Decoupling approach to modeling perforated tube muffler components

Abstract

A transformation is derived to decouple the two differential equations describing one-dimensional acoustic wave propagation in the presence of mean flow, in mufflers with partitioned, perforated tubes. The following analysis leads to compact and exact expressions for the matrix parameters of crossflow elements without any concern for convergence of infinite series or segmental analysis employed in earlier studies. The present analysis is, however, based on assumptions of a uniform perforate impedance on the tube, and of equal mean flow in the two ducts. The predicted transmission loss curves agree very well with published data. The decoupled equations make transparent the connection between high-frequency resonances of perforated elements and the axial propagation of radial velocity fluctuations through the holes, without mean flow. The resonance frequencies of a plug muffler are seen to coincide with resonance frequencies of crossflow elements, which in turn may be correlated very simply and accurately with the dimensionless group (ψl)2 defined in this work. This correlation bears out observed trends with variation of geometric parameters.