Experimental setup and data processing

Transcription

1 NEW CPV-RESULTS OF NACA 0012 TRAILING-EDGE NOISE A. Herrig, W. Würz and E. Krämer, S. Wagner Institute of Aerodynamics und Gas Dynamics (IAG), University of Stuttgart, Pfaffenwaldring 21, D Stuttgart, Germany Introduction Quantitative measurement of Turbulent Boundary-Layer Trailing-Edge (TBL-TE) noise in a non-aeroacoustic facility is a delicate task, as the airfoil self noise has to be separated from the typically higher background noise. At the Institute of Aerodynamics and Gas Dynamics (IAG) the Coherent Particle Velocity (CPV) method was developed [1] for two-dimensional airfoil trailing edge (TE) noise measurements in wind tunnels with high aerodynamic quality, which however often show high background noise levels. It is therefore specifically suited for aeroacoustic validation of low-noise airfoil sections under well defined aerodynamic boundary conditions. Cross-correlation of two hot-wire signals is used to measure the Coherent Particle Velocity of the sound waves. The setup can be compared to the Coherent Output Power (COP) method developed by Hutcheson and Brooks [2]. First CPV experiments were performed on a symmetric 4.2% thick flat plate like airfoil (c = 0.5 m) at zero angle of attack. This represents some benchmark case due to the low noise emission in comparison to practical airfoil sections. Subsequently the CPV-method was successfully applied for the validation of cambered wind turbine airfoils in the SIROCCO [3] project. In addition comparisons of CPV results to phased acoustic array measurements showed good agreement [4,5]. CPV-measurements on NACA 0012 airfoil sections have been performed [6] with the intent to validate absolute sound pressure levels in comparison to published results [7, 8]. The present paper concentrates on analysis of proven scaling laws applied to the measured data in order to obtain more insight into the ranges of applicability of the CPV method. In addition a background noise (BGN) correction scheme is proposed, extending the range of valid data to lower frequencies. Experimental setup and data processing LWT wind tunnel environment and airfoil sections The experiments were carried out in the Laminar Wind Tunnel (LWT) of the IAG. The LWT is an open return tunnel of Eiffel type. The test section is closed and has a rectangular m 2 shape and is 3.15 m long. The models span the short distance vertically and the gaps to the tunnel walls are sealed. A longitudinal turbulence level of about Tu x = could be determined with hot-wire measurements in the frequency range of Hz at U = 30 m/s. In the frequency range below 250 Hz the dominating part of the disturbances is of acoustic nature. This could be shown by correlation measurements with two hot-wires, traversed transversally. For frequencies of interest (>50 Hz) the turbulent longitudinal velocity fluctuations are correlated in the cross-flow direction over less than 15 mm. Despite the LWT is very well suited for aerodynamic measurements, it is not optimal for acoustic measurements. The fan is located 12 m downstream in the diffuser and in straight line to the test section. No acoustical damping measures are applied. An overall sound pressure level of L p = 94 db(a) at 60m/s was measured in-flow using a 1/2 B&K type 4190 microphone with standard nose cone. For the present tests NACA 0012 sections with three different chord lengths A. Herrig, W. Würz and E. Krämer, S. Wagner

