Robert P. Dougherty

OptiNav, Inc., Redmond, Washington

Bruce E. Walker

Channel Islands Acoustics, Camarillo, California

Daniel L. Sutliff

Glenn Research Center, Cleveland, Ohio

Locating and Quantifying Broadband Fan Sources 

Using In-Duct Microphones

NASA/TM—2010-216931

December 2010

AIAA–2010–3736
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Robert P. Dougherty

OptiNav, Inc., Redmond, Washington

Bruce E. Walker

Channel Islands Acoustics, Camarillo, California

Daniel L. Sutliff

Glenn Research Center, Cleveland, Ohio

Locating and Quantifying Broadband Fan Sources 

Using In-Duct Microphones

NASA/TM—2010-216931

December 2010

AIAA–2010–3736

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

16th Aeroacoustics Conference

cosponsored by the American Institute of Aeronautics and Astronautics

and the Confederation of European Aerospace Societies

Stockholm, Sweden, June 7–9, 2010
Acknowledgments

This work was supported by the NASA NRA Contract NNC07CB02C “Improved Phased Array Techniques

to Account for Extended Sources of Fan and Jet Noise.”

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

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Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2010-216931 1 

Locating and Quantifying Broadband Fan Sources 

Using In-Duct Microphones 

Robert P. Dougherty 

OptiNav, Inc. 

Redmond, Washington 98052 

Bruce E. Walker

Channel Islands Acoustics 

Camarillo, California 93010 

Daniel L. Sutliff 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

In-duct beamforming techniques have been developed for locating broadband noise sources on a lowspeed fan and quantifying the acoustic power in the inlet and aft fan ducts. The NASA Glenn Research 

Center’s Advanced Noise Control Fan was used as a test bed. Several of the blades were modified to 

provide a broadband source to evaluate the efficacy of the in-duct beamforming technique. Phased arrays 

consisting of rings and line arrays of microphones were employed. For the imaging, the data were 

mathematically resampled in the frame of reference of the rotating fan. For both the imaging and power 

measurement steps, array steering vectors were computed using annular duct modal expansions, selected 

subsets of the cross spectral matrix elements were used, and the DAMAS and CLEAN-SC deconvolution 

algorithms were applied. 

Introduction 

Significant reduction in aircraft noise is required to meet ongoing noise regulation in the USA and 

Europe. Since the turbofan engine is a large contributor to aircraft noise, any overall reduction in aircraft 

noise must include engine noise reduction. In order to efficiently achieve noise reduction, detailed 

understanding of the physics of noise source generation is required. The NASA focus area—Fundamental 

Aeronautics, Subsonic: Fixed Wing Program—emphasizes developing technologies for diagnostics of 

noise for subsonic aircraft. The work described here is intended to advance the state of the art for imaging 

broadband fan noise of turbofan engines using microphones that are flush mounted in the outer wall of the 

bypass flow path of the nacelle. The recordings are post-processed to form images of broadband noise 

sources on the rotating blades and to measure the modal amplitudes and the sound power in the inlet and 

aft fan ducts. The blade acoustic images and mode maps are intended to help clarify the mechanism for 

fan broadband noise generation and to identify any problem areas on a given set of blades. The sound 

power measurement may be a convenient and more-precise substitute for far field microphones. 
NASA/TM—2010-216931 2 

Nomenclature 





 a microphone location 





x a source point 

,  microphone indices 

S a set of array microphone pairs, (,) 

b beamforming result 

C cross spectral matrix 

C trimmed cross spectral matrix 

w beamforming weight vector 

g steering vector 

PSF array point spread function 

Jm , Ym Bessel functions 

mn mode function 

m spinning order 

n radial order 

Array Configuration and Approaches 

The NASA Glenn Research Center Aero-Acoustic Propulsion Laboratory is shown in Figure 1, and 

the Advanced Noise Control Fan rig (ANCF) therein is shown in Figure 2. The ANCF has an electrically 

driven fan, which, for this test, consisted of 16 blades. Four fan exit guide vanes, the minimum number 

allowed for vibration considerations, were installed. Arc arrays of external microphones, as shown in 

Figure 2, were used to determine the integrated sound power level in the inlet and aft sectors. Since no 

acoustic lining was installed, it is assumed that forward-propagating sound power in the inlet duct should 

equal the sound power derived from the forward-arc external array, and similarly for the sound power in 

the aft duct and the rear external microphones. 

