Milo D. Dahl, editor

Glenn Research Center, Cleveland, Ohio

Assessment of NASA’s Aircraft 

Noise Prediction Capability

NASA/TP—2012-215653

July 2012
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Milo D. Dahl, editor

Glenn Research Center, Cleveland, Ohio

Assessment of NASA’s Aircraft 

Noise Prediction Capability

NASA/TP—2012-215653

July 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identification 

only. Their usage does not constitute an official endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by expert reviewer(s). 

Contributions to this study were made by members of the Aeroacoustics, Computational Aerosciences, Configuration 

Aerodynamics and Structural Acoustics Branches at the NASA Langley Research Center and by members of the 

Acoustics, Multi-disciplinary Design Analysis Optimization, and Turbomachinary and Heat Transfer Branches at the NASA 

Glenn Research Center. The outstanding technical efforts of both NASA civil servants and contractors in completing this work 

is gratefully acknowledged. They are listed as authors for each of the chapters. Thanks are also extended to the following 

individuals for support of this effort: Dennis L. Huff, Charlotte E. Whitfield, Fayette S. Collier, E. Brian Fite, Michael A. Marcolini, 

Kevin P. Shepherd, Richard J. Silcox, Joseph H. Morrison, and Zachary T. Applin.

I also thank the following people from NASA, industry, and academia for reviewing and providing feedback on this document: 

Constantine Baltas, Stanley F. Birch, Eugene Chien, Michael J. Czech, Michael J. Doty, Fereidoun Farassat, Marvin E. Goldstein, 

Yueping Guo, Alan S. Hersh, Andrew J. Kempton, Donald C. Kenzakowski, Michelle R. Kirby, Eugene A. Krejsa, Dean F. Long, 

Justin H. Lan, Steven Martins, Joe E. Posey, Ramons A. Reba, Todd Schultz, Robert W. Stoker, Thomas Van de Ven, Donald S. 

Weir, Trevor H. Wood, and Jia Yu.

Finally, I am very grateful to Laura Becker, Lorie Passe, Nancy Mieczkowski, John Jindra, and Lorraine Feher for their help and 

careful effort in preparing this document.

Milo D. Dahl, editor
NASA/TP—2012-215653 iii

Preface

A goal of NASA’s Fundamental Aeronautics Program is the improvement of aircraft noise prediction. Within the Subsonic 

Fixed Wing, Subsonic Rotary Wing, and Supersonic projects, there are specific objectives to assess the accuracy of noise

prediction methods. NASA is uniquely positioned to provide this publication after years of developing codes and establishing 

experimental databases through in-house research and with numerous industrial and university partnerships.

The purpose of this document is to provide an assessment on the current state of the art for aircraft noise prediction by carefully 

analyzing the results from prediction tools and from the experimental databases to determine errors and uncertainties and compare 

results to validate the predictions. This assessment was performed over the time period from 2006 to 2009. The state of the art in 

this study is restricted to prediction methods and databases developed or sponsored by NASA, although in many cases they 

represent the current state of the art for industry. The scope of prediction tools range from semi-empirical methods to higher 

fidelity models that have matured to the level where they can be used for noise prediction. The error analysis is included for both 

the predictions and the experimental data. Gaps are identified where more work is needed to improve the prediction methods 

and/or the experimental databases. The results will be used to judge the progress of future work toward narrowing these gaps and 

reducing the levels of error and uncertainties by quantitatively tracking the improvements.

This report begins with an introduction that gives a general background for and a discussion on the process of this assessment 

followed by eight topic chapters. The topic areas are aircraft system noise, engine system noise, airframe noise, fan noise, liner 

physics, duct acoustics, jet noise, and propulsion airframe aeroacoustics.

NASA/TP—2012-215653 v

Contents

Preface ....................................................................................................................................................................iii

Chapter 1—Introduction..........................................................................................................................................1

Summary...........................................................................................................................................................1

1.1 Assessment Process................................................................................................................................1

1.2 Aircraft Noise Prediction Assessment .......................................................................................................5

Appendix A .—Nomenclature ..........................................................................................................................9

A.1 Acronyms..................................................................................................................................9

A.2 Symbols.....................................................................................................................................9

References ......................................................................................................................................................10

Chapter 2—Aircraft System Noise Prediction....................................................................................................... 11

Summary.........................................................................................................................................................11

2.1 Introduction...........................................................................................................................................11

2.2 ANOPP Code........................................................................................................................................12

2.2.1 ANOPP Source Noise Methods............................................................................................... 14

2.2.2 Installation Effects................................................................................................................... 17

2.2.3 ANOPP Computational Efficiency and Usage ........................................................................18

2.3 ANOPP Evaluation and Demonstration of Capabilities .......................................................................18

2.3.1 Vehicle Description................................................................................................................. 19

2.3.2 Engine Description.................................................................................................................. 19

2.3.3 Trajectory Description............................................................................................................. 19

2.3.4 Comparison of Measurements and Predictions.........................................................................21

2.3.5 Uncertainty Analysis............................................................................................................... 26

2.4 Recommendations.................................................................................................................................29

Appendix A.—Nomenclature .........................................................................................................................31

A.1 Acronyms................................................................................................................................ 31

A.2 Symbols................................................................................................................................... 31

References ......................................................................................................................................................32

Chapter 3—Engine System and Core Noise .......................................................................................................... 35

Summary and Recommendations...................................................................................................................35

3.1 Introduction...........................................................................................................................................35

3.2 Core-Noise Research ............................................................................................................................36

3.2.1 Compressor Noise ................................................................................................................... 36

3.2.2 Combustion Noise ................................................................................................................... 37

3.2.3 Turbine Noise.......................................................................................................................... 42

3.2.4 Current Prediction Codes ........................................................................................................42

3.3 Engine Noise Prediction Using ANOPP...............................................................................................43

3.3.1 ANOPP Static-Engine-Test Simulation...................................................................................43

3.3.2 Sensitivity................................................................................................................................ 44

3.4 Comparison of ANOPP–L25 Predictions and NASA-Honeywell EVNERT Engine TestStand Data ............................................................................................................................................46

3.4.1 Comparison of Total 1/3-Octave Results ................................................................................46

3.4.2 Comparison of Combustion-Noise 1/3-Octave Results...........................................................51

3.5 Concluding Remarks.............................................................................................................................58

Appendix A.—Nomenclature .........................................................................................................................59

A.1 Acronyms................................................................................................................................ 59

A.2 Symbols................................................................................................................................... 59

References ......................................................................................................................................................60

Chapter 4—Airframe Noise: A Prediction Capability Assessment .......................................................................63

Summary.........................................................................................................................................................63

4.1 Introduction...........................................................................................................................................63

4.1.1 Background ............................................................................................................................. 63

4.1.2 Assessment Overview ............................................................................................................. 64

4.2 Prediction Methodology .......................................................................................................................64

4.2.1 Modeling Approaches ............................................................................................................. 64
NASA/TP—2012-215653 vi

4.2.2 Prediction Tools ...................................................................................................................... 65

4.2.3 Test Facilities .......................................................................................................................... 65

4.2.4 Scaling Issues.......................................................................................................................... 65

4.2.5 Metrics..................................................................................................................................... 66

4.3 Airframe Noise Characteristics of a Gulfstream G550 Aircraft............................................................66

4.3.1 Discussion of Experimental Data ............................................................................................ 66

4.3.2 Metrics and Assessment .......................................................................................................... 68

4.3.3 Results and Findings ............................................................................................................... 69

4.3.4 Recommendations................................................................................................................... 70

4.4 Flap-Edge Noise Measurement and Prediction.....................................................................................71

4.4.1 Test Description ...................................................................................................................... 71

4.4.2 Results and Findings ............................................................................................................... 72

4.4.3 Metrics and Assessment .......................................................................................................... 73

4.4.4 Recommendations................................................................................................................... 73

4.5 Aeroacoustic Measurement and Prediction for Boeing 777 Landing Gear Model ...............................75

4.5.1 Discussion of Experimental Data ............................................................................................ 75

4.5.2 Results and Findings ............................................................................................................... 77

4.5.3 Sensitivity Study ..................................................................................................................... 78

4.5.4 Recommendations................................................................................................................... 81

4.6 Prototype for Airframe Component Interaction: Tandem Cylinders ....................................................81

4.6.1 Test Descriptions..................................................................................................................... 81

4.6.2 Computational Approach and Procedure.................................................................................82

4.6.3 Results and Findings ............................................................................................................... 83

4.6.4 Effect of Cylinder Spacing ...................................................................................................... 85

4.6.5 Recommendations................................................................................................................... 88

4.7 Aeroacoustic Analysis of Simplified Landing Gear Model..................................................................88

4.7.1 Test Description ...................................................................................................................... 88

4.7.2 Computational Approach and Procedure.................................................................................88

4.7.3 Results and Findings ............................................................................................................... 89

4.7.4 Recommendations................................................................................................................... 90

4.8 Aerodynamic Sources of Leading-Edge Slat Noise..............................................................................92

4.8.1 Discussion of Experimental Data ............................................................................................ 92

4.8.2 Metrics and Assessment .......................................................................................................... 92

4.8.3 Results and Findings ............................................................................................................... 93

4.8.4 Recommendations................................................................................................................... 98

4.9 Conclusions...........................................................................................................................................98

4.10 Recommendations.................................................................................................................................99

Appendix A.—Nomenclature .......................................................................................................................101

A.1 Acronyms.............................................................................................................................. 101

A.2 Symbols................................................................................................................................. 101

Appendix B.—Aircraft Noise Prediction Program.......................................................................................103

B.1 ANOPP: Fink’s Method ........................................................................................................ 103

B.2 ANOPP: Boeing’s Method, Landing Gear Noise..................................................................105

Appendix C.—CFL3D and Acoustic Analogy .............................................................................................107

Appendix D.—Test Facilities.......................................................................................................................109

D.1 Quiet Flow Facility................................................................................................................ 109

D.2 Basic Aerodynamic Research Tunnel....................................................................................110

References ....................................................................................................................................................111

Chapter 5—Fan Noise Prediction ........................................................................................................................ 115

Summary.......................................................................................................................................................115

5.1 Introduction.........................................................................................................................................115

5.2 Benchmark Test Cases........................................................................................................................116

5.3 Test Facility and Data Acquisition Systems .......................................................................................121

5.4 Wind Tunnel Acoustic Measurements................................................................................................121

5.5 Rotating Rake Acoustic Measurements..............................................................................................122

5.6 Uncertainty in Measurements.............................................................................................................122
NASA/TP—2012-215653 vii

5.6.1 Wind Tunnel Aerodynamic Data Uncertainty Analysis........................................................123

5.6.2 Wind Tunnel Sideline Acoustic Data Uncertainty Analysis .................................................123

5.6.3 Rotating Rake Acoustic Data Uncertainty Analysis..............................................................124

5.7 Prediction and Assessment .................................................................................................................125

5.7.1 Empirical Methods................................................................................................................ 126

5.7.2 Acoustic-Analogy-Based Methods........................................................................................ 126

5.7.3 Computational Methods........................................................................................................ 135

5.8 Conclusions.........................................................................................................................................141

5.9 Acknowledgments ..............................................................................................................................141

Appendix A.—Nomenclature .......................................................................................................................143

A.1 Acronyms.............................................................................................................................. 143

Appendix B.—Additional Data-Theory Comparisons for ANOPP..............................................................145

Appendix C.—Additional Data-Theory Comparisons for RSI Code ...........................................................151

References ....................................................................................................................................................155

Chapter 6—Uncertainty in Acoustic Liner Impedance Measurement and Prediction .........................................157

Summary.......................................................................................................................................................157

6.1 Introduction.........................................................................................................................................158

6.1.1 Challenge for Liner Design Improvement.............................................................................158

6.1.2 Viable Liners for Turbofan Engine Nacelles.........................................................................158

6.1.3 Perforated Plate Resistive Element in Multilayer Liners.......................................................159

6.1.4 Scope and Objective of This Assessment..............................................................................159

6.2 Impedance Uncertainty, Quantification, and Quality Control ............................................................160

6.2.1 Statistical Process Control: A Tool for Impedance Quality Control .....................................160

6.2.2 Specification Limits, Uncertainty Limits, and Confidence Intervals ....................................160

6.2.3 Uncertainty Metrics............................................................................................................... 160

6.2.4 Coverage Factor for Small Sample Sizes..............................................................................162

6.3 Impedance Concept and Measurement Issues ....................................................................................162

6.3.1 Nonlinearity Implication for Measurements and Prediction Models.....................................162

6.3.2 Grazing Flow Implication for Measurements and Prediction Models...................................163

6.3.3 Test Sample Size and Scale Implications..............................................................................163

6.3.4 Measurement Methodologies ................................................................................................ 164

6.3.5 Relevance of Laboratory Impedance Measurement ..............................................................166

6.3.6 Implementation of Rayleigh Absorber as Validation Liner...................................................167

6.4 Impedance Prediction Models for POHC Absorbers..........................................................................167

6.4.1 Phenomenological (Semi-Empirical) Models........................................................................167

6.4.2 Semi-Empirical Models for POHC Liners ............................................................................168

6.5 Database Creation for Uncertainty Assessment..................................................................................176

6.5.1 Assessment Liner Geometry and Input Preparation ..............................................................176

6.5.2 Quantifying Input Parameter Uncertainty .............................................................................176

6.6 Results and Discussion .......................................................................................................................179

6.6.1 Graphical Format and Interpretation .....................................................................................179

6.6.2 Comparison of NIT and GIT Measurements With No Flow.................................................180

6.6.3 Comparison of GIT Measurements With Flow .....................................................................181

6.6.4 Comparison of Predicted and Measured Results...................................................................182

6.7 Concluding Remarks and Recommendations.....................................................................................197

6.8 Acknowledgments ..............................................................................................................................199

Appendix A.—Nomenclature .......................................................................................................................201

A.1 Acronyms.............................................................................................................................. 201

A.2 Symbols................................................................................................................................. 201

References ....................................................................................................................................................203

Chapter 7—Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in 

Flow Ducts ..................................................................................................................................................... 205

Summary.......................................................................................................................................................205

7.1 Introduction.........................................................................................................................................205

7.2 Statement of Problem..........................................................................................................................206

7.3 Potential Flow Formulation ................................................................................................................207
NASA/TP—2012-215653 viii

7.3.1 Governing Differential Equations ......................................................................................... 207

7.3.2 The Linearized Acoustic Equations....................................................................................... 207

7.3.3 Derivation of Scalar Wave Equations ...................................................................................208

7.3.4 Scalar Wave Equation in Frequency Domain........................................................................208

7.3.5 Acoustic Boundary Conditions.............................................................................................. 209

7.4 Acoustic Liner Sound Attenuation......................................................................................................210

7.5 Potential Flow Computer Codes.........................................................................................................211

7.5.1 Quasi-Three-Dimensional Uniform-Flow Code....................................................................211

7.5.2 Axially Symmetric Code ....................................................................................................... 213

7.5.3 Three-Dimensional Uniform-Flow Code ..............................................................................214

7.5.4 Three-Dimensional Code With Parabolic Approximation ....................................................216

7.6 Rotational Flow Computer Codes.......................................................................................................218

7.6.1 Governing Differential Equations and Boundary Conditions................................................219

7.6.2 Quasi-Three-Dimensional Code............................................................................................ 220

7.6.3 Pseudo-Time Marching Codes.............................................................................................. 222

7.7 Results and Discussion .......................................................................................................................223

7.7.1 NASA Langley Grazing Incidence Tube Simulations...........................................................223

7.7.2 NASA Langley Curved Duct Test Rig Simulations..............................................................230

7.7.3 NASA Glenn Advanced Noise Control Fan Simulations......................................................232

7.8 Concluding Remarks and Recommendations.....................................................................................234

7.9 Acknowledgments ..............................................................................................................................235

Appendix A.—Nomenclature .......................................................................................................................237

A.1 Acronyms.............................................................................................................................. 237

A.2 Symbols................................................................................................................................. 237

References ....................................................................................................................................................239

Chapter 8—Jet Noise Prediction.......................................................................................................................... 241

Summary.......................................................................................................................................................241

8.1 Introduction.........................................................................................................................................242

8.2 Discussion of Codes............................................................................................................................242

8.2.1 Empirical Prediction Tool: Stone Jet Noise Module (ST2JET) Within ANOPP ..................243

8.2.2 Acoustic Analogy Prediction Tools....................................................................................... 244

8.2.3 Reynolds-Averaged Navier-Stokes (RANS) Tool: Wind-US ...............................................248

8.3 Identification of Test Programs ..........................................................................................................250

8.4 Jet Noise Case Taxonomy...................................................................................................................252

8.5 Description of Facilities......................................................................................................................252

8.6 Description of Test Hardware for Data Sources.................................................................................254

8.6.1 SHJAR................................................................................................................................... 254

8.6.2 Supersonic Dual-Flow Hardware (Test Program SDF07).....................................................257

8.6.3 Long Duct Internal Mixer Hardware (Test Program LDIM05).............................................257

8.6.4 High-Flow Cross-Facility Hardware (Test Program HFXF07).............................................259

8.7 Details of Measurements, Sensors, Transducers, and Placement........................................................259

8.8 Acoustic Data Collection and Processing ...........................................................................................260

8.9 Identifying Uncertainties in Acoustic Data.........................................................................................261

8.9.1 Measurement Uncertainties................................................................................................... 261

8.9.2 Experimental Uncertainties................................................................................................... 261

8.10 Flow Data Collection and Processing .................................................................................................264

8.10.1 Stereoscopic PIV System ...................................................................................................... 264

8.10.2 Optical Calibration and Verification .....................................................................................265

8.10.3 Three-Dimensional Vector Processing..................................................................................265

8.10.4 Flow Seeding......................................................................................................................... 265

8.11 Identifying Uncertainties in Flow Measurements...............................................................................266

8.12 Metrics................................................................................................................................................268

8.13 Description of Presentation Format for Acoustic Data .......................................................................268

8.14 Empirical Code Assessment Results...................................................................................................269

8.14.1 Case Listing........................................................................................................................... 269

8.14.2 Overall Results...................................................................................................................... 269
NASA/TP—2012-215653 ix

8.15 Acoustic Analogy Code Assessment Results: Jet3D ..........................................................................271

8.15.1 Case Listing........................................................................................................................... 271

8.15.2 Discussion of Jet3D Results.................................................................................................. 272

8.16 Acoustic Analogy Code Assessment Results: JeNo v1.0 ...................................................................276

8.16.1 Case Listing........................................................................................................................... 276

8.16.2 Discussion of JeNo v1.0 Results........................................................................................... 278

8.17 Conclusions.........................................................................................................................................290

8.17.1 Empirical code....................................................................................................................... 290

8.17.2 Acoustic Analogy Codes....................................................................................................... 291

8.17.3 Recommendations................................................................................................................. 291

Appendix A.—Nomenclature .......................................................................................................................293

A.1 Acronyms.............................................................................................................................. 293

A.2 Symbols................................................................................................................................. 293

Appendix B.—Jet Configurations Tested in NASA-Sponsored Test Programs...........................................295

Appendix C.—ANOPP Jet Noise Predictions and Comparison With Data..................................................305

References ....................................................................................................................................................329

Chapter 9—Propulsion Airframe Aeroacoustic Interactions...............................................................................331

Summary.......................................................................................................................................................331

9.1 Introduction.........................................................................................................................................331

9.2 Experiments........................................................................................................................................331

9.2.1 Pylon Effects Experiment...................................................................................................... 333

9.2.2 Experimental Facility ............................................................................................................ 333

9.2.3 Model Design and Experimental Configurations..................................................................334

9.2.4 Nozzle Operating Conditions................................................................................................ 335

9.2.5 Acoustic Data Processing...................................................................................................... 336

9.3 Prediction Method Overview..............................................................................................................336

9.4 Jet3D...................................................................................................................................................336

9.4.1 Guidelines for Applying Jet3D.............................................................................................. 339

9.4.2 Sensitivity to Input Settings................................................................................................... 340

9.4.3 Applications .......................................................................................................................... 340

9.4.4 Jet3D Challenges................................................................................................................... 351

9.5 Future PAA Experimental and Prediction Development ....................................................................351

Appendix A.—Nomenclature .......................................................................................................................353

A.1 Acronyms.............................................................................................................................. 353

A.2 Symbols................................................................................................................................. 353

References ....................................................................................................................................................354
NASA/TP—2012-215653 x

List of Tables

Table 1.1.—Codes assessed for aircraft noise predictive capability........................................................................6

Table 1.2.—List of codes and code types arranged by chapter topic.......................................................................6

Table 2.1.—Database used for “original” Heidmann method ...............................................................................15

Table 2.2.—Database used for “large fan” Heidmann method..............................................................................15

Table 2.3.—Database used for “small fan” Heidmann method .............................................................................15

Table 2.4.—ANOPP jet noise prediction methods ................................................................................................ 16

Table 2.5.—ANOPP modules used for predicting the noise from a generic Boeing 737–800 aircraft..................18

Table 2.6.—Monte Carlo simulation of Boeing 737 certification effective perceived noise levels 

(EPNL)............................................................................................................................................................. 27

Table 2.7.—Change in effective perceived noise level (EPNL) (dB) at approach location due to 

5-percent variations in aircraft velocity and power setting...............................................................................28

Table 2.8.—Change in effective perceived noise level (EPNL) (dB) at lateral sideline location due to 

5-percent variations in aircraft velocity and power setting...............................................................................29

Table 2.9.—Change in effective perceived noise level (EPNL) (dB) at flyover location due to 5-percent 

variations in aircraft velocity and power setting............................................................................................... 29

Table 3.1.—ANOPP nondimensional performance parameters ............................................................................45

Table 4.1.—G550 aircraft: characteristic dimensions............................................................................................ 66

Table 4.2.—Trailing-edge flap noise test: test conditions .....................................................................................72

Table 4.3.—Trailing-edge flap noise test: characteristic dimensions....................................................................72

Table 4.4.—Experimental repeatability analysis of sound pressure levels (in decibels) observed in flapedge beamforming............................................................................................................................................ 74

Table 4.5.—Major components of 6.3-percent-scale Boeing 777 landing gear.....................................................75

Table 4.6.—Test matrix for Boeing 777 landing gear noise study ........................................................................77

Table 4.7.—Boeing 777 main landing gear prediction input parameters ..............................................................77

Table 4.8.—Boeing 777 main landing gear component dimensions .....................................................................77

Table 5.1.—Model fan stage design parameters.................................................................................................. 117

Table 5.2.—Model fan tip speed conditions used in this study ...........................................................................117

Table 5.3.—Aerodynamic data uncertainty analysis results................................................................................123

Table 5.4.—Analysis of uncertainty in fan noise spectra ....................................................................................124

Table 5.5.—Representative uncertainty levels in mode sound power levels for second harmonic of bladepassing frequency computed from measured Rotating Rake data ....................................................................125

Table 5.6.—Modeling error from using hard-wall plug-flow basis function to fit shear-flow mode ..................125

Table 5.7.—Typical uncertainties in mode acoustic power level from all sources..............................................125

Table 5.8.—ANOPP L25v3 HDNFAN input parameters....................................................................................127

Table 5.9.—TURBO and LINFLUX grid sizes................................................................................................... 137

Table 6.1.—Geometric parameter statistical inputs............................................................................................. 177

Table 6.2.—Aeroacoustic parameter mean values............................................................................................... 177

Table 6.3.—Aeroacoustic parameter standard deviations....................................................................................177

Table 7.1.—Sound attenuation in decibels computed for plane wave in hard-wall duct with 

nonreflecting termination ............................................................................................................................... 224

Table 7.2.—Sound attenuation in decibels computed for least attenuated mode in soft-wall duct with 

nonreflecting termination ............................................................................................................................... 226

Table 7.3.—Wall clock time consumed on Columbia clusters computing sound attenuation with in-duct 

codes on baseline grid .................................................................................................................................... 227

Table 7.4.—Grazing incidence tube mean sound attenuation (μ) in decibels and 95% confidence 

interval uncertainty values (tn ∗ σ) ................................................................................................................. 230

Table 8.1.—Assessment cases for Jet3D predictions of jet noise spectra............................................................246

Table 8.2.—Taxonomy of test cases for assessment of jet noise prediction codes..............................................253

Table 8.3.—Design Mach numbers of single- flow convergent-divergent nozzles.............................................257

Table 8.4.—Analysis of uncertainty in measured jet noise spectra .....................................................................262

Table 8.5.—Assessment matrix for JeNo v1.0 predictions of jet noise spectra—axisymmetric 

geometries ...................................................................................................................................................... 276

Table 8.6.—Assessment matrix for JeNo v1.0 predictions of jet noise spectra—nonaxisymmetric 

geometries ...................................................................................................................................................... 277
NASA/TP—2012-215653 xi

Table 8.7.—Test case identifier within each configuration .................................................................................296

Table 9.1.—Separate-flow nozzle model areas for both cold and hot conditions and scale factors used 

for acoustic data processing............................................................................................................................ 335

Table 9.2.—Bypass ratio (BPR) 5 nozzle operating conditions ..........................................................................335
NASA/TP—2012-215653 xii

List of Figures

Figure 1.1.—Diagram of assessment process leading to validation of computed result by comparison to 

experimental data, where U is uncertainty. ........................................................................................................3

Figure 1.2.—Example of determining errors and uncertainties using a statistical approach for parameters 

X and dependent variable Y. (a) Raw measured and calculated data with computed means and 95% 

confidence intervals. (b) Computed comparison error and uncertainty band. (c) Point and line plot 

comparing calculated results and measured data, with “error bars.” (d) Comparison plot showing 

95% confidence interval (CI) and overlap regions. ............................................................................................4

Figure 2.1.—ANOPP Level 25.............................................................................................................................. 13

Figure 2.2.—Prediction flow within ANOPP Level 25 using CTOL source modules. .........................................13

Figure 2.3.—ANOPP coordinate system. .............................................................................................................. 14

Figure 2.4.—Analytical representation of CFM56–7B turbofan engine in Numerical Propulsion System 

Simulator (NPSS) (Ref. 41).............................................................................................................................. 19

Figure 2.5.—Cross-sectional view of NPSS/WATE aeromechanical and flow path simulation of 

CFM56–7B turbofan engine (drawing to scale). .............................................................................................. 20

Figure 2.6.—SAE AIR–1845 trajectory for the B737–800/CFM56–7B at 172 300 lb. (a) Altitude. (b) 

Airspeed. (c) Percent net engine thrust............................................................................................................. 21

Figure 2.7.—Noise certification measurement locations....................................................................................... 21

Figure 2.8.—Predicted tone-weighted perceived noise level (PNLT) time history at approach 

certification point. ............................................................................................................................................ 22

Figure 2.9.—Predicted sound pressure level (SPL) at approach certification point for three different polar 

directivity angles, θe. (a) 45°. (b) 90°. (c) 135°. .................................................................................................22

Figure 2.10.—Predicted tone-weighted perceived noise level (PLNT) time history at lateral sideline 

certification point. ............................................................................................................................................ 23

Figure 2.11.—Predicted sound pressure level (SPL) at lateral sideline certification point for three 

different polar directivity angles, θe. (a) 45°. (b) 90°. (c) 135°. .......................................................................23

Figure 2.12.—Predicted tone-weighted perceived noise level (PNLT) time history for flyover (with 

cutback) condition. ........................................................................................................................................... 24

Figure 2.13.—Predicted sound pressure level (SPL) at flyover (with cutback) location for three different 

polar directivity angles, θe. (a) 45°. (b) 90°. (c) 135°....................................................................................... 24

Figure 2.14.—Predicted contributions from each noise component to total effective perceived noise 

level (EPNL) at the three certification points. .................................................................................................. 25

Figure 2.15.—Comparison of predicted effective perceived noise level (EPNL) for B737–800/CFM56–7B 

and noise certification data of 73 certificated B737s equipped with CFM56–7B engines. Approach 

measurement location........................................................................................................................................ 26

Figure 2.16.—Comparison of predicted effective perceived noise level (EPNL) for B737–800/CFM56–7B 

and noise certification data of 73 certificated B737s equipped with CFM56–7B engines. Lateral 

sideline measurement location........................................................................................................................... 26

Figure 2.17.—Comparison of predicted effective perceived noise level (EPNL) for B737–800/CFM56–7B 

and noise certification data of 73 certificated B737s equipped with CFM56–7B engines. Flyover 

measurement location........................................................................................................................................ 26

Figure 3.1.—Coherence technique to determine combustion-noise component of far-field noise. 

Measurement stations C, T, and F are located in the engine combustor, core tail pipe, and far field, 

respectively. Signals x(t), y(t), and z(t) are directly measurable, are functions of time t, and are the 

sum of coherent combustion-noise signals u(t), v(t), and w(t) and uncorrelated signals m(t), n(t), and 

o(t) resulting from other noise sources; huv and hvw are impulse-response functions........................................39

Figure 3.2.—Three-signal coherence technique for noise rejection, where s(t) is the source signal as 

function of time t and hsu, hsv, and hsw are impulse-response functions. Coherent signals u(t), v(t), and 

w(t) of interest are not directly measurable; their addition to mutually uncorrelated signals m(t), n(t), 

and o(t) from other sources results in measurable signals x(t), y(t), and z(t).......................................................40

Figure 3.3.—ANOPP module flow chart for static-engine test. ............................................................................43

Figure 3.4.—Hard-wall case 1/3-octave surface plots comparing ANOPP predictions and EVNERT data 

of far-field sound from Honeywell TECH977 engine at various corrected fan speeds. SPL is sound 

pressure level, and f represents frequency. (a) 60 percent (approach). (b) 71 percent (cutback). (c) 87 

percent (takeoff). .............................................................................................................................................. 47
NASA/TP—2012-215653 xiii

Figure 3.5.—Comparison of ANOPP predictions and EVNERT data for hard-wall case of Honeywell 

TECH977 engine at approach condition, 60 percent corrected fan speed. Error bands for predictions 

are 1 and 3 percent uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated 

uncertainty from calibration and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) 

versus center frequency at different polar angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. 

(f) Overall SPL (OASPL) versus polar directivity angle..................................................................................48

Figure 3.6.—Comparison of ANOPP predictions and EVNERT data for hard-wall case of Honeywell 

TECH977 engine at cutback condition, 71 percent corrected fan speed. Error bands for predictions 

are 1 and 3 percent uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated 

uncertainty from calibration and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) 

versus center frequency at different polar angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. 

(f) Overall SPL (OASPL) versus polar directivity angle..................................................................................49

Figure 3.7.—Comparison of ANOPP predictions and EVNERT data for hard-wall case of Honeywell 

TECH977 engine at takeoff condition, 87 percent corrected fan speed. Error bands for predictions

are 1 and 3 percent uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated 

uncertainty from calibration and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) 

versus center frequency at different polar angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) 

Overall SPL (OASPL) versus polar directivity angle....................................................................................... 50

Figure 3.8.—Treated case 1/3-octave surface plots comparing ANOPP predictions and EVNERT data 

of far-field sound from Honeywell TECH977 engine at various corrected fan speeds. SPL is sound 

pressure level, and f represents frequency. (a) 60 percent (approach). (b) 71 percent (cutback). (c) 87 

percent (takeoff). .............................................................................................................................................. 52

Figure 3.9.—Comparison of ANOPP predictions and EVNERT data for treated case of Honeywell 

TECH977 engine at approach condition, 60 percent corrected fan speed. Error bands for predictions 

are 1 and 3 percent uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated 

uncertainty from calibration and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) 

versus center frequency at different polar angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. 

(f) Overall SPL (OASPL) versus polar directivity angle..................................................................................53

Figure 3.10.—Comparison of ANOPP predictions and EVNERT data for treated case of Honeywell 

TECH977 engine at cutback condition, 71 percent corrected fan speed. Error bands for predictions 

are 1 and 3 percent uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated 

uncertainty from calibration and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) 

versus center frequency at different polar angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. 

(f) Overall SPL (OASPL) versus polar directivity angle..................................................................................54

Figure 3.11.—Comparison of ANOPP predictions and EVNERT data for treated case of Honeywell 

TECH977 engine at takeoff condition, 87 percent corrected fan speed. Error bands for predictions 

are 1 and 3 percent uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated 

uncertainty from calibration and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) 

versus center frequency at different polar angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) 

Overall SPL (OASPL) versus polar directivity angle....................................................................................... 55

Figure 3.12.—Total- and combustion-noise 1/3-octave sound pressure level (SPL) versus 1/3-octave 

center frequency in 130° direction at different corrected fan speeds. ANOPP predictions and 

processed EVNERT data for Honeywell TECH977 engine configuration 35 (Ref. 57). Gzz refers to 

total noise spectrum; 2s-cip1, 2s-t551, and 3s refer to different processing techniques applied to the 

experimental data; and NOP refers to threshold values. (a) 48 percent (flight idle). (b) 60 percent 

(approach). (c) 71 percent (cutback). (d) 87 percent (takeoff). ........................................................................57

Figure 4.1.—Boeing 747 aircraft in landing configuration. Four main landing gear, nose landing gear, 

leading-edge slats and triple-slotted, trailing-edge flaps are deployed during airport approach. .....................64

Figure 4.2.—ANOPP source-observer geometry. R, θ, and φ are measured with respect to source 

emission time. V∞ is aircraft speed. .................................................................................................................. 65

Figure 4.3.—Gulfstream G550 aircraft planform. .................................................................................................66

Figure 4.4.—NASA microphone array and Gulfstream free-field (certification) microphone layout. ..................67

Figure 4.5.—Representative measured sound pressure level (SPL) spectra for two configurations of 

Gulfstream G550 aircraft.................................................................................................................................. 68

Figure 4.6.—Averaged measured sound pressure level (SPL) spectra for three selected airframe noise 

and clean configurations of Gulfstream G550 aircraft. ....................................................................................69
NASA/TP—2012-215653 xiv

Figure 4.7.—Predicted sound pressure level (SPL) spectra for three selected airframe noise and clean 

configurations of Gulfstream G550 aircraft. .................................................................................................... 69

Figure 4.8.—Uncertainties in predicted sound pressure level (SPL) spectra due to variations in speed 

and azimuthal angle, φ, for Gulfstream G550 aircraft. Configuration is flaps at 39° with landing gear 

down................................................................................................................................................................. 69

Figure 4.9.—Difference between measured and predicted absolute sound pressure level (SPL) spectra..............70

Figure 4.10.—Difference between measured and predicted relative sound pressure level (SPL) spectra.............70

Figure 4.11.—Flap overlap and gap definitions for flap-edge noise test with model airfoil in Quiet Flow 

Facility (QFF)................................................................................................................................................... 71

Figure 4.12.—Azimuthal (φ) locations of Small Aperture Directional Array (SADA) microphones for 

far-field tests with model airfoil in Quiet Flow Facility (QFF)........................................................................71

Figure 4.13.—Flap-edge noise sound pressure level (SPL) spectra at different Mach numbers M and 

deflection angles. Comparison of ANOPP predictions using Fink’s method and measurements from 

Quiet Flow Facility (QFF) experiments............................................................................................................. 73

Figure 4.14.—Discrepancy in airframe flap-edge noise sound pressure level (SPL) spectrum at Mach 

number M = 0.17 and 39° flap between ANOPP predictions using Fink’s method and measurements 

from Quiet Flow Facility (QFF) experiments................................................................................................... 73

Figure 4.15.—Boeing 777 main landing gear model. Baseline configuration, with door......................................75

Figure 4.16.—Boeing 777 main gear model assembly mounted in Quiet Flow Facility (QFF) for lateral 

“sideline” measurements by Medium Aperture Directional Array (MADA) microphones. ............................76

Figure 4.17.—Boeing 777 main gear model assembly mounted in Quiet Flow Facility (QFF) for 

“flyover” measurements by Medium Aperture Directional Array (MADA) microphones. .............................76

Figure 4.18.—Quiet Flow Facility (QFF) coordinates system for landing gear noise measurements. Re is 

source-to-observer distance, θe, is polar emission angle, and φe is azimuthal emission angle. ........................76

Figure 4.19.—Sound pressure level (SPL) of landing gear model. Comparison of measured spectrum and 

total scaled (Ref. 37) ANOPP predicted spectrum with its three separate frequency component spectra 

using Boeing-Guo method for Mach number 0.17 at two observer locations (see Figure 4.18). 

(a) Flyover position, θe = 87.1° and φe = 1.0°. (b) Forward-sideline position, θe = 59.3° and φe = 5.17°.............79

Figure 4.20.—Sound pressure level (SPL) of landing gear model. Comparison of measured spectrum and 

total ANOPP predicted spectrum with its separate component spectra using Fink method for Mach 

number 0.17 at two observer locations (see Figure 4.18). (a) Flyover position, θe = 87.1° and φe = 1.0°. 

(b) Forward-sideline position, θe = 59.3° and φe = 5.17°....................................................................................79

Figure 4.21.—Sound pressure level (SPL) of landing gear model for Mach number 0.17 and given polar 

angle at different azimuthal angles (see Figure 4.18). (a) Comparison of measured spectra and total 

scaled (Ref. 37) ANOPP-predicted spectra using Boeing-Guo method. (b) Comparison of measured 

spectra and total ANOPP-predicted spectra using Fink method.........................................................................80

Figure 4.22.—Sound pressure level (SPL) of landing gear model for Mach number 0.17 and given 

azimuthal angle at different polar angles (see Figure 4.18). (a) Comparison of measured spectra and 

total scaled (Ref. 37) ANOPP-predicted spectra using Boeing-Guo method. (b) Comparison of 

measured spectra and total ANOPP-predicted spectra using Fink method. .....................................................80

Figure 4.23.—Boeing-Guo method: Combined effects for variation in Mach number and landing gear 

angle of attack. ................................................................................................................................................. 81

Figure 4.24.—Tandem cylinder test configuration................................................................................................ 82

Figure 4.25.—Tandem cylinders installed in Basic Aerodynamic Research Tunnel (BART). .............................82

Figure 4.26.—Tandem cylinders installed in Quiet Flow Facility (QFF) tunnel for measurements with 

Medium Aperture Directional Array (MADA) microphones...........................................................................82

Figure 4.27.—Planar view of computational x,y-grid used for tandem cylinder computational fluid 

dynamics (CFD) simulations............................................................................................................................ 83

Figure 4.28.—Pressure coefficient Cp versus polar angle θ for the surfaces of the tandem cylinders. 

Comparison of results from Quiet Flow Facility (QFF) and Basic Aerodynamic Research Tunnel 

(BART) experiments and CFD simulations with grids of different spans. (a) Upstream cylinder. 

(b) Downstream cylinder.................................................................................................................................. 84

Figure 4.29.—Root-mean-squared (rms) value of perturbation pressure coefficient Cp′ versus polar angle θ

for the surfaces of the tandem cylinders. Comparison of results from Quiet Flow Facility (QFF) and 
NASA/TP—2012-215653 xv

Basic Aerodynamic Research Tunnel (BART) experiments and CFD simulations with grids of 

different resolutions and spans. (a) Upstream cylinder. (b) Downstream cylinder..............................................85

Figure 4.30.—Near-field tandem cylinder sound pressure level (SPL) contours, CFD predictions, where 

x and y are spatial coordinates and grid dimensions and Dt is cylinder diameter. ............................................85

Figure 4.31.—Power spectral density PSD for tandem cylinders. Comparison of CFD predictions using 

three grids and results from Quiet Flow Facility (QFF) experiments. ................................................................86

Figure 4.32.—Sound pressure level (SPL) spectra for tandem cylinders. Comparison of CFD predictions 

using three grids and measurements from Quiet Flow Facility (QFF) experiments............................................86

Figure 4.33.—Error in sound pressure level (SPL) spectra predictions for tandem cylinders. Difference 

between CFD predictions from MxyFz grid with span of 18 and experimental measurements...........................86

Figure 4.34.—Root-mean-squared (rms) value of tandem cylinder surface perturbation pressure 

coefficient Cp′ versus polar angle θ at two spacings Lt/Dt, where Lt is centroid-to-centroid distance 

and Dt is cylinder diameter (see Figure 4.24). Comparison of CFD predictions from MxyFz grid with 

span of 18 and measurements from Quiet Flow Facility (QFF) and Basic Aerodynamic Research 

Tunnel (BART) experiments............................................................................................................................ 87

Figure 4.35.—Power spectral density PSD for tandem cylinders at two spacings Lt/Dt, where Lt is 

centroid-to-centroid distance and Dt is cylinder diameter (Figure 4.24). Comparison of CFD 

predictions from MxyFz grid with span of 18 and measurements from Quiet Flow Facility (QFF) 

experiments. ..................................................................................................................................................... 87

Figure 4.36.—Sound pressure level (SPL) spectra for tandem cylinders at centroid separation distance

Lt/Dt = 1.435. Comparison of CFD predictions from MxyFz grid with span of 18 and measurements 

from Quiet Flow Facility (QFF) experiments................................................................................................... 87

Figure 4.37.—Error in sound pressure level (SPL) spectra predictions for tandem cylinders at centroid 

separation distance Lt/Dt = 1.435. Difference between CFD predictions from MxyFz grid with span 

of 18 and experimental measurements. ............................................................................................................ 87

Figure 4.38.—Geometry of simplified landing gear model...................................................................................88

Figure 4.39.—CFD surface grid of simplified landing gear model. ......................................................................89

Figure 4.40.—Sound pressure level (SPL) spectra for landing gear in overhead position at polar angle 

θ = 88° and azimuthal angle φ = –1° (see Figure 4.18). Comparison of CFL3D predictions, using gear 

surface with and without the ceiling surface, and measurements from Quiet Flow Facility (QFF) 

experiments, nontripped and tripped cases......................................................................................................... 89

Figure 4.41.—Power spectral density PSD for landing gear in overhead position at polar angle θ = 88° and 

azimuthal angle φ = –1° (see Figure 4.18). Comparison of CFL3D predictions, using gear surface with 

and without the ceiling surface, and measurements from Quiet Flow Facility (QFF) experiments, 

nontripped and tripped cases. ............................................................................................................................ 90

Figure 4.42.—Error in CFL3D sound pressure level (SPL) spectra predictions for landing gear in overhead 

position at polar angle θ = 88° and azimuthal angle φ = –1° (see Figure 4.18). Difference between 

predictions, using gear surface with and without the ceiling surface, and measurements from Quiet 

Flow Facility (QFF) experiments, tripped case..................................................................................................90

Figure 4.43.—Sound pressure level (SPL) spectra for landing gear in flyover positions (see Figure 4.18). 

Comparison of CFL3D predictions and measurements from Quiet Flow Facility (QFF) experiments, 

nontripped and tripped cases. (a) Upstream, polar angle θ = 58° and azimuthal angle φ = –1°. 

(b) Downstream, polar angle θ = 120° and azimuthal angle φ = –1°. .................................................................91

Figure 4.44.—Sound pressure level (SPL) spectra for landing gear in sideline positions (see Figure 4.18). 

Comparison of CFL3D predictions and measurements from Quiet Flow Facility (QFF) experiments, 

nontripped and tripped cases. (a) On door side, polar angle θ = 88° and azimuthal angle φ = –55°. 

(b) Opposite door side, polar angle θ = 88° and azimuthal angle φ = 55°...........................................................91

Figure 4.45.—Model three-element 30P/30N high-lift aircraft wing system. .......................................................92

Figure 4.46.—Instantaneous spanwise vorticity field downstream of leading-edge slat, based on CFL3D 

computations. (a) Planar cut resembling cove state I. (b) Planar cut somewhat resembling cove state 

II. ...................................................................................................................................................................... 94

Figure 4.47.—Sample snapshots of leading-edge slat spanwise vorticity field from particle imaging 

velocimetry (PIV) measurements (Ref. 35) with wing model configuration at 4° angle of attack in 

the Basic Aerodynamic Research Tunnel (BART). ωz is spanwise vorticity, cs is slat chord length, 

and V∞ is aircraft speed. (a) Cove state I. (b) Cove state II. .............................................................................94
NASA/TP—2012-215653 xvi

Figure 4.48.—Time-averaged velocity magnitude profiles across leading-edge slat shear layer. 

(a) Locations of mixing-layer profiles A through D superposed on contour of mean spanwise 

vorticity. (b) Comparison of CFL3D simulation results (based on spanwise grid) for locations A 

through D and particle imaging velocimetry (PIV) measurements (Ref. 35). The distance ε increases 

from left to right, along the cuts A through D. .................................................................................................95

Figure 4.49.—Time-averaged two-dimensional (2D) turbulent kinetic energy TKE distribution in 

leading-edge slat cover region, where V∞ is free-stream velocity. (a) Locations of mixing-layer 

profiles A through D superposed on particle imaging velocimetry (PIV) contours. (b) CFL3D 

predictions. (c) CFL3D results compared with (PIV) measurements along profiles A through D (Ref. 

35), where. Tu2D is the two-dimensional turbulence intensity..........................................................................96

Figure 4.50.—Peak two-dimensional turbulent intensity Tu2D along leading-edge slat cove mixing-layer 

trajectory versus distance s from slat cusp. Comparison of CFL3D Tu2D based on coarse (S1) and 

fine (S2) spanwise grids and particle imaging velocimetry (PIV) measurements derived from small 

and large fields of view (f.o.v.) (Ref. 35). ........................................................................................................ 97

Figure 4.51.—Acoustic radiation due to leading-edge slat cove unsteadiness. (a) CFL3D-computed 

acoustic spectra (product of frequency f and power spectral density PSD) at selected probe locations 

between one and two chords from trailing edge noting point at Strouhal number St = 2, where cs is slat 

chord length and V∞ is free-stream velocity. (b) Schematic for slat noise model in Reference 81. 

(c) Contours of instantaneous pressure perturbations from fine-spanwise-grid simulation. ................................97

Figure 4.52.—Medium Aperture Directional Array (MADA) with hood removed in Quiet Flow Facility 

(QFF).............................................................................................................................................................. 109

Figure 4.53.—MADA microphone arrangement................................................................................................. 109

Figure 4.54.—Basic Aerodynamic Research Tunnel (BART). Structure in front of test section is 

traverse for optical devices............................................................................................................................. 110

Figure 4.55.—Closeup: Basic Aerodynamics Research Tunnel (BART) test section with particle 

imaging velocimetry (PIV) camera on traverse system..................................................................................110

Figure 5.1.—The 22-in.-diameter Advanced Ducted Propulsor (ADP) Fan 1 installed in the NASA 9-

by 15-Foot Low-Speed Wind Tunnel. Traversing microphone (located on white stand) is visible to 

left of model. Microphone moves on track parallel with axis of fan..............................................................118

Figure 5.2.—Cross-sectional sketch of ADP Fan 1 model. ADP has 18 rotor blades, 45 fan exit guide 

vanes, and 63 core inlet guide vanes. ............................................................................................................. 119

Figure 5.3.—The 22-in.-diameter Source Diagnostic Test (SDT) fan installed in NASA 9- by 15-Foot 

Low-Speed Wind Tunnel. .............................................................................................................................. 119

Figure 5.4.—Cross-sectional sketch of SDT fan model. SDT has 22 rotor blades and 54 fan exit guide 

vanes............................................................................................................................................................... 120

Figure 5.5.—The 22-in.-diameter Quiet High-Speed Fan 2 (QHSF 2) fan installed in NASA 9- by 

15-Foot Low-Speed Wind Tunnel.................................................................................................................. 120

Figure 5.6.—Cross-sectional sketch of QHSF 2 model fan. QHSF 2 has 22 rotor blades, 50 fan exit 

guide vanes, 10 bypass duct struts, and 10 core duct struts............................................................................121

Figure 5.7.—Plan view of 9- by 15-ft test section showing model-scale fan acoustic installation, 2.3-m 

(89-in.) sideline traversing microphone, and fixed aft microphone locations. Dimensions are in 

meters (inches). .............................................................................................................................................. 122

Figure 5.8.—Rotating Rake ring assembly on 43-cm (17-in.) Advanced Ducted Propulsor (ADP) in 

NASA 9- by 15-Foot Low-Speed Wind Tunnel. (a) First-generation system. (b) Current-generation 

system............................................................................................................................................................. 123

Figure 5.9.—Sound pressure level (SPL) error in ANOPP predictions for all sideline emission angles 

for ADP fan at various tip speeds. Gray bar represents experimental uncertainty. (a) 5425 rpm. 

(b) 7525 rpm. (c) 8750 rpm. ........................................................................................................................... 128

Figure 5.10.—Sound pressure level (SPL) error in ANOPP predictions for all sideline emission angles 

for SDT fan at various tip speeds. Gray bar represents experimental uncertainty. (a) 7809 rpm. 

(b) 11 075 rpm. (c) 12 657 rpm. ..................................................................................................................... 129

Figure 5.11.—Sound pressure level (SPL) error in ANOPP predictions for all sideline emission angles 

for QHSF 2 fan at various tip speeds. Gray bar represents experimental uncertainty. (a) 9840 rpm. 

(b) 12 500 rpm. (c) 14 060 rpm. ..................................................................................................................... 130

Figure 5.12.—Computational domains for ADP fan used by TSWIFT code. (a) Rotor. (b) Stator.....................131
NASA/TP—2012-215653 xvii

Figure 5.13.—Flow field through ADP fan duct. Axisymmetric Mach number contours at 8750 rpm 

computed using TSWIFT code. External as well as internal flows included. Black lines indicate 

block boundaries............................................................................................................................................. 132

Figure 5.14.—Comparisons of measured and predicted turbulence intensity for three spanwise stations 

2.5 in. downstream of rotor tip trailing edge of SDT fan atapproach condition. Predictions made 

using NASA TSWIFT code; dashed curves are predicted levels raised so background level matches 

measured background. (a) 88 percent span. (b) 71 percent span. (c) 56 percent span....................................133

Figure 5.15.—Rotor-stator (R-S) interaction narrowband sound power level (PWL) for SDT fan at 

different speeds from measured stage and rotor-only PWLs: R-S = stage – rotor-only. Dashed line 

indicates data reliability is questioned (see Sec. 5.7.2). (a) 7809 rpm. (b) 9493 rpm. (c) 11 075 rpm. 

(d) 11 771 rpm. (e) 12 657 rpm. ..................................................................................................................... 134

Figure 5.16.—Comparison of predicted (using RSI code) and estimated narrowband sound power levels 

(PWLs) for SDT fan at different speeds. Estimates are rotor-stator (R-S) interaction PWLs taken 

from Figure 5.15. Dashed line indicates data reliability is questioned (see Sec. 5.7.2). (a) 7809 rpm. 

(b) 9493 rpm. (c) 11 075 rpm. (d) 11 771 rpm. (e) 12 657 rpm. ....................................................................136

Figure 5.17.—Error in predicted (using RSI code) narrowband sound power levels (PWLs) for SDT fan 

at different speeds (Figure 5.16). Gray bar represents experimental uncertainty. ..........................................137

Figure 5.18.—Comparison of measured and predicted sound power levels (PWLs) for exhaust 2×BPF 

tone (second harmonic of blade-passing frequency) for ADP fan at different tip speeds. Data from 

Rotating Rake (RR) and sideline microphone (SL). Predictions calculated using LINFLUX code. 

Results are for circumferential mode –9......................................................................................................... 138

Figure 5.19.—Comparison of measured and predicted sound power levels (PWLs) for exhaust 2×BPF 

tone (second harmonic of blade-passing frequency) for SDT fan at different tip speeds. Data from 

Rotating Rake (RR) and sideline microphone (SL). Predictions calculated using LINFLUX code. 

Results are for circumferential mode –10....................................................................................................... 139

Figure 5.20.—Error in prediction of sound power level (PWL) for 2×BPF tone (second harmonic of 

blade-passing frequency) using data from Rotating Rake. Data for ADP fan is from Figure 5.18 

(circumferential mode –9). Data for SDT fan is from Figure 5.19 (circumferential mode –10). Error 

is defined as (measured level) – (predicted level). Predictions calculated using LINFLUX code. Gray 

bar represents experimental uncertainty. ........................................................................................................ 140

Figure 5.21.—Error in prediction of sound power level (PWL) for 2×BPF tone (second harmonic of 

blade-passing frequency) using data from sideline microphone. Data for ADP fan is from 

Figure 5.18 (circumferential mode –9). Data for SDT fan is from Figure 5.19 (circumferential mode 

–10). Error is defined as (measured level) – (predicted level). Predictions calculated using 

LINFLUX code. Gray bar represents experimental uncertainty.....................................................................140

Figure 5.22.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for ADP fan in inlet and exhaust quadrants at 5425 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................145

Figure 5.23.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for ADP fan in inlet and exhaust quadrants at 7525 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................145

Figure 5.24.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for ADP fan in inlet and exhaust quadrants at 8750 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................146

Figure 5.25.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for SDT fan in inlet and exhaust quadrants at 7809 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................146

Figure 5.26.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for SDT fan in inlet and exhaust quadrants at 11 075 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................147

Figure 5.27.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from

ANOPP code for SDT fan in inlet and exhaust quadrants at 12 657 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................147

Figure 5.28.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for QHSF 2 fan in inlet and exhaust quadrants at 9840 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................148
NASA/TP—2012-215653 xviii

Figure 5.29.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for QHSF 2 fan in inlet and exhaust quadrants at 12 500 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................148

Figure 5.30.—Comparison of 1/3-octave measured sound pressure level (SPL) and SPL predicted from 

ANOPP code for QHSF 2 fan in inlet and exhaust quadrants at 14 060 rpm at Mach 0.1. (a) Inlet 

quadrant; emission angle 46°. (b) Exhaust quadrant; emission angle 136°....................................................149

Figure 5.31.—Comparison of measured narrowband sound power level (PWL) and PWL predicted 

using RSI code for ADP fan at various blade tip speeds. Data represent combined rotor and stator 

contributions. (a) 5425 rpm. (b) 6700 rpm. (c) 7525 rpm. (d) 8345 rpm. (e) 8750 rpm.................................152

Figure 5.32.—Comparison of measured narrowband sound power level (PWL) and PWL predicted 

using RSI code for SDT fan at various blade tip speeds. Data represent combined rotor and stator 

contributions. (a) 7809 rpm. (b) 9493 rpm. (c) 11 075 rpm. (d) 11 771 rpm. (e) 12 675 rpm........................153

Figure 5.33.—Comparison of measured narrowband sound power level (PWL) and PWL predicted 

using RSI code for QHSF 2 fan at various blade tip speeds. Data represent combined rotor and stator 

contributions. (a) 9840 rpm. (b) 10 935 rpm. (c) 12 500 rpm. (d) 13 280 rpm. (e) 14 060 rpm.....................154

Figure 6.1.—Turbofan engine nacelle with wall lining. ...................................................................................... 158

Figure 6.2.—Perforate-over-honeycomb core (POHC) liner...............................................................................159

Figure 6.3.—Depiction of accuracy versus precision for parameter x, as used in this chapter. (a) High 

accuracy, high precision; (b) High accuracy, low precision; (c) Low accuracy, high precision; 

(d) Low accuracy, low precision. ................................................................................................................... 161

Figure 6.4.—NASA Langley normal incidence tube (NIT). (a) Photograph. (b) Schematic...............................165

Figure 6.5.—NASA Langley grazing incidence tube (GIT). (a) Photograph. (b) Schematic. (c) Liner 

installed in top wall. ....................................................................................................................................... 166

Figure 6.6.—Representative format for comparison of impedance prediction and measurement means 

and 95% confidence intervals......................................................................................................................... 180

Figure 6.7.—Results from NIT impedance measurements with source excitation levels of 120 and 

140 dB conducted at 100-Hz increments. (a) Resistance. (b) Reactance. ......................................................180

Figure 6.8.—Results from GIT impedance measurements with source excitation levels of 120 and 

140 dB conducted at 500-Hz increments. (a) Resistance. (b) Reactance. ......................................................181

Figure 6.9.—Results from NIT and GIT impedance measurements with source excitation levels of 

120 dB conducted at 100- and 500-Hz increments, respectively. (a) Resistance. (b) Reactance. ..................181

Figure 6.10.—Results from NIT and GIT impedance measurements with source excitation levels of 

140 dB conducted at 100- and 500-Hz increments, respectively. (a) Resistance. (b) Reactance. ..................182

Figure 6.11.—Results from GIT impedance measurements with source excitation level of 140 dB 

conducted at 500-Hz increments for Mach numbers M = 0.3 and 0.475. (a) Resistance. (b) 

Reactance. ...................................................................................................................................................... 182

Figure 6.12.—Comparison of impedance results from 14 NIT measurements and 31 Two-Parameter 

model (TP) simulations with no flow and 120-dB source excitation level conducted at 100-Hz 

increments. (a) Resistance. (b) Reactance. ..................................................................................................... 183

Figure 6.13.—Comparison of impedance results from 14 NIT measurements and 31 Two-Parameter 

model (TP) simulations with no flow and 140-dB source excitation level conducted at 100-Hz 

increments. (a) Resistance. (b) Reactance. ..................................................................................................... 184

Figure 6.14.—Comparison of impedance results from 10 GIT measurements conducted at 500-Hz 

increments and 31 Two-Parameter model (TP) simulations conducted at 100-Hz increments with no 

flow and 120-dB source excitation level. (a) Resistance. (b) Reactance........................................................184

Figure 6.15.—Comparison of impedance results from 9 GIT measurements conducted at 500-Hz 

increments and 31 Two-Parameter model (TP) simulations conducted at 100-Hz increments with no 

flow and 140-dB source excitation level. (a) Resistance. (b) Reactance........................................................185

Figure 6.16.—Comparison of impedance results from 9 GIT measurements conducted at 500-Hz 

increments and 31 Two-Parameter model (TP) simulations conducted at 100-Hz increments with 

Mach number M = 0.3 and 140-dB source excitation level. (a) Resistance. (b) Reactance. ..........................185

Figure 6.17.—Comparison of impedance results from 9 GIT measurements conducted at 500-Hz 

increments and 31 Two-Parameter model (TP) simulations conducted at 100-Hz increments with 

Mach number M = 0.475 and 140-dB source excitation level. (a) Resistance. (b) Reactance. ......................186
NASA/TP—2012-215653 xix

Figure 6.18.—Comparison of impedance results from 14 NIT measurements and 31 Crandall FullSolution model (CF) simulations conducted at 100-Hz increments with no flow and 120-dB source 

excitation level. (a) Resistance. (b) Reactance. .............................................................................................. 186

Figure 6.19.—Comparison of impedance results from 14 NIT measurements and 31 Crandall FullSolution model (CF) simulations conducted at 100-Hz increments with no flow and 140-dB source 

excitation level. (a) Resistance. (b) Reactance. .............................................................................................. 187

Figure 6.20.—Comparison of impedance results from 10 GIT measurements conducted at 500-Hz 

increments and 31 Crandall Full-Solution model (CF) simulations conducted at 100-Hz increments 

with no flow and 120-dB source excitation level. (a) Resistance. (b) Reactance...........................................187

Figure 6.21.—Comparison of impedance results from 9 GIT measurements conducted at 500-Hz 

increments and 31 Crandall Full-Solution model (CF) simulations conducted at 100-Hz increments 

with no flow and 140-dB source excitation level. (a) Resistance. (b) Reactance...........................................188

Figure 6.22.—Comparison of impedance results from 9 GIT measurements conducted at 500-Hz 

increments and 31 Crandall Full-Solution model (CF) simulations conducted at 100-Hz increments 

with Mach number M = 0.3 and 140-dB source excitation level. (a) Resistance. (b) Reactance. ..................188

Figure 6.23.—Comparison of impedance results from 10 GIT measurements conducted at 500-Hz 

increments and 31 Crandall Full-Solution model (CF) simulations conducted at 100-Hz increments 

with Mach number M = 0.475 and 140-dB source excitation level. (a) Resistance. (b) Reactance. ..............189

Figure 6.24.—Comparison of impedance results from 14 NIT measurements and 31 Composite 

Empirical model (CE) simulations conducted at 100-Hz increments with no flow and 120-dB source 

excitation level. (a) Resistance. (b) Reactance. .............................................................................................. 189

Figure 6.25.—Comparison of impedance results from 14 NIT measurements and 31 Composite 

Empirical model (CE) simulations conducted at 100-Hz increments with no flow and 140-dB source 

excitation level. (a) Resistance. (b) Reactance. .............................................................................................. 190

Figure 6.26.—Comparison of impedance results from 10 GIT measurements conducted at 500-Hz 

increments and 31 Composite Empirical model (CE) simulations conducted at 100-Hz increments 

with no flow and 120-dB source excitation level. (a) Resistance. (b) Reactance...........................................190

Figure 6.27.—Comparison of impedance results from 9 GIT measurements conducted at 500-Hz 

increments and 31 Composite Empirical model (CE) simulations conducted at 100-Hz increments 

with no flow and 140-dB source excitation level. (a) Resistance. (b) Reactance...........................................191

Figure 6.28.—Comparison of impedance results from 9 GIT measurements conducted at 500-Hz 

increments and 31 Composite Empirical model (CE) simulations conducted at 100-Hz increments 

with Mach number M = 0.3 and 140-dB source excitation level. (a) Resistance. (b) Reactance. ..................191

Figure 6.29.—Comparison of impedance results from 10 GIT measurements conducted at 500-Hz 

increments and 31 Composite Empirical model (CE) simulations conducted at 100-Hz increments 

with Mach number M = 0.475 and 140-dB source excitation level. (a) Resistance. (b) Reactance. ..............192

Figure 6.30.—Comparison of impedance results from 14 NIT measurements and 31 Fluid Mechanical 

model (FM) simulations conducted at 100-Hz increments with no flow and 120-dB source excitation 

level. (a) Resistance. (b) Reactance................................................................................................................ 192

Figure 6.31.—Comparison of impedance results from 14 NIT measurements and 31 Fluid Mechanical 

model (FM) simulations conducted at 100-Hz increments with no flow and 140-dB source excitation 

level. (a) Resistance. (b) Reactance................................................................................................................ 193

Figure 6.32.—Comparison of average impedance values from Two-Parameter model (TP), Crandall 

Full-Solution model (CF), and Composite Empirical model (CE) simulations conducted at 100-Hz 

increments with no flow and 140-dB source excitation level. (a) Resistance. (b) Reactance. .......................193

Figure 6.33.—Comparison of average impedance values from Two-Parameter model (TP), Crandall 

Full-Solution model (CF), and Composite Empirical model (CE) simulations conducted at 100-Hz 

increments with Mach number M = 0.3 and 140-dB source excitation level. (a) Resistance. 

(b) Reactance.................................................................................................................................................. 194

Figure 6.34.—Comparison of average impedance values from Two-Parameter model (TP), Crandall 

Full-Solution model (CF), and Composite Empirical model (CE) simulations conducted at 100-Hz 

increments with Mach number M = 0.475 and 140-dB source excitation level. (a) Resistance. 

(b) Reactance.................................................................................................................................................. 194

Figure 7.1.—Turbofan engine nacelle with acoustic liner...................................................................................206
NASA/TP—2012-215653 xx

Figure 7.2.—Two types of acoustic propagation in flow ducts addressed in this chapter, showing source 

plane boundary Γs and termination plane boundary Γt. (a) Inlet propagation. (b) Aft-duct 

propagation..................................................................................................................................................... 206

Figure 7.3.—Finite-element discretization of two-dimensional duct...................................................................212

Figure 7.4.—Typical two-dimensional finite-element, [I,J], and local node numbering system.........................212

Figure 7.5.—Finite-element discretization of three-dimensional duct.................................................................215

Figure 7.6.—Typical three-dimensional finite-element, [I,J,K], and local node numbering system. ..................215

Figure 7.7.—Turbofan engine showing boundary regions of axisymmetric aft-fan geometry for 

parabolic approximation acoustic propagation and far-field radiation code FWH3D, where n is unit 

vector normal to outer shear layer. ................................................................................................................. 218

Figure 7.8.—Sound attenuation results from 8 grazing incidence tube (GIT) measurements and 31 

simulations with each sound propagation code for liner 1, no flow, and source sound pressure level 

of 140 dB........................................................................................................................................................ 228

Figure 7.9.—Sound attenuation results from 8 grazing incidence tube (GIT) measurements and 31 

simulations with each sound propagation code, resonance removed, for liner 1, no flow, and source 

sound pressure level of 140 dB. ..................................................................................................................... 228

Figure 7.10.—Sound attenuation results from 8 grazing incidence tube (GIT) measurements and 31 

simulations with each sound propagation code for liner 1, mean flow Mach number M0 = 0.25, and 

source sound pressure level of 140 dB. .......................................................................................................... 229

Figure 7.11.—Sound attenuation results from 8 grazing incidence tube (GIT) measurements and 31 

simulations with each sound propagation code for liner 1, mean flow Mach number M0 = 0.40, and 

source sound pressure level of 140 dB. .......................................................................................................... 229

Figure 7.12.—Sound attenuation results from 8 grazing incidence tube (GIT) measurements and 6 

simulations with each sound propagation code for liner 1, no flow, and source sound pressure level 

of 140 dB........................................................................................................................................................ 229

Figure 7.13.—Curved Duct Test Rig (CDTR) liner test section with straight liner installed, top 

removed, view looking downstream............................................................................................................... 231

Figure 7.14.—Curved Duct Test Rig (CDTR) sound attenuation measured and predicted with two sound 

propagation codes; no flow, incident mode (0,0), and source sound pressure level of 130 dB......................231

Figure 7.15.—Curved Duct Test Rig (CDTR) sound attenuation measured and predicted with two sound 

propagation codes; no flow, incident mode (1,0), and source sound pressure level of 130 dB......................232

Figure 7.16.—Curved Duct Test Rig (CDTR) sound attenuation measured and predicted with two sound 

propagation codes; no flow, incident mode (0,1), and source sound pressure level of 130 dB......................232

Figure 7.17.—NASA Glenn Advanced Noise Control Fan (ANCF) rig. ............................................................233

Figure 7.18.—Internal and pseudo-duct Advanced Noise Control Fan (ANCF) computational meshes. ...........233

Figure 7.19.—Comparison of FWH3D and CH2DIE predictions of sound radiated from a duct for 

Active Noise Control Fan (ANCF); mode (2,0) and blade-passing frequency (BPF) = 533 Hz. ...................234

Figure 8.1.—Turbulent kinetic energy (TKE) contours downstream from a nozzle. Comparison of 

predictions from different CFD codes, PAB3D and Wind-US, and experimental particle image 

velocimetry (PIV) data. .................................................................................................................................. 245

Figure 8.2.—Comparison of sound pressure levels (SPLs) predicted by Jet3D for a jet from a 

converging nozzle using input from different CFD codes, PAB3D and Wind-US, and experimental 

data. Case 037 from Table 8.1. Inlet angle θ = 90°. ....................................................................................... 246

Figure 8.3.—Power spectral density (PSD) versus Strouhal number St of cold jet, acoustic Mach 

number Ma = 0.5, predicted by JeNo using RANS input with three turbulence models; and largest 

difference Δ between predictions. (a) Inlet angle θ = 90°. (b) θ = 150°.........................................................247

Figure 8.4.—Power spectral density (PSD) versus Strouhal number St of cold jet, acoustic Mach 

number Ma = 0.9, predicted by JeNo using RANS input with three turbulence models; and largest 

difference Δ between predictions. (a) Inlet angle θ = 90°. (b) θ = 150°.........................................................248

Figure 8.5.—Overall sound pressure level (OASPL) predicted by JeNo for jets at changing inlet angle θ

using two different RANS code flow solutions; difference Δ in predictions is (Wind-US – Craft). (a) 

Acoustic Mach number Ma = 0.5. (b) Ma = 0.9.............................................................................................. 249

Figure 8.6.—Overall sound pressure level (OASPL) predicted by JeNo for cold jets at changing inlet 

angle θ with ±10 percent change in RANS code turbulent kinetic energy (TKE); and difference ∆ in 

predictions. (a) Acoustic Mach number Ma = 0.5. (b) Ma = 0.9.....................................................................250
NASA/TP—2012-215653 xxi

Figure 8.7.—Distribution of normalized turbulent kinetic energy (TKE) for 5-cm convergent nozzle; 

here, r is radial coordinate and x is axial distance, normalized over nozzle diameter D. Wind-US 

Reynolds-averaged Navier-Stokes (RANS) predictions and particle image velocimetry (PIV) 

measurements. (a) Acoustic Mach number Ma = 0.5 unheated jet (case 003, Table 8.1). (b) Ma = 0.9 

unheated jet (case 007). (c) Ma = 1.48 heated jet (case 040)..........................................................................251

Figure 8.8.—Small Hot Jet Acoustic Rig (SHJAR)............................................................................................. 254

Figure 8.9.—Inside Aero-Acoustic Propulsion Laboratory (AAPL), showing Nozzle Acoustic Test Rig 

(NATR) and overhead far-field microphone array used in NATR acoustic testing. ......................................255

Figure 8.10.—High Flow Jet Exit Rig (HFJER) in dual-flow mode. ..................................................................256

Figure 8.11.—SHJAR nozzle system with SMC000 nozzle attached. ................................................................256

Figure 8.12.—SHJAR nozzles used in this jet noise assessment.........................................................................257

Figure 8.13.—Convergent-divergent nozzle SMC014, design Mach number Md = 1.18. Dimensions are 

in centimeters (inches).................................................................................................................................... 257

Figure 8.14.—Internally mixed, axisymmetric, dual-flow exhaust system with convergent nozzle and 

different bypass ratios (BPRs). S1 to S3 are splitters, PE1 is center plug, and C4 is convergent 

nozzle. (a) Nozzle C4S1PE1, BPR = 0.2. (b) Nozzle C4S2PE1, BPR = 1. (c) Nozzle C4S3PE1, 

BPR = 3.......................................................................................................................................................... 258

Figure 8.15.—Internally mixed, axisymmetric, dual-flow exhaust system with convergent-divergent 

nozzle M8 shown with bypass ratio (BPR) = 0.2, splitter S1. PE2 is center plug..........................................259

Figure 8.16.—Internally mixed, dual-flow exhaust system with convergent nozzle and nonaxisymmetric 

splitters. (a) Lobed. (b) Chevron. ................................................................................................................... 259

Figure 8.17.—Externally mixed dual-flow exhaust systems. Dimensions are in centimeters (inches). 

(a) Nozzle PAA5. (b) Nozzle PAA8. (c) Nozzle PAA11. (d) Nozzle PAA14. ..............................................260

Figure 8.18.—Sound pressure level (SPL) versus Strouhal number St at inlet angle θ = 90° for different 

jet acoustic Mach numbers Ma. Comparison of results from current SHJAR experimental data, 

Reference 17, and Reference 18..................................................................................................................... 262

Figure 8.19.—Sound pressure level (SPL) versus Strouhal number St at jet acoustic Mach number 

Ma = 0.5 for inlet angles θ = 90° and 150°. Comparison of values from current SHJAR experimental 

data and Reference 17. (a) Static temperature ratio Ts,r = 0.86 (cold). (b) Ts,r = 1.76. (c) Ts,r = 2.27. ...........263

Figure 8.20.—Sound pressure level (SPL) versus Strouhal number St at jet acoustic Mach number 

Ma = 0.9 for inlet angles θ = 90° and 150°. Comparison of values from current SHJAR experimental 

data and Reference 17. (a) Static temperature ratio Ts,r = 0.86 (cold). (b) Ts,r = 1.76. (c) Ts,r = 2.27. ............263

Figure 8.21.—Hot jet sound pressure level (SPL) normalized to standard day at 4.6 m (15 ft) versus 

Strouhal number St for different nozzle diameters D at inlet angle θ = 90°, Mach number M = 0.7, 

and total temperature ratio Tt,r = 3.2. (a) Comparison of values from current SHJAR experimental 

data and Reference 18. (b) Difference between values of Reference 18 and SHJAR data.............................263

Figure 8.22.—Experimental arrangement for axial-flow stereo particle image velocimetry (PIV) 

measurements. ................................................................................................................................................ 264

Figure 8.23.—Axial velocity of cold jet, acoustic Mach number Ma = 0.5, measured along centerline 

x/D using conventional particle image velocimetry (PIV), time-resolved PIV (TRPIV), laser Doppler 

velocimetry (LDV), and hotwire anemometry. (a) Normalized mean axial velocity, uo/U. 

(b) Normalized root-mean-squared fluctuating axial velocity, u′2 /U ........................................................266

Figure 8.24.—Axial velocity of cold jet, static temperature ratio Ts,r = 0.84 and acoustic Mach number 

Ma = 0.9, measured along centerline x/D using particle image velocimetry (PIV) and laser Doppler 

velocimetry (LDV). T3 and T4 designate PIV measurements taken 1 year apart. (a) Normalized 

mean axial velocity uo/U. (b) Normalized root-mean-squared fluctuating velocity u′2 /U . .......................267

Figure 8.25.—Axial velocity of hot jet measured along centerline x/D using particle image velocimetry 

(PIV) (static temperature ratio Ts,r = 2.7 and acoustic Mach number Ma = 0.9) and laser Doppler 

velocimetry (LDV) (Ts,r = 2.7 and Ma = 0.78). (a) Normalized mean axial velocity uo/U. 

(b) Normalized root-mean-squared fluctuating velocity u′2 /U ..................................................................267

Figure 8.26.—Typical results for jet noise directivity analyses. (a) 1/3-octave sound pressure level 

(SPL) versus Strouhal number St for two inlet angles θ from SHJAR experimental data and ANOPP 

predictions. (b) Difference between predicted and measured SPL, with uncertainty bands. (c) Overall 

sound pressure level (OASPL) as function of θ. ............................................................................................ 269
NASA/TP—2012-215653 xxii

Figure 8.27.—Example of source noise component and total spectra computed by ANOPP for a shockfree jet at inlet angle θ = 90°. 1/3-octave sound pressure level (SPL) versus Strouhal number St.................269

Figure 8.28.—Average error μ in overall sound pressure level (OASPL) between ANOPP predictions 

and experimental data for all ANOPP assessment cases listed in Table 8.7 (Appendix B), grouped in 

configurations A through I with corresponding bypass ratio (BPR), azimuthal periodicity m, and 

Mach number M. ............................................................................................................................................ 270

Figure 8.29.—Standard deviation σ about the average overall sound pressure level (OASPL) error 

between ANOPP predictions and experimental data for all ANOPP assessment cases listed in 

Table 8.7 (Appendix B), grouped in configurations A through I with corresponding bypass ratio 

(BPR), azimuthal periodicity m, and Mach number M...................................................................................270

Figure 8.30.—Difference in effective perceived noise level (EPNL) between ANOPP predictions and 

experimental data for all ANOPP assessment cases listed in Table 8.7 (Appendix B), grouped in 

configurations A through I with corresponding bypass ratio (BPR), azimuthal periodicity m, and 

Mach number M. ............................................................................................................................................ 271

Figure 8.31.—Assessment of Jet3D jet noise predictions. Case 003 (see Table 8.1) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.51, acoustic Mach number 

Ma = 0.5, and static temperature ratio Ts,r = 0.955. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 272

Figure 8.32.—Assessment of Jet3D jet noise predictions. Case 007 (see Table 8.1) for convergent,

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.98, acoustic Mach number 

Ma = 0.902, and static temperature ratio Ts,r = 0.842. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 272

Figure 8.33.—Assessment of Jet3D jet noise predictions. Case 022 (see Table 8.1) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.37, acoustic Mach number 

Ma = 0.492, and static temperature ratio Ts,r = 1.767. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 273

Figure 8.34.—Assessment of Jet3D jet noise predictions. Case 025 (see Table 8.1) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.68, acoustic Mach number 

Ma = 0.901, and static temperature ratio Ts,r = 1.77. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 273

Figure 8.35.—Assessment of Jet3D jet noise predictions. Case 027 (see Table 8.1) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.01, acoustic Mach number 

Ma = 1.33, and static temperature ratio Ts,r = 1.759. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 274

Figure 8.36.—Assessment of Jet3D jet noise predictions. Case 034 (see Table 8.1) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.3, acoustic Mach number 

Ma = 0.484, and static temperature ratio Ts,r = 2.624. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 274

Figure 8.37.—Assessment of Jet3D jet noise predictions. Case 037 (see Table 8.1) for convergent,

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.56, acoustic Mach number 

Ma = 0.901, and static temperature ratio Ts,r = 2.702. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 
NASA/TP—2012-215653 xxiii

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 275

Figure 8.38.—Assessment of Jet3D jet noise predictions. Case 040 (see Table 8.1) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.92, acoustic Mach number 

Ma = 1.483, and static temperature ratio Ts,r = 2.703. Comparison between Jet3D predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 275

Figure 8.39.—Assessment of Jet3D jet noise predictions. Case 268 (see Table 8.1) for convergentdivergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.4, acoustic Mach 

number Ma = 2.2, and static temperature ratio Ts,r = 2.53. Comparison between Jet3D predictions 

and SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St 

for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 276

Figure 8.40.—Nozzles with offset stream technology used to assess the JeNo v1.0 code jet noise 

prediction capability. (a) Fan-wedge. (b) S-duct. ........................................................................................... 277

Figure 8.41.—Assessment of JeNo v1.0 jet noise predictions. Case 003 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.51, acoustic Mach number 

Ma = 0.5, and static temperature ratio Ts,r = 0.955. Comparison between JeNo predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 278

Figure 8.42.—Assessment of JeNo v1.0 jet noise predictions. Case 007 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.98, acoustic Mach number 

Ma = 0.902, and static temperature ratio Ts,r = 0.842. Comparison between JeNo predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 279

Figure 8.43.—Assessment of JeNo v1.0 jet noise predictions. Case 022 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.37, acoustic Mach number 

Ma = 0.492, and static temperature ratio Ts,r = 1.767. Comparison between JeNo predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 279

Figure 8.44.—Assessment of JeNo v1.0 jet noise predictions. Case 025 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.68, acoustic Mach number 

Ma = 0.901, and static temperature ratio Ts,r = 1.77. Comparison between JeNo predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 280

Figure 8.45.—Assessment of JeNo v1.0 jet noise predictions. Case 027 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.01, acoustic Mach number 

Ma = 1.33, and static temperature ratio Ts,r = 1.759. Comparison between JeNo predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 280

Figure 8.46.—Assessment of JeNo v1.0 jet noise predictions. Case 034 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.3, acoustic Mach number 

Ma = 0.484, and static temperature ratio Ts,r = 2.624. Comparison between JeNo predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................281

Figure 8.47.—Assessment of JeNo v1.0 jet noise predictions. Case 037 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.56, acoustic Mach number 

Ma = 0.901, and static temperature ratio Ts,r = 2.702. Comparison between JeNo predictions and 
NASA/TP—2012-215653 xxiv

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, and uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 281

Figure 8.48.—Assessment of JeNo v1.0 jet noise predictions. Case 040 (see Table 8.5) for convergent, 

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.92, acoustic Mach number 

Ma = 1.483, and static temperature ratio Ts,r = 2.703. Comparison between JeNo predictions and 

SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for 

inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 282

Figure 8.49.—Assessment of JeNo v1.0 jet noise predictions. Case 059 (see Table 8.5) for convergentdivergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.172, acoustic Mach 

number Ma = 1.047, and static temperature ratio Ts,r = 0.797. Comparison between JeNo predictions 

and SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St 

for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 282

Figure 8.50.—Assessment of JeNo v1.0 jet noise predictions. Case 068 (see Table 8.5) for convergentdivergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.394, acoustic Mach 

number Ma = 1.191, and static temperature ratio Ts,r = 0.73. Comparison between JeNo predictions 

and SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St 

for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 283

Figure 8.51.—Assessment of JeNo v1.0 jet noise predictions. Case 075 (see Table 8.5) for convergentdivergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.497, acoustic Mach 

number Ma = 1.251, and static temperature ratio Ts,r = 0.699. Comparison between JeNo predictions 

and SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St 

for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 283

Figure 8.52.—Assessment of JeNo v1.0 jet noise predictions. Case 083 (see Table 8.5) for convergentdivergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.659, acoustic Mach 

number Ma = 1.342, and static temperature ratio Ts,r = 0.654. Comparison between JeNo predictions 

and SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St 

for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 284

Figure 8.53.—Assessment of JeNo v1.0 jet noise predictions. Case 090 (see Table 8.5) for convergentdivergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.784, acoustic Mach 

number Ma = 1.403, and static temperature ratio Ts,r = 0.619. Comparison between JeNo predictions 

and SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St 

for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound 

pressure level (OASPL) as function of θ........................................................................................................ 284

Figure 8.54.—Comparison of lossless power spectral density (PSD) of jet noise versus Strouhal number 

St at different inlet angles θ on a 40D arc. NATR data and JeNo v1.0 predictions. (a) θ = 60°. 

(b) θ = 90°. (c) θ = 130°. (d) θ = 150°............................................................................................................ 286

Figure 8.55.—Comparison of lossless power spectral density (PSD) for offset nozzle versus Strouhal 

number St at different inlet angles θ on a 40D arc. NATR data and JeNo v1.0 predictions. 

(a) θ = 90°. (b) θ = 150°................................................................................................................................. 286

Figure 8.56.—Comparison of lossless power spectral density (PSD) for offset S-duct nozzle and 

axisymmetric geometry (see Table 8.6 and Figure 8.40(b)) at different inlet angles θ on 40D arc. 

(a) Nozzle geometries. (b) NATR experimental data, θ = 90° and 150°. (c) JeNo v1.0 predictions at 

90° using 2.5-dimensional approximation with line-of-sight method. (d) JeNo v1.0 predictions at 

150° using 2.5-dimensional approximation with line-of-sight method. .........................................................287

Figure 8.57.—Difference ∆ between power spectral density (PSD) measured on thick side of S-duct 

nozzle and axisymmetric nozzle. (a) JeNo v1.0 prediction at inlet angle θ = 150°. (b) NATR 

experimental data at θ = 150°. (c) Error estimate at θ = 150°; difference between NATR data and 

prediction. (d) Error estimate at θ = 90°......................................................................................................... 288
NASA/TP—2012-215653 xxv

Figure 8.58.—Lossless power spectral density (PSD) for offset fan-wedge nozzle and axisymmetric 

geometry (see Table 8.6 and Figure 8.40(a)) at different inlet angles θ on 24.46-m (80.24-ft) arc. 

(a) Nozzle geometries. (b) NATR experimental data. (c) JeNo v1.0 predictions at θ = 90° using 2.5-

dimensional approximation with line-of-sight method. (d) JeNo v1.0 predictions at θ = 150° using 

2.5-dimensional approximation with line-of-sight method. ...........................................................................289

Figure 8.59.—Difference ∆ between power spectral density (PSD) measured on thick (quiet) and thin 

(noisy) sides of fan-wedge nozzle and axisymmetric nozzle. (a) JeNo v1.0 prediction at inlet angle 

θ = 150°. (b) NATR experimental data at θ = 150°. (c) Error estimate at θ = 150°; difference 

between NATR data and prediction. (d) Error estimate at θ = 90°. ...............................................................290

Figure 8.60.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 003 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 0.51, acoustic Mach number Ma = 0.5, and static temperature ratio Ts,r = 0.955. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........306

Figure 8.61.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 007 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 0.98, acoustic Mach number Ma = 0.902, and static temperature ratio Ts,r = 0.842. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........307

Figure 8.62.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 022 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 0.37, acoustic Mach number Ma = 0.492, and static temperature ratio Ts,r = 1.767. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........307

Figure 8.63.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 025 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 0.68, acoustic Mach number Ma = 0.901, and static temperature ratio Ts,r = 1.77. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........308

Figure 8.64.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 027 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 1.01, acoustic Mach number Ma = 1.33, and static temperature ratio Ts,r = 1.759. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........308

Figure 8.65.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 034 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 0.3, acoustic Mach number Ma = 0.484, and static temperature ratio Ts,r = 2.624. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........309

Figure 8.66.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 037 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 0.56, acoustic Mach number Ma = 0.901, and static temperature ratio Ts,r = 2.702. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........309

Figure 8.67.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration A case 040 for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach 

number M = 0.92, acoustic Mach number Ma = 1.483, and static temperature ratio Ts,r = 2.703. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 
NASA/TP—2012-215653 xxvi

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........310

Figure 8.68.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration B case 042 for convergent, azimuthal periodicity m = 6 nozzle: bypass ratio (BPR) = 

0, Mach number M = 0.972, acoustic Mach number Ma = 0.902, and static temperature ratio Ts,r = 

0.837. Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 310

Figure 8.69.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration B case 057 for convergent, azimuthal periodicity m = 6 nozzle: bypass ratio (BPR) = 

0, Mach number M = 0.828, acoustic Mach number Ma = 1.309, and static temperature ratio Ts,r = 

2.571. Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 311

Figure 8.70.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration C case 059 for convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, 

Mach number M = 1.72, acoustic Mach number Ma = 1.047, and static temperature ratio Ts,r = 0.797. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........311

Figure 8.71.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration C case 068 for convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, 

Mach number M = 1.394, acoustic Mach number Ma = 1.191, and static temperature ratio Ts,r = 0.73. 

Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ........312

Figure 8.72.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration C case 075 for convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, 

Mach number M = 1.497, acoustic Mach number Ma = 1.251, and static temperature ratio Ts,r = 

0.699. Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 312

Figure 8.73.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration C case 083 for convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, 

Mach number M = 1.659, acoustic Mach number Ma = 1.342, and static temperature ratio Ts,r = 

0.654. Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 313

Figure 8.74.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration C case 090 for convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, 

Mach number M = 1.784, acoustic Mach number Ma = 1.403, and static temperature ratio Ts,r = 

0.619. Comparison between ANOPP predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 313

Figure 8.75.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration D case 104C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 0.2 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.184 and 

stagnation temperature ratio Tt,r = 1.546. For bypass, Ma = 0.955 and Tt,r = 1.006. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 
NASA/TP—2012-215653 xxvii

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 314

Figure 8.76.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration D case 104F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 0.2 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.184 and 

stagnation temperature ratio Tt,r = 1.546. For bypass, Ma = 0.955 and Tt,r = 1.006. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 314

Figure 8.77.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration D case 119C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 0.2 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 2.401 and 

stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.523 and Tt,r = 1.042. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 315

Figure 8.78.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B).

Configuration D case 119F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 0.2 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 2.401 and 

stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.523 and Tt,r = 1.042. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 315

Figure 8.79.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration E case 143C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 1 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.18 and 

stagnation temperature ratio Tt,r = 1.54. For bypass, Ma = 0.948 and Tt,r = 0.99. Comparison between 

ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 316

Figure 8.80.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration E case 143F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 1 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.18 and 

stagnation temperature ratio Tt,r = 1.54. For bypass, Ma = 0.948 and Tt,r = 0.99. Comparison between 

ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 316

Figure 8.81.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration E case 156C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 1 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 2.401 and 

stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.53 and Tt,r = 1.053. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 317

Figure 8.82.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration E case 156F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 1 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 2.401 and 

stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.53 and Tt,r = 1.053. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-
NASA/TP—2012-215653 xxviii

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 317

Figure 8.83.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration F case 175C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 3 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.183 and 

stagnation temperature ratio Tt,r = 1.541. For bypass, Ma = 0.94 and Tt,r = 0.977. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 318

Figure 8.84.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration F case 175F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 3 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.183 and 

stagnation temperature ratio Tt,r = 1.541. For bypass, Ma = 0.94 and Tt,r = 0.977. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 318

Figure 8.85.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration F case 188C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 3 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 2.385 and 

stagnation temperature ratio Tt,r = 2.589. For bypass, Ma = 1.487 and Tt,r = 1.012. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 319

Figure 8.86.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration F case 188F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 3 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 2.385 and 

stagnation temperature ratio Tt,r = 2.589. For bypass, Ma = 1.487 and Tt,r = 1.012. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 319

Figure 8.87.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 191N for externally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 5 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.265 and 

stagnation temperature ratio Tt,r = 2.663. For bypass, Ma = 0.935 and Tt,r = 1.822. Comparison 

between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level 

(SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ...................................320

Figure 8.88.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 200C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 5 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.637 and 

stagnation temperature ratio Tt,r = 3.543. For bypass, Ma = 0.984 and Tt,r = 1.302. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 320

Figure 8.89.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 200F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 5 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.637 and 

stagnation temperature ratio Tt,r = 3.543. For bypass, Ma = 0.984 and Tt,r = 1.302. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-
NASA/TP—2012-215653 xxix

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 321

Figure 8.90.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 211C for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: 

bypass ratio (BPR) = 5 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 

1.614 and stagnation temperature ratio Tt,r = 3.455. For bypass, Ma = 0.973 and Tt,r = 1.27. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90°

and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level 

(OASPL) as function of θ............................................................................................................................... 321

Figure 8.91.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 211F for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: 

bypass ratio (BPR) = 5 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 

1.614 and stagnation temperature ratio Tt,r = 3.455. For bypass, Ma = 0.973 and Tt,r = 1.27. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90°

and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level 

(OASPL) as function of θ............................................................................................................................... 322

Figure 8.92.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 218C for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass 

ratio (BPR) = 5 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.637 and 

stagnation temperature ratio Tt,r = 3.546. For bypass, Ma = 0.985 and Tt,r = 1.3. Comparison between 

ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 322

Figure 8.93.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 218F for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass 

ratio (BPR) = 5 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.637 and 

stagnation temperature ratio Tt,r = 3.546. For bypass, Ma = 0.985 and Tt,r = 1.3. Comparison between 

ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 323

Figure 8.94.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration G case 230N for externally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 5 and flight Mach number Mfl = 0.1. For core, acoustic Mach number Ma = 1.126 and 

stagnation temperature ratio Tt,r = 2.46. For bypass, Ma = 1.566 and Tt,r = 1.17. Comparison between 

ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level (SPL) versus 

Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, with 

uncertainty. (c) Overall sound pressure level (OASPL) as function of θ. ......................................................323

Figure 8.95.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration H case 235N for externally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 8 and flight Mach number Mfl = 0.01. For core, acoustic Mach number Ma = 1.002 and 

stagnation temperature ratio Tt,r = 2.447. For bypass, Ma = 0.812 and Tt,r = 1.114. Comparison 

between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level 

(SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ...................................324

Figure 8.96.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration H case 241C for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 8 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.366 and 

stagnation temperature ratio Tt,r = 3.211. For bypass, Ma = 0.902 and Tt,r = 1.296. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 
NASA/TP—2012-215653 xxx

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 324

Figure 8.97.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration H case 241F for internally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 8 and flight Mach number Mfl = 0. For core, acoustic Mach number Ma = 1.366 and 

stagnation temperature ratio Tt,r = 3.211. For bypass, Ma = 0.902 and Tt,r = 1.296. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 325

Figure 8.98.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration H case 253C for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: 

bypass ratio (BPR) = 8 and flight Mach number Mfl = 0.24. For core, acoustic Mach number Ma = 

1.371 and stagnation temperature ratio Tt,r = 3.237. For bypass, Ma = 0.906 and Tt,r = 1.3. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90°

and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level 

(OASPL) as function of θ............................................................................................................................... 325

Figure 8.99.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration H case 253F for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: 

bypass ratio (BPR) = 8 and flight Mach number Mfl = 0.24. For core, acoustic Mach number Ma = 

1.371 and stagnation temperature ratio Tt,r = 3.237. For bypass, Ma = 0.906 and Tt,r = 1.3. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90°

and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level 

(OASPL) as function of θ............................................................................................................................... 326

Figure 8.100.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration H case 257C for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass 

ratio (BPR) = 8 and flight Mach number Mfl = 0.24. For core, acoustic Mach number Ma = 1.376 and 

stagnation temperature ratio Tt,r = 3.254. For bypass, Ma = 0.906 and Tt,r = 1.309. Comparison 

between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 326

Figure 8.101.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration H case 257F for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass 

ratio (BPR) = 8 and flight Mach number Mfl = 0.24. For core, acoustic Mach number Ma = 1.376 and 

stagnation temperature ratio Tt,r = 3.254. For bypass, Ma = 0.906 and Tt,r = 1.309. Comparison 

between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-

octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) 

Difference in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as 

function of θ. .................................................................................................................................................. 327

Figure 8.102.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration I case 263N for externally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 11 and flight Mach number Mfl = 0.1. For core, acoustic Mach number Ma = 0.873 and 

stagnation temperature ratio Tt,r = 2.568. For bypass, Ma = 0.738 and Tt,r = 1.083. Comparison 

between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level 

(SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ...................................327

Figure 8.103.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). 

Configuration I case 267N for externally mixed, convergent, axisymmetric nozzle: bypass ratio 

(BPR) = 14 and flight Mach number Mfl = 0.1. For core, acoustic Mach number Ma = 0.859 and 

stagnation temperature ratio Tt,r = 2.53. For bypass, Ma = 0.686 and Tt,r = 1.071. Comparison 

between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level 
NASA/TP—2012-215653 xxxi

(SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ...................................328

Figure 9.1.—Propulsion airframe acoustics (PAA) classification tree. ...............................................................332

Figure 9.2.—NASA Langley’s Low Speed Aeroacoustic Wind Tunnel (LSAWT). Dimensions are in 

centimeters. (a) Side view of test section with flow from left to right. (b) End view looking upstream 

with microphone array in upper right-hand side............................................................................................. 333

Figure 9.3.—Bypass ratio 5 nozzle with eight-chevron core nozzle and baseline fan nozzle installed in 

the jet engine simulator (JES) in the LSAWT................................................................................................ 334

Figure 9.4.—Source-to-observer conventions in Jet3D’s implementation of Lighthill’s Acoustic 

Analogy (LAA). ............................................................................................................................................. 337

Figure 9.5.—Recommended shear layer grid topology for CFD predictions of jet flow.....................................340

Figure 9.6.—Effect of varying spatial correlation constant αL on Jet3D predictions of sound pressure 

level (SPL) for baseline round bypass ratio 5 dual-stream nozzle..................................................................341

Figure 9.7.—Effect of varying spatial correlation constant αL on Jet3D predictions of sound pressure 

level (SPL) for baseline round bypass ratio 5 dual-stream nozzle with pylon. ..............................................341

Figure 9.8.—Comparison of measured data and Jet3D predictions of sound pressure level (SPL) for 

convergent-divergent nozzle (jet stagnation temperature To ≈ 955.6 K (1720 °R), nozzle pressure 

ratio NPR = 3.18, and Mach number 1.4). Jet3D noise predictions are made at 13 observer locations 

(inlet angles). (a) 40°. (b) 50°. (c) 60°. (d) 70°............................................................................................... 342

Figure 9.8.—Continued. (e) 80°. (f) 90°. (g) 100°. (h) 110°................................................................................343

Figure 9.8.—Continued. (i) 120°. (j) 130°. (k) 140°. (l) 150°. ............................................................................344

Figure 9.8.—Concluded. (m) 160°. ..................................................................................................................... 345

Figure 9.9.—Comparison of measured data and Jet3D predictions of overall sound pressure level 

(OASPL) as function of inlet angle for convergent-divergent nozzle at jet stagnation temperature To

of approximately 955.6 K (1720 °R) operating at its design nozzle pressure ratio (NPR) of 3.18 and 

Mach number of 1.4. ...................................................................................................................................... 345

Figure 9.10.—Baseline separate-flow nozzle of BPR 5, configuration 1, for Jet3D jet noise prediction............346

Figure 9.11.—Baseline separate-flow nozzle of BPR 5 with pylon, configuration 6, for Jet3D jet noise 

prediction........................................................................................................................................................ 346

Figure 9.12.—Comparison of measured data and Jet3D predictions of sound pressure level (SPL) for 

baseline separate-flow nozzle of BPR 5, configuration 1, at different observer locations (inlet 

angles). From Reference 25. (a) 52°. (b) 62°. (c) 69°. (d) 78°. (e) 88°. (f) 98°. .............................................347

Figure 9.12.—Concluded. (g) 109°. (h) 121°. (i) 127°. (j) 134°. (k) 141°. (l) 148°. ...........................................348

Figure 9.13.—Comparison of measured data and Jet3D predictions of sound pressure level (SPL) for 

baseline separate-flow nozzle of BPR 5 with pylon, configuration 6, at different observer locations 

(inlet angles). From Reference 25. (a) 52°. (b) 62°. (c) 69°. (d) 78°. (e) 88°. (f) 98°.....................................349

Figure 9.13.—Concluded. (g) 109°. (h) 121°. (i) 127°. (j) 134°. (k) 141°. (l) 148°. ...........................................350

Figure 9.14.—Comparison of measured data and Jet3D predictions of effective perceived noise level 

(EPNL) for full-scale separate-flow nozzle of BPR 5, both configuration 1 and configuration 6 (with 

pylon). Standard deviation in data is ±0.36 EPNdB....................................................................................... 351

NASA/TP—2012-215653 1

Chapter 1—Introduction

Milo D. Dahl

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

The NASA Aeronautics Research Mission Directorate, under its Fundamental Aeronautics Program, is developing physicsbased multidisciplinary design, analysis, and optimization (MDAO) tools. At present, such tools are highly customized and 

focused on specific problems, configurations, and processes. Changing any of these usually requires extensive and complex 

redevelopment efforts to achieve new modeling solutions. The extent of these efforts can range from using analysis tools that are 

empirical in nature and do not handle unconventional geometries well without new experimental data, redesign, and recalibration 

to using highly intensive computational methods that take specialists to operate and take inordinate amounts of time to obtain a 

single solution set. The challenge is to create tools that have sufficient flexibility and fidelity to enable the study of the flight 

envelope and design space of new aircraft that may be outside of current convention. To achieve this objective, NASA needs 

computational tools and methods that are robust and highly accurate for performing these predictions. These tools require quantified levels of uncertainty and need to be validated with experimental data that also include established uncertainty levels. This 

emphasis on quantifying uncertainty establishes the credibility of the results.

The Fundamental Aeronautics Program contains four projects covering subsonic, supersonic, and hypersonic aircraft as well as 

subsonic rotorcraft. Each project is structured with a base of foundational research to provide knowledge for various disciplines to 

develop tools and technologies at the component level. These components will be integrated into subsystems and finally into full 

systems each with appropriate testing and validation programs. The MDAO capability will be a product of this development 

process. Among the disciplines defined in the program, the acoustics discipline focuses on developing improved noise prediction 

methods, at both the fundamental and component level, and on developing technologies to lower the overall noise radiated from 

the aircraft. To gauge its current capability, NASA undertook an assessment of its ability to predict the noise radiated from aircraft 

systems and components. The present chapter begins by outlining the process used in this assessment and describing how the 

errors and uncertainties were defined when comparing predicted results with measured results. This is followed by an introduction 

of the topics and the types of noise prediction codes assessed in the following eight chapters of this document.

Appendix A lists the acronyms and symbols found in this chapter.

1.1 Assessment Process

The process of the assessment is described in this section,

and terms are defined. Validation is a term often used to 

denote how well the computed results agree with experimental 

data. This is recognized as a continual process. As more data 

become available, it may become necessary to make code 

modifications leading to more validation. In this context, an 

assessment is a snapshot in time of the current state of a 

validation process. At all times in this process, data to quantify 

the errors and uncertainties are gathered to document progress 

in prediction capability.

The assessment of NASA’s current capability to predict 

aircraft noise is based on quantifying the differences between 

predictions of noise from computer codes and measurements 

of noise from experimental tests. The uncertainties associated 

with both the predictions and the measurements are also 

quantified. This further enhances the credibility of the 

assessment. The common approach of using “graphical 

validation” where only lines depicting predicted and measured 

results are placed on a plot is considered inadequate for true 

validation purposes (Ref. 1). An example will be given to 

illustrate the estimation of error and uncertainty in code 

prediction validation.

For the computed results, there are no methodologies for 

determining uncertainties that are unique to the computer 

codes related to aircraft noise prediction. These codes are built 

using common numerical methods and computing practices. 

Hence, we have followed well-documented practices that are 

found in the literature (Refs. 1 to 3), in technical guides 

(Refs. 4 and 5), and in engineering references (Refs. 6 to 8) for 

determining computational uncertainties and for determining 

experimental uncertainties.

The literature related to computer modeling and simulation 

validation uses terms like verification, validation, uncertainty, 

and error. Some of these terms are used interchangeably. The 

AIAA guide (G–077–1998, Ref. 4) on validating computational fluid dynamics simulations states that a failure to 

distinguish between these terms reduces the credibility of the 

computer modeling validation. To promote clarity and 

uniformity in performing this assessment of aircraft noise 

prediction codes, we adopted definitions for the terms given 

below that follow precedence in the cited literature:

(1) Verification is the process of determining if a model is 

implemented accurately. It includes ensuring that the controlling physical equations have been correctly implemented in a 

computer code, finding and removing mistakes and errors in 
NASA/TP—2012-215653 2

the numerical algorithm and in the code, making sure that the 

input data is accurate, and estimating the numerical solution 

error, as appropriate, through convergence studies.

(2) Validation is the process that gives the evidence demonstrating that the computer model is correct by comparing 

computed results with experimental data. The experimental 

data may be obtained from a variety of tests of differing 

complexity including fundamental experiments, subsystem 

tests, and complete system tests. However, it should be 

recognized that the complete correctness or accuracy of the 

computer model in all possible situations cannot be proven. 

Hence, validation is considered a process of determining

accuracy as evidence from experiments is accumulated, which 

may in turn require modifications to the computer model,

more validation, and so forth.

(3) Uncertainty is part of many aspects in obtaining the computed results and the experimental data. In a general definition, 

the AIAA guide suggests that uncertainty is a potential deficiency 

in any part of the computer modeling and the experimental data 

gathering process that is due to a lack of knowledge. Definitions 

for different types of uncertainties are given to help clarify the 

type of uncertainty being computed, for example:

Numerical Uncertainty: The uncertainty in computed results 

due to grid size, time steps, number of iterations, and other 

parameters that affect computationally based methods more 

than empirical methods. These uncertainties are typically 

estimated through code verification and convergence studies. 

Numerical uncertainty is assumed to be uncorrelated with 

model uncertainty and, if it is significant, may be combined 

with model uncertainty.

Model Uncertainty: The uncertainty in computed results 

due to initial conditions, boundary conditions, and model 

parameters. A deficiency or incomplete knowledge of a 

physical parameter, for instance, is often represented by a 

probability function. Thus, a statistical process is essentially 

used to determine model uncertainty. Estimates of the 

uncertainty of the code output can be obtained from variations

in these conditions and parameters, otherwise known as inputs 

to the code, using sensitivity analysis and uncertainty analysis. 

Computationally based codes are assumed to be converged for 

this type of analysis.

(a) Sensitivity Analysis: Codes may potentially have a large 

number of input parameters. A sensitivity analysis reveals 

which input parameters most affect the output results. This 

analysis has the potential of identifying and, hence, reducing the number of important parameters required in followon studies. The following basic steps are performed:

(i) Determine a range that each input parameter may 

have from experimental data or best estimate.

(ii) Perform computations to determine the output 

effects for the ranges of these input parameters using 

one of the many techniques ranging from single input 

parameter adjustments while all other input parameters 

are held constant to a variance-based technique (Ref. 8). 

Depending on the number of input parameters and the 

method chosen, the required number of calculations 

may be large.

(b) Uncertainty Analysis: Once the important input parameters are determined, the following procedure is used to 

determine the uncertainty of code output given the uncertainty in the input parameters:

(i) Characterize input parameter uncertainty using experimental data or best estimate. Essentially, the input 

parameters are described by a probability density function with mean and variance values.

(ii) Generate a series of input values using statistical 

sampling methods.

(iii) Create an ensemble set of output values using each 

sample set of input parameters in a computation.

(iv) Analyze the set of code outputs to quantify the uncertainty of the computed output. Realize that the accuracy 

of this analysis improves as the size of the sample set, and 

hence the number of computational runs, increases.

A similar process was followed for experimental results. For 

this assessment, data came from laboratory tests, wind tunnel 

tests, and flight vehicle tests. Thus, the determinations of 

experimental uncertainty were not unique. Therefore, 

appropriate estimates of the experimental uncertainty were 

determined, which depended on the particular situation and the 

methodology used, as discussed in each chapter.

(4) The AIAA guide defines error as a recognizable deficiency in modeling that is not due to a lack of knowledge. The error 

may be categorized as acknowledged and unacknowledged. 

Truncation error when discretizing equations and physical 

approximations to simplify equations are examples of acknowledged error. Blunders and mistakes are considered to be some 

of the unacknowledged errors. There are many other errors that 

one may identify with an appropriate descriptive adjective. For 

this assessment, the following general definition was used:

Error: The difference between the experimental measurement and the computed result.

Implicit in this definition is that both the experimental measurements and the computed results contain errors. Thus, the 

defined error is a resultant of all the errors that are associated 

with each, including the possibility that some errors may cancel. 

Ultimately, the effect of this error is to show the accuracy of the 

computer model. Given the uncertainties associated with both 

computations and experiments, if the error is much larger than 

the combined uncertainties, then the error is considered to be 

dominated by modeling error, assuming that what is measured 

in the experiment is actually what was intended to be modeled. 

This definition of error applies to a single comparison, but it 

also may apply to a series of similar comparisons, whereby an 

average error can be computed. 

The process outlined above is illustrated in Figure 1.1.

1

Reality is expressed by a particular component or system test

 1

Figure 1.1 is based on a figure given in a presentation by H.W. 

Coleman at the Foundations for Verification and Validation in the 21st 

Century Workshop, Johns Hopkins University, Laurel, Maryland, 

October 22–23, 2002.
Introduction

NASA/TP—2011-215653 3 Chapter 1

Figure 1.1.—Diagram of assessment process leading to validation of computed result by comparison to experimental data, 

where U is uncertainty.

configuration on which an experiment is to be conducted and 

for which a computer prediction is to be run. On the experimental side, certain approximations may be made as to what is 

being measured, and errors may be made during the experiment. 

For both, uncertainties U exist and are combined to obtain the 

total uncertainty associated with the experimental data. 

Uncertainties are also found on the computational side 

including those associated with modeling assumptions, code 

inputs, and verification of the code numerical process. Modeling 

of the physics requires the development of mathematical 

equations to describe the physical processes that are thought to 

occur. Sometimes simplifications are made to obtain a tractable 

formulation. For example, complex three-dimensional geometries may be reduced to one- or two-dimensional approximations. In other cases, empirical correlations may be used to 

represent the physical process and enable the problem to be 

solved, sometimes rapidly. Computer codes require input 

parameters to run including initial and boundary conditions and 

model parameters internal to the code. Modeling and input 

uncertainties propagate through the code to create output 

uncertainties. In addition, for highly intensive computationally

based codes, numerical uncertainties are defined through the 

verification process related to grid size, time step, iterations, and 

so forth, and are included in the total computational uncertainty. 

As indicated in Figure 1.1, the final comparison error is 

determined from the difference between the experimental and 

computed results, and the uncertainty associated with the 

comparison error is computed using the uncertainties from both 

the experimental and computed results.

To further illustrate and explain the results computed by this 

assessment process, we consider some example results, as 

illustrated in Figure 1.2. Figure 1.2(a) shows data for both 

multiple measurements of a dependent variable Y at three 

settings for the independent parameter X and multiple calculated 

predictions for the same parameter. There are 20 measurement 

points for each X parameter. For the computations, the inputs 

and modeling parameters were randomly varied in 21 separate 

code runs to provide the calculated results. These raw data 

points are shown plotted on the figure slightly offset from their

X-parameter value to better visualize the results. The mean 

values for these data and their 95% confidence intervals are 

shown as the small horizontal bars on the vertical lines. The 

confidence intervals indicate that the mean value has a 

95 percent chance of being within the confidence interval given 

that the variance of the sample is a good estimate of the true 

variance value. From these results, we now have the experimental results D and the computed results C based on the mean 

values and their associated uncertainties UD and UC based on 

the 95% confidence intervals. The remaining parts of the figure 

give different presentations of the comparison between the 

measured data and the calculated data. Figure 1.2(c) shows a 

presentation of mean value comparisons where the uncertainties
NASA/TP—2012-215653 4

Figure 1.2.—Example of determining errors and uncertainties using a statistical approach for parameters X and dependent 

variable Y. (a) Raw measured and calculated data with computed means and 95% confidence intervals. (b) Computed 

comparison error and uncertainty band. (c) Point and line plot comparing calculated results and measured data, with

“error bars.” (d) Comparison plot showing 95% confidence interval (CI) and overlap regions.

are plotted by using the classic error bars co-located with the 

mean data points. An alternative presentation of the same 

results is shown in Figure 1.2(d), where the confidence 

intervals are denoted by boundary lines and shading rather 

than using error bars. This type of plot more clearly shows the 

trends and overlap regions for easier assessment between the 

two data sets. The utility of a plot like Figure 1.2(d) becomes 

more apparent as the number of X points increases as in a 

comparison between measured and computed spectral data.

The result of combining the data shown in Figure 1.2(a) to 

obtain the comparison error and the combined uncertainty 

band is shown in Figure 1.2(b). This plot illustrates the level of 

comparison error, expressed as the difference between the 

measured mean values and the computed mean values, within 

a quantified level of combined uncertainty calculated from the 

square root of the sum of the squared uncertainties for the 

measured and computed results as noted in Figure 1.1. For 

parameter X1, the comparison error lies just outside the 

uncertainty band. For parameter X2, the comparison error lies 

within the uncertainty band and is perhaps indicative of a 

“good” prediction compared with the result for parameter X3,

where the comparison error lies well outside of the uncertainty 

band indicating that either the computer model is wrong or 

there is something wrong in the experimental measurement 

process. However, further explanation is required before 

judgment is made as to the goodness of this example assessment. The comparison error results at parameters X1 and X2

may be considered borderline and good, respectively, if the 

uncertainty band is judged to be relatively small. Then any 

comparison error result that lies within the uncertainty band is 

considered equally valid given the current known level of 

uncertainty in the experimentally measured data and in the 

computed results. Conversely, if the uncertainty band is 

judged to be large, then neither of the results for the X1 and X2

cases can be considered a good validation of the predictive 

capability. The results for the X3 parameter may always be 

regarded as a poor validation since the error is much larger 

than the uncertainty.
Introduction

NASA/TP—2011-215653 5 Chapter 1

1.2 Aircraft Noise Prediction Assessment

NASA’s Aircraft Noise Prediction Program (ANOPP) 

(Ref. 9) represents the current capability for system-level 

aircraft noise prediction. As discussed in Chapters 2 and 3, the 

ANOPP code, initially developed in the early 1970s (Refs. 10

and 11), is a semi-empirical, computational tool that assembles source prediction modules for engine and airframe 

components and links them to an acoustic propagation code to

obtain far-field noise levels and sound spectra. In addition, the 

combined noise source representation of an aircraft can be 

moved in time along simulated trajectories to obtain noise 

levels for various observers along or near this simulated flight 

path. ANOPP is composed of various modules that have been 

updated over the years as new data sets became available; 

however, the empirical nature of the program limits its 

usefulness. The ANOPP results typically show large discrepancies when attempting to predict radiated noise for aircraft 

designs outside of its database. Even with this limitation, 

ANOPP, in its current form, represents the state of the art in 

the ability to do rapid prediction estimates of aircraft system 

level noise. In addition, various subcomponents of aircraft 

noise may be predicted separately using the appropriate 

ANOPP source noise module as demonstrated in Chapters 4, 

5, and 8.

The computational approaches to predicting aircraft noise 

that rely more on using first-principal equations than on semiempirical source modeling, especially at the component level, 

use increasingly higher fidelity codes such as those categorized here as acoustic analogy and numerical methods. The 

acoustic analogy methods discussed in Chapters 5, 8, and 9

use a rearrangement of the governing equations. The resulting 

equation contains a linear operator on one side of the equation 

that reduces to the wave equation governing acoustic propagation at relatively large distances from the source region. On 

the other side of the equation are placed terms that are 

significant only within a relatively small region and are 

identified as the acoustic sources, or formally in this method, 

the equivalent or analogous acoustic sources. Thus, we obtain 

a linear, inhomogeneous equation that can be solved using a 

standard integral technique (Green’s function method), which 

may involve the introduction of simplifying assumptions and 

approximations in order to reduce the computational effort. 

The problem of solving the original exact equations is 

replaced by a modeling requirement to determine the unknown 

equivalent sources. For fan noise generation, the acoustic 

source is usually the unsteady pressure distribution generated 

on the surface of a blade when a vortical disturbance velocity 

field interacts with the blade surface (Ref. 12). This aerodynamic source may be obtained by measurements, through 

computations, or by modeling. The acoustic solution is 

obtained by first computing the acoustic source followed by 

solving an integral equation for the acoustic field. Depending 

how the solution is structured, one can, for example, compute 

the blade-passage-frequency tones associated with rotor-stator 

interaction (Ref. 13) or compute the fan broadband noise 

generated by the interaction of the fan rotor turbulent wake 

with the downstream stator vanes (Ref. 14). In the jet noise 

case, the sources are spatially distributed and identified with 

the turbulent fluctuations in the flow field. Computational 

fluid dynamics calculations using steady Reynolds-averaged 

Navier-Stokes (RANS) codes with turbulence models are 

currently being used to provide integral length and time scales 

that affect the functional descriptions characterizing the 

statistical behavior of the sources (Ref. 15). Computational 

methods do not require linearizing and rearranging the 

equations, but they are very expensive numerical methods for 

solving the unsteady noise generation problem directly from

the governing equations (Ref. 16) or for solving the propagation problem in complex geometries given a known source 

(Ref. 17). Presently, computational capabilities usually limit 

the unsteady solution to the source region. To obtain the farfield radiated noise, techniques such as the Kirchhoff or the 

Ffowcs Williams-Hawkings methods are used to propagate the 

sound outward from near the source region (Ref. 18). 

The prediction codes used in this assessment are listed in 

Table 1.1 with their abbreviated name followed by a brief 

description of the code. The codes are arranged in three 

categories: (1) The semi-empirical tools include all the noise 

prediction modules within the ANOPP code and models that 

predict the acoustic impedance of liner materials placed in the 

inlet, bypass, and exhaust ducts of aircraft engines. (2) The 

acoustic analogy tools compute the noise radiated from the 

equivalent sources of engine noise such as broadband fan noise 

and jet noise without and with the effects of installation 

hardware. These tools use turbulence and mean flow quantity 

inputs computed using steady RANS solvers. (3) The numerical 

tools include an unsteady RANS code to compute the noise 

generated by airframe components; a linearized Euler code to 

predict the engine fan tone frequencies, amplitudes, and modal 

content; and various codes to predict the propagation and 

attenuation of sound in ducts with flow and the radiation of 

sound to the far field from both the duct inlet and exit. Some of 

these codes were briefly described in the previous paragraphs. 

This listing does not contain all possible codes within NASA that 

relate to aircraft noise prediction; nor does it contain codes 

external to NASA in other government, industry, or academic 

organizations that may be similar or variations of these codes. 

Because of limitations on time and resources, the codes shown 

here were chosen as representative of the state-of-the-art or 

current capability in aircraft noise prediction at NASA. Many 

codes requiring intense computational resources such as codes 

using computational aeroacoustics and large eddy simulation 

techniques are considered to be part of ongoing research and thus 

not part of this assessment of aircraft noise prediction capability.

With these qualifications, the present document is an 

assessment of NASA’s capability to predict aircraft noise and

consists of eight chapters covering topics at both the system 

and the component levels. The chapter topics are listed in 

Table 1.2. In contrast to Table 1.1, the codes are listed by type 

according to the chapters in which they appear. Each chapter 

presents a discussion of the background, issues, codes, and
NASA/TP—2012-215653 6

TABLE 1.1.—CODES ASSESSED FOR AIRCRAFT NOISE PREDICTIVE CAPABILITY

Semi-Empirical Tools

ANOPP Level 25:

Applied to components: flaps, slats, landing gear, fan, jet 

Applied to systems: engine, aircraft 

Liner impedance models: 

Two-Parameter—uses linear and nonlinear steady-flow resistance 

Crandall Full Solution—uses Crandall oscillatory channel flow solution 

Composite Empirical—contains grazing-flow effects in resistance 

Fluid Mechanical—one-dimensional lumped element model

Acoustic Analogy Tools

RSI—rotor-stator interaction code for fan broadband noise 

JeNo—jet noise code for free jets 

Jet3D—jet noise code for free jets and propulsion airframe aeroacoustics 

Numerical Tools

CFL3D—unsteady RANS code for near-field noise sources 

LINFLUX—linearized Euler fan tone noise code 

Duct acoustic propagation codes: 

Based on convected Helmholtz equation: 

CH2DDS—two dimensional, uniform flow, finite element code, direct matrix solver 

CH3DDS—three dimensional, uniform flow, finite element code, direct matrix solver 

CH3DPA—three dimensional, uniform flow, parabolic approximation code 

Based on linearized Euler equations: 

LEE2DDS—two dimensional, finite element code, direct matrix solver 

LEE2DIS—two dimensional, finite difference code, iterative solver 

LEE3DIS—three dimensional, finite difference code, iterative solver

Duct acoustic radiation codes: 

Based on convected Helmholtz equation: 

CH2DIE—two dimensional, uniform flow, finite element code with infinite outer elements 

Based on convected Helmholtz and Ffowcs Williams-Hawkings equations: 

FWH3D—three dimensional, uniform flow, parabolic approximation code with time domain 

integral for radiation

TABLE 1.2.—LIST OF CODES AND CODE TYPES ARRANGED BY CHAPTER TOPIC

Chapter topic Codes

2. Aircraft system ANOPP–L25

3. Engine system ANOPP–L25 Semi-empirical 

4. Airframe

Flaps

Slats 

Landing gear

Acoustic analogy 

ANOPP–L25 Numerical 

ANOPP–L25 CFL3D

ANOPP–L25 CFL3D

5. Fan ANOPP–L25 RSI LINFLUX 

6. Liner physics Two-Parameter Crandall Full Solution Composite Empirical Fluid Mechanical

7. Duct acoustics

Propagation

Radiation

CH3DPA LEE2DDS CH2DDS CH3DDS LEE2DIS LEE3DIS

CH2DIE FWH3D

8. Jet ANOPP–L25 JeNo Jet3D 

9. Propulsion 

airframe 

aeroacoustics 

Jet3D

experiments for that chapter topic. With the possible exception 

of the minimal interaction between Chapter 6 on liners and 

Chapter 7 on duct acoustics, the chapters are essentially 

independent of one another. Chapter 2, which discusses 

aircraft system-level noise prediction, involves the assessment 

of the semi-empirical ANOPP code. A discussion of the 

structure, content, and operation of this code is presented. 

Next, Chapter 3 presents a system-level assessment of the 

ability to predict engine noise. This involves using only the 

ANOPP engine noise source modules. Chapter 3 also discusses research related to engine core noise and illustrates 

techniques to extract combustion noise levels from engine 

noise measurements. In a similar fashion, only the ANOPP 

airframe noise source modules are used in Chapter 4 to make 

noise predictions for individual components and for aircraft in

flight. In addition, predictions are compared to experimental 

data for idealized airframe components using a high-fidelity, 

numerical code.

The remaining five chapters relate to the prediction of the 

noise radiated from the propulsive components of an aircraft. 

Chapter 5 assesses predictions for the noise generated by the 

aircraft engine fan using codes that are in each of the three 
Introduction

NASA/TP—2011-215653 7 Chapter 1

listed categories. The next two chapters relate to the noise that 

propagates through and out the duct in which the fan noise 

source resides. Chapter 6 discusses the assessment of the 

semi-empirical models to predict the acoustic properties of the 

treatment that lines the duct, and Chapter 7 assesses the ability 

to predict the propagation and attenuation of sound within the 

duct using six different numerical codes. In addition, a 

comparison is made between the far-field radiated noise 

directivity patterns predicted by two duct noise radiation 

codes. The final two chapters discuss the prediction of jet 

noise and the changes that occur in jet noise because of the 

presence of a nearby airframe component. Chapter 8 assesses 

semi-empirical- and acoustic-analogy-type code predictions 

compared with measured data for many different nozzles and 

flow conditions. When airframe components are nearby, the 

interaction of aircraft noise sources with the airframe complicates the process for computing noise predictions. Using the 

example of a jet flow just downstream of a pylon, Chapter 9

assesses the ability to predict the resulting propulsion airframe 

interaction effect on the radiated noise.

Introduction

NASA/TP—2011-215653 9 Chapter 1

Appendix A.—Nomenclature

A.1 Acronyms

ANOPP Aircraft Noise Prediction Program (NASA)

CI confidence interval

MDAO multidisciplinary design, analysis, and

optimization

RANS Reynolds-averaged Navier-Stokes (code)

A.2 Symbols

C computed result

D experimental data

E comparison error

U uncertainty (see Figure 1.1)

X independent parameter

Y dependent variable

Subscripts:

A approximations

C computed result

D experimental data

E comparison error

I inputs

M modeling

N numeric

X experimental error
NASA/TP—2012-215653 10

References

1. Oberkampf, William L.; and Trucano, Timothy G.: Verification and Validation in Computational Fluid Dynamics. Prog. 

Aerosp. Sci., vol. 38, no. 3, 2002, pp. 209–272.

2. Stern, Fred, et al.: Comprehensive Approach to Verification 

and Validation of CFD Simulations—Part 1: Methodology and 

Procedures. J. Fluids Eng., vol. 123, no. 4, 2001, pp. 793–802.

3. McKay, Michael D.; Morrison, John D.; and Upton, Stephen 

C.: Evaluating Prediction Uncertainty in Simulation Models. 

Comput. Phys. Commun., vol. 117, no. 1, 1999, pp. 44–51.

4. AIAA Guide for the Verification and Validation of Computational Fluid Dynamics Simulation. AIAA Standards Series, 

AIAA G–077–1998, 1998.

5. NCSL International: American National Standard for Expressing Uncertainty—Calibration—U.S. Guide to the Expression of 

Uncertainty in Measurement. ANSI/NCSL Z540.2–1997, 1997.

6. Coleman, Hugh W.; and Steele, W. Glenn: Experimentation 

and Uncertainty Analysis for Engineers. Second ed., Wiley, 

New York, NY, 1999.

7. Taylor, John R.: An Introduction to Error Analysis. Second ed., 

University Science Books, Sausalito, CA, 1997.

8. Saltelli, A., et al.: Sensitivity Analysis in Practice: A Guide to 

Assessing Scientific Models. Wiley, Hoboken, NJ, 2004.

9. a. Zorumski, W.E.: Aircraft Noise Prediction Program Theoretical Manual. NASA TM–83199–PT–1, 1982. b. Zorumski, W.E.: 

Aircraft Noise Prediction Program Theoretical Manual. NASA 

TM–83199–PT–2, 1982.

10. Raney, J.P.: Development of a New Computer System for 

Aircraft Noise Prediction. AIAA–1975–536, 1975.

11. Raney, J.P.: Noise Prediction Technology for CTOL Aircraft. 

NASA TM–78700, 1978.

12. Ventres, C.S.; Theobald, M.A.; and Mark, W.D.: Turbofan Noise 

Generation—Volume 1: Analysis. NASA CR–167951, 1982.

13. Meyer, Harold D.; and Envia, Enmane: Aeroacoustic Analysis of 

Turbofan Noise Generation; Final Report. NASA CR–4715, 

1996.

14. Nallasamy, M.; and Envia, E.: Computation of Rotor Wake 

Turbulence Noise. J. Sound Vib., vol. 282, nos. 3–5, 2005, 

pp. 649–678.

15. Khavaran, Abbas; and Kenzakowski, Donald: Noise Prediction 

in Hot Jets. AIAA 2007–3640, 2007.

16. Tam, Christopher K.W.: Computational Aeroacoustics: An 

Overview of Computational Challenges and Applications. Int. 

J. Comput. Fluid Dyn., vol. 18, no. 6, 2004, pp. 547–567.

17. Nark, Douglas M., et al.: The Development of the Ducted Fan 

Noise Propagation and Radiation Code CDUCT-LaRC. AIAA 

2003–3242, 2003.

18. Lele, Sanjiva K.: Computational Aeroacoustics—A Review. 

AIAA–1997–0018, 1997.
NASA/TP—2012-215653 11

Chapter 2—Aircraft System Noise Prediction

Casey L. Burley2

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

John W. Rawls, Jr.

Lockheed Martin Space Operations Langley Program Office

Hampton, Virginia 23681

Jeffrey J. Berton

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Michael A. Marcolini

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

Summary

An investigation is undertaken to assess the current capability to predict aircraft noise using NASA’s Aircraft Noise Prediction 

Program (ANOPP). NASA initiated the development of ANOPP in the early 1970s to provide the U.S. Government with the 

ability to independently (1) assess aircraft system noise, (2) assess aircraft component noise, and (3) evaluate aircraft noise 

technologies and flight procedures. To meet these goals, the prediction methodologies that have been implemented within ANOPP

are predominantly empirical to semi-empirical in nature. Many of the methods predict well for conventional aircraft designs, but 

lack capability and fidelity required to predict for nonconventional configurations. The most accurate and robust predictions are for 

those configurations that assume conventional fuselage with wing-mounted engines. In this assessment predictions are made for a 

Boeing 737–800 with CFM56–7B engines for a certification flight procedure. The predictions are then compared with integrated 

noise metrics at the three certification points. A thorough validation of ANOPP was not possible because of the proprietary nature 

of the aircraft and engine design parameters and availability of acoustic measurements other than at the certification points.

An initial investigation is made to provide an estimate of the uncertainty in ANOPP full-aircraft noise predictions. This investigation is very limited because of lack of measured data. To perform a complete uncertainty and/or error analysis of ANOPP 

requires not only acoustic results, but also a full description of the engine, including engine state, and the airframe for a range of 

flight conditions. Since this was not available at the level of detail required, an analysis is performed to determine the uncertainty 

of ANOPP results for appropriate variations in aircraft velocity and throttle setting. It is found that for the variations examined, the 

ANOPP predictions are minimally sensitive. Because of the lack of data, it is not possible to determine the accuracy of this 

finding.

