Towards robust and accurate Reynolds-averaged closures for natural convection via multi-objective CFD-driven machine learning

Abstract

Robust and accurate Reynolds-averaged stresses and scalar fluxes closure models for natural convection developed by machine learning are presented in this work. In comparison to passive scalar flows, the complexity of turbulence modelling for natural convection problems is increased as the velocity and scalar fields are strongly coupled by the buoyancy force. Therefore, the appropriate Reynolds-averaged closure models for natural convection ought to capture this interaction within the second-moment terms. Previous data-driven turbulence modelling approaches have treated the unclosed terms of the velocity and thermal fields separately, which has lead to inaccurate predictions when handling natural convection problems. In this study, we therefore develop fully coupled buoyancy-extended models by using a novel multi-objective and multi-expression machine-learning framework that is based on CFD-driven training (Zhao et al., J. Comput. Phys., 411, 109413, (2020)). The model candidates obtained from a Gene-Expression Programming approach, and thus available in symbolic form, are evaluated by running RANS solvers for different Rayleigh number cases during the model training process. This novel framework is applied to vertical natural convection, with the emphasis of this paper on the importance of coupling the explicit closure model formulations, the choice of cost functions, and the appropriate input flow features (i.e. a generalised flux Richardson number) for developing accurate models. It is shown that the resulting machine-learnt models improve the predictions of quantities of interests, e.g. mean velocity and temperature profiles, across a wide range of Rayleigh numbers.