Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves

Abstract

An acoustic transmissivity method is proposed for measuring flow resistivity of porous materials having rigid frame. Flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The transmission scattering operator for a slab of porous material is derived from the response of the medium to an incident acoustic pulse. The flow resistivity is determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed.

Low-frequency sound wave parameter measurement in gravels

“…Such materials have been considered as media for the absorption of sound energy from military activities such as demolition and artillery training, and there is a paucity of available information on their sound absorption and propagation properties at the low frequencies characteristic of the noise of such activities. While theories exist for sound waves in porous media [1], very few have been tested for the prediction of propagation or absorption effects in the low-frequency range under consideration [2][3][4]. Thus there exists a need for basic experimental data that can be used for the prediction of sound absorption and propagation in various contexts.…”

Transient Acoustic Wave Propagation in Porous Media

“…An acoustic method [33][34][35][36][37] using transmitted and reflected waves is proposed for measuring static viscous permeability k 0 , flow resistivity σ, static thermal permeability k ′ 0 and the inertial factor α 0 (low frequency tortuosity), of porous materials having a rigid frame at low frequencies. Flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube.…”

“…For measuring the static thermal permeability and the inertial factor, a pipe of 3 m long, since the frequencies used in the experiment are between 1kHz and 4 kHz. However, for measuring the viscous permeability (and flow resistivity) [33,35,36], a pipe of 50 m long must be used (50Hz-1kHz) to avoid the reflections at its end. In this case, it is not important to keep the pipe straight, it can be rolled in order to save space without perturbations on experimental signals (the cut-off frequency of the tube f c ∼ 4kHz).…”

“…For its iterative solution, we used the simplex search method (Nedler Mead) [38] which does not require numerical or analytic gradients. Experiments are performed in a guide [33][34][35][36][37] (pipe), having a diameter of 5 cm. The experimental set up is given in Fig.…”

Technical Notes: Evaluation of Two Alternative Procedures for Measuring Airflow Resistance of Sound Absorbing Materials

“…The flow resistivity was estimated, solving an inverse scattering problem for the waves reflected by a homogeneous isotropic porous material with a rigid skeleton. Subsequently, an extension of this work was presented using an acoustic transmissivity method to determine flow resistivity (Fellah et al, 2006). Indirect methods for obtaining airflow resistance have also been developed based on measurements in an impedance tube and two side-mounted microphones (Picard et al, 1998;Panneton, Olny, 2006).…”