Due to increasing computer power, discrete particle models (DPM), or Lagrangian models, have become a very useful and versatile tool to study the hydrodynamic behavior of particulate flows. In these models, the Newtonian equations of motion are solved for each individual particle, and an interaction model is applied to handle particle encounters.
The fluid phase is described by the Navier-Stokes equations and is typically resolved on a much larger scale than an individual particle. Hence, sub-grid models are required to estimate the local fluid velocity at each particle in the domain.
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A fluidized bed
Ash particles above a combusting fluidized bed |
Collisions (particle-particle and particle-wall) are handled through a so-called "soft-sphere" or a "hard-sphere" approach, which takes particle elasticity, friction, rotational velocity and coefficient of restitution, amongst others, into account. The time-stepping routine for particle motion is decoupled from the fluid-phase and includes a choice of fixed and automated particle time-stepping. Automated time-stepping of the particle motion is based on the minimum elemental collision time, which is determined as a function of particle mass, velocity, elasticity and diameter, or can be selected to be event-driven. The Euler-Lagrangian module was specifically designed with a multiple and multi-grid approach. In addition to the irregular grid for fluid-phase motion a Cartesian grid, the particle grid, is used for particle tracking purposes. The overall calculation time can be significantly reduced by applying the algorithms referring to particle interactions, i.e.. the search algorithm for collision partners, on this grid. The cell-dimensions of the particle grid are on the order of magnitude of the largest particle in the simulation. Interaction between the fluid and the solid phase can be modelled with various drag relations, random walk models, and LES and LES de-filtering models are supported. The drag force on the particles is taken into account for every particle time-step. Re-coupling of the drag force to the fluid phase takes place before the fluid phase calculations, after which the drag force on the particles is updated. Modelling of non-spherical particles is supported as well. |
