×

An accurate and efficient computational method for time-domain aeroacoustic scattering. (English) Zbl 1436.76055

Summary: This paper presents a convective time-domain equivalent-source method for determining the scattered acoustic pressure field in a uniform moving medium. The proposed method is based on the solution of the time-domain convective Ffowcs Williams-Hawkings (FW-H) equation while the strengths of equivalent sources are determined by the required pressure gradient boundary condition on the scattering surface. The scattered acoustic pressure can be calculated once the strengths of equivalent sources have been determined. The current paper adopts the recently published analytical time-domain formulation for the acoustic pressure gradient in a moving medium to evaluate the incident pressure gradient on the scattering surface. This makes the proposed method considerably more efficient and accurate than a direct method. The total acoustic pressure consists of the scattered and the incident components. The latter can be obtained by the time-domain acoustic pressure formulation of the convective FW-H equation. Causes of possible instability in the proposed method are analyzed and an effective stabilizing method is proposed. Three test cases are considered to demonstrate the validity of the proposed method: a point monopole source field scattered by: (1) a rigid sphere in a stationary medium, (2) an infinite flat plate in uniform flow parallel to its surface, and (3) a cylinder of infinite length in axial uniform flow. To demonstrate the usefulness of the proposed method in practical engineering applications, the scattering of a point monopole source field by a slender wing in uniform flow is considered.

MSC:

76Q05 Hydro- and aero-acoustics
76M99 Basic methods in fluid mechanics
35P25 Scattering theory for PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Crighton, D. G.; Leppington, F. G., On the scattering of aerodynamic noise, J. Fluid Mech., 46, 3, 577-597 (1971) · Zbl 0224.76083
[2] Glegg, S. A.L., Effect of centerbody scattering on propeller noise, AIAA J., 29, 4, 572-576 (1991)
[3] Kingan, M. J.; Self, R. H., Open rotor tone scattering, J. Sound Vib., 331, 8, 1806-1828 (2012)
[4] Kingan, M. J.; Sureshkumar, P., Open rotor centrebody scattering, J. Sound Vib., 333, 2, 418-433 (2014)
[5] Atalla, N.; Glegg, S. A.L., Ray-acoustics approach to fuselage scattering of rotor noise, J. Am. Helicopter Soc., 38, 3, 56-63 (1993)
[6] Gennaretti, M.; Bernardini, G.; Poggi, C.; Testa, C., Velocity-potential boundary-field integral formulation for sound scattered by moving bodies, AIAA J., 56, 9, 3547-3557 (2018)
[7] Gaffney, J.; McAlpine, A.; Kingan, M. J., A theoretical model of fuselage pressure levels due to fan tones radiated from the intake of an installed turbofan aero-engine, J. Acoust. Soc. Am., 143, 6, 3394-3405 (2018)
[8] Huang, X., Theoretical model of acoustic scattering from a flat plate with serrations, J. Fluid Mech., 819, 228-257 (2017) · Zbl 1383.76419
[9] Agarwal, A.; Dowling, A. P.; Shin, H.-C.; Graham, W.; Sefi, S., Ray-tracing approach to calculate acoustic shielding by a flying wing airframe, AIAA J., 45, 5, 1080-1090 (2007)
[10] Roger, M.; Moreau, S.; Kucukcoskun, K., On sound scattering by rigid edges and wedges in a flow, with applications to high-lift device aeroacoustics, J. Sound Vib., 362, 252-275 (2016)
[11] Ffowcs Williams, J. E.; Hawkings, D. L., Sound generation by turbulence and surfaces in arbitrary motion, Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci., 264, 1151, 321-342 (1969) · Zbl 0182.59205
[12] Brentner, K. S.; Farassat, F., Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces, AIAA J., 36, 8, 1379-1386 (1998)
[13] Farassat, F., Derivation of formulations 1 and 1A of Farassat (2007), NASA Langley Research Center: NASA Langley Research Center Hampton, Virginia, Technical Report No. TM-2007-214853
