Simulation of a fluid flow and investigation of a permeability-porosity relationship in porous media with random circular obstacles using the curved boundary lattice Boltzmann method

Abstract

In this paper, the fluid flow between two parallel flat plates filled with porous media was investigated numerically using the Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM). The obstacles representing porous media were considered as random, circular, rigid and granular ones with uniform diameters and without overlap. The fluid was supposed to be a single-phase viscous Newtonian fluid and the flow to be incompressible, steady and laminar. The uniform velocity profile was considered at the entrance of the canal and the no-slip condition was imposed at solid walls. For applying curved boundary conditions, the linear interpolation method ( $ \Delta$ fraction) was used in this work. The effect of varying the Reynolds number on the pressure gradient and the Darcy drag was studied. The porous medium was supposed to be isotropic and having scalar permeability. The dimensionless permeability was calculated as a function of the Knudsen number. Also, the dimensionless permeability versus porosity was investigated and the results were compared with the Clague equation for different materials. Because of rather low precision of the Clague equation at high porosities, an extension to the Clague equation was presented. The permeability-porosity relationship was surveyed and the corresponding curve was plotted in the LBM scale. It was seen from numerical results that the enhancement of the Knudsen number increases the dimensionless permeability. The change of streamlines tortuosity in terms of porosity was explored and the results were compared with the revised Bruggeman equation. The obtained results demonstrate that the Lattice Boltzmann Method is very useful in the challenging problems of fluid dynamics such as fluid flow simulation through porous media.