Overdriven Detonation Velocity Dependence on Front Curvature

Abstract

Overdriven detonation is a forced detonation where the shock state is stronger than the CJ state of the explosive. Overdriven detonations are usually not steady but decaying towards the CJ state. It is however possible to have a steady overdriven detonation wave when the wave forcing agent is steady. For sub-CJ curved and steady detonations it is known that detonation velocity (D) is a decreasing function of front curvature (k). This D(k) relation is often used in an approximate and an efficient procedure, known as Detonation Shock Dynamics (DSD), to calculate the propagation of a quasi-steady curved detonation front, without having to solve the entire flow field behind it. In real situations, a divergent front going around an obstacle may become convergent (negative curvature). To tackle this part of the front propagation, people using DSD extrapolate the D(k) curve into the negative curvature region. Matignon et al. [2] performed a test in which they created a steady overdriven detonation with a negative curvature in an explosive rod. The forcing agent was a stronger explosive cylinder wrapped around the tested rod. In this way they were able to measure a point on the D(k) plane above the CJ velocity, to which they extrapolated the usual D(k) curve. Here we raise the question of the uniqueness of this extrapolated curve. It is hard to answer this question experimentally, as candidates to replace the outer explosive are hard to find. But as we show here, it is quite easy to answer this question computationally. We use our reactant temperature dependent reactive flow model TDRR [3-5], which we have calibrated and validated from many test results. As a forcing agent we put a travelling pressure boundary condition on the test rod. We change independently the pressure P and the travelling wave speed D, and in this way, we are able to obtain points on the D(k) plane for negative curvatures and above the CJ state. We show that these points do not fall on a single D(k) curve, and conclude that there is no unique D(k) relation for overdriven steady detonations.