Simulating Natural Turbulent Convection Fluid Flow In An Enclosure Using The Two-Equation Turbulent Models

ABSTRACT

This study assesses the performance of three numerical turbulence models; k -e ,

k -w and k -w - SST in predicting heat transfer due to natural convection inside an

air filled cavity. The heat transfer due to natural convection inside a rectangular

closed cavity should be modeled to include the effect of turbulence for Rayleigh

number greater than or equal to 9 10 .The non-linear terms i j u u and qi u in the

averaged momentum and energy equations respectively were modeled using the

k -e , k -w and k -w - SST models to close the governing equations. The cavity is

maintained at 283 K on the cold wall and 323 K on the opposite hot wall. The other

four walls are adiabatic.The vorticity-vector potential formulation has been used to

eliminate the need to solve the pressure term. The vorticity, vector potential, energy

and the two-equations for respective models together with their boundary conditions

were solved using finite difference approximations. The results obtained for velocity,

temperature, Nusselt number and turbulent kinetic energy for the three turbulence

models were compared to experimentally determined values. The comparisons

showed that k -w - SST model performs better than both k -e and k -w models in

the whole enclosure.The k -w - SST was then used in a test case problem of heating

and cooling on the same wall. For the test problem, it has been found that the room is

stratified into three regions: a cold upper region, a hot region in the area between the heater and window and a warm lower region.