Physics-constrained machine learning for thermal turbulence modelling at low Prandtl numbers

TL;DR

This paper introduces a physics-constrained machine learning approach using neural networks to accurately model turbulent heat flux in low Prandtl number liquid metals, relevant for nuclear reactor cooling systems.

Contribution

It develops a novel algebraic structure with physical constraints and trains an ANN with DNS data, improving turbulence modeling for low Prandtl number fluids.

Findings

Model accurately predicts turbulent heat flux across Pr=0.01-0.71

Method outperforms existing thermal models in validation tests

Provides a robust and stable vectorial heat flux model

Abstract

Liquid metals play a central role in new generation liquid metal cooled nuclear reactors, for which numerical investigations require the use of appropriate thermal turbulence models 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 applicability, robustness and stability. The closure coefficients of the model are predicted by an Artificial Neural Network (ANN) which is trained with DNS data at different Prandtl numbers. The validity of the approach was verified through a priori and a posteriori validation for two and three-dimensional liquid metal flows. The model provides a complete vectorial representation of the turbulent heat flux and the predictions fit the DNS data in a wide range of Prandtl numbers (Pr=0.01-0.71). The comparison with other existing thermal models shows that the methodology is very promising.