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.@en

The paper reports on the numerical turbulence model in predicting mass, momentum and heat transfer in a partially divided cavity heated from the side using buoyancy-extended eddy-viscosity and elliptic relaxation approach with the algebraic expressions for the Reynold stress tensor and turbulent heat flux vector. The CDS (central differencing scheme) and LUDS (linear upwind differencing scheme) were used as the discretization method and the governing equations were solved using the finite volume method and Navier-Stokes solver. Validation of the model has been carried out by experimental data of convective flow in the cavity as well as by numerical data DNS (direct numerical simulation). The model agrees very well with the experiment and DNS and it is also able to demonstrate the performance which is comparable to that of the previous advanced second-moment closure model (SMC) in the literature. The results show that the model is suitable for use in simulations of the turbulent convective flow in a cavity with partition and it has the potential to be applied to more complex cavities and a wide range of turbulence levels.@en