Page 274 - The Combined Finite-Discrete Element Method

INTRODUCTION 257

The coupling of the two requires a Lagrangian grid to be superimposed over the Eulerian
grid. As the solid particles are by definition of the problem loosely packed, and most of the
domain is filled by the fluid, the primary grid is the Eulerian CFD grid. As a consequence,
the primary solver is the Eulerian CFD solver. Thus, these are in essence CFD problems.
The influence of fluid on the motion of solid particles is obtained through transferring the
fluid pressure and drag forces onto the discrete elements.
There are two approaches available to take into account the influence of solid particles
on the CFD model:

• Resolving the interaction of each individual particle with the fluid.
• Averaging the interaction between solid particles and the fluid through introduction of
solid ‘density’. Introducing solid density goes against the spirit of the combined finite-
discrete element method, because it is in essence a continuum formulation. For it to
be valid, the continuum assumption must be valid, in which case the combined finite-
discrete element method is not necessary. If the continuum assumption is not valid,
by introducing a continuum based formulation for what is a discontinuum problem, all
discontinua-based phenomena may be automatically neglected, and the main purpose
of employing the combined finite discrete element method defeated.

8.1.2 Combined finite-discrete element method with CFD coupling

Problems of the second type are more common. A typical example of this type of problem
is fracture and fragmentation of solid using explosives. Fracture and fragmentation is the
result of the interaction of a detonation gas at high pressure with a fracturing solid.
After the initiation of the explosive charge, the detonation propagates through the charge
at the velocity of detonation. The detonation process results in a phase change of the
explosive material so that, as a result, hot detonation gas at high pressure is produced.
The energy released in the detonation process depends upon the type of explosive used,
and is usually expressed as specific explosive energy (i.e. energy per unit mass of explosive
charge). Through expansion of the detonation gas, part of this energy is transferred onto
the solid, causing it to break, fracture and/or fragment, depending on the amount of
explosive employed.
Detonation gas induced fracture and fragmentation involves interaction between the
detonation gas and fracturing solid. The gas exerts pressure onto the free surface of the
solid, causing the solid to accelerate, deform, fracture and displace at a velocity field that
changes with time. This in turn results in the expansion of the detonation gas, its partial
penetration into the cracks and voids created and its flow through the cracks and voids
and between fracturing solid blocks. The expansion of the detonation gas, flow of the
detonation gas and mechanical work done by the gas results in a decrease in the pressure
of the gas.
For this reason, the problem of detonation gas induced fracture and fragmentation is
employed in this chapter as a typical example of the combined finite-discrete element
method with fluid coupling. There are two aspects to this coupled problem:
• The evaluation of gas pressure as the surface load for a solid.
• The deformability, fracture and fragmentation of a solid under gas pressure.