On the aeroacoustic tonal noise generation mechanism of a sharp-edged plate Danielle J. Moreau, Laura A. Brooks and Con J. Doolan School of Mechanical Engineering, The University of Adelaide, South Australia, Australia 5005 danielle.moreau@adelaide.edu.au, laura.brooks@adelaide.edu.au, con.doolan@adelaide.edu.au 1
Abstract This letter presents an experimental study on the tonal noise generated by a sharp-edged flat plate at low-to-moderate Reynolds number. Flow and far-field noise data reveal that, in this particular case, the tonal noise appears to be governed by vortex shedding processes. Also related to the existence of the tonal noise is a region of separated flow slightly upstream of the trailing edge. Hydrodynamic fluctuations at selected vortex shedding frequencies are strongly amplified by the inflectional mean velocity profile in the separated shear layer. The amplified hydrodynamic fluctuations are diffracted by the trailing edge, producing strong tonal noise. c 2010 Acoustical Society of America PACS: 43.28.Ra 2
1. Introduction The noise radiated from airfoils operating at low-to-moderate Reynolds number (1 10 5 Re c 6 10 5, based on chord) may contain one or more high amplitude tonal components. While airfoil tonal noise has been the subject of many investigations over the years, there is no general consensus on the tonal noise generation mechanism. Furthermore, no experimental studies have conclusively verified any of the proposed hypotheses. The first known experimental study on airfoil tonal noise was conducted by Paterson et al. 1. Using the cross-correlation of boundary layer and far-field acoustic data, they concluded that airfoil tonal noise is governed by vortex shedding from the trailing edge. Tam 2 disagreed with this hypothesis and proposed that tonal noise is produced by an aeroacoustic feedback loop between the first point of boundary layer instability and a point in the wake which acts as the noise source. The acoustic waves emitted by the noise source travel upstream to enhance the hydrodynamic instabilities at their origin. Tam 2 and most subsequent researchers 3 8 have assumed that laminar boundary layer instabilities, known as Tollmien-Schlichting (T-S) waves, are responsible for the discrete frequency noise. The aeroacoustic feedback loop proposed by Tam 2 has since been modified by a number of researchers 3 5,9,10, who have suggested that airfoil tonal noise is produced by a feedback loop between instabilities in the laminar boundary layer and acoustic waves generated at the trailing edge. They suggest that the boundary-layer instabilities are diffracted at the trailing edge to produce acoustic waves that travel upstream and reinforce the hydrodynamic instabilities at their source. More recently, Nash et al. 6 and McAlpine et al. 7 stated that the feedback process is not a necessary condition for the generation of acoustic tones. They proposed that airfoil tonal noise is generated by the trailing edge diffrac- 3
tion of boundary layer T-S waves that are strongly amplified by the inflectional mean velocity profile in the separated shear layer at the trailing edge. Through analysis of experimental results, this letter presents a mechanism for the production of tonal noise based on vortex shedding processes at the trailing edge. 2. Experimental method Experiments were performed in the anechoic wind tunnel at the University of Adelaide. This facility contains a 75 mm x 275 mm test section with a free-stream turbulence intensity of 0.3%. The flat plate model used in this study has a chord of 200 mm, a span of 450 mm and a thickness of 5 mm. The flat plate leading edge is elliptical with semi-major axis of 8 mm and semi-minor axis of 2.5 mm while the trailing edge of the top surface is a wedge shape which forms a 12 angle with the lower flat surface of the plate as shown in Fig. 1 (a). The acoustic measurements were recorded using two B&K 1/2 microphones (Model No. 4190): one 585 mm directly above and one 585 mm directly below the trailing edge. As it is likely that the far-field noise measurements are contaminated by other noise sources such as background noise, the method for extracting and analysing trailing edge noise developed by