The cellular structure of an unstable gaseous detonation affected by a small obstacle on the sidewall

Abstract

This study investigated the influences of a small obstacle upon an unstable detonation front using the smoked-foil technique. In the present experiments, a stoichiometric propane–oxygen diluted with nitrogen mixture at initial pressure of 30 or 70 kPa was used as an explosive gas mixture and four types of obstacles were used: forward-facing steps and slopes and backward-facing steps and slopes. We used the propane-fuel gas mixture, because its non-dimensional activation energy is larger than that of the hydrogen-fuel gas mixture used in our previous study. In the cases of forward-facing steps and slopes, the detonation front structure was not significantly affected similarly to the previous study of hydrogen–oxygen diluted with argon mixture. The shock-tube model shows that the reflected shock wave from the forward-facing step does not drive a transverse wave obviously stronger than the intrinsic transverse wave. On the other hand, the detonation re-activation phenomena were observed in the vicinity of the sidewall downstream of the backward-facing steps and slopes. Although the cellular pattern was similar to the case of hydrogen gas mixture as a whole, the transverse waves were more attenuated behind the diffracted shock wave in the propane gas mixture. Moreover, the detonation re-activation also occurred in a far region from the sidewall in this study. However, noteworthy was that the distance between the backward-facing step and the re-activation position z_ra was expressed by the height of the step |h| and the CJ detonation cell width λ_CJ as z_ra/λ_CJ = 2.9(|h|/λ_CJ)^0.84 and this empirical formula well describes also the results of hydrogen gas mixture and many other mixtures, showing that the non-dimensional activation energy has little effect on the position where the detonation re-activation occurs. This implies that the detonation re-activation on the sidewall is predominantly governed by the transition from the regular reflection to the Mach reflection on the sidewall of the diffracted shock wave decoupled with chemical reaction through the slip-line formation, where the degree of the decay of the diffracted shock wave is influenced not by the stability of the detonation-front cellular structure but by λ_CJ, representing the induction-zone length between the leading shock wave and the subsequent exothermic reaction.