Effects of high activation energies on acoustic timescale detonation initiation

Abstract

Acoustic timescale Deflagration-to-Detonation Transition (DDT) has been shown to occur through the generation of compression waves emitted by a hot spot or reaction centre where the pressure and temperature increase with little diminution of density. In order to compensate for the multi-scale nature of the physico-chemical processes, previous numerical simulations in this area have been limited to relatively small activation energies. In this work, a computational study investigates the effect of increased activation energy on the time required to form a detonation wave and the change in behaviour of each hot spot as the activation energy is increased. The simulations use a localised spatially distributed thermal power deposition of limited duration into a finite volume of reactive gas to facilitate DDT. The Adaptive Wavelet-Collocation Method is used to solve efficiently the 1-D reactive Euler equations with one-step Arrhenius kinetics. The DDT process as described in previous work is characterised by the formation of hot spots during an initial transient period, explosion of the hot spots and creation of an accelerating reaction front that reaches the lead shock and forms an overdriven detonation wave. Current results indicate that as the activation energy is raised the chemical heat release becomes more temporally distributed. Hot spots that produce an accelerating reaction front with low activation energies change behaviour with increased activation energy so that no accelerating reaction front is created. An acoustic timescale ratio is defined that characterises the change in behaviour of each hot spot.

Keywords:

• detonation initiation
• deflagration-to-detonation transition
• acoustic timescale
• inertial confinement
• wavelets

Acknowledgements

JDR appreciates the guidance and support of OVV and DRK during his PhD thesis research project. Support for this work was provided by the National Science Foundation (NSF) under grants No. ACI-0242457 and No. CBET-0756046. DRK acknowledges support from Air Force STTR contact FA955010C0088 for the thermomechanical aspects of the current work.

Notes

¹Extensive discussions of both direct initiation of detonations and Deflagration-to-Detonation Transition (DDT), including references, are found in all of the aforementioned publications.

²Although the heat released in 25<t<30 does not create a true maximum, it still acts as an indication of an explosion that has occurred. Thus it will be referred to as a maximum in the heat release.

³The heat release time for hot spot 3 in Case 4 is not explicitly labelled, but it is to be understood as the time the induction period ends until the first shock interaction at .