On the noise reduction mechanism of a flat plate serrated trailing edge at low-to-moderate Reynolds number

On the noise reduction mechanism of a flat plate serrated trailing edge at low-to-moderate Reynolds number Danielle J. Moreau, Laura A. Brooks and Con J. Doolan The University of Adelaide, South Australia, Australia 5005 This paper presents the results of an experimental investigation exploring the noise reduction potential of sawtooth trailing edge serrations on a flat plate at low-to-moderate Reynolds number (1.6 10 5 < Re c < 4.2 10 5 ). Acoustic and aerodynamic measurements have been taken using a flat plate with both sharp and serrated trailing edges in the anechoic wind tunnel at the University of Adelaide. Trailing edge serrations are found to achieve up to 13 db of attenuation in the narrowband noise levels without modifying the directivity of the radiated noise. The noise reduction achieved with trailing edge serrations is found to be dependent on their geometrical wavelength and Strouhal number, St δ = fδ/u, where f is frequency, δ is boundary layer thickness and U is free-stream velocity. Far-field acoustic data are compared with theoretical noise reduction predictions showing that significant differences exist between measurements and theory. Velocity data measured in the very near trailing edge wake with hot-wire anemometry are related to the far-field noise measurements to give insight into the trailing edge serration noise reduction mechanism. The results suggest that for this particular configuration, the noise reduction capability of trailing edge serrations is related to their influence on the hydrodynamic field at the source location. I. Introduction Trailing edge noise is considered to be a major noise source in many aerodynamic applications for which sound production is problematic, such as fans, rotors and propellers, wind turbines and underwater vehicles. 1 3 Brooks et al. 4 classified airfoil self-noise mechanisms into five categories and showed that four of the five noise generation mechanisms are due to fluid-structure interaction at the trailing edge. Other studies 5, 6 have shown that trailing edge noise levels can be reduced by modifying the trailing edge geometry so that flow disturbances are scattered into sound with reduced efficiency. Modifying the trailing edge with the application of serrations has been shown theoretically, 5, 6 numerically 7, 8 and experimentally 3, 9 16 to reduce the trailing edge noise radiated into the far-field. Howe 5, 6 derived an analytical noise radiation model for a flat plate serrated trailing edge in low Mach number flow. According to Howe s 5, 6 theory, trailing edge noise is significantly reduced with the addition of trailing edge serrations due to a reduction in the effective spanwise length of the trailing edge that contributes to noise generation. Howe s 5, 6 theory states that the magnitude of this noise reduction is dependent on the height and geometrical wavelength of the serrations and on the frequency of sound. The sound generated by large eddies whose length scales are greater than the amplitude of the serrations (low frequency sound) is unaffected by the presence of the serrations and hence significant noise reductions are only expected in the high frequency region. A number of experimental studies on trailing edge serrations have examined their effect on full scale wind turbine blades or wind tunnel scale airfoil models at high Reynolds numbers (Re c > 5 10 5, based on chord). 3, 9 14 Oerlemans et al. 3, 12 investigated the reduction of trailing edge noise from a NACA 64418 airfoil and the blades of a full scale 2.3 MW wind turbine by shape optimisation and the application of Postdoctoral Research Associate, School of Mechanical Engineering, danielle.moreau@adelaide.edu.au, AIAA member Lecturer, School of Mechanical Engineering, laura.brooks@adelaide.edu.au, AIAA member Associate Professor, School of Mechanical Engineering, con.doolan@adelaide.edu.au, AIAA Senior member 1 of 20