To improve the accuracy of community noise predictions of aircraft, such as the noise of future aircraft with advanced, unconventional noise reduction technologies, or even for the B737’s certification noise levels estimated herein, NASA systems analysis 

tools will require significant upgrades. Some of the known issues and gaps in capabilities are identified that need to be addressed 

to use ANOPP in the prediction of next-generation aircraft.

2.1 Introduction

Aircraft system noise is the source noise emitted by an 

aircraft in flight, propagated through the atmosphere, and 

received by observers or sensors on the ground. The aircraft 

system noise includes source noise components associated 

with the propulsion system (such as jet, fan, compressor, 

combustor, propeller, and turbine noise), source noise 

components associated with the airframe (such as landing 

gear, flap, slat, and trailing-edge noise), and installation 

effects due to configuration (such as engine and wing 

shielding and reflection). The levels of each source may vary 

with aircraft configuration and operating condition. The 

combined acoustic signature of the source components 

propagates through the atmosphere to the observer. The 

observer receives the direct signal from the aircraft as well as 

indirect signals modified by the local terrain and surroundings. 

Taken together, this is the system noise of the aircraft at an 

observer.

Aircraft system noise predictions are used widely throughout the aerospace community to evaluate conceptual aircraft 

designs, for community airport planning, and to address 
NASA/TP—2012-215653 12

community noise issues. Civilian airframe and engine makers 

use system noise predictions to guide design parameter 

selections early in conceptual product design. Governmental 

regulatory agencies use system noise predictions to direct 

noise stringency rulemaking processes that protect the public 

health and welfare and to allocate resources for property and 

land use management near airports. Military researchers are 

interested in system noise predictions for reasons of low 

observability, the health of personnel, and to be good neighbors within the civilian communities in which they operate. 

Government research organizations such as NASA often make 

aircraft system noise predictions to guide aeroacoustic 

research investments as well as evaluate potential for noisereduction technologies, low-noise configurations, and lownoise procedures. 

Current aircraft systems noise prediction software lies on a 

hierarchy that trades fidelity for range of applicability. On one 

end of the hierarchy are acoustic research codes based on first 

principles. These codes require high-fidelity aerodynamic and 

geometric inputs and are used to model the physics responsible 

for the noise generation. They tend to be somewhat limited in 

range of applicability in that they address narrowly focused 

acoustic phenomena at a component or flow physics level. The 

results are often not readily or easily extended to community 

noise metrics. These research codes are usually noncommercial, 

of limited availability, require expert users, and are computationally expensive. On the opposite end of this hierarchy are 

prediction capabilities that are of low fidelity but have a large 

range of application. These codes may predict multiple-event 

noise metrics at the airport level for an entire fleet of aircraft 

and are typically widely available, empirically based, and quick 

to execute. However, they are often validated only for current 

aircraft configurations, where the noise characteristics are 

known. NASA’s aircraft system noise prediction tool, Aircraft 

Noise Prediction Program (ANOPP) (Refs. 1 and 2), lies 

somewhere between the low- and high-fidelity prediction 

methods, depending upon which modules are used. 

NASA initiated the development of ANOPP in the early 

1970s to provide the U.S. Government with the ability to 

independently assess aircraft system noise. NASA has 

continued to improve, extend, and add new prediction 

capabilities through validation and advanced modeling 

developments. ANOPP provides the capability to (1) assess 

aircraft system noise, (2) assess aircraft component noise, and 

(3) evaluate aircraft noise technologies and flight procedures. 

ANOPP consists of a set of modules (Refs. 1 to 3), which 

define the flight dynamics, noise sources of conventional 

takeoff and landing aircraft, and noise propagation effects, 

using various noise metrics. As a repository for current and 

future approaches to computerized study of aircraft noise, 

ANOPP provides maximum flexibility for updating and 

replacing the noise prediction methodology with state-of-theart prediction methods. ANOPP is continually updated by 

incorporating more physics-based theories into the modeling 

such that general scaling laws are utilized to cover a wide 

range of flow and geometric parameters and by incorporating 

new databases into the prediction schemes. 

One of the initial ANOPP validations in late 1970s for fullaircraft configurations was made for the Lockheed L–1011 

wide-body transport equipped with three RB.211–524B 

engines (Ref. 4). Predicted and measured noise comparisons 

were made for a range of Mach numbers (0.25 to 0.30) with 

engine pressure ratios ranging from 1.13 to 1.67. Comparisons 

of the predicted results with measurement were within several 

decibels in the aft quadrant, but large differences were found 

in the forward quadrant due to overprediction of the fan noise. 

Another validation study made during that time was for a 

McDonnell Douglas model DC–10–40 wide-body transport 

powered by three Pratt & Whitney JT9D–59A engines 

(Ref. 5). It was shown that for all power settings ANOPP 

consistently underpredicted the low frequency levels and 

overpredicted the higher frequency levels. The differences 

were dependent on flight condition (approach, flyover, and

takeoff), but ranged from a few decibels up to 15 dB. In these 

early studies the noise sources were modeled in isolation and 

did not include any installation effects. There was no capability within ANOPP to include effects of liners. Even though 

the comparison between measured and predicted levels was 

poor, the noise trends were captured. Since that time, methods 

to account for installation effects (although currently considered limited) and effects of liners (albeit quite limited) have 

been implemented, and there have been a number of studies 

performed using ANOPP. ANOPP has been used as part of 

aircraft design optimization (Refs. 6 to 9) and assessment of 

current and future noise reduction technologies (Refs. 10 and 

11). In addition to the subsonic aircraft (conventional takeoff 

and landing, CTOL) capability, a propeller analysis system 

(PAS) was also developed and became part of the ANOPP 

system (Ref. 3). Example validation efforts for this are 

provided in Reference 12 as well as Reference 13, for which 

the effect of propeller angle of attack on the noise was 

investigated. 

Acronyms and symbols used throughout this chapter are 

listed in Appendix A to aid the reader.

2.2 ANOPP Code

ANOPP is a state-of-the-art aircraft noise prediction tool 

that relies primarily on semi-empirical methods. A schematic 

of the ANOPP system is shown in Figure 2.1. ANOPP 

consists of a set of functional modules that predict atmospheric properties, the aircraft flight path, source-to-observer 

geometry, source noise of the aircraft components (propulsion

systems and airframe), propagation of the source noise to 

ground observers, and community noise metrics. The ANOPP 

executive is the part of the code that allows the user to 

interface with the other parts of ANOPP shown in Figure 2.1, 

This important part of the ANOPP capability not only controls 

the execution of modules but interprets and creates inputs for 

modules, provides data management for the functional
Aircraft System Noise Prediction

NASA/TP—2012-215653 13 Chapter 2

Figure 2.1.—ANOPP Level 25.

modules, and provides error handling and exit procedures to 

the host computer. Because of the ANOPP executive and 

modularity of the system, ANOPP prediction capabilities are 

flexible and appropriate for problems ranging from an isolated 

source to a full-aircraft system operating with complex flight 

regimes with varying conditions. The functional modules 

include those that can be used to set up the aircraft flight 

definition, the source noise modules for the CTOL, the PAS, 

the propagation modules, and the modules for determining 

noise metrics at specified far-field observer locations. A 

comprehensive discussion of the underlying theory, modeling, 

as well as ANOPP input and output is beyond the scope of this 

document. In summary however, the key geometric parameters and flow conditions to predict the acoustic strength and 

directivity required for each noise source are provided by the 

user and/or computed within the specific module. The details 

of the theory and modeling for each module can be found in 

Reference 2 and in the online-manual pages provided with the 

ANOPP code distribution. An example of the theory details 

provided in Reference 2 for ANOPP landing gear noise 

prediction can be found in Appendix B of Chapter 4, “Airframe Noise: A Prediction Capability Assessment.” 

The steps shown in Figure 2.2 can summarize the prediction 

of aircraft noise by the ANOPP system. These steps are used 

to determine the noise radiated from an aircraft that follows an 

arbitrary flight path in the presence of an observer on the 

ground. During this operation, noise sources on the aircraft 

emit acoustic radiation computed from models that determined

the power, directivity, and spectral distribution characteristics, 

all of which may vary with time. This source noise propagates 

through the atmosphere to the observer. The observer receives 

the noise signal from the direct ray plus a signal from a ray 

reflected by the local ground surface, if the observer is above 

the ground. The ANOPP computational process starts by first 

defining the aircraft flight profile. This requires that the 

atmosphere as well as the trajectory and operating conditions

Figure 2.2.—Prediction flow within ANOPP Level 25 

using CTOL source modules.

of the aircraft be defined. The Atmospheric Module (ATM) 

establishes the properties of the atmosphere (pressure, density, 

and humidity as functions of altitude). The Flight Dynamics 

Modules define the location and orientation of the aircraft as 

well as its operating state as a function of time relative to a 

ground fixed coordinate system. These modules also determine the engine throttle position and aircraft Mach number, 

which are used as control parameters for source noise 

predictions. The Geometry Module is then invoked to compute 

the time-dependent emission angles and source-to-observer 

distances. 

Once the aircraft flight path and conditions along that path 

are defined, the source noise modules are then used to 

compute the noise from each propulsion and airframe source. 

ANOPP assumes that each source can be modeled as a point 

source. Source noise predictions are made in several coordinate systems, which are attached to the aircraft. The airframe 

noise predictions are made in the wind axis coordinate system. 

The engine noise predictions are made in the body axis

system. Sources within the wind axis may be summed before 

propagation. Similarly sources within the body axis may be 

summed before propagation. Sources from the wind and body 

axis are propagated separately to a ground-fixed coordinate 

system and summed to obtain the total noise. Figure 2.3 shows 

the coordinate system for which the ground-fixed observers 

are defined. The ANOPP system internally handles the 

conversion between the source noise coordinate systems and 

the observer coordinate system. Using an assumption of 

acoustic superposition, the source noise spectra (mean-square 

pressures) are analytically summed in the vicinity of the 

aircraft and propagated to observers on the ground or may be 

summed at the ground observers.
NASA/TP—2012-215653 14

Figure 2.3.—ANOPP coordinate system.

2.2.1 ANOPP Source Noise Methods

In this section, the engine and airframe prediction capabilities contained in the ANOPP CTOL system are summarized. 

The ANOPP source noise prediction methods are implemented 

in separate modules for each of the engine and airframe noise 

sources. There are currently 13 source noise modules within 

the ANOPP CTOL system, with several of the modules 

including multiple methods. For instance, of the two fan noise 

modules in ANOPP, the fan noise module known as HDNFAN

contains three methods based on the original Heidmann 

method. One is the original method, and the other two are 

enhancements for large fans and enhancements for small fans. 

The other fan noise module known as BFN only contains one 

method. The details of the methods implemented can be found 

in the ANOPP theory manual electronically distributed with 

ANOPP Level 25. This document has been significantly 

updated from the original ANOPP theory manual of Reference 

2.

2.2.1.1 Fan

Fan noise radiates from the fan inlet and the bypass nozzle 

exit. The fan noise that radiates from the fan inlet is often 

modeled as three separate components, each associated with 

different noise-generation mechanisms. The first is the tone 

component, which is generated by steady and unsteady 

aerodynamic loading on rigid surfaces, such as the fan blades 

and the stator vanes. The second is the broadband noise 

component generated by unsteady aerodynamic loading 

associated with random flow fluctuations. These fluctuations 

may be caused by inflow turbulence impinging on rotor blades 

and stator vanes, rotor wake turbulence impinging on downstream stators, and interaction of the blade tip flow with the 

turbulent wall boundary layer. The third component is often 

referred to as “buzz saw” noise because of its distinct sound. 

This noise source is also referred to as multiple pure tone 

noise or combination tone noise. When the fan blades rotate at 

supersonic tip speeds, bow shocks form at the leading edges. 

These shocks interact nonlinearly with each other as they 

propagate upstream through the inlet. Slight variations in 

shock strengths result in a pressure spectrum with discrete 

multiple pure tones at the shaft rotational frequency as well as 

its harmonics and subharmonics. The fan noise that radiates 

from the fan exhaust duct is characterized by tone and 

broadband components. The mechanisms that generate this 

noise are similar to those that generate the forward-radiated 

noise. The total fan noise is predicted by summing the noise 

from three inlet radiated noise components and two aftradiated noise components.

The two fan noise modules implemented in ANOPP are the 

“Heidmann” module (HDNFAN) and the Boeing fan module 

(BFN). Both modules include methodologies to account for 

the inlet and aft radiated broadband noise, inlet and aft discrete 

interaction tones, and inlet combination tones. The original 

Heidmann method (which is one of the three options in the 

HDNFAN module) (Ref. 14) utilizes several acoustic 

relationships suggested by The Boeing Company as part of its 

underlying semi-empirical acoustic equation framework. This 

semi-empirical framework was calibrated to full-scale acoustic 

data obtained in the 1970s at NASA Lewis (now Glenn) 

Research Center under the direction of M.F. Heidmann. Two 

revisions have been made to the Heidmann method to improve 

the prediction method for fans outside the original database. 

Revisions made by AlliedSignal (Ref. 15) improve predictions 

for small turbofan engines in the 13- to 27-kN (3000- to

6000-lb) thrust range. Revisions made by GE Aircraft Engines 

(Ref. 16) improve predictions for large fans such as those 

found on the CF6–80C2, which has a rated thrust of about 

270 kN (60 000 lb). The data used to develop and validate the 

three methods are characterized in Table 2.1 to Table 2.3. All 

three methods employ empirical functions to predict the sound 

spectra as a function of frequency and polar directivity angle. 

Further details of the HDFAN module can be found later in

Chapter 5, “Fan Noise Prediction,” including a description of 

input parameters (in Table 5.8).

The Boeing fan noise module (BFN) (Refs. 17 and 18) 

computes forward and aft radiated fan noise for axial flow 

turbofans. The module was developed using five sets of 

component-modeled measurements that cover a wide range of 

fan diameters, including narrow- and wide-chord fans, and a 

range of power settings that include bypass ratios greater than 

8. The data used to evaluate the accuracy of the method 

consisted of 10 different engine data sets. These data sets 

included 127 individual power points, of which 48 were for 

bypass ratios greater than 8. Similar to the Heidmann methods, 

the BFN module utilizes empirical functions to predict sound 

spectra as a function of frequency and polar directivity angle.
Aircraft System Noise Prediction

NASA/TP—2012-215653 15 Chapter 2

TABLE 2.1.—DATABASE USED FOR “ORIGINAL” HEIDMANN METHOD

Fan Total 

pressure 

ratio

Mass flow

rate

Rotor tip 

Mach 

number

Rotor-relative 

tip Mach 

number

Number 

of

vanes

Number 

of

blades

Blade passage 

frequency,

Hz

Cutoff 

factor

Rotor-stator 

spacing 

kg/s lb/s factor

A 1.5 430 950 1.04 1.2 90 40 2420 0.83 200

B 1.5 430 950 1.04 1.2 60 26 1570 0.80 200

C 1.6 415 915 1.39 1.52 60 26 2250 N/A 200

QF–1 1.5 396 873 0.99 1.12 12 53 3120 0.89 367

QF–3 1.4 396 873 0.99 1.12 112 53 3120 0.89 367

QF–5 1.6 385 850 0.98 1.14 88 36 2080 0.68 227

QF–6 1.2 396 873 0.67 0.88 50 42 1670 3.53 400

QF–9 1.2 403 889 0.63 0.87 11 15 556 2.38 200

TABLE 2.2.—DATABASE USED FOR

“LARGE FAN” HEIDMANN METHOD

Fan Thrust,

104 N (103 lb)

Bypass

ratio

Tip speed,

m/s (ft/s)

Pressure

ratio

CF6 25 (57) 5 437 (1434) 1.8

E3 14 (32) 7.7 342 (1123) 1.4

QCSEE 8 (19) 12.1 291 (956) 1.3

TABLE 2.3.—DATABASE USED FOR “SMALL FAN” HEIDMANN METHOD

Fan Total 

pressure 

ratio

Mass flow 

rate,

kg/s (lb/s)

Rotor tip 

Mach 

number

Rotorrelative tip 

Mach 

number

Vane to 

blade 

ratio

Blade 

passage 

frequency,

Hz

Cutoff 

factor

Rotorstator 

spacing 

factor

1, 2, and 3 1.5 to 1.6 45 to 91

(100 to 200)

0.3 to 1.2 1.45 to 1.53 2.0 to 2.5 3600 to 5300 0.77 to 1.15 170 to 214

2.2.1.2 Jet

The characteristics of jet noise are determined by the operating conditions of the jet and the nozzle type. ANOPP offers six 

prediction methods to compute jet noise. These methods are 

identified along with their key features in Table 2.4. The range 

of application for each method varies depending on the 

operating condition and nozzle geometry. Jet noise is often 

characterized by three subcomponents: jet mixing noise, 

broadband shock noise, and screech tones. Jet turbulent mixing 

noise consists of that associated with the large turbulent 

structures and that due to the less directional fine-scale turbulence noise. The jet mixing noise is most intense in the downstream direction and peaks near 130° as measured from the 

engine inlet. The broadband shock noise, on the other hand, is 

most intense in the upstream direction near 30°. Noise from jets 

with supersonic exhaust velocity contain both jet mixing noise 

and broadband shock noise. Modern nozzles are commonly 

designed such that screech tones do not occur under normal 

operating conditions and therefore are not modeled.

Nozzle type also plays an important role in determining the 

jet noise characteristics. The most basic nozzle type is the

convergent circular nozzle. With the development of the

turbofan bypass engine, two nozzle configurations evolved—

the internally mixed nozzle and the externally mixed nozzle. 

Internally mixed jets exhaust the core and bypass flow through 

a single downstream nozzle with the internal primary nozzle 

located upstream of the bypass nozzle. In some cases, the 

internal nozzle may incorporate a lobed forced mixer to 

enhance the internal mixing. Internally mixed nozzles are not 

explicitly modeled within ANOPP; however, the effects of 

internal mixing may be estimated by computing mixed flow 

characteristics. The more common nozzle is the “separateflow coannular nozzle,” where the core and bypass flows 

exhaust through separate nozzles. The ANOPP modules 

STNJET and ST2JET model the separate-flow nozzle 

configurations, which include the coplanar nozzle, bypass 

nozzle that is offset (upstream) from the primary nozzle, and 

primary nozzle with a center plug. To add additional complexity, both the bypass nozzle and/or the primary nozzle can be 

fitted with exit perimeter suppression devices such as 

chevrons. Within ANOPP, ST2JET models the effect of 

chevrons as a correction to the source noise spectra of nozzles 

without chevrons. The following provides a short description 

of the noise prediction methods shown in Table 2.4: 

(1) One of the first empirical jet noise prediction methods to 

gain widespread acceptance is the SAE–ARP 876 method 

(Ref. 19). SAE–ARP 876 contains several methods of which 

only part are implemented within ANOPP. The mixing noise 
NASA/TP—2012-215653 16

for convergent circular jets is implemented in the SGLJET 

module, and the broadband shock noise for convergent 

circular jets is implemented in the SAESHK module. The SAE 

method for distributed jet noise is not currently implemented 

within ANOPP. Both of these methods are for the prediction 

of single (convergent) nozzle jets.

(2) The CNLJET module also known as the “Dual Stream 

Coannular Jet Noise Module,” predicts the jet mixing noise for 

a coannular jet exhaust nozzle with inverted velocity profiles 

(i.e., the bypass flow is greater than the core velocity). This 

prediction capability is based on the method developed by Pao 

and Russell, References 20 and 21, respectively. The method 

converts the coannular jet to an equivalent single stream jet 

with the same thrust, mass flow rate, and energy. 

(3) The TAMSHK module predicts the free-field lossless 

broadband shock noise for circular and rectangular nozzles. 

The circular jet theory, developed in References 22 and 23, is 

applicable to overexpanded and underexpanded jets and 

accounts for the effects of jet temperature and forward flight. 

The forward flight effects for the circular jet theory include 

both Doppler and convective amplification factors. The 

rectangular nozzle theory, developed by Tam and Reddy

(Ref. 24), contains essentially the same elements as the 

circular jet theory. Unlike circular jet noise though, rectangular jet noise is not symmetric in the azimuthal plane. An 

empirical correction factor developed by Ponton et al.

(Ref. 25) is used to extend the rectangular theory to azimuthal 

angles other than 0°. The rectangular nozzle theory is limited 

to nozzles with straight sidewalls and aspect ratios of 6 or less.

(4) Two ANOPP modules are associated with the work of 

Stone (Refs. 26 to 29). The original Stone method, STNJET,

(Refs. 26 and 27) predicts the far-field mean-square acoustic 

pressure for single- and dual-stream circular jets for either 

convergent or convergent-divergent nozzles. The method 

predicts both jet mixing noise and broadband shock noise. The 

method is limited to nozzles where the core velocity is greater 

than the bypass velocity. In addition, only the core velocity can 

be supersonic. The Stone method has been modified to improve 

jet noise predictions for small turbofan engines in the 13- to

27-kN (3000- to 6000-lb) thrust range (Ref. 28). The Stone Jet 

Noise module of 2003, ST2JET, is the most comprehensive of 

the jet noise prediction capabilities in ANOPP. A detailed 

assessment of the ST2JET module is presented later in Chapter 8, “Jet Noise Prediction.” The ST2JET module predicts jet 

noise for circular exhaust nozzles having single or dual streams, 

convergent or convergent-divergent geometry, and subcritical or 

supercritical pressure ratio. It also accounts for the presence of 

center plugs and exit plane perimeter noise suppression devices. 

The module is based on the semi-empirical model developed by 

J.R. Stone of Modern Technologies Corporation (Ref. 29). The 

method was developed from data with bypass ratios ranging 

from 5.0 to 14.9 obtained from the anechoic free-jet facilities at 

NASA Glenn Research Center, General Electric Company, and 

NASA Langley Research Center as well as free-jet facilities at 

Lockheed. The ST2JET module is an update to the STNJET 

module and extends the ANOPP jet noise prediction capability 

to higher bypass ratio engines for a full range of nozzle 

configurations including jets with inverted velocity profiles. 

TABLE 2.4.—ANOPP JET NOISE PREDICTION METHODS

SAE–ARP 876

Appendix A

(SGLJET)

Stone 1980

(STNJET)

Stone 2006

(ST2JET)

Pao-Russell

(CNLJET)

SAE–ARP 876

Appendix B

(SAESHK)

Tam

(TAMSHK)

Bypass ratio 0 0 to 5 0 to 14 0.1 to 5 0 0 to 5

Circular nozzle • • • • •

Coannular nozzle • • •

Rectangular nozzle •

Subsonic mixing (primary) • • • •

Supersonic mixing (primary) • • • •

Subsonic mixing (secondary) • • •

Supersonic mixing (secondary) • •

Broadband shock (primary) • •

Broadband shock (secondary) •

Point source • • • • • •

Distributed source •

Centerbody • •

Flight effects • • • • •

Chevrons •

Inverted velocity profile • •
Aircraft System Noise Prediction

NASA/TP—2012-215653 17 Chapter 2

2.2.1.3 Core

Combustion noise is computed using the GECOR module. 

This module predicts noise from conventional combustors 

installed in gas turbine engines. Three methods are available 

within the module and are known within ANOPP as the SAE 

method, the small engine method, and most currently the 

narrowband method. The SAE method, described in Reference 19 is based on methodology proposed by R.K. Matta 

(Ref. 30) and produces empirical 1/3-octave band spectra as a 

function of frequency and polar directivity angle. It is based on 

core noise data from turboshaft, turbojet, and turbofan engines. 

The small engine method, (Ref. 28) is a revision to the SAE 

method for small turbofan engines in the 13- to 27-kN (3000- to 

6000-lb) thrust class. The narrowband method predicts the noise 

generated by a combustor using empirical data and functions to 

compute sound spectra as a function of narrowband frequency 

and polar directivity angle (Ref. 31). The narrowband method 

follows a similar formulation to that of the ANOPP 1/3-octave 

band methods; however, the empirical directivity and spectrum 

factors are different and specific to the narrowband method. 

2.2.1.4 Turbine

Prediction methods for turbine noise have historically received 

limited attention due to its unimportance relative to the other 

engine sources. Prediction of the turbine noise is also difficult to 

assess since direct noise measurements are nonexistent and must 

be determined by indirect measurements or digitally extracting 

from the jet noise measurements. Two modules are available in 

ANOPP to predict turbine noise, TUR and SMBTUR. The TUR 

module predicts the free-field lossless far-field noise generated by 

the turbine of an aircraft engine. Turbine noise is modeled as two 

components, broadband noise and discrete tones. The broadband 

noise is the result of fluctuating lift on the rotors and stators, 

whereas the discrete tones are caused by the interaction of rotor 

wakes intersecting with following stator vanes and rotors. There 

are two options contained in this module. The first option is a 

semi-empirical prediction procedure based on the method 

developed by Dunn and Peart as described by Krejsa and 

Valerino in Reference 32. The second option is a revision to the 

Dunn and Peart method made by AlliedSignal (Ref. 28) to 

improve predictions for small turbofan engines in the 13- to

27-kN (3000- to 6000-lb) thrust class. This method is called the 

small engine method. Both methods use essentially the same form 

of equations. However, the small engine method uses different 

constants for the broadband and tone noise acoustic power terms. 

Also the spectrum shape is modified for the small engine method. 

The broadband and tone noise components are summed to 

determine the overall turbine noise level. 

The Smith and Bushell Turbine Noise Module or SMBTUR 

also predicts turbine noise, but only the broadband noise 

component. Similar to the TUR module, there are two options

contained in this module. The first option is based on the method 

developed by Smith and Bushell (Ref. 33) and employs empirical 

functions to produce sound spectra as a function of frequency and 

polar directivity angle. The second option is a revision to the 

Smith and Bushell method made by AlliedSignal (Ref. 28) to 

improve predictions for small turbofan engines in the 13- to

27-kN (3000- to 6000-lb) thrust class. Both of these options 

assume that the only significant noise source is the “vortex” 

component, which is the broadband noise due to the interaction of 

the rotating blades with random velocity patterns in the flow. 

2.2.1.5 Airframe

ANOPP currently has two methods for computing the noise 

from aircraft airframe components: the “Fink” method (computed using the FNKAFM module) and the “Boeing” method; each 

method is detailed in Chapter 4, “Airframe Noise: A Prediction 

Capability Assessment.” Both methods compute the 1/3-octave 

noise spectra based on fundamental parameters, which define the 

local flow conditions and the geometry of each component. The 

Fink method is based on a method developed by M.R. Fink of 

the United Technologies Research Center for the Federal 

Aviation Administration (FAA) (Ref. 34). The method employs 

empirical functions to model the far-field noise spectrum as a 

function of polar directivity angle and azimuthal directivity 

angle. Each spectrum is the sum of all the airframe component 

spectra produced by the wing, tail, landing gear, flaps, and 

leading-edge slats. 

The Boeing method also computes the noise from the airframe 

components; ailerons, trailing-edge flaps, leading-edge slats, and 

landing gear. The noise prediction methodology associated with 

the aerodynamic control surfaces (i.e., ailerons, flaps, and slats) 

was developed by Sen et al. (Ref. 35) using acoustic measurements from full- and model-scale commercial transports. The 

landing gear noise prediction method was developed by Guo 

(Ref. 36) and is based on measurements from model- and fullscale landing gear. The methods employ empirical functions to 

produce unattenuated 1/3-octave band acoustic spectra as a 

function of frequency and polar directivity angle. A Doppler 

frequency shift is included to account for forward flight effects. 

To define the airframe geometry, parameters such as wingspan, 

trailing-edge flap chord lengths, number of landing gear, tire 

sizes, and surface areas of the landing gear components must be 

provided by the user. 

2.2.2 Installation Effects

The aircraft configuration can significantly affect the radiated 

noise. The aircraft engines may be installed such that the wing 

shields (reduces) the noise generated by the engine from ground 

locations during the flight operation. Alternatively, the installation 

of the engines under the wing may result in reflection of the noise 

from the fuselage and/or wing-flap surface. ANOPP currently has 

limited capabilities to account for these effects. The following 

subsections provide an overview of engine liners and the module 

that is available to account for noise shielding and reflection.

2.2.2.1 Liners

The Fan Noise Treatment Module (TREAT) predicts the 

attenuation spectra for acoustic treatment in a turbofan inlet and 

aft fan bypass duct. The attenuation is estimated using methods 
NASA/TP—2012-215653 18

developed by Magliozzi (Ref. 37) or Kontos et al. (Ref. 38). 

The attenuation spectra are applied to separate predictions of the 

inlet- and aft-radiated source noise produced by a source noise 

module, such as the Heidmann Fan Noise Module (HDNFAN), 

and a total attenuated fan noise prediction is produced. The 

method accounts for a conventional (perforate) single- or 

double-degree-of-freedom liner of typical design. The aft duct 

treatment can be either single or double layered. The inlet 

treatment is always assumed to be single layered. The acoustic 

treatment is described geometrically by the duct radius or height 

and the treatment length. The acoustic treatment design is 

simply specified by the frequency of peak attenuation. The duct 

flow is determined from the mass flow and flow duct area. 

Hence it should be noted that these models are limited and that 

many important details about the liner design (such as modal 

content of the source) and implementation factors (location of 

liner, number of seams, etc.) of the designs are not included. 

Examples of predictions of engine noise with and without the 

TREAT module are shown in Chapter 3, “Engine System and 

Core Noise.”

2.2.2.2 Wing

The Wing Geometric Effects Module computes the effects of 

wing shielding and reflection on the propagation of noise from 

the engine. The wing shielding and the wing reflection effects 

are modeled separately and only for specific configurations. The 

wing shield model assumes the source (engine) is located above 

the wing. The wing reflection assumes the source (engine) is 

below the wing-flap system. Both models ignore the presence of 

the fuselage. The wing shielding model employs the Fresnel 

diffraction theory for a semi-infinite barrier, as described in 

Beranek (Ref. 39) and Maekawa (Ref. 40), with modifications 

to treat the finite barrier presented by the aircraft wing. The 

wing reflection model assumes that reflection can occur only 

from the wing-flap system, not the fuselage. A maximum of 

three wing-flap panels may be included in the model, and the 

effect of leading-edge slats on the wing is neglected. For both 

the wing shielding and reflection models the wing and flap 

panels are assumed to be perfectly planar surfaces.

2.2.3 ANOPP Computational Efficiency and Usage

ANOPP Level 25 is written in Fortran 77 and can be run on a 

desktop or personal computer. For most applications, ANOPP

will easily execute on modern personal computers with no special 

memory or disk requirements. Typical run times for ANOPP are 

on the order of seconds. For complex applications, where noise is 

computed at hundreds of observation points, the runtimes may be 

only on the order of minutes, which makes ANOPP very 

attractive for use in system and optimization studies. 

ANOPP requires that the user have a basic knowledge of 

aircraft aeroacoustics and propulsion systems. This is needed to 

properly select the appropriate prediction strategy and source 

noise modules. In addition the user needs to be familiar with the 

ANOPP executive programming language in order to customize 

standard input templates to solve specific problems. The 

ANOPP programming language is a powerful capability that

provides a unified system approach to prediction of noise from a 

full aircraft as well as from individual aircraft components.

2.3 ANOPP Evaluation and 

Demonstration of Capabilities

The ANOPP prediction capabilities are demonstrated for a 

Boeing 737–800 with CFM56–7B engines. The following 

section provides a description of the vehicle, the operating 

condition, and flight trajectory inputs used to compute noise 

metrics. A careful validation whereby detailed predictions are 

compared with a comprehensive acoustic database was not 

possible because of difficulties in obtaining the required 

vehicle state data and availability of validation quality 

measurements. Full-aircraft noise data available in the public 

domain and suitable for validation purposes are quite limited. 

The predictions in this chapter are compared with certification 

measurements taken for a number of Boeing 737–800 with 

CFM56–7B engines. In addition, an initial evaluation of the 

sensitivity of ANOPP predictions to small changes in aircraft 

Mach number and engine power setting is presented. 

The specific ANOPP functional modules and source noise 

modules used to predict the full-aircraft noise for each step 

indicated in Figure 2.2 are shown in Table 2.5 as all upper case 

identifiers. The ANOPP output for this study is the received 

noise that takes into account spherical spreading, atmospheric 

attenuation, ground effects, reflections, and lateral attenuation at 

certification locations. The ground was specified as soft, which 

is representative of the ground found at airports.

TABLE 2.5.—ANOPP MODULES USED FOR PREDICTING THE NOISE FROM A GENERIC BOEING 737–800 AIRCRAFT

Aircraft flight definition Source noise modelinga Propagation and received noise

Weather: ATM, ABS

Flight path definition: SFO

Source-to-observer geometry: GEO

Jet: ST2JET 

Fan: HDNFAN 

(General Electric large fan method)

Acoustic liner: TREAT 

(General Electric acoustic liner method)

Core: GECOR

(SAE ARP 876 Matta method)

Airframe: FNKAFM

(includes landing gear, slats, flaps, trailing-edge noise sources) 

Propagation: PRO

Noise metrics: LEV, EFF

a

Phrases in parentheses are options used within the module.
Aircraft System Noise Prediction

NASA/TP—2012-215653 19 Chapter 2

Figure 2.4.—Analytical representation of CFM56–7B turbofan engine in Numerical Propulsion System Simulator (NPSS) 

(Ref. 41).

2.3.1 Vehicle Description

The Boeing 737–800 is a short-to-medium-range aircraft, 

with a maximum range of about 5500 km (3000 nautical 

miles). It is equipped with two CFM56–7B engines capable of 

116 kN (26 091 lb) of thrust per engine at its sea level static 

flat rating, with a typical cruise Mach number of 0.785. The 

overall length of the B737–800 is about 39 m (129 ft) with a 

wingspan of over 34 m (112 ft). The B737–800 can seat 162 to 

189 passengers depending on the cabin class configuration. 

Gross airframe dimensions are required inputs for the Fink 

airframe noise prediction module used in this benchmarking 

assessment, and these inputs can be obtained from many 

public-domain aircraft information sources. A simple threeview drawing of the aircraft is often sufficient to provide the 

Fink airframe noise prediction method with proper input data.

2.3.2 Engine Description

The engine state for a range of Mach number and throttle 

settings is required input for ANOPP’s source noise prediction 

modules. Unfortunately, the propulsion system data that 

ANOPP needs are exceedingly difficult to obtain. Engine 

companies regard this information as highly proprietary 

company trade secrets. For this reason, propulsion data for the 

CFM56–7B was not available for this assessment. Fortunately, 

NASA has the capability to compute such propulsion data, 

using a thermodynamic cycle and aeromechanical engine 

simulation program known as the Numerical Propulsion 

System Simulator (NPSS, Ref. 41). The NPSS has been 

formally adopted by the U.S. aerospace industrial community, 

Government, and academia, and continues to be developed by 

a consortium of U.S. Government and industrial entities. 

Engine companies also use NPSS to create very elaborate 

models of their engines, since it allows for very accurate 

analytic predictions of the engine performance. 

The CFM56–7B was analytically modeled in NPSS using 

data available from several reliable public-domain sources, 

such as FAA-type certification data sheets, manufacturerprovided airport planning documents, technical reports, Jane’s 

Aero Engines, and manufacturers’ Web sites. No companyproprietary data were used. Performance data were computed 

throughout the flight operating envelope. The various 

components are linked together analytically in NPSS using 

coding constructs known as fluid ports and mechanical ports 

for flow and shaft connections within the engine, respectively. 

The analytical linkage of the CFM56–7B is shown in

Figure 2.4. 

An aeromechanical, weight, and flow path analysis was also 

conducted using other NPSS airbreathing elements collected 

in the Weight Analysis of Turbine Engines (WATE) library. 

One result of this analysis is the two-dimensional cross section 

of the engine shown in Figure 2.5. The analytical NASA 

representation of the engine is somewhat crude when compared with higher fidelity engine-company simulations. For 

example, an examination of the cross section suggests that the 

low-pressure turbine exit, the front frame, and duct flow paths, 

among other components, could be modeled with greater 

accuracy. However, it serves well enough to provide ANOPP 

with its basic requirements. The CFM56–7B NPSS simulation 

was easily configured to write the pressures, temperatures, 

rotational speeds, and flow areas for each flow station within 

the engine to an engine state table for inclusion in the ANOPP 

input file. 

2.3.3 Trajectory Description

The aircraft trajectory is important for accurate prediction 

of any time-dependent aircraft noise metric. The noise 

propagated through the atmosphere to the ground is dependent 

on the location, direction, orientation, airspeed, engine throttle 

setting, and operational configuration of the aircraft. These are
NASA/TP—2012-215653 20

Figure 2.5.—Cross-sectional view of NPSS/WATE aeromechanical and flow path simulation of CFM56–7B 

turbofan engine (drawing to scale).

all functions of time and aircraft position. For an existing 

aircraft, these data may be obtained from measurement, where 

an aircraft trajectory is tracked using radar equipment, optical 

systems, or by other means such as from trajectory simulations. Analytical trajectory simulations require solutions of 

equations of motion; using aircraft aerodynamics, thrust 

performance, stability and control moment, weight, and 

atmospheric data. The aircraft aerodynamics, in the form of 

so-called “drag polars,” and stability and control data are 

needed, but are often proprietary and difficult to obtain from 

airframe manufacturers for the same reasons as the propulsion 

data described above. The aerodynamic performance of an 

airplane with its high-lift devices (flaps and slats) deployed 

during takeoff and landing is particularly sensitive. For 

ANOPP predictions, the aircraft trajectory can be internally 

calculated using ANOPP modules or computed externally and 

entered in as input.

The B737–800’s departure and approach trajectories were 

simulated using the procedures described in the Society of 

Automotive Engineers (SAE) Aerospace Information Report 

(AIR), SAE–1845 (Ref. 42). The material in this document is 

similar to the material in related documents published by the 

European Civil Aviation Conference (ECAC) Document 29 

(Ref. 43). SAE–1845 describes a method where aircraft 

takeoff and approach trajectories may be empirically computed using aircraft and engine regression performance coefficients provided by industry. These performance coefficients 

are technical representations of the underlying proprietary data 

and hence are nonproprietary information. Engine thrust, for 

example, is represented by a simple regression model of lapses 

with airspeed, altitude, and ambient temperature with respect 

to a sea level static-rated thrust. These regression coefficients 

and methods for using them allow rapid aircraft trajectory 

computations in computer codes such as the FAA’s Integrated 

Noise Model (INM) (Ref. 44). The empirical methods are used 

to compute distance, altitude, speed, and throttle setting for the 

various flight segments encountered during approach and 

departure.

The approach and departure trajectories used within 

ANOPP for the B737–800/CFM56–7B operating from a sealevel field are shown in Figure 2.6. The conditions are for 

25 °C (77 °F) and 1.013 bar (29.92 in. Hg), with the airplane 

in departure configuration at its maximum takeoff gross 

weight of 78 150 kg (172 300 lb) and in approach configuration at its maximum landing weight of 66 360 kg (146 300 lb). 

The takeoff trajectory starts with the ground roll with engines 

at maximum takeoff rated thrust, then a rotation, followed by 

several climb and acceleration segments. It also includes a 

noise abatement throttle cutback procedure. This throttle 

cutback serves to reduce the noise perceived by the flyover 

observer and is allowed under 14 CFR Part 36 regulations 

(Ref. 45). After passing beyond the flyover observer, the 

engines are throttled up to their maximum continuous climb 

thrust for the remainder of the climb. Note the aircraft remains 

under 463 km/h (250 kn) calibrated airspeed under 3048 m 

(10 000 ft) per regulations. The approach has one constantaltitude, constant-calibrated-airspeed “step” that is typical of 

airport approach patterns. Afterwards, its descent follows a 

typical 3° glide slope to the runway threshold.

Certification noise levels are regulated by the requirements 

of the International Civil Aviation Organization (ICAO) 

Annex 16 noise regulations (Ref. 46) and in the United States 

by the Federal Aviation Regulations (FAR) Part 36 (Ref. 47). 

The regulations observed in this benchmarking assessment are
Aircraft System Noise Prediction

NASA/TP—2012-215653 21 Chapter 2

Figure 2.6.—SAE AIR–1845 trajectory for the

B737–800/CFM56–7B at 172 300 lb. (a) Altitude.

(b) Airspeed. (c) Percent net engine thrust.

those applicable for transport category large airplanes and jetpowered airplanes. An aircraft is flown through standardized 

takeoff and approach procedures, and the 1/3-octave band 

frequency spectrum time histories are measured at three 

locations identified as lateral sideline, flyover, and approach. 

These locations are shown in Figure 2.7. At each location the 

measurement microphone is located 4 ft above the ground. 

The certification noise metric used internationally is the 

effective perceived noise level (EPNL). During takeoff 

procedure this is measured at the flyover and lateral sideline 

observer points. The lateral sideline observer point is defined

where the EPNL is highest along the lateral sideline reference 

lines symmetrically located on either side of the flight path 

(running parallel to the runway at a distance of 450 m, or 

1476 ft). Within ANOPP, the sources are most often

colocated and axisymmetric, therefore only requiring the 

analysis to be made on one side of the aircraft. The flyover 

EPNL measurement is measured 6500 m (21 325 ft) from 

brake release on the runway centerline. (The flyover observer 

is also referred to as the “cutback,” “community,” “takeoff,”

or “centerline” observer.) The flyover measurement most 

often employs a noise abatement throttle cutback procedure 

that is allowed under certification rules. During approach the 

noise is measured at the approach point, located 2291 m 

(7518 ft) before the point of touchdown on the runway 

centerline. This corresponds to 2000 m (6562 ft) from the 

runway threshold, where the aircraft altitude over the observer 

is 120 m (394 ft).

2.3.4 Comparison of Measurements and Predictions

ANOPP predictions are made for the B737–800/CFM56–7B 

using the source noise modules identified in Table 2.5 and the 

flight procedure described above. The source noise from the 

engine and airframe are propagated to observers located 4 ft 

above the ground in accordance to the specifications for

Figure 2.7.—Noise certification measurement locations.
NASA/TP—2012-215653 22

Figure 2.8.—Predicted tone-weighted perceived noise level 

(PNLT) time history at approach certification point.

certification measurement procedure. Noise propagation 

effects accounted for include spherical spreading, Doppler 

shift and convective amplification, atmospheric attenuation,

and ground reflections based on data for grass-covered 

ground. The propagated acoustic spectra for each noise 

component are predicted at (user specified time increments) 

half-second intervals at each measurement location. From 

these spectra, ANOPP computes the perceived noise level 

(PNL), tone-weighted PNL (PNLT), and EPNL noise metrics 

for the individual sources and for the total aircraft.

The predicted PNLT time histories and 1/3-octave band 

spectra at the certification approach, lateral sideline, and 

flyover observer locations are shown in Figure 2.8 to Figure 2.13. The 1/3-octave band spectra results are only shown 

for the three polar emission angles θe = 45°, 90°, and 135°. 

For the approach flight segment, the PNLT time history 

predicted at the certification approach location is shown in 

Figure 2.8 and the associated 1/3-octave spectra at the three 

polar emission angles are shown in Figure 2.9. For polar 

angles prior to overhead (θe = 90°) the flap and slat noise 

dominates the airframe noise component. The engine sources 

are dominated by the fan inlet and discharge noise prior to and 

after the vehicle has passed overhead. The other engine noise 

components are minimal for the approach flight segment since 

the engine thrust is only at about 30 percent of the total 

available thrust. The PNLT time history predicted at the lateral 

sideline certification location is shown in Figure 2.10, and the 

associated 1/3-octave spectra at the three polar emission 

angles are shown in Figure 2.11. As expected, the engine noise 

sources dominate, particularly the jet and fan noise. The tonal 

character of the fan inlet can be seen in the PNLT time history 

by the spikes at polar angles less than 60°. The predicted 

results at the flyover location are shown in Figure 2.12 and

Figure 2.9.—Predicted sound pressure level (SPL) at 

approach certification point for three different polar 

directivity angles, θe. (a) 45°. (b) 90°. (c) 135°.

Figure 2.13. The trends are similar to those seen for the 

predictions at the lateral sideline location. The inlet fan noise 

dominates for polar angles less than θe = 90°, and the fan 

discharge and jet noise dominate for polar angles greater than

θe = 90°.
Aircraft System Noise Prediction

NASA/TP—2012-215653 23 Chapter 2

Figure 2.10.—Predicted tone-weighted perceived

noise level (PLNT) time history at lateral sideline 

certification point.

Figure 2.11.—Predicted sound pressure level (SPL) at 

lateral sideline certification point for three different 

polar directivity angles, θe. (a) 45°. (b) 90°. (c) 135°.
NASA/TP—2012-215653 24

Figure 2.12.—Predicted tone-weighted perceived 

noise level (PNLT) time history for flyover (with 

cutback) condition.

Figure 2.13.—Predicted sound pressure level (SPL) at 

flyover (with cutback) location for three different 

polar directivity angles, θe. (a) 45°. (b) 90°. (c) 135°.
Aircraft System Noise Prediction

NASA/TP—2012-215653 25 Chapter 2

The predicted EPNL results for each noise component 

contributing to the total aircraft noise are shown in Figure 2.14

for each certification measurement location. To compare the 

relative importance of the component noise sources on an 

EPNL basis, the noise from each source (fan inlet, fan 

discharge, jet, core, etc.) is analytically flown past each 

certification observer (lateral sideline, flyover, and approach). 

The EPNL for each source is computed as the difference 

between the full-system EPNL and the EPNL determined with 

all but the source component of interest included. (This is 

done on a pressure-squared basis.) This technique reduces the 

effect of duration and directivity discrepancies. As expected 

the airframe noise is nearly equivalent to the engine levels on 

approach and the engine sources dominate during the takeoff 

flight segment. The capability to identify the contribution of

individual noise components provides insight into the key

noise mechanisms contributing to the overall noise levels. 

Identification and reduction of these sources will allow for the 

development of quieter aircraft designs and flight procedures.

The predicted EPNL compared with certification measurements of this vehicle are shown in Figure 2.15 to Figure 2.17. 

The predicted results were made assuming the highest gross 

weight found for this vehicle and are indicated on the plots by 

the red square. These measurements were obtained from the 

FAA Web site and are the flight certification noise measurements obtained for Boeing 737–800 with CFM56–7B. The 

exact details of each vehicle configuration or engine operation 

are not known. The cause of the large scatter in the data, 

particularly for the lateral sideline and flyover locations can in 

part be attributed to model-type variations in the engine and 

airplane system, which cause differences in the measured 

certification noise. Airplane weight and thrust performance 

differences by type lead to changes in trajectory and throttle

history, which can produce measured noise differences of the

Figure 2.14.—Predicted contributions from each noise component to total effective perceived noise level (EPNL) at 

the three certification points.
NASA/TP—2012-215653 26

Figure 2.15.—Comparison of predicted effective

perceived noise level (EPNL) for B737–800/CFM56–7B 

and noise certification data of 73 certificated B737s 

equipped with CFM56–7B engines. Approach

measurement location.

Figure 2.16.—Comparison of predicted effective

perceived noise level (EPNL) for B737–800/CFM56–7B 

and noise certification data of 73 certificated B737s 

equipped with CFM56–7B engines. Lateral sideline 

measurement location.

Figure 2.17.—Comparison of predicted effective perceived 

noise level (EPNL) for B737–800/CFM56–7B and noise 

certification data of 73 certificated B737s equipped with 

CFM56–7B engines. Flyover measurement location.

first order. Differences in engine model architecture, even 

within a family of engine type, lead to the different enginetype ratings and may cause a substantial change in emitted 

noise. However, these engineering design implementations are 

often impossible to model without access to companyproprietary information. Also it should be noted that the 

manufacturers have some latitude in how the aircraft is flown 

in the vicinity of the flyover microphone, whereas little or no 

latitude exists near the other certification points. Therefore, 

they are likely to operate in an optimal manner that differs 

from the nominal takeoff procedure assumed. This could also 

explain the overprediction for the flyover point. The predictions shown, however, were not tweaked, but were created 

based on best available inputs and then directly compared with 

the data shown in Figure 2.15 to Figure 2.17. With many of 

the inputs not known exactly, the ANOPP results are considered fair to good in comparison with the data.

2.3.5 Uncertainty Analysis

An initial investigation is made to provide an estimate of the 

uncertainty in ANOPP full-aircraft noise EPNL predictions. 

This investigation is very limited because of the lack of 

measured data available. Performing a complete uncertainty 

and/or error analysis of ANOPP requires not only acoustic 

results, but also a full description of the engine, including 

engine state and airframe for a range of flight conditions. Since 

this is not available at the level of detail required, an analysis is 

performed to determine the uncertainty of ANOPP results for 

appropriate variations in aircraft velocity and throttle setting. 
Aircraft System Noise Prediction

NASA/TP—2012-215653 27 Chapter 2

Both of these variables may directly affect the noise generation 

from both the engine and airframe components.

Every module in the noise prediction process will introduce 

some uncertainty. The purpose of this analysis is to determine 

the sensitivity of the EPNL prediction due to uncertainty in 

specific key input parameters. Therefore, the analysis is 

performed with the assumption that atmospheric conditions and 

all geometric parameters relating to the aircraft are known. 

Approach and takeoff profiles are simulated by intervals 

between fixed points where the aircraft velocity, altitude, and 

angle of attack are specified. The aircraft velocity is allowed to 

vary but the altitude and angle of attack are held fixed. 

The aircraft velocity and engine power setting determine the 

engine performance, which is modeled in ANOPP through 

engine state tables. Engine state tables have two independent 

variables—aircraft Mach number and engine power setting—

and six dependent variables: area, fuel-to-air ratio, mass flow 

rate, total temperature, total pressure, and rotation speed. Engine 

state tables are provided for each noise source. Therefore, any 

change in the aircraft velocity or engine power setting will be 

reflected in the dependent variables. 

A Monte Carlo approach is used to determine the

95% confidence intervals based on a Gaussian distribution of 

the aircraft velocity and power setting. The aircraft velocity V

and the engine power setting Π are assumed to be uncorrelated 

and are allowed to vary according to 

Vi = V * +NV ,i∆V (2.1)

and 

Πi = Π * +NΠ,i∆Π (2.2)

where Vi is the simulated aircraft velocity, V* is the true aircraft 

velocity, NV,i is the random number associated with the variation 

in aircraft velocity, and ∆V = 15 ft/s is the maximum allowable 

variation in aircraft velocity. Similarly, Πi is the simulated power 

setting, Π* is the true power setting, NΠ,i is the random number 

associated with the variation in power setting, and ∆Π = 5 percent 

is the maximum allowable variation in power setting. Normally 

distributed random numbers NV,i and NΠ,i were generated with a 

maximum value of 1 and a minimum value of –1. Twenty-one 

simulations (i.e., predictions) are made from which the sample 

mean and sample standard deviation shown in Table 2.6 are 

computed. The Student’s t-factor for the 95% confidence interval 

with 20 degrees of freedom is 2.086 (Ref. 48). Therefore the

95% confidence interval CI about the mean is 

CI = ±tS (2.3)

where S is the sample standard deviation. The results shown in 

Table 2.6 state that with 95 percent confidence, the next

TABLE 2.6.—MONTE CARLO SIMULATION OF BOEING 737 CERTIFICATION

EFFECTIVE PERCEIVED NOISE LEVELS (EPNL)

Number of

simulations

Approach EPNL,

dB

Lateral sideline EPNL,

dB

Flyover EPNL,

dB

1 95.0 92.1 90.8

2 94.6 91.9 90.8

3 96.5 92.3 90.8

4 96.2 92.3 90.7

5 95.6 92.5 90.8

6 95.1 92.5 91.0

7 95.4 92.3 90.7

8 94.6 91.9 90.8

9 96.8 92.4 91.0

10 96.0 92.3 90.8

11 94.6 92.1 90.8

12 95.2 92.2 90.7

13 95.4 92.2 90.7

14 94.6 92.0 90.8

15 95.9 92.3 90.8

16 96.0 92.6 91.0

17 95.3 92.6 90.9

18 95.9 92.4 90.8

19 95.8 92.3 90.7

20 95.5 92.4 90.8

21 95.7 92.5 90.9

Sample mean 95.5 92.3 90.8

Sample standard deviation 0.6 0.2 0.1

95% confidence interval 1.3 0.4 0.2
NASA/TP—2012-215653 28

simulation at approach will fall between ±1.3 dB of the sample 

mean EPNL of 95.5 dB, the next simulation at the lateral 

sideline location will fall between ±0.4 dB of the sample mean 

EPNL of 92.3 dB, and the next simulation at the flyover 

location will fall between ±0.2 dB of the sample mean EPNL 

of 90.8 dB.

The noise levels are also computed for the extreme minimum and maximum values of aircraft velocity and engine 

power setting allowed in this analysis. This provides a 

minimum and maximum level of noise variation, based on 

these values. The results are shown in Table 2.7 to Table 2.9.

The sensitivity of ANOPP predictions to small variations in 

these two parameters is as expected for a robust system noise 

capability. To fully assess the sensitivity of all ANOPP 

modules to all inputs was not undertaken at this time because 

of the lack of data available for such a study and the limited 

resources available to perform the thorough analysis required. 

However, it is recognized that the there are several factors that 

can contribute to errors in predicting EPNL using ANOPP and 

some of these are as follows:

(1) ANOPP’s built-in source noise prediction models are 

based in most part on measured results. The empirical to semiempirical methods are hence inherently limited by the 

database used to develop and validate the methods. It is 

difficult to construct accurate analytical methods that are 

generically applicable to all varieties of noise sources. Fan 

noise, for example, is a strong function of fan design characteristics that are not necessarily captured by ANOPP’s

Heidmann module, which may fairly be called a generalized 

empirical fan noise prediction method. The prediction method 

is simply insensitive to airfoil geometry, positioning, and 

orientation; small-scale flow characteristics; specific acoustic 

treatment designs; and dozens of other attributes of the fan and 

ducts. In other words, since its framework is logically 

constructed and scalable, the Heidmann fan noise methodology may be a good tool to generically predict the noise for 

classes of fans, but it is most likely limited in its capabilities to 

accurately predict the noise of a specific fan design within a 

class. Similar arguments may be made for the other source 

noise prediction methods used in this benchmarking. 

(2) The propulsion cycle and aeromechanical information 

input to source noise prediction models has some associated 

error. Even the best, most accurate source noise predictions 

will be inaccurate if the propulsion system data feeding them 

has inaccuracies. There is certainly some propulsion data error 

involved in this benchmarking activity, and the difficulty in 

obtaining accurate propulsion system data due to its proprietary nature was described in detail in Section 2.3.2, “Engine 

Description.”

(3) ANOPP uses a paradigm of superposition, where multiple independent point noise sources are summed at the aircraft 

locale before propagating the combined signal to the ground. 

Real noise sources are complex, distributed sources (particularly jet noise) that are affected by the aircraft configuration 

and environment. The current capabilities within ANOPP do 

not adequately account for propulsion-source and airframe 

interactions, noise reflections, or complex acoustic phenomena 

such as refraction, diffraction, and other effects that can take 

place in the complex acoustic near field.

(4) Propagation modeling has some inherent error. ANOPP 

does capture the effects of a layered atmosphere, with 

procedures that correct the radiated signal for atmospheric 

attenuation and ground effects. Other, more complex propagation phenomena however, such as scattering, weather effects, 

and terrain are not adequately accounted for in the models. 

(5) The trajectory simulated by the SAE AIR–1845 method 

may not be precisely the same as the trajectory flown by the 

B737 during its noise certification tests. Trajectory has a firstorder influence on the outcome, and there will be some 

inherent error associated with this. Unfortunately, the exact 

details of the trajectory (vehicle orientation and engine 

operation) flown during certification are not available.

(6) The measured certification EPNLs to which comparisons are made have some error. For example, microphone 

measurements, equipment signal data processing, data 

corrections for ambient conditions, trajectory tracking, timing, 

weather, terrain, and complex propagation effects at the test 

site all contribute to the differences in this benchmarking. And 

the mathematical correction procedures specified by regulations to account for differences from the standard acoustic day 

accounts for some error in the published EPNLs.

TABLE 2.7.—CHANGE IN EFFECTIVE PERCEIVED NOISE LEVEL (EPNL) (dB)

AT APPROACH LOCATION DUE TO 5-PERCENT VARIATIONS

IN AIRCRAFT VELOCITY AND POWER SETTING

[Baseline represents nominal values of aircraft velocity and power setting.]

Aircraft velocity Power setting

Minimum

(–5 percent)

Baseline Maximum

(+5 percent)

Minimum (–4.6 m/s, or –15 ft/s) –1.8 –0.4 1.0

Baseline –1.3 0.0 1.3

Maximum (+4.6 m/s, or +15 ft/s) –0.7 0.5 1.5
Aircraft System Noise Prediction

NASA/TP—2012-215653 29 Chapter 2

TABLE 2.8.—CHANGE IN EFFECTIVE PERCEIVED NOISE LEVEL (EPNL) (dB)

AT LATERAL SIDELINE LOCATION DUE TO 5-PERCENT VARIATIONS

IN AIRCRAFT VELOCITY AND POWER SETTING

[Baseline represents nominal values of aircraft velocity and power setting.]

Aircraft velocity Power setting

Minimum

(–5 percent)

Baseline Maximum

(+5 percent)

Minimum (–4.6 m/s, or –15 ft/s) –0.7 0.1 0.2

Baseline –1.0 0.0 0.1

Maximum (+4.6 m/s, or +15 ft/s) –1.1 –0.2 –0.2

TABLE 2.9.—CHANGE IN EFFECTIVE PERCEIVED NOISE LEVEL (EPNL) (dB)

AT FLYOVER LOCATION DUE TO 5-PERCENT VARIATIONS

IN AIRCRAFT VELOCITY AND POWER SETTING

[Baseline represents nominal values of aircraft velocity and power setting.]

Aircraft velocity Power setting

Minimum

(–5 percent)

Baseline Maximum

(+5 percent)

Minimum (–4.6 m/s, or –15 ft/s) 0.3 0.2 0.4

Baseline 0.1 0.0 0.3

Maximum (+4.6 m/s, or +15 ft/s) 0.0 –0.1 0.2

Unfortunately, without access to proprietary data and more 

accurate prediction methods, we can only speculate as to the 

reasons for the error, or even if serendipity played a factor in 

the form of offsetting errors. The EPNL is a complex, highlevel, multidisciplinary metric with many independent 

variables affecting its outcome. To truly benchmark the 

ANOPP capabilities, the aircraft definition and measured 

noise must be known and to a much higher level of accuracy 

than was available for this assessment.

2.4 Recommendations

To improve the accuracy of community noise predictions of 

aircraft, such as the noise of future aircraft with advanced, 

unconventional noise reduction technologies, or even for the 

B737’s certification noise levels estimated herein, NASA 

systems analysis tools will require significant upgrades. 

Physics-based prediction tools do offer the promise of 

analytically developing and designing noise reduction 

concepts prior to testing. However, the field of first-principle, 

physics-based computational aeroacoustic tools is in its 

infancy because of the lack of knowledge required to develop 

accurate predictions of unsteady flow and acoustics. It will 

be quite some time before higher fidelity computational 

aeroacoustic tools become mature, accurate, robust, and 

fast enough to be used for noise estimates at the conceptual 

design level. Meeting the requirements for computing resource 

and computational efficiency will be key enablers for 

these advanced, high-fidelity solvers. Enhancements of the 

empirical and semi-empirical noise tools will continue, and 

they will become more robust and capable. In the near term, 

noise prediction methods based on first principles as well as 

improved semi-empirical analyses will be incorporated into a 

software framework in order to provide a capability for

assessing conventional and future nonconventional aircraft. 

There are undoubtedly gaps in NASA’s analytical acoustic 

toolset that are indicated by the shortcomings in evaluating 

many new and unconventional concepts. In addressing these 

gaps, NASA’s next-generation analysis tools must be flexible 

enough to incorporate new analytical acoustic methods as well 

as model the physics responsible for noise of current and 

future designs. 

The following gaps and issues need to be addressed to more 

accurately predict the system noise for conventional CTOL 

aircraft and to allow the prediction for nonconventional aircraft:

1. Develop aircraft noise prediction strategies that are 

multifidelity.

a. Address requirements at the fundamental noise technology level up through the system design and optimization level.

b. Address computational needs for accuracy and 

efficiency.

2. Extend jet noise capabilities.

a. Develop methods for internally mixed jets.

b. Develop methods for nonaxisymmetric nozzles.

3. Develop acoustic scattering methods that are based on 

first principles and those appropriate for system studies.
NASA/TP—2012-215653 30

a. Invest in fast multipole methods and efficient algorithms.

b. Develop intermediate methods that can account for 

noise shielding and/or reflecting effects using efficient 

method-ologies.

4. Invest in methods to account for propulsion-airframe and 

airframe-airframe interaction noise sources. These need to 

include not only methods based on first principles to allow for 

application to both conventional and nonconventional aircraft 

configurations, but also efficient methods that can account for 

the effects for system design purposes.

5. Advance atmospheric propagation methods to include 

effects of wind and terrain.

6. Obtain a comprehensive aircraft flight acoustic database 

that includes not only the noise at a number of ground 

measurement locations, but also the details on the engine and 

airframe geometries and engine operating states for the entire 

flight trajectory. 
Aircraft System Noise Prediction

NASA/TP—2012-215653 31 Chapter 2

Appendix A.—Nomenclature

A.1 Acronyms

AIR Aerospace Information Report (SAE)

ANOPP Aircraft Noise Prediction Program

CTOL conventional takeoff and landing

ECAC European Civil Aviation Conference

EPNL effective perceived noise level

FAA Federal Aviation Administration

FAR Federal Aviation Regulations

ICAO International Civil Aviation Organization

INM Integrated Noise Model

NPSS Numerical Propulsion System Simulator

PAS propeller analysis system

PNL perceived noise level

PNLT tone-weighted perceived noise level

SAE Society of Automotive Engineers

SPL sound pressure level

WATE Weight Analysis of Turbine Engines (library)

A.2 Symbols

CI confidence interval

N normally distributed random number, –1 ≤ N ≤ 1 

(see Eqs. (2.1) and (2.2))

R source-to-observer distance (see Figure 2.3)

S sample standard deviation

t Student’s t-factor

V aircraft velocity

x,y,z ANOPP coordinate system (see Figure 2.3)

θ polar angle (see Figure 2.3)

Π power setting

φ azimuthal angle (see Figure 2.3)

Subscripts:

e emission

i index

V aircraft velocity

Π power setting

Superscripts:

* true
NASA/TP—2012-215653 32

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NASA/TP—2012-215653 33 Chapter 2

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NASA/TP—2012-215653 35

Chapter 3—Engine System and Core Noise

Lennart S. Hultgren, Jeffrey Hilton Miles, and Philip C.E. Jorgenson3

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary and Recommendations

Noise generated in the turbofan engine core, by sources such as the compressor, combustor, and turbine, can make a significant 

contribution to the overall noise signature at low-power conditions, typical of approach flight. At high engine power during 

takeoff, jet and fan noise have traditionally dominated over core noise. However, current design trends and expected technological 

advances in engine-cycle design as well as noise-reduction methods are likely to reduce noncore noise even at engine-power points 

higher than approach. The result of such changes will be to elevate the importance of turbomachinery core noise. Also, future

airport regulations may force further noise reduction at the approach flight conditions, thus emphasizing the need for reductions in 

core noise.

A brief historical perspective and description of the development of the current state of the art in semi-empirical combustion 

noise prediction methods are given. The open issue of the relative importance of direct and indirect combustion noise is discussed. 

Noise-source separation techniques, which are essential in extracting the subdominant combustion noise from the total noise 

signatures obtained in static-engine tests, are described.

The ability of the Aircraft Noise Prediction Program (ANOPP) to predict static-engine test data is assessed with a comparison to 

results from such a test. The sensitivity of the predictions to uncertainties in the engine operational parameters is determined, and 

the effects of calibration and/or instrumentation uncertainty on the test data are estimated. There are cases where the predicted 

values differ from the test data by as much as 10 dB at certain frequencies. Clearly, there is room for improvement in those cases. 

However, considering the semi-empirical nature of the ANOPP algorithms and their inherent limitations in capturing all the 

physics of the noise sources, the ANOPP predictions do surprisingly well in many situations. Furthermore, when the prediction

captures the dominant feature of the sound-pressure-level spectrum, the corresponding integrated measure—the overall sound 

pressure level—agrees with the test results within the margin of uncertainty.

Better prediction methods and models need to be developed for turbine noise—a near-term issue already of importance for 

today’s turbofan engines. To enable future “quiet” engines, further progress must also be made in the understanding and modeling 

of combustion noise and its turbine transmission and interaction. The key is a robust, long-term research program comprising highfidelity computer simulation, careful experimental measurements in real engines (including refinement of source-separation 

techniques) for both validation and determination of required information, and concurrent development of reduced-order models 

for practical noise prediction methods. The numerical work needs to employ realistic geometries and multistage turbine simulations to better understand turbine self-generated noise and transmission and conversion effects on combustion noise. Similar 

integrated combustor-turbine simulations are needed to separate the direct and indirect source mechanisms for combustion noise.

3.1 Introduction

Gas turbine engines for commercial subsonic aircraft have 

undergone many changes in their operating cycle since their 

first introduction in the early 1950s. The early engines were of 

the turbojet type, but within a decade the design had changed 

to the turbofan type, which provided lower fuel consumption 

and reduced noise and emissions. The first-generation 

turbofan engines had bypass ratios near unity, where the 

bypass ratio is defined as the ratio of the mass-flow rates in 

the bypass and core streams. At takeoff, the perceived jet and 

fan noise components were typically about 15 and 8 dB 

greater, respectively, than the perceived core noise; and, at 

approach, the perceived fan noise commonly was about 10 dB 

greater than the (about equal) jet and core noise components 

(Ref. 1). The term “core noise” covers all noise generated in 

the engine core: compressor, combustion, and turbine noise. 

The first change in the turbofan-engine design was the 

introduction of acoustic liners (Ref. 2). This typically reduced 

the perceived fan noise at approach to a level below the jet and 

core noise components (Ref. 1). The next major change was 

the shift toward high-bypass-ratio engines, which took place 

during the 1970s. This change allowed as much thrust as 

previous engines by increasing the diameter of the jet while it 

reduced the jet exit velocity and as a consequence reduced the 

jet noise. This evolution led to the modern turbofan engine, 

which typically has a bypass ratio in the range of 5 to 8. For 

current engines, the perceived jet and fan noise are essentially 

on par at takeoff, and the core-noise level is about 10 to 20 dB 

lower (Ref. 3).

Because of the national interest in fast and efficient air 

transportation with minimal community impact, NASA has 

made large investments in noise research and noise-reduction 

technology. Fan noise has been studied since the mid 1960s, 

with its foundation based on earlier National Advisory 

Committee for Aeronautics (NACA) propeller- and helicopterblade noise work. Jet noise has been investigated since the 

early 1950s. The reduction of fan and jet noise remains a 
NASA/TP—2012-215653 36

major NASA research objective. Steady progress was made 

with higher bypass ratio engines, better fan and nozzle 

designs, and fan-noise acoustic-treatment technologies.

Core noise was vigorously investigated starting in the early 

1970s until the late 1980s, when it was concluded that its 

further study would have little additional impact on total 

engine noise and research was discontinued. However by the 

year 2000, it became clear that with further technology 

improvements, it is possible to build a much quieter turbofan 

engine in about a decade with fan noise, jet noise, and core 

noise of equal importance. Core noise would then provide a 

noise floor impacting any further advances in fan and jet noise 

reduction. It was also realized that core noise was an important 

contributor to airport ramp noise due to auxiliary power units 

(APUs). At that point, the NASA research effort to look at the 

core noise problem was restarted at a modest level.

In the collection by Hubbard (Ref. 4), Groeneweg et al. 

(Ref. 3), and Mahan and Karchmer (Ref. 5) summarize the 

status and understanding of turbomachinery contributions to 

flight vehicle noise at the beginning of the 1990s. Whereas jet 

and fan noise research and understanding have progressed, the 

state of the art in core-noise prediction has not been equally 

advanced. Of the core-noise components, compressor noise 

has received the least amount of recent modeling effort, 

partially because of the fact it has not been identified as a 

significant contributor to engine-system noise to date for highbypass-ratio turbofan engines. For this reason, compressornoise modeling is not emphasized here.

Low-frequency core noise up to about 1 kHz, particularly in 

aft quadrants, is generally attributed to combustion noise. Selfgenerated turbine (broadband and discrete-tone) noise normally 

falls in the frequency range of several kilohertz and above. 

High-frequency tones over 10 kHz are usually also attributed to 

the turbine. The discrete tones are caused by rotor wakes 

interacting with downstream stators and by stator potential 

fields interacting with upstream and downstream rotors (and 

stages). Turbine broadband noise is caused by rotor-stator lift 

fluctuations due to flow turbulence. There is also a significant 

broadband component in the far field associated with scattering 

of the discrete turbine tones by the jet shear layer(s). This socalled hay-stacking effect often dominates the broadband noise 

directly generated within the turbine.

Combustion noise is either of the direct or indirect type. 

The unsteady combustion process is the source of pressure, 

entropy, and vorticity fluctuations. Only the first two are 

commonly considered to be potential sources of far-field 

combustion noise. The frequency scale of these fluctuations is 

set by the unsteady combustion process and falls in the range 

of 400 to 500 Hz. A fraction of the pressure disturbances are 

acoustic pressure fluctuations with the balance being hydrodynamic unsteadiness. The former is referred to as “direct 

combustion noise.” Its spectrum is modified by the combustor 

geometry as well as pressure feedback on the unsteady 

combustion process itself. The direct combustion noise is 

reduced because of transmission effects during its propagation 

through the turbine stages. The entropy (temperature) 

fluctuations are convected downstream with the local mean 

velocity and get converted to acoustic pressure fluctuations in 

the turbine and other regions of rapid flow change. This is the 

indirect process of turbomachinery combustion noise generation. This is potentially a very effective mechanism and occurs 

at all turbine stages. The indirect combustion noise occurs in 

the same basic frequency range as the direct, but their spectral 

shapes could be quite different. The relative importance of 

direct and indirect combustion noise is still an unresolved 

issue. Any quasi-steady temperature streak ingested by the 

turbine would have an effect similar to a fan or compressor 

inlet disturbance and would generate noise in the bladepassing frequency range. This possibility should be classified 

as a turbine self-generated noise mechanism.

In this chapter, a brief historical perspective is given, which 

includes a discussion of noise-source separation techniques for 

application to engine test-stand data, and an assessment of a 

current prediction method applied to a static-engine test is 

presented. A list of the acronyms and symbols used in this 

chapter is given in Appendix A to aid the reader.

3.2 Core-Noise Research

The reduction of aircraft noise has long been an important 

technological challenge to the commercial air transport 

industry. The relative importance of different propulsion noise 

sources has changed with the evolution of the civilian-engine 

design. This has been reflected in the research efforts by 

industry, academia, and government institutions.

3.2.1 Compressor Noise

In addition to jet noise, inlet compressor noise was found to 

be a significant issue at approach for the first-generation jet 

aircraft powered by turbojet engines. The discrete-frequency 

compressor whine was discovered to be more annoying to 

airport neighbors than the broadband exhaust noise at landing 

(Ref. 6). The inlet tonal noise was mainly generated by the 

first two stages of the axial-flow compressors used in the 

turbojet engines (Ref. 7). Compressor noise was actively 

investigated during the transition from turbojet engines to 

turbofan engines. (Refs. 6 to 11). The bypass ratio of the early 

turbofan engines was initially low, and the inlet noise issue for 

these engines was sometimes referred to as fan-compressor 

noise (Ref. 11). However, as high-bypass-ratio turbofan 

engines were later introduced, fan noise and not compressor 

noise became the dominant feature of inlet noise.

The theory developed for compressor noise based on rotorstator interaction due to wakes, vortices, and turbulence also 

applies to fan and turbine noise. In the collection by Hubbard 

(Ref. 4), the chapter on turbomachinery noise (Ref. 3) describes 

the understanding in the early 1990s of compressor noise, as 

well as turbine and fan noise. Agarwal et al. (Ref. 12) have 

recently studied the compressor contribution to inlet noise. They 

point out that in current practice inlet noise is normally 

separated into fan-tone and fan-broadband components. The fan 

tones, occurring at the fan blade-passing frequency (BPF) and 
Engine System and Core Noise

NASA/TP—2012-215653 37 Chapter 3

its harmonics, are easily detected since their peak amplitude is 

normally well above the broadband noise level. However, if a 

sufficiently fine narrowband spectral analysis is carried out, the 

other component is often found to also contain many discrete 

frequencies; that is, it is not a true broadband component. The 

scattering of just a few compressor tones by upstream rotating 

blade rows, including the fan rotor, can lead to a large number 

of inlet tones originating from the compressor. Consequently, a 

significant portion of the inlet noise that is customarily identified as fan broadband noise then actually originates in the 

compressor. They also argue that higher fan-BPF harmonics 

may be dominated by contributions originating from the fan 

rotor wake interacting with the compressor stator rather than the 

interaction between the fan rotor wake and fan outlet guide 

vane.

It is clear that for further progress to be made in the modeling of compressor noise, the fan and compressor must be 

considered in an integrated fashion.

3.2.2 Combustion Noise

Major advances in combustion noise source modeling 

occurred during the 1970s and early 1980s and are discussed 

in the review chapter by Mahan and Karchmer (Ref. 5) and 

references therein. The approaches taken can broadly be 

divided into fundamental and applied research. Fundamental 

research activities attempt to develop first-principle theories 

by first considering simple situations and geometries and then 

successively increasing the level of complexity. Data is drawn 

from laboratory experiments and isolated component tests. 

This work has been carried out by both academic researchers 

and engine company investigators. Applied-research activities, 

in general, attempt to develop semi-empirical relations that 

correlate noise levels with engine operating parameters based 

on full-engine test data and has mainly been performed by 

aircraft engine companies, often with support from the 

Department of Transportation (DOT) Federal Aviation 

Administration (FAA) or NASA. Significant development of 

diagnostic techniques also took place during this time period.

3.2.2.1 Fundamental Research

One common fundamental-research approach (see the comprehensive review article by Strahle (Ref. 13)) is to make the 

simplifying assumption that combustor noise is closely related 

to that of an open flame. This successful avenue of research 

starts by developing theories and models for open-flame noise 

(Refs. 14 to 17) and validating those by correlating observations 

with variations in physical parameters. It then proceeds to more 

complex situations by addressing the effects of ducting on flame 

noise (Ref. 13) followed by combustor-rig experiments 

(Refs. 13, 18, and 19). There are some drawbacks to this 

approach: First, the combustion occurs at, or nearly at, open-air 

conditions and not at the pressure levels typical in engines. 

Second, the rigs generally exhaust directly to the atmosphere 

and, consequently, only information relevant to direct combustion noise is obtained. The conversion of entropy fluctuations to 

noise, caused by the unsteady combustion process, requires a 

significant mean axial pressure gradient to be effective 

(Refs. 13, 20, and 21). Third, attenuation effects occurring in the 

turbine of an actual engine installation are not included. Despite 

such limitations, it is generally accepted that this approach 

captures the main characteristic of the direct turbomachinery 

combustion noise; namely, a relatively universal (Ref. 22) lowfrequency (up to about 1 kHz) single-peak broadband spectrum, 

closely related to that of an open turbulent flame, modulated by 

geometry-dependent acoustic resonances (Refs. 19 and 23) and 

transmission effects.

In an experimental and theoretical investigation,

Muthukrishnan et al., (Ref. 18) added either a convergent nozzle 

or an orifice plate to a combustor can used in a previous 

experiment (Ref. 24) and found that indirect combustion noise 

became the prime component as the exit Mach number (≤1) was 

increased. This result suggested that indirect combustion noise 

is an important, if not the dominant, contribution to lowfrequency jet-engine core noise since typically the turbine 

(inlet) nozzle guide vanes operate at a choked, or nearly so, 

condition. However, as the authors pointed out, this result may 

depend somewhat on the fact that in the experiment the 

combustion took place at a fraction (10 to 20 percent) of the 

pressure in a real engine and the temperature fluctuations 

(12 percent) may have been up to six times as large as those in 

an actual engine situation. In addition, (Ref. 13) the nozzle 

exhausted into open space and not into a duct-like situation as 

would have been the case in an engine experiment.

Cumpsty and Marble (Refs. 25 and 26), showed good 

agreement between actual engine measurements and indirectcombustion-noise predictions based on a model for entropy 

fluctuations interacting with turbine blade rows. Cumpsty 

(Ref. 27), considered the interaction between a combustor and 

turbine and concluded that the indirect combustion noise 

dominates the direct. 

3.2.2.2 Applied Research

Semi-empirical models for the total acoustic power are 

developed based on physical considerations, with model 

coefficients determined using isolated-component and staticengine test data. Then the far-field directivity and universal 

spectral distribution are obtained empirically. In the case of 

full-engine tests, the measured total far-field acoustic signature normally is adjusted by subtracting the low-frequency jet 

noise using an appropriate model to reveal the core noise. This 

represents a weakness since combustion noise is not always a 

dominant noise source at low engine-power settings. 

Huff et al. (Ref. 28) reviewed the early 1970s state of the art 

in engine combustion-noise prediction and recommended an 

interim semi-empirical method to provide such a capability for 

the NASA Aircraft Noise Prediction Program (ANOPP) 

(Refs. 29 and 30). The proposed direct-combustion-noise 

method combined a formula developed by General Electric 

(Ref. 31) for the total acoustic power as a function of the engine 

operating condition, a Boeing (Ref. 32) obtained result for polar 
NASA/TP—2012-215653 38

directivity, and a single-peak spectral distribution based on the 

Society of Automotive Engineers SAE ARP876 in-flight jetnoise spectrum (Ref. 33). As recommended in the Boeing 

(Ref. 32) work, Huff et al. (Ref. 28) suggested using a fixed 

peak frequency of 400 Hz. Emmerling et al. (Ref. 34) improved 

the General Electric model by correlating the combustion-noise 

attenuation by the turbine with the design-point work extraction 

of the turbine and validated the resulting model using several 

sets of engine data. Ho and Doyle (Ref. 35) provided further 

validation and discussion of this model (see also Mahan and 

Karchmer (Ref. 5)). This simple direct combustion-noise model 

(Refs. 34 and 35) still forms the kernel of the ANOPP corenoise module and is referred to therein as the “SAE method.”

The current ANOPP module also contains a small-engine 

revision (Ref. 36) of this method and a narrowband method 

(Ref. 23) to account for tail-pipe resonances.

Also during the latter half of the 1970s, researchers at Pratt 

& Whitney (Refs. 37 and 38) developed a semi-empirical 

prediction method for direct combustion noise. They derived 

models for the total acoustic power level, turbine coupling and 

transmission losses, and peak frequency; and they empirically 

determined model constants, the directivity pattern, and a 

universal normalized spectral distribution using a range of 

burner-rig and full-scale static-engine tests. Mathews et al. 

(Ref. 37) also measured the dynamic temperature characteristics at the exit as well as inside of a burner in a rig experiment 

to provide inputs for an existing Pratt & Whitney indirect 

combustion noise model (Ref. 39). They found experimentally 

that the unsteady temperature level depended mainly on the 

total temperature increase across the burner (roughly 9 percent 

at the exit) and that the corresponding length scales were 

approximately proportional to a burner flow-rate parameter. 

Based on these measurements and the prediction codes, they 

found that indirect combustion noise should be 18 to 22 dB

lower than direct noise in the absence of turbine attenuation.

There are similarities and differences between the General 

Electric and Pratt & Whitney direct combustion-noise results 

(see also discussion in Mahan and Karchmer (Ref. 5)). In both, 

the total acoustic power level is proportional to the second 

power of the combustor pressure, the second power of the 

temperature rise across the combustor (the Pratt & Whitney 

model uses the air:fuel ratio which essentially is equivalent), 

and the inverse power of the combustor inlet temperature. The 

combustor mass-flow rate linearly affects the total acoustic 

power in the General Electric model, whereas in the Pratt & 

Whitney formula it enters through a burner flow parameter to 

the fourth power. The Pratt & Whitney result also depends on 

burner-geometry information such as the number of fuel nozzles 

and the burner cross-sectional area. Their formulas for turbine 

losses are different, but both are frequency independent. The 

latter fact implies that, in the absence of resonances, measured 

spectra for burner-rig and full-engine static tests should be quite 

similar. Furthermore, their directivity patterns are in good

agreement, and their single-peak universal spectral distributions

are similar when frequencies are normalized with the peak

frequency. The peak frequency in the General Electric model is 

always 400 Hz, but the corresponding Pratt & Whitney formula 

involves burner design and geometry parameters. In general, 

each of these prediction tools has shown good agreement with 

data from the engine manufacturer that developed the method, 

but not with data from other companies. The need for distinct 

models may be caused by differences in burner design philosophy (Ref. 40). Zuckerman (Ref. 40) summarized the history and 

results of the DOT/FAA sponsorship of core-noise research and 

provided further comments. The report also pointed out the need 

for continued improvements in turbine-attenuation and indirect 

combustion-noise source modeling.

3.2.2.3 Diagnostic Techniques

The direct measurement of turbofan-engine combustion 

noise is difficult because of the presence of jet noise in the 

frequency range of interest. Since in-flight effects reduce jet 

noise more than combustion noise, combustion noise can be a 

significant contributor to aircraft approach noise but be 

masked by jet noise under the corresponding static-engine test 

condition. To overcome this obstacle, researchers developed 

coherence techniques utilizing engine-internal as well as farfield measurements to identify the far-field combustion noise 

component. Modal analyses were also carried out to determine 

the source and propagation characteristics of combustion 

noise. As part of these efforts, NASA contracted with turbofan 

engine companies such as Avco Lycoming (Honeywell), 

General Electric Company, Pratt & Whitney, and AiResearch 

(Honeywell) between 1974 and 1980 to evaluate core noise.

3.2.2.3.1 Coherence Techniques

Figure 3.1 illustrates a typical three-sensor arrangement for 

a measurement utilizing correlation and coherence techniques 

to determine the combustion-noise component of the far-field 

noise signature. Measurement station C is located inside the 

combustor; station T, if present, is typically located in the core 

tail pipe; and station F is located in the far field. The signals 

u(t), v(t), and w(t) represent the combustion-noise signals at 

the three stations as functions of time t. These desired signals 

cannot be directly obtained by themselves because of the 

presence of the additional-noise signals m(t), n(t), and o(t) at 

the different stations. However, the downstream signals v(t) 

and w(t) are uniquely determined by the impulse-response 

functions huv and hvw and the previous-station signals u(t) and 

v(t), respectively. The measurable signal x(t), y(t), or z(t) at 

each station is the sum of the desired and corresponding 

additional-noise signals. The signals m(t), n(t), and o(t) can be 

taken as mutually uncorrelated as well as uncorrelated with the 

combustion-noise signal u(t), v(t), or w(t) at all the stations. 

The signal m(t) is to a large extent caused by hydrodynamic 

pressure fluctuations (pseudo-sound) in the combustor and

possibly also higher acoustic modes present in the combustor

but cut off in the downstream tail pipe and can potentially be
Engine System and Core Noise

NASA/TP—2012-215653 39 Chapter 3

Figure 3.1.—Coherence technique to determine combustion-noise component of far-field noise. Measurement stations C, T, and F are located in the engine combustor, core tail pipe, and far field, respectively. Signals x(t), y(t), 

and z(t) are directly measurable, are functions of time t, and are the sum of coherent combustion-noise signals 

u(t), v(t), and w(t) and uncorrelated signals m(t), n(t), and o(t) resulting from other noise sources; huv and hvw are 

impulse-response functions.

quite large. The signals n(t) and o(t) are mainly due to acoustic 

pressure fluctuations from other noise sources, and particularly 

o(t) can be dominant in the frequency range of interest because 

of the presence of jet noise. The goal is to determine the onesided auto-spectrum Gww(f), with f denoting frequency, the 

combustion-noise component of the total far-field noise 

signature Gzz(f). The diagnostic technique is commonly referred 

to as the “coherent-output-power method” when only one 

sensor inside the engine is utilized in combination with the farfield microphone and as the three-signal technique otherwise.

3.2.2.3.1.1 Coherent-Output-Power Method

Bendat and Piersol (Ref. 41) describe the basic formulation 

for the coherent-output-power method. If the sensor inside the 

combustor and one in the far field (Figure 3.1) are used in this 

technique, it follows that the coherent output spectrum is 

given by 

( ) ( )

( )

( )

( )

( )

( ) ( )

( )

( )

( f ) G (f )

G f

G f

G f G f

G f

G f

G f

G f

G f G f

xz zz

xx

xz

xx mm

xz

uu

xz

uu

uw ww

2

2 2

2

2

| | | |

| |

| |

= γ

≈ − =

=

=

(3.1)

regardless of the output noise Goo(f). Note Gαα, Gαβ, and 

γ αβ = | Gαβ | GααGββ denote the one-sided auto-spectrum, 

cross-spectrum, and coherence of the signals α and β, where α

and β are dummy indexes. Note that the measured Gxx is a 

positive-biased estimate for the unknown input spectrum Guu

and, consequently, the second-to-last step in Equation (3.1) is 

only a valid approximation when the unknown Gmm can be 

assumed to be small compared to Gxx. In view of the certain 

presence of nonpropagating pressure fluctuations in the combustor, i.e., Gmm ≠ 0, Equation (3.1) is quite likely to underpredict 

the actual coherent output spectrum. Furthermore, the spectra are 

estimated using a finite observation time, and consequently, the 

signal z(t) needs to be time shifted to account for the time delay 

of the disturbances in the computation of the cross-spectrum Gxz

in order to yield a meaningful result.

Karchmer and colleagues (Refs. 42 to 45) showed successful application of coherence techniques to measurements 

obtained using a static Avco Lycoming YF–102 turbofan 

engine instrumented with internal as well as far-field microphones. A typical result showed the combustion coherent 

output power in the 120° direction (aft quadrant) to roughly 

have a dome-shaped spectral distribution in the range 0 to 

200 Hz with the peak at about 125 Hz. At 43 percent engine 

speed, the peak was about 6 dB lower than the peak of the 

total far-field spectrum located at 120 Hz. The dome edges 

were about 20 dB lower at 40 and 200 Hz. Similar coherencefunction results also were obtained from static tests of Pratt & 

Whitney JT15D (Ref. 46) and General Electric CF6–50 

(Ref. 47) engines.

3.2.2.3.1.2 Three-Signal Coherence Method

Chung (Ref. 48) developed a three-signal coherence technique for microphone flow-noise rejection. Figure 3.2 shows 

the general block diagram for this method, where s(t) is the 

source signal and, as before, u(t), v(t), and w(t) are the 

coherent signals, m(t), n(t), and o(t) represent mutually 

uncorrelated noise, and x(t), y(t), and z(t) are the measurable 

signals. The coherent auto-spectra at the three measuring 

locations in Figure 3.2 are given by 

( ) ( ) ( )

| ( )|

| || |

G f

G f G f G f

yz

xy xz

uu = (3.2a)

( ) ( ) ( )

| ( )|

| || |

G f

G f G f G f xz

xy yz

vv = (3.2b)

( ) ( ) ( )

| ( )|

| || |

G f

G f G f G f

xy

xz yz

ww = (3.2c)
NASA/TP—2012-215653 40

Figure 3.2.—Three-signal coherence technique for noise 

rejection, where s(t) is the source signal as function of 

time t and hsu, hsv, and hsw are impulse-response

functions. Coherent signals u(t), v(t), and w(t) of interest 

are not directly measurable; their addition to mutually 

uncorrelated signals m(t), n(t), and o(t) from other 

sources results in measurable signals x(t), y(t), and z(t).

However, the three-signal method also applies to the situation shown in Figure 3.1, where the measuring stations and the 

signals x(t), y(t), and z(t) are “sequential” rather than “paralleloutput” measurements as in Figure 3.2. Krejsa (Ref. 49) 

independently considered the situation depicted in Figure 3.1

and obtained Equation (3.2c) as his far-field result. The threesignal coherence technique as applied by Krejsa (Refs. 49 to 51) 

eliminates the bias error in the coherent combustion-noise 

measurements due to nonpropagating pressure fluctuations 

within the engine.

The strength of the three-signal method is that it involves 

only measured cross-spectra. The measured cross-spectra are 

affected by extraneous noise only if this noise correlates 

between measurement locations. This can often be avoided by 

an appropriate spatial separation of the sensors involved; the 

three-signal method then provides unbiased estimates of the 

coherent auto-spectra. In contrast, measured auto-spectra will 

always include a positive definite contribution from the 

extraneous noise.

Krejsa compared results obtained using the earlier coherentoutput-power method with those using the new three-signal 

method for YF–102 (Refs. 49 to 51), JT15D (Ref. 50), and 

CF6–50 (Ref. 50) static-engine tests (Refs. 45 to 47). He 

found that the older method consistently underpredicted the 

combustion noise spectra by several dB at low engine speeds 

and of the order of 10 dB at a high engine speed. Krejsa 

(Ref. 51) also discussed two other techniques (Refs. 52 and 

53) for isolating the combustion noise using only far-field 

measurements, one of which introduced a model for the jet 

noise (Ref. 53). The three-signal coherence technique also was 

used by Shivashankara (Ref. 54) to study core noise in a Pratt 

& Whitney JT9D engine.

The three-signal coherence data for the YF–102, JT15D, 

and CF6–50 static-engine tests were further examined and 

correlated by von Glahn and Krejsa (Ref. 55). The suggested 

correlations utilized one, two, and four spectral segments to 

capture perceived peaks in the far-field core-noise spectra. 

Generally, the sound pressure levels at the single-segment 

spectrum peak, the higher frequency two-segment spectrum 

peak, and the two higher frequency four-segment spectrum 

peaks scaled with a heat-release parameter, as in the semiempirical models described in Section 3.2.2.2, whereas the 

low-frequency segments scaled with the combustor exit 

velocity to the fourth power. They stated that the four-segment 

spectra provided the best overall fit to the data, but also that 

the two-segment spectrum appeared to be a reasonable 

representation of the combustion noise. However, the data 

comparisons do not generally show the expected 3-dB 

increase at the intersection of the multisegment spectra, which 

renders their conclusions less clear. Nevertheless, their results 

show that the assumption of a single-peaked far-field

combustion-noise spectrum with the peak fixed at 400 Hz, as 

used in ANOPP, can be questioned.

It is also possible to separate core noise from jet noise using 

three far-field microphones since each would pick up correlated 

core noise and uncorrelated external noise from the jet (Refs. 54

and 56). As long as the spatial (polar angle) separation of the 

microphones is large enough, the jet noise at each location 

would be mutually uncorrelated and Equation (3.2) would 

apply. Mendoza et al. (Ref. 56) analyzed data from a Honeywell 

TECH977 static-engine test (Ref. 57) using a three-signal

far-field method, among other multiple-microphone

signal-processing techniques (Ref. 58). They found that the 

three-signal method works well in frequency regions where a 

single engine-internal noise source is dominant. The method did 

not work well for frequencies where multiple self-correlated 

noise sources are of comparable magnitude; for example, in the 

relatively limited range where combustion noise and turbine 

broadband noise overlap.

3.2.2.3.2 Modal and Other Analyses

In order to grasp the transmission of combustion noise to 

the engine-external flow region, the modal structure in the 

combustor and downstream passages as well as the turbine 

attenuation must be understood. Detailed diagnostic and 

analytical research efforts in these areas were carried out 

during the late 1970s and early 1980s.

An acoustic modal analysis was used to interpret experimental results from a full-scale (YF–102) annular combustorrig test by Karchmer (Ref. 59) and by Krejsa and Karchmer 

(Ref. 60) for the tailpipe unsteady pressure field of an 

AiResearch QCGAT turbojet engine. The method assumed 

randomly occurring equal-amplitude clockwise and 
Engine System and Core Noise

NASA/TP—2012-215653 41 Chapter 3

counter-clockwise propagating pressure fluctuations and 

statistical independence between the (μ,ν) modes, where μ and 

ν denote the azimuthal and radial mode numbers, respectively. 

An optimized least-square fit of the measured cross-spectra 

was then used to determine the modal amplitudes. For the 

frequencies (≤1500 Hz) of interest for combustion noise, only 

modes with ν = 0 and 0 ≤ μ ≤ 4 needed to be included in the 

analysis. They found that individual modes can be uniquely 

identified within separate frequency bands. The plane-wave 

(0,0) mode dominated for the lowest frequencies up to the cuton frequency of the (1,0) mode. For higher frequencies, the 

most recently cut-on mode dominated the unsteady pressure 

field; that is, successively higher azimuthal modes dominated 

with increasing frequency. Karchmer (Ref. 59) concluded that 

the basic source generating mechanism itself has a relatively 

smooth spectral shape, but the geometry of the combustor is 

extremely effective in promoting modes that are resonant in 

the combustor. Krejsa and Karchmer (Ref. 60) found that the 

(0,0) mode was dominant up to about 800 Hz at the tail-pipe 

exit.

Miles and Krejsa (Ref. 61) compared an analytical model 

for pressure propagation and convected-entropy conversion 

(with assumed input entropy) with core-nozzle data obtained 

for a JT15D turbofan engine. The model was found to be 

adequate for a low nozzle-exit Mach number of about 0.2, 

with the effect of the convected entropy being negligible. 

They found that a more accurate exit-impedance model and a 

better description of the incoming entropy would be needed at 

higher nozzle exit velocities and frequencies lower than about 

120 Hz. Miles et al. (Ref. 62) measured the pressuretemperature cross-spectra in a constant-area duct downstream 

of a General Electric J47 can combustor. Their results 

suggested that the pressure and temperature fluctuations 

correlate at the combustion source point for low frequencies 

and that the phase angles of the pressure and temperature are 

related by the convected-flow time delay. This result agrees 

with the earlier observation of Muthukrishnan et al. (Ref. 18) 

that at low frequencies indirect noise related to entropy and 

direct combustion noise are coherent (but become uncorrelated 

at moderate frequencies). Miles and Krejsa (Ref. 63) developed a one-dimensional model to calculate the relevant spectra 

in a ducted combustion system and compared predictions with 

experimental results (Ref. 62). Huff (Ref. 64) derived a 

simplified one-dimensional combustion-noise theory for a disk 

source in an infinite duct and predicted the pressure spectrum 

inside a CF6–50 engine (Ref. 47).

Matta and Mani (Ref. 65) developed a multistage actuator 

disk for low-frequency noise transmission through turbines. 

They found that the interaction effects of adjacent blade rows 

must be considered; that is, simply summing up attenuation 

from each blade row in isolation would have overpredicted the 

attenuation. A more complex finite-chord analysis also 

revealed that the actuator-disk theory remained valid for 

frequencies as high as about half the blade-passing frequency. 

Hence, the multistage actuator-disk theory is an adequate tool 

to predict direct combustion-noise attenuation by the turbine.

3.2.2.4 Low-Emission Combustors

Low-emission dual-annular combustors (DAC) under initial 

development in the 1990s produced significantly more noise 

(10 to 15 dB) than older production combustors at low-power 

operation, but with virtually no noise difference observed at 

full power (Ref. 66). Dual-annular combustors produce larger 

circumferential and radial variations of the total temperature in 

the combustor at partial-power conditions due to its firing 

pattern. Gliebe et al. (Ref. 66) argued that these spatially 

inhomogeneous, but steady, temperature distortions are 

effective sources for entropy fluctuations, which in turn induce 

pressure fluctuations (indirect noise) as they pass through the 

turbine and thus lead to the increased noise level. Mani 

(Ref. 67), on the other hand, expressed the opinion that the 

entropy waves are directly generated by the unsteady heat 

release and not as a consequence of the spatially inhomogeneous steady heat release. Nevertheless, the central point of both 

arguments is that the indirect-noise mechanism is responsible 

for the observed increase in noise. 

Gliebe et al. (Ref. 66) described an actuator-disk theory for 

the conversion of entropy fluctuations to sound by the turbine. 

The analysis starts at the combustor exit and requires 

knowledge of the rms level and axial and circumferential 

integral length scales of the temperature fluctuations at that 

location and mean-line flow information in the turbine. An 

accompanying computational fluid dynamics combustor 

simulation provided the rms temperature level but not the 

length scales, which had to be estimated based on other 

considerations. Mani (Ref. 67) provided a linearized twodimensional analysis of the combustor, which accounted for 

compressor and turbine boundary conditions and modeled the 

combustion zone as a flame sheet.

Gliebe et al. (Ref. 66) also developed empirical

combustion-noise correlations based on earlier obtained statictest data for a selection of modern high-bypass-ratio engines. 

The data used was from General Electric CF6–80C2 and CFM 

International CFM56–5B/7B engines equipped with standard 

single-annular combustors (SAC) and General Electric GE90 

and CFM56–5B/7B engines equipped with low-emission 

combustors. They adopted the multilobed spectrum ideas of 

von Glahn and Krejsa (Ref. 55) and found that the best fits 

were obtained by using a three-segment spectrum (peaks at 63, 

160, and 630 Hz) for SAC engines and two spectral segments 

(peaks at 160 and 500 Hz) for DAC engines.

3.2.2.5 Combustion Instability

Unstable combustion is an abnormal condition that is absent 

from a properly designed engine. Even though it can produce 

considerable noise, it is not a contributor under normal operating 

conditions. Strahle (Ref. 13) points out that combustion noise 

and combustion instability are only weakly related. Combustion 

noise is a random noise field containing a range of frequencies, 

each with random amplitude and phase. While there may be 

acoustic feedback on the unsteady combustion process, it is not 

of sufficient strength to give rise to a global phase-locked 
NASA/TP—2012-215653 42

oscillation. In contrast, combustion instability is characterized by 

a phase-coherent, single-frequency feedback oscillation. 

Typically (Ref. 13), 10–6 to 10–5 of the thermal input is converted 

to acoustic power in a combustor, and at an instability this 

number rises to about 10–4

. The latter thermoacoustic oscillations 

can limit combustor life, performance, and operating conditions. 

Current reviews of combustion instability, or thermoacoustic 

oscillations in combustors, are given by Dowling and Stow 

(Ref. 68), Lieuwen (Ref. 69), and Keller (Ref. 70).

3.2.3 Turbine Noise

By the end of the 1960s, it was realized that the turbine 

contribution to the overall engine noise could no longer be 

ignored because of reductions in jet and fan noise (Refs. 71 and 

72). Mathews et al. (Ref. 71) surveyed the early 1970s status of 

turbine-noise prediction and suggested research areas for further 

improvements in predictive capability. Krejsa and Valerino 

(Ref. 72) recommended an interim prediction method for 

turbine-noise prediction for the NASA ANOPP (Refs. 29 and 

30). The ANOPP turbine-noise prediction procedures have been 

refined over the years, but their roots are still in the methods 

described in those two references (Refs. 71 and 72). Groeneweg 

et al. (Ref. 3) described the early 1990s understanding of turbine 

noise and methods for its reduction. The major turbine contributions to the far-field noise signature originate in the lowpressure turbine (LPT) and manifest as both discrete-tone and 

broadband noise. The tones result from the interaction between 

rotating and stationary blades as well as struts and occur at the 

BPF and its harmonics. These acoustic pressure fluctuations 

propagate away from the generating blade or vane row, along 

spinning helical paths. Turbine broadband noise is internally 

generated by blade lift fluctuations caused by flow turbulence as 

well as by scattering of the turbine tones into sideband noise 

(commonly referred to as “haystacks”) by the turbulence in the 

external exhaust shear layers. The haystacking effect represents 

a redistribution of some of the acoustic power from tonal to 

broadband noise. The overall turbine-noise acoustic power is 

preserved, however. The far-field turbine broadband noise 

spectrum is commonly dominated by this haystacking phenomenon. Up to the early 1990s, LPTs were made quieter by using 

acoustic treatments and so-called cutoff and modal design 

techniques that were coupled with corporate in-house design 

rules. The high solidity of the LPT stages of that era also meant 

that transmission losses for tones generated by early stages were 

significant, and commonly the second-to-last stage was the 

loudest.

While turbine noise is not the dominant noise source for the 

current generation of aircraft engines, it is quite often the most 

miss-predicted one, which can lead to difficulties in meeting 

noise guarantees for some aircraft configurations (Ref. 73). 

Modern engine designs, including the LPT, are different from 

those of the 1990s and earlier and have resulted in a greater 

impact of the LPT noise component on total engine noise 

levels. Technology advances and cycle improvements have 

resulted in significantly lower levels of fan and jet noise. Also, 

the higher engine bypass ratios required for improved 

performance have resulted in larger engine diameters with 

lower rotational speeds, thus lowering the BPF and harmonic 

tone frequencies to more annoying bands where they lead to a 

higher effective perceived noise level, EPNL. Recent engine 

design and cycle changes are driven largely by cost, weight, 

performance, and maintainability. One result of this is a trend 

toward fewer LPT stages with reduced blade counts per stage. 

These lower airfoil counts lead to (1) higher blade loading, 

which produces stronger wakes and potentially increased tone 

intensities; (2) less stage solidity, which reduces attenuation of 

noise from earlier stages; and (3) a further reduction in the 

tone frequencies, to the point where the harmonics may now 

also fall into the more objectionable bands. Low cost and 

weight concerns have also led to a trend toward less spacing 

between stages as well as a decrease in the distance between 

the last-stage rotor and the exit struts. This decreases the decay 

(mixing) of wakes as well as increases the unsteady rotorblade loading due to potential pressure fields caused by

vanes and struts. In particular, the modes resulting from the 

interaction of the last-stage rotor and the exit struts will be 

stronger than for previous designs, and many of these modes 

are highly cut-on and are not subject to transmission losses 

that would occur through upstream stages (Ref. 74, personal 

communication).

Acoustic mode cutoff methodology, traditionally the first line 

of defense against tone noise, and the modal-design approach 

are now harder to implement because the newer LPT designs 

effectively increase the unsteady aerodynamic coupling of the 

turbine stages, which in turn introduces additional complexity in 

the tone generation mechanisms. Wake velocity defects are now 

more likely to propagate through one or more blade rows and 

create noise on several disks. With the trend of less attenuation 

per stage, the modification and/or scattering of the duct modes 

during their propagation through several static and rotating 

blade rows needs to be accounted for in the noise prediction. 

Furthermore, acoustic treatment is more of a challenge than it 

was previously. Exhaust temperatures at the design operating 

condition, as well as at the off-design noise generating conditions, have increased. Lightweight materials, suitable to be used 

for acoustic treatment and able to meet the temperature 

requirements, are not yet widely available.

3.2.4 Current Prediction Codes

The modular Aircraft Noise Prediction Program ANOPP 

was developed by NASA “to predict aircraft noise with the 

best currently available methods” (Ref. 75). An overview of 

ANOPP is presented in Chapter 2. In order to maintain and 

enhance the program, NASA has continued to contract with 

industry to evaluate ANOPP against flyover and real-engine 

data and to suggest improvements to its modules. These 

investments have over the years led to significant improvements in the capability of ANOPP.

Boeing (Ref. 76) in 1980 conducted a flyover test using a 

widebody 747–100 aircraft equipped with Pratt & Whitney 

JT9D engines. The data were acquired during level flight, using 
Engine System and Core Noise

NASA/TP—2012-215653 43 Chapter 3

12 ground-based microphones, with landing gear up and flaps 

set to minimize airframe noise, for corrected engine speeds in 

the 75.4 to 98.8 percent range. The tone-weighted perceived 

noise levels (PNLTs) were found to be consistently underpredicted in the aft direction by about 9 dB. The data also suggested a significant contribution in this quadrant from combustion 

noise in the 250 to 400 Hz range, with the peak occurring 

between 110° and 130°, for all power levels. Based on this 

observation, they concluded that the predictions would fit the 

test data better if in the combustion-noise module the peak 

frequency were shifted one 1/3-octave frequency band lower 

(from 400 to 315 Hz), and the power level were increased by 

about 3 dB. In addition, they stress that further development of 

accurate source separation techniques is an essential prerequisite 

for the potential improvement of component-prediction 

procedures.

In 1996, GE Aircraft Engines (Ref. 77) assessed ANOPP by a 

comparison with detailed static-engine measurements for a 

representative selection of high-bypass engines—CF6–80C2, E3

, 

and QCSEE—as well as with GE in-house prediction methods. 

They found that the ANOPP and GE in-house predictions for 

combustion noise agree closely. This is not surprising since both 

methods are practically identical. Furthermore, they state that “it 

is difficult to assess the absolute accuracy of the predicted levels 

and peak frequency” and continue on to conclude that “the 

combustion noise predictions do not cause the total predicted 

engine noise to assume an unreasonable spectral shape or to 

exceed the level of total measured engine noise.”

A contract effort (Refs. 36, 78, and 79) in the mid-1990s with 

AlliedSignal (Honeywell) led to a substantial extension of 

ANOPP fan, jet, core, and turbine modules to small turbofan 

engines such as those typically used by smaller regionaltransport and business aircraft. Acoustic measurements from 

static tests involving three AlliedSignal research engines were 

used in this effort.

Other computer codes for aircraft-noise prediction exist, but 

some may no longer be maintained. FOOTPR (Ref. 80) is a 

procedure for predicting flyover noise footprints for various 

engine installations and RADIUS (Ref. 80) is a tool for 

predicting the acoustic far-field signature of static-engine tests. 

These codes were created at the NASA Lewis (Glenn) Research 

Center as an aid during the early development stages of 

ANOPP, and they use common noise-source subroutines.

Another example is the HSRNOISE (Ref. 81) code, which is 

an outcome of noise studies by NASA and U.S. industry 

partners—Boeing, GE Aircraft Engines, and Pratt &

Whitney—during the course of the High Speed Research (HSR) 

Program (1989 to 1999). The goal of this program was to 

advance technology for supersonic commercial transport 

aircraft. New models for fan and jet noise were developed for 

the HSR technology-concept engine (Ref. 82), a mixed-flow 

turbofan engine with rectangular mixer-ejector nozzles. 

Combustor, turbine, airframe, and other models were adopted 

from existing methods used either by NASA (ANOPP) or its 

partners. In particular, the combustion noise module is based on 

the method developed by Mathews and Rekos (Ref. 38).

In addition, all major engine and airframe companies have 

proprietary in-house noise-prediction codes with capabilities 

similar to those of ANOPP.

3.3 Engine Noise Prediction Using 

ANOPP

The NASA system tool ANOPP (Ref. 75) (Aircraft Noise 

Prediction Program) is a highly modular code for the engineering prediction of aircraft flyover noise as well as static-engine 

noise. The basic philosophy of ANOPP is to use semi-empirical 

prediction methods for the different engine noise sources. The 

methods are based on engine data with parameters based on 

physical understanding of dominating processes. Directivity and 

spectral distribution vary from component to component and 

with noise source mechanisms for each component, but are 

generally independent of engine operational conditions. The 

acoustic power is correlated to engine operational conditions. 

ANOPP also has modules for airframe noise that depend on the 

aircraft characteristics and flight conditions.

This section presents the application of ANOPP to predict 

engine test-stand acoustic data. Community noise caused by 

takeoff, landing, or flyover are not addressed. Level 25v3 of 

ANOPP is used (see also the software distribution for up-todate documentation).

3.3.1 ANOPP Static-Engine-Test Simulation

Figure 3.3 illustrates a typical ANOPP model for a staticengine test. The first step involves defining the ambient 

conditions of pressure, temperature, relative humidity, density, 

and speed of sound using the atmospheric module (ATM). 

Sound attenuation by the atmosphere depends on frequency 

and these ambient conditions. Using these properties, the 

atmospheric absorption module (ABS) then constructs an 

absorption-coefficient table in terms of sound frequency and 

altitude, which is used in the propagation stage.

Figure 3.3.—ANOPP module flow chart for static-engine test.
NASA/TP—2012-215653 44

The second step utilizes modules for the fan (HDNFAN), 

combustor (GECOR), turbine (TUR), jet (STNJET or 

ST2JET), and the effects of fan-noise treatment (TREAT) to 

predict the source noise. Each source module provides a table 

of the mean-square acoustic pressure in 1/3-octave frequency 

bands as functions of polar directivity angle and azimuthal 

directivity angle at a virtual observer distance. The models 

used in these source modules are all azimuthal-angle independent. The fan-noise-treatment module estimates the 

attenuation by acoustic treatment in the inlet and aft bypass 

duct and updates the prediction from the fan-noise module.

The third step involves propagating the noise from the source 

(virtual observer) location to the actual observer location. The 

propagation is assumed to be linear. The propagation module 

(PRO) sums the noise data that are generated by the noisesource modules and propagates them to the observer positions. 

For a static-engine test, this includes accounting for spherical 

spreading and characteristic impedance change, atmospheric 

attenuation, and ground reflection and attenuation. The first 

effects are a consequence of the preservation of total acoustic 

power in the absence of losses. The computation of the 

atmospheric attenuation uses the coefficient table produced by 

the atmospheric and atmospheric-attenuation modules in step 

one. In a typical static-engine test, the engine is mounted on a 

stand a certain distance above a hard-surface ground, and the 

acoustic-measurement microphones are ground mounted to 

minimize, if not fully remove, the ground-reflection effect.

A brief summary of the source modules used for the engine 

noise predictions is given here. See Chapter 2, “Aircraft 

System Noise Prediction” for more detail on the modules.

3.3.1.1 HDNFAN and TREAT

The HDNFAN module predicts both pure tones and broadband noise for the fan as functions of 1/3-octave frequency 

band and polar directivity angle using empirical relationships. 

The module has the option to use the original Heidmann 

method (Ref. 83) or extensions for small (Ref. 78) and large 

(Ref. 77) engines, respectively. The module accounts for six 

separate physical noise-generating mechanisms: inlet broadband noise, inlet rotor-stator interaction tones, inlet flowdistortion tones, combination tone noise, discharge broadband 

noise, and discharge rotor-stator interaction tones. In a typical 

static-test situation, the engine is fitted with an inflow control 

device to remove extraneous inflow disturbances unrepresentative of flight. Consequently, inlet flow-distortion tones 

were not included here. In addition to geometric and design 

parameters, the prediction requires as input parameters the fan 

rotational rate, mass flow rate, and total temperature rise 

across the fan. Chapter 5, “Fan Noise Prediction,” provides an 

assessment of the HDNFAN module as well as examples of 

input parameters (Table 5.8).

The TREAT module updates the fan-noise prediction by 

accounting for acoustic treatment. The module has the option 

to use methods developed by Magliozzi (Ref. 84) or Kontos 

et al. (Ref. 77). It requires geometry and design parameters 

and the operation-point inlet and aft duct mass flow rates.

3.3.1.2 GECOR

The GECOR combustion-noise module predicts broadband 

noise as a function of 1/3-octave frequency band and polar 

directivity angle with a choice of using three empirical 

methods. The choices are (1) the SAE method (Ref. 34), (2) a 

small-engine revision (Ref. 36), or (3) an intermediate narrowband method (Ref. 23)

2 that includes tail-pipe modulation 

effects. The SAE and small-engine methods require as input 

parameters the combustor engine-state mass flow rate, inlet 

total pressure, and inlet and exit total temperatures, in addition 

to geometry and design parameters.

3.3.1.3 TUR

The turbine-noise module, TUR, predicts both broadband 

and tone noise as functions of 1/3-octave frequency band and 

polar directivity angle using empirical relationships (Ref. 72), 

with the option to use a small-engine extension (Ref. 36) of 

the method. In addition to geometry parameters, the module 

requires as input parameters the turbine shaft speed as well as 

exit total and static temperatures.

3.3.1.4 STNJET

The STNJET noise-source module predicts jet mixing noise 

and shock-associated noise for circular jets. The jets can be 

either single stream or coannular streams, with or without a 

center plug. The module has the option to use the original 

Stone (Refs. 85 and 86) empirical method or a small-engine 

extension (Ref. 36). In addition to geometry parameters, the 

module requires the nozzle exit flow conditions to be specified. For a subsonic single stream, with no center plug, these 

are the following parameters: jet total temperature and fully 

expanded jet density, velocity (acoustic Mach number), and 

Mach number.

3.3.2 Sensitivity

The influence of performance parameter uncertainties on 

the ANOPP total noise predictions is described here. The total 

mean-square pressure in a 1/3-octave frequency band b can be 

expressed as 

( ) (b)

c

c

b P p2

,

,

2 



=∑ (3.3)

where the brackets represent ensemble averaging, ( ) 2

,

b

pc  is the 

contribution to the total from each source and the indices c and 

indicate engine component (i.e., turbine, jet, etc.) and component 

noise source (i.e., rotor-stator interaction tones, broadband noise, 

etc.), respectively. The total relative difference in the prediction 

caused by a parameter change can be written as a weighted sum 

of the relative change in the component sources:

 2

See ANOPP L25v3 documentation.
Engine System and Core Noise

NASA/TP—2012-215653 45 Chapter 3

( ) 2

,

( ) 2

,

,

,

( ) 2

( ) 2 | | | |

b

c

b

c

c

c

b

b

p

p a

P

P









δ

≤

δ

∑ (3.4a)

( ) 2

( ) 2

,

, b

b

c

c

P

p a 

 = (3.4b)

where the δ indicates a difference and ac,l is a measure of the 

relative contribution from an individual component source to 

the total mean-square pressure. Since it can be assumed that 

each relative difference is finite, it follows that the overall 

change is determined by the difference in the prediction for 

the dominating noise source for a given operational condition. 

Since the sound-pressure level (SPL) in an 1/3-octave 

frequency band is given by 

















= 2

ref

( ) 2

( ) 10log P

P

SPL

b

b (3.5)

it follows that the change in SPL is given by 















 δ

δ = + ( ) 2

( ) 2

( ) 10log 1 b

b

b

P

P

SPL (3.6)

Note that a 1-dB difference in the SPL corresponds to about a 

26-percent change in the mean-square pressure.

For compactness of notation, let Φ denote either the

mean-square pressure in a particular 1/3-octave frequency

band or the mean-square pressure summed over all the bands; 

that is, either 

( ) 2 b

Φ = P or 

( ) 2 b

Φ = ∑b P along with 

ξ = (ξ1,ξ2,...,ξk) denote the ANOPP parameter vector. The 

ANOPP parameters are of three types: The first type is the 

engine-performance parameters (fan shaft speed, mass flow 

rates, etc.) that change with the engine operation point. The 

second type is the engine-design parameters (geometry, design 

turbine temperature extraction, etc.), and they do not change 

with the engine operation point. The third type is the ANOPP 

model coefficients, and they do not change with the engineoperation point nor within a given engine class. In what 

follows, the engine-design and ANOPP-model parameters are 

assumed to be known without uncertainty. The change in Φ

due to a small change in ξ is then given by k k k

δΦ = ∑ δξ ∂ξ

∂Φ . 

An upper bound on the change is given by 

( )

k k k

k k

k

k k

k k

ξ = ξ ± δξ

ξ − ξ ≈ Φ − Φ

∂ξ

∂Φ δΦ ≤

±

+ − + − ∑ 2∑

1

2

1

(3.7)

where Φk± denotes the value of Φ with only the kth parameter 

changed.

The sensitivity to uncertainty in the performance parameters for an ANOPP simulation is determined as follows: For a 

specific engine operation point, each performance parameter 

(see Table 3.1) is independently varied up and down by a 

small amount to determine the sensitivity to uncertainty in that 

parameter. Of course, parameters like the shaft speed in the 

fan and turbine modules are coupled; and mass flow rates in 

the fan, treatment, and combustor modules are also changed

together in a proportional fashion. The absolute values of the

TABLE 3.1.—ANOPP NONDIMENSIONAL PERFORMANCE PARAMETERS

Module Parameter Meaning

HDNFAN N Fan shaft speed, Strouhal number

MDOT Fan mass flow rate

DELTAT Total temperature rise across fan

TREAT MDOTIN Same as HDNFAN MDOT

MDOTAF Mass flow rate in aft duct

GECOR MDOT Combustor mass flow rate

PI Combustor inlet total pressure

TI Combustor inlet total temperature

TCJ Combustor exit total temperature

TUR ROTSP Turbine shaft speed, Strouhal number

TT Turbine exit total temperature

TSJ Turbine exit static temperature

STNJET T1 Jet total temperature

RHO1 Fully expanded jet density

V1 Fully expanded jet velocity, acoustic Mach number

M1 Fully expanded jet Mach number
NASA/TP—2012-215653 46

individual sensitivities are then added together to yield an 

upper bound on the prediction sensitivity to a relative 

uncertainty in the performance parameters. This is the 

procedure used below in the comparison of ANOPP predictions to engine test-stand data.

3.4 Comparison of ANOPP–L25 

Predictions and NASA-Honeywell 

EVNERT Engine Test-Stand Data

The EVNERT (Engine Validation of Noise and Emission 

Reduction Technology) program (Ref. 57) was a NASAfunded test program carried out by Honeywell Aerospace 

(Phoenix, AZ) during the period December 2004 through 

August 2007. It was an ambitious program of engine validations of integrated technologies that address the reduction of 

engine and propulsion-airframe integration noise. As part of 

this program, an extensive set of acoustic far-field data was 

taken to characterize engine noise sources, to gain insight in 

their mechanisms, and to evaluate select noise-reduction 

concepts. The tests were carried out in the Honeywell 

Aerospace’s San Tan outdoor engine test facility. The 

Honeywell TECH977 research engine, which is characteristic 

of small engines in the 6000- to 8000-lb thrust class, was used 

in these tests.

A combination of well-established industry-standard and 

leading-edge data acquisition, processing, reduction, and 

analysis techniques were used in the investigation. A wealth of 

information was generated that will serve noise researchers well 

for a considerable time and will have significant impact on the 

field. It is important to recognize, though, that even in a 

carefully executed engine-test-stand program, complete 

repeatability of the results cannot be expected. There is always 

the possibility of the temporary introduction of spurious noise 

sources caused by the many reconfigurations that take place 

during the course of a long investigation. Various degrees of 

agreement between predictions based on semi-empirical 

methods (which are based on engine-data correlations, presumably using results from many engines) and test results for a 

particular engine build, or between engine builds, are to be 

expected.

3.4.1 Comparison of Total 1/3-Octave Results

Constant-percentage-bandwidth, 1/3-octave, far-field noise 

data were obtained in the EVNERT program using groundlevel microphones located along a circular arc from 5° to 160°

with respect to the engine inlet direction, in 5° increments. 

The online data acquisition system also obtained narrowband 

data in parallel with the 1/3-octave data as well as sequentially

(Ref 87, personal communication) obtained pressure-time 

history data at select locations. Only the 1/3-octave data will 

be used here, however.

A sequence of “standard” engine power settings, characterized by the corrected fan speed, was used for the many 

configurations investigated during the EVNERT program. 

NASA was provided select engine operational parameters for 

the power settings for EVNERT configuration 31. The 

required nondimensional ANOPP performance parameters 

(see Table 3.1) were constructed from those. Even though, 

they were obtained for one particular configuration, the 

ANOPP nondimensional performance parameters are also 

representative of many of the other configurations.

Comparisons between ANOPP predictions and the 

EVNERT 1/3-octave data were made on an actual-day basis in 

the present work rather than on a standard-acoustic-day basis. 

This choice was based on the fact that NASA has access to the 

uncorrected actual-day EVNERT 1/3-octave data and 

converting the data would add further uncertainties to the 

experimental data. Consequently, the ambient (reference) 

conditions varied between cases (configurations and power 

settings) to reflect the actual conditions of the day. However, 

the same values of the nondimensional performance parameters were used in all cases for the ANOPP predictions carried 

out here.

Comparisons for configurations 25 and 31 are described in 

separate subsections below. Configuration 25 (October 2005) 

is a baseline case without any fan-noise acoustic treatment; 

that is, the fan flow path has all hard-wall conditions. Configuration 31 (March 2006) is identical except single-degree-offreedom acoustic liners are installed in the inlet, aft-fan c-duct, 

and nozzle. Configurations 25 and 31 will now be referred to 

as the “hard-wall” and “treated” cases, respectively.

3.4.1.1 Hard-Wall Case

To give a visual overview of the quality of the ANOPP 

predictions compared to the EVNERT measured data, side-byside 1/3-octave SPL carpet plots of predictions and test results 

are shown in Figure 3.4 for the approach, cutback, and takeoff 

conditions (60-, 71-, and 87-percent corrected fan speed). The 

horizontal axes are the base-10 logarithm of the center-band 

frequency and the directivity angle, and the vertical axis is the 

1/3-octave SPL. In general, the ANOPP predictions are in 

qualitative agreement with the EVNERT data. As can be seen 

in the figure, the EVNERT engine-test SPL values are higher 

than the ANOPP predictions for frequencies greater than about 

6 kHz in the downstream direction. This is believed to be 

caused by an underprediction of the turbine noise (Ref. 57). 

The EVNERT data is also contaminated in the 315 to 630 Hz 

1/3-octave frequency bands by an abnormal noise source. 

Honeywell (Ref. 57) identified this noise source to be caseradiated noise by using a tarmac-array beamforming technique. They found that this unwanted noise source was present 

during the 2005 EVNERT configurations 13 to 28, but was not 

seen again after a partial engine rebuild for instrumentation in 

early 2006.

Figure 3.5 to Figure 3.7 show the 1/3-octave SPL spectra in 

the 30°, 60°, 90°, 120°, and 150° directions in parts (a) 

through (e) and the overall SPL (OASPL) versus polar 

directivity angle in part (f) for the approach, cutback, and 

takeoff conditions, respectively. The ANOPP predictions have
Engine System and Core Noise

NASA/TP—2012-215653 47 Chapter 3

Figure 3.4.—Hard-wall case 1/3-octave surface plots comparing ANOPP predictions and EVNERT data of far-field 

sound from Honeywell TECH977 engine at various corrected fan speeds. SPL is sound pressure level, and f represents frequency. (a) 60 percent (approach). (b) 71 percent (cutback). (c) 87 percent (takeoff).
NASA/TP—2012-215653 48

Figure 3.5.—Comparison of ANOPP predictions and EVNERT data for hard-wall case of Honeywell TECH977

engine at approach condition, 60 percent corrected fan speed. Error bands for predictions are 1 and 3 percent 

uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated uncertainty from calibration 

and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) versus center frequency at different polar 

angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) Overall SPL (OASPL) versus polar directivity angle.
Engine System and Core Noise

NASA/TP—2012-215653 49 Chapter 3

Figure 3.6.—Comparison of ANOPP predictions and EVNERT data for hard-wall case of Honeywell TECH977

engine at cutback condition, 71 percent corrected fan speed. Error bands for predictions are 1 and 3 percent 

uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated uncertainty from calibration 

and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) versus center frequency at different polar 

angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) Overall SPL (OASPL) versus polar directivity angle.
NASA/TP—2012-215653 50

Figure 3.7.—Comparison of ANOPP predictions and EVNERT data for hard-wall case of Honeywell TECH977

engine at takeoff condition, 87 percent corrected fan speed. Error bands for predictions are 1 and 3 percent 

uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated uncertainty from calibration 

and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) versus center frequency at different polar 

angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) Overall SPL (OASPL) versus polar directivity angle.
Engine System and Core Noise

NASA/TP—2012-215653 51 Chapter 3

uncertainty bands (1 and 3 percent performance parameter 

uncertainty in blue and orange, respectively) and the staticengine-test data have ±1.25-dB bars based on estimated 

calibration and/or instrumentation uncertainty. The abnormal 

case-radiated sound and the high-frequency underprediction of 

the turbine noise are clearly visible in the SPL spectra shown 

in these figures. Nevertheless, the OASPL directivity and 

value are relatively well predicted for the cutback and takeoff 

conditions, with discrepancies mainly occurring close to the 

upstream and downstream directions. 

3.4.1.2 Treated Case

Figure 3.8 shows 1/3-octave SPL surface plots at the 

approach, cutback, and takeoff conditions of 60-, 71-, and

87-percent corrected fan speeds, respectively. The figure 

layout is the same as that used in Figure 3.4. The ANOPP 

predictions are in qualitative agreement with the EVNERT 

data, but with some exceptions. There is high-frequency noise, 

probably turbine-associated, present in the EVNERT data that 

is not reflected in the ANOPP predictions. In addition, there is 

a SPL peak in the EVNERT data at the compressor shaft 

frequency (≈400 Hz at approach). It is most visible in the data 

for the approach conditions and decreasingly so for the higher 

throttle settings. This spectral peak is most likely a

compressor-disk tone.3 The effect of the acoustic treatment in 

the inlet, c-duct, and nozzle can clearly be seen by comparing 

these results with those in Figure 3.4. The fan blade-passing 

frequency tone and its harmonics have clearly been reduced. 

The takeoff condition is dominated by jet noise, which 

somewhat masks the fan-noise attenuation due to the acoustic 

liners.

Figure 3.9 to Figure 3.11 show the 1/3-octave SPL

spectra in the 30°, 60°, 90°, 120°, and 150° directions in parts 

(a) through (e) and the OASPL versus polar directivity angle 

in part (f) for the approach, cutback, and takeoff conditions, 

respectively. The uncertainty bands and bars for the prediction 

and data, respectively, are the same as for the hard-wall case 

above. The compressor-disk tone and the high-frequency 

underprediction of the turbine noise are clearly visible in the 

SPL spectra shown in these figures. The OASPL directivity 

and value are relatively well predicted for all conditions. 

