Numerical simulations of Stokes Brinkman equations for permeability prediction of dual scale fibrous porous media

Abstract

A new finite-element scheme to solve the Stokes-Brinkman equation for flow analyses in dual scale porous media is presented and has been applied to predict the effective permeability of dual scale fibrous media Both continuous and discontinuous stress conditions at the interface between a porous media and a surrounding fluid are explored by introducing an equivalent momentum equation for the Brinkman equation The proposed scheme uses a uniform structured regular rectangular mesh to discretize the domain and employs the level-set method to describe the porous media allowing for inclusion of complex geometrical features easily Biperiodic boundary conditions have been applied to conduct the flow analysis in a representative volume of mesoscale porous structures Numerical solutions in a parallel channel flow over a porous media are presented and compared with analytic solutions to assess the accuracy of the proposed scheme The scheme is then applied to flow past two regular periodic geometries of elliptic porous media in two dimension, representing unidirectional fiber tow (bundle of aligned fibers) in a textile fabric, to predict the effective permeability and its dependence on the fiber volume fraction, the aspect ratio, the fiber tow permeability, and the degree of compaction of the fiber tows In addition, we propose a simple relationship between the effective permeability and the permeability of fiber tow, based on numerical and analytic results (C) 2010 American Institute of Physics [doi 10.1063/1.3484273]