Abstract

At critical conditions, the effect of instability plays a prominent role in the gaseous detonation transmission from a tube into an unconfined space. This study aims to clarify such an effect by investigating the critical tube diameter of quasi-detonations, i.e., detonations under the influence of minor perturbations along the tube walls. The strategy is to conduct two-dimensional numerical simulations using the reactive Euler equations with a two-step induction-reaction kinetic model. The chemical kinetic parameters were adapted to model the detonation wave in the stoichiometric hydrogen-oxygen mixture at 20 kPa and 300 K. The quasi-detonations are obtained in channels with obstacles (attached to the boundaries) of different sizes to mimic wall roughness, σ , which is defined as the ratio between the obstacle size δ and half of the channel width D1/2 . Below a critical value of σ , the rough wall creates only minor perturbations to the intrinsic cellular detonation. Apart from the velocity deficit, the degree of instability and cellular irregularity increases with roughness, resulting in a broader spectrum in the probability density function of the pressure and induction rate. For σ � 0.24, the intrinsic propagation dynamics are more significantly altered—the cellular structure vanishes locally or small cells re-appear from new re-initiation points. Detonations in these more significantly obstructed channels are not considered quasi-detonations subjected to minor boundary perturbations. The influence of small values of roughness on the critical tube diameter phenomenon is then examined. A shot-to-shot variation in cellular dynamics of quasi-detonations is considered by performing multiple simulations for each value of roughness to assess the probability of successful transmission into an unconfined space. For quasi-detonation diffraction at the sub-critical condition, despite a velocity deficit, increasingly higher instabilities resulting from a rough-walled geometry promote the re-initiation of a detonation in the open area. However, if the roughness increases beyond 0.24, both the velocity deficit and different propagation modes in a significantly obstructed channel lead to a lower probability of successful transmission.