Data-driven large eddy simulation modelling in natural convection

Natural convection is a commonly occurring heat-transfer problem in many industrial flows and its prediction with conventional large eddy simulations (LES) at higher Rayleigh numbers using progressively coarser grids leads to increasingly inaccurate estimates of important performance indicators, such as Nusselt number (Nu). Thus, to improve the heat transfer predictions, we utilize Gene Expression Programming (GEP) to develop sub-grid scale (SGS) stress and SGS heat-flux models simultaneously for LES. With that as the focus, in the present study, two geometrically distinct natural convection cases are considered to develop and generalize turbulence models. The Rayleigh-Benard Convection (RBC) is used to develop models, while the Concentric Horizontal Annulus (CHA) is used to test the model generalization. An in-house compressible solver, HiPSTAR, for simulating natural convection flows for low Mach number problems is benchmarked against the experiments and Direct Numerical Simulations (DNS) results. Subsequently, HiPSTAR is used to run simulations for the RBC and CHA configurations and the generated DNS database is then used to train and assess LES models. The models’ development starts with RBC, where the fluid is in a cubic box with the bottom wall as the hot wall and the top wall as the cold wall. The alignment between different basis functions and the Gaussian-filtered SGS stress and SGS heat flux is used to determine the most suitable training framework. The trained models in isotropic form, by utilizing the norm of the grid cell as the length scales demonstrate good performance in the bulk region, but less improved performance in the near wall region. It is shown, that for LES of wall-bounded flow, the GEP models in anisotropic form, i.e. using different grid length scales for the different spatial directions, are required to obtain generalized models suitable for different regions. Consequently, the a-priori results demonstrate a significant improvement in th