Thermal nonequilibrium detonation model of solid explosive

Abstract

A thermal nonequilibrium reactive flow model is proposed to deal with the detonation dynamics of solid explosive. For the detonation in solid explosive, the solid-phase reactant and gas-phase product in the chemically reactive mixture zone do not have molecular collisions as in the case of gaseous detonation, so the solid-phase reactant and gas-phase product can arrive at a mechanical equilibrium but cannot reach a thermal equilibrium when the detonation happens. The main properties of the present detonation model are as follows. The Euler equations for chemical mixture and the mass conservation equation for solid-phase reactant are used to express the chemically reactive flows in solid explosive detonation as a traditional way, and an additional set of governing equations of the species physical variables for solidphase reactant is derived to give an expression to the thermal nonequilibrium between the solid-phase reactant and gas-phase product. The chemical mixture within a control volume is defined as a collection of species which possess distinct internal energy or temperature, and the same pressure and velocity. For the explosive detonation, the species include solid-phase reactant and gas-phase product. Based on the mixing rule that every species can preserve the conservation of its internal energy in the reactive mixture zone, the evolution equation of internal energy for solid-phase reactant may be obtained, meanwhile, based on the property of mechanical equilibrium in the reactive mixture zone, the total volume fraction is equal to one, and the equation of state of every species, the evolution equation of volume fraction for solid-phase reactant and the evolution equation of pressure for chemical mixture can be derived. Thus, the theoretical model of solid explosive detonation includes the conservation equation of mass, momentum, total energy and the evolution equation of pressure for the chemical mixture, and the conservation equation of mass and the evolution equation of internal energy and volume fraction for the solid-phase reactant. The partially differential equations of the detonation model are numerically solved by a finite volume scheme with two-order spatiotemporal precision, through using a wave propagation algorithm by means of Strang splitting operator. The validation of the proposed detonation model is checked by the propagation of planar one-dimensional detonation, the propagation of cylindrically divergent detonation and the interaction between two cylindrically divergent detonations, and the typical examples demonstrate that the proposed theoretical model of solid explosive detonation is reasonable.