Extended Eddy-Viscosity Model to Rayleigh-Benard Convection in Cavity

Abstract

This paper presents a study of developing a numerical turbulent model in a cavity heated from below using eddy viscosity combined with elliptic relaxation approach. The model uses a set of differential equations that consist of kinetic energy, its dissipation, variance of temperature, velocity scale and elliptic relaxation parameter, which are solved using a finite-volume and Navier-Stokes solver. The unresolved stress tensors and heat flux vectors are modelled with an algebraic formula. The discretization method is carried out by CDS, or second-order differencing scheme, and LUDS, or second-order linear upwind scheme. The model is applied to the natural convection heated from below, known as Rayleigh-Benard convection, in a two-dimensional cavity with a height-to-length aspect ratio of 1:1.5, 1:4, and 1:8. The model has been validated using numerical data from DNS (direct numerical simulation) and experiments. The model produced similar results with both DNS and experiments. It was also shown that the model can visualize the main feature of turbulent convective flow in the enclosure for various aspect ratio.