The features of flame acceleration in channels with wall friction and the deflagration to detonation transition (DDT) are investigated theoretically and using high resolution numerical simulations of two-dimensional reactive Navier-Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, and a detailed chemical reaction mechanism for hydrogen-oxygen gaseous mixture. It is shown that in a wide channel, from the beginning, the flame velocity increases exponentially for a short time and then flame acceleration decreases, ending up with the abrupt increase of the combustion wave velocity and the actual transition to detonation. In a thin channel with a width smaller than the critical value, the exponential increase of the flame velocity is not bounded and ends up with the transition to detonation. The transition to detonation occurs due to the pressure pulse, which is formed at the tip of the accelerating flame. The amplitude of the pressure pulse grows exponentially due to a positive feedback coupling between the pressure pulse and the heat released in the reaction. Finally, large amplitude pressure pulse steepens into a strong shock coupled with the reaction zone forming the overdriven detonation. The evolution from a temperature gradient to a detonation via the Zeldovich gradient mechanism and its applicability to the deflagration-to-detonation transition is investigated for combustible materials whose chemistry is governed by chain-branching kinetics. The results of the high resolution simulations are fully consistent with experimental observations of the flame acceleration and DDT.
© 2011 American Physical Society