Fast, non-diffusive ignition of a gaseous reacting mixture subject to a point energy source

The ignition of a gaseous reactive mixture subject to a localized energy source is analysed using large activation energy asymptotics. The energy released by the source results in a thermal non-uniformity in a small region of the gas. We distinguish two different regimes, non-diffusive and diffusive, depending on the dominant cooling mechanism during the ignition stage: expansion effects or heat conduction. We focus on the non-diffusive ignition, considering the energy source as instantaneous. We show the existence of a critical value of a Damköhler number, defined as the ratio of the characteristic times of the expansion waves and chemical reaction, such that ignition only occurs for supercritical values at a well-defined ignition time, which is calculated numerically. The ignition process for a non-instantaneous energy source is also described in terms of an initial inert heating stage and a shorter reactive stage ending in thermal runaway for supercritical values of the Damköhler number.