A Reynolds-averaged Navier–Stokes closure model for natural convection based on Rayleigh–Prandtl scaling theory*

A new turbulence model has been developed for Reynolds-averaged Navier-Stokes (RANS) simulations of buoyancy-driven flows to overcome the incapability of existing models for accurately predicting Rayleigh-Bénard convection (RBC). In this study, the behavior of the commonly employed k-ε model for RBC is investigated at very high Rayleigh number (Ra) conditions. The present analysis reveals that the conventional k-ε model incorrectly predicts the turbulent heat flux as an exponentially growing solution, instead of converging to a correct finite value. To deal with this issue, a new model is proposed, aiming to accurately predict a steady-state heat transfer solution for RBC by applying the Grossmann and Lohse theory, which considers the Nusselt and Reynolds dependence on the Ra and Prandtl (Pr) numbers. The new model algebraically modifies the term in the ε equation that is related to buoyancy-induced turbulent kinetic energy production, allowing the new model to be used in conjunction with the k-ε model. The proposed modeling methodology for natural convection based on Ra-Pr scaling and dynamical systems theory, is expected to be applicable to other RANS models that include the buoyancy effect on turbulent kinetic energy.