A finite element analysis of the convected acoustic wave motion in dissipative silencers

A general finite element formulation for the analysis of the sound field in a flow duct with a surrounding volume filled with porous or fibrous absorbent material is given. The detailed, non-linear, steady flow field which is induced in the absorbent by the high speed mean flow in the central duct is evaluated. The induced steady flow field causes the acoustic field in the absorbent to be inhomogeneous, anisotropic and non-linear, even if the material is isotropic and homogeneous. Material anisotropy and inhomogeneity are also included in the formulation, which is therefore applicable to the most complex of dissipative silencers. Rapidly convergent solution schemes for the non-linear analyses are given and the merits of two different matching schemes between the acoustic fields of the flow duct and the absorption silencer are compared. Results are given which indicate the accuracy of the formulation and the necessity or otherwise to model accurately the induced steady flow field in the absorbent material.