Theory of two-phase detonation-Part I: Modeling

A new, one-dimensional, two-phase model appropriate for describing the detonation of granulated solid propellants or explosives is presented. The model satisfies the principle that the mixture mass, momentum, and energy are conserved, is strictly hyperbolic, and is frame indifferent. Conditions are presented for satisfying the second law of thermodynamics. It is shown that this and previous models do not satisfy the second law under all circumstances. It is shown that in the limit of no chemical reaction or gas phase effects that inclusion of compaction work is in violation of the energy conservation principle. It is also shown that a complete two-phase particle combustion model with constitutive functions dependent on particle radius requires an equation specifying the variation of particle radius; such a relation can be given by a number evolution equation. The model equations are solved in a subsequent study which follows as a separate article.