Influence of Higher Order Viscous and Thermal Effects on an Ultrasonic Wave Reflected from the First Interface of a Porous Material.

Zine El Abiddine Fellah,Claude Depollier,Nicholas O Ongwen,Erick Ogam,Mohamed Fellah,Rémi Roncen

doi:10.3390/ma15030798

Abstract

Ultrasound propagation in porous materials involves some higher order physical parameters whose importance depends on the acoustic characteristics of the materials. This article concerns the study of the influence of two parameters recently introduced, namely, the viscous and thermal surfaces, on the acoustic wave reflected by the first interface of a porous material with a rigid structure. These two parameters describe the fluid/structure interactions in a porous medium during the propagation of the acoustic wave in the high-frequency regime. Both viscous and thermal surfaces are involved in Laurent expansion, which is limited to the dynamic tortuosity and compressibility to a higher order and corrects the visco-thermal losses. A sensitivity study is performed on the modulus of the reflection coefficient at the first interface as a function of frequency and on the waveforms reflected by the porous material in the time domain. The results of this study show that highly absorbent porous materials are the most sensitive to viscous and thermal surfaces, which makes the consideration of these two parameters paramount for the characterization of highly absorbent porous materials using the waves reflected from the first interface.

Highlights

Air-saturated porous materials such as plastic foams or fibrous materials are widely used in the field of sound insulation and passive-noise control [1]
In this work, to see the effect of these viscous and thermal surfaces on the wave reflected by the first interface of the porous material, especially since the method using the wave reflected by the first interface has become a reference for the characterization of porous materials saturated with air in reflection, and it is interesting to see the influence of these surfaces on the reflected waves
What can be said about the different methods of characterization and inversion using experimental data? And where have these two surfaces been ignored? This work shows the importance of these two parameters Σ and Σ on the attenuation of waves reflected by the first interface of the porous material

Summary

Introduction

Air-saturated porous materials such as plastic foams or fibrous materials are widely used in the field of sound insulation and passive-noise control [1]. The viscous and thermal characteristic lengths have been measured experimentally using the waves reflected by the first interface of a porous material by solving the inverse problem using the Bayesian approach [49]. [21], the second order of the limited development of dynamic tortuosity (Equation (1)) and compressibility (Equation (2)) has been used for the calculation of the reflection coefficient, making it possible to study its sensitivity towards viscous and thermal characteristic lengths, and it has been shown that the viscous characteristic length has a significant effect on the amplitude of the wave reflected by the first interface, especially for highly absorbent porous materials. For that we will use the Laurent expansions given by relations (3) and (4) in the general expression of the reflection coefficient (6) and (7)

Sensitivity Analysis

Ultrasonic Measurement

Discussion and Conclusions