A new turbulent prandtl number model for forced fully-developed pipe heat transfer of liquid metals

With the proposal of liquid metals as coolant of the reactors , the use of accurate heat transfer correlation and reliable turbulent prandtl number（Prt）model of these low prandtl number fluids in turbulent flow is essential. The heat transfer of Liquid metals differ from traditional coolants for their good molecular heat conductivity and this property leads to a separation of the spatial extension of thermal and viscous boundary layers. A constant turbulent prandtl number is proved to be inappropriate for complex conditions for it depends on the Reynolds and molecular Prandtl number. This paper proposes a new turbulent prandtl number model Prt=C+B/Pet , which can be used for accurately predicting the heat transfer for liquid metal flows. The constants C and B of the expression are obtained from the analytic solution of renormalization group procedure. B is further corrected with the physical properties for different liquid metals. The results are in a good agreement with experimental data over the range of experimentally accessible Prandtl numbers. The Nusselt numbers calculated using the proposed model with the Lyon integral are found to be well consistent with the experimental data for forced fully-developed pipe flows with constant heat flow boundary conditions. Computational fluid dynamics(CFD) analysis is also carried out for pipe geometries. With the proposed model for turbulent prandtl number, CFD codes using RANS approach give similar results for local Nusselt numbers measured in the experiments.