In this paper, we apply sound source localization ... acoustic propagation to the microphone arrays in order to validate the source localization methods.
AIAA 2013-2213 Aeroacoustics Conferences May 27-29, 2013, Berlin, Germany 19th AIAA/CEAS Aeroacoustics Conference
3D Source localization in a closed wind-tunnel using microphone arrays T. Padois,∗ O. Robin∗ and A. Berry∗
Downloaded by Thomas Padois on September 19, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.2013-2213
GAUS, Sherbrooke, Quebec, J1K2R1, Canada
The detection of aeroacoustic sources in closed or open wind-tunnels usually involves microphone arrays. In this case, the source are searched in a planar two-dimensional grid. Recently, the potential of beamforming with a three-dimensional grid has been studied but with a two-dimensional planar array. In this paper, we apply sound source localization techniques to a three-dimensional array. First, a numerical solver is used to simulate the acoustic propagation to the microphone arrays in order to validate the source localization methods. The results show that the source position is localized accurately. An experiment in a closed wind-tunnel is presented. We use four microphone arrays installed on the sides of a wind-tunnel. Each microphone array has 48 microphones. Two types of acoustic sources are used. The first one is a monopolar sound source with known amplitude and position. Then a cylinder is mounted across the flow to generate dipolar radiation patterns.
Nomenclature Matrix or Vector Q Source power W Weight vector C Cross Spectral Matrix (CSM) G Green function L Regularization matrix J Hybrid Method weight vector U Vector of unknowns for LEE E Flux vectors for LEE F Flux vectors for LEE I Flux vectors for LEE H Gradient of the mean flow for LEE S Source term for LEE Parameter N Number of microphones L Number of scan points λ Penalization parameter ∆x Mesh size ∆y Mesh size ∆z Mesh size M Mach number Re Reynolds number St Strouhal number Upperscript H Hermitian transpose Subscript BF Beamforming ∗ GAUS,
University of Sherbrooke, Sherbrooke Quebec J1K2R1 Canada.
1 of 14 American Institute of Aeronautics and Astronautics Copyright © 2013 by T. Padois,[|#3#|] O. Robin[|#3#|] and A. Berry[|#3#|]. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
HM Hybrid Method
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I.
Introduction
Imaging exactly the noise coming from a complex sound source is a real challenge for acoustics. In 1976, Billingsley et al.1 have developed a tool called Acoustic Telescope to image the noise radiating by a full size jet-engine. They have used a linear array with 14 microphones and the source position was searched along a line. The source position was displayed on a TV screen. Then, nested array was introduced to overcome the high frequency limitations.2 This kind of array was used to detect sound source on by-pass train. With the improvement of the hardware, we see the increasing of number of microphones and so the microphone array are become two-dimensional. Different geometry 3 ´ was used, we can cite the X-shape of Elias and nowadays the most common used is the multi-arm spiral 4 array. With two-dimensional array the source position is searched on two dimensional plan closed to the object to scan. Now, most of the aeroacoustic applications use this technique to localize sound source on cars,5 trains6 or airplanes.7 The experiments are carried out in situ 8 or in an open9 or closed wind-tunnel.10 Although the in situ conditions are the best way to carry out an experiment, it is mostly expensive and weather depending, it is why experiments in a wind-tunnel are preferred. For open wind-tunnel, flow corrections have to be taken into account due to the propagation through the shear layer.11, 12 For closed wind-tunnel, high background noise and reflections occur.13 For each case the microphone array and the scan zone are two-dimensional. Only few papers deal with the potentiality of three-dimensional (3D) beamforming and it is mostly a 3D mapping zone with a 2D microphone array.14–16 In this paper we propose to realize a 3D microphone array in a closed wind-tunnel to localize a known acoustic source and then the noise generated by the interaction of a cylinder with flows In Section II of this paper, the beamforming, Clean-SC and the Hybrid Method are presented. Section III is devoted to a numerical example of 3D source localization based on Linearized Euler Equations (LEE) with and without flow. Finally Section IV presents the results of the 3D source localization in the closed windtunnel of the university of Sherbrooke. .
