Fluctuations, Clustering, and Interaction-Driven Dynamics in Sedimenting Particles at Low Galileo Numbers: A Neural Network Approach

TL;DR

This paper introduces a machine learning framework called IDNN to model hydrodynamic interactions in sedimenting particles, capturing force fluctuations and clustering effects that influence collective settling velocities.

Contribution

The novel IDNN approach replaces DNS for modeling particle interactions, enabling efficient prediction of force fluctuations and collective dynamics in sedimenting particles.

Findings

Increased settling velocity due to clustering and force fluctuations.

Force fluctuations originate from wake entrainment and ejection.

Energy spectra indicate a turbulent-like cascade in particle velocity fluctuations.

Abstract

In this study, we investigate the behaviour of sedimenting solid particles and the influence of microscopic particle dynamics on the collective motion of a sedimenting cloud. Departing from conventional direct numerical simulations (DNS), we introduce a novel machine learning framework, the Interaction-Decomposed Neural Network (IDNN), to model hydrodynamic particle interactions. The IDNN acts as a black-box module within a Lagrangian solver, predicting the particle drag force based on the relative positions of the nearest neighbours. This enables the recovery of force fluctuations, capturing effects previously accessible only through DNS. Our results show an increase in collective settling velocity in the dilute regime, consistent with earlier experimental and numerical studies, which we attribute to (i) fluctuations in the streamwise particle force around a value that is lower than the Stokes limit and (ii) the formation of particle clusters sedimenting at enhanced velocities. These fluctuations originate from persistent entrainment and ejection of particles in and out of the long, diffusive wakes generated by upstream particles at low Galileo numbers. Energy spectra of particle velocity fluctuations reveal a scale-dependent transfer of fluctuation energy, analogous to a turbulent-like cascade, with pronounced large-scale fluctuations at higher volume fractions. At very low volume fractions, fluctuation intensity and energy spectrum amplitudes diminish, though hydrodynamic interactions still remain appreciable.