[american institute of aeronautics and astronautics 16th aiaa/ceas aeroacoustics conference -...

American Institute of Aeronautics and Astronautics

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Reduction of Flow Induced Tonal Noise through Leading Edge Tubercle Modifications

K. L. Hansen1, R. M. Kelso2 and C.J. Doolan3

The University of Adelaide, Adelaide, Australia

A sinusoidal modification to the leading edge of an airfoil (tubercles) has led to the elimination of tonal noise for a NACA 0021 airfoil at a Reynolds number, Re ~ 120,000. It has also been found that the overall broadband noise is reduced for a considerable range of frequencies surrounding the peak in tonal noise. Investigations have also revealed that changing the amplitude and spacing between the tubercles has an effect on noise reduction. The mechanism of noise reduction is believed to be strongly related to the formation of streamwise vortices which are generated by tubercles. These vortices most likely have an effect on the stability characteristics of the boundary layer, hence influencing the velocity fluctuations of the shear layer near the trailing edge. In addition, spanwise variations in separation location are thought to affect the vortex shedding process, which could influence the feedback mechanism.

Nomenclature ρ = density [kgm-3] ν = dynamic viscosity [m2s-1] s = span [m] c = model chord [m] A = tubercle amplitude [mm] W = tubercle wavelength [mm] S = planform area [m2] L = lift force [N] D = drag force [N] α = angle of attack U∞ = free-stream velocity [ms-1] CL = lift coefficient, 2L/ρU∞

2S CD = drag coefficient, 2D/ρU∞

2S CLmax = maximum lift coefficient Re = Reynolds number, U∞c/ν α∗ = Corrected angle of attack αt = Geometric angle of attack H = Tunnel height [mm] fs = Tonal frequency [Hz] fn = Discrete frequency [Hz]

I. Introduction HIS paper presents an interesting and unique experimental study that investigates the effect of leading edge modifications in the form of sinusoidal protrusions (or tubercles) on airfoil flow and noise. Tubercles were

originally observed on Humpback whale flippers and have been identified as a lift-enhancing attribute connected with this animal’s feeding ecology.1, 2 However, there have been no previous studies of the effect of tubercles on airfoil self-noise. This is important, because if aspects of tubercles were to be incorporated into new hydrofoil, airfoil and rotor designs, then it is important to first understand how noise is modified and second, to exploit any 1 PhD Candidate, School of Mech. Eng., North Tce. Adelaide, 5005. 2 Associate Professor, School of Mech. Eng., North Tce. Adelaide, 5005. 3 Senior Lecturer, School of Mech. Eng., North Tce. Adelaide, 5005, Senior Member, AIAA.

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16th AIAA/CEAS Aeroacoustics Conference AIAA 2010-3700

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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noise-reduction capability that they may have. This paper reports the first measurements of noise from airfoils with tubercles. It is limited to the low-to-moderate Reynolds number regime where tonal noise is dominant.

Airfoil tonal noise is a high-pitched whistling sound that has been identified as a potential problem for wind turbines, gliders, small aircraft, rotors and fans.3, 4 According to McAlpine et al.3 tonal noise also occurs in underwater applications such as hydrofoils and propellers. The phenomenon has been investigated by numerous researchers and was first discussed in detail by Paterson et al.5

Paterson et al.5 proposed that the frequency of the tonal noise was related to the periodic vortex shedding experienced by an airfoil in a flow. The associated Strouhal number was based on twice the thickness of the boundary layer (99% velocity thickness) at the trailing edge for a flat plate. The researchers also mentioned that the tonal noise only occurred when the boundary layer on at least the pressure surface of the airfoil was laminar. In addition, it was shown that multiple tones could be generated simultaneously for a given flow condition.

Tam6 presented a comprehensive argument in opposition to the Strouhal number dependency discussed above. It was highlighted that the vortices initiated by wake instabilities would be formed considerably far from the trailing edge, making it difficult to associate them with the noise source, which is known to be close to the trailing edge. Additionally it was pointed out that a solid streamlined body is not known to generate two vortex systems at different frequencies coexisting with one other. Tam6 put forward an alternative theory involving the existence of a self-excited acoustic feedback loop. The proposed feedback loop is initiated by instabilities in a laminar boundary layer on the pressure surface of an airfoil, which become amplified as they move downstream. When these instabilities reach large enough amplitude, they cause a lateral oscillation of the wake, which induces acoustic wave emission in all directions. Increased boundary layer oscillation is instigated by the waves reaching the pressure surface of the airfoil near the trailing edge. For reinforcement to occur, the phase change around the loop should be an integral multiple of 2π. Tam6 highlighted that the frequency of the unstable disturbances is bounded by a neutral stability curve.

