Temperature cross-over and non-thermal runaway at two-stage ignition of n-heptane
Abstract To calculate ignition delay times a skeletal 56-step mechanism for n-heptane is further reduced to a short 30-step mechanism containing two isomers of the n-heptyl-redical and reactions describing both the high temperature and the low temperature chemistry. This mechanism reproduces ignition delay times at various pressures and temperatures reasonably well. Steady state assumptions for many of the intermediate species are introduced to derive separately two global mechanisms for the low temperature regime as well as for the intermediate and high temperature regime. In those formulations the OH radical is depleted by fast reactions with the fuel, as long as fuel is present. Its steady state relation shows that the OH concentration would blow up as soon as the fuel is depleted. Therefore the depletion of the fuel is used as a suitable criterion for ignition. In the intermediate temperature regime the first stage ignition is related to a change from chain-branching to chain-breaking as the temperature crosses a certain threshold. The chain branching reactions result in a build-up of ketohydroperoxides which dissociate to produce OH radicals. This is associated with a slight temperature rise which leads to a crossing of the threshold temperature with the consequence that the production of OH radicals by ketohydroperoxides suddenly ceases. The subsequent second stage is driven by the much slower production of OH radicals owing to the dissociation of hydrogen peroxide. The OH radicals react with the fuel at nearly constant temperature until the latter is fully depleted. In all three regimes analytical solutions for the ignition delay time are presented. The reduced 4-step mechanism of the low temperature regime leads with the assumption of constant temperature to linear differential equations, which are solved. The calculated ignition delay times at fuel depletion compares well with those of the 30-step mechanism. The analysis for the intermediate temperature regime starts from a 4-step subset of a 9-step reduced mechanism. It contains the cross-over dynamics in form of a temperature dependent stoichiometric coefficient which is analysed mathematically. The resulting closed form solutions describe the first stage ignition, the temperature cross-over and the second stage ignition. They also identify the rate determining reactions and quantify the influence of their rates on the first and the second ignition times. The high temperature regime is governed by a three-step mechanism leading to a nonlinear problem which is solved by asymptotic analysis. While the dissociation reaction of the ketohydroperoxide dominates the low temperature regime and the first stage ignition of the intermediate temperature regime, the hydrogen peroxide dissociation takes this role for the second stage of the intermediate and in the high temperature regime. The overall activation energy of the ignition delay time in the low temperature regime is the mean of the activation energies of two reactions only. The overall activation energy of the ignition delay time in the high temperature regime is shown to be related to the activation energies of only three but different rate determining reactions.