Numerical validation of a four parameter logarithmic turbulence model

Computational Fluid Dynamics codes are used in many industrial applications in order to evaluate interesting physical quantities, such as the heat transfer in turbulent flows. Commercial CFD codes use only turbulence models with an imposed constant turbulent Prandtl number Prt, which can give accurate results only for simulations when a strong similarity between the velocity field and the temperature field can be assumed. For fluids with a low Prandtl number, as for heavy liquid metals, a constant turbulent Prandtl number leads to an overestimation of the heat transfer, so experimental results and Direct Numerical Simulation cannot be reproduced. In this work we propose a new k-Ω-kθ-Ωθ turbulence model as an improvement of the k-ω-kθ-ωθ turbulence model, already validated by the authors, where Ω and Ωθ are calculated as the natural logarithm of the variables ω and ωθ. With this reformulation of the previous turbulence model we obtain some important advantages in numerical stability and robustness of the code. Results for the simulations of fully developed turbulent flows in two and three dimensional geometries are reported and compared with experimental correlations and DNS data, when available.