An experimental and theoretical investigation by Arbey and Bataille7 found that the noise spectrum associated with an airfoil in a laminar flow consists of a broadband contribution with a peak frequency at fs and a set of equally spaced, discrete frequencies, fn. The broadband contribution was attributed to diffraction of Tollmien-Schlichting (T-S) waves at the trailing edge, which was initially proposed as a noise radiation mechanism by Fink.8 The discrete frequencies fn, were believed to be the result of an aeroacoustic feedback loop between the maximum velocity point on the airfoil and the trailing edge.7 The proposed concept was similar to the one discussed by Tam6 however, the location of the feedback loop was quite different. Tam6 stipulated that the feedback loop was defined from a point very close to the trailing edge on the pressure surface of the airfoil to a point in the wake which acts as the noise source. This was justified by the observation that if a boundary layer trip were placed on the pressure surface of the airfoil, the tone would disappear.

A detailed study by McAlpine et al.3 found that tonal noise is closely related to a region of separated flow near the airfoil trailing edge and suggested that it is dependent on the existence of a separation bubble. It was proposed that tonal noise would be undetectable when transition to turbulence occurred sufficiently far upstream of the trailing edge of the airfoil. This was alluded to earlier by Tam6 who stated that the “no tone regime corresponds to a turbulent regime.” This idea is supported by the fact that tonal noise only occurs at low angles of attack. The authors used a linear stability model to predict the radiated tone frequency and found excellent agreement with their experimental results. The feedback model proposed by these researchers3 was similar to Tam6 except that it was specified as forced boundary layer receptivity (wavelengths of boundary layer and disturbance are comparable) in the region containing the separation bubble. Additionally, the “critical point” of coupling between the sound waves travelling upstream and the T-S waves travelling downstream in the boundary layer was suggested to be near the point of separation rather than where the flow initially became unstable.

It was emphasized in the experimental study by Nash et al.9 that the maximum amplification of T-S instabilities occurred in regions of the flow with inflectional velocity profiles caused by an adverse pressure gradient. For tonal noise generation, this region of inflected or separated flow should exist close to the trailing edge of the structure if it is to remain periodic. Also, the adverse pressure gradient should not be too severe, as this would initiate random turbulence having low coherence. In their theoretical analysis, the frequencies with maximum growth rates near the trailing edge corresponded closely with the observed acoustic tone. These researchers also carried out flow visualization with a strobed laser sheet, which showed a highly coherent wake structure at the frequency of the tone.

In the numerical study by Desquesnes et al.10 the mechanism of tonal noise generation detailed in Nash et al.9 was verified. In addition, an explanation for the secondary discrete vortices, fn, identified by Arbey and Bataille7 was provided. The researchers proposed that these discrete frequencies were the consequence of a periodic modulation of the amplitude of the main tonal frequency, fs. The observed secondary frequency spacing was identified to correspond to the period of this modulation. The role of the suction surface in the noise spectra was discussed for the first time since Arbey and Bataille7 and it was noted that the suction side boundary layer is highly receptive to the tone frequency. Visualization of flow at the trailing edge revealed that the phase difference between the instabilities on the pressure and suction sides


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(b) (a)

has a large impact on the acoustic waves generated. A phase difference of 180 degrees resulted in radiation of a higher-amplitude acoustic wave in contrast to phase locking which led to a weak acoustic wave radiation.

Kingan & Pearse4 developed a theoretical model based on the Orr-Sommerfield equation and compared it with existing empirical models3, 5, 7, 11 in regards to predicting tonal noise frequencies for four different sets of experimental results. It was shown that the theoretical model could be used to predict the boundary layer instability noise for arbitrary airfoil shapes with reasonable accuracy. By contrast, the empirical results gave varied results since they had been derived for a specific airfoil shape. They argued that this made the theoretical model much more widely applicable.

