Aeroacoustic Measurements in Open-jet Wind Tunnels - … · Aeroacoustic Measurements in Open-jet...

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American Institute of Aeronautics and Astronautics

Aeroacoustic Measurements in Open-jet Wind Tunnels – An

Evaluation of Methods Applied to Trailing Edge Noise

Chris Bahr,* Jian Li,

† and Louis Cattafesta

‡

Florida Center for Advanced Aero-Propulsion

Interdisciplinary Microsystems Group

University of Florida, Gainesville, FL 32611

Open jet wind tunnels have become commonplace in aeroacoustic testing, as having an

open-jet test section in an anechoic chamber can provide a near-anechoic environment when

attempting to measure acoustic field levels due to an aeroacoustic source. Additionally,

reduced flow is present over installation microphones, so SNR gains are observed versus

equivalent closed test section experiments. However, open-jet wind tunnels and their

acoustic treatment introduce additional noise sources which may contaminate a given signal

of interest. To overcome this limitation, multiple-microphone processing techniques

involving coherent power and/or beamforming are often leveraged. These techniques can

isolate the behavior of an aeroacoustic noise source using different types of assumptions.

However, depending on the facility background noise characteristics and measurement setup

these assumptions may be violated. A comparison of these techniques is conducted using a

NACA 63-215 Mod-B airfoil in UFAFF, and shows that when the signal of interest, trailing

edge noise, is not the dominant noise source, facility flow noise can introduce aberrant

behavior to the coherent power and array processing techniques. This behavior leads to

correspondingly large uncertainty bounds in output power spectra. Modifications to the

wind tunnel facility and experimental setup are proposed to mitigate these problems, and a

new experiment set with a smaller NACA 0012 airfoil is designed. Results show that

modifications appear to improve the behavior of coherent power methods, specifically those

tailored to trailing edge noise measurements, significantly. Major disagreement between

coherent power techniques and delay-and-sum integration is found even with significant

mitigation of facility contaminating noise sources. Uncertainty analysis does not account for

the difference visible between the methods, suggesting that further analysis involving

deconvolution and coherent source behavior is warranted.

I. Introduction

N experimental aeroacoustic analysis, open-jet wind tunnels are a common tool for performing measurements.

These facilities permit out-of-flow farfield acoustic measurements, significantly improving individual microphone

signal-to-noise ratios (SNRs) [1]. Additionally, these facilities can be constructed in anechoic chambers, thereby

permitting acoustic level analysis without contamination from acoustic reflections. However, this open-jet

configuration comes with a cost of additional flow-induced noise sources. A non-comprehensive list of such noise

sources includes:

* Former Post-Doctoral Associate, MAE Department, P.O. Box 116250, Member AIAA

† Professor, ECE Department, P.O. Box 116200

‡ Professor, MAE Department, P.O. Box 116250, Associate Fellow AIAA, [email protected]

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17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)05 - 08 June 2011, Portland, Oregon

AIAA 2011-2771

Copyright © 2011 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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• Edge noise from the open test section entrance/contraction exit

• Free shear-layer noise

• Shear layer/collector interaction noise

• Boundary layer noise from test section sidewalls (dependant on hard- or acoustically treated installation)

• Model-facility interactions, such as core flow deflection in high-lift configurations

A diagram of these sources for an example wind tunnel trailing edge noise measurement is shown in Figure 1. As

all of these signals can manifest themselves as real acoustic pressure fluctuations at a single microphone, multiple-

microphone processing techniques have been developed to mitigate these contaminating effects. Multiple-

microphone methods can give provide significantly more information about a given acoustic field, but they have

some inherent limiting assumptions. If violated, these assumptions can lead to erroneous conclusions about a given

aeroacoustics problem, especially with regard to true acoustic levels observed in a measurement induced by a

specific source. This research seeks to critically evaluate these methods in the context of a trailing edge noise

measurement by applying multiple methods to a given data set, comparing the results and their uncertainty bounds,

and evaluating disagreement between the methods.

Figure 1. Example background noise sources in a typical open-jet trailing edge noise experiment.

Trailing edge noise measurements offer a unique opportunity to study the interaction of these background noise

effects for an aeroacoustic problem of interest. Trailing edge noise is much quieter than many aeroacoustic sources,

for example landing gear, but are still an important source of interest [2]. These reduced levels can make it more

difficult to differentiate from facility noise sources. However, its well-known dipole-like radiation pattern allows

for specific implementations of coherent power methods which can show improved performance in extracting a

trailing edge noise signal [3]. Depending on the specific model and flow regime, trailing edge noise can exhibit

tonal noise from laminar instabilities and blunt vortex wake shedding; it can exhibit broadband characteristics from

turbulent boundary layer scattering; or even a combination of tonal and broadband characteristics [4]. These sources

Contraction Edge

Noise

Free Shear

Layer Noise

Collector

Interaction

Noise

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are generally spatially-distributed and partially-correlated [5,6]. An illustration of these sources in the vicinity of a

blunted trailing edge is shown in Figure 2. Note that both boundary layers and wakes may contribute to the

scattered field.

