Numerical Heat Transfer Study of Liquid Metal in Triangular Rod Bundle Based on k-ε-kθ-εθ Model

Abstract

Compared with the constant turbulent Prandtl number (Prt) model, a four-equation model considers the difference between the velocity and temperature boundary layer of liquid metals by introducing the turbulence time-scale, which is expected to improve the numerical heat transfer accuracy of liquid metals with low Prandtl number (Pr) heat transfer characteristics. However, the transport form of a four-equation model is limited by its complex turbulent boundary conditions. In order to simplify the boundary conditions of turbulent variables and improve numerical stability for a four-equation model, an isotropic four-equation model that can use natural near-wall boundary conditions was considered in the present work. So, based on Taylor series expansion and near-wall turbulence analysis method, an isotropic four-equation kkθεθ model was established and the kkθεθ model coefficients and key damping functions for liquid metals were obtained. Based on the opensource computational fluid dynamics program OpenFOAM and the kkθεθ model solver, the fullydeveloped flow and heat transfer processes of liquid metals (Pr＝0.01) in triangular rod bundles with different Peclet numbers (Pe＝2504 000) and different pitchdiameter ratios (P/D＝125146) were numerically calculated. The numerical Nusselt number results of the isotropic fourequation kkθεθ model, Prt＝0.85 model and Kays model were compared with the available experimental and derivation correlations. The results show that Prt＝0.85 model and Friedland correlation overestimate the Nusselt number of liquid metals, and the heat transfer results of the Kays model and the kkθεθ model are almost between the experimental correlation. The prediction Nusselt number results of the Kays model and the kkθεθ model are similar at low Peclet numbers, but the isotropic kkθεθ model is conservative compared with Kays model at high Peclet numbers. With the increase of P/D, the kkθεθ model gradually intersects with the Subbotin correlation at a certain Peclet number. If P/D is constant, the Nusselt number increases with the increase of the Peclet number. While the Peclet number is not changed, the Nusselt number increases with the increase of P/D. Then detailed local heat transfer phenomena for liquid metals in triangular rod bundles were analyzed, including dimensionless temperature, dimensionless temperature fluctuation, dimensionless thermal diffusion coefficient and dimensionless turbulent Prandtl number. Due to the large thermal conductivity and thick thermal boundary layer of liquid metals, the molecular heat conduction nearwall is stronger than the turbulent heat diffusion. When the Peclet number reaches a certain degree, the inflection point of turbulent heat diffusion greater than molecular heat conduction begins to appear. With the increase of Peclet number, the mean turbulent Prandtl number decreases. With the increase of P/D, the average turbulent Prandtl number increases. Based on the isotropic fourequation kkθεθ model, simple turbulent boundary conditions can be used and more references can be provided for the calculation of liquid metal flow and heat transfer.