James R. Stone, Eugene A. Krejsa, and Bruce J. Clark

MTC Technologies, Westlake, Ohio

Enhanced Core Noise Modeling for

Turbofan Engines

NASA/CR—2011-217026

June 2011
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James R. Stone, Eugene A. Krejsa, and Bruce J. Clark

MTC Technologies, Westlake, Ohio

Enhanced Core Noise Modeling for

Turbofan Engines

NASA/CR—2011-217026

June 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NAS3–00178, Task Order 15
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subject to revision as analysis proceeds.
NASA/CR—2011-217026 iii

Contents

Executive Summary......................................................................................................................................v

1.0 Introduction ..........................................................................................................................................1

1.1 Background.................................................................................................................................1

1.2 Approach.....................................................................................................................................2

1.3 Sample Extraction.......................................................................................................................3

2.0 Validation of Jet Noise Model..............................................................................................................4

2.1 CF6 Engine .................................................................................................................................4

2.2 CF34 Engine ...............................................................................................................................5

2.3 CFM56 Engine............................................................................................................................5

2.4 GE90 Engine...............................................................................................................................6

2.5 Accuracy of Jet Noise Prediction................................................................................................6

3.0 Core Noise Correlation.........................................................................................................................6

3.1 Component Level Correlations...................................................................................................6

3.1.1 Low Frequency Component.......................................................................................... 7

3.1.2 Middle Frequency Component...................................................................................... 7

3.1.3 High Frequency Component ......................................................................................... 7

3.2 Spectral Directivity Correlations ................................................................................................8

3.2.1 Low Frequency Component.......................................................................................... 8

3.2.2 Middle Frequency Component...................................................................................... 8

3.2.3 High Frequency Component ......................................................................................... 8

3.3 Statistical Evaluation ..................................................................................................................9

3.4 Application of Correlation to Other Engines..............................................................................9

3.4.1 JT15D.......................................................................................................................... 10

3.4.2 YF102.......................................................................................................................... 10

3.4.3 Prospects for Extension/Improvement ........................................................................ 10

4.0 Concluding Remarks..........................................................................................................................10

References...................................................................................................................................................11

Appendix A.—Nomenclature .....................................................................................................................47

List of Tables

Table I.—Spectral Directivity Relations For Low Frequency Core Noise (C1).........................................13

Table II.—Spectral Directivity Relations For Mid-Frequency Core Noise (C2)........................................15

Table III.—Spectral Directivity Relations For High Frequency Core Noise (C3) .....................................17

List of Figures

Figure 1.—Flight Effect Variables for Engine Exhaust Noise. ..................................................................19

Figure 2.—Typical Example Flight Effects on Exhaust Noise...................................................................19

Figure 3.—Typical Component Extraction for CF6-80C2A5F at Low Power, Vmix/camb = 0.402..............20

Figure 4.—Comparison of Experimental and Predicted Spectra for CF6-80C2A5F at High Power, 

Vmix/camb = 1.004.................................................................................................................................21

Figure 5.—Comparison of Experimental and Predicted OASPL Directivities for CF6-80C2A5F at 

3534 rpm and Vmix/camb = 1.004.....................................................................................................24

Figure 6.—Comparison of Experimental and Predicted Spectra for CF34-8C at High Power, 

Vmix/camb =1.049..................................................................................................................................24

Figure 7.—Comparison of Experimental and Predicted OASPL Directivities for CF34-9C at High 

Power, Vmix/camb = 1.049. ...................................................................................................................27
NASA/CR—2011-217026 iv

Figure 8.—Comparison of Experimental and Predicted Spectra for CFM56-5B/P High Power, 

Vmix/camb = 1.006.................................................................................................................................27

Figure 9.—Comparison of Experimental and Predicted OASPL Directivities for CFM56-5B/P at 

High Power, Vmix/camb = 1.006. ..........................................................................................................30

Figure 10.—Comparison of Experimental and Predicted Spectra for GE90 at High Power, 

Vmix/camb = 0.906.................................................................................................................................30

Figure 11.—Comparison of Experimental and Predicted OASPL Directivities for GE90 at High 

Power, Vmix/camb = 0.906. ...................................................................................................................33

Figure 12.—Core Noise Level Correlations. ..............................................................................................33

Figure 13.—Normalized Spectra for Low Frequency Core Noise. ............................................................35

Figure 14.—Normalized Spectra for Middle Frequency Core Noise. ........................................................37

Figure 15.—Normalized Spectra for High Frequency Core Noise.............................................................40

Figure 16.—Error (Experimental—Predicted) Versus Nondimensional Mixed Jet Velocity.....................42

Figure 17.—Standard Deviation Versus Nondimensional Mixed Jet Velocity. .........................................43

Figure 18.—Root-Mean-Square Error Versus Nondimensional Mixed Jet Velocity. ................................43

Figure 19.—Experimental 3-Signal Coherence Spectra Compared With Correlation at Directivity 

Angle θ = 120 deg for JT15D Engine. ...............................................................................................44

Figure 20.—Experimental Spectra Compared With Correlation at Directivity Angle θ = 120 deg 

for YF-102 Engine. ............................................................................................................................46
NASA/CR—2011-217026 v

Executive Summary

This report describes work performed by MTC Technologies (MTCT) for NASA Glenn Research 

Center (GRC) under Contract NAS3-00178, Task Order No. 15. MTCT previously developed a firstgeneration empirical model that correlates the core/combustion noise of four GE engines, the CF6, CF34, 

CFM56, and GE90 for General Electric (GE) under Contract No. 200-1X-14W53048, in support of GRC 

Contract NAS3-01135. MTCT has demonstrated in earlier noise modeling efforts that the improvement of 

predictive modeling is greatly enhanced by an iterative approach, so in support of NASA’s Quiet Aircraft 

Technology Project, GRC sponsored this effort to improve the model.

Since the noise data available for correlation are total engine noise spectra, it is total engine noise that 

must be predicted. Since the scope of this effort was not sufficient to explore fan and turbine noise, the 

most meaningful comparisons must be restricted to frequencies below the blade passage frequency.

Below the blade passage frequency and at relatively high power settings jet noise is expected to be the 

dominant source, and comparisons are shown that demonstrate the accuracy of the jet noise model 

recently developed by MTCT for NASA under Contract NAS3-00178, Task Order No. 10. At lower 

power settings the core noise became most apparent, and these data corrected for the contribution of jet 

noise were then used to establish the characteristics of core noise. There is clearly more than one spectral 

range where core noise is evident, so the spectral approach developed by von Glahn and Krejsa in 1982 

wherein four spectral regions overlap, was used in the GE effort. Further analysis indicates that the two 

higher frequency components, which are often somewhat masked by turbomachinery noise, can be treated 

as one component, and it is on that basis that the current model is formulated. The frequency scaling 

relationships are improved and are now based on combustor and core nozzle geometries.

In conjunction with the Task Order No. 10 jet noise model, this core noise model is shown to provide 

statistical accuracy comparable to the jet noise model for frequencies below blade passage. This model is 

incorporated in the NASA FOOTPR code and a user’s guide is provided.

NASA/CR—2011-217026 1

Enhanced Core Noise Modeling for Turbofan Engines

James R. Stone, Eugene A. Krejsa, and Bruce J. Clark

MTC Technologies

Westlake, Ohio 44145

1.0 Introduction

The introduction of high bypass ratio turbofan engines on modern aircraft has led to a substantial 

reduction of jet exhaust noise, in comparison to the older low bypass and turbojet engines. However, the 

growth of air traffic and the need to protect the environment in the vicinity of airports result in the need to 

further reduce jet noise. Local noise restrictions and the likelihood of international agreement on stricter 

noise rules in the near future make this need more urgent. Still higher bypass ratio engines and devices 

that can reduce noise without major weight or performance penalties are under development. As fan noise 

is reduced in these newer engines, jet exhaust noise reduces the system benefits that can be obtained.

With the evolution from turbojets to first low-bypass and then high-bypass turbofan engines, the 

importance of noise sources other than jet mixing became apparent. In addition to the fairly obvious fan 

noise, other internal sources became apparent throughout the spectrum. Since it was difficult to determine 

exactly what source or mechanism was responsible for each part of the spectrum, the term “core noise” 

was evolved to describe all noise generated within the engine core, or essentially all noise not generated 

by the fan or the jet. Mahan and Karchmer (Ref. 1) state, “Combustion noise in gas turbine engines is 

classified according to source mechanism as either direct or indirect. Direct combustion noise is produced 

by the combustion process itself, while indirect combustion noise occurs when the hot products of 

combustion pass through the turbine and exhaust nozzle. The combination of direct and indirect 

combustion noise in a gas turbine engine makes up an important part of what is generally called core 

noise. Depending on the authority cited, core noise may or may not include compressor noise as well as 

turbine noise not associated with the combustion process. In some quarters, core noise is defined as all 

noise exclusive of jet noise emitted into the rear arc of gas turbine engine.” To help quantify this 

somewhat elusive noise component so that it can be properly included in engine system noise 

assessments, a task was undertaken to develop a predictive model for combustion/core noise for General 

Electric (GE) with support from NASA Glenn Research Center (GRC) (Ref. 2). This effort is to develop 

an improved and more general model. For simplicity we will use the “core noise” identification.

1.1 Background

The real importance of core noise relative to jet noise for gas turbine engines did not become 

appreciated until relatively good quality flight data became available in the 1970s. Some of the 

terminology needed to describe flight effects is shown in Figure 1 (from Ref. 3). The cases considered in 

this discussion are level flyovers at airplane velocity V0, with the observer located at an angle θ from the 

inlet axis. According to classical jet noise theory (e.g., Ffowcs Williams, Ref. 4) in-flight noise should 

follow a fairly simple relation. For a given absolute jet velocity Vj, increasing the flight velocity V0

reduces the velocity of the jet relative to the air. This reduces the shear, and therefore the noise should be 

less in flight.

Interest in jet noise flight effects and in core noise was greatly stimulated when Rolls Royce (Refs. 5

and 6) reported results like those shown in Figure 2, where the overall sound pressure level OASPL is 

plotted against the directivity angle θ. The static case is shown by the solid curve, and the corresponding 

flight case is shown by the dash-dot curve. The noise in the rear quadrant was reduced, as expected.

However, in some cases, such as the one shown here, the noise in the forward quadrant increased in flight. 

Further confusing the issue is the fact that model-jet simulated flight tests indicate that in-flight noise 

should be reduced at all angles, roughly in agreement with theory, as shown by the dashed curve. Studies 
NASA/CR—2011-217026 2

conducted or sponsored by NASA suggest that these apparent anomalies can be resolved when the engine 

internal noise, or “core noise,” is considered (e.g., Refs. 7 to 13). The core noise is amplified by a 

sufficient amount (Ref. 14) in the forward quadrant (θ < 90 deg) that the total in-flight noise exceeds the 

static level even though the jet noise is reduced. The primary source of the low-to-middle frequency, 

broadband core noise is the combustor, including both “direct” and “indirect” combustion noise. Direct 

combustion noise is that generated by the mixing and burning processes, while indirect combustion noise 

results from the combustion-generated nonuniform flow through area changes such as the turbine and 

nozzle.

Engine ground tests are hard to interpret because of the tendency for jet mixing noise, which is 

reduced in flight, to obscure the core/combustion noise, which is not. Because both noise components are 

primarily broadband and peak at similar frequencies, it is very difficult to separate their contributions.

The earliest prediction procedures for core/combustion noise (Refs. 15 to 17) were based primarily on 

combustor rig data, but Reference 16 does include engine tests data. These predictive models do not agree 

on some parametric effects. It was in the late 1970s and early 1980s that the most relevant experimental 

work was done to determine the far-field noise emanating from the engine core for a turbofan engine 

(e.g., Refs. 18 to 20). Perhaps of greater concern is that recent tests indicate that combustion noise may be 

increased by as much as 10 to 15 dB for low emission combustors compared with conventional 

combustors for which predictive models, though crude, exist (Ref. 21).

1.2 Approach

This FOOTPR framework (Ref. 22) has been used by MTCT in developing noise prediction models 

for NASA and the industry. Most recently we have developed a model for predicting the jet noise for a 

wide variety of single and dual-stream nozzles (Ref. 23). Since the core/combustion noise is at low to 

moderately high frequencies, it is the jet noise that is most important to estimate correctly in order to 

isolate the core/combustion noise. However, for the middle frequency region fan noise can become in an 

important factor. In our initial analysis of the recent engine data, assuming that the combustion noise 

spectrum would have a rather broad, single-peaked spectrum as in earlier models (e.g., Refs. 15, 16, and 

24) was found not to be consistent with the data, as multiple peaks were apparent (Ref. 2). We reviewed 

the findings of von Glahn and Krejsa (Ref. 20) wherein as many as four core-related peaks were found for 

several turbofan engines from three-signal coherence analysis. We also noted that recent results for lowemissions combustors (Ref. 21) also exhibited such trends. Further analyses after the completion of the 

GE task (Ref. 2) led us to conclude that because of the partial masking of the two higher frequency core 

noise components by turbomachinery noise, a three-component core noise model was most appropriate.

For the current effort the noise for all the engine components was predicted, with the combustion core 

noise assumed to consist of three spectral regions. Since the engines tested had some acoustic treatment, 

some arbitrary adjustments had to be made for the fan noise (Ref. 25); turbine parameters were not 

provided, so turbine noise (Ref. 26) could not be predicted. It is likely that some of the high frequency 

noise currently attributed to plug separation noise is actually turbine noise.

