Computational analysis of re-ignition and re-initiation mechanisms of quenched detonation waves behind a backward facing step

Abstract

Re-ignition and re-initiation mechanisms of quenched detonation waves passing over a backward facing step are investigated using a high-resolution discontinuous Galerkin method, in which the reaction chemistry is described using a detailed chemical model. A stoichiometric Hydrogen/Oxygen mixture with different diluents (Argon and Nitrogen) is considered to assess effects of the mixture composition and reactivity on the initiation process. It is found that the mixture reactivity and the spatio-temporal evolution of the diffracted detonation wave are critical in controlling the development of the ignition kernels, and the possible transition to detonation. Due to curvature effects and the increasing shock angle, the incident shock wave transitions from a regular reflection to a Mach reflection. Through parametric studies, it is shown that for more reactive Argon-diluted mixtures, ignition first appears behind the regular shock reflection, which is followed by spontaneous re-initiation through the SWACER (Shock Wave Amplification by Coherent Energy Release) mechanism. By replacing Argon with Nitrogen, the reactivity reduces and re-ignition through Mach reflection is observed. The subsequent re-initiation is primarily controlled by flame-acoustic and wave-wave interactions. Hot-spot re-initiation behind the Mach stem is not found due to the short ignition window that exists over the limited range of shock angles. A theoretical model is developed to confirm these findings and to quantify the coupling among the incident shock angle, the thermodynamic state of the shock-compressed mixture, and the ignition delay. Effects of viscous-diffusive transport are also assessed, and it is shown that the viscous dissipation at the wall promotes ignition and transition to re-initiation.