2 Section I c=[0.2,0.4,0.6] m were manufactured. The hollow models are made from 6 mm thick GFRP shells built in CNC machined negative moulds. The surface of the models is polished to provide a typical remaining roughness height below 1.5 µm. The first set of airfoils was built according to the original NACA 0012 coordinates, which implies blunt trailing edges. The TE thicknesses realized were h=[0.42,1.02,1.45] mm. Later, to avoid the occurrence of blunt trailing-edge (BTE) noise, a second section with 0.4 m chord was built, which had a nearly sharp TE of 0.22 mm and also was equipped with pressure taps. The model with 0.6 m chord was extended by a small wedge of plastic material, sanded flush to the contour to obtain a TE thickness of <0.03 mm. The 0.2 m model didn t show significant BTE noise, so it was not necessary to build an additional one. Most of the tests were performed at U=60 m/s, corresponding to Ma and Re [0.8,1.6,2.4]x10 6, at zero degrees angle-of-attack. Measurement arrangement for CPV-method Two 45 degree slanted hot-wires (Dantec P12, 2.5 µm x 1.4 mm platinum-plated tungsten wires) are placed in one plane vertical to the trailing edge at a lateral distance of typically y = ±85 mm (Fig. 1), which is a multiple of the boundary layer thickness, and approximately 45 upstream of the TE. The wires are mounted in front of carbon tubes with about 0.7 m length, which are fixed to two streamlined stems and provide access to the mid-span of the model (Fig. 2). Fig. 1: Schematic of CPV setup, not to scale (above). Fig. 2: CPV setup in the test section of the LWT (left). The wake of the airfoil can pass between the stems. Dantec 55M10 CTA-bridges drive the hotwires at an overheat ratio of 1.8. The anemometers are adjusted for an almost flat frequency response up to a cut-off frequency of roughly 120 khz, determined from the response to step excitation by voltage injection. The signals are AC-amplified by AMI-321A ultra low-noise amplifiers (1 nv/hz 0.5 equiv. input noise) with a gain of 1,000. The 200 Hz high-pass behaviour of the amplifiers is used as a preemphasis filter to improve the dynamic range and is corrected later. Final AD-conversion is done by a 24 bit audio-system (RME-Hammerfall DSP) at a sampling rate of 44.1 khz per channel. The Σ- converters with 64 over-sampling provide excellent anti-aliasing filtering at half the data rate. Due to the large distance between the wires and their separation by the airfoil section, the influence of coherent parts in the signals resulting from wind tunnel turbulence and turbulent boundary layer (TBL) vortices is significantly reduced. Remaining coherent signals are therefore mainly due to acoustic particle velocity fluctuations. The strongly non-isotropic directional sensitivity of the wires (extended cosine law [9]) is exploited to improve the signal-to-noise ratio (SNR), which is the main advantage of using hot-wire sensors over omni-directional microphones. The wires are positioned such that reception of the airfoil noise is maximized, but background noise approaching from downstream is damped by 3 db. 2

3 Data processing and analysis Continuous time traces of 7 min were recorded and processed by fast Fourier transform of 4096 point blocks. The cross spectrum G 12 is calculated from the Fourier coefficients of the two simultaneous streams 1, 2 and averaged over the whole record length of n 4500 blocks [10]: G 1 ( f = (1) ϕ f ) = arctan(im( G 12 ) / Re( G )) (2) n * [ X 1, k ( f ) X 2, k ( f ] 12 ) ) n k = 1 ( 12 The cross-spectral analysis allows detection of TBL-TE noise because of its dipole characteristic. An observed 180 phase relationship of the radiated sound field on the two airfoil TE sides indicates its dominance over coherent background noise, which mainly shows up with nearly 0 phase difference. The cross-correlation allows a suppression of the incoherent noise, which is caused by the electronic noise of the hot-wire bridges or spurious random sound waves. For obtaining quantitative values of the far-field sound pressure, first the sensitivity of the hot-wires to velocity fluctuations U/ E is obtained from a one-point in-situ calibration. To compensate outliers caused by short-time ambient temperature changes during this procedure, sensitivity is also obtained by calibration constants determined from an empirical Nusselt relation [9]. The influence of the airfoil section on the local velocity at the wires is taken into account by XFOIL [11] calculations. Pollution of the wires is a serious problem, which can lead to a reduction of the frequency response for higher frequencies, not showing up in the static sensitivity. Because cleaning of the thin wires is hardly possible, regularly replacement solves this problem. Next a simulation of the response of the whole CPV system to the TE line source is performed. Incoherent point sources are uniformly distributed along the trailing edge and their particle velocity contributions at the position of the wires are added up. This way the non-isotropic sensor response, the near-field distance scaling and the source directivity are corrected. Sound pressure p is obtained from particle velocity v by the radial impedance p = Z R v a source model (monopole (epn. 3), dipole (eqn. 4), ) must be chosen here. Z R, mon. ic0 ic0 c0 c0 = ρ0c0 /( 1 ) (3) Z,. = 0 0( 1) /(2 2i 1) ωr ρ R dip c ωr ωr ωr (4) For the present investigations monopoles were selected like in all previous analyses, because better agreement to theoretically predicted spectra was found. The convection of the sound waves causes a retardation of the effective hot-wire position, which is also taken into account [7]. The results are finally given as the sound pressure level L p produced by a trailing edge of L=1 m at a distance of r=1 m and an observer placed at a reference angle of θ=90 to the TE. In principle the fluctuating voltage signal is composed of contributions from density, temperature and pressure fluctuations Eρ ρ E E p TT p E = Evv (5) Evv Evv Evv According to Davis [12] it is possible to choose a wire temperature so that the three terms on the right cancel each other and the velocity fluctuations indicated by the wire correspond to the true particle velocity fluctuations in a plane acoustic wave. For velocities of 60 m/s this results in an overheat ratio of about 1.7. Unfortunately, Davis presented only results for a 5 µm, 1.96 mm long 3

