Numerical Implementation and Performance of Macroscopic Models for Natural Convection in Square Cavities with Porous Inserts

Abstract

The study of problems dominated by natural convection through obstacles is of relevance in various fields of engineering. We may find examples where obstacles can be modeled explicitly (i.e. heat exchangers) and examples where it is convenient and practical to avoid this representation considering the obstacles as a porous medium (i.e. the cooling tank of an electrical power transformer). In this work, two-dimensional numerical solutions are presented for a variant of the classical problem of natural convection in a square cavity with Dirichlet boundary conditions. The cavity has been divided into two regions. In one region, the flow circulates in a clear space, while in the other one, the flow circulates through an array of circular solid obstacles. This can be simulated employing the actual geometry (direct simulation) or with a porous media model. In the last one, the region with obstacles is replaced by a homogeneous region where the conservation laws are affected by the interaction between the fluid and solid faces, and this interaction is represented by characteristics parameters of the medium, like the porosity and the permeability. A FEM-based program has been used to carry out the simulations. We have been able to verify the good performance of the porous model against the direct simulation in the laminar regime in terms of the velocity and temperature profiles, stratification levels and heat transfer through the vertical wall of the cavity. The main advantage in the use of porous models is the significant reduction in the computational cost. In this work we have been able to carry out porous model simulations in a third of the total time consumed by the direct simulation of the problem with the same amount of computational resources.