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Direct computation of the sound from a compressible co-rotating vortex pair

Published online by Cambridge University Press:  26 April 2006

Brian E. Mitchell ,
Sanjiva K. Lele  and
Parviz Moin
Brian E. Mitchell
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 far-field sound generated by compressible co-rotating vortices is computed by direct computation of the unsteady compressible Navier–Stokes equations on a computational domain that extends to two acoustic wavelengths in all directions. The vortices undergo a period of co-rotation followed by a sudden merger. The directly computed far-field sound is compared to the prediction of the acoustic analogy due to Möhring (1978, 1979), a modified form of the analogy developed by Lighthill (1952), and an acoustic analogy derived by Powell (1964). All three predictions are in excellent agreement with the simulation. Results of far-field pressure fluctuations from an acoustically non-compact, co-rotating vortex pair are also presented. In this case, the vortex sound theory over-predicts the sound by 65% in accordance with the analysis of Yates (1978).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 285 , 25 February 1995 , pp. 181 - 202
Copyright
© 1995 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1972 Handbook of Mathematical Functions. Dover.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Cantwell, B. 1986 Viscous starting jets. J. Fluid Mech. 173, 159–189.Google Scholar
Colonius, T., Lele, S. K. & Moin, P. 1991 Scattering of sound waves by a compressible vortex. AIAA Paper 91-0494.CrossRefGoogle Scholar
Colonius, T., Lele, S. K. & Moin, P. 1993 Boundary conditions for direct computation of aerodynamic sound generation. AIAA J. 31, 1574–1582.Google Scholar
Colonius, T., Lele, S. K. & Moin, P. 1994 The scattering of sound waves by a vortex – numerical simulations and analytical solutions. J. Fluid Mech. 260, 271–298.Google Scholar
Crighton, D. G. 1988 Goals for computational aeroacoustics. In Computational Acoustics: Algorithms and Applications (ed. J. C. Hardin & M. Y. Hussaini). Elsevier.Google Scholar
Crow, S. C. 1970 Aerodynamic sound emission as a singular perturbation problem. Stud. Appl. Math. 49, 21–44.Google Scholar
Engquist, B. & Majda, A. 1979 Radiation boundary conditions for acoustic and elastic wave calculations. Commun. Pure Applied Math. 23, 313–357.Google Scholar
Ffowcs Williams, J. E. & Hawkings, D. L. 1968 Shallow water wave generation by unsteady flow. J. Fluid Mech. 31, 779–788.Google Scholar
Giles, M. B. 1990 Nonreflecting boundary conditions for Euler equation calculations. AIAA J. 12, 2050–2058.Google Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw Hill.Google Scholar
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
Kambe, T. 1984 Influence of viscosity on aerodynamic sound emission in free space. J. Sound Vib. 95, 351–360.Google Scholar
Kambe, T. 1986 Acoustic emissions by vortex motions. J. Fluid Mech. 173, 643–666.Google Scholar
Kambe, T. & Minota, T. 1983 Acoustic wave radiated by head-on collisions of two vortex rings. Proc. R. Soc. Lond. A 386, 277–308.Google Scholar
Kambe, T., Minota, T. & Takaoka, M. 1993 Oblique collision of two vortex rings and its acoustic emission. Phys. Rev. E 48, 1866–1881.Google Scholar
Lamb, H. 1932 Hydrodynamics. Dover.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.Google Scholar
Lele, S. K. & Ho, C. M. 1994 Acoustic radiation from temporally evolving free shear layers. Internal Report, Stanford University.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically I. General theory. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Lyamshev, L. M. & Skvortsov, A. T. 1988 Sound radiation by localized vortices in a slightly compressible medium (Review). Sov. Phys. Acoust. 34, 447–59.Google Scholar
Melander, M. V., Zabusky, N. J. & McWilliams, J. C. 1988 Symmetric vortex merger in two dimensions: causes and conditions. J. Fluid Mech. 195, 303–340.Google Scholar
Mitchell, B. E., Lele, S. K. & Moin, P. 1992 Direct computation of the sound from a compressible co-rotating vortex pair. AIAA Paper 92-0374.CrossRefGoogle Scholar
Möhring, W. 1978 On vortex sound at low Mach number. J. Fluid Mech. 85, 685–691.Google Scholar
Möhring, W. 1979 Modelling low Mach number noise. In Mechanics of Sound Generation in Flows (ed. E.-A. Müller), pp. 85–96. Springer.CrossRefGoogle Scholar
Möller, E. A. & Obermeier, F. 1967 The spinning vortices as a source of sound. In Proc. Conf. on Fluid Dynamics of Rotor and Fan Supported Aircraft at Subsonic Speeds. AGARD.Google Scholar
Obermeier, F. 1985 Aerodynamic sound generation caused by viscous processes. J. Sound Vib. 99, 111–120.Google Scholar
Powell, A. 1964 Theory of vortex sound. J. Acoust. Soc. Am. 36, 177–195.Google Scholar
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions. Cambridge University Press.Google Scholar
Waugh, D. 1992 The efficiency of symmetric vortex merger. Phys. Fluids A 4, 1745–1758.Google Scholar
Weston, R. P. & Lu, C. H. 1982 Approximate boundary condition procedure for the two-dimensional numerical solution of vortex wakes. AIAA Paper 82-0951.CrossRefGoogle 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.Google Scholar