A-priori evaluation of data-driven models for large-eddy simulations in Rayleigh-Bénard 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. The models' development is performed using reference direct numerical simulation data of a typical natural convection case, i.e. the Rayleigh-B & eacute;nard convection (RBC). The training frameworks are built by using alignment as the evaluation metrics of the basis functions when comparing to the Gaussian-filtered SGS stress and SGS heat-flux. The trained models in isotropic form, by utilizing the L 2 norm of the grid cell 4 L 2 as the length scale, 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 scale 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 the prediction of both instantaneous and mean quantities for a wide range of filter widths.