Modeling hydrodynamic interactions in non-spherical particle-laden flows : numerical simulations and machine learning models

Particle-laden flows, involving solid particles suspended in a fluid, are prevalent in many natural and industrial applications. These flows manifest rich flow physics and pose unique modeling challenges. The dynamics of the two phases are strongly coupled, giving rise to spatio-temporal nonlinear interactions. This multi-scale nature poses significant challenges for achieving accurate two-way coupling in real-world applications. The key contributions of this PhD dissertation are twofold: (i) to deepen the understanding of the hydrodynamic forces driving the particle-fluid momentum transport in these flows, particularly focusing on non-spherical particles and (ii) to advance closure law modeling of these forces by integrating physical insights derived from high-fidelity numerical simulations into tailored architectures of Machine Learning (ML) methodologies. We first investigate the influence of shape using superquadric geometries, which allow controlled deviations from sphericity. We show that particle shape, orientation, and Reynolds number significantly affect the flow and hydrodynamic forces. Extending this to pairwise interactions, we show that neighboring particle arrangements drive local force disturbances. These interactions exhibit periodicity, which we capture using a Fourier series, offering a compact and interpretable modeling framework. We leverage ML to develop a multi-scale approach to modeling higher-order interactions. Building on a hierarchical model, we incorporate quaternary interactions and explicitly account for global and local heterogeneities. This significantly improves predictive accuracy, especially for streamwise drag, surpassing lower-order interaction models. Further, we introduce a novel attention-based Graph Neural Network architecture. This model captures complex spatial, geometric, and relational dependencies, demonstrating superior performance in predicting streamwise forces at low Reynolds numbers and volume fractions. While challenges remain in predicting transverse forces and torques at higher Reynolds numbers, this work lays the groundwork for data-driven multi-scale modeling of particle-laden flows. Overall, this dissertation offers new insights into the interplay of particle shape, flow structure, and hydrodynamic forces, advancing both our understanding and predictive capabilities in particle-laden suspensions.