A boundary element scheme for three-dimensional acoustic radiation with flow

Abstract

A boundary element approach is proposed for acoustical radiation in non-uniform, low Mach number flows. The formulation utilizes a transformation, valid at low Mach number for short wavelength disturbances, which converts this problem into an analogous no-flow problem for the same geometry. Two distinct boundary integral schemes are considered. An overdetermined combined surface-interior formulation and a combined surface-surface derivative formulation are both used to calculate the velocity potential due to the vibration of an arbitrary body in a uniform mean flow. Results are presented for the test cases of pulsating and juddering spheres in low Mach number flows. Good agreement is established between the results produced by the present boundary element formulations and those obtained from an analytic solution and an alternative numerical (finite element) scheme