Analytic Solutions to the Ignition Kinetics of the Hydrogen-Oxygen Reaction

Solutions have been obtained assuming isothermal conditions and negligible depletion of reactants during the induction period for the following scheme of reactions: O H + H 2 → k 1 H 2 O + H , H + O 2 → k 2 O H + O , O + H 2 → k 3 O H + H , H + O 2 + M → k 6 H O 2 + M , H O + H 2 → k 11 H 2 O 2 + H Three types of solutions have been deduced, corresponding to k 6 c M >2 k 2 (a low-temperature-high-pressure region of long ignition delays), 2 k 2 > k 6 c M (a high-temperature-low-pressure region of short delays), and 2 k 2 = k 6 c M (the boundary between the two regions). Experimental ignition delays in both long- and short-delay regions are adequately explained, and ignition delays computed by numerical integration of the rate equations are reproduced to within a few per cent. Finally, ignition delays for the Von Neumann spike condition in Chapman-Jouguet detonations in the neighborhood of the lean limit of detonability in air have been calculated. These delays decrease by two orders of magnitude as the hydrogen mole fraction increases from 0.135 to 0.145. This is very close to the experimental limit (hydrogen mole fraction 0.14 to 0.15) and thus supports the notion that the condition 2 k 2 > k 6 C M must be satisfied for a stable detonation.