Analysis of permeability and effective viscosity by CFD on isotropic and anisotropic metallic foams

Hydrodynamic properties of open-cell metallic foams are analyzed at the pore scale on a microtomographied sample from creeping flow to unsteady inertial flow. The influence of the anisotropy, obtained by shearing the initial sample, is also analyzed. The simulations show that the Darcy–Forchheimer law is valid at Redl>1Redl>1 and that the inertial coefficient tensor can be asymmetric as proved by Whitaker [1996. The Forchheimer equation: a theoretical development. Transp. Porous Media 25, 27–61] and checked by the lattice Boltzmann method. Despite this property, the eigen vectors are nearly orthogonal to each other and their orientation follows the shear angle. To evaluate the accuracy of the results, the analysis of the REV leads to a REV size lower than 2.5dp2.5dp for the velocity and is lower than 4.5dp4.5dp for the inertial flow permeability tensor. It is shown also that the CFD approach, validated by MRI investigation [Graf von den Schulenburg et al., 2007. Flow through an evolving porous media-compressed foam. J. Mater. Sci. 42 6541–6548], matches the 3D-Brinkman–Forchheimer model if the effective viscosity is close to two.