10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV13 Delft, The Netherlands, July 1-3, 2013
High-speed PIV analysis of trailing edge aeroacoustics
Stefan Pr ¨obsting1, Jacopo Serpieri2and Fulvio Scarano1
1Department of Aerodynamics, Delft University of Technology, Delft, The Netherlands s.probsting@tudelft.nl
2Department of Industrial Engineering, University of Naples Federico II, Naples, Italy
ABSTRACT
Tonal noise generated by airfoils observed at low to moderate Reynolds numbers is related to laminar boundary layer instabilities, which has lead to the term laminar boundary layer instability noise. The particular features of the acoustic spectrum have been discussed and a number of theories have been proposed in literature over the past 50 years. Previous research suggests that the appearance of tonal noise is related to a feedback between the acoustic waves scattered at the trailing edge and the receptive part of the boundary layer [4]. Reported studies have been performed on the basis of hot-wire anemometry, laser doppler velocimetry, phase-locked PIV, acoustic measurements, numerical simulations or theoretical models. In recent years, PIV has become an alternative for the investigation of aeroacoustic sources. In particular the aeroacoustic sources for trailing edge noise have been investigated by Schr¨oder et al. [10] using time-resolved PIV and Shannon and Morris [11] based on phase-locked PIV. Nakano et al. [8] focussed on the subject of laminar boundary layer instability noise on an airfoil and related their occurrence on the pressure side to noise emissions based on a correlation based technique.
In the present study, planar high-speed PIV is performed simultaneously with acoustic far-field measurements. This combination allows to associate features of the acoustic emissions to events in the source field near the trailing edge for a better understanding of the tonal noise generation on an airfoil. In the past a wide range of Reynolds numbers has been investigated for different airfoil models, most notably the NACA0012 which is also selected for the present study. In particular, it is found that a periodic amplitude modulation of rapidly growing instabilities on the pressure side of the airfoil is responsible for the occurrence of multiple tones for the present configuration.
Introduction
Tonal noise generated at the trailing edge of airfoils at low to moderate Reynolds numbers remains focus of research since decades. Paterson et al. [9] were first to report the tonal structure of the acoustic pressure power spectrum first, while Chong and Joseph [3] highlight the remaining controversies in a recent contribution. The broadband type spectrum encountered at higher Reynolds numbers is dominated by the interaction of the turbulent boundary layers with the trailing edge, while the tonal noise produced at moderate Reynolds numbers is often associated to the growth and convection of instabilities in the laminar boundary layer for airfoils with a sharp trailing edge. In the past, most studies have focussed on the NACA airfoils and therefore the NACA 0012 is selected for the present study.
For such airfoils at moderate Reynolds number a ”ladder” type acoustic spectrum is observed [9], containing a broadband hump centered at a frequency fsand a set of discrete tones at frequencies fn. The broadband contribution has been shown by Arbey and Bataille[1] to behave similar to the wall surface pressure spectrum and therefore it was suggested that it can be attributed to scattering at the trailing as outlined by models derived from diffraction theory [5]. In their early study, Paterson et al.[9] proposed a scaling rule Eq. 1, where u∞is the free stream velocity, c the chord, and ν the kinematic viscosity.
fs= 0.011u1.5∞ / (cν)
0.5 (1)
[12] proposed a feedback mechanism to explain the existence of the discrete tones and conjectured that instabilities are shed into the wake, some of which are unstable and radiate acoustic waves upstream, disturbing the boundary layer upstream of the trailing edge and thereby closing the loop. [12] points out the following velocity dependence of the discrete tones fn:
fn∼ nu0.8∞ (2)
The above empirical scaling laws show that the main tone frequency is reported to scale with the free stream velocity as fs∼ u1.5∞ , while individual discrete tones scale with fn∼ u0.8∞ . Due to this difference the main tone shifts towards higher orders n of the discrete tones with increasing free stream velocity.
(a) Schematic (not to scale) (b) Photograph Figure 1: Experimental set-up for PIV experiment.
Table 1: Parameters for planar PIV experiments.
