Forchheimer-type nonlinearities for high-intensity propagation of pure tones in air-saturated porous media

Abstract

A linear rigid frame, cylindrical capillary theory of sound propagation in porous media is extended to include nonlinear effects of the Forchheimer type, by making a particle velocity-dependent correction to the complex density. This type of nonlinearity becomes important at incident sound-pressure levels above approximately 120 dB re: 20 μPa for highly porous fibrous materials. Data from three experiments on air-saturated porous media and foams, at levels up to 170 dB, are compared to the rigid frame theory with Forchheimer-type extension. One of the experiments measured a low-frequency approximation for the complex density directly; the others measured internal attenuation and surface admittance (inverse impedance). The generally good agreement found between predictions based on the Forchheimer-type nonlinear theory and each of the experiments suggests that this type of nonlinearity is the dominant one for propagation in many types of air-saturated fibrous porous media. Some interesting surface absorption characteristics are predicted at incident sound-pressure levels above 140 dB, especially at lower frequencies.

Sound absorption of porous metals at high sound pressure levels

“…The two calculated curves follow almost exactly with the experimental data. Wilson et al 5 also calculated these trends, but their experimental data were unable to verify the trends because the range of their data was limited below SPL 140 dB. When the surface impedance instead of admittance is drawn, it will be clearly shown that if the acoustic resistance is larger than 0 c 0 the absorption coefficient will follow the trend of Fig.…”

“…This in a way also verifies the well known explanation that the nonlinearities are resulted from the inertia term in the Navier-Stokes equation, i.e., from drag instead of turbulence. 5 Two typical absorption curves of porous metals at resonance frequencies at high SPLs are shown in Fig. 2.…”

“…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:…”

“…A Forchheimer type nonlinearity was introduced by Nelson 4 to accommodate acoustic signals. Wilson et al 5 further extended the Forchheimer nonlinearity to the resistive damping and mass reactance terms in complex density. This model was later modified by McIntosh and Lambert.…”

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…”