Assessment of turbulence models in natural convection from two- and three-dimensional rectangular enclosures

In this study, unsteady turbulent natural convection heat transfer in two- and three-dimensional rectangular enclosures is investigated numerically. The enclosures are heated and cooled from the vertical opposing isothermal walls. All other side walls are assumed to be smooth and adiabatic. The working fluid is air (Pr = 0.71), and the flow is turbulent. Two- and three-dimensional unsteady-state continuity, Reynolds-Averaged Navier-Stokes (RANS), along with the averaged-energy equation, are solved using the commercial software - FLUENT 6.3.26®. Standard k−ε (SKE), Re-Normalization Group k−ε (RNGKE), Realizable k−ε (RKE), Reynolds Stress Model (RSM), Standard k-ω (SKW) and Shear Stress Transport k−ω (SSTKW) RANS models are used in conjunction with the two-layer (or Enhanced Wall Treatment, EWT) wall model for Rayleigh numbers ranging from 108 to 1013. The performance of the turbulence models on the heat transfer rate predictions is comparatively investigated for 2D square enclosure, as well as 3D rectangular enclosures having the slenderness ratio of H/W = 1 and H/W = 10. The heat transfer rate predictions are assessed for each case via surface-averaged mean Nusselt numbers over the hot wall, and empirical power-law correlations are derived for 2D and 3D enclosures for each turbulence model. The study reveals that 3D laminar and RANS models yield almost identical mean Nusselt number predictions up to Ra = 1010, and these predictions are compatible with those of obtained from 2D simulations. For larger Rayleigh numbers, the mean Nusselt numbers the flow becomes three-dimensional and 2D RANS models do not yield accurate predictions. The study reveals that 3D RANS models yield more accurate mean Nusselt numbers, and a mean Nusselt number correlation is proposed.