3.4.2 Comparison of Combustion-Noise 1/3-Octave 

Results

Data obtained for configuration 35 of the EVNERT 

(Ref. 57) program is used to assess the combustion-noise 

prediction capability of ANOPP. This engine-test configuration included engine-internal instrumentation in addition to the 

previously described far-field microphones. High-temperature 

pressure sensors with air cooling were located in a combustor 

 3

According to Reference 87 (personal communication), these tones are 

commonly seen in propulsion engines, auxiliary power units, and 

automobile turbochargers. They can be attributed to the geometric 

characteristics of the compressor system.

ignitor port (CIP1) and at the turbine exit (T551 and T552).4

Pressure-time histories at the internal sensors CIP1 and T551 

and the aft-quadrant far-field microphone located in the 130°

polar direction are used here. The EVNERT data acquisition 

system had a sampling rate of 65 536 Hz and a duration of 

about 70 s, leading to time histories with just over 4.5 million 

data points. Each time series is analyzed using a fast Fourier 

transform length of 8192 points (corresponding to an 8-Hz 

frequency resolution or bin width), Hanning windowing, and a 

50-percent data-segment overlap (leading to M = 1117 

segments). The resulting narrowband auto-spectra are then 

frequency summed up to yield the corresponding 1/3-octave 

SPL. The 1/3-octave far-field total SPL results are in full 

agreement with the Honeywell-provided 1/3-octave SPL data.

3.4.2.1 Source-Separation Implementation

Using the two- and three-signal coherence techniques 

described in Sections 3.2.2.3.1.1 and 3.2.2.3.1.2, the

combustion-noise component Gww(f) of the far-field noise 

signature Gzz(f) (see Figure 3.1) can be determined by 

Gww (f ) z (f )Gzz (f ), x, y 2 = γα α = (3.8a)

where either the combustor sensor CIP1 (α = x) or the turbineexit sensor T551 (α = y) is used in combination with the 130°

far-field microphone, and/or it can be determined by 

( ) ( ) ( )

( ) G ( f ) f

f f G f zz

xy

xz yz

ww γ

γ γ = (3.8b)

where signals from CIP1 sensor, T551 sensor, and the far-field 

microphone are utilized. These three choices will be referred 

to as the “2s-cip1,” “2s-t551,” and “3s” methods, respectively, 

in what follows. Equation (3.8a) is simply a restatement of 

Equation (3.1) allowing for a choice in engine-internal signal, 

and Equation (3.8b) follows directly from Equation (3.2c) by 

using the definition of coherence.

From a purely theoretical point of view, 0 ≤ γαβ ≤ 1, with 

γαβ = 0 meaning that the two signals α(t) and β(t) are completely uncorrelated and γαβ = 1 indicating perfectly correlated 

signals. In practice, only estimates αβ γˆ of the coherence can 

be obtained using finite data series. The estimated coherence 

will, in fact, be nonzero even for completely uncorrelated 

signals (Refs. 88 and 89); that is, only the interval 

ε < γˆαβ ≤ 1 (3.9)

is meaningful, where 

( ) 2 1 ( 1) 1 1 − ε = − − N I (3.10)

 4

The sensor labels here follow the naming convention in Reference 57.
NASA/TP—2012-215653 52

Figure 3.8.—Treated case 1/3-octave surface plots comparing ANOPP predictions and EVNERT data of far-field 

sound from Honeywell TECH977 engine at various corrected fan speeds. SPL is sound pressure level, and f

represents frequency. (a) 60 percent (approach). (b) 71 percent (cutback). (c) 87 percent (takeoff).
Engine System and Core Noise

NASA/TP—2012-215653 53 Chapter 3

Figure 3.9.—Comparison of ANOPP predictions and EVNERT data for treated case of Honeywell TECH977

engine at approach condition, 60 percent corrected fan speed. Error bands for predictions are 1 and 3 percent 

uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated uncertainty from calibration 

and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) versus center frequency at different polar 

angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) Overall SPL (OASPL) versus polar directivity angle.
NASA/TP—2012-215653 54

Figure 3.10.—Comparison of ANOPP predictions and EVNERT data for treated case of Honeywell TECH977

engine at cutback condition, 71 percent corrected fan speed. Error bands for predictions are 1 and 3 percent 

uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated uncertainty from calibration 

and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) versus center frequency at different polar 

angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) Overall SPL (OASPL) versus polar directivity angle.
Engine System and Core Noise

NASA/TP—2012-215653 55 Chapter 3

Figure 3.11.—Comparison of ANOPP predictions and EVNERT data for treated case of Honeywell TECH977

engine at takeoff condition, 87 percent corrected fan speed. Error bands for predictions are 1 and 3 percent 

uncertainties in performance parameters. Error bar for data is ±1.25 dB estimated uncertainty from calibration 

and instrumentation. (a) to (e) 1/3-octave sound pressure level (SPL) versus center frequency at different polar 

angles. (a) 30°. (b) 60°. (c) 90°. (d) 120°. (e) 150°. (f) Overall SPL (OASPL) versus polar directivity angle.
NASA/TP—2012-215653 56

I is the percent confidence interval if the true 2

αβ γ is zero, and 

N is the number of independent data segments used in 

obtaining 2ˆαβ γ . Welch (Ref. 90) showed, in the context of 

estimating auto power spectra, that N can be replaced by 

9M/11. Miles (Ref. 89) suggested that a better estimate for the 

coherence threshold value, or noise floor, ε can be obtained by 

purposely unaligning the two time series. That is, a time delay 

is deliberately introduced to make the two time series 

uncorrelated. The estimated unaligned coherence does not 

depend on any particular assumptions about the underlying 

statistical properties of the time series and accounts for any 

data-segment overlap and algorithms used in the analysis. The 

unaligned result captures the coherence of any discrete tones 

present in the signals and also provides an estimate of the 

minimum observable broadband coherence. Miles (Refs. 89

and 91) found that Equation (3.10) with N = M provided a 

good estimate of the noise floor. Following Miles, the 

estimated coherence threshold for the present study is 

ε = 0.00518. If the estimated coherence exceeds the threshold 

the two time series are coupled. If it is less than the threshold, 

the signals are random and appear independent for that 

particular number of segments.

In the two-signal (coherent-output-power) method calculations carried out here, the estimated coherence (f ) γαz ˆ is 

replaced by the threshold value ε if it falls below that value for 

a particular narrowband frequency. That is, the estimated 

narrowband combustion-noise component Gww (f ) ˆ is simply 

set to G (f ) zz 2 ˆ ε for the frequency in question. Otherwise it is 

given by the equivalent of Equation (3.8a). The narrowband 

estimate is then frequency summed to yield the corresponding 

1/3-octave result for the far-field combustion-noise

component.

Mathematically, it follows from Equation (3.9) that 

2 1

ˆ

ˆ ˆ − < ε

γ

γ γ

ε <

xy

xz yz (3.11)

The upper limit of this inequality is an unphysical result in 

view of Equation (3.8b) and the fact that Gww

ˆ cannot be 

larger than Gzz

ˆ . Clearly, an additional discriminator is needed 

to ensure a physically realistic three-signal combustion-noise 

estimate. This is provided by the following necessary condition for Equation (3.2) to be valid: 

Θ ≡ arg [Gxzconj(Gyz ) Gxy ] = 0 (3.12)

The standard deviation (in radians) of the estimate for the 

cross-spectrum phase angle Θαβ = arg(Gαβ ) is given by 

(Refs. 41 and 91).

( 2 ) 2 N 1 sin 1 2 αβ αβ

− σαβ = − γ γ (3.13)

Note that the standard deviation is zero for perfectly correlated 

signals and increases as the coherence is diminished. Consequently, in the three-signal method calculations carried out 

here, the estimated narrowband combustion-noise component 

for a particular narrowband frequency Gww (f ) ˆ is set to 

G (f ) zz 2 ˆ ε if any of the estimated coherence values xz γˆ , γ yz ˆ , 

or γ xy ˆ fall below the threshold value ε or if the estimated 

phase angle

Θ > σxz + σyz + σxy ˆ ˆ ˆ ˆ

where

[ ( )]

2N

1 max ˆ , 1 ˆ sin 2 2 1 γ ε − σ = αβ − αβ (3.14)

and α, β = x, y, z. Otherwise it is given by the equivalent of 

Equation (3.8b), utilizing the estimated values for the functions 

on the right-hand side. The narrowband estimate is then 

summed up to yield the corresponding 1/3-octave result for the 

combustion-noise contribution to the far-field noise signature.

3.4.2.2 Statistical Uncertainty

The textbook by Bendat and Piersol (Ref. 41) gives a

summary of statistical random error formulas for single 

input/output systems. From these, it follows that the statistical 

uncertainties for the present coherent-power-method estimates 

are given by

[ ( )] N

G f r zz

1 ˆ  = (3.15a)

[ ( )] N

G f r

αβ

αβ

γ = 1 ˆ  (3.15b)

[ ( )] [ ( )]

(f ) N

f f r

αβ

αβ

αβ γ

− γ

γ =

2

2

2 1

 ˆ (3.15c)

[ ( )] [ ( )]

(f ) N

f G f

z

z r ww

α

α

γ

− γ = 2

1 2 2 ˆ  (3.15d)

where r denotes the relative error or uncertainty. To evaluate 

these, the unknown true coherence γαβ is replaced by its 

computed value γαβ ˆ . Equation (3.15a) is the well known 

result that the uncertainty in an auto-spectrum estimation 

decreases as the inverse square root of the number averages 

used. This result shows that for the present computations, the 

statistical uncertainty of the total-noise auto-spectrum is about 

3.3 percent, which is an order of magnitude smaller than the 

33 percent (1.25 dB) estimated measurement uncertainty.
Engine System and Core Noise

NASA/TP—2012-215653 57 Chapter 3

Figure 3.12.—Total- and combustion-noise 1/3-octave sound pressure level (SPL) versus 1/3-octave

center frequency in 130° direction at different corrected fan speeds. ANOPP predictions and processed

EVNERT data for Honeywell TECH977 engine configuration 35 (Ref. 57). Gzz refers to total noise spectrum; 

2s-cip1, 2s-t551, and 3s refer to different processing techniques applied to the experimental data; and NOP 

refers to threshold values. (a) 48 percent (flight idle). (b) 60 percent (approach). (c) 71 percent (cutback).

(d) 87 percent (takeoff).

Equation (3.15c) shows that the uncertainty in the coherence

vanishes as the signals become correlated. This indicates that 

computed coherence values are more accurate than the 

quantities used in its evaluation. It is also important to realize 

that the estimate Equation (3.15d) also assumes that the input 

signal (see Figure 3.1) does not contain a noise component; 

that is, m(t) = 0 when α(t) = x(t) or n(t) = 0 for α(t) = y(t).

Using logarithmic differencing, it follows that the statistical 

uncertainty in the three-signal method can be expressed as 

[ ( )] [ ( )]

[ ( )] [ ( )]

[ ( )]. ˆ

ˆ 2

1 ˆ 21

ˆ 2

1 ˆ

2 2

2

G f

f f

G f f

r zz

r yz r xy

r ww r xz



 

� 

+

+ γ + γ

≤ γ

(3.16)
NASA/TP—2012-215653 58

For perfectly correlated signals, both Equations (3.15d) and 

(3.16) reduce to the equivalent of Equation (3.15a). As the 

signals become uncorrelated, Equations (3.15d) and (3.16) 

indicate a relative uncertainty of 2 ε2N and (3 2) 2 ε2N , 

respectively. Using the present number of data segments, the 

statistical uncertainty in the combustion-noise estimate is

about 3 percent when the signals are highly correlated and 

becomes roughly 80 and 120 percent (depending on sourceseparation method) as they become poorly correlated. This 

suggests that the three-signal method is less robust than the 

two-signal methods when the coherence is small.

3.4.2.3 Results

The far-field signal z(t) must be time shifted to account for 

the physical propagation delay between the engine-internal 

sensors and the 130° microphone. Following Miles (Ref. 91), 

the corresponding time series is shifted by 5800 points, which 

corresponds to an 88.5-ms time delay. Figure 3.12 shows the 

results of the source-separation procedures at the four engine 

power settings of 48-, 60-, 71-, and 87-percent corrected fan 

speed (flight-idle, approach, cutback, and takeoff conditions) 

for the 1/3-octave center frequency range of 20 to 1000 Hz.

The solid lines represent the ANOPP 1/3-octave SPL predictions for the total (dark grey) and combustion (red-brown) 

noise. The symbols correspond to results computed from the 

experimental time histories as described above. The black 

squares, labeled Gzz, represent the total noise signature, which 

is reasonably well predicted by the ANOPP results. The grey 

squares, labeled NOP, correspond to the threshold value for 

the coherent output power and any combustion-noise result

below these values would not be meaningful using the present 

number of data segments and source-separation techniques. 

The blue, red, and green squares correspond to the combustion 

noise detected using the three methods 2s-cip1, 2s-t551, and 

3s, respectively.

By comparing the results for the three different cases, the 

effect of the positive-bias error inherent in the two-signal 

method, not unexpectedly, leads to an underprediction of the 

peak value when the combustor-internal sensor CIP1 is used. 

The two-signal method utilizing the turbine-exit sensor T551 

and the three-signal method both clearly detect a single 

combustion noise peak, but indicate that the 400-Hz

combustion-peak location used in ANOPP is not adequate for 

this particular engine. The peak occurs at least two 1/3-octave 

bands lower. The ANOPP peak value also appears to be at 

least 3 dB too low.

3.5 Concluding Remarks

Within the limitations of static-engine measurements, the 

ANOPP total-noise predictions agree well with the EVNERT 

data, considering their semi-empirical base. In the near term, 

better prediction methods and models need to be developed for 

the nondominant turbine noise. The source-separation methods 

applied here to the EVNERT data show that the ANOPP 

combustion-noise predictions are not adequate for the 

particular engine used in the test. To enable future “quiet” 

aircraft engines, progress must be made in the understanding 

and modeling of the now subdominant combustion noise and 

its transmission and/or interaction with the turbine.
Engine System and Core Noise

NASA/TP—2012-215653 59 Chapter 3

Appendix A.—Nomenclature

A.1 Acronyms

ANOPP Aircraft Noise Prediction Program

APU auxiliary power unit

BPF blade-passing frequency

DAC dual-annular combustors

DOT Department of Transportation

EPNL effective perceived noise level

EVNERT Engine Validation of Noise and Emission 

Reduction Technology

FAA Federal Aviation Administration

HSR High Speed Research (Program)

LPT low-pressure turbine

NACA National Advisory Committee for Aeronautics

OASPL overall sound pressure level

PNLT tone-weighted perceived noise level

SAC single-annular combustors

SAE Society of Automotive Engineers

SPL sound pressure level

A.2 Symbols

a measure of relative contribution (from individual component source to total mean-square 

pressure)

I percent confidence interval

f frequency

G one-sided spectrum

h impulse-response function

M number of 50-percent-overlapped segments

m(t), n(t), o(t) uncorrelated signals from other sources than the 

one of interest

N number of independent data segments

P unsteady pressure

p contribution to unsteady pressure from individual noise source

s(t) source signal (see Figure 3.2)

SPL sound pressure level

t time

u(t), v(t), w(t) not directly measurable coherent signals (see 

Figure 3.1 and Figure 3.2) 

x(t), y(t), z(t) directly measurable signals (see Figure 3.1 and 

Figure 3.2); sum of not directly measurable coherent signal and uncorrelated signal from other 

sources. 

α(t), β(t) generic signals (could mean s, u, v, w, x, y, or z) 

γ coherence

ε small number >0 from Equation (3.9) 

 error or uncertainty

Θ phase angle

μ azimuthal mode number

ν radial mode number

ξ ANOPP parameter vector

^ estimate of quantity

ensemble average

Subscripts:

c engine component

r relative

ref reference

 engine-component noise source

α, β generic signals (could mean s, u, v, w, x, y, or z)
NASA/TP—2012-215653 60

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Engine System and Core Noise

NASA/TP—2012-215653 61 Chapter 3

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NASA/TP—2012-215653 62

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NASA/TP—2012-215653 63

Chapter 4—Airframe Noise: A Prediction Capability Assessment

Jay H. Casper, David P. Lockard, Casey L. Burley, Meelan M. Choudhari, William M. Humphreys,

Florence V. Hutcheson, Mehdi R. Khorrami, and Craig L. Streett4

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

Summary

Presented herein are the comprehensive findings of a 2006 investigation to determine NASA’s capability to predict airframe 

noise levels for aircraft that are configured for airport approach. During landing operations, the prominent components of airframe 

noise are the landing gear, along with the leading-edge slats and trailing-edge flaps of the aircraft’s high-lift system. The present 

assessment includes far-field predictions for these airframe components and their validation with experimental measurement. The 

test cases are chosen from previously identified experiments involving wind tunnel models and flight testing of operational 

aircraft. In a number of these cases, noise levels are predicted with semi-empirical methods that are based on rudimentary source 

models with considerable reliance upon an experimental database. The remaining predictions are from first principles, in which the 

acoustic source is simulated by computational fluid dynamics. While these latter methods are too computationally intensive to be 

considered practical prediction tools, the wealth of detailed information they yield can provide insight into the further development 

of existing modeling techniques. The present chapter contains a comprehensive overview of several investigations into airframe 

noise measurement and prediction, for both scale models and operational aircraft. Results and findings are discussed, and recommendations for extending the current state of the art for airframe noise prediction are provided.

4.1 Introduction

Airframe noise has been defined by Crighton as “the 

nonpropulsive noise of an aircraft in flight” (Ref. 1). The 

generation of such noise is driven by an aircraft’s geometry, 

resulting in acoustic sources associated with flow features 

such as boundary layer flow past trailing edges, incident 

turbulence, and wakes. Because of significant noise reduction 

in the propulsion systems of commercial aircraft during the 

past five decades, today’s airport noise levels are considerably 

influenced by airframe noise. In addition, it has been determined that compliance with increasingly stringent noise 

regulations cannot be achieved through reductions in the 

propulsion system alone (Ref. 1). As a result, the Federal 

Aviation Administration (FAA) requires planning and testing 

for airframe noise measurements to demonstrate compliance in 

its aircraft noise certification process (Ref. 2).

An aircraft’s radiated noise is most influenced by airframe 

sources during airport approach, when its engines are operating at reduced thrust, and the airframe itself is configured for 

landing. During landing operations, the aircraft’s wings are in 

high-lift configuration, and its landing gear is lowered, as 

illustrated in Figure 4.1. Flyover measurements (e.g., Refs. 3

to 11) and wind tunnel tests (e.g., Refs. 12 to 19) have 

revealed that the prominent sources of airframe noise are 

associated with the leading-edge slats, trailing-edge flaps, and 

landing gear of commercial transports.

4.1.1 Background

By 1970, as a result of research commissioned by the U.S. 

Air Force (Refs. 20 and 21), significant interest had arisen in 

airframe noise radiated by commercial transport aircraft. 

Measured noise levels for gliders and light aircraft, when 

scaled to commercial transports of the day, suggested that 

airframe noise levels during airport approach were of sufficient amplitude that compliance with ongoing FAA regulations would not be possible by engine noise control alone. At 

that same time, substantial reduction in propulsion noise was 

occurring with the introduction of the high-bypass turbofan 

engine, chosen by the U.S. Air Force to power its C–5 Galaxy 

transport. With the expectation of continued reduction in 

engine noise levels, airframe noise was perceived as the 

“ultimate noise barrier” (Ref. 22).

NASA initiated a flight research program in 1972 to investigate the nature and relative importance of airframe noise 

sources. During the following 10 years, NASA was involved 

in a significant effort that included full-scale flight testing, 

wind tunnel experiments, and the development of prediction 

tools. Flight testing involved the measurement of airframe 

noise levels for sailplanes, turboprops, and jet aircraft (Refs. 3

to 9). Wind tunnel research included anechoic testing of 

model-scale aircraft (Refs. 12 and 13), as well as fundamental 

studies to characterize acoustic source mechanisms (Refs. 23

to 26). This considerable body of experimental research 

spurred improved testing techniques (e.g., Refs. 27 to 29) and 

established an airframe noise database that was coordinated 

with the development of prediction methods (Refs. 30 to 32). 

Airframe noise research subsided during the 1980s, along with 

cutbacks in funding for aircraft noise research in general. 

Aircraft noise research at NASA was refocused in 1993, with 

the initiation of the Advanced Subsonic Transport (AST) 

Program, and continued through the Quiet Aircraft Technology (QAT) Program until 2005. Today, airframe noise research 

is conducted under the auspices of the Subsonic Fixed Wing
NASA/TP—2012-215653 64

Figure 4.1.—Boeing 747 aircraft in landing configuration. 

Four main landing gear, nose landing gear, leadingedge slats and triple-slotted, trailing-edge flaps are deployed during airport approach.

(SFW) project within NASA’s Fundamental Aeronautics 

Program (FAP). Efforts within the past decade have included 

important tests for aircraft configurations and component-level 

studies, throughout a considerable range of scale, to identify 

acoustic sources and implement noise reduction technology 

(Refs. 10, 11, 14 to 19, and 33 to 41).

4.1.2 Assessment Overview

The present chapter contains the findings of a 2006 study to 

assess NASA’s current capabilities in airframe noise prediction. 

This assessment includes calculations of acoustic radiation for 

airframe component models and an operational aircraft as well 

as comparison of the predictions with measurements obtained 

during various test programs. Also included are descriptions of 

the prediction methodologies, test facilities, and relevant 

experimental techniques and procedures.

The presentation of this chapter is organized as follows. In 

Section 4.2, airframe noise prediction methodology is discussed, 

including an introduction to the predictive and experimental 

tools that are relevant to the present study. Section 4.3 contains 

a description of a recent flight test (Ref. 11) involving a 

Gulfstream G550 aircraft, with associated airframe noise 

predictions. Test descriptions for various model-scale airframe 

components, and corresponding computational results, are 

presented in Sections 4.4 through 4.8. Two of the models are 

airfoil sections: a NACA 632-215 section with a part-span flap

(Ref. 34), and a 30P/30N section with a leading-edge slat 

(Ref. 35). The remaining models include two small-scale 

landing gears (Refs. 36 and 37) and a pair of tandem cylinders 

(Refs. 38 and 39). In Section 4.9, findings are summarized, and 

recommendations are made for improving current prediction 

methods and for future research. Lastly, Appendix A lists 

acronyms and symbols used in this chapter, and Appendix B to 

Appendix D contain pertinent details for the analytical and 

experimental tools that were employed to produce the results 

herein.

4.2 Prediction Methodology

Two significantly different approaches to problem modeling are represented by the acoustic predictions within this

chapter. These approaches are discussed below, including their 

relative strengths and weaknesses. The corresponding 

prediction methods for each of these modeling approaches are 

briefly described, with details contained in Appendix B and 

Appendix C. In each of the case studies (Secs. 4.3 to 4.8), a 

corresponding experiment is conducted to produce validation 

data for predictive comparison. The facilities employed to 

obtain these test results are identified, while more thorough 

descriptions can be found in Appendix D and associated 

references. Scaling issues and metrics (e.g., data variability, 

uncertainty) are also addressed.

4.2.1 Modeling Approaches

The first approach to airframe noise prediction involves the 

use of lower-order, semi-empirical source models. The term 

“lower order” here is used in the informal sense, to imply that 

the basis for the model’s formulation does not account for 

every important aspect of the problem. Therefore, these 

models typically rely upon experimental measurement for 

such critical characteristics as amplitude scaling or spectral 

shape. Computational efficiency is the primary advantage in 

the application of prediction methods based on lower-order 

models. However, an empirically based prediction method 

cannot be reliably applied to aircraft configurations that differ 

significantly from those contained within the method’s 

derivative database.

A second, and more fundamental, approach to modeling 

airframe noise relies on first principles. Specifically, an 

acoustic source is determined by solution of mathematical 

equations that accurately describe all significant aspects of the 

physical problem. In the present work, this “physics-based” 

approach requires that the source be simulated with a computational fluid dynamics (CFD) calculation. Such fundamental 

modeling avoids the constraints imposed by a preexisting 

database, but does not presently yield a practical approach on 

a routine basis, because of the computational effort involved. 

Typically, unsteady CFD calculations for noise prediction 

require the attention of expert users, tedious and timeconsuming grid generation, and access to supercomputers for 

weeks, if not months, depending upon the problem of interest. 

However, results obtained within this fundamental approach 

contain considerably more information than predictions based 

on lower-order models, and thereby lend support to further 

research in noise reduction techniques and tool development.

Today, lower-order, semi-empirical models continue to 

provide the prediction methods of choice with respect to 

design and technology development, because of their rapid 

execution and relative ease of application. As such, they are 

representative of the current state of the art, and half of the 

predictions in the present chapter are obtained with methods of 

this type. Also, note that the previously stated weakness in 

semi-empirical modeling has not heretofore been an issue, in 

that the basic configuration for transport aircraft has not been 

significantly altered since the advent of the jet airliner in the 

1950s. However, within NASA, there has been a growing 

interest in unconventional configurations, which are clearly 
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 65 Chapter 4

outside the realm of the current practical prediction methodology. Section 4.10 provides recommendations for the 

improvement of present prediction methods, including the 

extension of their application beyond conventional aircraft.

4.2.2 Prediction Tools

Half of the airframe noise predictions (Secs. 4.3 to 4.5) in the 

present chapter are obtained with the Aircraft Noise Prediction 

Program (ANOPP) (Ref. 42), developed at NASA Langley 

Research Center. An overview of ANOPP is presented in 

Chapter 2, “Aircraft System Noise Prediction.” ANOPP 

contains two airframe noise modules, both of which incorporate 

lower order, semi-empirical models. One module represents a 

prediction scheme developed by Fink (Ref. 32) for the FAA, 

and the other a method developed for NASA at Boeing Aircraft 

Company (Refs. 43 and 44). The specific formulations used to 

conduct the present study are provided in Appendix B. ANOPP 

uses the coordinate system shown in Figure 4.2, where R

represents the propagation distance, and θ and φ are the polar 

and azimuthal directivity angles, respectively. An additional 

convention used throughout the present work is the Strouhal 

number, which has the general form St = f L/V∞, where f is 

frequency, L is a characteristic length, and V∞ is the aircraft 

speed. Moreover, to be consistent with ANOPP’s documentation, airspeed is represented in Appendix B by the product 

M∞a∞, where the factors respectively denote the aircraft Mach 

number and the ambient sound speed.

In Sections 4.6 to 4.8, the physics-based approach is taken 

to predict aerodynamic noise to the far field. Conceptually, a 

CFD code that solves the Navier-Stokes equations can be used 

to model an aerodynamic source that produces sound as well 

as its propagation to any required point in the far field. 

However, such a straight-forward CFD approach to airframe 

noise prediction is, at present, computationally prohibitive. As 

such, the physics-based approach to airframe noise prediction 

currently results in a hybrid, two-step process: The acoustic 

source is simulated with a near-field CFD calculation, which 

is then used as input to an acoustic analogy to propagate the 

noise to the far field. In the present chapter, the near-field 

flow is computed with CFL3D (Refs. 45 and 46), and the 

propagated noise is obtained by integrating the Ffowcs 

Williams- Hawkings (FW–H) equation (Ref. 47). More 

information on these prediction tools can be found in Appendix C and the references therein.

4.2.3 Test Facilities

The testing and noise analysis associated with a full-scale, 

operational aircraft are discussed in Section 4.3. Airframe 

noise data were obtained during a flight test conducted at 

NASA’s Wallops Flight Facility at Wallops Island, Virginia. 

A brief description of this facility and the pertinent measurements are contained in Section 4.3, while further details can be 

found in Reference 11.

Figure 4.2.—ANOPP source-observer geometry. R, θ, 

and φ are measured with respect to source emission 

time. V∞ is aircraft speed.

All of the scaled model testing reported herein was conducted in two wind tunnel laboratories at NASA Langley 

Research Center: the Basic Aerodynamic Research Tunnel 

(BART) and the Quiet Flow Facility (QFF). The BART is a 

flow diagnostic facility that specializes in the acquisition of 

fundamental flow-field data (Ref. 48), and the QFF has an 

anechoic test section that is designed to obtain aerodynamic 

noise measurements (Ref. 49). These two experimental 

facilities are more fully described in Appendix D.

4.2.4 Scaling Issues

The ANOPP predictions are compared with measurements 

from both wind tunnel and flight tests in the present chapter. 

Although ANOPP was developed to compute noise (of all 

types) associated with full-scale aircraft in flight, predictions 

obtained with ANOPP’s airframe noise modules should scale 

with geometric dimension and flow speed (see Appendix B). 

Therefore, in concept ANOPP can be used to compute 

aerodynamic noise from aircraft of arbitrary size, including 

small-scale wind tunnel models. However, at least two 

potential issues arise when predicting noise from small-scale 

models with methods that are calibrated with flight test data. 

First, wind tunnel experiments may not include interaction 

effects, which are implicitly included in such semi-empirical 

models. Also, it is not clear how such small-scale predictions 

should be corrected to account for important differences that 

can occur between geometrically similar cases of significantly 

disparate Reynolds number.

Despite the issues involved in the use of wind tunnel experiments to develop aircraft noise prediction tools (as stated 

above), model tests are far less expensive to conduct than tests

with operational aircraft. Therefore, considerably more
NASA/TP—2012-215653 66

airframe noise data is available from model tests than from 

flight tests. Moreover, the bulk of available flight test data was 

obtained during the 1970s, when equipment and procedures 

were much less mature than today. Separation of the individual noise sources from flight tests is difficult, whereas wind 

tunnel tests often focus on individual components. Therefore, 

much of the current development in improved prediction 

methods, as well as the determination of potential noise 

reduction techniques, is based on wind tunnel data. The 

relevance of the small-scale tests is substantiated through 

comparisons with flight test data and measurements in those 

wind tunnels that simulate flight Reynolds numbers. Given the 

importance of both wind tunnel and flight tests, data from 

aircraft flyovers and ground-based testing are compared with 

ANOPP predictions.

4.2.5 Metrics

Unless otherwise noted, all acoustic results herein are 

presented in 1/3-octave sound pressure levels (SPLs), with the 

reference pressure taken as 20 μPa. “Error” is defined as the 

difference between a prediction and its associated experimental value. Only a limited uncertainty analysis has been 

performed: Data variability has been documented for experimental and computational test cases, contingent upon the 

availability of a sufficiently large database; for ANOPP 

predictions only, a limited analysis has been performed 

involving sensitivity to input parameters.

4.3 Airframe Noise Characteristics of a 

Gulfstream G550 Aircraft

An airframe noise flight test program was jointly conducted 

by NASA and Gulfstream Aerospace Corporation at NASA’s 

Wallops Flight Facility (WFF), from October 2 through 

November 1, 2006. The primary objective of this flight test 

was to acquire baseline airframe noise measurements for a 

regional jet class transport, using both a ground-based 

microphone array and individual microphones. The flight tests 

were executed in two phases, with each phase lasting approximately 10 days. Acoustic data for a Gulfstream G550 aircraft, 

on approach to landing, were acquired in Phase I. At least 24 

combinations of aircraft configurations and test conditions 

were flown. The test matrix, ranging from cruise to landing 

configurations, was designed to provide an acoustic characterization of both the full aircraft and individual airframe 

components. Noise sources were isolated by selectively 

deploying components (flaps, main landing gear, nose gear, 

spoilers, etc.) and altering the airspeed, glide path, and engine 

settings. A subset of the Phase I test matrix was repeated 

during Phase II with a smaller Gulfstream G450 aircraft. The 

Phase I and II tests confirmed that the airframe is a major 

contributor to the noise from regional jets during landing 

operations. Full details of the flight test program and post 

processing of the acoustic data have been documented in

Figure 4.3.—Gulfstream G550 aircraft planform.

Reference 11 and will not be repeated here. Only the salient 

features are presented in the present chapter.

4.3.1 Discussion of Experimental Data

For the present study, only the Phase I data acquired with 

the G550 are used to assess current airframe noise prediction 

capabilities. Gulfstream’s G550 is a T-tail, twin-engine jet 

aircraft marketed as a corporate class transport. However, with 

one of the largest wingspans in its class, the scale of the G550 

airframe approaches that of a regional jet, particularly in 

regard to the study of airframe noise. The aircraft’s planform 

is sketched in Figure 4.3, with relevant dimensions given in 

Table 4.1. 

TABLE 4.1.—G550 AIRCRAFT:

CHARACTERISTIC DIMENSIONS

Overall length, m (ft)....................................... 29.39 (96.42)

Height, m (ft)..................................................... 7.87 (25.83) 

Wingspan, m (ft).................................................. 28.5 (93.5)

Gross wing area, m2 (ft2) ................................ 105.63 (1137)

Mean aerodynamic chord, m (ft) ....................... 4.22 (13.86)

Flap span per side, m (ft)..................................... 7.8 (25.58)

Flap area per side, m2 (ft2).....................................8.8 (94.7)

Tail plane span, m (ft) ..................................... 10.72 (35.17)

Tail plane area, m2 (ft2).................................. 22.75 (244.86)

Max. gross takeoff weight, kg (lb)............... 41 300 (91 000)

The test was conducted on WFF’s Runway 4, the longest of 

the facility’s three available runways, with a length of 2667 m 

(8750 ft) and a width of 45.7 m (150 ft). This runway was 

selected to meet several essential criteria for successful test 

completion. The most critical elements under consideration 

were: (a) the availability of a large flat overrun section, where 

the NASA microphone array and Gulfstream free-field
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 67 Chapter 4

microphones could be placed adjacent to each other, along the 

aircraft approach direction, (b) the length of the runway to 

minimize potential risks during low-altitude, low-speed flyover at low engine power settings, and (c) the enforcement of 

a minimum distance between the installed microphones and 

any nearby roads, to reduce the impact on background noise 

levels from local traffic. 

The airframe noise test involved extensive noise measurements using NASA’s 167-microphone array system, as well as 

Gulfstream’s isolated, pole-mounted (certification) microphones. The layout of the microphone array and the individual 

microphones are shown in Figure 4.4, as installed on the 

overrun segment near the approach of Runway 4. The 

microphone array measurements are useful for noise source 

localization studies; noise source maps for the G550 from the 

Phase I flight test are presented in Reference 11. For the 

present discussion, the pole-mounted microphone data are 

more appropriate because the absolute noise levels for the 

various test configurations can be directly compared with the 

predictions. The mounting, operation, and processing of the 

data collected from the pole-mounted microphones were 

accomplished by Gulfstream engineers. Analysis of the 

individual microphone data followed the standard procedure 

typical of the aircraft certification process within the industry. 

Measured acoustical data (raw data) were adjusted for the 

effects of amplitude stability (calibration drift), microphone 

pressure response, microphone free-field-to-incidence 

correction, wind screen insertion loss, ambient barometric 

pressure correction, and system noise response. These 

computations were accomplished using a special version of 

Gulfstream’s noise certification analysis software.

Identification and determination of data errors and uncertainties for full-scale acoustic measurements is a challenging 

task. Unlike a highly controlled wind tunnel environment, 

flight tests occur in uncontrolled surroundings wherein the 

local atmospheric conditions do not remain constant. Although 

local conditions, up to an altitude of 152.5 m (500 ft), were 

recorded every hour using a combination of a weather balloon 

and a ground station, significant local atmospheric variations 

could occur within a short time period. The dominance of the 

errors introduced by the atmospheric effects (sound propagation, absorption, etc.) may mask other typical sources of error 

(e.g., instrumentation errors). To partially bracket the uncertainties introduced in the measured noise levels, repeat flights 

for each test condition were executed. For very few select 

configurations, repeat runs on a different day were performed 

to document day to day variability in the recorded noise levels.

Figure 4.4.—NASA microphone array and Gulfstream free-field (certification) microphone layout.
NASA/TP—2012-215653 68

In addition to the fully deployed (landing) and clean 

(cruise) configurations, Phase I covered numerous other 

configurations that were designed to isolate the noise sources 

associated with individual components (flap, nose gear, main 

gear, etc.). For each configuration, noise measurements were 

obtained at three distinct speeds with multiple runs at each 

speed in order to ensure that statistically meaningful data were 

obtained. Only a few select configurations at the nominal 

speed of 147 kn, for the time duration corresponding to an 

averaged emission (or polar overhead) angle θ = 86°, are used 

for the purposes of the present assessment. The selection of 

the candidate configurations was based on the desire to 

consider the more prominent airframe noise sources. The four 

selected configurations are (1) flaps deflected at 39° and gear 

down (landing configuration), (2) flaps deflected at 39° and 

gear up, (3) flaps retracted and only main gear down, and 

(4) flaps retracted and gear up (clean configuration). Note that 

the G550 wing has no leading-edge slat; therefore, slat noise is 

irrelevant to the current study.

4.3.2 Metrics and Assessment

As the primary NASA tool available for full-scale airframe 

noise prediction, ANOPP was utilized to perform the study. 

For the present full-scale noise assessment of regional jets, 

two distinct metrics are employed. The first metric involves 

comparison of the predicted absolute noise levels for the 

selected configurations and the levels obtained from the polemounted microphones. As an alternative criterion, the second 

assessment metric is based on comparison of relative noise 

levels, which are obtained as follows: The mean-square 

acoustic pressure for the clean (cruise) and each “dirty” 

(deflected surfaces) configuration under consideration are 

subtracted (dirty minus clean); the SPLs associated with these 

relative pressures are then calculated. This relative noise 

metric also partially eliminates any ambiguity attributed to the 

presence of residual engine noise or the background environmental noise within the measured signal.

Processing of the pole-mounted microphone data to extract 

the noise levels was accomplished by Gulfstream engineers. 

The processed data contain the appropriate corrections to 

account for absorption and propagation effects due to the 

variation in the local atmospheric conditions as well as 

variations in aircraft speed and altitude from the nominal 

values. Assuming a spherical spreading of the radiated noise 

and a 6 V∞ velocity dependence for the noise levels, the postprocessed 1/3-octave band spectra have been normalized to a 

common altitude of 120 m (394 ft) and aircraft speed of 

147 kn. However, the corresponding minor shift in the 

frequencies (less than 2 percent in most instances) was omitted 

during the normalization step.

Good data repeatability was demonstrated in Reference 11

where the variability in the measured SPLs was highlighted. 

The highest levels of variation in the measured SPL mostly 

shows up in the higher frequencies (above 3 to 4 kHz) where

Figure 4.5.—Representative measured sound pressure level (SPL) spectra for two configurations of 

Gulfstream G550 aircraft.

the levels are typically 10 to 15 dB below the peak and 

variation of the atmospheric conditions is the dominant factor. 

Thus, presentation of the results and comparison with the 

predicted sound levels are attempted for frequencies up to the 

1/3-octave band level 35 (3150 Hz center-frequency). 

Figure 4.5 compares the measured spectra for the full-dirty 

configuration (flaps-39 with landing-gear-down) with the 

spectra with only the main gear deployed. The primary 

(80 Hz) and secondary (250 Hz) dips as well as the lowfrequency peak (160 to 200 Hz) in the spectra are caused by 

the destructive or constructive superposition of groundreflected waves on the sound levels measured by the polemounted microphones. The prominent peak at 800 Hz is 

associated with a tone emanating from the main landing gear. 

At the time of this writing, its source has been identified, and a 

remedy for its elimination has been found. Therefore, for the 

purpose of comparison with predicted SPLs, the main gear 

tone has been removed from the spectra, and the corresponding frequency band is assigned a level that is linearly interpolated using the levels from the adjacent bands.

The SPLs for the four selected conditions are plotted in

Figure 4.6. Each curve represents the averaged value of all the 

accepted runs conducted for that particular configuration. 

Notice the absence of the main gear tone. Comparison of the 

levels for the landing (square symbols) and clean (circular 

symbols) configurations indicates that deploying the flaps and 

undercarriage results in an increase of 6 to 10 dB in the lowto mid-frequency range. Given that all the flights were 

executed with an approach-idle engine setting, Figure 4.6

shows residual engine noise not to be a factor within the 

frequency range displayed. Moreover, the main landing gear 

contributes less to the total noise than the flaps.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 69 Chapter 4

Figure 4.6.—Averaged measured sound pressure 

level (SPL) spectra for three selected airframe 

noise and clean configurations of Gulfstream 

G550 aircraft.

4.3.3 Results and Findings

ANOPP (Ref. 42), NASA’s foremost aircraft noise prediction 

tool, was used for predicting the full-scale airframe noise levels 

for the G550 aircraft. Some of the aerodynamic parameters 

required as input to the Boeing model (Refs. 43 and 44) could 

not be obtained for this study. Thus, only the airframe noise 

module based on Fink’s model (Refs. 32 and 42) was employed 

to compute the noise levels. In contrast to acoustic measurements in ground-based facilities, in flight the aircraft represents 

a moving noise source. To partially simulate the moving source 

behavior, several other ANOPP modules were utilized in 

addition to the airframe noise module. Listed in the sequence 

used in the prediction process, these modules were Atmospheric, Atmospheric Absorption, Steady Flyover, Geometry, 

Airframe Noise, and Propagation. Noise levels were predicted 

for a reference altitude of 120 m (394 ft), an aircraft speed of 

147 kn, an azimuthal (sideline) angle of 0°, a polar (overhead) 

angle of 86°, and acoustic standard day conditions (21 °C 

(70 °F) and 70 percent relative humidity).

The predicted SPLs for the four selected configurations are 

shown in Figure 4.7. In the low- to mid-frequency range, the 

spectra are similar in shape to the measured values. In 

particular, the frequencies corresponding to the peak SPL are 

well predicted. Note that by choosing a receiver located at the 

same height as the pole microphone, the low-frequency peaks 

and valleys caused by ground reflection are also captured. For 

frequencies above 800 Hz, however, the predicted spectra 

show a much steeper drop in SPL, with the decay becoming 

most rapid above 2 kHz. The effects of variations in aircraft 

speed and azimuthal angle (φ) on the predicted noise were also 

determined. The azimuthal variation was chosen as it directly 

corresponds to the aircraft’s roll angle as it passes over the 

measurement location. Figure 4.8 displays the effects of 

±5 percent variation in the nominal speed (147 kn) on the SPL

Figure 4.7.—Predicted sound pressure level (SPL) 

spectra for three selected airframe noise and clean 

configurations of Gulfstream G550 aircraft.

Figure 4.8.—Uncertainties in predicted sound 

pressure level (SPL) spectra due to variations 

in speed and azimuthal angle, φ, for Gulfstream 

G550 aircraft. Configuration is flaps at 39° with 

landing gear down.

for the landing configuration. The curves with square (red) 

and delta (blue) symbols bracket the extent of the variation in 

the SPL relative to the baseline (circular symbols) values. 

Also plotted in Figure 4.8 is the change in sound pressure 

levels predicted for the sideline angle of φ = 18°. From a 

geometrical point of view, this situation would be equivalent 

to the φ = 0 case while the aircraft moving over the microphones undergoes a roll (banked) angle of 18°. Selecting such

a large azimuth angle is a consequence of the insensitivity of 

the Fink model to small changes in φ. Moreover, the 

φ-dependency of the Fink model is symmetric and, therefore, 

the result is the same for φ = 342°.
NASA/TP—2012-215653 70

Figure 4.9.—Difference between measured and 

predicted absolute sound pressure level (SPL) 

spectra.

To assess the predicted absolute SPLs, a direct comparison 

between the measured (Figure 4.6) and computed values 

(Figure 4.7) is attempted. Subtracting the computed levels from 

the measured data, the differences in SPL are plotted in 

Figure 4.9 for the three airframe noise configurations. Positive 

values indicate that the simulated pressures underpredict the 

measurements, and negative values indicate overprediction. The 

underprediction and overprediction of the noise is on the order 

of 10 dB for frequencies below 300 Hz, but the variations 

become significantly smaller for higher frequencies up to 3 kHz. 

The trend towards larger errors for frequencies above 3 kHz 

must be viewed with suspicion due to engine noise and other 

forms of background noise inherent in the measured data. 

Nevertheless, the large errors at low to moderate frequencies 

clearly demonstrate the inadequacies of the present ANOPP 

airframe noise module to predict the full-scale absolute noise 

levels. Given the 1- to 2-dB uncertainties in most pole-mounted 

microphone measurements, predicted pressure levels that are 

within plus or minus 1 to 2 dB of the measured results would be 

considered ideal. Certainly, the observed 5- to 10-dB errors of 

the present assessment are considerably larger and point to the

need for improved prediction methods.

Results from the second assessment metric (based on 

changes relative to the clean configuration) are displayed in 

Figure 4.10. As before, positive values indicate underprediction and negative values, overprediction of the measured 

SPLs. Note that the trends are similar to those observed for the 

absolute level errors (Figure 4.9). The error for the flap at 0°, 

main gear down configuration shows very large oscillations at 

80 and 250 Hz. These extreme levels are caused by subtraction 

of pressures with very similar magnitudes (see data represented by circles and triangles in Figure 4.6) and have no physical 

meaning. The curve for the flaps at 39° and gear down 

configuration (square symbols) shows the least

Figure 4.10.—Difference between measured and 

predicted relative sound pressure level (SPL) 

spectra.

deviation from the 0-SPL line, indicating better agreement 

between the computed and measured SPL when all airframe 

noise sources are included. Once more, the errors in the 

relative noise levels at high frequencies (above 3 kHz) must be 

viewed with caution because of the presence of residual 

engine and high background noise levels. Comparing the 

results presented in Figure 4.9 and Figure 4.10, it is clear that 

ANOPP does a good job of predicting the relative SPL or the 

absolute levels in the mid-frequency range (500 to 2500 Hz). 

Nevertheless, the ultimate goal of having the capability to 

predict the SPL within 1 to 2 dB over the entire frequency 

range of interest eludes us. In this regard, the errors in the 

relative SPL (Figure 4.10) are still too high. 

4.3.4 Recommendations

The large errors in the predicted absolute and relative noise 

levels observed here are disappointing and point out the 

inherent risk of using empirically based predictive methods 

outside the range of the database from which they were 

originally derived. Fortunately, the overall magnitudes of the 

predicted changes in noise spectra are, for the most part, of the 

right order, and differ from the measured changes mostly by 

±8 dB. As indicated repeatedly in this chapter, for improvements in airframe noise prediction to occur, more details 

regarding the physical processes of noise generation in these 

complex, highly nonlinear flow fields must be elucidated, 

using coordinated experimental and computational studies. 

Empiricism in the predictive tools should be limited to more 

fundamental levels with the incorporation of configurationsensitive, local flow-field analyses. The ability to analyze 

airframe-noise-related flows at such intricate levels will 

require further investment in the development of advanced 

experimental and computational methods.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 71 Chapter 4

4.4 Flap-Edge Noise Measurement and 

Prediction

The component-based approach employed by Fink to predict 

total aircraft noise is now commonly used (Refs. 43, 44, and 50

to 52). Because individual components cannot be flight tested in 

isolation, difficulties in separating the contributions of all the 

sources leave some ambiguity when attempting to calibrate 

models for individual components. Ground-based testing allows 

components to be tested in isolation under controlled circumstances providing unambiguous data for calibration and model 

development. However, interactions effects, which are 

implicitly included in data from flight tests, must be explicitly 

accounted for if wind tunnel data are used for calibration. 

Furthermore, the physics in wind tunnels is not always representative of flight. Small-scale models typically result in much 

lower Reynolds numbers unless pressurized tunnels (Ref. 53) 

are employed. Very low Reynolds numbers can result in 

anomalous transition characteristics and thereby affect the flow

and radiated noise. Transition strips and grit-covered models are 

often used to simulate the effects of high-Reynolds-number 

flow. Although these techniques can be effective, the eventual 

connection back to flight is important (Ref. 54).

Because wind tunnel testing is being used as a source of data 

for the development of aircraft noise prediction methods, it is 

important to include comparisons between ANOPP predictions 

and acoustic measurements at model scale. Flap-edge noise 

spectra obtained from a QFF experiment are compared with 

predicted spectra, using ANOPP’s airframe noise modules. The 

acquisition and processing of the experimental data is described 

below, followed by predictions and comparisons. Additional 

information about the QFF can be found in Appendix D.

4.4.1 Test Description

The test model used in the QFF experiment (Ref. 34) was a 

NACA 632-215 main-element airfoil with an attached half-span 

Fowler flap of 12.2-cm (4.8-in.) chord. The chord and span of 

the main-element airfoil were 40.6 cm (16 in.) and 91.4 cm 

(36 in.), respectively. The flap was attached by an adjustable set 

of “U” brackets to minimize bracket interference with the ideal 

flap flow field. The model was held in place by vertical plates, 

which were rigidly mounted to the side-plate supports of the 

nozzle. The main element angle was set at 16°, which corresponds to a free-field angle of attack of 8.53°. Two flap angles, 

29° and 39°, were tested. The relative positions of the mainelement trailing edge and the leading edge of the flap are 

determined by measures of “gap” and “overlap,” as defined in 

Figure 4.11. Normalized with respect to the main-element chord 

length, the gap and overlap for the 29° flap angle were 0.0227 

and 0.0242, respectively. For the 39° flap angle, these parameters were, respectively, 0.0231 and 0.0132.

The far-field acoustics of the model were measured in the 

QFF using the Small Aperture Directional Array (SADA), 

which is discussed in Appendix D. The SADA was located 5 ft 

(1.5 m) from the center of the main element trailing edge, and in 

a plane perpendicular to, and centered on, the span of the model. 

This SADA position corresponds to zero azimuthal angle 

(φ = 0). The noise measurements were obtained for mean-flow 

Mach numbers of 0.07, 0.11, and 0.17 and for different flap side 

edge configurations, with the SADA positioned at 12 azimuthal 

positions, as shown in Figure 4.12. Note that, given the small 

QFF phased-array aperture, and thus limited solid collecting 

angle, “de-correlation” effects in the phased array data at high 

frequencies are expected to be very limited. The data chosen for 

comparison to prediction are SADA measurements from 

Reference 34, obtained for the baseline flap-edge configuration, 

on the pressure side of the model, at φ = 107° (Figure 4.12). 

Figure 4.11.—Flap overlap and gap definitions for 

flap-edge noise test with model airfoil in Quiet

Flow Facility (QFF).

Figure 4.12.—Azimuthal (φ) locations of Small Aperture 

Directional Array (SADA) microphones for far-field 

tests with model airfoil in Quiet Flow Facility (QFF).
NASA/TP—2012-215653 72

Signals from the array microphones were band-pass filtered 

over a pass band of 300 to 50 kHz and digitized using a 14-bit 

transient data recorder. A conventional beamforming approach 

(Refs. 55 and 56), employing matrices of cross-spectra 

between the array microphones, was used to electronically 

“steer” the array to chosen noise source locations. The spatial 

resolution (or sensing area over noise source regions) was 

controlled independently of frequency and steering-direction 

over broad frequency ranges. The array processing accounted 

for mean amplitude and phase changes due to refracted sound 

transmission through the shear layer to the individual microphones of the array. For each test case, the cross-spectral 

matrix had a corresponding background matrix subtracted 

from it to remove extraneous system noise (measured 

microphone and sensor noise for zero tunnel flow speed). 

Spectral data were determined for each narrowband frequency 

(34.88 Hz resolution bandwidth) of interest. The 1/3-octave 

band spectra were formed from the narrow-band spectra.

4.4.2 Results and Findings

The 1/3-octave band flap-edge noise spectra obtained for 

the test conditions listed in Table 4.2 were used for comparison to ANOPP predictions. Predicted spectra were obtained 

with the airframe noise module in ANOPP that implements 

Fink’s flap-noise model (Refs. 32 and 42). As ANOPP was 

initially developed to calculate noise levels for an aircraft in 

flight, relative to a stationary observer on the ground, Doppler 

frequency shifting is included as a default program condition. 

However, such phenomena do not occur during a typical wind 

tunnel measurement, where the model and microphone 

positions are in the same reference frame. Therefore, in order 

to appropriately compare ANOPP results with test measurements, the effects of Doppler shifting are excluded from the 

prediction methodology. For instance, the Strouhal number for 

the present test case is St = fAf /M∞a∞bf (subscript f denotes 

flap), which does not include the Doppler factor, 1–M∞cos θ 

(Eq. (4.17) in Appendix B). Note that the flap chord is the 

characteristic length in this case, and is determined by the 

ratio, Af /bf, of the surface area to the span. 

TABLE 4.2.—TRAILING-EDGE FLAP NOISE TEST:

TEST CONDITIONS

[See Figure 4.11 and Figure 4.12.]

Flap model configuration tested................Flat edge flap (baseline)

Flap chord, cm (ft) ...........................................................12.2 (0.4)

Flap span, cm (ft) .............................................................45.7 (1.5)

Flap deflection angles, deg.................................................... 29, 39

Main element angle of attack, dega .......................................... 8.53 

Mach numbers.........................................................0.07, 0.11, 0.17

Distance from flap side edge to SADA, m (ft)b...................1.52 (5)

SADA elevation angle (emission angle), degb .......................... 107

SADA Azimuthal angle (emission angle), degb ............................ 0

a

After wind tunnel correction.

b

SADA: Small Aperture Directional Array in Quiet Flow Facility (QFF).

The trailing-edge flap noise test characteristic dimensions 

listed in Table 4.3 were used as input to Fink’s trailing-edge 

flap model. Note that the observer polar directivity angle (θ) 

that is required as input to this module, is defined with respect 

to the wing axis and measured from the wing leading edge. 

Hence, the SADA elevation angle (φ = 107°) in the QFF 

experiment corresponds to a polar directivity angle of 81.53° 

in the ANOPP module.

TABLE 4.3.—TRAILING-EDGE FLAP NOISE TEST:

CHARACTERISTIC DIMENSIONS

Flap area, cm2 (ft2) ....................................... 557.4 (0.6)

Flap span, cm (ft) ........................................... 45.7 (1.5)

Flap deflection angles, deg...................................29, 39

Mach numbers....................................... 0.07, 0.11, 0.17

Distance from source to observer, m (ft)........... 1.52 (5)

Polar directivity angle, θ, deg................................81.53

Azimuthal directivity angle, φ, deg ..............................0

Number of slots for trailing-edge flap ..........................1

In Figure 4.13 the predicted spectra are compared with the 

QFF data. It is seen that the SPLs are very well predicted over 

a broad frequency range for the 39° flap, while the levels are 

overpredicted for most of the frequency range for the 29° flap 

case. It is also observed that agreement between the predictions and experimental data improves with decreasing Mach 

number. The discrepancy (∆dB) between the experimental and 

predicted spectra is plotted in Figure 4.14, for the 39° flap and 

a Mach number of 0.17. For this case, which is most representative of an aircraft flap during approach conditions, the 

∆dB is less than 4 dB from 1.5 to 25 kHz. Below 1.5 kHz, the 

discrepancy rises to a maximum of 6.3 dB. 

A sensitivity study was performed over a limited set of 

parameters for the 39° flap, at a Mach number of 0.17. The 

Mach number was varied ±1 percent (maximum error in the 

Mach number setting that could have occurred in the QFF 

experiment) and the wing angle of attack was varied by 

±5 percent (after wind tunnel correction was applied). 

Variations in the wing angle of attack only meant a change of 

±0.42° of the polar directivity angle θ, because the wing angle 

of attack is not a parameter used in the Fink method to define 

the acoustic amplitude and spectral shape. The effect from 

these parameter variations on the SPLs is shown as error bars 

in Figure 4.13.

The effect of flap deflection angle on the predicted spectral 

level was also examined. It was found that the Fink method is 

relatively insensitive to changes in flap deflection angle. As 

shown in Figure 4.13, the experimental data indicate a difference in noise level, between the 29° and 39° flap of less than 

4 dB below 1.5 kHz (for the three speeds tested). Above 2 kHz, 

the difference in noise level rises up to 8 dB. Additional 

predictions were performed for a 19° and a 49° flap deflection 

angle. The results indicated that increasing the flap deflection 

angle leads to a small increase in noise level that is uniform 

across the frequency range of interest (0.05 to 40 kHz). Thus, 
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 73 Chapter 4

Figure 4.13.—Flap-edge noise sound pressure level 

(SPL) spectra at different Mach numbers M and

deflection angles. Comparison of ANOPP predictions 

using Fink’s method and measurements from Quiet 

Flow Facility (QFF) experiments.

Figure 4.14.—Discrepancy in airframe flap-edge noise 

sound pressure level (SPL) spectrum at Mach number 

M = 0.17 and 39° flap between ANOPP predictions

using Fink’s method and measurements from Quiet 

Flow Facility (QFF) experiments.

increasing the flap deflection angle from 19° to 49°, in 10° 

increments, results in successive increases in noise level of 3 dB 

(19° to 29°), 1.5 dB (29° to 39°), and 0.5 dB (39° to 49°).

4.4.3 Metrics and Assessment

A limited study was conducted to determine the repeatability of SPLs derived from beamform analyses of phasedarray data acquired in 1997 for a flap noise model in the QFF 

(the last time such repeat data were available in the facility). A 

series of 16 repeat sets of phased-array data acquired for a 

baseline flat side-edge flap were processed using standard 

frequency-domain, delay-and-sum beamforming across a 

range of 1/3-octave center frequencies spanning 315 to 

40 000 Hz. These data sets represent repeat testing for a flap 

deflection of 39° and a wind tunnel Mach number of 0.17. 

Otherwise, relevant test conditions and array orientations for 

this repeatability study are identical to those in Table 4.2.

The results of the analysis are displayed in Table 4.4 where 

the peak SPL value observed in the beamforming presentation 

(centered on the flap side edge) for each frequency trial is 

tabulated. Also shown is the percent error in the peak of the 

pressure squared for each frequency. This error was derived 

from the standard deviation of the squared pressures obtained 

from measurements for each trial. The maximum observed 

repeatability error was 4.36 percent for the 25 kHz 1/3-octave 

frequency band with a typical error of approximately 2 to 

3 percent for the majority of the frequency bands. Therefore, a 

visual representation of the variation in the experimental 

spectra shown in Figure 4.13 would be within the displayed 

symbol sizes. 

Note that while the repeatability analysis was conducted 

using standard beamforming, it is reasonable to assume that an 

analysis using DAMAS deconvolution (Ref. 57) would yield 

similar results. When applied to leading- and trailing-edge 

noise sources, DAMAS was shown to give almost identical 

integrated SPLs across a wide frequency range when compared with results from beamform analyses. Given the duality 

between the two processing methods, it is expected that the 

repeatability errors would be similar. Finally, the present study 

only addresses simple repeatability of measurements. Topics 

for further research would include the identification of bias 

errors and a theoretical analysis involving a formal propagation of errors.

4.4.4 Recommendations

The Fink method was found to follow Strouhal scaling and, 

hence, allows for noise prediction of model-scale-size flaps. 

The predictions compared well with the experimental modelscale data for the higher flap deflection angle tested. The 

method was found, however, to be relatively insensitive to 

change in flap deflection angle, and thus overpredicted the 

noise level for the lower flap deflection angle tested. It is 

recommended that this ANOPP flap-noise prediction model be 

improved, to the extent possible, using the available database 

of model-scale measurements. One must keep in mind, 

however, that this database was generated from experiments at 

a relatively low Reynolds number and on a geometry that may 

be only partially representative of that encountered in 

engineering practice. While there are experimental databases 

that suggest the magnitude of the effects of these issues, they 

are judged inadequate in terms of absolute noise level 

measurements to be useful in this initial assessment.
NASA/TP—2012-215653 74

TABLE 4.4.—EXPERIMENTAL REPEATABILITY ANALYSIS OF SOUND PRESSURE

LEVELS (IN DECIBELS) OBSERVED IN FLAP-EDGE BEAMFORMING

Trial 1/3-Octave Frequency Band, Hz

315 400 500 630 800 1000 1250 1600 2000 2500 3150

1 74.53 73.79 72.64 73.63 74.08 71.69 72.25 74.39 73.26 74.70 74.17

2 74.27 73.79 72.63 73.43 73.79 71.60 72.10 74.39 73.36 74.67 74.06

3 74.70 73.99 72.99 73.28 73.91 71.40 72.21 74.22 73.18 74.59 74.12

4 74.25 73.69 72.79 73.32 73.86 71.42 72.09 74.27 73.16 74.60 74.05

5 74.28 73.62 72.50 73.36 73.72 71.69 72.03 74.02 73.38 74.59 74.10

6 74.08 73.63 72.57 73.37 73.76 71.36 71.86 74.15 73.16 74.40 73.98

7 74.46 73.79 72.42 73.09 73.91 71.65 71.87 74.26 73.20 74.63 74.16

8 74.03 73.30 72.41 73.30 73.90 71.45 72.12 74.17 73.00 74.57 73.98

9 74.18 73.72 72.31 73.20 73.84 71.52 72.24 74.13 73.20 74.72 74.05

10 74.23 73.63 72.69 73.28 73.84 71.56 72.08 74.16 73.29 74.56 74.19

11 74.19 73.68 72.60 73.28 73.82 71.47 72.06 73.94 73.19 74.55 74.15

12 74.21 73.62 72.55 73.37 73.95 71.54 72.08 74.27 73.37 74.48 74.16

13 74.11 73.44 72.27 73.34 73.78 71.46 72.02 74.31 73.20 74.51 74.16

14 74.26 73.65 72.66 73.14 73.62 71.40 71.99 74.12 73.17 74.45 73.98

15 73.99 73.48 72.40 73.11 73.64 71.35 71.99 74.08 73.16 74.59 74.09

16 74.16 73.67 72.66 73.21 73.93 71.45 71.83 74.18 73.13 74.51 73.89

Mean 74.24 73.66 72.57 73.29 73.83 71.50 72.05 74.19 73.21 74.57 74.08

STDVa 0.18 0.16 0.18 0.13 0.12 0.11 0.13 0.12 0.10 0.09 0.09

% Errorb 4.32 3.63 4.29 3.09 2.72 2.59 2.88 2.82 2.28 1.99 2.01

Trial 1/3-Octave Frequency Band, Hz

4000 5000 6300 8000 10 000 12 500 16 000 20 000 25 000 31 500 40 000

1 73.21 73.91 73.72 70.18 68.68 67.50 65.57 65.17 64.37 63.87 65.78

2 73.13 73.81 73.64 70.19 68.60 67.34 65.41 64.97 64.08 63.63 65.50

3 73.21 73.92 73.71 70.21 68.63 67.34 65.48 65.09 64.22 63.74 65.60

4 73.12 73.79 73.64 70.01 68.42 67.25 65.31 64.92 64.00 63.55 65.42

5 73.04 73.73 73.54 70.04 68.43 67.17 65.31 64.89 64.03 63.58 65.49

6 73.06 73.79 73.53 69.97 68.47 67.21 65.29 64.87 63.99 63.53 65.40

7 73.09 73.81 73.58 70.04 68.46 67.20 65.33 64.88 63.95 63.55 65.40

8 73.09 73.77 73.55 70.04 68.42 67.27 65.36 64.97 64.03 63.57 65.38

9 73.22 73.81 73.76 70.24 68.61 67.37 65.50 65.11 64.21 63.79 65.57

10 73.12 73.90 73.76 70.13 68.52 67.29 65.36 64.97 64.09 63.60 65.39

11 73.11 73.64 73.58 70.09 68.43 67.20 65.32 64.85 64.00 63.47 65.34

12 73.15 73.66 73.55 70.03 68.49 67.20 65.27 64.86 63.92 63.47 65.35

13 73.07 73.69 73.51 69.93 68.35 67.12 65.20 64.74 63.85 63.36 65.28

14 72.94 73.65 73.48 69.85 68.33 66.99 64.99 64.48 63.59 63.18 65.07

15 73.00 73.72 73.47 69.92 68.32 67.01 65.21 64.70 63.80 63.35 65.24

16 73.09 73.66 73.49 69.81 68.38 67.08 65.02 64.61 63.76 63.34 65.18

Mean 73.10 73.77 73.59 70.04 68.47 67.22 65.31 64.88 63.99 63.54 65.40

STDVa 0.08 0.09 0.10 0.13 0.11 0.13 0.15 0.18 0.19 0.18 0.17

% Errorb 1.73 2.15 2.30 2.93 2.52 3.08 3.52 4.15 4.36 4.13 3.93 a

STDV is standard deviation of the pressure squared values expressed in decibels.

b

The % Error is 100 times the standard deviation in the pressure squared divided by the mean pressure squared.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 75 Chapter 4

4.5 Aeroacoustic Measurement and 

Prediction for Boeing 777 Landing 

Gear Model

While most often used to predict the noise for a vehicle in 

flight, ANOPP can also be used to study a noise source 

associated with an individual component, such as an aircraft 

landing gear. In this mode, the sound is propagated to 

stationary observers located on a spherical surface that is 

centered at the source. To compare ANOPP predicted noise 

levels with wind tunnel data, when the source and microphone 

locations are fixed relative to each other, the effects of 

Doppler frequency shifting were removed by modifying the 

code. For example, the Strouhal number for the present test 

cases is St = fd/M∞a∞ which excludes the Doppler factor,

1–M∞cosθ (Eq. (4.23), Appendix B). The characteristic length 

d is the wheel diameter.

To facilitate the assessment of ANOPP’s ability to predict 

landing gear noise, an extensive experimental study was 

conducted using the Medium Aperture Directional Array 

(MADA) in the QFF to acquire detailed noise spectra and 

directivity data for a high-fidelity, 6.3-percent-scale Boeing 

777 main landing gear. The MADA and QFF are discussed in 

more detail in Appendix D. Straightforward individual 

microphone processing and DAMAS array processing were 

employed to compile unique flyover and sideline directivity 

databases for a range of free-stream Mach numbers that are 

relevant to airport approach conditions. Comprehensive 

corrections were applied to the test data to account for shear 

layer ray path and amplitude variations. This allowed proper 

beamforming at different measurement orientations, as well as 

directivity presentations in free-field emission coordinates. For 

the purposes of the assessment, the experimental spectral and 

directivity data were compared with predicted noise spectra 

and contours using the two ANOPP airframe noise modules. 

Details of the experimental data acquisition and processing 

and comparison with the ANOPP predicted noise follow.

4.5.1 Discussion of Experimental Data

The test model used for the assessment was a 6.3-percentscale high-fidelity Boeing 777 main gear assembly that was 

previously tested as part of an overall semi-span model 

(Ref. 16). The high-complexity gear was composed of a sixwheel bogie and a generally faithful representation of fullscale strut, oleo, braking, and hydraulic hardware. The exact 

configuration of the model used in the assessment is shown in 

Figure 4.15. The major component sizes for the model are 

listed in Table 4.5. The model was fabricated with loadbearing metal components and detailed stereo lithography 

components. Standard electrical wiring and pressure tubing 

(ranging from 1.2 to 2.0 mm, or 0.05 to 0.08 in.) were used to 

roughly simulate the hydraulic lines and cables. These were 

generally a little larger than scale. This is expected to have 

shifted the high-frequency content of the scale-model 

noise down slightly. The attached door for the baseline

Figure 4.15.—Boeing 777 main landing gear model. 

Baseline configuration, with door.

TABLE 4.5.—MAJOR COMPONENTS OF 6.3-PERCENT-SCALE

BOEING 777 LANDING GEAR

Model height, cm (in.)....................................................30.5 (12)

Side-to-side width, cm (in.)..............................................12.7 (5)

Length of oleo, cm (in.).................................................21.6 (8.5)

Diameter of oleo, cm (in.) ..................................................2.5 (1)

Strut component widths, cm (in.) ....................................1.3 (0.5)

Wheel width, cm (in.)....................................................3.2 (1.25)

Wheel diameter, cm (in.).............................................. 8.3 (3.25)

Truck length, cm (in.).......................................................20.3 (8)

configuration in Figure 4.15 had approximate dimensions of 

10.2 by 12.7 cm (4 by 5 in.) and a thickness of 3 mm (1/8 in.).

Figure 4.16 shows the model mounted to a treated portion of 

one of the QFF side-plates. The intent of the treatment was to 

create an acoustically compliant surface near the model while 

maintaining a flat boundary for the flow. The surface was 

created by stretching a thin Kevlar (DuPont) fabric over an 

open-backed ribbed frame, thus reducing acoustic surface 

reflections. Figure 4.16 represents the set-up for model 

“sideline” measurements with the boom-mounted MADA. For 

model “flyover” measurements, a removable 60-cm- (23.5-in.-) 

wide side-plate was especially constructed and mounted along a 

0.9-m (3-ft) side edge of the nozzle, as illustrated in Figure 4.17. 

This setup (Figure 4.17) enables “flyover” measurements, with 

the array positioned “underneath” the landing gear model. The 

flyover side-plate was correspondingly covered with Kevlar 

fabric over an open-backed ribbed frame.
NASA/TP—2012-215653 76

Figure 4.16.—Boeing 777 main gear model assembly 

mounted in Quiet Flow Facility (QFF) for lateral

“sideline” measurements by Medium Aperture

Directional Array (MADA) microphones.

Figure 4.17.—Boeing 777 main gear model assembly 

mounted in Quiet Flow Facility (QFF) for “flyover” 

measurements by Medium Aperture Directional Array 

(MADA) microphones.

For either orientation of the landing gear model, the coordinate system shown in Figure 4.18 was employed during 

analysis of the directivity data. The reference center of the 

landing gear was defined to be the center of the truck assembly. The coordinate system, defining the x-axis as being 

aligned with the direction of flight and the z-axis directed 

under the flight path, corresponds to the coordinate system 

used in ANOPP. Using this coordinate system, observer 

locations can be specified by an observer distance Re and two 

angles with θe denoting the polar flyover angle and φe 

denoting the azimuthal sideline angle. The “e” subscript 

indicates that these are emission coordinates determined from

Figure 4.18.—Quiet Flow Facility (QFF) coordinates 

system for landing gear noise measurements. Re is 

source-to-observer distance, θe, is polar emission 

angle, and φe is azimuthal emission angle.

tunnel, array, and landing gear mounting geometries, along 

with corresponding shear-layer acoustic refraction corrections. 

Reference 36 reports an extensive analysis used to derive 

equivalent emission coordinates in order to provide measurements in a coordinate system that can be used for free-field 

correlations.

Signals from the array microphones were band-pass filtered 

over a pass band of 300 Hz to 50 kHz and digitized using a 

14-bit transient data recorder. Postprocessing of the acquired 

array data included single microphone auto-spectrum analysis 

(using four microphones from the MADA identified in 

Appendix D and Ref. 36), conventional frequency-domain 

delay and sum beamforming, and DAMAS deconvolution. 

The processing accounted for mean amplitude and phase 

changes due to refracted sound transmission through the shear 

layer to the individual MADA microphones. A key feature of 

the beamforming and DAMAS processing was that the spatial 

resolution was controlled independently of steering frequency 

and direction over a broad frequency range. 

The test matrix for the assessment is summarized in

Table 4.6. A baseline landing gear configuration was 

employed with the side-mounted door and all detail hardware 

attached. The Mach numbers tested ranged from 0.11 to 0.17, 

corresponding to a Reynolds-number range of 2.1×105 to 

33×105

, based on wheel diameter. Although the nominal Mach 

number for a landing aircraft is around 0.2, the main landing 

gear experiences a slightly lower flow speed due to the 

circulation around the wing and flaps. Therefore, the tested 

Mach numbers are similar to what would be experienced by 

landing gear in flight. However, the test Reynolds numbers are 

only 6.3 percent of what would be experienced in flight.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 77 Chapter 4

Finally, a range of polar and azimuthal angles was chosen for 

acquisition such that a sizeable portion of the hemispherical 

directivity of the gear could be obtained and compared with 

ANOPP predictions.

TABLE 4.6.—TEST MATRIX FOR BOEING 777

LANDING GEAR NOISE STUDY

Model configuration tested ............................Baseline (with side door)

Model mounting, views............................................... Flyover, sideline

Mach numbers...................................................... 0.11, 0.13, 0.15, 0.17

Reynold’s numbers (based on wheel diameter)........ 2.1×105 to 3.3×105

Polar angular range (emission angles), deg.............................55 to 135

Azimuthal angular range (emission angles), deg...................–106 to 94

4.5.2 Results and Findings

The Boeing prediction method had been developed using 

full-scale landing gear noise data, whereas Fink’s method 

incorporated both model- and full-scale data during its 

development to define the noise spectral shape and amplitude. 

Note that difficulties in the matching of model- and full-scale 

landing-gear data have been encountered by other researchers 

(Refs. 41 and 58). However, the current comparisons between 

the predictions and the 6.3-percent-scale model data do not 

exhibit similar discrepancies. The Fink method (Refs. 32 and

42) is a pure Strouhal scaling approach that allows prediction 

of arbitrary landing gear size. The Boeing-Guo method 

(developed by Guo, Ref. 44) is also largely based on a 

Strouhal scaling approach. However, the use of “complexity 

factors” to ensure agreement with full-scale landing gear data, 

and the inclusion of a narrowband (versus 1/3 octaves) 

spectrum function in the source definition, prevent the 

prediction of arbitrary landing gear sizes. Therefore, a scaling 

method was developed to correctly compare Guo’s full-scale 

landing gear predictions with model-scale data. This scaling 

method is described in Reference 37.

The inputs to both prediction methods are extracted from 

the description of a full-scale Boeing 777 main landing gear 

provided in Reference 59, and given here in Table 4.7 and

Table 4.8. Fink’s method only requires as input the number of 

wheels and their diameter, the length of the main strut, and the 

free-stream Mach number. The Boeing-Guo method, which 

accounts for significantly more geometric detail, requires the 

entries in both tables as input.

TABLE 4.7.—BOEING 777 MAIN LANDING GEAR

PREDICTION INPUT PARAMETERSa

Free-stream Mach number............................................. 0.17

Source-to-observer distance, m (ft)......................24.3 (79.5)

Angle of attack, deg......................................................... 0.0

Wheel track angle, deg................................................... 13.0

Number of tires................................................................... 6

Tire diameter, cm (in.).......................................127.0 (50.0)

Tire width, cm (in.)..............................................50.8 (20.0) a

Full scale (Ref. 59).

TABLE 4.8.—BOEING 777 MAIN LANDING

GEAR COMPONENT DIMENSIONSa

Main gear components Length,

cm (in.)

Diameter or width,

cm (in.)

Thickness,

cm (in.)

Shock strut 388.6 (153.0) 40.6 (16.0) -----------

Upper hydraulic rod 76.2 (30.0) 30.5 (12.0) -----------

Lower hydraulic rod 88.9 (35.0) 7.6 (3.0) -----------

Axle 266.7 (105.0) 21.6 (8.5) -----------

Axle connection 304.8 (120.0) 33.0 (13.0) -----------

Front hydraulic rod 137.2 (54.0) 19.3 (7.6) -----------

Lower front side bar 127.0 (50.0) 17.8 (7.0) 15.2 (6.0)

Lower aft side bar 127.0 (50.0) 17.8 (7.0) 15.2 (6.0)

Upper front side bar 137.2 (54.0) 20.3 (8.0) 15.2 (6.0)

Upper aft side bar 137.2 (54.0) 20.3 (8.0) 15.2 (6.0)

Horizontal front side bar 121.9 (48.0) 10.2 (4.0) 10.2(4.0)

Horizontal aft side bar 109.2 (43.0) 10.2 (4.0) 10.2 (4.0)

Upper torque bar 147.3 (58.0) 12.7 (5.0) 7.6 (3.0)

Lower torque bar 162.6 (64.0) 12.7 (5.0) 7.6 (3.0)

Rear wheel steering 63.5 (25.0) 6.4 (2.5) -----------

Rear wheel hydraulic 50.8 (20.0) 12.7 (5.0) ----------- a

Full scale (Ref. 59).
NASA/TP—2012-215653 78

Figure 4.19 compares “scaled” Boeing-Guo predictions 

with experimental measurement at two different observer 

locations; Figure 4.19(a) is for the flyover position and 

Figure 4.19(b) is for the forward-sideline position. The total 

scaled spectrum and its three separate frequency component 

spectra are shown. At both locations, the high-frequency 

component overpredicts by about 2 to 5 dB at frequencies 

beyond 10 kHz. At frequencies less than 1250 Hz, the 

predictions underpredict the data. The peak in the total 

spectrum is around 5 kHz, but the curve is relatively flat 

between 1 and 10 kHz. The variation in the peaks of the low-, 

mid-, and high-frequency components produces the extended 

flat portion of the total, which is not borne out by the experimental data. At the forward-sideline location (Figure 4.19(b)) 

the overall spectrum is higher than at flyover location 

(Figure 4.19(a)), with the low- and mid-frequency components 

responsible for most of the increase. As the azimuthal angle 

increases, the contribution of the low- and mid-frequency 

components increases. For both the flyover and forwardsideline locations, the high-frequency component is responsible for the overprediction beyond 5 kHz.

Figure 4.20 is similar to Figure 4.19, but the predictions are 

from the Fink method. In Figure 4.20(a), at the flyover 

location, the predictions compare reasonably well over the full 

frequency range, but the high frequencies are overpredicted by 

1 to 3 dB. At this observer location, the wheel component 

totally dominates the predictions. In contrast, the component 

breakdown from the Guo method in Figure 4.19(a) is relatively 

balanced. Clearly, the breakdown of at least one of the 

methods does not correspond with the actual physics. At the 

forward-sideline location shown in Figure 4.20(b), the 

prediction is too low beyond 5 kHz and up to 6 dB too high 

for lower frequencies. Between the flyover and forwardsideline locations, the contribution of the wheels is nearly 

identical. The increase in the spectrum is achieved by a 

dramatic increase in the strut component (namely due to the 

directivity function), and most of the increase is at low 

frequency. 

The Fink and scaled Boeing-Guo predictions are compared 

with noise measurements for a range of azimuthal directivity 

angles in Figure 4.21. Both methods assume azimuthal 

symmetry and thus produce the same results at positive and 

negative azimuthal angles, as indicated in the figures. Note that

both prediction methods are based on data from landing gear 

that included a door, as does the scale model tested. Measured 

spectra for both the positive and negative azimuthal angles 

show the degree of asymmetry of the noise for the model. At 

φe = –59.1° for the observer on the door side, the noise is lower 

in level compared with that on the side opposite the door at φe = 

–57.8°, and the high-frequency levels are similar to those at the 

flyover location φe = –1.0°. The door and wheels appear to be 

responsible for 3 to 5 dB of shielding at high frequencies. 

Neither the Guo nor Fink model predicts this shielding effect. 

More details regarding azimuthal directivity and the effect of 

the door are found in Reference 36.

In Figure 4.22, the Fink and “scaled” Boeing-Guo predictions are compared with measurements for a range of flyover 

polar angles. The measured spectral shape is quite similar for 

the three angles. Although both the Fink and Guo predictions 

for the three angles are also similar in shape, the Fink 

predictions are in better overall agreement with the measurements. The measurements show a reduction of 5 dB between 

θe = 56.0° and θe = 87.1°, which is also observed in the 

Boeing-Guo predictions. However, the amplitude of the 

Boeing-Guo predictions is around 5 dB too high at higher 

frequencies. Almost no change is observed in the Fink 

predictions for these angles, but a reduction of around 3 dB is 

observed between θe = 87.1° and θe = 122.1°. At low frequencies, the experimental data shows a similar decrease, but 

almost no change at higher frequencies. Neither model appears 

to adequately model the polar variation in amplitude, which is 

at least partially caused by convective amplification. 

4.5.3 Sensitivity Study

The sensitivity of the Boeing-Guo and Fink landing-gear 

noise predictions to the Mach number and angle of attack was 

studied for the case with a nominal 0.17 Mach number. The 

observer for this sensitivity study was located at polar and 

azimuthal directivity angles, θe = 87.1° and φe = –1.0°, 

respectively. The Mach number was varied by ±1 percent 

(equivalent to the maximum Mach number error that could have 

occurred in the QFF experiment) about the mean value of 0.17. 

The landing gear angle of attack was varied by ±5 percent about 

the mean value of 13°. Only the Mach number sensitivity was 

considered for the Fink landing-gear noise model, as this model 

does not account for the angle of attack.

The effects of Mach number on the predicted levels for the 

Fink and Boeing-Guo methods were less than 0.3 and 0.4 dB, 

respectively, at all frequencies. The smallest differences were 

observed at the lower frequencies (on the order of 0.1 dB) and 

increased to a maximum at the higher frequencies. For the 

Boeing-Guo method, the level variations due to changes in the 

angle of attack were about ±0.1 dB at all frequencies. The 

combined (maximum) effects of Mach number and landing 

gear angle of attack for the Boeing-Guo method are shown in 

Figure 4.23. The variation in levels ranged from ±0.3 dB at the 

lower frequencies to about ±0.45 dB at the highest frequency. 

The two semi-empirical models follow expected 6 V∞ trends 

with respect to changes in Mach number, and these changes 

are substantial for just a 1-percent variation. The Mach 

number variation across the face of the gear is likely to be 

much larger than 1 percent for a gear mounted on a wing and 

experiencing flight conditions. Hence, accounting for this 

variation could significantly improve the ability to predict 

flight articles.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 79 Chapter 4

Figure 4.19.—Sound pressure level (SPL) of landing gear 

model. Comparison of measured spectrum and total 

scaled (Ref. 37) ANOPP predicted spectrum with its 

three separate frequency component spectra using 

Boeing-Guo method for Mach number 0.17 at two

observer locations (see Figure 4.18). (a) Flyover

position, θe = 87.1° and φe = 1.0°. (b) Forward-sideline 

position, θe = 59.3° and φe = 5.17°. 

Figure 4.20.—Sound pressure level (SPL) of landing 

gear model. Comparison of measured spectrum

and total ANOPP predicted spectrum with its

separate component spectra using Fink method

for Mach number 0.17 at two observer locations

(see Figure 4.18). (a) Flyover position, θe = 87.1°

and φe = 1.0°. (b) Forward-sideline position,

θe = 59.3° and φe = 5.17°. 
NASA/TP—2012-215653 80

Figure 4.21.—Sound pressure level (SPL) of landing 

gear model for Mach number 0.17 and given polar 

angle at different azimuthal angles (see Figure 4.18).

(a) Comparison of measured spectra and total 

scaled (Ref. 37) ANOPP-predicted spectra using 

Boeing-Guo method. (b) Comparison of measured 

spectra and total ANOPP-predicted spectra using 

Fink method.

Figure 4.22.—Sound pressure level (SPL) of landing 

gear model for Mach number 0.17 and given

azimuthal angle at different polar angles (see 

Figure 4.18). (a) Comparison of measured spectra 

and total scaled (Ref. 37) ANOPP-predicted spectra 

using Boeing-Guo method. (b) Comparison of

measured spectra and total ANOPP-predicted

spectra using Fink method.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 81 Chapter 4

Figure 4.23.—Boeing-Guo method: Combined effects 

for variation in Mach number and landing gear angle 

of attack.

4.5.4 Recommendations

NASA’s ANOPP offers two empirically based methods to 

predict landing gear noise: the Fink method and the BoeingGuo method. The Boeing-Guo method was developed almost 

exclusively using full-scale landing gear data. The Fink 

method was developed using both model- and full-scale data. 

Both methods have previously been shown to compare well 

with full-scale noise data. Application of these methods to a 

model-scale landing gear was investigated by comparing 

predictions from each method with measurements for a highfidelity, 6.3-percent-scale Boeing 777 main landing gear. The 

Fink method was found to follow Strouhal scaling and, hence, 

employed the scale model geometry as input. The Boeing-Guo 

method was found not to strictly follow Strouhal scaling and 

hence could not employ the scale model geometry as input. 

Hence, full-scale landing gear geometry was used as input to 

the Guo method, and the predicted results were then scaled to 

represent model-scale noise. Without this additional scaling, 

the Guo method cannot be used to compare with model-scale 

data. In this respect, Fink’s method is more general.

The measured polar and azimuthal directivity spectra reveal 

distinctive directivity patterns, with higher levels of noise 

directed forward and away from the door side of the landing 

gear. The Fink and “scaled” Boeing-Guo predictions show 

good comparisons for flyover polar angles and fair comparisons for overall directivity, particularly at the larger azimuthal 

angles. These comparisons suggest that noise measured for 

high-fidelity, scale-model landing gear is representative of that 

found for full-scale landing gear, as the prediction methods 

were developed and compared well with full-scale data. It is 

recommended that both ANOPP prediction methods be 

improved using the newly available extensive database of 

model-scale noise measurements. One obvious area of needed 

improvement lies in the models’ insensitivity to the presence 

or absence of the door, particularly in the prediction of 

azimuthal directivity.

4.6 Prototype for Airframe Component 

Interaction: Tandem Cylinders

The remaining test cases in the present assessment 

(Secs. 4.6 to 4.8) involve the more fundamental, physics-based 

modeling approach described in Section 4.2.1. As such, the 

near-field flow (including the acoustic source) is simulated 

with the Navier-Stokes code CFL3D (see Appendix C). The 

source simulation data is then used as input to an analytical 

formulation to propagate the noise to a predetermined 

observer location. The first such case involves a benchmark 

problem, two cylinders in tandem to an oncoming flow, for 

which the availability of detailed experimental data enables a 

thorough examination of the simulation’s capability to capture 

the relevant physics in the processes of noise generation and 

propagation. 

4.6.1 Test Descriptions

Experimental data have been obtained in the BART and 

QFF wind tunnel facilities at NASA Langley (see Appendix 

D). The test configuration comprises two cylinders of equal 

diameter (Dt), aligned in the streamwise direction. The 

configuration under consideration is shown in Figure 4.24. 

The separation distance between the cylinder centroids, Lt, and 

all other test parameters involving length are normalized with 

respect to Dt. The angle θ is measured from the upstream 

stagnation point and is positive in the clockwise direction.

Two experiments (Refs. 38 and 39) have been performed in 

the BART, providing steady and unsteady surface pressure 

data, detailed flow-field measurements using particle image 

velocimetry (PIV), and hot-wire measurements in the wake of 

the downstream cylinder. During Phase 1, the free-stream 

velocity was set to 56.1 m/s (184 ft/s), corresponding to a 

Mach number of 0.166. Each cylinder measured 44.45 mm 

(1.75 in.) in diameter, and spanned the test-section height 

(Figure 4.25), for an aspect ratio of b/Dt = 16 where b is the 

length of the span. The test Reynolds number, based on 

cylinder diameter, was 1.66×105

. Before the Phase 2 test runs, 

in order to accommodate more tubing and wiring for additional transducers, two new cylinders were manufactured, 

measuring 57.15 mm (2.25 in.) in diameter, thereby altering 

the value of b/Dt to 12.44. To maintain the Phase 1 Reynolds 

number, the tunnel speed was set to 43.89 m/s (144 ft/s), with 

a corresponding Mach number of M = 0.129. To ensure a fully 

turbulent shedding process, the boundary layers on the 

upstream cylinder were tripped between azimuthal locations of 

50° and 60° from the leading stagnation point. The measured 

surface pressure distribution for the large cylinder centroid 

separation case was nearly identical to that measured by 

previous investigators for a single, isolated cylinder at a 

Reynolds number greater than 8 million (Ref. 60).
NASA/TP—2012-215653 82

Upon conclusion of the Phase 2 BART test, the tandemcylinders model was removed and altered in length to mount 

in the QFF for acoustic measurements (Refs. 61 and 62). The 

model was supported above the open-jet nozzle by two 

vertical side plates that were mounted to the short sides of the 

nozzle (Figure 4.26). The cylinders spanned the 0.914-m (3-ft) 

section, yielding an aspect ratio of b/Dt = 16. To simulate the 

BART results as closely as possible, the trip arrangement on 

the front cylinder was duplicated, and the speed in the tunnel 

was adjusted until the shedding frequency was matched. The 

nominal Mach number for the test was 0.127 (43.4 m/s) with a 

dynamic pressure of 1145 Pa (0.166 psi). In addition to 

replicating the BART measurements of the steady and 

unsteady surface pressures, the acoustic radiation was 

measured using three pole-mounted microphones. Further 

details of the QFF test are reported in Reference 61.

4.6.2 Computational Approach and Procedure

The flow about tandem cylinders was simulated in free air, 

without any wind tunnel walls. All input parameters were 

based on wind tunnel test conditions during Phase 1 testing in 

the BART facility. The free-stream Mach number in the 

computations was 0.166, and the Reynolds number was 

1.66×105

, based on cylinder diameter. The separation distance 

between the centroids of the inline cylinders was Lt = 3.7Dt

(Figure 4.24). For this spacing, the flow is supercritical and 

both cylinders experience large-scale shedding. The experiments were run at different speeds, so the data have been 

corrected to an equivalent speed, with the QFF Mach number 

of 0.127 chosen as the reference to which the CFD calculations were scaled.

The calculations incorporate the shear stress transport 

(SST) k-ω turbulence model of Menter (Refs. 63 and 64), 

which was developed for steady flow. Because of the overly 

diffusive nature of the turbulence model, proper growth of 

unsteady phenomena can be inhibited. To remedy this 

shortcoming, a quasi-laminar approach, as described in 

Khorrami, et al. (Ref. 65), has been adopted. Following this 

approach, the flow field is assumed to be quasi-laminar, 

except for a narrow strip surrounding the cylinder surfaces 

where the SST turbulence model is used. Outside of this strip, 

the production term associated with the turbulence model is 

switched off. For computational convenience, the distance 

from the cylinder at which the switch occurs was set based on 

a set number of grid points from the surface. Because of the 

azimuthal nonuniformity in the grid stretching, the switch 

occurs between 0.01Dt and 0.04Dt, which includes the entire 

boundary layer within the region of attached flow. For 

different grid spacings, the number of points from the surface 

was changed to maintain the switching at the same physical 

distance. All of the simulations were run without specifying a 

transition location. The turbulence model in the Reynoldsaveraged Navier-Stokes (RANS) region was run in a fully 

turbulent mode and allowed to transition on its own.

Figure 4.24.—Tandem cylinder test configuration.

Figure 4.25.—Tandem cylinders installed in Basic 

Aerodynamic Research Tunnel (BART).

Figure 4.26.—Tandem cylinders installed in Quiet Flow 

Facility (QFF) tunnel for measurements with Medium 

Aperture Directional Array (MADA) microphones.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 83 Chapter 4

Figure 4.27.—Planar view of computational x,y-grid 

used for tandem cylinder computational fluid

dynamics (CFD) simulations.

Tandem cylinder grids were generated by replicating a 

404 000-point, block-structured, planar x,y-grid in the 

spanwise direction. The planar grid is shown in Figure 4.27. 

The total grid count for a span of 6 was 80 million. This grid is 

denoted as Fxyz. Care was taken so that the first point off the 

solid surfaces was at y

+ < 1. The reference length in the grid 

was the cylinder diameter, Dt. Hence, a span of 3 means 3 

diameters. Periodic boundary conditions were imposed in the 

spanwise direction. A Riemann condition was applied at the 

outer boundaries, except for a small region in the wake where 

extrapolation was employed. The no-slip condition with an 

adiabatic thermal condition was applied on all solid surfaces. 

Details about the boundary conditions can be found in the 

CFL3D user’s manual (Ref. 45). Simulations based on 

medium-level grids (derived from the finest grid by removing 

every other grid point in each direction) were performed to 

allow an assessment of the grid convergence of the computed 

solutions. This family of grids is denoted as Mxyz. A span of 

18, which is more representative of the experiment, has been 

examined with a 30-million-point grid. Although the planar 

resolution on the medium mesh was reasonable, the spanwise 

resolution did not seem to be sufficient. Therefore, a series of 

grids with the same spanwise resolution as the fine grid were 

generated. These grids, denoted as MxyFz, have nearly isotropic 

cell spacing in the wake region between the cylinders. Again,

a spanwise extent of 18 was examined, with 60 million

points in the grid. A constant, nondimensional time step of 

∆ta∞/Dt = 0.051 or ∆tV∞/Dt = 0.0855 (corresponding to 

approximately 520 time steps per period for the primary

shedding frequency) was used for all simulations, where V∞ is 

the free-stream velocity. Limited calculations were also 

performed with double and half the time step without any 

appreciable differences in the first- and second-moment 

statistics, although the required effort to obtain sufficient 

samples makes it problematic to be definitive about such 

statements. 

The simulation procedure includes several steps. First, a 

steady-state computation was used to set up the basic mean 

flow, followed by an unsteady calculation with random 

suction and blowing applied to different spanwise and 

azimuthal sections of both cylinder surfaces in order to 

accelerate the onset of three-dimensional unsteady flow 

structures. The forcing did not exceed 3 percent of the freestream velocity. The forcing was turned off after significant 

unsteadiness was observed, typically 200 time steps into the 

unsteady calculation. The simulations were then run for 5000 

to 10 000 time steps to allow the transient flow field to wash 

out before collecting time records. Data were collected every 

other time step.

The radiated noise is calculated using the FW–H approach 

(Refs. 47 and 66) described in Appendix C. The acoustic 

calculation uses unsteady, CFD simulation data on a surface 

surrounding the source. The FW–H noise calculations involve 

unsteady data collected on 32 total subsurfaces composing the 

impenetrable data surface, which lies on the cylinders. Only 

the pressure is needed on an impenetrable surface. Calculations with permeable surfaces away from the cylinders showed 

good agreement with those using the solid-surface data 

(Ref. 61). The 32 subsurfaces are a natural consequence of the 

block-structured grid used for the CFD calculations. Each 

subsurface is a boundary of one of the blocks comprising the 

grid. The complete time record of over 12 000 samples was 

subdivided into five segments of 4096 samples with 

50 percent overlap. A Hamming filter was applied to each 

segment. The FW–H code was used to calculate the noise at 

the exact locations of the pole-mounted microphones in the 

experiment. To account for differences in flow speed between 

the calculation and the experiments, frequencies were Strouhal 

scaled, and the acoustic power corrected by assuming 

proportionality to 2 6 St V∞ , where St = fDt /V∞.

4.6.3 Results and Findings

Extensive aerodynamic comparisons between the simulations and experiments can be found in References 61 and 65. 

Figure 4.28 presents the pressure coefficient results for the 

upstream and downstream cylinders. The pressure coefficient, 

Cp, is defined as ( ) ( ) 2

2

1 Cp = p − p∞ ρV∞ , where p, ρ, and V

are local values for the pressure, density, and speed of the 

airflow, respectively, and the subscript ∞ denotes a freestream value. Figure 4.28(a) shows that the base pressure on
NASA/TP—2012-215653 84

the upstream cylinder from the MxyFz grid matches slightly 

better with the QFF experimental data, whereas the Mxyz and

Fxyz results match better with the BART data. As the 

simulations were performed in free air, one might expect that 

the CFD should match the open-jet QFF results. On the 

downstream cylinder, there is very little difference among the 

various computed solutions, but the discrepancy with experiment is considerably larger. Solution variations among the 

different grids are more substantial when comparisons are 

based on perturbation pressure (denoted p′), which is determined from the Reynolds decomposition, p = p + p′ , where 

p denotes the mean (time-averaged) value of the pressure 

field. Such variations are shown in Figure 4.29, where the 

comparison quantity is the root-mean-squared (rms) value of 

the coefficient of perturbation pressure, ( ) 2

2

1 Cp′ = p′ ρV∞ . On 

the upstream cylinder (Figure 4.29(a)), the fluctuations on the 

MxyFz grid are considerably lower than on the other two grids 

and match extremely well with the experimental data. The 

levels on the finest grid Fxyz are the highest, but the Fxyz grid 

only has a span of 6, and there is a complex interaction 

between grid resolution and spanwise extent on the fluctuation 

levels. Note that the range for the downstream cylinder in 

Figure 4.29(b) is much larger than for the upstream cylinder. 

In general, the computations pick up the location of the peak 

fluctuations around θ = 45° because of the impingement of the 

wake on the downstream cylinder.

From a noise perspective, the downstream cylinder is going 

to dominate the radiation because the pressure fluctuations are 

10 to 15 dB higher than those on the upstream cylinder. The 

near-field SPL contours in Figure 4.30 resemble the directivity

from a dipole source just upstream of the downstream 

cylinder. Although CFD seems to have directly captured some 

of the radiated noise, this is still very much in the near field. 

The wavelength of the primary shedding frequency is larger 

than the size of the computational domain. The FW–H 

equation was used to make predictions of the noise at a 

microphone located at the downstream (x, y) location of the 

rear cylinder at (9.11Dt, 32.49 Dt). In the experiment, a

64-channel, 16-bit transient data recorder controlled by a 

workstation was used to acquire the data at a sampling rate of 

25 600 samples per second. High- and low-pass filters, set 

respectively at 5 Hz and 10 kHz, were used to condition the 

outputs from each microphone channel. The noise spectra 

were obtained by partitioning each time signal into 1000 nonoverlapping segments of 8192 samples, and each time history 

segment was Fourier transformed using a Hamming window 

for signal conditioning. The resulting frequency resolution 

was 3.125 Hz.

A comparison between the predictions using the three grids 

and the experimental results is shown using a narrowband 

analysis in Figure 4.31. All of the data have been scaled to an 

equivalent 1-Hz bin width, so the presentation is in power

spectral density. Both the experiment and predictions show a 

pronounced tone at low frequency. The prediction is only off 

by less than 20 Hz from what was observed in the experiment 

(178 Hz in the experiment and 160 Hz in the simulation). The 

Fxyz result was obtained by replicating the data from the span 

of 6 calculations 3 times to produce a span of 18, matching the 

length of the other calculations and the experiment. However, 

this results in an artificial spanwise correlation that produces 

more noise below 2000 Hz than the Mxyz grid. The elevated

Figure 4.28.—Pressure coefficient Cp versus polar angle 

θ for the surfaces of the tandem cylinders. Comparison 

of results from Quiet Flow Facility (QFF) and Basic 

Aerodynamic Research Tunnel (BART) experiments 

and CFD simulations with grids of different spans. 

(a) Upstream cylinder. (b) Downstream cylinder.
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NASA/TP—2012-215653 85 Chapter 4

Figure 4.29.—Root-mean-squared (rms) value of perturbation 

pressure coefficient Cp′ versus polar angle θ for the

surfaces of the tandem cylinders. Comparison of results 

from Quiet Flow Facility (QFF) and Basic Aerodynamic 

Research Tunnel (BART) experiments and CFD

simulations with grids of different resolutions and spans. 

(a) Upstream cylinder. (b) Downstream cylinder.

Figure 4.30.—Near-field tandem cylinder sound pressure 

level (SPL) contours, CFD predictions, where x and y

are spatial coordinates and grid dimensions and Dt is 

cylinder diameter.

levels are also evident in the 1/3-octave results shown in 

Figure 4.32. Bars are included in the plot representing the 

scatter between runs in the experiment and between different 

averaging segments in the predictions. The time record 

available from the CFD was short, so only five segments of 

4096 samples were used to obtain an average. The band shows 

the maximum and minimum values that were observed in the 

five segments. Although the CFD shows large variations, even 

the experiment shows considerable scatter because of the 

highly intermittent nature of the shedding process. Figure 4.33

shows the difference between the prediction from the MxyFz

grid and the experiment. Because the shedding frequency from 

the CFD and experiment were slightly different and the tone 

was near the edge of a 1/3-octave bin, the error plot shows 

large peaks at these frequencies. Other than missing the 

shedding frequency by about 20 Hz, the CFD prediction is 

actually in good agreement with the experiment.

4.6.4 Effect of Cylinder Spacing

Simulations and experiments have also been performed at 

other cylinder spacings. A detailed comparison between the 

results for a subcritical spacing of 1.435Dt is in Reference 62. 

In the subcritical state, large-scale shedding is suppressed. 

This state was experimentally observed with a cylinder 

centroid-to-centroid spacing of 1.435Dt, resulting in a more 

difficult flow field to simulate. Not only must the simulations 

correctly predict the reduced shedding, many frequencies must 

be resolved as they nearly equally contribute to the overall 

character of the flow. Often, however, the noise engineer is 

most interested in how the flow field and radiated noise 

change as a result of modifications to the geometric configuration. Thus, the computations are examined to assess how well
NASA/TP—2012-215653 86

Figure 4.31.—Power spectral density PSD for tandem 

cylinders. Comparison of CFD predictions using 

three grids and results from Quiet Flow Facility 

(QFF) experiments.

Figure 4.32.—Sound pressure level (SPL) spectra for 

tandem cylinders. Comparison of CFD predictions

using three grids and measurements from Quiet Flow 

Facility (QFF) experiments.

Figure 4.33.—Error in sound pressure level (SPL) 

spectra predictions for tandem cylinders. Difference 

between CFD predictions from MxyFz grid with span 

of 18 and experimental measurements.

the predictions respond to varying the spacing from supercritical (Lt/Dt = 3.7) to subcritical (Lt/Dt = 1.435). The levels of 

peak surface pressure on the downstream cylinder in both 

cases are used in the evaluation. Using the calculation on the 

MxyFz grid with a span of 18 as a reference, a comparison of 

experimental rms surface-pressure fluctuations for the two 

cylinder centroid separation distances is shown in Figure 4.34. 

The peak rms levels are different by a factor of 2 to 3 between 

the two configurations, and the CFD has picked up this effect. 

All of the CFD solutions from the different grids correctly 

capture the trend. Acoustic results for the different cylinder 

centroid separation distances are compared in Figure 4.35. 

Both the experimental and CFD results show that the tone and 

broadband amplitudes are significantly lower for the smaller 

spacing. A decrease of 20 dB represents an order of magnitude 

in reduction for the fluctuating pressure. Clearly, the CFD has 

predicted the correct trend in the far-field acoustics even 

though the details of the spectrum at the smaller spacing have 

not been captured. The spectral peak in the simulations is still 

10 dB above the rest of the spectrum, whereas the peak is 

barely discernible in the experiments. Figure 4.36 presents the 

1/3-octave SPL comparison between the simulations and 

experiment for the 1.435Dt spacing, and Figure 4.37 presents 

the corresponding error. Although the error exceeds 12 dB 

around the frequency of the peak in the predicted pressure 

spectra, the CFD has still correctly captured the dramatic 

reduction in the noise levels between the 3.7Dt and 1.435Dt

spacing cases. For some applications, capturing the trends is 

sufficient, but higher fidelity in predicting absolute noise 

levels is needed.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 87 Chapter 4

Figure 4.34.—Root-mean-squared (rms) value of

tandem cylinder surface perturbation pressure

coefficient Cp′ versus polar angle θ at two spacings 

Lt/Dt, where Lt is centroid-to-centroid distance and Dt

is cylinder diameter (see Figure 4.24). Comparison 

of CFD predictions from MxyFz grid with span of 18 

and measurements from Quiet Flow Facility (QFF) 

and Basic Aerodynamic Research Tunnel (BART) 

experiments.

Figure 4.35.—Power spectral density PSD for tandem 

cylinders at two spacings Lt/Dt, where Lt is centroidto-centroid distance and Dt is cylinder diameter 

(Figure 4.24). Comparison of CFD predictions from 

MxyFz grid with span of 18 and measurements from 

Quiet Flow Facility (QFF) experiments.

Figure 4.36.—Sound pressure level (SPL) spectra for 

tandem cylinders at centroid separation distance

Lt/Dt = 1.435. Comparison of CFD predictions from

MxyFz grid with span of 18 and measurements from 

Quiet Flow Facility (QFF) experiments.

Figure 4.37.—Error in sound pressure level (SPL)

spectra predictions for tandem cylinders at centroid 

separation distance Lt/Dt = 1.435. Difference between 

CFD predictions from MxyFz grid with span of 18 and 

experimental measurements.
NASA/TP—2012-215653 88

4.6.5 Recommendations

The tandem cylinder problem has proven to be an excellent 

and challenging dataset to test the ability of CFD to accurately 

predict the near-field aerodynamics and the resulting noise.

Although reasonable results were obtained with the MxyFz grid 

with a span of 18, the noise results for the Fxyz grid and a span 

of 6 overpredicted amplitudes. Unfortunately, the computational 

cost is prohibitive for a span of 18 on the Fxyz grid. Much faster 

flow solvers are needed to predict airframe noise when very 

complicated physics is responsible for the noise generation. 

Furthermore, robustness and the ability to model complex 

geometries are very important. It is imperative that resource 

investment be made in the development of fast, highly accurate 

flow solvers with robustness and geometric flexibility. Ideally, 

such solvers would adapt in an unsteady manner to the relevant 

flow features to maintain a desired level of accuracy. Benchmark problems like the tandem cylinders provide a means to 

assess the accuracy and efficiency of new methods.

4.7 Aeroacoustic Analysis of Simplified 

Landing Gear Model

Wind tunnel tests and computer simulations are conducted 

to study the aerodynamic noise generated by a Mach 0.2 flow 

over a simplified landing gear without small-scale parts, such 

as hydraulic lines and fasteners. An integral of the FW–H 

equation predicts the noise at far-field observer locations from 

surface-pressure data provided by an unsteady computational 

fluid dynamics calculation. The subsequent analysis includes 

the identification of geometric and aerodynamic characteristics that are responsible for various features in the computed 

noise spectra.

4.7.1 Test Description

The geometry of the test model, shown in Figure 4.38, 

approximately represents a 10-percent-scale Boeing 757 main 

landing gear. The model assembly is composed of four 

wheels, two side struts, an oleo, a side door, yokes, a pin, and 

other structures that join the system together. Tests were 

initiated in the Low-Turbulence Pressure Tunnel (LTPT) at 

NASA Langley, with the landing-gear model mounted on a 

three-element airfoil section (Ref. 67). The LTPT is a 

pressurized facility that enables model testing at increased 

Reynolds numbers while maintaining a constant Mach number 

(see Ref. 68 for facility details). The test conditions for the 

initial CFD analysis (Ref. 69), and those to follow, correspond 

to a free-stream Mach number of 0.2 at a static temperature of 

302.9 K (85.5 °F), and a free-stream stagnation pressure 

284 kPa (2.8 atm). Under these conditions, the Reynolds 

number is 1.23 million, relative to the landing-gear wheel 

diameter of 0.094 m (3.7 in.).

Most of the data from the LTPT test are unavailable, but 

acoustic measurements for the simplified landing-gear model 

were recently obtained in the QFF (see Appendix D). Although 

a comprehensive report on this QFF test is yet to be published, a 

few results are presented herein for prediction validation. 

Because of obvious similarities with the Boeing 777 model test 

in Section 4.5, aerodynamic noise associated with the present 

landing gear model was measured using the same setup and 

procedures described in References 36 and 37. The Reynolds 

number for the QFF test, based on wheel diameter, was 

370 000. 

4.7.2 Computational Approach and Procedure

Noise sources for this simplified landing gear have been 

simulated with CFL3D (Refs. 43 and 46) and a detached-eddy 

simulation (DES) (Ref. 70) methodology as proposed by Spalart 

(Refs. 71 and 72), coupled to a FW-H equation solver (Refs. 47

and 66) discussed in Appendix C. The DES model essentially 

reduces the level of eddy viscosity in regions away from solid 

surfaces when the grid is sufficiently fine. For the CFD 

simulations, the landing-gear model was mounted on a flat plate 

that represents the pressure surface of the aircraft wing. The 

flow calculations were run fully turbulent at a Reynolds number 

of 1.23×106

, based on the landing-gear wheel diameter. The 

structured grid consisted of 155 blocks possessing a total of 

13.3 million grid points. Figure 4.39 shows a coarsened grid 

distribution on the surface of the model. A Riemann condition 

was applied at the outer boundaries, except for a small region in 

the wake where extrapolation was employed. The no-slip 

condition with an adiabatic thermal condition was applied on all 

solid surfaces. Details of these boundary conditions can be 

found in the CFL3D User’s Manual (Ref. 45), and additional 

information in regard to the computations can be found in 

References 73 and 74.

Figure 4.38.—Geometry of simplified landing gear model.
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NASA/TP—2012-215653 89 Chapter 4

Figure 4.39.—CFD surface grid of simplified landing 

gear model.

Figure 4.40.—Sound pressure level (SPL) spectra

for landing gear in overhead position at polar angle

θ = 88° and azimuthal angle φ = –1° (see Figure 4.18). 

Comparison of CFL3D predictions, using gear

surface with and without the ceiling surface, and

measurements from Quiet Flow Facility (QFF)

experiments, nontripped and tripped cases.

The noise calculations involve unsteady flow data collected 

on 181 total subsurfaces comprising all the solid surfaces in 

the calculation. Only the pressure is required on impenetrable 

surfaces. One hundred forty-seven subsurfaces were on the 

gear itself, and thirty-four were on the plate above the gear. 

The subsurfaces are a natural consequence of the block 

structured grid used for the CFD calculation. Each subsurface 

is a boundary of 1 of the 155 blocks comprising the grid. Over 

12 000 nondimensional time samples were collected from the 

DES simulation. The computations were sampled at every 

fourth time step, with ∆ta∞/d = 0.02, where the tire diameter, 

d, was used as the reference length. All of the acoustic results 

represent an average over five segments with 50 percent 

overlap. Each segment consisted of 4096 samples. The 

observer was located 100 wheel diameters away from the 

model. To compare with the experimental data, the CFD 

results were scaled to a propagation distance of 1.52 m (5 ft, 

or 16.2 wheel diameters) and M = 0.17, by assuming that the 

acoustic power is proportional to V 6 R2 ∞ .

4.7.3 Results and Findings

The predictions are compared with the experimental values 

at five observer locations: overhead, two flyover positions, 

and two sideline positions. The comparison for the nominally 

overhead position (θ = 88°, φ = –1°) is presented in

Figure 4.40. The experimental data from the QFF includes 

both the nontripped and tripped cases. For the tripped case, the 

gear was coated in a fine grit to simulate the effects of higher 

Reynolds number. The amplitude of the noise is 1 to 3 dB 

lower with the grit, but the shapes of the curves are very 

similar. The results from the tripped case should be more 

similar to the computational results because the Reynolds 

number in the simulations was considerably higher. Two 

predictions using the CFL3D data are included: one using all 

solid surfaces (gear+ceiling), and one using only the surfaces 

on the gear. The grid is heavily patched in the vicinity of the 

ceiling, and disturbances passing through these interfaces are 

distorted and often artificially amplified. The noise levels 

obtained using only the ceiling is nearly identical to that from 

the gear+ceiling. The hump in the gear+ceiling spectra 

between 2 to 8 kHz is most likely caused by the artificial 

amplification. However, at lower frequencies, the gear+ceiling 

calculation is in much better agreement with the experiment 

relative to the gear-only prediction. The experiment employed 

a Kevlar sheet to prevent reflections from the mounting plate, 

which is the same as the ceiling in the computations. 

However, Kevlar is not completely acoustically transparent. 

Furthermore, most of the noise radiated from the ceiling in the 

computations is from the interaction of flow structures with 

the surface and not simple acoustic reflection. Therefore, it is 

hard to ascertain which of the calculations more faithfully 

represents the experiment.

A thorough perusal of the calculations indicates that the 

shed wake from the side bars is the source of the peak SPL at 

700 Hz in Figure 4.40. The peak at approximately 1300 Hz is 
NASA/TP—2012-215653 90

due to the wake from the main oleo. Most of the noise near 

1000 Hz is coming from the gear boxes and connectors. A 

narrowband presentation of the same data is given in Figure 4.41. Although there is not much change in the overall 

level of agreement, the differences in the peak frequencies are 

now evident. Beyond 10 000 Hz, the CFD data drops off 

rapidly. Because of the lack of resolution in the grid, the high 

frequencies are excessively damped. At full scale, the dropoff 

would begin around 1000 Hz, which is well below the 

maximum frequency at which landing gear contribute to the 

overall aircraft noise. The error in the overhead predictions is 

presented in Figure 4.42. The QFF tripped case is taken as the 

baseline for comparison purposes. The gear+ceiling calculation is within 2 dB of the experiment up to 2000 Hz, whereas 

the gear-only computation has errors between 3 and 6 dB. 

Beyond 10 000 Hz, the errors for both calculations approach 

10 dB.

Experimental data and predictions for polar angles of

θ = 58° (upstream) and 120° (downstream) are shown in 

Figure 4.43. Only the predictions using the CFD solutions 

from the gear alone are presented. In contrast to the experimental data, the CFD predicts only slightly lower levels 

downstream than upstream. However, Figure 4.44 shows that 

the CFD predicts the correct trend for the observers at

φ = –55° (door side) and 55° (opposite the door), with higher 

levels opposite the door. It is interesting that the CFD 

prediction for φ = 55° is in much better agreement with the 

data than φ = –55° and picks up the first two peaks. The door 

may be reflecting some of the signal from the interactions 

occurring near the ceiling resulting in a signal that is similar to 

the one seen in Figure 4.43(a) for the overhead position.

4.7.4 Recommendations

The CFD grid used in the computations was large when the 

calculation was performed, but much finer grids could be used 

today. Furthermore, the grid was heavily patched, especially in 

the vicinity of the ceiling. The patches resulted in obvious 

errors and large oscillations as strong disturbances passed 

through. Refining the grid should improve considerably the 

predictions and remove the ambiguity about the importance of 

flow interactions with the ceiling. However, a reasonable grid 

for a DES-type calculation would require on the order of 

150 million points. Running CFL3D with 150 million points 

on 493 cores on an SGI Altix ICE computer (using 3 of the 4 

cores on each Intel X5355 2.66 GHz processor), results in 

175 GB of total memory usage (365 MB per core). The code 

executes 1000 time steps in 70 hours. Completion of 50 000 

time steps would require 145 days. Although feasible, such a 

calculation is quite large by today’s standards, and the grid 

count is still insufficient to resolve the small scales generated 

around landing gear. Furthermore, the number of time steps 

would need to be increased by a couple of orders of magnitude 

to produce the same number of samples for averaging as are 

typically used in experiments.

Figure 4.41.—Power spectral density PSD for landing 

gear in overhead position at polar angle θ = 88° and 

azimuthal angle φ = –1° (see Figure 4.18). Comparison 

of CFL3D predictions, using gear surface with and 

without the ceiling surface, and measurements from 

Quiet Flow Facility (QFF) experiments, nontripped and 

tripped cases.

Figure 4.42.—Error in CFL3D sound pressure level 

(SPL) spectra predictions for landing gear in overhead 

position at polar angle θ = 88° and azimuthal angle

φ = –1° (see Figure 4.18). Difference between

predictions, using gear surface with and without the 

ceiling surface, and measurements from Quiet Flow 

Facility (QFF) experiments, tripped case.
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NASA/TP—2012-215653 91 Chapter 4

Figure 4.43.—Sound pressure level (SPL) spectra for 

landing gear in flyover positions (see Figure 4.18). 

Comparison of CFL3D predictions and measurements 

from Quiet Flow Facility (QFF) experiments, nontripped

and tripped cases. (a) Upstream, polar angle θ = 58° 

and azimuthal angle φ = –1°. (b) Downstream, polar

angle θ = 120° and azimuthal angle φ = –1°.

Figure 4.44.—Sound pressure level (SPL) spectra for 

landing gear in sideline positions (see Figure 4.18). 

Comparison of CFL3D predictions and measurements

from Quiet Flow Facility (QFF) experiments, nontripped 

and tripped cases. (a) On door side, polar angle 

θ = 88° and azimuthal angle φ = –55°. (b) Opposite 

door side, polar angle θ = 88° and azimuthal angle 

φ = 55°.
NASA/TP—2012-215653 92

Improvements in the turbulence model are also needed. The 

DES computation (Ref. 74) is a vast improvement over the 

original unsteady RANS computation reported in Reference 73. Nonetheless, there is still considerable room for 

improvement. The effects of the RANS region on the unsteady 

surface fluctuations, caused by impinging wakes, are still 

largely unknown. Experimentally, although the acoustic field 

has been mapped out, no near-field data have been obtained 

for the landing gear. A dataset with both near- and far-field 

information is needed to more clearly understand the flow 

phenomena and validate predictions.

Both the above computational study and the previous experimental one focused entirely on the noise generated by the 

flow field in the near vicinity of the landing gear itself. In a 

number of experimental studies of landing gear configurations 

mounted on wings with trailing-edge flaps deployed, microphone phased-array maps (Refs. 19 and 75) suggest that the 

collective unsteady wake of the gear, impinging on the leading 

edge and passing over the trailing edge of the flap, can 

produce significant radiated noise, presumably through a 

scattering process. Existing experimental and computational 

data should be examined in order to form a conclusion 

regarding the further study of this mechanism.

4.8 Aerodynamic Sources of LeadingEdge Slat Noise

In addition to trailing-edge flaps and landing gear (as previously discussed), leading-edge slats are also considered to be 

significant sources of aircraft noise during airport landing

operations. The present study is focused on three-dimensional 

simulations of the slat cove flow within a computational 

domain of limited spanwise extent. The results indicate that 

accounting for the three-dimensionality of flow fluctuations 

leads to considerable improvement in the accuracy of the 

unsteady, near-field solution. Validation data is provided by 

particle-image velocimetry measurements from a test conducted on a generic high-lift model in the BART facility.

4.8.1 Discussion of Experimental Data

The 30P/30N model tested in the BART at NASA Langley 

represents a generic, three-element, zero-sweep high-lift 

configuration with slat and flap deflections of 30° each 

(Figure 4.45). The slat chord, cs, and flap chord, cf, of the model 

are equal to 14.48 and 30 percent, respectively, of the 

stowed chord, c, of 0.457 m (18 in.). For the approach configuration, the slat gap is 2.95 percent; the flap gap is 1.27 percent; 

and the slat and flap overhang settings are equal to –2.95 and 

0.25 percent, respectively. (Ref. 76 provides a definition of 

these rigging parameters.) At the test Mach number of 

M = 0.17, the Reynolds number Rec based on the stowed chord 

of the BART model, corresponds to 1.7 million. While this 

Reynolds number is substantially lower in comparison to fullscale applications, the BART experiment is still suitable for 

validating numerical predictions of the slat cove noise sources 

as described in Reference 77.

The BART measurements (Ref. 35) consist of steady surface pressure measurements plus extensive two-dimensional

PIV data within the midspan plane of the model. To assess the 

accuracy of unsteady near-field predictions, calculations are 

performed for the configuration corresponding to a 4° angle of 

attack in BART, which approximates the mean slat loading for 

a free-flight configuration at a 5.5° angle of attack.

4.8.2 Metrics and Assessment

Previous studies (Refs. 78 and 79) have shown that many 

features of the unsteady slat cove flow may be inferred via 

planar (i.e., two-dimensional) computations that neglect both 

the local three-dimensionality of the unsteady flow structures 

within the slat cove and the large-scale three-dimensional 

effects due to the sidewalls of the tunnel. The origin of the 

dominant flow structures is linked to the Kelvin-Helmholtz 

instability of the shear layer emanating from the slat cusp. The 

two-dimensional computations capture the growth and 

evolution of large-scale coherent structures within the shear 

layer (including shear layer roll-up and vortex pairing) as well 

as their interaction with the slat surface. Following their 

impingement on the slat pressure surface, these vorticity 

structures either are advected past the slat trailing edge or 

migrate back to the slat cusp within the recirculating zone. 

Hybrid acoustic predictions, based on a combination of the 

two-dimensional near-field simulations and the FW–H 

equation, have been found to be consistent with the measured 

slat noise data in terms of both spectral shape and Mach 

number scaling (Refs. 78 and 80). However, the spectral 

intensity was overpredicted by greater than 10 dB in certain 

cases (Ref. 78). More importantly, the two-dimensional nearfield simulations predicted excessively energetic slat-cove 

flow structures, resulting in poor agreement with certain major 

aspects of the measured unsteady flow data (Ref. 80). 

The present assessment focuses on the comparison of 

BART measurements (Ref. 35) with three-dimensional 

simulations that account for the local three-dimensionality of 

the unsteady slat cove flow field. Because of limited

Figure 4.45.—Model three-element 30P/30N high-lift aircraft wing system.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 93 Chapter 4

computational resources, the spanwise width of the computational domain is set at 37.3 percent of the slat chord; that is, 

2.5 percent of the actual span. Given the complexity of the slat 

cove flow structures contributing to broadband noise radiation, 

the metrics chosen for this comparison correspond to

(1) Instantaneous spanwise vorticity distributions (compared visually with BART PIV data)

(2) First- and second-moment statistics of the velocity field

(3) The nature of the near-field acoustic radiation (compared with a DLR model (Ref. 81), based on ground 

test data)

Quantitative error measures have been employed in regard 

to (2); however, similar measures are not appropriate for (1) or 

(3), and therefore the comparisons between computations and 

measurements are purely qualitative.

4.8.3 Results and Findings

A general description of the computational methodology has 

already been discussed in Section 4.2.2; additional details may 

be found in Reference 77. Briefly, the CFL3D code is used with 

a zonal turbulence model to solve the unsteady, thin-layer 

Navier-Stokes equations for the 30P/30N configuration. The 

two-equation SST model of Menter (Refs. 63 and 64) is used to 

capture the mean flow behavior in regions away from the slat 

cove region, whereas the turbulence production term in the 

turbulence transport equations has been switched off within the 

cove region to eliminate the excessive diffusive effects of the 

turbulence model on the resolved unsteady flow structures. The 

design of the cross-sectional grid is based on prior experience, 

but limited grid sensitivity studies have been performed in 

regard to spanwise grid resolution and time step. Only the 

results obtained with the finest spanwise grid are typically used 

for this assessment, which focuses on the broadband sources of 

unsteadiness in the slat cove region. Additional sources of noise, 

such as vortex shedding from the finite thickness slat trailing 

edge, are not included in this assessment. 

The simulations were performed using characteristic boundary conditions at the far-field boundaries in the cross-sectional 

plane (which are positioned at a minimum of 10 chord lengths 

away from the center of the model), except for extrapolation 

from the interior at the downstream boundary. Periodic 

boundary conditions were employed across the spanwise 

boundaries of the computational domain. No-slip conditions 

were imposed at the solid surfaces, along with an adiabatic wall 

thermal boundary condition. 

Two representative snapshots of the spanwise vorticity, 

within a spanwise cut through the computational domain, are 

shown in Figure 4.46(a) and (b). Similar images based on the 

planar PIV data from Reference 35 are shown in Figure 4.47. 

The PIV measurements indicate a regular train of vortical 

structures along the slat shear layer. There is occasional 

entrainment of the vortical structures into the recirculation 

zone, which is the defining characteristic of “cove state I” in 

Figure 4.47(a); however, the majority of the vortices convect 

directly past the trailing edge, with no recirculation (“cove 

state II” in Figure 4.47(b)). The three-dimensional predictions 

in Figure 4.46 resemble the planar PIV data, indicating both 

states of the measured cove flow field. However, an inspection 

of several other three-dimensional computational snapshots 

suggests that the role of the recirculating vortices may be 

somewhat overemphasized within the narrow domain 

simulation, perhaps, because of its lack of large-scale threedimensional (i.e., model installation) effects. 

Time-averaged vorticity is used to derive what is referred to 

as the “shear-layer trajectory” in the slat cove. The notion of 

this trajectory is depicted in Figure 4.48(a), where it appears 

as a narrowband of time-averaged vorticity contours between 

the cusp and the reattachment point upstream of the trailing 

edge. Then, pictorially, the shear-layer trajectory is the curve 

segment that runs along the “center” of this band of contours, 

along a contour defined by local vorticity maxima. This curve 

segment is numerically determined by a collection of grid 

points that results from a search for local vorticity maxima, as 

directed along paths including points interior and exterior to 

the recirculation zone. The discrete distance s along the 

trajectory is determined by numerical arclength.

A comparison between the computed and measured mean 

shear-layer profiles at selected stations along the aft part of the 

shear layer trajectory is shown in Figure 4.48(b). The distance ε

in Figure 4.48(b) is measured along each of the four line 

segments (A, B, C, and D) in Figure 4.48(a) and is set to zero at 

the point of maximum mean velocity slope in the shear layer. The 

maximum slope of the computed velocity profiles agrees well 

with the measured data; however, computations underpredict the 

velocity differential across the mixing layer, again, presumably 

because of a lack of large-scale three-dimensional effects.

Contours of the measured and predicted distributions of twodimensional turbulent kinetic energy (TKE) are shown in 

Figure 4.49(a) and (b), respectively. This two-dimensional TKE

is defined by the quantity ( u′,u′ + v′,v′ ) 2 , where u′ and v′

are the Cartesian components of the two-dimensional velocity 

perturbation field, and the angular brackets represent the inner 

product operator. The peculiar “inverted λ” shape of the PIVbased contours of TKE distribution near the reattachment 

location is also captured within the three-dimensional simulation. However, in comparison with the PIV data, the computations indicate somewhat higher levels of turbulence intensity 

(Tu2D = TKE ) within the recirculation zone, as illustrated in 

Figure 4.49(c). Besides that, the TKE distribution based on the 

current three-dimensional time-accurate calculations is in good 

overall agreement with PIV data and, also, the steady-state 

predictions based on RANS calculations with a two-equation 

turbulence model active throughout the flow (i.e., including the 

cove region). The TKE from previous two-dimensional 

simulations showed significantly higher levels (Refs. 81 to 83)

than either of these results.
NASA/TP—2012-215653 94

Figure 4.46.—Instantaneous spanwise vorticity field 

downstream of leading-edge slat, based on CFL3D 

computations. (a) Planar cut resembling cove state I. 

(b) Planar cut somewhat resembling cove state II.

Figure 4.47.—Sample snapshots of leading-edge

slat spanwise vorticity field from particle imaging 

velocimetry (PIV) measurements (Ref. 35) with 

wing model configuration at 4° angle of attack in

the Basic Aerodynamic Research Tunnel (BART). 

ωz is spanwise vorticity, cs is slat chord length, and 

V∞ is aircraft speed. (a) Cove state I. (b) Cove 

state II.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 95 Chapter 4

Figure 4.48.—Time-averaged velocity magnitude profiles 

across leading-edge slat shear layer. (a) Locations

of mixing-layer profiles A through D superposed on contour of mean spanwise vorticity. (b) Comparison of 

CFL3D simulation results (based on spanwise grid) for 

locations A through D and particle imaging velocimetry 

(PIV) measurements (Ref. 35). The distance ε increases 

from left to right, along the cuts A through D.
NASA/TP—2012-215653 96

Figure 4.49.—Time-averaged two-dimensional (2D) turbulent kinetic energy TKE distribution in 

leading-edge slat cover region, where V∞ is free-stream velocity. (a) Locations of mixing-layer 

profiles A through D superposed on particle imaging velocimetry (PIV) contours. (b) CFL3D 

predictions. (c) CFL3D results compared with (PIV) measurements along profiles A through D 

(Ref. 35), where. Tu2D is the two-dimensional turbulence intensity.

