Natural Convection Modeling in an Open-Ended Square Cavity Partially Filled with Porous Media

Abstract

A two dimensional (2D) rectangular cavity with vertically partial filled porous media was proposed for modeling a Downhole Heat Exchanger in a well. The cavity has an open-ended boundary at the right side, and three non-slip flow boundaries on the others. The right part inside the cavity was filled with homogenous porous media, and the remained left part open free, which stands for the water in a well. The thermal boundary of the left side was given by a constant and low temperature, indicating the DHE extracting heat surface. The right side was open, which means that the fluid far from the reservoir can flow into the cavity or reversely. The powerful Lattice Boltzmann Method (LBM) was implemented to simulate the velocity and temperature profiles in the cavity, and the local Nusselt number at the left side of the cavity were numerically studied The influencing factors of Rayleigh number, Darcy number, porosity and width ratio on the Nusselt number were discussed. In addition, the position effect of interface separating the open fluid domain from the homogenous porous media on the Nusselt number has been investigated.