Nonlinear wave propagation through rigid porous materials. I: Nonlinear parametrization and numerical solutions

Abstract

It is well known that the flow resistance, as defined by Darcy's law, becomes a function of the fluid velocity when the fluid velocity becomes sufficiently large. For porous materials in air, there appears to be two separate nonlinear flow regimes: For low velocities, the resistance coefficient increases with the square of the fluid velocity; and, for high velocities, the resistance coefficient increases linearly with the magnitude of the fluid velocity. Similar regimes also exist for the mass coefficient; however, the mass coefficient is observed to decrease with increasing fluid velocity. (For pure-tone excitation, it is shown that these relationships then hold for the complex magnitude of the particle velocity. ) In this paper, the two nonlinear flow regimes are parametrized for several porous materials. Nonlinear corrections are made to linear wave theory, and numerical solutions for pure tones are obtained that are then used to predict surface admittance and internal pressures of finite length sample. A simple surface pressure criterion is put fourth based upon the materials nonlinear parameters that gives an approximate maximum surface pressure that a porous material could be exposed to before nonlinear phenomena become important in describing the material's characteristics. PACS numbers: 43.25.Ba, 43.25.Ed, 43.55.Ev

Measurement of Heat Flow Transmitted through a Stacked-Screen Regenerator of Thermoacoustic Engine

“…Thermoacoustic theory describes that the flow resistance of the regular flow channel is a constant [17][18][19], independent of the velocity amplitude, whereas that in the porous media with tortuous flow channels is shown to increase with the velocity [28][29][30] or Reynolds number [2][3][4][5]7]. From measurements of the acoustic field, we have proposed modification of the effective radius r 0 to have velocity dependence [16] as…”

Sound absorption of porous metals at high sound pressure levels

“…Following the one-dimensional acoustical equations of motion and continuity given by Wilson and McIntosh et al, 5,6 and taking exp͑it͒ time dependence, the equations describing sound wave propagating inside porous materials can be written in the following form:…”

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Sound absorption of a micro-perforated plate backed by a porous material under high sound excitation: measurement and prediction

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