Numerical simulation of a low Prandtl number flow with a four-parameters turbulence model through an explicit algebraic definition of Reynolds stress and turbulent heat flux

Computational Fluid Dynamics codes usually adopt the Reynolds analogy in order to simulate dynamic and thermal flow fields for ordinary fluids like water and air. On the other hand, in low Prandtl fluids, such as heavy liquid metals like Lead-Bismuth Eutectic (LBE), the time scales of temperature and velocity fields are rather different and therefore similarity hypothesis cannot be used. Furthermore, to properly predict a complex flow field characterized by anisotropic behavior, it is necessary to overcome eddy-viscosity models and move to more advanced turbulence models. In the present work, we propose a nonlinear method for the computation of the Reynolds stress tensor and of the turbulent heat flux. Explicit algebraic models (EAM) and new time scales have been implemented using a logarithmic four parameters turbulence model (i.e. K-ω-K θ -ω θ ). This new model is validated through the simulation of plane channel and cylinder flows and results are compared with DNS data.