Theory of two-phase detonation—Part II: Structure

Abstract

The structure of a two-phase steady detonation in a granulated solid propellant is studied, and existence conditions for a one-dimensional, steady two-phase detonation are given. Ordinary differential equations from continuum mixture theory are solved numerically to determine steady wave structure. In the limiting case where heat transfer and compaction effects are negligible, the model reduces to two ordinary differential equations that have a clear geometrical interpretation in a two-dimensional phase plane. This two-equation model predicts results that are quite similar to those of the full modeL This suggests that in the limited parameter space studied heat transfer and compaction are not important mechanisms in determining the detonation structure. It is found that strong and Chapman-Jouguet (CJ) detonation solutions with a leading gas phase shock and unshocked solid can be admitted, as can weak and CJ solutions with an unshocked gas and solid. As for one-phase materials, the CJ wave speed is the speed of propagation predicted for an unsupported, one-dimensional, two-phase detonation. It is predicted that there is no admissible CJ structure with a single leading gas phase shock and unshocked solid below a critical value of initial bulk density. This result cannot be predicted from equilibrium end state analysis. Thus it is concluded that it is essential to consider reaction zone structure when assessing potential solutions.

A High-Resolution Numerical Method for a Two-Phase Model of Deflagration-to-Detonation Transition

“…Together with Ref. [21], which gives predictions of the evolution of the steady CJ detonation structure identified by Powers et al [45], this work gives the only known detailed comparison between unsteady numerical predictions and steady-state results for two-phase detonation wave structure. Further, these comparisons conclusively show that all relevant detonation length scales are fully resolved, in contrast to most published work in this area, which is underresolved.…”

The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

“…While models of this kind arise in a number of applications, the context of deflagration-to-detonation transition in high-energy condensed-phase explosives provides the motivation for the present effort. A twophase continuum description of granular explosives has been provided by Baer and Nunziato [1]; also see the contemporaneous study of Butler and Krier [2], the earlier work of Gokhale and Krier [3], and the later papers of Powers, Stewart and Krier [4,5]. The model treats the explosive as a mixture of two phases, the unreacted granular solid and the gaseous product of combustion.…”

A Cell-Centered Multiphase ALE Scheme With Structural Coupling

“…This could have an adverse effect on the compaction of the solid material. Similarly, Powers et al [16,17] neglected the nozzling terms, but did use a compressible solid.…”