New Nusselt Number Correlation and Turbulent Prandtl Number Model for Turbulent Convection with Liquid Metal Based on Quasi-DNS Results

Liquid metal is widely used as the primary coolant in many advanced nuclear energy systems. Prandtl number of liquid metal is much lower than that of the conventional coolant of water or gas. Based on the Reynolds analogy, the turbulent Prandtl number is assumed to be a constant around unity. For the turbulent convection of liquid metal, dissipations of half the temperature variance are larger than those of turbulent kinetic energies. The dissimilarity between the thermal and momentum fields increases as Pr decreases. The turbulent Prandtl number is larger than one for the liquid metal. In the current investigation, the turbulent convection of liquid metal in the channel is quasi-directly simulated with OpenFOAM-7. The turbulent statistics of the momentum and the thermal field are compared with the existing database to validate the numerical model. The power law for dimensionless temperature distribution with different Prandtl numbers is obtained by regression analysis of numerical results. A new Nusselt number correlation is derived based on the power law. The new Nusselt number correlation agrees well with the DNS results in the literature. The momentum mixing process between different layers in the cross section is compared with the thermal mixing process. The effects of the Prandtl number on the difference between the turbulence time scale and scalar time scale are analyzed. A new turbulent Prandtl number model with local parameters is obtained for turbulent convection with liquid metal. Combined with the k − ω model, the temperature distributions with the new turbulent Prandtl number model agree well with the DNS results in the literature. The new turbulent Prandtl number model can be used for turbulent convection with different Prandtl and different Reynolds numbers.