A k-Ω-kθ-Ωθ four parameter logarithmic turbulence model for liquid metals

Turbulence modeling is one of the main issues when dealing with Computational Fluid Dynamics simulations. Models based on the Reynolds Averaged Navier Stokes equations are commonly used in several applications but, for liquid metals, the constant turbulent Prandtl number approximation leads to overestimate the heat transfer. In this work we propose a new k-Ω-kθ-Ωθ turbulence model which improves the k-ϵ-kθ-ϵθ four parameter model presented in [1]. The main difficulties encountered in the numerical implementation of the k-ϵ-kθ-ϵθ model are the nonlinear boundary conditions in kθ-ϵθ and the evaluation of the characteristic near wall times. By introducing the logarithmic variables Ω and Ωθ in order to avoid negative values, we can easily set appropriate boundary conditions and improve numerical stability. The new formulation of the model is validated and compared with Direct Numerical Simulation data and experimental correlations.