NeuralDEM – Real-time Simulation of Industrial Particulate Flows

Benedikt Alkin †, *, 1, 2, Tobias Kronlachner †, *, 1, 3, Samuele Papa †, 1, 4, 5,

Stefan Pirker 3, Thomas Lichtenegger 1, 3, Johannes Brandstetter @, 1, 2

core contributor, * equal contribution
1 NXAI GmbH, Linz, Austria
2 ELLIS Unit Linz, Institute for Machine Learning, JKU Linz, Austria
3 Department of Particulate Flow Modelling, JKU Linz, Austria
4 University of Amsterdam, Amsterdam, Netherlands
5 The Netherlands Cancer Institute, Amsterdam, Netherlands
@ Correspondence to: johannes.brandstetter@nx-ai.com

NeuralDEM presents an end-to-end approach to replace Discrete Element Method (DEM) routines and coupled multiphysics simulations with deep learning surrogates.

NeuralDEM

Abstract

Advancements in computing power have made it possible to numerically simulate large-scale fluid-mechanical and/or particulate systems, many of which are integral to core industrial processes. Among the different numerical methods available, the discrete element method (DEM) provides one of the most accurate representations of a wide range of physical systems involving granular and discontinuous materials. Consequently, DEM has become a widely accepted approach for tackling engineering problems connected to granular flows and powder mechanics. Additionally, DEM can be integrated with grid-based computational fluid dynamics (CFD) methods, enabling the simulation of chemical processes taking place, e.g., in fluidized beds. However, DEM is computationally intensive because of the intrinsic multiscale nature of particulate systems, restricting either the duration of simulations or the number of particles that can be simulated. Moreover, the non-trivial relationship between microscopic DEM and macroscopic material parameters necessitates extensive calibration procedures. Towards this end, NeuralDEM presents a first end-to-end approach to replace slow and computationally demanding numerical DEM routines with fast, adaptable deep learning surrogates. NeuralDEM is capable of picturing long-term transport processes across different regimes using macroscopic observables without any reference to microscopic model parameters. First, NeuralDEM treats the Lagrangian discretization of DEM as an underlying continuous field, while simultaneously modeling macroscopic behavior directly as additional auxiliary fields. Second, NeuralDEM introduces multi-branch neural operators scalable to real-time modeling of industrially-sized scenarios — from slow and pseudo-steady to fast and transient. Such scenarios have previously posed insurmountable challenges for deep learning models. Notably, our largest NeuralDEM model is able to faithfully model coupled CFD-DEM fluidized bed reactors of 160k CFD cells and 500k DEM particles for trajectories of 28s, which amounts to 2800 machine learning timesteps. NeuralDEM will open many new doors to advanced engineering and much faster process cycles.

NeuralDEM: the method

NeuralDEM method

NeuralDEM presents the first end-to-end solution for replacing computationally intensive numerical DEM routines and coupled DEM-CFD simulations with fast and flexible deep learning surrogates. NeuralDEM introduces two conceptually novel modeling paradigms:

  1. Physics representation: We model the Lagrangian discretization of DEM as an underlying continuous field, while simultaneously modeling macroscopic behavior directly as additional auxiliary fields. NeuralDEM encodes different physics inputs which are representative for DEM dynamics and/or multi-physics scenarios. Examples are particle displacement, particle mixing, solid fraction, or particle transport.
  2. Multi-branch neural operators: We introduce multi-branch neural operators scalable to real-time modeling of industrial-size scenarios. Multi-branch neural operators build on the flexible and scalable Universal Physics Transformer framework by enhancing encoder, decoder, and approximator components using multi-branch transformers to allow for modeling of multi-physics systems. The system quantities fundamental to predicting the evolution of the state in time are modeled in the main-branches, where they are tightly coupled. Additionally, auxiliary off-branches can be added to directly model macroscopic quantities by retrieving information from the main-branch state and further refining the prediction using relevant inputs.

Hopper discharge

Hoppers are industrially used for short as well as long term storage of particulate material, showcasing slow and pseudo-steady macroscopic behavior. DEM is the preferred method since the air around the particles can usually be neglected due to the slow velocities in the system. In our experiments, the hopper geometry is filled with 250k particles, which gradually exit the domain over the simulation duration when the hopper empties. Based on the material properties and the geometry properties, different flow regimes are obtained in a hopper.

Mass flow

DEM

NeuralDEM

When the hopper angle is high, it is very likely that the system exhibits mass flow, where the particles exit the hopper in the order in which they were filled. In this regime the full bulk of particles slides down the walls, as clearly visible in the DEM simulation, as well as, in the NeuralDEM trajectory.

Funnel flow

DEM

NeuralDEM

Contrast the previous simulation with this, where the hopper angle is very shallow. In this scenario, the material is likely to exhibit funnnel flow. Then the particles exit the hopper in the middle through a funnel built from the particles. This causes particles at the top to exit the hopper before those below them. In this cases, there is hardly any sliding on the wall as shown by both simulations.