II. A.
Source Localization algorithms
Beamforming
The most common technique to process phased array data is beamforming. This technique has been widely studied in the last two decades for aeroacoustic problems.10–12 For sake of conciseness, beamforming is only briefly presented. We consider an acoustic source radiating toward a microphone array. The microphone signals are used to compute the sound pressure Cross Spectral Matrix (CSM) denoted C, a [N × N ] matrix with N the number of microphones. The aim of beamforming is to delay and sum all microphone signals in relation to a virtual source position. When the source position coincides with the real source position, the sum is maximum. The source power map provided by beamforming QBF can be written QBF = WH CW,
(1)
where W is the normalized steering vector and (.)H the Hermitian transpose. The size of W is [N × L] where L is the number of scan points. The normalized steering vector is given by W=
G , |G|2
(2)
with G is the [N × L] free-field Green function. Basically, the beamforming source power map exhibits large main lobe at low frequency with strong side lobes. To improve the source power map, and therefore the source localization, deconvolution techniques such as Clean-SC have been developed. B.
Clean-SC
Clean-SC is one of the most commonly used deconvolution technique in aeroacoustics to discriminate several uncorrelated sources. Clean-SC removes side lobes and source spots spatially coherent with the main lobe.17 2 of 14 American Institute of Aeronautics and Astronautics
Moreover the size of the main lobe is clearly reduced. The iterative process of Clean-SC is briefly introduced here, for more information the reader is referred to.17 First of all, the beamforming source power map is computed, then the peak value is searched. A new CSM due to a single coherent source at this location is constructed. The new CSM is subtracted to the initial and the process is repeated. At the end, the peak value are replaced by a monopolar point source and added to the residual CSM. In this paper the source power maps given by Clean-SC are compared with beamforming and the Hybrid Method, which is described in the next section.
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C.
Hybrid Method with beamforming regularization matrix
The Hybrid Method is described in details in another AIAA paper conference.18 The Hybrid Method is based on an inverse problem. It is well known that inverse problem can be ill-conditioned,19–21 meaning that the solution can be very sensitive to measurement noise or model uncertainties. Using the Tikhonov regularization it is possible to prevent these errors and uncertainties. The Tikhonov regularization (using identity matrix) adds signals to the product (GH G) to well-conditioned the inverse problem. But no information about the acoustic problem is added. One way to perform a better regularization is to take into account the result obtained by beamforming.22 The main idea is to use a discrete smoothing norm depending on the beamforming results, given a priori information about the acoustic problem, instead of the identity matrix. The new discrete smoothing norm, denoted L, in relation to the beamforming, called beamforming regularization matrix, can be introduced by " L = diag
!#−1 p Diag(QBF ) p , kDiag(QBF )k∞
(3)
where diag(A) is the (L × L) matrix formed by the main diagonal of matrix A (all non-diagonal terms being 0). Finally, the normalized power of the general-form inverse problem, called Hybrid Method, is given by H −1 H ) QHM = L−1 kJλ k∞ (Jλ GH )C(GJH λ )kJλ k∞ (L
(4)
with Jλ = (GH G + λ2 I)−1 .
(5) −1
The parameter regularization is denoted λ and G is the regularized steering vector equal to G = WL . The Hybrid Method gives source power maps with a better resolution than beamforming and removed the side lobes.
III. A.
3D Source localization : a numerical example
Numerical solver : Linearized Euler Equations (LEE)
The first step of this study is to numerically validate the microphone array techniques for a 3D problem and to compare the source power maps obtained with the various techniques described previously. A code solving the LEE is used for the simulation of the acoustic propagation in flows and a 3D version is considered here. This code has been already used for source localization with beamforming11 or Time-Reversal.9 For more details, the reader is referred to.9 The LEE are commonly used for aeroacoustic simulation because it is not expensive in terms of computation time and memory requirement.23 The LEE are obtained by linearizing the standard Euler equations assuming isentropic fluctuations. The density, the three velocity components and the pressure U = (q, u, v, w, p) are split into mean and fluctuating quantities. The linearized equations of mass, momentum, and energy can be written as a first order linear system as follows ∂U ∂E ∂F ∂I + + + + H = S, ∂t ∂x ∂y ∂z
(6)
where U is the vector of unknowns, E, F and I are the three-dimensional flux vectors, H is the term containing the gradient of the mean flow and S is the source term. We use a a Dispersion Relation Preserving scheme24 (DRP) for the spatial discretization and a fourth-order Runge-Kutta scheme for the time integration. The free field conditions are simulated with non-reflecting boundary conditions.24
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B.
