Improving a Two-Equation Eddy-Viscosity Turbulence Model for High-Rayleigh-Number Natural-Convection Flows Using Machine Learning

This study presents data-driven modeling of the Reynolds stress tensor and turbulent heat flux vector for improving unsteady Reynolds-averaged Navier–Stokes (RANS) predictions of natural convection problems. While RANS-based calculations are cost-effective, conventional models fail to deliver the requisite predictive precision for high-Rayleigh-number practical engineering flows. To rectify this limitation, a gene-expression programing (GEP)-based machine-learning technique was employed to train novel models using a high-fidelity dataset from a vertical cylinder case with Ra = O(10¹³), which was generated using LES and validated against experimental data from Mitsubishi Heavy Industries (MHI). The newly developed data-driven closures for Reynolds stress and turbulent heat flux were then used to extend the realizable k-epsilon (RKE) turbulence model. The efficacy of these models was rigorously tested through a full a posteriori approach, involving URANS calculations with the newly constructed closures for the training case and two different testing cases. The results show that for cases with high Ra number (⁠$≥$10¹¹), the Nusselt number, temperature profiles, and velocity profiles exhibit significant enhancements due to the application of the GEP-based closures, initially developed using the Ra = O(10¹³) training case. However, for cases featuring lower Ra numbers, where standard RANS models already perform relatively well, the utilization of the current data-driven closures becomes un-necessary, potentially even leading to reduced simulation accuracy. This investigation carries implications for cost reduction in the design process of thermal engineering applications involving high-Rayleigh-number natural convection flows.