Inverse Measurement of the Thickness and Flow Resistivity of Porous Materials via Reflected Low Frequency Waves-Frequency Approach

A direct and inverse method is proposed for measuring the thickness and flow resistivity of a rigid air-saturated porous material using acoustic reflected waves at low frequency. The equivalent fluid model is considered. The interactions between the structure and the fluid are taken by the dynamic tortuosity of the medium introduced by Johnson et al. and the dynamic compressibility of the air introduced by Allard. A simplified expression of the reflection coefficient is obtained at very low frequencies domain (Darcy’s regime). This expression depends only on the thickness and flow resistivity of the porous medium. The simulated reflected signal of the direct problem is obtained by the product of the experimental incident signal and the theoretical reflection coefficient. The inverse problem is solved numerically by minimizing between simulated and experimental reflected signals. The tests are carried out using two samples of polyurethane plastic foam with different thicknesses and resistivity. The inverted values of thickness and flow resistivity are compared with those obtained by conventional methods giving good results.