Proposal of a turbulent Prandtl number model for Reynolds-averaged Navier-Stokes approach on the modeling of turbulent heat transfer of low-Prandtl number liquid metal

Because of their high molecular heat conductivity, low-Prandtl number liquid metal is a promising candidate coolant for various designs of advanced nuclear systems such as liquid metal-cooled fast reactors and accelerator-driven subcritical system (ADS). With the fast-growing computational capacity, more and more attention has been paid to applying computational fluid dynamics (CFD) methods in thermal design and safety assessment of such systems for a detailed analysis of three-dimensional thermal-hydraulic behaviors. However, numerical modeling of turbulent heat transfer for low-Prandtl number liquid metal remains a challenging task. Numerical approaches such as wall-resolved large eddy simulation (LES) or direct numerical simulation (DNS), which can provide detailed insight into the physics of the liquid metal flow and the associated heat transfer, were widely applied to investigate the turbulent heat transfer phenomenon. However, these approaches suffer from the enormous computational consumption and are hence limited only to simple geometrical configurations with low to moderate Reynolds numbers. The Reynolds-averaged Navier-Stokes (RANS) approach associated with a turbulent Prandtl number Pr-t accounting for the turbulent heat flux based on Reynolds analogy is still, at least in the current state in most of the circumstances, the only feasible approach for practical engineering applications. However, the conventional choice of Pr-t in the order of 0.9 similar to unity in many commercial computational fluid dynamics codes is not valid for the low-Prandtl number liquid metal. In this study, LES/DNS simulation results of a simple forced turbulent channel flow up to a friction Reynolds number Re-tau of 2000 at Pr of 0.01 and 0.025 were used as references, to which the Reynolds-averaged Navier-Stokes approach with varying Pr-t was compared. It was found that the appropriate Pr-t for the RANS approach decreases with bulk Peclet number Pe(b) and approaches a constant value of 1.5 when Pe(b) becomes larger than 2000. Based on this calibrated relation with Pe(b), a new model for Pr-t used in the RANS approach was proposed. Validation of the proposed model was carried out with available LES/DNS results on the local temperature profile in the concentric annulus and bare rod bundle, as well as with experimental correlations on the Nusselt number in a circular tube and bare rod bundle.