The Critical Transition Length from Chapman-Jouguet Deflagrations to Detonations

Abstract

In the process of deflagration-to-detonation transition (DDT) in reactive gases, the flame typ- ically accelerates first to the choked flame condition (known as a Chapman-Jouguet deflagra- tion), where it propagates at the sound speed with respect to the product gases. Subsequently, the choked flame may transit to a detonation. In the present study, the transition length from choked flames to detonations was measured experimentally in laboratory-scale experiments in methane, ethane, ethylene, acetylene, and propane with oxygen as oxidizer. The choked flames were first generated following the quenching of an incident detonation after its interaction with cylindrical obstacles. The subsequent acceleration was monitored via large-scale time-resolved shadowgraphy. The mechanism of transition was found to be through the amplification of trans- verse waves and hot spot ignition from local Mach reflections. The transition length was found to correlate very well with the mixture’s sensitivity to temperature fluctuations, reflected by the parameter introduced by Radulescu, which is the product of the non-dimensional activation energy (Ea/RT) and the ratio of chemical induction to reaction time (tig/tr). Mixtures with a higher parameter were found more susceptible to hot spot ignition and had a transition length much shorter than anticipated from a model neglecting the fluctuations in the choked flame structure. The correlation between transition length and the - parameter ob oxygen sub-atmospheric experiments was used to determine the critical DDT lengths in the same fuels with air as oxidizer at ambient pressures, thus providing an estimate for the critical charge dimension of reactive gases necessary to initiate a detonation.