Measuring static thermal permeability and inertial factor of rigid porous materials (L)

Abstract

An acoustic method based on sound transmission is proposed for deducing the static thermal permeability and the inertial factor of porous materials having a rigid frame at low frequencies. The static thermal permeability of porous material is a geometrical parameter equal to the inverse trapping constant of the solid frame [Lafarge et al., J. Acoust. Soc. Am. 102, 1995 (1997)] and is an important characteristic of the porous material. The inertial factor [Norris., J. Wave Mat. Interact. 1, 365 (1986)] describes the fluid structure interactions in the low frequency range (1-3 kHz). The proposed method is based on a temporal model of the direct and inverse scattering problems for the propagation of transient audible frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The static thermal permeability and the inertial factor are 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 theoretical data are in good agreement. Furthermore, the prospects are discussed. This method has the advantage of being simple, rapid, and efficient.

Generalized equation for transient-wave propagation in continuous inhomogeneous rigid-frame porous materials at low frequencies

“…In the time domain, the factors a(x) and b(x) are operators and their asymptotic expressions are given by 24,25 …”

A semi-empirical model relating micro structure to acoustic properties of bimodal porous material

“…(19d), effect of cell wall thickness is implied by r 0 and viscous characteristic length decreases by increasing thickness. 22,23 Increasing the reticulation rate on the other hand results in growing values for viscous length. The relation between viscous characteristic length and reticulation rate for bimodal foams with 10% and 15% polymer is illustrated in Figure 7.…”

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.…”

“…The inverse problem is to find the parameters k ′ and α 0 [37] which minimize numerically the discrepancy function…”

“…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.…”