Author(s)

R. Jecl, J. Kramer, J. Ravnik & L. ˇSkerget

Abstract

A thee-dimensional numerical simulation of convective flow in porous media using an algorithm based on a combination of a single domain and a subdomain boundary element method (BEM) is presented. The fluid flow in porous media is modeled with the modified Navier-Stokes equations (Brinkman-extended Darcy formulation with inertial term included) coupled with the energy and species equations using the Boussinesq approximation. The velocity-vorticity formulation is adopted to solve the governing set of equations, which results in decoupling of the computational scheme into the kinematic and kinetic computational parts. The boundary vorticity values are calculated by a single domain BEM solution of the kinematics equation, while the subdomain BEM is used to solve the vorticity, energy and species transport equations. Computations are performed for various governing parameters (Rayleigh number, Darcy number, Lewis number, buoyancy coefficient) and, simulation results are compared to the results of some published studies. Heat and mass flux through the cavity and flow fields are analyzed, focusing on the 3D nature of the phenomena. Keywords: boundary element method, porous medium, three-dimensional natural convection, Brinkman-extended Darcy formulation. 1 Introduction Problems of convective flow in saturated porous media can be found in a wide variety of engineering and natural applications, e.g. building thermal insulation, extraction of geothermal energy, heat exchangers, contaminant transport through water saturated soil. Most of the published studies, which are dealing with buoyancy induced flows in porous enclosures, are limited on the cases of two

Keywords

boundary element method, porous medium, three-dimensional natural convection, Brinkman-extended Darcy formulation