Influence of Shear Flow on Sound Attenuation in a Lined Duct

Abstract

A theoretical and experimental study of the influence of shear flow on the attenuation of sound in a lined duct is presented. Both upstream and downstream propagation are considered. Solutions of the linearized equations for acoustic-wave propagation in flow, based upon both uniform and power-law models of the mean-flow profile, are compared with attenuation measurements in a duct having two opposite side walls lined with a porous fiberglas® blanket for a frequency-geometry range kδ⩽1 and midstream Mach numbers Ml<0.2. Here, k is the plane wavenumber and δ is the aerodynamic boundary-layer thickness. Both profile models yield results in close agreement with experiments at low frequencies, kδ<0.1. For intermediate and high frequencies, 0.1 <kδ<1, the uniform-flow model fails, as expected, since it can only account for the convective effects of the flow upon attenuation of sound. It was not expected that the power-law model, which seemingly accounts for the effects of both convection and refraction within the shear layer upon the sound wave, would yield results much the same as those obtained for the uniform-flow profile, and thus fail in various degrees for this frequency range. Also, scattering of sound by turbulent flow does not appear to be strong enough to account for discrepancies between theory and experiment. As a result, the problem of accurately predicting the effects of refraction upon sound attenuation in the range 0.1 <kδ <1 remains unsolved. The uniform-flow model, for which solutions are easily obtained, proves useful from an acoustical-engineering point of view.