Parameters Symbol Value
Field of view FOV 32× 16mm2
Lens focal length f 200mm
Magnification M 0.65 Resolution δx 0.5mm Particle displacement ∆x 15px Acquisition frequency fs 6kHz Number of samples N 6,970 Velocity u∞ 16− 36m/s Angle of attack α 0◦, 1◦, 2◦, 4◦
As pointed out by Morris [7] PIV has become an alternative for the investigation of aeroacoustic in recent years. For the case of trailing edge noise, Schr¨oder et al.[10] performed a study based on time-resolved PIV. Phase-locked PIV provides an alternative for the assessment of the flow field within the active source region and has been applied for instance by Shannon and Morris[11] for noise generated at the blunt trailing edge of a flat plate. Nakano et al. [8] focussed on the subject of boundary layer instability noise on an airfoil by simultaneous PIV and microphone measurements, indicating the relation between the dominating frequency of the noise signal with fluctuations on the pressure side of the airfoil and in its wake. However, spectral data and the dynamics of the flow field in the aeroacoustic source region is not accessible using the phase-locked technique due to the inherent assumption of periodicity. Most studies up to date have been performed on the basis of hot-wire anemometry, LDV, phase-locked PIV, acoustic measurements, numerical simulations or theoretical models. In the current study, the recent approach of combining high-speed Particle Image Velocimetry (PIV) and simultaneous acoustic measurements is followed for the investigation of the flow field and associated acoustic sources and emissions. The objective of the present study is to identify and associate particular features of the flow field with features of the acoustic spectra for a better understanding of the tonal noise generation on an airfoil.
Experimental set-up
Simultaneous acoustic and PIV measurements are performed in a low-speed wind tunnel (V-Tunnel) at Delft University of Technology, an open section low turbulence facility with a circular cross section of diameter 60cm. Since the phenomenon is related to transition facility effects can influence the outcome of the experiment. In a study by Atobe et al. [2] performed in a closed section wind tunnel the discrete tones were found to be locked due to resonance. As will be shown later, such effects could not be identified in the present experiment. The NACA 0012 airfoil of 10cm chord and 40cm span is manufactured from plexiglass and mounted vertically at the center of the test section, 15cm above the nozzle exit. The angle of attack can be adjusted through rotation about the quarter chord point. In order to maintain 2D flow across the span under all angles of attack, plexiglass side plates of diameter 30cm are placed at the ends of the airfoil. Figure 1 shows a photograph of the set-up.
The field of view (approx. 3× 1.4cm2) is focussed center on the trailing edge containing both the airfoil’s pressure and suction surface. Images are acquired at an acquisition frequency of 6kHz (double frame) using a Photron FASTCAM SA1.1 (1024× 1024px2, pixel pitch 20µm) equipped with a Nikkor 200mm prime lens. Illumination is provided by a Quantronix Darwin Duo Nd:YLF laser (2× 25 mJ/pulse at 1kHz) and water-glycol based fog particles with a mean diameter of about 1µm seed the flow. Refraction of the light sheet at the trailing edge of finite thickness causes a shadow region on the suction surface of the airfoil. The pulse separation is adjusted such that the particle displacement in the free stream is approximately equal to 15px.
Two LinearX M51 microphones are positioned symmetrically and perpendicular with respect to the trailing edge at mid span and within the chord plane on opposite sides of the airfoil. Statistical measurements are performed at a sampling frequency of 40kHz for a period of 20s. The measurements are performed over a range of free stream velocities (u∞= 16m/s - 36m/s) and angles of attack (α = 0◦, 1◦, 2◦, and 4◦)in the mid-span plane around the trailing edge. Here, the acoustic results for α= 2◦and flow field results for 24m/s will be presented.
Φ a a [ d B ] f [Hz] 36m/s 32m/s 28m/s 24m/s 20m/s 16m/s 500 1000 1500 2000 2500 3000 3500 0 0 0 0 0 0 30 30 30 30 30 30
Figure 2: Sound pressure level for airfoil at angle of attack α= 2◦and free stream velocity u∞= 16m/s−36m/s. Dashed lines indicate u0.8scaling of the discrete tones with the free stream velocity. Thick lines indicate the dominating tone for each respective velocity.
f c/ u∞ tu∞/c pa /q∞ 62 64 66 68 70 72 74 76 78 80 ×10−3 0 5 10 −2 0 2
Figure 3: Time series and normalised square magnitude of wavelet coefficients of acoustic pressure. u∞= 24m/s, α = 2◦.