3D Source localization
The numerical solver is used to simulate the acoustic propagation to the microphone array. The cases of a monopole radiating white noise in free field condition with and without flow are studied to validate the source localization methods. The aim is to simulate the experiment without the hard wall and background noise of a closed wind-tunnel. The mesh size ∆x for the numerical simulation is chosen with respect to the smallest wavelength λmin that needs to be propagated. The mesh size in the three directions is ∆x = ∆y = ∆z = λmin /n where n is the number of points per wavelength. For the chosen spatial scheme, n = 10 is sufficient.24 We chose λmin = 0.15m, corresponding to a maximum frequency of approximately 2kHz. The size of the computational domain is (121 × 121 × 121) points, or (1.8m×1.8m×1.8m), which is similar to the size of the closed wind-tunnel. The simulation is performed over 3000 time steps. The flow is uniform and oriented along the X-axis. The Mach number M is set to M = 0.07 (equivalent to the experiment). An example of the sound pressure fields with and without flow is given on figure 1. The point source is located at the center of the numerical domain. The monopolar radiation pattern with no reflections at the boundaries of the calculation domain is clearly visible in each case. In the presence of flow, the acoustic waves are slightly convected in the downstream direction as expected. The acoustic pressure is recorded by 4 microphone arrays. The microphone arrays are 8-arm spiral array with 6 microphones on each arm, therefore 192 microphones are used. Each microphone array is located at the boundaries of the computational domain. The microphone arrays are presented on figure 2. This geometry corresponds to the microphone array geometry used in the closed wind-tunnel experiments.
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Figure 1. Sound pressure field radiated by a point source: a) without flow and b) with flow oriented along X > 0. The black and red dots are the positions of microphones.
Figure 2. Geometry of the microphone arrays used in numerical simulations and wind-tunnel experiments: four 8-arm spiral arrays with 6 microphones on each arm.
Then, beamforming, Clean-SC and the Hybrid Method are applied to detect the source position at the highest frequency of 2kHz. The scan zone is a cube centered on the source with 21 mesh points on each side. The source position is searched in this volume with the four microphone arrays. The source power maps are normalized by the peak value and are presented on figure 3 in the zero flow situation. It can be observed that each microphone array technique is able to detect the source position. To enhance visibility 4 of 14 American Institute of Aeronautics and Astronautics
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of the maps figure 4 and figure 5 show slices of the source power maps in the XY plane and Y Z plane at the position of the peak value (the results in the XZ plane are similar to the XY plane and are not shown here). In the two planes beamforming exhibits a large main lobe with strong side lobes whereas Clean-SC and the Hybrid Method show a narrow main lobe without side lobes. The main difference between the two slices is the size of the main lobe obtained by beamforming. The main lobe is larger along the X-axis due to the absence of microphone array in the Y Z plane. In the Y Z plane, the main lobe is a circle due to the presence of the four microphone arrays. It is well known that the spatial resolution of the sources is poor in the direction perpendicular to the array. In this case, the source maps, created by each array individually, combine to provide a smaller main lobe. This numerical example without flow validates the source localization techniques and shows the source pattern without hard wall reflections.
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Figure 3. 3D source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting white noise located at the center of the domain without flow. The source power maps are in dB and normalized by the peak value.
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Figure 4. XY plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting white noise located at the center of the domain without flow. The source power maps are in dB and normalized by the peak value.
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Figure 5. Y Z plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting white noise located at the center of the domain without flow. The source power maps are in dB and normalized by the peak value.
In the presence of flow, it has been shown that the source postion is shifted in the downstream direction 5 of 14 American Institute of Aeronautics and Astronautics
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due to flow convection. Therefore, we use a simple flow correction which takes into account the convection effect due to the mean flow by shifting the scan zone in the downstream direction.11 The shift is proportional to the product of the mean flow thickness by the Mach number. Figure 6, 7 and 8 present the 3D source power maps and the 2D source power maps in the XY and Y Z planes respectively. The source position is detected for the three microphone array techniques with an error less than three points (less than 5cm in the physical domain). Therefore, the simple flow correction compensates for the convection effect. Since the Mach number is low, the source power map pattern is quite similar to the case without flow. However, we can notice that the main lobe of the beamforming is larger along the flow direction. Finally, the three microphone array techniques accurately detect the source position with and without flow and Clean-SC and the Hybrid Method exhibit the best resolution without side lobes.
