A multiphysics model for the numerical simulation of wet balls mills

Abstract

There exists a need to understand the behaviour of wet mill loads by numerical simulation. However, the challenge is to adequately combine solid-based and liquid-based computer algorithms into one realistic framework. This study attempts to develop a computer framework that combines Discrete Element Modelling (DEM) and Computational Fluid Dynamics (CFD). Grinding media were modelled using a Lagrangian approach. In other words, the grinding charge was treated as a collection of distinct particles, each governed by Newton’s laws of motion. Particle-particle collisions were assumed to obey the Hertzian contact law. The model was then written using the open-source C++ based platform LIGGGTHS. The slurry phase, on the other hand, was modelled using the Navier-Stokes equation and solved using a finite volume element method. The presence of balls was accounted for by including a solid phase volume fraction in the Navier-Stokes equation. The model was then encoded into a C++ script using OpenFOAM®. The two-way interaction between grinding media and slurry or DEM-CFD coupling was described by buoyancy and drag forces. Upon running various simulations, the CFD-DEM simulated load positions were compared and validated against published experimental data from selected laboratory and pilot-scale ball mills. Simulated shoulder and toe of the media charge were found to match published results to within 10%. The calibrated CFD-DEM model also revealed little to no effects of slurry viscosity and material properties on load behaviour except for Young’s modulus. The shoulder position was also notably observed to increase with mill speed. It was concluded that the proposed framework was capable of simulating the mill charge motion. But further refinement is required in terms of modelling drag forces.