Finite element modeling of acoustic singularities with application to propeller noise

Abstract

Numerical formulations and results that expand on recent developments in finite element modeling of acoustic volume sources and acoustic dipoles are presented. It is shown that with a suitable structuring of the acoustic field equations it is possible to include monopoles and dipoles within the same analysis framework as has been extensively used for interior duct acoustic and duct inlet radiation problems. This allows the extension of the finite element modeling method to include the noise sources in such applications as propellers enclosed in a duct or in free space with mean flows. The necessary structuring of the acoustic field equations is shown, and example calculations are given for the case of one-dimension al sources and body forces in the presence of mean flow, two-dimensional sources, axial body forces, and transverse body forces in the presence of uniform mean flow. Three-dimensional sources and dipoles are modeled as the Fourier sum of axially symmetric solutions without the necessity of introducing singular elements. It is further demonstrated that distributions of singularities can be readily modeled, and an example is given of the computation of the near- and far-field radiation of a propeller. Comparison of the far-field radiation directivity is made with the Gutin theory.