A new numerical scheme for using the two-energy equation model for turbulent buoyant flow in a composite enclosure

Abstract

Walls made of layers of different materials and sizes, including empty spaces, can be used for modulating energy transfer across such composite structures. By changing layer thicknesses and by using distinct porous and solid materials, the overall cavity Nusselt number can be modified in regard to its traditional behavior found in cavities fully fitted with porous materials or with no obstructions. Numerical simulations of transport equations for such composite systems poses an additional difficulty if one considers the different layers, appropriate interface conditions between them and the need to use one single computational domain for simplicity. Motivated by such engineering application and numerical need, this work presents the analysis about natural convection in a two-dimensional horizontal composite square cavity, using laminar and k-ε turbulence models. Both the one energy equation (1EEM) and two energy equation (2EEM) closures are applied. The composite square cavity is equally divided and formed by three distinct regions. Non-dimensional temperatures are proposed such that the entire computational domain is handled in a single numerical scheme. It was found that the fluid begins to permeate the porous medium for values of Ra greater than 10⁶. Nusselt number values show that for the range of Ra analyzed there are no significant variation between the laminar/turbulent and 1EEM/2EEM model solution. When comparing the effects of Ra, thermal conductivity ratio $k_s/k_f$ and Da on Nu, results indicate that $k_s/k_f$ has a greater influence in controlling heat transfer rates across the composite cavity.

Acknowledgments

The authors would like to express their gratitude to CAPES, FAPESP and CNPq, research funding agencies in Brazil, for their consistent financial support during the last twenty years.