Acoustical determination of the parameters governing thermal dissipation in porous media

Abstract

In this paper, the question of the acoustical determination of macroscopic thermal parameters used to describe heat exchanges in rigid open-cell porous media subjected to acoustical excitations is addressed. The proposed method is based on the measurement of the dynamic bulk modulus of the material, and analytical inverse solutions derived from different semiphenomenological models governing the thermal dissipation of acoustic waves in the material. Three models are considered: (1) Champoux-Allard model [J. Appl. Phys. 20, 1975-1979 (1991)] requiring knowledge of the porosity and thermal characteristic length, (2) Lafarge et al. model [J. Acoust. Soc. Am. 102, 1995-2006 (1997)] using the same parameters and the thermal permeability, and (3) Wilson model [J. Acoust. Soc. Am. 94, 1136-1145 (1993)] that requires two adjusted parameters. Except for the porosity that is obtained from direct measurement, all the other thermal parameters are derived from the analytical inversion of the models. The method is applied to three porous materials-a foam, a glass wool, and a rock wool-with very different thermal properties. It is shown that the method can be used to assess the validity of the descriptive models for a given material.