Airfoil Trailing Edge Noise Source Location for Low to ...

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

AIAA 2011-2785

Airfoil Trailing Edge Noise Source Location at Low to Moderate Reynolds Number E.J.G. Arcondoulis*, C.J. Doolan†, L.A. Brooks‡ and A.C. Zander§ School of Mechanical Engineering, The University of Adelaide, South Australia, Australia 5005

A study of the effects of Reynolds number and angle of attack on the dominant acoustic source location relative to the trailing edge for airfoils at low-to-moderate Reynolds number is presented. This study, which was performed using acoustic beamforming in an anechoic wind tunnel, helps assess the influence of each test parameter on the distance of the acoustic source from the trailing edge thus improving our knowledge of how airfoils produce tonal noise. The results show that the acoustic source location of a NACA0012 airfoil varies along the chord for the frequency range 500 Hz to 3000 Hz at low-to-moderate Reynolds number. Changing the angle of attack and Reynolds number resulted in small changes to the acoustic source location within this frequency range. A modified flat plate, which only radiated broadband noise under similar flow conditions, presented a scattered distribution of source location between the range 300 Hz to 1200 Hz.

I. Introduction

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here are many differing theories surrounding the production of sound for an airfoil in low-to-moderate Reynolds number flows. Paterson et al.1 suggested that the observed tonal noise was due to a vortex shedding process, which would generate noise several chord lengths downstream of the trailing edge. Tam2 argued that an acoustic feedback mechanism was responsible for amplifying the effect of the noise diffracted by the trailing edge, based on a tonal frequency selection process. Tam postulated that the acoustic source was located at a fixed distance downstream of the trailing edge. Arbey3 and Gaudriot et al.4 claimed that the source of tonal noise was close to the trailing edge, as determined by an acoustic imaging technique. They did not, however, provide in-depth details on their measurements. Using Particle Image Velocimetry, Chong and Joseph5 identified a small, localized high amplitude region of rms velocity aft of the trailing edge of a NACA0012 airfoil at a Reynolds number of 149,000. By fixing the Reynolds number and investigating the effect of angle of attack, they observed that increasing the angle of attack from 0° to 5º forced the localized velocity source closer to the trailing edge. Above a critical angle of attack, the velocity fluctuations dispersed and a single, localized source was no longer observed. It is the aim of this paper to present an experimental study, detailing the effect of Reynolds number and angle of attack on the acoustic source location of a NACA0012 airfoil. Little experimental work has been performed to accurately locate acoustic sources resulting from an airfoil at low-to-moderate Reynolds number. Brooks and Humphreys6 identified the trailing edge noise sources of a NACA 63-216 airfoil using acoustic beamforming and a deconvolution algorithm called DAMAS (Deconvolution Approach for the Mapping of Acoustic Sources). They observed acoustic sources immediately downstream of the airfoil trailing edge; however, their results are for much higher Reynolds numbers which produce broadband airfoil self noise7, rather than tonal noise of interest here. Arcondoulis et al.8 presented a study of the effect of angle of attack and Reynolds number on the noise emissions of a NACA0012 airfoil at low-to-moderate Reynolds number. Their results did not, however, present any information about the acoustic source location, and the effect of angle of attack and Reynolds number. Moreau et al.9-11 investigated the noise emissions from a modified plate in low-to-moderate Reynolds number flow. They analyzed the locations of velocity fluctuation near the trailing edge but not the acoustic source location. Using acoustic

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Post Graduate Student, School of Mechanical Engineering, South Australia, Australia 5005, [email protected], AIAA member Student † Senior Lecturer, School of Mechanical Engineering, South Australia, Australia 5005, AIAA Senior member ‡ Lecturer, School of Mechanical Engineering, South Australia, Australia 5005, AIAA member § Senior Lecturer, School of Mechanical Engineering, South Australia, Australia 5005 1 American Institute of Aeronautics and Astronautics

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

beamforming, the acoustic sources can be located and compared with parameters such as Reynolds number and airfoil angle of attack, as will be presented here.

