A simulation-based analysis of the effect of a reflecting surface on aeroacoustic time-reversal source characterization and comparison with beamforming

Abstract This paper presents a simulation-based analysis of the effect of a reflecting surface on aeroacoustic Time-Reversal (TR) source localization/characterization and compares the results of TR with those obtained using cross-spectral Conventional Beamforming (CB). The TR technique is shown to require the use of at least two line arrays of microphones to accurately characterize the nature of aeroacoustic sources. This work, however, shows that in the presence of a rigid surface, only one line array of microphones is sufficient to accurately localize and characterize idealized aeroacoustic sources. Forward simulations were carried out using the 2-D Linearized Euler Equations on a rectangular domain with a rigid bottom boundary (modeling a 2-D semi-infinite space) for the test-cases of stationary idealized tonal aeroacoustic (monopole, dipole and lateral quadrupole) sources located in a fully-developed mean shear flow field wherein the acoustic pressure time–history was stored at the computational boundaries. A set of TR simulations are implemented that show for each test-case that only the top line array is required to accurately characterize the idealized aeroacoustic sources in the presence of a reflecting bottom boundary, thereby suggesting the redundancy of acoustic pressure measurement at the rigid surface. The test-case of convecting (moving) idealized aeroacoustic source was also considered and the TR simulation using only the top line array in the presence of reflecting bottom boundary was able to accurately retrieve the source trajectory and simultaneously characterize its nature. This numerical experiment demonstrates in principle that when a rigid surface is mounted on the floor of an Anechoic Wind Tunnel, the use of only one (top) line array of microphones should be sufficient to characterize the nature and location of experimental flow-induced noise source. Acoustic source maps were also obtained using the CB method based on the Method of Images (to model the reflecting surface) and incorporation of the Ray-Tracing algorithm necessary to account for the effect of mean flow. The CB results were found to be highly comparable to those obtained using TR for the test-cases of non-convecting sources; thereby demonstrating the conceptual equivalence of the Method of Images and directly implementing the rigid-wall condition during TR for source localization/characterization.

[1]  C. Burrus,et al.  Array Signal Processing , 1989 .

[2]  Allan D. Pierce,et al.  Acoustics: An Introduction to Its Physical Principles and Applications , 1981 .

[3]  Thomas Padois,et al.  Experimental localization of an acoustic sound source in a wind-tunnel flow by using a numerical time-reversal technique. , 2012, The Journal of the Acoustical Society of America.

[4]  Dan Givoli,et al.  Time Reversal as a Computational Tool in Acoustics and Elastodynamics , 2014 .

[5]  Jr William M. Humphreys,et al.  Design and Use of Microphone Directional Arrays for Aeroacoustic Measurements , 1998 .

[6]  A. Mimani,et al.  Enhancing the Resolution Characteristics of Aeroacoustic Time-Reversal Using a Point-Time-Reversal-Sponge-Layer , 2014 .

[7]  G. Lerosey,et al.  Time reversal of electromagnetic waves. , 2004, Physical review letters.

[8]  Pierre Sagaut,et al.  Localization of aeroacoustic sound sources in viscous flows by a time reversal method , 2013 .

[9]  A. Mimani,et al.  An experimental application of aeroacoustic time-reversal to the Aeolian tone. , 2016, The Journal of the Acoustical Society of America.

[10]  R. Amiet,et al.  Correction of open jet wind tunnel measurements for shear layer refraction , 1975 .

[11]  Mickael Tanter,et al.  Time-reversed acoustics , 2000 .

[12]  Fei Liu,et al.  Shear Layer Correction Validation Using A Non-Intrusive Acoustic Point Source , 2010 .

[13]  Derode,et al.  Limits of time-reversal focusing through multiple scattering: long-range correlation , 2000, The Journal of the Acoustical Society of America.

[14]  Damiano Casalino,et al.  A rod-airfoil experiment as a benchmark for broadband noise modeling , 2005 .

[15]  H. Ochi,et al.  Long-range time reversal communication in deep water: experimental results. , 2012, The Journal of the Acoustical Society of America.

[16]  Depth and range shifting of a focal spot using a time-reversal mirror in an acoustic waveguide , 2002 .

