Planar detonation structure for chain-branching kinetics with large activation energy and small initiation rate

Abstract

The structure of the steady planar detonation wave is analyzed for three-step chain-branching kinetics consistent with hydrogen–air chemistry. The initiation and chain-branching steps are described by an Arrhenius rate. Both are thermally neutral, so that heat release is due to termination. The initiation rate is typically very low and very stiff. As a result, a small fraction of the reactant is consumed in the initiation region, which is very long but ends in an exponential chain-branching explosion. Next, the reactant is rapidly converted into chain-branching radicals, within a very thin zone, which ends when the concentration of the chain-branching radical reaches a peak, because of reactant depletion. Finally, the termination step consumes the chain-branching radicals and releases heat within a region thicker than the peak zone, but much thinner than the initiation region. The analysis is based upon two assumptions: that the chain-branching activation energy is high and that initiation is slow. The structure of the initiation and chain-branching zones is different for post-shock states within or outside the explosion region in the chain-branching diagram. In the former situation, chain-branching is already stronger than termination at the von Neumann point, and vice versa. In the no-explosion case, the initiation zone becomes very long, while the little chain-branching specie produced by initiation is directly converted into product by the termination step. Temperature increases slowly until reaching the explosion curve, when chain-branching becomes stronger than termination. The subsequent structure is similar to the explosion case.