Experimental measurement of tortuosity, viscous, and thermal characteristic lengths of rigid porous material via ultrasonic transmitted waves

An inverse method is proposed for measuring tortuosity, viscous, and thermal characteristic lengths of air-saturated porous material with rigid frame via ultrasonic transmitted waves at normal incidence. The equivalent fluid model is considered. The interaction between the fluid saturated the pores and the structure are taken into account in two frequency response factors: the dynamic tortuosity of the medium introduced by Johnson et al. and the dynamic compressibility of the air introduced by Allard. Simplified expression of the transmission coefficient is obtained in frequency domain, and this expression depends on the porosity, tortuosity, viscous, and thermal characteristic lengths. The inverse problem is solved numerically in time domain by minimizing between simulated and experimental transmitted waves. The inverted parameters are in good agreement with those obtained using conventional methods. Simulated signals are reconstructed using the optimized values found and compared with the experimental signals. Tests are performed using three different plastic foam samples having low flow resistivity. The proposed technique has the advantage of being simple, fast, and not expensive.