Turbulent heat flux modelling in forced convection flows using artificial neural networks

Fluid dynamics of liquid metals plays a central role in new generation liquid metal cooled nuclear reactors, for which numerical investigations require the use of an appropriate thermal turbulence model for low Prandtl number fluids. Given the limitations of traditional modelling approaches and the increasing availability of high-fidelity data for this class of fluids, we propose a machine learning strategy for the modelling of the turbulent heat flux. A comprehensive algebraic mathematical structure is derived and physical constraints are imposed to ensure attractive properties promoting stability and realizability. The closure coefficients of the model are predicted by an Artificial Neural Network (ANN) which is trained with the available Direct Numerical Simulation (DNS) data at different Prandtl numbers. The validation shows that the ANN provides an accurate representation of the heat flux in a wide range of Prandtl numbers (Pr = 0.01–0.71) and compares well with other existing thermal closures. Nevertheless, simulations with different auxiliary models to compute the inputs of the ANN revealed a certain sensitivity of the data-driven formulation on the models used in combination with it. In particular, the ANN model strongly relies on the Reynolds stress anisotropy. Such a sensitivity limits the robustness of the model to the inaccuracies of the underline momentum field and the momentum turbulence model applied in combination with it