Numerical Simulation of Mixed Convection in a Lid Driven Cavity with Porous Obstacle Using (MRT-LBM)

Abstract

In this work, we study numerically a problem of mixed convection in lid driven square cavity, filled with air (Pr = 0.71), whose upper wall is movable and kept at constant cold temperature T_C. The cavity contains a porous obstacle of height h and width b, placed on the middle of bottom wall which maintained at a constant hot temperature TH. The side walls are adiabatic. Darcy-Brinkmann model is used for modeling the momentum equations in porous medium. The Boussinesq assumption is used and the viscous dissipation is assumed to be negligible. This numerical study is based on the multiple-relaxation-time Lattice Boltzmann method (MRT-LBM). The D2Q9 two-dimensional model is adopted to the dynamic part, while the D2Q5 model is applied for the thermal part. The objective of the study is to analyze the effect of Darcy number (10⁻⁶≼ Da ≼ 10⁻¹), Richardson number (0.01 ≼Ri≼ 10³) and the aspect ratio w = b/H (0.2 ≼ w ≼ 1) on the hydrodynamic and thermal characteristics in the cavity through the velocity and temperature as well as the average Nusselt number. The results obtained show a considerable effect of these parameters on the structure of the flow and the heat transfer in the cavity, which can not be neglected.