Figure 1.—Aero-Acoustic Propulsion Laboratory. Figure 2.—Advanced Noise Control Fan. 
NASA/TM—2010-216931 3 

Internal Microphone Arrays 

The microphones used for the internal measurements are shown in Figures 3 to 6. Six sub-arrays of 

wall microphones: four rings of 30 microphones each labeled A, B, C, and E, a forward axial array of 

16 microphones, and an aft axial array of 14 sensors are used for the current analysis. An additional 

30-microphone ring labeled D but not shown in Figure 3, was present in the interstage region. It was not 

used for the results presented here. The diameter of the ANCF duct is 48 in. The radius of the hub is 9 in. 

at the fan and 12 in. in the aft portion of the duct. Ring C is 5.875 in. forward of the fan centerline, and 

axial spacings A-B and B-C are 3 in. The spacing of the microphones in the axial arrays is 1.5 in. The 

forward axial array has a total length of 22.5 in. and the aft axial array is 19.5 in. long. Ring E is located 

19 in. aft the fan centerline, or 7.5 in. aft the centerline of the stator ring. 

The arrays were combined in different ways for the various types of analysis. Fan imaging made use 

of the 90-element array resulting from combing the three forward rings: A-B-C. The inlet mode 

measurements and power estimates used rings A and C together with the forward axial array: A-C-Axial 

Fwd (76 microphones). Finally, the 44- element array E-Axial Aft was used for the aft mode 

measurements and power estimates. 

Figure 3.—Microphone array locations in ANCF. 

Figure 4.—Microphone installation. 
NASA/TM—2010-216931 4 

Figure 5.—Inlet microphone arrays. 

Figure 6.—Aft microphone arrays. 

Beamforming Methods 

Using Subsets of the CSM Elements 

Beamforming in the frequency domain makes use of the array Cross Spectral Matrix (CSM). In wind 

tunnel beamforming, the diagonal elements of the CSM are usually deleted (Ref. 1) to remove the effect 

of boundary layer noise from the results. In the current work, it was observed that microphone pairs at the 

same clock angle showed much higher correlation than pairs corresponding to different angles. It is 

believed that the cause is convected boundary layer turbulence: two microphones experience nearly the 

same turbulence if they are aligned streamwise. In order to prevent this effect from contaminating the 

beamforming results, portions of the CSMs corresponding to streamwise-aligned microphones were set to 

zero. This modification of the CSM also improved the modal resolution characteristics of the arrays. The 

patterns used for the mode measurement arrays are shown in Figure 7. 
NASA/TM—2010-216931 5 

A compact treatment of adapting beamforming for deletion of CSM elements is given in References 2 

and 3. Following the notation in the references, deleting certain elements of the CSM produces the 

trimmed CSM, C , where the bar indicates that selected elements have been replaced by 0. Let the set of 

CSM elements that will be included in the beamforming be denoted S  ,v. Consider a particular 

source or mode with unit power and index k. Let the array response vector (“steering vector”) for this 

source be denoted gk. Given a measured CSM, the classical beamforming expression for estimating the 

power of this source is 

k w k k b  ' Cw (1) 

where the weight vector is a normalized version of the steering vector: 

 



  

 



S

g g

,

g w

2 2

 (2) 

Bessel Steering Vectors 

In many applications of beamforming, it is appropriate to compute g using free space propagation. 

This is not the best approach for in-duct beamforming at some frequencies because the duct walls alter the 

sound waves enough to produce confusing results. The current, in-duct, beamforming is based on 

hardwall annular duct modes with uniform flow (Ref. 3). For modal beamforming, the steering vector is 

simply a particular duct mode normalized to unit power and evaluated at the microphone locations. For 

the imaging function, an expression related to the Green’s function is used: 

        mn

v k mn k mn v g x x     * , (3) 

where 



 is a microphone location, x

 is a beamforming map point, and the sum includes the cuton and 

mildly cutoff annular duct modes with radial order n and spinning order m. As noted in Reference 3 an 

acoustic pressure normalization of the beamform map is used for the imaging case. 

