ANALYSIS OF THE UNSTEADY REYNOLDS­AVERAGED SIMULATION TECHNIQUE FOR RAYLEIGH-BéNARD CONVECTION

This study investigates the capability of unsteady Reynolds-averaged Navier-Stokes(URANS) simulations in predicting turbulent Rayleigh-Bénard convection, with a particular focus on the prediction of convective cells and turbulent heat transfer. Previous researchers have posited that URANS can accurately simulate convective rolls, which in turn may enable reliable predictions of heat transfer in turbulent regimes. The analysis distinguishes between the effects modeled and resolved by URANS—the latter capturing the unsteady fluid motions' contributions to heat transport. By simplifying the RANS model equations, the study estimates the turbulence diffusivities for momentum and heat, and derives scaling relationships for the Rayleigh, Prandtl, and Nusselt numbers that demonstrate the influence of large-scale convection cells. This approach qualitatively explains previous observations on the diminishing modeled effects on heat flux at higher Rayleigh numbers as observed in prior studies by Kenjereš and Hanjalić [2006, Int. J. Heat. Fluid. Fl., Vol. 27, No.5.]. Additionally, the study estimates the velocity scale of convective cells predicted by URANS, factoring in the modeled turbulent viscosity and thermal diffusivity alongside Rayleigh and Prandtl numbers. Findings suggest that the velocity scale, consistent across various turbulence models, can be approximated using the free-fall velocity concept, irrespective of the modeled turbulent viscosity.