In Figure 4.50, the peak two-dimensional turbulence intensity across the slat mixing layer is plotted against the distance 

s from the slat cusp along the mean shear-layer trajectory. 

Within the upstream portion of the shear-layer trajectory 

(s < 40 mm, or 1.6 in.), the measured PIV data based on a 

large field of view (f.o.v.) encompassing the entire slat cove 

indicate quite significant discrepancies with the numerical 

predictions. The relatively thin mixing layer near the cusp is 

poorly resolved by the large f.o.v. and is the likely cause of the 

observed differences. A portion of the mixing-layer evolution 

close to the slat cusp was included within a smaller f.o.v. (i.e., 

higher resolution) PIV measurement that is also included in 

Figure 4.50. The higher resolution PIV data seem to capture 

the fluctuation amplitudes near the predicted overshoot

(s ≈ 10), which is presumably associated with shear-layer 

transition from laminar to turbulent behavior. Unfortunately, 

the higher resolution data did not extend sufficiently far 

downstream to capture all of the shear-layer development.

Some preliminary insights concerning slat noise characteristics can also be gleaned from the subject computations. The 

frequency spectra of the computed pressure fluctuations at 

selected probe locations at distances between 1 and 2.5 slat 

chords away from the slat trailing edge are shown in

Figure 4.51(a). The ordinate in the figure is the frequency 

multiplied by the power spectral density PSD. With the 

frequency plotted on a log scale, the product f × PSD visually 

gives equal weighting to the energy at each frequency. Probes 

below the slat (at approximately 1.8 and 2.5 slat chords from 

the slat trailing edge) are to the rear of the overhead direction, 

whereas those above the slat (at approximately 1.1 slat chords 
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 97 Chapter 4

from the trailing edge) are in the forward arc. The acoustic 

spectra across the range of frequencies plotted in the

figure closely resemble the spectrum of pressure fluctuations 

near the reattachment location, emphasizing the prominence of 

this region in contributing to the slat’s broadband noise 

sources. The peak Strouhal number of the acoustic spectra

in Figure 4.51(a) lies within the Strouhal number range,

1 ≤ St ≤ 3, similar to the previous measurements of subscale 

high-lift configurations (Ref. 81). Beyond this peak (up to 

about 14 kHz), the rolloff in the computed acoustic spectra is 

not unlike the 1/f

2 decay predicted by Guo’s analytical model 

(Ref. 50). However, simulations on a domain of greater 

spanwise extent would be required to confirm this highfrequency rolloff.

Based partly on experimental measurements, Dobrzynski 

and Pott-Pollenske (Ref. 81) modeled the directivity of the 

broadband slat noise sources as that of an acoustic dipole that 

is normal to the slat surface near the trailing edge 

(Figure 4.51(b)). The orientation of the computed contours of 

the instantaneous pressure perturbations (Figure 4.51(c)) 

resembles the near-field propagating pressure waves from an 

acoustic dipole. However, far-field predictions are necessary 

to enable definitive comparisons with the above model, 

particularly in view of the multiple acoustic conversion 

mechanisms relevant to slat noise generation, such as scattering near the slat trailing edge and the gap region.

In summary, the favorable comparison with the planar PIV 

data represents a substantial improvement over previous twodimensional computations (Refs. 78 to 80), revealing the 

importance of three-dimensional fluctuations in determining

Figure 4.50.—Peak two-dimensional turbulent intensity 

Tu2D along leading-edge slat cove mixing-layer

trajectory versus distance s from slat cusp.

Comparison of CFL3D Tu2D based on coarse (S1) 

and fine (S2) spanwise grids and particle imaging 

velocimetry (PIV) measurements derived from small 

and large fields of view (f.o.v.) (Ref. 35).

Figure 4.51.—Acoustic radiation due to leading-edge

slat cove unsteadiness. (a) CFL3D-computed acoustic 

spectra (product of frequency f and power spectral 

density PSD) at selected probe locations between one 

and two chords from trailing edge noting point at 

Strouhal number St = 2, where cs is slat chord length 

and V∞ is free-stream velocity. (b) Schematic for

slat noise model in Reference 81. (c) Contours of

instantaneous pressure perturbations from finespanwise-grid simulation.
NASA/TP—2012-215653 98

the unsteady dynamics within the cove region. The computed 

acoustic characteristics (in terms of the frequency spectrum and 

spatial distribution) within short distances from the slat 

resemble the previously reported, subscale measurements of slat 

noise (Ref. 81). 

4.8.4 Recommendations

A more definitive assessment of the computational model 

will be enabled by acoustic measurements of the same 

configuration. Furthermore, additional measurements of the 

slat cove flow including the surface pressure fluctuations, 

especially just upstream of the slat trailing edge where the slat 

cove shear layer reattaches to the slat pressure surface, would 

be a crucial factor in evaluating the accuracy of both the 

computed frequency spectra and the spanwise coherence of 

the broadband noise sources in this acoustically significant 

region. Spanwise distribution of the acoustic sources has a 

direct impact on the far-field acoustic intensity, as the 

intensity is proportional to the spanwise coherence length.

Off-surface measurements using a hot wire would help 

overcome the limited spatial resolution of the current PIV 

data, especially near the slat cusp, and will also provide an 

additional means of validating the frequency spectra of 

computed fluctuations. Acquisition of three-dimensional PIV 

data across selected spanwise planes will contribute to a more 

complete assessment of the near-field computations by 

elucidating the spanwise structure of the slat flow fluctuations. 

After demonstrating that the relevant metrics of the

unsteady slat cove flow can be adequately predicted with such 

numerical simulations, the latter can be used to complement 

the typically sparse flow-field details available from experimental measurements. The simulation data can be used to 

develop and calibrate models for the spatio-temporal correlations used in low-order physics-based methods for airframe 

noise prediction. A promising approach of this type would 

involve the modeling of an acoustic source with fluctuation 

metrics derived from a stationary RANS computation along 

with a suitable model for the appropriate coherence functions. 

The sound can then be propagated to the far field by some 

method of choice; for example, by applying an acoustic 

analogy to a tailored Green’s function (Ref. 82), or solving the 

linearized Euler equations (Ref. 83).

A major drawback of the computation used during the 

present assessment corresponds to the limited spanwise extent 

of the computational domain. Appropriately validated 

computations of this type can still be used, even in their 

present form, to help refine the lower-order models for noise 

prediction (Refs. 82 and 83) and/or to help develop physicsbased noise reduction concepts. However, it is still desirable to 

extend such computations to larger spanwise domains, so that 

reliable acoustic predictions can be made without requiring

additional ad hoc assumptions. Increasing the computational 

efficiency by resorting to high-order accurate, yet robust, flow 

solvers (e.g., Ref. 84) should help accelerate the accomplishment of that goal; again, it is imperative that resource 

investment be made in this area.

There are two additional complications to the physics of 

slat-noise generation that must be investigated. One such 

complication can result from the wing’s leading-edge sweep, 

which could contribute to a spanwise velocity component that 

is large relative to that of the slat-cove flow in the plane 

normal to the leading edge. When this occurs, the cove flow 

no longer continually recirculates within the cove region 

(Figure 4.47(a)), and instead traverses a helical path to the 

outer tip of the slat. Such a phenomenon suggests that the flow 

in the cove shear layer is highly skewed, which could 

influence the structure of the fluctuations generated therein. 

Secondly, the potential effects of support brackets must be 

considered. In particular, the interaction of a strong spanwise 

cove flow with a bluff-body-like bracket geometry could have 

a measureable impact on slat noise radiation.

4.9 Conclusions

An investigation is undertaken to assess the current capability to predict airframe noise levels for aircraft that are 

configured for airport approach. During landing operations, 

the leading-edge slats and trailing-edge flaps of the aircraft’s 

high-lift system as well as the landing gear are the primary 

sources of airframe noise. The present assessment includes 

far-field predictions for these airframe components and their 

validation with experimental measurement. The test cases are 

chosen from previously identified experiments involving wind 

tunnel models as well as from flight testing of operational 

aircraft. In most of these cases, the generation and propagation 

of airframe noise are predicted with NASA’s Aircraft Noise 

Prediction Program (ANOPP). The remaining predictions are 

from first principles, in which the acoustic source is simulated 

by computational fluid dynamics. Although such methods 

cannot be considered practical prediction tools, the wealth of 

detailed information they yield regarding the physics of 

airframe noise sources can provide insight into the development of the next generation of prediction tools. 

Assessment metrics are defined to quantify the extent to 

which the computations and measurements are reliable and 

compare favorably. Predicted and measured results are 

subjected to various analyses to determine parametric ranges 

of applicability for each of the applied techniques. As the 

source models within ANOPP are largely empirical, comparisons of predictions with measurements of both total airframe 

noise and the noise from individual components ranged from 

acceptable to poor. For instance, in Section 4.4, “Flap-Edge 

Noise Measurement and Prediction,” Fink’s method was 

unable to adequately predict the noise increment due to an 

altered flap deflection (Figure 4.13). In Section 4.5, 

“Aeroacoustic Measurement and Prediction for Boeing 777 

Landing Gear Model,” both Fink’s and Boeing’s landing-gear 

source models were found lacking in regard to their insensitivity to the presence of a bay door (Figure 4.21). 

However, as stated by Gillian (Ref. 85), ANOPP’s primary 

function is “to predict aircraft noise with the best currently 

available methods.” Furthermore, the notion of a “best” 
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 99 Chapter 4

available method is predominantly influenced by the ability to 

use that method in a highly efficient manner. As of this 

writing, all such methods are based upon lower-order models 

and heavily reliant upon empiricism. Therefore, ANOPP (or 

any other present-day noise prediction tool) cannot be 

expected to provide design-level information on a case-bycase basis. Rather, ANOPP’s primary benefit lies in its ability 

to determine overall noise trends for full aircraft studies.

Nonetheless, such disappointing results as those cited above

indicate that the next generation of prediction methods must 

be responsive, in a fundamental way, to any geometric 

variation that alters the unsteady flow field. Also indicated is a 

need to pursue empirical relationships on a more basic level 

than previously investigated. Recommendations to achieve 

such advances in the present state of the art are given below.

4.10 Recommendations

The methods discussed within this chapter fall under the 

general classification of empirical prediction, wherein little 

information regarding the details of the actual physical 

processes that generate the noise is incorporated and predictions are based on correlations of experimental data. Although 

useful for rapid predictions in current engineering environments, the inability of the methods to predict even the change 

in noise due to an altered flap deflection—a most basic 

engineering parameter variation—demonstrates that such 

methods are not only prone to failure but also that an engineer 

may not know when the prediction is likely to fail.

Research in noise prediction methods must increasingly 

focus on utilizing more detailed descriptions of the noisegenerating physics. Examples of the development of such 

descriptions are discussed in References 86 to 88, involving 

coordinated experimental and computational studies on a range 

of simple geometries (called building-block problems). Indeed, 

the computational tools discussed in this chapter form a major 

component of such studies, but significant improvements are yet 

required for these tools to reliably and efficiently predict all 

required mechanisms of noise generation.

For engineering predictions, however, one can envision 

semiempirical tools, wherein the empiricism corresponds to 

aerodynamic noise sources on a more fundamental level. As 

an example, if empirical correlations could be developed for 

the noise amplitude and spectrum with respect to a set of 

generic flow-field features (e.g., the vorticity distribution of a 

shear layer in a separated flow), then such a semi-empirical 

method could begin with a computation of the steady flow 

field about the flap edge of a wing design under investigation. 

This computed flow field would then be examined for the 

corresponding correlation variables, and the noise predicted. 

The sensitivity of the noise prediction to engineering parameters would thus be contained in the computation of the steady 

flow field.

The suggested development effort requires a coordinated 

deployment of advanced experimental and computational tools 

in a series of fundamental studies that are carefully chosen and 

conducted, and for which sufficient time and resources are 

allotted. In order to make significant progress in the ability to 

accurately predict airframe noise for a wide range of configurations and flow conditions, it is clear that sufficient resources 

be invested in advancing the state of the art for numerical 

simulation and measurement of the unsteady flow fields that 

generate airframe noise. Specific recommendations include

1. Intensify development of numerical simulation tools, 

including Reynolds averaged Navier-Stokes (RANS), 

unsteady RANS (URANS), large-eddy simulation (LES), 

detached-eddy simulation (DES), and appropriate hybrids 

thereof. In addition, an efficient method for constructing 

tailored Green’s functions should be developed. RANS and 

tailored Green’s function development combined with 

improved models for the space-time coherence of the acoustic 

source would enable relatively rapid, medium-fidelity airframe 

noise predictions that could be calibrated and augmented using 

higher-fidelity, hybrid RANS/LES computations.

2. Continue development of hardware and processing 

methods for phased arrays and related measurement technologies, with such goals as higher sensor count, greater efficiency, and lower cost. Such development should include 

improvement to beamforming, deconvolution, and coherence 

detection algorithms, advanced methods to account for 

reflections and flow diffraction, and parallel distributed 

processing of array signals for real-time presentation of noise

levels and directivity. Ideally, such methods should be capable 

of simultaneous, nonintrusive measurement of fluctuating flow 

fields associated with multiple noise sources.

3. Conduct a portfolio of fundamental, “building-block” 

numerical simulations, in conjunction with detailed multiinstrumented experiments. Such a program is intended to 

generate an archival database of space-time correlation 

functions for flow-field fluctuations associated with aerodynamic noise sources, for eventual use in advanced prediction 

methods.

4. Intensify pertinent research in such areas as flow control, 

circulation control, and morphing structures to facilitate the 

development of noise reduction technology.

In closing, it is timely to comment on the outlook for 

extending the present prediction methodology beyond the 

realm of conventional aircraft configuration. At first glance, 

such an outlook is a contradiction in terms, as noted by 

Whitfield (Ref. 89):

Current aircraft system noise prediction tools (such 

as ANOPP) rely on current knowledge. Their ability 

to extrapolate to unconventional configurations is not 

to be trusted.
NASA/TP—2012-215653 100

Nonetheless, the aeroacoustic research community increasingly looks to unconventional aircraft to achieve long-term 

noise reduction goals. As stated by Posey, et al. (Ref. 90), with 

direct relevance to non-engine aircraft noise,

. . . as jet noise has decreased, noise from the fan and 

other engine components, as well as from flow over 

the airframe, has become unmasked, making further 

noise reduction much more difficult. Thus, a very 

large reduction in community noise due to an aircraft 

flyover will probably require an unconventional aircraft design that relies not only on a quiet engine 

design, but also on propulsion/airframe integration 

that minimizes noise production and shields the 

ground from the residual noise.

Such is the apparent conundrum, given the necessity to 

develop tomorrow’s quiet aircraft through unconventional 

design, while available noise prediction tools are presently 

unfit for the task. Clearly, methods that bring more of the 

physics into the prediction, and rely less on low-order 

modeling, are more extensible to unconventional configurations. However, only direct numerical simulation methods 

avoid modeling altogether. Every other methodology is 

limited by either the experimental database on which it is 

calibrated or the model itself, when physical attributes are not 

determined from first principles. For the foreseeable future, 

direct numerical simulation will not be a viable option due to 

its unacceptable consumption of computational resources 

when applied to problems involving turbulent flow on a fullscale aircraft. Therefore, more fundamental approaches to 

model development, such as those based on judiciously chosen

“building blocks” (Recommendation 3 above), will be the 

primary means of improving prediction accuracy and extending the methodology to unconventional configurations.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 101 Chapter 4

Appendix A.—Nomenclature

A.1 Acronyms

ANOPP Aircraft Noise Prediction Program

AST Advanced Subsonic Transport (Program)

BART Basic Aerodynamic Research Tunnel 

CFD computational fluid dynamics

DES detached-eddy simulation

FAA Federal Aviation Administration

FAP Fundamental Aeronautics Program

f.o.v. field of view

FW–H Ffowcs Williams-Hawkings

LES large-eddy simulation

LTPT Low-Turbulence Pressure Tunnel

MADA Medium Aperture Directional Array

PIV particle image velocimetry

PSD power spectral density

QAT Quiet Aircraft Technology (Program)

QFF Quiet Flow Facility

RANS Reynolds-averaged Navier-Stokes

rms root-mean-squared

SADA Small Aperture Directional Array

SST shear stress transport (model)

SFW Subsonic Fixed Wing (project)

SPL sound pressure level

TKE turbulent kinetic energy

URANS unsteady Reynolds-averaged Navier-Stokes

WFF Wallops Flight Facility

A.2 Symbols

a speed of sound

A planform area 

AG empirically derived constant in Equation (4.28), 

Appendix B

BG empirically derived constant in Equation (4.28), 

Appendix B

b span length 

C coefficient (e.g., pressure coefficient) 

c chord length

D diameter 

D directivity function 

d aircraft tire diameter 

F noise spectrum function 

Fxyz computational mesh with fine grid-point spacing in 

x,y,z-coordinates

f frequency 

K constant in Equation (4.19), Appendix B

L length 

L total length of all main struts

l strut length 

M Mach number 

Mxyz computational mesh with medium-level grid-point 

spacing in x,y,z-coordinates

MxyFz computational mesh with medium-level grid-point 

spacing in x,y-coordinates

and fine grid-point spacing in z-coordinate

n number of wheels on aircraft 

P spectral component of acoustic pressure in Equations (4.24) and (4.25), Appendix B

p aerodynamic pressure 

PSD power spectral density 

q empirical constant from Equation (4.28), Appendix B, 

that defines spectral shape 

R source-to-observer distance 

Re Reynolds number 

S aggregate surface-integration-effects parameter in 

Equation (4.25), Appendix B

St Strouhal number 

s distance along slat shear layer trajectory 

TKE turbulent kinetic energy 

Tu turbulence intensity 

t time 

u,v velocity components in the x- and y-directions

V velocity 

W aircraft maximum takeoff gross weight 

x, y, z Cartesian coordinates, in the streamwise, spanwise, 

and normal directions, respectively 

α quantity from Equation (4.27), Appendix B

β flow energy conversion efficiency parameter in 

Equation (4.25), Appendix B

γ empirically derived constant in Equation (4.28), 

Appendix B

δ boundary layer thickness 

ε distance across shear layer

η complexity factor, Equation (4.26), Appendix B

θ polar angle 

μ dynamic viscosity 

Π acoustic power 

ρ density of air 
NASA/TP—2012-215653 102

σ empirically derived constant in Equation (4.28), 

Appendix B

φ azimuthal angle 

ω vorticity

∂ deflection angle

Subscripts:

e emission 

f flap 

H high-frequency component 

h horizontal tail surface 

L low-frequency component 

M mid-frequency component 

O overall 

p pressure 

ref reference 

s slat

t tandem cylinder 

v vertical tail surface 

w wing 

z z-axis component 

2D two-dimensional 

∞ aircraft or free stream 

Superscripts:

* normalized (nondimensional) 

′ perturbation quantity
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 103 Chapter 4

Appendix B.—Aircraft Noise Prediction Program

Most of the acoustic predictions in the present work are 

obtained with semi-empirical methods in the Aircraft Noise 

Prediction Program (ANOPP) (Ref. 42). ANOPP was 

developed for general aircraft noise prediction, including the 

effects of an aircraft’s characteristics, engines, and operations 

as well as atmospheric and ground effects. As such, ANOPP is 

organized into modules that account for the flight operation of 

interest, describe the source-to-observer geometry, model the 

required noise-generating mechanism(s), propagate the noise 

through the atmosphere, and calculate the quantity of the noise 

received by the observer. Two airframe noise modules are 

available in ANOPP, each containing several component 

source models that can either be applied in isolation or 

summed to compute the total nonpropulsive noise for a given 

aircraft configuration. Only those airframe source models that 

are used in the present test cases are described below in a 

straightforward manner, with minimal discussion of theory or 

development. For a more thorough discussion of all available 

airframe noise source models, see Reference 42.

B.1 ANOPP: Fink’s Method

The earlier of the two airframe noise modules in ANOPP 

contains acoustic source models developed by Fink (Ref. 32) 

for the Federal Aviation Administration (FAA). In Fink’s 

“noise component method,” total airframe noise is calculated 

as an acoustic sum of component sources. It is, therefore, 

assumed that all component sources are mutually incoherent. 

In the development of his model, Fink formulated the noise 

contribution for each airframe component with an appropriate 

scaling law, and determined amplitudes by matching available 

experimental data. 

In ANOPP, the far-field noise associated with an airframe 

component source is computed in terms of a nondimensional, 

mean-square acoustic pressure. All of Fink’s component 

models can be expressed in the general form

2 4

2

(1 M cos )

( , ) (St)

4 − θ

θ φ

π

Π = ∗ ∞

∗ ∗ F

R

p

D (4.1)

In Equation (4.1), Π* is a nondimensional acoustic power, D

is a directivity function, F is a spectral shape function, and M∞

is the aircraft Mach number. The nondimensional variable R*

represents the physical propagation distance R normalized by 

the aircraft wingspan, and θ and φ represent the polar and 

azimuthal directivity angles, respectively; these dimensions 

are illustrated in Figure 4.2 (see Sec. 4.2.2). The argument St 

is a Strouhal number, defined by

= ( − ∞ θ) ∞ ∞1 M cos

M

St

a

f L (4.2)

where f is frequency, a∞ is the ambient sound speed, and L is a 

characteristic length scale of the airframe noise source. Note 

that the independent variables in Equations (4.1) and (4.2) are 

interpreted with respect to the visual position of the aircraft at 

signal emission time.

A prediction for an aircraft’s total airframe noise is ultimately a sum of the mean-square pressures, in Equation (4.1), 

that correspond to the individual airframe components 

described in the following three subsections. Although the 

methodology is presented within a nondimensional framework, the output from ANOPP is easily directed either to 

mean-square acoustic pressure in English or SI units or to a 

sound pressure level (SPL) in decibels, relative to a suitable reference pressure.

B.1.1 Clean Airframe Noise

The lower limit of an aircraft’s airframe noise is generated 

by its “clean” (cruise) configuration. In Fink’s method, the 

noise radiated by a “clean airframe” is composed entirely of 

trailing-edge sources; that is, those of the wings and tail 

surfaces. The theoretical basis for Fink’s clean airframe noise 

model is attributed to the trailing-edge noise analyses in 

References 91 and 92. For a conventionally constructed 

aircraft, the acoustic power associated with the wing’s trailingedge noise is

( ) * 5 M5 * Π = 4.464×10 ∞ δw − (4.3)

where * δw is a normalized boundary-layer thickness at the 

trailing edge, determined by a turbulent flat-plate model,

1/5

2

*

M

0.37 



 





ρ

μ δ = ∞ ∞ ∞

∞

w

w

w

w w a A

b

b

A (4.4)

The quantities Aw and bw are the area and span of the wing, 

respectively, while ρ∞ and μ∞ are the respective density and 

dynamic viscosity of the ambient medium.

The trailing-edge acoustic power for a horizontal tail surface (h) is similar to that of a clean wing,

( )

2

5 M5 * 4 464 10 



 



 Π = × ∞ δ ∗ −

w

h

h b

b . (4.5)

1/5

2

*

M

0.37 



 





ρ

μ δ = ∞ ∞ ∞

∞

h

h

h

h

h

a A

b

b

A

(4.6) 

The symbols * δh , Ah, and bh correspond to the horizontal

tail surface in the same way as their wing counterparts in 

Equations (4.3) and (4.4). The noise directivity function for 

the wing or horizontal tail surface is given by
NASA/TP—2012-215653 104

( , ) 4 cos cos ( 2) 2 2 D θ φ = φ θ (4.7)

Following the symbolic convention in Equations (4.3) to 

(4.7), the acoustic power formulation for a vertical tail surface 

(v) is

( )

2

5 M5 * 4.464 10 



 



 Π = × ∞ δ ∗ −

w

v v b

b (4.8)

1/5

2

*

M

0.37 



 





ρ

μ δ = ∞ ∞ ∞

∞

v

v

v

v v a A

b

b

A (4.9)

Because of its perpendicular orientation with respect to the 

planes of the wing and horizontal tail surfaces, the noise 

directivity function for a vertical tail surface is

( , ) 4 sin cos ( 2) 2 2 D θ φ = φ θ (4.10)

For conventionally constructed aircraft, the spectral shape 

function F(St) for trailing-edge noise associated with a clean 

airframe component is 

( )

4

1.5 10St 0.5

10St (St) 0.613

















+

F = (4.11)

( − θ) δ = ∞

∞ ∞

1 M cos

M

St *

a

f b (4.12)

where the values of the span b and the boundary layer 

thickness δ* correspond to any one of the three clean airframe 

components discussed above. Equations (4.3) to (4.12) yield 

the necessary input to Equation (4.1) to compute the far-field, 

mean-square acoustic pressure for each clean airframe 

component. A prediction for the total noise associated with the 

clean airframe is produced by summing these individual 

mean-square pressures.

B.1.2 Trailing-Edge Flap Noise 

Unlike the leading-edge slats, the additional noise radiated 

by the extension of trailing-edge flaps is not directly related to 

the clean wing noise. Instead, Fink regarded the flap panels as 

immersed in the turbulent wake of the main wing element and 

any additional upstream flap elements. Thus, trailing-edge flap 

noise is interpreted as the result of unsteady lift fluctuations 

due to incident turbulence. This model was entirely determined by scaling and curve-fitting available flight data 

(Refs. 5, 7, and 93). 

For a flap system (f) with one or two slots, the additional 

acoustic power can be expressed as

( ) f

f

f

b

A

Π = × ∞ ∂ ∗ − 2

2

4 6 2.787 10 M sin (4.13)

where Af, bf, and ∂f are the flap’s area, span, and deflection 

angle, respectively. The spectral shape for a system of singleor double-slotted flaps is described by the piecewise continuous function,





















>

≤ ≤

<

=

−

−

216.49 St (St 20)

0.1406 St (2 St 20)

0.0480 St (St 2)

(St)

3

F 0.55 (4.14)

For triple-slotted flaps, the overall acoustic power is

( ) f

f

f

b

A

Π = . × ∞ ∂ ∗ − 2

2

4 6 3509 10 M sin (4.15)

which represents an increase in power by 1 dB to account for 

the added flap complexity. The piecewise spectrum function 

for triple-slotted flaps is





















>

≤ ≤

<

=

−

−

17 078St (St 75)

0.0536St (2 St 75)

0.0257St (St 2)

(St)

3

F 1/16 (4.16)

For either trailing-edge flap case, the Strouhal number and 

noise directivity function are, respectively,

= ( − ∞ θ) ∞ ∞

1 M cos

M

St

f

f

a b

f A (4.17)

(θ,φ) = 3(sin ∂ cosθ + cos∂ sin θcosφ) D f f (4.18)

With the appropriate acoustic power and spectrum function 

from one of Equations (4.13) through (4.16), and the directivity 

in Equation (4.18), the flap’s contribution to the far-field 

acoustic pressure is then calculated with Equation (4.1).

B.1.3 Landing Gear Noise

The development of a general noise model for an aircraft’s 

landing gear is a particularly daunting task. The geometry of a 

given landing gear can be quite complex, containing many parts 

that vary significantly in shape, size, and flow orientation. 

Fink’s landing gear noise model is heavily reliant upon the 

experimental work of Heller and Dobrzynsky (Ref. 94). For 

instance, Fink incorporates the same Strouhal scaling, in which 

the landing gear tire diameter is chosen as the characteristic 

length scale. Heller and Dobrzynsky justified this scaling by 

noting “fairly constant” ratios of the tire diameter to the strut 

diameter, exposed strut length, wheel lateral spacing, and
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 105 Chapter 4

tire width, for landing gear on certain classes of aircraft 

(Ref. 94). Also, Fink’s model does not account for cavity 

noise due to landing gear bay doors remaining open, because 

the results in Reference 94 suggested that the noise radiated by 

an isolated cavity was mostly overwhelmed by that of the 

landing gear itself. Finally, Fink used the measured spectra in 

Reference 94 as a starting point for his own formulation, and 

approximated them with arbitrary empirical equations. Fink’s 

formulation, described below, is based on a characterization of 

the landing gear noise spectrum as the sum of two spectra, one 

representing a noise source that is independent of the azimuthal angle φ and another that varies as sin2

φ. Thus, Fink 

concluded that the prediction process for landing gear noise 

could be reasonably simplified by assuming that only two 

noise sources were significant: those arising from the wheels 

and the struts. 

In Fink’s airframe noise component method, the wheels and 

the strut of a landing-gear assembly each radiate an individual 

acoustic power, according to 

2

* 6 wheels M 













 Π = ∞ bw

d K n (4.19a)

d

l

b

d

w

2

* 4 6

strut 2.753 10 M 













 Π = × ∞ − (4.19b) 

where n is the number of wheels per landing gear, d is the tire 

diameter, and l is the strut length. The constant K is 4.349×10–4

for n = 1 or 2, and 3.414×10–4 for n = 4. Note that the ratio of 

exposed strut length to tire diameter is included in Equation (4.19b) to better predict noise from landing gear that may be 

significantly outside the presumed aircraft class; for example, 

those with a long-strut nose gear or a short-strut tail wheel. The 

directivity functions for the wheels and strut noise are

θ φ = θ2 wheels sin

2

3 D( , ) | (4.20a)

θ φ = θ φ 2 2 strut D( , ) | 3 sin sin (4.20b)

For one- or two-wheel landing gear, the wheel and strut 

noise spectra can be written

2 9 /4

2

wheels (St 12.5 )

13.59St (St) |

+

F = (4.21a)

St 30

5.325St (St) | 8

2

strut +

F = (4.21b)

while the corresponding spectra for a four-wheel landing gear 

are

2 3/ 2

2

wheels ( 0.25St 1 )

0.557St (St) |

+

F = (4.22a)

3

2 strut St 1.06

1.280St (St) | 



 





+

F = (4.22b)

The Strouhal number, in Equations (4.21) and (4.22) is 

referenced to the tire diameter:

= ( − ∞ θ) ∞ ∞1 M cos

M

St

a

f d (4.23)

The appropriate wheel and strut noise contributions are 

individually input to Equation (4.1), and then summed to 

compute the mean-square acoustic pressure for the landing 

gear in the far field.

B.2 ANOPP: Boeing’s Method, Landing Gear 

Noise

More recent airframe noise models (Refs. 43 and 44) have 

been developed by The Boeing Company and are incorporated 

into a separate ANOPP module. In some respects, Boeing’s 

approach to airframe noise is similar to Fink’s. Most importantly, the total noise is calculated as a sum of componentwise noise contributions that are generated by mutually 

incoherent sources. In addition, experimental measurement 

plays a critical role in Boeing’s semi-empirical method. 

However, the process and formulations are significantly 

different, as will become apparent below.

The application of Boeing’s airframe noise model in the 

present assessment involves the prediction of acoustic spectra 

for a model-scale Boeing 777 main landing gear. The relatively 

sparing use of this ANOPP module within the present assessment is, in part, due to difficulties with its implementation. 

These difficulties have arisen largely in two areas: unavailability of required input parameters and scaling issues, when 

wind tunnel models are involved (See Sec. 4.5.2, “Results and 

Findings.”). Therefore, these models will need to be reconsidered at a later date to determine their full effectiveness. 

Boeing’s landing gear noise model, developed by Guo 

(Ref. 44), is based on fundamental aerodynamic noise theory, 

statistical scaling laws derived from the theory, and correlations of these laws with full-scale landing gear noise tests. The 

method decomposes the landing gear noise into three spectral 

components. The low-frequency spectral component represents the noise generated by large-scale structures such as 

wheels. The mid- and high-frequency spectral components 

correspond to the main struts and the small-scale details such 

as hydraulic lines, respectively. The spectral shape, amplitude, 

and directivity of each component were derived separately, 

and each contains factors to allow modeling of the details of

each spectral component in an attempt to include more
NASA/TP—2012-215653 106

physics. The Boeing-Guo method requires significantly more 

detailed information to define the landing gear assembly than 

does Fink’s method, thus providing a higher fidelity prediction 

capability. These inputs include all the basic flow and 

geometric parameters used in Fink’s model: the number of 

wheels, wheel diameter, and main strut length. In addition, the 

Boeing-Guo model requires the wheel width, axle diameters, 

bogie length and width, as well as details on all other struts, 

shock struts, vertical bars, axles, torque bars, junction rods, 

and door details. Furthermore, and more importantly unlike 

Fink’s model, the Boeing-Guo model was developed in terms 

of a narrow-band spectrum, which is converted to 1/3 octaves 

as the last step. This has ramifications regarding frequency 

scaling as will be indicated later. The general form of the farfield, mean-square acoustic pressure formulation is

( M H ) L

e e

O e P P P

R

a

p + + − θ

ρ θ =

∞

∞ ∞

4 2

2 4 6

2

( 1 M cos )

M D ( ) (4.24)

where the parameters common to all three spectral components have been factored out, and those specific to a particular 

component are represented by the P terms. The subscripts L,

M, and H denote the low-, mid-, and high-frequency components, respectively. The overall directivity DO(θe) is in 

addition to the directivity function defined within each P term 

and is included to account for the effects of the landing gear 

installation. The propagation distance Re and angle θe are 

defined in Figure 4.18. To simulate wind tunnel conditions, 

the factor (1–M∞ cosθe)

4 is required to account for convective 

amplification, but was erroneously excluded from the method 

(Ref. 95). This factor has been incorporated for the predictions 

reported herein. Each P takes the form

P S ( , )F(St) = β D θe φe (4.25) 

where β is the flow energy conversion efficiency parameter, 

which models the efficiency of the process whereby the steady 

flow motion of the landing gear parts generates unsteady flow 

that radiates noise. Currently, this parameter can only be 

determined by matching prediction with data. In Equation (4.25), S is the aggregate surface-integration-effects 

parameter and is related to the aggregate surface area of the 

landing gear parts for each frequency component. For the lowfrequency component it is computed directly from the wheel 

dimensions. For the mid-frequency component it is computed 

by summing the surface areas of all main strut elements. For 

the high-frequency component, that approach is not practical 

because of the large number of small parts, which have 

various shapes and orientations. Hence, SH is modeled using 

an empirically defined length scale and “complexity factor” η

which has the following form for a main landing gear:





 





η = 1+ 0.15 − 1

ref ref nref

n

W

W

L

L

(4.26)

The terms W, L, and n are the maximum takeoff gross weight 

of the aircraft, the total length of all the main struts, and the 

number of wheels, respectively. The subscript “ref” indicates 

reference values, determined from full-scale data (Ref. 59). 

The functions D(θe,φe) and F(St) are the component specific 

directivity and spectrum functions, respectively. The general 

form of the directivity function is

( , ) (1 cos ) (1 sin ) 2 2 2 2 D θe φe = + α1 θe + α φe (4.27)

where α1 and α2 are unique for each of the three frequency 

domains. The values for the low-, mid-, and high-frequency 

domains, respectively, are α1 = (0.2, 0.6, 1.0) and α2 = (3.0, 

2.0, 0.1). The spectrum function F(St) is a narrowband power 

spectral density function and has the following form:

q G

G B

F A

( St )

St (St) γ

σ

+ = (4.28) 

where σ, γ, and q are empirical constants that define the spectral 

shape; and AG and BG are derived constants that set the peak 

value of the spectrum to unity at an empirically derived Strouhal 

number or the peak Strouhal number. For each of the three 

frequency-component spectra, a unique set of σ, γ, q, AG, and 

BG was determined for each peak Strouhal number by analyzing 

full-scale test data (Ref. 95). The Strouhal number St is 

determined using the characteristic length scale associated with 

the frequency range for which F(St) is being evaluated. The 

characteristic length scale for the low-frequency component 

spectrum is the wheel diameter; whereas, the characteristic 

length scale for the mid- and high-frequency component spectra 

are computed using the aggregate surface area parameter, an 

average length, and an empirical scale factor. Complete details 

on the development of these factors and parameters are fully 

documented in References 59 and 95.

Because F is defined as a narrowband spectral function, its 

shape is not invariant with respect to St, which undercuts the 

generality of using Strouhal scaling on which it is based. This 

effect, combined with the empirical function η used to define 

SH, makes the Boeing-Guo method, at present, only appropriate 

for full-scale landing gear. However, the model does attempt to 

incorporate as much physics as possible to reduce configuration 

dependence, but does not eliminate empiricism. Note that this 

method compares very well with full-scale landing gear 

measurements (Refs. 44 and 95) and is considered an improvement over existing semi-empirical prediction capabilities for 

full-scale Boeing 737 and 777 landing gear predictions. 
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 107 Chapter 4

Appendix C.—CFL3D and Acoustic Analogy

The acoustic predictions for the tandem cylinders and the 

simplified landing gear model in Sections 4.6 and 4.7, respectively, are modeled from first principles, beginning with the 

fundamental theory of aerodynamic sound proposed by 

Lighthill (Ref. 96). With the introduction of his “acoustic 

analogy,” followed by important extensions to solid surfaces 

(Ref. 96) in arbitrary motion (Ref. 47), Lighthill established a 

philosophy by which the noise associated with most problems 

of interest could be accurately predicted, provided that the 

“equivalent forces” and stresses representing the sources of 

sound could be accurately modeled. Within this approach to 

noise prediction, the objective is to model the actual flow 

mechanisms that give rise to the sources and propagation of 

radiated sound, thereby leading to the simulation of these 

sources with solutions of an appropriate set of fluid dynamics 

equations (e.g., unsteady Reynolds-averaged Navier-Stokes 

(URANS), large eddy simulation (LES), etc.). Such methods 

cannot presently be considered practical prediction tools, due to 

the turnaround times involved in their application. However, the 

wealth of detailed information they yield regarding the physics 

of airframe noise sources can provide insight into the development of the next generation of prediction tools.

Despite continued advances in computational resources and 

numerical algorithms, it is still prohibitively expensive, and 

often infeasible, to attempt to resolve wave propagation from 

near-field sources to far-field observers. Integral techniques 

that can predict the far-field signal based solely on near-field 

input are a means to overcome this difficulty. Here, the 

Ffowcs Williams-Hawkings (FW–H) equation (Ref. 47) 

solvers described by Lockard (Ref. 66) are used to predict the 

acoustic signature at various observer locations using unsteady 

flow data from the computational fluid dynamics (CFD) 

calculation. The FW–H equation is a rearrangement of the 

exact continuity and Navier-Stokes equations into a form with 

a wave equation on the left-hand side and a number of source 

terms on the right. Hence, the Navier-Stokes equations still 

need to be solved to determine the values for the source terms, 

but only where nonlinear and viscous effects are important; all 

of the linear propagation outside of this region can be 

determined by the FW–H equation. The solution to the FW–H 

equation is typically obtained using the free-space Green’s 

function. The resulting solution requires a surface integral and 

a volume integral over all space outside of the surface, but the 

solution is often well approximated by the surface integral 

alone. To perform the integrations, the time histories of all the 

flow variables are needed, but no spatial derivatives are 

explicitly required. The FW-H method has typically been 

applied by having the integration surface coincide with solid 

bodies, but the method is still applicable when the surface is 

off the body and penetrable. The codes used in this work are 

valid for both cases.

Certain flows exist where the volume integral cannot be 

ignored, such as those containing significant refraction of 

waves by shear layers and wakes or direct radiation of sound 

by turbulence. As long as the integration surface is placed 

outside of all regions where the volume source terms are large, 

the volume integral contribution can be neglected. In airframe 

noise problems where the flow speed is generally around 

Mach 0.2, most of the noise is generated by the interaction 

unsteadiness with solid surfaces. Refraction and the direct 

generation of noise by turbulence are generally much smaller 

effects. However, the common practice is to ignore the volume 

integral but compare the FW–H noise predictions obtained 

using the solid body as a surface with those from surfaces at 

varying distances away from the body. The predictions should 

agree if the volume source terms are negligible and the 

underlying CFD is sufficiently accurate. In addition, calculations using penetrable data surfaces are subject to additional 

sources of error caused when nonacoustic disturbances pass 

through the surface. Whether the error can be ignored is 

problem dependent and difficult to formally prove. However, 

the true radiated sound from airframe noise problems is often 

much larger than that of the spurious signal generated by 

disturbances passing through penetrable surfaces. Singer 

(Ref. 98) and Brentner and Farassat (Ref. 99) have shown that 

for different surfaces in the near field of solid bodies, the 

FW–H correctly calculates the radiated sound, whereas the 

linear Kirchhoff method produces erroneous results. Nonetheless, a rigorous description of the error incurred when wakes 

pass through penetrable FW–H surfaces is needed.

For three-dimensional flows with arbitrary motion, the timedomain FW–H formulations developed by Farassat (Ref. 100) 

are efficient and amenable to numerical computations. In 

retarded time formulations, the time of reception is known, and 

the time of emission is calculated. For arbitrary motion, the 

retarded time calculation requires a numerical root-finding 

technique. Alternatively, source time algorithms start with the 

source or emission time and then determine the reception time. 

For stationary observers, this involves a simple calculation. For 

a given source time, the arrival time at the observer is typically 

different for each source point on the mesh describing the 

FW–H surface. Therefore, the noise signal at the observer must 

be interpolated from the accumulated signals from all the source 

points. The forward-time algorithm has the advantage of only 

requiring the surface data from a single source time to calculate 

a contribution to the noise. Therefore, it can be directly coupled 

to CFD codes to compute the noise as the CFD computation 

proceeds and obviate the need to store all of the surface data. 

However, stored data allow for the scrutiny of the surface data 

and for additional observer locations to be included after the 

CFD computation finishes. 

Some simplifications to the retarded-time formulation can be 

applied for airframe noise problems based on restrictions of the

surface motion (Ref. 66) that obviate the need to numerically 

determine the retarded time. Furthermore, frequency-domain 

versions of the FW–H (Ref. 66) have been developed that are 

very efficient when only a limited number of frequencies are 

important. Additionally, the frequency-domain version is 
NASA/TP—2012-215653 108

applicable to two-dimensional problems where time-domain 

methods formally require an infinite time integration to account 

for all sources in the third spatial dimension.

The unsteady surface data for the FW–H solver is obtained 

from simulations with CFL3D (Refs. 45 and 46), a CFD code 

developed at NASA Langley Research Center. CFL3D uses a 

finite-volume formulation for the three-dimensional, timedependent, thin-layer Reynolds-averaged Navier-Stokes 

(RANS) equations. The code employs a third-order upwind 

difference for the convection terms that is nominally secondorder accurate on nonuniform grids. The viscous terms are 

discretized with second-order central differences. Time is 

advanced with a second-order backward difference. When 

running in time-accurate mode, the solution is converged within 

each physical time step by applying a dual time-stepping 

algorithm with multiple sub-iterations. Nominally, 20 to 30 subiterations per time step are required, but the number will vary 

depending on the grid and length of the time interval. CFL3D 

outputs the sub-iteration residual, lift, and drag after each subiteration, and the number of sub-iterations are chosen to ensure 

that the lift and drag have leveled off within each time step and 

that the residual has dropped by 2 to 3 orders of magnitude. 

However, the convergence of the turbulence quantities is 

typically worse than for the flow equations themselves.

Airframe-noise source regions usually involve unsteadiness 

in high Reynolds number, separated flows. Direct numerical 

simulations and LES of such flows are prohibitive because of 

the near-wall grid resolution requirements. Hybrid models that 

attempt to transition from an LES away from the geometry to 

a traditional turbulence model in the near wall region greatly 

reduces the grid requirement, but are still an active area of 

research. Even with hybrid models, the computations are 

resource intensive, requiring months on large Beowulf clusters 

or supercomputers.

The simulation procedure includes several steps. First, a 

steady-state computation is used to set up the basic mean flow, 

followed by an unsteady calculation with random suction and 

blowing applied to different sections of solid surfaces in order 

to accelerate the onset of three-dimensional, unsteady flow 

structures. In practice, the forcing does not exceed 3 percent of 

the free-stream velocity. Forcing is turned off after large-scale 

unsteadiness is observed, typically 200 time steps into the 

unsteady calculation. The simulations are then run for 5000 to 

10 000 time steps to allow initial transients in the flow field to 

dissipate, before collecting time records. Averaged flow 

quantities are produced by time-averaging over 20 000 to 

50 000 time steps.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 109 Chapter 4

Appendix D.—Test Facilities

All but two of the prediction assessments in the present 

chapter are based on experiments conducted in two wind 

tunnels: the Quiet Flow Facility and the Basic Aerodynamic 

Research Tunnel, both at NASA Langley Research Center. 

This appendix gives general descriptions for these test 

facilities and relevant measurement techniques. In the 

prediction assessments, additional details that apply to the 

specific test cases are mentioned as necessary. 

D.1 Quiet Flow Facility

The Quiet Flow Facility (QFF) is an open-jet wind tunnel 

that is specifically designed for anechoic testing. The facility 

is equipped with a 0.61- by 0.914-m (2- by 3-ft) rectangular 

open-jet nozzle, oriented vertically in a 407.8-m

3 (14 400-ft3

) 

chamber. The shorter sides of the nozzle are bounded by fixed 

side plates, to which various test articles can be mounted. The 

QFF is capable of sustaining a maximum free-stream Mach 

number of 0.17.

Acoustic spectra and directivity data in the QFF are

obtained using the Medium Aperture Directional Array 

(MADA). The MADA consists of 41 B&K Model 4138

0.318-cm (1/8-in.) microphones with 0.64 cm (1/4-in.) 

preamplifiers, mounted on an acoustically treated frame and 

covered with a hood of thin woven nylon fabric to reduce 

microphone self-noise due to recirculating air currents within 

the QFF. The hooded array is boom-mounted and faces the 

model region. Figure 4.52 is a photo of the MADA with the 

front hood removed to show the overall mounting. The 

schematic in Figure 4.53 shows the arrangement of the array 

microphones as viewed from the source region. The MADA

microphones are arranged in five concentric circles, each with 

eight equally spaced microphones, and one microphone 

mounted in the center (also serving as the phase center of the 

array). The inner four circles and the single central microphone correspond to the geometric arrangement for the Small 

Aperture Directional Array (SADA), used for legacy datasets 

(e.g., Ref. 55). The circles are irregular in the sense that the 

horizontal- and vertical-arm microphone spacings are slightly 

larger than those in the diagonal arms. The pivotal boom is 

attached to the fixed side plates and allows positioning of the 

array at a large range of polar and azimuthal angles, with 

respect to the test model. For the single-microphone analyses 

described in this chapter (e.g., Sec. 4.5; also, Refs. 36 and 37), 

the four MADA microphones shown circled in Figure 4.53 are 

used independently. At a nominal source distance of 1.5 m 

(5 ft), these microphones span polar and azimuthal ranges of 

approximately 10° in solid angle from the center of the boom 

rotation. 

In the course of each experiment, the SADA and MADA are 

carefully calibrated to check for deviations between experimental and theoretical array responses. Thus, injection calibrations that consist of inserting a known signal simultaneously 

into all microphone channels are performed to detect microphone sensitivity and phase drift. A series of point source tests 

is also performed by placing a calibrator source (intended to 

provide an omnidirectional sound source) in the test section at 

operational working distance from the array. Noise measurements are obtained across a broad frequency range and are 

compared with corresponding theoretical array responses.

Figure 4.52.—Medium Aperture Directional Array (MADA) 

with hood removed in Quiet Flow Facility (QFF).

Figure 4.53.—MADA microphone arrangement.
NASA/TP—2012-215653 110

Figure 4.54.—Basic Aerodynamic Research Tunnel (BART). Structure in front of test section is 

traverse for optical devices.

D.2 Basic Aerodynamic Research Tunnel

The Basic Aerodynamics Research Tunnel (BART) is a 

flow diagnostic facility that specializes in the acquisition of 

flow-field data to support the development and validation of 

computational fluid dynamics (CFD) models and techniques 

(Ref. 48). As such, this facility enables a researcher to 

undertake studies that require flow-field and surface measurements of high spatial and temporal resolution. The BART 

is equipped with highly automated data acquisition and control 

systems to efficiently process large experimental datasets, as 

well as large amounts of mass storage to maintain the facility 

database. This test facility and several instrumentation 

techniques are briefly described below. More detailed 

information can be found in References 48 and 101.

The BART is an atmospheric, open-return wind tunnel with 

a closed test section that measures 0.711 m (2.33 ft) in height, 

1.016 m (3.33 ft) in width, and 3.048 m (10 ft) in length. A 

tunnel schematic is sketched in Figure 4.54. During operation, 

air is drawn into the tunnel inlet by a 9-blade, 11-stator fan, 

which is powered by a 92-kW (125-hp), alternating-current 

motor that is coupled to a magnetic clutch. An electronic 

controller maintains the fan speed within 0.1 percent of full 

scale (less than 1 rpm variation). The tunnel flow is first 

conditioned by a 10-cm- (4-in.-) thick honeycomb that has a 

0.64-cm (1/4-in.) cell size, followed by four antiturbulence 

screens that are 20 mesh-per-inch with 64 percent porosity 

(ratio of open area to total area). The flow is then accelerated 

through an 11:1 contraction before entering the test section.

The maximum flow speed at the test section entrance is 

approximately 65 m/s (213 ft/s), with turbulence intensity 

varying from 0.03 percent at 15 m/s (49 ft/s) to 0.09 percent at 

maximum tunnel speed.

Optical access to the model and surrounding flow is provided by plexiglass (or glass, if required) windows in the test 

section walls and ceiling that are as large as structurally 

possible. Traditional diagnostic techniques available at the 

BART facility include titanium dioxide solution to reveal 

surface streaklines, five-hole probe surveys to record instantaneous velocity fields, pitot pressure surveys, and hot-wire 

anemometry. Within the more advanced techniques, a

Figure 4.55.—Closeup: Basic Aerodynamics Research 

Tunnel (BART) test section with particle imaging velocimetry (PIV) camera on traverse system.

three-component laser Doppler velocimeter is capable of 

obtaining accurate velocity measurements in flow fields with 

reverse flows, as well as large shear gradients and velocity 

fluctuations.

With particular relevance to the present assessment, flowfield velocity measurements were taken with a twodimensional digital particle image velocimetry (PIV) system 

(Refs. 35 and 38). The PIV system was deployed with either 

one or two high-resolution video cameras with a sensor size of 

1360 by 1024 pixels. Using a 50-mm (2-in.) lens, the field of 

view was approximately 80 by 60 mm (3.2 by 2.4 in.) for a 

single camera. With a second camera, two fields of view were 

overlapped to produce an expanded 156×60-mm field of view. 

The cameras were mounted to a traverse system (Figure 4.55) 

surrounding the tunnel, along with the laser and light-sheet 

optics. A 1.5-mm- (0.06-in.-) thick light sheet was generated 

using a pulsed, frequency-doubled, 200-mJ Nd-YAG laser, 

operated at 5 Hz. The experimental flow was seeded by 

disbursing particles with a theatrical fog machine throughout 

the entire room housing the tunnel. Further experimental 

details for the test cases associated with the present assessment 

are reported in References 35 and 38.
Airframe Noise: A Prediction Capability Assessment

NASA/TP—2012-215653 111 Chapter 4

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NASA/TP—2012-215653 115

Chapter 5—Fan Noise Prediction

Edmane Envia5

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Daniel L. Tweedt

AP Solutions Inc.

Cleveland, Ohio 44135

Richard P. Woodward, David M. Elliott, E. Brian Fite,

Christopher E. Hughes, Gary G. Podboy, and Daniel L. Sutliff

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

This chapter presents the results of an assessment of aircraft engine fan noise prediction capability at NASA. Representative

codes in the empirical, acoustic-analogy-based, and computational categories were exercised and assessed against a set of benchmark acoustic data obtained from wind tunnel tests of three model-scale fans representing the ultra-high-, high-, and moderatebypass-ratio designs. The chosen codes were the Aircraft Noise Prediction Program (ANOPP), representing an empirical

capability; RSI, representing an acoustic-analogy-based capability; and LINFLUX, representing a computational aeroacoustics 

capability. The selected benchmark fans cover a wide range of fan pressure ratios and tip speeds, and are representative of modern 

turbofan engine designs. The assessment results indicate that ANOPP can predict 1/3-octave fan noise spectra to within 4 dB of the 

measurement uncertainty band for ultra-high- and high-bypass-ratio fans except at the extreme aft emission angles, but the 

discrepancy between data and theory is considerably larger for the moderate-bypass-ratio fan. The RSI code can predict the rotorstator interaction broadband noise power level spectra to within 4 dB of the experimental uncertainty band for the high-bypassratio fan. The comparisons for the other two fans could not be carried out owing to lack of appropriate experimental data for those 

fans. The LINFLUX code can predict rotor-stator interaction tone noise power levels to within experimental uncertainties for the 

ultra-high-bypass-ratio fan, but deviates by as much as 7.6 dB outside the experimental uncertainty band for the high-bypass-ratio 

fan. LINFLUX results could not be computed for the moderate bypass-ratio-fan, since the mean flow solutions did not converge 

for that fan.

5.1 Introduction

The term fan noise is used here to denote the noise associated with the fan stage of a turbofan engine, which is produced 

by a number of different source mechanisms. For the most 

part, fan noise is produced through the interaction of unsteady 

flow perturbations with the fan rotor blades and fan exit guide 

vanes. These mechanisms include the interaction of inflow 

distortions and the inlet boundary layer with the fan rotor and 

the interaction of fan rotor flow perturbations (blade viscous 

wakes, tip clearance flow, etc.) with the bypass and core 

stators. The interaction can also be self-generated (often called 

self-noise) as in the case of noise produced by scattering of fan 

blade boundary layer turbulence at the blade trailing edge, 

noise due to local separation of the flow on the airfoil, or noise 

associated with vortex shedding at the blade trailing edge. 

Depending on the nature of the unsteady perturbations 

involved, the interaction sources generate discrete frequency 

tones, broadband noise, or in most cases, both. Fan noise can 

also be produced by the steady part of the flow within the fan 

stage. Examples include the interaction of the fan with the 

steady potential (i.e., pressure) field of the engine struts and 

the multiple pure tones (MPT) of the fan (also called buzz-saw 

noise) that are produced as a result of spatial non-uniformities 

in the rotor-locked pressure field. The fan-strut interaction 

produces discrete tones at the harmonics of the blade-passing 

frequency, while buzz-saw is produced at the multiples of fan 

shaft rotational frequency. It has been suggested that the 

fluctuating Reynolds stress (i.e., volume quadrupole) of the 

turbulent flow within the fan stage is also an important source 

of fan noise at high frequencies and high fan loading conditions. The strengths of fan noise sources depend on the fan 

rotational speed. As an example, the MPT noise is only 

significant when the fan tip speed is supersonic. At subsonic 

tip speeds, the rotor-locked pressure field is evanescent and 

contributes very little to the total noise signature of the fan. As 

the fan tip speed varies across the operating regime of the 

engine, the proportions of the contributions from various 

sources change. Measurements of fan noise from model-scale 

rigs and full-scale engines have provided indications of the 

relative importance of some of the fan noise sources as a 

function of the fan tip speed, but because of the overlapping 
NASA/TP—2012-215653 116

nature of the sources it is not always possible to differentiate 

between them.

Since the fan is a significant source of noise in a modern 

aircraft engine, it is important to assess the ability of the 

current codes to predict its noise contribution accurately. 

There is a variety of fan noise prediction methods, but in 

general, these methods can be grouped into three 

main categories: empirical, acoustic-analogy-based, and 

computational.

In the first category, experimental data are used to construct 

correlations between appropriate fan noise metrics and 

operating parameters. The correlations are often constructed 

for overall fan noise levels (i.e., the sum of contributions from 

all sources) since it is often not possible to conclusively isolate 

contributions of various noise sources from the total measured 

fan noise signature. These methods are widely used, principally, as part of system-level prediction codes for engine 

design evaluation studies. While it takes significant experience 

and skill to discern the appropriate correlation relationships 

from the mass of available information, once constructed, 

these methods are relatively easy to use, requiring a readily 

available set of input parameters. Codes based on empirical 

models tend to require minimal computer resources and run 

times, typically producing answers on a 1/3-octave spectral 

basis in a matter of seconds. ANOPP is the only empirical 

code currently in the NASA fan noise prediction inventory. As 

described in Chapter 2, “Aircraft System Noise Prediction,” 

ANOPP calculates fan noise through its HDNFAN module, 

which predicts fan noise inclusive of all fan noise sources. 

ANOPP, more generally, can be used to predict overall aircraft 

noise for the purposes of estimating aircraft community noise 

impact using the effective perceived noise level (EPNdB) 

metric.

As the name suggests, the methods in the second category 

are based on the acoustic analogy theory developed by 

Lighthill (Ref. 1). In this theory, the aerodynamic and acoustic 

aspects of the problem are treated separately. Mathematically, 

this is done by a rearrangement of the exact equations of the 

motion so that a linear wave equation is obtained whose lefthand side describes the propagation of sound and its righthand side represents a known aerodynamic source that 

generates the sound. The aerodynamic source is to be 

measured, computed, or otherwise modeled independently. 

The solution to the wave equation is given formally in terms 

of integrals that describe convolution of the source distribution 

and the acoustic propagation characteristics. Depending on the 

level of approximations involved in the description of the fan 

geometry and/or flow conditions, the solution can be

expressed either in closed form or may require the use of a 

quadrature scheme to evaluate the solution integrals. Such 

models have been developed for a number of fan noise 

sources, but most have been developed to predict the so-called 

rotor-stator interaction noise, which is produced as a result of 

the impingement of the fan rotor wakes on the fan exit guide 

vanes. The level of expertise needed to use this class of codes 

is more than the empirical models and often requires access to, 

or knowledge of, fairly detailed aerodynamic and geometric 

input parameters from independent measurements or computations. As such, acoustic-analogy-based codes tend to require 

more computer resources and run times, typically producing 

answers in a matter of minutes for tone noise and in a matter 

of hours for broadband noise. There are a number of NASA 

fan noise codes that fall in the acoustic analogy category. 

These include V072 (Refs. 2 and 3) and TFaNS (Refs. 4 to 7), 

which are used for rotor-stator interaction tone noise prediction; RSI (Ref. 8) and BFaNS (Refs. 9 to 11), which are used 

for rotor-stator interaction broadband-noise prediction; and 

Superpose (Ref. 12), which is used for rotor buzz-saw noise 

prediction.

The third category of fan noise prediction methods encompasses those approaches that—like the acoustic-analogy-based 

methods—start with the exact equations of motion, but require 

little or no approximations regarding the fan geometry or its 

flow field. The resulting coupled system of unsteady flow 

equations, therefore, retain their complexity and can only be 

solved numerically through the use of appropriate computational algorithms. These methods, generically called computational aeroacoustics (CAA) methods, include linearized 

frequency-domain methods as well as nonlinear time-domain 

methods. With recent advances in computing power and 

computational algorithms, CAA codes are beginning to gain a 

place in the toolbox of fan noise prediction methods. The use 

of CAA tools typically requires a high level of expertise and 

familiarity with the tools themselves and with computer 

hardware and software used to implement them. Depending on 

the particular code and application, these codes require 

significant computer resources, typically requiring tens of 

hours of computation time for tone noise prediction and tens 

of days for broadband noise prediction. NASA codes in this 

category include two Euler codes, LINFLUX (Refs. 13 to 15) 

and BASS (Refs. 16 to 20). LINFLUX is a linearized, 

frequency-domain, tone-noise prediction code, and BASS is a 

nonlinear, time-domain, broadband-noise prediction code. 

Both codes are currently used for rotor-stator interaction noise 

prediction.

In this chapter, a representative code in each category that 

is available in the public domain will be discussed and 

assessed against a set of benchmark fan noise data. In each 

case, a brief description of the code will be given including a 

discussion of the input parameters and the output produced by 

the code. It should be emphasized that the list of codes 

considered here is representative, not exhaustive. Each 

selected code typifies the current state of the art at NASA in 

each category and represents the capabilities of similar codes 

elsewhere that fall in that category. A list of acronyms and 

symbols used in this chapter is given in Appendix A.

5.2 Benchmark Test Cases

The selected test cases for this study include an ultra-highbypass-ratio fan stage, the NASA-Pratt & Whitney Advanced 

Ducted Propulsor (ADP) Fan 1; a high-bypass-ratio fan stage, 
Fan Noise Prediction

NASA/TP—2012-215653 117 Chapter 5

the NASA-General Electric Source Diagnostic Test (SDT) 

fan; and a moderate-bypass-ratio fan stage, the NASAHoneywell Quiet High Speed Fan 2 (QHSF 2). Again, the 

benchmark cases selected are not meant to be exhaustive, but 

representative. All three fans were tested in the NASA Glenn 

Research Center 9- by 15-Foot Low-Speed Wind Tunnel 

(9×15 LSWT) over the last decade. In all cases, sideline as 

well as in-duct acoustic measurements were acquired and have 

been used for the comparison purposes in this study. Owing to 

the limitations of the codes, only data from the so-called hardwall configurations, which do not include acoustic treatment 

inside the fan duct, have been considered in this study.

Table 5.1 shows select design parameters for these three 

model fans. The fan design conditions represent a significant 

value range. The ADP fan has a subsonic design tip speed in 

contrast to the supersonic design tip speeds for the SDT and 

QHSF 2 fans. Note the change in the fan bypass ratio, pressure 

ratio, and tip speed for these fans. The design point corrected 

inlet weight flows5 are similar for all three. The somewhat 

lower weight flow for the ADP fan is partly due to the higher 

rotor hub:tip radius ratio and consequent reduced flow area for 

that fan. All three fans have a 22-in.-diameter rotor and were 

tested at a number of fan tip speeds. For the purposes of this 

study, five fan tip speed conditions have been considered for 

each fan which include speeds that are representative of the 

three noise certification points; namely, approach, cutback and 

takeoff, and two additional intermediate tip speeds. The fan tip 

speeds investigated in this study are listed in Table 5.2.

 5 Corrected flow is the mass flow that would pass through the fan if 

the inlet pressure and temperature were at the standard day conditions 

(i.e., pressure = 101.4 kPa (14.696 lbf/in.2) and temperature = 288 K 

(518.7 °R)).

TABLE 5.1.—MODEL FAN STAGE DESIGN PARAMETERS

Parameter Fan stagea

ADP SDT QHSF 2

Fan speed, rpm 8750 12 656 15 625

Corrected tip speed, m/s (ft/s) 256 (840) 370 (1215) 449 (1474)

Stage pressure ratio 1.29 1.47 1.82

Rotor hub-to-tip radius ratio 0.43 0.30 0.35

Bypass ratio 13.3 8.9 3.8

Corrected specific weight flow, kg/m2-s (lbm/ft2-s) 180.2 (36.9) 204.1 (41.8) 213.4 (43.7)

Inlet corrected weight flow, kg/s (lbm/s) 38.9 (85.7) 45.6 (100.5) 44.9 (98.9)

Rotor blade count 18 22 22

Fan exit guide vane count 45 54 50

Core inlet guide vane count 63 None None

Bypass and core duct support struts None None 10 a

ADP is Advanced Ducted Propulsor, SDT is Source Diagnostic Test, and QHSF 2 is Quiet High Speed Fan 2. 

TABLE 5.2.—MODEL FAN TIP SPEED

CONDITIONS USED IN THIS STUDY

Fana Condition Corrected speed,

rpm

Design speed,

percent

ADP Approach 5 425 62.0

--- 6 700 76.6

Cutback 7 525 86.0

--- 8 345 95.4

Takeoff 8 750 100.0

SDT Approach 7 809 61.7

--- 9 493 75.0

Cutback 11 075 87.5

--- 11 771 93.0

Takeoff 12 657 100.0

QHSF 2 Approach 9 840 63.0

--- 10 935 70.0

Cutback 12 500 80.0

--- 13 280 85.0

Takeoff 14 060 90.0 a

ADP is Advanced Ducted Propulsor, SDT is Source Diagnostic 

Test, and QHSF 2 is Quiet High Speed Fan 2.
NASA/TP—2012-215653 118

A photograph of the ADP fan (Refs. 21 and 22), installed in 

the 9×15 LSWT, is shown in Figure 5.1. ADP has a relatively 

low stage pressure ratio of 1.29 and a subsonic design 

corrected tip speed of 256 m/s (840 ft/s), which avoids the 

generation of multiple pure tones. A three-dimensional 

exposed view of the fan stage is depicted in Figure 5.2. The 

fan stage has 18 rotor blades, 45 radial bypass stator vanes, 

and 63 radial core stator vanes (the core is passive). It has the 

highest design bypass ratio (13.3) of the three fans considered 

in this chapter. Figure 5.3 shows a photograph of the SDT fan 

(Refs. 23 and 24) installed in the 9×15 LSWT. A threedimensional exposed view of SDT is shown in Figure 5.4. The 

fan stage has 22 rotor blades (this rotor is called R4) and 54 

radial stator vanes. The SDT fan has a design corrected tip 

speed of 370.3 m/s (1215 ft/s) and a stage pressure ratio of 

1.47. Figure 5.5 shows a photograph of the QHSF 2 (Refs. 25

and 26) model installed in the 9×15 LSWT. The threedimensional exposed view of this fan is depicted in Figure 5.6

showing its relatively close rotor-stator spacing and its swept 

stator. The QHSF 2 has the highest design tip speed 

(449.3 m/s, or 1474 ft/s) of the three model fans in this study. 

It has 22 rotor blades, 50 swept stator vanes, 10 bypass struts, 

and 10 struts in its passive core. Its bypass ratio of 3.8,

well below that of the other two model fans, is considered 

moderate. 

Figure 5.1.—The 22-in.-diameter Advanced Ducted Propulsor (ADP) Fan 1 installed in 

the NASA 9- by 15-Foot Low-Speed Wind Tunnel. Traversing microphone (located on 

white stand) is visible to left of model. Microphone moves on track parallel with axis of 

fan.
Fan Noise Prediction

NASA/TP—2012-215653 119 Chapter 5

Figure 5.2.—Cross-sectional sketch of ADP Fan 1 model. ADP has 18 rotor 

blades, 45 fan exit guide vanes, and 63 core inlet guide vanes.

Figure 5.3.—The 22-in.-diameter Source Diagnostic Test (SDT) fan installed in 

NASA 9- by 15-Foot Low-Speed Wind Tunnel.
NASA/TP—2012-215653 120

Figure 5.4.—Cross-sectional sketch of SDT fan model. SDT has 22 rotor 

blades and 54 fan exit guide vanes.

Figure 5.5.—The 22-in.-diameter Quiet High-Speed Fan 2 (QHSF 2) fan installed 

in NASA 9- by 15-Foot Low-Speed Wind Tunnel.
Fan Noise Prediction

NASA/TP—2012-215653 121 Chapter 5

Figure 5.6.—Cross-sectional sketch of QHSF 2 model fan. QHSF 2 has 22 rotor 

blades, 50 fan exit guide vanes, 10 bypass duct struts, and 10 core duct struts.

5.3 Test Facility and Data Acquisition 

Systems

The 9×15 LSWT is a continuous-flow, anechoic wind tunnel 

facility located at the NASA Glenn Research Center (Ref. 27), 

and is part of the 8- by 6-Foot Supersonic Wind Tunnel 

complex. The 9×15 LSWT is capable of producing test section 

Mach numbers up to 0.23, as well as being used for static 

propulsion system performance testing. Acoustic-treatmentfilled boxes are installed on the test section flow surfaces, 

making the test section nominally anechoic down to 250 Hz 

(Refs. 28 to 31). Flow conditioning systems upstream of the test 

section reduce incoming turbulence and velocity distortion 

levels to very low values, making this facility ideally suited for 

establishing baseline acoustic levels and for noise source 

isolation testing of simulated propulsion systems. Figure 5.7 is a 

schematic showing a plan view of the 2.7- by 4.6-m (9- by 

15-ft) test section and the location of the installed model-scale 

fan hardware and the sideline acoustic measurement system 

(i.e., the traversing microphone and the fixed aft microphones). 

The fan models were all powered by the NASA Glenn Ultra 

High Bypass (UHB) Drive Rig propulsion simulator. A fourstage air turbine driven by high-pressure, high-temperature air 

through tubes in the support strut generates the power to drive 

the fan model through a common shaft connection. The UHB 

Drive Rig can deliver a maximum of 3766 kW, or 5050 shaft 

horsepower, at 16 850 rpm with air supplied at 1.6 MPa 

(230 psia) and 260 °C (500 °F).

5.4 Wind Tunnel Acoustic 

Measurements

Model fan acoustic sideline measurements in the 9×15 

LSWT are acquired using a traversing microphone probe at 

2.27-m (89.3-in.) sideline distance from the fan axis (see 

Figure 5.7). Data is taken from 48 positions at 2.5° intervals. 

Additionally, to obtain more angular coverage in the aft 

quadrant, three fixed microphone probes are placed in the rear 

of the test section. Together, the traversing probe and the fixed 

microphones cover 51 measurement locations. All acoustic 

data is obtained at the tunnel Mach number of 0.1, which is 

sufficient to establish acoustic flight effects (Ref. 32). The 

emitted angles corresponding to the 51 microphone locations 

at 0.1 Mach number range from 25° to 158° from the fan 

stacking axis with 0° being the forward position upstream of

the fan. The microphones used in the measurements are all 

0.6 cm (1/4 in.) in diameter.

Acoustic data in the 9×15 LSWT were acquired with two 

different sampling rates: 240 and 24 kHz. Both were acquired 

with a sample size of 4096, resulting in bandwidths of 

approximately 5.9 and 59 Hz, respectively. Allowing for 

the Nyquist limit and filter rolloff effects, typically, the range 

0 to 8 kHz for the bandwidth of 5.9 Hz, and the range 0 to 

80 kHz for the bandwidth of 59 Hz were used for analysis 

purposes.Corrections to the data have been made for microphone response, cable response, bullet nose cover receptivity,

filter response, atmospheric attenuation, and spherical
NASA/TP—2012-215653 122

Figure 5.7.—Plan view of 9- by 15-ft test section showing model-scale fan acoustic installation, 2.3-m (89-in.) 

sideline traversing microphone, and fixed aft microphone locations. Dimensions are in meters (inches).

spreading.6 Finally, for the purposes of comparison with 

predictions, the measured spectra shown here are presented at 

a distance of 0.3-m (1-ft) from the fan stacking axis without 

loss due to atmospheric absorption.

5.5 Rotating Rake Acoustic 

Measurements

An experimental measurement system was developed and 

implemented by NASA Glenn in the 1990s to measure 

turbofan duct acoustic modes. The system is a continuously 

rotating radial microphone rake that is inserted into the duct 

(see Figure 5.8). The Rotating Rake (Refs. 33 and 34) 

provides a complete map of the acoustic duct modes present in 

the fan duct and has been used on a variety of test articles 

including a low-speed concept test rig, several high-speed 

model-scale fans in the wind tunnel, and even on a full-scale 

production turbofan engine on an engine test stand. The 

Rotating Rake has been critical in developing and evaluating a 

number of noise reduction concepts as well as providing 

experimental databases for verification of fan noise prediction 

codes. 

Rotating Rake data is obtained from radially distributed 

high-response transducers mounted on a rake. Transducers 

used are 1.6 mm (0.062 in.) in diameter with a 34-kPa (5-psi) 

delta dynamic range. For inlet measurements, 12 to 14 

transducers are typically distributed in equal radial increments 

 6

Information regarding specific procedure used for correcting 9×15 

LSWT data may be obtained by contacting the NASA Glenn 

Acoustics Branch.

starting near the outer wall to the duct centerline at the throat. 

For exhaust measurements, six to eight transducers are 

typically distributed in equal radial increments starting near 

the outer wall to the near inner wall at the duct exit plane. 

The key concept of the Rotating Rake is that by slowly 

rotating the microphone rake, say, at 1/200 of the speed of the 

fan shaft, a Doppler shift is imparted to a given duct spinning 

mode that is uniquely related to its circumferential mode 

index. This allows the decomposition of the measured pressure 

profile into a collection of circumferential modes. The radial 

modes are then obtained by solving a least-squares-curve fit to 

each of these circumferential modes using the Bessel functions 

as the radial basis modes. The acoustic power level (PWL) for 

each radial mode is computed based on physical conditions 

directly from the mode pressure. Strictly speaking, this is valid 

only for a hard-wall cylindrical duct with a uniform (i.e., plug) 

flow through the duct and has implications for the accuracy of 

the fitted solution. The theory and implementation of the 

Rotating Rake with historical examples is documented in 

Reference 33.

5.6 Uncertainty in Measurements

The measurement values obtained from both of the facilities 

described above contain uncertainties that are documented in 

this section. The uncertainty analysis for measurements taken 

in the 9×15 LSWT facility includes both aerodynamic data 

and acoustic data. For the Rotating Rake facility, the uncertainty analysis is determined for the mode acoustic power 

levels computed from mode measurements.
Fan Noise Prediction

NASA/TP—2012-215653 123 Chapter 5

Figure 5.8.—Rotating Rake ring assembly on 43-cm (17-in.) Advanced Ducted Propulsor (ADP) in 

NASA 9- by 15-Foot Low-Speed Wind Tunnel. (a) First-generation system. (b) Currentgeneration system.

5.6.1 Wind Tunnel Aerodynamic Data Uncertainty 

Analysis

An error analysis using the standard ASME (American 

Society of Mechanical Engineers) measurement analysis 

techniques (Refs. 35 to 37) was conducted on the aerodynamic 

values used for reducing experimental far-field and Rotating 

Rake acoustic data. The measurement uncertainties of the data 

were first identified including the random and bias errors. A 

confidence level of 95 percent was then used corresponding to 

two standard deviations in a Gaussian error distribution with 

the number of degrees of freedom at least equal to 30. The 

random and bias errors from the uncorrelated sources were 

combined either linearly or in quadrature to produce an overall 

characterization for each variable. The computed uncertainties 

for aerodynamic variables important for acoustic data 

reduction are shown in the Table 5.3. It should be noted that 

these uncertainties are for a single point measurement and are 

based on manufacturer’s specifications of the various measurement system components.

TABLE 5.3.—AERODYNAMIC DATA

UNCERTAINTY ANALYSIS RESULTS

Variable name ±Uncertainty 

Tunnel total pressure, kPa (psia) 0.05 (0.0074)

Tunnel static pressure, kPa (psia) 0.05 (0.0074)

Tunnel total temperature, K (°R) 0.69 (1.25)

Tunnel static temperature, K (°R) 0.69 (1.25)

Tunnel Mach number 0.0016

Tunnel percent humidity, percent 0.022

Fan speed, rpm 4

Corrected fan speed, rpm 5

Inlet and exit duct Mach number 0.0004

Fan exit temperature, K (°R) 0.69 (1.25)

5.6.2 Wind Tunnel Sideline Acoustic Data

Uncertainty Analysis

The acoustic data system in the 9×15 LSWT consists of the 

following hardware from end to end: Brüel & Kjær (B&K) 

Type 4939 0.6-cm (1/4-in.) microphones; B&K 0.6- to 1.3-cm 

(1/4- to 1/2-in.) adapter cabling; B&K Type 2807 power 

supply; Stewart high-pass filters; DSP Technologies, Inc., 

analogue-to-digital and low-pass filter boards; and a Concurrent (Masscomp Computer Corporation) computer. The 

primary component, the B&K Type 4939 microphone, was 

calibrated by B&K before use and has an uncertainty shown in 

Table 5.4. This uncertainty is given for three representative 

frequencies corresponding to 300 Hz (low), 3000 Hz 

(medium), and 30 000 Hz (high). Every component introduces 

an amplitude uncertainty, which is eliminated by generating a 

calibration factor for the entire system at the beginning of 

every run using a known source. The calibration source is a 

B&K 4220 250-Hz, 124-dB pistonphone. The B&K pistonphone’s computed uncertainty is shown in Table 5.4.

For atmospheric attenuation, the ANSI S1.26–1995 Method 

for Calculation of the Absorption of Sound by the Atmosphere

(Ref. 38) claims an uncertainty of ±10 percent for the regime 

in which data is acquired in the 9×15 LSWT. The uncertainty 

levels for the ambient conditions of temperature and humidity 

were determined as ±0.69 °C (1.25 °F) and ±0.022 percent 

relative humidity (based on the instrument manufacturer’s 

specifications), respectively. Other errors in measurement 

include distance to the microphone from the assumed source 

and the uncertainty of the fan-model-corrected rpm, which is 

the controlling set point for the fan model. These uncertainty 

values are ±1.3 cm (0.5 in.) per 254 cm (100 in.) and ±5 rpm 

corrected, respectively.
NASA/TP—2012-215653 124

TABLE 5.4.—ANALYSIS OF UNCERTAINTY IN FAN NOISE SPECTRA

Source Uncertainty,

e,

dB

Basis for determining uncertainty

(Sec. 5.6.2)

Nominal frequency,

Hz

300 3000 30 000

Atmospheric attenuation 0.00001 0.001 0.1 ±0.69 °C (1.25 °F), ±2 percent relative humidity, hot and humid day

Distance 0.04 0.04 0.04 ±1.3 cm (0.5 in.) error in 254 cm (100 in.)

Set point 0.1 0.1 0.1 < ±0.25 percent error in rpm

Pistonphone 0.15 0.15 0.15 Brüel & Kjær (B&K) 4220, 124 dB, 250 Hz

Spectral response calibration 0.0 0.01 0.16 Certified by B&K calibration facility

1/3-octave-band averaging 0.33 0.1 0.01 Chi-squared analysis of 1/3-octave integration (five narrowbands minimum) 

at 90% confidence

– or –

Narrowband averaging 0.61 0.61 0.61 Chi-squared analysis of 194-average narrowband at 90% confidence

Totala 0.59 0.39 0.61 1/3-octave spectra

0.86 0.87 1.07 Narrowband spectra

a

Total uncertainty is summed according to 10 ( ) 10 10log 1 10 1 e   + −   ∑ .

Lastly, an error uncertainty is determined for the integration 

of the acquired data for averaging analysis purposes for both 

narrowband and 1/3-octave-band analysis. A chi-square 

analysis was done for 194-average narrow bands at a

90% confidence interval for the narrow-band uncertainty. A 

chi-square analysis was also done for a minimum of

5 narrowbands at 90% confidence interval for the

1/3-octave-band uncertainty. The uncertainty varies in the

1/3-octave-band analysis according to frequency because of 

the fact that fewer narrowbands are used in the lower frequencies, and the number of narrow bands combined to form single 

1/3-octave bands increases as frequency increases. The overall 

data measurement uncertainty was determined for three 

different frequency ranges and two noise-band-averaging 

methods. The results are shown in Table 5.4. 

The above analysis addresses the uncertainty in measured 

amplitude of the data. The measured frequency uncertainty is 

based on the uncertainty in the revolutions per minute of the 

fan model in the 9×15 LSWT. The calculated uncertainty of 

the fan model in the wind tunnel is ±5 corrected revolutions 

per minute. The highest uncertainty can be calculated for the 

lowest speed of interest here, which is 5425 rpm. This gives an 

uncertainty in the measured frequency of ~0.09 percent.

The list of uncertainties considered here, while not exhaustive, represents all the important measurement uncertainty 

factors. Finally, it should be noted again that these uncertainty 

levels were calculated based on manufacturer specifications of 

the various components of the measurement system.

5.6.3 Rotating Rake Acoustic Data Uncertainty 

Analysis

The uncertainty in the mode acoustic PWL computed from 

the Rotating Rake mode measurements arises from three basic 

components: instrumentation and calibration, data reduction, 

and modeling error. 

The instrumentation and calibration error arises from the errors 

associated with transducer and the telemetry transmission. The 

transducer uncertainty was determined by referencing to a 

pistonphone that was calibrated to a known transducer and the 

uncertainty assumed to be that of the pistonphone. The uncertainty induced by transmission through the telemetry system was 

obtained by placing a known signal across the telemetry and 

comparing this known signal with the telemetry output.

The data reduction uncertainty arises from the uncertainty 

in the inputs to the equation used for computation of mode 

power. Propagation of uncertainties through this equation may 

be calculated in the standard manner by analyzing the partial 

derivatives of the power equation with respect to all of the 

relevant parameters. The parameters that have a significant 

effect on mode PWL are mode pressure, duct Mach number, 

and mode cutoff ratio based on the corrected revolutions per 

minute. Errors in geometry (e.g., variations in blade and vane 

manufacturing, installation, etc.) are small for the three fans 

considered, particularly regarding their influence on the noise 

generation mechanisms considered in this study.7 As such, the 

influence of the geometric errors on mode PWL has been 

 7

This is not always true. Case in point is the buzz-saw noise resulting 

from small differences in blade manufacturing and installation. Buzzsaw noise is not considered in this study.
Fan Noise Prediction

NASA/TP—2012-215653 125 Chapter 5

TABLE 5.5.—REPRESENTATIVE UNCERTAINTY LEVELS IN 

MODE SOUND POWER LEVELS FOR SECOND HARMONIC 

OF BLADE-PASSING FREQUENCY COMPUTED FROM 

MEASURED ROTATING RAKE DATA 

[Data from Source Diagnostic Test (SDT) fan.]

Circumferential

mode number

Uncertainty level,

dB

Approach Cutback Takeoff

–8 1.26 1.10 1.47

18 0.27 0.51 0.91

–10 0.21 0.87 0.34

ignored here. The resulting uncertainties in rotor-stator 

interaction mode measurements that would arise for the SDT 

fan at three representative speeds points are shown in

Table 5.5. These are considered the representative levels and 

shall be used in subsequent analysis.

The uncertainty in modeling error is a result of using basis 

functions for plug flow when shear flow basis functions may 

be more appropriate. The shear flow basis functions can be 

computed using the methodology described in Reference 39. 

Table 5.6 shows the error that would result from fitting a plugflow basis function to a mode shape arising in shear flow. In 

this example, the computed zeroth-order radial acoustic mode 

in a duct with shear flow is used as measured values and fitted 

(i.e., approximated) by the zeroth-order radial acoustic mode 

when plug flow is assumed to be present in the duct. The last 

column on the right shows the percent error in acoustic 

pressure that occurs at the selected radial locations when 

making a plug flow assumption for a duct flow that physically 

is a shear flow. Clearly, the mismatch can lead to sizable 

discrepancies (3.2 dB in terms of mode amplitude). The 

modeling error depends on the particular mode under consideration, which means that an accurate estimate of the modeling error would require an exhaustive assessment of all rotorstator interaction modes present in the measured fan tone data 

for all of the fans and tip speeds under consideration here. 

Since such modal data is not available for all configurations 

and tip speeds of interest here, it was decided to use the 

uncertainty shown in Table 5.6 as the representative uncertainty for modeling error. 

The overall uncertainty is then the square root of the sum of 

the squares of the component uncertainties as shown in 

Table 5.7. Thus for each fan and operating point, an uncertainty can be computed for any given mode at each harmonic. 

This uncertainty can be expected to vary. In the absence of 

actual data for all modes and for all fans,8 it is proposed that 

the number obtained here for the case analyzed for SDT (i.e., 

±4.3 dB) be applied to the other fans as well. As such, this 

represents the uncertainty in mode PWL for an arbitrary mode 

in either inlet or exhaust.

 8

Individual mode power distributions for the ADP fan are not 

available.

TABLE 5.6.—MODELING ERROR FROM USING

HARD-WALL PLUG-FLOW BASIS FUNCTION

TO FIT SHEAR-FLOW MODEa

Radial

locationb

Shear flow mode Plug flow curve fit 

Pressure,

Pa (psi)

Pressure,

Pa (psi)

Percent 

errorc

0.000 0.000 0.000 0.0

0.040 0.000 0.000 0.0

0.106 0.002 (2.9×10–7

) 0.001 (1.5×10–7) 0.1

0.206 0.029 (4.2×10–6

) 0.010 (1.5×10–6) 1.5

0.341 0.196 (2.8×10–5

) 0.069 (1.0×10–5) 9.7

0.500 0.691 (1.0×10–4

) 0.260 (3.8×10–5) 32.9

0.659 1.260 (1.8×10–4

) 0.590 (8.6×10–5) 51.1

0.794 1.310 (1.9×10–4

) 0.901 (1.3×10–4) 31.2

0.894 0.925 (1.3×10–4

) 1.077 (1.6×10–4) 11.6

0.960 0.507 (7.3×10–5

) 1.140 (1.7×10–4) 48.3

Average error:d

18.6 percent

Mode amplitude 

pressure

Mode amplitude

pressure

Pa (psi) dB Pa (psi) dB

0.909 

(1.3×10–5)

91.8 0.536 (7.8×10–5

) 88.6

a

Number of radial nodes in mode is zero.

b

Normalized by duct radius.

c

Percent error calculated as 100 max.pressure(shear)

pressure(shear) pressure(plug) × −

d

Average error calculated as ∑i

percent errori 10

1 where i is an index 

representing the radial locations.

TABLE 5.7.—TYPICAL UNCERTAINTIES IN MODE 

ACOUSTIC POWER LEVEL FROM ALL SOURCES

Uncertainty source Uncertainty, 

e,

dB

10(e/10) – 1

Calibration 0.5 0.122

Telemetry 0.4 0.096

Data reduction 1.5 0.413

Modeling 3.2 1.089

Sum of component uncertainties 1.720

Total uncertainty = 10 log10(1+1.720) = 4.3 dB

5.7 Prediction and Assessment

In this section, the results of the assessment exercise are 

presented. The presentation is organized according to the 

categorization discussed earlier; namely, that we begin with 

the empirical results, followed by the acoustic-analogy-based 

results, and conclude with the computational aeroacoustics 

results. In each case, comparisons of the predicted levels and 
NASA/TP—2012-215653 126

the measured levels are presented. All comparisons include the 

calculated uncertainty of the experimental measurements as 

appropriate. In the interest of brevity, representative datatheory comparisons are shown in the main text, but all the rest 

are included in Appendix B and Appendix C. Depending on 

the particular fan noise code evaluated, the results are 

presented in terms of sound pressure level (SPL) or sound 

power level (PWL). The input requirements of each code are 

listed and discussed as appropriate.

5.7.1 Empirical Methods

As a representative code in the empirical methods category, 

the version (i.e., Level) 25 of the Aircraft Noise Prediction 

Program (ANOPP) was chosen to assess the accuracy of the 

empirical methods for predicting fan noise. ANOPP represents 

the state of the art at NASA in empirical methods for aircraft 

noise prediction. It can be used to predict the noise on the 

component basis as well as at the system level. Much literature 

has been devoted to describing the inner workings of ANOPP 

(see Refs. 40 to 44 for an in-depth understanding of ANOPP), 

so no details will be given here about the code. For the 

purposes of this study, the fan noise module in ANOPP, called 

HDNFAN (Ref. 45), was used to predict the sideline noise 

radiation for the test-bed fans. The HDNFAN fan noise 

prediction module, designated Level 25, version 3 (L25v3), 

was developed using data from a number of fans,

9 but this 

database does not include data from the model fans used in 

this study. HDNFAN predicts fan noise spectrum on a

1/3-octave-level basis inclusive of all fan noise sources and for 

both inlet and exhaust and includes the effects of acoustic 

transmission through the blade rows, scattering from the inlet 

and exhaust lips, and shear layer refraction in the exhaust 

stream.

ANOPP requires a host of geometric, environmental, and 

operational parameters as input. Table 5.8 lists these input 

parameters for each fan under consideration here. The ANOPP 

calculations for each of the three fans were carried out at the 

three fan tip speeds corresponding to the nominal approach, 

cutback, and takeoff conditions listed in Table 5.2. The actual 

revolutions per minute shown in Table 5.8 correspond to the 

corrected revolutions per minute listed in Table 5.2. The 

calculations and comparisons with the data were carried out 

for all emission angles as “lossless” on a 0.3-m (1-ft) radius 

centered on the fan pitch axis.

A sampling of the data-theory comparisons is presented in 

Appendix B in Figure 5.22 to Figure 5.30 for typical inlet and 

exhaust quadrant emission angles, namely 46° and 136°, 

respectively. The figures are organized as a function of fan tip 

speed for ADP, SDT, and QHSF 2, respectively. As shown in 

Table 5.4, the measured SPL data have a frequency-dependant 

1/3-octave uncertainty level of less than 1 dB over the entire 

 9

The fan noise module was developed using Marcus Heidmann’s 

method with revisions by General Electric (GE) Aircraft Engines for 

hard-wall modern fans including CF6, CFM56, E3

, and QCSEE (see 

Ref. 45).

range of frequencies of interest. However, for the sake of 

simplicity the uncertainty level is assumed to be a constant

±1-dB band for the entire frequency range as indicated by the 

error bars on the measured levels shown in these figures. It 

should be noted that the microphone measurements for both 

the inlet and exhaust below 2 kHz are contaminated by rig 

noise caused by the scrubbing of the exhaust flow over the 

drive rig assembly. This extraneous noise source has been 

robustly characterized in a recent investigation whose results 

have been documented in Reference 46. As a result, the 

portion of the data that is shown in Figure 5.22 to Figure 5.30

in Appendix B that is below 2 kHz should be ignored.

In Figure 5.9 to Figure 5.11, the results for all sideline 

(emission) angles have been summarized in the form of the 

decibel error in predicting the measured levels. Therefore, 

each point represents the difference between the measured and 

predicted SPL on a 1/3-octave basis. The gray band spanning 

the ±1-dB range represents the experimental uncertainty. 

Results below the 2-kHz band are not shown because of drive 

rig noise contamination. 

On average, the data-theory agreement falls well outside of 

the experimental uncertainty band for all three fans when all 

frequencies and angles are considered. In the extreme aft 

angles, in particular, ANOPP tends to underpredict the 

measured levels by sizable margins. However, with the 

exception of a few isolated frequency bands, the data-theory 

deltas are within ±4 dB of the experimental uncertainty margin 

for ADP and SDT for nearly all frequency and angle combinations. The deltas also tend to be clustered together and follow 

the same general trends for nearly all frequencies. The same is 

not true for QHSF 2 for which the deltas are outside the ±4-dB 

range (especially for the 12 500 rpm case) and there is far 

more scatter in the deltas. As noted in Table 5.8, the ANOPP 

predictions were all generated using the “GE revised method” 

within HDNFAN module and represent the best comparisons 

of all available options in ANOPP L25v3.

In summary, the data-theory comparisons indicate that 

ANOPP predictions are within ±4 dB of the measurement 

uncertainty band for most fan tip speed, 1/3-octave frequency 

band, and emission angle combinations for the ADP and SDT 

fans. However, the data-theory discrepancy is considerably 

larger for the QHSF 2 fan.

5.7.2 Acoustic-Analogy-Based Methods

As a representative code in this category, the most recent 

version of the RSI (i.e., rotor-stator interaction) code

was chosen to predict broadband noise generated by the 

interaction of rotor turbulence impinging on the downstream 

stator in the bypass duct. The underlying theory for this code 

has been described in detail in Reference 8 and will not be 

repeated here. The RSI code computes in-duct narrowband 

distribution of PWL as a function of frequency. It computes 

the PWL upstream and downstream of the stator. The 

upstream portion contributes to the fan inlet noise, and the 

downstream portion is the main source of the fan exhaust
Fan Noise Prediction

NASA/TP—2012-215653 127 Chapter 5

TABLE 5.8.—ANOPP L25V3 HDNFAN INPUT PARAMETERS

[Using GE revised method.]a

Input parameterb Fanc

ADP SDT QHSF 2

Approach Cutback Takeoff Approach Cutback Takeoff Approach Cutback Takeoff

Ambient temperature,

K (°R)

297.3 

(535.2)

296.4 

(533.5)

297.1 

(534.8)

295.7 

(532.2)

295.5 

(531.9)

295.3 

(531.5)

297.4 

(535.3)

297.2 

(534.9)

297.4 

(536.3)

Ambient pressure,

kPa (lb/ft2)

97.67

(2039.9)

97.63

(2039.0)

97.59

(2038.3)

98.44

(2056.0)

98.30

(2053.1)

98.25

(2052.0)

99.46

(2077.2)

99.35

(2075.0)

99.32

(2074.3)

Ambient speed of 

sound, m/s (ft/s)

345.6

(1134.1)

345.1

(1132.2)

345.5

(1133.6)

340.3

(1116.4)

340.3

(1116.4)

340.3

(1116.4)

345.6

(1134.1)

345.6

(1133.7)

346.0

(1135.2)

Ambient density, 

kg/m3 (slug/ft3

)

1.182

(0.00229)

1.182

(0.00229)

1.182

(0.00229)

1.167

(0.00226)

1.167

(0.00226)

1.167

(0.00226)

1.197

(0.00233)

1.197

(0.00233)

1.197

(0.00233)

Blade count 18 18 18 22 22 22 22 22 22

Vane count 45 45 45 54 54 54 50 50 50

Revolutions per 

minute (actual) 5510 7630 8885 7910 11 205 12 810 9995 12 690 14 295

Inlet cross-sectional 

area, m2 (ft2)

0.200 

(2.15)

0.200 

(2.15)

0.200

(2.15)

0.222

(2.39)

0.222

(2.39)

0.222

(2.39)

0.215

(2.32)

0.215

(2.32)

0.215

(2.32)

Design relative tip 

Mach number 0.86 0.86 0.86 1.20 1.20 1.20 1.52 1.52 1.52

Axial rotor-stator 

spacing (in rotor tip 

chords)

1.42 1.42 1.42 3.14 3.14 3.14 2.32 2.32 2.32

Fan inlet flow, kg/s 

(lb/s)

11.16

(24.60)

17.70

(39.02)

20.66

(45.54)

25.46

(56.14)

36.82

(81.17)

42.75

(94.24)

27.03

(59.60)

34.84

(76.8)

39.96

(88.1)

Fan inlet total 

temperature, K (°R)

297.3 

(535.2)

296.4 

(533.5)

297.1 

(534.8)

295.7 

(532.2)

295.5 

(531.9)

295.3 

(531.5)

297.4 

(535.3)

279.2 

(534.9)

297.4 

(536.3)

Fan exit total 

temperature, K (°R)

306.0 

(550.8)

31.5 

(564.3)

320.4 

(576.7)

310.3 

(558.6)

325.6 

(586.1)

335.6 

(604.0)

320.7 

(577.3)

337.1 

(605.8)

349.1 

(628.4)

GE flight cleanup

(takeoff, cutback = 

1; approach = 2)

2 1 1 2 1 1 2 1 1

a

GE is General Electric Company.

b

Source-to-observer distance set to 0.3 m (1 ft).

Fan reference diameter set to 0.56 m (1.83 ft).

Flight Mach number set to 0.0 to avoid “flyover” Doppler frequency shift in output spectra.

Prediction method flag set to GE revised method.

Inlet guide vane index set to 1 (no vanes).

Inlet flow distortion index set to 1 (no distortion).

Fan inlet broadband switch set to “true.”

Fan inlet R/S discrete tone switch set to “true.”

Fan inlet combination tone switch set to “false.”

Fan inlet distortion tone switch set to “false.”

Fan discharge broadband switch set to “true.”

Fan discharge rotor-stator discrete tone set to “true.” c

ADP is the NASA-Pratt & Whitney Advanced Ducted Propulsor Fan 1; SDT, the NASA-General Electric Source Diagnostic Test fan; and QHSF 2, the 

NASA-Honeywell Quiet High Speed Fan 2.
NASA/TP—2012-215653 128

Figure 5.9.—Sound pressure level (SPL) error in ANOPP predictions for

all sideline emission angles for ADP fan at various tip speeds. Gray

bar represents experimental uncertainty. (a) 5425 rpm. (b) 7525 rpm. 

(c) 8750 rpm.
Fan Noise Prediction

NASA/TP—2012-215653 129 Chapter 5

Figure 5.10.—Sound pressure level (SPL) error in ANOPP predictions

for all sideline emission angles for SDT fan at various tip speeds. Gray 

bar represents experimental uncertainty. (a) 7809 rpm. (b) 11 075 rpm. 

(c) 12 657 rpm.
NASA/TP—2012-215653 130

Figure 5.11.—Sound pressure level (SPL) error in ANOPP predictions for 

all sideline emission angles for QHSF 2 fan at various tip speeds. Gray 

bar represents experimental uncertainty. (a) 9840 rpm. (b) 12 500 rpm. 

(c) 14 060 rpm.
Fan Noise Prediction

NASA/TP—2012-215653 131 Chapter 5

noise. It should be noted that the predicted upstream PWL does 

not include the effects of acoustic transmission loss through the 

rotor and, therefore, would overestimate the upstream level 

noise. It should also be noted here that the measured PWL, 

which is calculated by integrating the measured sideline SPL 

over a sphere enclosing the fan model, includes contributions 

from the rotor-stator interaction source as well as the rotor-only 

source(s) (i.e., the contribution of the rotor by itself). As such, a 

direct comparison of the RSI code PWL predictions to the 

measured PWL is not fruitful. However, if rotor-stator interaction PWL contribution could be estimated, then meaningful 

comparisons could be carried out. 

Like similar codes, RSI requires a description of the basic 

blade row geometry, mean flow quantities, and impinging 

turbulence characteristics as input for computing broadband noise 

spectra. Specifically, RSI requires the radial variations of the vane 

chord and stagger angle, radial distributions of the axial and 

tangential components of the mean flow, radial distributions of 

the root-mean-squared (rms) turbulence intensity, and the integral 

length scales of turbulence. Turbulence information is sometimes 

available from experiments or more typically is heuristically 

modeled to provide the best fit of the predicted noise spectra to 

the measured levels. An alternative approach is to compute the 

turbulence characteristics using Reynolds-averaged Navier–

Stokes (RANS) calculations, since measuring the turbulence 

integral length scales is not an easy task especially in high-speed 

flow environments. The RANS code utilized in this study is 

TSWIFT, which is a derivative of a code developed at NASA 

Glenn over the past several years (see Ref. 47). For each fan 

under consideration in this study, the TSWIFT code was used to 

compute the flow field at all tip speeds of interest. This represents 

a large and detailed investigation of the fan aerodynamics for the 

three fans used in this study and served as an invaluable resource 

for generating the input for this assessment.

Shown in Figure 5.12 are the three-dimensional computational blocks for the rotor and stator (in this case for the ADP 

fan). The full simulation includes additional blocks enclosing 

not only the two blade rows, but also the entire flow path 

inside the nacelle as well as the external flow field within the 

tunnel. The blocks are a mix of axisymmetric and full threedimensional flow-field volumes. In Figure 5.13 axisymmetric 

Mach number contours computed using the TSWIFT code for 

the ADP fan at the takeoff condition (i.e., 8750 rpm) are 

shown as an example of the level of detail that is available 

from these simulations. All geometric, mean flow, and 

turbulence information needed to run the RSI code were 

obtained by interrogating the rotor, stator, and the rotor-stator 

intermediate blocks. As described in Reference 8 the turbulence and kinetic energy information are used to construct 

both an analytic description of the rms turbulence intensity 

across the blade pitch and to estimate the integral length scales 

of turbulence using the isotropic assumption. In the RSI code a 

distinction is made between the distributions of the turbulence 

intensity within the background flow and within the rotor 

wake flow (see Ref. 8). Background turbulence refers to that 

portion of turbulence that was not generated by the rotor 

blades, but originated upstream of the fan and was drawn into 

the fan disc. It should be noted that we define the background 

turbulence region as spanning the entire blade pitch and that 

its level is uniform across the blade pitch. Any excess level 

above the background produced downstream of the fan blade 

is considered to be the wake turbulence contribution. Because 

the RSI predictions are sensitive to the input turbulence 

information, it is desirable to check the accuracy of the 

computed turbulence characteristics from the TSWIFT code 

by comparing them with the experimental data.

Figure 5.12.—Computational domains for ADP fan used by TSWIFT code. (a) Rotor. (b) Stator.
NASA/TP—2012-215653 132

Figure 5.13.—Flow field through ADP fan duct. Axisymmetric Mach number contours 

at 8750 rpm computed using TSWIFT code. External as well as internal flows

included. Black lines indicate block boundaries.

In Figure 5.14 comparisons of the predicted and measured 

total turbulence intensity 6.4 cm (2.5 in.) downstream of the 

fan rotor tip trailing edge are plotted at three spanwise 

stations. The results correspond to the approach condition 

(7809 rpm) for the SDT fan and are the most reliable available 

data for this purpose. The comparisons are shown for three 

spanwise stations; namely, 88 percent shown in the top plot 

for the outboard region, 71 percent span shown in the middle 

plot for an intermediate region, and 56 percent shown in the 

bottom plot for an inboard region. Note that the locations of 

the inboard and outboard stations were selected to avoid the 

disturbed flow regions near the inner and outer walls where it 

is hard to make a distinction between the background turbulence and wake turbulence. The intermediate station was 

chosen since it falls between the other two. Whereas the 

TSWIFT code seems to predict reasonable levels of turbulence 

within the wake region, it predicts much lower levels for the 

background turbulence by as much as 90 percent. The cause of 

this shortfall is not entirely clear at this point and warrants 

further investigation. In the meantime, for the purposes of this 

study, the measured background turbulence level, which turns 

out to be about 1.5 m/s (5 ft/s) at all spanwise stations and all 

the measured conditions,10 was used as the input for the

 10Note that on a percent basis, the background turbulence intensity 

level changes as a function of spanwise station and fan tip speed.

background turbulence level for all RSI test cases. Otherwise, 

the RANS results were used “as is,” meaning that the distribution of the wake turbulence intensity as well as the integral 

length scale were used from the RANS simulation results 

without any change. It should be emphasized that in the 

TSWIFT code, the background turbulence level is set a priori 

on the outer boundaries of the computational domain11 and 

remains essentially unaffected in absolute terms (not percent 

basis) by the flow through the fan rotor. Therefore, the 

computed wake turbulence level (as we have defined it here) 

would have not changed had a 5-ft/s background level been 

used in TSWIFT simulations in the first place.

Finally, it should be noted that the turbulence information 

used here was extracted at the exit plane of the rotor block 

since TSWIFT uses a mixing plane strategy to couple the rotor 

and the stator and, as such, smears the turbulence information 

at the inlet plane of the stator block. To ensure accuracy, the 

rotor block exit plane was placed very close to the stator 

leading edge (approximately 1.3 cm (0.5 in.)).

The PWL predictions from the RSI code for all cases considered in this chapter are compared with the measured PWL 

and the results are shown in Figure 5.31 to Figure 5.33 in 

Appendix C. Note that the measured PWL spectra include

 11The 1990s vintage measurements reported 0.25-percent free-stream 

turbulence level at Mach number = 0.1 (i.e., ~0.09 m/s, or ~0.28 ft/s).
Fan Noise Prediction

NASA/TP—2012-215653 133 Chapter 5

Figure 5.14.—Comparisons of measured and predicted 

turbulence intensity for three spanwise stations 

2.5 in. downstream of rotor tip trailing edge of SDT 

fan atapproach condition. Predictions made using 

NASA TSWIFT code; dashed curves are predicted 

levels raised so background level matches

measured background. (a) 88 percent span.

(b) 71 percent span. (c) 56 percent span.

only broadband contribution since tone content was removed 

from the measured data.12 The RSI predictions were calculated 

for 50 frequency values, roughly covering the range between 1 

and 50 kHz. The actual RSI acoustic power level predictions 

at each frequency value are shown as open red circles in these 

figures. There is some scatter in predictions because RSI 

couples a two-dimensional stripwise unsteady aerodynamic 

response to a three-dimensional acoustic modal description. 

Because there is an inherent mismatch between the cutoff 

phenomena in two- and three-dimensional unsteady responses, 

there sometimes occurs exaggerated two-dimensional 

aerodynamic response near a two-dimensional mode cutoff 

condition that would not have occurred for a threedimensional mode. The result is a somewhat erratic PWL 

variation as a function of frequency. This is more noticeable at 

lower frequencies where fewer modes propagate at each 

frequency, and therefore the power sum is more sensitive to 

the variations in each mode level. To mitigate the effect of the 

cutoff mismatch, in this study, a polynomial curve was fitted 

through the predicted points to smooth out the scatter.13

It should be noted that the predicted PWL spectra shown 

here include only the exhaust contribution since stator inlet 

noise is negligible compared with the stator exhaust noise 

(Ref. 23). From the information in Table 5.4, an error band of 

±1 dB is assigned to the measured PWLs. The reader is 

reminded that the measurements below 2 kHz are contaminated by the extraneous drive rig noise mentioned in the previous 

section, “5.7.1 Empirical Methods.” Furthermore, the RSI 

acoustic power level predictions do not include the rotor-only 

contribution. In contrast, the measured PWL data (henceforth 

referred to as “stage PWL”) include both the rotor-stator 

interaction noise PWL and rotor-only noise PWL.

To gauge the relative magnitude of the rotor-only contribution, we have plotted in Figure 5.15 the measured rotor-only 

PWL for the SDT fan along with the stage PWL. Note that the 

stage PWL data are the same as those plotted in Figure 5.32

(Appendix C). The rotor-only PWL data were acquired for the 

SDT fan (but not the other two fans) by removing the stator 

and independently supporting the nacelle and the centerbody 

(see Ref. 49). With both sets of PWL spectra available, one 

can calculate the rotor-stator interaction contribution by 

spectral subtraction of the two (i.e., antilogarithmic difference 

converted back to decibels). The result, shown in blue, 

represents only an estimate because rotor transmission loss 

effects are still present in the difference spectra. Nonetheless, 

these estimates provide a better benchmark for evaluating the 

RSI predictions than the stage PWL data do. Naturally, the

 12The tone extraction procedure is somewhat subjective without the 

use of time-domain averaging, which is only possible if long time 

series data were acquired together with the once-per-revolution signal 

from the fan rotor. Such data are not available for all fan configurations investigated here.

13A more elegant and mathematically robust fix may be that 

suggested by Atassi and Hamad in Reference 48, which ameliorates 

the cutoff mismatch.
NASA/TP—2012-215653 134

Figure 5.15.—Rotor-stator (R-S) interaction narrowband sound power level (PWL) for SDT fan at different 

speeds from measured stage and rotor-only PWLs: R-S = stage – rotor-only. Dashed line indicates data 

reliability is questioned (see Sec. 5.7.2). (a) 7809 rpm. (b) 9493 rpm. (c) 11 075 rpm. (d) 11 771 rpm. 

(e) 12 657 rpm.
Fan Noise Prediction

NASA/TP—2012-215653 135 Chapter 5

benchmarking will be limited to the SDT data, but even this 

limited assessment is still useful.

It should be noted that the rotor-only PWL data include a 

higher proportion of drive rig noise contamination because of 

the high-speed swirling flow exiting the duct and impinging 

on the drive rig. The contamination levels are higher—since 

the absolute exit velocities are higher—for the rotor-only 

configuration compared with the stage configuration for the 

same fan tip speed. The difference is clearly evident by 

examining the crossover point where rotor-only noise power 

levels exceed the stage power levels as the tip speed increases. 

As a result, the range of frequencies where the rotor-stator 

interaction PWL estimates are valid decreases as the fan tip 

speed increases. Specifically, at the lowest tip speed (i.e.,

7809 rpm) the spectral differencing results are valid starting at 

2 kHz, while for the highest tip speed (i.e., 12 657 rpm) they 

are valid starting at 6 kHz.

Another important aspect of the spectral differencing has to 

do with the interpretation of the difference when the rotor-only 

PWLs are close to the stage PWLs, even if the rotor-only 

noise levels are less than the stage noise levels. Given the

±1-dB measurement uncertainty band, when the constituent 

spectra are within 2 dB of each other, the resulting difference 

is suspect. In order to ensure unambiguous results, we have 

chosen to use 3 dB as the criterion to accept the difference as 

reliable. Put differently, we accept the rotor-stator interaction 

PWL as free from ambiguity only when the difference PWL is 

equal to or larger than the rotor-only PWL. In Figure 5.15, 

where this criterion is not met, the rotor-stator interaction 

PWL is shown as a dotted line. An examination of the results 

in these figures indicates that the frequency range where the 

rotor-stator interaction PWL is reliable shrinks as the tip speed 

increases until eventually, at the highest fan tip speed, the 

resulting spectrum is entirely unreliable.

Although somewhat limited, these rotor-stator interaction 

estimates can still serve to assess the validity of the RSI 

predictions. The RSI acoustic power level predictions are 

compared with the estimated rotor-stator interaction acoustic 

power level in Figure 5.16. As before, only the reliable portion 

of the estimated rotor-stator interaction PWL spectrum is 

shown as a solid line. Where comparisons are possible, the 

data-theory agreement is fair at low tip speeds, but deteriorates 

with increasing tip speed.

The results of the data-theory comparisons for the SDT fan 

are summarized in Figure 5.17. Generally speaking, the RSI 

predictions overestimate the level of measured sound power 

level generated by rotor-stator interaction noise by as much as 

4 dB beyond the uncertainty margin. Surprisingly, the datatheory agreement is better when the RSI predictions are 

compared with the measured stage PWL as shown in 

Figure 5.32 (Appendix C). In addition to the shortcoming of 

the RSI code, it is also entirely possible that the procedure 

used to isolate the measured rotor-stator interaction noise 

described earlier may be partially responsible for the relatively 

poor data-theory agreement summarized in Figure 5.17. 

Therefore, the principal conclusion here is that rotor-only 

source contribution must be modeled in order to get a better 

assessment of the accuracy of the RSI code for predicting fan 

broadband noise.

5.7.3 Computational Methods

As an example of computationally intensive methods, the 

LINFLUX code (see Ref. 15) was selected for this assessment 

exercise. The choice was dictated for two main reasons. First, 

LINFLUX has been in use since the late 1990s and has been 

rigorously exercised and even used in design work. Second, 

computational codes tend to require significant user experience to be reliably used for analysis and design purposes. At 

NASA, LINFLUX has been extensively used and is the tool of 

choice when high-fidelity predictions are required.14 NASA 

has been developing a more advanced code in this category 

(i.e., BASS, see Ref. 20), but it is still in the late development 

stages and not yet ready for routine use.

LINFLUX is a frequency-domain, three-dimensional, 

linearized inviscid description of the unsteady flow. In this 

study it was used to compute the rotor-stator interaction tones 

generated as a result of the mean perturbations in the fan rotor 

wake impinging on the stator. The underlying mean flow (also 

three-dimensional and inviscid) is representative of the flow 

through a realistic stator. The required nonlinear mean flow 

can be computed using any suitable inviscid code, but for the 

purposes of this study a serial version of the TURBO inviscid 

steady aerodynamic code was used. Both LINFLUX and 

TURBO use an implicit and finite-volume description of the 

flow, which makes for better consistency in describing and 

analyzing both the mean and perturbation components of the 

flow. A detailed description of the LINFLUX code (and to 

some extent the version of the TURBO code used here) can be 

found in Reference 15 and other works cited in that document. 

The LINFLUX code calculates perturbation density, momenta, 

and internal energy everywhere in the domain subject to 

specified wake perturbation input, which are supplied in terms 

of the fan blade-passing harmonic content. In this study, these 

were generated from the TSWIFT simulations discussed 

earlier. The TSWIFT simulations were used to supply the 

inflow conditions for the mean flow calculations. These 

include the radial profiles of the circumferentially averaged 

total pressure, total temperature, and the swirl angle at the 

inflow plane of the computational domain for TURBO. The 

harmonic content of the wake perturbation were also computed from the TSWIFT solutions by extracting wake perturbation velocities at the exit plan of the rotor block and Fourier 

decomposing them. 

In addition to the field solution, LINFLUX also calculates 

the tone SPL and PWL upstream and downstream of the 

stator.15 Since the computational inflow and outflow boundaries fall well short of the Rotating Rake measurement stations,

 14The well-known NASA tone noise prediction codes V072 and 

TFaNS were not assessed, since LINFLUX, by comparison, has been

shown to produce more robust results in both trend and absolute sense.

15LINFLUX does not account for rotor transmission effects.
NASA/TP—2012-215653 136

Figure 5.16.—Comparison of predicted (using RSI code) and estimated narrowband sound power

levels (PWLs) for SDT fan at different speeds. Estimates are rotor-stator (R-S) interaction PWLs taken 

from Figure 5.15. Dashed line indicates data reliability is questioned (see Sec. 5.7.2). (a) 7809 rpm. 

(b) 9493 rpm. (c) 11 075 rpm. (d) 11 771 rpm. (e) 12 657 rpm.
Fan Noise Prediction

NASA/TP—2012-215653 137 Chapter 5

Figure 5.17.—Error in predicted (using RSI code) narrowband sound power levels 

(PWLs) for SDT fan at different speeds (Figure 5.16). Gray bar represents

experimental uncertainty.

the data-theory comparisons shown here are on the acoustic 

power level basis, which is thought to be conserved, at least 

for the nonswirling flow downstream of the stator.

Both the mean and perturbation flows are discretized on a 

regular H-mesh topology, which needs to be dense enough to 

resolve the perturbations of interest. Therefore, the size of the 

grid depends on the frequency content under consideration. In 

this study, the goal was to resolve rigorously the second 

harmonic of the blade-passing frequency (i.e., 2×BPF) tone.16

The documentation for the LINFLUX code calls for a 

minimum of 40 grid points per acoustic wavelength to 

adequately resolve the perturbations. Each grid extends axially 

one vane chord upstream and one vane chord downstream to 

allow the mean flow to become axisymmetric at the inflow 

and outflow planes. In the radial direction nearly the same 

number of grid points were used in all cases because the vane 

span (measured vertically) is nearly the same for all three 

stators. In the tangential direction, the grid spans one blade 

passage because LINFLUX uses the known interblade phase 

angle as a means of relating the boundary conditions on one 

side of the passage to those on the other side. The grid sizes 

used for the three fans in this study are listed in Table 5.9. The 

larger axial grid size for QHSF 2 is a consequence of the 

swept geometry of the stator for this fan, which necessitates a 

larger axial domain if the one vane chord upstream

and downstream “rule” were to be enforced. Finally, the 

 16Blade-passing frequency tone is cut off for all three fans, given their 

blade/vane ratios.

differences in the tangential direction are due to differences in 

the vane counts. In the interest of reducing the number of grids 

that had to be generated and the mean flow fields that had to 

be computed for each fan, the grid corresponding to the 

highest fan tip speed (and hence highest frequency) was 

chosen as the common grid for all speeds for that fan.

TABLE 5.9.—TURBO AND LINFLUX GRID SIZES

Fana Axial Radial Tangential

ADP 181 49 43

SDT 181 51 37

QHSF 2 211 51 39 a

ADP is the NASA-Pratt & Whitney Advanced Ducted 

Propulsor Fan 1; SDT, the NASA-General Electric Source 

Diagnostic Test fan; and QHSF 2, the NASA-Honeywell 

Quiet High-Speed Fan 2.

In all cases, the TURBO and LINFLUX calculations were 

run to convergence (i.e., at least 4 orders of magnitude reduction 

in the maximum residual). This involved running the TURBO 

simulations at least 40 000 iterations and the LINFLUX 

calculations a minimum of 5000 iterations unless the solution 

converged sooner. The characteristics of the converged mean 

flowfields were closely examined in each case to ensure that the 

flow was well behaved especially near the blade surface. This 

turned out to be possible only for the ADP and SDT fans, but 

not the QHSF 2 fan. For the latter fan, the flow develops a small 

recirculation zone near the leading edge on the pressure side 

and/or near the trailing edge on the suction side of the vane. An 
NASA/TP—2012-215653 138

examination of the TSWIFT simulation results indicates that the 

same phenomena are present in the viscous solutions and, 

hence, they are not artifacts of the inviscid calculations. When 

such recirculation zones are present in the mean flow, the 

perturbation calculations do not behave well and sometimes do 

not even converge. As a result, the QHSF 2 results are not 

included in this chapter, but might be included in a separate 

report if they can be converged through reasonable changes in 

the inflow conditions.

The results of the data-theory comparisons for the 2×BPF 

tones of the ADP and SDT fans are shown in Figure 5.18 and 

Figure 5.19. The comparisons shown here are only for the 

downstream-radiated noise (i.e., the exhaust noise), since the 

three-dimensional rotor acoustic transmission loss through the 

fan rotor cannot be accounted for using the LINFLUX code at 

the present time. Figure 5.18 shows the variations in the level 

of the acoustic power at the 2×BPF as a function of the tip 

speed for the ADP fan, and Figure 5.19 shows the results for 

the SDT fan. Acoustic power levels based on SPL measurements from both the Rotating Rake system (designated RR 

data) and the 9x15 wind tunnel sideline microphone system 

(designated SL data) are shown in both figures. As indicated 

in Table 5.4 and Table 5.7, the uncertainty margin in measuring the sideline acoustic data is ±1 dB, and for the Rotating 

Rake system it is ±4.3 dB. Both sets of uncertainties are 

indicated in the figures also.

Note that, in general, there are noticeable differences between the acoustic power levels obtained via the Rotating Rake 

and sideline microphone systems. This is in part due to the fact 

that while the Rotating Rake system can measure a specific 

circumferential mode at a given frequency (i.e., the rotor-stator 

Tyler-Sofrin interaction mode with a circumferential mode 

number of –9 at 2×BPF for ADP), the sideline measurements 

include—in addition to the Tyler-Sofrin mode—extraneous 

modes generated at 2×BPF. The extraneous modes, which are 

always produced in a fan rig, are a result of manufacturing and 

installation imperfections that prevent precise phasing amongst 

corresponding wakes from various fan blades and amongst 

unsteady pressure responses from various vanes. The end result 

is imperfect cancellations and reinforcements giving rise to 

circumferential modes that do not obey the Tyler-Sofrin rule 

based on the blade and vane counts (see Ref. 50). Fortunately, 

in most cases the extraneous modes are much less energetic than 

the Tyler-Sofrin mode(s), and in aggregate, they contribute only

Figure 5.18.—Comparison of measured and predicted sound power levels 

(PWLs) for exhaust 2×BPF tone (second harmonic of blade-passing 

frequency) for ADP fan at different tip speeds. Data from Rotating Rake (RR) 

and sideline microphone (SL). Predictions calculated using LINFLUX code. 

Results are for circumferential mode –9.
Fan Noise Prediction

NASA/TP—2012-215653 139 Chapter 5

Figure 5.19.—Comparison of measured and predicted sound power levels 

(PWLs) for exhaust 2×BPF tone (second harmonic of blade-passing 

frequency) for SDT fan at different tip speeds. Data from Rotating Rake (RR) 

and sideline microphone (SL). Predictions calculated using LINFLUX code. 

Results are for circumferential mode –10.

a modest extra amount of acoustic power beyond that contained 

in the Tyler-Sofrin mode(s). For example, for SDT fan, where 

detailed Rotating Rake mode data are available, it turns out that 

the extraneous modes typically contribute less than 2 dB to the 

total acoustic power at 2×BPF. Therefore, the sizable discrepancies between the PWLs for the Rotating Rake and sideline data 

cannot be entirely explained by the presence of the extraneous 

modes. This makes a conclusive determination of the

LINFLUX prediction accuracy problematic since the measured 

data are somewhat suspect. However, given the relatively large 

uncertainties in the Rotating Rake data compared with the 

sideline data, it is likely that the sideline data is a better measure 

of the acoustic power at the target frequencies. Nonetheless, in 

the interest of completeness, data-theory comparisons for both 

measurements systems are included here.

Returning to Figure 5.18 and Figure 5.19, it is typically the 

case that there is good agreement between the predictions 

from LINFLUX and the sideline data for the ADP fan for all 

tip speed conditions. The agreement for the SDT fan is not as 

good and generally comparable to that using the Rotating 

Rake data. In contrast, the data-theory agreement for the 

Rotating Rake data is quite poor for both fans. The results of 

the prediction error analysis are presented in Figure 5.20 for 

the data based on the Rotating Rake measurement system, and 

in Figure 5.21 for the data based on the sideline measurement 

system. In both figures, the gray bar signifies the experimental 

uncertainty. In the case of the Rotating Rake data 

(Figure 5.20) for the majority of the cases, the prediction error 

lies well outside of the uncertainty band (by as much as 5.7 dB 

for the ADP fan at takeoff condition). In contrast, the margin 

of error is much smaller and mostly within the uncertainty 

band for the ADP fan when the predictions are compared with 

the sideline data. The error for the SDT fan is large even when 

compared with the sideline data (by as much as 7.6 dB for the

11 771-rpm tip speed condition). Therefore, taking the sideline 

data as the benchmark, there is excellent agreement between 

data and theory for the ADP fan mostly within the uncertainty 

band, but a rather poor agreement for the SDT fan with errors 

as large as 7.6 dB outside of the sideline measurements 

uncertainty band.

Finally, additional studies were carried out to investigate 

the dependence of the LINFLUX predictions on the grid size. 

The results of these studies indicate that the solutions presented here are grid independent such that halving the grid size for 

the ADP fan (i.e., using a 181×25×43 grid) changed the 

predictions by less than 1 dB. It should be noted that this 

conclusion is based on running both TURBO and LINFLUX 

on the coarser mesh for all five ADP fan speeds.
NASA/TP—2012-215653 140

Figure 5.20.—Error in prediction of sound power level (PWL) for 2×BPF tone 

(second harmonic of blade-passing frequency) using data from Rotating 

Rake. Data for ADP fan is from Figure 5.18 (circumferential mode –9). Data 

for SDT fan is from Figure 5.19 (circumferential mode –10). Error is defined 

as (measured level) – (predicted level). Predictions calculated using LINFLUX 

code. Gray bar represents experimental uncertainty.

Figure 5.21.—Error in prediction of sound power level (PWL) for 2×BPF tone 

(second harmonic of blade-passing frequency) using data from sideline

microphone. Data for ADP fan is from Figure 5.18 (circumferential mode –9). 

Data for SDT fan is from Figure 5.19 (circumferential mode –10). Error is

defined as (measured level) – (predicted level). Predictions calculated using 

LINFLUX code. Gray bar represents experimental uncertainty.
Fan Noise Prediction

NASA/TP—2012-215653 141 Chapter 5

5.8 Conclusions

NASA fan prediction codes in the empirical, acousticanalogy-based, and computational categories were exercised 

and assessed against a set of benchmark fan acoustic data. The 

codes included ANOPP (an empirical code), RSI (an acousticanalogy-based code), and LINFLUX (a computational 

aeroacoustics code). The benchmark fans cover a wide range 

of fan bypass ratios, pressure ratios, and tip speeds. The 

assessment results indicate that the ANOPP code can predict 

the fan noise spectrum to within 4 dB of the measurement 

uncertainty band on a 1/3-octave basis for the ultra-high- and 

high-bypass-ratio fans. The RSI code can predict rotor-stator 

interaction broadband noise spectrum to within 4 dB of 

experimental uncertainty band for the high-bypass ratio fan. 

The LINFLUX code can predict interaction tone power levels 

to within experimental uncertainties at low and moderate fan 

tip speeds, but could deviate by as much as 7.6 dB outside the 

experimental uncertainty band at the highest tip speeds in 

some cases.

The results of this assessment report will guide the course 

of the future developments in the area of fan noise modeling 

and prediction at NASA. In the short term, the goal is to 

continue to improve the RSI code while also adopting and/or 

developing a rotor-only noise prediction capability that can be 

combined with RSI to provide an improved fan broadband 

noise prediction tool set. In parallel, work is underway to 

develop a rotor acoustic transmission capability that can be 

used in conjunction with both the RSI and LINFLUX codes to 

improve inlet noise prediction. In the meantime, the ongoing 

work in developing a numerically based approach to predicting rotor-stator interaction broadband noise has been completed, and initial code validation exercises are underway. It is 

hoped that, when it is ready, this code (currently called BASS) 

together with LINFLUX will represent the state of the art in 

fan noise prediction for subsonic-tip-speed fans. In the long 

term, the aim is to revisit supersonic rotor noise and improve 

the Superpose code to tackle MPT noise. As for ANOPP, 

NASA continues to maintain and improve it, but plans are in 

place to eventually supplant this code with a multifidelity 

capability that accounts for source distribution and source 

noncompactness as well as installation, reflection, refraction, 

and scattering effects.

5.9 Acknowledgments

Edmane Envia thanks Dr. Christopher J. Miller for his 

invaluable suggestions for improving the quality of the mean 

flow solutions used in the LINFLUX assessment studies.

Fan Noise Prediction

NASA/TP—2012-215653 143 Chapter 5

Appendix A.—Nomenclature

A.1 Acronyms

ADP Advanced Ducted Propulsor 

ANOPP Aircraft Noise Prediction Program

ASME American Society of Mechanical Engineers

BPF blade-passing frequency

CAA computational aeroacoustics

GE General Electric

LSWT Low-Speed Wind Tunnel

MPT multiple pure tones

PWL power level

QHSF 2 Quiet High Speed Fan 2

RANS Reynolds-averaged Navier–Stokes

rms root-mean-squared

SDT Source Diagnostic Test

SPL sound pressure level

UHB ultrahigh bypass

Fan Noise Prediction

NASA/TP—2012-215653 145 Chapter 5

Appendix B.—Additional Data-Theory Comparisons for ANOPP 

In this appendix, Figure 5.22 to Figure 5.30 present additional comparisons between experimental and theoretical 

(using the Aircraft Noise Prediction Program (ANOPP) code) 

sound pressure level (SPL) data for the NASA-Pratt & 

Whitney Advanced Ducted Propulsor (ADP) Fan 1, the 

NASA-General Electric Source Diagnostic Test (SDT) fan, 

and NASA-Honeywell Quiet High Speed Fan 2 (QHSF 2) 

model fans at typical inlet and exhaust emission angles of 46°

and 136°, respectively.