II. Experimental Facility The Anechoic Wind Tunnel (AWT), located in the Holden Lab at the University of Adelaide, is a low-speed wind tunnel, designed for scale model testing, with a total room size of approximately 2 m3. The walls are acoustically treated with foam wedges, providing an (ideally) anechoic environment above 200 Hz. The contraction outlet (test section) has a working area of 75 mm (height) × 275 mm (width). The AWT facility including the contraction and the airfoil housing are shown in Figure 1.

Acoustic Beamformer

Flow Contraction

Figure 1. AWT facility, The University of Adelaide. From preliminary testing, the range of frequencies measured from the airfoil section was 500 Hz – 5000 Hz (Arcondoulis et al.8). A measurement of background noise with no airflow in the AWT was recorded by the center microphone of the beamforming array presented in Section III.B. The results of this measurement are provided in Figure 2. This figure shows that this microphone self-noise is relatively uniform and small. The AWT was then operated at all fan speeds equivalent to the experimentally chosen Reynolds numbers, without the airfoil, to acquire the background spectra. It can be seen that the airflow of 22.6 m/s in the AWT (corresponding to an airfoil Reynolds number of 100,000 if a 67 mm airfoil were in place) results in a very small increase in background noise above the no-flow case. As the airflow velocity was increased to 33.8 m/s (corresponding to an airfoil Reynolds number of 150,000 if a 67 mm airfoil were in place), there was a marked noise increase at frequencies less than 1000 Hz, as shown in Figure 2.

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0 m/s

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Figure 2. Background AWT noise with no airflow and Reynolds numbers of 100,000 and 150,000 (freestream velocities 22.6 m/s and 33.8 m/s, respectively).

III. Experimental Method A. Experimental Equipment A NACA0012 airfoil section was used for the experiments presented in this paper. The chord is 67 mm, with a span of 275 mm, which is the same width as the working section. The airfoil is secured in its housing 50 mm from the plane of the contraction outlet using a rod protruding through the airfoil along its axis of maximum thickness. This rod is then fastened to the housing at both ends of the airfoil span, which is directly attached to the contraction, as shown in Figure 3.

Airfoil Housing

NACA0012 Airfoil Figure 3. NACA0012 airfoil secured to the AWT contraction. The flow speed was varied so that results at Reynolds numbers 100,000, 125,000 and 150,000 were obtained. For each Reynolds number, results were obtained for three geometric angles of attack, being 0°, 5° and 10°. Due to the AWT jet being finite, two-dimensional correction factors were applied to determine the true effect of the airfoil angle of attack7. The airfoil was placed in the middle of the jet, which was assumed to be 75 mm in height. Note that the airfoil is placed 50 mm from the contraction outlet and it is assumed that the flow jet height does not expand significantly by the time it reaches the airfoil. Thus, the actual angles of attack presented in this paper are calculated as 0°, 1.58° and 3.16°. To provide more beamforming results using a different geometry, a modified flat plate was placed in the AWT (this work follows the results of Moreau et al.9,10). The modified flat plate has a circular leading edge, with a radius 3 American Institute of Aeronautics and Astronautics

of 2.5 mm. The trailing edge has a symmetrical wedge shape, with an apex angle of 12°. The plate has a chord of 200 mm, a span of 450 mm and a thickness of 5 mm. Under appropriate flow conditions this flat plate radiates broadband noise 9,10. A schematic diagram of the plate is shown in Figure 4.