[14] Brentner, K. S.; Farassat, F., Modeling aerodynamically generated sound of helicopter rotors, Prog. Aerosp. Sci., 39, 2-3, 83-120 (2003)
[15] Brentner, K. S., Numerical algorithms for acoustic integrals with examples for rotor noise prediction, AIAA J., 35, 4, 625-630 (1997) · Zbl 0907.76060
[16] Hanson, D. B., Direct frequency domain calculation of open rotor noise, AIAA J., 30, 9, 2334-2337 (1992)
[17] Khelladi, S.; Kouidri, S.; Bakir, F.; Rey, R., Predicting tonal noise from a high rotational speed centrifugal fan, J. Sound Vib., 313, 1-2, 113-133 (2008)
[18] Tang, H.; Qi, D.; Mao, Y., Analysis on the frequency-domain numerical method to compute the noise radiated from rotating sources, J. Sound Vib., 332, 23, 6093-6103 (2013)
[19] Wells, V. L.; Han, A. Y., Acoustics of a moving source in a moving medium with application to propeller noise, J. Sound Vib., 184, 4, 651-663 (1995) · Zbl 0982.76553
[20] Najafi-Yazdi, A.; Brès, G. A.; Mongeau, L., An acoustic analogy formulation for moving sources in uniformly moving media, Proc. R. Soc. A, Math. Phys. Eng. Sci., 467, 2125, 144-165 (2011) · Zbl 1219.76046
[21] Ghorbaniasl, G.; Lacor, C., A moving medium formulation for prediction of propeller noise at incidence, J. Sound Vib., 331, 1, 117-137 (2012)
[22] Xu, C.; Mao, Y.; Qi, D., Frequency-domain acoustic pressure formulation for rotating source in uniform subsonic inflow with arbitrary direction, J. Sound Vib., 333, 14, 3081-3091 (2014)
[23] Dowling, A. P.; Ffowcs Williams, J. E.; Goldstein, M. E., Sound production in a moving stream, Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci., 288, 1353, 321-349 (1978) · Zbl 0378.76055
[24] Bogey, C.; Bailly, C., A family of low dispersive and low dissipative explicit schemes for flow and noise computations, J. Comput. Phys., 194, 1, 194-214 (2004) · Zbl 1042.76044
[25] Tam, C. K.W.; Webb, J. C., Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys., 107, 2, 262-281 (1993) · Zbl 0790.76057
[26] Rao, P. P.; Morris, P. J., Use of finite element methods in frequency domain aeroacoustics, AIAA J., 44, 7, 1643-1652 (2006)
[27] Guo, Y., Computation of sound propagation by boundary element method (2005), The Boeing Company: The Boeing Company Huntington Beach, California, NASA Contract Report No. NAS1-00086-A003
[28] Astley, R. J.; Sugimoto, R.; Mustafi, P., Computational aero-acoustics for fan duct propagation and radiation. Current status and application to turbofan liner optimisation, J. Sound Vib., 330, 16, 3832-3845 (2011)
[29] Hu, F. Q.; Pizzo, M. E.; Nark, D. M., On a time domain boundary integral equation formulation for acoustic scattering by rigid bodies in uniform mean flow, J. Acoust. Soc. Am., 142, 6, 3624-3636 (2017)
[30] Kropp, W.; Svensson, U. P., Application of the time domain formulation of the method of equivalent sources to radiation and scattering problems, Acustica, 81, 6, 528-543 (1995) · Zbl 0860.76067
[31] Lee, S.; Brentner, K. S.; Morris, P. J., Acoustic scattering in the time domain using an equivalent source method, AIAA J., 48, 12, 2772-2780 (2010)
[32] Dunn, M. H.; Tinetti, A. F., Aeroacoustic scattering via the equivalent source method, (10th AIAA/CEAS Aeroacoutics Conference, AIAA Paper 2004-2937, American Institute of Aeronautics and Astronautics. 10th AIAA/CEAS Aeroacoutics Conference, AIAA Paper 2004-2937, American Institute of Aeronautics and Astronautics, Manchester, United Kingdom (2004))
[33] Mao, Y.; Gu, Y.; Xu, C., Validation of frequency-domain method to compute noise radiated from rotating source and scattered by surface, AIAA J., 54, 4, 1188-1197 (2016)
[34] Siozos-Rousoulis, L.; Troyer, T. D.; Ghorbaniasl, G., Scattered noise prediction using acoustic velocity formulations V1A and KV1A, Wave Motion, 72, 363-376 (2017) · Zbl 1524.76418
