Wavefront Acceleration and the (Dn-kappa) Relationship in the Evolution of a Detonation

A detonation propagating across multiple HE regions usually creates a concave shock front due to the different detonation speeds. We will show theoretical and numerical evidence that the effect of front acceleration is necessary to correctly predict the motion of a concave detonation. We derive the initiation-zone of a traveling concave front taking into account acceleration. We demonstrate that in the case of a diverging front, such as in a rate-stick test, the solution of a detonation can be improved by adding the acceleration effect to a (D, κ) relation which is precisely defined as the zero-acceleration contour. In addition, we show that a (D, κ) relation describing a quasi-steady diverging wave has a form consistent with an evolution equation previously proposed for a converging wave in the limit of small acceleration.

We perform direct numerical simulations using reactive flow models (Ignition and Growth and CHEETAH) and front tracking using the meshless detonation tracker SDOT developed at LLNL with an evolution equation calibrated for LX-17, for the dual-HE concave detonation test described in the “French Experiment” by Matignon (IDS 2010). Our results show close agreement between SDOT DSD tracking and DNS with clear appearance of an ‘initiation zone”, and consistency with the original experiment.