A Study of the Occurrence of DDT in an Array of Obstacles: Combined Effects of Longitudinal and Transverse Obstacle Spacings

Combustion wave propagation in a channel containing a stoichiometric hydrogen-air mixture and an array of obstacles was investigated, aiming to explore the effects of longitudinal (ls) and transverse (ts) spacings of the obstacles on the occurrence of deflagration-to-detonation transition (DDT). A high-order numerical algorithm and adaptive mesh refinement were adopted to solve reactive Navier-Stokes equations. The spacings, ls and ts, are varied from 1.2 to 6 times the obstacle diameter (d(o) = 12.7 mm). The results show that the occurrence of DDT is largely dependent on ts. The DDT is likely to occur when the ratio of transverse obstacle gap to detonation cell size d/lambda >= 0.64. The DDT run-up distance and time are closely related to ls and ts. For large ts, the DDT occurrence time increases with ls. However, the DDT distance may decrease significantly as ls increases when ls is relatively small, due to frequent local explosions in the isolated pockets of unreacted material. A requirement for the generation of these isolated explosions can be quantified as (ls/ts)(2)(12-4br) < 1, where br is the blockage ratio of the channel. For small ts, the increase of DDT distance with ls/ts slows down notably when ls/ts exceeds a threshold, because there is a mechanism characterized by large fluctuations in flame surface area that promotes the occurrence of DDT in the case with a large enough ls/ts.