Numerical mode matching in dissipative silencers with temperature gradients and mean flow

Abstract

This work presents a mathematical approach based on the mode matching method to compute the transmission loss of perforated dissipative silencers with temperature gradients and mean flow. Three-dimensional wave propagation is considered in silencer geometries with arbitrary, but axially uniform, cross section. To reduce the computational requirements of a full multidimensional finite element calculation, a method is developed combining axial and transversal solutions of the wave equation. First, the finite element method is employed in a twodimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as radial temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. Assuming a low acoustic influence of axial gradients (compared to radial variations), an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A weighted residual approach is then used to match the acoustic fields (pressure and axial acoustic velocity) at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes. Transmission loss predictions are compared favourably with a general three-dimensional finite element approach, offering a reduction in the computational effort.