Moreau et al. 11 has been used to process the far-field noise measurements. However, as the tonal noise levels are much higher than the background noise levels, the effect of the correction was seen to be negligible. Hot-wire anemometry was used to measure both unsteady velocity data in the streamwise direction, and the boundary layer profile at the trailing edge. A TSI 1210- T1.5 single wire probe with a wire length of 1.27 mm and a wire diameter of 3.81 µm was used. The probe was positioned using a Dantec automatic traverse which allowed continuous movement in the streamwise (x), vertical (y) and spanwise (z) directions. The origin of the co-ordinate system is located at the centre of the trailing edge. Both 4
the far-field noise measurements and the velocity data were collected using a National Instruments board at a sampling frequency of 2 15 Hz for a sample time of 8 s. Experiments were conducted with the flat plate positioned at zero angle of attack at free-stream velocities between U = 5 and 15 m/s, corresponding to Reynolds numbers of Re c 0.7 10 5 2.0 10 5. 3. Experimental results and discussion The far-field acoustic spectra for the flat plate at U = 15 m/s is compared with background noise spectra in Fig. 1 (b). The background noise was measured with the top trailing edge microphone. The far-field noise spectrum is composed of a broadband contribution centered around the peak tone and a number of discrete equi spaced tones. The value of the difference between two consecutive discrete frequencies is f 244 Hz. The tones observed in the far-field noise spectra are the 2nd 5th harmonics: f 2 = 480 Hz; f 3 = 729; f 4 = 960 Hz and f 5 = 1212 Hz, of the fundamental with frequency f 1 = 244 Hz. The frequencies of the dominant tones radiated by the flat plate as a function of free-stream velocity are shown in Fig. 1 (c). In this figure, a major tone refers to a tone that is clearly visible but lower in amplitude than the peak tone. At flow speeds between U = 8 and 15 m/s, multiple tones are produced by the flat plate. Below U = 8 m/s, only a single tone is visible in the far-field noise spectra. The tonal frequencies in Fig. 1 (c) display a clear ladder-type structure consistent with the results of previous researchers 1,5,6. Paterson et al. 1 found that the frequencies of the discrete tones radiated by airfoils at low angles of attack displayed a dependence on the U 0.8 power law and that the frequency scaling law of U 1.5 described the relationship between the average behaviour of the tonal noise and the free-stream velocity. These scaling laws for an airfoil do 5
not describe the ladder structure of the flat plate tonal noise frequencies in Fig. 1 (c). Instead, the frequencies of the flat plate tones are seen to scale with free-stream velocity according to U 1.25. The discrepancy in the frequency scaling law is attributed to significant differences in the geometry of the NACA 0012 and NACA 0018 airfoils used by Paterson et al. 1 and the flat plate studied here. Fig. 1 (d) shows the amplitude of the peak tonal component as a function of freestream velocity. At very low flow speeds, the amplitude of the peak tone increases with an increase in flow velocity. The intensity of the peak tone reaches a maximum at U = 12 m/s, before decreasing with a further increase in flow speed and becoming undetectable at U = 16 m/s. This trend is again consistent with the findings of others 1,5 suggesting that although the geometry differs, the mechanism studied here is the same as that investigated by previous researchers. To gain further insight into the tonal noise generation mechanism, simultaneous flow and velocity data were measured at the free-stream velocity of U = 15 m/s. Fig. 2 shows spectral maps of the fluctuating velocity measured in the streamwise direction below the lower flat surface of the plate at y/c = 0.0035. High intensity velocity fluctuations are visible at the far-field tonal noise frequencies, f 2 to f 5, both upstream and downstream of the trailing edge. In the wake, an additional high energy peak is observed at the fundamental frequency of f 1 = 244 Hz (see Fig. 2 (b)). This fundamental tone is not observed in either the flow field upstream of the trailing edge or in the far-field noise spectra. The high intensity velocity fluctuations in the wake at the fundamental frequency, f 1, and at the far-field tonal noise frequencies, f 2 to f 5, are attributed to vortex shedding from the trailing edge. Upstream of the trailing edge, the high intensity fluctuations at the tonal noise frequencies, f 2 to f 5, are dominated by acoustic disturbances, as discussed later. Recent studies 6,7 have highlighted the importance of flow separation upstream of 6
