Quasi-steady combustion of normal-alkane droplets supported by Cool-Flame chemistry near diffusive extinction

Two steady-state chemical-kinetic approximations are introduced into the apparently most relevant five cool-flame steps of the latest San Diego mechanism for n-heptane, supplemented by a sixth step chosen to capture the influence of hot-flame chemistry on the cool flame in that mechanism, in order to obtain an effectively four-step chemical-kinetic description for addressing quasi-steady combustion of normal-alkane droplets in the lower-temperature part of the negative-temperature-coefficient (NTC) range, where cool-flame extinction is observed to occur. A development paralleling the classical activation-energy-asymptotic (AEA) analysis of the partial-burning regime, accompanied by an approximate description of a distributed reaction, is then pursued to make predictions of the combustion process, accounting for the large Lewis numbers of the fuel and intermediate species for the first time. The predictions are compared with results of droplet-combustion experiments performed in the International Space Station (ISS), showing reasonable agreement between theory and experiment and pointing to some needed future improvements in values of rate parameters. In addition, the theory predicts, for the first time, a limiting oxygen index (LOI) for droplet combustion of normal alkanes, giving, for example, for heptane burning in oxygen-nitrogen mixtures at normal room temperature, a corresponding oxygen mole fraction on the order of 0.10 in the ambient atmosphere, below which cool-flame-supported combustion cannot occur.