Numerical simulation of buoyant, turbulent flow—II. Free and mixed convection in a heated cavity

Abstract

In Part I of this study two models were developed for predicting free and mixed convection low Reynolds number turbulent flows. Detailed comparisons between measurements and predictions for the case of free convection along a heated, vertical, flat plate showed that both models yield accurate results for the mean flow and heat transfer. As a result, the simpler of the two (a k- ε formulation based on the notion of eddy diffusivities for momentum and heat) was extended to predict steady free and mixed convection flows of air in a strongly heated cavity of arbitrary rectangular cross-section and orientation. This is the subject of the present communication. Numerical calculations show that the details of free convection flow in a heated cavity are strongly governed by the characteristics of the local heat transfer. The characteristics depend on the cavity aspect ratio, a b , the inclination angle, α, and the Grashof number, Gr b . For example, stable stratification of heated fluid inside a tilted cavity strongly dampens the turbulent fluctuations, thus reducing convective heat losses from the cavity. Calculations performed for the free convection cases investigated experimentally by Humphrey et al [Sandia Report No. SAND 84–8192 (1985) ; Phil. Trans. R. Soc. A316, 57–84, (1985)] show good qualitative agreement with measurements of the velocity and temperature distributions. Predictions of the Nusselt number, Nu b , display trends which are also in accord with the measurements. For mixed convection, the details of the flow become asymptotically independent of a as the ratio of inertia to buoyant forces, characterized by Re 2 b Gr b , is increased. For a b = 1 and α = 45°, predictions reveal a minimum in Nu b when Re 2 b Gr b ~ 1 . Many of the complex flow patterns revealed experimentally, for both free and mixed convection, are reproduced numerically.