The field of view (approx. 3.2× 1.6cm2) is focussed center on the trailing edge, resulting in a transverse magnification of about M= 0.65 and showing both the airfoil’s pressure and suction surface (figure 1). Images are acquired at an acquisition frequency of 6kHz (double frame mode) using a Photron FASTCAM SA1.1 (1024× 1024px2at 5.4kHz, pixel pitch 20µm) equipped with a Nikon Nikkor200mm prime lens operated at a numerical aperture of f#= 4. At such a value of the numerical aperture the particle image diameter is smaller than 1 pixel at the plane of focus, which would lead to large bias errors. Therefore, the plane of focus is slightly shifted away from the illumination plane leading to defocused particle images encompassing approximately 2 pixels and as a result the measurement is not affected by peak-locking errors. Illumination is provided by a Quantronix Darwin Duo Nd:YLF laser (2× 25 mJ/pulse at 1kHz) and water-glycol based fog particles with a mean diameter of about 1µm are used for seeding the flow. Refraction of the light sheet at the trailing edge of finite thickness causes a shadow region on the suction surface of the airfoil. The pulse separation is adjusted such that the particle displacement in the free stream is approximately equal to 15px. Tbl. 1 provides an overview of the planar PIV experiment performed for this study. For image acquisition as well as correlation LaVision DAVIS 8.1 is employed. Images are processed using a multi-pass technique with elliptical windows (2:1) and 75% overlap, resulting in a final window size of approximately 0.5mm . The surface attached coordinate system is defined separately for both sides such that xn indicates the wall-normal location with respect to the surface at the trailing edge and xtindicates the respective tangential coordinate, where the trailing edge is chosen as origin.
Noise emissions
The principal features of the acoustic emission as reported by Chong and Joseph [3] and others for an airfoil at low Reynolds number and angle of attack can be confirmed with the results in the present study. Figure 2 shows spectra of the acoustic pressure measured in the far field, estimated using the coherent output power method (COP)[6] for angle of attack α= 2◦. The spectra are shown for a range
y
/c
x/c
×10
−3×10
−3-200
-150
-100
-60
-40
-20
x/c
×10
−3-200
-150
-100
−100
0
100
Figure 4: Contours of vorticity ωc/u∞during the high amplitude phase (a) and low amplitude phase (b), α= 2◦, u∞= 24m/s.
of free stream velocities between 16m/s and 36m/s and normalised (sound pressure level, SPL). Additionally, the empirical fit based on the relation fn∼ nu0.8∞ (dashed lines) and the dominating tone for each respective velocity is indicated (thick line). Unlike in the study of Atobe et al.[2], who also performed tests in a non-anechoic environment and attributed the deviating behaviour to facility resonance, the tonal frequencies are not constant but follow the dependency reported by others before [9, 3].
For low velocities a number of discrete tones can be observed, showing a strong peak below 1000Hz with an upper harmonic. The upper harmonic of this peak shows side peaks spaced evenly, providing evidence of multiple tones. With increasing velocity this second harmonic starts to dominate, while the energy of the first harmonic is reduced. Comparing to the fn∼ nu0.8∞ scaling rule (dashed lines), the discrete tones can be seen to follow this relation to a good approximation. For the second harmonic, transitions of the main tone to higher order n of the discrete tone can be observed. These transitions are indications for the ladder type structure already observed by Paterson et al. [9]. Thus, both discrete tones and transitions of the main tone can be observed in the present data and are consistent with literature. For the case of α= 2◦at u∞= 24m/s the main tonal frequency is fsc/u∞= 7.71 (1850Hz) and the frequency separation of the side peaks is ∆ f c/u∞= 0.56 (135Hz).