trailing edge serrations. At high Reynolds numbers (Re c 1.6 10 6 ), optimising the airfoil shape for low noise emission and adding trailing edge serrations achieved an average reduction of 6 db in the radiated noise levels over a variety of flow conditions. Trailing edge serrations applied to the full-scale wind turbine blade were found to decrease noise levels by 3 db at frequencies below 1 khz and increase the noise levels above this frequency without any adverse effect on aerodynamic performance. Gruber et al. 14 examined the noise reduction achieved with sawtooth serrations on a NACA 651-210 airfoil at Reynolds numbers of 2.0 10 5 < Re c < 8.3 10 5 and found that noise reductions of up to 7 db were achieved at low frequencies (< 2 khz) and an increase in noise level was observed at high frequencies. The frequency delimiting a noise reduction and a noise increase was found to correspond to a constant Strouhal number of St δ = 1, where St δ is Strouhal number based on boundary layer thickness. Previous investigations on trailing edge serrations suggest they are a valid means of airfoil self-noise reduction. The mechanism responsible for this noise reduction is, however, still unclear. Howe s model 6 provides some insight into the serration noise reduction mechanism but all experimental studies conducted on trailing edge serrations in the past have reported some discrepancy between their measurements and Howe s theory. In all cases, the predicted noise reduction levels far exceeded those measured. In addition, contrary to Howe s 6 theory, trailing edge serrations on airfoils have been found to produce a noise reduction 3, 10 14 at low frequencies and a noise increase at high frequencies. This suggests that there is a need to further investigate the physical mechanisms by which trailing edge serrations reduce airfoil self-noise. This paper presents the results of an experimental study that explores the noise reduction potential of sawtooth trailing edge serrations on a flat plate at low-to-moderate Reynolds number (1.6 10 5 < Re c < 4.2 10 5 ). This experimental study has relevance to applications employing small sized airfoils such as small scale wind turbines, unmanned air vehicles (UAVs) and computer and automotive fans, all of which operate at lower Reynolds numbers. Acoustic test data have been measured for a flat plate with both sharp and serrated trailing edges in an anechoic wind tunnel. In addition, velocity data about the flat plate trailing edge have been measured using hot-wire anemometry, providing information on the turbulent noise sources. The overall aims of this paper are: (1) to present acoustic and flow data for two different serration geometries at a variety of flow speeds; (2) to compare experimental measurements with theoretical noise reductions predicted using the theory of Howe; 5, 6 and (3) to investigate how serrations affect noise production at the trailing edge. This paper is structured as follows: Section II presents the theoretical background; the experimental method is described in Section III; Section IV presents the experimental results including far-field acoustic data, comparison with the theoretical predictions of Howe 5, 6 and velocity spectra in the wake; and the conclusion is given in Section V. II. Theoretical background Howe 6 derived an analytical model to predict the effect on noise radiation of sawtooth serrations at the trailing edge of a flat plate in low Mach number flow. The acoustic pressure frequency spectrum, Φ(x, ω), of a flat plate with a serrated trailing edge at an observer location a distance x from the trailing edge is given by 6 Φ(x, ω) (ρv 2 ) 2 (l/c 0 )(δ/ x ) 2 = ( Cm π ) ( ) θ sin 2 sin(α)ψ(ω), (1) 2 where ρ is the fluid density, v 0.03U, l is the plate span, c 0 is the speed of sound, δ is the boundary layer thickness, C m 0.1553, θ and α are the polar and azimuthal observer angles respectively, Ψ(ω) is the non-dimensional edge noise spectrum and ω = 2πf, where f is the frequency. The polar and azimuthal observer angles, θ and α, are defined according to the co-ordinate system of Fig. 1. Consider the serrated trailing edge to have a root-to-tip amplitude of 2h and wavelength of λ, as shown in Fig. 2. The non-dimensional edge noise spectrum for the serrated trailing edge is defined as Ψ(ω) = f ( 1 + 1 2 ɛ ɛ ( ωδ, h U c λ, h ) δ ; ɛ = ) f ( ωδ, h U c λ, h ) δ ; ɛ, (2) (1 + 64(h/λ)3 (δ/h) ( cosh(c A + ɛ 2 ) cos(2ωh/u c ) ) ) 1 AB + ɛ 2 ( A + ɛ 2 )(AB + ɛ 2 ) sinh(c A + ɛ 2 ), (3) 2 of 20

where A = (ωδ/u c ) 2, B = 1 + (4h/λ) 2, C = λ/2δ and ɛ = 1.33. For the case when h 0, Eqs. (3) and (4) reduce to the following non-dimensional edge noise spectrum for an unserrated trailing edge Ψ(ω) = A (A + ɛ 2 ) 2. (4) According to Howe s 6 theory, when the acoustic frequency is high such that ωh/u >> 1, the theoretical maximum reduction in radiated mean square pressure is proportional to 10 log 10 [1 + (4h/λ) 2 ] for serrations with a sawtooth profile. The largest noise reductions occur when the dimensions of the serrations are of the order of the turbulent boundary layer thickness and when the angle between the mean flow and the local tangent to the wetted surface is less than 45. This suggests that sharper serrations with a smaller wavelength to amplitude ratio, λ/h, will result in greater noise reduction. z Plate Trailing edge Observer x x y Figure 1: Flat plate co-ordinate system. Flow Plate 2h Root of sawtooth Tip of sawtooth Figure 2: Sawtooth serrations at the trailing edge of a flat plate with root-to-tip amplitude of 2h and wavelength of λ. III. Experimental method Experiments were performed in the anechoic wind tunnel at the University of Adelaide. The anechoic wind tunnel test chamber is 1.4 m 1.4 m 1.6 m (internal dimensions) and has walls that are acoustically 3 of 20