This paper first discusses the analysis methodologies used herein and then presents existing experimental data

from the University of Florida Aeroacoustic Flow Facility (UFAFF) acquired with a NACA 63-215 Mod-B airfoil.

The results are analyzed, and lessons learned from this data set are used to propose modifications to the experiment

setup and analysis using a new NACA 0012 airfoil.

Figure 2. Schematic of sources in the vicinity of a trailing edge.

II. Analysis Techniques

A brief discussion of the analysis techniques used in this study is given. Basic formulations of the techniques are

listed. All presented analysis occurs in the frequency domain with RMS-averaged power spectra.

A. Coherence-Based Techniques

Coherent power analysis, a common form of source identification [7], has frequently been applied to the analysis

of trailing edge noise [3,4,8-10]. Coherence-based techniques make few assumptions concerning the nature of the

source, aside from the linearity of signal behavior between one or multiple sources. However, implicit within the

use of such techniques is the assumption that there is either a single, dominant, coherent source, or that the multiple

coherent, incoherent or partially coherent sources generating the measured field can be spatially lumped relative to

the measurement domain [11]. In essence, these methods make a compact source assumption. Unfortunately, in

many open-jet aeroacoustic facilities, this may not always hold true. For instance in UFAFF a microphone placed 1

m from a model trailing edge may also be observing collector noise - located ~ 2 m from the microphone - at a

significantly different angle of incidence. The severity of this violation of the lumped assumption is dependent on

the relative levels of the contaminating sources.

For simplicity of discussion, a two-microphone measurement is discussed. A pair of microphone signals, ( )1y t

and ( )2y t , are assumed to measure a stationary random process ( )x t . These signals have Fourier transforms ( )1Y f

and ( )2Y f . As defined in detail elsewhere [7], with appropriate data segmenting, windowing and block averaging,

auto- and cross-spectral estimates can be constructed. The estimated autospectra (suppressing frequency

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dependence) are given as 1 1y yG and

2 2y yG . The cross-spectrum estimate is 1 2y yG , and the corresponding ordinary

coherence function is 1 2

2

y yγ . Autospectra and the coherence function are real quantities, while the cross spectrum is

complex. The autospectrum of a given channel is treated as the sum of two signals, as shown in Equation (1). The

first signal, i iu uG , is the signal which is due to a source observed by both microphones and is the signal of interest.

The second, i in nG , is only locally observed by the given channel and is considered noise.

i i i i i iy y u u n nG G G= + (1)

A generalized coherent power statement can be constructed to define the component of a given autospectrum

which is related between channels and is given in Equation (2), where XX

G is the autospectrum of the source of

interest and 1

H models the propagation from the source to the first observer. However, as Equation (2) shows, this

definition suffers an SNR bias dependant on the opposing channel from that being analyzed. As classically applied

for system identification [7], where the input signal is measured and assumed low-noise, the output bias disappears.

1 2

1 2 1 2 2 2 1 1

1 11 2 2 22 2 2 2 2 2

2 2

2

2 22

2 11

2 2

1 11 11

u u

y y u u u u u uxxy yy y n ny y u u n n

u u

G

G G G GH GCOP G

GG G GSNR SNRG

γ= = = = = =+ + ++

(2)

Alternatively, if the dipole-like nature of the trailing edge noise source is leveraged, the microphones can be located

such that the propagation models 1

H and 2

H are equal in magnitude but opposite in phase. This leads to an

unbiased calculation of the coherent power in Equation (3) [3].

1 21 1 2 2y yu u u u

G G G= = (3)

If three microphones are used, a system of equations can be defined which directly solves for channel SNRs

based on coherence functions, which can then be used to calculate the coherent power at each microphone without a

noise bias.

2 3 1 3 1 2

1 2 1 3 1 2 2 3 1 3 2 3

2 2 2

2 2 2 2 2 21 2 3

1 1 11 , 1 , 1

y y y y y y

y y y y y y y y y y y ySNR SNR SNR

γ γ γ

γ γ γ γ γ γ= − = − = − (4)

, 1, 2, 311

i i

i i

y y

u u

i

GG i

SNR

= = +

(5)

While this formulation is exact, strictly it only applies when the signal of interest is observed by all three

microphones, and noise is local to each. It does not, for example, address situations where there is coherent noise

observed by two of the microphones.

If more microphone measurements are considered for a single input, the number of equations quickly outpaces

the number of unknowns [10]. Several efficient methods have recently been developed to analyze this problem

using covariance-based techniques [12]. The first of these methods minimizes the Frobenius Norm of the difference

between the cross-spectral matrix (CSM) of the microphone signals and the modeled signal and noise matrices. The

second method leverages the Rank-1(i.e., single source) behavior of the signal matrix to model the difference

between the CSM and the noise data. The third method, a Maximum Likelihood method, assumes independent and

identically distributed random Gaussian processes and minimizes a log-likelihood function. All three methods are

designed to find the optimal single coherent signal present in a multi-microphone CSM.

