The Propagation of Sound in Cylindrical Ducts with Mean Flow and Bulk-reacting Lining

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Abstract
We consider the transmission and reflexion of sound at sudden area changes in a cylindrical waveguide, which consists of two semi-infinite ducts. One duct is composed of two coaxial cylinders; the outer is sound-hard and the inner is perforated, and the space between the cylinders is filled with a sound-absorbing material. The other duct is a sound-hard cylinder with the same radius and axis as the perforated tube. A uniform gas flow is assumed in this duct and inside the perf⊙rated tube. Transmission and reflexion matrices are calculated for the causal solution. Causality and the boundary conditions imply a convective instability wave (Helmholtz instability) when the perforate is downstream the junction. (We have chosen the parameter values in order to avoid so-called absolute instabilities.) Calculations of the reflexion coefficient for the abrupt area expansion show good agreement with experiments.

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