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

Nejc Vovk, Jana Wedel, Paul Steinmann, Jure Ravnik

TL;DR

A novel machine learning framework is introduced, the Interaction-Decomposed Neural Network (IDNN), to model hydrodynamic particle interactions, which acts as a black-box module within a Lagrangian solver, predicting the particle drag force based on the relative positions of the nearest neighbours.

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.

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

TL;DR

A novel machine learning framework is introduced, the Interaction-Decomposed Neural Network (IDNN), to model hydrodynamic particle interactions, which acts as a black-box module within a Lagrangian solver, predicting the particle drag force based on the relative positions of the nearest neighbours.

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.
Paper Structure (3 sections, 16 equations, 3 figures, 1 table)

This paper contains 3 sections, 16 equations, 3 figures, 1 table.

Table of Contents

  1. Particle force computation with BEM
  2. Mesh validation study
  3. Coordinate system transformations

Figures (3)

  • Figure 1: Force exerted by the fluid on a single particle during plug flow versus the number of mesh nodes used. The symbol labels refer to the share of nodes used to discretize the particle, while the rest was used to discretize the outer spherical domain. The mesh chosen for further simulations is shown in red.
  • Figure 2: The mesh, recognized as a good compromise between the accuracy and the computational cost, that was used for running numerous simulations during the training database generation. The colour on the particle surface demonstrates the pressure distribution on the particle surface, as a result of the BEM simulation.
  • Figure 3: Visualization of the GCS and the LCS.