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Figure 6. 3D source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting white noise located at the center of the domain with flow. The source power maps are in dB and normalized by the peak value.
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Figure 7. XY plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting white noise located at the center of the domain with flow. The source power maps are in dB and normalized by the peak value.
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Figure 8. Y Z plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting white noise located at the center of the domain with flow. The source power maps are in dB and normalized by the peak value.
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IV.
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A.
3D experimental source localization
Experimental set-up
An experiment has been carried out in the closed wind-tunnel of the university of Sherbrooke to perform 3D source localization. The test section is 10 meters long and the flow is generated by a 1.8m diameter vane axial fan driven by a 200 hp electric motor. The rotational speed of the fan, and consequently the flow velocity in the test section, can be varied using a frequency control. The air velocity in the empty 1.82m×1.82m test section is close to 25m/sec. The level of turbulence is less than 0.3%. Four microphone arrays are installed on the sides of the closed wind-tunnel. Each microphone array consists in 48 microphones with 8-arm-spiral and 6 microphones per arm. Therefore, an array of 192 microphones is used to perform sound source localization. The microphones are Br¨ uel&Kjaer phased microphones model No. 4957 and the signals are aquired with 16 LAN-XI modules. The acoustic signals are sampled at 32768Hz during 10 seconds. The test section with the four microphone arrays is shown on figure 9.a. The microphones are flush-mounted in a bushing slotted in the plywood. The airtightness is ensured with silicone between the plywood and the bushing and with o-rings between the bushing and the microphones. The microphones are recessed in cylindrical apertures as proposed in25 and opening in the wind-tunnel side walls are covered by a film of Kapton to protect from the hydrodynamic fluctuations. Kapton is a very thin film (0.0025cm) similar to Kevlar. Finally, facing arrays have their microphones rotated by 10˚ to avoid similar microphone positions. Two types of sources are used to generate acoustic waves. The first one is a LMS Mid High Frequency Volume source, that behaves as a monopolar volume acceleration source. The spherical wave spreading (6 dB reduction per distance doubling), and the constant directivity of the volume velocity source have been experimentally verified in an anechoic room. The source temination is placed in the center of the cross test section using a rod fixed in the floor panel. The second source is a cylinder immersed in the flow to generate a dipolar radiation pattern. The cylinder diameter is 6.35mm (1/4inch) and the length is 0.45m. The cylinder is fixed to the right and left side walls using two rods (diameter is 5cm). Aerodynamic measurements have been carried out to characterize the flow. A Cobra probe able to resolve the three components of velocity is used. The time signal is sampled at 2500Hz during 10 seconds. Therefore, mean velocity, turbulence intensity and power spectral density can be measured. A picture of the Cobra Probe is presented on figure 9.b. An example of aerodynamic results (axial mean velocity, turbulence intensity and power spectral density) is presented on figure 10. The Cobra Probe is located at 8.5cm behind the cylinder and moved vertically. The profile of the axial mean velocity shows a minimum behind the cylinder whereas the turbulence intensity is maximal as expected. The mean flow velocity is set to 23m/s, corresponding to a Reynolds number of Re = 9362 and a Strouhal number of St = 0.21.26 Therefore the vortex shedding frequency can be estimated at 760Hz. The power spectral density of the axial velocity is computed with 1024 points, Hanning window and 50% overlap and exhibits a peak at 732Hz. The slight difference between the experimental and theoretical vortex shedding frequency can be attributed to installation effects. B.
