Overdriven detonation is a forced detonation where the shock state is stronger than the CJ state. Overdriven detonations are usually non steady, decaying towards the CJ state. But it’s possible to have a steady overdriven detonation when the forcing agent is steady.
For sub CJ curved and steady detonations it is known that detonation velocity is a decreasing function of front curvature. This D(k) relation is often used in an approximate and 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. (2010) 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’s hard to answer this experimentally, as candidates to replace the outer explosive are hard to find. But it’s quite easy to answer this computationally.
We use our temperature dependent reactive flow model TDRR, which we calibrated and validated from many tests. As a forcing agent we put a travelling pressure boundary condition on the test rod. We change independently the pressure P and the travelling speed D, and in this way we are able to obtain many points on the D(k) plane for negative curvature 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.