Physics validation and macroscopic quantities

Most macroscopic quantities of interest to engineering applications emerge from the microscopic particle-particle interactions modeled by DEM. To re-generate these emerging phenomena with NeuralDEM, we train our model to predict auxiliary fields at each timestep of the simulation.

Flow regime

Mass flow

Hopper mass flow

Funnel flow

Hopper mass flow

In the funnel flow regime particle layer inversion happens, i.e., particles from higher layers overtake particles from the lower layers through the funnel. This emerging macroscopic phenomena is perfectly modeled by NeuralDEM.

Global quantities

Outflow rate

Hopper mass flow

Drainage time

Hopper mass flow

Residual volume

Hopper mass flow

NeuralDEM can evaluate global measurements from the learned dynamics. The outflow rate, drainage time, and residual volume, that stays in the hopper does not empty, can be predicted with high accuracy.

Fluidized bed reactors

Fluidized bed reactors are characterized by fast and transient phenomena and are widely used in industry for a variety of processes. Fluidized bed reactors showcase strong interactions of the particles with the surrounding fluid, necessitating an accurate modeling of particles, the gas phase, as well as particle-gas interactions. Thus, modeling approaches need to combine DEM parts with simulations of the surrounding fluid. Simulation are performed with a coupled CFD-DEM method, using 500k particles and the fluid, i.e., air, that is uniformly pushed into the reactor from the bottom is modeled on a grid of 160k hexahedral cells.

CFD-DEM

Particles

Solid fraction

Fluid velocity

NeuralDEM

Iso-surface

Solid fraction

Fluid velocity

The iso-surface shows the bubble structure that the model is predicting. Particles in the CFD-DEM simulation shows all 500k particles used. Solid fraction and fluid velocity are shown on the surface of the reactor.

A fluidized bed reactor simulation exhibits fast and transient dynamics with many physically possible trajectories, i.e., fluidized bed reactor trajectories are chaotic. This means that — also for numerical solvers — starting a fluidized bed simulation with different initial particle packings will yield different trajectories.

Long-term stability

Fluidized bed statistics - slow inlet velocity

Slow inlet velocity

Fluidized bed statistics - fast inlet velocity

Fast inlet velocity

The solid fraction is the ratio of volume which is occupied by particles, aka solids. When averaged over the entire volume this is effectively a mass conservation test. Here we see how NeuralDEM keeps the same initial mass throughout the entire simulation, which lasts 28s or 2800 machine learning timesteps.

Fluidized bed: a chaotic system

The fast and chaotic nature of fluidized bed also means that numerical differences will result in sharp changes in the simulation. Both different initial conditions and slight differences in the numberical choices made during the simulation will lead, in the long term, to different rollouts. NeuralDEM captures these physics very well. Would you be able to distinguish between the CFD-DEM simulation and the NeuralDEM simulation?

NeuralDEM - Initialization 1

CFD-DEM - Initialization 2

CFD-DEM - Initialization 1

NeuralDEM - Initialization 2

CFD-DEM - Initialization 2

NeuralDEM - Initialization 1

CFD-DEM - Initialization 1

NeuralDEM - Initialization 2

Those with a sharp eye will already have spotted that some simulations are more smooth than others. It turns out that the smoother simulations are actually from NeuralDEM, thanks to its neural field-based decoder, which has a desireable continuity bias.

Fluidized bed: Generzation to differet inlet velocities

Low inlet velocity

CFD-DEM

NeuralDEM

Medium inlet velocity

CFD-DEM

NeuralDEM

Fast inlet velocity

CFD-DEM

NeuralDEM

With slow inlet velocity the particles still exhibit a fluidized behavior, with bubbling cearly visible. Instead, with higher inlet velocities the particles move faster and the fluidized bed is more chaotic. NeuralDEM is capable of capturing all regimes.

Fluidized bed: particle mixing behavior

Particle mixing behavior modeled by NeuralDEM.

The slow inlet velocity simulation shows slow mixing, and NeuralDEM can match the same mixing rate (the two lines are overlapping). Notice here that the purple particles appear at the back of the fluidized bed towards the end of the simulation.

For high inlet velocity the particle mixing concentration rises more quickly at the beginning, slowing down towards the end. The model matches the prediction very well.

These simulations are run for 3s real-time (or 300 machine learning timesteps) and are here slowed-down to last 15s. Additionally, we want to note that the particle mixing is not a time-averaged statistic, so it is strongly dependent on the exact bubbles and position of the particles. We do not expect the model to be able to match the CFD-DEM particle mixing curve exactly, but only to do that at the beginning of the simulation. After a few tens of steps, the system is chaotic enough that divergence caused by numerical differences are expected.

BibTeX

@article{alkin2024neuraldem,
      title={{NeuralDEM} - Real-time Simulation of Industrial Particulate Flows},
      author={Benedikt Alkin and Tobias Kronlachner and Samuele Papa and Stefan Pirker and Thomas Lichtenegger and Johannes Brandstetter},
      journal={arXiv preprint arXiv:2411.09678},
      year={2024}
}