4 wire operated at a=2.26 and there is no direct relation for transfering the result to a 2.5 µm x 1.4 mm wire. The main unknown is the change of the sensitivity to pressure, which is influenced by the Knudsen number Kn being the ratio of molecular mean free path to wire diameter. With the larger Kn of the thinner wires the pressure term is expected to rise, which would mean that the measured velocity fluctuations are somewhat too high. So in the experiments a might be chosen too large, but it reduces the sensitivity to temperature fluctuations from the ambient air on the other hand. The influence of a phase shift between v and p in the acoustic near field still is to be investigated. Boundary-layer measurements To verify values for the displacement thickness δ 1 subsequently used in noise scaling relations, hot-wire measurements 1 mm downstream of the TE were performed for chord-based Reynolds numbers [1.0,1.3,1.5,1.6,1.7]x10 6 on the 0.4 m section with nearly sharp TE. The model was equipped with 62 pressure taps and angle of attack was adjusted for achieving a symmetric pressure distribution with the hot-wire traverse installed. The BL profiles measured with a single-normal hotwire (Fig. 3) were processed to derive integral BL parameters and fluctuation spectra. The obtained δ 1 -values are in good agreement to XFOIL [11], with a trend to slightly higher values. Brooks [7] values obtained with a heavy trip, i.e. sandpaper of #60 grit from the LE to x/c=0.2, are significantly larger, because the turbulent boundary layer is additionally thickened. The light trip values of δ 1 obtained as 60% of the heavy trip values however are noticably smaller. The clean data match relatively well at Re=1.5e6. Fig. 3: Measured boundary layer profiles 1 mm downstream of TE for various Reynolds numbers (left). Comparison of displacement thickness to data from BPM [7] and predictions using Xfoil (right). Discussion of acoustic results Narrow-band spectra In Fig. 4 an example CPV measurement is shown. The auto-spectra of the two hot-wires are shown as dotted lines (basically identical), the cross-spectrum as solid line. Airfoil noise clearly dominates for frequencies from 1 to 6 khz, visible from the phase difference (circles) of

5 Fig. 4: Measured single and cross-spectra (lines) and phase difference (circles) for 0.4 m NACA 0012 at zero angle of attack. On the low-frequency end the background noise level dominates over the airfoil noise and the phase difference tends to zero. On the high-frequency side typically coherence of the signals is reduced due to domination of incoherent electronic noise, which makes the phase difference become random. This upper limit of measurement frequency range is influenced by signal-to-noise ratio and can be improved with increased averaging time. For selection of valid third-octave bands originating from TE noise a phase threshold of ϕ(f) 2.2 rad for more than 80% of the narrow band points was defined. Background noise correction The presence of coherent background noise G BG leads to a reduction of the measured spectrum G 12 compared to the true TE noise G TE. This is illustrated in Fig. 5. In particular around the crossover frequency f CO, where G BG and G TE intersect, the noise components cancel each other as the complex phasors are pointing in the opposite direction. The reason why there is no exact zero at f CO is, that also other signal components and a noise floor are present, causing a non-zero amplitude. To correct G 12, it is necessary to estimate the BGN, which unfortunately is unknown at f >f CO. Possibilities to estimate G BG include: a) Empty test section CPV measurements for each flow velocity. However the BGN will be changed removing the model and accuracy is not necessarily high. b) Establishing a universal model from microphone BGN measurements L p,bg(b&k) (f). A simple approach is L p,bg(theo) = L p0 + K 1 log10(u) + K 2 log10(f). Fig. 6 shows, that it fits the measured levels quite well in the range 500 Hz f 2000 Hz. However for direct application for all velocities this approach alone is too inaccurate. c) Extrapolating G 12 from f<f CO, where it mainly contains BGN, to higher frequencies. This can be done by a model like in b) or by shifting the measured BGN spectra of a) or b) to match G 12 at a low frequency. In practice the lower branch levels are often influenced by other coherent signal contributions than pure BGN. E.g. it could be shown by Laser Scanning Vibrometry, that the hotwire mounting tubes are subject to vibrations. So the frequency from where the BGN is extrapolated must be chosen carefully. 5