As the review above demonstrates, there are still some aspects of tonal airfoil noise generation that remain to be explained or experimentally confirmed. Furthermore, there has been no study of the effect of leading edge modifications on tonal noise. Therefore, the aims of this paper are to describe an experimental investigation into the effects of leading edge modifications on airfoil self noise, aerodynamic performance and flow structure at low-to-moderate Reynolds numbers. The ability of tubercles to eliminate tonal noise is demonstrated for both a closed-section wind tunnel and an anechoic wind tunnel. The observed results are related back to the existing body of evidence in order to shed light on the airfoil tonal noise generation mechanism.

II. Experimental Technique

A. Airfoil Design Tubercle configurations were incorporated into a NACA 0021 airfoil profile and a baseline airfoil was manufactured

for comparison. Airfoils were machined from aluminum and all airfoils have a mean chord of c̄ = 70mm and span of s = 495mm, giving a plan-form area of S = 0.035m2. The limited width of the anechoic wind tunnel, restricted the span to s = 275mm, with corresponding plan-form area, S = 0.019m2. Sinusoidal tubercle configurations are illustrated in Fig. 1 and the dimensions are summarized in Table 1.

Table 1 Tubercle configurations and adopted terminology

Configuration Label 0021 unmodified airfoil 0021 unmod

A = 2mm (0.03c) W = 7.5mm (0.11c) A2W7.5

A = 4mm (0.06c) W = 7.5mm (0.11c) A4W7.5

A = 4mm (0.06c) W = 15mm (0.21c) A4W15

A = 4mm (0.06c) W = 30mm (0.43c) A4W30

A = 4mm (0.06c) W = 60mm (0.86c) A4W60

A = 8mm (0.11c) W = 30mm (0.43c) A8W30

Fig. 1 Section view of airfoil with tubercles (a) 3D view, (b) Plan view with characteristic dimensions

Amplitude, A

Wavelength, W


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B. Aerodynamic Force and Acoustic Measurements

Aerodynamic force and acoustic measurements were carried out using a low-speed wind tunnel at the University of Adelaide, which has a 0.5 m square cross-section and a turbulence intensity of ~ 0.8%. The working section (Fig. 3) was bolted to the exit of the wind tunnel and the top of the airfoil was located very close (5mm) to the ceiling of the duct to minimize three-dimensional effects. The working section did not have any form of acoustic treatment.

Lift and drag forces were measured using a 6-component load cell from JR3 with external digital electronics (Fig. 4). This was fixed to a rotary table and rotated together with the airfoil. Care was taken to ensure the airfoil was mounted as accurately as possible with regard to the free-stream flow. Maximum blockage occurred at an angle of attack of α = 20º and is calculated to be 5% and thus small enough to be ignored in this investigation.

Acoustic measurements were carried out in the wind tunnel described above using two microphones located outside

of the working section, which were fixed in the same positions for all experiments. One microphone was positioned at a perpendicular distance of 280mm from the trailing edge of the airfoil, opposite a Perspex window. The other was located near the atmospheric reference slot at the downstream end of the working section at a perpendicular distance of 400mm and a downstream distance of 280mm from the working section exit.

Further acoustic results were obtained using the anechoic wind tunnel (AWT) at the University of Adelaide, which has a room size of approximately 2m3 and walls acoustically treated with foam wedges. The contraction outlet has dimensions of 75mm (height) and 275mm (width). End-plates were manufactured for the model to reduce three-dimensional effects and a circular cut-out section with a ‘running fit’ tolerance allowed the angle of attack to be adjusted (Fig. 5). For these measurements, a single microphone was positioned at a height of 650mm above the airfoil trailing edge and 50mm posterior to the trailing edge.

Working section

U∞

Rotating table Load cell

Base plate Stiff

Airfoil

Fig. 3 Sketch of experimental set-up Fig. 4 Load cell arrangement

Fig. 5 Mount for anechoic wind tunnel

U∞

Running fit tolerance


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To account for the downwash and flow curvature of the airflow around the model associated with the finite size of the open jet, a correction factor was applied to determine the true angle of attack, α*.12 The true angle of attack was reduced by approximately a factor of three as a result of these calculations.

