A numerical study on the influence of increased instability of quasi-detonation on the critical tube diameter phenomenon

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 D_1/2. 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.