State relations for a two-phase mixture of reacting explosives and applications

To assess the assumptions behind the two phase mixture rule for reacting explosives, the shock-to-detonation transition process was calculated for high explosives using a finite difference method. An ignition and growth model and the Jones–Wilkins–Lee (JWL) equations of state were employed. The simple mixture rule assumes that the reacting explosive is a simple mixture of the reactant and product components. Four different assumptions, such as that of thermal equilibrium and isotropy, were adopted to calculate the pressure. The main purpose of this paper is to present the answer to the question of why the numerical results of shock-initiation are insensitive to the assumptions adopted. The equations of state for reactants and products were assessed by considering plots of the specific internal energy E and specific volume V. If the slopes of the constant-pressure lines for both components in the E–V plane are almost the same, it is demonstrated that the numerical results are insensitive to the assumptions adopted. We have found that the relation for the specific volumes of the two components can be approximately expressed by a single curve of the specific volume of the reactant vs that of the products. We discuss this relationship in terms of the results of the numerical simulation.