Introducing Sphero-cylinders in EDEM 2022
Particle shape plays a fundamental role in the behavior of granular materials. When using the Discrete Element Method (DEM) for computational modelling of granular materials, however, the use of a realistic particle-shape description has to be balanced with the need for good computational performance. This results in a wide range of potential ways to model particle shape in DEM.
At one end, spherical particles provide the simplest but most computationally efficient modelling method. Using spherical particles means that there is lack of interlocking between the elements which can generally lead to unrealistic results. Even though in most cases this issue can be addressed through friction coefficients in combination with the appropriate contact model, in many practical applications a more detailed shape description is needed.
At the other end of the modelling choices, generic methods exist to represent arbitrary particle shapes. The most widely used is multi-spheres, which has long been supported in Altair EDEM. Recently, in its 2021 release, EDEM also added support for polyhedral particles in its GPU-based solver.
In between these two extremes (spheres vs generic methods), there is the choice to use specific particle shapes, defined by only few parameters, such as superquadrics, ellipsoids, cylinders, sphero-cylinders, etc. These specific shapes attempt to strike a better balance between realistic representation and computational performance for a range of granular material simulations.
The new sphero-cylinder particle shape in EDEM
We had recently the pleasure to collaborate with Dr Stefanos Papanicolopulos to implement sphero-cylinder particles in EDEM. Dr Papanicolopulos was seconded from the University of Edinburgh to Altair, with funding by the Royal Academy of Engineering under its Industrial Fellowships scheme. This is one of the non-spherical particle shapes now available in EDEM.
Figure 1 Spherocylindrical particles in EDEM [2]
Sphero-cylinders are cylinders capped at their two ends with hemispherical caps [1]. Compared to other particles shapes, they strike a very good balance between efficiency (low computational cost) and versatility. While some industrial applications involve particles that are true sphero-cylinders (e.g. handling of pharmaceutical capsules), the versatility of sphero-cylinders is due to their ability to efficiently approximate elongated, rod-like particles (e.g. grass or plant stems).
The new sphero-cylinder particle shape solver runs on the EDEM CUDA solver, thus maximizing the computational performance. Additionally, sphero-cylinders have been integrated throughout the EDEM software, so that for example particle shapes can be created in the EDEM Creator and the particles are compatible with EDEM’s coupling interface for coupled simulations with Finite Element Method (FEM), Multi-body Dynamics (MBD) and custom scripts. Sphero-cylinder particles can make use of a variety of contact models available on the CUDA Multi-Sphere engine, and they can be assigned size distributions allowing for the real-world variation in materials.
Example results
Sphero-cylinders are especially suited to modelling rod-like particles with a very high aspect ratio, as in the following simulations:
Figure 2: Simulation of rod-like particles in a rotating drum (left) and sticks being poured from a cylindrical container (right).
It is important to note that since EDEM is providing multiple particle shape options to represent the material, the user needs to make the appropriate choice. Sometimes the choice is obvious, such as particles with relatively smooth surface where spherocylinders with even low aspect ratio are better to get chosen as coarser multi-sphere approximation will introduce unwanted “bumpiness” of the lateral surface of particle, resulting in a non-smooth, stick-and-slip behaviour. But there are other cases when there is a fine balance between accuracy in results and computational efficiency. Below is an example of a hopper discharge replicating experimental steel rod-like sticks [3]. The simulation was repeated choosing both a spherocylinderical shape and multi-sphere approximations with different number of spheres.
It was observed that the spherocylinders described well the experimental data and also as the multi-sphere fidelity increased the results converged towards the spherocylinder, with best accuracy when 60 or more spheres where chosen. However, this led to an increased computational cost when running with multi-sphere particles. Choosing a spherocylinder instead gave more than 5 times speed up, highlighting the clear benefit of choosing the appropriate shape. This work was presented in the CHoPS 2022 10th International Conference on Conveying and Handling of Particulate Solids, Salerno, Italy, 5–9 July 2022
Figure 3: Comparison of simulation time between spherocylinder (red) and multi-sphere particles of different fidelity.
As always, the simulation capabilities of DEM can be greatly extended by combining features, as in the following simulation where sphero-cylinders are used together with the built-in Bonding V2 model to simulate grass-cutting.
Figure 4: Grass-cutting simulation in EDEM using spherocylinders. The image is taken from the EDEM Tutorial 19 - Bonded MetaParticle Spherocylinder.
Summary and upcoming features
Sphero-cylinders provide an efficient yet versatile method to model granular materials with elongated particles, especially for cases with highly elongated particles or where we wish to avoid the bumpiness associated with a coarse multi-sphere approximation.
This versatility will be further extended with the upcoming support for Meta-Particles for Sphero-Cylinders. Meta-Particles can bond and flex using the built-in Bonding V2 model, and can therefore be used to efficiently model elongated structures with branches (e.g. crop stems).
Figure 5: Template for meta-particles using sphero-cylinders.
References
[1] L. Pournin, M. Weber, M. Tsukahara, J.-A. Ferrez, M. Ramaioli, Th. M. Liebling (2005) Three-dimensional distinct element simulation of spherocylinder crystallization, Granular Matter, 7, 119–126, https://doi.org/10.1007/s10035-004-0188-4
[2] M. Sousani, S. A. Papanicolopoulos, A. Piskopakis (2022) Modelling hopper discharge of elongated particles with different shape representation methods, in: CHoPS 2022 10th International Conference on Conveying and Handling of Particulate Solids, Salerno, Italy, 5–9 July 2022.
[3] Tangri, H., Curtis, S. J. (2019) Hopper discharge of elongated particles of varying aspect ratio: Experiments and DEM simulations. Chemical Engineering Science:X, Vol 4, https://doi.org/10.1016/j.cesx.2019.100040