# (442n) Discrete Element Method Simulation of Non-Sphere Particles Using Super-Ellipsoids

- Conference: AIChE Annual Meeting
- Year: 2015
- Proceeding: 2015 AIChE Annual Meeting
- Group: Particle Technology Forum
- Session:
- Time:
Tuesday, November 10, 2015 - 6:15pm-8:00pm

Discrete element method simulation of non-sphere

particles using super-ellipsoids

Yongzhi Zhao

(yzzhao@zju.edu.cn), Lei Xu

*Institute
of Process Equipment, Zhejiang University, Hangzhou 310027, China*

Since granular systems

is common in many industrial processes and the movement of the particles is

extremely complicated, it's meaningful to study the physics of the granular

materials by discrete element method (DEM), which has been recognized as an

effective and efficient way. A series of models have been proposed to simulate

the non-sphere particles, such as glued spheres, polyhedral, super-ellipsoids,

and some kinds of real shape models like ellipsoid. Among them,

super-ellipsoids model has advantages on many aspects.

In

this work, a contact model of discrete element method using the

super-ellipsoids was proposed. The mathematical model of the particles is based

on the function of the super-ellipsoids. For the algorithm of super-ellipsoids

particles, the most important steps are contact detection and contact

evaluation. In current research, the particles were supposed to be rigid bodies

to simplify the detection. Thus, when two particles are in contact, they must

have an overlap between each other. Using the super-ellipsoids function

mentioned above, it's easy to find it out whether the two particles are in

contact or not. Once they are contacted, it's necessary to get the overlap

quantitatively for the following calculation. In the simulation, the overlap is

represented by the line joining the two deepest points of the two particles

inside each other. In order to find the two points, a special optimization algorithm

was adopted and it was proved to be an efficient way for the simulation. After

the two points were found, the overlap between the two particles was obtained, and

then the force between them can be calculated using the spring model. Finally, the

velocity of the particles can be get and the new position of the particles is

easy to be acquired before the next time step.

A

program has been developed and in order to test the mathematical model and the

algorithm, two cases have been carried out. In the first case, four kinds of

particles, spherical particles, cylindrical particles, cubic particles, and ellipsoid

particles were used. The particles were put into a rotating drum. When the drum

is running, the particles inside the drum will have a dynamic angle of repose.

The results of the simulation are nearly the same as that of the experiments.

In the second case, spherical particles, cylindrical particles, cubic particles

and ellipsoid particles were used and the particles are packed in a box in the

simulations. The efficiency of the algorithm will be got by a series of

simulations. For the cubic particles, with the increase of the shape index,

i.e. when the particles get closer to real cube, the efficiency came down. For

the cylindrical particles, the results are nearly the same. For the ellipsoid

particle, with the increase of the difference of the half-length, the time

consumption also increased.

The

mathematical model and the algorithm were approved to be high efficient, high accurate,

and robust. The motion of many kinds of non-sphere particles can be simulated

by the present model and the algorithm in this paper.

Fig. 1 Packing

in a box with different kinds of particles modeled by super-ellipsoid