Auto-ignition of a homogeneous hydrogen-air mixture subjected to unsteady temperature fluctuations

The effect of unsteady temperature oscillations on the ignition of a homogeneous constant-volume hydrogen-air mixture is studied computationally with detailed chemical kinetics, and theoretically using asymptotic analysis. The study is of practical importance in the recent development of low-temperature combustion engines (such as homogeneous charge compression ignition engines) in which control of ignition timing and burn duration in the presence of temporal and spatial temperature variations becomes a technical challenge. Both low-temperature and high-temperature regimes of hydrogen ignition are studied. The asymptotic analysis is used to derive a closed-form solution for the ignition delay, showing excellent agreement with direct numerical calculations with detailed chemistry. It is found that ignition delay shows a harmonic response to the frequency of the imposed temperature oscillation and the response monotonically attenuates as the frequency increases. For frequencies of oscillation lower than the first harmonic, the unsteady ignition behavior correlates strongly with the cumulative mean temperature during the induction period. On the other hand, for higher frequencies the ignition behavior is dictated by the instantaneous gradient of the temperature fluctuation at the onset of ignition.