Controlled acoustic source
First of all, we used a controlled acoustic source with known position in order to validate the microphone array technique and estimate the installation effects on the acoustic propagation (hard wall reflections for example). The origin of the domain is set at the bottom right of the cross test section. The X-axis corresponds to the flow direction. The Y -axis and Z-axis are respectively the horizontal and vertical directions. The source is located at (Xs = 0.96m; Ys = 0.92m; Zs = 0.90m), which almost corresponds to the center of the cross test section. The acoustic source is driven by a sine-wave at 1kHz that is close to the vortex shedding frequency determined by flow measurements. The acoustic signal is sampled at 32768Hz during 10 seconds. The CSM is computed with 4096 points, Hanning window and 50% overlap. The scan zone is a cube with the origin located at (Xc = 0.6m; Yc = 0.6m; Zc = 0.6m). The side length of the cube is 0.6m. The scan zone is sampled with 21 points in each direction, which corresponds to a total number of 9261 scan points. The 3D source power maps obtained with the three microphone array techniques previously presented are shown on figure 11. In each case the source position is well detected. The position error is less than 3cm. The sound power level of the source maps is rounded to the nearest integer and 1dB is associated to one color level. The last color level is set to white to enhance visibility. The sound power levels are equivalent for the three microphone array techniques. Slices in the XY and Y Z planes are shown on figure 12 and figure 13. The source map pattern is equivalent to the numerical case (figure 3 to 5). The main lobe is larger along the
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Figure 9. a) Picture of the cross test section of the closed wind-tunnel with the four microphone arrays. b) Close view of the Cobra Probe for aerodynamic measurement.
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Figure 10. a) Profile of the axial mean flow velocity, b) profile of the turbulence intensity and c) power spectral density of the axial velocity.
X-axis due to the absence of microphone array and the side lobes are larger in the Y Z plane. The Hybrid Method gives a result similar to Clean-SC with side lobes removed. Therefore, we can conclude that the hard wall reflections do not disturb the source power map at this frequency. The same experiment was repeated with flow (M = 0.07). The power spectral density of the sound pressure measured by all microphones with and without the Kapton film is shown on figure 14. The peaks correspond to the blade passage frequency of the blower and its harmonics. The sheet of Kapton clearly reduces the flow noise at low frequency but is not effective for all microphones. The Kapton film is taped on the microphone bushings and it is possible that the flow degrades the airtightness. However, the mean sound pressure level of all microphones is more than 5dB lower with Kapton and the 1kHz sine-wave is dominates the harmonics of the blade passage frequency. The acoustic signal is processed in the same way than without flow and the simple flow correction is used. In each case the source position is well detected, the simple flow corrects the source position shift due to the convection effect (figure 15). The slices (figure 16 and figure 17) show that the source power map pattern is not disturbed by the flow. Finally Clean-SC and Hybrid Method
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Figure 11. 3D source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting sine wave at 1kHz located at (Xs = 0.96m; Ys = 0.92m; Zs = 0.90m) without flow. The source power maps are in dB.
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Figure 12. XY plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting sine wave at 1kHz located at (Xs = 0.96m; Ys = 0.92m; Zs = 0.90m) without flow. The source power maps are in dB.
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Figure 13. Y Z plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting sine wave at 1kHz located at (Xs = 0.96m; Ys = 0.92m; Zs = 0.90m) without flow. The source power maps are in dB.
provide the best source power maps without side lobes and a smaller main lobe. C.
Aero-Acoustic source
The previous section shows that the microphone array techniques are able to accurately detect the position of a controlled acoustic source with and without flow. To demonstrate the ability of the 3D source localization, the controlled acoustic source is replaced by a cylinder perpendicular to the flow direction. The noise generated by the vortex shedding behind a cylinder has been extensively studied.27, 28 It is well known vortex shedding generates a pure-tone with the directivity of a dipole in the direction perpendicular to the flow and cylinder axis. Moreover the vortex shedding frequency is related to the acoustic frequency. The aerodynamic measurements show that the vortex shedding frequency is 760Hz. The Reynolds number is
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Figure 14. Power spectral density of the sound pressure measured by all microphones a) without Kapton and b) with Kapton. The source is a monopole emitting sine wave at 1kHz. The bottom, middle and top red lines are respectively the minimum, mean and maximum shape of the power spectral density.
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Figure 15. 3D source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting sine wave at 1kHz located at (Xs = 0.96m; Ys = 0.92m; Zs = 0.90m) with flow M = 0.07. The source power maps are in dB.