treated with foam wedges to approximate a free environment at frequencies above 250 Hz. The facility contains a contraction outlet that is rectangular in cross-section with dimensions of 75 mm x 275 mm. The maximum flow velocity of the free jet is 40 m/s and the free-stream turbulence intensity is 0.33%. 17 The flat plate model used in this study is composed of a main steel body and a detachable trailing edge plate made from brushed aluminum, as shown in Fig. 3. The main body has a span of 450 mm and a thickness of 6 mm. The leading edge (LE) of the main body is elliptical with a semi-major axis of 8 mm and a semi-minor axis of 3 mm while the trailing edge (TE) is asymmetrically bevelled at an angle of 12. Three 0.5 mm thick trailing edge plates were used (one at a time) as shown in Fig. 4 (a): one with a straight, unserrated configuration and two with serrations. The flat plate model with the straight unserrated trailing edge is used as the reference configuration for all tests and so will be referred to as the reference plate hereafter. Two different serration geometries are compared in this study, both with root-to-tip amplitude of 2h = 30 mm: one with a wavelength of λ = 3 mm (λ/h = 0.2, termed narrow serrations) and the other with λ = 9 mm (λ/h = 0.6, termed wide serrations). As shown in Fig. 4 (b), the root of the serrations is aligned with the trailing edge of the main body so that only the serrated component of the trailing edge plate is exposed to the flow. The area of the reference plate is equivalent to that of the flat plate with serrated trailing edges giving the same effective wetted surface area in all three test cases. The serrated and reference plate models all have the same mean chord of 165 mm. The trailing edge plate is fastened to the main body with 24 M2 0.4 screws. These screws protruded slightly (< 0.4 mm) into the flow below the lower flat surface of the plate model; however, this was consistent for all three plate configurations. Hot-wire measurements within the boundary layer on the lower flat surface of the plate downstream of the screws confirmed that any flow disturbances created at the screws dissipated well before the trailing edge. The method of trailing edge attachment used in this study avoids bluntness at the root of the serrations that may produce vortex shedding and a tonal noise component. The flat plate model was then held between two side plates and attached to the contraction at zero angle of attack as shown in Fig. 4 (b). The span of the flat plate models extends beyond the width of the contraction outlet (see Fig. 4 (b)) to eliminate the noise produced by the interaction of the side plate boundary layers with the model leading edge. Unless otherwise stated, acoustic measurements were recorded at a single observer location using a B&K 1/2 microphone (Model No. 4190) located 554 mm directly below the trailing edge of the reference plate. Hot-wire anemometry was used to obtain unsteady velocity data in the wake of the serrated and reference plate models. A TSI 1210-T1.5 single wire probe with wire length of L = 1.27 mm and a wire diameter of d = 3.81 µm was used in experiments. The sensor was connected to a TSI IFA300 constant temperature anemometer system and positioned using a Dantec automatic traverse with 6.25 µm positional accuracy. The traverse allowed continuous movement in the streamwise (x), spanwise (y) and vertical (z) directions. The co-ordinate system used in this study is shown in Fig. 1. The origin of the co-ordinate system is located at the centre of the trailing edge of the reference plate. Experiments were conducted at free-stream velocities between U = 15 and 38 m/s corresponding to Reynolds numbers, Re c = 1.6 10 5 and 4.2 10 5, respectively. Acoustic and flow data were recorded for each flat plate model using a National Instruments board at a sampling frequency of 5 10 4 Hz for a sample time of 8 s. LE 3 mm 8 mm Main body 12 TE Trailing edge plate 0.5 mm Figure 3: Schematic diagram of the flat plate model. 4 of 20

(a) Trailing edge plates. Top: straight unserrated trailing edge (reference), middle: narrow serrations with λ = 3 mm, bottom: wide serrations with λ = 9 mm. (b) The flat plate model with wide trailing edge serrations held between the side plates and attached to the contraction outlet. Figure 4: The trailing edge plates and the flat plate model in situ. 5 of 20

IV. Experimental results A. Acoustic data 1. Reference plate acoustic spectra The far-field acoustic spectra for the reference plate with a straight trailing edge at free-stream velocities between U = 15 and 38 m/s are shown in Fig. 5. This figure shows a clear trend with broadband noise levels decreasing for a reduction in flow velocity. This is particularly evident at lower frequencies (< 1 khz) where high noise levels are measured. In addition, a broad peak is observed in the noise spectra at high frequencies (at 8.5 khz for U = 38 m/s) and this peak reduces in frequency and amplitude with decreasing flow speed. The high frequency peak observed in the reference plate noise spectra in Fig. 5 is attributed to vortex shedding from the trailing edge. According to Blake, 1 narrowband blunt trailing edge vortex shedding noise is negligible if the trailing edge is sufficiently sharp such that the bluntness parameter t/δ < 0.3 where t is the thickness of the trailing edge and δ is the boundary layer displacement thickness. While the boundary layer properties have not been directly measured in this study, they can be approximated using the expressions for a turbulent boundary layer at zero pressure gradient on a flat plate as follows 18 δ = 8δ, and (5) δ c = 0.37 Re 1/5 c, (6) where δ is the boundary layer thickness and c is the plate chord. Table 1 shows the flat plate boundary layer properties and bluntness parameter calculated using Eqns. (5) and (6) at flow speeds between U = 15 and 38 m/s. As stated in this table, the bluntness parameter t/δ > 0.3 for all free-stream velocities between U = 15 and 38 m/s indicating that narrowband noise contributions due to blunt trailing edge vortex shedding can be expected. The centre frequency, f c, of the vortex shedding peak in the noise spectra (see Fig. 5) and the associated Strouhal number based on trailing edge thickness, St t = f c t/u, are given in Table 2. This table shows that between U = 15 and 38 m/s, the vortex shedding peak occurs at a Strouhal number of between 0.08 and 0.11. This is in agreement with the findings of Herr and Dobrzynski 19 who also reported flat plate blunt trailing edge vortex shedding noise to occur at St t 0.1. Figure 5: Far-field acoustic spectra for the reference plate with a straight trailing edge at flow speeds between U = 15 and 38 m/s. 2. Noise reduction achieved with trailing edge serrations Figure 6 shows the narrowband far-field acoustic spectra for the reference plate and the two plates with trailing edge serrations at free stream velocities of U = 15 and 38 m/s. The background noise spectra 6 of 20

