Discrete element method simulation of non-sphere particles using super-ellipsoids
Yongzhi Zhao (email@example.com), 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