 (a) (b) 

Figure 7.—CSM elements sets S. Elements included are white. (a) A-CAxial Fwd. array, (b) E-Axial Aft.
NASA/TM—2010-216931 6 

DAMAS Deconvolution 

If only a single source is present, the beamform map will typically show that source with a peak level 

indicating the correct power. However, it will also incorrectly show both nearby sources (beamwidth) and 

remote sources (sidelobes) with nonzero power. This is described by the array point spread function 

(PSF), denoted by matrix A, which can be calculated from 

Ajk j Ck w j  w ' (4) 

where j is the beamforming point, the source is at k, and the single-source CSM (before trimming) is 

Ck  gk g'k (5) 

The diagonal elements of A are unity by construction. The matrix can be very large, and is not 

necessarily symmetric. Suppose there are mutually incoherent sources at the beamforming points, or 

modes, and that the source powers are used to make a column vector, X. Source incoherence means that 

the CSM can be written 

C Ck Xk (6) 

Using Y to represent the classical beamform map, the source powers, the PSF, and the beamforming 

results are related by 

Y  AX (7) 

The DAMAS deconvolution algorithm (Ref. 4) consists of beamforming to create Y and then solving 

Equation (7) iteratively for X, subject to the constraint Xk0. In the current work, like Reference 4, 

Gauss-Seidel iteration was used, with alternating forward and backward loops over the indices. In some 

cases, it was found necessary to apply Successive Under Relaxation (SUR) with relaxation parameter 

 = 0.1 in order to achieve convergence. 

CLEAN-SC Deconvolution 

Like DAMAS, CLEAN-SC (Ref. 2)is an algorithm that computes a set of source powers to account 

for an initial, classical, beamform map. The result, a “clean” map is constructed from the original, “dirty,” 

map using an iterative procedure. During each iteration, the highest point in the dirty map is identified 

and a portion of the power at this grid point is transferred to the clean map. A model for the portion of the 

CSM associated with this partial source is constructed. The model is computed from the (dirty) CSM and 

the steering vectors in such a way that any sources coherent with the identified peak are included in the 

model. The last steps in the iteration are to subtract the beamform map of the model CSM from the dirty 

map and model CSM from the dirty CSM. The iteration is complete when no significant sources remain 

in the dirty map. Like the DAMAS result, the clean map is intended to represent the true source 

distribution. One important difference between CLEAN-SC and DAMAS is that multiple coherent 

sources will probably be represented as a single source in the CLEAN-SC map, with a power matching 

the highest classical beamform point for the sources. The version of DAMAS used here is not formulated 

to operate correctly for the coherent case, but it is at least possible that the multiple sources will be give 

rise to distinct peaks in the DAMAS result. Efforts are underway to extend DAMAS to the coherent case 

(Ref. 5). 
NASA/TM—2010-216931 7 

Fan Source Imaging 

The computation of the fan source images makes use of the microphone rings ahead of the fan, array 

A-B-C. Tone noise is removed and the broadband data set is resampled to a coordinate system that rotates 

with the fan. As discussed in Reference 3, each 30-microphone, real, subarray is replaced with a 

32-element ring of virtual microphones. The coordinates of the virtual microphones are fixed relative to 

the fan blades. Beamforming is then performed as if the array were a conventional, fixed, phased array. 

The only modification to the process needed for the rotation is to account for the apparent swirl in the 

rotating coordinate system in determining the set of cuton annular duct modes and their axial propagation 

constants when evaluating Equation (3). DAMAS or CLEAN-SC deconvolution is sometimes applied to 

produce the final results. 

As presented in Reference 3, the annular duct modes in the rotating coordinate system are 

characterized by an effective wave number 

c

m k k    ' 0eff 0 (8) 

where 

c

k 

0  , m is the spinning order in the rotating coordinate system (which is the same as m, the 

spinning order in the stationary system), and  is the fan rotation frequency. Multiplying by the speed of 

sound, Equation (8) becomes 

eff   m (9) 

The spinning order and effective wave number eff 0k are used to determine the radial eigenvalues and the 

axial propagation constants. In this work, the values of m are limited by the spacing of the virtual 

microphones to –16 < m < 16. Using the corrected speed as an approximation,  is 188.5 radians/sec. The 

largest value of m is therefore 2827 radians/sec. or 450 Hz. Potential difficulties with a negative 

effective wavenumber were avoided by limiting the analysis to frequencies above 450 Hz. In higherspeed applications, it has been found useful to constrain the spinning orders included in the steering 

vector calculation to m < /2. 

