Lattice Boltzmann methods for modeling microscale flow in fibrous porous media

Abstract

A lattice Boltzmann description of fluid flow in heterogeneous porous media is presented which is intended for modeling flow processes which occur in liquid composite molding applications. The lattice Boltzmann method is equivalent to solving a hybrid method of the Stokes and Brinkman equations, with the Brinkman equation being implemented to model flow through porous structures, while the Stokes equation is applied to the open regions outside the porous structures. The Brinkman equation is recovered through a modification of the particle equilibrium distribution function, which reduces the magnitude of momentum at specified lattice sites, while leaving the direction of momentum unchanged. As a test of the new lattice Boltzmann model, steady transverse flow (saturated) through a square array of porous cylinders of elliptical cross section is investigated. Cell permeabilities obtained from the lattice Boltzmann simulations are in excellent agreement with a lubrication model, validating the lattice Boltzmann formulation of the Stokes and Brinkman equations.