Turbulent natural convection in a differentially heated square cavity

Abstract

Natural convection in a side or differentially heated cavity is a classical problem in heat transfer. The problem represents a wide range of engineering applications and has also been commonly used as a benchmark problem for validating Computational Fluid Dynamics (CFD) computer programs. This study investigates turbulent natural convection of a fluid with a Prandtl number of 0.71 in a differentially heated square cavity with adiabatic top and bottom walls. Two different boundary conditions are applied to the side walls; (1) the standard isothermal side wall problem, and (2) the mixed isoflux/isothermal problem, which has a constant heat flux on the heated side wall with an isothermal cold wall on the opposite side. An experimental study is carried out to determine the net convective heat transfer between isothermal hot and cold walls for a range of wall temperature differences in the laminar flow regime. The experiment data is compared with CFD predictions, and they are found to be in reasonable agreement. The ANSYS Fluent CFD package is used for numerical modelling in this study. Turbulent natural convection in the standard isothermal and the mixed isoflux/isothermal cavity are modelled with the two-dimensional Reynolds Averaged Navier-Stokes (RANS) equations using the standard k-ω turbulence model, and in three-dimensions using Large Eddy Simulation (LES) with the Dynamic Smagorinsky-Lilly subgrid scale model, for Rayleigh numbers of 107 to 1012. Both turbulence models predict a similar Nusselt and Rayleigh number relationship for the standard isothermal problem. However, LES predicts a constant vertical velocity scale for all Rayleigh numbers, while RANS predicts a thicker velocity boundary layer with a decrease in vertical velocity with increasing Rayleigh number. For the mixed isoflux/isothermal problem, the Nusselt and Rayleigh number relationship predicted by RANS and LES are identical with the laminar solution for Rayleigh numbers less than 107. But at higher Rayleigh numbers, LES predicts a lower Nusselt number than the RANS model. For the mixed isoflux/isothermal problem, the normalised temperature at mid-height of the cavity is less than that for the standard problem, and consequently the vertical velocity is also smaller since there is a smaller buoyancy force. Moreover, the asymmetric boundary conditions lead to an asymmetric velocity profile, with the upward vertical velocity near the isoflux heated wall being slightly less than the downward velocity near the isothermal cold wall.