Figure 5.22.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for ADP fan in inlet and exhaust quadrants at 

5425 rpm at Mach 0.1. (a) Inlet quadrant; emission

angle 46°. (b) Exhaust quadrant; emission angle 136°.

Figure 5.23.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for ADP fan in inlet and exhaust quadrants at 

7525 rpm at Mach 0.1. (a) Inlet quadrant; emission

angle 46°. (b) Exhaust quadrant; emission angle 136°.
NASA/TP—2012-215653 146

Figure 5.24.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for ADP fan in inlet and exhaust quadrants at 

8750 rpm at Mach 0.1. (a) Inlet quadrant; emission

angle 46°. (b) Exhaust quadrant; emission angle 136°.

Figure 5.25.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for SDT fan in inlet and exhaust quadrants at 

7809 rpm at Mach 0.1. (a) Inlet quadrant; emission

angle 46°. (b) Exhaust quadrant; emission angle 136°.
Fan Noise Prediction

NASA/TP—2012-215653 147 Chapter 5

Figure 5.26.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for SDT fan in inlet and exhaust quadrants at 

11 075 rpm at Mach 0.1. (a) Inlet quadrant; emission

angle 46°. (b) Exhaust quadrant; emission angle 136°.

Figure 5.27.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for SDT fan in inlet and exhaust quadrants at 

12 657 rpm at Mach 0.1. (a) Inlet quadrant; emission 

angle 46°. (b) Exhaust quadrant; emission angle 136°.
NASA/TP—2012-215653 148

Figure 5.28.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for QHSF 2 fan in inlet and exhaust quadrants at 

9840 rpm at Mach 0.1. (a) Inlet quadrant; emission

angle 46°. (b) Exhaust quadrant; emission angle 136°.

Figure 5.29.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for QHSF 2 fan in inlet and exhaust quadrants at 

12 500 rpm at Mach 0.1. (a) Inlet quadrant; emission 

angle 46°. (b) Exhaust quadrant; emission angle 136°.
Fan Noise Prediction

NASA/TP—2012-215653 149 Chapter 5

Figure 5.30.—Comparison of 1/3-octave measured sound 

pressure level (SPL) and SPL predicted from ANOPP 

code for QHSF 2 fan in inlet and exhaust quadrants at 

14 060 rpm at Mach 0.1. (a) Inlet quadrant; emission 

angle 46°. (b) Exhaust quadrant; emission angle 136°.

Fan Noise Prediction

NASA/TP—2012-215653 151 Chapter 5

Appendix C.—Additional Data-Theory Comparisons for RSI Code

In this appendix, Figure 5.31 to Figure 5.33 present additional comparisons between experimental and theoretical 

(using RSI code) narrowband sound power level (PWL) data 

for the NASA-Pratt & Whitney Advanced Ducted Propulsor 

(ADP) Fan 1, the NASA-General Electric Source Diagnostic 

Test (SDT) fan, and NASA-Honeywell Quiet High Speed Fan 

2 (QHSF 2) model fans at various blade tip speeds.
NASA/TP—2012-215653 152

Figure 5.31.—Comparison of measured narrowband sound power level (PWL) and PWL predicted using 

RSI code for ADP fan at various blade tip speeds. Data represent combined rotor and stator

contributions. (a) 5425 rpm. (b) 6700 rpm. (c) 7525 rpm. (d) 8345 rpm. (e) 8750 rpm.
Fan Noise Prediction

NASA/TP—2012-215653 153 Chapter 5

Figure 5.32.—Comparison of measured narrowband sound power level (PWL) and PWL predicted using 

RSI code for SDT fan at various blade tip speeds. Data represent combined rotor and stator

contributions. (a) 7809 rpm. (b) 9493 rpm. (c) 11 075 rpm. (d) 11 771 rpm. (e) 12 675 rpm.
NASA/TP—2012-215653 154

Figure 5.33.—Comparison of measured narrowband sound power level (PWL) and PWL predicted

using RSI code for QHSF 2 fan at various blade tip speeds. Data represent combined rotor and

stator contributions. (a) 9840 rpm. (b) 10 935 rpm. (c) 12 500 rpm. (d) 13 280 rpm. (e) 14 060 rpm.
Fan Noise Prediction

NASA/TP—2012-215653 155 Chapter 5

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From Duct Rake Instrumentation on 1.294 Pressure Ratio, 8.06 

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39. Dahl, Milo; and Sutliff, Daniel: Numerical Technique for 

Analyzing Rotating Rake Mode Measurements in a Duct With 

Passive Treatment and Shear Flow. AIAA–2007–3679, 2007.
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40. Gillian, R.E.: Aircraft Noise Prediction Program User’s Manual. NASA TM–84486, 1982.

41. Zorumski, W.E.: Aircraft Noise Prediction Program Theoretical Manual. NASA TM–83199–PT–1, 1982.

42. Wilson, Mark R.: An Introduction to High Speed Aircraft 

Noise Prediction. NASA CR–189582, 1992.

43. Kontos, K.B.; Janardan, B.A.; and Gliebe, P.R.: Improved 

NASA–ANOPP Noise Prediction Computer Code for Advanced Subsonic Propulsion Systems. Volume 1: ANOPP 

Evaluation and Fan Noise Model Improvement. NASA CR–

195480, 1996.

44. Kontos, Karen B.; Kraft, Robert E.; and Gliebe, Philip R.: 

Improved NASA–ANOPP Noise Prediction Computer Code 

for Advanced Subsonic Propulsion Systems. Volume 2: Fan 

Suppression Model Development. NASA CR–202309, 1996.

45. Heidmann, Marcus F.: Interim Prediction Method for Fan and 

Compressor Source Noise. NASA TM X–71763, 1979.

46. Brown, Clifford A.; and Schifer, Nicholas A.: Low Frequency 

Noise Contamination in Fan Model Testing. ASME GT2008–

50850, 2008, pp. 849–862.

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Three-Dimensional Disturbances Convected in a Subsonic 

Flow. AIAA–1981–2046, 1981.

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Test—Rotor Alone Aerodynamic Performance Results. AIAA–

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NASA/TP—2012-215653 157

Chapter 6—Uncertainty in Acoustic Liner

Impedance Measurement and Prediction

Tony L. Parrott and Michael G. Jones6

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681–2199

Summary

For nearly five decades, passive acoustic liners have been the mainstay for attenuation of tone-dominated fan noise propagated 

through aircraft engine nacelles, both in the inlet and the aft-fan duct. For the most part, these liners consist of one- to three-layer 

perforate-over-honeycomb structures. Besides the desire to attain a target attenuation spectrum, several environmental and 

structural considerations drive liner design. Early in the history of liner development, the convergence of these considerations led 

to the resistive-facesheet resonator as the key functional element. From the acoustician’s viewpoint, such structures are locally 

reacting; that is, lateral wave propagation in the liner is prohibited. This means that the normal incidence acoustic impedance 

becomes the key design parameter governing sound attenuation in the duct airway. As such, an impedance boundary condition on 

the acoustic wave propagation process allows the nuances of the duct propagation problem to be isolated. This is especially 

relevant to understanding how uncertainties in the propagation process interact with uncertainties in the duct boundary conditions 

(i.e., liner impedance).

This chapter focuses on prediction and measurement uncertainties of the local-reacting impedance boundary condition, as 

employed in duct propagation models to predict acoustic attenuation spectra for nacelle liners. Given an attenuation spectrum

target, the liner designer is tasked with providing a realizable, optimal liner design. Over the past five decades, numerous semiempirical impedance prediction models have been proposed by academia and aircraft industry researchers. During this time, 

NASA Langley Research Center has focused mainly on the development of impedance measurement technology. This separation 

between measurement technology and modeling has placed Langley’s measurement capability in the role of validating prediction 

models generated by its industry and academia partners. Clearly, such validations need to be supported by accompanying statements concerning error bounds or limits. The basis for the current assessment consists of 95% confidence interval estimates of 

impedance measurements for a representative single-layer perforate-over-honeycomb core (POHC) test liner.

There are a wide variety of acoustic liners available today; thus it is not possible to make general statements about sources of 

error in their performance or the quantification thereof. Instead, this study addresses a conventional, single-layer POHC-type liner. 

A POHC liner typifies the issues that arise when attempting to apply uncertainty analysis to liner design and fabrication as it 

relates to quality control on the end product; that is, installed liner impedance. To accomplish this, statistical process control (SPC)

concepts are used where confidence intervals for predicted and measured impedances for this POHC test liner represent the 

variability in the liner development process (i.e., the “voice of the process”) that is being monitored using SPC. It is argued that 

with sufficient validation, prediction models can serve to quantify uncertainty metrics of liner fabrication processes for compliance 

with the “voice of the customer”; that is, the end-user-imposed confidence interval that contains the target design impedance.

In general, confidence intervals for the measurements and model predictions do not center on the same mean values, which is 

indicative of systematic error (in either or both the measurement process and prediction model). Also, the prediction model 

confidence intervals for the resistance component vary greatly and do not always encompass those for the measurements. Although 

systematic error is present for the reactance component, it is contained within the model confidence intervals. As expected, 

confidence intervals grow monotonically with frequency for all models.

There is a strong connection between this chapter and Chapter 7, “Assessment of Acoustic Propagation and Radiation Codes for 

Locally Reacting Liners in Flow Ducts,” which focuses on the prediction and measurement of sound propagation through engine 

nacelles. It is noteworthy that, over some bandwidths, small uncertainty in the impedance boundary condition may correlate with 

large uncertainty in the predicted attenuation. Conversely, in other bandwidths, a small uncertainty in the predicted attenuation 

may correlate with relatively large uncertainty in the liner impedance. Clearly, the relationship between confidence intervals on the 

impedance and the predicted attenuation is not uniform with frequency and is likely to be highly dependent on the duct configuration and/or source.

One of the main achievements of this assessment is to propose the applicability of the SPC paradigm to deliver an installed liner 

impedance spectrum to within accompanying customer-specified uncertainty limits. This assessment also highlights current 

capabilities and limitations of impedance measurement processes and prediction models. Finally, it provides guidance toward 

future model development and measurement process enhancements needed to improve the state of the art in acoustic liner design 

and measurement.
NASA/TP—2012-215653 158

6.1 Introduction

Beginning in the 1960s, attention became focused on tonedominated engine noise radiated to airport communities from 

turbofan-powered aircraft (Ref. 1). In the late 1960s, the 

potential for reducing tone noise with passive acoustic treatments (see Figure 6.1), as applied to a turbofan nacelle, was 

dramatically demonstrated via flight tests conducted using a 

Boeing 707–320C powered by JT3D–7 engines. Results from 

this flight test showed that acoustic liners could achieve tonal 

noise reduction on landing approach (dominant tone reduction 

of 32 dB at 2.7 kHz) (Ref. 2). The liner structure consisted of a 

honeycomb core bonded between a porous facesheet and an 

impervious back plate. Such structures are resonant absorbers, 

with the facesheet porosity controlling the peak absorption and 

the honeycomb depth controlling the absorption peak frequency. As such, they are well suited for tonal noise reduction. 

The flight test results clearly demonstrated that suppression of 

noise radiated from the JT3D–7 inlet was enhanced by using 

two treated splitter rings and treated support struts to increase 

the effective treatment-length-to-duct-height ratio (L/H). 

(Geometric L/H was approximately 3.25 for the JT3D–7 inlet.) 

Approximately three decades later, tests were conducted in the 

9- by 15-ft Low-Speed Wind Tunnel at the NASA Glenn 

Research Center with the Advanced Ducted Propulsor (22-in. 

ADP fan rig), a very large bypass ratio turbofan engine (Ref. 3). 

The single-layer liner used in this test was representative of 

1992 liner technology, and the ADP engine had an L/H of 

approximately 0.5 (a factor of 6.5 less than that of the JT3D–7 

flight test engine). When scaled up to a 267-kN (60 000-lb) 

thrust engine, a noise reduction of 5.2 dB was computed for a 

457-m (1500-ft) flyover approach at Mach 0.1. Maximum 

single-tone reduction (at a full-scale frequency of about 600 Hz) 

was estimated to be about 10 dB, and broadband noise attenuation ranged from 2 to 3 dB. The L/H ratio is the key metric for 

estimating the effectiveness of liners to reduce the amount of 

noise radiated from the engine nacelle. As L/H increases, the 

corresponding noise reduction also increases. It is a testimonial 

to the advancing liner technology over the three decades 

separating these two tests that, in spite of an L/H reduction by a 

factor of 6.5, significant tonal and broadband noise reductions 

were achieved.

Acronyms and symbols used in this chapter are listed in 

Appendix A to aid the reader.

6.1.1 Challenge for Liner Design Improvement

The progress in improving liner efficiency over the past 

four decades, as described above, places in perspective the 

challenge of achieving even greater liner efficiency in the face 

of decreasing L/H and the changing character of turbofan 

noise spectra (broadband noise increase and spectrum shift to 

lower frequencies). Success is contingent on advances in 

materials technology, liner fabrication processes, liner 

architecture, liner impedance prediction models, and—perhaps 

most critically—the validation of such models via impedance

Figure 6.1.—Turbofan engine nacelle with wall lining.

measurements. As mentioned previously, the L/H ratio for a 

lined duct is a key metric for estimating relative performance. 

Historically, an off-optimum liner design could still achieve a 

desired noise reduction provided there was sufficient L/H

available. As L/H becomes more restricted, off-optimum 

design becomes less tolerable. The continuing evolution of the 

high-bypass engine, along with greater political pressure to 

reduce the noise footprint in spite of the persistent increase in 

the number of airport operations, combine to provide great 

stimulus to improve liner efficiency. Notwithstanding past 

turbofan noise source reductions credited to improvements in 

fan blade design, passive liner technology continues to be an 

important tool for reducing turbofan noise emission. Consistent with the foregoing issues, the implication is that future 

liner design will become far less forgiving than was the case 

historically. Thus there is a need for more efficient designs 

that provide more attenuation per L/H, as well as an increased 

emphasis on ensuring that a target design is realized in the 

operational engine nacelle. To that end, the objective of the 

uncertainty analysis described in this chapter lays out a 

framework for assessing the effects of environmental and 

geometric parameters on liner design.

6.1.2 Viable Liners for Turbofan Engine Nacelles

For application in turbofan engines, viable liner designs must 

function in harsh aeroacoustic environments to provide efficient 

noise attenuation while complying with stringent mechanical 

and environmental constraints. Historically, these constraints 

have ruled out bulk absorbers such as foam and fiberglass, 

which are excellent choices for broadband attenuation, but are 

unsuitable for nacelle environments due to fluid retention, 

debris contamination, lack of load-bearing capacity and 

maintenance concerns (Refs. 1 and 4). Instead, liner designers 

were compelled to explore other acoustic dissipation mechanisms. To that end, the thin, porous facesheet (typically realized 

as a perforate) over honeycomb core (POHC, see Figure 6.2) 

liner offers a suitable alternative, as it is a lightweight, loadbearing, low-maintenance structural component. It is derived 

from its purely structural counterpart that consists of a
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NASA/TP—2012-215653 159 Chapter 6

Figure 6.2.—Perforate-over-honeycomb core (POHC) liner.

honeycomb core bonded between two thin, impervious 

facesheets, with consequent low area density and high bending 

stiffness. By making one of the facesheets porous, it is 

transformed into a local-reacting acoustic absorber for incident

waves on the porous side; that is, acoustic waves interior to 

the structure are restricted from propagating lateral to the 

facesheet surface. This local reaction aspect provides an 

enormous simplification for calculating the duct airway sound 

attenuation because an impedance boundary condition suffices 

to couple the acoustically absorbing structure to the wave 

propagation process in the duct airway. Fortuitously, this 

“tried and tested” load-bearing structure provides the mechanical properties to make it an excellent choice for duct liner 

treatments. The structure can be fabricated using a wide 

variety of facesheet materials to provide the desired porosity; 

for example, fibermetals, woven wire mesh combined with 

perforates, or stand-alone perforates (as illustrated in Figure 6.2). New fabrication methodologies for manufacturing 

perforates, such as electron-beam and laser-beam drilling, 

have developed in recent years to supplement the more 

traditional technologies such as shear-punched and pin 

mandrel-formed holes.

6.1.3 Perforated Plate Resistive Element in

Multilayer Liners

In its simplest form, a POHC absorbing structure provides 

significant attenuation over a relatively narrow bandwidth, 

making it an excellent noise reduction choice for tonedominated, low-bypass turbofan engines. These sandwich-type 

structures can also be stacked into multiple layers to enhance 

attenuation bandwidth via additional degrees of freedom, to 

allow tuning of the absorption spectrum. Multiple layers can 

extend attenuation bandwidth by at least one octave. For 

current high-bypass engines, up to three-layer liners are in use. 

While these multilayer systems have greater bandwidth than

the single-layer resonant structure, they are also more complex 

to fabricate, and their increased weight translates into greater 

cost and reduced payload. Two recent developments offer the 

possibility of improved bandwidth while retaining the 

structural simplicity and mechanical advantages of the singlelayer liner. The first involves the insertion of multiple porous 

septa (cellular caps) into individual honeycomb cells at 

selected depths (Ref. 5). The second involves the implementation of a specified porosity (e.g., laser-drilled perforations) in 

the honeycomb cell walls (Refs. 6 and 7). These two innovations portend the advent of a “designer bulk absorber,” 

wherein anisotropic, bulk acoustic properties can be specified 

(e.g., flow resistivity). This means that liners can be designed 

to range from local reacting to extended reacting in two 

independent directions. Further, because the fundamental 

resistance element in such liners is a thin porous material, 

acoustic property modeling builds on existing empirical 

impedance prediction models. As previously noted, the 

modeling of such liners is likely to be more computationally 

intense than for the single-layer, local-reacting liner. However, 

in view of the continuing decline of computational costs, 

bandwidth control to optimally attenuate both tonal and 

broadband noise may become feasible in the future.

6.1.4 Scope and Objective of This Assessment

In summary, for about five decades, continuing advances in 

materials technology have provided an increasing number of 

choices for resistive elements in nacelle liner treatments. 

These have included fibermetal products (originally targeted 

to industrial filtering processes), woven wire meshes, synthetic 

meshes, and metal foams. Although many of these advances 

continue to be explored for potential usage in liner designs, the 

perforated facesheet continues to be a commonly employed 

resistance element, mainly because of its structural simplicity 

and strength, mechanical durability, easily quantifiable 

geometric properties, and low cost. Consequently, the aircraft 

industry has accumulated an extensive database, whereby 

semi-empirical impedance prediction models have been 

developed for liner design. Because of the continuing 

relevance of the POHC liner, in both its single-layer and 

multilayer configurations, and because of time constraints, the 

scope of this assessment will be limited to a single-layer 

POHC test liner configuration. This absorbing structure is 

representative of the issues encountered in an uncertainty 

analysis. The main objective of this assessment is to provide a 

statistical approach for assessing the quality of an impedance 

“product” in the same manner as statistical process control is 

used for a manufacturing process. In the next section, the 

metrics of uncertainty are discussed, along with their implication for the measurement and prediction of liner impedance 

spectra.
NASA/TP—2012-215653 160

6.2 Impedance Uncertainty, 

Quantification, and Quality Control

This section addresses the metrics used to quantify impedance uncertainty and the relevance of such metrics to the task 

of applying statistical process control technology to achieving 

target liner impedance spectra in an operational aircraft engine 

to within a specified range of uncertainty.

6.2.1 Statistical Process Control: A Tool for 

Impedance Quality Control

A single realization of a liner design in an operational 

engine is subject to random and systematic errors that result in 

frequency-dependent deviation of the installed impedance 

from the targeted values. The limiting of such errors to an 

interval centered on the target impedance is traditionally the 

task of manufacturing quality control. Traditional quality 

control is based on a statistical sampling of the final product 

and thus does not detect an out-of-compliance condition until 

after it occurs. Statistical process control (SPC) monitors the 

inherent variability of a manufacturing process at critical 

points (“voice of the process”) to provide a warning of an 

impending out-of-compliance condition (Refs. 8 and 9). The 

power of SPC is to provide a basis to intervene in the manufacturing processes at critical points to prevent production of 

out-of-compliance units. This approach to quality control 

would achieve an installed liner impedance under operational 

conditions to within some specified total error. The userspecified variation of the end product from the target (“voice 

of the customer”) is what makes SPC an attractive approach 

for impedance quality control. It fits well with the SPC 

concept because the statistical sampling of the installed liner 

impedance is impractical on a routine basis. It is the judicious 

sampling of the manufacturing process that is the critical 

aspect of SPC, and that makes it an attractive conceptual 

framework for specifying installed impedance uncertainty in 

operational aircraft engines. As with SPC applied to widget 

production, the task is to anticipate an impending out-ofcompliance condition at selected stages in the design and 

fabrication process. To some degree, manufacturing process 

monitoring is already being implemented in current acoustic 

liner production. What may be missing, however, is a robust 

statistical database for the various subprocesses which 

constitute the voice of the process and that may be used in 

conjunction with a user-defined uncertainty limit such as a 

confidence interval centered on the desired impedance. For a 

liner impedance spectrum, such confidence intervals are 

frequency dependent. The most critical (and potentially 

useful) aspect of applying the SPC paradigm to assure 

performance compliance is the creation of a laboratoryvalidated, semi-empirical impedance prediction model that 

serves as a kind of proxy for impedance measurements on the 

installed product (assumed inaccessible on a routine basis). 

Thus, in what follows, we apply uncertainty analyses to 

impedance predictions and measurements for the POHC 

single-layer liner.

6.2.2 Specification Limits, Uncertainty Limits, and 

Confidence Intervals

The goal of SPC, for liner implementation on an operational 

engine, is to estimate the confidence with which an installed 

impedance complies with an end-user-defined uncertainty 

range centered on the target impedance. When quantified in 

terms of a probabilistic statement this uncertainty range is 

generally called a confidence interval because it estimates the 

level of confidence that the implemented impedance will fall 

within the stated uncertainty interval. Because it is not 

practical to “measure” the impedance of the finished product 

(i.e., installed impedance), a semi-empirical impedance 

prediction model provides the basis for estimating not only 

impedance mean values but also the standard deviation about 

the mean. These two statistical quantities are crucial to 

estimating compliance of the process with a user-specified 

uncertainty limit. Thus SPC is a statistical tool and for its 

successful application relies on a sufficiently robust statistical 

database. Both the statistical database and the selected semiempirical liner impedance prediction model are crucial for the 

successful application of SPC to estimating installed impedance uncertainty.

The success of a quality control program, in the SPC context, depends upon a validated impedance prediction model 

and an informed customer specification limit. Model validation is done in a laboratory environment and is the basis for 

employing the model as a kind of proxy for the voice of the 

process. Given a creditable voice of the process, an informed 

customer specification limit on a target impedance spectrum 

translates into an optimal choice (both technically and 

economically) for the entity ultimately responsible for 

compliance of an aircraft engine noise certification requirement. Without realistic specification limits, presumably 

determined from allowable uncertainty contributed by the 

turbofan noise to the aircraft footprint, the liner producer 

simply does not know how “tight” the process input parameters need to be! Thus, since there are no a priori specification 

limits provided for the POHC liner studied in this assessment, 

the focus is on the credibility of the voice of the process. This 

takes the form of comparisons of semi-empirical impedance 

prediction models and laboratory measurements. These 

comparisons are done in terms of an uncertainty analysis on 

statistical datasets of measured impedance spectra and Monte 

Carlo simulations applied to impedance prediction models.

6.2.3 Uncertainty Metrics

An unbiased measurement repeated N times on a hypothetical, statistically stable, parent population exhibits random 

fluctuations about the mean of the N sample values. For 

unimodal (e.g., Gaussian) statistical distributions, the sample 

mean approaches that of the parent population mean
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NASA/TP—2012-215653 161 Chapter 6

(sometimes denoted “true value”), as N increases without 

limit. In practice, the sample mean, as well as other statistical 

parameters of interest, is always an estimate of the parent 

population counterpart. Real measurement processes (and 

predictive models) may impose unknown bias error (also 

called systematic error) on the sample statistics to cause a 

nonrandom shift in sample statistical parameters relative to 

their true values. This fact constitutes the major challenge for 

uncertainty analysis as systematic error is not known a priori

and is thus not easily separated out from random error. 

Conceptually, at least, the total error in a single measurement 

(or prediction) comprises an unknown combination of 

systematic and random errors (Ref. 10). Again, because the 

true value is unknown, the total error is also unknown. 

However difficult the distinction between systematic and 

random errors may be in practice, these distinctions are 

nevertheless helpful. Hence, systematic errors are said to be 

due to assignable causes, and random errors are said to be due 

to unassignable causes.

Systematic and random errors are sometimes differentiated 

by the terms accuracy and precision that, in conventional 

usage, are synonymous. In the technical context here, accuracy 

denotes closeness to the true value and precision denotes the 

degree of clustering around a mean value (not necessarily the 

true value). In this document, we find it convenient to use all 

of these descriptors. There are four combinations of precision 

and accuracy as illustrated in Figure 6.3. Generally, improving 

measurement methodology increases accuracy, whereas 

improving measurement technique increases precision. The 

reader will note that increasing accuracy or precision corresponds to an improved measurement, but not in the same 

manner. Correspondingly, a decrease in systematic error or 

random error corresponds to an improved measurement. Thus,

these descriptors bear an inverse relationship to each other. 

While the above definitions have been discussed in terms of 

measurements, we also intend to apply them to impedance 

model predictions.

As will be discussed in Section 6.3.5, “Relevance of Laboratory Impedance Measurement,” a propagation model must be 

employed to measure (educe) the impedance of a test liner. 

This indirect measurement process affords ample opportunity 

for accuracy and precision errors to arise. To help mitigate 

these errors, at least for the impedance measurement technologies employed at the NASA Langley Research Center, studies 

have been conducted via well-understood absorbing structures 

(validation liners) consisting of parallel, capillary-like 

channels embedded in a rigid matrix (Ref. 11). The impedance 

behavior of such structures is nearly linear (impedance 

independent of excitation level and mean flow speed),

making the impedance predictable from first principles. This

Figure 6.3.—Depiction of accuracy versus precision for parameter x, as used in this chapter. (a) High accuracy, 

high precision; (b) High accuracy, low precision; (c) Low accuracy, high precision; (d) Low accuracy, low

precision.
NASA/TP—2012-215653 162

prediction capability allows very accurate and precise 

impedance spectra to be determined. This capability allows 

these liners to be used to establish a baseline uncertainty for 

validating the impedance measurement methodologies and 

processes at Langley (Ref. 12), which have been used to 

validate both normal incidence and grazing incidence 

impedance measurement processes (Refs. 13 and 14).

For the purposes of this study, the metric for uncertainty is 

chosen to be the 95% confidence interval (Ref. 10). These 

intervals are calculated from the statistics generated by 

repeated impedance measurements and predictions. Calculation of 95% confidence intervals, as used here, assumes input 

parameter statistics to be Gaussian distributed. The precision 

part (random error) of the uncertainty analysis consists of 

simply comparing 95% confidence intervals for impedance 

measurements and predictions. The accuracy part (systematic 

error) of the uncertainty analysis consists of comparing the 

measured and predicted mean values. These confidence 

intervals are deemed to have a 95-percent probability of 

containing the “truth.” For the purposes of this study, the truth 

is assumed to be the mean values that would be attained with a 

large number (parent population) of measurements or 

predictions. Correspondingly, there is a 95-percent confidence 

that the next measurement (or simulation, in the case of 

prediction models) will fall within the 95% confidence 

interval. Any difference between the measured and predicted 

mean values is deemed to be systematic error (due to assignable causes). The confidence interval widths are deemed to 

arise from unassignable causes (random variability). These 

definitions are the bases for all the commentary on the many 

data charts to follow in Section 6.6, “Results and Discussion.”

6.2.4 Coverage Factor for Small Sample Sizes

When estimating a confidence interval for a small sample 

size taken from a normally distributed parent population, a 

coverage factor is introduced to account for the fact that the 

sample probability density function follows a Student’s

t-distribution for small sample sizes (Ref. 10). Because 

sufficiently large sample sizes (number of tests or simulations) 

are generally impractical, especially in experimental work, the 

underlying assumption of parent population normality cannot 

be confirmed. In the present task, this situation arises both in 

the use of the nonlinear data reduction equation for the 

impedance measurement methodologies and in the prediction 

models. The impedance prediction models presented in this 

assessment involve nonlinear equations and are thus almost 

guaranteed to generate non-Gaussian output distributions for 

sufficiently large excursions of the inputs from their respective 

means. This is true even when the input distributions (probability distributions of the input parameters used in the 

prediction model) are Gaussian and large sample sizes are 

employed. To allay the concern for the usage of a coverage 

factor under these circumstances, a Monte Carlo process was 

used to acquire a large number of simulations (impedance 

predictions). Excellent agreement between the coverage 

factor-based confidence intervals and those calculated directly 

from the Monte Carlo simulations is achieved.

6.3 Impedance Concept and 

Measurement Issues

Mathematically, acoustic impedance can be defined as the 

ratio of the frequency transforms of the acoustic pressure and 

acoustic particle velocity (hereinafter called the acoustic 

velocity when appropriate) at a point of interest in an acoustic 

field (Ref. 15). As a result of the directional nature of acoustic 

velocity, the acoustic impedance is also directional. Thus, at 

the surface of a local-reacting liner, the normal incidence 

impedance boundary condition is relevant at all incidence 

angles, even at grazing incidence. This is a result of the 

pressure being a scalar and the acoustic velocity being a vector 

constrained to be normal to the surface. Conversely, if the 

normal incidence impedance for a purportedly local-reacting 

material is found not to hold at grazing incidence, then the 

material (liner) is judged to depart from the local reaction 

assumption. Few materials (or absorbing structures) are 

ideally locally reacting; however, many approximate this 

condition. This is generally the case for POHC liners in 

operational nacelle liner treatments, even though cell-to-cell 

drainage slots are present in the circumferential direction. 

Departure from a local reaction assumption at grazing 

incidence is a source of systematic error for conventional 

POHC liners. If an absorbing structure is locally reacting, and 

its impedance is independent of the aeroacoustic environment, 

then the impedance is an intrinsic property of that structure. 

However, the nonlinear acoustic response of a typical POHC 

liner and its sensitivity to grazing flow makes its impedance a 

joint property of the structure and aeroacoustic environment. 

The fundamental indirectness of acoustic impedance measurement is a key contributor to the difficulty of making these 

measurements in the presence of high acoustic excitation 

levels and grazing flows. As mentioned previously in Section 

6.2.3, “Uncertainty Metrics,” Langley employs a validation 

liner to provide a measure of confidence in the various 

measurement methodologies. This liner exhibits a high degree 

of linearity and insensitivity to grazing flow and is discussed 

further in Section 6.3.6, “Implementation of Rayleigh 

Absorber as Validation Liner.” It consists of a number of 

parallel tubes embedded in a ceramic matrix that are oriented 

normal to the surface (Refs. 11 and 13). Historically, such 

structures have been called Rayleigh absorbers (Ref. 16). 

6.3.1 Nonlinearity Implication for Measurements 

and Prediction Models

As noted above, the classical impedance boundary condition breaks down for POHC liners because the impedance 

increases with increasing acoustic excitation. The nonlinearity 

poses an issue for using the classical frequency-domain 

concept of impedance as an experimental characterization of a 

perforate, because the impedance is no longer a unique 
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NASA/TP—2012-215653 163 Chapter 6

property of the perforate: it is also dependent on the excitation 

spectrum. Under the current physics-based modeling paradigm, this excitation-spectrum dependence is manifested 

entirely by the total root-mean-squared (rms) velocity through 

the perforate (both acoustically and turbulence driven). Thus 

the shape of the excitation test spectrum is not relevant so long 

as the resulting rms acoustic velocity is kept invariant. 

Researchers have found it advantageous to use both broadband 

and isolated tones as excitation sources. Broadband excitation 

is less labor intensive and equipment demanding (compression 

driver limitations). Detailed excitation spectrum control is lost 

with broadband excitation, and extraction of broadband 

acoustic signals in the presence of grazing-flow noise becomes 

more challenging. Discrete tone excitation avoids the control 

and signal extraction issues but tends to be labor intensive. At 

Langley, the authors have chosen to employ single-tonedominated excitation spectra for impedance prediction model 

validation investigations and broadband excitation for system 

diagnostic testing. Separations of at least 20 dB between the 

target and spurious tones are easily achieved. This choice 

allows different test liners to be compared on a frequency-byfrequency basis with greater control of excitation level. Tonal 

excitation also allows more in-depth investigations of the 

assumptions that undergird the impedance prediction models 

now used by industry. Such investigations are yet to be 

performed in a systematic manner.

6.3.2 Grazing Flow Implication for Measurements 

and Prediction Models

For conventional POHC liners, the facesheet aspect ratio 

(thickness to hole diameter) t/d ranges from about 0.2 to 1.5, 

in which case grazing flow over the liner dominates the 

resistance, with a contribution roughly proportional to the 

Mach number. This effect can easily overwhelm the viscous 

and acoustic nonlinearity contributions and tends to subdue 

the nonlinear response to high acoustic excitation levels. 

Grazing flow tends to have comparatively little effect on the 

perforate mass reactance (a limiting reduction to not less than 

one-half its no-flow value at high flow speeds). It thus follows 

that the challenge for a perforate impedance prediction model 

is to accurately account for the grazing-flow effect. There are 

two prevailing theories regarding the basis of the grazing-flow

effect. The first assumes it to be driven by the interaction of 

the acoustically driven oscillatory orifice flow with the 

grazing-flow boundary layer. The second assumes the 

dominant grazing-flow effect to be the combination, on an 

energy basis, of acoustic excitation with pseudo-excitation due 

to turbulence. There is considerable connectivity between the 

two approaches (Refs. 17 to 19). 

Although high-speed grazing flows and high acoustic 

excitation levels complicate frequency-domain impedance 

prediction models for perforates, their continued use for a 

POHC liner has provided notable success in advancing passive 

liner technology for application in turbofan engines. Ongoing 

advances in perforate manufacturing technology have allowed 

a t/d of up to at least 5 to be attained (i.e., a microperforate), 

wherein viscous resistance becomes a significant contributor 

to the total resistance.

It should also be noted that a more rigorous way to characterize a nonlinear duct liner boundary condition is via a timedomain impedance operator that relates the instantaneous 

acoustic velocity at the liner surface to the excitation pressure 

(Ref. 20). Sporadic research on this approach has produced 

mixed results. To exploit this approach, time-domain models 

of the source and the duct airway propagation process are 

required. Although the time-domain impedance boundary 

condition remains a topic of research interest, the frequencydomain approach remains the basis for most impedance 

prediction models relevant to liner design.

6.3.3 Test Sample Size and Scale Implications

When conducting tests in a laboratory environment, one 

must be mindful that there are some characteristics of the fullscale environment (in this case, an aircraft engine nacelle) that 

cannot be fully simulated. For instance, it is important to 

attempt to maintain a sufficiently large test sample such that 

the measured results are representative of those that would be 

expected in the full-scale environment. This was not a 

problem for the samples used to validate the impedance 

eduction processes with the two Langley waveguides (normal

incidence tube (NIT) and grazing incidence tube (GIT)), as 

these samples contain hundreds of small-diameter channels 

distributed across their surfaces, such that any edge effects 

(e.g., partially blocked channels) represent a very small 

portion of the total surface area. Similarly, it is expected that 

microperforate samples, with their high hole densities, should 

be representative of larger surfaces used in the full-scale 

environment. However, for the assessment liner used in the 

current investigation, there are two key concerns. The first is 

associated with hole blockage, and the second is due to partial 

cells along the edges of liner test samples.

A number of holes in the facesheet are at least partially 

blocked by the interface between the honeycomb core and the 

facesheet. Of course, this is not unique to test samples, as 

honeycomb cores are an integral part of all POHC liners. 

However, this blockage can cause some variation in the 

number of holes per cell, thereby causing a variation in local 

or cell-to-cell impedance. If the size of the sample (assumed 

taken from the parent material) is sufficiently large, these 

variations will average out over the entire surface, and will be 

representative of the full-scale liner (ignoring, for the moment, 

the changes in impedance along the axial length of the liner 

due to nonlinearity effects). However, for sufficiently small 

samples, random variations of impedance will be measured 

with nominally identical samples.

The effect described above is particularly troublesome 

along the test sample edges. Unavoidable partial cells that 

occur at the liner edges at full scale represent a small percentage of the entire liner surface, but may represent a substantial 

percentage of the surface for small samples. If only one test
NASA/TP—2012-215653 164

sample is employed, this leads to a systematic error in the 

impedance measurement with respect to the full-scale liner. 

One way to avoid this issue is to perform measurements on a 

statistically significant number of nominally identical test 

samples, each fabricated by randomly orienting the honeycomb core with respect to the perforate hole pattern.

A consideration of the issues listed above led to the choices 

of dimensions for the NIT and GIT samples. These choices 

represent a compromise between the issues regarding representative sample size and a desire to study the effects of planewave sources (no higher-order modes) on these liners up to a 

frequency of 3 kHz. In the comparisons between measured 

and predicted impedances presented later in this chapter, the 

effects described above manifest themselves as a systematic 

error because only one sample is evaluated. This error can be 

viewed in two ways. In one sense, the test sample can be 

considered as not representative of the full-scale environment, 

in that it does not present the same average impedance across 

its surface as would be observed in the engine. Alternatively, 

the prediction model can be viewed as not including all of the 

detailed geometry of the test sample. Regardless, this sample 

is viewed as sufficiently representative of the full-scale 

environment to allow useful comparison.

Impedance spectra for full-scale liners are generally desired 

over a frequency range of at least 0.4 to 4 kHz. One way of 

achieving this goal, while maintaining the capability to use 

only plane-wave sources, is to reduce the dimensions of the 

acoustic waveguide. Of course, this further exacerbates the 

effects of sample size, as described above. Another way to 

extend the frequency range is to incorporate higher-order 

modes into the measurement and analysis methods. Schultz, 

et al. (Ref. 12), conducted an analytical uncertainty analysis, 

in which extremely tight 95% confidence intervals on the 

measured impedances were computed in a 25.4- by 25.4-mm 

(1- by 1-in.) normal incidence tube up to frequencies above 

6 kHz.

It is often useful to conduct model-scale testing, such as 

tests with a fan rig that is a scaled version of the full-scale 

engine, as it allows testing at greatly reduced expense. 

However, it is not a trivial matter to fabricate liners to reduced 

scale, as each of the geometric components should be reduced 

by the same scale factor. In addition, this requires the test 

regime (frequency range) in the fan rig to be scaled as well, 

thereby requiring the frequency range to be translated to 

higher frequencies. For example, if 1/5-scale models are used, 

the 0.4 to 4 kHz, full-scale frequency range is translated to a 2 

to 20 kHz range. To support this type of testing, component 

liners must also be tested over this scale-model frequency 

range. This extension has not been pursued at Langley, as the 

emphasis has instead been placed on methods that use the fullscale frequency range at laboratory scale. One attempt to 

extend the frequency range in this manner was developed by 

Schultz, et al. (Ref. 21). They used a modal decomposition 

method with their 25.4- by 25.4-mm (1- by 1-in.) normal 

incidence tube to extend the frequency range to 13.5 kHz. The 

results they acquired with a plane-wave source (out to about 

6 kHz) were excellent, while the data acquired, with higherorder modes present, exhibited some effects of mode scatter.

6.3.4 Measurement Methodologies

Impedance measurement methodologies are divided into two 

categories: (1) those that are invasive to the test sample and 

(2) those that are noninvasive. Invasive methods run the risk of 

perturbing the structure and acoustic field, thus introducing 

systematic error that can be notoriously difficult to isolate and 

correct. Noninvasive methods provide a global impedance 

measurement, but have the disadvantage of requiring an 

acoustic field model to mediate between acoustic pressure 

measurements and the surface impedance of the test sample. At 

Langley, global methods have been used almost exclusively. In 

the following subsections, two invasive and two noninvasive 

methods are described. The two invasive methods are included 

because they offer capabilities that cannot be achieved with the 

two noninvasive methods currently employed by Langley. In 

contrast with the noninvasive methods employed by Langley, 

these two methods offer the potential for direct impedance 

measurements in full-scale engine nacelles. Of the two invasive 

methods, the in situ method has been used to a much greater 

extent than the T-tube method.

6.3.4.1 Invasive Methods

The in situ method (ISM), originally investigated by Dean 

(Ref. 22) and later by Kraft, et al. (Ref. 23) requires pressure 

measurements at the backing cavity surface and at a representative location on the facesheet surface. The facesheet 

measurement can be measured with a single, flush-mounted 

microphone or by means of a traversing probe. In any case, a 

large systematic error can be incurred if the facesheet pressure 

is not measured with care. This is particularly true for 

perforates because of the hydrodynamic near field of oscillatory orifice flows. The advantages of the ISM are (1) it does 

not require a model for the acoustic field, external to the liner, 

to mediate between pressure measurements and the local 

impedance of the targeted cell, (2) measurements can be 

conducted in difficult environments, such as an operational 

engine, and (3) it requires no supporting test duct (waveguide). 

Disadvantages are (1) the measured impedance is local to a 

cell and may not be representative of a global impedance (e.g., 

POHC liners where hole counts, and thus blockage, vary from 

cell-to-cell), (2) the intrinsic cell impedance is almost certainly 

disturbed to some unknown degree by the intrusive microphones, (3) the precision required for microphone installation 

requires mechanical skill, is tedious and time consuming, and 

(4) an assumption must be made about the acoustic field 

within the measurement cell.

The ISM has acquired a reputation for being labor and skill 

intensive, along with having a lack of accuracy, precision, and 

robustness. This has prompted Langley to avoid this methodology. In spite of the large systematic and random error 

reported for this method, (Ref. 23) its capability of measuring 

a point-like impedance, albeit contaminated by hydrodynamic 
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NASA/TP—2012-215653 165 Chapter 6

effects, is of interest for studying the details of the near-field 

impedance variability at microscale and for validating direct 

numerical simulation of such flows via the Navier-Stokes 

equations (Ref. 24). 

The T-tube method (TTM) described by Dean and Feder 

(Ref. 25) employs a normal incidence tube mounted normal to 

a flow duct. A small test sample with no back plate is mounted 

flush with the flow duct wall, such that grazing flow sweeps 

across its face while sound is incident on the open back side 

(thus the invasive nature of this method). The total impedance 

of the test sample plus that of the duct environment is 

measured by standard means in the normal incidence tube (see 

next section). Its chief merit is that it requires no inflow 

acoustic measurements, as do the waveguide methods (see 

next section). Another merit of the TTM is that it gives a 

global impedance (in contrast with a point-like impedance 

from the ISM) over a facesheet geometry suitable for a normal 

incidence tube. This feature avoids the systematic error that 

arises from averaging out nonlinear effects along a test sample 

length, typically required in a waveguide measurement. Aside 

from being an invasive method (i.e., removal of the back 

plate), the big disadvantage of the TTM is the inclusion of the 

generally unknown radiation impedance looking into the flow 

duct. This constitutes a very significant source of systematic 

error unless carefully “calibrated out.” This issue notwithstanding, the TTM can be useful as a means of measuring 

impedance changes due to grazing flow and can serve as 

complement to the waveguide methods.

6.3.4.2 Noninvasive Waveguide Methods

Noninvasive methods require a field propagation model to 

mediate between complex acoustic excitation pressures 

measured well away from the test sample surface in a control 

volume adjacent to the test sample. These methods generally 

provide an average surface impedance over the test sample 

surface, making this method a global determination of 

impedance. However, they require detailed modeling of each 

of the boundary conditions of the computational domain used 

to represent in the test environment. For the grazing-flow

environment, the boundary conditions used in the Langley 

methodology include (1) the source plane, which can contain 

one or more modes, (2) the exit plane, either an impedance or 

pressure condition, (3) rigid boundaries along the two 

sidewalls, the bottom wall, and the portion of the upper wall 

that does not contain the test liner, (4) the complex acoustic 

pressure field along the wall opposite the liner, and (5) the 

surface impedance of the test liner.

The overriding advantage of the waveguide method, as seen 

from the Langley perspective, is that it provides the only 

possibility of measuring the global impedance of an intact, test 

liner sample in a simulated environment representative of an 

operational engine environment. Clearly, none of the invasive 

methods discussed above can do this. However, the invasive 

methods remain of interest because they may have a role to 

play in certain impedance prediction model development 

issues. NASA Langley employs two hardware implementations of noninvasive, impedance measurement: a deterministic, two-microphone method (TMM) (Refs. 26 to 28) as 

implemented in a normal incidence tube (NIT, see Figure 6.4), 

and an over-determined, multimicrophone method (MMM) 

that employs a microphone array embedded in the walls of a 

grazing incidence waveguide with or without grazing flow 

(grazing incidence tube, GIT, see Figure 6.5).

Error sources specific to the TMM and MMM are well 

documented in the literature (Refs. 12, 26, and 27). Here, we 

focus on error sources that are likely to arise when results 

using the two methodologies are compared for the specific 

apparatuses employed at Langley, the NIT and GIT. The NIT 

accommodates a test sample size of 50.8 by 50.8 mm

(2 by 2 in.). The GIT accommodates sample sizes that can 

range from 50.8 by 50.8 mm (2 by 2 in.) to 50.8 by 406.4 mm 

(2 by 16 in.). Although the GIT can accommodate the same 

sample size as the NIT, data quality suffers because the 

decaying wave field adjacent to a 50.8 by 50.8 mm (2 by 2 in.) 

sample in the GIT cannot be well resolved, at least with the 

current arrangement of microphone locations. This means that 

test sample interchangeability between the NIT and GIT is not 

a suitable way to compare sample impedance data for normal 

and grazing incidence. Instead, two test samples, one 50.8 by 

50.8 mm (2 by 2 in.) and the other 50.8 by 406.4 mm (2 by 

16 in.), are fabricated to nominally the same specifications. 

Any random variability between such samples appears as a

Figure 6.4.—NASA Langley normal incidence tube (NIT). 

(a) Photograph. (b) Schematic.
NASA/TP—2012-215653 166

Figure 6.5.—NASA Langley grazing incidence tube 

(GIT). (a) Photograph. (b) Schematic. (c) Liner installed in top wall.

systematic error, unless a statistically significant number of 

nominally identical samples are tested. This is believed not to 

be a significant source of error for the validation test samples. 

However, random error may be aliased into a systematic error 

when POHC test liner results are compared for the two 

methodologies on a paired, sample-to-sample basis.

The TMM, as implemented at Langley, has been demonstrated to provide high-quality normal-incidence impedance 

measurements from 400 to 3000 Hz, over a range of normalized resistance and reactance values of 0 to 10 and

–10 to 10, respectively. However, a potentially significant 

source of systematic error for the GIT is related to the global 

nature of the impedance measurement when performed on a 

nonlinear test liner. Significant attenuations can occur over the 

standard test liner length. This can cause the acoustic resistance to decrease from the leading to trailing edge. Because 

the MMM assigns an average (smeared) impedance over the 

entire liner length, a significant systematic error can be 

incurred. One strategy for dealing with this error consists of 

dividing the liner into multiple axial segments that are 

sufficiently small to render a uniform-impedance assumption 

(different impedance for each segment) acceptable. A 

preliminary effort has been made to implement this strategy 

(Ref. 29). 

For the GIT, grazing flow complicates the field model and 

the source and exit plane boundary conditions on the control 

volume. These source and exit boundary conditions constitute 

a daunting measurement challenge, especially in the presence 

of flow. In addition to these ancillary boundary conditions, the 

flow field profile throughout the control volume adjacent to, 

and centered on, the test liner (Figure 6.5(c)) is an input 

parameter. These issues notwithstanding and for the reasons 

stated previously, NASA Langley has chosen to invest great 

effort in the development of this impedance measurement 

technology as implemented in the GIT (Refs. 26 to 28, 13, 30, 

and 31). The GIT is currently being upgraded to provide 

acoustic excitation levels up to 150 dB over a frequency range 

of 400 to 6000 Hz, grazing flow up to a Mach number of 0.6, 

and sound propagation with and against the grazing flow 

(simulates aft and inlet conditions).

6.3.5 Relevance of Laboratory Impedance

Measurement

As previously stated, the key motivation for implementing 

the waveguide-based methodology is to simulate, insofar as is 

feasible, a test liner subjected to realistic aeroacoustic 

environments and to determine its impedance in this environment. Thus, it is intended for a waveguide propagation model 

to capture the salient features of the aeroacoustic environment. 

This requires input parameters on a control volume with some, 

as yet unknown, level of accuracy and precision. Whereas an 

analytical data reduction equation connects a transfer function 

measurement to the test sample impedance for no-flow, 

normal-incidence impedance measurements, an iterative 

numerical algorithm is required for grazing flow. Wave 

propagation in the waveguide has been modeled by the 

convected Helmholtz equation (CHE) and the linearized Euler 

equations (LEE) (Refs. 14, 31, and 32). The CHE model 

captures the full three-dimensional aspects of the aeroacoustic 

field in the control volume, centered on the test liner, for 

uniform mean flows. Alternatively, the current implementation of the LEE model can capture the effects of the boundary 

layer, but only in a two-dimensional aeroacoustic environment. The iterative scheme requires that an initial impedance 

be arbitrarily set to a convenient value, and then iterated upon 

until the computed complex acoustic pressures at the microphone locations converge to the corresponding measured 

acoustic pressures, in a mean square sense, to within a 

specified tolerance (thus the over-determined character of this 

methodology relative to the TMM as applied in the NIT). The 

liner impedance for which the measured and predicted 
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 167 Chapter 6

acoustic pressures converge is taken to be the measured 

impedance. These codes have been validated (Ref. 14) via an 

implementation of the Rayleigh absorber described previously. 

The data reduction equations for the CHE and LEE propagation models are discussed in Chapter 7 on duct acoustics.

It is important to note that the sole justification for the large 

effort, over the past four decades, to experimentally evaluate 

liner response in realistic environments at laboratory scale has 

been driven by the liner nonlinearity and the need to describe 

these effects via semi-empirical impedance prediction models. 

Should advances in materials science and fabrication technologies allow the development of linear liners that are suitable 

for aircraft nacelles, the need for simulating harsh aeroacoustic 

environments at laboratory scale will cease, with the consequence that impedance prediction models can be enormously 

simplified. Some indication of that trend is evidenced in the 

high t/d perforates available via laser hole drilling. However, 

the current focus remains on liners that exhibit significant 

nonlinearity. To that end, the uncertainty analysis employed 

here focuses on a representative perforate.

6.3.6 Implementation of Rayleigh Absorber as 

Validation Liner

From what has been said previously, it is clear that the 

indirect nature of impedance measurement (eduction) is 

complicated by the addition of high-speed grazing flows 

combined with intrinsic liner nonlinearity. It is therefore 

important that the aforementioned impedance measurement 

methodologies be verified via a liner whose impedance can be 

predicted from first principles. This has been accomplished at 

NASA Langley by implementing the so-called Rayleigh 

absorber concept (Ref. 16), an absorber that dissipates 

acoustic energy by means of acoustic boundary layers in a 

geometrically well defined internal structure (e.g., narrow, 

capillary-like channels (Ref. 16)). As alluded to previously, 

the NASA Langley implementation of the Rayleigh absorber 

is achieved by densely packed, parallel cylindrical channels in 

an impervious ceramic matrix material (Ref. 11). The material 

is precision cut to conform to test liner dimensions for the NIT 

(active face 50.8 by 50.8 mm, or 2 by 2 in.) and GIT (50.8 by 

406.4 mm, or 2 by 16 in.). The channels are rigidly terminated 

at lengths up to about 82 mm (3.2 in.) to give a channel 

length-to-diameter ratio up to 130. The various implementations of the Rayleigh absorber will henceforth be called 

validation liners.

Accurate impedance prediction of the validation liner 

depends critically upon ascertaining the channel propagation 

constant and characteristic impedance. The theory for performing this calculation is classical and is thoroughly reviewed by 

Tijdeman (Ref. 33). Any acoustic nonlinearity or grazing-flow

effect on the impedance of such an absorber can arise only at 

the liner surface where the channels interface with the aeroacoustic field. It is intuitively clear that the scale of dissipation at 

this interface must be small compared with the interior dissipation. Thus acoustic nonlinearity and grazing-flow effects are 

minimized, but not entirely eliminated by the small scale of the 

individual channel openings and relative large composite open 

area ratio (better than 50 percent, compared with conventional 

POHC liners). Numerous comparisons between predictions and 

measurements in both the NIT and GIT have justified the use of 

this implementation of the Rayleigh absorber as a validation 

liner (Refs. 13 and 14). 

6.4 Impedance Prediction Models for 

POHC Absorbers

For the purposes of this discussion, first-principles acoustic 

impedance prediction models for POHC liners are those for 

which the impedance can be related to the acoustic energy 

dissipation physics in the perforate via the fluid dynamic 

equations of motion of the unsteady flow. It is also assumed 

that the structure is mechanically rigid, but possibly heat 

conducting, and that no empirical parameters are needed; that 

is, only tabulated physical constants are to be used. The only 

absorbing structure that qualifies for this kind of prediction 

model in the work at Langley is the ceramic tubular material 

implementation of the so-called Rayleigh absorber, as 

discussed in the previous section. The application of firstprinciples models to realistic absorbers, such as POHC liners, 

gives rise to nonlinear, differential equations that require 

several simplifications and approximations to achieve a 

computationally practical result. Thus, as a practical matter, 

there has been a bias toward phenomenological, or semiempirical, models with concomitant heavy reliance upon 

empirically determined parameters.

6.4.1 Phenomenological (Semi-Empirical) Models

Phenomenological acoustic impedance prediction models 

are based on easily measured parameters that are relevant to 

the phenomenon of interest, as per the relationship between 

acoustic resistance and direct current (DC) flow resistance. 

Unlike first-principles models, which imply a detailed 

description of the phenomenon of interest, phenomenological 

models make use of dimensional analysis to identify dimensionless groupings of parameters. These parameter groups are 

then used to provide guidance for experimental testing to flesh 

out the details of the phenomenon: for example, the classical 

Reynolds number dependence of laminar to turbulent transition in pipe flow. Phenomenological models are also denoted 

as semi-empirical. For acoustic impedance modeling, the 

empirical parameters are usually determined from a combination of nonacoustic and acoustic measurements. Historically, 

the acoustic resistance part of the impedance prediction 

models can be related to the modeling concepts used to study

flow losses through metering orifices and percolation through 

porous media of interest in fluid filtering and seepage flow in 

aquifers (Refs. 34 and 35). This is possible because of the 

commonality between the fluid flow regimes in these structures, such as the transition from laminar to turbulent flow at a 

critical Reynolds number based upon a characteristic length 
NASA/TP—2012-215653 168

scale (micropore diameter for foam-like structures, fiber 

diameter for fibrous materials, or hole diameter for perforates). It is this commonality of flow regimes at the microscale 

that allows impedance prediction models for perforates to 

employ generally the same phenomenological framework as 

do micropore structures. Although the physics of flow losses 

in porous materials is generally well understood, a semiempirical impedance prediction model must be employed if 

the nonlinear contribution to resistance is important. This 

happens when, at the hole scale, acoustic excitation pressure p

is such that the terms v(∂v/∂x) and ∂v/∂τ become comparable 

in the fluid dynamic equation of motion

= 0

∂

∂  +



 





∂

∂

+

∂τ

∂

ρ

x

p

x

v

v

v

(6.1)

that describes the acoustic velocity v through the perforate 

where ρ is the constant ambient density. This criterion for 

significant nonlinearity in perforates is discussed at length by 

Melling (Ref. 36) and Kraft (Ref. 37). The importance of 

resistance nonlinearity for a POHC liner depends not only on 

acoustic excitation level and frequency, but also upon 

perforate geometry (e.g., hole aspect ratio, t/d, and open-area 

ratio, σ). Generally, the nonlinear contribution to resistance is 

reduced by increasing the hole aspect ratio and the open area 

ratio, which reduces particle velocity in the perforate holes for 

a given excitation. It should be noted that the terms “open area 

ratio” and “porosity” are often used interchangeably, with 

porosity generally expressed as a percentage and open area 

ratio expressed as a fraction.

It is expected that semi-empirical models will continue to 

play a major role in POHC impedance prediction for the 

foreseeable future. However, there are three caveats to this 

forecast. One is that viscous losses within microperforates, 

which contain holes with large hole aspect ratios, may be 

exploited to dominate nonlinear losses and thus exhibit 

insignificant response to grazing flow (Ref. 5). Second, 

advances in computational technology may permit firstprinciples models to be employed in routine liner design. A 

third possibility is that electromechanical liner technology 

(Ref. 38) may emerge to make the design of targeted liner 

impedance spectra less critical. However, even for the selfadjusting or “smart liner,” it will be necessary to achieve a 

mean impedance spectrum, about which an onboard intelligence implements adjustments in response to a changing 

environment. In the interim, the refinement of semi-empirical 

impedance prediction models to meet targeted impedance 

spectra to within an appropriate specification range will 

continue to be sought. The objective of this assessment is to 

lay a foundation for discriminating among the merits of such 

competing models.

6.4.2 Semi-Empirical Models for POHC Liners

Perforates used in POHC liners are assumed to satisfy the 

lumped-element and quasi-steady-flow assumptions. Thus, a 

measurement of DC flow resistance (a nonacoustic parameter) 

is generally assumed to translate into an effective dynamic, or 

acoustic, resistance (both linear and nonlinear contributions). 

The empiricism of such models limits their range of applicability. For example, one model may hold for facesheet 

thicknesses less than the hole diameter (t/d < 1), whereas 

another model may hold for facesheet thicknesses greater than 

the hole diameter (t/d > 1). They may also employ parameter 

groupings derived from dimensional analysis, as previously 

mentioned. The lumped-element model holds when the local 

fluid motion associated with a perforate hole can be regarded 

as moving as a unit: that is, there is no wave motion on the 

scale of the fluid motion affected by the hole. This would 

include the fluid contained within the hole and the induced 

flow-field distortion in the vicinity of the hole. The mathematical criterion for lumped-element modeling is that the product 

of the acoustic wavenumber and the effective hole length be 

much less than unity (Ref. 15). Thus, the lumped-element 

assumption implies that the perforate has zero thickness. For a 

single-layer impedance prediction model, this assumption has 

been observed to generate significant systematic errors in the 

antiresonance region. Another important assumption for many 

perforate acoustic impedance models is that the rms acoustic 

velocity can be equated to a DC (or steady) flow velocity. This 

rests upon the quasi-steady-flow assumption and is key to 

modeling the nonlinear part of the resistance in a frequency 

domain sense. This assumption is violated if the excitation 

time scale becomes too small (high frequencies), such that 

flow profiles within an orifice do not develop to near a steadystate condition.

For conventional POHC liners, as currently used in aircraft 

engine nacelles, the perforate hole aspect ratio t/d ranges from 

about 0.5 to 1.5. Consequently, the nonlinear contribution to 

resistance dominates the viscous contribution. For this range 

of hole aspect ratio, grazing flow has a large effect on the 

nonlinear resistance because it significantly perturbs the 

entire, oscillatory flow field associated with the hole. As an 

aside, it should be intuitively clear that as hole aspect ratio 

increases, response sensitivity to grazing flow decreases. 

Correspondingly, the viscous contribution to resistance 

increases to the point that it can dominate the total resistance 

when the hole aspect ratio reaches about 50, as is the case for 

the Rayleigh absorber previously discussed. From these 

remarks, it should be clear that a viable impedance prediction 

model for POHC liners must deal with both nonlinearity and 

grazing-flow effects, in addition to the more classical viscous 

dissipation contribution to resistance. Aside from their 

mechanical advantages, perforates offer more precise control 

of governing parameters (e.g., porosity and hole geometry) 

than do micropore-type structures. (In this context, “micropore” is intended to convey the concept of a rigid, porous 

matrix that supports randomly dispersed, tortuous fluid paths 

as provided by reticulated foams, granulated materials, or 

compacted fibers—microperforates excluded.) The added 

complication of nonlinearity and grazing-flow effects 

notwithstanding, the impedance prediction models for POHC 
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 169 Chapter 6

liners allow them to employ generally the same phenomenological framework as do micropore structures.

Another limiting feature of any semi-empirical POHC 

impedance prediction model is that the various empirical 

parameters are specific to the perforate fabrication process 

(e.g., shear punching, pin-mandrel forming, or electron-beam 

drilling). Further, the accuracy and precision of their predictions are conditioned upon the variability (i.e., quality) of the 

perforate fabrication process and the test data used to support 

the model empiricism. This is one reason for the propensity of 

industry to treat such models as proprietary in order to 

preserve their competitive status. When such models are used 

outside their empirical support base, the utmost caution should 

be exercised. With these caveats in mind, the models discussed here have been selected to focus on POHC structures 

consisting of punched aluminum facesheets bonded to 

honeycomb core via a sheet reticulation bonding process 

(Ref. 39). The authors believe that the chosen POHC test liner 

(assessment liner) for this project is representative of this 

fabrication class. However, it does not necessarily follow that 

the assessment liner complies with all the assumptions 

underlying the empiricism in the various prediction models. 

Also, it should be noted that none of the empirical parameters 

have been adjusted to bring about improved agreement with 

the measured results.

In what follows, four semi-empirical impedance prediction 

models are presented that are believed to represent those 

currently used by industry. The model descriptions are 

intended to capture their salient features, and are not to be 

construed as a critical analysis of their differences and 

similarities. The names given to these models, described in the 

subsequent sections, are the Two-Parameter (TP) model, the 

Crandall Full-Solution (CF) model, the Composite Empirical

(CE) model, and the Fluid Mechanical (FM) model.

6.4.2.1 Two-Parameter Model (TP)

The TP and CF impedance prediction models share a commonality in that they parse the liner impedance (normalized by 

ρc, where ρ is the ambient density and c is the ambient speed 

of sound) as follows

ζ = θ + iχ = θlin + θnonlin + θgf + i{χ fs − cot(kh)} (6.2)

where θlin and θnonlin are the viscous and nonlinear contributions to the facesheet resistance, respectively. The grazingflow contribution is given by θgf. The reactance is given by the 

expression in brackets, from the facesheet mass reactance and 

cavity compliance via the terms χfs and cot(kh), respectively.

Note that an e

iωτ time convention is used (where ω is the 

angular frequency and τ is time) throughout this paper, and all 

impedances are normalized by ρc.

A lumped-element assumption for a perforate allows the 

acoustic oscillatory flow through the perforate to be treated as 

locally incompressible and quasi-steady. Thus, a DC flow 

resistance measurement on the perforate provides the basis for 

an empirical model of the acoustic resistance. No dynamic 

information related to the mass reactance is available by this 

means. If the honeycomb cell depth (backing cavity) h

is sufficiently small relative to the acoustic wavelength, it

can also be treated as a lumped compliance element, or a 

Helmholtz resonator. If this is not the case, then it is modeled 

as a rigidly terminated transmission line. The cell reactance is 

then given by χcav = –cot(kh), where k is the wavenumber and 

h is the cell depth. This is the cell reactance model used in this 

document. It holds for excitation frequencies that are low 

enough that cross modes are not supported in an individual 

cell, which is generally not a serious limitation. For perforates 

in which the viscous contribution to resistance is small, 

viscous losses in the honeycomb core may become evident as 

systematic errors that add a small resistance to the total 

resistance of the liner.

The simplest of the four models evaluated in this document is 

the so-called Two-Parameter impedance prediction model. It 

gets its name from parsing the DC flow resistance Rf into linear 

and nonlinear contributions, most simply expressed as

Rf A B Vinc = + ⋅ (6.3)

Experimentally, Rf is determined using Rf = ∆P/Vinc, where 

Vinc is the measured incident flow velocity through the test 

specimen and ∆P is the measured pressure drop across the 

specimen. Such measurements should be conducted over an 

incident velocity range commensurate with that expected for 

acoustic excitation. The constants A and B can be determined 

directly by fitting Equation (6.3) to the measured values of Rf

and Vinc. This purely empirical curve fit constitutes the 

simplest characterization of thin facesheet resistance behavior. 

It is not restricted to perforates, but must be repeated for each 

facesheet structure of interest (e.g., fibermetal sheet). Because 

of its intensely empirical nature, this form of the twoparameter flow resistance characterization is not pursued 

further in this document.

Alternatively, a semi-empirical model for the flow resistance can be inferred from the one-dimensional momentum 

equation (Ref. 35) for the pressure loss in a porous material. 

From Green’s analysis (Ref. 35), the pressure gradient in a 

porous material can be characterized by an equation of the 

form

2

d

d V V xP − = αμ + βρ (6.4)

where μ is the ambient dynamic viscosity, x corresponds to the 

direction of interest, and α and β are used to characterize the 

internal geometry of the material. These coefficients relate to 

the pressure losses due to viscosity and fluid inertia, respectively. Inertia-related pressure loss arises from flow path 

tortuosity. At sufficiently low Reynolds numbers based on a 

suitable characteristic length, the pressure gradient is controlled entirely by the first term. At higher flow speeds, the 
NASA/TP—2012-215653 170

inertial effects come into play to eventually dominate the 

pressure gradient. In smooth pipe flow, this behavior corresponds to the transition from laminar to turbulent flow and 

occurs abruptly at a Reynolds number of about 2300. In 

porous materials, the transition is gradual with increasing 

Reynolds number, which necessitates the usage of both terms 

to characterize the pressure losses in a porous material.

The above model for the pressure gradient (or flow resistance) through a porous material has served as the inspiration for flow resistance characterization of perforated plates. 

For perforates, the internal geometry is macroscopically 

regular and well defined, in contrast with porous foams or 

fibrous materials. Nevertheless, flow path regularity of 

perforates does not remove the gradual laminar-to-turbulent 

transition response with respect to Reynolds number as might 

be expected based on pipe flow. Thus, the pressure loss (flow 

resistance) across perforates generally tends to behave more 

like a high-inertia-dominated porous material than a collection 

of parallel pipe flows. This tendency is believed associated 

with geometric irregularities at the perforate hole subscale and 

their effect on flow losses generated by vorticity.

As noted above and in contrast with conventional porous 

materials (e.g., foams or loosely packed particles), the inertiarelated pressure losses for a perforated plate arise mainly from 

vorticity that is generated exterior to the perforate holes (i.e., 

exiting jet-like flows). The character of these flows is 

controlled by the hole Reynolds number, discharge coefficient, 

and hole aspect ratio. Other microscopic details of the hole 

geometry may also be involved, such as roughness and hole 

edge curvature. From the above background, it should be clear 

that a semi-empirical model for a thin perforate plate, in the 

paradigm described above, is likely to involve ingredients 

from pipe flow theory and orifice metering theory. In that 

vein, a two-parameter flow resistance model for perforated 

plates of thickness t is given by

( ) ( ) inc 2 2 2 2

V

c C d c C

a t

c

R

D

i e

D

f

f

σ

κ + κ

+

ρ σ

μ = ρ

θ = (6.5)

where the empirical constant a is assigned a value of 64. As 

suggested above, the first term in Equation (6.5) has its roots 

in Hagen-Poiseuille pipe flow (Refs. 34 and 40) or in Darcy’s 

law governing seepage through porous media (Ref. 35). The 

second term can also be derived from orifice metering theory 

(Ref. 34). Empirical constants (κi + κe) account for entrance

and exit end effects, whereas the discharge coefficient, CD, 

accounts for vorticity-associated losses both at the hole walls 

and exterior to the holes. The quantity (κi + κe) is taken as 

unity and a default value for CD is 0.76 for a sharp-edged 

orifice. In addition to being dependent on Reynolds number 

and hole geometry, the discharge coefficient is greatly affected 

by grazing flow and is therefore a source of systematic and 

random error in any impedance prediction model. It may also 

depend weakly on porosity (via hole separation) because of 

interference between entry and exit flows through adjacent 

holes.

In the TP model for resistance, the effect of grazing flow is 

taken into account by the Rice-Heidelberg model as given by

c { ( d )}

Rgf

gf

1

C L

2 1.256

M

σ + δ = ρ

θ = (6.6)

where Rgf is the grazing-flow resistance, MC/L is the freestream (centerline) Mach number, and δ1 is the boundary layer 

displacement thickness. Again, this is a single-hole model that 

accounts for multiple holes via mass conservation via the open 

area ratio, σ, as shown in Equation (6.5). The fact that grazing 

flow affects the discharge coefficient means there should be a 

direct modification of the contribution from Equation (6.3) 

when grazing flow is present. This is a significant shortcoming 

of the TP model as well as the CF model described in the next 

section. In practice, it is likely a moot issue for many conventional perforates as applied in nacelle ducts because the 

resistance increase due to grazing flow is the dominant 

contributor to total resistance. When the quantity δ1/d is near 

unity and the grazing-flow effect is dominant, the total 

perforate resistance from Equation (6.6) is instead approximated by

σ

θ = 3

MC L

gf (6.7)

In summary, the complete normalized resistance component 

is given by

( ) ( ) gf

D

i e

D

v

c C d c C

a t

+ θ

σ

κ + κ

+

ρ σ

μ θ = rms 2 2 2 2

(6.8)

where θgf is provided by Equation (6.6) or (6.7), depending on 

the magnitude of grazing-flow velocity. Note that Vinc has now 

been replaced by the rms acoustic velocity, vrms. The presence 

of vrms forces the calculation of the impedance to use an 

iterative procedure (described in greater detail below). It is 

also of interest to note that the nonlinear term scales on the 

inverse of the square of the open area ratio, whereas the linear 

and grazing-flow terms scale on the first power of the inverse 

of the open area ratio. This accentuates the role of the open 

area ratio when the nonlinear term is a significant contributor 

relative to the other two terms.

As previously noted, the POHC liner compliance is supplied by the cavity, and is modeled as

cot(kh) χcav = − (6.9)

The remaining contributor to the acoustic reactance is the 

normalized mass reactance due to the perforate facesheet, and 

is taken to be
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 171 Chapter 6

( )

D fs C

k t d

σ

+ ε

χ = (6.10)

where εd is the hole length end correction and

( )

3

C L 1 305

0.85 1 0.7

+ M

− σ

ε = (6.11)

A discussion of this end correction is provided in Reference 41. Early literature (Ref. 36) suggests a value of 0.85 for 

the no-flow, linear end correction for a single (isolated) 

orifice. The factor (1− 0.7 σ ) was provided by Ingard 

(Ref. 42) to account for open area ratio, and the grazing-flow

effect (1 305M ) 3 + C/L is due to Rice (Ref. 19). In summary, the 

complete acoustic reactance is given by

( ) ( )

CD

k t d kh

σ

+ ε

χ = −cot + (6.12)

This is the only component of the model in which the 

interaction among neighboring holes is taken into account, 

albeit implicitly, via the end correction, εd. The total acoustic 

impedance ζ is given by the combination of Equations (6.8) 

and (6.12).

6.4.2.2 Crandall Full-Solution Model (CF)

The distinguishing feature for the next model (Ref. 43)

is the use of a purely analytical solution for oscillatory flow in 

a circular channel to produce both Poiseuille-type and 

frequency-dependent viscous losses. Melling (Ref. 36) cites 

Crandall as the first to give this problem a modern treatment, 

thus the name for this model. A disadvantage of this approach 

is that both the resistance and mass reactance components 

internal to the hole use Bessel functions to describe the in-hole 

velocity profile. This is handled by defining two different hole 

end corrections, one for resistance and one for reactance. The 

model introduces a purely empirical dependence of discharge 

coefficient CD upon the t/d ratio and perforate open area ratio 

σ. The discharge coefficient is employed in the nonlinear 

resistance contribution as well as the perforate mass reactance. 

Hole interaction is included via the factor (1− 0.7 σ ) in mass 

reactance, and via the factor (1 – σ

2

) in the nonlinear resistance. Aside from these differences, this model is very 

similar in its phenomenological basis to the TP model 

described earlier. However, there is no explicit use of DC flow 

resistance data. Also, similar to the TP model, the grazingflow effects are simply superimposed via the Rice-Heidelberg 

model. 

The full equation for normalized liner acoustic impedance 

is given as

i[ S v (kh)]

S v

m me m

R gf

cot rms

0 0, rms

+ χ + χ + −

ζ = θ + θ ω + + θ

(6.13)

The contributing terms are described below with their 

individual derivations.

For a single tone source, as was used in the current investigation, the total (incident plus reflected) sound pressure level 

SPL at the surface of the liner with a known impedance ζ is 

used to compute the rms acoustic velocity vrms as

| |

10 20 ref rms ρ ζ = c

P

v

SPL

(6.14)

where the reference pressure Pref has a value of 20 μPa 

(2.9×10–9 psi). For multitone or broadband sources, the 

measured overall SPL and the frequency-dependent surface 

impedance ζ(f) are used to determine the frequency-dependent 

acoustic velocity vrms(f) similar to that shown in Equation (6.14). These frequency-dependent components are then 

combined to determine the rms acoustic velocity used in the 

current model. Because of the nature of Equation (6.14), an 

iterative approach must be used to simultaneously determine 

vrms and ζ.

The effective mass end correction, εd, has different contributions to the resistance and reactance terms. Let

ζ ω = (θ + θ ω )+ i (χm + χme ) 0, 0 0, (6.15)

where θ0 and θ0,ω represent the frequency-independent and 

frequency-dependent components of the normalized linear 

acoustic resistance, respectively; χm is the normalized mass 

reactance; and χme is the corresponding mass reactance due to 

the end correction. The real and imaginary components of ζ0,ω

are computed as follows:

( ) ( ) ( )

( ) 













 ω + ε σ θ + θ = μ

ω k r

i t Red c

F 0 0, Re (6.16)

( ) ( ) ( )

( ) 













 ω + ε σ

χ + χ = μk r

i t Imd c m me F

Im (6.17)

where r is the hole radius (r = d/2) and εRe is given by

3 MC L 1 305

1 0.7

+

− σ

εRe = (6.18)

and εIm is given by

εIm = 85εRe 0. (6.19)

Equation (6.13) can now be rewritten as
NASA/TP—2012-215653 172

ζ = ζ0,ω + SRvrms + θgf + i{Smvrms − cot(kh)} (6.20)

The derivations for nonlinear resistance slope, SR, and 

nonlinear mass reactance slope, Sm, are given by

















σ

ρ − σ

ρ = 2

2

2

1

2

133.6541

D

R c C

S (6.21)

2 0.00207

σ = − k Sm (6.22)

and the normalized grazing-flow-induced acoustic resistance, 

θgf, is provided by Equation (6.6). It should be noted that 

Equations (6.21) and (6.22) are empirically derived formulas, 

with units of seconds per meter. Thus, the numerical coefficient for SR is dimensionless, and the numerical coefficient for 

Sm has units of seconds. Finally, F(kμr) is defined (Ref. 33) as

( ) ( )

k rJ (k r)

J k r k r μ μ

μ

μ = − 0

2 1 F 1 (6.23)

where J0 and J1 are zero- and first-order Bessel functions, and kμ

is the wavenumber of the viscous Stokes wave computed from

μ

ωρ kμ = −i 2 (6.24)

Finally, the discharge coefficient is a function of t/d. For 

t/d ≤ 1, it is given by

(t d ) CD e 0.1 0.5072 0.80695 σ − = (6.25)

However, for perforated plates with t/d > 1, the discharge 

coefficient will vary based on skin material and perforation 

method. A sufficient database is necessary to establish an 

adequate empirical equation in each case. For example, the 

following relation is used for electro-deposited nickel-based 

microperforate plates.

(d t) CD e 0.1 1.151 0.584854 σ − = (6.26)

6.4.2.3 Composite Empirical Model (CE)

The Composite Empirical model (CE) (Ref. 44, private 

communication) blends resistance contributions from a DC 

flow resistance model with grazing-flow effects due to an 

effective acoustic velocity (in turn, due to the turbulent 

boundary layer) in a way that the TP and CF models do not. 

The grazing-flow resistance appears as a cross-term derived 

by invoking contributions from the DC flow resistance and the 

effective acoustic velocity (calculated as root-square-sum of 

the purely acoustic particle velocity), as well as an equivalent 

particle velocity generated by the turbulent flow. The detailed 

structure of this model is as follows:

( ) 25 eff , cav ζ = θDC + θ AC +1. θI v CD ω + i χm + χme + χ (6.27)

where θDC is the steady flow resistance, and θAC and θI are the 

frequency-dependent and inertial contributions to the resistance, respectively. veff is an effective rms acoustic velocity, 

CD,ω is a discharge coefficient correction for unsteady flow, 

χm is the internal mass reactance, χme is the attached mass 

reactance, and χcav is the classical cavity reactance given by 

Equation (6.9). Expressions for the above impedance components are

















ρ σ

μ θ = 2

32 1.75

c d

t

DC (6.28a)





 





σ

+

ρ

μω θ = ct d

AC

1 2.82 (6.28b)













σ

θ = 2 2 ( )

1

D

I c C (6.28c)

































σ ω = − −

1.2

eff ,

0.53 1 exp fdv CD (6.29)

2 2 2 2 eff 0.2 D gf v = v + BC σ V (6.30a)

( ) 11 2 B = 0.05 + 0. d δ (6.30b)

where v is the acoustic velocity at a given frequency, Vgf is the 

grazing-flow speed, and δ2 is the boundary layer momentum 

thickness. For a given incident sound excitation level (in 

decibels), the effective rms acoustic velocity can also be 

computed as

| |

10 20 ref

eff

ρ ζ

⋅ = cP

v

SPL

(6.31)

and can be used to determine the impedance via an iterative 

process. The mass reactance terms are given by

( )















 − σ  + 

 



 ω

χ + χ = z m me e

d

t

c

0.85 1 0.9 1.11 (6.32)

where

















+ 















+

σ

 + 

 



 ω =

c

V

c

V

fd

v

c

z

gf gf 8.65 0.8192

0.035 0.275

2

eff

2

(6.33)

and the cavity reactance χcav is given by Equation (6.9).
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 173 Chapter 6

6.4.2.4 Fluid Mechanical Model (FM)

The Fluid Mechanical model (FM) (Ref. 45) employs an 

orifice-centered control volume to describe the acoustically 

driven unsteady flow into the orifice-cavity system. Although 

the model employs five empirically determined parameters, it 

is also the most “first principles based” of the four models 

considered in this investigation. To keep the model onedimensional, equations employing conservation of mass and 

momentum (the component normal to the surface) are used to 

parse the flow into inviscid-core and boundary-layer components. Viscous scrubbing losses and inertial losses are 

restricted to the boundary-layer and inviscid-core flows, 

respectively. Consequently, the resulting time-domain 

equation of motion for fluid momentum is nonlinear in 

velocity, arising from momentum flux terms at the control 

volume surfaces. Five simplifications are employed to make 

the differential equation amenable to solution for a timeharmonic excitation. Thus, the following empirical parameters 

are introduced:

(1) Kss and Kac steady-state and acoustic viscous loss 

parameters, respectively

(2) CD orifice discharge coefficient

(3) H orifice nonlinear inertial length

Parameters Kss and Kac are dependent upon t/d, the orifice 

thickness-to-diameter ratio, and CD is dependent upon a 

nondimensional orifice velocity (like a Reynolds number) and 

frequency. The parameter H is an orifice inertial length 

parameter that is unknown and must be modeled experimentally (Ref. 46), and the ratio H/d is strongly dependent upon 

acoustic excitation and frequency. All of these model parameters have been derived using POHCs with the following 

conditions:

0.4 ≤ t ≤ 129 mm (0.02 ≤ t ≤ 5.1 in.)

0.8 ≤ d ≤ 1.6 mm (0.03 ≤ d ≤ 0.06 in.)

0.5 ≤ t/d ≤ 16

0.0039 ≤ σ ≤ 0.0156

75 ≤ SPL ≤ 140 dB

Therefore, application of this model outside these parameter 

ranges should be used with caution.

The resistance component of the FM model is given by





 



 θ  +  



 θ

+















ρ σ 













 − θ = 2 2

1 2

2 2

pk L L

D

D

c

p

C

C

(6.34)

where ppk is the peak acoustic excitation pressure at the 

surface of the liner and

















μ

ω ρ +

ρ σ

μ θ = 2

2

d

cd

t

L Kss Kac (6.35)

The reactance component for a resonator with a cavity length 

of h is given by

(kh) c − cot

σ

ω

χ = H (6.36)

As mentioned previously, Kss and Kac are related to viscous losses and have a simple dependency upon the ratio of 

plate thickness to orifice diameter, t/d, given by

1.44

13 10.23

−





 



 = +

d

t Kss (6.37a)

and 

1

3 2.32

−





 



 = +

d

t Kac (6.37b)

The orifice nonlinear inertial length, H, is given by 

( ) 

















































 = − − − − −

4

1 1 res exp 1 0f f

f

NL

H D H M (6.38)

where the single hole orifice inertial length for low sound 

pressure level (SPL), D, is

( )

( )

2

1 0.2554 1

0.0263 1 1

1 1.25

0.85 −













+ −

− + 















+ σ = +

N

N D d

t (6.39)

and N is the number of holes in the perforated plate 

(facesheet). Nondimensional parameters M, and V are 

defined as































 



 



 + − −











 



 



 = + −η

4.365

13.06 1 exp 64.9

0.011 2.086

d

t

d

t M V 0

(6.40a)

0.0325 3.4

3.7

0  + 

 





η =

−

d

t (6.40b)

and

2

ref v

p pk

ρ

V = (6.40c)

where
NASA/TP—2012-215653 174

















+ σ = π +1 1.25

0.85

ref 2 d

v f L t (6.40d)

The three frequency parameters, f0, fL, and fNL, are given by

( ) 0.264{1 } 0.436

1 18.81

1.34

4.49

0

+ − −











 



 



 +





 





=

− d

t

e

d

t

d

t

f

V (6.41a)

( )

( )

1

1 1.25

0.85

1 0.2554 1

0.0263 1 1

2

−

















+ σ

+

σ ×













+ −

− +

π =

d

t

h

c f L N

N

(6.41b)

and















































 



 × − −

























 



 



 



 = + − − −

V 2

0.6

1 exp 3.63

1 0.785 0.76 1 exp 3.63

d

t

d

t fNL fL

(6.41c)

The nonlinear inertial length at the resonance condition is 

given by

1

1

V

V

H

η

−

η

−





 



 +





 



 +

= 1.411

1.227

res

1 1.018

1 0.7254

d

t

d

t

(6.42)

where

( ) d

t

e

0.1174

1 3.419 − η = (6.43)

CD is determined by curve fitting to data taken at the

resonant frequency of the liner. First, a curve fit to CD at 

resonance, CD,res, is determined for selected resonators to get

2

2

V

V

res

res ,res 1

1

n

m CD

+

+ = (6.44)

where

( )

( ) d

t

d

t

e

e

m

0.647

0.647

res

1 0.109

1 110.5

+

+ = (6.45a)

( )

( ) d

t

d

t

e

e

n

0.647

0.647

res

1 0.109

1 168.5

+

+ = (6.45b)

Further curve fits for a range of selected resonators have 

been obtained to construct the general discharge coefficient, 

which is given by

2 0 non 0 non

2 ,res 0 non

1 n f m f

C m f C D

D

+ +

+ = (6.46)

where fnon is a nondimensional frequency given by

non = −1

f

f f NL (6.47)

and the curve-fitting parameters m0 and n0 for CD include

3V 0 1 2 m m m m e− = + (6.48)

where

( ) { } d

t

e

d

t

m d

t 0.18

1 18.81 57.11 1 −  − − 

 



 = (6.49a)

































 



 +





 



  + 

 



  +  



  −



 





= 4

2 3 4

2

1 148

33.5 78 131 917

exp

d

t

d

t

d

t

d

t

d

t

m (6.49b)

( )

d

t

e

d

t

m d

t





 



  − − 

 



 = −0.19

3 43.2 147.1 1 (6.49c)

and

V

V

3

1 2

0 1 n

n n

n

+

+ = (6.50)

where





 



 +





 



 − −

=

d

t

d

t

n

1 0.342

3.44 0.182

1 (6.51a)





 



 +





 



 +

=

d

t

d

t

n

1 0.151

18.23 1.33

2 (6.51b)

2

7

3

1 1.3 10

38





 



 + ×

=

−

d

t

n (6.51c)
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 175 Chapter 6

6.4.2.5 Grazing-flow Contribution to Resistance: Comparison of Models

The grazing-flow contribution to perforate resistance is 

included in the TP and CF models via the Rice-Heidelberg 

grazing-flow resistance model (Refs. 41 and 43). It is simply 

superimposed onto the respective no-flow models as

( ( d )) gf

1

C L

2 1.256

M

σ + δ

θ = (6.52)

where θgf is the grazing-flow resistance, MC/L is the freestream Mach number (at duct centerline), σ is the open area 

ratio (porosity) of the perforate, δ1 is the boundary layer 

displacement thickness, and d is the hole diameter. The

porosity in the denominator accounts for the difference 

between a single hole and the entire perforate, but it does not 

account for hole-to-hole interactions. The boundary layer 

correction term, involving δ1/d, is based on empirical correlations with data and is attributed to Hersh (Ref. 46). It is of 

interest to note that in the limiting case as δ1 approaches 0, θgf

reduces to exactly one-half the free-stream Mach number 

(with due accounting for porosity):

σ

θ →

δ →

C L

0

M

2

1 lim

1

gf (6.53)

The above limiting value is 20 percent less than that predicted by a purely theoretical, inviscid flow dissipation model 

of Baumeister (Ref. 47). His model is based on the hypothesis 

that the grazing flow sweeps nearly all the orifice jet kinetic 

energy into the mean flow when the orifice jet velocity is 

nearly the same as the mean-flow velocity. Under this 

circumstance, the Baumeister model predicts a grazing-flow

contribution to resistance of

σ

θ = MC L

1.6

1

gf (6.54)

Thus, under the inviscid flow model restrictions, the dominant term in the Rice-Heidelberg model can be viewed as 

being due to an inviscid flow dissipation mechanism. The term 

involving boundary layer displacement δ1 can be interpreted 

as a correction on an inviscid flow dissipation mechanism. As 

a matter of consistency, the Rice-Heidelberg grazing-flow

resistance tends to 0 in the limit of increasing δ1/d.

A worrisome issue arises with the “tacked-on” nature of the 

Rice-Heidelberg model to account for the grazing-flow

resistance in the TP and CF models. The discharge coefficient 

CD in the TP and CF models is inferred from DC flow resistance measurements. When such measurements are conducted with grazing flow, the discharge coefficient will typically be 

substantially different from the corresponding value observed in 

the absence of grazing flow. This dependence of the discharge 

coefficient on the grazing flow is not captured in the TP and CF 

models. As a result, the grazing-flow effect is isolated to the 

Rice-Heidelberg contribution. Correspondingly, the counterpart 

of a discharge coefficient does not appear in the inviscid 

dissipation part of the Rice-Heidelberg model. For those cases 

where the grazing-flow contribution dominates the resistance, 

this decoupling of the grazing-flow effect and acoustics may not 

appreciably affect the total resistance for conventional perforates. However, for low to modest grazing-flow speeds, the 

respective contributions to the acoustic resistance by acoustics 

and the grazing flow may be sufficiently close to cause 

measurable systematic error. Similarly, the respective contributions of acoustics and grazing flow to the acoustic resistance are 

nearly the same for microperforates, which have a relatively 

large facesheet thickness-to-hole diameter ratio (t/d). Thus, 

significant systematic error can be incurred for these types of 

liners as well.

The CE model avoids the issue discussed above. In this 

model, the acoustic and fluid dynamic effects are integrated, 

and the discharge coefficient appears explicitly in the inertial 

loss and grazing-flow resistance terms. Green (Ref. 35) 

provides the phenomenological basis for the flow losses 

through a general porous medium, and Eversman (Ref. 17) 

describes the inclusion of grazing flow for thin porous 

materials suitable for the resonant liners of interest here. The 

grazing-flow resistance is assumed to derive from a pseudoacoustic pressure given by





 



 ∆ = ρ 2 rms 2

1

p K V (6.55)

where K is an empirical function of the grazing-flow boundary 

layer, facesheet geometry and effective roughness. This 

pseudo-acoustic pressure, ∆prms, combines with the acoustic 

excitation pressure in a root-sum-squared fashion to define an 

increment in the total rms particle velocity through the 

perforate. This is an essential difference between the CE 

model and the other two (TP and CF) models.

6.4.2.6 Summary of Salient Features of Models

In this section, we contrast some of the similarities and 

distinctions among the above four models. 

Similarities:

(1) Each acoustic resistance model for the perforate 

facesheet is physics based and employs lumped-element and 

quasi-steady flow assumptions to model unsteady flow losses. 

This is justified because all dissipation is confined to a layer, 

centered at the perforate thickness midspan, with thickness 

much smaller than the shortest wavelength of interest.

(2) These assumptions allow an effective lumped-element 

resistance, Reff, to be calculated from a knowledge of the DC 

flow resistance and a prescribed unsteady velocity through the 

perforate, as follows:
NASA/TP—2012-215653 176

( ) ( )

∫ (τ) τ

∫ τ τ = d

d

2

0

2

0

eff

v

R v v

R

T

f

T

(6.56)

where T is the period of the longest wavelength of interest.

Each of the four models employ an iterative scheme to 

determine a velocity time history consistent with a flow 

resistance model and specified acoustic excitation.

(3) Based on a Fok’s formula (Ref. 36), hole-to-hole interactions are assumed to be weak for conventional POHC liners. 

As such, both multihole effects and hole-to-hole interactions 

are included via the facesheet porosity parameter for the

resistance component.

(4) Grazing-flow effects are decoupled from viscous and 

inertial resistance contributions.

(5) The cavity is purely compliant and therefore provides 

no dissipation.

Distinctions:

(1) TP (Two-Parameter): The TP model is the simplest of 

the four models included in this study. It makes minimum use 

of empirical parameters, the most prominent being the HagenPoiseuille laminar flow friction factor, a, and orifice discharge 

coefficient, CD, to predict frequency-independent linear and 

nonlinear contributions to resistance, respectively. A modest 

hole-interaction effect is included in the reactance, where the 

hole end correction is decreased by the factor (1− 0.7 σ) (see 

Eq. (6.11)).

(2) CF (Crandall Full-Solution): The CF model includes a 

frequency-dependent viscous resistance contribution via the 

full Navier-Stokes solution (due to Crandall) for oscillatory 

flow in a circular channel. Separate end corrections are used 

for resistance and reactance. Also, orifice thickness-to-hole 

diameter ratio and porosity dependence are incorporated into 

the discharge coefficient parameter.

(3) CE (Composite Empirical): The CE model integrates 

effects of grazing flow on resistance by adding a turbulent 

boundary-layer-driven excitation onto the acoustic excitation 

on an energy basis.

(4) FM (Fluid Mechanical): The FM model employs a firstprinciples-based application of the mass and momentum 

equations to an orifice-centered control volume. These 

equations are manipulated and combined into a time-domain, 

nonlinear, differential equation. Five assumptions are applied 

to solve this equation. This solution characterizes the unsteady 

orifice flow for harmonic acoustic excitation. The solution 

procedure gives rise to five empirical parameters that must be 

evaluated experimentally via acoustic impedance measurements. Unlike the other three models, it does not include 

grazing-flow effects.

6.5 Database Creation for Uncertainty 

Assessment 

This section describes the creation of a statistical database 

for both the input parameters and the processing of those 

parameters through the prediction model. 

6.5.1 Assessment Liner Geometry and Input 

Preparation

During the late 1990s, a study was conducted by four organizations (NASA, Boeing, GE, and Goodrich) to compare 

impedance measurement methodologies (Ref. 48). The 

facesheet geometry (see Table 6.1) for the single-layer 

baseline liner used in that study was considered to be at or 

near the median for each geometric parameter (hole diameter, 

facesheet thickness, and porosity). This same liner configuration was chosen as the assessment liner for the current 

investigation, such that results from this study could be 

compared with those from previous studies conducted by each 

of these organizations. This assessment liner was fabricated in 

two configurations (50.8- by 50.8-mm and 50.8- by 406.4-mm 

active surface areas) to allow testing in the NASA Langley 

normal incidence tube (NIT) and grazing incidence tube 

(GIT), respectively. Each configuration was fabricated from 

the same parent material, using the same fabrication processes. 

In the several graphics that follow, statistical metrics

(95% confidence intervals) are presented. The 50.8- by 50.8-

mm configuration was tested 14 times in the NIT at each test 

condition. Similarly, the 50.8- by 406.4-mm configuration was 

tested 8 to 10 times in the GIT at each test condition of interest 

to provide meaningful statistical metrics. Repeat runs were 

conducted at different times of the year, and the assessment 

liner of interest was removed and reinstalled between tests.

6.5.2 Quantifying Input Parameter Uncertainty

In what follows, a brief description is provided of how each 

input parameter was measured along with a description of how 

the uncertainty in that parameter was determined. For those 

parameters that were measured at least once per test (between 

8 and 14 times), the mean and standard deviation were 

computed in the classical manner. For parameters that were 

determined to be independent of any particular test, the 

methods chosen for estimating their means and standard 

deviations are included with the description below. The 

resultant means and standard deviations for the geometrical 

parameters associated with the assessment liner are provided 

in Table 6.1. Limited tests with other liners showed very 

similar results. Because of time constraints, this was the only 

liner tested a sufficient number of times to support meaningful

statistical estimates. Thus, only the results for this liner are
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 177 Chapter 6

discussed in the remainder of this chapter. The aeroacoustic 

parameter mean values and standard deviations for the 

assessment liner are provided in Table 6.2 and Table 6.3, 

respectively.

6.5.2.1 Geometric Parameters

As mentioned earlier, each configuration (50.8 by 50.8 mm

and 50.8 by 406.4 mm) was fabricated from the same

parent material. Thus, it was assumed that the geometric 

parameters have the same values for either configuration. For

convenience, these parameters were measured on the smaller

samples. The following parameters were measured at 10

randomly selected locations across the sample surface. The 

corresponding means and standard deviations computed from 

these measurements are provided in Table 6.1.

(1) Facesheet thickness (t): The thickness was measured 

using a computer-aided system that allows the user to move a

probe until it makes contact with a surface and then records 

the location in a three-dimensional coordinate system. The 

facesheet thickness was determined by taking the difference 

between the results from measurements taken in this manner 

from both sides of the facesheet.

(2) Cavity depth (h): The cavity depth was measured with 

the same contact probe system described above.

TABLE 6.1.—GEOMETRIC PARAMETER STATISTICAL INPUTSa

Facesheet thickness,

t,

mm (in.)

Hole diameter,

d,

mm (in.)

Cavity depth,

h,

mm (in.)

Open area ratio,

σ

Mean StDev Mean StDev Mean StDev Mean StDev 

0.813 (0.032) 0.025 (9.8×10–4

) 0.965 (0.038) 0.000 38.176 (1.50) 0.076 (3×10–3) 0.089 0.002 a

Mean indicates mean value and StDev, the standard deviation.

TABLE 6.2.—AEROACOUSTIC PARAMETER MEAN VALUES 

Test

case

Test

riga

Average 

Mach 

number,

Mave

Sound 

pressure 

level,

SPL,

dB

Static pressure,

Ps,

Pa (psi)

Static

temperature,

Ts,

K (°R)

Discharge

coefficient,

CD

Boundary-layer 

displacement 

thickness

δ1,

mm (in.)

Boundary-layer 

momentum 

thickness,

δ2,

mm (in.)

1 NIT 0.000 120.0 101 601 (14.736) 295.8 (532.4) 0.771 0.00 0.00

2 NIT 0.000 140.0 101 438 (14.712) 295.4 (531.7) 0.771 0.00 0.00

3 GIT 0.000 122.3 101 701 (14.751) 295.8 (532.4) 0.771 0.00 0.00

4 GIT 0.000 140.5 101 686 (14.748) 295.8 (532.4) 0.771 0.00 0.00

5 GIT 0.252 121.3 101 687 (14.495) 295.3 (531.5) 0.771 0.05 (0.002) 1.75 (0.07)

6 GIT 0.251 140.7 101 933 (14.784) 295.2 (531.4) 0.771 0.05 (0.002) 1.75 (0.07)

7 GIT 0.400 120.2 101 839 (14.771) 293.8 (528.8) 0.771 0.05 (0.002) 1.75 (0.07)

8 GIT 0.400 140.6 101 823 (14.768) 293.8 (528.8) 0.771 0.05 (0.002) 1.75 (0.07) a

The NASA Langley normal incidence tube (NIT) or grazing incidence tube (GIT).

TABLE 6.3.—AEROACOUSTIC PARAMETER STANDARD DEVIATIONS 

Test

case

Test

riga

Average 

Mach 

number,

Mave

Sound 

pressure 

level,

SPL,

dB

Static pressure,

Ps,

Pa (psi)

Static 

temperature,

Ts,

K (°R)

Discharge

coefficient,

CD

Boundary-layer 

displacement

thickness

δ1,

mm (in.)

Boundary-layer 

momentum 

thickness,

δ2,

mm (in.)

1 NIT 0.0000 0.2 611 (0.089) 0.8 (1.4) 0.135 0.000 0.000

2 NIT 0.0000 0.4 810 (0.118) 1.3 (2.3) 0.135 0.000 0.000

3 GIT 0.0000 1.6 387 (0.056) 0.9 (1.6) 0.135 0.000 0.000

4 GIT 0.0000 1.1 485 (0.070) 0.6 (1.1) 0.135 0.000 0.000

5 GIT 0.0012 0.9 790 (0.115) 0.3 (0.5) 0.135 0.004 (0.00016) 0.102 (0.004)

6 GIT 0.0012 0.8 862 (0.125) 0.2 (0.4) 0.135 0.004 (0.00016) 0.102 (0.004)

7 GIT 0.0007 1.6 783 (0.114) 0.2 (0.4) 0.135 0.001 (0.00004) 0.102 (0.004)

8 GIT 0.0006 1.2 754 (0.109) 0.2 (0.4) 0.135 0.001 (0.00004) 0.102 (0.004) a

The NASA Langley normal incidence tube (NIT) or grazing incidence tube (GIT).
NASA/TP—2012-215653 178

(3) Hole diameter (d): A set of precision pins was used to 

determine the hole diameter of each of the 10 randomly 

selected holes. The outer diameter of the largest pin that would 

fit through a hole was used as the diameter. All holes were 

observed to have the same diameter. It should be noted that 

this assumes the holes to be perfectly round. If they are not, 

the precision pins provide a measure of the minimum width of 

the hole opening.

(4) Open area ratio (σ): This parameter is a function of the 

hole diameter and the distances between adjacent rows and 

columns of holes (staggered rows to form equilateral hole 

patterns). The mean and standard deviation of the hole 

diameters were computed based on measurements described 

above. The distance between adjacent rows and columns was 

determined using the contact probe system described above. 

The open area ratio mean was then computed using

r c s s

d

4

2 π

σ = (6.57)

where sr and sc are the row and column separation distances, 

respectively. The mean open area ratio is taken to be the value 

computed using the mean values of the corresponding 

parameters (d, sr and sc). Also, since these parameters are 

assumed to be uncorrelated, the standard deviation is given by

( ) ( ) ( )

( ) ( )

0.5

2

2

1 1

2

























+ 















+







  + 

 





σ = σ

c

c

r

r

Var s

s

Var s

s

Var d

d

StDev Mean

(6.58)

where Mean, StDev, and Var represent the mean, standard 

deviation, and variance of the selected parameter.

6.5.2.2 Aeroacoustic Parameters

These parameters are associated with the aeroacoustic 

environment in which a test was conducted. The following 

provides a description of how each parameter is “measured” in 

the NASA Langley NIT and GIT.

(1) Static pressure (Ps):

(a) The atmospheric pressure in the test facility is recorded prior to each test in the NIT; this is taken to 

be the static pressure for the NIT tests.

(b) A pitot-static probe mounted in the center of the GIT, 

downstream of the test window, is used to record the 

static pressure at the beginning of each test. It is of 

interest to note that at a centerline Mach number of 

0.3, the static pressure gradient in the hard-wall section has been reported as 1733 Pa/m (0.08 psi/ft). 

This corresponds to a variation of about 704 Pa 

(0.102 psi) over a distance equal to the assessment 

liner length, comparable to a range of standard deviations in static pressures from Table 6.3 of 387 to 862 

Pa (0.056 to 0.125 psi) (Ref. 13). 

(2) Static temperature (Ts):

(a) The static temperature for NIT tests is taken to be 

the room temperature in the test facility.

(b) The static temperature in the GIT is recorded with 

the pitot-static probe mentioned above.

(3) Centerline and average Mach numbers (MC/L and Mave):

(a) The Mach number in the NIT is 0.

(b) When flow is turned on in the GIT, the prediction 

models require either a centerline Mach number or a 

cross-section-averaged Mach number. Since the 

flow profile changes lengthwise along the liner, the 

centerline Mach number also changes, and to a lesser extent, the cross-section-averaged Mach number 

changes. Thus, when a prediction code requires a 

centerline Mach number as input, this is determined 

by averaging the centerline Mach number at three 

locations: just upstream of the liner leading edge, at 

the length-wise mid-span, and just downstream of 

the trailing edge. The downstream location, centerline Mach number is used as the facility set point, 

and is indexed to the average of the three centerline 

Mach numbers via a curve fit. When the crosssection-averaged Mach number is required, the same 

procedure is adopted, except that cross-sectionaveraged Mach numbers replace the centerline 

Mach numbers.

(4) Boundary layer displacement thickness (δ1):

(a) The boundary layer displacement thickness in the 

NIT is 0.

(b) For the GIT tests, this parameter was assumed to be 

correlated with the centerline Mach number as 

determined in the earlier test (Ref. 49). This parameter was not measured during each test, but was 

assumed to be solely a function of the target MC/L. 

As such, the variability was taken to be the range of 

boundary layer displacement thickness over the 

length of the liner (i.e., difference between values 

computed at the upstream and downstream planes). 

This range was assumed to span the full range of 

uncertainty for this parameter, ±3 ⋅ StDev(δ1).

(5) Boundary layer momentum thickness (δ2):

This parameter was handled in the same manner 

as described above for boundary layer displacement 

thickness.

(6) Discharge coefficient (CD): 

During the late 1990s, a study was conducted by four 

organizations (NASA, Boeing, GE, and Goodrich) 

to compare impedance measurement methodologies. 
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 179 Chapter 6

During this study (Ref. 39), tests were conducted with 

liners made from the same parent materials as those 

used in the current study. To improve statistical confidence, a number of samples fabricated using the same 

manufacturing process were added to this database, and 

DC flow resistance measurements were conducted to 

educe the discharge coefficient for each sample. The 

mean (0.771) and standard deviation (0.135) reported 

for this series of tests are used in the current investigation. The reader will note that the standard deviation on 

CD is 17.5 percent of the mean value. This percent 

standard deviation is greater than that for any other 

input variable, by about a factor of 3 (see Table 6.2 and

Table 6.3). It should also be noted that there are 

multiple methods in use to determine the discharge coefficient of a conventional liner. These methods tend to 

be paired with corresponding impedance prediction 

models, such that the discharge coefficients are only 

applicable to the paired impedance prediction model. 

Given the importance of the discharge coefficient in 

most impedance prediction models, it is our view that 

significant benefit could be gained by settling on a 

single methodology. In the absence of this consensus, 

the discharge coefficient provided in Reference 39 is 

used in all impedance prediction models that do not 

offer an explicit, independent method of calculation.

(7) Excitation level (SPL):

(a) A reference microphone flush mounted in the NIT 

duct wall 6.35 mm (0.25 in.) from the surface of the 

liner is used to record the sound pressure level SPL.

(b) A microphone mounted in the lower wall of the GIT 

at the “computational source plane” (101.6 mm 

(4 in.) upstream of the liner leading edge) is used to 

record the source SPL. Since the SPL is reset for 

each frequency of interest (in the NIT and GIT), this 

frequency dependence of the SPL variability is 

included in the current investigation. Thus, an 

independent set of means and standard deviations is 

used at each frequency (based on corresponding 

measurements in the NIT and GIT). Note the GIT 

computational domain used in the current investigation is of shorter axial extent than that typically 

reported. A problem in the test setup resulted in an 

SPL variation that is larger than that typically 

observed (±0.5 dB) in this test apparatus.

6.5.2.3 Processing Input Parameter Uncertainty Through 

Impedance Prediction Models

A Monte Carlo approach was used to estimate the

95% confidence intervals for the impedance prediction 

models, which were compared with 95% confidence intervals 

derived from zero-order replication tests (Ref. 10) conducted 

in the NASA Langley test rigs (NIT and GIT). As mentioned 

earlier, between 8 and 14 tests were conducted in the NIT and 

GIT at each aeroacoustic set point of interest (i.e., at each

frequency, SPL, and Mach number). The frequency was 

assumed to be deterministic (i.e., StDev = 0), but all other 

parameters were assumed to vary about their respective 

means. Thirty-one simulations were then conducted for each 

impedance prediction code, with their respective inputs based 

on these Gaussian distributions for each parameter of interest. 

For example, 31 values of static pressure were randomly 

selected from the Gaussian distribution generated by the 

procedure described above. This process was used for all of 

the geometric and aeroacoustic parameters except the source 

excitation level (SPL). In order to capture the additional 

variability in the SPL, a set of 31 (1 per simulation) values of 

SPL was randomly selected from the SPL Gaussian distribution at each test frequency of interest (i.e., the SPL at each 

frequency was independent of that selected for all other 

frequencies). The impedance prediction codes were then used 

to perform simulations based on these inputs, for 100 Hz 

increments from 400 to 3000 Hz. The means and standard 

deviations of the predicted impedance at each test frequency 

were then used to compute 95% confidence intervals; 

comparisons of these prediction confidence intervals with the 

corresponding measurement confidence intervals are used to 

highlight capabilities and limitations of the existing processes.

6.6 Results and Discussion

A number of tests and model simulations were conducted to 

evaluate the measurement processes and impedance prediction 

models presented above. This section provides results of these 

evaluations.

6.6.1 Graphical Format and Interpretation

Monte-Carlo simulations performed on the impedance prediction models are used to compute means and 95% confidence 

intervals (CIs). Figure 6.6 provides an example of how these 

results are compared with those from statistical sampling 

generated by repeated impedance measurements. The graphic 

format described below is information intensive and is key to 

interpreting the results. This format is used for comparisons of 

measured and predicted results. A similar format is also used to 

describe comparisons of two measured results.

The graphic ordinate is in normalized impedance units (in 

Figure 6.6, resistance), and the abscissa is frequency in hertz. 

The shaded regions indicate the measured and predicted CIs. 

A red region, bounded by dotted lines, represents a measured 

CI. Correspondingly, a green region, bounded by dashed lines, 

represents a predicted CI. Solid red and green lines depict the 

mean values for the measured and predicted impedances, 

respectively. Regions where the measured and predicted CIs 

overlap are shaded yellow. Thus, perfect agreement between 

the measured and predicted impedances would result in 

coincident means and CIs. However, it should be noted that 

coincidence between measured and predicted means does not 

imply the absence of systematic error, but rather that the 

systematic errors of the measurements and prediction are 

exactly the same. These systematic errors can be zero, but do
NASA/TP—2012-215653 180

Figure 6.6.—Representative format for comparison of 

impedance prediction and measurement means and 

95% confidence intervals.

not have to be. The reader should also note that measurements 

were taken in 100-Hz increments in the NIT and in 500-Hz 

increments in the GIT because data acquisition and processing 

is more labor and computation intensive for the GIT. The 

predictions were performed at 100-Hz increments.

In pursuit of the final goal to relate uncertainty analysis, as 

described here, to as-yet-unknown specification limits, the

following language convention is adopted for comparing 

measurements with predictions. It is supposed that the prediction CIs are to be taken as the provisional or default specification limits, in the SPC sense. The objective is then to ascertain 

to what degree the prediction CIs subsume the measurement 

CIs, as would be the case if they were true specification limits. 

It is not known a priori how to parse systematic error between 

measurements and predictions. Thus, an out-of-compliance 

condition signifies that accuracy and precision of both the 

prediction and the measurement are to be scrutinized. Ultimately, both predictions and measurements should be independently validated to a level such that an out-of-compliance 

condition can be attributed to the liner fabrication process 

(assignable causes) at some stage prior to final product 

production. An important aspect of this approach to uncertainty 

is the inherent tradeoff between accuracy and precision to 

achieve compliance within specification limits.

6.6.2 Comparison of NIT and GIT Measurements 

With No Flow

In this section, we focus on the measurements conducted in 

the NIT and GIT. Comparisons between measured and predicted 

results are discussed in a subsequent section. For a local-reacting 

liner, there should be no difference between normal incidence 

impedance spectra measured in a normal incidence or grazing 

incidence environment. Thus, any differences between the 

impedances measured in the two test rigs are indicative of either 

systematic or random error. We begin with a discussion of the 

results in the vicinity of the zero reactance crossing point (i.e., 

the liner resonance), as POHC liners are generally most effective 

for frequencies near resonance.

Figure 6.7.—Results from NIT impedance measurements 

with source excitation levels of 120 and 140 dB conducted 

at 100-Hz increments. (a) Resistance. (b) Reactance.

The NIT measurements for 120- and 140-dB excitations are 

shown in Figure 6.7. The resistance CIs (red and blue shading 

for 120 and 140 dB excitations, respectively) are very tightly 

centered on the measured means, with very modest CI growth 

at the low end of the frequency range. The resonance peak

mean resistance increases from 0.16 to 0.45 with an excitation 

increase from 120 to 140 dB. For the reactance spectra, the 

measured CIs essentially collapse onto the means at the 

graphical resolution used here. Note that the reactance zero 

crossing occurs about 115 Hz above the peak resistance. Also, 

the mean resistance clearly increases at either end of the 

frequency range.

The corresponding GIT measurements for 120- and 140-dB 

excitations are provided in Figure 6.8. Very modest growth of 

the reactance CIs is noted, relative to those for the NIT, 

especially for the 120-dB excitation. The resistance CIs are 

noticeably greater across the entire frequency range for the 

GIT relative to the NIT. Also, in contrast with the very tight 

CIs for the NIT, the CIs for the lower excitation (120 dB) in 

the GIT are about 0.16 and 0.02 for 500 and 1000 Hz, 

respectively. The CIs for the remaining frequencies range 

from about 0.05 to 0.09, with no definite trend. For the higher 

excitation (140 dB), the CIs are generally less than 0.1, with
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 181 Chapter 6

Figure 6.8.—Results from GIT impedance measurements with source excitation levels of 120 and 140 dB 

conducted at 500-Hz increments. (a) Resistance.

(b) Reactance.

the exception of a CI of 0.28 at 500 Hz. The resonance mean 

resistance values of 0.14 and 0.38 for 120- and 140-dB 

excitations, respectively, compare with the corresponding 

values of 0.16 and 0.45 for the NIT. Also, increases in the 

resistance at the frequency extremes are more evident in the 

GIT results. The reactance zero-crossing frequencies measured 

in the GIT are very consistent with those observed from the 

NIT measurements. Also, there appears to be more separation 

between the reactance zero crossings and the peak resistances 

measured in the GIT than was the case for the NIT measurements. However, given the 500-Hz resolution of the GIT 

measurements, it is not clear whether this is truly the case.

These same results are presented in a different format in 

Figure 6.9 and Figure 6.10. Figure 6.9 presents comparisons of 

the NIT and GIT results for an excitation of 120 dB, while 

Figure 6.10 presents similar comparisons for an excitation of 

140 dB. Because of the expanded scale of the graphical 

results, there appear to be substantial differences between the 

ranges of the resistance means measured with the two test rigs. 

In reality, the range are quite similar. For an excitation of 

120 dB, the mean resistance ranges from 0.1 to 0.2 for the NIT 

measurements, and from 0.1 to 0.3 for the GIT measurements.

Figure 6.9.—Results from NIT and GIT impedance

measurements with source excitation levels of

120 dB conducted at 100- and 500-Hz increments,

respectively. (a) Resistance. (b) Reactance.

There is a slightly larger difference for an excitation of 

140 dB, with the mean resistances measured in the NIT 

ranging from 0.1 to 0.5, while the corresponding results in the 

GIT range from 0.2 to 0.4.

6.6.3 Comparison of GIT Measurements With 

Flow

Impedance measurements acquired in the GIT with flow 

(see Figure 6.11) are reported at two centerline Mach numbers 

(0.3 and 0.475) and one excitation level (140 dB). These 

conditions were chosen as representative of the most realistic 

simulations of the aeroacoustic environment of full-scale 

aircraft engine nacelles. A comparison of Figure 6.10 and 

Figure 6.11 indicates a broadband increase in resistance with 

increasing Mach number, accompanied by a general flattening 

of the resistance spectra relative to the no-flow results in the 

vicinity of the reactance zero crossing (liner resonance). The 

mean resistances are approximately 0.5, 0.9, and 1.2 for 

centerline Mach numbers of 0.0, 0.3, and 0.475, respectively.

Clearly, the effects of mean flow on the resistance spectra 

mask the resonance-related peak exhibited for no-flow at near 

1500 Hz in the NIT.
NASA/TP—2012-215653 182

Figure 6.10.—Results from NIT and GIT impedance 

measurements with source excitation levels of

140 dB conducted at 100- and 500-Hz increments, 

respectively. (a) Resistance. (b) Reactance.

Significant variability is also evident in the mean resistance 

values across the frequency range. On the other hand, the 

reactance is less affected by mean flow. For frequencies near 

resonance, the reactance is virtually identical across the range 

of mean-flow velocities. However, the reactance is observed 

to increase with increasing mean flow at the lower frequencies, and to decrease with increasing mean flow at the higher 

frequencies. This results in a flattening of the reactance 

spectrum as the Mach number is increased. It is perhaps 

important to note that this flattening of the reactance at high 

excitation levels and grazing-flow velocities is a useful 

feature, in that it tends to make single-layer, POHC liners 

more viable for broadband turbofan noise attenuation.

In general, the resistance confidence intervals are relatively 

unchanged with flow (referring now to the ranges of the CIs, 

in contrast with their respective means). They tend to be very 

tight at the mid-range frequencies for a flow Mach number of 

0.3, and somewhat greater at a flow Mach number of 0.475. 

They also show modest growth well away from resonance, 

especially toward the higher frequencies. Confidence intervals

on the reactance nearly collapse on the mean values for a flow 

Mach number of 0.3 and are only slightly larger at a Mach 

number of 0.475.

Figure 6.11.—Results from GIT impedance measurements 

with source excitation level of 140 dB conducted at

500-Hz increments for Mach numbers M = 0.3 and 

0.475. (a) Resistance. (b) Reactance.

6.6.4 Comparison of Predicted and Measured 

Results

This section presents comparisons of measured and predicted statistical parameters relevant to establishing the voice of 

the process with the “voice of the customer” with respect to 

the SPC paradigm. The main objective of the comparison is to 

demonstrate the shortfall in attaining an adequate voice of the 

process whereby a negotiation can happen between the end 

user (voice of the customer) and liner fabrication process 

(voice of the process).

6.6.4.1 Effects of Sample Size on Impedance Prediction

Models

The reader will recall from Section 6.2 regarding statistical 

metrics that the computation of 95% confidence intervals on 

small samples involves the use of a coverage factor to account 

for the fact that small sample sizes generally deviate from the 

Gaussian behavior that is assumed to govern their parent 

population (Ref. 10). In the spirit of strict mathematical rigor, 

the application of a coverage factor to the small sample sizes, 

adopted for the prediction statistics to be consistent with the 

measurement statistics, violates the Gaussian distribution 
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 183 Chapter 6

assumption for the parent population. The possibility of a nonGaussian predicted impedance distribution arises from the 

perforate nonlinearity incorporated into all four impedance 

prediction models. This concern is allayed via a Monte Carlo 

simulation, in which a large number of model predictions is 

used to determine the probability distribution associated with 

the underlying prediction model for a realistic set of Gaussiandistributed input parameters. In contrast, it was not possible to 

conduct a large number of measurements because of time and 

cost limitations. However, since the measured parameters do 

not vary over a large range, the “assumption” of Gaussian 

distribution was deemed acceptable. Of the impedance 

prediction models, the TP model was chosen for this more 

detailed coverage factor evaluation. The TP model was chosen 

because of its relative simplicity and straightforward algorithmic implementation of the model nonlinearity. This model 

was used to provide 10 000 simulations corresponding to the 

most nonlinear case included in this study, a target SPL of 

140 dB and an average Mach number of 0.4. These simulations were conducted at 500-Hz increments from 500 to 

3000 Hz. According to Reference 10, the coverage factor of 

1.96 can be used for this large sample population; that is, 

95 percent of the simulations should provide results that are 

within the mean ±1.96 times the standard deviation. The mean 

and standard deviation for each of the six frequencies were 

computed, and the results from each of the 10 000 simulations 

were compared against this range. For these six frequencies, at 

least 95 percent of the acoustic resistances and reactances 

computed with the TP model were within this range. Thus, the 

use of the coverage factor to gain statistical results with small 

sample populations was deemed acceptable.

6.6.4.2 Order of Graphical Results

Comparisons between the measured and predicted impedance spectra are provided in the following sections. Each 

figure provides the results based on the following choices:

(1) Prediction model: Two-Parameter (TP), Crandall FullSolution (CF), Composite Empirical (CE), or Fluid

Mechanical (FM)

(2) Test rig: normal incidence tube (NIT) or grazing incidence tube (GIT)

(3) Centerline Mach number: 0.0, 0.3, or 0.475

(4) Source excitation level (SPL): 120 or 140 dB

In an attempt to add clarity to the graphical results, the 

figures are provided in the following order. First, comparisons 

are provided between the measured impedances and those 

predicted with the TP model. We begin with comparisons of 

the TP model with the NIT measurements, and follow with 

similar comparisons for the GIT measurements, with the 

centerline Mach number set to 0. Results are provided for each 

of the source excitation levels. Next, comparisons of the TP 

model with GIT measurements in the presence of mean flow 

are provided, for centerline Mach numbers of 0.3 and 0.475. 

For these flow cases, only the 140 dB source excitation results 

are provided. This choice is made for the sake of brevity, as 

well as to focus attention on the test conditions that are most 

closely matched to those present in an aircraft engine nacelle 

(i.e., maximum SPL and MC/L). This sequence of graphical 

results is then repeated for the CF and CE impedance prediction models. Finally, since the FM model does not handle 

mean flow, the results for this model are only compared with 

measurements acquired in the NIT.

Instead of a detailed, figure-to-figure discussion of the 

model predictions and their comparisons with measured data, 

the trends of the predicted CIs (shaded green areas) and means 

(heavy green lines) are discussed in a general way with the aid 

of a perusal of all the relevant Figure 6.12 to Figure 6.31. 

Salient features are singled out for more detailed commentary. 

The discussion will close with remarks on model-to-model 

comparisons with the aid of Figure 6.32 to Figure 6.34. The 

reader is reminded that the figures follow the test parameter 

sequence previously indicated and that all predicted CIs and 

means are based upon 31 Monte Carlo simulations (large 

sample statistics) on the relevant prediction model.

Figure 6.12.—Comparison of impedance results from 14 

NIT measurements and 31 Two-Parameter model (TP) 

simulations with no flow and 120-dB source excitation 

level conducted at 100-Hz increments. (a) Resistance. 

(b) Reactance.
NASA/TP—2012-215653 184

Figure 6.13.—Comparison of impedance results from 14 NIT 

measurements and 31 Two-Parameter model (TP)

simulations with no flow and 140-dB source excitation

level conducted at 100-Hz increments. (a) Resistance. 

(b) Reactance.

Figure 6.14.—Comparison of impedance results from 10 GIT 

measurements conducted at 500-Hz increments and 31 

Two-Parameter model (TP) simulations conducted at

100-Hz increments with no flow and 120-dB source

excitation level. (a) Resistance. (b) Reactance.
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NASA/TP—2012-215653 185 Chapter 6

Figure 6.15.—Comparison of impedance results from 9 GIT 

measurements conducted at 500-Hz increments and 31 

Two-Parameter model (TP) simulations conducted at

100-Hz increments with no flow and 140-dB source

excitation level. (a) Resistance. (b) Reactance.

Figure 6.16.—Comparison of impedance results from 9 GIT 

measurements conducted at 500-Hz increments and 31 

Two-Parameter model (TP) simulations conducted at

100-Hz increments with Mach number M = 0.3 and 140-dB 

source excitation level. (a) Resistance. (b) Reactance.
NASA/TP—2012-215653 186

Figure 6.17.—Comparison of impedance results from 9 GIT 

measurements conducted at 500-Hz increments and 31 

Two-Parameter model (TP) simulations conducted at

100-Hz increments with Mach number M = 0.475 and

140-dB source excitation level. (a) Resistance.

(b) Reactance.

Figure 6.18.—Comparison of impedance results from 14 NIT 

measurements and 31 Crandall Full-Solution model (CF) 

simulations conducted at 100-Hz increments with no flow 

and 120-dB source excitation level. (a) Resistance.

(b) Reactance.
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NASA/TP—2012-215653 187 Chapter 6

Figure 6.19.—Comparison of impedance results from 14 NIT 

measurements and 31 Crandall Full-Solution model (CF) 

simulations conducted at 100-Hz increments with no flow 

and 140-dB source excitation level. (a) Resistance. 

(b) Reactance.

Figure 6.20.—Comparison of impedance results from 10 GIT 

measurements conducted at 500-Hz increments and 31 

Crandall Full-Solution model (CF) simulations conducted

at 100-Hz increments with no flow and 120-dB source

excitation level. (a) Resistance. (b) Reactance.
NASA/TP—2012-215653 188

Figure 6.21.—Comparison of impedance results from 9 GIT 

measurements conducted at 500-Hz increments and 31 

Crandall Full-Solution model (CF) simulations conducted

at 100-Hz increments with no flow and 140-dB source 

excitation level. (a) Resistance. (b) Reactance.

Figure 6.22.—Comparison of impedance results from 9 GIT 

measurements conducted at 500-Hz increments and 31 

Crandall Full-Solution model (CF) simulations conducted at 

100-Hz increments with Mach number M = 0.3 and 140-dB 

source excitation level. (a) Resistance. (b) Reactance.
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NASA/TP—2012-215653 189 Chapter 6

Figure 6.23.—Comparison of impedance results from 10 GIT 

measurements conducted at 500-Hz increments and 31 

Crandall Full-Solution model (CF) simulations conducted

at 100-Hz increments with Mach number M = 0.475 and 

140-dB source excitation level. (a) Resistance. 

(b) Reactance.

Figure 6.24.—Comparison of impedance results from 14 NIT 

measurements and 31 Composite Empirical model (CE) 

simulations conducted at 100-Hz increments with no flow 

and 120-dB source excitation level. (a) Resistance. 

(b) Reactance.
NASA/TP—2012-215653 190

Figure 6.25.—Comparison of impedance results from 14 NIT 

measurements and 31 Composite Empirical model (CE) 

simulations conducted at 100-Hz increments with no flow 

and 140-dB source excitation level. (a) Resistance. 

(b) Reactance.

Figure 6.26.—Comparison of impedance results from 10 GIT 

measurements conducted at 500-Hz increments and 31 

Composite Empirical model (CE) simulations conducted

at 100-Hz increments with no flow and 120-dB source

excitation level. (a) Resistance. (b) Reactance.
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NASA/TP—2012-215653 191 Chapter 6

Figure 6.27.—Comparison of impedance results from 9 GIT 

measurements conducted at 500-Hz increments and 31 

Composite Empirical model (CE) simulations conducted

at 100-Hz increments with no flow and 140-dB source 

excitation level. (a) Resistance. (b) Reactance.

Figure 6.28.—Comparison of impedance results from 9 GIT 

measurements conducted at 500-Hz increments and 31 

Composite Empirical model (CE) simulations conducted at 

100-Hz increments with Mach number M = 0.3 and 140-dB 

source excitation level. (a) Resistance. (b) Reactance.
NASA/TP—2012-215653 192

Figure 6.29.—Comparison of impedance results from 10 GIT 

measurements conducted at 500-Hz increments and 31 

Composite Empirical model (CE) simulations conducted at 

100-Hz increments with Mach number M = 0.475 and

140-dB source excitation level. (a) Resistance.

(b) Reactance.

Figure 6.30.—Comparison of impedance results from 14 NIT 

measurements and 31 Fluid Mechanical model (FM)

simulations conducted at 100-Hz increments with no

flow and 120-dB source excitation level. (a) Resistance. 

(b) Reactance.
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NASA/TP—2012-215653 193 Chapter 6

Figure 6.31.—Comparison of impedance results from 14 NIT 

measurements and 31 Fluid Mechanical model (FM)

simulations conducted at 100-Hz increments with no flow 

and 140-dB source excitation level. (a) Resistance. 

(b) Reactance.

Figure 6.32.—Comparison of average impedance values from 

Two-Parameter model (TP), Crandall Full-Solution model 

(CF), and Composite Empirical model (CE) simulations 

conducted at 100-Hz increments with no flow and 140-dB 

source excitation level. (a) Resistance. (b) Reactance.
NASA/TP—2012-215653 194

Figure 6.33.—Comparison of average impedance values from 

Two-Parameter model (TP), Crandall Full-Solution model 

(CF), and Composite Empirical model (CE) simulations 

conducted at 100-Hz increments with Mach number

M = 0.3 and 140-dB source excitation level. (a) Resistance. 

(b) Reactance.

Figure 6.34.—Comparison of average impedance values from 

Two-Parameter model (TP), Crandall Full-Solution model 

(CF), and Composite Empirical model (CE) simulations 

conducted at 100-Hz increments with Mach number

M = 0.475 and 140-dB source excitation level.