ζαα t=* (1)

where, ( ) σσζ 1221 2 ++= (2)

and ( )( )22 48 Hcπσ = (3)

For both wind tunnel configurations, the free-stream velocity was measured using a Pitot tube and recorded with a sampling rate of 1000 Hz. The velocity data were averaged over a period of one minute and collected via a National Instruments USB-6008/6009 data acquisition system. The Reynolds number based on the free-stream velocity of U∞ = 25m/s and mean chord length was Re ~ 120,000.

Acoustic data were measured in the wind tunnels using two half-inch Brüel & Kjær condenser microphones attached to a Brüel & Kjær power supply and amplifier. The signals were processed using an Ace spectrum analyzer, which gave an output of the power spectral density. A stable averaging process was used, with a bandwidth of 1.6 Hz and a total of 100 averages per measurement, which took about 30 seconds to acquire. The frequency range of 0-2.5 kHz was selected based on preliminary measurements with the baseline NACA 0021 airfoil, which indicated that all tones existed in this range. The angle of attack, α, was increased incrementally by one degree increments from α = 0 to α = 12. Some further measurements were taken in the stall regime but it was found that all tones occurred at α ≤ 8 degrees, and were absent when the wings were stalled.

C. Flow visualization Flow visualization was carried out in a 0.5 m square cross-section water tunnel using the hydrogen bubble flow visualization technique. The water tunnel velocity was selected to give suitable flow conditions for visualization with the hydrogen bubble method. Thus velocities of U∞= 70mm/s and 84mm/s were utilized, corresponding to Re = 4370 and 5250 respectively. A platinum wire of diameter 40µm was bent into a sinusoidal shape and then a low current was passed through it, leading to the generation of hydrogen bubbles, which formed streaklines. The flow was illuminated using a thin light sheet and digitally recorded via a SONY Mini-DV video camera, which was connected to a laptop computer. Footage was recorded from different orientations to highlight specific features. The side view shows the separation point as well as the downwash angle. The angled top view enables observation of vortex structures. In all cases, the flow was visualized as close as possible to the mid-span location to minimize 3-D flow effects.

D. Results/Discussion

A. Aerodynamics It is useful to study the variation of lift and drag coefficients with angle of attack (Fig. 6, Fig. 7) to gain an

understanding of the aerodynamic performance of the various profiles. Whereas the airfoils with tubercles show some disadvantages such as a reduction in maximum lift coefficient, CLmax and an increase in drag near the stall point, there are also some considerable advantages. More specifically, the modified airfoils exhibit a more gradual stall and a higher lift coefficient post-stall. The most successful tubercle configuration, in terms of both favorable lift and drag characteristics, is the smallest wavelength and smallest amplitude configuration. By increasing the amplitude of the tubercles, a smoother stall characteristic is achieved but there is an associated penalty of a drop in CLmax and a decrease in maximum stall angle. The least successful tubercle configuration was the one with the largest wavelength.


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B. Flow Visualization Hydrogen bubble flow visualization highlights some of the unusual flow characteristics of airfoils with tubercles.

Some features of interest include the presence of stream-wise vortices, which appear to form in counter-rotating pairs in the troughs between tubercles (Fig. 8(a)). These stream-wise vortices are likely to increase the momentum exchange in the boundary layer, thus delaying stall13 and changing the stability characteristics of the boundary layer. Additionally, it is evident that the flow separates behind the troughs earlier than behind the peaks (Fig. 8(b), (c)). This would most likely lead to an interrupted separation line, which was noted in the numerical study by Pedro and Kobayashi14 for analysis of a model Humpback whale flipper. Buresti15 mentioned that positioning protuberances along the span of a body in a flow could avoid the occurrence of boundary layer separation along a straight line, hence interfering with the vortex-shedding process.

C. Acoustic Measurements in Hard-Walled Wind Tunnel With regards to tonal noise generation, Fig. 9 and Fig. 10 illustrate that the unmodified NACA 0021 airfoil

produces tones at each angle of attack from α = 1 to α = 8. These results were obtained from the microphone nearest the airfoil as well as the microphone at the exit of the working section.

