Discrete Element Modelling
As computer power has increased, Lagrangian models, or distinct element models (DEM), have become more popular. These models calculate the path and motion of the individual particle and particle interactions are modeled through specified collision rules. One of the advantages of the Lagrangian approach is the ability to very easily vary the physical properties associated with individual particles, such as size, friction and density. For validation purposes, the local physical phenomena related to the particle flow behavior can be easily probed. Moreover, the type of interaction between two colliding particles can be accurately specified. The interaction models can be divided into two groups, hard-sphere models, and soft-sphere models. In the hard-sphere approach, collisions between two particles are assumed binary and instantaneous, and the velocities of the particles emerging from a collision are calculated by considering a balance of linear and angular momentum in the collision.
Hopper Animation: Animation of a hopper with bimodal particle distributionHopper Animation: Animation of a hopper with bimodal particle distribution
The basis of the soft-sphere approach implemented in MultiFlow is outlined in the seminal work of Mindlin (1953) where the time-dependent interaction of elastic spheres is considered. The local deformation of the sphere is described by the contact theory of Hertz, in which the forces resulting from the deformation are described by Poisson's ratio and Young's modulus for the specific particulate material. The original theory from Mindlin is simplified by describing the forces associated with particle interactions and deformation using three physical elements: a spring, dashpot, and slider, which are integrated in time for each particle-particle interaction. On the basis of numerous investigations, it has become clear that the soft-sphere models of incorporate the correct physics for individual particle interaction in the dense as well as dilute particulate flow regime.
The DEM models are coupled with single-phase type Navier-Stokes equation, including source terms and sources linear in all velocity components, and ensemble averaged volume fractions. The DEM model is coupled with a so-called Particle Mesh with the fluid mesh,
Particle-Fluid Mesh CouplingParticle-Fluid Mesh Coupling
to facilitate optimal calculation of particle-particle interactions.