[35] Keller, J. B.; Givoli, D., Exact non-reflecting boundary conditions, J. Comput. Phys., 82, 1, 172-192 (1989) · Zbl 0671.65094
[36] Berenger, J.-P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 2, 185-200 (1994) · Zbl 0814.65129
[37] Koopmann, G. H.; Song, L.; Fahnline, J. B., A method for computing acoustic fields based on the principle of wave superposition, J. Acoust. Soc. Am., 86, 6, 2433-2438 (1989)
[38] Song, L.; Koopmann, G. H.; Fahnline, J. B., Numerical errors associated with the method of superposition for computing acoustic fields, J. Acoust. Soc. Am., 89, 6, 2625-2633 (1991)
[39] Wang, Z.-H.; Bi, C.-X.; Zhang, X.-Z.; Zhang, Y.-B., Sound field prediction and separation in a moving medium using the time-domain equivalent source method, Acta Acust. Acust., 103, 3, 401-410 (2017)
[40] Bi, C.-X.; Geng, L.; Zhang, X.-Z., Cubic spline interpolation-based time-domain equivalent source method for modeling transient acoustic radiation, J. Sound Vib., 332, 22, 5939-5952 (2013)
[41] Zhang, X.-Z.; Bi, C.-X.; Zhang, Y.-B.; Xu, L., Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method, J. Acoust. Soc. Am., 130, 3, 1430-1440 (2011)
[42] Zhang, X.-Z.; Bi, C.-X.; Zhang, Y.-B.; Xu, L., A time-domain inverse technique for the localization and quantification of rotating sound sources, Mech. Syst. Signal Process., 90, 15-29 (2017)
[43] Tinetti, A. F.; Dunn, M. H., Aeroacoustic noise prediction using the fast scattering code, (11th AIAA/CEAS Aeroacoutics Conference, AIAA Paper 2005-3061, American Institute of Aeronautics and Astronautics. 11th AIAA/CEAS Aeroacoutics Conference, AIAA Paper 2005-3061, American Institute of Aeronautics and Astronautics, Monterey, California (2005))
[44] Lee, S.; Brentner, K. S.; Morris, P. J., Assessment of time-domain equivalent source method for acoustic scattering, AIAA J., 49, 9, 1897-1906 (2011)
[45] Swift, S. H.; Blaisdell, G. A.; Lyrintzis, A. S., An efficient time-domain equivalent source method for acoustic scattering, Int. J. Aeroacoust., 14, 1-2, 133-160 (2015)
[46] Mao, Y.; Hu, Z.; Gu, Y., Efficient method to predict rotor noise scattered by an axisymmetric body, AIAA J., 55, 10, 3458-3466 (2017)
[47] Amoiridis, O.; Siozos-Rousoulis, L.; Huang, Z.; Ricks, N.; Kalfas, A.; Ghorbaniasl, G., Aeroacoustic scattering of rotating sources using a frequency-domain acoustic pressure gradient formulation, Appl. Acoust., 130, 99-106 (2018)
[48] Lee, S., Review: the use of equivalent source method in computational acoustics, J. Comput. Acoust., 25, 1, Article 1630001 pp. (2017)
[49] Hu, F.; Pizzo, M. E.; Nark, D. M., On the use of a Prandtl-Glauert-Lorentz transformation for acoustic scattering by rigid bodies with a uniform flow, J. Sound Vib., 443, 198-211 (2019)
[50] Rienstra, S. W.; Hirschberg, A., An Introduction to Acoustics, 214-217 (2018), Eindhoven University of Technology: Eindhoven University of Technology Eindhoven, the Netherlands, Ch. 9.1, available at
[51] Ghorbaniasl, G.; Huang, Z.; Siozos-Rousoulis, L.; Lacor, C., Analytical acoustic pressure gradient prediction for moving medium problems, Proc. R. Soc. A, Math. Phys. Eng. Sci., 471, 2184, 1-14 (2015) · Zbl 1371.76117
[52] Bi, C.-X.; Wang, Z.-H.; Zhang, X.-Z., Analytic time-domain formulation for acoustic pressure gradient prediction in a moving medium, AIAA J., 55, 8, 2607-2616 (2017)
[53] Siozos-Rousoulis, L.; Amoiridis, O.; Huang, Z.; Troyer, T. D.; Kalfas, A. I.; Ghorbaniasl, G., A convected frequency-domain equivalent source approach for aeroacoustic scattering prediction of sources in a moving medium, J. Sound Vib., 431, 88-104 (2018)
[54] Mao, Y.; Hu, Z.; Xu, C.; Ghorbaniasl, G., Vector aeroacoustics for uniform mean flow: acoustic velocity and vortical velocity, AIAA J., 56, 7, 2782-2793 (2018)
[55] Myers, M. K.; Hausmann, J. S., Computation of acoustic scattering from a moving rigid surface, J. Acoust. Soc. Am., 91, 5, 2594-2605 (1992)
