Resolved Reaction Zone Detonations in One Dimension

The nature of a reaction zone depends on the chemical decomposition rates and the equation of state used to describe the undecomposed explosive, the detonation products, and the mixtures of undecomposed explosive and detonation products. As shown in section 1.4, the nature of the reaction zone also strongly depends upon whether the explosive is homogeneous or heterogeneous (whether density discontinuties are present). The Arrhenius rate law was used in the numerical modeling of the reaction zone, and the HOM equation of state described in Appendix A was used for condensed explosive, the detonation products, and any mixture of condensed explosive and detonation products, assuming pressure and temperature equilibrium. 

Up to 2500 mesh points were used in the calculations. The number of mesh points in a reaction zone depends upon the initial size of the mesh, the thickness of the reaction zone, and the amount the mesh is compressed. For example, a 620-A reaction zone in nitromethane has 120 mesh points whose initial thickness was 10-A. The equation-of-state constants used are described in Table 1.1 and on the CD-ROM. 

The details of the reaction zone structure are very dependent on the properties of the equation of state for the mixture of undecomposed explosive and detonation products. The amount of overdrive necessary to obtain a steady detonation and the period and magnitude of the oscillation of an unstable detonation are not as dependent upon the equation of state details, but they are very dependent on the activation energy. 

The period for the C-J case is about 1 x 10 //sec, as estimated from the overdriven cases. 

The amount of overdrive necessary to stabilize the nitromethane detonation decreases with decreasing activation energy and is independent of the frequency factor. If one assumes an activation energy of 40 kcal/mole instead of the experimental value of 53.6, the nitromethane detonation for a 7 of 0.68 is stable at the C-J velocity of 0.6460 cm//Lisec. The nitromethane detonation for a 7 of 1.7 and an activation energy of 40 kcal/mole is unstable at 0.6550 cm//rsec and stable at 0.6640 cm//rsec. 

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