(194a) Geometric Similarity on Force Evaluation for Scaled-up Particle Model in DEM

Discrete Element Method (DEM) are used to simulate various kinds of particulate systems. In DEM, it is straightforward to consider complex inter-particle forces such as contact, liquid bridge and cohesion forces in simulation, which may be difficult to achieve with other methods including the continuum method. One of the major challenges in DEM is the high computational cost to track the movement of all individual particles in a system. This makes it difficult or practically impossible to perform simulation of fine particles in industrial-scale systems.

The scaled-up particle model, which is sometimes referred to as the coarse grain and/or the discrete parcel models, has been increasingly popular to overcome the aforementioned problem: large particles are used in simulation to mimic the behaviour of the original small particles. The scaled-up particle model in the literature may be largely classified into the parameter scaling and the direct force scaling approaches. The former employs scaled-up physical properties and parameters (often based on some dimensionless parameters) to achieve similarity to the original particle system, whilst the latter first estimates the forces acting on the original particles using the original physical properties and variables, and then the resultant forces are directly scaled.

In the scaled-up particle model, the original particles are not explicitly simulated but represented by scaled-up particles. Therefore, particularly in the direct force scaling approach, it is important to accurately evaluate the original particle variables related to the force calculation, such as the translational velocity, angular velocity, particle overlap and inter-particle separation distance, from the scaled-up particle variables. While some correlations for translational and angular velocities are derived based on the conservation of total kinetic energy, those for overlap and inter-particle separation distance are not well-grounded in theory. However, little attention has been paid to this topic in the literature.

The present work discusses the evaluation method of original particle variables for the force calculation in the scaled-up particle model. The most notable difference from the previous work in the literature is that the overlap and inter-particle separation distance of original particle are evaluated based on geometric similarity. Simulations of uniaxial compression of a particle bed as well as adhesive/cohesive particles in a mixer are performed with the proposed approach which sees a good agreement with the original simulations in terms of the stress-strain relationship and velocity distribution.