Numerical validation of a k-w-kt-wt heat transfer turbulence model for heavy liquid metals

The correct prediction of heat transfer in turbulent flows is relevant in almost all industrial applications but many of the heat transfer models available in literature are validated only for ordinary fluids with Pr=1. In commercial Computational Fluid Dynamics codes only turbulence models with a constant turbulent Prandtl number of 0.85-0.9 are usually implemented but in heavy liquid metals with low Prandtl numbers it is well known that these models fail to reproduce correlations based on experimental data. In these fluids heat transfer is mainly due to molecular diffusion and the time scales of temperature and velocity fields are rather different, so simple turbulence models based on similarity between temperature and velocity cannot reproduce experimental correlations. In order to reproduce experimental results and Direct Numerical Simulation data obtained for fluids with Pr=0.025 we introduce a k-e-kt-et turbulence model. This model, however, shows some numerical instabilities mainly due to the strong coupling between κ and on the walls. In order to fix this problem we reformulate the model into a new four parameter k-w-kt-wt where the dissipation rate on the wall is completely independent on the fluctuations. The model improves numerical stability and convergence. Numerical simulations in plane and channel geometries are reported and compared with experimental, Direct Numerical Simulation results and with results obtained with the k-e formulation, in order to show the model capabilities and validate the improved k-w model.