12° 2.5 mm

Leading Edge

Trailing Edge

Figure 4. Flat plate geometry used for beamforming investigation. Adapted from Moreau et al.9,10. B. Acoustic Beamformer An acoustic beamformer was designed and manufactured for aeroacoustic experiments in the AWT12,13. The array contains 63 microphones, arranged in a modified logarithmic spiral12,13. The array covers an approximate area of 700 mm × 700 mm and is located 600 mm from the centerline of the working section. The beamformer installed in the AWT is shown in Figure 5. A beamforming algorithm was written to acquire and process the data, producing both cross-spectral and DAMAS beamformer outputs6,12. The scanning grid for the NACA0012 airfoil is 300 mm × 300 mm. This is the minimum practical scanning grid size which encloses the airfoil span of 275 mm. This creates a scanning grid resolution of 6 mm, where the grid contains 51 × 51 grid lines (2601 points). A preliminary study of the uncertainty of the source location capability of the beamforming array has been performed for a single frequency13. The source location capability of the array has not been evaluated for a range of acoustic frequencies; this will be performed in the future to understand the capability of the array in more detail. The beamformer has, however, been shown to accurately locate acoustic sources under still (zero-velocity) conditions12. In an attempt to improve the resolution of the acoustic sources, the harmonic frequencies of the noise structure were beamformed because the main lobe of the beamformer output is decreased in size at higher frequencies. Unfortunately, the signal-to-noise ratio at these higher frequencies was insufficient to provide meaningful beamforming results and hence the higher frequency results were not considered further at this stage.

Figure 5. Beamformer installed in the AWT. The effect of refraction of the acoustic waves through the AWT jet shear layer is significant as it changes the apparent acoustic source location. The shear layer refraction beamforming algorithm by Brooks and Humphreys6 modifies the beamformer output to account for the shear layer refraction at each scanning grid point. To save computational resources, the calculated shear layer refraction at the center microphone due to an acoustic source directly beneath it was computed. This offset value was applied to all of the cross-spectral beamformer outputs, resulting in a net shift of the cross-spectral beamformer output in the direction of the flow (being from top to bottom). This method, compared to the shear layer refraction beamforming algorithm by Brooks and Humphreys6, showed little difference in the computation of the maximum acoustic source locations. The beamformer output 4 American Institute of Aeronautics and Astronautics

image near the upper and lower bounds of the scanning grid showed some minor differences; however, these locations are not the primary focus of this paper. The acoustic source location at each frequency was calculated by finding the scanning grid point location corresponding to the maximum cross-spectral value in the beamformer output. This scanning grid location was converted into x and y coordinates. The DAMAS algorithm was also used to locate the acoustic source, but it was found that there was no difference between the maximum cross-spectral and the maximum DAMAS output locations. Thus, to save computational resources and time, the cross-spectral algorithm was employed for subsequent calculations of acoustic source locations. The DAMAS plots are presented in the following sections at 2000 Hz to help visualize the source locations relative to the airfoil. Each DAMAS simulation required 1000 iterations and was computed over a scanning grid containing 31 × 31 grid lines (961 grid points). C. Data Acquisition The data acquisition (DAQ) system used for this study consists of a National Instruments (NI) PXI-1042Q Chassis, with four PXI-4496 DAQ cards. Each card is capable of storing 16 channels of data, thus allowing up to 64 channels of real-time data total. A MATLAB DAQ interface was used to collect these data at a sampling frequency of 215 Hz for 5 seconds. The data were converted into Pascals, band-pass filtered between 50 Hz and 10 kHz and passed through a Fast Fourier Transform (FFT) algorithm. This data were input into a cross-spectral matrix, which contains the product of the complex pressure of each microphone multiplied by its conjugate. The autospectra were removed and the complex pressures were input into a cross-spectral beamforming algorithm6. All beamforming results are normalized relative to the maximum output, displayed as acoustic pressure (dB) relative to 20 × 10-6 Pa. The noise spectra presented in this paper are taken from the center microphone of the array, with a frequency resolution of 1Hz and the units are dB/Hz, relative to 20 × 10-6 Pa.

