Effectiveness of several turbulence models in natural convection

Heat transfer due to natural convection inside a closed cavity must be modeled to include the effects of turbulence if the Rayleigh number is sufficiently large. This study assesses the performance of several commonly used numerical turbulence models such as k-epsilon, Renormalized Group k-epsilon and Reynolds stress model, in predicting heat transfer due to natural convection inside an air-filled cubic cavity. The cavity is maintained at 307 K on one side and 300 K on the opposite side with a linear temperature variation between these values on the remaining walls. Two cases are considered, one in which the heated side is vertical, and the other in which it is inclined at 45degrees from the horizontal. Rayleigh numbers of 10(7) 10(8), 10(9) and 10(10) are considered. Results of the three turbulence models are compared to experimentally determined values or values from correlations. It was found that the standard k-epsilon model was the most effective model in terms of accuracy and computational economy.