Microstructure and Acoustical Macro-Behavior: Approach by Reconstruction of a Representative Elementary Cell

Abstract

The fundamental issue of determining acoustic properties of porous media from their local geometry is examined in this Ph.D. dissertation thesis, thanks to a sample of open-cell aluminium foam analyzed by axial computed microtomography. Various geometric properties are measured to characterize the experimental sample at the cell size level. This is done in order to reconstruct a porous medium by means of idealized three- and two-dimensional unit cells. The frequency dependent thermal and velocity fields governing the propagation and dissipation of acoustic waves through rigid porous media are computed by Brownian motion simulation and the finite element method, respectively. Macroscopic behavior is derived by spatial averaging of the local fields. Our results are compared to experimental data obtained from impedance tube measurements. First, this approach leads to the identification of the macroscopic parameters involved in Pride and Lafarge semiphenomenological models. Second, it yields a direct access to thermal and viscous dynamic permeabilities. However, the bidimensional model underestimates the static viscous permeability as well as the viscous characteristic length; what thus require a three-dimensional implementation.