Simulation Example 

The theoretical resolution of the VRM array with several beamforming techniques is shown in 

Figures 8 and 9. A mathematical point source was positioned in the fan plane, close to the outer wall, and 

the steering vector for this source and a synthetic CSM were computed according to Equations (3) and 

(5). The circumferential location of the source was near the trailing edge of blade 15. The numbering of 

the blades is such that blades with successively increasing numbers pass a given point in the duct. The 

trailing edge of blade 15 is therefore the edge near blade 16. The fan rotation speed used in computing the 

steering vector was 1780 rpm. Using the synthetic CSM in classical beamforming gives the results in 

Figure 8(a) to (c). There are high sidelobe levels, the radial resolution is poor, and apparent sources exist 

outside the duct. Using the annular duct steering vectors gives the results in Figures 8(d) to (f). The 

sidelobes are improved and the map is confined to the duct (by construction). The peak is slightly rotated, 

to the correct angle, because apparent swirl is taken into account. The radial resolution is still poor. 

Applying DAMAS gives the results in Figure 9. The resolution is much sharper. A maximum filter with a 

radius of 2 pixels was applied to Figure 9 and all of the other DAMAS and CLEAN-SC plots in order to 

show isolated point sources more clearly. There is still evidence of sidelobes in Figure 9(c) and (b). This 

is believed to be caused by the fact that a trimmed CSM was used in the beamforming, but not in the 

computation of the PSF for DAMAS in this case. This can be regarded as an illustration of the sensitivity 

of DAMAS to the accuracy of the PSF. 
NASA/TM—2010-216931 8 

Figure 8.—Beamforming a simulated source. Free space steering vectors, (a) to (c); annular 

duct mode steering vectors, (e) to (f). 

 
NASA/TM—2010-216931 9 

Figure 9.—Beamforming a simulated source: DAMAS. Maximum filter with a radius of 

2 pixels applied to make small spots visible. 

Mode and Power Measurements 

Mode maps and power estimates are made using data from the inlet array A-C-Axial Fwd and the aft 

array E-Axial Aft. Tone removal is performed and the broadband microphone signals are use to compute 

CSMs. Outward- propagating cuton modes are considered for each frequency. The steering vector for 

mode (m,n) (spinning order, radial order) and microphone location v 

 is 

     mn v

mn

v P g  m n     1  , , (10) 

where Pmn is the power of the mode that was initially normalized to unity average-square pressure over a 

cross section of the duct. Beamforming with Equation (1) using these steering vectors produces the mode 

map. A power estimate is obtained by summing the powers of the determined modes. Since the arrays do 

not have perfect modal resolution, is it not strictly appropriate to sum the powers of modes in the raw 

beamform map; this would be expected give a result that is too high. Deconvolution should be applied 

first. The modes may be mutually coherent or incoherent. (To see that it is possible to have coherent 

modes, suppose hypothetically that all of the sound is created by a single point source. Since all of the 
NASA/TM—2010-216931 10 

modes have the same origin, they must be temporally coherent.) Inspection of the power integral and 

application of the mutual orthogonality of the modes shows that mode powers should be summed whether 

the modes are coherent or incoherent. The available deconvolution techniques include DAMAS and 

CLEAN-SC. DAMAS is not strictly appropriate if the modes are coherent, but the powers in the resulting 

deconvolved maps are the appropriate quantities to sum. CLEAN-SC may apply in the coherent case, but 

does not account for coherent mode powers appropriately to support the final power estimate. 

Simulation Example 

Figure 10 gives beamforming results for a simulated (7,1) mode with a power of 100 dB re. 1 pW. 

Figures 10(a) to (c) represent the inlet and Figures 10(d) to (e) are simulations of the aft duct. The cuton 

modes at the analysis frequency of 1503 Hz are shown in blue. The aft duct has fewer cuton radial modes 

because of its smaller duct height (12 in. vs. 15 in. forward of the fan) and the direction of the flow, 

assumed to be Mach 0.1. The classical beamforming plots show that both arrays have excellent resolution 

in m (as they should, since they contain complete rings), but poor resolution in the n. The correct power, 

100 dB re. 1 pW, was determined for the true mode, but the total power for the classical beamforming 

overestimates the true value as a result of including the radial-order sidelobes. As an aside, deleting the 

axial-axial portion of the CSM is critical to the good m-order resolution of these arrays. If the full CSMs 

are included, apart from the diagonals, of course, the resolution in spinning order becomes poor. This is 

similar to cross array beamforming (Ref. 6). 