Table 1: Flat plate boundary layer properties between U = 15 and 38 m/s. U, m/s δ, mm δ, mm t/δ 38 4.7 0.53 0.84 35 4.8 0.60 0.82 30 5.0 0.62 0.80 25 5.2 0.64 0.77 20 5.4 0.67 0.74 15 5.7 0.71 0.70 Table 2: Centre frequency, f c, and Strouhal number, St t, of trailing edge vortex shedding noise peak between U = 15 and 38 m/s. U, m/s f c, Hz St t = f c t/u 38 8540 0.11 35 7750 0.11 30 6680 0.11 25 4900 0.10 20 3980 0.10 15 2530 0.08 are also shown in these figures for comparison. Figure 6 clearly shows that both serration geometries are effective in reducing the high frequency trailing edge vortex shedding noise component. Reductions of up to 13 db are achieved at frequencies where trailing edge vortex shedding noise is dominant. (a) U = 38 m/s. (b) U = 15 m/s. Figure 6: Far field acoustic spectra for the reference plate and the plates with trailing edge serrations at U = 15 and 38 m/s compared to background noise levels. For clearer comparison, Figs. 7 and 8 show one-third-octave band spectra for the reference plate and the flat plate with trailing edge serrations at flow speeds between U = 15 and 38 m/s. The one-third-octave band spectra at all flow speeds in Fig. 7 show that the narrow serrations slightly reduce broadband noise levels by up to 2.5 db at low frequencies (R1). In the mid-frequency range, a minor noise increase of up to 3 db is observed with narrow serrations (R2). In the high frequency region, narrow serrations produce a significant noise reduction of up to 10 db in the trailing edge vortex shedding noise component (R3). It 7 of 20

