Machine-learnt closure models based on computational space training frameworks for large-eddy simulations in natural convection

Natural convection heat transfer at very high Rayleigh numbers ( Ra ) is a commonly occurring phenomenon in many industry applications. Practically, Large Eddy Simulations (LES) are often chosen as an economical method for the numerical prediction of these flows. However, developing accurate LES models that generalize well to complex geometries poses a challenge, particularly for data-driven methods. Thus, in the current study, machine-learnt closure models with the general choice of length scales for different geometries are proposed, where the subgrid-scale (SGS) stress and heat-flux models developed by using Gene Expression Programming (GEP) are built in the computational space. Two geometrically distinct natural convection cases (Rayleigh–Bénard convection and the concentric horizontal annulus) are chosen to develop and generalize the models. Subsequently, the formulation between the SGS closures, the total and the resolved large-scale turbulent stress and heat-flux is derived in the compressible LES context. The a-priori results show that the GEP models developed in computational space significantly improve both the SGS stress and SGS heat-flux prediction while being robust to complex flows. Similarly, the a-posteriori results demonstrate that the GEP models perform better than the wall-adapting local eddy-viscosity (WALE) model in the prediction of the mean SGS stress and the SGS heat-flux. The data-driven approach for turbulence model development presented clearly offers a promising models’ generalization for LES in the prediction of SGS stress and heat-flux. • A direct numerical simulation of natural convection in concentric horizontal annulus. • Machine learned non-linear SGS models for natural convection based on the computational space are developed for complex flow. • A-posteriori evaluation of the GEP models by comparing the total turbulent stress and heat-flux to DNS.