A data-driven approach for predicting hydrodynamic forces on spherical particles using volume fraction representations

Particle-laden flows are simulated at various scales using numerical techniques that range from particle-resolved direct numerical simulations (pr-DNS) for small-scale systems to Lagrange point–particle methods for laboratory-scale problems, and Euler–Euler approaches for larger-scale applications. Recent research has been particularly focused on the development of both physics-based and data-driven closures to enhance the accuracy of the Lagrangian point–particle approach by leveraging highly resolved data from pr-DNS. In this study, a data-driven methodology is presented for the prediction of hydrodynamic forces acting on spherical particles immersed in an ambient flow field, where neighboring particle information is represented by volume fractions. The volume fractions are computed on an auxiliary grid with cell sizes on the order of the particle diameter. The volume fraction values in the vicinity of each particle are used as input features for the data-driven model to predict the corresponding hydrodynamic forces and moments. The training data were generated by a series of pr-DNS of flow through arrays of randomly distributed, fixed-position particles at various Reynolds numbers and particle volume fractions. The data-driven model is built using fully connected neural networks (FCNN). Improved prediction accuracy of hydrodynamic forces and torques is demonstrated in comparison to FCNN models that rely on direct particle position inputs. In addition, the proposed volume-fraction-based approach exhibits greater flexibility than previously introduced models by accommodating systems with particles of different sizes and shapes.