An analytical approximation for high-temperature autoignition times of higher alkanes

It is shown that, above about 1000 K, ignition delay times for propane and all higher alkanes, as well as for a number of other fuels, can be calculated well by employing rate parameters of only three types of elementary steps, namely CmHn + HO2 → CmHn−1 + H2O2, H2O2 + M→2OH + M and 2HO2 → H2O2 + O2, only the first of which is fuel specific, the other two clearly being common to all fuels. The prediction of this remarkably simple result relies on a steady-state approximation for HO2, as well as steady states for more active radicals during induction. The resulting approximation to the chemistry exhibits a slow, finite-rate buildup of H2O2 and removal of fuel during the induction period. The criterion employed for termination of the induction period is the complete depletion of the original fuel subject to the approximations introduced. Numerical comparisons of the ignition-time formula with the experiments show that the predictions work well not only for higher alkanes but also for propene and JP-10. The analytical approximation thus produces reasonable results for a wide range of fuels.