Flame acceleration and DDT in channels with obstacles: Effect of obstacle spacing

We study flame acceleration and deflagration-to-detonation transition (DDT) in obstructed channels using 2D reactive Navier–Stokes numerical simulations. The energy release rate for the stoichiometric hydrogen–air mixture is modeled by one-step Arrhenius kinetics. Computations performed for channels with symmetrical and staggered obstacle configurations show two main effects of obstacle spacing S. First, more obstacles per unit length create more perturbations that increase the flame surface area more quickly, and therefore the flame speed grows faster. Second, DDT occurs more easily when the obstacle spacing is large enough for Mach stems to form between obstacles. These two effects are responsible for three different regimes of flame acceleration and DDT observed in simulations: (1) Detonation is ignited when a Mach stem formed by the diffracting shock reflecting from the side wall collides with an obstacle, (2) Mach stems do not form, and the detonation is not ignited, and (3) Mach stems do not form, but the leading shock becomes strong enough to ignite a detonation by direct collision with the top of an obstacle. Regime 3 is observed for small S and involves multiple isolated detonations that appear between obstacles and play a key role in final stages of flame and shock acceleration. For Regime 1 and staggered obstacle configurations, we observe resonance phenomena that significantly reduce the DDT time when S/2 is comparable to the channel width. Effects of imposed symmetry and stochasticity on DDT phenomena are also considered.