should be noted that in Fig. 7 (e), only a very minor noise reduction of 0.3 db is measured in region R1. The one-third-octave band spectra for the reference plate and the flat plate with wide serrations are shown in Fig. 8. This figure shows that at all flow speeds between U = 15 and 38 m/s, the wide serrations attenuate broadband noise levels by up to 3 db at low frequencies (R1). In the mid frequency range, wide serrations have little affect on the radiated noise with the noise levels of the reference plate and the flat plate with wide serrations being approximately equal (R4). At high frequencies, the wide serrations significantly attenuate the trailing edge vortex shedding noise component by up to 10 db (R3). For both serration geometries in Figs. 7 and 8, the regions of noise attenuation (R1 and R3) reduce in frequency and amplitude with decreasing flow speed. Comparing Figs. 7 and 8 shows that wide serrations outperform the narrow ones by achieving higher levels of low frequency attenuation over a larger frequency range and no noise increase in the mid frequency region. 3. Variation in noise reduction with Strouhal number Figure 9 shows 2D contour plots of the measured attenuation achieved with the trailing edge serrations at flow speeds between U = 15 and 38 m/s. The attenuation in these figures has been calculated by dividing the power spectral density of the serrated plates by that of the reference plate. Three separate regions of noise reduction are identifiable in the attenuation maps in Fig. 9 and each of these regions is bounded by a constant Strouhal number based on boundary layer thickness at the trailing edge, δ. For narrow serrations in Fig. 9 (a): St δ < 0.13 : Region of noise attenuation (R1). 0.13 < St δ < 0.7 : Region of noise increase (R2). 0.7 < St δ < 0.14 : Region of attenuation in the blunt trailing edge vortex shedding noise component (R3). For wide serrations in Fig. 9 (b): St δ < 0.2 : Region of noise attenuation (R1). 0.2 < St δ < 0.7 : Region of equivalent noise levels (R4). 0.7 < St δ < 0.14 : Region of attenuation in the blunt trailing edge vortex shedding noise component (R3). In their experiments on a NACA 651-210 airfoil with trailing edge serrations, Gruber et al. 14 found that for a range of serration geometries (λ/h = 0.1 0.6) the frequency delimiting a noise reduction and a noise increase followed a constant Strouhal number dependency of St δ = 1. This Strouhal number scaling does not describe the trends observed in the flat plate data in Fig. 9. Discrepancies in the Strouhal number scaling is attributed to significant differences in Reynolds number and between the geometry of the airfoil used in the study of Gruber et al. 14 and the flat plate studied here. 4. Noise directivity Figure 10 shows the sound pressure level directivity pattern for the reference plate and the plates with trailing edge serrations at three selected one-third octave band centre frequencies at U = 38 m/s. To obtain these measurements, the microphone was fastened to the traverse arm and the traverse was then used to position the microphone at a number of locations on an arc at a radial distance of 300 mm from the trailing edge of the reference plate. The measurements in Fig. 10 have been corrected to account for shear layer refraction. 20 At the one-third-octave band centre frequency of 0.4 khz, Fig. 10 (a) shows that both serration geometries reduce the noise levels of the reference plate (region R1 in Figs. 7 (a) and 8 (a)) at all angular locations, with the wide serrations outperforming the narrow ones. In Fig. 10 (b) at 2 khz, the wide serrations produce equivalent noise levels to the reference plate (region R4 in Fig. 8 (a)) while a noise increase is observed with the narrow serrations (region R2 in Fig. 7 (a)) at all angular locations. At 8 khz in Fig. 10 (c), both serration geometries significantly attenuate the trailing edge vortex shedding noise component (region R3 in Figs. 7 (a) and 8 (a)) at all angular locations. Figure 10 shows that the trailing edge serrations do not significantly modify the directivity of the radiated trailing edge noise. This was found to be the case at all one-third-octave band frequencies, whether a noise reduction occurred or not. 8 of 20

(a) U = 38 m/s. (b) U = 35 m/s. (c) U = 30 m/s. (d) U = 25 m/s. (e) U = 20 m/s. (f) U = 15 m/s. Figure 7: One-third-octave band spectra for the reference plate and the plate with narrow serrations at U = 15 38 m/s. R1: region of noise reduction, R2: region of noise increase, R3: region of noise reduction in the blunt trailing edge vortex shedding component and R4: region of equivalent noise levels. 9 of 20

(a) U = 38 m/s. (b) U = 35 m/s. (c) U = 30 m/s. (d) U = 25 m/s. (e) U = 20 m/s. (f) U = 15 m/s. Figure 8: One-third-octave band spectra for the reference plate and the plate with wide serrations at U = 15 38 m/s. R1: region of noise reduction, R2: region of noise increase, R3: region of noise reduction in the blunt trailing edge vortex shedding component and R4: region of equivalent noise levels. 10 of 20

(a) Narrow serrations with λ = 3 mm. (b) Wide serrations with λ = 9 mm. Figure 9: Noise reduction achieved with serrations at U = 15 38 m/s. Dashed lines are lines of constant Strouhal number, St δ. R1: region of noise reduction, R2: region of noise increase, R3: region of noise reduction in the blunt trailing edge vortex shedding component and R4: region of equivalent noise levels. 11 of 20

(a) f = 0.4 khz. (b) f = 2 khz. (c) f = 8 khz. Figure 10: Trailing edge noise directivity pattern for the reference plate and the plates with trailing edge serrations at selected one-third-octave band centre frequencies for U = 38 m/s. Dashed circular contours denote the sound pressure level in db. An angular position of 180 relates to a position upstream of the trailing edge at x = 300 mm, y = 0, z = 0, 270 relates to a position directly below the trailing edge at x = 0, y = 0, z = 300 mm and 0 relates to a position downstream of the trailing edge at x = 300 mm, y = 0, z = 0. 12 of 20

