From the microstructure to condensed equivalent fluid models, by Fabien Chevillotte (Matelys – Research Lab) Jan. 24, 2017
DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017
Session on New trends in traditional noise treatments – porous materials and microperforated plates
Speaker: Fabien Chevillotte (Matelys – Research Lab)
The present work focuses on the modeling of visco-thermal dissipations of acoustical energy within porous media. Considering long wavelengths, a rigid porous medium can be seen as an equivalent fluid which is modeled by two complex frequency-dependent functions: the dynamic density and the dynamic bulk modulus. First, two methods for calculating these equivalent properties from the microstructural description of porous media will be presented: the direct approach which solves the linearized Navier-Stokes and the heat equations in harmonic regime and the hybrid method which relies on approximate but robust semi-phenomenological models as Johnson-Champoux-Allard (JCA) model. Then, it will be shown how to take into account additional phenomena such as pressure diffusion or inner resonance using simple equivalent fluid representations. This enables to add complex physical phenomena to equivalent fluid models in order to reduce the numerical cost e.g. finite element models (FEM). In addition, based on the Biot's theory, it will be recalled how to add elastic effects and their coupling to any visco-thermal dissipation models. The advantage of this formalism is to be directly suitable for modeling porous media in complex systems and submitted to various excitations. Practical examples will be given for a broad range of microstructures from simple perforated plates to deformable porous media with inner resonators.