Analytical solution of sound propagation in lined or unlined circular ducts with laminar mean flow

Abstract

Lined ducts often form a part of practical flow duct acoustic systems. The prediction of attenuation in such a duct has been a topic of research for many years. As far as the authors' knowledge goes, the analysis of lined ducts with sheared mean flow has always been done numerically. In this paper, an analytical solution for the wave propagation in lined ducts with laminar mean flow is presented. The effect of the laminar mean flow Mach number is investigated for both downstream and upstream wave propagation. Results are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.