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This study presents two different machine learning approaches for themodeling of hydrodynamic force on particles in a particle-laden multiphaseflow. Results from particle-resolved direct numerical simulations (PR-DNS) offlow over a random array of stationary particles for eight combinations ofparticle Reynolds number ($Re$) and volume fraction ($\phi$) are used in thedevelopment of the models. The first approach follows a two step process. Inthe first flow prediction step, the perturbation flow due to a particle isobtained as an axisymmetric superposable wake using linear regression. In thesecond force prediction step, the force on a particle is evaluated in terms ofthe perturbation flow induced by all its neighbors using the generalizedFax\'en form of the force expression. In the second approach, the force data onall the particles from the PR-DNS simulations is used to develop an artificialneural network (ANN) model for direct prediction of force on a particle. Due tothe unavoidable limitation on the number of fully resolved particles in thePR-DNS simulations, direct force prediction with the ANN model tends toover-fit the data and performs poorly in the prediction of test data. Incontrast, due to the millions of grid points used in the PR-DNS simulations,accurate flow prediction is possible, which then allows accurate prediction ofparticle force. This hybridization of multiphase physics and machine learningis particularly important, since it blends the strength of each, and theresulting pairwise interaction extended point-particle (PIEP) model cannot bedeveloped by either physics or machine learning alone.

theoretical and computational fluid dynamics

Towards Particle-Resolved Accuracy in Euler-Lagrange Simulations of  Multiphase Flow Using Machine Learning and Pairwise Interaction Extended  Point-particle (PIEP) Approximation