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Propagation of Sound Waves in a Cylindrical Tube Filled with a Porous Medium

Том 12, Выпуск 6, 2009, pp. 537-548
DOI: 10.1615/JPorMedia.v12.i6.40
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Краткое описание

It is shown that the three main parameters governing the propagation of sound waves in a fluid contained in rigid cylindrical tubes filled with a saturated porous medium are the shear wave number s = R√(ρω/μ), the porosity ε, and the Darcy number Da = R/√(K). A variational solution of the problem with an isentropic wave's propagation in a cylindrical tube in the presence or absence of a convective steady flow is presented. The manner in which the flow influences the attenuation and the phase velocity of the forward and backward propagating acoustic waves is deduced. It is found that the increasing of porosity increases the wave's attenuations and enhances phase shift for both the forward and backward propagated sound waves for either case of absent or present steady flow; this is due to the favorable effect of the solid matrix in damping sound waves. It is also found that as the Darcy number is increased the attenuation and phase shift are increased for both the forward and backward sound waves for the case of absent steady flow, while for the case of present steady flow the attenuation is increased and phase shift is decreased for the forward sound waves, and both the attenuation and phase shift are decreased for the backward sound waves; this is due to the favorable retarding effect of the solid matrix on the forward sound waves and unfavorable collision effect on the backward sound waves.

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