Explicit analytic prediction for hydrogen–oxygen ignition times at temperatures below crossover

This paper addresses homogeneous ignition of hydrogen–oxygen mixtures when the initial conditions of temperature and pressure place the system below the crossover temperature associated with the second explosion limit. A three-step reduced mechanism involving H2, O2, H2O, H2O2 and HO2, derived previously from a skeletal mechanism of eight elementary steps by assuming O, OH and H to follow steady state, is seen to describe accurately the associated thermal explosion. At sufficiently low temperatures, HO2 consumption through HO2 + HO2 → H2O2 + O2 is fast enough to place this intermediate in steady state after a short build-up period, thereby reducing further the chemistry description to the two global steps 2H2 + O2 → 2H2O and 2H2O → H2O2 + H2. The strong temperature sensitivity of the corresponding overall rates enables activation-energy asymptotics to be used in describing the resulting thermal runaway, yielding an explicit expression that predicts with excellent accuracy the ignition time for different conditions of initial temperature, composition, and pressure.