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.

Effects of Flow Profile on Educed Acoustic Liner Impedance

“…He observed that the flow gradient tends to channel the sound energy into a narrow layer next to the wall for downstream propagation. Tack et al 2 conducted theoretical and experimental investigations of the influence of shear flow on the attenuation of sound in a lined duct, for upstream and downstream sound propagation. They observed that a uniform-flow assumption is adequate for low-frequency propagation, but were unable to accurately predict high-frequency attenuation with either uniform or shear-flow models.…”

A measurement method of the flow rate in a pipe using a microphone array

“…Also, in the range k␦ a Ӷ1, where sound wavelength is larger than the aerodynamic boundary-layer thickness, ␦ a , refraction by flow gradient becomes quite negligible; thus, the flow velocity profile can be regarded to be uniform when estimating sound attenuation. 8,9 Here, k is the wave number and the value of ␦ a can be considered to be equal to the radius of the pipe when the flow is a fully developed turbulent flow. 9 Therefore, the only one-dimensional plane wave satisfying the above-mentioned conditions is dealt with; the acoustic pressure and the flow velocity profile may be regarded as uniform over the cross section of the pipe when estimating acoustic properties.…”

On Physical Aeroacoustics with Some Implications for Low-Noise Aircraft Design and Airport Operations

“…Apart from this exceptional case acoustic-vortical waves have a critical layer and a continuous spectrum associated with either shear flow or non-rigid body rotation or both [216][217][218][219][220][221][222][223][224][225][226][227][228]. Figure 3 is shown an annular duct.…”

“…Both the acoustic-shear waves in a fan inlet duct, and the acoustic-swirl waves in a turbine exaust duct are acoustic-vortical waves [216][217][218][219][220][221][222][223][224][225][226][227][228] with vorticity due to shear or swirl or both. An axisymmetric mean flow (Figure 3) with Equation (11a) an axial shear flow with velocity U(r) and an azimuthal swirling flow with angular velocity Ω(r):…”