The normalized random uncertainty of the coherence function is calculated directly using experimental quantities

in Equation (6), where d

n is the effective number of block averages [7]. While equations exist for directly

computing the uncertainty of coherent output power and cross-spectral magnitude, these break down under low-

coherence conditions. This is because at low coherence the 95% confidence interval can cover negative power

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regimes, which is non-physical, and thus the uncertainty region when expressed for polar terms such as magnitude

and phase are not Gaussian. Instead these, along with three-microphone uncertainties, are computed by perturbing

co-(12

C ) and quad-(12

Q ) spectral terms from the cross-spectra by their uncertainties, given in Equations (7) and (8)

[7], inside a Monte-Carlo loop [13].

( )2

122

12

12

2 1

dn

γε γ

γ

− = (6)

[ ]2 2

11 22 12 12

12

12 2 d

G G C QC

C nε

+ −= (7)

[ ]2 2

11 22 12 12

12

12 2 d

G G Q CQ

Q nε

+ −= (8)

Bias uncertainty for these analyses is neglected. Due to computational expense, uncertainties in the covariance-

based methods are not computed.

B. Beamforming

Traditional beamforming techniques as applied to aeroacoustic testing involve the assumption of a source field

consisting of a sum of monopoles, generally incoherent when addressed in the power domain. Beamforming can be

used to estimate the locations of acoustic sources, as well as the field level at the array center due to each source.

This technique has been applied often to analysis of trailing edge noise experimental data with various modifications

[9,14,15]. For an open-jet facility, shear-layer corrections are applied to each microphone’s signal prior to the

application of beamforming algorithms [16]. Alternative array calibration techniques involving acoustic point

sources can be used to correct for shear-layer effects [17,18]. Diagonal removal is often applied to negate the effects

of microphone self noise [19,20]. Erroneous negative powers may be computed when using diagonal removal [19],

but can be set to zero in subsequent power summation [22].

The power P at a given point in a scan plane l can be computed by constructing the CSM of an array

measurement G�

as defined in Equation (9), and multiplying it by the steering vector l

a�

, defined in Equation (11)

using the microphone-to-scan-location distances. The steering vector’s conjugate transpose is multiplied by this

resultant vector, with appropriate normalization for the number of the microphones in the array M [20].

1 1 1

1

M

M M M

y y y y

y y y y

G G

G

G G

=

…�

⋮ ⋱ ⋮

⋯

(9)

2

1 H

l l lP a GaM

=��

(10)

,1 ,,1 ,

,0

1,...,l l M

Tjkr jkr

l l Mll

a r e r er

= �

(11)

For traditional beamforming the total power at the array face due to sources in a given region can be estimated

by summing the power from every scan point within the region and normalizing by the array point spread function

(PSF) [22].

( )PSF

ll LL

l L

PP

l∈

∈

∑=∑

(12)

More advanced power estimation techniques often involve deconvolution. A non-exhaustive list of the current

methods in use includes DAMAS [14], DAMAS2 [23], FFT-NNLS [24], CLEAN-SC [25], CMF [26], LORE [27]

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and MACS [28]. These are, with the exception of DAMAS usage for NACA 63-215 data, beyond the scope of this

work.

Uncertainty calculations for beamforming can be difficult and computationally intensive. Recently, a Monte-

Carlo method was devised for computing power uncertainties of the conventional beamformer [29]. This method is

used in the present work. Uncertainties for DAMAS results are computationally infeasible at the present time.

III. Initial Experiments

All experiments are conducted in UFAFF. The original facility characteristics have been presented in several

references [30,31]. After some facility modifications, up-to-date background noise levels have also been published

[32]. A NACA 63-215 Mod-B airfoil [33] is used in these experiments, with a zig-zag trip tape applied at 5% chord

on the suction and pressure sides of the model. The airfoil is selected for comparison with existing research [9,21],

and the results show qualitative agreement [10]. A photograph of the airfoil is shown in Figure 3. The facility is

operated at Mach numbers ranging from 0.05 to 0.17 in 0.01 increments. The airfoil geometric angle of attack is set

to -1.5°, 0° and 1.5°. For brevity’s sake, the data presented are for Mach 0.17 at 0° angle of attack.

A 45-element multi-arm logarithmic spiral array [34]

is located 1 m below the model trailing edge. Opposite

the array are three G.R.A.S. 40 BE ¼” free field

condenser microphones, as shown in Figure 4. The array

consists of Panasonic WM-61a electret microphones and

is shown in Figure 5 along with its PSF at a characteristic

frequency of the experiment. A Brüel &Kjær (B&K)

4138 1/8” pressure field microphone is located at the

center of the array. When only coherent power methods

are considered, a B&K 4939 microphone is positioned 1

m below the model instead of the array. Schematically,

the array shown in Figure 4 is replaced with a single free-

field microphone at the equivalent location of the array’c center. All methods are applied such that they attempt to

educe the acoustic field 1 m below the model trailing edge. The most basic method, a single microphone

measurement, is simply the reading from the B&K 4138 or B&K 4939. Coherent power is calculated between this

microphone and the opposing center G.R.A.S. microphone. The three-microphone results are computed using these

first two microphones and the downstream G.R.A.S. microphone. Finally, phased array results are computed using

the 45 microphones from the array assembly, such that the beamforming output is the power observed at the B&K

4138 face.