Applying DAMAS or CLEAN-SC (Figs. 10(b), (c), (e), and (f)) removes the radial order peak 

spreading and restores the correct total power, although CLEAN-SC loses 0.08 dB in this case. 

Figure 10.—Mode plots for a simulated source. Inlet, (a) to (c); aft, (d) to (f). 
NASA/TM—2010-216931 11 

Data and Configurations 

Results are given for 1800 rpm (corrected) and five configurations. The baseline configuration, 

A-I has 16 nominally identical blades. The blades used for the test were old and had a number of 

nonuniformities such as chipped corners and loose pieces of tape (Fig. 11(b) to (d)). The second 

configuration for the results, A-II had blades #6 and #14 replaced with alternate blades with missing 

trailing edges (Fig. 11(a)). In configuration A-III, two plastic bolts were installed in each of blades #6 and 

#14 to create flow noise at part-span locations (Fig. 11(e)). Configuration A-VII was similar to 

configuration A-III, except the bolts were removed, leaving two holes in blade #6 and two holes in 

blade #14. In configuration, A-VIII, blades #6 and #14 were removed entirely. The data for blade imaging 

(Array A-B-C) were acquired synchronously at 600 samples per revolution for a nominal sampling rate of 

18,000 Hz. The data for mode and power measurement (arrays A-C-Axial Fwd and E-Axial Aft) were 

acquired asynchronously at 20,000 Hz. The analysis makes use of 20 sec of data from each condition. 

Figure 11.—Blade details. Removed trailing edge, (a), loose tape, (b) and (c), chipped corner, 

(d), added bolts, (e). 
NASA/TM—2010-216931 12 

Results 

Imaging Results 

VRM imaging plots for the baseline configuration at three frequencies using two sets of beamforming 

steering vectors are shown in Figure 12. As in Figure 8, parts (a) to (c) give results at approximately 1000, 

1500, and 2000 Hz using free space steering vectors, and parts (d) to (f) represent steering vectors derived 

from annular duct modes. Individual blade images can be seen clearly using both sets of steering vectors, 

but only the annular duct results show the blades at the higher and lower frequencies as well. The annular 

duct results indicate that the primary source region is the trailing edge of the blades. (The direction of fan 

rotation is counterclockwise in all of the imaging figures.) The plots using the free space steering vectors 

show incorrect circumferential source locations because of the effect of apparent swirl. The radial 

distribution of the apparent source is unclear at the highest frequency. 

VRM and VRM/CLEAN-SC results are given for configuration A-II in Figure 13. The part of the 

blade modification that creates the most noise appears to be the near the hub. As shown in Figure 11(a), 

the carved blades have sharp corners in the trailing edges near the hub. Figure 13(d)) shows bright spots 

on the modified blades at approximately the radius of the corners, but the spots seem to be closer to the 

leading edges of the blades than the trailing edges. The direction of the offset is consistent with the inflow 

swirl created by the fan, i.e., the spots are displaced counterclockwise from the probable source locations. 

The analysis assumes that the flow is axial in the nacelle coordinate system. (This swirl is physical and is 

distinct from the apparent swirl of the axial flow in the rotating coordinate system that was taken into 

account in the mode-based beamforming.) Sources near the blade tips, such as spots at the outer wall in 

Figure 13(d)) are not expected to be strongly influenced by inflow swirl because the propagation distance 

through the flow to the nearest virtual rotating microphone is relatively short. 

Figure 14 shows one frequency from Configuration A-VIII: blades #6 and #14 removed. As expected, 

the spots at the blade tip trailing edges are missing. It also appears that the main source locations for the 

following blades, #7, #8, #15, and #16 are displaced away from the wall, presumably as a result of the 

altered aerodynamic environment seen by these blades. 

The configuration with plastic bolts in blades #6 and #14, A-III, is treated in Figure 15. The strongest 

source at the lower frequencies is on blade #2. Sources like this appeared when pieces of tape pulled loose 

from the fan, as shown in Figure 11(b). The bolts are represented by spots on blades #7 and #15 at 1096 

and 1164 Hz, and blades #6 and #14 at 3972 Hz. Viewed in the fan coordinate system, the bolt source 

location appears father downstream at lower frequency. This phenomenon is familiar in, for example, flap 

edge noise (Ref. 7) and jet mixing noise (Ref. 8). At the lowest frequency shown in Figure 15, the bolt 

source appears at the outer wall and extends from the blade with the bolt to the following blade. This may 

be caused by interaction between the wakes of the bolts and the blade tip vortices. At 4451 Hz, sources 

appear near the roots of the leading edges of blades #6 and #14. These appear similar to the case of the 

missing trailing edge (Fig. 13(d)). The trailing edges of blades #6 and #14 in Configuration A-III were 

present, but featured a different design from the other blades. These, nonuniform, trailing edges may act 

as noise sources similar to Configuration A-II. 

