a1 Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK
a2 Department of Mechanical and Manufacturing Engineering, Aalborg University, 9220 Aalborg, Denmark
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.
(Received April 25 2011)
(Reviewed August 25 2011)
(Accepted October 11 2011)
(Online publication December 01 2011)