Data are acquired simultaneously via an NI PXI 1045 chassis populated with 17 NI PXI 4462 4-channel DAQ

cards. All DAQ occurs at 102,400 samples/sec, with ac-coupling enabled on all channels. Appropriate microphone

calibration frequency response functions, calculated separately [32] are applied to the array microphone signals prior

to beamforming, while 1 kHz calibration corrections are applied to G.R.A.S. and B&K microphones.

In post-processing, a beamforming integration region encompassing the trailing edge is selected for the

computation of total power. While the test section span is 1.12 m, the integration region for the NACA 63-215 data

only spans 1.06 m, to exclude some observed sidewall noise. The integration region extends 0.2 m upstream and

downstream from the trailing edge.

Figure 3. UF’s NACA 63-215 Mod-B airfoil.

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Figure 4. Initial experimental configuration.

(a)

(b)

Figure 5. Phased array plate (a), shown with 2,512 Hz

PSF (b), in relative dB.

IV. Initial Results

Initial 95% confidence interval results for the two-microphone methods are compared in Figure 6. Note the

distinct separation between the curves is expected, due to the general method’s SNR bias underprediction.

Uncertainties become large around 3.5 kHz, which as shown in Figure 7 is where the ordinary coherence function

approaches zero, invalidating coherent power methods. This no-coherence condition does not necessarily mean that

no acoustic field is present. It can instead be indicative of the extent of the spectrum in wavenumber space. In other

words, the spatially lumped assumption required for multi-source inputs to coherent power methods has broken

down. For example, as shown by Capon [35], the coherence function between two observers of a diffuse noise field

trends as a first-order Bessel function of the first kind (J1),

( )( )

( )2

2

1 02

0

4ij ij

ij

J k xk x

γ ω = ∆∆

, (13)

where k0 is the acoustic wavenumber 0 0k cω= and ∆xij is the spatial separation between the observers. The

behavior of the coherence function for a distributed noise field of similar bandwidth and geometry to that in these

UFAFF experiments has been evaluated computationally, and compares closely with experiment even for uniform-

strength source fields with no effort to match true acoustic levels or source correlation length scales [36].

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Figure 6. Coherent power confidence intervals for B&K

4939 measurements.

Figure 7. Coherence between B&K 4939 and center

G.R.A.S. 40BE.

As discussed in reference 36, in computing the coherence between the B&K 4939 and G.R.A.S. 40BE microphones,

if trailing edge noise were dominant at higher frequencies, the coherence function would not decay as it does.

Mathematically, under the simplifying assumption of plane-wave behavior, the coherence function between two

center-span microphones observing a line source defined as the coordinate system axis manifests as

( )2

2 sinci j

ij

y ykφγ ω

π

− =

. (14)

Here kφ is the wavenumber defined by the acoustic wavenumber and the angle made by the ray extending from the

end of the line source (trailing edge/sidewall junction) to the observer (microphone), with respect to the line source

(trailing edge), 0 sink kφ φ= . The parameters yi and yj are the respective distances from the first and the second

microphones to the trailing edge. In the case of an ideal trailing edge noise measurement where the microphones are

equidistant from the airfoil trailing edge, yi and yj are equal and Equation (14) is identically unity. A coherence

breakdown as shown in Figure 7 would require off-axis sources from other regions of the facility, such as sidewall

noise or jet collector noise.

A comparison of the two-microphone dipole

assumption case and the three-microphone case is

shown in Figure 8. Both methods are clearly in

agreement at the airfoil blunt trailing edge shedding

peak near 2.5 kHz. This has been qualitatively

validated through comparison with DAS beam map

results [32]. Again at high frequencies uncertainties

become large due to coherence breakdown. However,

disagreement at lower frequencies is also indicative of

a violation of coherent power assumptions, as in

Section II it was shown that the two methods should

arrive at the same result when assumptions are obeyed.

Disagreement at lower frequencies is unlikely due solely to a diffuse wavespace field, as from Equation (14),

coherence breakdown at low frequencies requires large microphone separation. Instead, it is possible that there is

disagreement between methods because the overall test section acoustic field is not behaving as a line source

centered at the trailing edge at these lower frequencies. This could indicate that other facility noise sources, such as

the sidewalls or the facility jet collector, are dominant at these frequencies. Finally, a comparison of the covariance-

based approaches is shown in Figure 9. Where the coherence function is not dominated by diffuse wavenumber

Figure 8. Data for 2- and 3-mic B&K 4939.