Plots from Configuration A-VII, bolt holes in blades #6 and #14, are shown in Figure 16. The low 

frequency spot on blade #2 is missing because the tape on this blade was repaired between the runs for 

Configurations A-III and A-VII. Spots near the leading edge of the tip of blades #7 and #15 are apparent 

at 935 Hz, but the sources are more compact and lower in level than the case with the bolts installed 

(69 dB vs. about 74 dB at 890 Hz in Fig. 15). The plot for 1136 Hz in Figure 16 shows the blade tip 

trailing edges more clearly than the corresponding plot for the bolts, 1164 Hz in Figure 15, which is 

dominated by the source on blade #2 and the bolt noise that appears on blades #7 and #14. Bolt hole noise 

is evident at 3808 and 4008 Hz. The high frequency noise seen at the leading edges of blades #6 and #14 

in Figure 15 is not evident in Figure 16. This may be a result of masking by a new source that appeared 

on blade #3. 
NASA/TM—2010-216931 13 

Figure 12.—Beamforming the baseline configuration. Free space steering vectors, (a) to (c); 

annular duct mode steering vectors, (d) to (f). 
NASA/TM—2010-216931 14 

Figure 13.—Configuration A-II (TE missing on blades #6 and #14). VRM, (a) and (b); 

VRM/CLEAN-SC, (c) and (d). 

Figure 14.—Beamforming for Configuration A-VIII. Blades #6 and 14 removed, VRM. (a); 

VRM/DAMAS, (b). 
NASA/TM—2010-216931 15 

Figure 15.—VRM/CLEAN-SC beamforming for configuration A-III. Bolts in blades #6 and #14. 
NASA/TM—2010-216931 16 

Figure 16.—VRM/CLEAN-SC beamforming for configuration A-VII. Bolt holes in blades #6 and #14. 
NASA/TM—2010-216931 17 

Modes 

Mode plots for Configuration A-I at 1503 Hz are given in Figure 17. Parts (a) to (c) present modes in 

the inlet and (d) and (e) represent the fan duct. In each case, three types of beamforming are shown: 

classical, DAMAS, and CLEAN-SC. The plots also note the estimate for the total power obtained by 

summing the mode powers for this 9.76 Hz (20,000 Hz/2048) frequency bin. The DAMAS results show 

reduced levels for some of the modes such as (m,n) = (–5,1) in the inlet and (4,1) in the fan duct that 

represent imperfect radial order resolution in classical beamforming. The power results for DAMAS are 

consequently lower than the classical values by 1.77 dB in the inlet and 1.35 dB in the fan duct. 

The CLEAN-SC plots, Figures 17(c) and (f), show significantly fewer modes than the classical or the 

DAMAS plots. The interpretation is that modes present in the baseline plots but missing from the 

CLEAN-SC plots were coherent with other modes that are shown in the CLEAN-SC plots. The power of 

these missing modes is also missing from the total power results, which are consequently much lower 

than the classical values (by 4.02 dB for the inlet and 5.33 dB for the aft case). 

Total Power 

The inlet and aft power levels for three frequency bands are shown in Figure 18. The bands are 

1: 237-711, 2: 711-1186, and 3: 1186-1659 Hz. These bands are centered at the nominal blade passage 

frequency and its second and third harmonics. The bars in Figure 18 correspond to the integrated power 

levels from the far field microphones (blue), the mode results from classical beamforming (red), and the 

DAMAS mode results (yellow). The rms errors, taken as the differences between the far field and the 

modal results over all three configurations, inlet and aft, and the three frequency bands (18 data points) 

are 1.05 dB for classical beamforming and 1.907 dB for DAMAS. 