the trailing edge in the generation of acoustic tones. The inflectional mean velocity profile in the separated laminar shear layer acts as a tonal selection and amplification mechanism. Many experimental studies on airfoil tonal noise have measured a region of flow separation on the airfoil laminar flow surface upstream of the trailing edge using a variety of techniques including laser velocimetry, hot-wire anemometry and flow visualization 6,13 15. While concerns have been raised over the possible influence of hot-wire measurement techniques on the flow in the vicinity of the separation region 6,7, a comparative study by Brendel and Mueller 13 demonstrated that hot-wire anemometry was as accurate as laser velocimetry in the detection of flow separation. This is on the proviso that the probe is positioned at an angle of less than 10 to the horizontal, as was done here. In this work, the hot-wire probe was kept outside of the separation bubble at all times. Examination of the mean velocity underneath the plate (Fig. 3 (a)) clearly shows a small region of flow separation is located upstream of the trailing edge, very close to the surface of the plate. The velocity is observed to accelerate as it approaches the trailing edge, reach a peak and decelerate, consistent with flow outside of a separation bubble. Only tones at harmonics of the vortex shedding frequency, f 2 to f 5, are visible upstream of the trailing edge and in the far-field noise spectrum suggesting that velocity fluctuations at these frequencies are strongly amplified by the inflectional mean velocity profile in the shear layer associated with the separation bubble as per the mechanism discussed by Nash et al. 6 and McAlpine et al. 7. High amplitude tonal sound is produced as these amplified hydrodynamic fluctuations are diffracted by the trailing edge 16. No high amplitude tone is observed in the far-field noise spectra at the fundamental, f 1, as fluctuations at this frequency are not amplified by the inflectional mean velocity profile in the shear layer. Most previous researchers 2 7 have assumed that T-S waves are responsible for 7
the tonal noise components. For the case of a laminar flat plate boundary layer, the frequencies of unstable disturbances are restricted to the region within the neutral stability curve for Blasius flow. The boundary layer profile was measured below the trailing edge of the flat plate and was found to have a Blasius velocity profile above the small region of flow separation. This indicates that the flow is therefore laminar through the boundary layer on the lower flat surface of the plate upstream of the separation bubble. Fig. 3 (b) shows the neutral stability curve for Blasius flow 12. In this figure, ω is the angular frequency, ν is the kinematic viscosity and Re δ is the Reynolds number based on boundary layer displacement thickness at the trailing edge. The boundary layer displacement thickness was measured to be δ = 0.96 10 3 mm at the trailing edge. The tonal noise frequencies, f 2 to f 5, all lie outside the region of instability, showing that T-S waves should not exist at these frequencies in the laminar boundary layer upstream of the separation bubble. While the fundamental frequency, f 1, does lie within the bounds of the instability region, high intensity velocity fluctuations are not observed at this frequency upstream of the trailing edge. In Fig. 2 (a), an additional high energy peak is visible in the laminar boundary layer upstream of the separation bubble at a frequency of 140 Hz. This high energy peak is believed to be a T-S wave as its frequency sits within the region of instability, as shown in Fig. 3 (b). The frequencies of the tonal noise components in the far-field noise spectra do not correspond to that of the T-S wave indicating that T-S waves are not involved in the tonal noise production process. Fig. 4 shows the coherence and phase difference between the fluctuating velocity measured in the streamwise direction and the far-field acoustic noise at the peak tonal frequency of f 3 = 729 Hz. Phase and coherence measurements at the other far-field tonal noise frequencies, f 2, f 4 and f 5, follow the same trend as those for f 3. Fig. 4 (a) shows that the coherence between the far-field acoustic and velocity 8