6 f CO Fig. 5: Correction of measured TE noise spectrum by adding extrapolated background noise phasor, that otherwise leads to reduced spectral levels. Fig. 6: Example of BGN correction. Third-octave band levels are raised slightly, in particular on the lowfrequency side. A mix of b) and c) is used in the present approach to increase accuracy and it is worked on the basis of third-octave band levels. For each CPV measurement the average of L p,bg(theo) and L p,bg(b&k) shifted to match L p,12 at f=200 Hz is evaluated at the lowest valid third-octave band frequency (as an approximation for f CO ) to obtain a more reliable estimate of the background noise L p,bg *. Compare Fig. 6. The BGN corrected sound pressure levels are then calculated as: P, corr L, / 10, / 10 ( p m L p BG + 10 ) L = 10 lg 10 (3) Scaling of TE noise third-octave spectra To validate applicability range of the CPV method, investigations on the nondimensionalisation of third-octave SPL spectra were performed for three different chord lengths and velocities of [40,50,60,70] m/s. This should capture possible effects of chord length and variable background noise level, i.e. signal-to-noise ratio. The results for the test cases at α=0 are shown in Fig. 7 (left), exhibiting the expected level staggering with velocity. With increasing chord length the maxima shift to lower frequencies, but only a minor increase in level occurs. Considerable BTE noise contributions at frequencies of about 2-5 khz are visible for the 0.4 and 0.6 m airfoil sections with blunt TE (dashed lines), becoming higher for the larger chords as the bluntness parameter h/δ 1 [7] increases. For the sharp sections these humps disappear practically completely, h/δ 1 values drop below 0.1. For comparison, latest data from the Aeroacoustic Windtunnel Braunschweig (AWB) [8] for a sharp-te NACA 0012 with 0.4 m chord and zig-zag tripping at x/c=0.1 are plotted in Fig. 7 (right). An elliptic mirror directional microphone system was used for these measurements, applying corrections for frequency dependend gain and shear layer influence. Conversion to the same level basis db/m (r=1m) required adding 2.18 db to correct for the different reference TE length of 0.8 m and observer distance of 1.15 m. The absolute levels match very well around the maxima. From a CPV study of the effect of tripping position it is known, that sensitivity of TBL-TE noise spectra to trip parameters is significant. Using the CPV method a comparison between the two trippings was performed at α=0. It showed, that the more downstream trip position in the AWB leads to approximately 0.5 db reduction of the spectral maximum, which is very much in line with the observed differences and the sligthly smaller decay of the AWB measurements to higher frequencies. 6

7 The presence of BTE noise occuring for the blunt-te 0.4 m model is more clearly visible in Fig. 7 (right). With h/δ 1 increasing from 0.35 to 0.39 the BTE contributions change from a relatively undefined broadband hump to a more clearly separated hump at a flow speed of 60 m/s. In case of the blunt TE a small reduction of peak levels seems to occur in the frame of the given measurement accuracy. An explanation could be slightly smaller boundary layer displacement thicknesses at the TE due to the less adverse pressure gradients. At least XFOIL calculations show a reduction of δ 1 of 10% at the TE and 5% at x/c=0.986, which could be responsible for db change in level. Fig. 7: Comparison of measured NACA 0012 third-octave spectra from LWT (left) for the three chord lengths and various velocities; α=0, 2d trip 0.36 x 1.5 mm at x/c=0.05. Blunt model produces BTE noise humps around 3-5 khz, not present for the sharp-te section. Right: Comparison to AWB measurements (sharp TE) shows good agreement. The collapse of CPV data scaled with the measured boundary layer displacement thickness δ 1 is shown in Fig. 8. The most commonly assumed dependency of radiated TBL-TE sound pressures in the acoustically non-compact frequency range, p²~u 5 δ 1, has been applied, with δ 1,ref taken for the 0.4 m model at 60 m/s. For completeness the BTE noise spectra are also plotted. The agreement in the range of the maximum SPL is not particularily good, the spectra seem over-corrected for the different chords. However it cannot be expected, that this simple scaling approach, neglecting detailed information on the distribution of turbulent fluctuations in the boundary layer profiles, is very accurate. Comparison to theoretical predictions of TBL-TE noise with the semi-empirical XEnoise code based on EDDYBL, which was developed at IAG [13], in Fig. 8 shows that the observed spread of the levels can indeed be expected. Only in the low-frequency region below ωδ 1 /U = 0.2, where according to Blake [14] the surface pressure fluctuations are dominated by the wake region of the BL profile, the outer variable scaling collapses the theoretical spectra to one line. Unfortunately reliable CPV data could not yet be obtained here, especially for the larger chord lengths, because background noise levels are too high. Inner variable scaling with the viscous length scale ν/uτ based on the shear velocity becomes appropriate for higher dimensionless frequencies ωδ 1 /U > 2 only and scaling with this length scale 7