The jet noise, consisting of four components, is calculated using the model of Reference 27 with very 

limited adjustments depending on the confidence we have in the individual component predictions. For 

the large-scale (“merged”) turbulent mixing noise generated well downstream of the nozzle exits, only

±1.0 dB is used in fitting the individual test cases. For small-scale turbulent mixing noise generated near 

the nozzle exits, ±2.0 dB is tolerated, while for transitional/intermediate scale (“premerged”) turbulent 

mixing noise, and plug separation noise, the tolerances are ±3.0 and 4.0 dB, respectively. 

An important point to understanding our analysis approach is to recognize that for each component, at 

any angle and at any frequency, the sound pressure level SPLcomp,EE is always directly proportional to the 

component coefficient, Ccomp,exp. The process is iterative. We initially compare the experimental results 

with absolute prediction (Ref. 27 for jet noise, Ref. 25 for fan noise, and Ref. 2 modified to three 

components for core noise). We next adjust the five coefficients in the fan noise prediction (forward 

broadband, forward tone, multiple pure tones, aft broadband and aft tone) to provide reasonable
NASA/CR—2011-217026 3

“eye-ball” agreement in the vicinity of the BPF; since many of the test cases involve some degree of fan 

acoustic treatment, this process is rather crude. We do not attempt to minimize the errors at very high 

frequencies, since turbine noise is likely to be a major factor there. At this point we establish the 

frequency range over which each of the core noise components is most important and calculate the 

statistical relations between experimental and predicted total levels across these frequency bands. Finally, 

we vary the jet and core noise coefficients carefully in small increments (with jet coefficients constrained 

as mentioned above) to produce the minimum average error ∆ over each of these frequency ranges, often 

being able to achieve ∆ = 0.0 dB. This yields the experimental component coefficients CC1,exp, CC2,exp, and 

CC3,exp for core noise, along with CL,exp (large-scale mixing), CS,exp (small-scale mixing), CT,exp

(transitional/intermediate scale mixing) and CP,exp (plug separation).

From these calculations the predicted contribution of each component to the total is calculated. This 

calculated difference, SPL(total)—SPL(component), is then applied to the experimental spectra to 

produce experimental/extracted spectra for each component, SPLcomp,EE. These component SPLs are 

significant only where the component SPL is close to the total, and it is on such data that our correlations 

are based.

As a starting point, we made the assumption that core noise should correlate with the same parameters 

included in the original NASA ANOPP core noise prediction (Ref. 15), where overall sound power level 

OAPWL was correlated as follows:

OAPWL = Constant + 10 log WI {[TC,o – TC,i] [PC,i/Pamb] [Tamb/TC,i]}2 (1)

Where WI is the total core mass flow rate (fuel and air), TC,o is the combustor outlet temperature, TC,i is 

the combustor inlet temperature, Tamb is the ambient temperature, PC,i is the combustor inlet pressure, and 

Pamb is the ambient pressure.

1.3 Sample Extraction

A sample of our component noise extraction procedure, discussed above, is shown in Figure 3 for one 

specific engine. (The values of SPL on the figure are relative, as the exact values are proprietary to GE).

Total experimental spectra and experimental/extracted (denoted EE) component spectra are shown for 

nominal directivity angles (with respect to the inlet axis) θ = 90, 120, and 150 deg are shown in

Figure 3(a) to (c). Note that we break the core noise contributions into three regions, denoted C1, C2, and 

C3. The jet noise components are denoted L for large scale mixing, S for small scale mixing, T for 

transitional mixing, and P for plug separation; turbomachinery noise is denoted by tm. (Note that software 

limitations cause subscripts to appear as normal text in figure legends.) The turbomachinery noise tends to 

dominate at frequencies above the blade passage frequency, in this case 1045 Hz, with jet and core noise 

dominating at lower frequencies, especially toward the sideline and in the rear quadrant, as shown here.

At this very low power setting, the total engine noise below 1000 Hz is well above that predicted for jet 

noise, except at very low frequency and as we approach the jet axis (Fig. 3(c)). The coefficients for the 

three core noise components are adjusted to minimize the error between experimental and predicted total 

SPLs over the appropriate frequency ranges. The adjustments to the jet noise model in this case were

1.0 dB for large scale mixing noise, 0.0 dB on small scale mixing noise, 3.0 dB, and 4.0 dB on plug 

separation noise (which may also include turbine noise.)

For this particular case, the middle and high frequency core noise components are quite evident at

θ = 90 and 120 deg (Figs. 3(a) and (b)), and the third is clearly evident even at θ = 150 deg (Fig. 3(c)).

The low frequency core noise component is on the same order as the large scale mixing noise at θ = 90 

and 120 deg (Fig. 3(a) and (b)) and is obscured by this jet noise component at θ = 150 deg (Fig. 3(c)).

These observations are not general; each case must be considered individually.

The component coefficients obtained in this manner for the full set of cases analyzed are correlated as 

a function of combustor design and aerothermodynamic variables to yield the final predictive model.
NASA/CR—2011-217026 4

2.0 Validation of Jet Noise Model

The development of the core noise model from total engine noise data requires the accurate prediction 

of jet noise. It is at high power that jet noise is expected to be most evident, so this section shows 

comparisons of experimental data with predictions for all four engines at the highest power setting. The 

jet noise components, large scale mixing (SPLL,Pred), small scale mixing (SPLS,Pred), transitional/

intermediate scale mixing (SPLT,Pred), and the plug separation noise (SPLP,Pred) are all predicted using the 

relations of Reference 27 exactly, with no adjustment. The turbomachinery noise (SPLtm,Pred) is very 

crudely predicted/fit by a temporary method. Even though jet noise is expected to be dominant below the 

blade passage frequency, core noise is estimated using the finalized model exactly as described later in 

this report; these components are SPLC1,Pred, SPLC2,Pred, and SPLC3,Pred. The point of the comparisons in this 

section is that the jet noise model of Reference 27 is valid for these engines.

2.1 CF6 Engine

Figure 4 presents a comparison of the experimental spectra with prediction at the highest power 

setting tested, 3534 rpm. Blade passage frequency (BPF) is 2238 Hz.

It appears that the SPL is slightly over-predicted at low frequency, where large-scale turbulent mixing 

noise is expected to be dominant at all angles. At θ = 30 deg (Fig. 4(a)) the noise from about 200 Hz up to 

the BPF is predicted with reasonable accuracy, with a significant contribution from core noise even at this 

high power. These observations are also appropriate at θ = 60 deg (Fig. 4(b)) and θ = 90 deg (Fig. 4(c)), 

but the accuracy is better. At high frequencies, it is difficult to separate the relative contributions of small 

scale mixing noise, plug separation noise and turbomachinery noise. The large scale mixing prediction 

appears to be reasonably well validated over this angular range.

In the aft quadrant the jet mixing noise components are expected to become more dominant. At

θ = 120 deg (Fig. 4(d)) the agreement below BPF is quite good, with large scale mixing noise predicted to 

dominate at f < 630 Hz, and with small scale mixing predicted to be most important at 1000 to 6300 Hz, 

except where fan tones appear. The under-prediction at f > BPF is likely due mainly to the 

turbomachinery noise or plug separation noise. At θ = 150 deg (Fig. 4(e)) the spectrum is predicted to be 

dominated by large scale mixing noise for f ≤ 1000 Hz and by small scale mixing noise at 1250 ≤ f ≤

8000 Hz (again with the exception of fan tones). The agreement for f < BPF is very good, and at higher 

frequencies plug separation and/or turbomachinery noises appear to be somewhat under-predicted.

Overall there is an average over-prediction of the SPLs at all angles and f < BPF of 0.5 dB, with a 

standard deviation (σ) of 1.1 dB and a RMS error (ε) of 1.2 dB. This is quite good when it is recognized 

that most of the inaccuracy is in the crude core noise model. In comparison, as shown in Reference 27 in 

comparing repeat model tests for a nominal BPR = 5 external plug nozzle (Ref. 28) at Vmix/camb = 

1.072±0.014 and Mf = 0.28, it was observed that when the data at all frequencies and all angles are 

considered the average error is ±0.9 dB, with σ = ε = 1.2 dB. When the component coefficients are 

adjusted as in Reference 27 the over-prediction is reduced to 0.1 dB, with σ = 0.9 dB and ε = 0.9 dB.

Because of the improvements included in the present core noise model the statistical accuracy is 

significantly improved over that shown in Reference 2.

The OASPL directivity comparison is shown in Figure 5. Large scale mixing is the dominant 

component for all angles, and the agreement is good at all angles except very near the jet axis. The 

disagreement that exists at high angle is related to the fact that the jet noise model is calibrated to give 

reasonable results at these angles for both static and simulated (free jet) flight test. It is the contention of 

at least one of us (Stone) that the problem probably lies in the infinitesimally thin shear layer assumed in 

the transformation procedure; it is in the rear quadrant that the effects of the thick and spreading shear 

layer would be greatest.
NASA/CR—2011-217026 5

2.2 CF34 Engine

Analogous comparisons are shown in Figures 6 and 7 for a CF34-8C engine at the highest power 

setting tested, 7225 rpm, with BPF = 3372 Hz.

Spectral comparisons are shown at θ = 30 deg (Fig. 6(a)), and agreement below BPF is fairly good 

except for an under-prediction on the order of 2 dB at 125 to 250 Hz, probably due as much to the core 

noise as large-scale turbulent mixing noise. The agreement is a little better at θ = 60 deg (Fig. 6(b)), 

except for a near-tone at 125 Hz with the experimental SPL 3.4 dB above prediction. At θ = 90 deg

(Fig. 6(c)) the agreement is excellent. At this angle large scale mixing noise is predicted to dominate up to 

f = 800 Hz, with the intermediate/transitional scales dominating from 800 ≤ f ≤ 2500 Hz, and small scale 

mixing being the strongest at 3150 to 8,000 Hz. The small scale mixing appears to be under-predicted by 

about 1.0 dB (This could also be due to fan noise.), with the lower frequency components being predicted 

very accurately. At θ = 120 deg (Fig. 6(d)) the mixing noise components are again predicted to dominate 

and the agreement is very good. At θ = 150 deg (Fig. 6(e)) the mixing noise components are still 

predicted to dominate, but the agreement is not as good and it appears that the large scale mixing noise is 

over-predicted. As discussed earlier, these aft angle problems may be due to the accommodation of the 

predictive model for simulated flight data. Looking at the full range of angles, the three components 

predicted for mixing noise agree rather well with the experimental data.

Overall there is an average over-prediction of the SPLs at all angles and f < BPF of 0.3 dB, with

σ = 1.5 dB and ε = 1.8 dB. When the component coefficients are adjusted (slightly) the average is now 

exactly predicted (instead of over-predicted), with σ = 1.5 dB and ε = 1.7 dB. Again this is somewhat 

better agreement than shown in Reference 2.

The OASPL directivity comparison is shown in Figure 7. Large scale mixing is the dominant 

component, or nearly so for all θ, and the agreement is good except beyond θ = 140 deg. The aft angle 

disagreement is a little worse than for the CF6 case (Fig. 5), probably for the same reasons.

2.3 CFM56 Engine

Analogous comparisons are shown in Figures 8 and 9 for a CFM56-5B/P engine at the highest power 

setting tested, 5053 rpm, with BPF = 3032 Hz.

Spectral comparisons are shown at θ = 30 deg (Fig. 8(a)) where the only jet noise predicted to be the 

strongest component is large scale mixing at f ≤ 160 Hz, and in that range the agreement is quite good.

Through the middle frequencies where core noise is predicted to be the strongest contributor, there is 

fairly good agreement. Some over-prediction is evident at the higher frequencies where turbomachinery 

noise is most evident. At θ = 60 deg (Fig. 8(b)) there is some under-prediction across parts of the 

spectrum, with large scale mixing noise predicted to be strongest component for f ≤ 160 Hz and 

transitional/intermediate scale mixing significant over the 500 ≤ f ≤ 2000 Hz range. At θ = 90 deg

(Fig. 8(c)) there is a 1 to 2 dB under-prediction over much of the spectrum. At θ = 120 deg (Fig. 8(d)) the 

spectral shape is predicted fairly well, but there is an under-prediction of about 1 to 2 dB. Large scale 

mixing noise is predicted to be dominant for f ≤ 400 Hz and transitional/intermediate scale mixing is 

predicted to be the strongest contributor for 631 ≤ f ≤ 1595 Hz. At θ = 150 deg (Fig. 8(e)) the agreement 

is fairly good up to BPF, although it appears that large scale mixing and transitional/intermediate scale 

mixing noises may be over-predicted by about 1 to 2 dB.

Overall there is an average under-prediction of the SPLs at all angles and f < BPF of 1.0 dB, with

σ = 1.8 dB and ε = 1.8 dB. When the component coefficients are adjusted (slightly) the average is overpredicted by 0.1 dB, but with σ = 1.4 dB and ε = 1.5 dB.

The OASPL directivity comparison is shown in Figure 9. The agreement is not bad, but not quite as 

good as for the CF6 and CF34, with a fairly consistent over-prediction of about 1.5 dB for 40 ≤ θ ≤

140 deg. 
NASA/CR—2011-217026 6

2.4 GE90 Engine

Analogous comparisons are shown in Figures 10 and 11 for a GE90 engine at the highest power 

setting tested, 2400 rpm, with BPF = 880 Hz. For this large, slowly rotating engine, turbomachinery noise 

is expected to obscure jet and core noise more than for the smaller engines, furthermore fan multiple pure 

tones appear to generate significant noise at f < BPF.

