From the Microstructure to Condensed Equivalent Fluid Models

This work focuses on the modeling of visco-thermal dissipations within porous media used in automotive sound packages. This paper mainly presents a review of works which enable to condense complex physical phenomena in a simple formalism. Rigid porous media are usually modeled as equivalent fluids using two complex and frequency-dependent functions: the dynamic density and the dynamic bulk modulus. Two methods for calculating these equivalent properties from the microstructural are recalled. Then, it is shown how to take into account additional phenomena such as pressure diffusion, tortuous effect at the mesoscopic scale, or inner resonators using simple equivalent fluid representations. This enables to add complex physical phenomena to equivalent fluid models in order to reduce the numerical cost for e.g. finite element models (FEM). The advantage of this formalism is being directly suitable for modeling porous media in complex systems and submitted to various excitations.