Shock-wave initiation of heterogeneous reactive solids

Abstract

Shock-wave initiation of solid explosives depends on localized regions of high temperature (hot spots) created by heterogeneous deformation in the vicinity of various defects. Current mathematical models of shock initiation tend to fall into two broad categories: (1) thermodynamic-state-dependent reaction-rate models, and (2) the continuum theory of multiphase mixtures. The level of generality possessed by (1) appears to be insufficient for representation of observed initiation phenomena, while that of (2) may exceed necessary requirements based on present measurement capabilities. As a means of bridging the gap between these two models, we present an internal-state-variable theory based on elementary physical principles, relying on specific limiting cases for the determination of functional forms. The appropriate minimum set of internal-state variables are the mass fraction of hot spots p, their degree of reaction J, and their average creation temperature e. The overall reaction rate A, then depends on /1-, f, and e in addition to the usual macroscopic thermodynamic variables (current state as well as their history). Two specific forms of this set of equations are applied to timeresolved shock-initiation data on PBX-9404. Numerical solution is achieved by the method of characteristics for rate-dependent chemical reaction. Additional questions such as the effect of thermal equilibrium between phases (solid reactants and gaseous products) on the theoretical results are discussed quantitatively.

Effect of Reaction Rate Periodicity on Detonation Propagation

“…Two models of this type are Lee and Tarver [3] and Johnson et al [4]. The advantage of this approach is that the standard single-fluid hydrodynamic (Euler) equations govern the flow evolution.…”

“…The issue we are studying is the role of explicit reaction rate spatial dependence. Existing models [3,4] homogenize the rate and treat the presence of hot-spots by terms in the reaction rate that represent the initiation or creation of hot-spots and the subsequent growth. In the present study, we have introduced an explicit spatial dependence of the reaction rate and have carried out numerical experiments to determine the effect on detonation initiation and propagation simulations.…”

Compaction waves in granular HMX

“…Models motivated by hot spots, such as the growth and ignition model [5] or the JTF model [6], are largely heuristic in nature. In effect, they use a sequence of reactions to simulate the effect of hot spots.…”

“…The average effect of the heterogeneities can be judged by comparing with the predictions of the porous Hugoniot for uniaxial-strain listed in table 6 below. In addition, we describe the fluctuations resulting from the granular structure of the bed.…”

Adding kinetics and hydrodynamics to the CHEETAH thermochemical code

“…3 In Cheetah's kinetic module only forward reactions are specified. The backward reaction is calculated through the detailed balance condition…”