Spectral comparisons throughout the forward quadrant, shown at θ = 30, 60 and 90 deg (Figs. 10(a) to

(c)), indicate that large-scale turbulent mixing noise should predominate for f ≤ 200Hz; these low 

frequency levels are somewhat under-predicted at θ = 30 deg (Fig. 10(a)) but are in good agreement at 

higher angles. Inaccurate prediction of fan multiple pure tones appears at θ = 30 and 60 deg (Figs. 10(a)

to (b)), but at θ = 90 deg (Fig. 10(c)) the predicted multiple pure tones are low enough that the 

transitional/intermediate mixing noise is predicted to be the strongest component between about 251 and 

631 Hz, and the agreement is good up to BPF. At θ = 120 and 150 deg (Figs. 10(d) to (e)) agreement is 

good for f ≤ BPF, indicating reasonably good agreement with the jet noise model.

Overall there is an average over-prediction of the SPLs at all angles and f < BPF of 0.5 dB, with

σ = 1.7 dB and ε = 1.9 dB; this is primarily due to non-jet components. At the lowest frequencies, 50 to 

126 Hz, there is an under-prediction of 0.5 dB, with σ = 1.2 dB and ε = 1.2 dB. When the component 

coefficients are adjusted (mainly combustion noise) the average for f < BPF is now predicted accurately 

to 0.1 dB, with slightly reduced scatter, σ = 1.6 dB and ε = 1.8 dB.

The OASPL directivity comparison is shown in Figure 11. The agreement is not bad, but not quite as 

good as for the CF6 and CF34. The agreement is about the same or little better than CFM56.

2.5 Accuracy of Jet Noise Prediction

From these comparisons we conclude that the jet noise model is sufficiently accurate to enable 

reasonably accurate extraction of the core/combustor noise. When the statistics are averaged for these 

four cases in terms of all frequencies below BPF and all angles, the average predicted within less than

0.1 dB, with σ = 1.5 and ε = 1.6 dB. Considering that some of these errors are due to the core and 

turbomachinery contributions, it is not unreasonable to claim very good agreement for the jet noise model 

in regions where it is the dominant source.

3.0 Core Noise Correlation

The experimental data for a wide range of test conditions on the various engines were analyzed in the 

“extraction” process described in Section 1.3. This resulted in “experimental/extracted” spectra as a 

function of corrected directivity angle for each noise component. The correlation of the core noise 

component results is described in this section. First the component level coefficients, CC1, CC2, CC3, are 

determined using the following type of assumed relation.

UOLC(i),EE = CC(i),exp – 20 log R + 10 log WI {[TC,o – TC,i] [PC,i/Pamb] [Tamb/TC,i]}2 (2)

Where R is the source-to-observer distance, and UOLC(i),EE is the experimental/extracted overall sound 

pressure level for that component at a corrected directivity angle θ = 90 deg, but recall as explained 

earlier that CC(i),exp is determined to minimize the average error at all angles over the frequency range 

considered. These coefficients are then correlated as described in the following.

3.1 Component Level Correlations

Although the coefficients are defined as above (Eq. (2)), we observed that the variation of the 

component levels UOLC(i),EE with the NASA core noise parameter, log WI {[TC,o – TC,i] [PC,i/Pamb] 
NASA/CR—2011-217026 7

[Tamb/TC,i]}2, does not always have a slope of 10 and may be a function of other variables. The approach 

we use is to plot the distance-corrected level (which is the value at θC,cor minimizing the error at all 

angles), UOLC(i),EE + 20 log R, versus 10 log WI {[TC,o – TC,i] [PC,i/Pamb] [Tamb/TC,i]}2 for each component 

and determining the effects of other variables by comparing the results for the different engines. Fuel 

nozzle number nf emerged as a possible correlating parameter (Fig. 12), as discussed below, but further 

analyses might yield better alternative approaches. The following general form is used for all three 

components:

UOLC(i) = CC(i) – 20 log R + NC(i) log (WI {[TC,o – TC,i][PC,i/Pamb] [Tamb/TC,i]}2

) – FC(i) log nf (3)

3.1.1 Low Frequency Component

The normalized (distance-corrected) component level, UOLC1,EE + 20 log R, was plotted against

10 log WI {[TC,o – TC,i] [PC,i/Pamb] [Tamb/TC,i]}2 for the four engines, with differences between engines 

being evident. To bring the data bands closer together, the term – 20 log nf was added to the correlating 

parameter, as shown in Figure 12(a). To help emphasize the cases where this noise component is most 

important, the experimental data for each engine are divided into as many as three categories: significant, 

where this component is the strongest noise component at some angles and frequencies; marginal or tone 

contaminated, where exact correlation is not meaningful; and minor, where significant changes in the 

level of this component has very little effect on the total noise level at any angle or frequency, meaning 

that only very crude correlation of these levels is needed to provide accurate total noise prediction. As an 

example of a “minor” effect, the point falling 10 dB below the correlation line for the CF6 is so 

insensitive to this component that increasing its level by 10 dB (to the correlation value) would only 

increase the average error in total noise in this frequency range by 0.5 dB. The observed slope is less than 

the original NASA model predicts, and the following set of correlation parameters based on Equation (3) 

is obtained:

UOLC1 = 78.0 – 20 log R + 7.0 log (WI {[TC,o – TC,i][PC,i/Pamb] [Tamb/TC,i]}2

) – 14.0 log nf (5)

3.1.2 Middle Frequency Component

The normalized component level was plotted against the core noise parameter, as was done for the 

low frequency component. Again engine-to-engine differences were observed. In this case the term – 18 

log nf was added to the correlating parameter, as shown in Figure 12(b). The same symbol convention is 

used to identify the relative sensitivity of each data point. For the “significant” cases, the scatter appears 

to be more than for the low frequency component; the middle frequency component is more difficult to 

extract since both large-scale and transitional jet noise, both of the other core noise components, and in 

some cases fan noise, can all contribute in this frequency range. The observed slope is as in the original 

NASA model, and the following set of correlation parameters based on Equation (3) is obtained: 

UOLC2 = 60.3 – 20 log R + 10.0 log (WI {[TC,o – TC,i][PC,i/Pamb] [Tamb/TC,i]}2

) – 18.0 log nf (6)

3.1.3 High Frequency Component

The normalized component level was plotted against the core noise parameter, as was done for the 

two lower frequency components. In this case there did not appear to be any significant engine-to-engine 

differences, so the correlating parameter was not modified with a fuel nozzle number term. The results are 

shown in Figure 12(c). The same symbol convention is again used to identify the relative sensitivity of 

each data point. For the “significant” cases, the scatter appears to be more than for the low frequency

component but somewhat less than for the middle frequency component. The slope is better defined than 

for any other component and is slightly less than the original NASA model; the following set of 

correlation parameters based on Equation (3) is obtained:
NASA/CR—2011-217026 8

UOLC3 = 42.5 – 20 log R + 9.0 log (WI {[TC,o – TC,i][PC,i/Pamb] [Tamb/TC,i]}2) (7)

3.2 Spectral Directivity Correlations 

Correlations of the spectral directivity characteristics of the three core noise component are shown in 

Figures 13 to 15. For each component the normalized spectra are shown at θ = 30, 60, 90, 120 and

150 deg in parts (a), (b), (c), (d), and (e) of each figure. The component experimental extracted level at 

each angle and frequency, SPLC(i),EE, is normalized by subtracting the adjusted overall level for that 

component at θC = 90 deg, UOLC(i),EE. The normalized SPL is plotted versus the logarithmic Strouhal 

number for each component. Note that for all data plotted, the experimental extracted level is within 7 dB 

of the total. Data where this difference is greater than 7 dB are dominated by other noise components.

3.2.1 Low Frequency Component

For the lowest frequency core noise (Fig. 13), the Strouhal number is based on core nozzle hydraulic 

diameter (Dh,I) and ambient sonic velocity (camb), as follows:

SC1 = fDh,I/camb (8)

The agreement with prediction is reasonably good except at θ ≅ 150 deg, where jet noise is most 

dominant, making core noise inaccurate to extract. Even though the general agreement is reasonably 

good, it is possible that there are engine-to-engine effects that are not totally correlated. The sound 

pressure level of the low-frequency core noise component (SPLC1) is presented as a function of UOLC1

and SC1 in Table 1.

3.2.2 Middle Frequency Component

For the middle frequency core noise (Fig. 14), the Strouhal number, is based on combustor diameter 

(DC) and combustor exit sonic velocity (cC,o), as follows:

SC2 = fDC/cC,o (9)

Except at θ ≅ 150 deg, the agreement is not as good as for the lowest frequency component; largely due to 

the existence of strong tones for the CFM56. Also contributing to this is that fact there are more noise 

components overlapping in this range, both lowest and highest frequency core noise, as well as jet noise, 

making this component more inaccurate to extract. The sound pressure level of the middle-frequency core 

noise component (SPLC2) is presented as a function of UOLC2 and SC2 in Table 2.

3.2.3 High Frequency Component

For the highest frequency core noise (Fig. 15), the Strouhal number is calculated as for the middle 

frequency component, as follows:

SC2 = fDC/cC,o (10)

The agreement is not quite as good as for the middle frequency core noise, which is not surprising since 

fan noise can be a significant contributor in this frequency range, complicating the extraction process. 

The characteristic lengths and velocities used in these Strouhal relations may very well change if data 

for other engines over a wider range of correlating variables become available. The selection of the 

currently used characteristic velocities and lengths was based simply on identifying a set that 

approximately correlated engine-to-engine trends and the fairly small trends with engine power. No claim 

is made that better relationships cannot be found with further study. The sound pressure level of the highfrequency core noise component (SPLC3) is presented as a function of UOLC3 and SC3 in Table 3.
NASA/CR—2011-217026 9

3.3 Statistical Evaluation

We view the process of developing an empirical predictive model as an evolutionary process, 

particularly for such a complex situation as a turbofan engine. Certainly the model in its current state is an 

advancement over the earlier models (Refs. 15 to 17 and even 2), so it is appropriate to establish 

comparisons now against which to judge future progress. These comparisons are all on an absolute basis, 

not adjusted as in Figure 3. The only adjustment is to the fan noise model, to minimize the errors in the 

vicinity of the blade passage frequency. In each plot the solid symbols are for the average measure at all 

angles and at frequencies below blade passage. The heavily shaded symbols are for all angles and the 

frequency range where the low frequency component is the greatest core noise contributor. The lightly 

shaded symbols are for the frequency range of middle frequency core noise, and the open symbols are for 

the frequency range of high frequency core noise.

Absolute errors ∆ (experimental minus predicted) are shown plotted versus nondimensional mixed jet 

velocity, Vmix/camb, in Figure 16. (Note that Vmix is the mass averaged jet velocity). With our current 

model we predict the noise below the blade passage frequency correctly on average for all engines. With 

∆ = –0.1, –0.5, 0.2, and 0.3 dB for the CF6, CF34, CFM56, and GE90, respectively. These differences 

suggest that there may be effects of combustor variables not yet correlated completely. The tendency to 

under-predict is most pronounced at low power. The lowest frequency component is predicted quite well 

except for CF6. For the middle frequency components the agreement is very good except for the CF34.

For the high frequency component the agreement is fairly good for all engines.

Standard deviation, σ, is shown in Figure 17 versus Vmix/camb. On average for frequencies below blade 

passage, σ = 1.4 dB. Since the standard deviation corrects for the mean error, these results are indicative 

of what may be achieved as the model is evolved; such σ values are lower than we observe in correlating 

model jet noise experimental data.

The more difficult root-mean-square error, ε, is shown in Figure 18. The average for all cases at 

frequencies below blade passage is 1.7 dB, which is comparable to model scale jet noise accuracy.

However, there is clearly room for considerable progress. Since some of the differences appear to be 

systematic, further iteration will likely lead to an improved model.

3.4 Application of Correlation to Other Engines

Previous experience with other combustion noise correlations has been that, while they work well for 

the engines of a given manufacturer, they do not necessarily apply to the engines of a different 

manufacturer. One hypothesis for this disagreement is that different aircraft engine manufacturers have 

different combustion design approaches that result in different combustor noise characteristics. Thus in 

order to test the generality of the combustion noise prediction procedure presented in this report an 

attempt was made to apply it to aircraft engines from different manufactures. One of the difficulties in 

doing this is finding both the noise data and the required cycle data and engine geometry, especially data 

and geometry related to the combustor. Fortunately, sufficient data to perform a preliminary evaluation of 

the prediction method were found for two engines not manufactured by General Electric. These are the 

Avco Lycoming YF102 engine and the Pratt and Whitney JT15D engine. For these two engines, some of 

the geometric parameters, such as combustor diameter, were obtained from report figures using known 

dimensions to determine the scale. Thus these dimensions are at best approximate and assumed that the 

report figures accurately depicted the engine geometry. In addition, the number of fuel nozzles was not 

immediately obtainable in time for this study for the JT15D and YF102 engines. This parameter is used in 

the determination of the levels of the first two predicted peaks, but is not needed for the level of the third 

peak or for the prediction of the frequencies of the three peaks. For the analysis presented here, a value of 

18 fuel nozzles was used for both engines.

Noise data for the JT15D engine were obtained from Reference 20 and that for the YF102 were 

obtained from Reference 19. Both sets of data were obtained using the three-signal coherence method 

developed by Krejsa (Ref. 19). In this method combustion noise levels were determined from cross-
NASA/CR—2011-217026 10

correlations between internal engine and far-field noise measurements. The resultant levels are due only 

to sources within the engine core, which at the low frequencies analyzed in this report are combustion 

noise sources. However, results were reported only at an angle of 120 degrees from the engine inlet. 

Predicted levels for the two engines are compared with data in Figures 19 and 20. In these figures the 

levels of the predicted lowest frequency combustion noise component were adjusted to match the data but 

the peak frequencies of all three components and the levels of the two higher frequency components were 

those predicted by the correlation. 

