A comprehensive, data-driven, universal force modeling approach for dense particle-laden flows

Current models for dense, particle-laden, non-stationary flow force predictions have been subject to scrutiny from the multiphase flow community in recent years. Much innovation has occurred through the use of particle-resolved direct numerical simulation (PR-DNS) methods in developing empirical formulas via volume averaging the force for all the particles in a domain; however, machine learning (ML) offers a promising avenue for statistically inferring individual particle properties over a wide range of parameters, improving the viability of these closure models for Euler-Lagrange (EL) simulations. With data paucity remaining an issue for most ML researchers, this approach overcomes it through two avenues. One is by running 48 PR-DNS simulations, covering volume fractions between 1.68%-26.22%, particle density ratios between 2.56-256, and Reynolds numbers between 10-60. The second is by using an interpretable and hierarchical equivariant neural network to preserve rotational and reflectional symmetries which simplifies the necessity for larger datasets as these equivariant forces do not need physical representation within the data. Preliminary results of this force closure model are promising, with over 80% accuracy in predicting lift and drag when compared against PR-DNS results. This highly interpretable and generalizable physics-informed hierarchical network is also under investigation for the novel implementation of its framework's inference capabilities in EL simulations.