Fig. 6 Lift Coefficient vs. Angle of Attack for NACA 0021

Fig. 7 Drag Coefficient vs. Angle of Attack for NACA 0021

(a)(b)

Fig. 8 Hydrogen bubble visualisation (a) angled top view showing stream-wise vortices, (b) side view in plane of trough and (c) side view in plane of peak (Re = 4370 (a) and Re = 5250 (b,c), α = 10°)

(c)


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As expected, the overall noise level detected by the microphone closest to the duct exit is higher since for the

microphone closest to the airfoil, there is a transmission loss associated with the Perspex window that the sound must pass through. There were some slight variations in the two sets of results which can be attributed to absorption at some frequencies and reinforcement at others, however there was only one tonal noise which was measured for one location and not the other. This was a secondary tone at α = 5º with a frequency of 1863Hz and was measured at the exit only. It was only observed at one angle of attack and is therefore unrelated to potential noise sources from the wind tunnel itself.

The most significant tone was observed to be just over 30dB above the equivalent broadband SPL at that frequency as measured by the microphone near the window. The microphone near the working section exit measured this tone to be around 40dB above broadband.

The results shown below in Fig. 11-16 were obtained using the microphone near the window due to its closer proximity to the airfoil and because it was located approximately 2m upstream from the other microphone, thus reducing the possibility for reflection and absorption by the duct walls. Since the highest amplitude tone was detected at α = 5º, the acoustic spectra comparison with the modified airfoils is made at this angle of attack. It should be noted that in their experimental study with a NACA 0018 airfoil, Nakano et al.16 found maximum tonal noise amplification at α = 6º, which is very similar to the current results. Fig. 11 is a plot of three separate runs at α = 5º which were taken at different times but with exactly the same set-up. The measured SPL and frequency of the tones show good repeatability and for a conservative estimate, the measurement with the lowest SPL at the main tone was used to compare with the results from the modified airfoils.

Fig. 11 SPL vs. Frequency for NACA 0021 at α = 5 for three separate runs

Fig. 12 SPL vs. Frequency for Variation of Amplitude of Tubercles (Small Amplitude)

Fig. 9 SPL vs. Frequency for NACA 0021 at angle of attack, α = 1-8° (window position)

Fig. 10 SPL vs. Frequency for NACA 0021 at angle of attack, α = 1-8° (exit position)


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Figures 12 and 13 present the effects on the acoustic spectra of changing the amplitude of the tubercles, whereas Fig. 14 shows results for variation of the wavelength. In general, the airfoils with the smallest wavelength and largest amplitude tubercles are the most effective at eliminating tonal noise at α = 5º. Interestingly, some of the other tubercle configurations successfully removed tonal noise at the problematic frequency but then generated another tone at a different frequency. In all cases, however, the amplitude of the new tone above the equivalent broadband SPL at that frequency was much lower than that of the original tone for the unmodified airfoil.

Results were also obtained for other angles of attack but to provide a brief overview, will be presented in a

condensed format. Figures 15 and 16 show that in general, the frequency of the tonal noise is higher for airfoils with tubercles and the SPL is lower. It can be seen that from the remaining tubercle configurations with tonal noise (two configurations showed no clear tones for all angles of attack), the smallest wavelength case has the highest frequency and lowest SPL amplitude at the two angles of attack that it produces tonal noise. Note that the results in Fig. 16 are obtained by subtracting the broadband SPL for the corresponding angle of attack and frequency. It was considered that a suitable broadband level for measurements including the airfoil would be α = 0º since no tones occur at this angle of attack.

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9Angle of Attack, α

Str

ouha

l no.

(fc

/U)

0021 unmodA2W7.5A4W15A4W30A4W60

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9Angle of Attack, α

SP

Lrm

s ab

ove

back

grou

nd (d

B) 0021 unmod

A2W7.5

A4W15

A4W30

A4W60

Fig. 13 SPL vs. Frequency for Variation of Amplitude of Tubercles (Large Amplitude)

Fig. 14 SPL vs. Frequency for Variation of Wavelength of Tubercles

Fig. 15 Strouhal no. vs. Angle of Attack for Tubercle Configurations with Tonal Noise

Fig. 16 SPL vs. Angle of Attack for Tubercle Configurations with Tonal Noise


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D. Acoustic Measurements in Anechoic Wind Tunnel (AWT) Further acoustic measurements were conducted in the AWT to investigate whether the mechanism of tonal noise

elimination for various tubercle configurations was influenced by the presence of the tunnel walls. Consistent with the results in the hard-walled wind tunnel, the most successful tubercle configurations for tonal noise elimination are the smaller wavelength and larger amplitude tubercles (Fig. 17 b, c & g). Additionally, the largest amplitude tone occurs at α = 5º (Fig. 17a), which is also in agreement with the previous results. However, the tonal frequency for the AWT was slightly higher (2125Hz compared with 1675Hz in the hard-walled wind tunnel). This is an interesting discrepancy and highlights the sensitivity of the tonal noise generating mechanism to changes in experimental parameters, even after appropriate corrections have been applied. Another difference between the sets of results is that tonal noise appeared over a much wider range of angles when testing in the hard-walled wind tunnel.

