Analysis of multiple-duct variable area perforated tube resonators

Abstract

Conical concentric tube resonators are often used in commercial automotive mufflers. These are characterised by wave-coupling phenomenon across interacting ducts. Using a one-dimensional control volume approach, a mathematical model is presented for a generalised configuration of variable area perforated tube resonators. The analysis is applied to different configurations that account for waves in the incompressible mean flow and in the acoustic coupling between the interacting ducts due to the admittance of the intervening perforates. The problem has been solved by means of the Peano-Baker's series of matrix calculus, and the transmission loss results have been outlined. The predictions have been validated against the three-dimensional finite element analysis.