The transition from deflagration to detonation in thin channels

A numerical study of a two-dimensional model for premixed gas combustion in a thin, semi-infinite and thermally-insulated channel is performed. The work is motivated by recent theoretical advances revealing the important role of hydraulic resistance in deflagration-to-detonation transition, one of the central yet still poorly understood phenomena of gaseous combustion. The two-dimensional formulation reproduces the formation of the so-called tulip flame and its predetonational acceleration, well-known experimentally but unattainable within the quasi-one-dimensional approach employed previously. It is shown that the detonation first develops in the boundary layer where the effect of hydraulic resistance is stronger, and thereupon spreads over the channel's interior. However, the second stage of the transition does not proceed gradually but rather through a localized auto-ignition within the tulip.