signals is at a maximum when the hot-wire is located close to the trailing edge. The coherence plot displays a clear minimum at x/c = 0.1, with the coherence falling to 0.1 at this position. This is observed in the velocity spectra in Fig. 2 (b) as a significant decrease in the amplitude of the velocity fluctuations of f 3 at the point of minimum coherence. Locating the hot-wire at this position has likely disturbed the vortex formation process, resulting in lower amplitude velocity fluctuations at this frequency and thus lower coherence. As the hot-wire moves downstream of x/c = 0.1, the velocity fluctuations at f 3 regain their amplitude as the vortex has formed and continues downstream and the coherence is observed to increase. Far upstream and downstream of the trailing edge the velocity fluctuations at f 3 become almost undetectable and thus low coherence levels are observed at these locations. The spanwise coherence was measured in the very near wake of the trailing edge and showed that highly coherent spanwise vortical structures were present. Even if a vortex is disturbed at its point of formation in the wake by the hot-wire probe or the probe holder, the strong spanwise vortical structures will induce similar fluid mechanics about the plate trailing edge as evidenced by the velocity profile in Fig. 3 (a). Fig. 4 (b) shows that when the hot-wire is located upstream of the separation bubble, the phase difference between the fluctuating velocity and far-field acoustic signals at the peak tonal frequency of f 3 = 729 Hz is nearly constant. This indicates that the acoustic component of velocity is dominant there. The high amplitude velocity fluctuations at the far-field tonal frequencies, f 2 to f 5, measured upstream of separation in Fig. 2 (a) are therefore acoustic disturbances. Acoustic waves are produced at the trailing edge at the selected vortex shedding frequencies of f 2 to f 5 and these acoustic waves are radiated upstream along the lower flat surface of the plate. Both Paterson et al. 1 and Sunyach et al. 17 also detected acoustic waves traveling 9
upstream from the trailing edge inside the boundary layer in their experiments on airfoils in low Reynolds number flow. Downstream of the trailing edge, the phase difference between the fluctuating velocity and far-field acoustic signals varies linearly (see Fig. 4 (b)) indicating the development of strong hydrodynamic fluctuations. It is worth noting, that the authors used similar analysis to that of Tam 2 to investigate the possibility of an aeroacoustic feedback loop between the hydrodynamic fluctuations and the acoustic waves generated at the trailing edge or at a point in the wake. Tam 2 derived equations describing the total phase change around the aeroacoustic loop. In the present study, no aeroacoustic feedback loop was identified that agreed with the phase and coherence information of Fig. 4 or with other experimental observations. The results presented here instead agree with the findings of Nash et al. 6 and McAlpine et al. 7 who suggest that the feedback process is not a necessary condition for the generation of acoustic tones. Recently, Jones et al. 10 identified a feedback mechanism that involves the generation of boundary layer disturbances at the leading edge through acoustic excitation from the trailing edge. This feedback loop was shown to exist only in certain flow conditions 18. It is possible that the present results are an example of flow conditions where the loop cannot be supported. More work is required to experimentally confirm if the new loop proposed by Jones et al. 10 can explain these and previously reported results. 4. Conclusion This paper has presented results of an experimental investigation on the tonal noise generated by a sharp-edged flat plate at low-to-moderate Reynolds number. Experimental results have indicated that in this particular case, the tonal noise generation mechanism appears to be governed by vortex shedding processes at the trailing edge. Velocity fluctuations at the selected vortex shedding harmonics are strongly 10
