RESUMEN
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.
RESUMEN
Analytical solutions are derived to extract from dynamic density the macroscopic parameters governing viscous dissipation of sound waves in open-cell porous media. While dynamic density is obtained from acoustical techniques, the analytical solutions are derived from the model describing this dynamic density. Here, semiphenomenological models by Johnson et al. and by Wilson are investigated. Assuming dynamic density, open porosity, and static airflow resistivity known, analytical solutions derived from the Johnson et al. model yield geometrical tortuosity and viscous characteristic dimension. For the Wilson model, only dynamic density needs to be known. In this case, analytical solutions yield-for the first time-Wilson's density parameter and vorticity-mode relaxation time. To alleviate constraints on the Johnson et al. model, an extrapolation approach is proposed to avoid prior knowledge of static resistivity. This approach may also be used to determine this latter parameter. The characterization methods are tested on three materials covering a wide range of static airflow resistivities (2300-150 100 Ns/m4), frame rigidities (soft and rigid), and pore geometries (cells and fibers). It is shown that the analytical solutions can be used to assess the validity of the descriptive models for a given material.
RESUMEN
A study of the propagation of waves in porous media with an interconnected network of pores and micropores of very different characteristic sizes, saturated by a compressible Newtonian fluid, is proposed. With this aim, the homogenization technique for periodic separated scales media, is applied to realistic double porosity materials with motionless skeleton. From preliminary explicit estimations of wavelengths in the two fluid networks, it is shown that the macroscopic descriptions depend on the contrast of static permeability between pores and micropores and on frequency. The local equations are solved in the cases of low and high contrasts of permeability, and two main macroscopic behaviors are obtained. In the low contrast situation, the macroscopic flow is given by a kind of generalized Darcy's law involving both pores and micropores, and their respective characteristic frequencies. Regarding compressibility effects, both pore networks act in parallel. The high permeability contrast reveals that the macroscopic flow law is governed by the pores. The microporous part of the material is submitted to pressure diffusion effects, bringing dissipation, and modifying the dynamic bulk modulus of the material. The two situations of coupling are illustrated for simple geometry of double porosity materials, including perforated--and slits--microporous materials.