Acoustic wave motion along a narrow cylindrical duct in the presence of an axial mean flow and temperature gradient

Abstract

A numerical solution is presented to the problem of non-isentropic acoustic wave motion in a circular capillary tube in the presence of both axial mean flow and a background axial temperature gradient. The effects of the radial components of the acoustic velocity are included in the analysis. The main application area is in the study of the acoustic effects of catalytic converters. The solution makes use of a series expansion and is valid for small relative changes in the background temperature, which are typical of this application area. Various solutions to the problem have been obtained previously, using different simplifications to the complete problem which is considered here. It is shown that each of the simplifications results in errors for the predicted attenuation of at least 20 dB/m, using conditions typical for catalytic converters. In particular the isentropic assumption is shown to be invalid.