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Figure 16. XY plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting sine wave at 1kHz located at (Xs = 0.96m; Ys = 0.92m; Zs = 0.90m) without flow M = 0.07. The source power maps are in dB.
Re = 9362, corresponding to a subcritical regime where the vortex shedding noise is strong.27 The power spectral density of sound pressures measured by all microphones (with Kapton film) is presented on figure 18. Even the background noise is high, a slight bump appears at 768Hz close to the vortex shedding frequency. Therefore, the microphone array techniques are performed at this frequency. The positions of the cylinder are (Xs = 1m; Zs = 0.95m). The length of the cylinder is 0.45m and is placed between Ys = 0.70m and Ys = 1.15m. The scan zone is slightly moved close to the cylinder but the number of scan points is the same as in the acoustic source case. Figure 19 shows the 3D source power maps. The source position along the X-axis (flow direction) is well detected with the three microphone array techniques. In each case the Z source position is found slightly over the cylinder and the Y peak value is detected close to the cylinder center. Beamforming and the Hybrid Method clearly exhibit a dipolar radiation pattern whereas Clean-SC shows only a single spot. Slices are presented on figure 20 and figure 21. From the top view (XY plane), the 10 of 14 American Institute of Aeronautics and Astronautics
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Figure 17. Y Z plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a monopole emitting sine wave at 1kHz located at (Xs = 0.96m; Ys = 0.92m; Zs = 0.90m) without flow M = 0.07. The source power maps are in dB.
three microphone array techniques present a spot at source position corresponding to a monopolar radiation. In this case, it is impossible to detect the dipolar radiation and Clean-SC provides the best resolution. From the side view (Y Z plane), Clean-SC provides only a single spot at the cylinder position and removes the second spot, which can be interpreted as a coherent source, characteristic of a the dipolar radiation. The Hybrid Method provides the best source power map with side lobes removed and dipolar radiation pattern.
Figure 18. Power spectral density of the sound pressure measured by all microphones (with Kapton). The source is a cylinder immersed in a flow at M = 0.07. The bottom, middle and top red lines are respectively the minimum, mean and maximum shape of the power spectral density
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Figure 19. 3D source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a cylinder immersed in a flow at M = 0.07 (Xs = 1m; Ys = [0.70 − 1.15]m; Zs = 0.95m).
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Figure 20. XY plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a cylinder immersed in a flow at M = 0.07 (Xs = 1m; Ys = [0.70 − 1.15]m; Zs = 0.95m).
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Figure 21. Y Z plane source power map: a) beamforming, b) Clean-SC and c) Hybrid Method. The source is a cylinder immersed in a flow at M = 0.07 (Xs = 1m; Ys = [0.70 − 1.15]m; Zs = 0.95m).
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V.
Conclusion
This paper investigates the potential of 3D source localization with different microphone array technique. First, beamforming and Clean-SC algorithms were presented and a method, called Hybrid Method, based on the regularization by beamforming of an inverse problem is introduced. A numerical solver based on linearized Euler equations was used to simulate 3D acoustic propagation in a flow. The three microphone array methods accurately detect the source position with and without flow. Clean-SC and the Hybrid Method provide the best results with a better spatial resolution and less side lobes than conventional beamforming. An experiment in the closed wind-tunnel of the university of Sherbrooke has been carried out with a controlled acoustic source and an aeroacoustic source. The controlled acoustic source is a monopolar source located at the center of the test cross section. Despite the high background noise and the hard wall reflections, the source position was well detected and the simple flow model corrects the shift in source position due to convection effect. Finally, a cylinder was immersed in the flow. Aerodynamic measurements were performed to characterize the flow. The power spectral density of the axial flow velocity exhibits a peak at the vortex shedding frequency at wich the microphone array techniques were tested. The beamforming source power map provided the correct dipolar radiation pattern but with a large main lobe. Clean-SC detected only one source and did not highlight the dipolar pattern. Finally, the Hybrid Method clearly improved the source power map by reducing the size of the main lobe and revealing the dipolar pattern.
Acknowledgments The authors wish to thank NSERC and Pratt&Whitney Canada for their financial support and Patrick L´evesque for his technical support to the experimental work.
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