5. Comparison with serrations theory Figure 11 shows 2D contour plots of the noise reduction predicted with Howe s 6 theory as presented in Section II for the two different serration geometries used in this study. The predicted attenuation in Fig. 11 has been calculated by dividing the edge spectra of the serrated plates (Eqs. (2) and (3)) with that of the reference plate (Eq. (4)). The oscillations in the theoretical noise reduction map for narrow serrations in Fig. 11 (a) are due to interference between acoustic radiation produced at the root and the tip of the serrations. The experimental measurements in Fig. 9 do not agree with Howe s theory (see Fig. 11) in terms of absolute noise levels or in terms of the variation in noise reduction with flow velocity and frequency. Compared with measured attenuation levels, the theoretical noise reduction predictions are much higher and occur over a much larger frequency range at all flow velocities considered in this study. In addition, some attenuation is measured at low frequencies contrary to Howe s model that predicts noise reductions to occur only at high frequencies (ωh/u >> 1). This is however, in agreement with a number of other experimental studies that 10, 11, 13, 14 have found trailing edge serrations to attenuate low frequency airfoil self-noise. According to Howe, 6 the serration geometry determines the magnitude of the noise reduction. The theoretical maximum attenuation in the radiated mean square pressure is 10 log 10 (1+(4h/λ) 2 ) for serrations with a sawtooth profile. The noise reduction is therefore expected to increase as λ/h decreases. For the narrow serrations with λ = 3 mm, the maximum attenuation is predicted to be 26 db while for the wide serrations with λ = 9 mm, the maximum theoretical attenuation is 17 db. As shown in Fig. 11, narrow serrations are predicted to clearly outperform wide serrations in terms of the level of attenuation achieved at all frequencies and flow speeds. In this study however, wide serrations were found to achieve higher attenuation levels than narrow serrations which actually cause a slight noise increase in the mid frequency range (see Figs. 7-9). While contrary to Howe s 6 theory, this does agree with the experimental findings of 15, 16 who Chong et al. found wider serrations to be the more effective in reducing tonal instability noise at low Reynolds numbers. In deriving the serration noise reduction model, Howe 6 made numerous assumptions and approximations. One such assumption is that the surface pressure frequency spectrum close to the trailing edge is unchanged by the presence of trailing edge serrations. A number of experimental studies have however, shown that this assumption is inaccurate. 11, 13 This may explain the considerable over-prediction of noise reduction observed 10, 11, 13, 14 in this and many other experimental studies. (a) Narrow serrations with λ = 3 mm. (b) Wide serrations with λ = 9 mm. Figure 11: Noise reduction for sawtooth serrations predicted with the theory of Howe 6 at U = 15 38 m/s. Note the differing colorbar scales. 13 of 20

B. Velocity data As the turbulent flow field about the trailing edge is the source of trailing edge noise, velocity measurements in the very near wake of the straight and serrated trailing edges are examined in this section to gain insight into the serration noise reduction mechanism. While velocity measurements are presented at the selected flow speed of U = 38 m/s only, measurements at flow speeds to U = 15 m/s follow the same trend. 1. Velocity spectra Figures 12 and 13 show spectral maps of the fluctuating velocity (u 2 /Hz) measured in the spanwise (y) and vertical (z) directions in the near wake of the plate with straight and serrated trailing edges at U = 38 m/s. The spectra for all three plates in these figures show high energy levels at low frequencies. This corresponds to the high levels of low frequency trailing edge noise measured in the far-field at U = 38 m/s (see Fig. 6 (a)). The high levels of low frequency energy are likely due to eddies or convected flow perturbations in the boundary layer as it negotiates the adverse pressure gradient on the top beveled surface of the plate. This is evidenced by the spectral maps in Figs. 13 (a), (b) and (d) which shows slightly higher energy levels on the top surface of the plates near the trailing edge than in the region below the trailing edge. The spectral maps measured in the spanwise direction in the near wake of the two plates with serrated trailing edges in Figs. 12 (b) and (c) clearly show features that occur due to flow interaction with the serrations. Higher levels of turbulent energy are measured at locations that correspond to the tip of a serrated tooth. This is to be expected as the measurement locations are physically closer to the model at the tip of a serrated tooth, thus are closer to an attached boundary layer and its more energetic, small scale turbulence, compared with measurements taken in the space between two serrated teeth, where the probe is relatively far away from the attached boundary layer and can be considered to be in a wake. Figure 12 shows that the trailing edge serrations affect the flow field in the vicinity of the trailing edge which is the source of the trailing edge noise in Fig. 6 (a). The spectral maps for the reference plate in Figs. 12 (a) and 13 (a) support the theory that vortex shedding at the trailing edge is the source of the broad high frequency peak in the reference plate noise spectra (see Fig. 5). High energy velocity fluctuations at frequencies corresponding to those of the broad peak in the reference plate noise spectra are observed along the span and close to the trailing edge of the reference plate in Figs. 12 (a) and 13 (a) respectively. These high energy velocity fluctuations are however, not observed in the spectral maps for the flat plate with serrated trailing edges (see Figs. 12 (b), (c) and 13 (b) - (e)). This agrees with the noise spectra in Fig. 6 (a) which shows that serrations attenuate the vortex shedding noise component. Trailing edge serrations therefore reduce trailing edge vortex shedding noise by suppressing vortex shedding from the trailing edge. This indicates that trailing edge serrations reduce this trailing edge noise component by changing the behaviour of the hydrodynamic field at the source location. 2. Turbulent length scale Figures 14 and 15 show the streamwise turbulent length scale across the span and in the vertical direction in the near wake of the reference plate and the plates with trailing edge serrations at U = 38 m/s. The turbulent length scale, L u, is a measure of the longest correlation distance between two points in the flow. Assuming frozen turbulence, the turbulent length scale, L u, can be calculated as L u = U R 0 uu (x, y, z, τ)dτ, (7) R uu (x, y, z, 0) where U is the local mean flow velocity and R uu (x, y, z, τ) is the temporal autocorrelation function. Calculating L u using Eq. (7) requires integration of the autocorrelation function over an infinite domain. In practice, the domain of the autocorrelation function calculated from experimental data is finite. The integration domain used here to evaluate the integral length scale is from x = 0 to the first zero crossing of the autocorrelation function. 21 Figures 14 and 15 show that the trailing edge serrations increase the streamwise turbulent length scale along the span at the trailing edge position relative to the reference plate. A significantly higher turbulent length scale is measured in the valley between two serrated teeth compared to at the tip of a serrated tooth. This suggests that large coherent structures are formed in the space between the trailing edge serrations. This is in agreement with the work of Jones and Sandberg 7 who observed horseshoe vortices between serrated 14 of 20

