Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-uniform Heating of the Bottom Wall

Abstract

Numerical study on three-dimensional (3D), incompressible, four-sided lid (FSL) driven cavity flows has been conducted to show the effects of the transverse aspect ratio, K, on the flow field by using a multiple relaxation time lattice Boltzmann equation. The top wall is driven from left to right, the left wall is moved downward, whereas the right wall is driven upward, and the bottom wall is moved from right to left, all the four moving walls have the same speed and the others boundaries are fixed. Numerical computations are performed for several Reynolds numbers for laminar flows, up to 1000, with various transverse aspect ratios. The flow can reach a steady state and the flow pattern is symmetric with respect to the two cavity diagonals (i.e., the center of the cavity). At Reynolds number=300, the flow structures of the 3D FSL cavity flow at steady state with various transverse aspect ratio, i.e., 3, 2, 1, 0.75, 0.5 and 0.25 only show the unstable symmetrical flow pattern. The stable asymmetrical flow pattern could be reproduced only by increasing the Reynolds number that is above a critical value which is dependent on the aspect ratio. It is found that an aspect ratio of more than 5 is needed to reproduce flow patterns, both symmetric and asymmetric flows, simulated by using 2D numerical models.

壁面漏热的冷却腔体内增加薄壁隔板引起的热效应数值研究

“…LBM has been found to be an efficient tool for solving natural convection (Bararnia et al, 2011;Kefayati, 2016;Ren and Chan, 2016) and mixed convection (Kefayati et al, 2012;Bettaibi et al, 2015). Unlike conventional numerical methods based upon the NavierStokes equation, the LBM uses pseudo particles that represent information of the distribution function to simulate the flow field.…”

Mixed convection in a driven cavity with an internal obstacle using the lattice Boltzmann method

“…To cover the larger spectrum of flow characteristics, they employed a wide range of Re and Ra. In the last two decades, mixed convection had been studied using LBM in a driven cavity with various types of fluids and boundary conditions [12][13][14][15][16]. Karimipour et al [12] used a copper-water nanofluid to study mixed convection in an inclined cavity.…”

“…They discovered that the Richardson number can be used to determine the relative significance of natural and forced convection modes in heat transport. Bettaibi et al [14] used multiple relaxation time LBM to investigate mixed convection in a differentially heated cavity and discovered that heat transmitted in terms of Nusselt number rose as Ri decreased. Abu-Nada et al [15] investigated mixed convection by flowing a nanofluid through a square chamber with a wavy bottom wall.…”