Data-Driven Turbulence Modelling of Transient Unsteady Flow in Stratified Water Storage Tanks

The flow and thermal characteristics of thermal stratification appears in a wide range of industrial applications related to energy storage. In a previous study (Xu et al. submitted to Flow, Turbulence and Combustion), it has been shown that linear closure models in unsteady Reynolds averaged Navier–Stokes (RANS) calculations are unable to accurately capture the transient flow and thermal characteristics occurring in stratified water storage tank configurations. In the current study, we extend a data-driven framework to develop turbulence and heat flux closures for a three-dimensional (3D) geometry of a stratified water storage tank, using data from a highly resolved large eddy simulation. The transient high-fidelity data set is partitioned into several time-intervals used for closure development and testing. In detail, we first present the model formulations for 3D buoyant flow. We then use the reference data to extract the most suitable input features, i.e. variables used to regress the data driven model. In order to reduce the complexity of the resulting models and accelerate the training process, a recursive basis function elimination is performed, using alignment of the different basis functions with the target turbulence stress and heat flux as metric. Using the identified features and the subsets of basis functions, novel closures are then developed using a symbolic regression framework, based on Gene Expression Programming (GEP). Models are developed either for each time interval or for all intervals at once. The different machine-learnt turbulence and heat-flux closure models are then tested for two different tank configurations where the thermal stratification is affected by positively/negatively buoyant jets within simple or complex three-dimensional geometries. It is demonstrated that the extended GEP-based data-driven turbulence modelling approach is able to create models that can accurately predict flow with inherent unsteadiness in three dimensional complex-geometry cases.