(a) Resistance. (b) Reactance.
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NASA/TP—2012-215653 195 Chapter 6

6.6.4.3 Results for MC/L = 0.0

At least for no flow, the presence of a peak resistance centered on the zero reactance crossing is a general feature of all 

the prediction models employed in this study, as is the monotonic decrease of resistance to either side of the peak resistance 

to the extremities of the test frequency range. This behavior 

serves as a context for further commentary on the measured

impedance spectra. It arises from the absorption physics of a 

single-degree-of-freedom (SDOF) liner, because the facesheet 

experiences higher acoustically driven particle velocities in the 

vicinity of zero reactance. Thus, when exposed to a single, 

dominant tone, the peak resistance for an SDOF liner is a direct 

manifestation of the facesheet nonlinearity. As such, this is one 

reason to employ a test protocol utilizing a single tone at a time 

for prediction model validation.

When mean flow is present, the resistance peaks become 

greatly subdued because of a broadband increase in resistance. 

This results in a nearly uniform resistance spectrum that is still 

characterized by a broad peak resistance. With the addition of 

grazing-flow, boundary layer turbulence generates a random 

fluctuating fluid velocity through the facesheet that combines 

with the acoustically driven fluctuating velocity. These 

fluctuating velocities are assumed to combine on an energy 

basis, in a root-sum-squared sense, to create a broadband 

increase in resistance across the entire frequency spectrum. 

The empirical quantification of the grazing-flow “forcing 

potential” is a likely source of systematic error, as is the rootsum-squared assumption. Because of the assumed physics of 

the grazing-flow contribution, the liner resistance must still 

exhibit a single peak at the excitation frequency with a 

monotonic decrease on either side, however slight. In the limit 

of low acoustic rms velocity relative to that attributable to 

flow, the resistance becomes essentially uniform. Any 

departure of the means from this general behavior, in either 

the predicted or measured values, suggests the presence of 

systematic error in one or both. The reader will recall the 

discussion in Section 6.3.3, “Test Sample Size and Scale 

Implications,” in which a few potential sources of systematic 

error related to sample size effects are provided.

It is not known a priori how systematic errors, attributable 

to differences between prediction and measurement means, are 

to be parsed. Such parsing must be based on scrutinizing the 

physical basis for the model and measurement methodologies. 

Previous observations have indicated that, even in the absence 

of facesheet nonlinearity, the measured resistance of a singlelayer liner exhibits a spike at its antiresonance frequencies,

including a pseudo-antiresonance at 0 Hz. The width of this 

antiresonance can vary depending upon several factors,

not yet well understood, and can influence the resistance well 

away from the antiresonance (Ref. 6). None of the models 

discussed here account for this effect, which the authors 

believe is responsible for a portion of the systematic error 

observed between predicted and measured resistances at the 

frequency range extremities.

To the graphical resolution provided in the enclosed figures, the peak resistance and the zero crossing of the reactance 

occur at essentially the same frequency for each of the 

impedance prediction models. However, the measured 

resistance peaks generally occur at frequencies approximately 

50 to 100 Hz below their corresponding reactance zero 

crossings. The measured resistance peaks also tend to occur at 

lower frequencies than the corresponding predicted resistance 

peaks. An exception to this is shown in Figure 6.13 for a

140-dB excitation level in the NIT, where the measured and 

predicted (TP model) resistance peaks are nearly equal, but the 

measured zero reactance crossing is nearly 200 Hz greater 

than the predicted zero crossing. Other features of this figure 

are also noteworthy: First, the systematic error, shared 

between measurements and the TP model prediction, is 

roughly uniform across the entire frequency spectrum and 

never exceeds about 0.1. Second, the measurement resistance 

CIs cluster tightly on the means (pastel yellow region centered 

on red curve). However, the prediction CIs are relatively large 

and subsume the measurement CIs up to about 2500 Hz. 

Correspondingly, the shared reactance systematic error (i.e., 

the difference between the predicted and measured reactance 

mean values) increases with frequency and never exceeds 

about 0.4. The prediction reactance CIs also increase with 

frequency and generally subsume the measurement CIs, which 

collapse on their respective means.

The relative behavior of CIs and systematic errors in

Figure 6.13 illustrates the potential of uncertainty analysis in 

the context of SPC. If the prediction CI limits are construed as 

specification limits (a default in the absence of actual customer specification limits), then the measurement process 

(yielding a combined systematic and random error, taken as a 

proxy for the voice of the process) is said to be in compliance 

with the specification limits when the specification limits 

(prediction CIs) subsume the voice of the process (measurement CIs). Focusing on resistance, this is the case in

Figure 6.13 (excluding the lowest and highest frequencies 

where an out-of-compliance is evident). Clearly, both 

systematic error and prediction uncertainty are issues that need 

to be addressed in this proxy for SPC application to a liner 

fabrication process. The reader will recall that an out-ofcompliance condition can be driven by an arbitrary combination of random and/or systematic error, as is the case in

Figure 6.12, where a relatively large systematic error and 

relatively small random error drive the out-of-compliance 

condition at the low and high ends of the frequency range.

Attention was drawn above to the observation that the 

prediction CIs for resistance in Figure 6.13 were sufficiently 

large to subsume (for most of the frequency range) the 

combined systematic and random error associated with the 

measured resistance (the same is also true for reactance). It is 

of interest to note the large increase in the resistance CIs for 

the TP model prediction as the excitation level is increased 

from 120 to 140 dB (compare Figure 6.12 and Figure 6.13). It 

is also of interest to note that the peaks in lower and upper CI
NASA/TP—2012-215653 196

limits differ by about 300 Hz. This observation is consistent 

with the zero-crossing of the CI limits associated with the 

reactance. The corresponding no-flow results for the other 

three models do not show this trend. Instead, the lower and 

upper bounds of the prediction resistance CIs are well aligned 

for each of the other models (see Figure 6.18 and Figure 6.19

for the CF model, Figure 6.24 and Figure 6.25 for the CE 

model, and Figure 6.30 and Figure 6.31 for the FM model). 

This misalignment of the prediction CI limits is an artifact of 

the TP model that is not yet fully understood.

It is also interesting to note that, whereas the peak in the 

prediction mean resistance for each model occurs at the 

frequency corresponding to the zero-crossing of the prediction 

mean reactance, the same is not true of the measured results. 

In fact, the peak in the measurement mean resistance often 

occurs at a frequency well below the zero-crossing of the 

measurement mean reactance, for many of the comparisons 

between predicted and measured results. The resulting 

misalignment between the predicted and measured resistance 

peaks exaggerates the differences between their corresponding 

CIs. In fact, if this misalignment of predicted and measured 

resistance peaks was removed (slide the measurement 

spectrum to the right in Figure 6.19), the prediction CIs would 

nearly subsume the measurement CIs.

Notwithstanding the systematic error evidenced by the 

differences between the prediction and measurement resistance mean values of Figure 6.19, the comparability of their 

trends and the ranges of their CIs illustrate a near-ideal 

distribution of systematic and random error suitable for 

applying the specification limit concept of the SPC paradigm 

as discussed earlier. The prediction reactance CIs for the CF 

model essentially collapse onto their respective reactance 

mean values for each of the conditions evaluated (all three 

Mach numbers and both excitation levels). This is also 

observed for the results with the CE model, with inputs based 

on measurements in the NIT (Figure 6.24 and Figure 6.25). In 

this case, the maximum resistance CI (maximum difference 

between the upper and lower bounds) increases from about 0.1 

to 0.3 as the source excitation level is increased from 120 to 

140 dB. For the FM model (see Figure 6.30 and Figure 6.31), 

the maximum resistance CI hovers at around 0.04 for both 

excitation levels.

6.6.4.4 Results for MC/L >0.0

As previously noted, impedance means and CIs were measured and predicted for one excitation level (140 dB) and two 

flow Mach numbers (0.3 and 0.475). Both the TP model 

(Figure 6.16 and Figure 6.17) and the CF model (Figure 6.22

and Figure 6.23) predict measurement resistance means very 

well in the midfrequency range at the lower Mach number of 

0.3, but suffer some separation from the measured results at 

the higher Mach number of 0.475. As was observed for the noflow condition, the measurement mean resistances are 

generally higher than the prediction mean resistances at the 

frequency range extremes.

In all cases, the spans of the prediction CIs are relatively 

small, and yet they generally subsume the measurement CIs in 

the midfrequency range. However, there is clearly a divergence of measurement and prediction reactance means at the 

lowest frequencies for the lower Mach number of 0.3. This 

divergence grows for the higher Mach number of 0.475, for 

which a divergence also occurs at the highest frequencies. 

Again, the prediction reactance CIs vary substantially from 

model to model.

The above comparisons of prediction and measurement 

impedance means and CIs provide the framework for systematically identifying sources of systematic errors in both 

prediction models and measurements. The choice of a POHC 

assessment liner with conventional perforate geometry has 

demonstrated strengths and weaknesses of both the Langley 

measurement methodologies and the various predictive 

models considered. Clearly, it would appear there are 

systematic errors in both the measurement methodologies and 

the prediction models that warrant further study.

6.6.4.5 Effects of Impedance Measurement (Eduction)

Methodology

Comparisons of the results provided above with those in 

Chapter 7, “Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts,” 

provide additional insight. It is interesting to note that the 

measurement impedance CI at a test condition tends to be 

inversely proportional to the prediction SPL attenuation CI. At 

first glance, this result appears counterintuitive and somewhat 

negative. Upon further review, it is noted that (at least for the 

test conditions evaluated in the current investigation) the 

prediction SPL attenuation CI tends to grow as the mean value 

increases (see Figure 7.8 in Chapter 7). In other words, at test 

conditions where a liner provides minimal attenuation (i.e., 

frequencies away from resonance), the prediction SPL 

attenuation CI is small, and the measurement impedance CI is 

large. Conversely, at test conditions where the prediction SPL 

CI is large, the measurement impedance CI is small. It should 

also be noted that these differences between the prediction 

SPL CI and the measurement impedance CI are accentuated 

by the choice of a single-layer configuration, since the 

attenuation is significantly larger at resonance for this liner 

geometry.

If the attenuation provided by an acoustic liner is low in a 

duct with a specified geometry, the impedance measurement 

process becomes less robust because large impedance changes 

produce small changes in attenuation. If this measured 

impedance were intended to be used only in ducts of the same 

geometry, this would be acceptable. However, the goal is to 

determine the impedance at each frequency of interest as 

accurately as possible. In order to improve the quality of the 

NASA Langley measurement process, it appears important 

that efforts be made to achieve sufficient attenuation at

each test condition to minimize the size of the measurement 

impedance CI. Based on the results of the current
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NASA/TP—2012-215653 197 Chapter 6

investigation, one approach that is currently being considered 

is to design test liners such that the resonance occurs near the 

frequency of interest. For those cases where the frequency 

range of interest is broad, this will require multiple liners to be 

tested. Each liner would be constructed with the same 

perforate facesheet material, but would have a cavity depth 

selected to “cover” a different portion of the frequency range. 

By combining the results from multiple liner tests, it is 

expected that the measurement impedance CI can be reduced 

to an acceptable range over the entire frequency range of 

interest.

6.6.4.6 Model-to-Model Comparisons

Model-to-model comparisons are shown in Figure 6.32 to 

Figure 6.34 for 140 dB excitation and grazing-flow Mach 

numbers of 0, 0.3, and 0.475. At zero flow, all of the models 

are in reasonably good agreement below the reactance zerocrossing frequency for the TP model. Above the zero-crossing 

frequency for the TP model, the agreement is not as good. The 

CE model forms an upper bound and the TP model forms a 

lower bound on the resistance spectra graphic of Figure 6.32. 

The spread in resistance above the reactance zero crossing 

averages about 0.2. Predicted reactance spectra are in excellent agreement for the CF and CE models. The TP model is 

the reactance spectrum outlier, with a positive divergence

of about 0.4 from the CF and CE models at the highest 

frequency. This divergence gives rise to a delta in zerocrossing frequency between the TP and the (CF, CE) pair of 

nearly 200 Hz.

At a Mach number of 0.3, the predicted resistance spectra 

of the TP and CF models essentially coalesce. The CE model 

resistance is the outlier below the other two models, with a 

resistance delta of about 0.3 at the broad peak to about 0.32 at 

the lowest frequency. The small reactance spread on the three 

models is sufficient to generate a delta in the reactance zero 

crossing of about 80 Hz.

At a Mach number of 0.475, the trends for the 0.3 Mach 

number measurements are continued with the CE model now 

underpredicting resistance (relative to the TP and CF results) 

uniformly by about 0.7. Again, the reactance predictions 

virtually coalesce, to give a zero crossing delta of about 30 Hz 

(see Figure 6.34).

When compared with the near coalescence of the TP and 

CF predictions at flow Mach numbers of 0.3 and 0.475, the 

uniform discrepancies in predicted resistance spectra for the 

CE model of 0.3 and 0.7 are at first glance somewhat surprising. However, it should be recalled that the TP and CF models 

share several similarities, the most relevant being an identical 

model for the contribution of grazing flow to the resistance, 

the Rice-Heidelberg model. Thus, any difference between the 

TP and CF models is due to their respective no-flow model 

component contribution. Except for minor differences in 

empirical tweaking factors, the main difference in the TP and 

CF models is the way the viscous resistance is modeled. In the

TP model, the viscous resistance comes from a HagenPoiseuille type model for pipe flow. In the CF model, a 

frequency-dependent viscous resistance is derived from a full 

Navier-Stokes solution for oscillatory flow in a pipe. Differences in these two contributions would be expected to arise 

only for high frequencies and/or for large perforate thickness 

relative to hole diameter. That is assuredly not the case for the 

selected assessment liner, which has a t/d ratio close to unity. 

Thus, to understand the differences between the CE model and 

the other two models in the presence of mean flow, the 

physics underlying the Rice-Heidelberg resistance model and 

the empirical model for the boundary layer, turbulence-driven 

rms velocity through the perforate must be further analyzed.

In summary, the trends of the prediction and measurement 

resistance means are generally in agreement, while the details 

of how well the predicted values track the measurements differ 

from model to model. The bias error (with respect to measurements) for some models tends to be uniform, but is 

frequency-region selective for others. This frequency-region 

selective bias is generally excitation-level dependent. The 

prediction resistance CI spectra differ dramatically from 

model to model, but the corresponding reactance CI spectra 

are generally very tight. The sole exception to this is the TP 

model, which predicts CI growth with increasing frequency. 

The CIs grow with increasing excitation level for some of the 

models, but remain relatively constant for others. Those 

models for which the CIs grow with excitation level (especially through the resonance region) make explicit use of a 

discharge coefficient that, as mentioned previously, was 

characterized by a rather large standard deviation in the 

current investigation. A detailed input parameter sensitivity 

study was conducted with the TP model, which demonstrated 

a significant portion of the observed growth of prediction CIs 

is attributable to discharge coefficient uncertainty (Ref. 50). 

6.7 Concluding Remarks and 

Recommendations

This chapter has provided the results of uncertainty analyses conducted by NASA Langley, cast in the statistical metrics 

of means and confidence intervals. This was done in anticipation of the usage of statistical process control (SPC) to predict 

out-of-compliance conditions for a target impedance spectrum 

during liner fabrication. These analyses have been conducted 

with four impedance prediction models, and the results have 

been compared with impedances measured in the NASA 

Langley normal incidence tube and grazing incidence tube. A 

number of findings have been highlighted by the current 

investigation. Some of the more salient ones include

1. A key focus of this document has been to propose an 

adaptation of the SPC paradigm to the production of an 

impedance target spectrum to within specifications defined by 

the customer. It offers a tool whereby the liner designer
NASA/TP—2012-215653 198

negotiates a target design uncertainty with the customer. In 

SPC theory, the voice of the process is a sequence of component parameter measurements (e.g., flow resistance and hole 

geometry) prior to liner fabrication. A successful adaptation of 

the SPC paradigm to complying with the voice of the customer relies critically upon known accuracy and precision of the 

relevant impedance prediction models. This investigation is a 

first step toward this goal: systematic errors and uncertainties 

for four prediction models and two measurement processes 

have been compared. This exercise has demonstrated that 

much work remains to be done on both the predictive models 

and the measurement process in a grazing-flow environment.

2. Consistent trends are observed for the four impedance 

prediction models (Two-Parameter, Crandall Full-Solution, 

Composite Empirical, and Fluid Mechanical) in the absence of 

flow, and for the first three models in the presence of mean flow:

a. The resistance increases with increasing mean flow.

b. The reactance becomes flatter with increasing mean 

flow.

c. The Two-Parameter and Crandall Full-Solution models produce very similar resistances, below the Composite Empirical resistances in the absence of mean flow 

and above the Composite Empirical resistances in the 

presence of mean flow (difference increases with 

increasing mean flow).

3. Confidence intervals for measured impedances tend to 

increase with increasing mean flow, and tend to be much 

larger for resistance than for reactance.

4. Differences between predicted and measured impedances generally increase with increases in mean-flow velocity.

5. Impedance prediction and sound pressure level (SPL) 

attenuation confidence intervals are inversely related. As the 

attenuation is reduced (at frequencies away from resonance), 

the impedance measurement process becomes less robust 

(since large impedance changes only produce small changes in 

attenuation). Correspondingly, these impedances become less 

critical (when applied in the current duct) at these frequencies 

of less attenuation. Differences between predicted and 

measured SPL attenuations are accentuated by the choice of a 

single-layer configuration, since the attenuation is significantly larger at resonance for this liner geometry.

This investigation has provided valuable insight with regards to impedance measurement and prediction methodologies and their shortcomings. The following items are 

recommended for further research, and will form the basis of 

continued liner physics research at NASA Langley:

1. Incorporate three-dimensional aeroacoustic effects into 

the impedance measurement (eduction) model, including

a. Nonuniform mean flow

b. Boundary-layer growth

c. Duct geometry

d. Higher-order modes (at the source plane, upstream of 

the liner)

Plans are underway to implement two test ducts (50.8- by 

63.5-mm (2- by 2.5-in.) and 152.4- by 381.0-mm (6- by 15-

in.) cross sections) designed to evaluate each of these effects, 

both individually and jointly. It is expected that measurements 

in these ducts will provide data of increased fidelity that can in 

turn be used to improve current impedance prediction models.

2. Conduct tests with additional validation liners to exercise a wider range of impedance variability. These liners 

should be linear (independent of mean-flow velocity and 

source excitation level) and predictable from first principles. 

Liner segmentation should also be exploited to achieve 

impedance variability along the liner length, such that the 

ability of the impedance measurement methodology to account 

for axial impedance spectra changes that occur with conventional, nonlinear liners can be thoroughly evaluated.

3. Conduct tests with multiple samples of the same geometry, such that the effects of manufacturing repeatability can 

be properly assessed (i.e., application of SPC).

4. Conduct detailed sensitivity studies with each impedance prediction model, and with the impedance measurement 

methodology, to determine which parameters are of greatest 

importance to the final results. In the SPC paradigm, results 

from these studies would provide a measure of the voice of the 

process. They should also be used to guide future tests in the 

two test rigs mentioned above.

5. Extend the measurement range to higher mean-flow 

velocity, source excitation level, and frequency to more 

closely simulate the realistic aircraft engine nacelle environment. One of the new test ducts mentioned above is a grazingflow impedance tube and is expected to support each of these 

goals. This test duct is expected to support up to Mach 0.6 

flow, with source levels up to at least 150 dB for frequencies 

up to 3000 Hz. It will also support analysis at frequencies up 

to 6000 Hz, although initially at perhaps limited source SPLs.

6. Extend the evaluation to incorporate a broadband noise 

source into the impedance eduction method. Modern aircraft

engines produce a combination of tones and broadband noise. 

As the tonal content has gradually been reduced, the importance of the broadband noise has increased. As such, there 

is a need to include both in future liner evaluations.

7. Extend the evaluation to include other liner types. These are expected to include multilayer perforate-overhoneycomb liners and extended-reaction liners, each of which 

provides increased broadband attenuation. Multilayer 

perforate-over-honeycomb liners are commonly used in 

current engine nacelles, and multiple extended-reaction liner 

concepts are currently being investigated.

8. Conduct studies to identify the sources of discrepancy 

between the various methods for including grazing-flow

effects in the acoustic resistance prediction. This should 

include investigation of the effects of boundary layer profile 

on the measured impedance.
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6.8 Acknowledgments

The authors extend sincere gratitude to Carol Harrison for 

the care in which she conducted extensive tests to generate the 

measurement database used in this investigation. They also 

wish to express appreciation to Willie Watson for his assistance with the impedance eduction methodology, to Carl 

Gerhold and Martha Brown for their assistance with the 

impedance prediction models, and to Brian Howerton for his 

assistance with the measurement process.

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NASA/TP—2012-215653 201 Chapter 6

Appendix A.—Nomenclature

A.1 Acronyms

ADP Advanced Ducted Propulsor

CE Composite Empirical model

CF Crandall Full-Solution model

CHE convected Helmholtz equation

CI confidence interval

DC direct current

FM Fluid Mechanical model

GIT grazing incidence tube

ISM in situ method

LEE linearized Euler equations

MMM multimicrophone method

NIT normal incidence tube

POHC perforate-over-honeycomb core

rms root-mean-squared

SDOF single degree of freedom

SPC statistical process control

SPL sound pressure level

TMM two-microphone method

TTM T-tube method

TP Two-Parameter model

A.2 Symbols

A constant from Equation (6.3)

a Hagen-Poiseuille laminar flow friction factor, 

empirical constant from Equation (6.5)

B constant from Equation (6.3)

B model coefficient defined in Equation (6.30b)

CD perforate hole discharge coefficient

c ambient speed of sound

D single hole orifice inertial length parameter 

defined by Equation (6.39)

d liner facesheet hole diameter

F function defined by Equation (6.23)

f frequency

f0 frequency parameter defined by Equation (6.41a)

H duct height

H orifice nonlinear inertial length defined by 

Equation (6.38)

h honeycomb cell depth

i −1

J0 zeroth-order Bessel function of the first kind

J1 first-order Bessel function of the first kind

K viscous loss parameter from Fluid Mechanical 

model (FM)

k acoustic wavenumber

κ end effect empirical constant

L duct length

M Mach number

M nondimensional curve fit parameter for H

defined by Equation (6.40a)

Mean(*) mean of parameter *

m,n CD-related nondimensional curve fit components

N number of samples

N number of holes in perforated sheet

P steady pressure

p acoustic pressure

R resistance

r liner facesheet hole radius

S nonlinear slope parameter

s orifice separation distance

SPL sound pressure level in decibels

StDev(*) standard deviation of parameter *

T wavelength period

Ts static temperature

t liner facesheet thickness

V steady fluid velocity

V nondimensional acoustic velocity parameter 

defined by Equation (6.40c)

v acoustic velocity

Var(*) variance of parameter *

x distance or direction of interest

z model coefficient defined in Equation (6.33)

α steady pressure loss coefficient due to viscosity

in Equation (6.4)

β steady pressure loss coefficient due to fluid 

inertia in Equation (6.4)

δ1 boundary layer displacement thickness

δ2 boundary layer momentum thickness

ε coefficient for hole length end correction factor

ζ normalized complex acoustic impedance

η H-related nondimensional curve fit components 

with subscripts 0 and 1

θ normalized acoustic resistance
NASA/TP—2012-215653 202

ρ ambient fluid density

σ perforate open area ratio (porosity)

τ time

μ ambient dynamic viscosity

χ normalized acoustic reactance

ω radial frequency

Subscripts:

AC frequency dependent

ac acoustic

ave cross-sectional area averaged

c column

cav cavity

C/L centerline

DC frequency independent

e exit end effects

eff effective

f steady flow

fs facesheet

gf grazing flow

I inertial contribution

Im imaginary part

i entrance end effects

inc incident

L linear

lin linear

m mass

me mass end effects

NL nonlinear

non nondimensional

nonlin nonlinear

pk peak

R resistance

res at resonant conditions

ref reference

r row

Re real part

rms root-mean-squared

s static

ss steady state

μ viscous Stokes wave

ω unsteady, or frequency dependent

0 frequency independent
Uncertainty in Acoustic Liner Impedance Measurement and Prediction

NASA/TP—2012-215653 203 Chapter 6

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in Square Ducts. J. Acoust. Soc. Am., vol. 120, no. 6, 2006.

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Measurement in Flow Ducts. J. Sound Vib., vol. 34, no. 1, 

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Studies for Predicting Noise Attenuation in Acoustically Treated Ducts for Turbofan Engines. NASA CR–1373, 1969.

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Frequency Analysis System. Annual Book of ASTM Standards 

2000, ASTM E1050–08, vol. 04.06, 2000, pp. 962–972.

27. Jones, Michael G.; and Parrott, Tony L.: Evaluation of a MultiPoint Method for Determining Acoustic Impedance. Mech. 

Syst. Sig. Process., vol. 3, no. 1, 1989, pp. 15–35.

28. Jones, Michael G.; and Stiede, Patricia E.: Comparison of 

Methods for Determining Specific Acoustic Impedance. J. 

Acoust. Soc. Am., vol. 101, no. 5, 1997, pp. 2694–2704. 

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Optimization Method for Educing Variable-Impedance Liner 

Properties. AIAA J., vol. 36, no. 1, 1998, pp. 18–23.

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2001–2266, 2001.

31. Watson, Willie R., et al.: Validation of a Numerical Method for 

Extracting Liner Impedance. AIAA J., vol. 34, no. 3, 1996, pp. 

548–554.

32. Watson, Willie R., et al.: A Finite Element Propagation Model 

for Extracting Normal Incidence Impedance in Nonprogressive 

Acoustic Wave Fields. J. Comput. Acoust., vol. 125, no. 1, 

1996, pp. 177–186.

33. Tijdeman, H.: On the Propagation of Sound Waves in Cylindrical Tubes. J. Sound Vib., vol. 39, no. l, 1975, pp. 1–33.

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Englewood Cliffs, NJ, 1967.

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Metals. J. Appl. Phys., vol. 18, 1951, pp. 39–45.

36. Melling, T.H.: The Acoustic Impendance of Perforates at Medium and High Sound Pressure Levels. J. Sound Vib., vol. 29, 

no. 1, 1973, pp. 1–65.

37. Kraft, R.E.; Yu, J.; and Kwan, H.W.: Acoustic Treatment 

Design Scaling Methods. NASA/CR—1999-209120/VOL2, 

1999.

38. Liu, Fei, et al.: A Multiple Degree of Freedom Electromechanical Helmholtz Resonator. J. Acoust. Soc. Am., vol. 122, no. 1, 

2007, pp. 291–301.

39. Syed, Asif A., et al.: The Steady Flow Resistance of Perforated 

Sheet Materials in High Speed Grazing Flows. NASA/CR—

2002-211749, 2002.

40. Guess, A.W.: Calculation of Perforated Plate Liner Parameters 

From Specified Acoustic Resistance and Reactance. J. Sound 

Vib., vol. 40, no. 1, 1975, pp. 119–137.

41. Hubbard, Harvey H., ed.: Aeroacoustics of Flight Vehicles: 

Theory and Practice. Volume 2: Noise Control. NASA RP–

1258–VOL–2, 1991.

42. Ingard, U.: On the Theory and Design of Acoustic Resonators. 

J. Acoust. Soc. Am., vol. 25, 1953, pp. 1037–1061.
NASA/TP—2012-215653 204

43. Yu, Jia; Ruiz, Marta; and Kwan, Hwa-Wan: Validation of 

Goodrich Perforate Liner Impedance Model Using NASA 

Langley Test Data. AIAA–2008–2930, 2008.

44. Premo, John: The Boeing Company, Seattle, WA, personal 

communication, 2007.

45. Hersh, A.S.; Walker, B.E.; and Celano, J.W.: Helmholtz Resonator Impedance Model, Part 1: Nonlinear Behavior. AIAA J., 

vol. 41, no. 5, 2003, pp. 795–808.

46. Hersh, A.S.; and Walker, B.: Effect of Grazing Flow on the 

Acoustic Impedance of Helmholtz Resonators Consisting of 

Single and Clustered Orifices; Final Report. NASA CR–3177, 

1979.

47. Baumeister, K.J.: Orifice Resistance for Ejection Into a Grazing 

Flow. Advances in Engineering Sciences, NASA CP–2001, 

vol. 3, 1976, pp. 895–905.

48. Jones, Michael; Parrott, Tony; and Watson, Willie: Comparison 

of Acoustic Impedance Eduction Techniques for LocallyReacting Liners. AIAA–2003–3306, 2003.

49. Jones, Michael; Watson, Willie; and Parrott, Tony: Benchmark 

Data for Evaluation of Aeroacoustic Propagation Codes With 

Grazing Flow. AIAA–2005–2853, 2005.

50. Jones, Michael; Parrott, Tony; and Watson, Willie: Uncertainty 

and Sensitivity Analyses of a Two-Parameter Impedance Prediction Model. AIAA–2008–2928, 2008.
NASA/TP—2012-215653 205

Chapter 7—Assessment of Acoustic Propagation and

Radiation Codes for Locally Reacting Liners in Flow Ducts

Willie R. Watson and Douglas M. Nark7

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

Summary

A suite of duct acoustic propagation and radiation codes is assembled, consisting of the four most commonly used NASA

Langley Research Center codes, a code from academia, and three codes recently developed at Boeing. These codes support 

propagation through acoustically treated inlet and aft-fan ducts with locally reacting liners in the presence of irrotational or 

rotational mean flow, as well as radiation to the far field. Collectively, they are a representative cross section of the state of the art 

in the liner industry. This chapter reviews the basic assumptions, governing differential equations, acoustic boundary conditions, 

and numerical methods underlying the development of each code. An assessment of each code is then provided using the accuracy 

of the predicted attenuation, computational efficiency, and effects of input uncertainties as the primary metrics. Each assessment is 

performed on the same problem, same computer, and grid. Code results are compared with each other and to analytical and 

measured data.

Several primary conclusions are drawn from the assessment. First, wall clock time increases of an order of magnitude or more 

are observed for three-dimensional codes relative to the corresponding two-dimensional versions of the same codes. Second, of all 

codes in the suite the one based on the parabolic approximation is the most efficient but is of low fidelity. Third, predicted results 

from codes are in excellent agreement with exact analytical results for hard-wall ducts. Fourth, when liners are included, most 

codes compare well with each other and to analytical results except at a frequency where the attenuation is quite large. However, it 

is observed that results from one code in the suite tend to diverge from that of others at the higher Mach number. Fifth, attenuations predicted for a conventional perforate-over-honeycomb liner installed in the Langley “grazing incidence tube” compare well 

with measured attenuations for a plane wave source. As expected, the uncertainty (attenuation 95% confidence interval) is 

proportional to the amount of attenuation (i.e., small changes in the code inputs at a frequency where significant attenuation occurs 

result in sizable changes in attenuation). Finally, code results compare well to measurements in the Langley Research Center

Curved Duct Test Rig for lower-order mode sources, but errors in the comparisons occur when higher-order modes are present.

The following items are recommended for further research, and are expected to form the basis for continuing code development 

at NASA: First, more efficient three-dimensional solvers should be incorporated into the three-dimensional propagation codes, 

such that these codes can be used to efficiently perform parameter studies and to model engine nacelles closer to full scale. A 

reduction in wall clock time by at least 2 to 3 orders of magnitude is desired. Second, many of the codes included in the current 

investigation were not initially designed to take advantage of current and future computer architectures. Where possible, these 

codes should be upgraded to take advantage of these architectures. Third, the effects of the mean boundary layer should be 

incorporated into the three-dimensional propagation codes to improve their fidelity. Finally, a parallel effort should be conducted 

to develop propagation codes for the evaluation of extended-reaction liners. It is expected that these propagation codes would be 

based on approaches described herein for locally reacting liners.

7.1 Introduction

High levels of engine noise radiated from modern turbofan 

engine nacelles, especially at approach and cutback conditions, threaten to curtail much needed growth in commercial 

air transportation systems both in the United States and 

abroad. Engine fan noise is acoustic energy generated at the 

fan or exit guide vanes of a turbofan engine. It radiates 

forward via the nacelle inlet duct and rearward by propagating 

through the aft nacelle duct and ambient shear layer, ultimately reaching observers on the ground. Fan noise from earlier 

versions of the turbofan engine was dominated by tones 

associated with the blade passage frequency and its harmonics; however, broadband noise has become an increasingly 

important component of fan noise from recent engines 

incorporating increased fan bypass ratios and modified fan 

designs.

One of the most effective means for reducing levels of 

engine noise from commercial aircraft engines is the installation of acoustic treatment into the walls of the inlet and aft fan 

ducts. Such treatments significantly reduce radiated noise by 

attenuating both the inlet and aft duct noise as it propagates 

through the engine nacelle. Suitable aircraft noise prediction 

codes are required to optimally design the acoustic treatment 

for maximum attenuation within specified nacelle geometry. 

Some codes predict the attenuation achieved by the acoustic 

treatment within the nacelle, while others predict the amount 

of noise radiated to observers on the ground.

Noise prediction codes for aircraft nacelles are divided into 

potential and rotational flow codes. Each code has advantages 
NASA/TP—2012-215653 206

and disadvantages depending upon the problem being 

modeled, assumptions that are made, and computer facilities 

available to code users. At the current time, information 

available to users of these codes is often fragmented and 

incomplete. The purpose of this chapter is to assemble a 

number of noise propagation and radiation codes together 

under a single umbrella, to describe their basic assumptions, 

and to give an assessment of each code using predefined 

metrics. The codes detailed in this chapter represent a broad 

spectrum of approaches and are validated against a number of 

test configurations. The three primary metrics chosen for this 

assessment are (1) accuracy of the predicted attenuation, 

(2) computational efficiency, and (3) effects of input uncertainties on the predicted attenuations. Readers are assumed to 

have some background in vector calculus, fluid dynamics, 

aeroacoustics, numerical methods, computer science, and 

statistics. Although many duct propagation codes exist in the 

literature that are based on modal analysis, such codes are 

generally not applicable to the variable cross-sectional area 

distribution encountered in aircraft engine nacelles. Therefore, 

only the nonmodal duct propagation codes that can accommodate variable cross-sectional area distributions are considered 

in this chapter.

This chapter begins by presenting the basic assumptions, 

the governing differential equations, and duct boundary 

conditions for each of the two classes of flows. A description 

of the numerical method used to solve these equations is then 

presented for each code. Because considerable economy is 

often achieved by writing the equations in a vector format, a 

standard vector format is used throughout this chapter. Each of 

the three primary assessment metrics is evaluated (for each 

code) on the same problem, using identical grids, and on the 

same computer. Whenever appropriate, results are compared 

to measured data. The chapter closes with recommendations 

on necessary code improvements and suggestions for new 

models or approaches. A list of the symbols used in this 

chapter is given in Appendix A.

7.2 Statement of Problem

Figure 7.1 shows a sketch of a typical three-dimensional, 

finite length, nacelle duct geometry. The duct carries a 

nonuniform, subsonic mean flow that flows from left to right. 

A Cartesian coordinate system (x,y,z) is used, in which the 

axial coordinate is z and the two transverse coordinates are x

and y. The source plane is defined to be at the fan face and as 

seen in Figure 7.2, is denoted by an imaginary plane Γs. Codes 

discussed in this chapter consider two types of acoustic 

propagation. For inlet propagation, the sound propagates 

upstream of the fan against the flow and exits the duct as 

shown in Figure 7.2(a). In this case, the duct termination is 

located at the entrance to the inlet and is denoted by the plane 

Γt. The second type of propagation is aft-duct propagation, in 

which the sound propagates downstream of the fan face and 

exits the duct via the aft-fan duct as shown in Figure 7.2(b). 

For aft propagation, the termination plane Γt is located

Figure 7.1.—Turbofan engine nacelle with acoustic liner.

Figure 7.2.—Two types of acoustic propagation in flow 

ducts addressed in this chapter, showing source plane 

boundary Γs and termination plane boundary Γt.

(a) Inlet propagation. (b) Aft-duct propagation.

downstream of the fan face in the exhaust duct. In both inlet 

and aft-duct propagation the computational volume is denoted 

by Ω, and the perimeter of the duct containing the physical 

duct walls will be denoted by Γw. Let the surface bounding Ω

(for inlet or aft-duct propagation) be denoted by Γ, such that 

the union of Γs, Γt, and Γw is Γ: 

Γ = Γs ∪ Γt ∪ Γw (7.1)

Further, the perimeter of the duct is lined with acoustic 

material that is assumed to be locally reacting (i.e., acoustic 

waves propagate through it normal to the surface). The 

normalized acoustic impedance of the wall lining will be 

denoted by ζ. The wall impedance contains real and imaginary 

components (i.e., ζ = R[ζ] + iI[ζ]) and is generally a function 

of wall location. Here R[...] and I[...] denote the real and 
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 207 Chapter 7

imaginary part of a complex quantity, respectively, and i

denotes the unit imaginary number. The real component of the 

normalized impedance R[ζ] is the normalized resistance, and 

the imaginary component I[ζ] is the normalized reactance. 

Throughout this chapter, all impedances are normalized with 

respect to the characteristic impedance of the air flowing in 

the duct. The problem to be addressed is to describe the basic 

assumptions and give an assessment of available nonmodal 

duct propagation codes that predict the noise attenuated by the 

acoustic treatment in the inlet (see Figure 7.2(a)) or the aft 

duct (see Figure 7.2(b)). In addition, codes that predict the 

level of sound radiated to observers on the ground are also 

described.

7.3 Potential Flow Formulation

The basic assumption of potential flow is that the fluid in 

the duct is an ideal gas and the flow is reversible, adiabatic, 

and irrotational. These assumptions allow one to write a 

single, scalar wave equation that governs the sound field in the 

duct. The nonmodal potential flow codes discussed in this 

chapter compute a solution to this wave equation that satisfies 

the appropriate acoustic boundary conditions at the source 

plane, duct wall, and duct termination. The derivation of this 

wave equation and the relevant acoustic boundary conditions 

are presented in this section.

7.3.1 Governing Differential Equations

The starting point for the potential flow formulation is the 

equations that govern conservation of mass and momentum in 

the flow duct based on an assumption of adiabatic reversible 

flow (Ref. 1):

(ˆ )ˆ ˆ ˆ 0 ˆ + • ρ + ρ • = ∂

∂ρ u ∇ ∇ u

t

(7.2)

(ˆ )ˆ ˆ 0 ˆ ˆ + = 



 



 + • ∂

∂

ρ p

t

u ∇ u ∇ u

(7.3)

where, ρ, u, and p are the fluid density, fluid velocity vector, 

and fluid pressure, respectively. Further, the superscript ^ 

denotes a total quantity, the boldface characters denote a vector 

quantity, t denotes dimensional time, and • denotes the vector 

dot product. Throughout this chapter, the components of the 

fluid velocity vector u in the x-, y-, and z-directions are referred 

to as “u,” “v,” and “w,” respectively. In addition to the assumptions that the flow is reversible and adiabatic, other assumptions 

used in deriving the equations governing conservation of mass 

(Eq. (7.2)) and momentum (Eq. (7.3)) are

(1) The fluid is a continuum.

(2) There are no effective gravity forces acting on the fluid.

Instead of using the full energy equation to close the system of 

equations, the much simpler isentropic relation for an ideal gas 

is assumed: 

γ pˆ = C ρˆ (7.4)

where C is a constant and γ is the ratio of the specific heat at 

constant pressure to that at constant volume.

7.3.2 The Linearized Acoustic Equations

The effects of acoustic perturbations within the flow are 

now determined by decomposing the flow into a time 

independent mean flow and a time-dependent acoustic 

perturbation 

u u u

~ , ˆ ~ , ˆ ~ ˆρ = ρ0 + ρ p = p0 + p = 0 + (7.5)

where the mean (or steady-flow) quantities ρ0, p0 and u0 are 

solutions to the steady form of Equations (7.2) and (7.3) and 

the perturbations, p

~, ~

ρ and u

~ are considered small with 

respect to the mean quantities. Substituting Equation (7.5) into 

Equations (7.2) and (7.3) allows the equations for mass and 

momentum continuity to be rewritten in terms of the perturbation variables 

( )





 



 + ρ • ρ = −

+ • ρ + ρ • + ρ

0 0

0

0 0

D

D

1 ~ ~

D

~ D

u

u u

∇

∇ ∇

t

NL

t (7.6)

( )





 



 = − ρ +

ρ + ρ • + ρ + +

0 0 0

0 0 0 0

D

D

2 ~

D

~ ~ D

D

~ D

p

t

p NL

t t

∇

∇ ∇

u

u

u u

u

(7.7)

where the material derivative is taken following the mean flow 

+ •∇

∂

∂ = 0 D

D

u

t t

(7.8)

and the nonlinear terms are 

= ρ( • ) + ( • ) ρ ~ ~ ~ ~ NL1 ∇ u u ∇ (7.9) 

( ) ( )

(u )u (u )u

u u u u

u

~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ 2

0

0 0

∇ ∇

∇ ∇

+ρ • + ρ •

+ ρ • + ρ • ∂

∂ = ρ

t

NL (7.10)

Although Equations (7.6) and (7.7) are exact, the difficulty 

lies in the nonlinear terms. A considerable simplification can 

be realized by linearizing these equations about the steady 

flow. This is achieved by neglecting the nonlinear terms 

(NL1 = NL2 ≈ 0) and recalling that the right-hand sides of 

Equations (7.6) and (7.7) are zero since the steady flow is the 

solution to the steady form of Equations (7.2) and (7.3). Thus, 

the exact equations for mass and momentum continuity are 

now approximated using much simpler equations that contain 

no nonlinear terms:
NASA/TP—2012-215653 208

( ) 0 ~ ~ ~

D

~ D

+ ρ0 • + ρ • 0 + • ρ0 = ρ ∇ u ∇ u u ∇

t

(7.11)

( ) 0 ~

D

~ ~ D

D

~ D 0 ρ0 + ρ0 • 0 + ρ + p = t t

∇ ∇ uu u

u (7.12)

In component form, a combination of the scalar Equation 

(7.11) along with the vector Equation (7.12) constitutes four 

equations in the five unknown perturbation variables 

, ~ , ~ , ~ , ~p ρ u v and w

~ . To close the system of equations, it is 

necessary to establish a relationship between p

~ and ρ

~ . This 

is achieved by linearizing Equation (7.4) to obtain 

0

2 0

0

2

0 , ~ ~

ρ = ρ = γ p p c c (7.13)

where c0 is the speed of sound waves in the flow.

7.3.3 Derivation of Scalar Wave Equations

Potential flow follows from the assumption that the vorticity, ∇ × uˆ , equals zero

= φ ~ ~ u ∇ (7.14)

c Dt

~ ~ D

2

0

ρ0 φ ρ = − (7.15)

where φ

~ is the acoustic velocity potential. Substituting 

Equations (7.14) and (7.15) into the linearized continuity 

equation (Eq. (7.11)) and simplifying gives a single scalar 

equation on the acoustic velocity potential in a nonuniform 

flow: 

( ) 0 1 ~

D

~ 1 D

D

D

0

0 2

0

• ρ φ = ρ+































 φ − ∇ ∇

t c t

(7.16)

It is often desirable to solve for the acoustic pressure field 

in the presence of an assumed uniform mean flow. When the 

mean flow is uniform, it is convenient to express the scalar 

wave equation (Eq. (7.16)) as an equation on acoustic 

pressure. Such an approach is desirable because the acoustic 

pressure field is directly measurable in laboratory experiments 

and is therefore available for comparison with numerical 

computations. To begin, the linearized continuity equation 

(Eq. (7.11)) and momentum equations (Eq. (7.12)) for an 

assumed uniform mean flow imply that 

0 ~

D

~ 1 D

0 2

0

+ ρ ∇ • u = t

p

c

(7.17)

p

t

~

D

~ D

ρ0 = −∇ u (7.18)

Taking the material derivative of Equation (7.17) gives 

( ) 0 ~

D

D

D

~ 1 D 0 2

2

2

0

+ ρ ∇ • u = t t

p

c

(7.19)

Now taking the divergence of Equation (7.18) gives 

p

t

~

D

~ D 2

0∇  = −∇ 

 





ρ • u

(7.20)

Recalling that the gradient operator commutes with the 

material derivative of the acoustic velocity field in a uniform 

flow, 

( ) 



 





ρ • = ρ • t Dt

~ ~ D

D

D

0 0

u ∇ u ∇ (7.21)

and substituting Equation (7.21) into Equation (7.19) gives 

0

D

~ D

D

~ 1 D

0 2

2

2

0

 =



 



 + ρ • t t

p

c

u ∇ (7.22)

Now substituting Equation (7.20) into Equation (7.22) gives a 

scalar wave equation on the acoustic pressure for uniform 

mean flow, 

p

t

p

c

~

D

~ 1 D 2

2

2

2

0

= ∇ (7.23)

It is noted that a second order wave equation on the acoustic 

pressure field is not derivable in three space dimensions for 

nonuniform mean flows.

7.3.4 Scalar Wave Equation in Frequency Domain

Time-harmonic (i.e., frequency domain) solutions to Equations (7.16) and (7.23) are sought so that 

, where 1 ~

~

= −











φ =















φ ω e i

p p

i t (7.24)

where ω is the circular frequency and φ and p are now understood to be frequency dependent. It should be noted that the 

+iωt sign convention is employed throughout this chapter unless 

explicitly stated otherwise. Substituting Equation (7.24) into 

Equation (7.23) gives the differential equation that governs the 

time-harmonic acoustic pressure field in a uniform flow, 

p

t

p

c

2

2

2

2

0 D

1 D = ∇ (7.25)
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 209 Chapter 7

Similarly, substituting Equation (7.24) into Equation (7.16) 

gives the differential equation for the time-harmonic acoustic 

potential in a nonuniform flow, 

( ) 0 1

D

1 D

D

D

0

0

2

0

• ρ φ = ρ

 +



 



 



 



 φ − ∇ ∇

t c t

(7.26)

where the material derivative in Equations (7.25) and (7.26) is 

now expressed in the frequency domain 

= ω+ 0 • ∇

D

D i u

t

(7.27)

The single scalar wave equation for uniform (Eq. (7.25)) or 

nonuniform mean flow (Eq. (7.26)) may now be solved 

(subject to acoustic boundary conditions) to obtain the timeharmonic acoustic pressure or acoustic velocity potential. The 

appropriate acoustic boundary conditions for both scalar wave 

equations are the subject of the following subsection.

7.3.5 Acoustic Boundary Conditions

In the current subsonic flow problem, the linearized acoustic problem in three space dimensions requires one boundary 

condition at the source boundary and another at the duct 

termination. Codes that solve the uniform-flow, timeharmonic acoustic pressure equation (Eq. (7.25)) often have 

the time-harmonic acoustic pressure ps specified directly at the 

source plane:

p = ps along Γs (7.28)

Alternatively, the source plane acoustic pressure may be split 

into incident, pinc, and reflected, pref, components with the 

incident component specified as the source plane condition 

ps = pinc + pref along Γs (7.29)

In Equation (7.29) the reflected acoustic pressure pref is 

obtained as part of the solution procedure. The two approaches 

to acoustic source specification are generally driven by either 

the desire to support experimental facilities or to perform 

parameter studies. In experimental facilities, the sum of the 

incident and reflected source plane acoustic pressure ps is 

measured and readily available for code input, and Equation 

(7.28) is therefore used as the source plane condition. 

However, in parameter studies, only the incident part of the 

source plane acoustic pressure pinc is generally known (the 

reflected wave pref is a function of the liner impedance, duct 

termination, and geometry and cannot be known a priori), and 

Equation (7.29) is therefore implemented. Either method for 

specifying the source plane boundary condition (Eq. (7.28) or 

(7.29)) is mathematically correct and leads to an identical 

solution (provided other conditions are the same within Ω).

At the duct termination, a boundary condition is specified in 

the form of either an acoustic pressure, where the incident 

acoustic pressure is given as 

p = pinc + pref along Γt (7.30)

or as a termination boundary condition of the form 

[ t]{ p } {p} t

ic ζ • = Γ

ω

along 0 ∇ n (7.31)

One important point that can be easily overlooked is that 

the termination boundary condition defined by Equation (7.31) 

is a nonlocal condition. That is, the normal gradient of the 

acoustic pressure field at a point along the boundary depends 

upon the collective influence of the acoustic pressure field at 

all other points along the boundary. The square matrix [ζt] is 

the dimensionless node impedance matrix, n is the outward 

unit normal vector to Γt, {p} and {∇p •n} are column 

vectors containing the acoustic pressure and its normal 

derivative at points along Γt. Further, when the exit boundary 

is discretized with N grid points, the dimensionless node 

impedance matrix is of order N, the vector {p} is a column 

vector of length N that contains the acoustic pressure at the N

grid points along Γt, and {∇p •n} is a column vector of 

length N that contains the normal derivative of the acoustic 

pressure at the N grid points along Γt. The elements in the 

matrix [ζt] may be chosen so that the termination is modeled 

as reflecting or nonreflecting; the choice for elements in [ζt] 

will be discussed in more detail later when results are 

presented. A more detailed discussion of Equation (7.31) 

along with its derivation is given in Reference 2. It is also 

worth noting that Equation (7.30) is often used by codes in 

which only the incident wave pinc is known. Equation (7.31), 

on the other hand, is used mostly by codes that support 

experimental facilities where the total pressure field (i.e., the 

sum of incident and reflected pressure field) and dimensionless node impedance matrix can be measured.

There has been considerable discussion in the literature 

during the past half century concerning the acoustic boundary 

condition for general surface shapes with mean flow. Myers 

(Ref. 3) resolved this controversy a quarter of a century ago 

and his boundary condition has been generally accepted as 

correct in modern duct acoustic literature. Thus, all codes 

discussed in this chapter employ the Myers boundary condition, which in its most general time-harmonic form is 

( )

( ) w i

p

c

p

i

p c c

• • Γ

ωζ

+

















ρ ζ • ω

ρ − ζ − ρ • = −

0 on

0 0

0

0 0

0 0

n n u

u n u

∇

∇

(7.32)
NASA/TP—2012-215653 210

It is noted that Equation (7.32) is restricted to locally reacting acoustic treatment and will not be valid for those absorbers 

that allow wave propagation through the material in directions 

parallel to the flow path. To write the impedance boundary 

condition (Eq. (7.32)) in terms of acoustic pressure in the 

presence of uniform flow, take the normal component of the 

linearized momentum equation (Eq. (7.18)) to obtain 

(− ρ • ) = • in Ω

D

D

0c0u n c0 p n

t

∇ (7.33)

Substituting Equation (7.32) into Equation (7.33) and 

assuming a uniform flow gives 

( ) c p w c

p

i

p c

t  = − • Γ



 





















ρ ζ • ω

ρ +

ζ

on

D

D 0

0 0

0 0 0 u ∇ ∇ n (7.34)

Equation (7.34) is the appropriate wall impedance boundary 

condition for the scalar pressure equation (Eq. (7.25)).

Returning now to solutions for the acoustic potential equation in nonuniform mean flow (Eq. (7.26)), we specify either 

the acoustic potential at the source plane 

φ = φs along Γs (7.35)

or the source plane acoustic potential is split into an incident 

and reflected source plane potential 

φ = φinc + φref along Γs (7.36)

with the incident source plane potential φinc specified and the 

reflected potential φref obtained as part of the solution. Along 

the duct termination, a nonlocal boundary condition similar to 

Equation (7.31) is specified in the form 

[ t]{ } { } t

ic ζ φ • = φ Γ

ω

along 0 ∇ n (7.37)

The Myers boundary condition (Eq. (7.32)) is applied along 

the duct wall. When written in terms of the time-harmonic

acoustic potential, this boundary condition is 

( ) 0 0

0

0

0 0

0

D

1 D

D

1 D

D

1 D

n n M

M

n

c i c t

i c t

c

c t

∇

∇ ∇

• • φ

ω ζ −















 φ

ζ 



 



 • ω

+ φ

ζ − φ • =

(7.38)

where the mean-flow Mach number vector, M0 is defined as 

0

0

0

c

u M = (7.39)

7.4 Acoustic Liner Sound Attenuation

The acoustic intensity I at any axial plane can be evaluated 

using the Morfey expression (Ref. 4): 

( )( )

( ) ( )( )







 • + • • ρ

+





 = R • + ρ • •

∗ ∗

∗ ∗

u n u u u n

u n u u u n

0 0 2

0

0 2 0 0

0 0 2

1

c

p

c

pp

I p

(7.40)

where the asterisk superscript denotes the complex conjugate. 

Furthermore, the total acoustic power at the source or duct 

termination is the integral of the acoustic intensity across the 

cross section 

= Γ ∫ΓE I d s

s (7.41)

= Γ ∫Γ

E I d t

t (7.42)

and the decrease in decibels of the acoustic power from the 

source to the duct termination (i.e., the liner attenuation) can 

be written as 















 ∆ = t

s

E

E E 10log10 (7.43)

It should be noted that ∆E represents that portion of the acoustic 

energy in decibels that is attenuated by the liner and does not 

propagate away from the duct exit to the far field. The goal of 

optimum liner design is to maximize the liner attenuation.

Unfortunately, the normal component of acoustic velocity, 

u • n, needed to evaluate the acoustic intensity in Equation (7.40) is generally not available. In this situation, it is 

convenient to use the difference in the integrated (i.e., 

average) sound pressure level (SPL) between the source and 

duct termination ∆SPL as a measure of lining performance. 

This expression is 

∆SPL = SPLs − SPLt (7.44)

















∫ Γ

∫ Γ =

Γ

∗ Γ

d

d

10log 2

reference

10

p

pp

SPL

s

s

s (7.45)

















∫ Γ

∫ Γ =

Γ

∗ Γ

d

d

10log 2

reference

10

p

pp

SPL

s

t

t (7.46)

where SPLs and SPLt are the average SPLs at the source and 

duct termination, respectively, and preference is a reference 

pressure usually taken as 20 μPa. Equation (7.44) is used 

throughout this chapter to compute the performance of the 
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 211 Chapter 7

wall lining when only the acoustic pressure is known (such as 

with experimental measurements). On the other hand, 

Equation (7.43) can be used when both the acoustic pressure 

and the normal component of acoustic velocity are known 

(such as in numerical simulations).

7.5 Potential Flow Computer Codes

Obtaining solutions to the potential flow scalar wave equation (Eq. (7.25) or Eq. (7.26)), when coupled with the appropriate source, termination, and wall impedance boundary 

condition, remains a formidable task. Exact solutions for 

arbitrary sources and mean flows have thus far not been found. 

However, the introduction of large-scale digital computers has 

allowed for numerical solutions to be obtained. These numerical 

solutions are essential for optimum design of noise-efficient 

aircraft. Over the past two decades, a number of computer codes 

have emerged for the numerical solution of these scalar wave 

equations when coupled to the appropriate boundary conditions. 

The remaining subsections discuss the various computer codes 

along with their salient features and limitations. There are four 

potential flow codes discussed in this chapter:

(1) Quasi-three-dimensional uniform-flow code

(2) Axially symmetric code

(3) Three-dimensional uniform-flow code

(4) Three-dimensional code with the parabolic approximation

Readers are reminded that the code descriptions presented in 

this chapter are intended as a review only and more technical 

details are provided on the quasi-three-dimensional code in 

Reference 5, the axially symmetric code in Reference 6, and 

the three-dimensional code with the parabolic approximation 

in Reference 7. Details of the three-dimensional uniform-flow 

code have not been published and are provided in this chapter 

for the first time. Each of these codes is discussed in the above 

order in the following subsections.

7.5.1 Quasi-Three-Dimensional Uniform-Flow 

Code

The quasi-three-dimensional approximation is applicable to 

duct geometries and flows for which the acoustic solution in one 

orthogonal direction (assumed to be the y direction in this 

chapter) is separable due to the fact that the sidewalls are both 

rigid and orthogonal to that direction. Quasi-three-dimensional 

acoustic analysis is restricted to a liner impedance that depends 

only on the axial coordinate z (ζ = ζ(z)), and mean velocity 

fields that have only a uniform axial component. Further, the 

mean static pressure, and mean static density are constant 

constant

constant

constant

0

0

0

0

0

0

0

=

ρ =

=

=

=

p

w

u

v

(7.47)

so that the uniform-flow pressure equation (Eq. (7.25)) and 

acoustic pressure boundary conditions (Eqs. (7.28), (7.31), and 

(7.34)) may be used. Physically, the quasi-three-dimensional 

approximation is applicable to laboratory experiments 

conducted in constant-area, rectangular geometries such as 

grazing-flow impedance tubes where the mean-flow velocity 

is fairly low and boundary layer effects can be neglected.

The weighted residual approximate solution to Equation 

(7.25) requires that the time-harmonic acoustic pressure p be 

first approximated by a trial solution p and that the resulting 

error in the governing differential equation (Eq. (7.25)) be 

minimized by requiring that it be orthogonal to a complete set 

of basis functions WJ, 

d 0

D

1 D

2

2

2

0

Ω = 













 − • ∫Ω p WJ

t

p

c

∇ ∇ (7.48)

where 

Dt

D is expressed in the frequency domain by Equation (7.27). The above formulation has the restriction that ∇p

must be continuous in Ω before p can converge to p. This 

restriction can be relaxed by applying the Stokes theorem to 

Equation (7.48) so that the order of the highest derivatives are 

reduced. This results in the weak form 

[ ( )

( )( ) ( ) ( )]

= [ − ( • )]• Γ

− • • − • Ω

− − •

∫

∫

Γ

Ω

d

d

2

0 0

0 0

0 2

J

J J

J J

p p W

W p p W

k pW ik p W

M M n

M M

M

∇ ∇

∇ ∇ ∇ ∇

∇

(7.49)

where M0 is the mean-flow Mach number vector defined in 

Equation (7.39) and the freespace wave number k is 

c0

k ω = (7.50)

Equation (7.49) is solved numerically using a quasi-threedimensional, Galerkin finite element method with rectangular 

finite elements. A full discussion of the theory underlying the 

development of the finite element method may be found in 

Reference 8. The method as used here assumes that there are 

N nodes in the axial direction (i.e., the z-direction) and M

nodes in the transverse direction (i.e., the x-direction) of the 

duct as shown in Figure 7.3. Because the solution in the 

spanwise direction (i.e., the y-direction) is separable and 

contains rigid sidewalls, it is expanded into a series of hardwall duct modes. Thus, the finite element solution needs to be 

obtained only in the x,z-plane. A typical two-dimensional 

rectangular element [I,J] is shown in Figure 7.4. Each element 

consists of four local node numbers labeled 1, 2, 3, and 4. 

Each element is considered to have length in z-direction
NASA/TP—2012-215653 212

Figure 7.3.—Finite-element discretization of twodimensional duct.

Figure 7.4.—Typical two-dimensional finite-element, 

[I,J], and local node numbering system.

of a = (zI+1 – zI) and length in x-direction of

b = (xJ+1 – xJ) as shown. The objective of the method is to 

obtain the unknown acoustic pressure and its derivatives at the 

nodes of each of the (N – 1) × (M – 1) elements.

Within each finite element, p is represented as a linear 

combination of 16 cubic functions, N1, N2, N3,..., N16, 

which compose a complete set of basis functions:

I I

I

I

z x

D

m y p z x y  Φ 

 



 π = ∑

=

=

( , , ) cos ( , )

16

1

N (7.51)

where D is the distance between the rigid sidewalls, and 

the node coefficients ΦI are understood to depend on the 

hard-wall-mode order m. We use a Galerkin finite element 

method so that the set of weighting functions WJ equals the 

basis functions used in the expansion for p :





 



 π = D

m y WJ NJ (z,x) cos (7.52)

The 16 two-dimensional basis functions NI and nodal 

parameters ΦI are easily constructed from the products of the 

four cubic Hermite polynomial basis functions in the two 

coordinate directions,

( )

( )

( )

( ) 



 



 − 













 =





 



  −  



 =





 



 = −





 



  +  



 = −

, 1

2 , 3

, 1

, 1 3 2

2

4

2

3

2

2

2 3

1

a

z

a

z f z a

a

z

a

z f z a

a

z f z a z

a

z

a

z f z a

(7.53)

and the requirement that ∇p be continuous within each 

element and along inter-element boundaries 

( , ) ( , )

( , ) ( , )

( , ) ( , )

16 4 4

2 2 1

1 1 1

f z a f x b

f z a f x b

f z a f x b

=

=

=

N

N

N

 (7.54)

( )

( )

( )

z x

p z x

z

p z x

p z x

I J

I J

I J

∂ ∂

∂ Φ =

∂

∂ Φ =

Φ =

+1 2

16

2

1

,

,

,

 (7.55)

The variable impedance ζ(z) is represented in a similar manner 

along each boundary element: 

( , ) ( )

1 ( , ) ( )

1

( , ) ( )

1 ( , ) ( )

1

( )

1

4

1

3

1

1 2

f z a

z

f z a

z

f z a

z

f z a

z z

I I

I I

+ ζ + ′ +

ζ

+

ζ′ +

ζ = ζ (7.56)

where ζ′ represents the derivative of ζ with respect to z. The 

importance of the choice of the trial solution and basis 

functions given in Equations (7.51) and (7.52) is that they 

satisfy the convergence and continuity requirements of the 

finite element method (Ref. 8). Thus by substituting Equations 

(7.51) to (7.56) into Equation (7.49) and setting the weighting 

function WJ to the basis function NJ allows one to compute 

the contributions to the minimization of the total error from 

each individual element, 
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 213 Chapter 7

[ ( )

( )( ) ( )]

∑ [ ( )] ∫

∑ ∫

= − • • Γ

− • • − • Ω

− − •

Γ

Ω

elements

0 0

0 0

0

elements

2

 d

 d

2

J e

J J e

J J

e

e

p p

p p

k p ik p

N

N N

N N

M M n

M M

M

∇ ∇

∇ ∇ ∇ ∇

∇

(7.57)

where the sum in Equation (7.57) is carried out over all finite 

elements using the usual rules of finite element assembly. In 

Equation (7.57), Ωe is now interpreted as the element volume 

and Γe is the surface that bounds the element volume. The 

surface integral on the right-hand side of Equation (7.57) 

produces no net contribution except at the source plane, at the 

duct termination, and along the perimeter of the duct. This 

occurs because, away from these boundaries, adjoining finite 

elements produce surface integral contributions on the righthand side of Equation (7.57) that are equal in magnitude and 

opposite in direction. Effects of the wall impedance boundary 

condition is included in weak form at the element level by 

substituting the uniform-flow form of the Myers boundary 

condition (see Eq. (7.34)) 

[ ( )] 















ζ • = − + • ik

p p ik 2 ∇ n M0 ∇ (7.58)

directly into the surface integral on the right-hand side of 

Equation (7.57). A similar procedure is used to implement the 

exit impedance boundary condition (Eq. (7.31)). Because of 

the orthogonality of the hard-wall duct modes, Equation (7.57) 

with appropriate substitution from Equation (7.58) will hold 

for each spanwise mode m so that it needs to be constructed 

only in the z,x-plane. Contributions to Equation (7.57) from a 

typical element [I,J] are of the form [S]{Φ} where [S] is a 

16×16 complex matrix for each element [I,J], and {Φ} is a 

16×1 column vector containing the unknown acoustic pressure 

and its derivatives at the four nodes of the element. The 

coefficients in the local stiffness matrix, [S], are computed in 

closed form using Mathematica (Ref. 9) intrinsic functions.

Assembly of the global equations for the computational 

domain is a basic procedure in the finite element method. 

Appropriate shifting of rows and columns is all that is required 

to add the local element matrix, [S], directly into the global 

stiffness matrix. Assembling the elements for the entire 

domain results in a global matrix equation of the form: 

[SCH2D ]{Φ} = {FCH2D} (7.59)

where the global stiffness matrix [SCH2D] is a complex square 

matrix whose order is 4MN, and {Φ} and {FCH2D} are 4MN×1 

column vectors. The vector {Φ} contains the nodal values of 

the unknown acoustic pressure and its derivatives at the nodes 

of the elements and {FCH2D} is the null vector.

It is necessary to apply the source pressure condition 

(Eq. (7.28)) to the system of Equations (7.59) before a unique 

solution can be obtained. Satisfying the noise source boundary 

condition consists simply of constraining all nodal values of 

acoustic pressure and its derivative at the source plane Γs to 

the known value of source pressure, ps, and its derivative. This 

procedure introduces nonzero elements into the first 4M

components of the vector {FCH2D}.

After implementation of source boundary condition, Equation (7.59) remains block tridiagonal. Much practical importance arises from this matrix structure, as it is convenient for 

minimizing storage and maximizing computational efficiency. 

Special matrix techniques exist for a solution of this structure.

An unsymmetrical parallel sparse solver with equation reordering to minimize fill is used to decompose [SCH2D] into the 

products of a unit lower ([L]) and a unit upper ([U]) triangular 

matrices, and a nonsingular diagonal matrix ([DD]) 

[SCH2D ] = [L][DD][U] (7.60)

Equation (7.60) now decomposes into two triangular systems 

[L]{Φ} = {FCH2D} (7.61)

[DD][U]{Φ} = {Φ} (7.62)

The sequential operations of forward and backward substitution are used to obtain the solution vector, {Φ}. In this work,

all computations are performed on a parallel computer and 

only the nonzero elements in [SCH2D] are stored and operated 

upon during the solution stage. The computer code developed 

for the solution of the convected Helmholtz uniform-flow 

equation following the aforementioned two-dimensional finite 

element approach with a direct solve strategy is referred to as 

the CH2DDS code in subsequent discussion.

7.5.2 Axially Symmetric Code

The axially symmetric code was developed in academia 

(Ref. 6), is written in cylindrical coordinates, and is termed 

axially symmetric because the nacelle geometry and the mean 

flow field in and around the nacelle are axially symmetric. 

Unlike the quasi-three-dimensional code that computes only the 

in-duct propagation, the axially symmetric code allows the 

noise field in the nacelle to radiate to the far field. The cylindrical coordinates are z, r, and θ, where the axial coordinate is z, 

the radial coordinate is r, and θ is the angular or circumferential 

coordinate. Acoustic solutions are sought in terms of the angular 

harmonics of a Fourier series with angular mode m. This 

reduces the acoustic solution to a two-dimensional problem in 

the z, r-plane. The inlet and aft radiation are treated similarly in 

the code. The exception is that the jet is included in the aft fan 

radiation by separating the interior and exterior flow outside the 

aft fan duct with a thin barrier created by disconnecting the 

interior and exterior domain. In what follows, a discussion of 

the inlet radiation code is performed in detail. Afterwards, we 

show how to include the effects of the jet in the formulation for 

aft radiation.
NASA/TP—2012-215653 214

For inlet radiation, the sound fields in the duct and far field are 

extracted using a weighted residual formulation for which the 

acoustic potential is φ and the weighting functions are WJ. Thus, 

the weighted residual formulation of Equation (7.26) gives 

d 0

D

D

D

D 2

2 0

0

0  Ω =



 



  − • φ 

 



ρ  φ

∫Ω c WJ c t t

∇ ∇ (7.63)

where Ω consists of the entire domain (interior and exterior to 

the nacelle). Applying the Stokes theorem to Equation (7.63) 

and simplifying as shown above in the quasi-threedimensional discussion gives the weak formulation 

[ ( ) ( )

( )( ) ( ) ( )]

[− ω φ + ω φ − ( • φ)]• Γ ρ =

− • • φ − φ • Ω

−ω φ + ω • φ − ω • φ ρ

∫

∫

Γ

Ω

d

d

0 0 2

2 0 0

0

0

2 0 0 0

0 0 2

2

0

0

J

J J

J J J

i c W c

W c W

W i W i W c

u u u n

u u

u u

∇ ∇

∇ ∇ ∇ ∇

∇ ∇

(7.64)

Solutions are sought in cylindrical coordinates in terms of 

angular harmonics of the form 

( )

( )

( )

( ) 











φ =













φ θ

θ

− θ

θ

im m

m im J J

z r e

W z r e

z r

W z r

,

,

, ,

, , (7.65)

and the gradient operators are defined as 

z J J r JJ

z

W

r

imW

r

W W e e e

∂

∂

+ +

∂

∂ ∇ = θ (7.66)

z m m r m m r z

im

r

e e e

∂

∂φ + φ − ∂∂φ ∇φ = θ (7.67)

where er, eθ and ez, are unit vectors in the r-, θ-, and 

z-directions. The irrotational mean flow, u0, is the gradient of 

the axially symmetric mean flow potential φ0(r,z):

r z r z

u e e

∂

∂φ +

∂

∂φ = φ = 0 0

0 ∇ 0 (7.68)

Note that the factors e

±imθ cancel out of Equation (7.64) and 

the problem is reduced to one in two spatial coordinates r and 

z for each Fourier mode m.

In a steady, nonuniform flow field, Equation (7.64) is 

solved using a conventional Galerkin finite element method, 

where the weighting functions WJ are identical to the finite 

element basis functions. The finite element basis functions in 

this region (i.e., where the mean flow is nonuniform) are 

rectangular, eight noded, isoparametric serendipity elements 

(elements without interior nodes). Thus, a quadratic

expression is used to approximate the acoustic potential within 

each finite element. The near field (where the flow is nonuniform) is terminated on a boundary Γr, beyond which a single 

layer of far-field or infinite elements is used. An artificial 

baffle Γb formed by a ray from the origin is used to limit the 

domain. In the far field, Equation (7.64) is discretized using 

mapped wave envelope elements. The basis functions in the 

infinite elements are constructed to display the characteristics 

of the fundamental source solution at large distances from the 

source. The weighting functions in the far field are chosen so 

that the boundary integrals in Equation (7.64) have no 

contribution along Γr. The details of the mapped wave 

envelope implementation are rather lengthy and are discussed 

in further detail in Reference 6. The effects of the wall 

impedance and the sound source are included by substitution 

into the boundary integrals in Equation (7.64), just as in the 

quasi-three-dimensional formulation. Only the incoming 

waves are specified at the source plane (i.e., Eq. (7.36)), and 

the reflected portion of the solution is captured as part of the 

solution procedure.

Assembling the elements together leads to a linear matrix 

equation similar in form to Equation (7.59), but different in 

structure. The axially symmetric solver uses a frontal solver 

by Irons (Ref. 10) to solve this matrix equation. Modifications 

have been made to the original solver of Irons so that all 

direct-access inputs and outputs are eliminated in favor of 

active storage or sequential inputs and outputs. This has 

resulted in as much as 50 percent reduction in computation 

time, dependent mainly on available fast memory.

For the aft radiation code, the acoustic potential is discontinuous across the shear layer dividing the extended jet from 

the external flow. Therefore, elements above and below the 

shear layer have additional degrees of freedom on the shear 

layer boundaries that contain the acoustic particle displacement. Because the acoustic pressure and particle displacement 

are continuous across the shear layer, a penalty constraint in 

the form of a surface integral is added to the surface integrals 

on the right-hand side of Equation (7.64) to enforce the proper 

conditions across the shear layer. The penalty constraint 

simply modifies the coefficient matrix, [SCH2D]. The computer 

code developed based on the aforementioned axially symmetric formulation with inlet or aft radiation is referred to as the 

CH2DIE code in subsequent discussion.

7.5.3 Three-Dimensional Uniform-Flow Code

The three-dimensional uniform-flow code makes assumptions similar to the quasi-three-dimensional formulation, with 

the exception that all four walls of the duct may be lined and 

the liner impedance is a function of both wall coordinates. 

Consequently, the solution in the y (or any other) dimension is 

not separable, and a fully three-dimensional model is required 

to compute the acoustic field.

The three-dimensional weighted residual approximate 

solution to Equation (7.25) in weak form is still given by 

Equation (7.49):
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 215 Chapter 7

[ ( )

( )( ) ( ) ( )]

= [ − ( • )]• Γ

− • • − • Ω

− − •

∫

∫

Γ

Ω

d

d

2

0 0

0 0

0 2

J

J J

J J

p p W

W p p W

k pW ik p W

M M n

M M

M

∇ ∇

∇ ∇ ∇ ∇

∇

(7.49)

Here, Equation (7.49) is solved numerically using a threedimensional Galerkin finite element method. The threedimensional finite element method assumes that there are N

nodes in the axial, or z-direction, M nodes in the x-direction, 

and Q nodes in the y-direction of the duct as shown in 

Figure 7.5. Brick elements with eight nodes are used in the 

analysis. A typical brick element, [I,J,K], is shown in Figure 7.6. Each element consists of eight local node numbers 

labeled 1, 2,..., 8. Each element is considered to have length

a = (zI+1 – zI), height b = (xJ+1 – xJ) and width d = (yK+1 – yK) 

as shown. The objective of the three-dimensional method is to 

obtain the unknown acoustic pressure and its derivatives at the 

nodes of each of the (N–1) × (M–1) × (Q–1) elements.

Within each element, p is represented as linear combinations of 64 cubic functions, N1, N2, N3,..., N64 that 

compose a complete set of basis functions:

I I

I

I

p z x y = ∑ z x y Φ

=

=

( , , ) ( , , )

64

1

N (7.69)

A Galerkin finite element method is used so that the set of 

weighting functions WJ equals the basis functions: 

W (z,x,y) J = NJ (7.70)

The 64 three-dimensional basis functions NI and node 

coefficients ΦI are easily constructed from the products of the 

four cubic Hermite polynomial basis functions (Eq. (7.53)) in 

the three coordinate directions and the requirement that p

and ∇p be continuous within and along inter-element 

boundaries:

( , ) ( , ) ( , )

( , ) ( , ) ( , )

( , ) ( , ) ( , )

64 4 4 4

2 2 1 1

1 1 1 1

f z a f x b f y d

f z a f x b f y d

f z a f x b f y d

=

=

=

N

N

N

 (7.71)

z x y

p z x y

z

p z x y

p z x y

I J K

I J K

I J K

∂ ∂ ∂

∂ Φ =

∂

∂ Φ =

Φ =

( , + , + )

( , , )

( , , )

1 1 3

64

2

1

 (7.72)

The variable impedance ζ is represented in a similar manner 

for elements along Γw: 

Figure 7.5.—Finite-element discretization of threedimensional duct.

Figure 7.6.—Typical three-dimensional finite-element, 

[I,J,K], and local node numbering system.

w

I

I

I

I

z x y Γ

ζ = ζ ∑

=

=

, along 1 ( , , ) 1 64

1

N (7.73)

where ζI are values of the impedance function and its derivatives at nodes along Γw. Only 16 of the basis functions NI are 

nonzero along Γw.

Substituting Equations (7.69) to (7.73) into Equation (7.49) 

and setting the weighting function WJ to the basis functions 

allows one to compute the contributions to the minimization of 

the total error from each individual element as 

[ ( )

( )( ) ( ) ( )]

= [ − ( • )]• Γ

− • • − • Ω

− − •

∑ ∫

∑ ∫

Γ

Ω

d

d

2

0 0

elements

0 0

0 2

elements

J

J J

J J

p p

p p

k p ik p

N

N N

N N

M M n

M M

M

∇ ∇

∇ ∇ ∇ ∇

∇

(7.74)
NASA/TP—2012-215653 216

where the sum in Equation (7.74) is again carried out over all 

finite elements using the usual rules of finite element assembly. Effects of the wall impedance boundary condition are 

included in weak form at the element level by substituting the 

Myers boundary condition directly into the surface integral on 

the right-hand side of Equation (7.74):

[ ( )] 















ζ • = − + • ik

p p ik 2 ∇ n M0 ∇ (7.75)

A similar procedure is used to implement the duct termination boundary condition. Contributions to Equation (7.74) 

from a typical element [I,J,K] are of the form [S]{Φ}, where 

[S] is a 64×64 complex square matrix for each element [I,J,K], 

and {Φ} is a 64×1 column vector containing the unknown 

acoustic pressure and its derivatives at the eight nodes of the 

element. The coefficients in the local stiffness matrix [S] are 

computed in closed form just as in the quasi-three-dimensional 

analysis.

Assembling the elements for the entire domain results in a 

matrix equation that is again of the form

[SCH3D ]{Φ} = {FCH3D} (7.76)

where [SCH3D] is a complex, square, block tridiagonal matrix 

whose order is 8MNQ, and {Φ} and {FCH3D} are 8MNQ×1 

column vectors. The vector {Φ} contains the nodal values of 

the unknown acoustic pressure and its derivatives at the nodes 

of the element, and {FCH3D} is the zero vector. The source 

plane boundary condition is introduced into Equation (7.76) 

by constraining the nodal degrees of freedom just as in the 

quasi-three-dimensional case. This introduces 4QM nonzero 

elements into {FCH3D}. The same unsymmetrical parallel 

sparse solver used in the quasi-three-dimensional case is used 

to solve the fully three-dimensional system. However, the 

three-dimensional system has a much larger bandwidth. The 

computer code developed for the solution of the convected 

Helmholtz uniform-flow equation following the aforementioned three-dimensional finite element approach with a direct 

solver strategy is referred to as the “CH3DDS” code in 

subsequent discussion.

7.5.4 Three-Dimensional Code With Parabolic 

Approximation

A duct fan noise propagation and radiation code has been 

developed that utilizes a parabolic approximation to the 

convected Helmholtz equation (Ref. 11). The code is composed 

of five distinct modules: (1) input and output specification, 

(2) mean flow and acoustic grid generation, (3) background 

flow calculation, (4) duct acoustic propagation, and (5) acoustic 

radiation. The propagation module, which is the focus of 

this section, incorporates the work of Dougherty 

(Refs. 7 and 12) and utilizes a parabolic approximation to the 

convected Helmholtz equation. This approach affords very 

efficient propagation calculations, thus allowing solutions for 

complex three-dimensional geometries to be handled with 

relatively low computational costs. This efficiency comes at the 

expense of reduced accuracy as the direction of propagation of 

an acoustic mode diverges from the preferred angle of the 

parabolic approximation. Additionally, loss of accuracy may 

occur when reflection of acoustic waves in the axial direction 

becomes important, as these effects are not captured in this 

formulation. Nevertheless, if appropriate care is taken to 

account for these limitations, this code can provide an efficient 

environment in which to perform three-dimensional propagation 

calculations. Thus, an additional aspect of this assessment is the 

continuation of a systematic study to identify a “working 

envelope” within which to use the various approaches to 

modeling duct propagation.

Although the parabolic approximation and general splitting 

technique were discussed in detail in previous work, a brief 

introduction is useful in understanding the approach. The full 

formulation is carried out in terms of the acoustic velocity 

potential φ and is based on the convected Helmholtz equation 

(Eq. 7.26). However, for simplicity, a rectangular duct is 

considered in which a steady mean-flow Mach number M0

aligned with the duct z-axis is present. Thus, the initial 

governing equation of the analysis is the convected Helmholtz 

equation in the form 

( ) − φ ∂

∂φ 



 





∂

∂ = − φ + +

∂

∂ φ − ⊥

0 2

0 0

2

2

2

2

0

M 1 M 2 M M k

z z

ik

z

∇ (7.77)

where 2 ∇⊥ is the transverse Laplacian defined as 

2

2

2

2

2

x ∂y

∂

+

∂

∂ ∇⊥ = ∇⊥ • ∇⊥ = (7.78)

and an e

iωt time dependence has again been assumed. As 

discussed by Dougherty (Ref. 12) and outlined by Corones 

(Ref. 13), a derivation based on splitting the solution of the 

governing equation (Eq. 7.77) into “positive” and “negative” 

traveling waves is proposed. This general splitting may be 

represented as

[ ] [ ] 











φ

φ =

















∂

∂φ

φ

















∂

∂φ

φ

=













φ

φ

−

+ −

−

+ 1 ( ) or T(z)

z z

T z (7.79)

where the splitting matrix [T(z)] is arbitrary. Substitution of 

the general variable splitting (Eq. (7.79)) into the convected 

Helmholtz equation (Eq. (7.77)) leads to a coupled pair of 

differential equations for φ± of the form
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 217 Chapter 7

( )

( ) [ ]

[ ] ( ) [ ] 











φ

φ



































 





∂

∂ − + +

−

+















 





∂

∂ = −













φ

φ

∂

∂ −

−

+ −

⊥

−

−

+

1

0

0 0 2 2

2

0

1 2

0

2

0

M 2 M M

0 1 M

1 M

1 M

T

z

k ik T

T

z

T

z

∇

(7.80)

Dougherty considered plane waves to produce a splitting of 

the form













φ

φ

















+ −

= −

















∂

∂φ

φ

−

+

1 M0 1 M0

1 1

ik ik

z

(7.81)

Typically, at this point in the derivation, the terms that couple 

the equations for φ± are neglected to produce a single parabolic 

equation for the “positive” or “negative” traveling wave.

The general formulation outlined by Dougherty considers a 

system of orthogonal, curvilinear coordinates (ξ1, ξ2, ξ3) 

defined so that ξ3 is aligned with the steady potential mean 

flow. Following the aforementioned splitting process and 

neglecting the off-diagonal terms in the resulting matrix 

equation gives the parabolic approximation 

( ) + + ⊥ + +

φ ∂ξ

∂ φ − φ − + = ∂ξ

∂φ 1 2

1 2 3

3 2

0

3

3 2

1

1 M 2

h h

ik h h

h ik h ∇ (7.82)

where hi is the element of length given by 

for 1, 2, 3

2

3

1

= 















∂ξ

∂ = ∑

=

i x h

i

j

j

i (7.83)

The source boundary condition is given by 

inc 0 φ = φ =

+

z (7.84)

and the solution for φ+ is marched from the source to the exit 

plane, where the source is taken to be a specified φ+ distribution and no exit impedance is required, as φ± coupling is not 

considered.

The effects of acoustic treatment on the duct walls are 

included by assuming locally reacting impedance surfaces, 

which are out of the flow. The acoustic pressure and the 

normal acoustic particle displacement are continuous across an 

infinitely thin boundary layer. Denoting quantities within the

duct interior with subscript “I” and those outside the infinitely 

thin boundary layer with subscript “II,” the impedance 

boundary condition may be written as 

ζ

φ = ∂ξ∂φ ± + + 1 II II ik

hj j

(7.85)

where + φII is the acoustic velocity potential below the 

boundary layer, ζ is the normalized impedance, and the sign is 

negative for minimum ξj and positive for maximum ξj. The 

continuity of pressure condition leads to 

t ∂t

∂φ = φ+ + I II

D

D (7.86)

and the normal particle displacement condition leads to 

( n)  ( φ • n) 

 





∂

∂  φ • = 

 



 +

−

+

−

II

1

I

1

D

D ∇ ∇

t t

(7.87)

where the material and time derivatives in Equations (7.86) 

and (7.87) are expressed in the frequency domain. Eliminating 

+ φII and neglecting derivatives of the Mach number in the 

direction of the flow leads to 

( ) + + +

φ















∂ξ ζ

∂

+

φ ζ + = ±

∂ξ

∂φ

I

0 3

0

2 I

0

1

1 M

M

1 M

j j

j

ik h h

 (7.88)

The code that implements the aforementioned parabolic 

approximation method without computing the far-field 

radiation is referred to as “CH3DPA.”

As mentioned above, the code suite also contains an acoustic radiation module for the prediction of far-field noise

(Ref. 11). The approach is based on a time-domain integral 

representation of the solution of the Ffowcs WilliamsHawkings equation with penetrable data surfaces (FW-Hpds)

(Refs. 14 and 15). Here, acoustic quantities and mean flow 

conditions are provided on a penetrable source surface. This 

surface is typically defined by extending the aforementioned 

in-duct propagation calculations a short distance beyond the 

inlet or exhaust planes for inlet or aft-fan cases, respectively. 

At the termination of the in-duct prediction domain, the 

necessary input information is transferred to the FW-Hpds 

domain for subsequent use in radiation predictions.

For aft-fan cases, the shear layer between the bypass flow 

and external stream can refract the sound waves radiated to the 

far field. Radiation results can be improved by including this 

effect as well as the reflection of the sound in the bypass 

region from the solid surface external to the bypass duct
NASA/TP—2012-215653 218

Figure 7.7.—Turbofan engine showing boundary regions of axisymmetric

aft-fan geometry for parabolic approximation acoustic propagation and

far-field radiation code FWH3D, where n is unit vector normal to outer

shear layer.

surrounding the core flow (see Figure 7.7). As described in 

Section 7.5.2, “Axially Symmetric Code,” this is taken into 

account in the axially symmetric finite element code by the 

inclusion of additional degrees of freedom on the shear layer 

boundaries that contain the acoustic velocity. For the base 

implementation described above, this effect is not taken into 

account. However, one possible method of modeling this 

effect has been proposed. It entails extending the bypass duct 

propagation calculation into a “pseudo-duct” beyond the 

exhaust plane. This pseudo-duct extends axially from the 

exhaust plane of the bypass duct to the trailing edge of the 

core cowl; its inner and outer radii are defined by the core 

cowl and shear layer, respectively, as indicated in Figure 7.7. 

Acoustic treatment may be included on the core cowl and an 

acoustic-liner-type boundary condition is applied to the shear 

layer surface.

Although presented previously in Reference 16, a brief 

review of this boundary condition may be useful. The 

development is based on the satisfaction of two conditions on

the shear layer, which is assumed to be infinitely thin:

(1) The particle displacement must be continuous across the 

shear layer.

(2) The acoustic pressure must be continuous across the 

shear layer.

First, an expression relating the normal components of the 

acoustic velocity on the opposing sides of the shear layer is 

developed. Second, assuming that duct modal patterns persist 

within the shear layer flow region, an expression for the 

impedance on the external surface of the shear layer is 

derived. Finally, the impedance on the internal surface of the 

shear layer is given as 

II

I

II

I ζ •

• ζ = n)n)

(u

(u (7.89)

where the subscripts I and II indicate the corresponding 

regions shown in Figure 7.7, u is the acoustic velocity vector, 

n is the unit normal vector to the shear layer’s external

surface, and ζ is the acoustic impedance. The computer code

developed for the solution of the convected Helmholtz 

equation in three dimensions following the aforementioned 

parabolic approximation with the acoustic radiation module 

used to predict the far-field noise is referred to as the 

“FWH3D” code in subsequent discussion.

7.6 Rotational Flow Computer Codes

This section presents the governing differential equations, 

duct boundary conditions, and numerical methods for the suite 

of duct propagation models that allow for rotational flow. Four 

codes are discussed:

(1) Two-dimensional code

(2) Quasi-three-dimensional code

(3) Axially symmetric code

(4) Three-dimensional code

The quasi-three-dimensional code is based upon a finite 

element simulation of the linearized equations that govern 

conservation of mass and momentum for the fluid in the duct. 

Readers interested in more technical details concerning the 

quasi-three-dimensional code than presented in this chapter 

may consult (Ref. 17). The other three rotational flow codes 

were developed at Boeing with partial funding from NASA. 

Each of these three codes use a pseudo-time marching scheme 

to solve the linearized equations governing the conservation of 

mass and momentum either in two-dimensional, axially 

symmetric, or three-dimensional flows. More technical details 

on the pseudo-time marching codes are provided in (Refs. 18

and 19). In this section, the governing equations and boundary 

conditions for three-dimensional rotational flows are first 

presented. Next, we discuss the quasi-three-dimensional finite 

element code and its assumptions. Finally, we discuss the 

recently developed pseudo-time marching method that is used 

for the remaining three codes.
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 219 Chapter 7

7.6.1 Governing Differential Equations and 

Boundary Conditions

The equations that govern conservation of mass and 

momentum in a flow duct with viscous effects are (Ref. 1) 

(ˆ )ˆ ˆ ˆ 0 ˆ

+ • ρ + ρ • = ∂

∂ρ u ∇ ∇ u

t

(7.2)

(ˆ )ˆ ˆ [ˆ] 0 ˆ ˆ + − • = 



 



 + • ∂

∂

ρ ∇ ∇p ∇ τ

t

u u

u

(7.90)

At this point, the assumptions and equations governing 

continuity of mass and momentum in the fluid are the same as 

those presented in Section 7.3, “Potential Flow Formulation,” 

except for the additional matrix, [τˆ], which is the shear stress 

tensor. Thus, Equation (7.90) is now the Navier-Stokes 

equation, which accounts for viscous effects.

Decomposing the flow into a time independent mean flow 

and a time dependent acoustic perturbation gives 

] ~ , [ˆ] [ ] [ ~ , ˆ ~ , ˆ ~ ˆρ = ρ0 + ρ p = p0 + p u = u0 + u τ = τ0 + τ (7.91)

Substituting Equation (7.91) into Equations (7.2) and (7.90) 

allows the equations for mass and momentum conti-nuity to be 

rewritten in terms of the perturbation variables 

( )





 



 + ρ • ρ + = −

+ ρ • + ρ • + • ρ ρ

0 0

0

0 0 0

D

D 1

~ ~ ~

D

~ D

u

u u u

∇

∇ ∇ ∇

t

NL

t (7.6)

( )

[ ] [ ]





 



 − • + = − ρ + − •

ρ + ρ • + ρ +

0 0

0

0

0

0 0 0

D

D 2 ~

~

D

~ ~ D

D

~ D

∇ τ ∇ ∇ τ

∇ ∇

p

t

NL

p

t t

u

u

u u

u

(7.92)

and the nonlinear terms are 

= ρ( • )+ ( • )ρ ~ ~ ~ ~ NL1 ∇ u u ∇ (7.9)

( ) ( )

(u )u (u )u

u u u u

u

~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ 2

0

0 0

∇ ∇

∇ ∇

+ ρ • + ρ •

+ ρ • + ρ • ∂

∂ = ρ

t

NL (7.10)

By neglecting the nonlinear terms (NL1 = NL2 ≈ 0) in 

Equations (7.6) and (7.92), and recalling that the right-hand 

side of Equations (7.6) and (7.92) are zero since the viscous 

mean flow is the solution to the steady form of Equations (7.2) 

and (7.90), the linearized form of the perturbation equations

becomes

( ) 0 ~ ~ ~

D

~ D

+ ρ0 • + ρ • 0 + • ρ0 = ρ ∇ u ∇ u u ∇

t

(7.11)

( ) [ ] 0 ~ ~

D

~ ~ D

D

~ D 0 ρ0 + ρ0 •∇ 0 + ρ + ∇p − ∇ • τ = t t

u

u u

u

(7.93)

In order to close the system of equations, it is necessary to 

establish a relationship between p

~ and ρ

~ and establish 

transport properties relating the coefficient of viscosity to the 

velocity field. Here, it is assumed that the disturbance takes 

place homentropically in an ideal gas, so that 

0

2 0

0

2

0 , ~ ~

ρ

γ = ρ = p

p c c (7.13)

Note that the homentropic relation (Eq. (7.13)) neglects the 

effects of viscous and heat conduction effects on the perturbations ( [ ] 0 ~ ∇ • τ ≈ ). This leads to a linear system of four 

perturbation equations in four unknown variables (often 

referred to as the “linearized Euler equations”):

( ) ( ) 0 ~ ~ ~ ~

D

D

2

0

2 0

0 0 0 2

0

2

0 + γ • + • + γ • = 















c

p

p p c

c

p

t

c ∇ u ∇ u u ∇ (7.94)

( ) 0 ~

D

~ ~ ~ D

D

~ D 2

0

0

0 0 0  + = 

 





γ + γ • + c p

t

p p

t

p ∇ ∇ uu u

u

(7.95)

We now seek time-harmonic solutions to Equations (7.94) 

and (7.95) so that 

, 1 ~, ~ = = = − ω ω p pe e i i t i t u u (7.96)

where p and u are now understood to be frequency dependent. 

Substituting Equation (7.96) into Equations (7.94) and (7.95) 

gives the following system of four equations in four unknown 

variables:

( ) 0

D

D

2

0

2 0

0 0 0 2

0

2

0 + γ • + • + γ • = 















c

p

p p c

c

p

t

c ∇ u ∇ u u ∇ (7.97)

( ) 0

D

D

D

D 2

0

0 γ 0 + γ 0 • 0 + + c p = t

p p

t

p ∇ ∇ uu u

u

(7.98)

Equations (7.97) and (7.98) are referred to here as the “timeharmonic linearized Euler equations.” These equations can be 

solved uniquely to determine the perturbation variables, 

provided the appropriate boundary conditions are prescribed.

In the current subsonic flow problem, the linearized Euler 

equations in three space dimensions require three boundary
NASA/TP—2012-215653 220

conditions at the inflow (i.e., the source boundary), one 

boundary condition at the outflow (i.e., the termination 

boundary), and a boundary condition at the acoustically lined 

wall. The wall impedance boundary condition remains the 

Myers time-harmonic boundary condition (Eq. (7.32)). Two 

implementations of the inflow and outflow boundary conditions are presented in this section. The first implementation 

(Ref. 17) specifies the acoustic pressure and the two transverse 

perturbation velocity components at the source boundary Γs: 

s

s

s

s

v

u

p

v

u

p

Γ





















=





















along (7.99)

where ps, us, and vs are the known values of p, u, and v at 

points along Γs. Along the duct termination, a boundary 

condition of the form 

ρ0c0 [ζt]{w} = {p}alongΓt (7.100)

is specified. In Equation (7.100) {p} and {w} are vectors 

containing the values of p and w at nodes along Γt, and [ζt] is 

the normalized node impedance matrix that is either calculated 

from mode theory or measured. The second implementation of 

the boundary conditions (Ref. 18) splits ps, us, and vs into 

incident and reflected waves and specifies only the incident 

wave. The reflected wave is computed by invoking a nonreflecting boundary condition at the source plane. At the duct 

termination, a nonreflecting boundary condition is also 

specified, the details of which are discussed further in 

Reference 18.

7.6.2 Quasi-Three-Dimensional Code

The quasi-three-dimensional rotational flow code is applicable to duct geometries and flows for which the solution in 

one orthogonal direction (assumed to be the y-direction in this 

chapter) is separable, due to the fact that the sidewalls are both 

rigid and orthogonal to that direction. Quasi-three-dimensional 

analysis is valid only if the mean velocity field u0 does not 

have a component in the separable dimension and the other 

mean flow quantities are also independent of that dimension:

( , )

( , )

( , )

( , )

0

0 0

0 0

0 0

0 0

0

p p x z

x z

w w x z

u u x z

v

=

ρ = ρ

=

=

=

(7.101)

For the solution to be separable (as required in the quasi-threedimensional theory) the wall impedance must also be solely a 

function of the axial coordinate (i.e., ζ = ζ(z)). Further, the 

quasi-three-dimensional theory is mostly applicable to 

laboratory experiments conducted in rectangular geometries 

such as grazing-flow impedance tubes. Therefore, the quasithree-dimensional formulation is presented in Cartesian 

coordinates.

In the case of quasi-three-dimensional acoustics, the timeharmonic acoustic pressure and velocity field components are 

expanded into the following series of hard-wall duct modes:





 



 π = ∑

=∞

= D

m y p z x y pm x z

m

m

( , , ) ( , )cos

0

(7.102)





 



 π = ∑

=∞

= D

m y u z x y um x z

m

m

( , , ) ( , )cos

0

(7.103)





 



 π = ∑

=∞

= D

m y

v z x y vm x z

m

m

( , , ) ( , )sin

1

(7.104)





 



 π = ∑

=∞

= D

m y w z x y wm x z

m

m

( , , ) ( , )cos

0

(7.105)

where the hard-wall duct mode m takes on integer values and

D is the distance between the parallel rigid duct walls. 

Substituting Equations (7.101) to (7.105) into Equations (7.97) 

and (7.98) and writing the resulting equations in component 

form yields the following system of four equations in four 

unknown variables for each m.

{ }





























=





























=

0

0

0

0

w

v

u

p

E

E

E

E

E (7.106)

































∂

∂

+















∂

∂

+ γ





 





∂

∂

+

∂

∂  +



 





∂

∂

+

π

+

∂

∂

+ γ

































∂

∂

+















∂

∂ = ω +

2

0

0

2

0

2 0

0

0 0

0

2

0

0 2

0

0 2

0

c

p

z

w

c

p

x

c u

z

w

x

u

p

z

w

v

D

m

x

u

p

c

p

z

w

c

p

x

E i p c u

m m

m m m m

m m p m

(7.107)

x

p c zu w xu p u

z

u w xu p u

z

u w xu E i p u p u

m m

m m

m m u m

∂

∂  +



 





∂

∂

+

∂

∂

+





 





∂

∂

+

∂

∂

+ γ





 





∂

∂

+

∂

∂ = ωγ + γ

2

0

0

0

0

0

0 0

0

0 0 0 0

(7.108)
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 221 Chapter 7

m m m v m p D

m c

z

v

w

x

v E i p v p u

2

0

0 0 0 0

− π  +



 





∂

∂

+

∂

∂ = ωγ + γ (7.109)

z

p c zw

w x

w

p u

z

w

w x

w

p u

z

w

w x

w E i p w p u

m m

m m

m m w m

∂

∂  +



 





∂

∂

+

∂

∂

+





 





∂

∂

+

∂

∂

+ γ





 





∂

∂

+

∂

∂ = ωγ + γ

2

0

0

0

0

0

0 0

0

0 0 0 0

(7.110)

The computational domain is divided into N–1 elements in 

the axial direction and M–1 elements in the x-direction, as 

shown in Figure 7.3. These elements need not be equally 

spaced. Within each element, each acoustic variable is 

expanded as a series 

I I

I

I I

I

I I

I

I I

I

w w

v v

u u

p p

N

N

N

N

∑

∑

∑

∑

=

=

=

=

=

=

=

=

4

1

4

1

4

1

4

1

(7.111)

where NI, pI, uI, vI, and wI are the basis functions and nodal 

values of p, u, v, and w, respectively, at local node I. Here the 

subscript m has been dropped for the sake of brevity and the 

basis functions NI are linear two-dimensional polynomials 

a

z f a z

a

z f a z

f a z f b x

f a z f b x

f a z f b x

f a z f b x

=

= −

=

=

=

=

( , )

( , ) 1

( , ) ( , )

( , ) ( , )

( , ) ( , )

( , ) ( , )

2

1

4 1 2

3 2 2

2 2 1

1 1 1

N

N

N

N

(7.112)

The variable impedance ζ and mean flow quantities are 

represented in similar series but the nodal values of these 

quantities are known.

The discrete equation system that governs the quasi-threedimensional formulation is obtained by using a Galerkin finite 

element method to minimize the field residual error vector 

{E}. This is achieved by requiring that {E} be orthogonal to 

each basis function NI. The contribution to the minimization 

of the field error for each element is expressed in matrix form 

as 

{ } d d [ ]{ } 0 0

= Φ ∫ ∫ E I z x S b a

N (7.113)

where [S] is a 16×16 complex matrix for each element [I,J] 

and {Φ} is a 16×1 column vector that contains the unknown 

acoustic pressures, axial acoustic velocities, and transverse 

acoustic velocities at the four nodes of the element. The 

coefficients in the local stiffness matrix, [S], are computed in 

closed form. Appropriate shifting of rows and columns is all 

that is required to add the local element matrix [S] directly into 

the global matrix [SLEE2D]. This process leads to a set of linear 

matrix equations of the form 

[SLEE2D]{Φ} = {0} (7.114)

Here, the matrix [SLEE2D] is singular until boundary conditions 

are applied.

Before a nontrivial solution to Equation (7.114) can be 

obtained, the source, termination, and wall impedance 

boundary conditions must be imposed. Minimizing the 

boundary residual along the wall satisfies the wall impedance 

boundary condition 

( ) d 0

0 0

0 0

0 0

wallelements

 Γ =





















ρ ζ • ω

ρ +







ζ − ρ • + ∑ ∫Γ

I w c

p

i

c

p c w

u ∇ N

u n

(7.115)

Equation (7.115) is rewritten as a matrix equation 

{ }

{ }









 Φ = Φ = W

W w W W

u

p [S ]{ } {0},{ } (7.116)

where {pW} and {uW} are 2N×1 vectors containing the values of 

the normal component of acoustic velocities and acoustic 

pressures at the 2N nodes along Γw. Here, [Sw] is a complex 

2N×4N matrix containing the values of the wall impedance ζ at 

the 2N nodes of Γw and {0} is a null column vector of length 2N. 

The discrete form of the wall impedance boundary condition 

(Eq. (7.116)) is imposed on Equation (7.115) as a set of constraints. Likewise, the sound source boundary condition 

(Eq. (7.99)) and duct termination boundary conditions 

(Eq. (7.100)) are implemented as constraints on Equation (7.114).

Imposing the wall impedance, sound source, and duct 

termination boundary condition into Equation (7.115) leads to 

a modified system of equations of the form 

[SLEE2D]{Φ} = {FLEE2D} (7.117)
NASA/TP—2012-215653 222

where [SLEE2D] is a complex, asymmetric matrix with an order 

of 4NM, and {Φ} is a 4NM×1 column vector that contains the 

nodal values of the unknown acoustic variables (p, u, v, and w) 

at the NM nodes of the duct. The vector {FLEE2D} is a 4NM×1 

column vector that contains source effects. Equation (7.117) is 

solved using a standard band solver to extract the solution 

vector {Φ}. The computer code developed for the solution of 

the linearized Euler equations following the aforementioned 

two-dimensional finite element approach with a direct solve 

strategy is referred to as the “LEE2DDS” code in subsequent 

discussion.

7.6.3 Pseudo-Time Marching Codes

Pseudo-time marching codes have also been developed for 

solutions of the linearized Euler equations (Eqs. (7.97) and 

(7.98)) when coupled with the source, termination, and wall 

impedance (Eq. (7.32)) boundary conditions. The pseudo-time 

marching codes are available in three-dimensional, twodimensional, or axially symmetric form. The starting point for 

the pseudo-time marching method is to rewrite Equations (7.97) and (7.98) in a compact vector format for either 

three-dimensional, two-dimensional, or axially symmetric 

flows. In three dimensions, the compact vector format at a 

location (x, y, z) is 

{ }





























=

+ = 











∂

∂

+













∂

∂

+













∂

∂ − ω +

w

v

u

p

Q

D Q

z

Q C

y

Q B

x

Q i Q A

[ ] [ ]{ } 0

{ } [ ] [ ]

(7.118)

where [A], [B], and [C] are 4×4 matrices that contain mean 

flow effects and [D] is a 4×4 matrix containing terms related 

to the gradient of the mean flow field. (See Ref. 18 for the 

definition of these matrices.) For axially symmetric flows in 

cylindrical coordinates (r, θ, z) with spinning modes of the 

form e

imθ

, the compact vector format is 

{ }





























=

+ = 











∂

∂

+













∂

∂ − ω +

w

v

u

p

Q

D Q

z

Q C rQ i {Q} [A] [ ] [ ]{ } 0

(7.119)

and for two-dimensional flows the vector format is 

{ } 



















=

+ = 











∂

∂

+













∂

∂ − ω +

v

u

p

Q

D Q

z

Q C

x

Q i {Q} [A] [ ] [ ]{ } 0

(7.120)

For two-dimensional flows, [A], [C], and [D] are 3×3 

matrices. However, in axially symmetric and threedimensional flows [A], [C], and [D] are 4×4 matrices. Further, 

although the coefficients in these matrices are not explicitly 

written in this chapter, these coefficients are different in threedimensional, two-dimensional, and axially symmetric flows.

Adding a pseudo-time derivative to the compact vector 

form of the linearized Euler equations gives in three dimensions, 

[ ] [ ] [ ]{ }

{ } [ ]

D Q

z

Q C

y

Q B

x

Q i Q A Q

+













∂

∂

+













∂

∂

+













∂

∂ = − ω + 











∂τ

∂

(7.121)

in axially symmetric flows, 

{ } [ ] [ ] [D]{Q}

z

Q C

r

Q i Q A Q +













∂

∂

+













∂

∂ = − ω + 











∂τ

∂

(7.122)

and in two-dimensional flows 

{ } [ ] [ ] [D]{Q}

z

Q C

x

Q i Q A Q +













∂

∂

+













∂

∂ = − ω + 











∂τ

∂

(7.123)

where τ is the pseudo-time variable. The pseudo-time 

derivative is introduced so that Equations (7.121) to (7.123) 

may be marched in pseudo-time until the solution is steady. 

Thus, the steady solution to Equations (7.121) to (7.123) is the 

solution to Equations (7.118) to (7.120). In the following, we 

describe the pseudo-time marching procedure only in three 

dimensions (see Eq. (7.121)), since its simplification to axially 

symmetric flows (Eq. (7.122)) and two-dimensional flows 

(Eq. (7.123)) is relatively straightforward.

To begin, Equation (7.121) is discretized in pseudo-time 

using a forward-Euler scheme: 

[ ] [ ] [ ]{ }

{ } [ ] 1

1

n n n

n n n n

D Q

z

Q C

y

Q B

x

Q i Q A Q Q

+













∂

∂

+













∂

∂

+













∂

∂

+ ω =













∆τ

− + +

(7.124)
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 223 Chapter 7

where n is the pseudo-time index, ∆τ is the pseudo-time step, 

and the first term on the right-hand side of Equation (7.121) is 

treated implicitly. Equation (7.124) can then be written in a 

delta form 

[ ] [ ] [ ]{ }

{ } [ ] 1 { }

n n n

n n

D Q

z

Q C

y

Q B

x

Q Q i i Q A

+













∂

∂

+













∂

∂

+













∂

∂  = − ω + 

 



 + ω

∆τ

∆

(7.125)

Q Qn Qn ∆ = − +1 (7.126)

Upon approximating the spatial derivatives and implementation of boundary conditions, Equation (7.125) can be 

marched iteratively in pseudo-time until the solution is steady 

(i.e., until {∆Q} = {0}) to achieve the frequency domain 

solution. The spatial gradients are approximated using a 

fourth-order optimized finite difference technique, referred to 

as the “dispersion-relation-preserving” (DRP) scheme 

(Ref. 20). The DRP scheme is a central difference approximation to the gradient in each coordinate direction that uses a 

seven-point stencil. The DRP scheme is especially designed to 

minimize dissipation and dispersion errors with a resolution of 

eight points per wavelength. At and near boundaries of the 

computational domain, the DRP central difference scheme 

requires points from outside the computational domain. This is 

avoided by switching to a fourth-order optimized one-sided 

difference at and near these boundaries. Further, an eighthorder filtering scheme is applied to prevent spurious waves 

from contaminating the solution domain, as the solution is 

advanced forward in pseudo-time. The source, liner, and duct 

termination boundary condition are inserted into the pseudotime marching method by replacing each derivative (i.e., in 

these boundary conditions) by a fourth-order optimized onesided difference. All of the intricate details involved in the 

implementation of the DRP scheme to the acoustic equations, 

as well as implementation of other acoustic boundary 

conditions (these are not considered in this text), are described 

in detail in Reference 18 and are not presented herein.

The three-dimensional, axially symmetric, and twodimensional pseudo-time marching methods are implemented 

on a curvilinear mesh using uniform computational coordinates. Thus, solutions using arbitrary geometries are possible. 

In addition, the three-dimensional pseudo-time marching code 

uses a domain decomposition scheme that utilizes the 

message-passing interface (MPI) method to reduce wall clock 

time on parallel computers. The domain decomposition is only 

in the axial direction so that the other two dimensions are not 

parallelized. It should be noted that the two-dimensional and 

axially symmetric versions of the pseudo-time marching code 

available for this study are not currently parallelized. The 

computer codes developed for the solution of the linearized 

Euler equations in two-dimensions and three dimensions 

following the aforementioned pseudo-time approach with an 

iterative solve strategy are referred to in subsequent discussion 

as the “LEE2DIS” and “LEE3DIS” codes, respectively.

7.7 Results and Discussion

This section provides an assessment of the potential and 

rotational flow codes discussed in this chapter. This assessment uses the accuracy of the predicted attenuation, the 

computational efficiency, and the effects of input uncertainties 

as its primary metrics. Code results are compared with each 

other and to analytical solutions when they are available. For 

duct configurations where analytical solutions are not 

available, code results are compared with measured data 

acquired in either the NASA Langley grazing incidence tube, 

the NASA Langley Curved Duct Test Rig, or the NASA 

Glenn Advanced Noise Control Fan Rig.

7.7.1 NASA Langley Grazing Incidence Tube 

Simulations

A number of the codes were run for a geometry corresponding to the NASA Langley Research Center grazing incidence 

tube (GIT). This geometry was chosen for the following 

reasons:

(1) Experimental data was available to compare with code 

predictions.

(2) A detailed description of the apparatus and its capabilities already exists in the literature (Ref. 21).

(3) Currently, some of the codes only support a rectangular 

geometry.

(4) The GIT is frequently used to educe liner impedance (as 

discussed in detail in Chapter 6, “Uncertainty in Acoustic 

Liner Impedance Measurement and Prediction”) and the 

accuracy of the resulting impedance estimates is dependent 

upon the accuracy of the propagation model.

Sound and flow are directed in the same direction (only aftduct propagation was modeled), and the centerline Mach 

numbers range from 0.0 to 0.5. Results are presented for six 

selected excitation frequencies (500, 1000, 1500, 2000, 2500, 

and 3000 Hz).

Results are presented for the following three lining 

configurations:

(1) A hard-wall duct

(2) An infinitely long duct for which the lower and two 

sidewalls are rigid, and the upper wall contains a uniform liner. 

The impedance values of the uniform liner were judiciously 

chosen so that they spanned the ranges of resistance and 

reactance observed for a number of liners tested in the GIT.

(3) A 71.12-cm-long portion of a duct for which the lower 

wall and two sidewalls are rigid. The upper wall is also rigid, 

except for a 40.64-cm-long, uniformly treated section that is 

positioned 10.16 cm downstream of the source plane. The test 

liner was a conventional perforate-over-honeycomb material 

whose impedance was obtained from measurements in the 
NASA/TP—2012-215653 224

GIT. Because the upper wall of this duct incorporates a hardwall section, followed by a soft-wall section, followed again 

with a hard-wall section, it is referred to as the “segmented 

liner” example in the following discussion.

7.7.1.1 Accuracy Assessment

The most important metric in assessing a propagation code 

is the accuracy of the predicted attenuation. To assess the 

accuracy of the predicted attenuation, two example problems 

were chosen for which the attenuation could be determined 

analytically. The first example problem tests the ability of the 

in-duct codes to predict the attenuation of a plane wave 

propagating through a hard-wall duct with flow. It is well 

known that a plane wave does not attenuate as it propagates 

along a hard-wall duct, and therefore the codes should predict 

zero attenuation. The second example problem tests the ability 

of each code to predict the finite attenuation of a cut-on mode 

in a softwall duct with a uniform lining. For this case, an exact 

value for the attenuation is obtained using mode theory.

In the first example problem, the hard-wall attenuations 

were simulated for nine different conditions obtained from 

three excitation frequencies (1000, 2000, and 3000 Hz) and 

three mean-flow Mach numbers (0.0, 0.3, and 0.5). For each 

simulation, the source was planar (i.e., ps = 1) and the 

termination was nonreflecting (i.e., [ζt] = [I]). Simulations 

were run at standard atmospheric conditions: the mean static 

pressure was 101325.0 N/m2

, density was 1.2 kg/m3, and 

temperature was 293.0 K.

Predicted sound pressure level (SPL) attenuations from 

Equation (7.44) for the three Mach numbers and three 

frequencies are presented in Table 7.1 for the hard-wall duct. 

The first column in the table gives the excitation frequency in 

Hertz, and the second column gives the attenuation in decibels 

(exactly 0 for a hard wall). The predicted in-duct attenuations 

are presented for six of the eight codes in the suite. Note that 

predicted hard-wall attenuations are for three potential flow 

and three rotational flow codes from the suite. The three 

potential flow codes were the quasi-three-dimensional flow 

code (CH2DDS), the three-dimensional uniform-flow code 

(CH3DDS), and the three-dimensional code with the parabolic 

approximation (CH3DPA). The axially symmetric code (see 

Sec. 7.5.2) was used to compute radiated sound and therefore 

is not included in this comparison. The three rotational flow 

codes used to predict the in-duct attenuation were the 

quasi-three-dimensional rotational code (LEE2DDS), the twodimensional rotational flow code (LEE2DIS), and the threedimensional rotational flow code (LEE3DIS). The axially 

symmetric rotational flow code (see Sec. 7.6.3) was not run 

because the GIT is not an axially symmetric geometry. 

Table 7.1 shows that the predicted hard-wall attenuations from 

each of the six in-duct codes are in excellent agreement with 

the exact value of 0.

The second example tests the ability of each code to predict 

the finite attenuation of a cut-on mode in a softwall duct with 

a uniform lining. In this case, an exact value for the attenuation is obtained using mode theory. It is easily shown that the 

exact value of the SPL attenuation from Equation (7.44) for 

this configuration is 

∆SPL = 20log10 (e)I[Km,nL] (7.127)

where Km,n is the axial propagation constant. The transverse 

wavenumber λm,n satisfies the transcendental equation 

ikαm,n = ζ λm,n tan(λm,nH ) (7.128)

where 

c0

k ω =

(7.50)

2

0 , 0 ,

,

M M

1 2 















+















α = − k

K

k

K m n m n

m n (7.129)

TABLE 7.1.—SOUND ATTENUATION IN DECIBELS COMPUTED FOR PLANE WAVE

IN HARD-WALL DUCT WITH NONREFLECTING TERMINATION

[For different values of mean-flow Mach number M0.]

Excitation frequency,

Hz

Exact Acoustic propagation code

CH2DDS LEE2DDS LEE2DIS CH3DPA CH3DDS LEE3DIS

M0 = 0.0

1000 0.00 0.00 0.01 0.00 0.00 0.00 0.00

2000 0.00 0.00 0.02 0.00 0.00 0.00 0.00

3000 0.00 0.00 0.00 0.05 0.00 0.00 0.09

M0 = 0.3

1000 0.00 0.00 0.01 0.00 0.00 0.00 0.00

2000 0.00 0.00 0.01 0.00 0.00 0.00 0.00

3000 0.00 0.00 0.21 0.01 0.00 0.00 0.01

M0 = 0.5

1000 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2000 0.00 0.00 0.02 0.00 0.00 0.00 0.00

3000 0.00 0.00 0.06 0.00 0.00 0.00 0.00
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 225 Chapter 7

The λm,n and axial propagation constant Km,n are related by 

the dispersion relation 

( ) [( ) ( ) ]

( ) 2

0

2

,

2 2

0 0 ,

1 M

M 1 1 M

− −

± − − π + λ = m kD k

k

Km n m n (7.130)

The axial propagation constant Km,n is approximated by 

finding the roots of the transcendental equation (Eq. (7.128)). 

Note that for a given value of λm,n, the Km,n satisfying 

Equation (7.130) has two roots. Here, the root that corresponds to right-moving waves in the duct is chosen. It is easily 

shown that right-moving waves are identified as those waves 

for which the axial propagation constant Km,n has a zero or 

negative imaginary part and a positive real part. The method 

used to obtain the eigenvalues parallels the analytic continuation method discussed in Reference 22. However, we replace 

Mullers’ iterative scheme (Ref. 23) with Stewart’s adaptation 

of the Davidon-Fletcher-Powell method (Ref. 24) during the 

iteration phase of the analytic continuation method.

Attenuations due to a softwall were computed for 36 different conditions. These 36 conditions correspond to the same 

frequencies and Mach numbers as presented in Table 7.1. Four 

softwall impedances were used with each combination of 

Mach number and frequency. The sound source ps was chosen 

to be the least attenuated mode in the duct, the termination 

was chosen to be nonreflecting (i.e., [ζt] = ζexit[I]), and the 

mean static pressure, density, and temperature were those at 

the standard atmospheric conditions used in the hard-wall 

simulations. Here, ζexit is the characteristic impedance for the 

least attenuated right-moving wave and was computed from 

the exact expression for the outgoing wave impedance: 

m n

m n

K

k K

,

0 ,

exit

− M

ζ = (7.131)

Softwall attenuations predicted from CH2DDS, LEE2DDS, 

LEE2DIS, CH3DPA, and CH3DDS for the softwall duct with 

an anechoic (i.e., nonreflecting) termination and zero flow are 

compared to the exact attenuations in Table 7.2. The normalized resistance and reactance of the wall lining are given in the 

second and third columns, respectively, of the table. Recall 

that the sound source in this second example was a softwall 

duct mode. Results from LEE3DIS were not computed 

because the available version of LEE3DIS was designed to 

take source inputs in the form of hard-wall duct modes only. 

As shown in Table 7.2, CH2DDS, LEE2DDS, and CH3DDS 

are in excellent agreement with the exact results with one 

exception. Note that at 2000 Hz, LEE2DDS fails to predict the 

large attenuation of 143 dB when the impedance is

ζ = 0.5 – 0.5i. Attenuations predicted with LEE2DIS and 

CH3DPA are in good agreement with the exact attenuation 

except at the frequency and impedance corresponding to the 

peak attenuation of 143 dB. The failure of three of the codes 

(LEE2DDS, LEE2DIS, and CH3DPA) to predict the peak 

attenuation of 143 dB was somewhat surprising and should be 

further investigated. Generally speaking, LEE2DIS and 

CH3DPA are slightly less accurate than the other three in-duct 

codes in the absence of flow. Given the parabolic approximation of the CH3DPA code, its performance is quite good.

Softwall attenuations predicted at Mach 0.3 and Mach 0.5 

are also given in Table 7.2. Several high-Mach-number 

observations are noted. First, a significant reduction in the 

peak attenuation is observed at the higher Mach numbers (e.g., 

the highest attenuation is slightly more than 56 dB, compared 

with 143 dB at Mach 0.0). Second, CH2DDS, LEE2DDS, and 

CH3DDS are in excellent agreement with the exact results at 

each Mach number (note that LEE2DDS is in agreement with 

the exact attenuation now that the peak attenuation is much 

lower). Third, given the lower fidelity of the CH3DPA 

compared with the other codes, its predicted attenuation is still 

quite good, except at a few frequencies where wide-angle 

effects are more pronounced. Fourth, the attenuation of 

LEE2DIS is diverging from the exact attenuation and from the 

attenuation predicted by other codes as Mach number 

increases. This is an unexpected result, but may be due to use 

of the LEE2DIS plane-wave nonreflecting boundary condition. Recall that the exact attenuation (see the fourth column in 

Table 7.2) is computed assuming that the duct termination is 

nonreflecting. However, the LEE2DIS boundary condition 

that is used to predict the LEE2DIS attenuation will yield a 

nonreflecting termination only if the termination is located in a 

hard-wall section of duct. Because the duct termination was 

located in a softwall section of duct, this may explain the 

divergence of the LEE2DIS results.

7.7.1.2 Efficiency Assessment

Two important metrics often used to determine the efficiency of a computer code are wall clock time per central processing unit (CPU) and computer memory requirements. The 

suite of codes presented in this chapter solve a discrete set of 

acoustic equations using either a direct solve (e.g., CH2DDS, 

LEE2DDS, CH3DPA, or CH3DDS) or an iterative solve (e.g., 

LEE2DIS or LEE3DIS) strategy to compute the acoustic 

solution. The codes that are based on an iterative solve 

strategy were designed for computers with low memory (e.g.,

workstations and small clusters), whereas those that implement direct solve strategies are designed for high-memory 

machines (e.g., large clusters). Generally speaking, the wall 

clock time is not as important on low-memory machines 

because they are often under the control of a single user and 

there is little competition for CPU usage from other users. 

However, high-memory machines often support many users 

that compete for available wall clock time and CPUs. In this 

chapter, we choose to place focus on how these codes are used 

at Langley, where the most important metrics for deciding 

on the choice of a code are the wall clock time and number 

of CPUs. This occurs for three primary reasons:
NASA/TP—2012-215653 226

TABLE 7.2.—SOUND ATTENUATION IN DECIBELS COMPUTED FOR LEAST ATTENUATED

MODE IN SOFT-WALL DUCT WITH NONREFLECTING TERMINATION

[For different values of mean-flow Mach number M0.]

Excitation

frequency,

Hz

Normalized

resistance,

R[ζ ]

Normalized

reactance,

I[ζ ]

Exact Sound propagation code

CH2DDS LEE2DDS LEE2DIS CH3DPA CH3DDS

M0 = 0.0

1000 0.50 –0.50 61.70 61.70 59.50 56.22 68.77 61.10 

1000 0.50 0.50 50.00 50.00 49.80 48.32 43.15 49.50 

1000 2.00 –0.50 24.60 24.60 24.40 24.90 25.73 24.30 

1000 2.00 0.50 24.00 24.00 23.90 23.78 24.25 23.80 

2000 0.50 –0.50 143.00 143.00 61.70 66.26 79.00 142.00 

2000 0.50 0.50 19.30 19.30 19.20 19.19 35.52 19.10 

2000 2.00 –0.50 26.50 26.50 26.30 28.33 25.39 26.20 

2000 2.00 0.50 21.00 21.00 20.90 22.53 22.71 20.80 

3000 0.50 –0.50 36.10 36.10 35.90 39.53 24.06 35.70 

3000 0.50 0.50 10.30 10.30 10.20 14.18 8.35 10.20 

3000 2.00 –0.50 26.40 26.40 26.30 31.01 27.63 26.10 

3000 2.00 0.50 17.90 17.90 17.70 22.87 17.63 17.70 

M0 = 0.3

1000 0.50 –0.50 21.20 21.20 20.80 10.60 39.76 21.00 

1000 0.50 0.50 44.10 44.10 44.10 16.94 29.85 43.70 

1000 2.00 –0.50 13.70 13.70 13.60 15.81 15.57 13.50 

1000 2.00 0.50 15.00 15.00 15.00 15.00 15.03 14.90 

2000 0.50 –0.50 39.10 39.10 40.70 49.83 43.01 38.70 

2000 0.50 0.50 19.20 19.20 19.30 19.02 24.90 19.00 

2000 2.00 –0.50 15.20 15.20 15.10 21.53 15.31 15.00 

2000 2.00 0.50 14.00 14.00 14.00 18.37 14.28 13.80 

3000 0.50 –0.50 52.30 52.30 52.50 52.57 56.22 51.70 

3000 0.50 0.50 11.50 11.50 11.70 15.68 9.78 11.40 

3000 2.00 –0.50 15.80 15.80 15.80 26.46 16.73 15.60 

3000 2.00 0.50 12.80 12.80 12.90 21.62 12.72 12.70 

M0 = 0.5

1000 0.50 –0.50 13.30 13.30 13.00 8.69 31.12 13.10 

1000 0.50 0.50 38.90 39.00 39.10 15.83 25.53 38.50 

1000 2.00 –0.50 9.93 9.93 9.87 13.50 12.05 9.83 

1000 2.00 0.50 11.40 11.40 11.40 14.85 11.74 11.30 

2000 0.50 –0.50 23.20 23.20 23.10 14.34 31.47 23.00 

2000 0.50 0.50 18.50 18.50 18.70 15.22 20.48 18.30 

2000 2.00 –0.50 11.10 11.10 11.10 9.66 11.63 11.00 

2000 2.00 0.50 10.90 10.90 10.90 9.49 11.03 10.70 

3000 0.50 –0.50 46.80 46.80 45.60 36.99 51.67 46.30 

3000 0.50 0.50 11.60 11.60 11.90 16.16 9.80 11.40 

3000 2.00 –0.50 11.60 11.60 11.60 24.40 12.44 11.50 

3000 2.00 0.50 10.20 10.20 10.30 21.60 10.12 10.10 
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 227 Chapter 7

(1) codes are often run on a massively parallel computer 

within a multiuser environment where users must compete for 

both wall clock time and CPUs, (2) much emphasis is placed 

on impedance eduction, in which the selected propagation 

code must be run hundreds (sometimes thousands) of times to 

educe the unknown impedance of a test liner, and (3) Langley 

is working toward the ability to model full-scale, large 

commercial engine nacelles with high-fidelity codes to get a 

quality prediction (high-fidelity codes require significantly 

more wall clock time and CPUs than low-fidelity codes). 

Again, it is reemphasized that other research organizations 

may utilize these codes for other reasons or may have different 

computing facilities that may dictate choosing different 

metrics for deciding on the choice of a code.

Each computer code was converted to the same operating 

system, and an attempt was made to compare wall clock time 

per CPU for each code. Assessment of wall clock time was 

conducted with the Columbia clusters. Each Columbia cluster 

is an Altix 3700 system that uses the Itantium2 processor by 

Madison and has a clock speed of 1.5 GHz. One thousand 

CPUs (each with 2 GB RAM, random-access memory) are 

available on each cluster. Unfortunately, some of the codes 

were designed to run only on sequential machines (e.g., 

CH3DPA and LEE2DDIS), while others were designed to run 

on parallel machines (e.g., CH2DDS, CH3DDS, LEE2DDS, 

and LEE3DIS). Further, many of the parallel codes scale 

poorly with the number of CPUs (e.g., CH2DDS, CH3DDS,

and LEE2DDS), and others (e.g., LEE3DIS) have not been 

fully parallelized. Therefore, comparison of codes using wall 

clock time per CPU as a metric proved difficult. The decision 

was made, therefore, to run each code using the least amount 

of CPUs possible for a chosen grid, and to simply record the 

wall clock time for interested users.

A grid refinement study showed that all codes were converged on a uniform computational grid with 97 points in the 

axial and 21 points in the two transverse directions for all Mach 

numbers and frequencies. Thus, the three-dimensional and twodimensional codes were run on uniform 97×21×21 and 97×21 

baseline grids, respectively. Table 7.3 gives the wall clock time

on the baseline grid for three two-dimensional codes and three 

three-dimensional codes. The six columns in the table correspond to (1) the code name, (2) the number of spatial dimensions considered by the code, (3) the governing differential 

equations that are solved by the code, (4) the type of numerical 

method used to solve the governing differential equations, (5) 

the minimum number of CPUs required for the grid, and (6) the 

wall clock time consumed (in seconds). Although the wall clock 

times are those necessary to obtain the solution in the hard-wall 

duct, there was almost no change when the wall was lined with 

acoustic material. Note that the wall clock time increases by a 

factor of 19 when the cubic finite element analysis (i.e., with a 

direct solve strategy) is increased from two-dimensional 

(CH2DDS) to three-dimensional (CH3DDS). When the pseudotime marching code (i.e., with an iterative solve strategy) is 

increased from two-dimensional (LEE2DIS) to threedimensional (LEE3DIS), the wall clock time increases by a 

factor of 26. As expected, the lowest fidelity three-dimensional 

code in the suite (CH3DPA, using the parabolic approximation) 

is the most time efficient of the three-dimensional codes. 