8 leads to some satisfactory collapse of the theoretical spectra at the high frequency end (not shown), supporting the apparently early drop of the 0.2 m spectra. Again according to Blake, the surface pressure fluctuations in the region around the spectral maximum are more controlled by the log-law layer of the BL profile close to the wall. So it seems, that displacement thickness is not the optimal estimate for the length scales responsible for the region around the maximum level. Fig. 8: Measured third-octave spectra scaled on (U,δ 1 ) compared to predictions using IAG s XEnoise code. Including δ 1 in the level scaling, the groups of different chord are spread slightly in the region of the maximum, but collapse in the low frequency region. Conclusions A hot-wire based CPV-method is presented for the measurement of trailing edge noise in noisy aerodynamic wind tunnels. For two-dimensional airfoil sections the measurement of absolute sound pressure levels, due to a detailed sensitivity analysis of the setup. A simplified approach for the correction of amplitude biases caused by the presence of coherent background noise contributions is applied. The experimental procedure, including the necessary theoretical approach for obtaining quantitative noise spectra, is validated by analysis of known scaling relations of measured TE noise spectra from NACA 0012 sections. The observed spread of levels for the different chords is in line with theoretical predictions taking into account the detailed turbulence properties in the BL profiles. Comparison of CPV data to independent elliptic mirror measurements in the AWB shows very good agreement of absolute levels and spectral shape. 8

9 Acknowledgements The author would like to thank the German Research Council (DFG) for funding the further investigation of the CPV method. Further thanks go to M. Herr from the Institute of Aerodynamics and Flow Technology, Braunschweig, for providing NACA 0012 reference data from their aeroacoustic facility. REFERENCES 1. Würz W., Guidati S., Herrig A., Lutz Th., Wagner S. Measurement of Trailing Edge Noise by a Coherent Particle Velocity Method, ICMAR 2004, , Novosibirsk 2. Hutcheson F.V. and Brooks T.F. Measurement of Trailing Edge Noise using Directional Array and Coherent Output Power Methods, AIAA-paper , 8th AIAA/CEAS Aeroacoustics Conference 3. Schepers J.G. et al. Sirocco: Silent rotors by acoustic optimization, Contribution to the 2 nd International Meeting on Wind Turbine Noise, September 20-21, Herrig, A., Würz, W., Lutz, T., Braun, K., Krämer, E., and Oerlemans, S. Trailing Edge Noise Measurements of Wind Turbine Airfoils in Open and Closed Test Section Wind Tunnels, First International Meeting on Wind Turbine Noise: Perspectives for Control, Berlin, Germany, Herrig A., Würz W., Lutz T., Braun K., Krämer E. Trailing-Edge Noise Measurements Using a Hot-Wire Based Coherent Particle Velocity Method, AIAA , 24th Appl. Aerod. Conf., June, Herrig A., Würz W., Lutz T., Krämer E., Wagner S. Trailing-Edge Noise Measurements of a NACA 0012 Airfoil using the Coherent Particle Velocity Method, Int. Conf. on Methods of Aerophysical Research ICMAR 2007, Novosibirsk, Russia, February 5-10, Brooks T.F., Pope D.S., Marcolini M.A.: Airfoil Self-Noise and Prediction. NASA RP-1218, Herr M. Design Criteria for Low-Noise Trailing-Edges, AIAA , 13 th AIAA/CEAS Aeroacoustics Conference, Rome, Italy, May 21-23, Bruun, H. H. Hot-Wire Anemometry: Principles and Signal Analysis, Oxford University Press, Oxford OX2 6DP, Bendat, J. S. and Piersol, A. G. Random Data, Analysis and Measurement Procedures, John Wiley & Sons Inc., 3 rd ed., Drela M. XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils, In: "Low Reynolds Number Aerodynamics (Conference Proceedings)", pp. 1-12, ed. T. J. Mueller, June, Davis M. R. Hot Wire Anemometer Response in a Flow with Acoustic Disturbances, Journal of Sound and Vibration, Vol. 56, No. 4, 1978, pp Lutz Th., Herrig A., Würz W., Kamruzzaman M., Krämer E. Design and wind tunnel verification of low noise airfoils for wind turbines, AIAA journal, Vol 45, No. 4 pp , April Blake W.K. Mechanics of Flow-Induced Sound and Vibration, Vol. I, II. Academic Press Inc., NY, 1986 A. Herrig, W. Würz and E. Krämer, S. Wagner