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field effects, the methods show near-agreement with the three microphone method. However, as the coherence

function breaks down, the behavior of the methods becomes erratic.

Beamforming is now evaluated in comparison to coherent power methods. First, a comparison between the

three-microphone method and conventional integrated beamforming is shown in Figure 10. Note the ripple in the

integrated spectra is due to a standing wave pattern between the solid array face and airfoil model. The methods

agree at the trailing edge shedding peak, and are in nominal agreement when uncertainties become large, but

elsewhere disagree. A beam map for 1,204 Hz is shown in Figure 11, where the solid rectangle indicates the airfoil

cross-section, longer dashed line facility sidewalls, shorter dashed line the inlet, and green box the integration

region. The diffuser, not shown to clarify flow direction on this scale, is located at -0.92 m in the x-direction. The

color scale is in dB ref 20 µPa. While the array resolution is insufficient to separate out noise sources in the

installation, the measured field does appear to originate from well behind the model at this frequency, indicating that

diffuser-related phenomena are dominant at lower frequencies, agreeing with the assessment from the coherent

power method behavior. A beam map of the airfoil shedding peak frequency in Figure 12 shows that the airfoil

trailing edge is the dominant noise source.

Figure 9. Comparison of covariance methods. Figure 10. Data for 3-mic B&K 4138 and DAS.

Figure 11. Beamforming output at 1,024 Hz.

Figure 12. Beamforming output at 2,512 Hz

Finally, a frequency bin with large uncertainties, > 20 dB, in the integrated beam map level is selected. This beam

map, shown in Figure 13. Here, it is evident that sidewall scrubbing noise and a leading edge interaction are

dominant, and on the plotted scale trailing edge noise is not even visible. The large uncertainties in the conventional

beamforming output appear to be due to the Monte Carlo perturbations causing the sidewall noise sources to

fluctuate into and out of the beamforming integration region. The geometry of the sidewalls and extent of the noise

field in the beam map is sufficient at these higher frequencies to generate an acoustic field that is highly diffuse in

wavespace.

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Beamforming methods are also compared. Conventional

beamforming confidence intervals are compared to DAMAS

solutions both with a smaller scan grid, selected for reduced

computational cost, equal to the selected integration region, as

well as the solution using the full scan plane. These results are

shown in Figure 14. Here they appear to be in close agreement,

but an examination of the DAMAS beam maps shows non-

physical source locations. The full scan grid shows reduced

noise predictions from DAS outside of the shedding peak band,

again indicating major noise sources outside of the trailing edge

region are contaminating many of the analysis techniques The

sensitivity of deconvolution to beam map domain size is also

evident. A 1/3rd

-octave band comparison to the airfoil noise prediction code NAFNoise is shown in Figure 15 [37].

This work is based on previous research [4] involving a NACA 0012 airfoil, and uses computed boundary layer

parameters as inputs to estimate airfoil noise levels. Aside from the airfoil shedding peak, the code output is in

dramatic disagreement with the experimental data. This could indicate significant differences in facility background

noise, but previous research [10] has shown agreement between NACA 63-215 Mod-B data acquired in UFAFF and

in NASA’s Quiet Flow Facility using the same processing techniques.

Figure 14. Comparison of conventional beamforming and

DAMAS.

Figure 15. 1/3rd octave comparisons.

V. Modified Experiments

Clearly, at many frequencies of interest, facility background noise overwhelms trailing edge noise, making

quantitative analyses of multiple-microphone methods difficult at best, if not invalid. The next step of this research

plan is to see if, using the analysis of these older contaminated results, modifications can be made to the

experimental setup to mitigate the contaminants and improve the behavior of coherent power and beamforming

methods.

The first targeted noise source is the diffuser jet collector. This noise source appears to dominate lower

frequencies, and when evaluating autospectra appears louder than even the airfoil blunt shedding peak. The

treatment of this is twofold. First, the diffuser of the facility is reduced in length by 1.2 m. This modification makes

it easier for beamforming methods to exclude the noise source. Also it gives more room for the facility open jet to

gradually curve into the ductwork after being deflected by a model, possibly reducing the severity of the

impingement noise which would benefit both beamforming and coherent power methods. Secondly, a smaller

Figure 13. Beamforming output at 7,600 Hz.

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airfoil model has been selected for subsequent research. The previous NACA 63-215 Mod-B has been determined

to be too large for UFAFF. While the large chord allowed for high Reynolds numbers, the blockage ratio and 0.74

m chord make it very easy for the model to deflect the test section open jet into the diffuser even at low angles of

attack. A new NACA 0012 with a 0.3048 m chord has been fabricated for subsequent experiments. The reduced

chord and cross-sectional area dramatically improve the blockage ratio. Additionally, the model has a 0.74 m span,

allowing for vertical mounting in the 0.74 m by 1.12 m test section of UFAFF. Vertical mounting further improves

the blockage ratio of the experiment. The overall blockage ratio changes from 0.153 to 0.033. The old installation

is shown in Figure 16, and the new in Figure 17

Sidewall treatment is more problematic. Previous research studies have used both solid sidewalls [3] and

