On the estimation of wall pressure coherence using time-resolved tomographic PIV

Three-dimensional time-resolved velocity field measurements are obtained using a high-speed tomographic Particle Image Velocimetry (PIV) system on a fully developed flat plate turbulent boundary layer for the estimation of wall pressure fluctuations. The work focuses on the applicability of tomographic PIV to compute the coherence of pressure fluctuations, with attention to the estimation of the stream and spanwise coherence length. The latter is required for estimations of aeroacoustic noise radiation by boundary layers and trailing edge flows, but is also of interest for vibro-structural problems. The pressure field is obtained by solving the Poisson equation for incompressible flows, where the source terms are provided by time-resolved velocity field measurements. Measured 3D velocity data is compared to results obtained from planar PIV, and a Direct Numerical Simulation (DNS) at similar Reynolds number. An improved method for the estimation of the material based on a least squares estimator of the velocity derivative along a particle trajectory is proposed and applied. Computed surface pressure fluctuations are further verified by means of simultaneous measurements by a pinhole microphone and compared to the DNS results and a semi-empirical model available from literature. The correlation coefficient for the reconstructed pressure time series with respect to pinhole microphone measurements attains approximately 0.5 for the band-pass filtered signal over the range of frequencies resolved by the velocity field measurements. Scaled power spectra of the pressure at a single point compare favorably to the DNS results and those available from literature. Finally, the coherence of surface pressure fluctuations and the resulting span- and streamwise coherence lengths are estimated and compared to semi-empirical models and DNS results.

[1]  D. Palumbo,et al.  Determining correlation and coherence lengths in turbulent boundary layer flight data , 2012 .

[2]  Jerry Westerweel,et al.  High speed PIV applied to aerodynamic noise investigation , 2011 .

[3]  Joseph Katz,et al.  Instantaneous pressure and material acceleration measurements using a four-exposure PIV system , 2006 .

[4]  M. Gad-el-Hak,et al.  Debate Concerning the Mean-Velocity Profile of a Turbulent Boundary Layer , 2003 .

[5]  Bernhard Wieneke,et al.  Multi-frame pyramid correlation for time-resolved PIV , 2012 .

[6]  Matteo Bernardini,et al.  Wall pressure fluctuations beneath supersonic turbulent boundary layers , 2011 .

[7]  Fulvio Scarano,et al.  PIV-based pressure fluctuations in the turbulent boundary layer , 2012 .

[8]  S. Pirozzoli.  On the size of the energy-containing eddies in the outer turbulent wall layer , 2012, Journal of Fluid Mechanics.

[9]  F. Clauser.  The Turbulent Boundary Layer , 1956 .

[10]  Raf Theunissen,et al.  On improvement of PIV image interrogation near stationary interfaces , 2008 .

[11]  Scott C. Morris,et al.  Shear-Layer Instabilities: Particle Image Velocimetry Measurements and Implications for Acoustics , 2011 .

[12]  S. K. Robinson,et al.  Coherent Motions in the Turbulent Boundary Layer , 1991 .

[13]  Fulvio Scarano,et al.  3D pressure imaging of an aircraft propeller blade-tip flow by phase-locked stereoscopic PIV , 2011 .

[14]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[15]  Bernhard Wieneke,et al.  Tomographic particle image velocimetry , 2006 .

[16]  Bernhard Wieneke,et al.  Volume self-calibration for 3D particle image velocimetry , 2008 .

[17]  Fulvio Scarano,et al.  Multi-pass light amplification for tomographic particle image velocimetry applications , 2010 .

[18]  M. S. Howe.  TRAILING EDGE NOISE AT LOW MACH NUMBERS , 1999 .

[19]  Günter Schewe,et al.  On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow , 1983, Journal of Fluid Mechanics.

[20]  R. Kat,et al.  Instantaneous planar pressure determination from PIV in turbulent flow , 2011, Experiments in Fluids.

[21]  Fulvio Scarano,et al.  Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV , 2011 .

[22]  Tommaso Astarita,et al.  Analysis of weighting windows for image deformation methods in PIV , 2007 .

[23]  R. Amiet.  Noise due to turbulent flow past a trailing edge , 1976 .

[24]  Michel Stanislas,et al.  The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer , 2011 .

[25]  S. Hambric,et al.  Comparison of semi-empirical models for turbulent boundary layer wall pressure spectra , 2009 .

[26]  M. Bull.  Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow , 1967, Journal of Fluid Mechanics.

[27]  Fulvio Scarano,et al.  On the use of time-resolved particle image velocimetry for the investigation of rod–airfoil aeroacoustics , 2012 .

[28]  Julien Christophe,et al.  Application of hybrid methods to high frequency aeroacoustics , 2011 .

[29]  M. Goody.  Empirical Spectral Model of Surface Pressure Fluctuations , 2004 .

[30]  Cameron V. King,et al.  Assessment of pressure field calculations from particle image velocimetry measurements , 2010 .

[31]  Wr Graham,et al.  A comparison of models for the wavenumber-frequency spectrum of turbulent boundary layer pressures (Reprinted from Proceedings of First CEAS/AIAA Aeroacoustics Conference, June, 1995) , 1997 .

[32]  T. Brooks,et al.  Trailing edge noise prediction from measured surface pressures , 1981 .

[33]  M. Bull.  WALL-PRESSURE FLUCTUATIONS BENEATH TURBULENT BOUNDARY LAYERS: SOME REFLECTIONS ON FORTY YEARS OF RESEARCH , 1996 .

[34]  Andreas Schröder,et al.  Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV , 2008 .

[35]  G. Corcos.  The structure of the turbulent pressure field in boundary-layer flows , 1964, Journal of Fluid Mechanics.

[36]  R. Kat.  Instantaneous planar pressure determination from particle image velocimetry , 2012 .

[37]  Sergio Pirozzoli,et al.  Generalized conservative approximations of split convective derivative operators , 2010, J. Comput. Phys..