A Generalised Gruneisen Equation of State for Non-Reacted Explosives

A condition for compatibility between the non-reacted (NR) and detonation products (DP) equations of state (EOS) in a reactive burn model is that the two EOS surfaces in pressure -- specific volume -- specific internal energy space should not cross.~ Crossovers can lead to hydrocode calculation failures or non-physical results. At any specific volume for a Mie-Gruneisen EOS, pressure is linear in specific internal energy, with a slope equal to the Gruneisen Gamma divided by the specific volume. This causes a problem when both EOS are of Mie-Gruneisen form, as experiments suggest that the Gruneisen Gamma for the NR EOS is greater than for the DP EOS, which inevitably leads to a crossover at positive pressures.~ Equally there is a problem when a Mie-Gruneisen NR EOS is combined with tabular data from a chemical equilibrium DP EOS, in which Gruneisen Gamma varies with pressure at each specific volume.~ This work describes a new Generalised Gruneisen form for an NR EOS, in which Gruneisen Gamma varies with entropy as well as specific volume.~ It is shown that the new EOS has the potential to avoid the crossover with the detonation products EOS, whether this is of Mie-Gruneisen or chemical equilibrium form.