acoustically treated sidewalls [38]. Some studies have shown that acoustic foam sidewalls are desired to avoid

acoustic reflections, which can interfere with beamforming levels [38] if not properly accounted for in steering

vector corrections [39]. While a study of which sidewalls produce the least scrubbing noise while maintaining

beamformer integrity would be technically worthwhile, the required test matrix places it beyond the scope of the

current research plan. Instead, an attempt to reduce sidewall noise contribution is made by reducing the size of the

sidewalls. Previously, the test section sidewalls were continuous from the exit of the test section contraction to the

entrance of the diffuser. As visible in Figure 17 for the modified research plan, they are cut just over two chord

lengths downstream of the trailing edge. Again this points to the benefits of a smaller model. Additionally, with the

sideline installation, microphones can be installed further from the facility test section based on the UFAFF chamber

geometry. This increased distance from the source should partially mitigate the diffuse wave field behavior of the

ordinary coherence function, thus increasing the frequency to which coherent power methods are reliable.

Finally, a new array is necessary for the measurements. The previous array was machined into a plate for

minimal uncertainty in microphone locations, and designed with a small aperture to minimize source directivity

effects on level measurements. Unfortunately as shown the solid array plate induced a standing wave pattern which

had a significant effect on observed levels. The new array, shown prior to acoustic treatment in Figure 18, consists

of G.R.A.S. 40BE and B&K 4958 ¼” free-field microphones installed on a sparse grid, with a B&K 4954 ¼” free-

field installed in the array center for calibration reference [40]. While free-field installations suffer directivity issues

at higher frequencies due to acoustic scattering off of the individual microphone heads, the frequencies of interest in

this research study have been below 10 kHz, so such effects should be minimal. The calibration of this array and

correction methods are discussed elsewhere [18]. The array pattern is shown in Figure 19. The array is installed

1.13 m away from the model trailing edge, at an angle of 90° from the flow direction based on the trailing-edge

centered coordinates in Figure 4. As before, reference microphones are mounted opposite the model trailing edge

from the array. In this case, a B&K 4939 ¼” free field microphone is installed at -90°, 1.13 m away. A second

B&K 4939 is installed 0.2 m downstream of the first.

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Figure 16. NACA 63-215 installation, prior to insertion of

sidewalls.

Figure 17. NACA 0012 installation.

The experiments discussed above in the previous installation are repeated with the new setup. Reynolds number

matching is not possible given the new model size for any but the lowest Reynolds number from the 63-215 cases,

so Mach numbers are varied, as before, from 0.05 to 0.17. Angles of attack of -5°, 0° and 5° are evaluated. As with

the previous cases, the model is tripped at 5% chord on both the suction and pressure sides. Again, only the 0° AoA,

Mach 0.17 (Rec = 1.08x106) case is shown. The final experimental configuration, prior to model installation is

shown in Figure 20 to clarify the array beamforming coordinate system.

Figure 18. Example free-field microphone array, prior to

application of acoustic treatment (red circles denote

microphone locations).

Figure 19. Microphone coordinates and example spiral

arm for array from Figure 18.

Figure 20. Installation and coordinate system in sideline setup (array to test section centerline distance of 1.13 m).

VI. Updated Results

Coherent power techniques are first considered. As the general COP method is shown to suffer a universal bias,

it is not considered here. The dipole-specific COP is compared with the three-microphone method in Figure 21.

The uncertainty bounds of the dipole-based COP method have dramatically improved, but the three-microphone

method still shows some breakdown above 4 kHz, as well as disagreement at lower frequencies. As uncertainty

z

y x

Array Face (Microphone

1 at Center)

1.13 m Microphone 3

Microphone 2

1.12 m

0.74 m

Sidewall

NACA 0012

NACA 63-215

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bounds are driven by coherence functions, these coherence functions are evaluated next in Figure 22. The coherence

is plotted on a logarithmic scale here to emphasize a significant behavior. The coherence between microphones 1 &

2 and microphones 1 & 3 (labeled in previous figures) show a similar, slow roll-off as a function of frequency. To

re-iterate, microphone 1 is directly below the model trailing edge, 1.13 m away, while microphone 2 is directly

above it, 1.13 m away. Microphone 3 is downstream of microphone 2 by 0.2 m. The similar behavior of the first

two coherence functions is indicative that the relationship of microphone 1 to microphones 2 and 3 is very similar,

as might be expected for a line dipole. The coherence between microphones 2 and 3, however, acts very different.

The drop-off starting above 4 kHz is consistent with where the three-microphone method’s uncertainty bounds

become large. The oscillatory structure which develops for higher frequencies appears consistent with the behavior

expected for diffuse acoustic fields [36], and is expected as microphone 3 is further from the airfoil trailing edge

than microphone 2, assuming the trailing edge acts as a distributed noise source. However, Equation (14) would

suggest a 5% coherence roll-off at 10 kHz for the installation locations of microphones 2 and 3 relative to the

trailing edge. The lobe structure evident in Figure 22 is far more dramatic, indicative of a more diffuse acoustic

field and suggesting that the trailing edge noise source is not the only significant noise source present at these higher

frequencies, making further evaluation of these bands with array data valuable.