IV. Experimental Results A. Conditions A parametric investigation of Reynolds number and angle of attack is presented, allowing an evaluation of the effect of each parameter on the location of the acoustic source. The results in this paper were measured on the pressure side of the airfoil and are separated into three angles of attack cases: 0°, 1.58° and 3.16°. These results are a continuation of previous research by Arcondoulis et al.8. The same angles of attack and Reynolds number cases are analyzed; however, this current paper provides beamforming results of the airfoil, identifying the acoustic source locations. For each angle of attack case, the noise spectra are presented at Reynolds numbers of 100,000, 125,000 and 150,000. Cross-spectral and DAMAS beamforming results for an acoustic frequency of 2000 Hz are also presented. The process of obtaining the location of maximum noise within the beamformer output has been automated for each frequency between 500 Hz and 3000 Hz. B. NACA0012 0° Angle of Attack This section details the results of the beamforming testing at zero angle of attack. Figure 6 shows beamforming results at 2000 Hz. The greatest acoustic source at this frequency is upstream of the trailing edge. The cross-spectral and DAMAS plots in Figure 6 show a maximum acoustic source strength at the same location.


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Figure 6. Beamforming results for a NACA0012 airfoil, placed at 0° angle of attack and a Reynolds number of 100,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively. Figure 7a presents the acoustic source locations for the NACA0012 airfoil with a 67 mm chord, placed at zero degrees angle of attack and Reynolds number 100,000. The y-axis represents the distance of that frequency source from the trailing edge, where positive is upstream and negative is downstream.

(a)

(b) Figure 7. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 100,000 and zero angle of attack. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. The distribution of the acoustic source locations across the range of frequencies is interesting. The acoustic source location seems to oscillate about the trailing edge. For frequencies between 500 Hz and 800 Hz, the acoustic source location is widely scattered and any pattern in the acoustic source location is smeared. This is due to the broadband nature of the noise in this frequency range as well as the expected uncertainty of the beamformer measurement in this relatively low frequency range and also due to lower signal-to-noise ratio. 6 American Institute of Aeronautics and Astronautics

Observing frequencies between approximately 800 Hz and 2200 Hz, there exists a clear trend of the acoustic source location. This frequency range coincides with the amplified noise spectrum shown in Figure 7b, containing tones and a broadband hump, as typically observed for this Reynolds number flow regime8,14. At frequencies between approximately 2200 Hz and 3000 Hz, the trend begins to spread about the trailing edge. The spread of acoustic source locations about the trailing edge may be due to a poor spanwise coherence of the broadband noise sources in this frequency range. This would affect the ability of the beamformer to resolve the acoustic source locations. The Reynolds number was increased to 125,000 and the resulting beamformer outputs at 2000 Hz are provided in Figure 8. At 2000 Hz, the acoustic source location has moved downstream relative to the Reynolds number of 100,000 case (by observation of Figure 6 and Figure 8). Figure 9a presents the acoustic source locations for the NACA0012 airfoil with a 67 mm chord, placed at zero degrees angle of attack and Reynolds number 125,000. The acoustic spectrum of the noise emission is shown in Figure 9b.

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Figure 8. Beamforming results for a NACA0012 airfoil, placed at 0° angle of attack and a Reynolds number of 125,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively. The locations of the acoustic sources for the flow conditions of Figure 9a are similar to those shown in Figure 7a, with the exception of the sources measured at approximately 1750 Hz. For the flow conditions relevant to Figure 9a, 1750 Hz corresponds to the primary tone of the noise structure, whereas in Figure 7a, 1750 Hz is part of the broadband hump. The differences between the two results is a slight spread of acoustic source locations for frequencies between approximately 1700 Hz to 1800 Hz, as shown in Figure 9a. This spread is not apparent in Figure 7a. In addition, the primary tone shown in Figure 9b has both increased in frequency and magnitude, which corresponds to the results presented in Arcondoulis et al.8.


