Acoustic transmission in non-uniform ducts with mean flow, part II: The finite element method

Abstract

This second paper in a two part series describes the implementation of the finite element method for the solution of the problem of acoustic transmission through a non-uniform duct carrying a high speed subsonic compressible flow. A finite element scheme based on both the Galerkin method and the residual least squares method and with eight noded isoparametric elements is described. Multi-modal propagation is investigated by coupling of the solution in the duct non-uniform section to modal expansions in uniform sections. The accuracy of the finite element results for both the eigenvalue and transmission problems is assessed by comparison with exact solutions and with results from the method of weighted residuals in the form of a modified Galerkin method as introduced in Part I of this pair of papers. The results of calculations show that modal interactions, particularly in transmitted modes, become increasingly important with increasing duct flow Mach number. Power transmission coefficient calculations for the geometries studied reveal no indication of a linear basis for the phenomenon of subsonic acoustic choking.