3.4.1 JT15D

In Figure 19, combustion noise levels determined using the three-signal coherence method are 

compared with predictions, with the levels for the lowest frequency component decreased by 8 dB, for the 

JT15D engine at four engine speeds. This reduction in peak level was made to allow the degree of 

spectral agreement to be observed. At all speeds, the peak frequencies appear to be high by 1 or 2 1/3 

octave bands. At the two lowest speeds, the levels are within 2 to 3 dB of the measured levels. At the 

higher speeds, the difference between the predicted and measured levels is larger, but the sharper peaks in 

the measured spectra indicate that combustor instabilities may be present. The combustion noise method 

presented in this report is not intended to predict levels associated with combustor instabilities.

3.4.2 YF102

In Figure 20, the adjusted prediction is compared with data for the YF102 engine at 37 percent engine 

speed. In Figure 20(a), the measured levels are those determined using the three-signal coherence 

technique and those in Figure 20(b) are the total measured levels. For this engine, the levels for the lowest 

frequency were decreased by 15 dB. All other levels and frequencies were as predicted. Similar to the 

JT15D engine, the frequencies of the two higher peaks appear to be about 1/3 octave band high and the 

levels are within a few dB of the data.

3.4.3 Prospects for Extension/Improvement

The two comparisons presented in this section indicate that, except for the level of the lowest 

frequency noise component, the combustion noise prediction methodology presented in this report is 

capable of predicting the combustion noise associated with engines from several manufactures. At 

present, the reason for the substantial adjustment required for the level of the lowest frequency component 

is unknown. The comparisons for the JT15D and YF102 are not affected by the jet noise model since the 

experimental technique yields core noise only. However, for the other engines, relatively small changes in 

the large-scale jet mixing noise model could have a significant effect on experimental/extracted low 

frequency core noise. It will probably be necessary to adjust both the jet and core noise models to 

improve the accuracy and generality of the model.

Differences for the other components may be due to approximations in the combustor parameters, 

including frequency-scaling effects. Data from more engine geometries and manufacturers would be 

useful to resolve these issues.

4.0 Concluding Remarks

MTC Technologies (MTCT) has developed a prediction model for core/combustion noise in turbofan 

engines based on experimental data for four General Electric (GE) engines. The model is based on core 

noise components peaking at low, medium and fairly high (~1 kHz) frequency based on extensive 

analysis of these data. Since it is impossible to exactly determine the contribution of core noise, statistical 

accuracy is evaluated on the basis of total noise at frequencies below blade passage. On this basis, the 

prediction agrees with the data for the four GE engines exactly on average, with root-mean-square error 

of 1.7 dB. Very limited comparisons with data for engines from other manufacturers indicate rough 
NASA/CR—2011-217026 11

agreement with the two higher-frequency components, but fall significantly below the current prediction 

for the low frequency component.

The statistical accuracy of the model is documented so that users may apply it with quantifiable 

confidence. Overall the accuracy is comparable to correlation of model-scale jet noise, but since 

systematic trends appear to be present, improvement is achievable. We feel that further iteration is 

warranted, but comparison with data for other engines would be even more valuable.

References

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1991.

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Report to GE (Contract 200-1X-14W53048) in support of NASA Contract NAS3-01135, June 14, 

2004.

3. Stone, J.R., and Feiler, C.J., “Recent Developments in Aircraft Engine Noise Reduction Technology,” 

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Philosophical 

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8. Merriman, J.E., et al., “Forward Motion and Installation Effects on Engine Noise,” AIAA-76-584, 

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(MDC-J7708, Douglas Aircraft Co., Inc., NASA Contract NAS3-20031).

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Control Engineering

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on Jet Noise,” NASA CR-3056, 1978.

13. Burcham, F.W., Jr., Lasagna, P.L. and Oas, S.C., “Measurements and Predictions of Flyover and 

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14. Morse, P.M. and Ingard, K.U., “Theoretical Acoustics,” McGraw-Hill Book Co., Inc., 1968.

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Noise,” NASA TM-71627, 1974.

16. Matta, R.K., Sandusky, G.T. and Doyle, V.L., “GE Core Noise Investigation – Low Emission 

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17. Mathews, D.C. and Rekos, N.F., Jr., “Prediction and Measurement of Direct Combustion Noise in 

Turbopropulsion Systems,” J. Aircraft

18. Karchmer, A.M., Reshotko, M. and Montegani, F.J., “Measurement of Far-Field Combustion Noise 

from a Turbofan Engine Using Coherence Functions,” NASA TM-73748, 1977.

, Vol. 14, No. 9, September 1977, pp. 850–859.

19. Krejsa, E.A., “New Technique for the Direct Measurement of Core Noise from Aircraft Engines,” 

NASA TM-82634, July 1981.

20. von Glahn, U.H. and Krejsa, E.A., “Correlation of Core Noise Obtained by Three-Signal Coherence 

Techniques,” NASA TM-83012, November 1982.
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21. Gliebe, P., Mani, R., Shin, H., Mitchell, B., Ashford, G., Salamah, S. and Connell, S. “AST Critical 

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Area of Interest 13, December 1999.

22. Clark, B.J., “Computer Program to Predict Aircraft Noise Levels,” NASA TP-1913, September 1981.

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Jet Noise Prediction,” AIAA-2004-0361, January 2004.

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AIAA-80-1008, June 1980.

25. Heidmann, M.F., “Interim Prediction Method for Fan and Compressor Source Noise,” NASA TM X71763, 1979.

26. Krejsa, E.A. and Valerino, M.F., “Interim Prediction Method for Turbine Noise,” NASA TM X73566, 1976.

27. Stone, J.R., Krejsa, E.A. and Clark, B.J., “Jet Noise Modeling for Suppressed and Unsuppressed 

Aircraft in Flight,” MTC Final Report to NASA, Contract NAS3-10078, Task Order No. 10, October 

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NASA/CR—2011-217026 13

TABLE I.—SPECTRAL DIRECTIVITY RELATIONS FOR LOW FREQUENCY CORE NOISE (C1) 

Frequency Normalized sound pressure level, SPLC1-UOLC1, dB as function of corrected directivity angle 

parameter Corrected directivity angle, θC, deg 

log SC1 0 10 20 30 40 50 60 70 80 90

-3.6 -59.0 -59.0 -59.0 -59.0 -59.0 -58.5 -58.0 -57.5 -56.5 -55.5

-2.2 -31.0 -31.0 -31.0 -31.0 -31.0 -30.5 -30.0 -29.5 -28.5 -27.5

-2.1 -29.0 -29.0 -29.0 -29.0 -29.0 -28.5 -28.0 -27.5 -26.5 -25.5

-2.0 -27.0 -27.0 -27.0 -27.0 -27.0 -26.5 -26.0 -25.5 -24.5 -23.5

-1.9 -25.0 -25.0 -25.0 -25.0 -25.0 -24.5 -24.0 -23.5 -22.5 -21.5

-1.8 -23.0 -23.0 -23.0 -23.0 -23.0 -22.5 -22.0 -21.5 -20.5 -19.5

-1.7 -21.0 -21.0 -21.0 -21.0 -21.0 -20.5 -20.0 -19.5 -18.5 -17.5

-1.6 -19.0 -19.0 -19.0 -19.0 -19.0 -18.5 -18.0 -17.5 -16.5 -15.5

-1.5 -17.0 -17.0 -17.0 -17.0 -17.0 -16.5 -16.0 -15.5 -14.5 -13.5

-1.4 -15.0 -15.0 -15.0 -15.0 -15.0 -14.5 -14.0 -13.5 -12.5 -11.5

-1.3 -13.0 -13.0 -13.0 -13.0 -13.0 -12.5 -12.0 -11.5 -10.5 -9.5

-1.2 -11.0 -11.0 -11.0 -11.0 -11.0 -10.5 -10.0 -9.5 -8.5 -7.5

-1.1 -9.0 -9.0 -9.0 -9.0 -9.0 -8.5 -8.0 -7.5 -6.5 -5.5

-1.0 -10.1 -10.1 -10.1 -10.1 -10.1 -9.6 -9.1 -8.6 -7.6 -6.6

-0.9 -12.6 -12.6 -12.6 -12.6 -12.6 -12.1 -11.6 -11.1 -10.1 -9.1

-0.8 -16.6 -16.6 -16.6 -16.6 -16.6 -16.1 -15.6 -15.1 -14.1 -13.1

-0.7 -21.6 -21.6 -21.6 -21.6 -21.6 -21.1 -20.6 -20.1 -19.1 -18.1

-0.6 -27.6 -27.6 -27.6 -27.6 -27.6 -27.1 -26.6 -26.1 -25.1 -24.1

-0.5 -33.6 -33.6 -33.6 -33.6 -33.6 -33.1 -32.6 -32.1 -31.1 -30.1

-0.4 -39.6 -39.6 -39.6 -39.6 -39.6 -39.1 -38.6 -38.1 -37.1 -36.1

-0.3 -45.6 -45.6 -45.6 -45.6 -45.6 -45.1 -44.6 -44.1 -43.1 -42.1

-0.2 -51.6 -51.6 -51.6 -51.6 -51.6 -51.1 -50.6 -50.1 -49.1 -48.1

-0.1 -57.6 -57.6 -57.6 -57.6 -57.6 -57.1 -56.6 -56.1 -55.1 -54.1

0.0 -63.6 -63.6 -63.6 -63.6 -63.6 -63.1 -62.6 -62.1 -61.1 -60.1

0.1 -69.6 -69.6 -69.6 -69.6 -69.6 -69.1 -68.6 -68.1 -67.1 -66.1

0.2 -75.6 -75.6 -75.6 -75.6 -75.6 -75.1 -74.6 -74.1 -73.1 -72.1

0.3 -81.6 -81.6 -81.6 -81.6 -81.6 -81.1 -80.6 -80.1 -79.1 -78.1

0.4 -87.6 -87.6 -87.6 -87.6 -87.6 -87.1 -86.6 -86.1 -85.1 -84.1

0.5 -93.6 -93.6 -93.6 -93.6 -93.6 -93.1 -92.6 -92.1 -91.1 -90.1

0.6 -99.6 -99.6 -99.6 -99.6 -99.6 -99.1 -98.6 -98.1 -97.1 -96.1

0.7 -105.6 -105.6 -105.6 -105.6 -105.6 -105.1 -104.6 -104.1 -103.1 -102.1

0.8 -111.6 -111.6 -111.6 -111.6 -111.6 -111.1 -110.6 -110.1 -109.1 -108.1

0.9 -117.6 -117.6 -117.6 -117.6 -117.6 -117.1 -116.6 -116.1 -115.1 -114.1

1.0 -123.6 -123.6 -123.6 -123.6 -123.6 -123.1 -122.6 -122.1 -121.1 -120.1

1.1 -129.6 -129.6 -129.6 -129.6 -129.6 -129.1 -128.6 -128.1 -127.1 -126.1

1.2 -135.6 -135.6 -135.6 -135.6 -135.6 -135.1 -134.6 -134.1 -133.1 -132.1

1.3 -141.6 -141.6 -141.6 -141.6 -141.6 -141.1 -140.6 -140.1 -139.1 -138.1

1.4 -147.6 -147.6 -147.6 -147.6 -147.6 -147.1 -146.6 -146.1 -145.1 -144.1

1.5 -153.6 -153.6 -153.6 -153.6 -153.6 -153.1 -152.6 -152.1 -151.1 -150.1

1.6 -159.6 -159.6 -159.6 -159.6 -159.6 -159.1 -158.6 -158.1 -157.1 -156.1

1.7 -165.6 -165.6 -165.6 -165.6 -165.6 -165.1 -164.6 -164.1 -163.1 -162.1

1.8 -171.6 -171.6 -171.6 -171.6 -171.6 -171.1 -170.6 -170.1 -169.1 -168.1

1.9 -177.6 -177.6 -177.6 -177.6 -177.6 -177.1 -176.6 -176.1 -175.1 -174.1

2.0 -183.6 -183.6 -183.6 -183.6 -183.6 -183.1 -182.6 -182.1 -181.1 -180.1

3.6 -279.6 -279.6 -279.6 -279.6 -279.6 -279.1 -278.6 -278.1 -277.1 -276.1

OASPLC1-UOL1 -2.8 -2.8 -2.8 -2.8 -2.8 -2.3 -1.8 -1.3 -0.3 0.7
NASA/CR—2011-217026 14

TABLE I.—Concluded. 

