Spherical ignition of oxyhydrogen behind a reflected shock wave

Abstract

Nonsteady one-dimensional hydrodynamic equations of plane and spherical symmetry are solved on the both sides of the extended second explosion limit of oxyhydrogen mixtures. Ignition is produced by the arrival and reflection of a shock wave at the shock tube end. Ignition delay, generation of pressure waves and development of subsequent reactions naturally result from the numerical integration of basic equations including twenty-two elementary reactions. It has become clear from the plane ignition model that at the wall itself the reaction is mild and produces no shock waves or shock-like discontinuity on either side of the extended second explosion limit. However, it is observed that the compression waves continue to build up and that in the meantime a detonation wave is formed at a distance of the order of centimeters from the reflection wall. The newly formed detonation soon catches up with the preceding shock wave and is merged into a single detonation wave. It is concluded from such results that the weak ignition observed by Meyer, Oppenheim and Vermeer is not the result of plane ignition. Spherical ignition from a point on the shock reflection wall is also simulated on both sides of the extended second explosion limit. It was found that for single spherical ignition of equimolar oxyhydrogen at 1000°K, mild reactions occur both below and above the second explosion limit. Although accumulation of pressure waves and acceleration of the reaction front are observed, their magnitudes are still considerably below the pressure and velocity of a self-sustaining detonation. Finally, some consideration is given to the origin of reaction centers. The possibility of statistical fluctuations of rate constants is discussed. It is shown numerically that order-unity change of the rate constant of O2+H→OH+O considerably affects the ignition delay of oxyhydrogen mixtures.