(a)

(b) Figure 9. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 125,000 and zero angle of attack. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. The Reynolds number was increased to 150,000. The beamformer output at 2000 Hz, presented in Figure 10, shows a maximum amplitude further downstream than the Reynolds number of 100,000 and 125,000 cases. Figure 11a presents the acoustic source locations for this test case. Observing Figure 11a, there now exists a greater spread of acoustic source locations, for frequencies of 500 Hz to approximately 1000 Hz which is due to the lower signalto-noise ratio. This is most likely due to a low signal-to-noise ratio. From Figure 11b, there is also no clear, defined primary tone at this Reynolds number; however, there exist tones of lesser magnitude at higher frequencies, such as 2050 Hz.

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Figure 10. Beamforming results for a NACA0012 airfoil, placed at 0° angle of attack and a Reynolds number of 150,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively.


(a)

(b) Figure 11. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 150,000 and zero angle of attack. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. C. NACA0012 1.58° Angle of Attack The airfoil was placed at a 5° geometric angle (1.58° true angle) of attack. The Reynolds number was set at 100,000 and the resulting 2000 Hz beamforming results are displayed in Figure 12. Increasing the angle of attack for this airfoil at a Reynolds number of 100,000 appears to only have minor effects on the location of the acoustic sources near the trailing edge. This can be observed by comparing Figure 7a with Figure 13a which shows a similar trend of acoustic source location between 1000 Hz and 2000 Hz. The notable differences occur at frequencies greater than approximately 2500 Hz, where the acoustic source appears much further downstream for the 1.58° angle of attack case, whereas the zero angle of attack case shows the acoustic source remaining close to the trailing edge. This is probably due to poor signal-to-noise ratio in this frequency range for the 1.58° angle of attack.

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Figure 12. Beamforming results for a NACA0012 airfoil, placed at 1.58° angle of attack and a Reynolds number of 100,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively. 9 American Institute of Aeronautics and Astronautics

By comparing the spectra of the zero and 1.58° cases, the zero angle of attack case has a higher noise emission at 3000 Hz (approx 30 dB) whereas the 1.58° angle of attack case has less than 20 dB, as shown in Figure 13b. The noise spectra do not contain the clear, defined tone as shown in Figure 7b for the same Reynolds number case.

(a)

(b) Figure 13. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 100,000 and angle of attack 1.58°. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. The flow speed was increased to achieve a Reynolds number of 125,000 and the beamforming results at 2000 Hz are shown in Figure 14. From observation of the cross-spectral and DAMAS outputs, the acoustic source location at 2000 Hz is similar to the Reynolds number 100,000 case. Figure 15a shows a similar acoustic source location distribution to Figure 13a. There is a strong trend of distance of the acoustic source from the trailing edge with frequency. By observing the noise spectra in Figure 15b, the tones have increased in both magnitude and frequency, as compared with the Reynolds number of 100,000 case shown in Figure 13b.

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Figure 14. Beamforming results for a NACA0012 airfoil, placed at 1.58° angle of attack and a Reynolds number of 125,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively. 10 American Institute of Aeronautics and Astronautics

(a)

(b) Figure 15. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 125,000 and angle of attack 1.58°. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. The flow was increased to produce a Reynolds number of 150,000. The measured beamforming results at 2000 Hz are shown in Figure 16. The acoustic source at 2000 Hz has moved slightly downstream relative to the Reynolds number 100,000 and 125,000 cases.

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Figure 16. Beamforming results for a NACA0012 airfoil, placed at 1.58° angle of attack and a Reynolds number of 150,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively. The acoustic source locations for the Reynolds number of 150,000 case differ from the Reynolds number of 100,000 and 125,000 cases, in the frequency range of 500 Hz to approximately 1600 Hz, as observed by comparing Figure 13a, Figure 15a and Figure 17a. The trend that was observed in the lower Reynolds number cases is spread over the airfoil chord in the Reynolds number 150,000 case, shown in Figure 17a, is likely due to the lower signalto-noise ratio. The trend of acoustic source location relative to the trailing edge from approximately 1300 Hz is less defined than the Reynolds number of 100,000 and 125,000 cases. For frequencies between approximately 1300 Hz 11 American Institute of Aeronautics and Astronautics

and 3000 Hz, the results at Reynolds numbers of 125,000 and 150,000 are similar, but the variation in the acoustic source location across the airfoil chord is slightly more apparent at frequencies greater than 2500 Hz for the Reynolds number of 150,000 case. There is less scatter of the acoustic source location due to the tones in the higher frequency range. From observation of Figure 17b, there are now fewer dominant tones in the noise spectrum and the primary tone has increased in magnitude for the presented frequency range.

