A Generalised Lattice-Boltzmann Model of Fluid Flow and Heat Transfer with Porous Media

Abstract

A numerical model, based on the Lattice Boltzmann Method, is presented for simulating two dimensional flow and heat-transfer in porous media. The drag effect of the porous medium is accounted by an additional force term. To deal with the heat transfer, a temperature distribution function is incorporated, which is additional to the usual density distribution function for velocity. The numerical model was demonstrated on a few simple geometries filled fully or partially with a porous medium: channel with fixed walls, channel with a moving wall, and cavity with a moving wall.The numerical results confirmed the importance of the nonlinear drag force of the porous media at high Reynolds or Darcy numbers. For flow through a full porous medium, the results shows an increase of velocity with porosity. The velocity profile for the partial porous medium, shows a discontinuity of velocity gradient at the interface when the porosity is very small. At higher Peclet number, the temperature in full and partial porous media is slightly higher, more so for the case of high heat dissipation at the wall.The good agreement of the GLBM solution with finite difference solutions and experimental results demonstrated the accuracy and reliability of the present model. Previous studies have been mainly focused on the effect of different Reynolds and Darcy numbers. In this thesis, it is extended to investigate the effect of different porosity and Peclet number.