Frequency Normalized sound pressure level, SPLC1-UOLC1, dB as function of corrected directivity a 

parameter Corrected directivity angle, θC, deg 

log SC1 100 110 120 130 140 150 160 170 180

-3.6 -54.0 -52.3 -49.8 -46.2 -47.2 -50.2 -55.2 -60.2 -65.2

-2.2 -26.0 -24.3 -21.8 -18.2 -19.2 -22.2 -27.2 -32.2 -37.2

-2.1 -24.0 -22.3 -19.8 -16.2 -17.2 -20.2 -25.2 -30.2 -35.2

-2.0 -22.0 -20.3 -17.8 -14.3 -15.3 -18.3 -23.3 -28.3 -33.3

-1.9 -20.0 -18.3 -15.8 -12.5 -13.5 -16.5 -21.5 -26.5 -31.5

-1.8 -18.0 -16.3 -13.8 -10.8 -11.8 -14.8 -19.8 -24.8 -29.8

-1.7 -16.0 -14.3 -11.8 -9.2 -10.2 -13.2 -18.2 -23.2 -28.2

-1.6 -14.0 -12.3 -9.8 -7.7 -8.7 -11.7 -16.7 -21.7 -26.7

-1.5 -12.0 -10.3 -7.9 -6.2 -7.2 -10.2 -15.2 -20.2 -25.2

-1.4 -10.0 -8.3 -6.1 -4.7 -5.7 -8.7 -13.7 -18.7 -23.7

-1.3 -8.0 -6.3 -4.4 -3.2 -4.2 -7.2 -12.2 -17.2 -22.2

-1.2 -6.0 -4.5 -3.1 -2.0 -3.0 -6.0 -11.0 -16.0 -21.0

-1.1 -4.2 -3.0 -2.0 -1.0 -2.0 -5.0 -10.0 -15.0 -20.0

-1.0 -5.3 -4.0 -2.9 -1.8 -2.8 -5.8 -10.8 -15.8 -20.8

-0.9 -7.8 -6.5 -5.4 -4.3 -5.3 -8.3 -13.3 -18.3 -23.3

-0.8 -11.8 -10.5 -9.4 -8.3 -9.3 -12.3 -17.3 -22.3 -27.3

-0.7 -16.8 -15.5 -14.4 -13.3 -14.3 -17.3 -22.3 -27.3 -32.3

-0.6 -22.8 -21.5 -20.4 -19.3 -20.3 -23.3 -28.3 -33.3 -38.3

-0.5 -28.8 -27.5 -26.4 -25.3 -26.3 -29.3 -34.3 -39.3 -44.3

-0.4 -34.8 -33.5 -32.4 -31.3 -32.3 -35.3 -40.3 -45.3 -50.3

-0.3 -40.8 -39.5 -38.4 -37.3 -38.3 -41.3 -46.3 -51.3 -56.3

-0.2 -46.8 -45.5 -44.4 -43.3 -44.3 -47.3 -52.3 -57.3 -62.3

-0.1 -52.8 -51.5 -50.4 -49.3 -50.3 -53.3 -58.3 -63.3 -68.3

0.0 -58.8 -57.5 -56.4 -55.3 -56.3 -59.3 -64.3 -69.3 -74.3

0.1 -64.8 -63.5 -62.4 -61.3 -62.3 -65.3 -70.3 -75.3 -80.3

0.2 -70.8 -69.5 -68.4 -67.3 -68.3 -71.3 -76.3 -81.3 -86.3

0.3 -76.8 -75.5 -74.4 -73.3 -74.3 -77.3 -82.3 -87.3 -92.3

0.4 -82.8 -81.5 -80.4 -79.3 -80.3 -83.3 -88.3 -93.3 -98.3

0.5 -88.8 -87.5 -86.4 -85.3 -86.3 -89.3 -94.3 -99.3 -104.3

0.6 -94.8 -93.5 -92.4 -91.3 -92.3 -95.3 -100.3 -105.3 -110.3

0.7 -100.8 -99.5 -98.4 -97.3 -98.3 -101.3 -106.3 -111.3 -116.3

0.8 -106.8 -105.5 -104.4 -103.3 -104.3 -107.3 -112.3 -117.3 -122.3

0.9 -112.8 -111.5 -110.4 -109.3 -110.3 -113.3 -118.3 -123.3 -128.3

1.0 -118.8 -117.5 -116.4 -115.3 -116.3 -119.3 -124.3 -129.3 -134.3

1.1 -124.8 -123.5 -122.4 -121.3 -122.3 -125.3 -130.3 -135.3 -140.3

1.2 -130.8 -129.5 -128.4 -127.3 -128.3 -131.3 -136.3 -141.3 -146.3

1.3 -136.8 -135.5 -134.4 -133.3 -134.3 -137.3 -142.3 -147.3 -152.3

1.4 -142.8 -141.5 -140.4 -139.3 -140.3 -143.3 -148.3 -153.3 -158.3

1.5 -148.8 -147.5 -146.4 -145.3 -146.3 -149.3 -154.3 -159.3 -164.3

1.6 -154.8 -153.5 -152.4 -151.3 -152.3 -155.3 -160.3 -165.3 -170.3

1.7 -160.8 -159.5 -158.4 -157.3 -158.3 -161.3 -166.3 -171.3 -176.3

1.8 -166.8 -165.5 -164.4 -163.3 -164.3 -167.3 -172.3 -177.3 -182.3

1.9 -172.8 -171.5 -170.4 -169.3 -170.3 -173.3 -178.3 -183.3 -188.3

2.0 -178.8 -177.5 -176.4 -175.3 -176.3 -179.3 -184.3 -189.3 -194.3

3.6 -274.8 -273.5 -272.4 -271.3 -272.3 -275.3 -280.3 -285.3 -290.3

OASPLC1-UOL1 2.1 3.5 5.0 6.3 5.3 2.3 -2.7 -7.7 -12.7
NASA/CR—2011-217026 15

TABLE II.—SPECTRAL DIRECTIVITY RELATIONS FOR MID-FREQUENCY CORE NOISE (C2) 

Frequency Normalized sound pressure level, SPLC2-UOLC2, dB as function of corrected directivity angle 

parameter Corrected directivity angle, θC, deg 

log SC2 0 10 20 30 40 50 60 70 80 90

-3.6 -176.3 -175.3 -174.3 -173.3 -172.3 -170.8 -169.8 -168.8 -168.3 -167.8

-2.2 -92.3 -91.3 -90.3 -89.3 -88.3 -86.8 -85.8 -84.8 -84.3 -83.8

-2.1 -86.3 -85.3 -84.3 -83.3 -82.3 -80.8 -79.8 -78.8 -78.3 -77.8

-2.0 -80.3 -79.3 -78.3 -77.3 -76.3 -74.8 -73.8 -72.8 -72.3 -71.8

-1.9 -74.3 -73.3 -72.3 -71.3 -70.3 -68.8 -67.8 -66.8 -66.3 -65.8

-1.8 -68.3 -67.3 -66.3 -65.3 -64.3 -62.8 -61.8 -60.8 -60.3 -59.8

-1.7 -62.3 -61.3 -60.3 -59.3 -58.3 -56.8 -55.8 -54.8 -54.3 -53.8

-1.6 -56.3 -55.3 -54.3 -53.3 -52.3 -50.8 -49.8 -48.8 -48.3 -47.8

-1.5 -50.3 -49.3 -48.3 -47.3 -46.3 -44.8 -43.8 -42.8 -42.3 -41.8

-1.4 -44.3 -43.3 -42.3 -41.3 -40.3 -38.8 -37.8 -36.8 -36.3 -35.8

-1.3 -38.3 -37.3 -36.3 -35.3 -34.3 -32.8 -31.8 -30.8 -30.3 -29.8

-1.2 -32.3 -31.3 -30.3 -29.3 -28.3 -26.8 -25.8 -24.8 -24.3 -23.8

-1.1 -26.3 -25.3 -24.3 -23.3 -22.3 -20.8 -19.8 -18.8 -18.3 -17.8

-1.0 -20.3 -19.3 -18.3 -17.3 -16.3 -14.8 -13.8 -12.8 -12.3 -11.8

-0.9 -16.3 -15.3 -14.3 -13.3 -12.3 -10.8 -9.8 -8.8 -8.3 -7.8

-0.8 -14.3 -13.3 -12.3 -11.3 -10.3 -8.8 -7.8 -6.8 -6.3 -5.8

-0.7 -15.0 -14.0 -13.0 -12.0 -11.0 -9.5 -8.5 -7.5 -7.0 -6.5

-0.6 -16.9 -15.9 -14.9 -13.9 -12.9 -11.4 -10.4 -9.4 -8.9 -8.4

-0.5 -19.8 -18.8 -17.8 -16.8 -15.8 -14.3 -13.3 -12.3 -11.8 -11.3

-0.4 -23.8 -22.8 -21.8 -20.8 -19.8 -18.3 -17.3 -16.3 -15.8 -15.3

-0.3 -28.8 -27.8 -26.8 -25.8 -24.8 -23.3 -22.3 -21.3 -20.8 -20.3

-0.2 -34.1 -33.1 -32.1 -31.1 -30.1 -28.6 -27.6 -26.6 -26.1 -25.6

-0.1 -39.7 -38.7 -37.7 -36.7 -35.7 -34.2 -33.2 -32.2 -31.7 -31.2

0.0 -45.7 -44.7 -43.7 -42.7 -41.7 -40.2 -39.2 -38.2 -37.7 -37.2

0.1 -51.7 -50.7 -49.7 -48.7 -47.7 -46.2 -45.2 -44.2 -43.7 -43.2

0.2 -57.7 -56.7 -55.7 -54.7 -53.7 -52.2 -51.2 -50.2 -49.7 -49.2

0.3 -63.7 -62.7 -61.7 -60.7 -59.7 -58.2 -57.2 -56.2 -55.7 -55.2

0.4 -69.7 -68.7 -67.7 -66.7 -65.7 -64.2 -63.2 -62.2 -61.7 -61.2

0.5 -75.7 -74.7 -73.7 -72.7 -71.7 -70.2 -69.2 -68.2 -67.7 -67.2

0.6 -81.7 -80.7 -79.7 -78.7 -77.7 -76.2 -75.2 -74.2 -73.7 -73.2

0.7 -87.7 -86.7 -85.7 -84.7 -83.7 -82.2 -81.2 -80.2 -79.7 -79.2

0.8 -93.7 -92.7 -91.7 -90.7 -89.7 -88.2 -87.2 -86.2 -85.7 -85.2

0.9 -99.7 -98.7 -97.7 -96.7 -95.7 -94.2 -93.2 -92.2 -91.7 -91.2

1.0 -105.7 -104.7 -103.7 -102.7 -101.7 -100.2 -99.2 -98.2 -97.7 -97.2

1.1 -111.7 -110.7 -109.7 -108.7 -107.7 -106.2 -105.2 -104.2 -103.7 -103.2

1.2 -117.7 -116.7 -115.7 -114.7 -113.7 -112.2 -111.2 -110.2 -109.7 -109.2

1.3 -123.7 -122.7 -121.7 -120.7 -119.7 -118.2 -117.2 -116.2 -115.7 -115.2

1.4 -129.7 -128.7 -127.7 -126.7 -125.7 -124.2 -123.2 -122.2 -121.7 -121.2

1.5 -135.7 -134.7 -133.7 -132.7 -131.7 -130.2 -129.2 -128.2 -127.7 -127.2

1.6 -141.7 -140.7 -139.7 -138.7 -137.7 -136.2 -135.2 -134.2 -133.7 -133.2

1.7 -147.7 -146.7 -145.7 -144.7 -143.7 -142.2 -141.2 -140.2 -139.7 -139.2

1.8 -153.7 -152.7 -151.7 -150.7 -149.7 -148.2 -147.2 -146.2 -145.7 -145.2

1.9 -159.7 -158.7 -157.7 -156.7 -155.7 -154.2 -153.2 -152.2 -151.7 -151.2

2.0 -165.7 -164.7 -163.7 -162.7 -161.7 -160.2 -159.2 -158.2 -157.7 -157.2

3.6 -261.7 -260.7 -259.7 -258.7 -257.7 -256.2 -255.2 -254.2 -253.7 -253.2

OASPLC2-UOLC2 -8.5 -7.5 -6.5 -5.5 -4.5 -3.0 -2.0 -1.0 -0.5 0.0
NASA/CR—2011-217026 16

TABLE II.—Concluded. 

Frequency Normalized sound pressure level, SPLC2-UOLC2, dB as function of corrected directivity a 