At this point it is of interest to investigate the origin of the discrete tones corresponding to the side peaks of the second harmonic. Wavelet analysis based on the Morlet wavelet[13] reveals the time dependent characteristics of the acoustic pressure fluctuations in the far field (figure 3) presented here for α= 2◦and u∞= 24m/s. The time series shows high frequency oscillations with a period of about ∆tu∞/c = 0.13, corresponding to a frequency of fsc/u∞= 7.71 (1850Hz), which is consistent with the highest peak in the power spectra of acoustic pressure (figure 2). The amplitude of these fluctuations is modulated periodically at at a lower frequency of ∆ f c/u∞= 0.56 (135Hz). Indeed, this periodic amplitude modulation explains the occurrence of multiple discrete tones in the power specturm and has been observed for the noise emitted by an airfoil under similar conditions in a numerical study by Desquesnes et al.[4], who provided an explanation based on a varying phase difference between instability waves passing the trailing edge on the two sides of the trailing edge. However, the particular reasons for this amplitude fluctuation can be manifold and require further investigation of the flow field in the aeroacoustic source region.
Analysis of PIV data
Figure 4 shows two instantaneous visualizations of the spanwise component of vorticity for α= 2◦and u∞= 24m/s. Note that the masked region is due to a shadow over this region originating from the refraction of light at the trailing edge. Figure 4a) shows the flow field around the trailing edge during a period of high amplitude acoustic emissions. The visualization implies that relatively coherent vortical structures on both pressure and suction side of the airfoil might be responsible for these strong emissions. As will be shown later, the saturated vortices on the suction side mostly convect downstream past the trailing edge, while a strong amplification is observed on the pressure side. Consistently, a decreased signal to noise ratio is observed for locations close to the trailing edge on the suction side, which might imply 3D breakdown and therefore out of plane motion of the particles.
During the phase of low amplitude noise emission the vorticity field around the trailing edge appears substantially changed as figure 5b) shows. Convecting vortical structures are barely visible on either side of the airfoil, supporting the hypothesis that an amplitude modulation of the instability waves and their convection past the trailing edge might the source of the multiple discrete tones observed in the spectrum. However, the amplitude modulation implied by these instantaneous visualizations of the flow field requires further analysis. In contrast to the assertion of Desquesnes et al. [4] not only the relative phase of such convecting instabilities on the two sides of the trailing edge, but also their respective strength can be the cause of the amplitude modulation of the acoustic pressure in the far-field.
The power spectrum of the of the wall normal velocity component for u= 24m/s and α = 2◦sampled at xn/c = 0.038 along the surface of the airfoil (figure 5) reveals a similar structure when compared to the spectrum of acoustic pressure (figure 2). In both cases the frequency of the dominating peaks are found at fsc/u∞= 7.71 (1850Hz) and clearly visible side peaks appear with a frequency separation of ∆ f c/u∞= 0.56 (135Hz). As explained before, the occurrence of such symmetric side peaks is a strong indication for a periodic amplitude modulation of the signal. Note however the particular difference between suction side (top) and pressure side (bottom): While no amplification is present on the suction side, indicating a saturated state and dominating convection, the instability waves on the pressure side show a strong amplification towards the trailing edge sustained by the separated flow on this side of the airfoil.
The wavenumber-frequency spectrum of the wall-normal velocity component (figure 6) gives an indication of the propagation velocity associated to the convecting instability waves. This convection velocity is indicated by the slope of the solid line intersecting the maxima
Φ u n un [d B ] −70 −60 −50 −40 −30 xt/c =-0.055 xt/c =-0.027 xt/c =0.017 Φ un un [d B ] 2 4 6 8 10 12 −70 −60 −50 −40 −30
Figure 5: Normalised power spectra of wall normal velocity component unat different locations xt/c on the suction (top) and pressure (bottom) side of the airfoil for u∞= 24m/s. α = 2◦, xn/c = 0.038.
of the energy content for positive wavenumber k. Note that positive wavenumbers are associated to convection in the downstream direction, while the opposite holds true for negative wavenumbers. The dashed lines therefore relate to aliased energy content resulting in upstream travelling waves, which are not physical but yield spurious peaks in the power spectrum. Note the large difference in convection velocity between the suction side (15.4m/s, uc/u∞= 0.63) and pressure side (7.7m/s, uc/u∞= 0.32). For the dominating frequency ( fsc/u∞= 7.71, 1850Hz) these convection velocities provide an estimation of the length scale for the corresponding flow structures, namely uc/ fs= 8.2mm on the suction side and about half, uc/ fs= 4mm, on the pressure side. These estimations match well the wavelength of the clearly identifiable vortical structures in figure 4, and therefore the dominating frequency ( fsc/u∞= 7.71, 1850Hz) can definitely be associated with the frequency at which such structures pass the trailing edge.
