An efficient frequency-domain prediction method for aeroacoustic radiation and scattering using equivalent sources

Abstract

An efficient radiation and scattering prediction method is proposed in the frequency domain based on the convective Ffowcs Williams–Hawkings (FW–H) equation and the convective equivalent-source method (ESM). In this work, the convective FW–H equation and its spatial derivatives are adopted to develop ESM-I and ESM-S for predicting incident acoustic pressure and acoustic pressure gradient, respectively. The equivalent sources strength of ESM-I and ESM-S are determined by matching the pressure and pressure gradient boundary conditions on the integral surface of FW–H equation. The pressure gradient from ESM-S constructs a hard-wall boundary on a solid surface for the prediction of scattered pressure. Since then the total acoustic pressure can be efficiently evaluated from the incident and scattered components. An energy-based singular value decomposition method is adopted to filter the small singular values that probably lead to solution instability. Convective Green functions are suggested, which allow the final prediction methodology to be suitable for situations in different dimensions with the inclusion of moving-medium effects. Available analytical solutions for point sources as well as a monopole scattered by a cylinder, a sphere and a plane are used to examine the parameter sensitivity and accuracy of the proposed methodology.