[17]  M Fink,et al.  Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink. , 2002, Physical review letters.

[18]  Con J. Doolan,et al.  A sponge-layer damping technique for aeroacoustic Time-Reversal , 2015 .

[19]  A. Mimani,et al.  Experimental Application of Aeroacoustic Time-Reversal , 2015 .

[20]  Arnaud Derode.  NUMERICAL AND EXPERIMENTAL TIME-REVERSAL OF ACOUSTIC WAVES IN RANDOM MEDIA , 2001 .

[21]  Takao Suzuki.  A review of diagnostic studies on jet-noise sources and generation mechanisms of subsonically convecting jets , 2010 .

[22]  Con J. Doolan,et al.  Enhanced focal-resolution of dipole sources using aeroacoustic time-reversal in a wind tunnel , 2016 .

[23]  Pierre Sagaut,et al.  Pseudo‐characteristic formulation and dynamic boundary conditions for computational aeroacoustics , 2007 .

[24]  M. Fink,et al.  Time reversal of water waves. , 2012, Physical review letters.

[25]  Mathias Fink,et al.  One-channel time-reversal in chaotic cavities: Theoretical limits , 1999 .

[26]  K. Viswanathan.  Aeroacoustics of hot jets , 2002, Journal of Fluid Mechanics.

[27]  A. Majda,et al.  Radiation boundary conditions for acoustic and elastic wave calculations , 1979 .

[28]  M. Fink,et al.  Subwavelength sound focusing using a time-reversal acoustic sink , 2007 .

[29]  A Mimani,et al.  Multiple line arrays for the characterization of aeroacoustic sources using a time-reversal method. , 2013, The Journal of the Acoustical Society of America.

[30]  Laura A. Brooks,et al.  The effect of boundary layer type on trailing edge noise from sharp-edged flat plates at low-to-moderate Reynolds number , 2012 .

[31]  Soogab Lee,et al.  Computation of aeolian tone from a circular cylinder using source models , 2008 .

[32]  M. Fink,et al.  One-Channel Time Reversal of Elastic Waves in a Chaotic 2D-Silicon Cavity , 1997 .

[33]  A. Mimani,et al.  Stability and Accuracy of Aeroacoustic Time- Reversal using the Pseudo-Characteristic Formulation , 2015 .

[34]  J. Sochacki.  Absorbing boundary conditions for the elastic wave equations , 1988 .

[35]  Lanbo Liu,et al.  Time reversal processing for source location in an urban environmenta) , 2005 .

[36]  Thomas J. R. Hughes,et al.  Computation of trailing-edge noise due to turbulent flow over an airfoil , 2004 .

[37]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[38]  Christopher K. W. Tam,et al.  Computational aeroacoustics - Issues and methods , 1995 .

[39]  Brian E Anderson,et al.  Optimization of the array mirror for time reversal techniques used in a half-space environment. , 2013, The Journal of the Acoustical Society of America.

[40]  Pierre Sagaut,et al.  A coupled time-reversal/complex differentiation method for aeroacoustic sensitivity analysis: towards a source detection procedure , 2009, Journal of Fluid Mechanics.

[41]  M. Zhuang,et al.  Applications of High-Order Optimized Upwind Schemes for Computational Aeroacoustics , 2002 .

[42]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[43]  Mathias Fink,et al.  One-channel time-reversal in chaotic cavities: Experimental results , 1999 .

[44]  H. Sohn,et al.  Understanding a time reversal process in Lamb wave propagation , 2009 .

[45]  Con J. Doolan,et al.  Three-dimensional beamforming of dipolar aeroacoustic sources , 2015 .

[46]  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 .

[47]  Tze Pei Chong,et al.  An experimental study of airfoil instability tonal noise with trailing edge serrations , 2013 .

[48]  Con J. Doolan,et al.  Flow-Induced Sound of Wall-Mounted Finite Length Cylinders , 2013 .

[49]  Jörn Sesterhenn,et al.  A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes , 2000 .

[50]  A Mimani,et al.  Enhancing the focal-resolution of aeroacoustic time-reversal using a point sponge-layer damping technique. , 2014, The Journal of the Acoustical Society of America.