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The effects of viscosity on sound radiation near solid surfaces

Published online by Cambridge University Press:  01 December 2011

C. L. Morfey ,
S. V. Sorokin  and
G. Gabard
C. L. Morfey
Affiliation:
Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK
S. V. Sorokin
Affiliation:
Department of Mechanical and Manufacturing Engineering, Aalborg University, 9220 Aalborg, Denmark
G. Gabard*
Affiliation:
Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: g.gabard@soton.ac.uk
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Abstract

Although the acoustic analogy developed by Lighthill, Curle, and Ffowcs Williams and Hawkings for sound generation by unsteady flow past solid surfaces is formally exact, it has become accepted practice in aeroacoustics to use an approximate version in which viscous quadrupoles are neglected. Here we show that, when sound is radiated by non-rigid surfaces, and the smallest dimension is comparable to or less than the viscous penetration depth, neglect of the viscous-quadrupole term can cause large errors in the sound field. In addition, the interpretation of the viscous quadrupoles as contributing only to sound absorption is shown to be inaccurate. Comparisons are made with the scalar wave equation for linear waves in a viscous fluid, which is extended using generalized functions to describe the effects of solid surfaces. Results are also presented for two model problems, one in a half-space and one with simple cylindrical geometry, for which analytical solutions are available.

JFM classification

Acoustics: Aeroacoustics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 690 , 10 January 2012 , pp. 441 - 460
Copyright
Copyright © Cambridge University Press 2011

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