Figure 21. Coherent power confidence intervals for NACA

0012 experiments.

Figure 22. Coherence functions for NACA 0012

experiments.

Figure 23. Phase between opposing trailing edge mic pairs.

Figure 24. Phase between same-side pair of microphones.

Additional field characterization can be conducted by assessing the phase relationship of each microphone pair.

Unwrapped phase angles of microphone pairs opposing each other across the airfoil trailing edge are shown in

Figure 23. These angles are shown without any shear layer correction for time delay, which would alter the slope of

the plots, but not the oscillatory behavior. Oscillations aside, the phase data follow a linear trend up to near 7 kHz

14


suggesting a single dominant source field. Unwrapping the angle helps clarify this behavior. The 180° offset for the

pairing of microphones 1 and 2, equidistant from the airfoil trailing edge, is again indicative of a dipole-like

radiation pattern. However, as shown in Figure 24, such behavior does not hold for the microphones on the same

side. For an acoustic field dominated by a line dipole, the phase angle between two same-side microphones, one

downstream from the other, should show a linear trend starting with zero phase offset at dc. Instead, the phase

relationship breaks down above 4 kHz. As an aside, note that the phase relationship between opposing microphones

has a large structure in the vicinity of 2 kHz. This may relate to subsequent observed beam map behavior.

These data suggest that up to 7 kHz, there may be a single, dominant acoustic source acting as a line dipole.

However, the behavior of the three-microphone method and corresponding coherence and phase relationships

indicates that from 4 kHz to 7 kHz some source dynamics are present which violate the assumptions involved in the

three-microphone coherence method. The coherence and phase relationships also indicate that this breakdown

occurs between same-side microphone pairings.

This supposition of additional noise sources, of course, requires validation. Beam maps of select frequencies are

now considered. The integration bounds are geometrically scaled to the new test section dimensions and model size,

such that the integration bounds extend upstream and downstream of the model by 0.1 m, and are inset from the

sidewall by 0.02 m (covering 0.7 m of the model’s 0.74 m span). Integrated levels are shown for use with spectral

comparisons later in the document. The line usage to denote facility bounds and model footprint are the same as

used for the NACA 63-215 beam maps, although a bold black line is used in to show the integration region, as it

contrasts better with the particular data. Point source calibration is applied for shear layer correction [18].

Figure 25. Beamforming output for NACA 0012 at 2 kHz.




15


Figure 25 and Figure 26 show beam maps where the behaviors of the two-microphone and three-microphone

methods are both well-behaved. As is clearly visible, the airfoil trailing edge is the dominant noise source at these

frequencies, although some sidewall effects are beginning to become evident at 4 kHz. As shown in the beam maps,

any diffuser noise which may be present is more easily separable. Figure 27 shows the beam map at 6 kHz.

Sidewall noise is becoming more dominant in this frequency bin. However, the character of the trailing edge noise

source is also changing. It is no longer uniform across the span of the model, but shows dominance at the model-

wall junction. Such a behavior, if still maintaining a local dipole radiation pattern, may explain why the phase

behavior of opposite pairs of microphones appears as trailing edge noise, but the same side pairs of microphones see

behavior more like that of a diffuse sound field. Finally, Figure 28 shows the beam map at 8 kHz. Here, where both

two-microphone and three-microphone methods become unreliable due to large uncertainties, the sidewalls and

leading edge interaction source are dominant, and no (mid-span) trailing edge noise is visible.

Integrated spectra are now considered for the NACA 0012 experiments. The integrated DAS output for a the

static integration regions used in Figure 25 through Figure 28 is shown in Figure 29. As plotted here, the data show

poor agreement with the two-microphone and three-microphone analyses aside from the 4 kHz band where, as the

beam maps show, trailing edge noise is clearly dominant. However, for the low frequency data the array resolution

is too poor for the selected size of the integration region, while for the high frequency data the sidewall-junction

noise sources are near the edge of the integration bounds.

Because of these junction noise sources, the integration bounds must be re-evaluated. In attempting to match the

integrated spectra to the two- and three-microphone data, at least for bands where these methods appear valid, two

different approaches are possible. One approach would suggest including these junction noise sources completely,

as they are legitimate noise sources in a trailing edge noise aeroacoustic experiment. The other would suggest

completely removing them to isolate “true” two-dimensional trailing edge noise. In both cases the integration

bounds should be tailored as functions of array beamwidth, and thus functions of frequency. For both cases the

bounds are specified such that the integration region extends upstream and downstream of the trailing edge by one

beamwidth (half a beamwidth nominally, plus another half to account for offset in the data from the nominal airfoil

location). For the first case, the bounds are set such that the integration region extends beyond the sidewalls by a

beamwidth, to capture any junction noise sources, while for the second the bounds are set to extend inward from the

sidewalls by a beamwidth (with a minimum value of half the test section span), to reject junction noise sources.