[56] Lee, S.; Brentner, K. S.; Farassat, F.; Morris, P. J., Analytic formulation and numerical implementation of an acoustic pressure gradient prediction, J. Sound Vib., 319, 3-5, 1200-1221 (2009)
[57] Carley, M.; Fitzpatrick, J., Linear acoustic formulae for calculation of rotating blade noise with asymmetric inflow, (2nd AIAA/CEAS Aeroacoutics Conference, AIAA Paper 1996-1789, American Institute of Aeronautics and Astronautics, State College. 2nd AIAA/CEAS Aeroacoutics Conference, AIAA Paper 1996-1789, American Institute of Aeronautics and Astronautics, State College, Pennsylvania (1996))
[58] Farassat, F., Introduction to generalized functions with applications in aerodynamics and aeroacoustics (1996), NASA Langley Research Center: NASA Langley Research Center Hampton, Virginia, Technical Report No. TP-3428
[59] Jones, D. S., Acoustics and Electromagnetic Waves, 127-128 (1986), Clarendon Press: Clarendon Press Oxford, Ch. 3.2
[60] Crighton, D. G.; Dowling, A. P.; Ffowcs Williams, J. E.; Heckl, M.; Leppington, F. G., Modern Methods in Analytical Acoustics, 530-538 (1992), Springer-Verlag: Springer-Verlag London, Ch. 18.2
[61] Zhang, X.-Z.; Bi, C.-X.; Zhang, Y.-B.; Xu, L., On the stability of transient nearfield acoustic holography based on the time domain equivalent source method, J. Acoust. Soc. Am., 146, 1335-1349 (2019)
[62] Wang, H.; Henwood, D. J.; Harris, P. J.; Chakrabarti, R., Concerning the cause of instability in time-stepping boundary element methods applied to the exterior acoustic problem, J. Sound Vib., 305, 1-2, 289-297 (2007) · Zbl 1242.65213
[63] Jang, H.-W.; Ih, J.-G., Stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions, J. Acoust. Soc. Am., 131, 2742-2752 (2012)
[64] Trefethen, L. N.; Embree, M., Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, 1-46 (2005), Princeton University Press: Princeton University Press Princeton, New Jersey, Ch. I · Zbl 1085.15009
[65] Parot, J.-M.; Thirard, C., A numerical algorithm to damp instabilities of a retarded potential integral equation, Eng. Anal. Bound. Elem., 35, 4, 691-699 (2011) · Zbl 1259.76032
[66] van’t Wout, E.; van der Heul, D. R.; van der Ven, H.; Vuik, C., Stability analysis of the marching-on-in-time boundary element method for electromagnetics, J. Comput. Appl. Math., 294, 358-371 (2016) · Zbl 1336.78016
[67] Hansen, P. C.; Sekii, T.; Shibahashi, H., The modified truncated SVD method for regularization in general form, SIAM J. Sci. Stat. Comput., 13, 5, 1142-1150 (1992) · Zbl 0760.65044
[68] Hansen, P. C., Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems, Numer. Algorithms, 6, 1, 1-35 (1994) · Zbl 0789.65029
[69] Ochmann, M., The complex equivalent source method for sound propagation over an impedance plane, J. Acoust. Soc. Am., 116, 6, 3304-3311 (2004)
[70] Brouwer, H. H., The scattering of open rotor tones by a cylindrical fuselage and its boundary layer, (22nd AIAA/CEAS Aeroacoutics Conference, AIAA Paper 2016-2741, American Institute of Aeronautics and Astronautics. 22nd AIAA/CEAS Aeroacoutics Conference, AIAA Paper 2016-2741, American Institute of Aeronautics and Astronautics, Lyon, France (2016))
[71] Kingan, M. J.; Powles, C.; Self, R. H., Effect of centerbody scattering on advanced open-rotor noise, AIAA J., 48, 5, 975-980 (2010)
[72] Bouwkamp, C. J., A note on singularities occurring at sharp edges in electromagnetic diffraction theory, Physica, 12, 7, 467-474 (1946) · Zbl 0063.00574
[73] Jones, D. S., The Theory of Electromagnetism, 566-569 (1964), Pergamon Press, Ch. 9.2 · Zbl 0121.21604
[74] Crighton, D. G., The Kutta condition in unsteady flow, Annu. Rev. Fluid Mech., 17, 411-445 (1985) · Zbl 0596.76037
[75] Rienstra, S. W., Sound diffraction at a trailing edge, J. Fluid Mech., 108, 443-460 (1981) · Zbl 0473.76061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.