The role of permeability in lid-driven cavity flow containing a cluster of hot solids

Abstract

The flow behavior of particle clusters with thermal convection in confined fluid flow has garnered considerable attention. One of the remaining challenges is to understand the role of a porous structure of particle clusters in the confined thermal fluid flow. In present work, a numerical study based on a double distribution function lattice Boltzmann model has been conducted to unveil the two-sided lid-driven cavity flow containing a hot cluster formed by an array of center-placed solids. First, we investigated the heat transfer by varying the Richardson number (Ri, from 0.01 to 1.0) and the solid fraction of the cluster (ϕ, from 0.0143 to 0.6734) with fixed cavity Reynolds number (Re=1000) and Prandtl number (Pr=0.7). The increase in Ri would lead to the formation of non-centrosymmetric streamlines and isotherms and an increase in the total averaged Nusselt number Nu¯a, in which several vortex structures being identified at high Ri and ϕ. Then, we explored the influence of permeability, quantified by the Darcy number (Da), by changing the porous structure of cluster via rearranging the array of solids. It is found that a higher permeability could enhance heat transfer of particle cluster due to the increase in convection, but the smaller surface area of solid particles would limit heat transfer. A correlation of Nu¯a with respect to Ri and Da could be developed based on our two-dimensional simulation results, allowing the evaluation of involved interplay between the porous structure of particle cluster and thermal convection in confined flow via a simple yet effective way.