Referring to Fig. 17 b-g), it can be seen that all tubercle configurations experience significantly reduced SPL at the tonal frequency and in most cases the tonal noise is eliminated altogether. A result that was not observable using the hard-walled wind tunnel is a small reduction in broadband noise, which occurs between 1500 and 2500Hz for the airfoils with tubercles. Closer inspection also reveals a broadband contribution around the tonal frequency, fs, as well as equi-distant discrete frequencies, fn, which is consistent with the results from Arbey & Bataille7. The reduction in broadband noise for the modified airfoils between 1500 & 2500Hz most likely occurs because a higher broadband component is directly related to the presence of a 2125Hz tone for the baseline airfoil.

Fig. 17 SPL vs. Frequency measured for Re = 120,000 in AWT

0021 unmod A2W7.5 A4W7.5

A4W15 A4W30 A4W60

A8W30

a) b) c)

d) e) f)

g)


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E. Conclusions The results of an experimental study investigating the flow and noise characteristics of airfoils with tubercles

have been presented. It has been found that the larger amplitude and smaller wavelength tubercles are the most effective configurations for eliminating tonal noise. From the remaining cases, reduction in wavelength appears to increase the frequency at which tonal noise is detected. There is a corresponding decrease in sound pressure level. Lift and drag measurements indicate that the tubercle configuration with the smallest wavelength is also the most effective in terms of aerodynamic performance. Hydrogen bubble visualization illustrates the flow pattern associated with the modified airfoils and stream-wise vortices have been identified in the regions behind the troughs between tubercles. It is postulated that these vortices create increased momentum exchange within the boundary layer, changing the stability characteristics of the boundary layer and hence the frequency of velocity fluctuations in the shear layer near the trailing edge. In addition, due to varying locations of separation along the span-wise direction, the separation line becomes somewhat interrupted and this is thought to affect the stability and velocity fluctuation frequency of the shear layer. An interesting discrepancy has been found between the tonal frequencies measured in the hard-walled wind tunnel and the anechoic wind tunnel. However, results are in agreement with regards to the angle of attack with maximum tonal noise as well as the demonstration of tonal noise elimination through incorporating tubercles into the leading edge of the model.

Acknowledgments Thanks to Colin Hansen for invaluable technical support and to members of the mechanical workshop at

Adelaide University for their efficiency and precision, especially Bill Finch.

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Whale Flippers,” Physics of Fluids, Vol. 16, No. 5, 2004, pp. L39-L42, 2004. 3McAlpine, A., Nash, E.C. and Lowson, M.V., “On the Generation of Discrete Frequency Tones by the Flow Around an

Airfoil,” Journal of Sound and Vibration, Vol. 222, No. 5, 1999, pp. 753-779 4Kingan, M.J. and Pearse, J.R., “Laminar Boundary Layer Instability Noise Produced by an Aerofoil,” Journal of Sound and

Vibration, Vol. 322, 2009, pp. 808-828. 5Paterson, R.W., Vogt, P.G., Fink, M.R. and Munch, C.L., “Vortex Noise of Isolated Airfoils,” Journal of Aircraft, Vol. 10,

No. 5, 1973, pp. 296-302 6Tam, C. K. W., “Discrete Tones of Isolated Airfoils”, Journal of the Acoustical Society of America, Vol. 55, No. 6, 1974,

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Vol. 24, No. 8, 1986, pp. 1245 1251. 13Fish, F.E., Howle, L.E. and Murray, M.M., “Hydrodynamic Control in Marine Mammals,” Integrative and Comparative

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A.G., Eds.), Balkema, Rotterdam, 1998, pp. 61-95. 16Nakano, T., Fujisawa, S. and Lee, S., “Measurements of Tonal-Noise Characteristics and Periodic Flow Structure around

NACA 0018 Airfoil,” Experiments in Fluids, Vol. 40, 2006, pp. 482-490.

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