Machine Learning Approaches to Close the Filtered Two-Fluid Model for Gas-Solid Flows: Models for Subgrid Drag Force and Solid Phase Stress

Gas-particle flows are commonly simulated through a two-fluid model at the industrial scale. However, these simulations need a very fine grid to have accurate flow predictions, which is prohibitively demanding in terms of computational resources. To circumvent this problem, the filtered two-fluid model has been developed, where the large-scale flow field is numerically resolved and small-scale fluctuations are accounted for through subgrid-scale modeling. In this study, we have performed fine-grid two-fluid simulations of dilute gas-particle flows in periodic domains and applied explicit filtering to generate data sets. Then, these data sets have been used to develop artificial neural network (ANN) models for closures such as the filtered drag force and solid phase stress for the filtered two-fluid model. The set of input variables for the subgrid drag force ANN model that has been found previously to work well for dense flow regimes is found to work as well for the dilute regime. In addition, we present a Galilean invariant tensor basis neural network (TBNN) model for the filtered solid phase stress, which can nicely capture the anisotropic nature of the solid phase stress arising from subgrid-scale velocity fluctuations. Finally, the predictions provided by this new TBNN model are compared to those obtained from a simple eddy-viscosity ANN model.