amplified by the inflectional mean velocity profile in the separated shear layer on the plate laminar flow surface. High amplitude tonal sound is produced when the amplified hydrodynamic fluctuations are diffracted by the trailing edge. Acknowledgments This work has been supported by the Australian Research Council under grant DP1094015 The mechanics of quiet airfoils. References and links 1 R. Paterson, P. Vogt, and M. Fink, Vortex noise of isolated airfoils, J. Aircraft 10(5), 296 302 (1973). 2 C. Tam, Discrete tones of isolated airfoils, J. Acoust. Soc. Am. 55(6), 1173 1177 (1974). 3 M. Fink, Prediction of airfoil tone frequencies, J. Aircraft 12(2), 118 120 (1975). 4 R. Longhouse, Vortex shedding noise of low tip speed, axial flow fans, J. Sound Vib. 53, 25 46 (1977). 5 H. Arbey and J. Bataille, Noise generated by airfoil profiles placed in a uniform laminar flow, J. Fluid Mech. 134, 33 47 (1983). 6 E. Nash, M. Lowson, and A. McAlpine, Boundary-layer instability noise on airfoils, J. Fluid Mech. 382, 27 61 (1999). 7 A. McAlpine, E. Nash, and M. Lowson, On the generation of discrete frequency tones by the flow around an airfoil, J. Sound Vib. 222(5), 753 779 (1999). 8 M. Kingan and J. Pearse, Laminar boundary layer instability noise produced by an aerofoil, J. Sound Vib. 322, 808 828 (2009). 9 S. Wright, The acoustic spectrum of axial flow machines, J. Sound Vib. 45, 165 223 (1976). 11
10 L. Jones, R. Sandberg, and N. Sandham, Stability and receptivity characteristics of a laminar separation bubble on an aerofoil, J. Fluid Mech. 648, 257 296 (2010). 11 D. Moreau, M. Tetlow, L. Brooks, and C. Doolan, Acoustic analysis of flat plate trailing edge noise, in 20th International Congress on Acoustics, ICA 2010 (2010). 12 C. Lin, Theory of hydrodynamic stability (Cambridge University Press, Great Britain) 67 68 (1955). 13 M. Brendel and T. J. Mueller, Boundary-layer measurements on an airfoil at low Reynolds numbers, J. Aircraft 25, 612 617 (1988). 14 S. Yarusevych, J. Kawall, and P. Sullivan, Unsteady separated flow characterisation on airfoils using time-resolved surface pressure measurements, AIAA J. 46(2), 508 516 (2008). 15 S. Makiya, A. Inasawa, and M. Asai, Vortex shedding noise and noise radiation from a slat trailing edge, AIAA J. 48(2), 502 509 (2010). 16 J. Ffowcs Williams and L. Hall, Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane, J. Fluid Mech. 40, 657 670 (1970). 17 M. Sunyach, H. Arbey, D. Robert, J. Bataille, and G. Comte-Bellot, Correlations between far field acoustic pressure and flow characteristics for a single airfoil, in AGARD Conference No. 131, Noise Mechanisms, Paper No. 5 (1973). 18 L. Jones and R. Sandberg, Numerical investigation of tonal airfoil self-noise generated by an acoustic feedback-loop, in 16th AIAA/CEAS Aeroacoustics Conference (2010). 12
List of Figures Fig. 1 Flat plate geometry and corresponding far-field acoustic data: (a) flat plate geometry, (b) far-field acoustic spectra compared to background noise spectra for U = 15 m/s, (c) tonal frequency relationship and (d) amplitude of the peak tonal component. (Color online)...... 14 Fig. 2 Spectral maps of the fluctuating velocity, U, measured in the streamwise direction at y/c = 0.0035 for U = 15 m/s: (a) upstream, and (b) downstream of the trailing edge. (Color online).......... 14 Fig. 3 (a) The mean velocity measured in the streamwise direction at y/c = 0.0035 for U = 15 m/s and (b) the curve of neutral stability for Blasius flow 12. (Color online)...................... 15 Fig. 4 (a) Coherence and (b) phase difference between the fluctuating velocity measured in the streamwise direction at y/c = 0.0035 and the farfield acoustic noise at f 3 = 729 Hz for U = 15 m/s. (Color online). 15 13
(a) LE 12 TE Fig. 1. Fig. 2. 14
Fig. 3. Fig. 4. 15