parameter Corrected directivity angle, θC, deg 

log SC2 100 110 120 130 140 150 160 170 180

-3.6 -167.3 -166.8 -166.3 -165.8 -167.3 -169.5 -171.7 -173.9 -176.1

-2.2 -83.3 -82.8 -82.3 -81.8 -83.3 -85.5 -87.7 -89.9 -92.1

-2.1 -77.3 -76.8 -76.3 -75.8 -77.3 -79.5 -81.7 -83.9 -86.1

-2.0 -71.3 -70.8 -70.3 -69.8 -71.3 -73.5 -75.7 -77.9 -80.1

-1.9 -65.3 -64.8 -64.3 -63.8 -65.3 -67.5 -69.7 -71.9 -74.1

-1.8 -59.3 -58.8 -58.3 -57.8 -59.3 -61.5 -63.7 -65.9 -68.1

-1.7 -53.3 -52.8 -52.3 -51.8 -53.3 -55.5 -57.7 -59.9 -62.1

-1.6 -47.3 -46.8 -46.3 -45.8 -47.3 -49.5 -51.7 -53.9 -56.1

-1.5 -41.3 -40.8 -40.3 -39.8 -41.3 -43.5 -45.7 -47.9 -50.1

-1.4 -35.3 -34.8 -34.3 -33.8 -35.3 -37.5 -39.7 -41.9 -44.1

-1.3 -29.3 -28.8 -28.3 -27.8 -29.3 -31.5 -33.7 -35.9 -38.1

-1.2 -23.3 -22.8 -22.3 -21.8 -23.3 -25.5 -27.7 -29.9 -32.1

-1.1 -17.3 -16.8 -16.3 -15.8 -17.3 -19.5 -21.7 -23.9 -26.1

-1.0 -11.3 -10.8 -10.3 -9.8 -11.3 -13.5 -15.7 -17.9 -20.1

-0.9 -7.3 -6.8 -6.3 -5.8 -7.3 -9.5 -11.7 -13.9 -16.1

-0.8 -5.3 -4.8 -4.3 -3.8 -5.3 -7.5 -9.7 -11.9 -14.1

-0.7 -6.0 -5.5 -5.0 -4.5 -6.0 -8.2 -10.4 -12.6 -14.8

-0.6 -7.9 -7.4 -6.9 -6.4 -7.9 -10.1 -12.3 -14.5 -16.7

-0.5 -10.8 -10.3 -9.8 -9.3 -10.8 -13.0 -15.2 -17.4 -19.6

-0.4 -14.8 -14.3 -13.8 -13.3 -14.8 -17.0 -19.2 -21.4 -23.6

-0.3 -19.8 -19.3 -18.8 -18.3 -19.8 -22.0 -24.2 -26.4 -28.6

-0.2 -25.1 -24.6 -24.1 -23.6 -25.1 -27.3 -29.5 -31.7 -33.9

-0.1 -30.7 -30.2 -29.7 -29.2 -30.7 -32.9 -35.1 -37.3 -39.5

0.0 -36.7 -36.2 -35.7 -35.2 -36.7 -38.9 -41.1 -43.3 -45.5

0.1 -42.7 -42.2 -41.7 -41.2 -42.7 -44.9 -47.1 -49.3 -51.5

0.2 -48.7 -48.2 -47.7 -47.2 -48.7 -50.9 -53.1 -55.3 -57.5

0.3 -54.7 -54.2 -53.7 -53.2 -54.7 -56.9 -59.1 -61.3 -63.5

0.4 -60.7 -60.2 -59.7 -59.2 -60.7 -62.9 -65.1 -67.3 -69.5

0.5 -66.7 -66.2 -65.7 -65.2 -66.7 -68.9 -71.1 -73.3 -75.5

0.6 -72.7 -72.2 -71.7 -71.2 -72.7 -74.9 -77.1 -79.3 -81.5

0.7 -78.7 -78.2 -77.7 -77.2 -78.7 -80.9 -83.1 -85.3 -87.5

0.8 -84.7 -84.2 -83.7 -83.2 -84.7 -86.9 -89.1 -91.3 -93.5

0.9 -90.7 -90.2 -89.7 -89.2 -90.7 -92.9 -95.1 -97.3 -99.5

1.0 -96.7 -96.2 -95.7 -95.2 -96.7 -98.9 -101.1 -103.3 -105.5

1.1 -102.7 -102.2 -101.7 -101.2 -102.7 -104.9 -107.1 -109.3 -111.5

1.2 -108.7 -108.2 -107.7 -107.2 -108.7 -110.9 -113.1 -115.3 -117.5

1.3 -114.7 -114.2 -113.7 -113.2 -114.7 -116.9 -119.1 -121.3 -123.5

1.4 -120.7 -120.2 -119.7 -119.2 -120.7 -122.9 -125.1 -127.3 -129.5

1.5 -126.7 -126.2 -125.7 -125.2 -126.7 -128.9 -131.1 -133.3 -135.5

1.6 -132.7 -132.2 -131.7 -131.2 -132.7 -134.9 -137.1 -139.3 -141.5

1.7 -138.7 -138.2 -137.7 -137.2 -138.7 -140.9 -143.1 -145.3 -147.5

1.8 -144.7 -144.2 -143.7 -143.2 -144.7 -146.9 -149.1 -151.3 -153.5

1.9 -150.7 -150.2 -149.7 -149.2 -150.7 -152.9 -155.1 -157.3 -159.5

2.0 -156.7 -156.2 -155.7 -155.2 -156.7 -158.9 -161.1 -163.3 -165.5

3.6 -252.7 -252.2 -251.7 -251.2 -252.7 -254.9 -257.1 -259.3 -261.5

OASPLC2-UOLC2 0.5 1.0 1.5 2.0 0.5 -1.7 -3.9 -6.1 -8.3
NASA/CR—2011-217026 17

TABLE III.—SPECTRAL DIRECTIVITY RELATIONS FOR HIGH FREQUENCY CORE NOISE (C3)

 

Frequency Normalized sound pressure level, SPLC3-UOLC3, dB as function of corrected directivity angle

parameter Corrected directivity angle, θc, deg

log Sc 0 10 20 30 40 50 60 70 80 90

-3.6 -198.8 -198.2 -197.6 -197.0 -196.4 -195.7 -195.0 -194.8 -194.4 -193.6

-2.2 -114.8 -114.2 -113.6 -113.0 -112.4 -111.7 -111.0 -110.8 -110.4 -109.6

-2.1 -108.8 -108.2 -107.6 -107.0 -106.4 -105.7 -105.0 -104.8 -104.4 -103.6

-2.0 -102.8 -102.2 -101.6 -101.0 -100.4 -99.7 -99.0 -98.8 -98.4 -97.6

-1.9 -96.8 -96.2 -95.6 -95.0 -94.4 -93.7 -93.0 -92.8 -92.4 -91.6

-1.8 -90.8 -90.2 -89.6 -89.0 -88.4 -87.7 -87.0 -86.8 -86.4 -85.6

-1.7 -84.8 -84.2 -83.6 -83.0 -82.4 -81.7 -81.0 -80.8 -80.4 -79.6

-1.6 -78.8 -78.2 -77.6 -77.0 -76.4 -75.7 -75.0 -74.8 -74.4 -73.6

-1.5 -72.8 -72.2 -71.6 -71.0 -70.4 -69.7 -69.0 -68.8 -68.4 -67.6

-1.4 -66.8 -66.2 -65.6 -65.0 -64.4 -63.7 -63.0 -62.8 -62.4 -61.6

-1.3 -60.8 -60.2 -59.6 -59.0 -58.4 -57.7 -57.0 -56.8 -56.4 -55.6

-1.2 -54.8 -54.2 -53.6 -53.0 -52.4 -51.7 -51.0 -50.8 -50.4 -49.6

-1.1 -48.8 -48.2 -47.6 -47.0 -46.4 -45.7 -45.0 -44.8 -44.4 -43.6

-1.0 -42.8 -42.2 -41.6 -41.0 -40.4 -39.7 -39.0 -38.8 -38.4 -37.6

-0.9 -36.8 -36.2 -35.6 -35.0 -34.4 -33.7 -33.0 -32.8 -32.4 -31.6

-0.8 -30.8 -30.2 -29.6 -29.0 -28.4 -27.7 -27.0 -26.8 -26.4 -25.6

-0.7 -24.8 -24.2 -23.6 -23.0 -22.4 -21.7 -21.0 -20.8 -20.4 -19.6

-0.6 -19.6 -19.0 -18.4 -17.8 -17.2 -16.5 -15.8 -15.6 -15.2 -14.4

-0.5 -15.5 -14.9 -14.3 -13.7 -13.1 -12.4 -11.7 -11.5 -11.1 -10.3

-0.4 -12.6 -12.0 -11.4 -10.8 -10.2 -9.5 -8.8 -8.6 -8.2 -7.4

-0.3 -11.6 -11.0 -10.4 -9.8 -9.2 -8.5 -7.8 -7.6 -7.2 -6.4

-0.2 -11.9 -11.3 -10.7 -10.1 -9.5 -8.8 -8.1 -7.9 -7.5 -6.7

-0.1 -12.9 -12.3 -11.7 -11.1 -10.5 -9.8 -9.1 -8.9 -8.5 -7.7

0.0 -15.1 -14.5 -13.9 -13.3 -12.7 -12.0 -11.3 -11.1 -10.7 -9.9

0.1 -18.7 -18.1 -17.5 -16.9 -16.3 -15.6 -14.9 -14.7 -14.3 -13.5

0.2 -23.2 -22.6 -22.0 -21.4 -20.8 -20.1 -19.4 -19.2 -18.8 -18.0

0.3 -29.2 -28.6 -28.0 -27.4 -26.8 -26.1 -25.4 -25.2 -24.8 -24.0

0.4 -35.2 -34.6 -34.0 -33.4 -32.8 -32.1 -31.4 -31.2 -30.8 -30.0

0.5 -41.2 -40.6 -40.0 -39.4 -38.8 -38.1 -37.4 -37.2 -36.8 -36.0

0.6 -47.2 -46.6 -46.0 -45.4 -44.8 -44.1 -43.4 -43.2 -42.8 -42.0

0.7 -53.2 -52.6 -52.0 -51.4 -50.8 -50.1 -49.4 -49.2 -48.8 -48.0

0.8 -59.2 -58.6 -58.0 -57.4 -56.8 -56.1 -55.4 -55.2 -54.8 -54.0

0.9 -65.2 -64.6 -64.0 -63.4 -62.8 -62.1 -61.4 -61.2 -60.8 -60.0

1.0 -71.2 -70.6 -70.0 -69.4 -68.8 -68.1 -67.4 -67.2 -66.8 -66.0

1.1 -77.2 -76.6 -76.0 -75.4 -74.8 -74.1 -73.4 -73.2 -72.8 -72.0

1.2 -83.2 -82.6 -82.0 -81.4 -80.8 -80.1 -79.4 -79.2 -78.8 -78.0

1.3 -89.2 -88.6 -88.0 -87.4 -86.8 -86.1 -85.4 -85.2 -84.8 -84.0

1.4 -95.2 -94.6 -94.0 -93.4 -92.8 -92.1 -91.4 -91.2 -90.8 -90.0

1.5 -101.2 -100.6 -100.0 -99.4 -98.8 -98.1 -97.4 -97.2 -96.8 -96.0

1.6 -107.2 -106.6 -106.0 -105.4 -104.8 -104.1 -103.4 -103.2 -102.8 -102.0

1.7 -113.2 -112.6 -112.0 -111.4 -110.8 -110.1 -109.4 -109.2 -108.8 -108.0

1.8 -119.2 -118.6 -118.0 -117.4 -116.8 -116.1 -115.4 -115.2 -114.8 -114.0

1.9 -125.2 -124.6 -124.0 -123.4 -122.8 -122.1 -121.4 -121.2 -120.8 -120.0

2.0 -131.2 -130.6 -130.0 -129.4 -128.8 -128.1 -127.4 -127.2 -126.8 -126.0

3.6 -227.2 -226.6 -226.0 -225.4 -224.8 -224.1 -223.4 -223.2 -222.8 -222.0

OASPLc3-UOL3 -4.8 -4.2 -3.6 -3.0 -2.4 -1.7 -1.0 -0.8 -0.4 0.4
NASA/CR—2011-217026 18

TABLE III.—Concluded. 

Frequency Normalized sound pressure level, SPLC3-UOLC3, dB as function of corrected directivity 

parameter Corrected directivity angle, θc, deg

log SC2 100 110 120 130 140 150 160 170 180

-3.6 -192.1 -190.4 -188.6 -187.2 -190.7 -193.2 -195.2 -197.2 -199.2

-2.2 -108.1 -106.4 -104.6 -103.2 -106.7 -109.2 -111.2 -113.2 -115.2

-2.1 -102.1 -100.4 -98.6 -97.2 -100.7 -103.2 -105.2 -107.2 -109.2

-2.0 -96.1 -94.4 -92.6 -91.2 -94.7 -97.2 -99.2 -101.2 -103.2

-1.9 -90.1 -88.4 -86.6 -85.2 -88.7 -91.2 -93.2 -95.2 -97.2

-1.8 -84.1 -82.4 -80.6 -79.2 -82.7 -85.2 -87.2 -89.2 -91.2

-1.7 -78.1 -76.4 -74.6 -73.2 -76.7 -79.2 -81.2 -83.2 -85.2

-1.6 -72.1 -70.4 -68.6 -67.2 -70.7 -73.2 -75.2 -77.2 -79.2

-1.5 -66.1 -64.4 -62.6 -61.2 -64.7 -67.2 -69.2 -71.2 -73.2

-1.4 -60.1 -58.4 -56.6 -55.2 -58.7 -61.2 -63.2 -65.2 -67.2

-1.3 -54.1 -52.4 -50.6 -49.2 -52.7 -55.2 -57.2 -59.2 -61.2

-1.2 -48.1 -46.4 -44.6 -43.2 -46.7 -49.2 -51.2 -53.2 -55.2

-1.1 -42.1 -40.4 -38.6 -37.2 -40.7 -43.2 -45.2 -47.2 -49.2

-1.0 -36.1 -34.4 -32.6 -31.2 -34.7 -37.2 -39.2 -41.2 -43.2

-0.9 -30.1 -28.4 -26.6 -25.2 -28.7 -31.2 -33.2 -35.2 -37.2

-0.8 -24.1 -22.4 -20.6 -19.2 -22.7 -25.2 -27.2 -29.2 -31.2

-0.7 -18.1 -16.4 -14.6 -13.2 -16.7 -19.2 -21.2 -23.2 -25.2

-0.6 -12.9 -11.2 -9.4 -8.0 -11.5 -14.0 -16.0 -18.0 -20.0

-0.5 -8.8 -7.1 -5.3 -3.9 -7.4 -9.9 -11.9 -13.9 -15.9

-0.4 -5.9 -4.2 -2.4 -1.0 -4.5 -7.0 -9.0 -11.0 -13.0

-0.3 -4.9 -3.2 -1.4 0.0 -3.5 -6.0 -8.0 -10.0 -12.0

-0.2 -5.2 -3.5 -1.7 -0.3 -3.8 -6.3 -8.3 -10.7 -12.7

-0.1 -6.2 -4.5 -2.7 -1.3 -4.8 -7.3 -9.3 -12.2 -14.2

0.0 -8.4 -6.7 -4.9 -3.5 -7.0 -9.5 -11.5 -15.0 -17.0

0.1 -12.0 -10.3 -8.5 -7.1 -10.6 -13.1 -15.1 -19.3 -21.3

0.2 -16.5 -14.8 -13.0 -11.6 -15.1 -17.6 -19.6 -25.1 -27.1

0.3 -22.5 -20.8 -19.0 -17.6 -21.1 -23.6 -25.6 -31.1 -33.1

0.4 -28.5 -26.8 -25.0 -23.6 -27.1 -29.6 -31.6 -37.1 -39.1

0.5 -34.5 -32.8 -31.0 -29.6 -33.1 -35.6 -37.6 -43.1 -45.1

0.6 -40.5 -38.8 -37.0 -35.6 -39.1 -41.6 -43.6 -49.1 -51.1

0.7 -46.5 -44.8 -43.0 -41.6 -45.1 -47.6 -49.6 -55.1 -57.1

0.8 -52.5 -50.8 -49.0 -47.6 -51.1 -53.6 -55.6 -61.1 -63.1

0.9 -58.5 -56.8 -55.0 -53.6 -57.1 -59.6 -61.6 -67.1 -69.1

1.0 -64.5 -62.8 -61.0 -59.6 -63.1 -65.6 -67.6 -73.1 -75.1

1.1 -70.5 -68.8 -67.0 -65.6 -69.1 -71.6 -73.6 -79.1 -81.1

1.2 -76.5 -74.8 -73.0 -71.6 -75.1 -77.6 -79.6 -85.1 -87.1

1.3 -82.5 -80.8 -79.0 -77.6 -81.1 -83.6 -85.6 -91.1 -93.1

1.4 -88.5 -86.8 -85.0 -83.6 -87.1 -89.6 -91.6 -97.1 -99.1

1.5 -94.5 -92.8 -91.0 -89.6 -93.1 -95.6 -97.6 -103.1 -105.1

1.6 -100.5 -98.8 -97.0 -95.6 -99.1 -101.6 -103.6 -109.1 -111.1

1.7 -106.5 -104.8 -103.0 -101.6 -105.1 -107.6 -109.6 -115.1 -117.1

1.8 -112.5 -110.8 -109.0 -107.6 -111.1 -113.6 -115.6 -121.1 -123.1

1.9 -118.5 -116.8 -115.0 -113.6 -117.1 -119.6 -121.6 -127.1 -129.1

2.0 -124.5 -122.8 -121.0 -119.6 -123.1 -125.6 -127.6 -133.1 -135.1

3.6 -220.5 -218.8 -217.0 -215.6 -219.1 -221.6 -223.6 -229.1 -231.1

OASPLc3-UOL3 1.9 3.6 5.4 6.8 3.3 0.8 -1.2 -3.6 -5.6
NASA/CR—2011-217026 19

Figure 1.—Flight Effect Variables for Engine Exhaust Noise.

