EFFECTIVE TOOL
Discrete Element Modelling: Overcoming the Challenges The behaviour of bulk granular material is different from that of solids and fluids, making it difficult to predict the dynamic and even static behaviour. Until fairly recently, the design of bulk materials handling equipment relied on empirical-analytical approaches.
T
he Discrete Element Method (DEM) was introduced in the 1970’s as a numerical method for the modelling of granular materials as discrete particles. Over the years, advances in computer technologies have made it possible to use DEM as a design tool, either to solve existing problems in bulk handling systems or as a predictive tool to model and investigate the performance of new concepts and developments. However, there are still challenges that need to be overcome for DEM to be an effective tool in analysing large scale industrial applications.
Introduction
DEM models granular material as an assembly of individual or are discrete particles. The interaction between the particles
and between the particles and walls (used to define containing structures, equipment, etc) is described by a contact model as shown in Figure 1. The particles are considered rigid and allowed to overlap at the contact instead of deforming, as the physical particles would do. The contact model defines the relation between the forces and the overlap as defined by the stiffness, damping and friction at the point of contact. A single DEM time step consists of three phases: contact detection, calculation of contact forces and the integration of the equations of motion which includes updating the position and orientation of the particles. The most commonly used contact models include the linear and Hertz-Mindlin models. In the case of the linear model, the contact force is a linear function of the overlap while in the Hertz-Mindlin model the force is a function of the overlap to the power 1.5, resulting in a non-linear response or stiffness. In both models, the contact stiffness can be related to a combination of the elastic properties of the individual elements (particle and/or wall) in contact, namely Young’s modulus, the shear modulus and Poisson’s ratio. The force in the tangential direction is limited by a Coulomb type friction coefficient which allows for relative sliding between the elements at the contact. The friction is responsible for the dissipation of energy from the system which can be increased by introducing a damper (dashpot) at each contact.
Figure 1 – Schematic representation of the typical normal, tangential and rolling contact models for cohesionless materials
Rolling resistance in the form of a moment acting at the point of contact can also be introduced. Similar to sliding
Figure 2 – The large scale laboratory conveyor transfer facility at Stellenbosch University for testing chute designs and validating DEM models
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BULK HANDLING TODAY
August 2019