The periodogram obtained through wavelet analysis provides information on the time-dependent development of the flow field. Here, the analysis based on the Morlet wavelet[13] is shown for the wall-normal velocity component with u∞= 24m/s (figure 7). The signal on the suction side (top) shows a weak indication of a periodic amplitude modulation, but does not appear to be very coherent. This lack in coherence is possibly due to the 3D breakdown as indicated earlier. On the pressure side, the dominating frequency fsc/u∞= 7.71 (1850Hz) and a near periodic amplitude modulation with a modulation frequency of roughly ∆ f c/u∞= 0.56 (135Hz) can clearly be observed. This periodic amplitude modulation appears in the acoustic pressure (figure 2) and velocity spectra (figure 5) as side peaks of the second harmonic with frequency separation equal to the modulation frequency. Therefore it can be concluded that the instabilities near the trailing edge show a similar periodic amplitude modulation as the acoustic pressure. Furthermore, the strong resemblance of the velocity signal on the pressure side of near the trailing edge with the acoustic pressure in the far-field suggests a strong influence of the pressure side instability on the noise generation mechanism.
15.36m/s k c f c/u∞ 0 2 4 6 8 10 12 −0.4 −0.3−0.2 −0.1 0 0.1 0.2 0.3 0.4 7.68m/s k c f c/u∞ 0 2 4 6 8 10 12 −0.4 −0.3−0.2 −0.1 0 0.1 0.2 0.3 0.4
Figure 6: Wavenumber-frequency spectra of wall normal velocity component unon the suction side (top) and pressure side (bottom). Solid line indicates convection velocity of downstream travelling vortex structures. Dashed line indicates upstream travelling waves due to aliased energy content above the Nyquist frequency. u∞= 24m/s, α = 2◦.
Conclusion
High-speed PIV and acoustic measurements have been performed to investigate the tonal noise generation as well as the related flow structure and aeroacoustic sources on an airfoil profile. Both types of measurements have been performed over a larger range of angles of attack and velocities. The frequency scaling on velocity of individual tones follows approximately the u0.8∞ relation reported in literature for the NACA 0012 airfoil series and evidence of a ladder structure of the acoustic spectrum is found.
At angle of attack α= 2◦and free stream velocity u∞= 24m/s similar features can be observed in the velocity spectra on both pressure and suction side. Tonal peaks in the acoustic spectra are found to coincide with peaks in the power spectra of the velocity fluctuations and their respective frequency. The dominating peak has been associated to the convection of vortical structures past the trailing on both the suction and pressure side with different convection velocities and wavelengths. Symmetric side peaks at a frequency separation of multiples of ∆ f are present in the spectra, indicating a periodic amplitude modulation at this frequency, which has been confirmed through a time-dependent spectral analysis. This amplitude modulation embeds within the concept of a existing feedback loop between the noise generated at the edge and the receptivity region of the boundary layer providing an explanation for the presence of the discrete tones in the spectrum.
Acknowledgments
This research is supported by the European Communitys Seventh Framework Programme (FP7/2007-2013) under the AFDAR project (Advanced Flow Diagnostics for Aeronautical Research). Grant agreement No.265695.
f c/ u∞ tu∞/c un /u ∞ 62 64 66 68 70 72 74 76 78 80 0 5 10 −0.2 0 0.2 f c/ u∞ tu∞/c un /u ∞ 62 64 66 68 70 72 74 76 78 80 0 5 10 −0.2 0 0.2
Figure 7: Time series and normalised square magnitude of wavelet coefficients of wall-normal velocity component unon suction side. u∞= 24m/s, α = 2◦.
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