A non-linear turbulence model of supercritical fluid considering local non-equilibrium of Reynolds stress transport

For supercritical fluid turbulence, the traditional Reynolds-averaged Navier–Stokes models cannot yield satisfying predictions under the heat transfer deterioration condition due to the modifications of the buoyancy on turbulence. Direct numerical simulation results reveal that in the buoyancy flow, the linear Reynolds stress constitutive equation in the eddy viscosity model (EVM) is invalidated, and the pressure fluctuation contributes to Reynolds stress transport. A new modeling approach for the EVM of supercritical flow is investigated in two aspects: (i) the analytical solution of the pressure strain term in the Reynolds stress transport equation is obtained by solving the Poisson equation of the pressure fluctuation of supercritical flow, and then, the models of the slow term and rapid term are proposed and (ii) a non-linear constitutive equation between the Reynolds stress and the mean strain rate is proposed. Combining these two points, the modified expressions for the eddy viscosity and turbulent Prandtl number are finally developed. We find that the accuracy of the prediction by the new model on supercritical fluid heat transfer and turbulence statistics in vertical flow and horizontal flow can be significantly improved.