An analytical fractal model for permeability in isotropic open-cell metal foam with surface roughness

This paper develops analytically a fractal model for estimating flow permeability of open-cell foam with rough surfaces. Fractal theory is employed for better characterize the randomness of pore distribution in the porous media and for describing particularly the micro roughness on the metallic ligaments. This provides a closer look at the actual situation of pore distribution of open-cell foams. The permeability can mainly be expressed with porosity, average tortuosity, and micro-rods geometric parameters, without any empirical or fitting parameters. The analytical model is verified through comparison to existing experimental data. To further explain the influence of micro-rods on the permeability, a tetradecahedral unit cell is used for pore-scale simulation. It is found that the reduced permeability is caused mainly by the increased flow tortuosity and the surface friction between fluid transport and the micro roughness.