(a) Reference plate at x/c = 0.006. (b) Narrow serrations with λ = 3 mm at x/c = 0.1. (c) Wide serrations with λ = 9 mm at x/c = 0.1. Figure 12: Velocity spectral maps in the wake measured in the spanwise (y) direction from centre span at z/c = 0 at U = 38 m/s. For subfigures (b) and (c), position y/c = 0 corresponds to a serration peak. A position of x/c = 0.006 corresponds to 1 mm downstream from the trailing edge of the reference plate and x/c = 0.1 corresponds to 1 mm downstream from the serrated trailing edge. teeth during direct numerical simulations of the flow around a NACA 0012 airfoil with trailing edge serrations at Re c = 5 10 4. As the wide serrations have a larger wavelength and more space between them to promote growth of these large coherent flow structures it follows that a larger turbulent length scale is measured for the wide serrations than for the narrow serrations. In the vertical direction, Fig. 15 shows that a higher streamwise turbulent length scale is measured in the region above the trailing edge for the trailing edge serrations and in the region below the trailing edge for the reference plate. 15 of 20

(a) Reference plate at x/c = 0.006. (b) Peak of narrow serrations with λ = 3 mm at x/c = 0.1. (c) Valley of narrow serrations with λ = 3 mm at x/c = 0.1. (d) Peak of wide serrations with λ = 9 mm at x/c = 0.1. (e) Valley of wide serrations with λ = 9 mm at x/c = 0.1. Figure 13: Velocity spectral maps in the wake measured in the vertical (z) direction at centre span at U = 38 m/s. A position of x/c = 0.006 corresponds to 1 mm downstream from the trailing edge of the reference plate and x/c = 0.1 corresponds to 1 mm downstream from the serrated trailing edge. 16 of 20

(a) Narrow serrations with λ = 3 mm. (b) Wide serrations with λ = 9 mm. Figure 14: Streamwise turbulent length scale, L u, in the spanwise (y) direction for the trailing edge serrations compared to the reference plate at U = 38 m/s. The reference plate turbulent length scale has been measured at x/c = 0.006, z/c = 0 corresponding to 1 mm downstream from the trailing edge of the reference plate. The turbulent length scale for the trailing edge serrations has been measured at x/c = 0.1, z/c = 0 corresponding to 1 mm downstream from the serrated trailing edge. 17 of 20

(a) Peak of narrow serrations with λ = 3 mm. (b) Valley of narrow serrations with λ = 3 mm. (c) Peak of wide serrations with λ = 9 mm. (d) Valley of wide serrations with λ = 9 mm. Figure 15: Streamwise turbulent length scale, L u, at centre span in the vertical (z) direction for trailing edge serrations compared to the reference plate at U = 38 m/s. The reference plate turbulent length scale has been measured at x/c = 0.006 corresponding to 1 mm downstream from the trailing edge of the reference plate. The turbulent length scale for the trailing edge serrations has been measured at x/c = 0.1 corresponding to 1 mm downstream from the serrated trailing edge. 18 of 20

