Eigenvalue Theory for Aluminized Explosives

The addition of aluminum to an explosive mixture can result in a discrepancy between the experimentally observed detonation velocity and the Chapman-Jouguet (CJ) detonation velocity. Classical CJ theory assumes that chemical reaction reaches completion at the sonic point in the flow, but that is generally not the case for aluminized explosives. A more suitable model to consider in these situations is eigenvalue detonation, as described by Fickett and Davis in "Detonation Theory and Experiment", 1979. In an eigenvalue detonation, the explosive is modelled at a minimum by two sequential reactions; an exothermic reaction followed by a net endothermic reaction. Then the reaction to equilibrium products at the sonic point, is not complete, and is dependent on the reaction rates. As a result, reactions involving aluminum may occur after the flow has passed the sonic point as afterburn. To enhance the aluminum reactions' contribution to the shock wave and minimize their occurrence as afterburn, one possible solution is to increase the reaction rate of the aluminum-involved reactions such that the energy is incorporated into the flow before it reaches the sonic point. Alternatively, overdriving the explosive prevents the flow from becoming sonic within the reaction zone and the slower aluminum-involved reactions stay within the sub-sonic flow. This can result in a strong branch detonation as opposed to a weak branch detonation. The reaction zone structure of strong and weak branch detonation are explored analytically through steady eigenvalue detonation theory, and validated by reverse impact and flyer impact numerical simulations.