CH3DPA is observed to be more than 2 orders of magnitude 

faster than CH3DDS, and nearly 3 orders of magnitude faster 

than LEE3DIS.

7.7.1.3 Uncertainty Assessment

The first example problem contained a hard-wall configuration, while the second considered a uniform liner. In these two 

example problems, the inputs to the prediction codes were 

known exactly, and exact solutions for the attenuations were 

determined analytically for comparison with code predictions. 

In this section, a third example is presented for which the 

upper wall incorporates the segmented lining configuration. 

Unfortunately, exact values for the attenuation were not 

available for this configuration, and predicted attenuations 

were therefore compared to measured data. Additionally, 

because the code inputs must be measured, they were not 

known exactly, but were subject to measurement uncertainty.

The measured attenuation values also carried uncertainty.

Therefore, comparisons between measured and predicted

attenuations are made on a statistical basis, and uncertainty 

bounds placed on both quantities. When taken in conjunction

TABLE 7.3.—WALL CLOCK TIME CONSUMED ON COLUMBIA CLUSTERS COMPUTING

SOUND ATTENUATION WITH IN-DUCT CODES ON BASELINE GRID 

Sound propagation code Number of

CPUsa

Wall clock time,

Code s

name

Spatial

dimensions

Governing differential

equations

Numerical method

CH2DDS 2 Convected Helmholtz Cubic finite element 8 48

LEE2DDS 2 Linearized Euler Linear finite element 8 60

LEE2DIS 2 Linearized Euler Pseudo-time-stepping 1 210

CH3DPA 3 Convected Helmholtz Parabolic approximation 1 7

CH3DDS 3 Convected Helmholtz Cubic finite element 32 912

LEE3DIS 3 Linearized Euler Pseudo-time-stepping 4 5400 a

Number of central processing units (CPUs) on Columbia clusters used for sound attenuation calculations.
NASA/TP—2012-215653 228

with Chapter 6, “Uncertainty in Acoustic Liner Impedance 

Measurement and Prediction,” these comparisons provide 

valuable insights into uncertainties expected from the 

impedance eduction process.

For this configuration, attenuation predictions were performed for a 140-dB plane-wave source in the GIT, in which 

the upper wall contains a 40.16-cm-long single-degree-offreedom (SDOF) liner as described in Table 6.1 of Chapter 6.

Results were acquired at three flow rates for frequencies ranging 

from 500 to 3000 Hz, in steps of 500 Hz. Data were acquired at 

each of these conditions at least eight times in order to allow for 

a small-sample statistical evaluation (Ref. 25). These tests were 

conducted at different times over a period of 1 year to minimize 

systematic errors due to atmospheric effects. Uncertainty 

intervals (95% confidence intervals) were computed for a 

number of parameters based on these measured results. The 

attenuation uncertainty intervals are represented as black 

squares in Figure 7.8 to Figure 7.12 (i.e., the separation 

between two black squares at a particular frequency represents 

the range of uncertainty in the measured attenuation). Similarly, 

uncertainty intervals for the following parameters were computed from these measurements in the GIT:

(1) Source SPL

(2) Average Mach number

(3) Liner impedance

(4) Exit impedance

(5) Mean static pressure

(6) Mean static temperature

Each of these parameters, which were used as inputs to the 

propagation codes, was assumed to be Gaussian distributed 

about their respective mean values.

Next, 31 simulations were conducted at each nominal test 

condition of interest (SPL, M0, and ζ) using a Monte Carlo 

approach. For each simulation, each input parameter was 

randomly selected from its respective Gaussian distribution, 

and the set of inputs was used with each of the propagation 

codes of interest. It should be noted that two of the codes 

(CH3DPA and LEE2DIS) could not take advantage of the 

measured exit impedance because they assumed anechoic 

terminations. Each simulation was run on the baseline grid 

discussed in the previous subsection.

Figure 7.8 to Figure 7.11 provide comparisons of measured 

and predicted attenuations (see Eq. (7.44)) when 31 simulations 

with each code were considered. The 95% confidence intervals 

for measurements and predictions are provided at each frequency of interest in each figure. The 95% confidence interval was 

the primary statistical metric of interest in this investigation, and 

the upper and lower bounds for each interval are represented by 

the same symbol in each figure. Essentially, this interval 

indicates that if another simulation were conducted, there is a 

95-percent confidence that the resulting attenuation would fall 

between these limits. In general, the mean values of the 

simulations are observed to track the mean values of the 

measured data quite well.

Figure 7.8.—Sound attenuation results from 8 grazing 

incidence tube (GIT) measurements and 31 simulations 

with each sound propagation code for liner 1, no flow, and 

source sound pressure level of 140 dB.

Figure 7.9.—Sound attenuation results from 8 grazing 

incidence tube (GIT) measurements and 31 simulations 

with each sound propagation code, resonance removed, 

for liner 1, no flow, and source sound pressure level of 

140 dB.
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 229 Chapter 7

Figure 7.10.—Sound attenuation results from 8 grazing 

incidence tube (GIT) measurements and 31 simulations 

with each sound propagation code for liner 1, mean flow 

Mach number M0 = 0.25, and source sound pressure level 

of 140 dB.

Figure 7.11.—Sound attenuation results from 8 grazing 

incidence tube (GIT) measurements and 31 simulations 

with each sound propagation code for liner 1, mean flow 

Mach number M0 = 0.40, and source sound pressure level 

of 140 dB.

It should be noted that the propagation codes assumed a 

uniform-flow profile. Thus, it is expected that part of the 

reason for the differences in the mean predicted and measured 

attenuation values is the absence of the mean-flow boundary 

layer in the predictive methods. In addition, the resonant

Figure 7.12.—Sound attenuation results from 8 grazing 

incidence tube (GIT) measurements and 6 simulations 

with each sound propagation code for liner 1, no flow, and 

source sound pressure level of 140 dB.

behavior of this SDOF liner is clearly evident at 1500 Hz in 

Figure 7.8 (no flow, SPL = 140 dB). The differences between 

predicted and measured SPL attenuations are accentuated at 

resonance because of the intrinsic behavior of single-layer 

liners. When one notes the levels of measured and predicted 

attenuation at 1500 Hz of at least 60 dB, these differences 

between predicted and measured results are of limited 

concern. Certainly, if a 40.64-cm-long liner provides greater 

than 60 dB (predicted or measured), it is performing quite 

well. It is anticipated that differences between predicted and 

measured attenuations would be significantly reduced for 

multilayer liners because the resonant behavior of such liners 

is a less dominant contributor to attenuation.

Because of the large confidence interval at resonance 

(1500 Hz) in Figure 7.8 (no flow, 140 dB), the attenuation 

scale is expanded in Figure 7.9 to more clearly show the 

results at the remaining frequencies. As expected, the 

confidence intervals grow as the mean-flow velocity is 

increased (see Figure 7.8 to Figure 7.11). Also, the confidence 

intervals for the measured data are observed to be less than for 

the predictive methods as Mach number increases. Figure 7.12

shows results for 6 simulations at Mach 0.0 with each code, 

for comparison with the 31 simulations shown in Figure 7.8. 

This information is also provided in tabular form in Table 7.4. 

Here, the mean attenuation and 95% confidence interval 

uncertainty (in dB) are given for the predicted attenuations 

when 31 and 6 simulations were considered. As described in 

Coleman and Steele (Ref. 25), the uncertainty values are the 

product of the Student’s t factor and standard deviation σ in 

the predicted attenuation. As expected, the scatter (confidence 

interval) is observed to decrease as the number of simulations
NASA/TP—2012-215653 230

TABLE 7.4.—GRAZING INCIDENCE TUBE MEAN SOUND ATTENUATION (μ) IN DECIBELS

AND 95% CONFIDENCE INTERVAL UNCERTAINTY VALUES (tn ∗ σ)

a

[For Liner 1, mean-flow Mach number M0= 0.00, and source sound pressure level = 140 dB.]

Excitation

frequency,

Hz

Sound propagation code

CH2DDS LEE2DDS LEE2DIS CH3DPA

μ |tn ∗ σ| μ |tn ∗ σ| μ |tn ∗ σ| μ |tn ∗ σ|

31 simulations (tn = 2.042)

500 2.22 0.35 2.16 0.35 2.36 0.35 1.22 0.52

1000 10.12 0.88 10.30 0.90 10.14 0.90 11.90 0.97

1500 80.78 23.35 61.02 3.64 41.27 0.31 68.99 2.21

2000 8.00 0.77 8.09 0.79 8.60 0.74 22.07 1.23

2500 1.91 0.29 2.01 0.29 2.29 0.27 1.76 0.24

3000 2.01 0.26 2.05 0.20 1.90 0.17 1.56 0.17

6 simulations (tn = 2.571)

500 2.11 0.56 2.05 0.57 2.26 0.58 1.05 0.84

1000 10.14 0.90 10.32 0.88 10.14 0.84 11.90 0.87

1500 83.18 43.00 60.98 6.80 41.25 0.39 68.17 3.40

2000 8.23 0.97 8.32 1.01 8.79 0.94 22.36 2.05

2500 1.91 0.35 2.00 0.31 2.33 0.20 1.80 0.18

3000 2.05 0.22 2.06 0.20 1.92 0.13 1.58 0.13

a

tn is Student’s t factor and σ is standard deviation.

is increased. This decrease in scatter with an increase in the 

number of simulations was observed for all conditions 

evaluated. It is noted that the Monte Carlo approach used 

herein has assumed that all input parameters were uncorrelated. In fact, this assumption is likely to be incorrect (i.e., some 

of the parameters may be correlated). If they are correlated, 

inclusion of this information would likely cause the uncertainty intervals to decrease.

7.7.2 NASA Langley Curved Duct Test Rig

Simulations

To illustrate the progression of testing that may be performed in other facilities, a series of predictions was also 

carried out for the NASA Langley Curved Duct Test Rig 

(CDTR) (Ref. 26). The CDTR affords the opportunity to test 

the codes in a larger geometry than the GIT, and in an 

aeroacoustic environment for which the effects of higher-order 

propagating modes can be isolated and evaluated. Some 

insight into the potential use of the CDTR for impedance 

eduction may also be obtained from this study. Although a 

further uncertainty analysis is desirable, this was precluded by 

the availability of only one data set. As time was also limited, 

only the two codes (i.e., CH3DPA and CH2DDS) requiring 

the least wall clock time were considered. In addition to 

allowing investigation of higher-order mode effects, the 

CDTR is also intended to improve the understanding of the 

behavior of duct treatment in curved ducts. For example, the 

aft bypass duct flow path of aircraft engines is often curved to 

accommodate the engine core. Therefore, the design of the 

CDTR allows the baseline straight rectangular design to be 

modified with horizontal offsets of up to one duct width, with 

the aim of determining whether use can be made of curvature 

to enhance liner performance. The test section cross section is 

rectangular in order to facilitate the design and manufacture of 

candidate duct liner configurations, and it is relatively large 

(scaled to between 25 and 50 percent of the bypass duct of 

most modern engines). Airflow through the duct is designed to 

be typical of bypass duct flow. In this subsection, attenuations 

measured with the straight CDTR configuration are compared 

with those predicted using the in-duct codes.

The CDTR test section modeled in each code is 38.10 cm 

high, 15.54 cm wide, and 197.36 cm long. A 81.28-cm-long 

test liner was inserted into the left sidewall so that the leading 

and trailing edges of the liner were located 58.29 and 

57.81 cm from the source and termination planes, respectively. 

The right sidewall consists of another liner sample, which was 

covered with tape to simulate an acoustically hard wall. The 

test liner consists of an impervious backing sheet, a 2.8-cmthick honeycomb core, and a perforate cover sheet (i.e., 

similar to the SDOF liner of the previous section). An 

illustrative test configuration is shown in Figure 7.13. 

Frequencies from 500 to 2400 Hz were generated upstream of 

the liner test section, and the relative amplitudes and phases at 

each of the acoustic drivers were chosen such that the (0,0), 

(1,0), or (0,1) mode was dominant. (Note: First index refers to 

vertical (parallel to the liner) mode and second index refers to 

the spanwise (perpendicular to the liner) mode.) The results 

provided here are for the “no flow” condition.
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 231 Chapter 7

Figure 7.13.—Curved Duct Test Rig (CDTR) liner test section 

with straight liner installed, top removed, view looking 

downstream.

Figure 7.14.—Curved Duct Test Rig (CDTR) sound attenuation 

measured and predicted with two sound propagation codes; 

no flow, incident mode (0,0), and source sound pressure 

level of 130 dB.

A 51×1555 (spanwise and axial directions) evenly spaced 

grid was used to model the CDTR in CH2DDS, whereas the 

CH3DPA grid utilized 17, 33, and 81 points in the spanwise, 

vertical, and axial directions, respectively. Both CH3DPA and 

CH2DDS use the modal amplitudes and phases in the hardwall section upstream of the liner as source input. These were 

obtained from acoustic pressures measured with flushmounted microphones in the walls of the CDTR. The codes

also require the impedance of the test liner as input. The test 

liner impedance values were educed from measurements in the 

GIT using a sample liner of the same design as that placed in 

the CDTR left sidewall. The CH3DPA assumes a nonreflecting termination, whereas CH2DDS uses the measured 

termination impedance to construct the node impedance 

matrix ([ζt]). In the attenuation comparison to follow, the 

measured mode amplitudes in the hard-wall sections upstream 

and downstream of the liner were used to determine the 

acoustic pressure field present in the CDTR via modal 

expansion. The axial velocity needed to compute the intensity 

(Eq. (7.40)) was determined from this modal expansion. 

Similarly, the numerical solutions obtained from CH2DDS in 

the hard-wall sections of the duct upstream and downstream of 

the liner were decomposed into hard-wall duct modes, and the 

axial velocity was computed using this mode expansion. The 

CH3DPA code is formulated in terms of acoustic potential, 

from which the acoustic pressure and velocity may be directly 

computed. Based on the acoustic pressure and axial velocity 

field, Equation (7.43) was then used to compute both the 

measured and numerical values of attenuation. It is these 

quantities that are compared in this section.

Figure 7.14 compares the attenuation measured in the 

CDTR to that computed using the CH3DPA and CH2DDS 

computer codes with a plane-wave source. The plane wave 

had 130 dB incidence SPL and was isolated approximately 

20 dB above all other modes. Discrepancies in measured and 

predicted attenuation are quite small except near the peak of 

the attenuation curve. An impedance variability study has been 

performed, and it has been observed that in the vicinity of the 

sharp attenuation peak, normalized educed reactance changes 

of ±0.1 lead to significantly different attenuations predicted by 

the in-duct codes. The effect of an error in the educed 

impedance was barely noticeable at frequencies away from the 

frequency of peak attenuation. This behavior is very similar to 

that observed in the GIT results of Figure 7.8 and is due to the 

SDOF liner considered.

Until now, no results have been presented for sources other 

than plane waves. Figure 7.15 compares the measured and 

predicted attenuations for the first nonplanar mode to cut on 

(i.e., the (1,0) mode) in the CDTR. Again, the first index refers 

to the vertical-mode order (i.e., in the long dimension) and the 

second index refers to the spanwise-mode order (i.e., in the 

short dimension). This vertical mode was isolated at least 

10 dB above all other propagating modes. As shown in 

Figure 7.15, the measured attenuation and that predicted by 

the in-duct codes are in very good agreement. Note that the 

attenuation for this nonplanar mode is observed to peak at 

approximately the same frequency as the plane-wave mode 

(between 1000 and 1100 Hz). It is not surprising that the shape 

of the attenuation spectrum for the (1,0) mode source would 

be similar to that for the (0,0) mode source, as the mode 

number in the direction normal to the liner is the same. At 

frequencies above 1500 Hz, the measured attenuation is 

slightly greater than the predictions, but by no more than 2 dB.
NASA/TP—2012-215653 232

Figure 7.15.—Curved Duct Test Rig (CDTR) sound attenuation 

measured and predicted with two sound propagation codes; 

no flow, incident mode (1,0), and source sound pressure 

level of 130 dB.

Figure 7.16.—Curved Duct Test Rig (CDTR) sound attenuation 

measured and predicted with two sound propagation codes; 

no flow, incident mode (0,1), and source sound pressure 

level of 130 dB.

For a source consisting of the spanwise mode closest to the 

plane-wave mode (i.e., the (0,1) mode), the attenuation does 

not show the same “peak-dominated” behavior, and the 

measured and in-duct code attenuations do not agree as well as 

for previous source specifications. This is the case in

Figure 7.16, where the (0,1) mode was generated and isolated 

at least 10 dB above other propagating modes in the CDTR. 

Although there is some similarity between the measured and 

predicted data trends, the magnitude of the predicted attenuation is approximately half of the measured values at frequencies above mode cut-on. Similar trends were observed when 

the (1,1) mode was isolated in the duct, although these results 

are not presented. Currently, indications are that the primary 

cause of the discrepancy is likely compliance of the taped 

right sidewall. This appears possible because the predicted 

attenuations, which assume a rigid sidewall, fall below the 

measured attenuations (except for the CH3DPA code at the 

frequencies of 1500 and 1600 Hz).

7.7.3 NASA Glenn Advanced Noise Control Fan 

Simulations

Section 7.7.1.3, “Uncertainty Assessment,” focused on induct attenuation prediction uncertainties based on input 

parameters, because it relates directly to the impedance 

modeling and eduction discussed in Chapter 6, “Uncertainty in 

Acoustic Liner Impedance Measurement and Prediction.” In 

many instances, efficient prediction of the far-field radiated 

noise is also of interest. In fact, it is an essential tool in

assessing the community noise impact of low-noise concepts. 

Therefore, for completeness, example acoustic radiation 

predictions are presented that employ the approaches of 

Section 7.5.2, “Axially Symmetric Code,” and Section 7.5.4, 

“Three-Dimensional Code With Parabolic Approximation,” 

referred to here as “CH2DIE” and “FWH3D,” respectively. 

Currently, the FWH3D is connected to the in-duct results of 

CH3DPA. However, development is underway to allow for 

use with the CH2DDS, CH3DDS, and LEE2DDS propagation 

codes. It should also be noted that the pseudo-time marching 

codes described in Section 7.6.3 follow the FWH3D paradigm 

and implement a frequency-domain Ffowcs WilliamsHawkings formulation. However, predictions are not presented because of time constraints and the similarity with the 

FWH3D approach.

Predictions were made for the NASA Glenn Advanced 

Noise Control Fan (ANCF) rig, which is a low-speed fan 

testbed designed for noise reduction concept testing (Ref. 27). 

In addition to collection of far-field data, the ANCF allows for 

the insertion of a rotating microphone rake (Ref. 28) to 

measure the interaction modes of the ducted fan. Therefore, 

for selected test configurations, in-duct rotating rake measurements and far-field acoustics measurements may be 

obtained. A general schematic of the axisymmetric rig is 

presented in Figure 7.17.

The example cases considered are the by-product of calculations performed in conjunction with colleagues at the NASA 

Glenn Research Center. Based on rotating rake data, inlet and 

aft predictions were performed for the (2,0) mode at the bladepassing frequency (BPF) of 533 Hz. For the inlet case, the 

source mode was prescribed at an axial location of –30 cm 

(see Figure 7.17), with an amplitude of 6.27 Pa, phase of

–121.6°, and duct Mach number of 0.130. Predictions were 
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 233 Chapter 7

obtained at 15 equally spaced locations on a 366-cm arc 

centered on the inlet plane origin. For the aft case, the source 

mode was prescribed at an axial location of 156 cm, with an 

amplitude of 8.14 Pa, phase of 2.3°, and duct Mach number of 

0.175. Predictions were obtained at 15 equally spaced 

locations on a 457-cm arc centered on the exhaust plane 

origin. The proximity of the source location to the inlet or 

exhaust planes leads to the use of a short duct section for the 

internal propagation calculations, thereby minimizing the 

influence of any in-duct propagation errors. For the aft case, 

the CH2DIE predictions include shear layer modeling by 

default. For the FWH3D model, both aft-baseline and shearlayer-corrected predictions were performed. Illustrative 

internal and pseudo-duct meshes are shown in Figure 7.18 and 

are represented with white and green wireframe, respectively. 

Note that although the geometry is axisymmetric, the FWH3D 

calculations were performed over the fully three-dimensional 

geometry. Comparisons for the full prediction set are provided 

in Figure 7.19. Some of the discrepancy at large off-axis 

radiation angles may be due to differing extents to which the 

models are able to account for engine cowl shielding and edge 

effects. For the aft predictions, differences in nacelle trailingedge thickness used in each model may also be the cause 

of some discrepancy in the peak levels. Note that for the

FWH3D aft results, inclusion of the shear-layer correction 

increases the peak directivity level and shifts its location 

forward. The comparisons are encouraging and provide 

motivation for the further use of the approaches. It is expected 

that recent ANCF data collected under the Engine Validation 

of Noise and Emissions Reduction Technology (EVNERT) 

task of the Quiet Aircraft Technology (QAT) Program will 

provide an excellent opportunity for further validation work.

Figure 7.17.—NASA Glenn Advanced Noise Control Fan 

(ANCF) rig.

Figure 7.18.—Internal and pseudo-duct Advanced Noise Control Fan (ANCF) computational 

meshes.
NASA/TP—2012-215653 234

Figure 7.19.—Comparison of FWH3D and CH2DIE predictions 

of sound radiated from a duct for Active Noise Control Fan 

(ANCF); mode (2,0) and blade-passing frequency (BPF) = 

533 Hz.

7.8 Concluding Remarks and 

Recommendations

This chapter has been used as a research umbrella, underneath which a suite of acoustic duct propagation and radiation 

codes has been gathered together for the first time. The suite 

consists of the most commonly used NASA Langley codes, a 

code from academia, and three codes recently developed at 

Boeing with partial NASA funding. These codes support 

propagation through acoustically treated inlet and aft-fan ducts 

in the presence of mean flow, as well as radiation to the far 

field. Collectively, they are believed to be a representative 

cross section of the state-of-art in the liner industry. The 

following is a brief summary of contributions provided in this 

chapter:

1. The basic assumptions underlying each code were 

quantified.

2. Each code was evaluated on the same massively parallel 

computer system (i.e., the Columbia clusters) using identical 

grids.

3. The predicted attenuations in a hard-wall duct were 

computed for nine combinations of frequencies and Mach 

numbers, and were compared to known values determined 

from analytical models.

4. The predicted attenuations (for each code) over a section 

of an infinitely long duct with a uniform impedance liner 

along the top wall were computed for 36 combinations of 

Mach number, frequency, and lining impedance, and were 

compared to values obtained from mode theory.

5. Attenuation measurements were made with a conventional perforate-over-honeycomb liner in the NASA Langley 

grazing incidence tube (GIT) and were compared to code 

predictions. Results were compared for a 140-dB incident 

sound pressure level for three flow rates and for source 

excitation frequencies from 500 to 3000 Hz in 500-Hz 

increments.

6. Limited code predictions were compared with attenuations measured in the NASA Langley Curved Duct Test Rig, 

which has a geometry closer to that of a full-scale engine than 

the GIT and allows for higher-order mode effects to be 

evaluated.

7. Example far-field acoustic predictions were conducted 

for the NASA Glenn Advanced Noise Control Fan Rig 

geometry.

The following primary conclusions have resulted from this 

investigation:

1. Increases in wall clock time of an order of magnitude or 

more are observed for three-dimensional codes relative to the 

corresponding two-dimensional versions of the same codes.

2. Attenuations predicted with each code are in excellent 

agreement with exact results for the hard-wall duct.

3. Attenuations predicted with the CH2DDS, LEE2DDS, 

CH3DDS, and CH3DPA codes over a portion of an infinitely 

long duct with uniform acoustic treatment compare well with 

results from mode theory for the 36 combinations of Mach 

number, frequency, and wall impedance used in this study. Of 

these four codes, the CH3DPA is considerably more time 

efficient and is only slightly less accurate. The LEE2DIS 

attenuation predictions compare well with mode theory at low 

Mach numbers, but tend to diverge from mode theory as the 

flow Mach number is increased.

4. Attenuations predicted for a conventional perforate-overhoneycomb liner installed in the GIT compare well with 

measured attenuations. As expected, the uncertainty (attenuation 95% confidence interval) is proportional to the amount of 

attenuation (i.e., small changes in the code inputs at a 

frequency where significant attenuation occurs will result in 

sizable changes in attenuation).

5. Attenuations were predicted with the CH3DPA and 

CH2DDS codes for planar and higher-order vertical modes 

(zero-order spanwise mode) in the CDTR. These predictions 

were based on liner impedances educed for a similar liner in 

the GIT and are observed to agree well with measured 

attenuations.

This investigation has provided valuable insights with 

regards to strengths and weakness of several propagation 

codes. The following items are recommended for further 

research and are expected to form the basis for continuing 

code development at NASA Langley Research Center.

1. More efficient three-dimensional solvers should be 

incorporated into the three-dimensional propagation codes,
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 235 Chapter 7

such that these codes can be used to efficiently perform 

parameter studies and to model engine nacelles closer to full 

scale. A reduction in wall clock time by at least 2 to 3 orders 

of magnitude is desired.

2. Many of the codes included in the current investigation 

were not initially designed to take advantage of current and 

future computer architectures. Where possible, these codes 

should be upgraded to take advantage of these architectures.

3. The effects of the mean boundary layer should be incorporated into the three-dimensional propagation codes to 

improve their fidelity.

4. If possible, the fidelity of the CH3DPA code should be 

increased (while maintaining its current efficiency). An 

ongoing effort is underway to develop a multipass version of 

this code, which is expected to significantly increase the 

fidelity of the results with minimal reductions in efficiency.

5. Discrepancies between attenuations measured in the 

CDTR and those predicted with the CH3DPA and CH2DDS 

codes, for sources with a dominant, higher-order spanwise 

mode, should be further evaluated. This should include an 

uncertainty analysis of the measurement and prediction 

processes for this duct geometry.

6. The divergence between LEE2DIS results and those 

computed with the other codes as the mean-flow Mach 

number is increased should be further evaluated. Every 

indication is that the source of the discrepancy is the termination boundary condition.

7. Initial far-field prediction comparisons were encouraging, and it is expected that recent ACNF data collected under 

the QAT Program will be a source for further validation.

In addition, a parallel effort will be conducted to develop a 

propagation code for the evaluation of extended-reaction 

liners. It is expected that this code will be based on approaches 

described herein for evaluation of locally reacting liners.

7.9 Acknowledgments

The authors wish to express appreciation to Tony Parrott 

and Mike Jones for their time and input in connecting this 

effort to Chapter 6, “Uncertainty in Acoustic Liner Impedance 

Measurement and Prediction.” The authors also extend sincere 

gratitude to Carol Harrison for the care in which she conducted extensive tests to generate the measurement database used 

in this investigation. They also thank Carl Gerhold, Brian 

Howerton, and Martha Brown for their assistance in the 

measurement and impedance prediction processes.

Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 237 Chapter 7

Appendix A.—Nomenclature

A.1 Acronyms

ANCF Advanced Noise Control Fan

BPF blade-passing frequency

CDTR Curved Duct Test Rig

CH2DDS convected Helmholtz two-dimensional direct 

solver

CH2DIE convected Helmholtz two-dimensional infinite 

element

CH3DDS convected Helmholtz three-dimensional direct 

solver

CH3DPA convected Helmholtz three-dimensional 

parabolic approximation

CPU central processing unit

DRP dispersion-relation-preserving

EVNERT Engine Validation of Noise and Emissions 

Reduction Technology 

FWH3D Ffowcs Williams-Hawkings three-dimensional

FW-Hpds Ffowcs Williams-Hawkings (equation) with 

penetrable data surfaces

GIT grazing incidence tube

LEE2DDS linearized Euler equations two-dimensional

direct solver

LEE2DIS linearized Euler equations two-dimensional

iterative solver

LEE3DIS linearized Euler equations three-dimensional

iterative solver

MPI message-passing interface

QAT Quiet Aircraft Technology

RAM random-access memory

SDOF single degree of freedom

SPL sound pressure level

A.2 Symbols

[A], [B] matrices for constructing the linearized Euler 

equations 

a width of finite element

b height of finite element

c speed of sound

C constant in Equation (7.4)

[C], [D] matrices for constructing the linearized Euler 

equations 

D distance between two parallel rigid sidewalls

[DD] diagonal matrix in decomposition of [S]

Dt

D material derivative

d length of a finite element

E total acoustic power

{E} error residual vector

e unit vector in cylindrical coordinate system

{F} column vector containing source effects

f linear or cubic polynomials

H height of duct

h arc length in a coordinate direction

I acoustic intensity

[I] identity matrix

i unit imaginary number

I[⋅⋅⋅] imaginary part of complex expression ⋅⋅⋅

K axial propagation constant 

k freespace wave number 

L length of duct

[L] lower triangular matrix in decomposition of [S] 

M number of nodes in transverse x-direction

M0 uniform-flow Mach number

M0 Mach number vector

m mode number 

N number of nodes in z-direction

N finite element basis function

n pseudo-time index

n outward unit normal vector to Γt

NL1 nonlinear term from Equation (7.6) defined in 

Equation (7.9)

NL2 nonlinear term from Equation (7.7) defined in 

Equation (7.10)

p fluid pressure

Q number of nodes in the transverse y-direction of 

the duct

(r, θ, z) cylindrical coordinates 

R[⋅⋅⋅] real part of complex expression ⋅⋅⋅

SPL sound pressure level 

[S] finite element stiffness matrix

[T(z)] splitting matrix

tn Student’s t factor

t time

[U] upper triangular matrix in decomposition of [S]

u scalar component of u in x-direction

u particle velocity vector 

v scalar component of u in y-direction

W weighting function 
NASA/TP—2012-215653 238

w scalar component of u in z-direction

(x, y, z) Cartesian coordinates 

γ ratio of specific heat at constant pressure to that 

at constant volume in fluid 

λ transverse wavenumber 

ζ normalized acoustic impedance of wall lining 

θ angular cylindrical coordinate

Γ surface bounding Ω; union of Γs, Γt, and Γw

(ξ1, ξ2, ξ3) generalized curvilinear coordinates 

ρ fluid density 

σ standard deviation 

τ pseudo-time variable in rotational pseudo-time 

marching codes 

[τ] shear stress tensor 

Φ node coefficients 

φ acoustic velocity potential 

ω circular frequency

Ω computational volume

∇ gradient vector 

Subscripts:

b baffle 

CH2D convected Helmholtz equation, two-dimensional

CH3D convected Helmholtz equation, threedimensional

exit exit 

e element 

I index 

inc incident 

J index 

LEE2D linearized Eulers equations, two-dimensional

m mode number 

n mode number 

(r, θ, z) cylindrical coordinate

ref reflected 

reference reference 

s source 

t duct termination 

w duct walls 

0 mean or steady flow 

I inner region

II outer region 

Superscripts:

~ an acoustic or perturbation quantity 

(

–

) a trial solution 

^ a total fluid quantity 

+ positive traveling – negative traveling 

* complex conjugate 
Assessment of Acoustic Propagation and Radiation Codes for Locally Reacting Liners in Flow Ducts

NASA/TP—2012-215653 239 Chapter 7

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Status—Shear Layer Refraction and Noise Radiation. AIAA–

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NASA/TP—2012-215653 241

Chapter 8—Jet Noise Prediction

James E. Bridges and Abbas Khavaran8

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Craig A. Hunter

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

Summary

An assessment exercise investigated three jet noise prediction methods that are in NASA’s possession: an empirically based 

model and two models based on the acoustic analogy theory. The assessment started by identifying a suite of jet flows covering a 

wide range of nozzle geometries, bypass ratios, flow speeds, temperatures, and flight speeds. The data from far-field acoustic 

measurements, and for some cases advanced flow measurements, were assembled. The accuracy of the measured data was 

established by comparing measured data taken in different facilities, using different measurement techniques, and documented by 

different authors. In addition, comparisons of measured data were made with analytical results. This determined experimental 

uncertainty bands about the acoustic data and established the uncertainty in the input flow solutions used in the acoustic analogy 

noise prediction codes. Finally, the results of the prediction codes were directly compared with far-field acoustic data, with the 

error being directly computed and compared over the entire range of jet flows for all codes. From this overview, recommendations 

for future improvements in jet noise prediction methods are made.

The empirical code assessed was the Stone Jet Noise module (ST2JET) contained within the Aircraft Noise Prediction Program 

(ANOPP) Level 25 aircraft noise prediction code. This code predicts both jet mixing noise and shock-associated noise. It is well 

documented and represents the state of the art in acoustic prediction codes where virtual sources are associated with various 

aspects of noise generation and are combined to predict the noise spectral directivity for a given jet plume. A total of 265 jet noise 

cases were run on the ST2JET code, with run times of the order of fractions of a second apiece and with no additional input 

beyond simple geometric and flow parameters. Considering that the internally mixed nozzle systems are approximated two 

different ways by the code, 408 runs were actually performed and analyzed here. 

Two acoustic analogy jet noise prediction codes were also evaluated. These codes predict the jet mixing noise, but not the 

shock-associated noise component. Fewer cases were examined with the acoustic analogy prediction codes because these methods 

require substantially more resources, typically an external Reynolds-averaged Navier-Stokes (RANS) solution to the jet plume, 

followed by numerical processing of the plume data for source strength as well as the propagation effects, integrated over the 

entire jet plume. The cases evaluated do span much of the parameter space but much more sparsely than in the empirical model.

All predictions were compared against experimental data from the NASA Glenn Research Center jet noise rigs. Far-field noise 

data were themselves validated against other high-quality published jet noise datasets. In addition, a large amount of flow-field 

data was obtained using the NASA facility, which was required to validate the RANS solutions that were used as input for the 

acoustic analogy codes. The flow-field data were also validated against available published data. The cross-facility comparisons 

were used, in conjunction with component analysis, to establish the experimental uncertainty of the data.

Neither empirical nor acoustic analogy models predicted the overall acoustic power of subsonic axisymmetric nozzle flows to 

within the experimental uncertainty for all cases. The empirical code ANOPP did not predict the spectral directivity within 

experimental uncertainty for most cases, having systematic disagreements at high frequencies especially at downstream angles. 

Consequently, the projected effective perceived noise level (EPNL) values were off by several decibels for sample cases studied, 

an intolerable situation in practice, where EPNL values need to be known to within fractions of a decibel. However, for axisymmetric jets, the ANOPP code was more robust than the acoustic analogy codes, and produced a consistent level of error for a broad 

range of jet flows. The acoustic analogy code JeNo v1.0 predicted noise spectral directivity to within experimental uncertainty for 

subsonic cold jets, but deviated when either the jet speed approached or exceeded the speed of sound or the jet temperature was 

elevated. JeNo did capture the impact of nonaxisymmetric jets with azimuthal periodicity greater than 4, but did not capture the 

azimuthal directivity effect from low-order asymmetries such as offset nozzles. The acoustic analogy code Jet3D was able to 

predict the noise level and the spectral content of high-speed hot jets at forward and side angles, but incorrectly predicted the noise 

level and its peak frequency at aft angles. The Jet3D code did not predict cold jets very well, missing both the spectral shape and 

the peak frequency.
NASA/TP—2012-215653 242

8.1 Introduction

When jet aircraft were first introduced, observers were 

awed by their potential for high levels of thrust as well as the 

incredible sound levels they generated. The level of effort to 

tame this source of noise quickly elevated from an engineering 

problem to a full research topic as it became clear that the 

major source of the tremendous noise was not the vibrating 

surfaces as envisioned by classical acoustics and noise 

engineering, but the turbulent mixing of the exhaust plume. 

Thus understanding the noise generation mechanism in the 

absence of solid surfaces became the primary problem in jet 

noise. Considerable resources have been devoted to the topic, 

and many research papers have been written on the subject, 

yet aeronautical engineers acknowledge that prediction of jet 

noise remains a highly empirical art compared to other 

engineering disciplines. Unlike solid mechanics and computational fluid dynamics (CFD), where complex designs have 

benefited strongly from the advent of the computer, the same 

is not true in aeroacoustics. The problem may be attributed to 

the complicated and poorly understood relationship between 

turbulence and noise and our limited ability to accurately 

compute certain turbulence parameters.

Jet noise is a byproduct of turbulent flow, a nearly negligible fraction of the flow energy as the thrust of the aircraft 

engine converts from steady kinetic energy to unsteady fluid 

motion and heat via viscous dissipation. Since turbulence 

remains difficult to robustly quantify, jet noise is equally 

difficult to predict. Empirical relations have yielded certain 

scaling laws for simple exhaust geometries. Yet first-principle 

theoretical approaches have not benefited from the same level 

of success, and have often been frustrating to researchers in 

the field. For basic engineering work, empirical methods (e.g., 

programmed interpolations between measured cases) remain 

at the forefront, with occasional unpleasant surprises, especially when subtle changes in the flow produce unexpected noise 

changes. 

Many years of research have finally produced relative 

success in implementing the acoustic analogy models in jet 

noise prediction using Reynolds-averaged Navier-Stokes 

(RANS) code flow solutions as input. Such methods make an 

attempt to define a closed-form relationship for certain 

statistical parameters of interest in turbulence, such as spacetime correlations, preferably in compliance with available 

data. Since statistical measurements are often carried out 

under restrictive flow conditions due to lab and instrumentation limits, it is not uncommon for such models to be pushed 

beyond their intended envelope and include assumptions that 

are true only at limited or special cases. Parameters not 

available in the data bank may also rely solely on the physical 

intuition of the researcher. But how well do these methods 

predict the spectral directivity of jet noise over a broad range 

of jet flow conditions, and how successful are they in transforming predictions of the turbulent kinetic energy into 

predictions of jet noise? These are questions to be answered, 

quantitatively, in this assessment.

This chapter will introduce jet noise prediction codes that 

were available in the assessment exercise. These codes are 

discussed briefly, and references are provided for more indepth discussions of their development and modeling details. 

Sample runs illustrate the sensitivity of each code relative to 

input parameters. The CFD code Wind-US, which generated 

the mean flow and turbulence information for the acoustic 

analogy codes is also discussed briefly with an overview of 

the validation work that puts an error bar on the input to the 

acoustic analogy codes. Next, experimental data sources are 

introduced and details of the measurement systems are given. 

This information is used to determine the uncertainties in both 

acoustic predictions and the CFD input to the acoustic codes. 

A set of metrics is then established by which the predictions 

and experimental results are compared, and the results of each 

code are catalogued. The chapter closes with a summary of 

each code’s performance and an overview of the state of the 

art in jet noise prediction. Appendix A lists the acronyms and 

symbols used in this chapter.

8.2 Discussion of Codes

Jet noise predictive codes fall into three categories:

(1) Empirical—based on scaling laws and interpolations on 

measured data

(2) Acoustic analogy—based on a RANS solution to the 

mean flow and turbulence

(3) Direct—based on direct numerical solution to the set of 

Navier-Stokes equations 

The first category describes the majority of codes used in 

practice today, whether they are simple interpolations across 

existing corporate databases, such as the ESDU method 

(Ref. 1), or more complicated schemes that attempt to 

subdivide the jet into a number of noise sources depending on 

the geometric details and operating conditions of each jet, 

such as the Stone jet method (Ref. 2). The latter code is 

currently contained within the NASA Aircraft Noise Prediction Program (ANOPP) code (Ref. 3). These codes typically 

require as input parameters some description of the flow 

condition such as velocity and temperature plus geometric 

parameters such as nozzle areas, extension lengths, and 

perhaps hydraulic perimeter in the case of enhanced mixing 

devices. Empirical codes are quick to run and are typically 

suitable for large systems studies where thousands of evaluations of overall system noise and performance may have to be 

carried out to find an optimal design space with less emphasis 

on the details.

Codes in the second category attempt to make use of formulations such as acoustic analogy theories that describe the 

transfer of energy from turbulence to noise. Typically these 

codes require as input a RANS CFD solution for the mean 

velocities, temperatures, turbulent kinetic energy, and length 

and time scales. Models are proposed for the space-time 

correlations of noise generating turbulent eddies in the jet, and 
Jet Noise Prediction

NASA/TP—2012-215653 243 Chapter 8

subsequently the noise produced from each volume element is 

propagated through the inhomogeneous acoustic medium to 

the far-field observer. As long as the statistical properties of 

turbulence are correctly incorporated into the source model, 

the acoustic analogy approaches are expected to provide the 

noise estimate using a superposition of noise emitted from 

independent correlation volume elements that comprise the jet. 

Details of the source correlations as related to velocityvelocity or velocity-temperature fluctuations at two points 

separated in space and time are still unresolved, and it is not 

uncommon to see some important source terms discarded due 

to lack of data for validation and/or the inability of the RANS 

solvers to provide the required input parameters. Aside from 

the generation mechanism associated with the source, 

propagation of sound through the non-uniform base flow also 

poses computational challenges in a general three-dimensional 

jet. Even in the relatively subtle axisymmetric jets, effects 

such as scattering of sound by turbulence are completely 

overlooked and the effects on the sound propagation are 

attributed only to non-uniformities in mean velocity and 

temperature.

Codes in the third category compute the time-dependent 

turbulent flow directly, resolving scales of motion as small as 

permitted by the grid density and computer storage capacity. 

In large eddy simulations (LES), the smaller scales (subgrid 

scale terms) are modeled, and the Navier Stokes equations are 

filtered for the larger scales that are considered as sources of 

jet noise. Consequently, predicted noise levels tend to be much 

lower at high frequency compared to data. In principle, one 

should be able to compute the pressure fluctuations directly 

along with other variables of interest. Because our interest is 

usually the far field, computationally it is advantageous if the 

flow calculation is stopped outside the hydrodynamic domain 

and matched with an acoustic solution to propagate to a farfield observer point. This type of calculation as exemplified by 

LES requires massive computational resources and is still in 

its infancy. For these reasons, this category of predictive code 

is not considered in the present assessment exercise.

8.2.1 Empirical Prediction Tool: Stone Jet Noise 

Module (ST2JET) Within ANOPP

The purpose of the NASA Aircraft Noise Prediction Program ANOPP is to predict noise from aircraft, accounting for 

the effects of the aircraft characteristics, its engines, its 

operations, and the atmosphere, in an attempt to meet noise 

certification rules. During certification exercises, the aircraft 

follows an arbitrary flight path in the presence of an observer 

on the ground. Throughout this operation, various noise 

sources on the aircraft emit noise with defined power, 

directional, and spectral distribution characteristics, all of 

which may depend on time. Noise propagates through the 

atmosphere subject to the atmospheric attenuations, and 

reaches to the vicinity of the observer. The observer receives 

noise signals from the direct ray as well as ground reflection. 

A complete background on ANOPP is given in Chapter 2, 

“Aircraft System Noise Prediction.”

The ST2JET module is based on the semi-empirical model 

developed by J.R. Stone of Modern Technologies Corporation 

(Ref. 4). The method was developed from data with bypass 

ratios ranging from 5.0 to 14.9 obtained from free-jet facilities 

at NASA Glenn and NASA Langley Research Centers as

well as the anechoic free-jet facilities at Lockheed Martin 

Corporation and General Electric Company. The ST2JET 

module is an update to the older STNJET module in ANOPP 

and extends the ANOPP jet noise prediction capability to 

higher bypass ratio engines for a full range of nozzle configurations including jets with inverted velocity profiles. The jet 

mixing noise and broadband shock noise components 

(associated with supersonic jets) also include corrections for 

forward flight effects. 

The components of jet mixing noise are inner stream mixing noise, outer stream mixing noise, and merged stream 

mixing noise. The inner stream mixing noise (intermediatescale mixing noise) is a mid- to high-frequency-range noise 

source generated by the shear between the primary jet stream 

and either the secondary jet stream or the ambient air for a 

circular single-stream jet. The outer stream mixing noise 

(small-scale mixing noise) is relatively high-frequency noise 

generated by the small-scale turbulent mixing near the nozzle 

exit. The merged mixing noise (large-scale mixing noise) is 

the lowest frequency noise source generated by the mixing of 

the large-scale coherent structures in the jet with the ambient 

flow well downstream of the nozzle exit. Nozzles with center 

plugs have an additional plug separation noise component 

caused by the flow disturbance at the tip of the center plug. 

The plug separation noise is a high-frequency component 

associated with the primary stream. The method also includes 

procedures for computing nozzle exit perimeter suppression 

effects, such as might be found with chevrons, tabs, chutes, or 

other exit suppression devices that do not separate the flow 

stream. These effects are applied to the three mixing noise 

components. 

Broadband shock noise is evaluated for supersonic shockcontaining jets in the primary and/or the secondary stream. 

Co-annular nozzles with a center plug but without exit perimeter suppression devices are treated as a special case. For such 

nozzle configurations, if both streams are supersonic and the 

secondary stream total pressure is greater than the primary 

stream total pressure, the outer stream shock noise is replaced 

with the downstream merged shock noise. Otherwise shock 

noise is predicted using the outer stream shock component only.

8.2.1.1 Description of Input Parameters

The ST2JET module requires nozzle flow properties and 

geometric dimensions of the nozzle. The nozzle exit flow 

parameters can be provided by the “Jet Noise Parameters 

Module” within ANOPP or specified by the user directly. The 

main input parameters are nozzle diameters at exit and throat
NASA/TP—2012-215653 244

of core and bypass streams, plus temperature and jet velocity 

for both streams as well as the flight Mach number. 

8.2.1.2 Description of Output and Options Used

The ST2JET prediction method combines the component 

noise from sources described above into a single 1/3-octave 

band spectrum at each polar angle. The output is a table of the 

mean-square acoustic pressure as a function of frequency, 

polar directivity angle as measured from jet inlet axis, and 

azimuthal directivity angle when the noise field is not 

axisymmetric. Jet exhaust noise from circular nozzles is 

independent of the azimuthal directivity angle; however, it is 

tabulated as a constant function of azimuthal angle so that the 

output table is compatible with other noise tables generated by 

ANOPP. For the definition of these angles, see Figure 2.3 in 

Chapter 2, “Aircraft System Noise Prediction.”

In this assessment exercise, only the ST2JET source module was invoked, and the main ANOPP code was used to 

propagate the sound to a set of observers at the same far-field 

locations and frequencies as the experimental measurement. In 

cases involving simulated forward flight, ANOPP output as 

expressed in a fixed-observer frame of reference was postprocessed, and transformed to “infinite wind tunnel” coordinates with the observer moving with the source, essentially 

removing the Doppler shift from the data. In all cases,

1/3-octave data from ANOPP were imported into the NASA 

Glenn digital acoustic data system (DADS) where it was 

converted to narrowband power spectral density for later 

manipulation. The frequency f was normalized using nozzle 

diameter D (based on total area) and jet velocity U (ideally 

expanded), and expressed as a Strouhal number St = fD/U. 

The sound spectral density was also integrated over each

1/3-octave frequency band for smooth presentation of data. 

8.2.2 Acoustic Analogy Prediction Tools

Flow-induced noise, in principle, is associated with small 

pressure fluctuations that radiate at the speed of sound from a 

turbulent flow to a distant observer. Rather than solving the 

governing fluid dynamic equations directly from a noisegenerating region to the far field, an equivalent problem may 

be posed in the form of an inhomogeneous wave equation. 

Subsequently, a solution is written in closed form as a 

convolution of the source with an appropriate Green’s 

function as is done in classical acoustics. Lighthill’s secondorder wave equation (Ref. 5 and 6) is the simplest form of the 

acoustic analogy because its Green’s function, at any frequency of interest, is that of the reduced Helmholtz equation. A 

successful implementation of this particular analogy is rather 

difficult because of the complexity of the source term and the 

simplifying assumption required to model the source. Other 

variants of the wave operator were later proposed that place 

less demand on the source but also require a more complicated 

Green’s function. Lilley’s third-order wave equation (Ref. 7)

is an example of such an analogy where flow effects such as 

source convection and mean-flow refraction are explicitly 

described by the operator part of the equation. A practical 

implementation of any acoustic analogy involves several 

steps: (1) computation of a nonradiating base flow, 

(2) modeling of the source term(s), and (3) computation of the 

Green’s function. In general, step (1) is achieved by considering the base flow as the mean flow computed by a RANS 

solver. A two-equation turbulence model is also used to 

evaluate the turbulent kinetic energy and its dissipation rate as 

needed for the source modeling. Step (3) in general, is 

computationally intensive and in some instances high- or lowfrequency analytical approximations to the Green’s function 

are sufficient and computationally efficient.

A formal solution to any acoustic analogy model may be 

written as

p t Gt q ( , d ,| , , d ) ( ) ( )

∞

−∞

′ =τ τ τ ∫ ∫y

x xy y y (8.1)

where p′ denotes the fluctuations in pressure p at the observer 

location x and at time t; q is the source intensity per unit 

volume at source location y at the time of emission τ, and G is 

the relevant Green’s function. Following the computation of 

the autocorrelation function 

( ) ( ) ( ) 2 , 1 , ,d 2 p p tp t t

−

τ = ′ ′ + τ ∫ x x x

T

T T (8.2)

the Fourier transform is used to compute the acoustic spectrum

( ) ( ) 2 2 1 , ,d 2 P pei

∞

ωτ

−∞

ω= τ τ

π ∫ x x (8.3)

where T denotes some large but finite time and ω is the radian 

frequency. The two acoustic analogy tools described next, 

Jet3D and JeNo v1.0, use Lighthill’s and Lilley’s formulations, respectively.

8.2.2.1 Jet3D

The Jet3D code (Ref. 8) is based on a straightforward 

application of Lighthill’s Acoustic Analogy (Ref. 5 and 6) in 

three dimensions. Manipulating the equations of motion, a 

second-order, inhomogeneous wave equation is derived,

2 2 2

2

2 2

ij

j i j

T

c

t x xx ∞

∂ρ ∂ρ ′ ′ ∂ − = ∂ ∂ ∂∂ (8.4)

where 2 ( ) T uu p c ij i j = + ρ − ρ δ −σ ∞ ij ij is the Lighthill stress 

tensor, ui is the fluid velocity vector, c∞ is the ambient speed 

of sound, ρ is the fluid density, p is pressure, δij is the 

Kronecker delta, and σij is the viscous stress tensor. In the far

field, pressure and density fluctuations are related by 2 p c∞ ′ ′ = ρ . The source term
Jet Noise Prediction

NASA/TP—2012-215653 245 Chapter 8

( ) ( ) 2 , , ij

i j

T

q

y y

∂ τ

τ =

∂ ∂

y

y (8.5)

and the corresponding Green’s function

( ) ( )

R

t R c G t t

π

δ − τ − = ∞

4

x, y, (8.6)

where the distance between the source and receiver R = |x – y|. 

Substituting Equations (8.5) and (8.6) into Equation (8.1) 

formally solves for the far-field pressure p′. In deriving the 

acoustic analogy, Lighthill cast the complicated nonlinear jet 

noise problem into a simple analogy within the scope of 

classical acoustics; the flow field and complex flow-acoustic 

interactions (such as source convection and mean-flow 

refraction) in a real jet are replaced by a fictitious volume 

source distribution of acoustic quadrupoles radiating into a 

uniform ambient medium with a free-space Green’s function. 

This formulation makes the calculation of propagation a simple 

matter, but puts weight on modeling of the source terms to 

accommodate for flow-sound interaction. In practice, the 

viscous stress σij is neglected because of its small contribution, 

and the entropy source term ( ) 2 p c − ρ∞ is also neglected in 

unheated jets, although it could potentially become significant 

in heated jets. Of note in this assessment, the source modeling 

does not include the impact of the entropy source term; rather,

the source is represented by the Reynolds stress term ρuiuj. 

Specific details of the implementation of the Lighthill theory in 

the Jet3D code can be found in Chapter 9, “Propulsion Airframe

Aeroacoustic Interactions.”

Early validation of Jet3D was done using the Yamamoto 

et al. dataset (Ref. 9). Noise predictions were made for a 

heated Mach number M = 1.4 jet issuing from a convergentdivergent nozzle, exit diameter 13.7 cm (5.4 in.), operating at 

its design nozzle pressure ratio of 3.18, with a jet total 

temperature of approximately 956 K (1720 °R). The Jet3D 

noise predictions were made for 13 observer locations along a 

12-m (40-ft) radius arc (approximately 88 nozzle diameters) 

centered on the nozzle exit. For each observer, 1/3-octave 

band frequency sound pressure levels (SPLs) were computed 

over bands from 50 Hz to 80 kHz. 

For this assessment exercise, Jet3D was run using RANS 

CFD input from the Wind-US CFD code (Ref. 10). This led to 

some concern since Jet3D was calibrated using the PAB3D 

CFD code (Ref. 11). As a cross check, two of the nine cases 

listed in Table 8.1 were recomputed using Jet3D with RANS 

input from the PAB3D code. As expected, using the different 

flow solutions from the RANS codes caused differences in the 

computed noise spectra. Also, one of the cases was repeated 

with a higher resolution grid, but the changes in noise 

prediction were minimal. Figure 8.1 illustrates the differences 

in a typical computed flow solution by comparing

the predicted turbulent kinetic energy from the PAB3D and 

Wind-US codes with particle image velocimetry (PIV) data 

from the same facility as the noise data were acquired. 

Figure 8.2 shows the impact on the predicted noise when using 

two different computed flow solutions for the conditions of 

case 037 from Table 8.1.

Figure 8.1.—Turbulent kinetic energy (TKE) contours downstream from a nozzle. Comparison of

predictions from different CFD codes, PAB3D and Wind-US, and experimental particle image

velocimetry (PIV) data.
NASA/TP—2012-215653 246

TABLE 8.1.—ASSESSMENT CASES FOR JET3D

PREDICTIONS OF JET NOISE SPECTRAa

Case M Axial geometry Ma Ts,r nozid

003 0.51 Convergent 0.500 0.955 SMC000

007 0.98 0.902 0.842

022 0.37 0.492 1.767

025 0.68 0.901 1.770

027 1.01 1.330 1.759

034 0.30 0.484 2.624

037 0.56 0.901 2.702

040 0.92 1.483 2.703

268 1.40 C-D 2.20 2.530 SMC015 a

Nomenclature for table headings:

M ideally expanded Mach number

Axial geometry indicates if nozzle was convergent or convergentdivergent (C-D) 

Ma acoustic Mach number, U/c∞

Ts,r static temperature ratio, Ts/T∞

nozid nozzle identification

8.2.2.2 JeNo v1.0

JeNo v1.0 (hereafter referred to as “JeNo”) is also an embodiment of an acoustic analogy. Unlike the Jet3D code that 

follows the Lighthill analogy, JeNo follows a third-order 

convective wave equation associated with Lilley (Ref. 7). 

When this equation is linearized about a unidirectional 

transversely sheared mean flow, it may be expressed as

L qt Π = (x, ) (8.7)

where ( )

1

p po 1 Π= −γ is the pressure variable, po is the 

mean pressure, and p = p′ + po. Since the ratio p′/po is very 

small compared to 1 (on the order of 10–5

), the dominating 

term in the series expansion of the pressure variable Π

becomes p po Π≅ γ ′ where γ is the specific heat ratio of air. 

The operator L depends on the convective derivative

D D u x1 t t = ∂ ∂ + o∂ ∂ , where uo is the mean axial velocity, 

and x1 is the streamwise direction

2 2

2 2

2

1

D D 2

D D o o

j j jj

u

o L cc

t t x x x xx

− +

    ∂ ∂∂ ∂ ≡     ∂ ∂ ∂ ∂∂    

(8.8)

and the source term may be written as

1

D (,) 2 D

j j o

j j

u

q t

tx x x

∂ξ ∂ξ ∂ = − ∂ ∂∂

x (8.9)

where

(1 ) ( 1) j i j

i j

uu h

x x

∂ ∂Π ξ ≡ +Π + γ− ′′ ′ ∂ ∂ (8.10)

Figure 8.2.—Comparison of sound pressure levels (SPLs) 

predicted by Jet3D for a jet from a converging nozzle using 

input from different CFD codes, PAB3D and Wind-US, and 

experimental data. Case 037 from Table 8.1. Inlet angle 

θ = 90°.

Lilley’s formulation of the wave equation accounts for both 

the convection effect and the refraction of the sound that is 

caused by gradients in the jet mean velocity uo and sound 

speed co. Here ui

′ is a fluctuating velocity vector and h′ is 

enthalpy fluctuations in the flow. The entropy source term that 

was associated with the ( ) 2 p c − ρ∞ term in Lighthill’s acoustic 

analogy is now written in a more transparent form by using the 

energy equation. As seen above, this source relates to 

fluctuations in temperature through h′. When a nonradiating 

base flow is additionally subtracted from the governing 

equations, as described by Goldstein’s generalized acoustic 

analogy (Ref. 12), this source is shown to depend on fluctuations in total enthalpy. A full derivation of the theory behind 

JeNo, development of the propagator and source modeling is 

provided in References 13 and 14. 

In axisymmetric jets, the reduced form of the wave operator 

(Eq. (8.8)) at any frequency ω becomes the second-order, selfadjoint, compressible Rayleigh equation. Once the radial 

distribution of the mean velocity and temperature are specified, this equation is solved numerically at each frequency of 

interest to obtain the Green’s function, G(x y;ω). For 

comparison, the corresponding Green’s function in Lighthill’s 

acoustic analogy is simply the Fourier transform of Equation (8.6); that is, G(x y;ω) = exp(iωR/c∞)/(4πR).

As in Jet3D, JeNo does not model the enthalpy-related term 

in its source model and approximates the source term as 

( ) ( ) ( ) 2 2

1

D , 2 D

i j i j o

ij i j

u u u u u q t

t xx x xx

∂ ∂ ′ ′ ∂ ′ ′ ≅ −

∂∂ ∂ ∂∂ x (8.11)
Jet Noise Prediction

NASA/TP—2012-215653 247 Chapter 8

To include the enthalpy-related source term, dedicated 

RANS solvers are needed to provide the variance in total 

enthalpy as an additional input parameter to the noise code. 

Such solvers are currently under development and will not be 

discussed here. The source volume integration (dy) in 

Equation (8.1) may be subdivided into a composite of ring 

volume elements if the jet is axisymmetric. Nonaxisymmetric 

jets, however, pose additional difficulties, and in general five 

linear equations need to be solved in generalized threedimensional coordinates for the five components of a vector 

Green’s function. Such a vector function should be able to 

address the azimuthal variation of the sound field in both polar 

θ and azimuthal directions φ in unconventional (nonaxisymmetric) jets. A more practical type of computation currently 

employed in JeNo is a so-called 2.5-dimensional approximation that extends the axisymmetric Green’s function to a threedimensional jet. Such an approximation allows for the 

variation in source strength in the azimuthal direction, but 

convolves that with a Green’s function that is calculated along 

a specified azimuthal plane. For example, in the “line-ofsight” approach the Green’s function is calculated along a 

predefined azimuthal plane, referred to as the “line of sight,”

while the source density is allowed to change azimuthally as 

the volume integration is carried out. An alternative

2.5-dimensional approximation evaluates the Green’s function 

at the same azimuthal plane as the source (i.e., φ = φs

) and 

computes a new Green’s function at each azimuthal plane 

using the corresponding flow profile into the second-order 

compressible Rayleigh equation. This method resembles some 

form of azimuthal averaging of the sound field and is referred 

to as the “line-of-source” approximation.

Calibration constants for source amplitude, length scale, 

and time scale were determined for the best fit with a Mach 

0.51 unheated jet. Two of these constants work with the input 

turbulent kinetic energy and dissipation rate to set the local 

time- and length-scales. Subsequently, these parameters show 

sensitivity with respect to the specific RANS solver as well as 

the particular turbulence model within a single flow solver. 

For example, Figure 8.3 shows the spectral density computed 

by the JeNo code at 90° and 150° using the Wind-US RANS 

code to compute the flow for a cold jet with an acoustic Mach 

number of 0.5 with three different turbulence models: the

Figure 8.3.—Power spectral density (PSD) versus Strouhal number St of cold jet, acoustic Mach number Ma = 0.5, 

predicted by JeNo using RANS input with three turbulence models; and largest difference Δ between predictions. 

(a) Inlet angle θ = 90°. (b) θ = 150°.
NASA/TP—2012-215653 248

Figure 8.4.—Power spectral density (PSD) versus Strouhal number St of cold jet, acoustic Mach number Ma = 0.9, 

predicted by JeNo using RANS input with three turbulence models; and largest difference Δ between predictions. 

(a) Inlet angle θ = 90°. (b) θ = 150°.

standard Chien k–ε model, Mentor shear stress transport (SST) 

model, and the variable diffusion model. The details of each 

model, and sample velocity and turbulence comparisons, are 

examined in Georgiadis et al. (Ref. 15). Noise predictions that 

use the solutions from the same RANS solver but with the

three turbulence models are in close agreement, and the largest 

differences are at the lower frequencies. The difference in 

decibels is computed between the largest and smallest spectral 

value at each frequency among the three predicted spectral 

densities. Figure 8.4 shows a similar set of results for a cold 

jet with a 0.9 acoustic Mach number.

An alternative uncertainty assessment is shown for JeNo 

predictions in Figure 8.5, using flow input from two different 

RANS solvers. Here the flow-field simulation is achieved 

using identical grids and similar turbulence models (standard 

Chien k–ε model) but different flow solvers, Wind-US 

(Ref. 10) and Craft (Ref. 16). Parameter ∆ measures the 

difference in decibels between the JeNo predicted overall 

sound pressure levels (OASPLs)—Wind-US minus Craft—

and should be related to numerical algorithm and convergence 

criteria in each flow simulation.

The effect of the turbulent kinetic energy on the predicted 

OASPL directivity is shown in Figure 8.6. The input level of 

turbulent kinetic energy has been intentionally modified by 

±10 percent to show that it could have a 3.5- to 5.0-dB impact 

on the predicted noise level. 

8.2.3 Reynolds-Averaged Navier-Stokes (RANS) 

Tool: Wind-US

Input to acoustic analogy jet noise prediction codes consist 

of the grid file, the mean-flow parameters, plus turbulent 

kinetic energy k and its dissipation rate ε. Prior to evaluating 

the acoustic codes’ predictive capability, it was critical to 

assess the accuracy of the flow field. The degree to which the 

CFD predictions impact the accuracy of the acoustic predictions is determined once we know the noise code sensitivities 

to errors in the input flow parameters. As shown in the 

descriptions of the Jet3D and JeNo codes, the mean-flow 

parameters such as mean Mach number (velocity and temperature) could affect the propagation portion of the acoustic 

solution whereas parameters such as density, turbulent kinetic
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NASA/TP—2012-215653 249 Chapter 8

Figure 8.5.—Overall sound pressure level (OASPL) predicted by JeNo for jets at changing inlet angle

θ using two different RANS code flow solutions; difference Δ in predictions is (Wind-US – Craft).

(a) Acoustic Mach number Ma = 0.5. (b) Ma = 0.9.
NASA/TP—2012-215653 250

Figure 8.6.—Overall sound pressure level (OASPL) predicted by JeNo for cold jets at changing inlet

angle θ with ±10 percent change in RANS code turbulent kinetic energy (TKE); and difference ∆

in predictions. (a) Acoustic Mach number Ma = 0.5. (b) Ma = 0.9.

energy, and dissipation rate affect the predicted source

strength. Mean velocity and temperature and turbulent 

velocity have been measured for validation purposes. However, dissipation is very difficult to measure, and the quantity 

labeled as dissipation in most CFD codes is more a surrogate 

factor than a physically realizable quantity. Thus it is difficult 

to validate the dissipation fields from various CFD codes, and 

indeed this parameter is observed to vary most between 

different flow solvers. Hence (1) noise prediction codes were 

mostly evaluated using the CFD code on which they had been 

calibrated, and (2) only mean velocity and turbulent kinetic 

energy were directly compared with experimental data.

Jet3D has been used mostly with the flow solver PAB3D, 

and JeNo has been calibrated using the code Wind-US. Both 

codes are available to United States concerns and are open to 

researchers working to improve and modify the turbulence 

models and other aspects of the codes. A great deal of 

documentation exists for these codes and will not be repeated 

here. An in-depth analysis of the suitability of different 

turbulence models was carried out by Georgiadis et al. 

(Ref. 15) and should be referred to. Note that all CFD 

predictions for jet noise assessment were performed using the 

Mentor SST turbulence model. 

Shown in Figure 8.7 are the predicted turbulent kinetic 

energy distributions—in normalized form as k U —for the 

5.1-cm (2-in.) convergent nozzle operated at the conditions 

listed as cases 003, 007, and 040 in Table 8.1 corresponding to 

acoustic Mach numbers of 0.50, 0.90, and 1.48, respectively. 

The first two jets are unheated, and the last jet is at exit static 

temperature ratio of Ts,r = 2.70. Favorable agreement with the 

PIV measurements are observed in the turbulence levels, as well 

as the shortening of the core length due to the heat—which is 

the product of a faster jet spread and improved mixing.

8.3 Identification of Test Programs

In large part, jets chosen for the assessment were selected 

from datasets that had well-known uncertainties in noise 

measurement. First, the idiosyncrasies of the facilities, such as 

internal rig noise, anechoic character, and microphone 

placements, must be known. Issues such as sample time, 

accuracy of the set point over the duration of sampling, 

stability of the air supply controls, transfer functions of the 

signal conditioning equipment, calibration procedures and

policies all can play a role and produce subtle changes in the 

data. A very significant factor that has noticeable impact on
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NASA/TP—2012-215653 251 Chapter 8

Figure 8.7.—Distribution of normalized turbulent kinetic energy (TKE) for 5-cm

convergent nozzle; here, r is radial coordinate and x is axial distance, normalized 

over nozzle diameter D. Wind-US Reynolds-averaged Navier-Stokes (RANS)

predictions and particle image velocimetry (PIV) measurements. (a) Acoustic 

Mach number Ma = 0.5 unheated jet (case 003, Table 8.1). (b) Ma = 0.9 unheated 

jet (case 007). (c) Ma = 1.48 heated jet (case 040).
NASA/TP—2012-215653 252

the jet noise spectrum is whether the boundary layer at the 

nozzle exit is turbulent or laminar. Accuracy of ambient 

conditions during noise measurements and proper correction 

for atmospheric attenuation must also be documented. 

To properly evaluate the acoustic predictions, input parameters as predicted with the CFD codes had to be evaluated 

against data. This implied a comprehensive measurement of 

parameters such as mean velocity and turbulent kinetic energy 

at a wide range of temperatures and velocities of interest—in 

addition to the far-field noise for each jet. Very few datasets 

exist containing both turbulence and noise, especially in hot 

and/or supersonic flows. 

Over the years from 2002 to 2009, such a dataset has been 

compiled at NASA Glenn to be used in guiding prediction and 

validation efforts. Substantial effort has gone into quantifying 

the internal rig noise, electronic noise sources, and in comparing measurements of both flow and noise with highly qualified 

facilities that do not have the capability to measure both flow 

and noise. Both single- and dual-flow jet rigs were utilized 

with cross-rig comparisons used to reassure rig-independent 

measurements. Comparisons of single-stream jets were carried 

out against results from Boeing’s Low-Speed Aeroacoustic 

Facility jet rig, where the quality of the facility has been well 

documented. To validate dual-stream results, the test nozzles 

for several separate-flow configurations were tested at NASA 

Langley’s Low Speed Aeroacoustic Wind Tunnel to ensure 

that the internal rig noise was well understood and removed 

from data prior to the assessment exercise. 

8.4 Jet Noise Case Taxonomy

To parameterize the jet noise cases of interest, the following 

jet parameters were considered:

• Bypass ratio (BPR)

• Mach number (M = ideally expanded value computed 

using nozzle pressure ratio and total temperature)

• Acoustic Mach number (Ma = ideally expanded jet 

velocity/sound speed at ambient temperature)

• Static temperature ratio (Ts,r = ideally expanded static 

temperature/ambient temperature) 

• Total temperature ratio (Tt,r = total temperature/ambient 

temperature)

• Flight Mach number (Mfl = flight speed/ambient sound 

speed)

• Convergent and convergent-divergent (C-D) nozzles

• Internally and externally mixed nozzles

• Azimuthal base periodicity (m)

With this selection of parameters, taxonomy was established according to Table 8.2. Essentially, the cases include 

single-stream jets (BPR at 0) that are subsonic with

convergent nozzles (Configuration A, axisymmetric,

and Configuration B with chevrons) and supersonic with 

convergent-divergent nozzles (Configuration C). Different 

internal splitters changed the BPRs from 0.2 to 1.0 and 3.0 

(Configurations D, E, and F, respectively) for both subsonic 

and supersonic conditions. At BPRs of 5 and 8 (Configurations G and H) the data were obtained from an internally 

mixed nozzle test with axisymmetric splitter, and with 

strongly mixed lobed mixer and an externally mixed separate 

flow nozzle. At BPRs of 11 and above (Configuration I) all 

the data were acquired at externally mixed, separate-flow 

nozzle systems with two different area ratios. Several of the jet 

conditions with externally mixed nozzle systems at BPRs 5 

and above have datasets with and without forward flight.

8.5 Description of Facilities

Single-stream data primarily came from measurements on 

the Small Hot Jet Acoustic Rig (SHJAR, Figure 8.8). The 

SHJAR, located in the Aero-Acoustic Propulsion Laboratory 

(AAPL, Figure 8.9) at the NASA Glenn Research Center in 

Cleveland, Ohio, was developed to test jet-noise-reduction 

concepts at a low technology readiness level (TRL 1 to 3) and 

at minimum expense. As a jet-noise testing rig, the SHJAR 

was designed to minimize rig noise sources, incorporating the 

work of Viswanathan (Ref. 19) and Ahuja (Ref. 20) to achieve 

this goal. The rig is a single-flow jet rig that used 1034-kPa 

(150-psi) air supplied by several remotely located compressors. The maximum mass flow rate was 2.7 kg/s (6 lbm/s) and 

the maximum temperature air was 700 °C (1300 °F). A 

hydrogen-burning combustor, permitting a large range of 

temperatures, provided the heat. The air passed through a 

baffled muffler, followed by a settling chamber before 

reaching the nozzle. Two valves, a large main valve and a 

small vernier valve, controlled the rate of airflow, providing 

precise control over the entire range of operating conditions. 

Nozzle sizes from 2.5 to 7.6 cm (1 to 3 in.) in diameter were 

supported, although most data for this assessment was 

acquired using a 5.1-cm (2-in.) nozzle. The AAPL, which 

houses the SHJAR, is an 18.3-m (60-ft) radius geodesic dome 

lined with sound absorbing wedges that reduce sound 

reflection at all frequencies above 200 Hz. The jet exhaust is 

directed outside through a large door. An extensive study of 

the acoustic properties of the SHJAR rig and its validation are 

given in Brown and Bridges (Ref. 21).
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NASA/TP—2012-215653 253 Chapter 8

TABLE 8.2.—TAXONOMY OF TEST CASES FOR ASSESSMENT OF JET NOISE PREDICTION CODESa

Configuration BPR M Geometry Ma Ts,r Data sourceb

Axial Azimuthal

A 0 0.3 to 1.0 Convergent m = 0 0.35 to 1.5 0.85 to 2.7 SHJAR, Ref. 17, Ref. 18

B 0 0.5 to 1.0 Convergent m = 6 0.5 to 1.3 0.85 to 2.6 SHJAR

C 0 1.2 to 1.8 C-D m = 0 1.0 to 2.4 0.6 to 2.7 SHJAR, Ref. 17

D 0.2

0.6 to 1.0 Internal,

convergent

m = 0 0.8 to 1.5 0.8 to 2.9 SDF07

1.0 to 2.0 m = 0 1.0 to 2.4 1.0 to 2.9 SDF07

1.2 to 21.8 Internal, C-D m = 0 1.4 to 2.4 1.0 to 2.3 SDF07

E 1

0.6 to 1.0 Internal,

convergent

m = 0 0.8 to 1.5 0.8 to 2.9 SDF07

1.0 to 2.0 m = 0 0.9 to 2.4 0.8 to 2.3 SDF07

1.2 to 2.0 Internal, C-D m = 0 1.4 to 2.4 1.0 to 2.3 SDF07

F 3

0.6 to 1.0 Internal,

convergent

m = 0 0.9 to 1.5 0.9 to 2.9 SDF07

1.0 to 2.0 m = 0 1.0 to 2.4 0.8 to 2.3 SDF07

G 5

0.6 to 1.0

Internal,

convergent

m = 0 0.9 to 1.7 2.5 to 3.1 LDIM05

0.6 to 0.9 m = 8 0.9 to 1.7 2.6 to 3.1 LDIM05

0.6 to 0.9 m = 20 0.9 to 1.6 2.6 to 3.1 LDIM05

0.8 to 1.1 External,

convergent m = 0 1.0 to 1.6 1.8 to 2.4 HFXF07

H 8

0.6 to 1.0

Internal,

convergent

m = 0 0.9 to 1.7 2.5 to 3.1 LDIM05

0.8 to 0.9 m = 8 1.27 to 1.4 2.8 to 3.0 LDIM05

0.8 to 0.9 m = 20 1.3 to 1.4 2.8 to 3.0 LDIM05

0.7 to 0.8 External,

convergent m = 0 0.7 to 1.0 2.1 to 2.3 HFXF07

I

11 0.7 External,

convergent

m = 0 0.9 2.3 to 2.4 HFXF07

14 0.7 m = 0 0.8 to 0.9 2.4 HFXF07 a

Nomenclature for table headings:

BPR is bypass ratio. Values in table are approximate.

C-D is convergent-divergent.

M is ideally expanded Mach number; for dual stream flows, it is the higher M.

m is azimuthal base periodicity.

Ma is acoustic Mach number, U/c∞.

Ts,r is static temperature ratio, Ts/T∞.

b

Data sources are listed in Section 8.6, “Description of Test Hardware for Data Sources.”
NASA/TP—2012-215653 254

Figure 8.8.—Small Hot Jet Acoustic Rig (SHJAR).

For dual-stream test cases, data were acquired using the 

High Flow Jet Exit Rig (HFJER), which supplied air to the 

nozzle model at conditions similar to an aircraft engine. The 

HFJER sat at the exit of the Nozzle Acoustic Test Rig (NATR, 

Figure 8.9), a 1.3-m (53-in.) free-jet that provided the forward 

flight airflow around the nozzle at speeds up to Mach 0.35. 

The NATR sat in the middle of the AAPL mentioned above. A 

cutaway view of the HFJER is shown in Figure 8.10. Capabilities of the facilities are detailed in Reference 22. The use of 

NATR’s simulated forward flight conforms to industry 

standard practice, such as General Electric’s Cell 41 facility in 

Evandale, Ohio, and Boeing’s larger Low-Speed Aeroacoustic 

Facility in Seattle, Washington. 

8.6 Description of Test Hardware for 

Data Sources

All data used in this assessment were acquired within 

NASA-sponsored test programs over the period 2004 to 2007. 

Each data source is identified with a particular test set facility, 

and is intended to address a subset of cases, loosely grouped 

by BPR, illustrated in Table 8.2.

8.6.1 SHJAR

Most single-stream jet data acquired with nozzles attached 

to the SHJAR used the SMCxxx series model system. 

Originally conceived as a model system for parametric testing 

of chevron nozzles, its modular design allowed for a large 

number of nozzle concepts to be mounted such as chevrons 

and convergent-divergent nozzles in addition to the baseline 

axisymmetric convergent nozzle SMC000 (see Figure 8.11

and Figure 8.12).

Examples of nonaxisymmetric nozzles are SMC001, 

SMC005, and SMC006, each with six chevrons of identical 

dimensions except for the bending shape of the chevrons that 

determines the degree to which the chevron penetrates the 

flow (see Figure 8.12). For fully expanded supersonic jets, a 

family of five single-flow convergent-divergent nozzles was 

designed applying the method of characteristics (Ref. 23), 

each nozzle flow reaching a full expansion at the exit at a 

specified design Mach number Md. Figure 8.13 shows the 

cross section of the convergent-divergent nozzle SMC014 

with the lowest Md of 1.18. All five single-flow convergentdivergent nozzles are identified in Table 8.3.
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NASA/TP—2012-215653 255 Chapter 8

Figure 8.9.—Inside Aero-Acoustic Propulsion Laboratory (AAPL), showing Nozzle

Acoustic Test Rig (NATR) and overhead far-field microphone array used in NATR 

acoustic testing.
NASA/TP—2012-215653 256

Figure 8.10.—High Flow Jet Exit Rig (HFJER) in dual-flow mode.

Figure 8.11.—SHJAR nozzle system with SMC000 nozzle attached.
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NASA/TP—2012-215653 257 Chapter 8

Figure 8.12.—SHJAR nozzles used in this jet noise assessment.

Figure 8.13.—Convergent-divergent nozzle SMC014, design Mach number 

Md = 1.18. Dimensions are in centimeters (inches).

TABLE 8.3.—DESIGN MACH NUMBERS OF SINGLEFLOW CONVERGENT-DIVERGENT NOZZLES 

[Used for SHJAR jet noise measurements.]

Nozzle Design Mach number,

Md

SMC014 1.18

SMC015 1.4

SMC016 1.5

SMC017 1.66

SMC018 1.8

8.6.2 Supersonic Dual-Flow Hardware (Test 

Program SDF07)

For dual flows, several different exhaust systems were 

employed. The family of models from the supersonic dualflow tests SDF07 (see Table 8.2) featured internally mixed 

flows with variable bypass ratios. A series of splitters were 

fabricated which, when coupled with a special contraction 

section, produced four secondary to primary area ratios 

ranging from 0.2 to 2.0, designated as S1 to S3 in Figure 8.14, 

and with a convergent nozzle exhaust (C4) of diameter

10.2-cm (4-in.). To obtain fully expanded, dual flows, a series 

of convergent divergent nozzles with exit diameter of 10.2 cm 

were fabricated. The method of characteristics (Ref. 23) was 

used to design these nozzles for the fully expanded Mach 

numbers of 1.18, 1.4, 1.5, 1.6, 1.8, and 2.0. An example of a 

dual stream nozzle with area ratio of 0.2 (splitter configuration 

S1), and convergent-divergent exhaust at design Mach number 

of 1.18 (M8) is shown in Figure 8.15. Between variations in 

splitters to give area ratios and variations in nozzles to give 

different fully expanded Mach numbers, a wide range of 

supersonic and subsonic jet flows were obtained from 

approximate bypass ratio 0.2 to 4.7.

8.6.3 Long Duct Internal Mixer Hardware (Test 

Program LDIM05)

Examples of dual-flow nozzles with internal mixing from 

nonaxisymmetric splitters, both lobed mixers and chevrons, 

are shown in Figure 8.16. The nozzle system designated 

5000.00 had a convergent common nozzle and an axisymmetric splitter with plug sized to produce flows of roughly bypass 

ratio 5. In nozzle 5001.04 the splitter of 5000.00 is replaced 

with a chevron mixer having 6 outward and 6 inward chevrons, and in nozzle 5002.02 it is replaced with a lobed mixer 

having 20 deep lobes. Nozzles designated as 8000.00, 

8001.04, and 8002.02 followed the same convention, but with 

a larger plug to produce a bypass ratio of approximately 8.
NASA/TP—2012-215653 258

Figure 8.14.—Internally mixed, axisymmetric, dual-flow exhaust system with convergent nozzle and different bypass ratios 

(BPRs). S1 to S3 are splitters, PE1 is center plug, and C4 is convergent nozzle. (a) Nozzle C4S1PE1, BPR = 0.2.

(b) Nozzle C4S2PE1, BPR = 1. (c) Nozzle C4S3PE1, BPR = 3.
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NASA/TP—2012-215653 259 Chapter 8

Figure 8.15.—Internally mixed, axisymmetric, dual-flow 

exhaust system with convergent-divergent nozzle M8

shown with bypass ratio (BPR) = 0.2, splitter S1.

PE2 is center plug.

8.6.4 High-Flow Cross-Facility Hardware (Test 

Program HFXF07)

Externally mixed exhaust systems, both with internal plugs 

and external plugs, had fan nozzle diameters of 24.4 cm 

(9.6 in.) and different core nozzles and plugs to achieve 

bypass ratios from 5 to roughly 14. Figure 8.17 gives the 

cross-sectional views of the four separate flow nozzles tested 

in the High Flow Cross-Facility Test (HFXF07). The data 

used in this assessment were acquired at the NASA AAPL, but 

most of the nozzles and test conditions were also run at NASA 

Langley Jet Noise Laboratory, hence the designation of crossfacility test.

8.7 Details of Measurements, Sensors, 

Transducers, and Placement

Acoustic measurements on SHJAR were recorded by an 

array of 24 microphones placed on an arc with a radius of 

2.54 m (100 in.) at 5° intervals from 50° to 165° measured 

from the inlet. The microphones were Brüel & Kjær (B&K) 

1/4-in. microphones (model 4939, with a B&K Model 2670 

preamp), used without grid caps and pointed at the nozzle exit. 

To minimize reflection from the microphone stands, six 

stands—each holding four microphones—were used. On the 

HFJER, a similar arc array was deployed, with a nominal 

radius of 13.7 m (45 ft). On HFJER, the microphones were 

located on 1.9-cm (0.75-in.) pipe-frame carts, which were 

located on a track across the ceiling of the NATR (see 

Figure 8.9). 

A DataMAX Instrumentation Recorder (RC Electronics 

Inc.) simultaneously recorded data from all microphones, 

using a 90-kHz low-pass filter to limit the bandwidth (at 

200 kHz sample rate). B&K Nexus amplifiers provided

Figure 8.16.—Internally mixed, dual-flow exhaust system with 

convergent nozzle and nonaxisymmetric splitters. (a) Lobed. 

(b) Chevron.

the signal conditioning. Eight seconds of data were recorded at 

each point. The high-frequency response of the Nexus 

amplifiers and DataMAX recorder had been documented using 

a white noise generator. When a 100-kHz signal from a white 

noise generator was directly input into the DataMAX, the 

recorded signal had a 1-dB down point at 63 kHz compared to 

70 kHz for the signal generator itself. When the white noise 

first passed through the Nexus amplifier, the recorded signal 

was further decreased above 74 kHz. In practice the trusted 

bandwidth was closer to 75 kHz than the 90 kHz set on the 

recorder itself. 

To record flow conditions during the acoustic data acquisition, a facility computer called ESCORT recorded variables 

such as rig temperatures, pressures, and mass flows, as well as 

ambient temperature, pressure, and humidity. The ESCORT 

averaged the data over the same time that the acoustic record 

was recorded, giving one value per variable per acoustic data 

point.
NASA/TP—2012-215653 260

Figure 8.17.—Externally mixed dual-flow exhaust systems. Dimensions are in centimeters (inches). (a) Nozzle PAA5.

(b) Nozzle PAA8. (c) Nozzle PAA11. (d) Nozzle PAA14.

8.8 Acoustic Data Collection and 

Processing

The far-field microphone data were processed in a series of 

procedures given below:

(1) Time series were multiplied by amplification factors 

from the variable gain Nexus signal conditioners and by the 

calibration factor determined by in situ recording of the B&K 

pistonphone.

(2) Fourier transforms were computed using fast Fourier 

transform algorithms and 10th-order Kaiser-Bessel windowing 

on 16384-point records with 50 percent overlapping.

(3) Background noise, measured immediately before the 

data set was acquired, was subtracted, and any frequency band 

within 3 dB of the background was flagged and was not 

considered for future processing and final plotting. Note that 

for conditions with simulated forward flight the background 

noise included the noise of the large free jet.

(4) Data were corrected for microphone spectral response 

characteristics based on the manufacturer’s documentation of 

each individual microphone obtained during calibration 

performed within 1 year of the test.

(5) Data were converted to a 0.3-m (1-ft) lossless condition 

using the ANSI S1.26–1995 standard atmospheric corrections 

(Ref. 24). 

(6) Data have been reported as lossless, and scaled to an 

arc distance of 100D based on the nozzle diameter D. Note 

that scaling the sound amplitude to a distance based on a 

constant number of nozzle diameters is mathematically 

identical to scaling the data to a common nozzle size.

(7) The frequency is normalized as Strouhal number when 

multiplied by the factor [(nozzle diameter)/(jet velocity)]. The 

spectra are also normalized and stored as power spectral 

density per Strouhal number.

(8) Power spectral density was later integrated over

1/3-octave bands, using a method consistent with the IEC 

1260:1995 standard (Ref. 25)—specifically an ideal

1/3-octave filter, for presentation and comparison.

(9) For those datasets involving forward-flight simulation 

(free-jet operation), corrections for the refraction of sound 

through the free-jet shear layer were made using the method 

documented in NASA CR–3056 (Ref. 26). The method is 
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NASA/TP—2012-215653 261 Chapter 8

equivalent to the technique commonly referred to as “Amiet’s 

method” when the source location is taken to be at the nozzle 

exit for all frequencies. This step was carried out prior to 

corrections for atmospheric attenuation. 

Processing of the far-field acoustic data to correct for the 

refraction of sound is handled differently at different facilities 

because of differences in philosophy in handling the distributed, directional sources of the jet plume. However, all facilities 

can, and have, used the Amiet’s correction method as used in 

this chapter. There is still substantial concern about the 

relationship between model-scale acoustic data obtained in 

this manner and the full-scale flight data, but the resolution of 

this problem is beyond the scope of this chapter.

8.9 Identifying Uncertainties in 

Acoustic Data

The procedure established to identify and eliminate external 

and background noise sources addressed the issue of data 

accuracy. This section will address the precision of the 

measured jet noise data using two methods. First, direct 

analysis of the primary sources of precision error, using 

manufacturers specifications, gives the worst-case error band. 

Second, data points recorded during different test programs 

but using the same nozzle and jet condition are considered to 

establish the actual precision observed under complete test 

conditions.

8.9.1 Measurement Uncertainties

The measurement uncertainties were determined by identifying the sources of uncertainty that affect the data and then 

averaging the data. The results of this analysis are shown in 

Table 8.4 with the following descriptions for the sources of 

uncertainty:

(1) Measurement of atmospheric conditions, which feed the 

calculation of atmospheric attenuation. This turns out to be a

rather small error, ~0.1 dB, because the measurement 

uncertainties of 0.6 °C (1 °F) and 2 percent relative humidity 

only impact the highest frequencies; that is, the last few

1/3-octave bands. 

(2) Location of the microphones. Using gyro-stabilized 

laser alignment tools allows microphones to be positioned to 

within 1.3 cm out of 250 cm (0.5 in. out of 100 in.) on the 

SHJAR and a comparable 2.5 cm out of 15 m (1 in. out of 

50 ft) on the HFJER. This translates into 0.04 dB uncertainty.

(3) Accuracy of the jet flow condition settings and maintaining them during data acquisition. The test procedure in 

both SHJAR and HFJER maintained a 0.5 percent tolerance 

on the jet velocity. Transducers were calibrated to assure this 

tolerance level, which translated into noise uncertainty of 

±0.17 dB. 

(4) Pistonphone calibration, a value that is easily determined from the manufacturer’s specifications. Note that most 

calibrators have a higher uncertainty than the 4220 pistonphone.

(5) Spectral calibration that relates the microphone response 

from 250 Hz, where the pistonphone signal is generated, to all 

the other frequencies. The calibration laboratory that provides 

this spectral response also includes the uncertainty. Values 

shown are typical for the indicated frequencies.

(6) Averaging of the spectral data.

Using chi-square analysis on 1/3-octave bands, which are 

the result of many narrowband estimates of power spectral 

density, the biggest uncertainty appears at the low-frequency 

end, where relatively few narrowbands are available for 

integration and statistical analysis. Here, at a 90% confidence 

interval, the uncertainty for the roughly 450-sample measurement (5 narrow bands with 90 ensembles each) is ±0.33 dB. 

As each 1/3-octave band picks up 1.25 times as many samples 

as a previous band, the error estimated within a decade is of 

the order of ±0.1 dB. The cumulative uncertainty, as shown in 

Table 8.4 at three representative frequencies, is 0.66 dB at the 

lower 1/3-octave frequency bands, reduces to 0.46 dB by the 

mid-frequency bands, and rises to 0.60 dB at the highest 

frequency bands.

8.9.2 Experimental Uncertainties

A final and larger source of uncertainty in jet noise measurements emerges when jet flows are scaled from experimental model size (order of centimeters) to that of the 

application size (order of meters). The imperfect scaling of 

nozzle lip thickness to jet diameter, internal and external 

boundary layer properties, and core turbulence intensities are 

but a few of the documented scaling parameters that cause jet 

rig experiments to differ from aircraft engines.

In addition, variations in jet noise facilities, especially 

subtle aspects such as flow collectors, entrainment air, size of 

free stream in simulated flight experiments, and distance from 

microphones to jet contribute to the so-called site-related 

errors. When uncertainties are added together it is no surprise 

that people who have compared experimental facilities have 

also experienced a renewed sense of humility considering 

many challenges present in measuring the true source of jet 

noise. Several excellent references have examined these issues 

in detail (Refs. 18 to 21, and 27) and the lessons shared in 

those efforts have been observed in this work. Comparison 

with measurements from alternative facilities also provides 

some level of confidence in one’s own data quality, and helps 

to establish an overall measure of experimental uncertainty. 

Assuming compliance with best practices, this uncertainty 

represents an estimate of noise measurement errors due to 

hardware, data processing, corrections, and so forth in two 

nominally identical jets at two different facilities.
NASA/TP—2012-215653 262

TABLE 8.4.—ANALYSIS OF UNCERTAINTY IN MEASURED JET NOISE SPECTRA

Measurement uncertainty,

e,

dB

Basis for determining uncertainty

Source Nominal frequency,

Hz

300 3000 30 000

Atmospheric attenuation 0.00001 0.001 0.1 ±0.56 °C (1 °F), ±2 percent relative humidity

Distance 0.04 0.04 0.04 ±1.3-cm (0.5-in.) error in 254 cm (100 in.)

Setpoint 0.17 0.17 0.17 ±0.5-percent error in jet velocity U

Pistonphone 0.15 0.15 0.15 B&K 4220 specification

Spectral calibration 0.0 0.01 0.16 B&K calibration laboratory specification

1/3- octave-band 

averaging

0.33 0.1 0.01 Chi-squared analysis of 1/3 octave integration at 90 percent confidence.

Lowest 1/3-octave band has 450 measurements (5 narrowbands with 90 ensembles each). 

Each higher frequency band has 1.25 more measurements than previous band, resulting in less 

uncertainty.

- or -

Narrow-band averaging 0.61 0.61 0.61 Chi-squared analysis of 194-average narrow band at 90 percent confidence

Totala 0.66 0.45 0.60 1/3-octave SPL (dB)

0.92 0.93 1.13 Narrowband power spectral density (dB)

a

Total uncertainty is summed according to 10 ( ) 10 10log 1 10 1 e   + −   ∑ .

As an example, consider three well-documented datasets 

acquired 30 years apart. The far-field spectra of Tanna 

(Ref. 17) and Viswanathan (Ref. 18) are reproduced in 

Figure 8.18, and are compared with the current SHJAR dataset 

(shown in blue) at 90° for three unheated jets at acoustic Mach 

numbers of Ma = 0.50, 0.70, and 0.90. The data from SHJAR 

fit to within 1 dB of the other two facilities, mostly splitting 

the difference, but exhibits lower amplitude at the highest 

frequencies where rig noise is most commonly observed. 

There is some concern that the Tanna dataset may have been 

improperly corrected for atmospheric attenuation at the 

highest frequencies due to the inaccurate methods utilized at 

the time. There is also concern that the Tanna and SHJAR 

datasets may contain some additional high-frequency noise 

due to low-Reynolds-number effects (i.e., smaller diameter 

nozzles compared with those tested by Viswanathan). That 

said, the variation observed between the SHJAR data and the 

other datasets is less than 1 dB below a Strouhal number of 

0.40 and less than 2 dB above this number. 

Similar comparisons are also carried out at heated conditions. Figure 8.19 and Figure 8.20 compare the data of Tanna 

and that of the current SHJAR dataset at three different 

temperature ratios, and at acoustic Mach numbers of Ma = 0.5 

and 0.90 respectively. As documented in Reference 28, there 

are concerns regarding the relatively low Reynolds numbers of 

some heated jets (below 500 000 for Ma = 0.5 jets), which 

may have an impact on SHJAR data at Strouhal numbers

Figure 8.18.—Sound pressure level (SPL) versus Strouhal 

number St at inlet angle θ = 90° for different jet acoustic 

Mach numbers Ma. Comparison of results from current 

SHJAR experimental data, Reference 17, and Reference 18.

above 5.0. However, the discrepancies in SHJAR measurements are within 2 dB, and at 150° the results agree within 

less than 1 dB—better than expected considering measurement 

uncertainties!
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NASA/TP—2012-215653 263 Chapter 8

Figure 8.19.—Sound pressure level (SPL) versus Strouhal number St at jet acoustic Mach number Ma = 0.5 for inlet

angles θ = 90° and 150°. Comparison of values from current SHJAR experimental data and Reference 17.

(a) Static temperature ratio Ts,r = 0.86 (cold). (b) Ts,r = 1.76. (c) Ts,r = 2.27.

Figure 8.20.—Sound pressure level (SPL) versus Strouhal number St at jet acoustic Mach number Ma = 0.9 for inlet

angles θ = 90° and 150°. Comparison of values from current SHJAR experimental data and Reference 17.

(a) Static temperature ratio Ts,r = 0.86 (cold). (b) Ts,r = 1.76. (c) Ts,r = 2.27.

Figure 8.21.—Hot jet sound pressure level (SPL) normalized to standard day at 4.6 m (15 ft) versus Strouhal number St

for different nozzle diameters D at inlet angle θ = 90°, Mach number M = 0.7, and total temperature ratio Tt,r = 3.2.

(a) Comparison of values from current SHJAR experimental data and Reference 18. (b) Difference between

values of Reference 18 and SHJAR data.
NASA/TP—2012-215653 264

Reference 18 provides several interesting test cases to 

demonstrate the scale independence in hot jets. Figure 8.21(a) 

shows the 90° noise measurements in a Mach 0.70 heated jet 

at a total temperature ratio of 3.20 using three different jet 

diameters of 3.81, 6.22, and 8.79 cm (1.50, 2.45, and 3.46 in.) 

(in Ref. 18). This data is compared with the present jet data 

after SHJAR measurements were normalized to conditions 

specified in Reference 18. The level of agreement is a 

testimony to the quality of SHJAR data compared to other 

high-quality jet rigs. Shown in Figure 8.21(b) are delta dB 

noise difference between SHJAR data and the three jets 

examined in Reference 18. The difference is roughly 1.0 dB 

except at very high frequencies. This is the best one would 

hope; an expected difference closer to 2 dB, as demonstrated 

in the earlier Tanna comparisons, and will be adopted in the 

following assessment exercise as the experimental uncertainty 

for a 1/3-octave SPL spectrum.

8.10 Flow Data Collection and 

Processing

To properly validate the acoustic analogy noise prediction 

codes, the flow solutions used as input to these codes had to be 

validated as well. From analysis of the code’s sensitivities it 

seems that the most critical flow parameters for acoustic 

accuracy are mean and turbulent velocities predicted by the 

RANS solver. To measure these quantities in hot, high-speed 

jets, PIV was deployed in the same facility and rigs where the 

acoustic measurements were made. Details of the PIV 

implementation are provided in Reference 29. The major 

issues related to data quality are also explained in this 

reference. Not all 265 jets considered in the assessment 

exercise have flow measurements available, but a substantial 

number have and those were used to assess the accuracy of the 

CFD predictions, and hence the input to the acoustic analogy 

prediction tools.

8.10.1 Stereoscopic PIV System

Flow datasets used in validating the RANS solutions were 

obtained using stereoscopic PIV. In this configuration, shown 

in Figure 8.22, the cameras are located on opposite sides of the 

light sheet. This arrangement is suitable for streamwise (axialplane) measurements. The system consisted of a dual-head 

pulsed Nd:YAG laser (Continuum Surelite III) operating at 

508 nm (2×10–5 in.), which generated a 400 mJ per pulse pair 

of light sheets defining the measurement plane orientation. 

The light-sheet-forming optics consisted of a spherical lens 

with a 1200-mm (47.2-in.) focal length followed by two 

cylindrical lenses, –75- and –40-mm (–3- and –1.6-in.) focal 

length. 

Each laser pulse was synchronized with a pair of 2048- by 

2048-pixel cross-correlation cameras (Redlake Megaplus ES 

4.0) viewing the laser sheet at oblique angles. Image frame 

pairs from each camera were obtained by straddling adjacent 

frame exposures. PCI (peripheral component interconnect) 

frame grabbers were used to acquire and stream the image 

data directly to disk in 200 image-pair sequences (for each 

camera). Image acquisition occurred at a nominal camera 

frame rate of ~5 Hz. Each camera and PCI board was connected to individual dual-processor 3.1-GHz Pentium computers, 

configured in a master-slave mode of operation. The entire 

system was controlled using NASA-developed PIV image 

acquisition software PIVACQ (Ref. 30).

Two Nikon 105-mm (4-in.) f/2.5 lenses were used with 2×

teleconverters. An f/5.6 setting was preferred in this case 

because of the enhanced light collection from the particle 

forward-scattering orientation. The cameras were positioned 

approximately 1.8 m from the measurement plane, roughly 

45° from vertical as shown in Figure 8.22. The cameras and 

lenses were adjusted to satisfy the Scheimpflug condition for 

stereo viewing of a plane; the angle between the camera lens 

and image planes was below 5°.

Since the AAPL is open to the environment during testing, 

the SHJAR could not be operated in complete darkness. To 

accommodate this situation, optical backdrops for the cameras 

were provided. These darkened camera backgrounds were 

positioned such that they were aligned with each camera view 

behind the measurement plane. The backgrounds were offset a 

suitable distance to minimize any influence on the ambient 

seeded flow distribution. 

The complete stereo digital PIV system (Ref. 30), including 

all cameras and backdrops, data acquisition computers, laser 

hardware, and optics, was rigidly mounted on a large axial 

traverse located downstream of the nozzle exit plane. The 

travel range of the traverse was approximately 2.5 m (8.2 ft), 

with a positioning accuracy of 1.0 mm (0.04 in.). Rezeroing of 

the traverse to coincide with the trailing edge of individual 

chevron nozzles was aided by the installation of a calibration 

target, required in stereo PIV, on a fixture secured to the 

traverse. This enabled highly repeatable cross- and axial-flow 

measurement plane locations with numerous chevron nozzle

Figure 8.22.—Experimental arrangement for axial-flow stereo 

particle image velocimetry (PIV) measurements.
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NASA/TP—2012-215653 265 Chapter 8

configuration changes. Following a cold start-up, the entire 

test rig experiences axial growth when operating at elevatedtemperature set points. Thus, a rezeroing adjustment of the 

transverse rig was required and performed by optical means, 

using the current camera nozzle views to reference known 

chevron trailing edge tip locations at the nozzle exit planes.

8.10.2 Optical Calibration and Verification

Each camera was oriented at a certain angle with respect to 

the laser sheet to obtain a stereo view of the measurement 

plane. Because of the incorporation of the Scheimpflug 

condition, magnification factors between the image and object 

planes are variable due to perspective distortion. In order to 

combine camera measurements from both views into a single, 

three-component velocity vector map in the fluid plane, 

camera calibrations were required. The three-dimensional in 

situ calibration procedure as outlined by Soloff et al. (Ref. 31) 

was performed.

Prior to each day’s collection of test runs, both cameras 

were precalibrated at the same time using the existing optical 

setup and the introduction of a calibration target into the 

measurement plane. The target was positioned in the same 

orientation, and at the same location, as the laser light sheet. A 

commercial dual-sided, four-plane target manufactured by TSI 

Incorporated was used. The identically sized target, also with 

marker locations on 10-mm centers, in this case was fixed, 

with its centerline positioned along the nozzle jet axis 

centerline during calibration image acquisition. Both “A” and 

“B” light sheets were centered on the target, with the thinner 

“A” sheet precisely aligned and centered within the wider “B” 

sheet. Polynomial mapping functions were determined using 

the known marker locations in the fluid and the recorded 

locations in the image planes to uniquely characterize the 

camera to fluid mapping functions for particle displacement 

(Ref. 29). Polynomial mapping orders of 2 and 1 were selected 

for mapping the displacement components in the laser

light sheet plane and normal to the laser light sheet plane, 

respectively. 

In this calibration verification procedure, particle images 

from each camera illuminated by the same laser pulse are 

warped to the fluid plane using the existing calibration 

equations. If the laser light sheet were of zero thickness and 

the calibration perfectly accurate, the particle images from 

each camera would map to the same location in the warped 

images. By using cross-correlation processing (the same 

processing used to measure the flow velocity) to measure the 

displacements in the warped images, a target-to-light sheet 

alignment error can be determined. All measured warped pixel 

displacements are assumed to be caused by errors in the axial

location of the calibration target due to an x-axis translation 

and/or out-of-measurement-plane tilt (see Figure 8.22). This 

information reveals the actual position of the target relative to 

the light sheet and permits the finding of a best-fit solution 

through an iteration procedure to correct the calibration target 

position marker locations in the fluid coordinate system.

8.10.3 Three-Dimensional Vector Processing

Velocity vector maps for each camera were computed (in 

the image planes) from the image pairs using NASAdeveloped PIVPROC software (Ref. 30). The software utilizes 

conventional multipass PIV cross-correlation processing 

algorithms and incorporates error detection based on image 

correlation signal-to-noise ratio. First-pass interrogation 

region sizes of 64 by 64 pixels on 32-pixel centers and finalpass interrogation region sizes of 32 by 32 pixels on 16-pixel 

centers were used to process image pairs from the cameras in 

both stereo configurations.

After processing the images acquired by each camera, the 

pixel displacement data from the left and right views were 

combined to obtain the three-component velocity vector field 

at the measurement plane in the fluid. The equations that 

govern the transformation of the image plane data to the object 

plane are those given following the verified calibration 

procedures noted above. The software used to perform these

operations was developed in-house to permit execution via 

command line processing. Some notable features include the 

ability to perform bicubic vector interpolation of the neighboring vector data in the image plane prior to being mapped back 

into the fluid space, as well as the ability to calculate threedimensional vectors in the fluid on arbitrarily defined 

rectangular grids of any size—useful for nonsquare correlation 

region processing.

As the u-, v-, and w-components of each three-dimensional 

flow velocity vector are computed using a linear least-squares 

fit (singular value decomposition) of the left and right twodimensional vector, a residual error is found by substituting 

each solution back into the least-squares equations. The total 

residual error for each vector is given as the square root of the 

sum of these residual errors squared. This error, given in 

pixels, is indicative of the total mismatch between left and 

right vectors. A residual pixel threshold of 0.5 pixels was 

specified for validating the solution vector. For the cross-flow 

configuration, solutions exceeding this threshold indicate the 

v-components of velocity between the two vectors differed by 

more than 0.5 pixel.

Ensemble averaging of the 200 individual vector maps was 

performed to obtain statistical information at each measurement plane. The averaging procedure incorporated both hard 

velocity cutoff limits and Chauvenet’s criterion for data outlier 

removal (Ref. 30). This ensemble averaging was also performed using in-house developed software, with any threedimensional vector data that exceeded the residual pixel 

threshold (0.5 pixels) being excluded from the ensemble 

averaging procedures. 

8.10.4 Flow Seeding

As is typical in all PIV applications, quality flow seeding 

was an essential factor in obtaining high-accuracy results. 

Because of the elevated operating temperatures, a refractory 

seed material was required for the core jet flow. The flow 

seeding material utilized was ~0.5-μm (~2×10–5 in.) powdered 
NASA/TP—2012-215653 266

alumina particles. This material, contained within a pHadjusted ethanol solution, was delivered to the core flow 

upstream of the flow conditioning screens. Uniform dispersion 

was provided by a pair of air-assisted, atomizing nozzles. As 

determined from a particle frequency response analysis, the 

core flow particles were expected to be able to accurately 

follow the jet flows over the complete range of nozzle 

operating conditions considered in this test program.

The ambient air was seeded with ~0.2 μm (~8×10–6 in.) 

mineral oil droplets produced by a commercial smoke 

generator. This ambient smoke system was located in a 

partially enclosed rig support structure upstream of the nozzle. 

Entrainment of the particles around the nozzles was aided by 

the use of two circulating fans. This provided a very low 

velocity (<5 m/s, or <16 ft/s) airstream surrounding the nozzle 

core jet flows. The performance of this flow seeding arrangement has been previously applied to PIV measurements with 

successful results (Ref. 29).

8.11 Identifying Uncertainties in Flow 

Measurements

Beyond internal calibrations and checks on data quality, the 

PIV results were compared with data obtained with conventional measurement techniques to estimate experimental 

uncertainties. Similar to acoustic results, comparisons with 

measurements made at other facilities using other measurement techniques give a more complete determination of 

overall experimental error. Measurements made in a cold 

Ma = 0.50 jet using PIV were compared with the same facility 

data using conventional hotwire anemometry as well as data 

obtained elsewhere using laser Doppler velocimetry (LDV) 

(Ref. 32). The results are displayed in Figure 8.23 as PIV for 

conventional PIV data, TRPIV for time-resolved PIV, hotwire, 

and LDV data. While the mean velocity agreement between 

the LDV and PIV is to within a few percent, the turbulence 

levels differ by as much as 10 percent (the hotwire turbulence 

measurements agree better with the PIV). At a higher acoustic 

Mach number of Ma = 0.90, which is beyond the functionality 

range of the hotwire anemometry, the LDV data was compared with two PIV datasets taken a year apart, denoted as 

PIV(T3) and PIV(T4). As seen in Figure 8.24, the difference 

in mean velocities is less than 5 percent. The root-meansquared (rms) velocities agree within 5 to 10 percent. Finally, 

to evaluate the accuracy of PIV data in a high-speed hot jet, 

the PIV data is compared with LDV data for nearly comparable jets at Ma = 0.90 and Ts,r = 2.7 for the PIV tests and at

Ma = 0.78 and Ts,r = 2.7 for the LDV tests (see Figure 8.25). 

Discrepancies in the centerline velocity decay appear mostly 

well past the end of the potential core, leading to concerns 

about the equivalence of the two jet flows rather than differences in the measurement techniques. The rms values as a 

percentage of jet exit velocity agree much better to within 

5 percent, except for a limited segment near the ending of the 

potential core—and subsequent internal examination of the 

PIV data based on the particle images confirmed data to be 

somewhat questionable.

Figure 8.23.—Axial velocity of cold jet, acoustic Mach number Ma = 0.5, measured along centerline x/D using

conventional particle image velocimetry (PIV), time-resolved PIV (TRPIV), laser Doppler velocimetry (LDV), 

and hotwire anemometry. (a) Normalized mean axial velocity, uo/U. (b) Normalized root-mean-squared

fluctuating axial velocity, u′2 /U .
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NASA/TP—2012-215653 267 Chapter 8

Figure 8.24.—Axial velocity of cold jet, static temperature ratio Ts,r = 0.84 and acoustic Mach number Ma = 0.9, 

measured along centerline x/D using particle image velocimetry (PIV) and laser Doppler velocimetry (LDV).

T3 and T4 designate PIV measurements taken 1 year apart. (a) Normalized mean axial velocity uo/U.

(b) Normalized root-mean-squared fluctuating velocity u′2 /U .

Figure 8.25.—Axial velocity of hot jet measured along centerline x/D using particle image velocimetry (PIV) (static 

temperature ratio Ts,r = 2.7 and acoustic Mach number Ma = 0.9) and laser Doppler velocimetry (LDV) (Ts,r = 2.7 

and Ma = 0.78). (a) Normalized mean axial velocity uo/U. (b) Normalized root-mean-squared fluctuating velocity 

u′2 /U .

Assumptions regarding flow axisymmetry or location of the 

jet centerline could also lead to additional subtle errors. This is 

especially true in the case of dual-stream jets with a hot core 

flow as documented by Birch et al. (Ref. 33). In the referenced 

work, azimuthal variations of 12 percent in turbulence 

intensity were observed in nominally axisymmetric separate 

flow nozzles. Much of the CFD validation in the present 

chapter was achieved with single-stream jets where such 

azimuthal variations are much less important. Typically when 

measurements are carried out along the opposite mixing 

planes in a single-stream jet, the turbulence intensities agree to 

within experimental error. Validating CFD results in dualstream jets requires much more care. Adding a fixed known 

asymmetry such as a pylon is likely to reduce the

error introduced by the sensitivity of the dual-stream jet to 

asymmetries. 

From above comparisons, we estimate that the mean and 

rms velocity measurements are accurate to within 3 and 
NASA/TP—2012-215653 268

5 percent, respectively. While this puts the uncertainty near 

10 percent for the turbulent kinetic energy, it is noted that 

most RANS solvers do not come this close to the measured 

data.

8.12 Metrics

In all cases and for all codes, 1/3-octave spectral directivity 

comparisons were made. For simplicity, only two spectra, at 

polar angles of either 90° and 150° or 90° and 130° from the 

inlet axis, are shown in plots. All spectra have been normalized to power spectra versus Strouhal number, removing 

atmospheric attenuation, to the condition of an observer at 100 

jet diameters. First, the predictions were compared with the 

data in standard overlay plots for the two angles, and then the 

difference between the prediction and the data was plotted as a 

function of Strouhal number St. This second plot contains 

dashed lines representing the upper and lower uncertainty 

band of the experimental data. If the difference lies within 

these lines, the prediction is projected as within experimental 

uncertainty. 

Similarly, to judge the ability of the codes to predict the 

OASPL directivity, the predicted and measured spectra are 

integrated within the frequency range 0.05 < St < 30. Again, 

the predicted and measured OASPL directivities are plotted 

together, and their difference is examined in relation to 

experimental uncertainty bars. 

To help summarize the data collection, the average μ and 

variance σ

2 of error ∆ in the OASPL between ANOPP 

predictions and experimental data were computed over a jet 

sample case at N polar angles (24 polar angles θ, 50° to 165° 

in 5° increments)

ANOPP expt at ∆ ≡i i OASPL OASPL − θ=θ (8.12)

1

1 N

i N i=

μ= ∆ ∑ (8.13a)

( )

2 2

1

1 N

i N i=

σ = ∆ −μ ∑ (8.13b)

The average error μ gives an indication of how close the 

prediction comes to the data in overall sound power, and the 

variance σ

2 (or its square root σ, the standard deviation) of the 

error in OASPL could be interpreted as the ability to predict 

directivity. It is possible for the error in predicting OASPL to 

average to zero even if the prediction has the wrong directivity. 

In this case the standard deviation of the error would be 

nonzero. Conversely, the standard deviation could be very small 

if the prediction were correct in directivity but wrong in overall 

sound power. Combined, these two metrics give a strong insight 

into the accuracy of the prediction compared with the experiment. Distilling the voluminous data from all the cases into 

these two metrics helps spot trends across all cases.

Another significant measure of great interest to practicing 

engineers in jet noise is the effective perceived noise level 

(EPNL). This metric is tied to the scale of the jet and weighs 

frequency bands near 2000 Hz full-scale much more heavily 

than the typical peak of jet noise. To get a feel for the error in 

EPNL, all cases were transformed to a 1-m- (3.3-ft-) diameter 

nozzle in level flight at 0.28 Mach number and an altitude of 

500 m (1640 ft). This parameter penalizes codes that do well 

in capturing the peak jet noise but do not perform as well at 

off-peak high frequencies.

8.13 Description of Presentation Format 

for Acoustic Data

Because of the large volume of the illustrations, it was 

important to choose a legend consistent throughout the 

presentations. A typical illustration, such as Figure 8.26, 

consists of 1/3-octave SPL spectra at two inlet angles (such as 

θ = 90° and 150°). Figure 8.26(a) examines the predictions 

(lines) versus measurements (symbols). The difference 

between prediction and data is compared with the experimental uncertainty bars (dashed lines) in Figure 8.26(b). The 

uncertainty band labeled “Measurement” is the uncertainty

of the measurement at the facility, and that marked as 

“Experimental” represents the variation observed between 

facilities for nominally the same experiment. To provide an 

assessment over a broad range of angles, Figure 8.26(c) 

examines the OASPL directivity (i.e., the integrated spectrum 

at each angle). This figure also serves as a “typical” spectral 

result for many of the shock-free flows. Because it encompasses measurement uncertainty, only experimental uncertainty will be plotted in the prediction and measurement 

comparisons and labeled as “Uncertainty.”

Without getting into the specifics of the jet that Figure 8.26

represents, it is seen that the predicted spectra agree with the 

experimental data relatively well in the peak amplitude and the 

peak frequency, but then fall too sharply and depict a second 

hump at St = 10. The experimental data, on the other hand, 

show steady high frequency decay at both angles. This pattern 

is observed in many ANOPP spectral predictions and represents a consistent error in the source modeling. 

Using the jet noise component controls for the ST2JET 

module, it is possible to turn various sources on and off to 

discern the origin of this high-frequency hump. The three 

spectral components in a shock-free jet, as predicted by 

ANOPP, are labeled as “Inner Stream,” “Outer Stream,” and 

“Merged Stream,” intended to model jet noise from different 

scales of turbulence associated with three shear layers due to 

bypass-core, ambient-bypass, and the fully merged regions, 

respectively. These components are shown separately in 

Figure 8.27. The suspect high-frequency hump at Strouhal 

number 10 is identified as part of the “Outer Stream,” which 

points to the source modeling deficiencies in the ambientbypass mixing region.
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NASA/TP—2012-215653 269 Chapter 8

Figure 8.26.—Typical results for jet noise directivity analyses. (a) 1/3-octave sound pressure level (SPL) versus Strouhal 

number St for two inlet angles θ from SHJAR experimental data and ANOPP predictions. (b) Difference between

predicted and measured SPL, with uncertainty bands. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.27.—Example of source noise component and total spectra 

computed by ANOPP for a shock-free jet at inlet angle θ = 90°.

1/3-octave sound pressure level (SPL) versus Strouhal number St.

8.14 Empirical Code Assessment Results

The only empirical model available during this assessment 

exercise was the jet noise routine within the ANOPP code. 

Section 8.2.1 briefly outlined the origin of the ST2JET 

module. This section examines sample cases in an attempt to 

provide a direction for future improvements. 

8.14.1 Case Listing

Table 8.7 in Appendix B details nine jet configurations 

(identified alphabetically as A through I) considered in the 

ANOPP ST2JET assessment exercise. These configurations 

encompass a broad range of operating conditions (jet temperature and velocity) in both subsonic and supersonic jets. In 

addition to the convergent nozzles, a number of single-stream 

convergent-divergent nozzles were also designed to generate 

shock-free jets at exhaust Mach numbers shown in Table 8.3. 

Aside from single stream jets, dual stream nozzles were also 

examined with a BPR as high as 14.

8.14.2 Overall Results

Figure 8.28 to Figure 8.30 are an attempt to distill the

results for the 265 cases listed in Table 8.7 into a few figures 

that answer the question, “How well does ANOPP predict jet 

noise?” The metrics used are defined in Equation (8.13). 

Figure 8.28 shows the average difference μ in the OASPL 

between ANOPP and experiments, and is essentially a 

measure of how well ANOPP predicts the total noise of the 

jet. First, with the exception of configuration B, which 

represents convergent nozzles with chevron mixers, it appears 

that ANOPP predicted the OASPL to within a few decibels 

and within experimental uncertainty for most configurations. 

Second, given that the jet velocity generally increases

with case number within each configuration group, it
NASA/TP—2012-215653 270

Figure 8.28.—Average error μ in overall sound pressure level (OASPL) between ANOPP

predictions and experimental data for all ANOPP assessment cases listed in Table 8.7

(Appendix B), grouped in configurations A through I with corresponding bypass ratio (BPR), azimuthal periodicity m, and Mach number M.

Figure 8.29.—Standard deviation σ about the average overall sound

pressure level (OASPL) error between ANOPP predictions and

experimental data for all ANOPP assessment cases listed in Table 8.7

(Appendix B), grouped in configurations A through I with corresponding 

bypass ratio (BPR), azimuthal periodicity m, and Mach number M.
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NASA/TP—2012-215653 271 Chapter 8

Figure 8.30.—Difference in effective perceived noise level (EPNL) between ANOPP predictions 

and experimental data for all ANOPP assessment cases listed in Table 8.7 (Appendix B), 

grouped in configurations A through I with corresponding bypass ratio (BPR), azimuthal

periodicity m, and Mach number M.

appears that ANOPP tends to do a better job of predicting 

OASPL at lower speeds. Third, configuration groups E and F 

have less accuracy because most of these cases were shockcontaining jets where the noise prediction was dominated by 

the prediction of broadband shock noise. Apparently the 

broadband shock noise prediction code is less accurate than 

the mixing noise code that dominates in most jet noise 

predictions. 

To assess how well ANOPP predicted the directivity in 

OASPL, the standard deviation σ of the difference in OASPL 

over the polar angles is plotted in Figure 8.29. The discrepancy in predicting directivity is similar across all configurations, 

even configuration B in which predictions credited the 

chevrons with much more reduction of sound power than was 

measured but properly predicted the directivity. As in the 

average error μ, the overall upward trend in σ with increasing 

case number within each configuration points to a decline in 

the prediction quality with increasing jet speed. 

Figure 8.30 is similar to Figure 8.28, but measures the 

average difference in the EPNL between predictions and data 

assuming an arbitrary nozzle area of 0.7854 m2 (1217 in.

2

) 

flown at Mach 0.28 in level flight of 500 m (1640 ft) altitude. 

The EPNL of predictions shows slightly less discrepancy with 

data compared to predictions of OASPL shown in Figure 8.28; 

however, this assessment is dependent upon scale factor. 

Looking across all configurations the predicted EPNL 

generally matches the measured EPNL within 2 EPNdB.

Results comparing measured and predicted 1/3-octave spectra and OASPL directivities for a representative subset of 265 

cases appear in Figure 8.60 to Figure 8.103 in Appendix C.

8.15 Acoustic Analogy Code Assessment 

Results: Jet3D

In the Jet3D code, computation of the jet mixing noise is 

carried out according to Lighthill’s acoustic analogy as 

described in Section 8.2.2, “Acoustic Analogy Prediction 

Tools.” The spectral density of the far-field noise is evaluated 

following Equation (8.3) using the source and the Green’s 

function as defined in Section 8.2.2.1. The Wind-US CFD 

solver (Ref. 10) supplied the RANS solution files for cases 

shown here. 

8.15.1 Case Listing

The acoustic analogy code Jet3D was assessed at singleflow subsonic, and shock-free supersonic jet conditions listed 

in Table 8.1. The table represents only a limited subset of the 

full assessment matrix (cases listed in Table 8.7). This was 

partially due to the relatively large resources—gridding and 

CFD computation—required for each test case. In addition, 

Jet3D is not equipped with modeling tools to evaluate 

broadband shock associated noise hence none of the shockcontaining jets were included.
NASA/TP—2012-215653 272

8.15.2 Discussion of Jet3D Results

Of nine single-stream axisymmetric cases examined with 

Jet3D, the first two (003 and 007) represent unheated subsonic 

jets. These presented the least agreeable Jet3D performances, 

with OASPL overpredictions that exceeded above 10.0 dB at 

most angles (Figure 8.31 and Figure 8.32). This was partially 

due to the fact that the code was originally calibrated around 

hot jets and the heat-related sources were also considered as 

small and dismissed as a source. Subsequently, it was 

anticipated to see improved predictions at heated conditions. 

The next six cases present heated jets at a static temperature 

ratio ranging from 1.76 to 2.70. At the highest temperature, 

the overpredictions diminished to an average of ~5.0 dB above

measurements, but the peak frequency was off by as much as a 

full octave as seen in Figure 8.33 to Figure 8.38. The last 

example (case 268) was a shock-free supersonic jet at Mach 

1.40. This case (see Figure 8.39) presented the best performance of the Jet3D in terms of the OASPL directivity; 

however, the details of the spectrum were not correct, and the 

spectral peak at 130° was off by ~0.80 of a full octave below 

measured data. This was the case for which Jet3D had been 

calibrated in Reference 8.

In general, Jet3D did better at low-Mach-number heated 

conditions. Given that the usual approximation of the Lighthill 

stress tensor neglects enthalpy related terms as a source, it was 

not surprising to see prediction inconsistencies across 

temperatures. 

It is noted that the prediction shortfalls were not related to 

the particular CFD solver or the grid-density, as sensitivity to 

both were explored earlier in the discussion of Jet3D code in 

Section 8.2.2.1 (Figure 8.2).

Figure 8.31.—Assessment of Jet3D jet noise predictions. Case 003 (see Table 8.1) for convergent, axisymmetric nozzle:

bypass ratio (BPR) = 0, Mach number M = 0.51, acoustic Mach number Ma = 0.5, and static temperature ratio

Ts,r = 0.955. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure level 

(SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.32.—Assessment of Jet3D jet noise predictions. Case 007 (see Table 8.1) for convergent, axisymmetric nozzle:

bypass ratio (BPR) = 0, Mach number M = 0.98, acoustic Mach number Ma = 0.902, and static temperature ratio

Ts,r = 0.842. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.33.—Assessment of Jet3D jet noise predictions. Case 022 (see Table 8.1) for convergent, axisymmetric nozzle:

bypass ratio (BPR) = 0, Mach number M = 0.37, acoustic Mach number Ma = 0.492, and static temperature ratio

Ts,r = 1.767. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure 

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.34.—Assessment of Jet3D jet noise predictions. Case 025 (see Table 8.1) for convergent, axisymmetric nozzle: 

bypass ratio (BPR) = 0, Mach number M = 0.68, acoustic Mach number Ma = 0.901, and static temperature ratio

Ts,r = 1.77. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty.

(c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.35.—Assessment of Jet3D jet noise predictions. Case 027 (see Table 8.1) for convergent, axisymmetric nozzle: 

bypass ratio (BPR) = 0, Mach number M = 1.01, acoustic Mach number Ma = 1.33, and static temperature ratio

Ts,r = 1.759. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure 

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.36.—Assessment of Jet3D jet noise predictions. Case 034 (see Table 8.1) for convergent, axisymmetric nozzle: 

bypass ratio (BPR) = 0, Mach number M = 0.3, acoustic Mach number Ma = 0.484, and static temperature ratio

Ts,r = 2.624. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure 

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.37.—Assessment of Jet3D jet noise predictions. Case 037 (see Table 8.1) for convergent, axisymmetric nozzle: 

bypass ratio (BPR) = 0, Mach number M = 0.56, acoustic Mach number Ma = 0.901, and static temperature ratio

Ts,r = 2.702. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure 

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.38.—Assessment of Jet3D jet noise predictions. Case 040 (see Table 8.1) for convergent, axisymmetric nozzle: 

bypass ratio (BPR) = 0, Mach number M = 0.92, acoustic Mach number Ma = 1.483, and static temperature ratio

Ts,r = 2.703. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure 

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.39.—Assessment of Jet3D jet noise predictions. Case 268 (see Table 8.1) for convergent-divergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 1.4, acoustic Mach number Ma = 2.2, and static temperature ratio

Ts,r = 2.53. Comparison between Jet3D predictions and SHJAR experimental data. (a) 1/3-octave sound pressure level 

(SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty.

(c) Overall sound pressure level (OASPL) as function of θ.

8.16 Acoustic Analogy Code Assessment 

Results: JeNo v1.0

In JeNo, computations of the turbulent mixing noise are 

carried out according to Lilley’s acoustic analogy, and the 

spectral density of the far-field noise is evaluated following 

Equation (8.3) using the source and the Green’s function as 

defined in Section 8.2.2.2. The version considered in the 

assessment exercise (i.e., JeNo v1.0) does not address the 

heat-related sources that are associated with enthalpy fluctuation in a jet. Consequently, source term q relates to second 

rank velocity tensors as shown in Equation (8.11). Aside from 

differences in their source modeling, the major difference 

between the two acoustic analogy codes Jet3D and JeNo is 

their Green’s functions. While Jet3D used a free space 

Green’s function, JeNo solves the second-order compressible 

Rayleigh equation numerically at each frequency and at each 

source location (Ref. 13). The Wind-US CFD solver (Ref. 10) 

supplied the RANS solution files for cases shown here.

8.16.1 Case Listing

The acoustic analogy code JeNo v1.0 was assessed only on 

a subset of the full assessment matrix. These consist of 13 

axisymmetric, convergent and convergent-divergent nozzles 

as listed in Table 8.5, plus additional cases with nonaxisymmetric geometries as listed in Table 8.6. JeNo is not presently 

equipped with modeling tools to evaluate the broadband shock 

associated noise hence none of the shock-containing jets were 

included in the list.

