A computational method of evaluating noncompact sound based on vortex sound theory

Abstract

A numerical investigation is made of the production of sound by turbulence interacting with a noncompact body. The problem is formulated in the frequency domain by extending the theory of vortex sound proposed by Howe. The anomalous "numerical" generation of sound by the sudden termination of Lighthill's stress tensor at the outer boundary of a finite computational domain is avoided by identification of "scattered" sound sources that generate sound principally by interaction with the solid surface. It is argued that the boundary element method is the most efficient means of computing the aeroacoustic Green's function for the problem, because it requires a minimum of CPU time, is not prone to numerical errors such as dispersion and dissipation during propagation, and the radiation condition is easily applied at the outer boundary. The method is applied to the problem of sound generation by high Reynolds number flow past a circular cylinder. The "scattered" sources are shown to be confined to the vicinity of the cylinder surface. At low frequencies the radiation has a dipole-like directivity in agreement with the compact approximation. However, the directivity is quite different at high frequencies, where our noncompact method predicts a more complicated "leaf-like" radiation pattern.