Direct Numerical Simulation and RANS Modeling of Turbulent Natural Convection for Low Prandtl Number Fluids

Abstract

Results of direct numerical simulation (DNS) of turbulent Rayleigh-Be´nard convection for a Prandtl number Pr = 0.025 and a Rayleigh number Ra = 105 are used to evaluate the turbulent heat flux and the temperature variance. The DNS evaluated turbulent heat flux is compared with the DNS based results of a standard gradient diffusion turbulent heat flux model and with the DNS based results of a standard algebraic turbulent heat flux model. The influence of the turbulence time scales on the predictions by the standard algebraic heat flux model at these Rayleigh- and Prandtl numbers is investigated. A four equation algebraic turbulent heat flux model based on the transport equations for the turbulent kinetic energy k, for the dissipation of the turbulent kinetic energy ε, for the temperature variance θ2, and for the temperature variance dissipation rate εθ is proposed. This model should be applicable to a wide range of low Prandtl number flows.