Page 276 - The Combined Finite-Discrete Element Method

EXPANSION OF THE DETONATION GAS 259

8.2 EXPANSION OF THE DETONATION GAS

Once the explosive charge is initiated through the detonation process, hot detonation gas
at high pressure is created. The pressure of the detonation gas can exceed 10 GPa. The
detonation process is characterised by the Velocity Of Detonation (VOD). The velocity
of detonation of modern explosives can exceed 7000 m/s. This means that the detonation
process is in general very fast in comparison to the fracture and fragmentation pro-
cesses. An acceptable approximation in such cases would be that the detonation process
is completed instantaneously. With this assumption, the combined finite-discrete element
simulation starts with a borehole filled with detonation gas at high pressure. An alterna-
tive approach is to consider the detonation process while at the same time considering
coupled combined finite-discrete element simulation. In such a case, the mass of det-
onation gas and the spatial distribution of the gas within the borehole changes as the
detonation progresses.
In both cases, the coupled combined finite-discrete element simulation of interaction of
the detonation gas with a fracturing and fragmenting solid must consider:

• Expansion of the detonation gas, coupled with cooling of the detonation gas and rapid
pressure drop. The gas pushes against the free surfaces of the solid, thus transferring
part of its energy onto the solid in the form of mechanical work.
• Penetration of detonation gas into cracks and voids coupled with escape of the gas
through these cracks and voids. This is in essence a fluid flow problem of the second
type, as defined above.

8.2.1 Equation of state

The gas side of the coupled combined finite-discrete element simulation is subject to
the same CPU and RAM requirements to which the rest of the combined finite-discrete
element procedures are subject. From this point of view, it is ideal if expansion of the
detonation gas is described in analytical form. To facilitate this, the following equation
of state for the detonation gas is assumed:

'
b (
1 1
p = + a RT (8.6)
v v
where p is the pressure of the detonation gas, v is the specific volume of the detonation
gas, T is the temperature of the detonation gas, while a, b and R are constants.
The same equation can be written in terms of the density of detonation gas ρ = 1/v:

p = ρ + aρ b RT (8.7)

8.2.2 Rigid chamber

The simplest case of detonation gas expansion is the hypothetical case of an explosive
charge being placed in a rigid thermally insulated chamber, and filling only a part of