Efficient simulation of nonspherical particles using the discrete element method
The discrete element method (DEM) is a numerical simulation approach for particulate systems proposed during the 1970s. The computational expense of DEM traditionally limited the simulations to small numbers of highly-idealised particles, typically disks or spheres. However, continual increases of computational power means that it is now feasible to incorporate nonspherical particles in DEM simulations. However, there are still significant gaps in the theory that need to be addressed before nonspherical particles find widespread adoption, particularly in industry. This thesis sought to develop some important theoretical aspects of nonspherical particle simulations, and increase the efficiency of these simulations. Contact detection is a major issue in simulating nonspherical particles. The first original scientific chapter of this thesis describes a novel contact-detection algorithm between convex polyhedra and superquadrics, which generally refer to blocky and round particles, respectively. The contact detection is based on a highly efficient ‘search and return’ method. The algorithm has been successfully validated for all types of contact between polyhedra and superquadrics. This algorithm makes it possible to simulate a system containing particles of both blocky and round shapes. Selecting a stable, efficient time step is essential for any DEM simulation; choosing a larger time step will increase a simulation’s efficiency. The second scientific chapter of this thesis presents a method for calculating the critical time step for systems of nonspherical particles in DEM analyses. The critical time step was analytically derived from the amplification matrix of the simulation and is explicit with damping considered. For underdamped cases, this approach gives a similar critical time step for spheres compared with previous studies. Moreover, this approach is applicable to underdamped, critically-damped and overdamped cases while previous studies were restricted to underdamped cases. The final scientific chapter of this thesis is an application: simulating ellipsoidal beans in a rotating drum. Laboratory experiments were performed in which the system was recorded by a high-speed camera and the images were analysed with particle image velocimetry (PIV) for validation of DEM results. The interaction of particles with the drum’s surface was the main focus of this study. Both soybeans and red beans slide along the drum in the simulation and experiment. This was observed from velocity analysis of the PIV data and mobilised friction using the DEM data. This sliding was relative to the dynamic angle of repose, but the particle translational velocities predicted from DEM and PIV differed while the simulated dynamic angle of repose was close to that in experiments, indicating that the DEM model did not exactly match the physical experiment. Other micro-scale behaviours in the system were also investigated. This thesis consists of both theoretical development and a practical application. The former provides some indication of how to simulate nonspherical particle systems in DEM more efficiently and more possibilities to simulate systems of diverse particle shapes, while the latter provides insights into a common engineering system of industrial relevance.