(a)

(b) Figure 17. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 150,000 and angle of attack 1.58°. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. D. NACA0012 3.16° Angle of Attack The largest angle of attack considered in this research was 10° geometric (3.16° true). It was found that increasing the angle of attack resulted in broadband noise generation for Reynolds numbers 150,000 and less. The flow speed in the AWT was set to generate a Reynolds number of 100,000. The measured beamforming results at 2000 Hz are shown in Figure 18. The location of the acoustic source at 2000 Hz is located between the leading and trailing edge of the airfoil. This is slightly further upstream than the other angle of attack cases for all Reynolds number flow conditions. Figure 19a presents the acoustic source locations for the airfoil placed at 3.16°. There exists a greater variation along the chord of the airfoil as compared to the results for the airfoil placed at zero and 1.58° again likely due to the far lower signal-to-noise ratio. A trend can be detected between the frequencies of approximately 1000 Hz and 2500 Hz, however it is not clear. Results for frequencies between 2500 Hz and 3000 Hz show that the source is pushed further downstream. The acoustic spectrum shown in Figure 19b at this Reynolds number is markedly different in structure compared to the zero and 1.58° angle of attack cases. There are no tones present and the magnitude of the broadband hump is diminished.


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Figure 18. Beamforming results for a NACA0012 airfoil, placed at 3.16° angle of attack and a Reynolds number of 100,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively.

(a)

(b) Figure 19. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 100,000 and angle of attack 3.16°. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. The Reynolds number was increased to 125,000. The measured beamforming results at 2000 Hz are shown in Figure 20. The acoustic source location at 2000 Hz is downstream of the trailing edge, as seen in the beamformer output in Figure 20. There appears to be a source concentration near the left-side (negative x) trailing edge corner and a weaker source distribution along the airfoil trailing edge. It is believed that the acoustic sources are distributed evenly across the span of the airfoil trailing edge region; however it is currently unknown why the source is more concentrated on one side than the other (this is part of the authors’ ongoing analysis).


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Figure 20. Beamforming results for a NACA0012 airfoil, placed at 3.16° angle of attack and a Reynolds number of 125,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively. Figure 21a shows the acoustic source location for a Reynolds number of 125,000. Compared with the Reynolds number of 100,000 case shown in Figure 19a, there appears to be a varying trend of acoustic source location along the airfoil chord, similar to the zero and 1.58° cases. The frequency range 1000 Hz to 2500 Hz coincides with the range of the broadband hump in the noise spectrum. At higher frequencies, between 2700 Hz and 3000 Hz, the sources are measured to be closer to the trailing edge than the Reynolds number of 100,000 case. This may be due to a higher signal-to-noise ratio in than the Reynolds number of 100,000 case. By observation of Figure 21b, increasing the Reynolds number to 125,000 caused the broadband hump in the noise spectrum to increase in magnitude and increase the center frequency of the broadband noise hump. However, the magnitude of the noise only slightly exceeds the background noise.

(a)

(b) Figure 21. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 125,000 and angle of attack 3.16°. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone. 14 American Institute of Aeronautics and Astronautics

The flow speed was increased to produce a Reynolds number of 150,000. The measured beamforming results at 2000 Hz are shown in Figure 22. The acoustic source location at 2000 Hz is centered about the airfoil trailing edge. The acoustic source locations for the airfoil at a Reynolds number of 150,000 are presented in Figure 23a. This plot shows a weakened trend of acoustic source locations with frequency compared to the previous Reynolds number of 125,000 case. By observation of Figure 23b, the broadband hump has narrowed in width and slightly increased in magnitude, centered between 2000 Hz and 3000 Hz.