Figure 2.—Typical Example Flight Effects on Exhaust Noise.
NASA/CR—2011-217026 20

(a) Directivity Angle θ = 90 deg

(b) Directivity Angle θ = 120 deg

Figure 3.—Typical Component Extraction for CF6-80C2A5F at Low Power, Vmix/camb = 0.402.

0

5

10

15

20

25

30

35

40

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLC1,EE

SPLC2,EE

SPLC3,EE

SPLtm,EE

SPLP,EE

SPLL,EE

SPLS,EE

SPLT,EE

0

5

10

15

20

25

30

35

40

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLC1,EE

SPLC2,EE

SPLC3,EE

SPLtm,EE

SPLP,EE

SPLL,EE

SPLS,EE

SPLT,EE
NASA/CR—2011-217026 21

(c) Directivity Angle θ = 150 deg

Figure 3.—Concluded.

(a) Directivity Angle θ = 30 deg

Figure 4.—Comparison of Experimental and Predicted Spectra for CF6-80C2A5F at

High Power, Vmix/camb = 1.004.

0

5

10

15

20

25

30

35

40

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLC1,EE

SPLC2,EE

SPLC3,EE

SPLtm,EE

SPLP,EE

SPLL,EE

SPLS,EE

SPLT,EE

10

15

20

25

30

35

40

45

50

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 22

(b) Directivity Angle θ = 60 deg

(c) Directivity Angle θ = 90 deg

Figure 4.—Continued.

20

25

30

35

40

45

50

55

60

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

20

25

30

35

40

45

50

55

60

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 23

(d) Directivity Angle θ = 120 deg

(e) Directivity Angle θ = 150 deg

Figure 4.—Concluded.

30

35

40

45

50

55

60

65

70

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

25

30

35

40

45

50

55

60

65

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 24

Figure 5.—Comparison of Experimental and Predicted OASPL Directivities for CF6-80C2A5F at

3534 rpm and Vmix/camb = 1.004.

(a) Directivity Angle θ = 30 deg

Figure 6.—Comparison of Experimental and Predicted Spectra for CF34-8C at High Power, 

Vmix/camb =1.049.

40

45

50

55

60

65

70

75

80

0 20 40 60 80 100 120 140 160 180

Directivity Angle, θ, deg

Relative OASPL, dB

OASPLexp

OASPLPred

OASPLC1,Pred

OASPLC2,Pred

OASPLC3,Pred

OASPLF,Pred

OASPLP,Pred

OASPLL,Pred

OASPLS,Pred

OASPLT,Pred

15

20

25

30

35

40

45

50

55

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 25

(b) Directivity Angle θ = 60 deg

(c) Directivity Angle θ = 90 deg

Figure 6.—Continued.

25

30

35

40

45

50

55

60

65

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

20

25

30

35

40

45

50

55

60

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 26

(d) Directivity Angle θ = 120 deg

(e) Directivity Angle θ = 150 deg

Figure 6.—Concluded.

30

35

40

45

50

55

60

65

70

75

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

30

35

40

45

50

55

60

65

70

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 27

Figure 7.—Comparison of Experimental and Predicted OASPL Directivities for CF34-9C at High Power, 

Vmix/camb = 1.049.

(a) Directivity Angle θ = 30 deg

Figure 8.—Comparison of Experimental and Predicted Spectra for CFM56-5B/P High Power, 

Vmix/camb = 1.006.

45

50

55

60

65

70

75

80

85

0 20 40 60 80 100 120 140 160 180

Directivity Angle, θ, deg

Relative OASPL, dB

OASPLexp

OASPLPred

OASPLC1,Pred

OASPLC2,Pred

OASPLC3,Pred

OASPLF,Pred

OASPLP,Pred

OASPLL,Pred

OASPLS,Pred

OASPLT,Pred

20

25

30

35

40

45

50

55

60

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 28

(b) Directivity Angle θ = 60 deg

(c) Directivity Angle θ = 90 deg

Figure 8.—Continued.

25

30

35

40

45

50

55

60

65

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

25

30

35

40

45

50

55

60

65

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 29

(d) Directivity Angle θ = 120 deg

(e) Directivity Angle θ = 150 deg

Figure 8.—Concluded.

35

40

45

50

55

60

65

70

75

80

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

35

40

45

50

55

60

65

70

75

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 30

Figure 9.—Comparison of Experimental and Predicted OASPL Directivities for CFM56-5B/P at

High Power, Vmix/camb = 1.006.

(a) Directivity Angle θ = 30 deg

Figure 10.—Comparison of Experimental and Predicted Spectra for GE90 at High Power,

Vmix/camb = 0.906.

30

35

40

45

50

55

60

65

70

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

50

55

60

65

70

75

80

85

90

0 20 40 60 80 100 120 140 160 180

Directivity Angle, θ, deg

Relative OASPL, dB

OASPLexp

OASPLPred

OASPLC1,Pred

OASPLC2,Pred

OASPLC3,Pred

OASPLF,Pred

OASPLP,Pred

OASPLL,Pred

OASPLS,Pred

OASPLT,Pred
NASA/CR—2011-217026 31

(b) Directivity Angle θ = 60 deg

(c) Directivity Angle θ = 90 deg

Figure 10.—Continued.

40

45

50

55

60

65

70

75

80

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

35

40

45

50

55

60

65

70

75

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 32

(d) Directivity Angle θ = 120 deg

(e) Directivity Angle θ = 150 deg

Figure 10.—Concluded.

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Relative SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLtm,Pred

SPLP,Pred

SPLL,Pred

SPLS,Pred

SPLT,Pred
NASA/CR—2011-217026 33

Figure 11.—Comparison of Experimental and Predicted OASPL Directivities for GE90 at High Power, 

Vmix/camb = 0.906.

(a) Low Frequency Component

Figure 12.—Core Noise Level Correlations.

60

65

70

75

80

85

90

95

100

0 20 40 60 80 100 120 140 160 180

Directivity Angle, θ, deg

Relative OASPL, dB

OASPLexp

OASPLPred

OASPLC1,Pred

OASPLC2,Pred

OASPLC3,Pred

OASPLF,Pred

OASPLP,Pred

OASPLL,Pred

OASPLS,Pred

OASPLT,Pred

105

110

115

120

125

130

135

140

145

50 55 60 65 70 75 80 85 90

Modified Core Noise Parameter, 10 log WI [(TC,o - TC,i)(PC,i/Pamb)(Tamb/TC,i)]2} - 

20 log nf, dB

Normailized Component Level, UOLC1 + 20 log R, 

dB

CF6

CF6

CF34

CF34

CFM56

CFM56

GE90

GE90

GE90

Corr

Corr + 3

Corr - 3

Correlation: UOLC1 = CC1 - 20 log R - FC1 log nf

 + 

NC1 log {WI

 [(TC,o - TC,i)(PC,i/Pamb)(Tamb/TC,i)]2}

Where: CC1 = 78.0; FC1 = 14.0; NC1 = 7.0

Note: small solid symbols denote this 

component is significant, medium gray symbols 

denote component marginal or tone 

contaminated; large open symbols denote 

minor component - approximate value
NASA/CR—2011-217026 34

(b) Middle Frequency Component

(c) High Frequency Component

Figure 12.—Concluded.

105

110

115

120

125

130

135

140

145

150

155

50 55 60 65 70 75 80 85 90

Modifeied Core Noise Parameter, 10 log {WI

 [(TC,o - 

TC,i)(PC,i/Pamb)(Tamb/TC,i)]2

} - 18 log nf, dB

Normalized Component Level, UOLC2 + 20 log R, 

dB

CF6

CF34

CFM56

GE90

CF6

CFM56

CFM56

GE90

GE90

Corr

Corr + 3

Corr - 3

Correlation: UOLC2 = CC2 - 20 log R - FC2 log nf + NC2 

log {WI [(TC,o - TC,i)(PC,i/Pamb)(Tamb/TC,i)]2

}

Where: CC2= 60.3; FC2 = 18; NC2 = 10.0 

Note: small solid symbols denote this component is 

significant, medium gray symbols denote component 

marginal or tone contaminated; large open symbols 

denote minor component - approximate value

110

115

120

125

130

135

140

145

150

155

80 85 90 95 100 105 110 115 120

Core Noise Parameter, 10 log {WI [(TC,o - TC,i)(PC,i/Pamb)(Tamb/TC,i)]2}, dB

Normalized Component Level, CC3 + 20 log R, 

dB

CF6

CF34

CFM56

GE90

CFM56

CFM56

GE90

Corr

Corr + 3

Corr - 3

Correlation: UOLC3 = CC3 - 20 log R - FC3 log nf

 + 

NC3 log {WI

 [(TC,o - TC,i)(PC,i/Pamb)(Tamb/TC,i)]2

}

Where: CC3 = 42.5; FC3 = 0.0; NC3 = 9.0 

Note: small solid symbols denote this component is 

significant, medium gray symbols denote component 

marginal or tone contaminated; large open symbols 

denote minor component - approximate value
NASA/CR—2011-217026 35

(a) Corrected Directivity Angle θC,cor = 29.4-29.7 deg

(b) Corrected Directivity Angle θC,cor = 59.0-59.4 deg

Figure 13.—Normalized Spectra for Low Frequency Core Noise.

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-1.6 -1.4 -1.2 -1.0 -0.8 -0.6

Core Strouhal Parameter, log SC1, dimensionless 

Normalized Sound Pressure Level, SPLC1,EE - UOLC1,EE, 

dB

Corr 60

Corr + 3

Corr - 3

CF6, 1650

CF6, 1800

CF6, 2100

CF34, 4000

CF34, 4200

CF34, 4400

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

StC1 = fDh,I/camb

Note: data plotted only if SPLC1 is within 7.0 dB of total

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-1.6 -1.4 -1.2 -1.0 -0.8 -0.6

Core Strouhal Parameter, log SC1, dimensionless 

Normalized Sound Pressure Level, SPLC1,EE - UOLC1,EE, 

dB

Corr 30

Corr + 3

Corr - 3

CF6, 1650

CF6, 1800

CF6, 2100

CF34, 4000

CF34, 4200

CF34, 4400

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

StC1 = fDh,I/camb

Note: data plotted only if SPLC1 is within 7.0 dB of total
NASA/CR—2011-217026 36

(c) Corrected Directivity Angle θC,cor = 88.8-89.3 deg

(d) Corrected Directivity Angle θC,cor = 119.0-119.4 deg

Figure 13.—Continued.

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

-1.6 -1.4 -1.2 -1.0 -0.8 -0.6

Core Strouhal Parameter, log SC1, dimensionless 

Normalized Sound Pressure Level, SPLC1,EE - 

UOLC1,EE, dB

Corr 120

Corr + 3

Corr - 3

CF6, 1650

CF6, 1800

CF6, 2100

CF34, 4000

CF34, 4200

CF34, 4400

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

StC1 = fDh,I/camb

Note: data plotted only if SPLC1 is within 7.0 dB of total

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-1.6 -1.4 -1.2 -1.0 -0.8 -0.6

Core Strouhal Parameter, log SC1, dimensionless 

Normalized Sound Pressure Level, SPLC1,EE - UOLC1,EE, 

dB

Corr 90

Corr + 3

Corr - 3

CF6, 1650

CF6, 1800

CF6, 2100

CF34, 4000

CF34, 4200

CF34, 4400

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

StC1 = fDh,I/camb

Note: data plotted only if SPLC1 is within 7.0 dB of total
NASA/CR—2011-217026 37

(e) Corrected Directivity Angle θC,cor = 149.4-149.6 deg

Figure 13.—Concluded.

(a) Corrected Directivity Angle θC,cor = 29.4-29.7 deg

Figure 14.—Normalized Spectra for Middle Frequency Core Noise.

