COMPUTATION OF TURBULENT NATURAL CONVECTION IN A RECTANGULAR CAVITY WITH THE k–ϵ––f MODEL

Abstract

A numerical study of natural convection in a rectangular cavity with the k − ϵ– − f model is presented. The primary emphasis of the study is placed on the investigation of accuracy and numerical stability of the k–ϵ––f models for a natural-convection problem. Both the original –f model [1] and its modified one [2] are considered. Both models are applied to the prediction of natural convection in a rectangular cavity together with the two-layer model. The original model exhibits the numerical stiffness problem when used with a segregate solution procedure such as the SIMPLE algorithm, and a simple remedy for this problem is proposed. The computed results are compared with the experimental data commonly used for validation of turbulence models. It is shown that the original –f model predicts accurately the mean velocity, velocity fluctuation, Reynolds shear stress, turbulent heat flux, and local Nusselt number at the hot wall. The modified –f model predicts all the quantities well, but the accuracy of solution is a little less than that of the original model. The two-layer model predicts the mean vertical velocity component poorly and underpredicts the turbulent quantities. As is already known from the literature, the modified –f model greatly enhances the numerical stiffness problem of the original model.

This study has been supported by the Nuclear Research and Development Program of the Ministry of Science and Technology of Korea. The authors are grateful to Prof. P. A. Durbin of Stanford University for kindly answering our questions about the –f model and the elliptic relaxation method by E-mail throughout the present work.