A CFD four parameter heat transfer turbulence model for engineering applications in heavy liquid metals

In ordinary fluids, such as water or air, similarity between thermal and dynamical fields holds and it is commonly accepted that implementing a Computational Fluid Dynamics (CFD) code for a two-equation turbulence model with the hypothesis of a constant turbulent Prandtl number in the range 0.85–0.9 is sufficient to obtain reliable results both for velocity and temperature fields. In heavy liquid metals such as sodium, lead and Lead–Bismuth Eutectic (LBE) with low Prandtl number (Pr ≈ 0.025) the time scales of temperature and velocity fields are rather different, because heat transfer is due mainly to molecular diffusion. In these fluids a standard constant turbulent Prandtl number model fails to reproduce correlations build from experimental data and predicts a too high heat transfer. Heavy liquid metals are promising coolant fluids for achieving the necessary requirements of fast nuclear reactors and many European projects have been started with the purpose of developing CFD codes able to correctly predict turbulent heat transfer for these fluids. The present work addresses an effort to improve the prediction of turbulent heat transfer for liquid metal flows in plane and cylindrical geometries assessing a κ–∊–κθ–∊θ four parameter turbulence model. In particular the simulations aim to reproduce fully developed thermal and velocity profiles by using a standard finite element implementation of the Navier–Stokes equations coupled with the energy and momentum turbulence models. A modified κ–∊ system with low-Reynolds model functions is used for the turbulent velocity field while a κθ–∊θ system is employed to compute the turbulent temperature field. The results of the simulations are compared with Direct Numerical Simulations (DNS) data and with heat transfer experimental correlations in order to validate the four parameter turbulence model. Different uniform heat flux boundary conditions with zero and constant temperature fluctuations at the wall are presented.