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-1.6 -1.4 -1.2 -1.0 -0.8 -0.6

Core Strouhal Parameter, log SC1, dimensionless 

Normalized Sound Pressure Level, SPLC1,EE - 

UOLC1,EE, dB

Corr 150

Corr + 3

Corr - 3

CF34, 4000

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

GE90, 1200

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

StC1 = fDh,I/camb

Note: data plotted only if SPLC1 is within 7.0 dB of total

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

-1.2 -1.0 -0.8 -0.6 -0.4

Core Strouhal Parameter, log SC2, dimensionless 

Normalized Sound Pressure Level, SPLC2,EE - 

UOLC2,EE, dB

Corr 30

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF6, 3534

CF34, 4000

CF34, 4200

CF34, 4400

CF34, 6800

CF34, 7225

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1880

GE90, 2200

GE90-cfg5, 1200

GE90-Blkiv, 1200

SC2 = fDC/cC,o

Note: data plotted only if

SPLC2 is within 7.0 dB of total
NASA/CR—2011-217026 38

(b) Corrected Directivity Angle θC,cor = 59.0-59.4 deg

(c) Corrected Directivity Angle θC,cor = 88.8-89.3 deg

Figure 14.—Continued.

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

-1.2 -1.0 -0.8 -0.6 -0.4

Core Strouhal Parameter, log SC2, dimensionless 

Normalized Sound Pressure Level, SPLC2,EE - 

UOLC2,EE, dB

Corr 90

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF6, 3534

CF34, 4000

CF34, 4200

CF34, 4400

CF34, 6800

CF34, 7225

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90, 1880

GE90, 2200

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

SC2 = fDC/cC,o

Note: data plotted only if SPLC2 is within 7.0 dB of total

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

-1.2 -1.0 -0.8 -0.6 -0.4

Core Strouhal Parameter, log SC2, dimensionless 

Normalized Sound Pressure Level, SPLC2,EE - 

UOLC2,EE, dB

Corr 60

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF6, 3534

CF34, 4000

CF34, 4200

CF34, 4400

CF34, 6800

CF34, 7225

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90, 1880

GE90, 2200

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

SC2 = fDC/cC,o

Note: data plotted only if SPLC2

 is within 7.0 dB of total
NASA/CR—2011-217026 39

(d) Corrected Directivity Angle θC,cor = 119.0-119.4 deg

(e) Corrected Directivity Angle θC,cor = 149.4-149.6 deg

Figure 14.—Concluded.

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

-1.2 -1.0 -0.8 -0.6 -0.4

Core Strouhal Parameter, log SC2, dimensionless 

Normalized Sound Pressure Level, SPLC2,EE - 

UOLC2,EE, dB

Corr 150

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF34, 4000

CF34, 4200

CF34, 4400

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

GE90, 1200

GE90, 1320

GE90, 1720

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

SC2 = fDC/cC,o

Note: data plotted only if SPLC2

is within 7.0 dB of total

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

-1.2 -1.0 -0.8 -0.6 -0.4

Core Strouhal Parameter, log SC2, dimensionless 

Normalized Sound Pressure Level, SPLC2,EE - 

UOLC2,EE, dB

Corr 120

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF34, 4000

CF34, 4200

CF34, 4400

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

CFM56, 5053

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1880

GE90, 2200

GE90-cfg5, 1200

GE90-Blkiv, 1200

GE90-Blkiv, 710

SC2 = fDC/cC,o

Note: data plotted only if SPLC2 is within 7.0 dB of total
NASA/CR—2011-217026 40

(a) Corrected Directivity Angle θC,cor = 29.4-29.7 deg

(b) Corrected Directivity Angle θC,cor = 59.0-59.4 deg

Figure 15.—Normalized Spectra for High Frequency Core Noise.

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Core Strouhal Parameter, log SC3, dimensionless 

Normalized Sound Pressure Level, SPLC3,EE - 

UOLC3,EE, dB

Pred 60

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF6, 3534

CF34, 4000

CF34, 4200

CF34, 4400

CF34, 6800

CF34, 7225

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90, 1880

GE90, 2200

GE90, 2400

GE90-Blkiv, 1200

SC3 = fDC/cC,o

Note: data plotted only if

SPLC3 is within 7.0 dB of total

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Core Strouhal Parameter, log SC3, dimensionless 

Normalized Sound Pressure Level, SPLC3,EE - 

UOLC3,EE, dB

Pred 30

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF6, 3534

CF34, 4000

CF34, 4200

CF34, 4400

CF34, 6800

CF34, 7225

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90, 1880

GE90, 2200

GE90, 2400

SC3 = fDC/cC,o

Note: data plotted only if

SPLC3 is within 7.0 dB of total
NASA/CR—2011-217026 41

(c) Corrected Directivity Angle θC,cor = 88.8-89.3 deg

(d) Corrected Directivity Angle θC,cor = 119.0-119.4 deg

Figure 15.—Continued.

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Core Strouhal Parameter, log SC3, dimensionless 

Normalized Sound Pressure Level, SPLC3,EE - 

UOLC3,EE, dB

Pred 120

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF6, 3534

CF34, 4000

CF34, 4200

CF34, 4400

CF34, 6800

CF34, 7225

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90, 1880

GE90, 2200

GE90, 2400

GE90-Blkiv, 1200

SC3 = fDC/cC,o

Note: data plotted only if SPLC3 is within 7.0 dB of total

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Core Strouhal Parameter, log SC3, dimensionless 

Normalized Sound Pressure Level, SPLC3,EE - 

UOLC3,EE, dB

Pred 90

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF6, 3534

CF34, 4000

CF34, 4200

CF34, 4400

CF34, 6800

CF34, 7225

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90, 1880

GE90, 2200

GE90, 2400

GE90-Blkiv, 1200

SC3 = fDC/cC,o

Note: data plotted only if

SPLC3 is within 7.0 dB of total
NASA/CR—2011-217026 42

(e) Corrected Directivity Angle θC,cor = 149.4-149.6 deg

Figure 15.—Concluded.

Figure 16.—Error (Experimental—Predicted) Versus Nondimensional Mixed Jet Velocity.

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Core Strouhal Parameter, log SC3, dimensionless 

Normaized Sound Pressure Level, SPLC3,EE - 

UOLC3,EE, dB

Pred 150

Corr + 3.0

Corr - 3.0

CF6, 1650

CF6, 1800

CF6, 2100

CF6, 2700

CF34, 4000

CF34, 4200

CF34, 4400

CFM56, 1375

CFM56, 2000

CFM56, 2150

CFM56, 2450

GE90, 1200

GE90, 1320

GE90, 1720

GE90, 1800

GE90, 1880

GE90, 2200

GE90, 2400

GE90-Blkiv, 1200

SC3 = fDC/cC,o

Note: data plotted only if SPLC3 is within 7.0 dB of total

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.200 0.400 0.600 0.800 1.000 1.200

Nondimensional Mixed Jet Velocity, Vmix/camb

Error 

∆ (Experimental - Predicted), dB

Sub-BPF:CF6

Sub-BPF:CF34

Sub-BPF:CFM56

Sub-BPF:GE90

C1:CF6

C1:CF34

C1:CFM56

C1:GE90

C2:CF6

C2:CF34

C2:CFM56

C2:GE90

C3:CF6

C3:CF34

C3:CFM56

C3:GE90
NASA/CR—2011-217026 43

Figure 17.—Standard Deviation Versus Nondimensional Mixed Jet Velocity.

Figure 18.—Root-Mean-Square Error Versus Nondimensional Mixed Jet Velocity.

0.0

0.5

1.0

1.5

2.0

2.5

0.200 0.400 0.600 0.800 1.000 1.200

Nondimensional Mixed Jet Velocity, Vmix/camb

Standard Deviation, 

σ, dB

Sub-BPF:CF6

Sub-BPF:CF34

Sub-BPF:CFM56

Sub-BPF:GE90

C1:CF6

C1:CF34

C1:CFM56

C1:GE90

C2:CF6

C2:CF34

C2:CFM56

C2:GE90

C3:ACF6

C3:CF34

C3:CFM56

C3:GE90

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.200 0.400 0.600 0.800 1.000 1.200

Nondimensional Mixed Jet Velocity, Vmix/camb

Root-Mean-Square Error, ε, dB

Sub-BPF:CF6

Sub-BPF:CF34

Sub-BPF:CFM56

Sub-BPF:GE90

C1:CF6

C1:CF34

C1:CFM56

C1:GE90

C2:CF6

C2:CF34

C2:CFM56

C2:GE90

C3:CF6

C3:CF34

C3:CFM56

C3:GE90
NASA/CR—2011-217026 44

(a) 33 Percent rpm

(b) 40 Percent rpm

Figure 19.—Experimental 3-Signal Coherence Spectra Compared With Correlation at Directivity 

Angle θ = 120 deg for JT15D Engine.

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Free-Field SPL at 100 ft, SPL, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Free-Field SPL at 100 ft, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred
NASA/CR—2011-217026 45

(c) 55 Percent rpm

(d) 73 Percent rpm

Figure 19.—Concluded.

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Free-Field SPL at 100 ft, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Free-Field Lossless SPL at 100 ft, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred
NASA/CR—2011-217026 46

(a) Three-Signal Coherence Data

(b) Total Engine Noise Data

Figure 20.—Experimental Spectra Compared With Correlation at Directivity Angle θ = 120 deg for

YF-102 Engine.

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Free-Field Lossless SPL at 100 ft, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred

SPLF,Pred

SPLL,Pred

SPLT,Pred

45

50

55

60

65

70

75

80

85

10 100 1000 10000

1/3-Octave-Band Center Frequency, f, Hz

Free-Field Lossless SPL at 100 ft, dB

SPLexp

SPLPred

SPLC1,Pred

SPLC2,Pred

SPLC3,Pred
NASA/CR—2011-217026 47

Appendix A.—Nomenclature

ANOPP Aircraft Noise Prediction Program

BPF Blade passage frequency, Hz

BPR Bypass ratio

C Noise component coefficient

c Sonic velocity

D Diameter, ft

F (Negative) slope of UOL versus nf relationships

f Frequency, Hz

GE General Electric

GRC Glenn Research Center

M Mach number

MTCT MTC Technologies

N Core noise component slope (UOL vs. core parameter)

nf Number of fuel nozzles

NASA National Aeronautics and Space Administration

OAPWL Overall sound power level, dB

OASPL Overall sound pressure level, dB re 20 μPa

P Total pressure (absolute), psia

R Source-to-observer distance, ft

S Strouhal number, dimensionless

SPL Sound pressure level, dB re 20 μPa

T Total temperature (absolute), deg R

UOL OASPL at θ = 90 deg

V Velocity, ft/sec

W Mass flow rate, lbm/sec

∆ Error, experimental minus predicted value, dB

ε Root-mean-square (RMS) error, dB

θ Directivity angle (relative to engine inlet), deg

σ Standard deviation, dB

Subscripts:

0 Flight

amb Ambient

C Combustor

C1 Low frequency core noise component

C2 Middle frequency core noise component

C3 High frequency core noise component

C,i Combustor inlet

C,o Combustor outlet

C(i) “i”th core noise component

comp Component
NASA/CR—2011-217026 48

cor Corrected for source location

EE Experimental/extracted

exp Experimental

f Simulated flight

h Hydraulic

I Inner (core, total into nozzle)

j Jet

L Large scale mixing

mix Mass-averaged mixed flow

P Plug separation

Pred Predicted

S Small scale mixing

T Transitional mixing

tm Turbomachinery
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2. REPORT TYPE

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3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Enhanced Core Noise Modeling for Turbofan Engines 

5a. CONTRACT NUMBER

NAS3-00178 

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Stone, James, R.; Krejsa, Eugene, A.; Clark, Bruce, J. 

5d. PROJECT NUMBER

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15 

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WU 22-781-20-01 

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MTC Technologies 

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E-17691 

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This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

This report describes work performed by MTC Technologies (MTCT) for NASA Glenn Research Center (GRC) under Contract NAS3-00178, Task Order No. 15. MTCT 

previously developed a first-generation empirical model that correlates the core/combustion noise of four GE engines, the CF6, CF34, CFM56, and GE90 for General Electric 

(GE) under Contract No. 200-1X-14W53048, in support of GRC Contract NAS3-01135. MTCT has demonstrated in earlier noise modeling efforts that the improvement of 

predictive modeling is greatly enhanced by an iterative approach, so in support of NASA’s Quiet Aircraft Technology Project, GRC sponsored this effort to improve the model. 

Since the noise data available for correlation are total engine noise spectra, it is total engine noise that must be predicted. Since the scope of this effort was not sufficient to 

explore fan and turbine noise, the most meaningful comparisons must be restricted to frequencies below the blade passage frequency. Below the blade passage frequency and at 

relatively high power settings jet noise is expected to be the dominant source, and comparisons are shown that demonstrate the accuracy of the jet noise model recently 

developed by MTCT for NASA under Contract NAS3-00178, Task Order No. 10. At lower power settings the core noise became most apparent, and these data corrected for 

the contribution of jet noise were then used to establish the characteristics of core noise. There is clearly more than one spectral range where core noise is evident, so the 

spectral approach developed by von Glahn and Krejsa in 1982 wherein four spectral regions overlap, was used in the GE effort. Further analysis indicates that the two higher 

frequency components, which are often somewhat masked by turbomachinery noise, can be treated as one component, and it is on that basis that the current model is 

formulated. The frequency scaling relationships are improved and are now based on combustor and core nozzle geometries. In conjunction with the Task Order No. 10 jet noise 

model, this core noise model is shown to provide statistical accuracy comparable to the jet noise model for frequencies below blade passage. This model is incorporated in the 

NASA FOOTPR code and a user’s guide is provided.

15. SUBJECT TERMS

Aeroacoustics; Aircraft noise; Jet aircraft noise; Noise prediction (aircraft) 

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