Heat Transfer Numerical Simulations with the Four Parameter k-w-kt-et Model for Low-Prandtl Number Liquid Metals

The present work addresses a new effort towards the improvement of turbulence models for low-Prandtl number fluids, like heavy liquid metals, whose interest arises in many fields such as in the study of innovative nuclear fission reactors. The commonly used turbulence models are based on a similarity between the modeling of the velocity and energy Reynolds stress tensors that relies on the constant turbulent Prandtl number hypothesis. Unfortunately, for low-Prandtl number fluids, this assumption fails to reproduce the available experimental correlations and a rather different convective heat transfer behavior is observed. In order to simulate accurately liquid metal turbulent flows, in this work we consider the algebraic flux model (AFM) together with the four parameter k-w-kt-et model. We show some finite element numerical results by investigating the case of a vertical annular geometry. These results are compared with the simple eddy diffusivity (SED) and the generalized gradient diffusion hypothesis (GGDH) models. For a large range of forced flows the k-w-kt-et model is a powerful tool for predicting the heat transfer in flows with large dissimilarity between velocity and thermal fields.