The numerical tools that are integrated in the M5 model of stirred media milling include the Discrete Element Method (DEM) for macroscale simulations, Finite Element Method (FEM) based Fluid-Structure Interaction (FSI) for mesoscale simulations and combined FEM and DEM for microscale simulation of grinding bead impacts. Statistical analyses of the impacts derived by DEM at a macro-level are used for optimization of the mill design and its operational parameters. The thermo-mechanical and hydrodynamical phenomena that occur at the mesoscopic FSI scale between the approaching grinding beads are analyzed by FEM for various impact scenarios with different combinations of impact velocity, direction and rotation as a function of macroscopic mill design. Therefore, the M5 concept takes into account global-local coupling so that the influences of macroscopic design can be derived at nano levels by downscale coupling of influential phenomena.
IntroductionThe basic principle in scales separation that allows explicit modeling of the stirred media milling process is shown in Fig. 1. On the macroscale, DEM was used to simulate the motion of thousands of grinding beads in a grinding chamber. Statistical analysis of the bead trajectories yields several interesting impact statistics, e.g., distribution of impact velocities, etc., that are very difficult to obtain with other observation methods. Statistical results strongly depend both on the design of the mill and the operating conditions. Thus, they can be used to optimize both mill design and operation.Mesoscale simulations of motion and impacts of beads in a fluid medium were undertaken using a dedicated Fluid-Structure Interaction (FSI) code based on FEM [1]. The experimental values of the coefficient of restitution (COR), i.e., the ratio of the normal velocity of a bead after and before the impact, and which was experimentally measured as described by Yang and Hunt [2], were reproduced by semi-analytical modeling of the interaction force between two beads moving in a liquid medium.Macro-and mesoscale simulations were performed primarily to retrieve the boundary conditions for microscale simulations. Typical impact scenarios (velocity and angle) were taken from the impact statistics. These scenarios were then used as boundary conditions in the microscale simulations. On the microscale, irregularly shaped product particles were inserted at different locations between two approaching bead surfaces. All expected events, i.e., particle trapping and breakage as well as particles being washed away, were observed. Product particles were modeled using FEM with plastic material properties in order to allow deformation and damage accumulation.M5 numerical problems are inherently difficult to solve with a single numerical tool as they are often specialized for one particular class of problems, and thus, the need to integrate several different numerical tools in solving M5 problems is unavoidable. In the present work, DEM and FEM simulations were performed with the DEM software system ...