High Rayleigh Number Natural Convection Inside 2D Porous Enclosures Using the Lattice Boltzmann Method

TLDR: In this article, a lattice Boltzmann method was employed to investigate natural convection inside porous medium enclosures at high Rayleigh numbers, and the effect of the form drag on the Nusselt number was studied by using a form drag modified Rayleigh number Ra C (extended from Ra m ).

Abstract: Lattice Boltzmann method (LBM) is employed to investigate natural convection inside porous medium enclosures at high Rayleigh numbers. Volume averaged porous medium model is coupled with the lattice Boltzmann formulation of the momentum and energy equations for fluid flow. A parallel implementation of the single relaxation time LBM is used, which allows the porous medium modified Rayleigh number Ra m to be as high as 10 8 . Heat transfer results in the form of the enclosure averaged Nusselt number Nu are obtained for higher modified Rayleigh numbers 10 4 ≤Ra m ≤ 10 8 . The Nu values are compared with values in the absence of the form drag term. The form drag due to the porous medium is found to influence Nu considerably. The effect of the form drag on Nu is studied by using a form drag modified Rayleigh number Ra C (extended from Ra m ). Utilizing the results for Nu in the high Ra m range, a correlation is proposed between Nu and Ra C for Darcy numbers 10 ―6 ≤ Da ≤ 10 ―2 , encompassing the non-Darcy flow regime.