Detonation theory of liquid and aluminized liquid explosives

Non-ideal behavior of condensed explosives with metal particle additives has been observed experimentally. In general, adding metal particles to a homogeneous explosive leads to a reduction in the detonation velocity and pressure, depending on the charge diameter, the concentration of the additive, and the particle size. To investigate these phenomena, detonation propagation in liquid and aluminized liquid explosives has been studied theoretically by including source terms in the 1-D conservation equations for mass, momentum and energy. To predict the steady state detonation parameters and the detailed structure of the detonation, the generalized C-J condition has been used to obtain a unique solution from the spectrum of possible solutions to the differential equations.The eigenvalue detonation solution is first determined for a weakly confined, cylindrical liquid explosive charge. The steady-state analysis assuming an Arrhenius reaction rate predicts the detonation failure diameter which depends on the curvature of the detonation wave, wall friction, and heat loss to the wall. The calculated detonation velocity deficit for liquid nitromethane (NM) is less than 2.1 % near the failure diameter. The predicted failure diameter for liquid NM varies from 15--18 mm for activation energy E*, ranging from 30--40 kcal/mol. These results agree well with the experimental data. A second form for the reaction rate law is also considered (i.e., the so-called "simple" law in which the reaction rate is not dependent on temperature). In this case, the detonation failure is not correctly predicted, and hence this rate law is not appropriate for liquid NM.Detonation propagation in an aluminized liquid explosive involves complex exothermic and endothermic processes. A two-phase flow model is proposed to take into account the non-equilibrium processes which determine the differences in velocity and temperature between the liquid explosive detonation products and solid particles. The onset of reaction of the Al particles in the detonation zone is set based on a simple ignition criterion.The calculations show that micron-sized Al particles are chemically inert whereas nanoscale particles may react within the detonation zone. For an explosive with nanoscale additives, the reaction heat of the particles in the detonation zone, if any, contributes to an increase in the detonation temperature. The large detonation velocity deficit for an aluminized liquid explosive is primarily due to momentum losses to the particles, with heat losses playing a relatively minor role, unless the particles are very small. The calculations also reproduce the measured effects of particle size and concentration on detonation velocity. From Chariton's theory of failure diameter, the comparison of the measured failure diameter to the prediction of the detonation zone timescales by the two-phase model with an Arrhenius reaction rate law suggests that the addition of solid particles alters the chemical kinetics of the liquid explosive. A so-called "hot spot" reaction rate law is proposed. With this new reaction rate law, the model predicts the effects of particle size and concentration on the detonation velocity and the detonation zone timescale, in general agreement with the experimental observations