V. Conclusion This paper has presented results of an experimental investigation of the acoustic and aerodynamic effects of trailing edge serrations on a flat plate at low-to-moderate Reynolds number. Trailing edge serrations were found to minimise broadband noise levels at low frequencies (by up to 3 db at the reference measurement location) and achieve significant attenuation (of up to 13 db at the reference measurement location) of blunt vortex shedding noise at high frequencies without modifying the directivity of the radiated noise. The noise reduction achieved with trailing edge serrations was found to depend on Strouhal number, St δ = fδ/u, and serration wavelength. Theoretical predictions of the noise reductions using the theory of Howe 6 were in poor agreement with experimental data. Contrary to theory, wide serrations with larger wavelength to amplitude ratio, λ/h, were found to outperform narrow ones by achieving higher attenuation levels and no noise increase in the mid frequency region. Unsteady velocity measurements in the very near wake of the straight and serrated trailing edges suggest that for this particular configuration, the noise reduction capability of trailing edge serrations is related to their influence on the hydrodynamic field at the source location rather than on a reduction in sound radiation efficiency at the trailing edge. Acknowledgments This work has been supported by the Australian Research Council under grant DP1094015 The mechanics of quiet airfoils. References 1 Blake, W., Mechanics of Flow Induced Sound and Vibration, Vol. II: Complex flow-structure interactions, Academic Press, New York, 1986. 2 Lockard, D. and Lilley, G., The Airframe Noise Reduction Challenge, Tech. Rep. NASA/TM-2004-213013, NASA Langley Research Center, 2004. 3 Oerlemans, S., Fisher, M., Maeder, T., and Kogler, K., Reduction of wind turbine noise using optimized airfoils and trailing-edge serrations, AIAA Journal, Vol. 47(6), 2009, pp. 1470 1481. 4 Brooks, T., Pope, S., and Marcolini, M., Airfoil self-noise and prediction, Tech. rep., NASA Reference Publication 1218, 1989. 5 Howe, M., Aerodynamic noise of a serrated trailing edge, Journal of Fluids and Structures, Vol. 5(1), 1991, pp. 33 45. 6 Howe, M., Noise produced by a sawtooth trailing edge, Journal of the Acoustical Society of America, Vol. 90, 1991, pp. 482 487. 7 Jones, L. and Sandberg, R., Numerical investigation of airfoil self-noise reduction by addition of trailing-edge serrations, 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7-9 June 2010. 8 Sandberg, R. and Jones, L., Direct numerical simulations of low Reynolds number flow over airfoils with trailing-edge serrations, Journal of Sound and Vibration, Vol. 330(16), 2011, pp. 3813 3831. 9 Dassen, T., Parchen, R., Bruggeman, J., and Hagg, F., Results of a wind tunnel study on the reduction of airfoil self-noise by the application of serrated blade trailing edges, European Union Wind Energy Conference and Exhibition, Gothenburg, Sweden, 20-24 May 1996. 10 Braun, K., Van der Borg, N., Dassen, A., Doorenspleet, F., Gordner, A., Ocker, J., and Parchen, R., Serrated trailing edge noise (STENO), European Wind Energy Conference, Nice, France, 1-5 March 1999. 11 Parchen, R., Hoffmans, W., Gordner, Q., Braun, K., van der Borg, N., and Dassen, A., Reduction of airfoil self-noise at low Mach number with a serrated trailing edge, Sixth International Congress on Sound and Vibration, Copenhagen, Denmark, 5-8 July 1999. 12 Oerlemans, S., Schepers, J., Guidati, G., and Wagner, S., Experimental demonstration of wind turbine noise reduction through optimized airfoil shape and trailing-edge serrations, European Wind Energy Conference, Copenhagen, Denmark, 2-6 July 2001. 13 Gruber, M., Joseph, P., and Chong, T., Experimental investigation of airfoil self noise and turbulent wake reduction by the use of trailing edge serrations, 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7-9 June 2010. 14 Gruber, M., Joseph, P., and Chong, T., On the mechanisms of serrated airfoil trailing edge noise reduction, 17th AIAA/CEAS Aeroacoustics Conference, Portland, Oregon, 5-8 June 2011. 15 Chong, T., Joseph, P., and Gruber, M., An experimental study of airfoil instability noise with trailing edge serrations, 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7-9 June 2010. 16 Chong, T., Joseph, P., and Gruber, M., On the noise and wake flow of an airfoil with broken and serrated trailing edges, 17th AIAA/CEAS Aeroacoustics Conference, Portland, Oregon, 5-8 June 2011. 19 of 20

17 Moreau, D., Brooks, L., and Doolan, C., Broadband trailing edge noise from a sharp-edged strut, Journal of the Acoustical Society of America, Vol. 129(5), 2011, pp. 2820 2829. 18 Cebeci, T. and Bradshaw, P., Momentum Transfer in Boundary Layers, Hemisphere Publishing Corporation, Washington, 1977. 19 Herr, M. and Dobrzynski, W., Experimental investigations in low-noise trailing-edge design, AIAA Journal, Vol. 43(6), 2005, pp. 1167 1175. 20 Amiet, R., Correction of open jet wind tunnel measurements for shear layer refraction, 2nd AIAA Aeroacoustics Conference, Hampton, VA, 24-26 March 1975. 21 O Neill, P., Nicolaides, D., Honnery, D., and Soria, J., Autocorrelation functions and the determination of integral length with reference to experimental and numerical data, 15th Australasian Fluid Mechanics Conference, Sydney, Australia, 13-17 December 2004. 20 of 20