Theoretical prediction of sound attenuation in acoustically lined annular ducts in the presence of uniform flow and shear flow

Abstract

An investigation is made of the sound attenuation in a lined annular duct with flow. The eigenvalue equation in the presence of uniform flow is derived by matching the radial component of the particle displacement and acoustic pressure across a vortex sheet located an infinitely small distance from the facing sheet of an acoustic lining. The eigenvalue equation in the presence of shear flow is developed by matching the acoustic pressure and the radial component of the particle displacement at the interface between the regions of uniform flow and shear flow. Theoretical prediction of the sound-attenuation spectrum is based on an acoustic-energy flow in which the effect of the mean flow is taken into account. The results presented in this paper are limited to those which are typical for the geometry of an annular duct. Effects of mean flow Mach number, boundary-layer refraction, and acoustic impedance on the sound attenuation for a given duct configuration are found to be similar to those in rectangular- and circular-duct problems.