Computational study of gaseous cellular detonation diffraction and re-initiation by small obstacle induced perturbations

A gaseous detonation wave that emerges from a channel into an unconfined space is known as detonation diffraction. If the dimension of the channel exit is below some critical value, the incident detonation fails to re-initiate (i.e., transmit into a self-sustained detonation propagating) in the unconfined area. In a previous study, Xu et al. ["The role of cellular instability on the critical tube diameter problem for unstable gaseous detonations," Proc. Combust. Inst. 37(3), 3545-3533 (2019)] experimentally demonstrated that, for an unstable detonable mixture (i.e., stoichiometric acetylene-oxygen), a small obstacle near the channel exit promotes the re-initiation capability for cases with a sub-critical channel size. In the current study, two-dimensional numerical simulations were performed to reveal this obstacle-triggered re-initiation process in greater detail. Parametric studies were carried out to examine the influence of obstacle position on the re-initiation capability. The results show that a collision between a triple-point wave complex at the diffracting shock front and the obstacle is required for a successful re-initiation. If an obstacle is placed too close or too far away from the channel exit, the diffracting detonation cannot be re-initiated. Since shot-to-shot variation in the cellular wave structure of the incident detonation results in different triple-point trajectories, for an obstacle at a fixed position, the occurrence of re-initiation is of a stochastic nature. The findings of this study highlight that flow instability generated by a local perturbation is effective in enhancing the re-initiation capability of a diffracting cellular detonation wave in an unstable mixture.