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Figure 22. Beamforming results for a NACA0012 airfoil, placed at 3.16° angle of attack and a Reynolds number of 150,000. Cross-spectral beamforming result (dB relative to the maximum output) at 2000 Hz (left image) and DAMAS result (dB relative to the maximum output) at 2000 Hz (right image). The flow direction is from positive to negative chordwise direction and the airfoil location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively.

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(b) Figure 23. (a) Acoustic source location relative to the airfoil trailing edge for a NACA0012 airfoil, Reynolds number 150,000 and angle of attack 3.16°. Lines at 0 and 0.067 m have been drawn to help identify the airfoil trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone.


E. Modified Plate Geometry A test was performed using the modified plate of Moreau et al.9,10 which is described in Section III.A. The flow speed was set at 15.25 m/s, so that a Reynolds number of approximately 200,000 was achieved, making any results produced here comparable with Moreau et al.9,10. The location of the maximum acoustic source for each frequency appears to be clustered near the plate trailing edge, as expected15. The beamforming results at 910 Hz are presented in Figure 24. Note that the scanning grid area was increased to 1000 mm × 1000 mm to allow for the span of the plate.

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Figure 24. Beamforming results for a modified plate, at a Reynolds number of 200,000. Cross-spectral beamforming result (dB relative to the maximum output) at 910 Hz (left image) and DAMAS result (dB relative to the maximum output) at 910 Hz (right image). The flow direction is from positive to negative chordwise direction and the plate location has been superimposed for observation purposes. LE and TE denote Leading Edge and Trailing Edge respectively. The acoustic source location was measured and plotted over the frequency range 300 Hz to 1200 Hz, as shown in Figure 25a. The acoustic spectrum of the plate is shown in Figure 25b. The upper frequency limit was reduced from 3000 Hz as the highest frequency with an acceptable signal-to-noise ratio was 1200 Hz. The lower frequency range was reduced to 300 Hz to increase the data set size and due to the plate being larger (450 mm span), beamforming plots of 300 Hz fit within a 1000 mm × 1000 mm scanning grid. The acoustic sources are mainly centered about the plate trailing edge. There is some spread across the plate chord, but there is not a distinct trend as shown in the results of the NACA0012 airfoil at zero and 1.58° angles of attack.


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(b) Figure 25. (a) Acoustic source location relative to the plate trailing edge, Reynolds number 200,000. Lines at 0 and 0.2 m have been drawn to help identify the plate trailing and leading edges respectively. (b) Background (blue) and airfoil flow noise (black) spectra measured at the array center microphone.

V. Conclusions This paper provides a comparison of acoustic source locations of a NACA0102 airfoil for varying angles of attack and Reynolds number using acoustic beamforming. Observation of the acoustic source locations showed variation of the source location along the airfoil chord for varying frequencies between 500 Hz to 3000 Hz. The zero and 1.58° cases showed similar trends and there was less scatter of the acoustic source locations when tones were measured in the noise emissions. The 3.16° case and the modified plate geometry showed weaker trends of acoustic source location. More work is required with other airfoil profiles to evaluate whether the observed trends of acoustic source location along the airfoil chord with frequency is relevant to a NACA0012 airfoil only or is a generalized behaviour for all airfoils at low-to-moderate Reynolds number. Analyzing a modified flat plate geometry, which radiated only broadband noise, presented little variation in the acoustic source location. More work is required to establish a connection between the acoustic source location information with models of how tonal noise is created by airfoils in uniform flow.

Acknowledgments The authors would like to thank the School of Mechanical Engineering at the University of Adelaide for access and use of the facilities and equipment detailed in this paper. The authors would also like to extend their sincere gratitude toward Mr. Silvio De Ieso and Mr. Norrio Itsumi for their insight and tireless work in the electronics workshop. Without their efforts, the construction of a 63 channel microphone array would not have been possible.

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