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The scattering of sound waves by a vortex: numerical simulations and analytical solutions

Published online by Cambridge University Press:  26 April 2006

Tim Colonius ,
Sanjiva K. Lele  and
Parviz Moin
Tim Colonius
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Sanjiva K. Lele
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Parviz Moin
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier–-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 260 , 10 February 1994 , pp. 271 - 298
Copyright
© 1994 Cambridge University Press

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References

Abramowitz, M. A. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.
Broadbent, E. G. & Moore, D. W. 1979 Acoustic destabilization of vortices. Phil. Trans. R. Soc. Lond. A 290, 353–371.Google Scholar
Candel, S. M. 1979 Numerical solution of wave scattering problems in the parabolic approximation. J. Fluid. Mech. 90, 465–507.Google Scholar
Colonius, T., Lele, S.K. & Moin, P. 1991a Scattering of sound waves by a compressible vortex. AIAA Paper 91–0494.
Colonius, T., Lele, S.K. & Moin, P. 1991b The free compressible viscous vortex. J. Fluid. Mech. 230, 45–73.Google Scholar
Colonius, T., Lele, S. K. & Moin, P. 1992 Boundary conditions for direct computation of aerodynamic sound. AIAA J. 31, 1574–1582.Google Scholar
Crighton, D. G. 1975 Basic principles of aerodynamic noise generation. Prog. Aerospace Sci. 16, 31–96.Google Scholar
Crighton, D. G. 1988 Goals for computational aeroacoustics. In Computational Acoustics: Algorithms and Applications (ed. D. Lee, R. L. Sternberg & M. H. Schultz). Elsevier.
Ferziger, J. H. 1974 Low-frequency acoustic scattering from a trailing vortex. J. Acoust. Soc. Am. 56, 1705–1707.Google Scholar
Georges, T. M. 1972 Acoustic ray paths through a model vortex with a viscous core. J. Acoust. Soc. Am. 51, 206–209.Google Scholar
Giles, M. B. 1990 Non-reflecting boundary conditions for Euler equation calculations. AIAA J. 12, 2050–2058.Google Scholar
Horne, W. C. 1983 Measurements of the scattering of sound by a line vortex. AIAA Paper 83–0676.
Howe, M. S. 1975 Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid. Mech. 71, 625–673.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.Google Scholar
Lighthill, M J. 1952 On sound generated aerodynamically. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Müller, E. A. & Matschat, K. R. 1959 The scattering of sound by a single vortex and by turbulence. Tech. Re p. Max-Planck-Inst. für Strömungsforschung, Göttingen..
O'shea, S. 1975 Sound scattering by a potential vortex. J. Sound Vib. 43, 109–116.Google Scholar
Tanaka, K. & Ishii, S. 1981 Scattering of a plane sound wave by a vortex pair. J. Phys. Soc. Japan 51, 1992–1999.Google Scholar
Taylor, G. I. 1918 On the dissipation of eddies. Aero. Res. Comm., R and M 598.Google Scholar
Yates, J. E. 1978 Application of the Bernoulli enthalpy concept to the study of vortex noise and jet impingement noise. NASA Contractor Rep. 2987.