TABLE 8.5.—ASSESSMENT MATRIX FOR JeNo v1.0 

PREDICTIONS OF JET NOISE SPECTRA—

AXISYMMETRIC GEOMETRIESa

Case M Axial 

geometry

Ma Ts,r nozid

003 0.51 Convergent 0.500 0.955 SMC000

007 0.98 0.902 0.842

022 0.37 0.492 1.767

025 0.68 0.901 1.770

027 1.01 1.330 1.759

034 0.30 0.484 2.624

037 0.56 0.901 2.702

040 0.92 1.483 2.703

059 1.172 C-D 1.047 0.797 SMC014

068 1.394 1.191 0.730 SMC015

075 1.497 1.251 0.699 SMC016

083 1.659 1.342 0.654 SMC017

090 1.784 1.403 0.619 SMC018 a

Nomenclature for table headings:

M ideally expanded Mach number

Axial geometry indicates if nozzle was convergent or convergentdivergent (C-D) 

Ma acoustic Mach number, U/c∞

Ts,r static temperature ratio, Ts/T∞

nozid nozzle identification
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TABLE 8.6.—ASSESSMENT MATRIX FOR JeNo v1.0 PREDICTIONS

OF JET NOISE SPECTRA—NONAXISYMMETRIC GEOMETRIESa

Case Geometry M Ma Ts,r nozid

Axial Azimuthal

042 Convergent m = 6 0.972 0.902 0.837 SMC001

Geometry BPR M Core Bypass Mfl nozid

Axial Azimuthal Ma Tt,r Ma Tt,r

Separate flow Axisymmetric 2.84 0.82 0.888 1.004 0.701 1.001 0.28 5000

Fan-wedge 2.43 0.83 0.901 1.002 0.711 0.999 0.28 520x

Axisymmetric 2.09 0.73 0.909 1.039 0.530 0.999 0.0 5000

S-duct 2.04 0.73 0.904 1.003 0.527 1.006 0.0 50Sx a

Nomenclature for table headings:

BPR bypass ratio

M ideally expanded Mach number; for dual stream, mass averaged

Axial geometry indicates convergent or externally mixed separate flow

Azimuthal geometry indicates nozzle is axisymmetric or defined as shown in Figure 8.40, or single stream, azimuthal base 

periodicity m

Ma acoustic Mach number U/c∞

Ts,r static temperature ratio Ts/T∞

Tt,r total temperature ratio Tt/T∞, for dual stream cases 

Mfl flight Mach number

nozid nozzle identification

Figure 8.40.—Nozzles with offset stream technology used to assess the JeNo v1.0 code jet noise prediction capability. 

(a) Fan-wedge. (b) S-duct.

8.16.1.1 Axisymmetric Jets

Cases listed in Table 8.5 are made up of seven unheated, 

and six heated jets. Unheated cases consist of two subsonic 

jets at acoustic Mach numbers of 0.50 and 0.90 (cases 003 and 

007), and five supersonic flows at ideally expanded Mach 

numbers from 1.17 to 1.78 (cases 059, 068, 075, 083, and 

090). An additional six heated cases (022, 025, 027, 034, 037, 

and 040) were also considered with static temperature ratios 

from 1.76 to 2.70 to highlight the shortcomings in hot jet 

predictions and needed future improvements. The RANS 

solutions were generated using the Wind-US code and the 

Mentor SST turbulence model as discussed previously in 

Sections 8.2.2.2 and 8.2.3. Upstream nozzle conditions were 

specified in terms of plenum total temperature ratio and the 

nozzle pressure ratio in computing the CFD solutions, 

however, only the external flow downstream of the nozzle exit 

plane was integrated in noise computations.

8.16.1.2 Nonaxisymmetric Jets

One of the main promises of the RANS-based acoustic 

analogy models is their ability to predict the variations in 

noise generation due to subtle changes in the nozzle geometry 

and jet flow. One obvious and historically productive geometrical change has been azimuthal variations in the nozzle lip 

geometry (i.e., lobed mixers, chevrons, and pylons). 

The ability of the codes to predict the impact on noise of 
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alterations to nozzle axisymmetry is almost as useful as their 

ability to predict the absolute jet noise itself. A tool that could 

predict noise modification due to geometric changes is 

satisfactory for engineering quieter nozzles.

8.16.1.2.1 Chevron Nozzles

Chevron nozzles have the potential to reduce jet noise at its 

peak directivity angle near the downstream jet axis with 

minimal benefit or even slight noise increase along the 

sideline. They are designed with the premise that the strengthened axial vorticity generated by the chevrons would decay 

the centerline velocity faster, enhance mixing, and help reduce 

the core length. Chevron nozzle SMC001 was a litmus test 

case that examined the ability of RANS-based acoustic 

analogy codes to capture noise trends in nonaxisymmetric 

configurations. This particular nozzle design (see Figure 8.12) 

consists of six identical chevrons at 5° penetration angle, and 

with an effective nozzle exit diameter of 5.1 cm (2 in.). The 

details of the geometry and its aeroacoustics performance 

compared to the base nozzle as well as alternative chevron 

designs are discussed in Reference 34. For the purpose of this 

assessment, only one operating condition was considered (case

042, Table 8.6).

8.16.1.2.2 Offset Nozzles

The offset streams are designed primarily in dual-flow 

nozzles in an attempt to modify the fan stream and to divert 

the core-fan shear noise in a favorable direction away from an 

observer on the ground. These designs usually result in a noise 

increase in the opposite direction. Two offset-stream concepts 

are discussed here (Figure 8.40): (1) the “fan-wedge” design

places a 20° wedge in the fan stream with the wedge tip 

pointing upstream and (2) the “S-duct” design shifts the flow 

centerlines to create 5 percent offset while allowing for the 

two streams to remain parallel at the jet exit. Both designs 

create a relatively thicker flow with less turbulence on one 

side relative to the opposite side (Ref. 35) when compared to 

the flow of the dual stream geometry without offset or fanwedge. The operating conditions for the two concepts are very 

similar (see Table 8.6). This operating condition was chosen to 

have similar velocity gradients as many commercial aviation 

jet cycles but with a cold core flow, knowing that the JeNo 

code was not calibrated for hot jets. The Wind-US RANS 

solver provided the mean flow and turbulence for offset 

nozzles as well as the base configuration.

8.16.2 Discussion of JeNo v1.0 Results

Figure 8.41 to Figure 8.53 show comparisons of measured 

data and predicted results for the cases listed in Table 8.5 and 

Table 8.6.

The subsonic cold jet comparisons (cases 003 and 007) are 

very good, generally within the experimental uncertainty 

(Figure 8.41 and Figure 8.42). The hot jet cases (Figure 8.43

to Figure 8.48) are off by as much as 10 dB, depending upon 

the jet speed. The discrepancy is always an underprediction, 

and gets worse with increased heating, and the aft angle has an 

incorrect peak frequency at the highest speeds (cases 027 and 

040). On the other hand, the supersonic cold jet predictions 

(cases 059, 068, 075, 083, and 090) are not too bad, typically 

within 5 dB of data (Figure 8.49 to Figure 8.53). This was not 

surprising, as this version of JeNo was expected to do 

relatively well in the unheated jet cases. The discrepancies are 

mostly at aft angles and become more prominent at higher 

supersonic speeds. 

Figure 8.41.—Assessment of JeNo v1.0 jet noise predictions. Case 003 (see Table 8.5) for convergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 0.51, acoustic Mach number Ma = 0.5, and static temperature ratio 

Ts,r = 0.955. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound pressure 

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with

uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.42.—Assessment of JeNo v1.0 jet noise predictions. Case 007 (see Table 8.5) for convergent, axisymmetric nozzle:

bypass ratio (BPR) = 0, Mach number M = 0.98, acoustic Mach number Ma = 0.902, and static temperature ratio Ts,r = 0.842. 

Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound pressure level (SPL) versus 

Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. (c) Overall sound

pressure level (OASPL) as function of θ.

Figure 8.43.—Assessment of JeNo v1.0 jet noise predictions. Case 022 (see Table 8.5) for convergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 0.37, acoustic Mach number Ma = 0.492, and static temperature

ratio Ts,r = 1.767. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with 

uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.44.—Assessment of JeNo v1.0 jet noise predictions. Case 025 (see Table 8.5) for convergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 0.68, acoustic Mach number Ma = 0.901, and static temperature

ratio Ts,r = 1.77. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound pressure 

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.45.—Assessment of JeNo v1.0 jet noise predictions. Case 027 (see Table 8.5) for convergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 1.01, acoustic Mach number Ma = 1.33, and static temperature ratio 

Ts,r = 1.759. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound pressure

level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with uncertainty. 

(c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.46.—Assessment of JeNo v1.0 jet noise predictions. Case 034 (see Table 8.5) for convergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 0.3, acoustic Mach number Ma = 0.484, and static temperature

ratio Ts,r = 2.624. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, with 

uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.47.—Assessment of JeNo v1.0 jet noise predictions. Case 037 (see Table 8.5) for convergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 0.56, acoustic Mach number Ma = 0.901, and static temperature

ratio Ts,r = 2.702. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, and 

uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.48.—Assessment of JeNo v1.0 jet noise predictions. Case 040 (see Table 8.5) for convergent, axisymmetric 

nozzle: bypass ratio (BPR) = 0, Mach number M = 0.92, acoustic Mach number Ma = 1.483, and static temperature 

ratio Ts,r = 2.703. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave sound

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values,

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.49.—Assessment of JeNo v1.0 jet noise predictions. Case 059 (see Table 8.5) for convergent-divergent,

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.172, acoustic Mach number Ma = 1.047, and static 

temperature ratio Ts,r = 0.797. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.50.—Assessment of JeNo v1.0 jet noise predictions. Case 068 (see Table 8.5) for convergent-divergent,

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.394, acoustic Mach number Ma = 1.191, and static 

temperature ratio Ts,r = 0.73. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.51.—Assessment of JeNo v1.0 jet noise predictions. Case 075 (see Table 8.5) for convergent-divergent,

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.497, acoustic Mach number Ma = 1.251, and static 

temperature ratio Ts,r = 0.699. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.52.—Assessment of JeNo v1.0 jet noise predictions. Case 083 (see Table 8.5) for convergent-divergent,

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.659, acoustic Mach number Ma = 1.342, and static 

temperature ratio Ts,r = 0.654. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.53.—Assessment of JeNo v1.0 jet noise predictions. Case 090 (see Table 8.5) for convergent-divergent,

axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.784, acoustic Mach number Ma = 1.403, and static 

temperature ratio Ts,r = 0.619. Comparison between JeNo predictions and SHJAR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 130°. (b) Difference in SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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The 130° spectra peaked at a lower frequency relative to 

measurements and showed a deficit in noise level at all speeds. 

One might conclude that the parallel flow assumption in the 

Green’s function predicts a larger cone of silence near the 

downstream jet axis. Spreading jets are expected to generate a 

much shallower zone of silence as seen in measured data.

The presence of residual shock noise—a noise generation 

mechanism not modeled in the code—is also quite visible in 

the experimental spectra. This accounts for some of the 

“underprediction” at the upstream angles, meaning that in 

reality the mixing noise predictions may be quite better than 

what data projects at such angles. Still, the aft angle predictions were not as good.

In carrying out the source volume integration in axisymmetric jets, JeNo considers the source as a superposition of ring 

volume elements. Radial distributions of the axial mean 

velocity and temperature are used to evaluate the Green’s 

function at each frequency. As pointed out in Section 8.2.2.2, 

rather than solving for the five components of a vector 

Green’s function, propagation effects in nonaxisymmeteric 

geometries are treated with a more robust approach using

either the line-of-sight or the line-of-source method. These 

methods, also referred to as 2.5-dimensional approximation, 

allow for the azimuthal variation of the source strength in such 

jets; however, the Green’s function is evaluated along a userdefined azimuthal plane. 

A single-stream chevron nozzle represents the first example 

of such nonaxisymmetic nozzle concepts. Figure 8.54 shows 

the power spectral density (PSD) in an SMC001 nozzle with 

six chevrons (see Figure 8.12 for geometry). JeNo predictions 

in a 2.5-dimensional approximation are shown with the line of 

sight placed either at the chevron tip or its valley. The spectra 

are compared with both measured data and prediction for a 

base axisymmetric geometry (no chevrons). The differences 

between the two lines of sight emerge primarily at aft angles. 

At 150°, significantly more high frequency noise is projected 

when the line of sight is placed at the chevron tip compared to 

the chevron valley. The reality may be somewhere between 

these two extremes. This is illustrated in Figure 8.55 when the 

2.5-dimensional concept is carried out using line-of-source 

model. Such an approximation removes any azimuthal 

dependency from the final result and resembles some form of 

azimuthal averaging of the sound field. Measurements show 

that the sound field for a six-chevron nozzle is nearly

axisymmetric.

Computational study of the offset nozzle designs (Ref. 36), 

and experimental results (Refs. 37 and 38), indicate that 

modifications in the fan stream could provide noise benefits 

on one side of a separate flow jet at the expense of increased 

noise on the opposite side. A qualitative assessment of such 

concepts is shown here using the 2.5-dimensional approximation and the line-of-sight method. Figure 8.56 shows JeNo 

predictions for the S-duct concept. Lossless spectra are shown 

on an arc at 24.46 m (80.24 ft) at 90° and 150° inlet angles, 

respectively, with the line-of-sight placed either along the 

thick or thin sides of the fan flow. Experimental data are also 

shown separately in Figure 8.56(b). Measures of noise benefit 

(reduction), or penalty (increase) at 150° between the base 

geometry and the thick side of S-duct concept are shown 

separately in Figure 8.57(a) and (b) as the decibel difference 

between the thick side spectrum and the baseline, axisymmetric spectrum for the predictions and the experimental data, 

respectively. A positive delta dB indicates noise penalty. The 

task of error analysis may be accomplished if the error band is 

defined as the difference between the trends suggested by 

Figure 8.57(a) and (b), as seen in part (c). A similar error band 

is shown at 90° in part (d).

An assessment of the fan-wedge concept is presented in 

Figure 8.58. In this exercise, the spectra are shown along the 

opposing sides using two lines of sight separated by 180°, and 

are compared with the base geometry operating at a similar 

condition. Again 90° and 150° power spectral density 

predictions are presented and similar data illustrations are also 

provided for comparison. The delta dB difference in noise 

between the two sides of the fan-wedge concept at 150° inlet 

angle is shown in Figure 8.59(a), with similar representation 

of the experimental data in Figure 8.59(b). An error band that 

displays the difference between the two is shown in 

Figure 8.59(c), and an additional error band at 90° inlet angle 

is also seen in Figure 8.59(d).

A realistic assessment of the three-dimensional effects, as 

indicated earlier, requires a full three-dimensional propagation 

Green’s function. The present exercise shows that the 

2.5-dimensional concept and extension of the axisymmetric 

Green’s function to three-dimensional jets is rather successful 

in capturing the observed trends.
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Figure 8.54.—Comparison of lossless power spectral density (PSD) of jet noise versus Strouhal number St at different

inlet angles θ on a 40D arc. NATR data and JeNo v1.0 predictions. (a) θ = 60°. (b) θ = 90°. (c) θ = 130°. (d) θ = 150°.

Figure 8.55.—Comparison of lossless power spectral density (PSD) for offset nozzle versus Strouhal number St at different 

inlet angles θ on a 40D arc. NATR data and JeNo v1.0 predictions. (a) θ = 90°. (b) θ = 150°.
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Figure 8.56.—Comparison of lossless power spectral density (PSD) for offset S-duct nozzle and

axisymmetric geometry (see Table 8.6 and Figure 8.40(b)) at different inlet angles θ on 40D arc.

(a) Nozzle geometries. (b) NATR experimental data, θ = 90° and 150°. (c) JeNo v1.0 predictions at 90°

using 2.5-dimensional approximation with line-of-sight method. (d) JeNo v1.0 predictions at 150° using 

2.5-dimensional approximation with line-of-sight method.
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Figure 8.57.—Difference ∆ between power spectral density (PSD) measured on thick side of S-duct nozzle and 

axisymmetric nozzle. (a) JeNo v1.0 prediction at inlet angle θ = 150°. (b) NATR experimental data at θ = 150°. 

(c) Error estimate at θ = 150°; difference between NATR data and prediction. (d) Error estimate at θ = 90°.
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Figure 8.58.—Lossless power spectral density (PSD) for offset fan-wedge nozzle and axisymmetric geometry (see

Table 8.6 and Figure 8.40(a)) at different inlet angles θ on 24.46-m (80.24-ft) arc. (a) Nozzle geometries. (b) NATR 

experimental data. (c) JeNo v1.0 predictions at θ = 90° using 2.5-dimensional approximation with line-of-sight

method. (d) JeNo v1.0 predictions at θ = 150° using 2.5-dimensional approximation with line-of-sight method.
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Figure 8.59.—Difference ∆ between power spectral density (PSD) measured on thick (quiet) and thin (noisy) 

sides of fan-wedge nozzle and axisymmetric nozzle. (a) JeNo v1.0 prediction at inlet angle θ = 150°.

(b) NATR experimental data at θ = 150°. (c) Error estimate at θ = 150°; difference between NATR data

and prediction. (d) Error estimate at θ = 90°.

8.17 Conclusions

Neither empirical nor acoustic analogy models predicted 

overall acoustic power of subsonic axisymmetric nozzle flows 

within experimental uncertainty for all cases examined in this 

assessment exercise. The empirical code ANOPP did not 

predict spectral directivity within experimental uncertainty for 

most cases, and displayed systematic errors leading to spectral 

disagreement at high frequencies, especially at downstream 

angles. Sample-case EPNL predictions were off by several 

decibels, an intolerable situation in practice where EPNL 

values need to be known to within fractions of a decibel. 

However, for axisymmetric jets, the ANOPP code was more 

robust than the acoustic analogy codes, and displayed a 

consistent level of error—slightly overpredicting the peak and 

displaying an erroneously large amplitude at high frequency 

near the Strouhal number 10.0—for a broad range of jet flows. 

At 150° the prediction was very good except for this highfrequency component. 

The acoustic analogy code JeNo v1.0 predicted noise spectral directivity to within experimental uncertainty for subsonic 

cold jets, but deviated when either jet speed approached the 

speed of sound or the jet temperature was elevated. Also, JeNo 

did capture the impact of nonaxisymmetric jets with azimuthal 

periodicity greater than 4, but did not capture the azimuthal 

directivity effect from low-order asymmetries such as offset 

nozzles. 

The acoustic analogy code Jet3D was able to predict the 

noise and spectral content from a high-speed hot jet at forward 

and side angles, but incorrectly predicted noise and peak 

frequency at angles in the aft arc. Jet3D did not predict cold 

jets very well, missing the spectral shape, peak frequency, and 

amplitude.

8.17.1 Empirical Code 

1. The Stone Jet Noise module (ST2JET) contained within 

ANOPP was applicable to a wide range of flow conditions, 

predicting OASPLs only slightly outside of experimental 

uncertainty for most axisymmetric jets. 

2. The error in the prediction first became apparent in 

OASPL directivity, where the aft angle noise was predicted to 

change more radically with angle than the data supports. 

Spectrally, the main problem was with a predicted highfrequency noise component, the “outer stream mixing noise” 

from the ambient-bypass mixing region, which caused a highfrequency hump in the spectra not observed in the data.

3. The model for predicting the impact of chevrons did not 

successfully predict the noise produced by an external chevron 

nozzle, overpredicting the noise reduction by 15 dB or so.
Jet Noise Prediction

NASA/TP—2012-215653 291 Chapter 8

8.17.2 Acoustic Analogy Codes

Both acoustic analogy codes suffered from their inability to 

predict the jet mixing noise consistently across heated and 

unheated jet conditions. 

8.17.2.1 JeNo v1.0

1. The JeNo version 1.0 code predicted noise from cold, 

shock-free jets within experimental uncertainty at both 

broadside and aft angles. 

2. As jet speed increased past the sonic speed, the broadside spectra maintained their accuracy; however, the aft angle 

spectra displayed inaccurate peak frequency and amplitude. 

3. As jet temperature increased, underpredictions in noise 

amplitude emerged at both broadside and aft angles. Since 

JeNo v1.0 does not contain enthalpic sources, this was 

expected.

4. Predicted far-field noise from nonaxisymmetric nozzles 

with azimuthal-mode order greater than 4 was axisymmetric 

and consistent with data. Jets with low-order asymmetries and 

nonaxisymmetric noise field, such as offset streams, pylons, or 

rectangular nozzles were not predicted well. Ideally, a full 

three-dimensional calculation of the Green’s function is 

required in three-dimensional jets. This capability was not 

available in JeNo v1.0.

8.17.2.2 Jet3D

1. The Jet3D code predicted noise for cold, shock-free jets 

that differed from the experimental data by 5 dB or more in 

peak amplitude at broadside angles. Spectral shape was 

grossly incorrect for these cases. 

2. As temperature increased, overpredictions diminished 

to an average of 5 dB above measurements, but the peak 

frequency was off by a significant margin.

3. Jet3D did predict jet noise within experimental uncertainty for high-speed hot jets at broadside angles. At a total 

temperature ratio above 2 and jet velocity exceeding twice the 

ambient sound speed, the broadside spectra were within 

experimental uncertainty, although aft angle noise amplitudes 

were in error by 10 dB or more.

8.17.3 Recommendations

1. The empirical jet noise prediction code ST2JET within 

ANOPP Level 25 should be used for high-speed, system-level 

design studies with the understanding that it produces results 

only accurate to within 2 decibels in EPNL. The ANOPP code 

could be improved using the current database if the predicted 

noise accuracy is not satisfactory for system studies. 

2. Both acoustic analogy codes JeNo v1.0 and Jet3D need 

to include additional source terms associated with unsteady 

temperature (i.e., enthalpy related sources). 

3. Both acoustic analogy codes—especially Jet3D—need 

improved directivity factors. To improve JeNo v1.0 it may be 

necessary to examine the significance of source noncompactness in high-speed jets. Relaxing the parallel flow assumption 

in favor of a spreading jet could also improve predictions at 

small aft angles.

4. A three-dimensional vector Green’s function is required 

as a propagator to correctly predict the propagation of sound 

from unconventional nozzle geometries.

Jet Noise Prediction

NASA/TP—2012-215653 293 Chapter 8

Appendix A.—Nomenclature

A.1 Acronyms

AAPL Aero-Acoustic Propulsion Laboratory

ANOPP Aircraft Noise Prediction Program

B&K Brüel & Kjær 

BBSN broadband shock-associated noise

BPR bypass ratio

C-D convergent-divergent

CFD computational fluid dynamics

DADS digital acoustic data system

EPNL effective perceived noise level

HFJER High Flow Jet Exit Rig

LDV laser Doppler velocimetry

LES large eddy simulations

NATR Nozzle Acoustic Test Rig

NPR nozzle pressure ratio

OASPL overall sound pressure level

PCI peripheral component interconnect

PIV particle image velocimetry

RANS Reynolds-averaged Navier-Stokes

rms root-mean-squared

SHJAR Small Hot Jet Acoustic Rig

SPL sound pressure level

SST shear stress transport

TKE turbulent kinetic energy

TRL technology readiness level

TRPIV time-resolved PIV

A.2 Symbols

c speed of sound

D nozzle diameter 

f frequency

G Green’s function

h enthalpy

i unit imaginary number

k turbulent kinetic energy

L linear differential operator, Eq. (8.8)

M Mach number

m azimuthal base periodicity

N number of polar angles

P Fourier transform of p

p pressure

q source term

R distance between source and receiver

r radial coordinate

St Strouhal number

T temperature

T large period of integration 

t time

Tij Lighthill stress tensor

U fully expanded jet velocity

u,v,w components of flow velocity vector

x axial direction

x observer spatial position vector

y source spatial position vector

γ specific heat ratio of air

∆ error (difference between measurements and 

predictions)

δ Dirac delta function

δij Kronecker delta

ε turbulent kinetic energy dissipation rate

θ polar (or inlet) angle

μ average error, Eq (8.13a)

Π pressure variable in Eq. (8.7)

ρ fluid density

σij viscous stress tensor

σ

2 variance, Eq. (8.13b)

τ time of emission

φ azimuthal angle

ω radian frequency

( ) mean value

Subscripts:

a acoustic

ANOPP predicted with ANOPP code

d design

expt experimental value

fl flight

o mean

r ratio

s static

t total

∞ ambient

Superscripts:

s source

′ fluctuating

Jet Noise Prediction

NASA/TP—2012-215653 295 Chapter 8

Appendix B.—Jet Configurations Tested in NASA-Sponsored Test Programs 

Details of the operating conditions for nine test categories 

are identified as configurations A through I. Tests were carried 

out at NASA Glenn Research Center over a period of four 

years (2004 to 2007), and extensive aerodynamic and noise 

data have been compiled to guide model development and 

validation efforts.

Nomenclature for the table:

BPR bypass ratio

M ideally expanded Mach number; for 

dual stream flows, it is the higher M

Axial geometry indicates if nozzle was convergent or 

convergent-divergent (C-D) or if it was 

internally or externally mixed

Azimuthal geometry azimuthal base periodicity, indicates 

nozzle was axisymmetric (m = 0) or 

had lobes or chevrons

Ma acoustic Mach number U/c∞

Ts,r static temperature ratio Ts/T∞

Tt,r total temperature ratio Tt/T∞; for dual 

stream cases 

Mfl flight Mach number

nozid nozzle identification
NASA/TP—2012-215653 296

TABLE 8.7.—TEST CASE IDENTIFIER WITHIN EACH CONFIGURATION

(a) Configuration A: BPR = 0, convergent axisymmetric nozzles, hot subsonic flowa

Case M Geometry Ma Ts,r Mfl nozid

Axial Azimuthal

001 0.35 Convergent m = 0 0.350 0.980 0 SMC000

002 0.41 0.401 0.972 0 SMC000

003 0.51 0.500 0.955 0 SMC000

004 0.62 0.601 0.932 0 SMC000

005 0.74 0.701 0.906 0 SMC000

006 0.85 0.799 0.877 0 SMC000

007 0.98 0.902 0.842 0 SMC000

008 0.80 0.798 1.001 0 SMC000

009 0.90 0.897 0.997 0 SMC000

010 0.55 0.599 1.202 0 SMC000

011 0.64 0.701 1.198 0 SMC000

012 0.73 0.799 1.204 0 SMC000

013 0.82 0.899 1.203 0 SMC000

014 0.91 1.001 1.203 0 SMC000

015 0.33 0.399 1.431 0 SMC000

016 0.42 0.502 1.430 0 SMC000

017 0.50 0.599 1.430 0 SMC000

018 0.59 0.698 1.428 0 SMC000

019 0.67 0.802 1.428 0 SMC000

020 0.75 0.897 1.428 0 SMC000

021 0.99 1.185 1.426 0 SMC000

022 0.37 0.492 1.767 0 SMC000

023 0.53 0.698 1.764 0 SMC000

024 0.61 0.801 1.768 0 SMC000

025 0.68 0.901 1.770 0 SMC000

026 0.89 1.184 1.771 0 SMC000

027 1.01 1.330 1.759 0 SMC000

028 0.47 0.699 2.267 0 SMC000

029 0.54 0.801 2.272 0 SMC000

030 0.60 0.899 2.269 0 SMC000

031 0.78 1.158 2.270 0 SMC000

032 0.89 1.329 2.263 0 SMC000

033 0.99 1.483 2.277 0 SMC000

034 0.30 0.484 2.624 0 SMC000

035 0.43 0.700 2.707 0 SMC000

036 0.49 0.800 2.699 0 SMC000

037 0.56 0.901 2.702 0 SMC000

038 0.73 1.187 2.695 0 SMC000

039 0.82 1.329 2.704 0 SMC000

040 0.92 1.483 2.703 0 SMC000

a

See the beginning of this appendix for definitions of table columns.
Jet Noise Prediction

NASA/TP—2012-215653 297 Chapter 8

TABLE 8.7.—Continued.

(b) Configuration B: BPR = 0, convergent chevron nozzles, hot subsonic flowa

Case M Geometry Ma Ts,r Mfl nozid

Axial Azimuthal

041 0.50 Convergent m = 6 0.499 0.958 0 SMC001

042 0.972 0.902 0.837 0 SMC001

043 0.668 0.881 1.752 0 SMC001

044 1.006 1.320 1.734 0 SMC001

045 0.551 0.883 2.639 0 SMC001

046 0.827 1.308 2.576 0 SMC001

047 0.506 Convergent m = 6 0.494 0.953 0 SMC005

048 0.972 0.893 0.844 0 SMC005

049 0.674 0.884 1.740 0 SMC005

050 1.008 1.325 1.743 0 SMC005

051 0.549 0.879 2.649 0 SMC005

052 0.823 1.304 2.585 0 SMC005

053 0.977 Convergent m = 6 0.898 0.844 0 SMC006

054 0.673 0.885 1.745 0 SMC006

055 1.006 1.320 1.736 0 SMC006

056 0.555 0.891 2.651 0 SMC006

057 0.828 1.309 2.571 0 SMC006 a

See the beginning of this appendix for definitions of table columns.
NASA/TP—2012-215653 298

TABLE 8.7.—Continued.

(c) Configuration C: BPR = 0, convergent-divergent axisymmetric nozzles, hot supersonic flowa

Case M Geometry Ma Ts,r Mfl nozid

Axial Azimuthal 

058 1.174 C-D m = 0 1.178 1.007 0 SMC014

059 1.172 1.047 0.797 0 SMC014

060 1.170 1.171 1.003 0 SMC014

061 1.171 1.401 1.436 0 SMC014

062 1.172 1.469 1.578 0 SMC014

063 1.177 1.554 1.759 0 SMC014

064 1.175 1.663 2.032 0 SMC014

065 1.170 1.746 2.271 0 SMC014

066 1.169 1.828 2.509 0 SMC014

067 1.174 1.897 2.693 0 SMC014

068 1.394 C-D m = 0 1.191 0.730 0 SMC015

069 1.381 1.381 0.998 0 SMC015

070 1.392 1.489 1.145 0 SMC015

071 1.384 1.826 1.757 0 SMC015

072 1.384 2.058 2.262 0 SMC015

073 1.384 1.652 1.430 0 SMC015

074 1.395 2.132 2.397 0 SMC015

075 1.497 C-D m = 0 1.251 0.699 0 SMC016

076 1.484 1.485 1.002 0 SMC016

077 1.488 1.657 1.242 0 SMC016

078 1.482 1.773 1.436 0 SMC016

079 1.501 1.841 1.510 0 SMC016

080 1.484 1.966 1.771 0 SMC016

081 1.488 2.134 2.090 0 SMC016

082 1.538 2.268 2.218 0 SMC016

083 1.659 C-D m = 0 1.342 0.654 0 SMC017

084 1.666 1.484 0.793 0 SMC017

085 1.658 1.657 0.999 0 SMC017

086 1.659 1.983 1.433 0 SMC017

087 1.656 2.191 1.767 0 SMC017

088 1.789 C-D m = 0 2.136 1.429 0 SMC018

089 1.786 2.359 1.760 0 SMC018

090 1.784 1.403 0.619 0 SMC018

091 1.785 1.403 0.618 0 SMC018

092 1.779 1.778 0.999 0 SMC018 a

See the beginning of this appendix for definitions of table columns.
Jet Noise Prediction

NASA/TP—2012-215653 299 Chapter 8

TABLE 8.7.—Continued.

(d) Configuration D: BPR = 0.2, axisymmetric internally mixed nozzles, hot flowa

[Coplanar and fully mixed approximations.]

Case M Geometry Core Bypass Mfl nozid

Axial Azimuthal Ma Tt.r Ma Tt,r

093 0.6 Internal splitter,

convergent m = 0 0.902 2.450 0.607 1.088 0.0 C4S1PE1

094 0.6 1.001 3.038 0.611 1.099 0.0 C4S1PE1

095 0.8 0.898 1.433 0.758 1.010 0.0 C4S1PE1

096 0.8 1.197 2.576 0.780 1.072 0.0 C4S1PE1

097 0.9 0.834 1.002 0.835 1.008 0.0 C4S1PE1

098 0.9 1.197 2.078 0.853 1.045 0.0 C4S1PE1

099 0.9 1.498 3.293 0.874 1.094 0.0 C4S1PE1

100 1 0.906 0.988 0.910 0.995 0.0 C4S1PE1

101 1 1.000 1.200 0.979 1.149 0.0 C4S1PE1

102 1 1.500 2.724 0.944 1.068 0.0 C4S1PE1

103 1.05 1.051 1.221 1.031 1.173 0.0 C4S1PE1

104 1.05 1.184 1.546 0.955 1.006 0.0 C4S1PE1

105 1.18 1.400 1.748 1.071 1.023 0.0 C4S1PE1

106 1.18 1.601 2.296 1.083 1.044 0.0 C4S1PE1

107 1.18 1.801 2.910 1.094 1.071 0.0 C4S1PE1

108 1.18 2.000 3.592 1.110 1.102 0.0 C4S1PE1

109 1.4 1.400 1.392 1.188 1.003 0.0 C4S1PE1

110 1.5 1.503 1.455 1.262 1.026 0.0 C4S1PE1

111 1.5 1.799 2.087 1.268 1.035 0.0 C4S1PE1

112 1.5 2.004 2.578 1.274 1.044 0.0 C4S1PE1

113 1.6 1.603 1.513 1.310 1.013 0.0 C4S1PE1

114 1.6 1.803 1.916 1.322 1.031 0.0 C4S1PE1

115 1.6 2.406 3.393 1.346 1.065 0.0 C4S1PE1

116 1.8 1.801 1.650 1.415 1.017 0.0 C4S1PE1

117 1.8 2.402 2.917 1.441 1.053 0.0 C4S1PE1

118 2 1.999 1.794 1.511 1.026 0.0 C4S1PE1

119 2 2.401 2.581 1.523 1.042 0.0 C4S1PE1

120 1.18 Internal splitter,

C-D m = 0 1.401 1.750 1.061 1.004 0.0 M2S1PE2

121 1.18 1.603 2.291 1.067 1.016 0.0 M2S1PE2

122 1.18 1.808 2.916 1.073 1.030 0.0 M2S1PE2

123 1.4 1.399 1.397 1.176 0.987 0.0 M4S1PE2

124 1.5 1.504 1.463 1.236 0.988 0.0 M5S1PE2

125 1.5 1.804 2.097 1.245 1.002 0.0 M5S1PE2

126 1.5 2.008 2.595 1.257 1.019 0.0 M5S1PE2

127 1.6 1.601 1.516 1.286 0.979 0.0 M6S1PE2

128 1.6 1.805 1.925 1.294 0.989 0.0 M6S1PE2

129 1.6 2.407 3.398 1.334 1.054 0.0 M6S1PE2

130 1.8 1.801 1.647 1.421 1.027 0.0 M8S1PE2

131 1.8 2.402 2.913 1.441 1.055 0.0 M8S1PE2 a

See the beginning of this appendix for definitions of table columns.
NASA/TP—2012-215653 300

TABLE 8.7.—Continued.

(e) Configuration E: BPR = 1, axisymmetric internally mixed nozzles, hot flowa

[Coplanar and fully mixed approximations.]

Case M Geometry Core Bypass Mfl nozid

Axial Azimuthal Ma Tt.r Ma Tt.r

132 0.6 Internal splitter,

convergent m = 0 0.902 2.449 0.576 1.001 0.0 C4S2PE1

133 0.6 1.003 3.052 0.582 1.011 0.0 C4S2PE1

134 0.8 0.900 1.429 0.748 0.985 0.0 C4S2PE1

135 0.8 1.201 2.573 0.748 0.992 0.0 C4S2PE1

136 0.9 0.829 0.983 0.824 0.977 0.0 C4S2PE1

137 0.9 1.203 2.078 0.829 0.991 0.0 C4S2PE1

138 0.9 1.508 3.293 0.839 1.009 0.0 C4S2PE1

139 1 0.902 0.978 0.899 0.976 0.0 C4S2PE1

140 1 0.998 1.195 1.003 1.209 0.0 C4S2PE1

141 1 1.503 2.726 0.909 0.995 0.0 C4S2PE1

142 1.05 0.939 0.978 0.937 0.976 0.0 C4S2PE1

143 1.05 1.180 1.540 0.948 0.990 0.0 C4S2PE1

144 1.18 1.605 2.300 1.070 1.022 0.0 C4S2PE1

145 1.18 1.805 2.910 1.068 1.022 0.0 C4S2PE1

146 1.4 1.404 1.397 1.191 1.006 0.0 C4S2PE1

147 1.5 1.504 1.456 1.252 1.012 0.0 C4S2PE1

148 1.5 1.799 2.084 1.241 0.991 0.0 C4S2PE1

149 1.5 2.000 2.572 1.256 1.014 0.0 C4S2PE1

150 1.6 1.604 1.515 1.312 1.013 0.0 C4S2PE1

151 1.6 1.803 1.916 1.298 0.992 0.0 C4S2PE1

152 1.6 2.406 3.384 1.339 1.055 0.0 C4S2PE1

153 1.8 1.805 1.655 1.420 1.026 0.0 C4S2PE1

154 1.8 2.403 2.911 1.442 1.056 0.0 C4S2PE1

155 2 2.006 1.808 1.521 1.041 0.0 C4S2PE1

156 2 2.401 2.581 1.530 1.053 0.0 C4S2PE1

157 1.18 Internal splitter,

C-D m = 0 1.404 1.754 1.057 0.995 0.0 M2S2PE2

158 1.18 1.605 2.305 1.059 1.003 0.0 M2S2PE2

159 1.18 1.806 2.919 1.063 1.009 0.0 M2S2PE2

160 1.4 1.402 1.402 1.184 1.000 0.0 M4S2PE2

161 1.5 1.502 1.461 1.240 0.995 0.0 M5S2PE2

162 1.5 1.800 2.094 1.244 1.003 0.0 M5S2PE2

163 1.5 2.003 2.589 1.248 1.009 0.0 M5S2PE2

164 2 2.003 1.802 1.496 1.006 0.0 MTS2PE2

165 2 2.403 2.580 1.500 1.012 0.0 MTS2PE2 a

See the beginning of this appendix for definitions of table columns.
Jet Noise Prediction

NASA/TP—2012-215653 301 Chapter 8

TABLE 8.7.—Continued.

(f) Configuration F: BPR = 3, convergent axisymmetric internally mixed nozzles, hot flowa

[Coplanar and fully mixed approximations.]

Case M Geometry Core Bypass Mfl nozid

Axial Azimuthal Ma Tt.r Ma Tt.r

166 0.6 Internal splitter m = 0 0.896 2.439 0.573 0.977 0.0 C4S3PE1

167 0.6 1.000 3.057 0.579 0.992 0.0 C4S3PE1

168 0.8 0.902 1.435 0.760 1.024 0.0 C4S3PE1

169 0.8 1.194 2.568 0.746 0.981 0.0 C4S3PE1

170 0.9 0.857 1.057 0.835 0.998 0.0 C4S3PE1

171 0.9 1.202 2.082 0.826 0.977 0.0 C4S3PE1

172 1 0.925 1.031 0.912 0.999 0.0 C4S3PE1

173 1 1.497 2.726 0.907 0.983 0.0 C4S3PE1

174 1.05 0.960 1.025 0.951 0.999 0.0 C4S3PE1

175 1.05 1.183 1.541 0.940 0.977 0.0 C4S3PE1

176 1.18 1.603 2.290 1.071 1.023 0.0 C4S3PE1

177 1.18 1.801 2.903 1.072 1.024 0.0 C4S3PE1

178 1.4 1.399 1.389 1.176 0.982 0.0 C4S3PE1

179 1.5 1.502 1.452 1.237 0.984 0.0 C4S3PE1

180 1.5 1.805 2.095 1.262 1.025 0.0 C4S3PE1

181 1.5 2.000 2.573 1.263 1.028 0.0 C4S3PE1

182 1.6 1.601 1.515 1.295 0.990 0.0 C4S3PE1

183 1.6 1.804 1.919 1.322 1.032 0.0 C4S3PE1

184 1.6 2.402 3.377 1.332 1.046 0.0 C4S3PE1

185 1.8 1.800 1.649 1.400 0.998 0.0 C4S3PE1

186 1.8 2.412 2.931 1.410 1.010 0.0 C4S3PE1

187 2 1.987 1.805 1.483 1.009 0.0 C4S3PE1

188 2 2.385 2.589 1.487 1.012 0.0 C4S3PE1 a

See the beginning of this appendix for definitions of table columns.
NASA/TP—2012-215653 302

TABLE 8.7.—Continued.

(g) Configuration G: BPR = 5, convergent internally or externally mixed nozzles, hot flowa

Case M Geometry Core Bypass Mfl nozid

Axial Azimuthal Ma Tt.r Ma Tt.r

Externally mixed

189 0.80 Separate flow m = 0 0.956 2.327 0.791 1.112 0.0 PAA5

190 0.87 1.120 2.482 0.871 1.146 0.0 PAA5

191 0.93 1.265 2.663 0.935 1.182 0.0 PAA5

192 0.80 0.959 2.335 0.790 1.113 0.1 PAA5

193 0.87 1.119 2.481 0.866 1.142 0.1 PAA5

194 0.93 1.264 2.662 0.938 1.182 0.1 PAA5

195 0.88 1.119 2.506 0.878 1.161 0.2 PAA5

196 0.94 1.272 2.676 0.940 1.190 0.2 PAA5

197 0.94 1.268 2.670 0.938 1.186 0.3 PAA5

Coplanar and fully mixed approximations

198 0.6 Internal splitter m = 0 0.886 2.691 0.674 1.258 0.0 5000.00

199 1.343 3.119 0.885 1.250 0.0 5000.00

200 1.637 3.543 0.984 1.302 0.0 5000.00

201 1.248 3.013 0.904 1.249 0.0 5000.00

202 1.401 3.176 0.872 1.249 0.0 5000.00

203 0.894 2.687 0.675 1.254 0.3 5000.00

204 1.334 3.055 0.879 1.230 0.3 5000.00

205 1.637 3.548 0.987 1.302 0.3 5000.00

206 1.245 3.015 0.906 1.254 0.3 5000.00

207 1.530 3.322 0.993 1.252 0.3 5000.00

208 1.407 3.184 0.878 1.256 0.3 5000.00

209 1.662 3.487 0.977 1.254 0.3 5000.00

210 Internal chevron m = 8 0.913 2.790 0.690 1.309 0.0 5001.04

211 1.614 3.455 0.973 1.270 0.0 5001.04

212 0.908 2.790 0.687 1.306 0.3 5001.04

213 1.375 3.260 0.906 1.309 0.3 5001.04

214 1.651 3.596 0.992 1.317 0.3 5001.04

215 1.271 3.132 0.926 1.309 0.3 5001.04

216 1.406 3.202 0.878 1.260 0.3 5001.04

217 Internal deep 

scalloped lobes m = 20 0.901 2.765 0.682 1.294 0.0 5002.02

218 1.637 3.546 0.985 1.300 0.0 5002.02

219 0.906 2.762 0.681 1.290 0.3 5002.02

220 1.366 3.214 0.902 1.294 0.3 5002.02

221 1.633 3.540 0.986 1.303 0.3 5002.02

222 1.269 3.111 0.919 1.294 0.3 5002.02

223 1.429 3.297 0.893 1.297 0.3 5002.02

Externally mixed

224 Separate flow m = 0 1.037 2.130 1.165 1.050 0.1 PAA5

225 1.037 2.130 1.295 1.050 0.1 PAA5

226 1.037 2.390 1.487 1.050 0.1 PAA5

227 1.126 2.260 1.200 1.170 0.1 PAA5

228 1.126 2.260 1.335 1.170 0.1 PAA5

229 1.126 2.390 1.487 1.170 0.1 PAA5

230 1.126 2.460 1.566 1.170 0.1 PAA5 a

See the beginning of this appendix for definitions of table columns.
Jet Noise Prediction

NASA/TP—2012-215653 303 Chapter 8

TABLE 8.7.—Continued.

(h) Configuration H: BPR = 8, convergent internally or externally mixed nozzles, hot subsonic flowa

Case M Geometry Core Bypass Mfl nozid

Axial Azimuthal Ma Tt.r Ma Tt.r

Externally mixed

233 0.68 Separate flow m = 0 0.688 2.231 0.667 1.059 0.01 PAA8

234 0.76 0.859 2.356 0.746 1.078 0.01 PAA8

235 0.82 1.002 2.447 0.812 1.114 0.01 PAA8

236 0.68 0.690 2.238 0.665 1.057 0.10 PAA8

237 0.76 0.858 2.350 0.744 1.078 0.10 PAA8

238 0.82 1.002 2.455 0.814 1.115 0.10 PAA8

239 0.82 1.010 2.455 0.816 1.116 0.20 PAA8

Coplanar and fully mixed approximations

240 0.6 Internal splitter m = 0 0.912 2.773 0.686 1.296 0.0 8000.00

241 1.366 3.211 0.902 1.296 0.0 8000.00

242 1.637 3.549 0.988 1.307 0.0 8000.00

243 1.272 3.118 0.920 1.294 0.0 8000.00

244 1.428 3.286 0.891 1.295 0.0 8000.00

245 0.879 2.608 0.664 1.222 0.24 8000.00

246 1.328 3.043 0.878 1.222 0.24 8000.00

247 1.642 3.559 0.990 1.307 0.24 8000.00

248 1.225 2.937 0.892 1.220 0.24 8000.00

249 1.563 3.450 1.013 1.301 0.24 8000.00

250 1.387 3.096 0.863 1.220 0.24 8000.00

251 1.695 3.620 0.996 1.302 0.24 8000.00

252 Internal chevron m = 8 1.371 3.225 0.900 1.294 0.0 8001.04

253 1.371 3.237 0.906 1.300 0.24 8001.04

254 1.271 3.114 0.919 1.296 0.24 8001.04

255 1.426 3.295 0.891 1.296 0.24 8001.04

256 Internal deep 

scalloped lobes m = 20 1.375 3.240 0.906 1.305 0.0 8002.02

257 1.376 3.254 0.906 1.309 0.24 8002.02

258 1.267 3.135 0.926 1.306 0.24 8002.02

259 1.434 3.323 0.894 1.304 0.24 8002.02 a

See the beginning of this appendix for definitions of table columns.
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TABLE 8.7.—Concluded.

(i) Configuration I: BPR = 11+, convergent externally mixed nozzles, hot subsonic flowa

Case BPR M Geometry Core Bypass Mfl nozid

Axial Azimuthal Ma Tt.r Ma Tt.r

260 11 0.74 Separate flow m = 0 0.867 2.425 0.734 1.085 0.00 PAA11

261 0.75 0.881 2.579 0.736 1.084 0.01 PAA11

262 0.75 0.861 2.425 0.735 1.082 0.10 PAA11

263 0.75 0.873 2.568 0.738 1.083 0.10 PAA11

264 14 0.70 Separate flow m = 0 0.757 2.468 0.686 1.072 0.01 PAA14

265 0.69 0.853 2.534 0.683 1.074 0.01 PAA14

266 0.69 0.751 2.464 0.684 1.073 0.10 PAA14

267 0.69 0.859 2.530 0.686 1.071 0.10 PAA14 a

See the beginning of this appendix for definitions of table columns.
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Appendix C.—ANOPP Jet Noise Predictions and Comparison With Data

A selective number of jet cases from each of the nine configurations listed in Table 8.7 in Appendix B were assessed 

with the empirical code ANOPP. Jet noise predictions and 

comparisons with measured data are shown in Figure 8.60 to 

Figure 8.103.

Studying the sound pressure level (SPL) and overall SPL 

(OASPL) plots for each case in detail bears out the overall 

observations made in the plots of OASPL error shown in 

Figure 8.28 and Figure 8.29. Looking at details in the spectra 

at broadside (90°) and peak angles (150°) reveals trends that 

could be investigated in future generations of the ANOPP 

ST2JET code.

For configurations with internally mixed exhaust systems 

two approximations were used within ANOPP to predict the 

radiated noise: (1) configurations assuming coplanar nozzle 

flow (fully unmixed streams), which are denoted by a “C” in 

their case numbers, and (2) configurations assuming fully 

mixed flow at the nozzle exit, which are denoted by an “F” in 

their case numbers. The few dual-stream jet examples with 

external mixing are denoted by an “N” in their case numbers.

Details shown in the following illustrations—spectral plots 

at broadside (90°) and peak (150°) inlet angles as well as the 

OASPL directivity—examine the ANOPP code performance 

at different jet conditions for nine jet configurations listed in 

Table 8.7. The goal is to equip researchers with a guide in 

their attempt for the future improvements of the ANOPP 

ST2JET code.

Figure 8.60 to Figure 8.67 apply to Configuration A from 

Table 8.7 in Appendix B: single-stream, convergent axisymmetric nozzles. The details of the operating conditions for 

these eight jets can also be found in Table 8.5 under case 

numbers 003 through 040, respectively.

The comparisons show that ANOPP does fairly well at 90°, 

often slightly overpredicting the peak and displaying an 

erroneously large amplitude at high frequency near the 

Strouhal number 10.0. At 150° the prediction is very good 

except for this high-frequency component. 

Configuration B covers subsonic single-flow jets with six 

equally spaced chevrons at the nozzle lip. Two examples are 

presented in Figure 8.68 and Figure 8.69 at Mach numbers of 

0.972 and 0.828, and static temperature ratios of 0.837 and 

2.571, respectively. These examples exhibit a major weakness 

of the ANOPP prediction method—in spectral shape and noise 

amplitude—with the OASPL directivity underpredictions of 

10.0 dB or more throughout the angle range. The relevant 

module in the ANOPP code is calibrated to predict noise 

reduction produced by chevrons in separate flow nozzle 

configurations. Apparently, the module performs poorly when 

chevrons are placed on the external nozzle, such as internally 

mixed nozzle configurations. In order to model the impact of 

the chevrons on the exhaust noise, ANOPP correlates the 

hydraulic diameter of the chevron to the jet equivalent 

diameter. Examination of the parameter space demonstrated 

that this may be an inappropriate parameter. For instance, 

nozzles used within Configuration B had identical hydraulic 

diameters but different penetration—a parameter that certainly 

impacts noise but is not present in the prediction model.

Within the next grouping, Configuration C, five

convergent-divergent (C-D) nozzles are considered. The 

operating conditions for these axisymmetric supersonic jets 

are detailed in Table 8.5 under case 059 through case 090. The 

design Mach number for each nozzle is also given in 

Table 8.3. Noise predictions and comparisons with data are 

shown in Figure 8.70 to Figure 8.74. The key question here 

was to examine the code’s ability to predict the jet mixing 

noise at high speeds. It should be noted that experimental data 

were not entirely shock-free, even though pressure ratios were 

set to their design values for the respective nozzles. Subsequently, broadband shock-associated noise (BBSN) was 

present in the spectra especially at upstream angles. Some of 

the ANOPP underpredictions in the OASPL at angles less than 

100° could be attributed to the experimental data especially at 

lower Mach numbers where BBSN was relatively stronger. As 

for the spectral shapes at two angles of 90° and 150°, the peak 

amplitude was in good agreement with data and showed 

improvement with increased Mach number. However, the 

spectral decay at high frequency and near the downstream 

angles produced a dual peak feature, a shortfall also witnessed 

in subsonic jets. 

Configuration D deals with internally mixed jets at very 

low bypass ratio, such as those associated with military 

aircraft. Because the flow is very similar to single-flow 

axisymmetric jets, ANOPP predictions are expected to be 

similar in quality to those in single stream nozzles. Two 

sample cases are illustrated here, both at a bypass ratio of 

0.20. Since the core flow is supersonic, a shock noise module 

within ANOPP was invoked to predict the BBSN, and a sum 

of mixing and shock noise components is shown at each angle. 

As pointed out earlier, ANOPP provides two different source 

models for internally mixed jets, leading to a total of four 

comparisons in Figure 8.75 to Figure 8.78. Internally mixed 

jets can be treated either as fully mixed (designation “F” in the 

case number) single-stream jets, substituting in the fully mixed 

flow conditions, or can be treated as a co-flow nozzle with no 

internal mixing (designation “C” in the case number). For 

these low-bypass ratio jets the difference between the two 

models is insignificant because the bypass stream contributes 

very little to the fully mixed jet conditions. The main difference is in the predicted high-frequency noise associated with 

the higher speed outer shear layer when the fully mixed 

approximation is used. ANOPP missed predicting the peak 

spectra of higher temperature jets at downstream angles, 

overpredicting the levels by 5 to 10 dB. In addition, supersonic shock-containing jets were strongly underpredicted at high 

frequencies.

Configuration E also covers internally mixed jets, with 

bypass ratios near unity. Two examples are shown in 

Figure 8.79 to Figure 8.82. As before, two source models were 
NASA/TP—2012-215653 306

implemented in each example; the co-flow approximation 

produced better results probably because the amount of 

internal mixing is negligible. The peak frequency of the 

broadband shock noise was not accurately predicted over the 

range of conditions. The noise spectra from low-speed hightemperature jets were not predicted well either.

Configuration F was similar to Configuration E, but at a 

higher BPR of 3. Two examples are presented in Figure 8.83

to Figure 8.86 using two different models available in 

ANOPP. Prediction issues were similar to those cases under 

Configuration E. In general, low-supersonic jets were not well 

predicted, mostly because of mistakes in predicting the 

broadband shock associated noise.

Configuration G covers BPR 5 dual stream convergent 

axisymmetric nozzles. Five cases are presented—the first and 

last cases represent externally mixed flows “N”; while the 

remaining three cases are internally mixed streams, and are 

examined using both unmixed coplanar ”C” and the fully 

mixed “F” approximation models available within ANOPP. 

These are shown in Figure 8.87 to Figure 8.94. Since the 

ST2JET code within ANOPP was originally calibrated for jets 

similar to this configuration, the predicted results were also 

the best among all dual flow configurations. For the internally 

mixed jets, both approximations give surprisingly similar 

results—often missing the experimental data by similar 

margins. As before, the peak frequency of the broadband 

shock noise was poorly predicted.

Within Configuration H, one axisymmetric, separate-flow 

nozzle and three internally mixed convergent nozzles at BPR 8 

are presented: (1) axisymmetric splitter, (2) mixer with eight 

equally spaced chevrons, and (3) mixer with 20 lobes. Each case 

was examined using two available approximation models within 

ANOPP for a total of seven illustrations as seen in Figure 8.95

to Figure 8.101. Since both streams were at subsonic Mach 

numbers (~0.81 for the core and ~0.85 for the bypass), and the 

code had been calibrated against subsonic cases matching these 

conditions, expectations were high for success. These expectations were largely met in axisymmetric nozzles as seen in 

Figure 8.96 and Figure 8.97, and discrepancies were mostly at 

the high frequency. The chevron- and lobed-mixer predictions 

did not fare as well and overpredictions as large as 7.0 dB were 

observed at aft angles near 140°. These latter jets also included 

a flight Mach number Mfl = 0.24.

Configuration I examines the largest bypass ratio in

separate-flow axisymmetric nozzles at BPR of 11 and 14. At 

these large bypass ratios the unheated, subsonic, outer stream 

is expected to dominate the flow and noise; subsequently, 

predictions resembled the cold subsonic single-flow cases of 

Configuration A. Two examples are shown in Figure 8.102

and Figure 8.103 at Mfl = 0.10. 

Figure 8.60.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 003

for convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.51, acoustic Mach number Ma = 0.5,

and static temperature ratio Ts,r = 0.955. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.61.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 007 for

convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.98, acoustic Mach number Ma = 0.902,

and static temperature ratio Ts,r = 0.842. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.62.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 022 for

convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.37, acoustic Mach number Ma = 0.492,

and static temperature ratio Ts,r = 1.767. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.63.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 025 for

convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.68, acoustic Mach number Ma = 0.901,

and static temperature ratio Ts,r = 1.77. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.64.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 027 for 

convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.01, acoustic Mach number Ma = 1.33,

and static temperature ratio Ts,r = 1.759. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.65.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 034 for 

convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.3, acoustic Mach number Ma = 0.484,

and static temperature ratio Ts,r = 2.624. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.66.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 037 for 

convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.56, acoustic Mach number Ma = 0.901,

and static temperature ratio Ts,r = 2.702. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.67.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration A case 040 for

convergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 0.92, acoustic Mach number Ma = 1.483,

and static temperature ratio Ts,r = 2.703. Comparison between ANOPP predictions and SHJAR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 

1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.68.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration B case 042 for

convergent, azimuthal periodicity m = 6 nozzle: bypass ratio (BPR) = 0, Mach number M = 0.972, acoustic Mach number 

Ma = 0.902, and static temperature ratio Ts,r = 0.837. Comparison between ANOPP predictions and SHJAR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference 

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.69.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration B case 057 for

convergent, azimuthal periodicity m = 6 nozzle: bypass ratio (BPR) = 0, Mach number M = 0.828, acoustic Mach number 

Ma = 1.309, and static temperature ratio Ts,r = 2.571. Comparison between ANOPP predictions and SHJAR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference 

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.70.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration C case 059 for

convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.72, acoustic Mach number

Ma = 1.047, and static temperature ratio Ts,r = 0.797. Comparison between ANOPP predictions and SHJAR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference 

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.71.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration C case 068 for

convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.394, acoustic Mach number

Ma = 1.191, and static temperature ratio Ts,r = 0.73. Comparison between ANOPP predictions and SHJAR experimental

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference 

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.72.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration C case 075 for

convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.497, acoustic Mach number

Ma = 1.251, and static temperature ratio Ts,r = 0.699. Comparison between ANOPP predictions and SHJAR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference 

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.73.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration C case 083 for

convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.659, acoustic Mach number

Ma = 1.342, and static temperature ratio Ts,r = 0.654. Comparison between ANOPP predictions and SHJAR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference 

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.74.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration C case 090 for

convergent-divergent, axisymmetric nozzle: bypass ratio (BPR) = 0, Mach number M = 1.784, acoustic Mach number

Ma = 1.403, and static temperature ratio Ts,r = 0.619. Comparison between ANOPP predictions and SHJAR experimental 

data. (a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference 

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.75.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration D case 104C for

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 0.2 and flight Mach number Mfl = 0. For core, 

acoustic Mach number Ma = 1.184 and stagnation temperature ratio Tt,r = 1.546. For bypass, Ma = 0.955 and Tt,r = 1.006. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.76.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration D case 104F for

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 0.2 and flight Mach number Mfl = 0. For core, 

acoustic Mach number Ma = 1.184 and stagnation temperature ratio Tt,r = 1.546. For bypass, Ma = 0.955 and Tt,r = 1.006. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.77.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration D case 119C for

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 0.2 and flight Mach number Mfl = 0. For core, 

acoustic Mach number Ma = 2.401 and stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.523 and Tt,r = 1.042. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.78.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration D case 119F for

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 0.2 and flight Mach number Mfl = 0. For core, 

acoustic Mach number Ma = 2.401 and stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.523 and Tt,r = 1.042. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.79.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration E case 143C for

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 1 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 1.18 and stagnation temperature ratio Tt,r = 1.54. For bypass, Ma = 0.948 and Tt,r = 0.99. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.80.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration E case 143F for

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 1 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 1.18 and stagnation temperature ratio Tt,r = 1.54. For bypass, Ma = 0.948 and Tt,r = 0.99. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.81.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration E case 156C for

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 1 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 2.401 and stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.53 and Tt,r = 1.053. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.82.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration E case 156F for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 1 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 2.401 and stagnation temperature ratio Tt,r = 2.581. For bypass, Ma = 1.53 and Tt,r = 1.053. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.83.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration F case 175C for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 3 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 1.183 and stagnation temperature ratio Tt,r = 1.541. For bypass, Ma = 0.94 and Tt,r = 0.977. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.84.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration F case 175F for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 3 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 1.183 and stagnation temperature ratio Tt,r = 1.541. For bypass, Ma = 0.94 and Tt,r = 0.977. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.85.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration F case 188C for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 3 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 2.385 and stagnation temperature ratio Tt,r = 2.589. For bypass, Ma = 1.487 and Tt,r = 1.012. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.86.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration F case 188F for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 3 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 2.385 and stagnation temperature ratio Tt,r = 2.589. For bypass, Ma = 1.487 and Tt,r = 1.012. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
NASA/TP—2012-215653 320

Figure 8.87.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 191N for 

externally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0. For core, 

acoustic Mach number Ma = 1.265 and stagnation temperature ratio Tt,r = 2.663. For bypass, Ma = 0.935 and Tt,r = 1.822. 

Comparison between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level (SPL) versus 

Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall 

sound pressure level (OASPL) as function of θ.

Figure 8.88.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 200C for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 1.637 and stagnation temperature ratio Tt,r = 3.543. For bypass, Ma = 0.984 and Tt,r = 1.302. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.89.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 200F for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 1.637 and stagnation temperature ratio Tt,r = 3.543. For bypass, Ma = 0.984 and Tt,r = 1.302. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.90.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 211C

for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0. 

For core, acoustic Mach number Ma = 1.614 and stagnation temperature ratio Tt,r = 3.455. For bypass, Ma = 0.973 and

Tt,r = 1.27. Comparison between ANOPP predictions with coplanar approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
NASA/TP—2012-215653 322

Figure 8.91.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 211F

for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0. 

For core, acoustic Mach number Ma = 1.614 and stagnation temperature ratio Tt,r = 3.455. For bypass, Ma = 0.973 and

Tt,r = 1.27. Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.92.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 218C

for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0.

For core, acoustic Mach number Ma = 1.637 and stagnation temperature ratio Tt,r = 3.546. For bypass, Ma = 0.985 and

Tt,r = 1.3. Comparison between ANOPP predictions with coplanar approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.93.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 218F

for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0.

For core, acoustic Mach number Ma = 1.637 and stagnation temperature ratio Tt,r = 3.546. For bypass, Ma = 0.985 and

Tt,r = 1.3. Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.94.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration G case 230N for 

externally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 5 and flight Mach number Mfl = 0.1. For core, 

acoustic Mach number Ma = 1.126 and stagnation temperature ratio Tt,r = 2.46. For bypass, Ma = 1.566 and Tt,r = 1.17. 

Comparison between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level (SPL) versus 

Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall 

sound pressure level (OASPL) as function of θ.
NASA/TP—2012-215653 324

Figure 8.95.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration H case 235N for 

externally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 8 and flight Mach number Mfl = 0.01. For core, 

acoustic Mach number Ma = 1.002 and stagnation temperature ratio Tt,r = 2.447. For bypass, Ma = 0.812 and Tt,r = 1.114. 

Comparison between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level (SPL) versus 

Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall 

sound pressure level (OASPL) as function of θ.

Figure 8.96.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration H case 241C

for internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 8 and flight Mach number Mfl = 0. For core, 

acoustic Mach number Ma = 1.366 and stagnation temperature ratio Tt,r = 3.211. For bypass, Ma = 0.902 and Tt,r = 1.296. 

Comparison between ANOPP predictions with coplanar approximation and NATR experimental data. (a) 1/3-octave sound 

pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, 

with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.97.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration H case 241F for 

internally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 8 and flight Mach number Mfl = 0. For core,

acoustic Mach number Ma = 1.366 and stagnation temperature ratio Tt,r = 3.211. For bypass, Ma = 0.902 and Tt,r = 1.296. 

Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data. (a) 1/3-octave 

sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL 

values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.98.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration H case 253C

for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: bypass ratio (BPR) = 8 and flight Mach number Mfl = 0.24. 

For core, acoustic Mach number Ma = 1.371 and stagnation temperature ratio Tt,r = 3.237. For bypass, Ma = 0.906 and

Tt,r = 1.3. Comparison between ANOPP predictions with coplanar approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
NASA/TP—2012-215653 326

Figure 8.99.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration H case 253F

for internally mixed, chevron, azimuthal periodicity m = 8 nozzle: bypass ratio (BPR) = 8 and flight Mach number Mfl = 0.24. 

For core, acoustic Mach number Ma = 1.371 and stagnation temperature ratio Tt,r = 3.237. For bypass, Ma = 0.906 and

Tt,r = 1.3. Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.100.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration H case 257C

for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass ratio (BPR) = 8 and flight Mach number Mfl = 0.24. 

For core, acoustic Mach number Ma = 1.376 and stagnation temperature ratio Tt,r = 3.254. For bypass, Ma = 0.906 and

Tt,r = 1.309. Comparison between ANOPP predictions with coplanar approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.
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Figure 8.101.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration H case 257F

for internally mixed, lobed, azimuthal periodicity m = 20 nozzle: bypass ratio (BPR) = 8 and flight Mach number Mfl = 0.24. 

For core, acoustic Mach number Ma = 1.376 and stagnation temperature ratio Tt,r = 3.254. For bypass, Ma = 0.906 and

Tt,r = 1.309. Comparison between ANOPP predictions with fully mixed approximation and NATR experimental data.

(a) 1/3-octave sound pressure level (SPL) versus Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference

in 1/3-octave SPL values, with uncertainty. (c) Overall sound pressure level (OASPL) as function of θ.

Figure 8.102.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration I case 263N for 

externally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 11 and flight Mach number Mfl = 0.1. For core, 

acoustic Mach number Ma = 0.873 and stagnation temperature ratio Tt,r = 2.568. For bypass, Ma = 0.738 and Tt,r = 1.083. 

Comparison between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level (SPL) versus 

Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall 

sound pressure level (OASPL) as function of θ.
NASA/TP—2012-215653 328

Figure 8.103.—Assessment of ANOPP ST2JET jet noise predictions (Table 8.7, Appendix B). Configuration I case 267N for 

externally mixed, convergent, axisymmetric nozzle: bypass ratio (BPR) = 14 and flight Mach number Mfl = 0.1. For core, 

acoustic Mach number Ma = 0.859 and stagnation temperature ratio Tt,r = 2.53. For bypass, Ma = 0.686 and Tt,r = 1.071. 

Comparison between ANOPP predictions and NATR experimental data. (a) 1/3-octave sound pressure level (SPL) versus 

Strouhal number St for inlet angles θ = 90° and 150°. (b) Difference in 1/3-octave SPL values, with uncertainty. (c) Overall 

sound pressure level (OASPL) as function of θ.
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NASA/TP—2012-215653 329 Chapter 8

References

1. Engineering Sciences Data Unit: ESDU Aircraft Noise Series. 

April 2000.

2. Stone, James R., et al.: Jet Noise Modeling for Suppressed and 

Unsuppressed Aircraft in Simulated Flight. NASA/TM—2009-

215524, 2009. 

3. Zorumski, W.E.: Aircraft Noise Prediction Program Theoretical 

Manual. NASA TM–83199, pts. 1 and 2, 1982.

4. Stone, James; Krejsa, Eugene; and Clark, Bruce: SemiEmpirical Model for Coannular Nozzle Component Noise Extraction and Correlation Including the Effects of Noise Reduction Devices. AIAA–2003–1060, 2003.

5. Lighthill, M.J.: On Sound Generated Aerodynamically. 1. General Theory. Proc. Royal Soc. London Series A, vol. 211, no. 

1107, 1952, pp. 564–587.

6. Lighthill, M.J.: On Sound Generated Aerodynamically. 2. Turbulence as a Source of Sound. Proc. R. Soc. London, Ser. B, vol. 

222, no. 1148, 1954, pp. 1–32.

7. Lilley, G.M.: On the Noise From Jets, Proceedings of Noise

Mechanisms, AGARD CP–131, 1973.

8. Hunter, Craig A.: An Approximate Jet Noise Prediction Method 

Based on Reynolds-Averaged Navier-Stokes Computational 

Fluid Dynamics Simulation. D.Sc. Thesis, George Washington 

University, 2002.

9. Yamamoto, K., et al.: Experimental Investigation of Shock-Cell 

Noise Reduction for Single-Stream Nozzles in Simulated Flight, 

Comprehensive Data Report. NASA CR–168234, vols. 1–3, 

1984.

10. Nelson, C.C.; and Power, G.D.: CHSSI Project CFD–7: The 

NPARC Alliance Flow Simulation System. AIAA–2001–594, 

2001.

11. Abdol-Hamid, Khaled, S., et al.: PAB3D: Its History in the Use 

of Turbulence Models in the Simulation of Jet and Nozzle 

Flows. AIAA–2006–489, 2006.

12. Goldstein, M.E.: A Generalized Acoustic Analogy. J. Fluid 

Mech., vol. 488, 2003, pp. 315–333.

13. Khavaran, Abbas; Bridges, James; and Georgiadis, Nicholas: 

Prediction of Turbulence-Generated Noise in Unheated Jets. Part 

1: JeNo Technical Manual (Version 1.0), NASA/TM—2005-

213827, 2005.

14. Khavaran, Abbas; Wolter, John D.; and Koch, L. Danielle: 

Prediction of Turbulence-Generated Noise in Unheated Jets. Part 

2: JeNo Users’ Manual (Version 1.0), NASA/TM—2009-

213827/PART2, 2009.

15. Georgiadis, Nicholas; Yoder, Dennis; and Engblom, William: 

Evaluation of Modified Two-Equation Turbulence Models for 

Jet Flow Predictions. AIAA J., vol. 44, no. 12, 2006, pp. 3107–

3114.

16. Dash, S.M., et al.: Recent Advances in Jet Flowfield Simulation:

Part I—Steady Flows. AIAA–1993–4390, 1993.

17. Tanna, H.K.; Dean, P.D.; and Burrin, R.H.: The Generation and 

Radiation of Supersonic Jet Noise. Final Technical Report, 

AFAPL–TR–76–65–VOL–3, 1976.

18. Viswanathan, K.: Aeroacoustics of Hot Jets. J. Fluid Mech., vol. 

516, 2004, pp. 39–82.

19. Viswanathan. K.: Jet Aeroacoustic Testing: Issues and Implications. AIAA J., vol. 41, no. 9, 2003, pp. 1674–1689.

20. Ahuja, K.K.: Designing Clean Jet-Noise Facilities and Making 

Accurate Jet-Noise Measurements. International J. Aeroacoustics, vol. 2, nos. 3 and 4, 2003, pp. 371–412. 

21. Brown, Clifford; and Bridges, James: Acoustic Efficiency of 

Azimuthal Modes in Jet Noise Using Chevron Nozzles. AIAA–

2006–2645, 2006.

22. Soeder, Ronald H.; Wnuk, Stephen P.; and Loew, Raymond A.: 

Aero-Acoustic Propulsion Laboratory Nozzle Acoustic Test Rig 

User Manual. NASA/TM—2006-212939, 2006. Available from 

the Center for AeroSpace Information.

23. Thompson, Phillip, A.: Compressible Fluid Dynamics (Advanced Engineering Series), McGraw Hill, 1972.

24. Acoustical Society of America: Calculation of the Absorption of 

Sound by the Atmosphere. ANSI/ASA S1.26–1995 (R2009), 

2010.

25. International Electrotechnical Commission: Electroacoustics 

Octave-Band and Fractional-Octave-Band Filters. International 

Standard IEC 1260, First ed., 1995.

26. Ahuja, K.K.; Tester, B.J.; and Tanna, H.K.: The Free Jet as a 

Simulator of Forward Velocity Effects on Jet Noise. NASA CR–

3056, 1978.

27. Viswanathan, K.; and Clark, L.T.: Effect of Nozzle Internal 

Contour on Jet Aeroacoustics. Intl. J. Aeroacoustics, vol. 3, no. 

2, 2004, pp. 103–135. 

28. Brown, Cliff; and Bridges, James: Small Hot Jet Acoustic Rig 

Validation. NASA/TM—2006-214234, 2006.

29. Opalski, Anthony; Wernet, Mark; and Bridges, James: Chevron 

Nozzle Performance Characterization Using Stereoscopic DPIV. 

AIAA–2005–444, 2005.

30. Wernet, Mark P.: Fuzzy Logic Enhanced Digital PIV Processing 

Software. NASA/TM—1999-209274, 1999.

31. Soloff, S.M.; Adrian, R.J.; and Liu, Z.-C.: Distortion Compensation for Generalized Stereoscopic Particle Image Velocimetry. 

Meas. Sci. Technol., vol. 8, no. 12, 1997, pp. 1441–1454.

32. Ahuja, K.K., et al.: Tone-Excited Jet: Theory and Experiments; 

Final Report. NASA CR–3538, 1982.

33. Birch, Stanley, et al.: An Experimental Study of Flow Asymmetry in Co-Axial Jets. AIAA–2005–2845, 2005.

34. Bridges, James; and Brown, Clifford: Parametric Testing of 

Chevrons on Single Flow Hot Jets. AIAA–2004–2824, 2004.

35. Brown, Clifford; Bridges, James; and Henderson, Brenda: Offset 

Stream Technologies Test—Summary of Results. AIAA–2007–

3664, 2007.

36. Dippold, Vance; Foster, Lancert; and Wiese, Michael: Computational Analyses of Offset Stream Nozzles for Noise Reduction. 

AIAA–2007–3589, 2007.

37. Papamoschou, Dimitri: Parametric Study of Fan Flow Deflectors 

for Jet Noise Suppression. AIAA–2005–2890, 2005.

38. Zaman, Khairul: Noise- and Flow-Field of Jets From an Eccentric Coannular Nozzle. AIAA–2004–5, 2004.

NASA/TP—2012-215653 331

Chapter 9—Propulsion Airframe Aeroacoustic Interactions

Craig A. Hunter and Russell H. Thomas9

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

Summary

State-of-the-art propulsion airframe aeroacoustic interaction experiments and prediction methods constitute important first steps 

leading towards the development of more comprehensive methods. Preliminary experiments have been done on the jet-pylon 

interaction and acoustic scattering in a static environment. While useful, these experiments have lacked many of the key interaction effects that occur in realistic environments. In the future, there will be a need for aircraft system level experiments (including 

fuselage, wing, high-lift system, etc.) with important parameters included such as angle of attack, and with more thorough far-field 

acoustic source characterization and flow-field data.

Prediction methods for propulsion airframe aeroacoustics (PAA) are lacking even a basic empirical or semi-empirical basis 

suitable for system noise tools. Higher fidelity methods have made progress in the area of PAA flow interactions focused on jetpylon interaction. The future of propulsion airframe aeroacoustics methods is aimed at simulating the full aircraft configuration 

with flow interaction and acoustic scattering effects.

9.1 Introduction

Relative to other areas of aircraft acoustics, there has been 

too little research focused on the aeroacoustic effects of 

propulsion airframe integration, distinguished by the term 

“propulsion airframe aeroacoustics” (PAA). From a technology development point of view, this has largely been the 

result of limited prediction method capabilities, limited 

computational resources, and the more complex experimental 

approaches required to address fully integrated systems 

requiring full-scale flight experiments.

In general, the aeroacoustic effects related to propulsion 

airframe integration, or PAA effects, can be classified in 

various ways. The following classification begins with a 

fundamental division of PAA effects into those effects having 

to do with flow interaction and those having to do with 

acoustic propagation. However, it is important to remember 

that in many cases these are not entirely unrelated issues. With 

these two fundamental divisions, the classification can be 

extended to the next level. For flow interaction the next 

important division concerns the flow direction: upstream or 

inlet, and downstream or exhaust. Since turbomachinery and 

jet noise sources have different characteristics, acoustic 

propagation effects are more importantly divided along noise 

sources. The next lowest level of the classification tree is 

composed of identifying interactions between general engine 

and airframe components. And finally, some specific interactions are given along with key parameters. This classification 

tree is shown in Figure 9.1 and represents a general way of

identifying and organizing PAA effects. However, at the same 

time, it is not meant to imply that these effects can necessarily 

be studied or addressed separate from the aircraft system as a 

whole.

Flow interaction effects are caused by the flow field of one 

component interacting with another specifically because of the 

location or orientation of installation. An example of this is the 

influence of the engine mounting pylon on the core jet exhaust 

flow. The influence of the pylon creates flow features in the 

jet that are not present in an isolated jet. These features are 

then also influenced by aircraft attitude. Another example is 

the possible interaction of the fan or core jet exhaust flow with 

an extended flap and its flow; for example, with the typical 

engine-under-wing configuration. These types of flow 

interaction effects from installation can create new acoustic 

sources, or they can modify existing acoustic sources already 

associated with components.

Acoustic propagation effects arise when noise generated 

from various components propagates and interacts either with 

structures or with flow features created by flow over the 

airframe and propulsion device. The acoustic propagation of 

fan noise along the exhaust duct, for example, is altered by the 

presence of the bifurcator and pylon. Furthermore, the fan 

noise propagation can be scattered off deployed flaps compared to propagation of fan noise in isolation. Reflection of jet 

noise off of the underside of the wing for the typical engineunder-wing configuration is another example. Acoustic 

propagation effects are unlikely to create new noise sources 

specifically due to installation effects; however, these effects 

can conceivably modify existing component noise sources. An 

example of this modification could be reflected jet noise 

interacting with jet noise sources.

Overviews of PAA effects and some recent research can be 

found in References 1 to 3.

Acronyms and symbols used in this chapter are listed in 

Appendix A.

9.2 Experiments

There are several experiments that have been performed 

specifically as PAA studies in recent years as part of research 

by NASA and partners. The 2002 Pylon Effects test was 

conducted in the NASA Langley Research Center Jet Noise
Figure 9.1.—Propulsion airframe acoustics (PAA) classification tree.

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NASA/TP—2012-215653 333 Chapter 9

Laboratory and provided basic mean-flow-field and acoustic 

far-field data for a jet-pylon interaction study (Ref. 4). The 

2004 NASA-Boeing PAA experiment in the Boeing LowSpeed Aeroacoustic Facility (LSAF) was an extensive 

experiment involving nozzle, pylon, and flaperon trailing-edge 

modifications and effects (Refs. 5 to 8). As part of the same 

partnership, there was a PAA element to the Boeing-led Quiet 

Technology Demonstrator 2 (QTD2) flight test project 

(Ref. 9). Finally, specifically in the area of acoustic shielding, 

the 2003 blended wing body (BWB) acoustic shielding 

experiment was conducted using a broadband point source to 

document the shielding of the BWB airframe under static 

conditions; this is described together with predictions in 

Reference 10.

In general, more complex aircraft-system-level experiments, such as the 2004 NASA-Boeing LSAF PAA experiment and the QTD2 flight experiment, include the realistic 

PAA effects but are too complex for PAA prediction methods 

that are available to date. The 2002 Pylon Effects experiment 

with its limitation to the interaction of jet and pylon was used 

as the primary validation of the Jet3D prediction code, and 

that code and experiment are described in the following 

sections and are the focus of this chapter.

9.2.1 Pylon Effects Experiment

The experiments reported here were carried out at NASA 

Langley’s Jet Noise Laboratory (JNL) and were concluded by 

the summer of 2002. The purpose was to provide an experimental database of acoustic and mean-flow surveys of a basic 

building block of propulsion airframe integration, the jetpylon interaction. The components of the experiment consisted of the jet engine simulator, the Low Speed Aeroacoustic 

Wind Tunnel, and the model hardware.

The experimental investigation of jet-pylon effects included 

separate flow and chevron nozzles of bypass ratio (BPR) 5 and 

8. These experiments measured the mean-flow quantities of 

pressure and temperature and acoustic effects. The mean-flow 

measurements were reported in Reference 11, and the full 

report of the acoustic measurements has been reported in 

Reference 4. The models corresponded to an approximate “full 

scale to model scale” factor of 9. Operating conditions 

representing those from a typical subsonic aircraft at approach 

to takeoff were tested at wind tunnel free-jet Mach numbers of 

0.1, 0.2, and 0.28. An eight-chevron nozzle and a pylon were 

primary configuration variables. In addition, two orientations 

of the chevrons relative to the pylon were tested. The effect of 

the pylon and the azimuthal directivity were investigated for 

the baseline nozzles and the chevron nozzles.

9.2.2 Experimental Facility

The jet engine simulator (JES) is installed in the NASA 

Langley Low Speed Aeroacoustic Wind Tunnel (LSAWT) as 

shown in Figure 9.2 to produce two streams and accurately 

simulate engine nozzle systems. The JES has two propanefired sudden expansion burners to heat fan and core nozzle 

streams separately. Each stream can flow air up to a maximum 

of 7.7 kg/s (17 lbm/s). In addition, each stream has an electric 

pre-heater for low temperature operation and for burner 

stability. Airflow is straightened before transitioning to the 

nozzle. The JES is equipped with a six-component load cell 

for thrust measurements, although that capability was not used 

in this experiment. Airflow is measured by critical venturi 

meters in each stream. Airflow pressure and temperature rakes 

are positioned just upstream of the nozzle contraction to 

measure nozzle conditions.

The LSAWT is a continuous-flow in-draft wind tunnel that 

provides a free jet surrounding the JES exhaust flow. The free 

jet is produced by a 0.44-m

2 (4.7-ft2

) nozzle. As shown in 

Figure 9.2, the JES is positioned in the free-jet nozzle and test 

section as it was configured in 2002. Wind tunnel speed can 

be varied from a Mach number of 0.1 up to 0.32. For this 

experiment the wind tunnel free jet was run at three Mach 

numbers: 0.1, 0.2, and 0.28.

Figure 9.2.—NASA Langley’s Low Speed Aeroacoustic Wind Tunnel (LSAWT). Dimensions are in centimeters. (a) Side view 

of test section with flow from left to right. (b) End view looking upstream with microphone array in upper right-hand side.
NASA/TP—2012-215653 334

The test section has anechoic treatment from fiberglass 

wedges with a cutoff frequency of 250 Hz. Dimensions of the 

test cell, measured from tip to tip of the wedges is 10.4 m long 

by 5.2 m high by 5.2 m wide (34 by 17 by 17 ft). The 

downstream flow collector regulates flow recirculation in the 

test cell. Both the wind tunnel nozzle and the flow collector 

are acoustically treated to minimize reverberations.

9.2.3 Model Design and Experimental

Configurations

The baseline configurations are two separate flow nozzles 

with BPR 5 and 8, each with an external plug. The nozzle

and pylon design are from a nozzle study performed by 

McDonnell Douglas (now Boeing) in 1996 and represent a 

generic design of conventional nozzles for commercial 

subsonic transports. The baseline nozzle is modified by 

attaching a pylon and/or chevrons to the core nozzle; the fan 

nozzle remains the same for both BPR 5 and 8. The higher 

bypass ratio is achieved by reducing the diameter of the core 

nozzle from 12.8 to 11.9 cm (5.04 to 4.70 in.).

Chevrons are a noise-reduction technology that is rapidly 

being applied to newer engine nozzles, and since the pylon is 

an integral part of the nozzle, core and fan chevrons were 

tested with and without a pylon at both bypass ratios. On the 

baseline nozzles, when fan and core chevrons were installed, 

the orientation of the core and fan chevrons relative to each 

other was tested. When a pylon was installed, two orientations 

of the core chevrons relative to the pylon were tested. These 

two orientations occur when a chevron trough is aligned with 

the pylon centerline and again when a chevron tip is aligned 

with the pylon centerline.

The chevrons were designed for the core nozzle using 

guidelines similar to those used in studies during the NASA 

Advanced Subsonic Technology (AST) program. The 

chevrons were designed to penetrate into the core flow by 

approximately the estimated thickness of the boundary layer 

for the BPR 5 nozzle. For the BPR 8 nozzle the core chevrons 

did not penetrate the core flow. The trailing edge of the 

baseline nozzle is chosen to correspond to the midpoint of the 

chevron axial length.

Since the pylon clearly creates a nonaxisymmetric geometry, azimuthal angle was also variable in the experimental 

matrix. Three azimuthal angles were tested, including an 

orientation corresponding to a flyover (90°), a sideline or 

takeoff angle (34°), and a third angle at 0° that is normal to the 

line from the microphones to the nozzle centerline. To achieve 

the different azimuthal angles the microphones remain fixed 

and the model with pylon was rotated.

The pylon in these configurations has a diverging angle of 

1.5° for the shelf of the pylon that the core flow follows. The 

junction of the core nozzle with chevrons and the pylon shelf 

is simply the result of a separate chevron and pylon design 

combined with no added design feature for the junction. A 

typical nozzle configuration used in this experiment is shown 

in Figure 9.3. This picture shows the BPR 5 nozzle with a 

baseline fan nozzle, and an eight-chevron core nozzle with a 

chevron tip aligned with the pylon. The pylon was added to 

the same baseline fan nozzle. Therefore, the fan nozzle area 

for a configuration with a pylon is less than the fan nozzle area 

for a baseline configuration. As will be described in sections 

below, the reduced area, for the same nozzle flow condition, 

means less fan area and less thrust.

Figure 9.3.—Bypass ratio 5 nozzle with eight-chevron core nozzle and baseline 

fan nozzle installed in the jet engine simulator (JES) in the LSAWT.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 335 Chapter 9

Table 9.1 summarizes the total nozzle areas for both BPR 5 

and 8 baseline and pylon configurations. The model-scale area 

at cold (room-temperature) conditions are based on measurements of the nozzles and are of the area normal to the inner 

surface at the exit of the nozzle as opposed to an area in the 

vertical plane at the exit. During the experiment, the nozzle 

operates at elevated temperatures, and thermal expansion 

causes the nozzle system dimensions to change slightly. The 

dimensions under hot operating conditions are not measured, 

but are estimated based on the known thermal expansion 

coefficients. These estimated areas under hot operating 

conditions are also shown in Table 9.1. The pylon has an axial 

split line that allows for thermal growth between the core and 

fan nozzles. The gap between the two parts of the pylon is 

typically less than 0.1 cm (0.04 in.) and is sealed to prevent air 

leakage. Chevron nozzles were assumed to have the same exit 

area as the corresponding baseline nozzle. Also in Table 9.1

are the scale factors (based on hot areas) used for processing 

of the acoustic data as will be described later.

Flow was varied by the nozzle operating conditions and 

the wind tunnel Mach numbers of 0.1, 0.2, and 0.28. Since 

the wind tunnel is open to the atmosphere, the ambient 

temperature and pressure fluctuate with prevailing conditions. 

However, the ambient temperature turned out to be 

remarkably stable during the course of the experiment and 

only varied by about ±5.6 K (±10 °R) from day to day.

Detailed geometry modifications were also tested, including 

a fillet on the pylon-core nozzle body junction and an 

extended pylon. Not all of the results of the modifications are 

reported here since the general conclusions are not altered.

9.2.4 Nozzle Operating Conditions

The nozzle operating conditions for BPR 5 (see Table 9.2) 

were taken from the same AST study that produced the 

original hardware design for the baseline nozzles. These 

operating conditions have been used previously in a study of 

high-BPR jet noise during the AST program (Ref. 12). The 

BPR 8 operating conditions used in the experiment were 

updated to reflect more realistic conditions but were not used 

in the prediction method validation phase. The same operating 

conditions were used whether the configuration had a pylon or 

not, and therefore the nozzle exit conditions were also the 

same. As described in the discussion of Table 9.1, this meant 

that for a given baseline-to-pylon configuration comparison 

the fan area was different and therefore the actual thrust of the 

pylon configuration was less. As will be discussed in the next 

section, the acoustic data were scaled differently in order to 

allow an acoustic comparison on an equal thrust basis.

TABLE 9.1.—SEPARATE-FLOW NOZZLE MODEL AREAS FOR BOTH COLD AND HOT CONDITIONS

AND SCALE FACTORS USED FOR ACOUSTIC DATA PROCESSING

Bypass

ratio

Pylon Test

point

Cold model 

fan area,

cm2 (in.2

)

Cold model 

core area,

cm2 (in.2

)

Total cold model 

nozzle area,

cm2 (in.2)

Estimated total 

hot model area,

cm2 (in.2

)

Scale

factor

Full size total area,

cm2 (in.2)

5 Yes 15 173.4 (26.87) 69.35 (10.75) 242.7 (37.62) 240.2 (37.23) 9.00 19455.6 (3015.63)

5 No 15 186.1 (28.84) 69.35 (10.75) 255.4 (39.59) 253.0 (39.21) 8.77 19456.4 (3015.75)

8 Yes 5 194.0 (30.07) 48.80 (7.56) 242.8 (37.63) 241.5 (37.43) 9.72 22815.0 (3536.33)

8 No 5 208.5 (32.32) 48.80 (7.56) 257.3 (39.88) 256.1 (39.69) 9.44 22815.0 (3536.33)

TABLE 9.2.—BYPASS RATIO (BPR) 5 NOZZLE OPERATING CONDITIONSa

Condition Test 

point

Fan Core BPR Estimated

mixed 

velocity,

m/s (ft/s)

NPR To,

°R

Estimated 

velocity,

m/s (ft/s)

Estimated 

flow rate,

kg/s (lb/s)

NPR To,

°R

Estimated

velocity,

m/s (ft/s)

Estimated 

flow rate,

kg/s (lb/s)

Approach 1 1.27 582 207 (680) 4.16 (9.16) 1.15 1190 228 (749) 0.68 (1.51) 6.07 210 (690)

2 1.39 596 244 (802) 4.92 (10.84) 1.24 1240 288 (944) 0.90 (1.98) 5.47 251 (824)

Cutback 5 1.51 612 276 (904) 5.53 (12.18) 1.33 1300 337 (1107) 1.03 (2.28) 5.34 285 (936)

12 1.63 629 303 (993) 6.03 (13.3) 1.445 1390 394 (1294) 1.18 (2.61) 5.1 318 (1042)

Takeoff 15 1.75 647 327 (1072) 6.46 (14.25) 1.56 1491 447 (1466) 1.30 (2.87) 4.97 347 (1138) a

NPR is nozzle pressure ratio.

To is stagnation temperature.
NASA/TP—2012-215653 336

9.2.5 Acoustic Data Processing

Acoustic data were collected with a 28-microphone sideline 

array located 3.52 m (11.54 ft) from the centerline axis of the 

model. Microphones were 0.64 cm (0.25 in.) in diameter, 

operated with the grid caps removed, and calibrated with a 

pistonphone and electrostatic calibrator before and after the 

test. Acoustic data was processed using both General Electric 

Company (GE) and NASA procedures and using different 

shear-layer corrections. In general, although there are 

differences in the results from the different processing, the 

conclusions concerning changes between configurations are 

not altered. Therefore, data presented in this paper uses the GE 

process with the Amiet (Ref. 13) point-source model for the 

shear layer correction. Acoustic data shown in subsequent 

sections are processed to 1/3-octave bands and include 

corrections for the microphone calibration, wind tunnel 

background noise, a Doppler shift to the spectral data, and 

atmospheric absorption to acoustic standard day conditions 

using the Shields and Bass methodology (Ref. 14). The data 

were scaled to the full-scale engine size using the varying 

scale factors of Table 9.1, and extrapolated to a distance of 

543.2 m (1782 ft), typical of certification. This corresponds to 

an altitude of 304.8 m (1000 ft) and a ground sideline distance 

of 449.9 m (1476 ft). After the model-scale data were 

transformed to full scale, the effective perceived noise level 

(EPNL) was calculated by simulating an aircraft flyover at 

Mach 0.28 and using the procedure described in Reference 15.

The repeatability of the acoustic measurements is approximately ± 0.4 dB. Most of the test points were repeated several 

times. For the PNL and EPNL plotted here as a function of 

operating condition, a linear fit is made through all available 

data points so differences between configurations can be made 

with more confidence by considering the trends demonstrated 

by all points along the operating line.

The model-scale nozzles are of almost identical total area as 

seen in Table 9.1. This implies less thrust from the nozzles 

with a higher BPR. To make comparisons meaningful, the 

acoustic results were scaled to achieve equivalent ideal thrust 

at the takeoff condition. This would, in theory, allow either of 

the two BPR nozzles to power the same aircraft with other 

practical issues ignored. This also means that for an equivalent 

ideal thrust, the mixed-jet velocity of each BPR nozzle will 

not necessarily be the same. With a scale factor of 9 fixed for 

the BPR 5 baseline nozzle, different scale factors were 

calculated for the BPR 5 nozzle with a pylon, the BPR 8 

baseline, and the BPR 8 nozzle with a pylon. This allows for 

the acoustic data to be scaled to a representative full scale at 

equivalent ideal thrust.

9.3 Prediction Method Overview

The PAA prediction methods are grouped in several categories in parallel with the prior classification of PAA effects. An 

efficient tool and one suited to current system noise prediction 

methods would be an empirical or semi-empirical method 

based primarily on experimental data. With the appropriate 

benchmark experiment, it would be possible to develop such 

an empirical or semi-empirical model for integration in a 

system noise prediction method like NASA’s Aircraft Noise 

Prediction Program (see Chapter 2). Many parameters could 

be included in such a model addressing installation effects; 

however, no such comprehensive model has been developed in 

NASA efforts yet. Moving to higher fidelity methods, for 

PAA effects of the flow interaction type involving primarily 

jet and pylon, wing, and flap interaction, for example, methods 

based on computational fluid dynamics (CFD) exist using a 

flow solver (PAB3D, USM3D, etc.) in combination with a 

noise prediction code like Jet3D. For PAA effects of the 

acoustic interaction type there are a number of methods in 

various stages of development and use such as methods based 

on ray tracing, energy elements, or boundary elements, the 

latter being used in the NASA-sponsored acoustic scattering 

code described in Reference 10 together with comparison with 

the 2003 BWB acoustic scattering experiment.

9.4 Jet3D

Jet3D (Ref. 16) is based on a straightforward application of 

Lighthill’s Acoustic Analogy (LAA) in three dimensions, 

solved and manipulated (according to Ffowcs Williams, 

Ref. 17) to give the far-field acoustic pressure p correlation as 

a function of spatial observer position x and time delay τ:

( ) 

⌡

⌠ ′ ∂τ

∂ 

⌡

⌠

π

τ =

∞

−∞ ∞ ∞

x dζdz ~

ˆ ˆ ˆ ˆ

16

1 , 4

4

jet

2 4 5 2

2 i j mn

i j m n T T

C C r

r r r r

c p (9.1)

where c∞ is the ambient speed of sound, , ˆri are components of 

the acoustic radius unit vector, C is the jet convection factor, 

C∞ is the flight convection factor, r is the magnitude of the 

acoustic radius, τ

~ is the time delay in the moving frame, Tij

is the Lighthill stress tensor, Tmn′ is the stress tensor at a 

different spatial position, ζ is the moving frame separation 

vector, and z is the moving frame source position vector. Here 

( ) Ti j = p − c∞ρ δi j − σi j + ρuiu j 2 where ρ is the density of air, 

δij is the Kronecker delta function, σij is the viscous stress 

tensor, and ui are components of the total velocity; quantities 

inside integrals are to be evaluated at a retarded time and 

corresponding position. The indices i, j, m, and n are integers 

that vary from 1 to 3. Developed over 50 years ago (Refs. 18

and 19), this elegant theory unified the fields of aerodynamics 

and acoustics. In deriving the acoustic analogy, Lighthill cast 

the complicated nonlinear jet noise problem into a simple 

analogy with classical acoustics; the flow field and complex 

flow-acoustic interactions (such as sound wave convection and 

refraction) in a real jet are replaced by a fictitious volume 

source distribution of acoustic quadrupoles radiating into a 

uniform ambient medium.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 337 Chapter 9

By formulating the jet noise problem into an equivalent 

linear acoustics problem, LAA makes it possible to handle 

complex three-dimensional flows and arbitrary nozzle 

configurations with ease, thus making it a good choice for 

PAA applications. Compared to other methods based on nonlinear acoustic propagation and convected wave equation 

formulations, simplifying jet flow assumptions are not needed 

in LAA, and complicated ray-tracing or flow-acoustic 

interaction models are not required. The tradeoff, of course, is 

that LAA places a much heavier burden on source modeling, 

since the sources themselves produce analogous “propagation” 

effects through temporal and spatial phasing.

This leads to the chief difficulty in implementing LAA over 

the past 50+ years: the tacit assumption that the mean-flow 

and fluctuating turbulent fields in a jet—namely, components 

of the Lighthill stress tensor Tij—are known. Full knowledge 

of the jet flow field would be equivalent to a full solution of 

the Navier-Stokes equation, which remains elusive to this day. 

However, advances in computational fluid dynamics have 

closed the gap quite a bit. The fidelity and quality of information available in a Reynolds-averaged Navier-Stokes 

(RANS) CFD simulation has improved to the point where it is 

now possible to develop better models and make educated 

assumptions about any remaining unknowns.

The source-to-observer conventions in Jet3D’s LAA 

implementation are shown in Figure 9.4, where effects of both 

aircraft motion (at Mach number M∞) and source convection 

(at Mach number Mc) are included. All Mach numbers are 

relative to a fixed observer, and are based on the ambient 

speed of sound c∞. It is important to note the relationship 

between source motion and convection: because acoustic 

sources in a jet (essentially convecting turbulent eddies) have 

a finite lifetime, they possess a convective effect and Doppler 

shift that goes according to the convection Mach number Mc, 

but retarded time effects come in mainly through motion of 

the aircraft. Thus, the retarded time position of sources 

depends primarily on the flight Mach number M∞. Following 

the illustration in Figure 9.4, the geometric observer radius r* 

and geometric observer angle θ* can be used to give the 

effective acoustic radius r and observer angle θ at the retarded 

time (results shown assume subsonic M∞):

( ) ( )

( ) 2

2 2 2 2

1 M

M * cos * M *cos * 1 M *

∞

∞ ∞ ∞

−

− θ + θ + − = r r r r (9.2)





 



 θ = θ − ∞ − cos * M * cos 1

r

r (9.3)

Figure 9.4.—Source-to-observer conventions in Jet3D’s implementation of

Lighthill’s Acoustic Analogy (LAA).
NASA/TP—2012-215653 338

By following Lighthill’s assumption that the stress tensor 

can be approximated as Tij ~ ρuiuj, breaking velocities out into 

mean and fluctuating components ui(z,t) = Vi(z) + vi(z,t), and 

assuming that density is only a function of space (i.e., 

ρ(z,t) ≈ ρ(z)) the two-point time-delayed correlation of the 

Lighthill stress tensor becomes

Ti jTmn [ VjVn

′ vivm′ + vivjvm′ vn′ ] ∂τ

∂ ′ = ρρ′ ∂τ

∂ 4 ~ ~4

4

4

4

(9.4)

Note that odd terms involving triple correlations of the form 

vivmvn ′ ′ have been dropped, on the assumption that they 

would integrate to zero under the correlation integral. Of the 

two remaining terms, the first is known as the “shear noise” 

term, since it arises from interactions between turbulent and 

mean-flow velocities. The second term is the “self noise” term, 

as it arises from interactions between the turbulent velocities 

themselves. Under the assumption that the joint probability 

distribution of turbulent velocities is normal, the quadruple self 

noise correlation can be expanded into the product of double 

correlations as shown by Batchelor (Ref. 20):

viv jv′

mvn

′ = viv j vm′ vn′ + vivm′ v jvn′ + viv′

n v jvm′ (9.5)

From this point onward, implementation of the Lighthill 

theory in Jet3D centers on the modeling of two-point spacetime correlations for shear and self noise terms. Mean-flow 

correlations for velocity and density are modeled using a 

Taylor series expansion, written in terms of local mean-flow 

gradients and the separation vector between the two points of 

the mean-flow correlation:

k

n n n k

z

V V V

∂

∂ ′ ~ + ζ

(9.6)

k

k ∂z

∂ρ ρ′ ~ ρ + ζ

(9.7)

where k = 1, 2, and 3 to carry out a dot product.

Turbulent velocity correlations are separated into space and 

time factors and modeled using the local one-point correlation 

(related to the Reynolds stress tensor) and a combination of 

Gaussian-type exponential functions and quadratic functions:

) ~ vivm

′ = vivm R(z, ζ)g(z, τ (9.8)

where































 ζ + ζ + ζ − π































 ζ + ζ + ζ

μ −

=

2

3

2

3

2

2

2

2

2

1

2

1

2

3

2

3

2

2

2

2

2

1

2

1

2 exp

1 1

( , )

     

R z ζ

(9.9)

{ }2

0

~2 ) exp ~ g(z, τ = − τ τ (9.10)

τ = τ C ~ (9.11)

and C is defined in Equation (9.18). Here, τ0 is a characteristic 

time scale of turbulence

ε

τ = ατ

k

0 (9.12)

where k is the turbulent kinetic energy (TKE) per unit mass 

and ε is its dissipation rate, and 1, 2, and 3 are characteristic 

length scales of turbulence

ε = α

3 2 2

1

1

v

 L (9.13a) 

ε = α

3 2 2

2

2

v

 L (9.13b)

ε = α

3 2 2

3

3

v

 L (9.13c)

The specific form of the correlation functions is not so 

important, as discussed in Reference 21, as long as the spatial 

correlation function is integrable in ζ and the temporal 

correlation function is amenable to Fourier transforms. 

Generally, any reasonable correlation function can be used and 

calibrated to give good results, with the majority of noise 

prediction accuracy and correct spectrum shape depending on 

the CFD solution.

For the correlation functions given above, early calibration 

work determined fixed values for the correlation calibration 

constant μ and the time scale calibration constant ατ of 0.735 

and 0.15, respectively. Over the past 7 years, values of the 

length scale calibration constant αL between 0.3 and 0.34 have 

been used to predict noise for a wide range of nozzle configurations and flow conditions.

After carrying out tensor products with i j m n rˆ rˆ rˆ rˆ , and putting everything together, the acoustic pressure correlation can 

be written as

( ) ( ) ( )

self

2

shear

2 2 p x, τ = p x, τ + p x, τ (9.14)

where

( )

( ) ( ) ∫

∞

−∞ ∞ ∞ 

⌡

⌠

τ

ρ

π

τ =

x z ζ ζ z

x

, d d ~, 4

16

1

,

shear

jet

shear 2 4 5 2

shear

2

G F

C C r

V v v

c

p

r r r (9.15a)
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 339 Chapter 9

( )

( ) ( ) ∫

∞

−∞ ∞ ∞

 τ ζ ζ

⌡

⌠ ρ

π

τ =

x z z

x

, d d ~, 2

16

1

,

self self

jet

5 2

2

2 4

self

2

G F

C C r

v v

c

p

r r (9.15b)

r jV j V = rˆ (9.16)

vrvr rirm vivm = ˆ ˆ (9.17)

and the various functions are defined in Reference 16. The 

remaining analysis is straightforward but tedious, so the reader 

is referred to Reference 16 for details. In summary, the 

following steps are carried out:

(1) The ζ correlation integrals are evaluated analytically.

(2) A Fourier transform is applied to obtain the spectral 

density of the mean-square acoustic pressure.

(3) The spectral density is integrated over a frequency band 

to obtain the mean-square acoustic pressure spectrum in that 

band.

The remaining z integration over the jet is evaluated numerically. Thus, the Jet3D noise prediction algorithm is based on 

the volume integration over a set of equations giving the bandintegrated acoustic pressure correlation spectrum for the shear 

and self noise. The integration is carried out for each volume 

element in a discretized jet flow field using data obtained from 

a CFD solution. Within the integration routine, turbulent 

Reynolds stresses are computed using one of several linear or 

nonlinear anisotropic models (Ref. 16), atmospheric absorption effects are calculated with the Shields and Bass attenuation model (Ref. 14), mean-flow gradients are computed with 

a finite volume scheme (Ref. 16), and local convection Mach 

number (Mc) is modeled empirically using correlated data 

trends from the classic Davies experiment (Ref. 22). The 

present formulation of Jet3D uses the Ribner/Ffowcs Williams 

(Ref. 23) jet convection factor 

[( ) ]

1/ 2 2 2 2 C = 1− Mc cosθ + αcMc (9.18)

where αc = 0.58, along with the C∞ = 1 + M∞ cosθ forward 

flight convection factor.

Jet3D is written in FORTRAN 77/90/95 with dynamic 

memory allocation, and is easily ported across numerous 

computing platforms. The main algorithms in Jet3D are 

vectorized to take advantage of compiler optimizations and 

vector processing on certain architectures. Jet3D also 

implements a low-level multiprocessing capability, where 

noise for multiple observers can be computed in parallel. 

Generally, noise predictions require on the order of 2 to 

10 minutes per observer for the types of PAA applications 

discussed in this chapter. In addition to a prediction mode, 

Jet3D can be run in one of several diagnostic modes to output 

noise source maps for follow-on analysis.

9.4.1 Guidelines for Applying Jet3D

As alluded to above, the basic burden for noise prediction 

quality and accuracy falls on the CFD solution. Ultimately, the 

distribution of noise sources in a CFD solution determines 

sound pressure level (SPL) spectrum shape far more than the 

modeling assumptions in Jet3D. This leads to a few important 

guidelines:

(1) The CFD grid should extend at least 30 jet diameters 

downstream for subsonic jets, and 40 to 50 diameters downstream for supersonic jets. Jet3D noise source maps can be 

used to verify that desired low-frequency sources are being 

captured within the computational domain.

(2) Grid resolution around nozzle lips is critical to resolving high-frequency noise sources and predicting the correct 

high-frequency spectrum shape. On the order of 40 grid points 

across each boundary layer and 20 grid points across a nozzle 

lip are required to resolve this region and ensure suitable 

transition from nozzle boundary layer flows to shear layer 

flows.

(3) Grid density should be fanned out from nozzle lips to 

cover developing shear layer regions. On the order of 40 grid 

points across a shear layer is appropriate. See Figure 9.5 for an 

example of this topology.

(4) Whenever possible, CFD solutions should be compared 

with experimental mean-flow and turbulence data to ensure 

that the CFD-predicted jet flow field is valid and reasonable 

(i.e., correct potential core length, proper turbulence levels, 

etc.). Issues in the CFD solution should be resolved before 

proceeding to noise prediction.

(5) RANS turbulence models have known deficiencies in 

predicting the correct potential core length for heated jets. In 

general, mixing is underpredicted and the jet potential core is 

too long (by several nozzle diameters), resulting in an 

incorrect mean flow and turbulence field. Proper steps should 

be taken to avoid this problem, using a correction such as the 

one suggested by Abdol-Hamid et al. (Ref. 24). This correction increases the mixing rate in the hot part of a jet flow with 

a minimally invasive modification to turbulent eddy viscosity. 

The correction is implemented in a way that is equally valid 

for wall-bounded and free shear flows, which is important for 

installed jet simulations of interest to PAA.
NASA/TP—2012-215653 340

Figure 9.5.—Recommended shear layer grid topology for CFD predictions of jet flow.

In addition to these CFD guidelines, a few acoustic guidelines are worth noting:

(1) Observers must be at least 50 nozzle diameters from the 

nozzle exit to truly be in the far field of Jet3D’s implementation of LAA.

(2) Best predictions are from 0° to 100° inlet angle. Predictions beyond a 110° inlet angle are generally not reliable, 

because of shortcomings in the Jet3D implementation of LAA 

(terms neglected in the Lighthill stress tensor).

(3) Noise analysis should begin with an observer at an inlet 

angle of 90°, where jet noise is least affected by convection 

and refraction effects and noise sources in Jet3D take on their 

simplest form. If the results at 90° do not correlate with the 

measured spectrum, the CFD solution should be analyzed for 

problems and deficiencies before proceeding to other observer 

angles.

9.4.2 Sensitivity to Input Settings

Most of the input settings for Jet3D are based on nozzle 

operating conditions and acoustic data reduction conventions. 

Of the various calibration constants in Jet3D, all have been 

frozen except for the spatial correlation constant αL, which 

generally varies between 0.3 and 0.34 for most cases. Using 

the equations for predicted SPL from Reference 16, the 

sensitivity to αL can be computed:

L L L

SPL

α ≈ α = ∂α

∂ 13.029

ln10

30

(9.19)

More simply, the change in SPL for a change in αL is

















α

∆α ∆ = + L

L SPL 30log 1

(9.20)

Thus, the SPL changes by –1 dB for a –7.39 percent change 

in αL, or it changes by 1 dB for a 7.98 percent change in αL. 

The αL constant can be used to calibrate noise prediction 

results to experimental data (most appropriately done at 90° 

observer angle) by shifting the SPL spectrum up or down as 

needed.

The effect of varying αL is shown in Figure 9.6 and 

Figure 9.7, based on cases discussed in Reference 25. 

Figure 9.6 shows Jet3D predictions at a 90° observer angle for 

a baseline round BPR 5 dual-stream nozzle, and Figure 9.7

shows the same prediction for a BPR 5 nozzle with a pylon.

9.4.3 Applications

Early validation of Jet3D was done using the Yamamoto 

et al. dataset (Ref. 26). Noise predictions were made for a 

heated convergent-divergent nozzle with an exit diameter of 

13.7 cm (5.4 in.) operating at its design nozzle pressure ratio 

(NPR) of 3.18, a Mach number of 1.4, and a jet stagnation 

temperature To of approximately 955.6 K (1720 °R). Jet3D 

noise predictions were made for 13 observer locations along a 

40-ft-radius arc (approximately 88 nozzle diameters) centered 

on the nozzle exit. For each observer, 1/3-octave band 

frequency SPL was computed over bands from 50 Hz to 

80 kHz.

Results from one of the validation cases, with a static free

stream, are shown in Figure 9.8 and Figure 9.9. Jet3D did a 

reasonable job predicting SPL for inlet angles of 40° to 100°, 

but shows a frequency shift for inlet angles beyond 100°. This 

is due to flow acoustic interaction effects as the observer nears 

the jet axis. These interactions are not adequately handled in 

the present form of Jet3D, because of the neglect of terms 

from the Lighthill stress tensor. Overall sound pressure level 

(OASPL) results in Figure 9.9 are slightly more forgiving, 

showing decent OASPL prediction to an inlet angle of about 

130°.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 341 Chapter 9

Figure 9.6.—Effect of varying spatial correlation constant αL on Jet3D 

predictions of sound pressure level (SPL) for baseline round bypass 

ratio 5 dual-stream nozzle.

Figure 9.7.—Effect of varying spatial correlation constant αL on Jet3D 

predictions of sound pressure level (SPL) for baseline round bypass 

ratio 5 dual-stream nozzle with pylon.
NASA/TP—2012-215653 342

Figure 9.8.—Comparison of measured data and Jet3D predictions of sound pressure level (SPL) for convergentdivergent nozzle (jet stagnation temperature To ≈ 955.6 K (1720 °R), nozzle pressure ratio NPR = 3.18, and Mach 

number 1.4). Jet3D noise predictions are made at 13 observer locations (inlet angles). (a) 40°. (b) 50°. (c) 60°.

(d) 70°.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 343 Chapter 9

Figure 9.8.—Continued. (e) 80°. (f) 90°. (g) 100°. (h) 110°.
NASA/TP—2012-215653 344

Figure 9.8.—Continued. (i) 120°. (j) 130°. (k) 140°. (l) 150°.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 345 Chapter 9

Figure 9.8.—Concluded. (m) 160°.

Figure 9.9.—Comparison of measured data and Jet3D predictions of overall sound pressure level (OASPL) as function of inlet angle for convergent-divergent nozzle at jet 

stagnation temperature To of approximately 955.6 K (1720 °R) operating at its design 

nozzle pressure ratio (NPR) of 3.18 and Mach number of 1.4.

The first PAA application of Jet3D (Ref. 25) focused on 

dual-stream BPR 5 nozzles, shown in Figure 9.10 (baseline 

round nozzle, configuration 1) and Figure 9.11 (pylon nozzle, 

configuration 6). The primary interest was in using Jet3D to 

examine the pylon installation effect, later covered in more 

detail in Reference 27. Jet3D noise predictions were compared 

to experimental acoustic data obtained in the LSAWT at 

NASA Langley’s Jet Noise Laboratory (JNL), for nozzle 

configurations operating at the takeoff cycle point (core 

nozzle: NPR = 1.56 and To = 827.8 K (1490 °R); fan nozzle: 

NPR = 1.75 and To = 359 K (646 °R)) with a free-stream 

Mach number of 0.28. Each 1/9-scale nozzle has a nominal 

core exit diameter of D = 12.8 cm (5.04 in.).
NASA/TP—2012-215653 346

For SPL comparisons, Jet3D noise predictions were made 

at 24 observer locations along a 100D-radius arc, at inlet 

angles ranging from 52° to 148°. At each observer point, 1/3-

octave band frequency spectrum SPL were computed over 

center frequencies ranging from 200 Hz to 100 kHz. Additional sideline predictions were made at full scale (scale factor 

9.0) and fed through JNL data processing routines to come up 

with EPNL predictions. 

The SPL predictions for configuration 1 are shown in 

Figure 9.12, and predictions for configuration 6 are shown in 

Figure 9.13. Predictions are compared with JNL model-scale 

data (with standard deviation of ±0.47 dB) at observer inlet 

angles of 52°, 62°, 69°, 78°, and 88° in the inlet arc, and inlet 

angles of 98°, 109°, 121°, 127°, 134°, 141°, and 148° in the jet 

arc. For both configurations, Jet3D predictions are in good to 

excellent agreement with JNL data in the inlet arc, but the 

agreement progressively deteriorates in the jet arc past about 

121°, again, where flow-acoustic interaction issues come into 

play. The EPNL predictions for full-scale nozzle systems are 

compared with data in Figure 9.14. For both configurations, 

Jet3D predictions are within the ±0.36 dB standard deviation 

for the EPNL determined from the JNL measurements. 

Furthermore, Jet3D properly captures the effect of the pylon 

(due in part to the reduced thrust of that configuration), 

predicting 0.69 EPNdB noise reduction.

Figure 9.10.—Baseline separate-flow nozzle of BPR 5, 

configuration 1, for Jet3D jet noise prediction.

Figure 9.11.—Baseline separate-flow nozzle of BPR 5 with pylon, configuration 6, 

for Jet3D jet noise prediction.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 347 Chapter 9

Figure 9.12.—Comparison of measured data and Jet3D predictions of sound pressure level (SPL)

for baseline separate-flow nozzle of BPR 5, configuration 1, at different observer locations (inlet

angles). From Reference 25. (a) 52°. (b) 62°. (c) 69°. (d) 78°. (e) 88°. (f) 98°.
NASA/TP—2012-215653 348

Figure 9.12.—Concluded. (g) 109°. (h) 121°. (i) 127°. (j) 134°. (k) 141°. (l) 148°.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 349 Chapter 9

Figure 9.13.—Comparison of measured data and Jet3D predictions of sound pressure level (SPL) 

for baseline separate-flow nozzle of BPR 5 with pylon, configuration 6, at different observer

locations (inlet angles). From Reference 25. (a) 52°. (b) 62°. (c) 69°. (d) 78°. (e) 88°. (f) 98°.
NASA/TP—2012-215653 350

Figure 9.13.—Concluded. (g) 109°. (h) 121°. (i) 127°. (j) 134°. (k) 141°. (l) 148°.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 351 Chapter 9

Figure 9.14.—Comparison of measured data and Jet3D 

predictions of effective perceived noise level (EPNL)

for full-scale separate-flow nozzle of BPR 5, both

configuration 1 and configuration 6 (with pylon).

Standard deviation in data is ±0.36 EPNdB.

9.4.4 Jet3D Challenges

Two challenges face Jet3D, the first being the poor aft arc 

prediction seen in previous examples. Past about 110° inlet 

angle, Jet3D SPL predictions are generally missing the 

experimental data in both amplitude and frequency. As 

mentioned previously, this is due to incomplete modeling of 

the Lighthill stress tensor in Jet3D—that is, the neglect of 

terms other than ρuiuj—in combination with the two-point 

space-time correlation formulation. Unfortunately, it is not 

practical to fix this modeling issue as long as RANS–CFD is 

used for flow input; however, ad hoc aft-arc corrections have 

been somewhat successful on a case-by-case basis.

For a more permanent, long-term improvement, Jet3D will 

transition to using data from nonaveraged simulations 

including large eddy simulation (LES), direct numerical 

simulation (DNS), and partially-averaged Navier-Stokes 

(PANS). Of these methods, PANS holds the most promise 

because it combines the affordability of RANS with the higher 

fidelity of LES and DNS. With any of these methods, the 

Lighthill stress tensor will be computed directly, with minimal 

need for approximations and modeling, and no need for twopoint correlations.

The other challenge facing Jet3D is midfrequency SPL 

overprediction in dual-stream core-fan nozzles. This has been 

traced back to CFD overprediction of turbulent kinetic energy 

(TKE) near the end of the annular fan stream’s potential core 

and is present in solutions from a wide range of RANS solvers 

and turbulence models. The localized boost in TKE results in a 

corresponding increase in noise sources and a 5- to 6-dB spike 

in SPL around 1600 to 3000 Hz (model scale). Presently, the 

problem is addressed on a case-by-case basis (using experimental data for guidance) by smoothing or filtering the TKEspike portion of the CFD solution and its corresponding noise 

sources.

Going forward, the midfrequency overprediction problem is 

being investigated as a turbulence modeling issue. Though 

RANS turbulence modeling is not entirely appropriate near the 

end of a jet potential core, it is hoped that some improvement 

can be made. Early indications suggest that the TKE overprediction may be due to inflow turbulence initialization, with 

low initial levels resulting in higher-than-normal TKE growth 

at the end of the fan’s annular potential core.

9.5 Future PAA Experimental and 

Prediction Development

In addition to the underlying challenges of the noise source 

components (jet, fan, airframe, etc.), propulsion airframe 

aeroacoustics interaction experiments face many challenges to 

develop more comprehensive prediction methodologies.

One challenge involves the need for a benchmark PAA 

experiment on the prolific engine-under-wing configuration. 

This experiment would include variation of the major 

parameters from pylon length (jet-wing spacing), pylon 

thickness, jet exhaust plane to flap trailing-edge spacing, flap 

settings, nozzle types (conventional and chevron), and so 
NASA/TP—2012-215653 352

forth. Detailed acoustic and flow-field measurements would 

be required to provide the complete documentation that

is missing to date. Both polar and azimuthal far-field acoustic 

measurements would be necessary with phased-array

measurements. Flow-field measurements should include both 

surface pressures as well as mean-flow and turbulence 

measurements at key locations where the jet exhaust interacts 

with the flap and wing downwash. A comprehensive experiment of this type, at large scale (3 percent or larger) with highfidelity geometry, does not appear to be available in the 

literature.

For the engine-under-wing configuration there should also 

be an experimental documentation of the fan noise reflection 

from the wing and fuselage. Clearly, for unconventional 

configurations that mount engines on top of the wing and 

fuselage, documentation of the shielding and reflection of 

propulsion noise sources, both fan and jet, is key. This 

includes parameters like forward flight effects and angle of

attack. The flow interactions of such unconventional configurations should be investigated particularly on configurations 

that require highly integrated propulsion systems with 

embedded engines.

Future challenges for PAA prediction methods cover almost 

the full range because of the early state of development of 

methods that are focused on predictions of this kind. The PAA 

predictions must move toward predictions of the complete 

aircraft configuration because of the complex geometries 

required and the basic fact that it is only with the full aircraft 

configuration that the multiple flow and acoustic PAA effects 

are present. This overall challenge drives the needs for 

multiple improvements in prediction capabilities starting with 

issues of a fundamental nature including the improved RANS 

turbulence models, the use of time-dependent flow information for acoustic predictions, and the deployment of fast, 

efficient, flexible unstructured grid generation methods and 

CFD solutions.

On the way to this full aircraft configuration PAA prediction, the next major step will likely be the prediction of the jetflap interaction for the engine-under-wing configuration. 

Including the nozzle, pylon, wing, and deployed flaps at 

relevant angle-of-attack, this problem will require significant 

effort just to obtain time-dependent flow-field solutions. These 

solutions must include aeroacoustics-relevant refinements 

such as off-body grid adaptation to noise-producing shear 

layers downstream of the jet-flap interaction. The flow-field 

solution is, of course, the essential prerequisite to the eventual 

CFD-based noise prediction.

Ultimately, the prediction method for jet-flap interaction 

will probably require the Jet3D approach described above, 

including the time-dependent flow field, to accurately predict 

the multiple jet and jet-airframe interactions sources present in 

the jet-flap interaction problem. Once this prediction capability for jet-flap interaction is in place for the engine-underwing configuration, it will probably represent the basic 

capability needed for a flow-interaction PAA prediction 

method usable for more general configurations. For a less 

computationally intensive approach using a RANS flow-field 

solution, it remains to be seen how well such methods can do 

on the jet-flap interaction problem.

For the full PAA prediction capability, flow-interaction 

PAA effects prediction (such as three-dimensional jet-pylon 

and jet-flap interactions) will have to be linked to acoustic 

propagation and interaction, shielding, and reflection prediction. The needs for acoustic scattering prediction are focused 

in the foreseeable future on increasing the frequency range, 

including the effects of the mean nonuniform flow field, and 

on the computational resource and efficiency issues resulting 

from complex configuration geometry.

Finally, with such a flow and acoustic interaction PAA 

prediction capability, the overall requirement will be to 

integrate these methods into an effective aircraft system noise 

prediction tool.
Propulsion Airframe Aeroacoustic Interactions

NASA/TP—2012-215653 353 Chapter 9

Appendix A.—Nomenclature

A.1 Acronyms

AST Advanced Subsonic Technology 

BPR bypass ratio

BWB blended wing body

CFD computational fluid dynamics

DNS direct numerical simulation

EPNL effective perceived noise level

GE General Electric Company

JES jet engine simulator

JNL Jet Noise Laboratory

LAA Lighthill’s Acoustic Analogy

LES large eddy simulation

LSAF Low-Speed Aeroacoustic Facility

LSAWT Low Speed Aeroacoustic Wind Tunnel

NPR nozzle pressure ratio

OASPL overall sound pressure level

PAA propulsion airframe acoustics

PANS partially-averaged Navier-Stokes

PNL perceived noise level

QTD2 Quiet Technology Demonstrator 2

RANS Reynolds-averaged Navier-Stokes

SPL sound pressure level

TKE turbulent kinetic energy

A.2 Symbols

c local speed of sound 

C jet convection factor

C∞ flight convection factor

D core nozzle diameter

g temporal correlation function, g = g( τ

~ )

k turbulent kinetic energy (TKE) per unit mass

1, 2, 3 turbulence length scales

M Mach number

p acoustic pressure 

r acoustic radius vector, r = x – z

r magnitude of acoustic radius r

rˆ acoustic radius unit vector, rˆ = r r

R spatial correlation function

SPL sound pressure level

t time

T temperature

Ti j Lighthill stress tensor

ui total velocity vector component

vi turbulent velocity vector component

Vi mean flow velocity vector component

vivm one-point turbulent velocity correlation

vivm

′ two-point turbulent velocity correlation 

x fixed observer position vector

z moving frame source position vector

αc jet convection factor parameter

αL length scale calibration constant

ατ time scale calibration constant

δij Kronecker delta function

ε dissipation rate of k

ζ moving frame separation vector

θ observer angle from jet axis

μ correlation calibration constant

ρ density

σij viscous stress tensor

τ time delay in observer frame

τ

~ moving frame time delay, τ~ = t/C

τ0 characteristic time scale of turbulence

Subscripts:

c convection

o stagnation

∞ ambient or free-stream conditions

Superscripts:

* geometric observer

′ denotes spatial change for variable in a two-point 

correlation
NASA/TP—2012-215653 354

References 

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Investigation. AIAA–2005–2807, 2005.

2. Thomas, R.H.; and Hill, G.A.: Challenges and Opportunities 

for Noise Reduction Through Advanced Aircraft Propulsion 

Airframe Integration and Configurations. Presented at the 8th 

ASC–CEAS Workshop on Aeroacoustics of New Aircraft and 

Engine Configurations, Budapest, Hungary, 2004.

3. Thomas, Russell H.: Aeroacoustics of Propulsion Airframe 

Integration: Overview of NASA’s Research. Presented at the 

NOISE–CON 2003 Conference, NOISE–CON 2003 Paper 105, 

Cleveland, OH, 2003.

4. Thomas, Russell; and Kinzie, Kevin W.: Jet-Pylon Interaction 

of High Bypass Ratio Separate Flow Nozzle Configurations. 

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5. Mengle, Vinod, et al.: Reducing Propulsion Airframe Aeroacoustic Interactions With Uniquely Tailored Chevrons: 1. Isolated Nozzles. AIAA–2006–2467, 2006.

6. Mengle, Vinod, et al.: Reducing Propulsion Airframe Aeroacoustic Interactions With Uniquely Tailored Chevrons: 2. Installed Nozzles. AIAA–2006–2434, 2006.

7. Mengle, Vinod, et al.: Reducing Propulsion Airframe Aeroacoustic Interactions With Uniquely Tailored Chevrons: 3. JetFlap Interaction. AIAA–2006–2435, 2006.

8. Mengle, Vinod, et al.: Flaperon Modification Effect on Jet-Flap 

Interaction Noise Reduction for Chevron Nozzles. AIAA–

2007–3666, 2007.

9. Nesbitt, Eric, et al.: Flight Test Results for Uniquely Tailored 

Propulsion Airframe Aeroacoustic Chevrons: Community 

Noise. AIAA–2006–2438, 2006.

10. Reimann, Craig; Tinetti, Ana; and Dunn, M.: Noise Prediction 

Studies for the Blended Wing Body Using the Fast Scattering 

Code. AIAA–2005–2980, 2005.

11. Massey, Steven, et al.: Computational and Experimental Flowfield Analyses of Separate Flow Chevron Nozzles and Pylon 

Interaction. AIAA–2003–3212, 2003.

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Society of America, Pittsburgh, PA, 2002.

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14. ABSTRACT

A goal of NASA’s Fundamental Aeronautics Program is the improvement of aircraft noise prediction. This document provides an 

assessment, conducted from 2006 to 2009, on the current state of the art for aircraft noise prediction by carefully analyzing the results from 

prediction tools and from the experimental databases to determine errors and uncertainties and compare results to validate the predictions. 

The error analysis is included for both the predictions and the experimental data and helps identify where improvements are required. This 

study is restricted to prediction methods and databases developed or sponsored by NASA, although in many cases they represent the current 

state of the art for industry. The present document begins with an intrduction giving a general background for and a discussion on the 

process of this assessment followed by eight chapters covering topics at both the system and the component levels. The topic areas, each 

with multiple contributors, are aircraft system noise, engine system noise, airframe noise, fan noise, liner physics, duct acoustics, jet noise, 

and propulsion airframe aeroacoustics.

15. SUBJECT TERMS

Noise prediction; Aircraft noise; Engine noise; Computer simulation; Sensitivity analysis; Statistical analysis; Accuracy; Acoustic 

ducts; Acoustic attenuation 

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