This study aims to analyze the permeability behavior of porous media with the help of a numerical simulation which can represent microscopic flow behaviors. 3D Navier-Stokes equation is employed for the governing equation of fluid movement in the simulation, while the immersed boundary method is utilized to embed spherical boundary on the grains' surface in the finite difference formulation with the staggered grid system. In present study, a series of numerical permeability tests were carried out on the representing volume unit (RVE) of granular material, expressed as a cuboid region where solid spheres were randomly packed. Unidirectional flow was considered and static pressure gradient is applied as the boundary condition, while the other perpendicular directions were treated as periodic. The profile of each RVE as a granular material was controlled with its void ratio and distribution of inner particle diameter. Also, in order to compare results from different simulation conditions and inner structures, the Reynolds number for the porous media is taken into account.
The results were compared to the former simulations with grid-wise uniformed inner structures conducted by the corresponding author [3] and several popular empirical formulae for an estimation of macroscopic permeability coefficient. The discussion is aimed at clarifying the relationship between present results and existing empirical formulae of permeability coefficient for soils within wide range of material profile index.
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