Figure 17.—Mode plots for the baseline configuration. Inlet, (a) to (c); aft, (d) to (f).
NASA/TM—2010-216931 18 

Figure 18.—Power results for the inlet (I) and the Aft duct (A) for 

three frequency bands: 1: 237-711 Hz, 2: 711-1186 Hz, and 3: 1186-

1659 Hz. Far field reference values and modal results using classical 

beamforming and DAMAS. 
NASA/TM—2010-216931 19 

Analysis of the Power Results 

The classical power results appear to be more accurate than the DAMAS results, but this may 

represent cancellation of two sources of error: extra power from imperfect resolution of radial modes, as 

discussed previously (increases power values) and decorrelation of the CSM elements by propagation 

through boundary layer turbulence (Ref. 9), which decreases the power results. Both error sources 

increase with frequency. The modal resolution effect becomes more important at higher frequency 

because there are more radial modes cuton, and the decorrelation becomes more important because the 

propagation time shifts are a lager portion of an acoustic period. The DAMAS results contain only the 

decorrelation error, so they are lower than the far field values, and the difference is greater at higher 

frequency. 

Conclusions 

Virtual rotating microphone arrays can be used to image broadband fan source distributions. Steering 

vectors computed from annular duct modes and the DAMAS and CLEAN-SC deconvolution increase the 

frequency range of applicability and the resolution of the method. The VRM/deconvolution images 

showed noise from blade tip trailing edges, bolts installed in blades, pieces of loose tape, and 

nonuniformities near the root of blade trailing edges. Circumferential and radial resolution were 

demonstrated. 

In-duct arrays combining rings and axial line arrays are effective for broadband mode measurements 

and sound power calculations. It is appropriate to delete the portion of the CSM representing the cross 

powers of microphones within the line array. In-duct power estimates obtained from the classical 

beamforming mode measurements agree with the far field sound power measurements to within about 

1 dB. 

References 

1. Dougherty, R.P., “Beamforming in acoustic testing,” Chapter 2 in Aeroacoustic Testing, T.J. Mueller, 

ed., Springer-Verlag, 2002. 

2. Sijtsma, P., “CLEAN Based on Spatial Source Coherence,” AIAA Paper 2007-3436, May, 2007. 

3. Dougherty, R.P. and B.E. Walker, “Virtual rotating microphone imaging of broadband fan noise,” 

AIAA Paper 2009-3121, May 2009. 

4. Brooks, T., and W. Humphreys, “A Deconvolution Approach for the Mapping of Acoustic Sources 

(DAMAS) Determined from Phased Microphone Arrays,” AIAA Paper 2004-2954, May, 2004. 

5. Brooks, T., and W. Humphreys, “Extension of DAMAS phased array processing for spatial coherence 

determination (DAMAS-C),” AIAA Paper 2006-2654, May 2006. 

6. Piet, J.-F., and J. Elias, “Airframe Noise Source Localization Using a Microphone Array,” AIAA 

Paper 97-1643, Atlanta, GA, May 12–14, 1997. 

7. Kendall, J.M. and W.F. Ahtye, “Noise Generation by a Lifting Wing/Flap Combination at Reynolds 

Numbers to 2.8×106,” AIAA Paper 80-0035, Jan. 1980. 

8. Dougherty, R.P. and G.G. Podboy, “Improved Phased Array Imaging of a Model Jet,” AIAA Paper 

2009-3186, May 2009. 

9. Dougehrty, R.P., “Turbulent decorrelation of aeroacoustic phased arrays: lessons from atmospheric 

science and astronomy,” AIAA Paper 2003-3200, May 2003. 
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Locating and Quantifying Broadband Fan Sources Using In-Duct Microphones 

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Dougherty, Robert, P.; Walker, Bruce, E.; Sutliff, Daniel, L. 

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John H. Glenn Research Center at Lewis Field 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

In-duct beamforming techniques have been developed for locating broadband noise sources on a low-speed fan and quantifying the acoustic 

power in the inlet and aft fan ducts. The NASA Glenn Research Center’s Advanced Noise Control Fan was used as a test bed. Several of the 

blades were modified to provide a broadband source to evaluate the efficacy of the in-duct beamforming technique. Phased arrays consisting 

of rings and line arrays of microphones were employed. For the imaging, the data were mathematically resampled in the frame of reference 

of the rotating fan. For both the imaging and power measurement steps, array steering vectors were computed using annular duct modal 

expansions, selected subsets of the cross spectral matrix elements were used, and the DAMAS and CLEAN-SC deconvolution algorithms 

were applied. 

15. SUBJECT TERMS

Fan noise; Phased array 

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