Acceleration of laminar hydrogen/oxygen flames in a tube and the possible onset of detonation

The possibility is analysed of a laminar flame accelerating along a cylindrical tube, closed at one end, and inducing a deflagration to detonation transition in a stoichiometric H₂/O₂ mixture. The pressure and temperature ratios at the ensuing shock wave increase, as do laminar burning velocities, while autoignition delay times decrease. Combined with appreciable elongation of the flame, these enhance the strength of the shock. The conditions necessary for delay times of 0.05, 0.1, 1.0 and 5.0 ms, at an unburned mixture critical Reynolds number of 2300, are computed for different tube diameters. Probable consequences of the different delay times and hot spot reactivity gradients, including detonation, are all considered. The probability of a purely laminar propagation leading to a detonation is marginal. Only when the initial temperature is raised to 375 K, do purely laminar detonations become possible in tubes of between about 0.5 and 1.35 mm diameter.