Measuring flow resistivity of porous material via acoustic reflected waves

Abstract

An acoustic reflectivity method is proposed for measuring flow resistivity of porous materials having rigid frame. The 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. It is important as one of the several parameters required by acoustical theory to characterize porous materials like plastic foams and fibrous or granular materials. 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. This time domain model of wave propagation was initially introduced by the authors ͓Z.E.A. Fellah and C. Depollier, J. Acoust. Soc. Am. 107, 683 ͑2000͔͒. The viscous losses of the medium are described by the model devised by Johnson et al. ͓D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid. Mech.176, 379 ͑1987͔͒. Reflection and transmission scattering operators for a slab of porous material are derived from the responses of the medium to an incident acoustic pulse. The flow resistivity is determined from the expression of the reflection operator. Experimental and numerical validation results of this method are presented. A guide ͑pipe͒ is used in the experiment for obtaining a plane wave. This method has the advantage of being simple, rapid, and efficient.

Wave Propagation in Porous Materials

“…The expression of the reflection coefficient Rz ðÞin Laplace domain (put z ¼ jω for obtaining the frequency domain of R ω ðÞ ), is given by [32] …”

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

“…A procedure for measuring the airflow resistance was also proposed by Woodcock and Hodgson (1992) using the inversion of the Delany and Bazley (1970), expression of the characteristic impedance as a function of airflow resistivity. Another technique was proposed by Sebaa et al (2005) who used the physical property that in low frequencies the resistivity to the flow has a significant influence on the sound waves reflected. The flow resistivity was estimated, solving an inverse scattering problem for the waves reflected by a homogeneous isotropic porous material with a rigid skeleton.…”