Hydrogen-Oxygen Flame Acceleration in Channels of Different Widths with No-Slip Walls and the Deflagration-to-Detonation Transition

Abstract

A propagating flame initiated near the closed end of the channel controls the flow forming ahead of it, which results in the flame acceleration compatible with the physical boundary conditions. The first qualitative study of the flame acceleration caused by the flame interaction with the upstream flow in a channel with no-slip walls has been done by Zeldovich [1], who emphasized that stretching of the flame front due to the interaction with a nonuniform distribution of the upstream flow velocity is the main cause of the flame acceleration, while turbulence can play only a minor supplementary role if any. The accelerating flame acts as a piston producing compression waves in the upstream flow which steepen into the shocks. Dynamics of the accelerating flame, the intensity and location of the shock waves in the upstream flow with respect to the flame front, are obviously crucial for the mechanism of the transition from deflagration to detonation (DDT). Over the years DDT was one of the least understood processes in combustion science in spite of its extreme importance. Significant efforts have been devoted to understand the nature of the flame acceleration and mechanism of DDT using CFD with a simplified onestep chemical model (see [2] for recent review). However, a single-step reaction model cannot reproduce the main properties of the combustion such as the induction time in chain-branching kinetics and detonation initiation. The primary cause for disagreement comes not from three dimensional effects in the experiment but from a one-step Arrhenius kinetics which was employed for CFD simulations. It is therefore important to investigate the qualitative and quantitative differences of the processes between chain-branching kinetics and the predictions from one-step models. In the present paper we show that the flame acceleration in channels with no-slip walls is entirely determined by the features of the flow formed ahead of the flame. It is shown that the transition to detonation occurs due to the pressure pulse, which is formed at the tip of accelerating flame, grows exponentially and steepens into a strong shock coupled with the reaction zone.