New Turbulent Prandtl Number Model for Liquid Metal Based on DNS Results

Abstract Liquid metal is widely used as the primary coolant in many advanced nuclear energy systems. Prandtl number of liquid metal is much lower than the conventional coolant of water. Due to the high molecular thermal diffusion coefficients of liquid metal, the thermal conduction dominated region of liquid metal is much thicker than that of water. Logarithmic region for dimensionless temperature in the cross section is diminished due to the low Prandtl number effects. Conventional Nusselt number correlations derived from the logarithmic temperature distribution can not be used for liquid metal. For conventional coolant of water or air, the turbulent momentum field is similar with turbulent scalar field. Based on Reynolds analogy, the turbulent Prandtl number is assumed as one for the Reynolds Averaged Navier Stokes method. For turbulent convection of liquid metal, dissipations of turbulent scalar energies are larger than that of turbulent kinetic energies. Dissimilarity between the thermal and momentum field increases with the decreasing of Prandtl number. For turbulent convection of liquid metal, the turbulent Prandtl number is larger than one. In the current investigation, turbulent convection of liquid metal in channel is directly simulated with OpenFOAM. Turbulent statistics of the momentum and the thermal field are compared with the existed database to validate the numerical model. Power law for dimensionless temperature distribution with different Prandtl number is obtained by regression analysis of DNS results. New Nusselt number correlation is derived based on the power law of temperature distribution. The new Nusselt number correlation agrees well with the DNS results in the literature. Using the method of order magnitude analysis, relationships between the turbulent heat flux and turbulent scalar energy is analysed. Turbulent scalar energy is used to calculate the turbulent thermal diffusion coefficients. New correlation is proposed to consider Prandtl number effects on dissimilarity between the turbulent kinetic energy and the turbulent scalar energy. Then, new turbulent Prandtl number model for liquid metal is obtained. Combined with SST turbulence model, numerical results with the new turbulent Prandtl number model agree well with DNS results. The new Prandtl number model can be used for turbulent convection with different Prandtl number and with different Reynolds number.