Data-driven modeling of apparent added mass force in filtered two-fluid models for densely loaded gas-particle flows

Filtered two-fluid models (fTFMs) for gas-solid flows, supplemented with models for the effects of subgrid-scale structures, are frequently used to simulate industrial-scale fluidized beds because of the prohibitively high cost of fine-grid simulations of two-fluid models (TFMs). Previous studies have shown that the subgrid correction to the interphase interaction force (specifically, the drag force) is critical for accurate prediction of the flow hydrodynamics via fTFM simulations. Although early studies focused on analytical models for subgrid contributions, machine learning-based models have appeared in recent years. In the present study, an automated framework based on Bayesian optimization was used to train an artificial neural network (ANN) to predict the drag force in fTFMs. This optimized ANN model revealed a linear dependence of the filtered drag force on the filtered gas pressure gradient over most of the particle volume fraction range and filter sizes for various gas-solid systems. A constrained ANN model in which the linear dependence of the drag force on the filtered gas pressure gradient was explicitly enforced was found to be comparable to that of the unconstrained ANN model in accuracy, but its on-the-fly utilization in simulations could be less expensive from a computational perspective. The constrained ANN model, when introduced into the fTFM, shows that the overall dependence on the gas pressure gradient is altered upon filtering the drag force term, which has previously been shown to be equivalent to the emergence of an apparent added mass force term.