On hydrodynamic effects of exothermic power in condensed explosives

Abstract

The initial flow produced in an explosive by the impulsive action of a constant velocity rear-boundary is considered to provide a better understanding of the coupling between hydrodynamic flow and chemical reaction and the shock initiation of detonation in explosives impacted by flying plates. Equations determining the initial shape of the reactive shock are derived from the equations of motion for an arbitrary specific energy-pressure-specific volume-extent of reaction equation of state and an arbitrary energy release rate. These expressions for the flow derivatives define the relationship between hydrodynamic flow and energy release rate induced by a constant velocity rear boundary, and demonstrate the dependence of the shock initiation process on the equation of state of an explosive and its energy release rate. The equations for the first derivatives show that the shock accelerates with a positive particle velocity gradient; those for the second derivatives show that the wave can develop with a positive, negative, or zero pressure gradient and account for the flows observed by Bernier, Wackerle and Johnson, and Kennedy respectively. The equation determining the pressure gradient was used to check the results of numerical studies of initiation and to determine the relationship between the pressure gradient and the initial shock pressure for a series of condensed explosives. Calculations on cast TNT, PBX9404, and Composition B based on reasonable assumptions about their equations of state and energy release rates predict that the sign of the initial pressure gradient in these explosives will change from negative to positive as the initial shock pressure is increased in a series of shock initiation experiments.