As shown in Figure 30, varying the domain of the integration region to account for the sidewall-junction noise

sources, either to include or exclude them, has little effect on the overall shape of the integrated spectrum. Including

the sources shows a larger offset from the nominal integration at lower frequencies but close agreement at higher

frequencies, while excluding the sources shows agreement with nominal integration at lower frequencies while

lower levels at higher frequencies. None of the cases explain the disagreement of the 2 kHz data between coherent

power data and DAS integration. This may be an issue of array resolution relative to the size of the overall trailing

edge. Dramatically increasing the integration region size to encompass all visible noise near the trailing edge in the

full test section beam map only raises the DAS output by 3.5 dB, so the bounds do not explain the discrepancy. The

array calibration procedure itself could be suspect, but as shown in the reference [18], for this particular case

applying calibration has little effect on beam map levels, primarily shifting apparent source locations and acting as

an alternative to classic shear layer correction.

Nominal experimental data are compared with the NAFNoise code output for a NACA 0012 airfoil. Results are

plotted in Figure 31. As shown, the prediction does not trend well with any method below 1 kHz, but does follow

coherence-based methods, specifically the two-microphone method, above 1 kHz. This may be due to NAFNoise’s

dependence on a two-microphone empirical database. Finally, the DAS 95% confidence interval is shown in

16


comparison to the nominal coherent power method solutions. As with the NACA 63-215 data, aside from the band

of coherence breakdown, the DAS results are distinct from the coherent power predictions at all frequency bands

aside from the one where the array beamwidth is small and the trailing edge is dominant. However, in the case of

the NACA 63-215 data, the trailing edge blunt shedding peak provided a high SNR for all techniques, leading to

improved agreement in a wide band around the peak. No such condition exists with the NACA 0012 data, so even

frequencies where the trailing edge is visibly the dominant noise source are in disagreement. This is best seen near 2

kHz. Here, as already addressed, the discrepancy is likely not related to array calibration or integration region size,

so alternative possibilities must be explored. One such possibility is the presence of coherent reflected sources in

the 2 kHz band. This might explain the phase behavior observed in Figure 23 and Figure 24. As has been noted

elsewhere, correlated and coherent source fields can lead to erroneous source level calculations [41]. Alternatively,

if the problem is an array resolution issue, deconvolution may provide additional useful information.

Figure 29. NACA 0012 analyses comparison.

Figure 30. Evaluation of effect of integration region bounds.

Figure 31. 1/3rd Octave comparisons for NACA 0012 data.

Figure 32. DAS uncertainty compared to autospectral level

and nominal coherence techniques.

VII. Conclusions and Future Work

The NACA 0012 results show high variability in the analysis of the trailing edge noise source, even with a

modified experimental design based on the lessons learned from previous work. For coherent power methods,

placing two microphones equidistant from the airfoil trailing edge appears to provide superior isolation of the

trailing edge noise signal when contaminating noise sources are present. This conclusion is based on the behavior of

17


both the phase and the coherence function between the two microphones. Three-microphone analysis appears more

sensitive to additional sources, depending on microphone installation location, but provides a useful tool for

assessing the presence of these additional noise sources. Simple DAS integration disagrees with both other

techniques but as always provides an image of the acoustic field, which is extremely useful for assessing the state of

source distributions. Uncertainty estimates do not properly explain the discrepancy between DAS integration and

coherent power methods. When contaminating facility noise sources are addressed and reduced, the trailing-edge

specific formulation of a two-microphone coherent power method shows the best agreement with existing empirical

codes.

If anything, this research shows the importance of utilizing multiple analysis techniques when studying a given

data set with the selected methods. For example, if the two-microphone method were the only analysis applied to

the NACA 0012 data, one might conclude that trailing edge noise is the sole source of interest up to 7 kHz.

However, the coherence breakdown and subsequent high uncertainty in the three-microphone results suggested that

much of the data above 4 kHz are questionable. Beamforming allowed for the assessment of this questionable

frequency range to find the sidewall-junction noise sources. However, the volume of beam maps needed to blindly

locate frequency bins with interesting shifts in source field character would have been prohibitive without the

application of the two- and three-microphone methods. Channel-to-channel phase and coherence can provide

invaluable tools for determining source characteristics and the applicability of data analysis methods.

The major discrepancies between DAS and coherent power methods must be addressed in future work. Simple

integration may prove insufficient. As such, future research must also include the application of deconvolution-

based methods like DAMAS, as were applied to the NACA 63-215 data set. Additionally, source correlation must

be considered. These should remove the question of variation in the beamforming integration region based on

beamwidth, and clarify the behavior of an array power estimate as compared to more classic techniques.

Acknowledgements

The authors gratefully acknowledge the financial support provided by NASA Langley Research Center Grant

NAG1-03044 as well as that from the Florida Center for Advanced Aero-Propulsion.

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