Prediction of Darcy-Forchheimer drag for micro-porous structures of complex geometry using the lattice Boltzmann method

The micro flows through two-dimensional and three-dimensional granular and fibrous porous media at various Knudsen numbers are studied by using the lattice Boltzmann method. For the granular materials, the results for the medium of rounded inclusions agree well with the existing empirical and numerical correlations between the permeability and the Reynolds number. However, the agreement becomes poor for the medium of sharp-cornered inclusions. A new correlation for the Darcy-Forchheimer drag for various inclusion shapes and arrangements is then proposed. For the fibrous materials, the current results are also compared with existing experimental and numerical data. They are in good agreement. The calculations are further carried out for these porous media in the slip-flow regime. The effect of rarefaction on the permeability in different porous media is discussed. A new correlation between the permeability, the porosity and the Knudsen number for both granular and fibrous porous media is presented.