Asymptotic analysis of cool-flame propagation in mixtures of an n-alkane, oxygen, and nitrogen

A simplified chemical-kinetic cool-flame mechanism for n-alkanes has recently been developed and applied to the description of quasi-steady droplet combustion. Chemistry of this same general type can support premixed laminar cool-flame deflagrations. The present contribution derives the structure of the associated freely propagating cool premixed flame controlled by the low-temperature chemistry and develops formulas for calculating the corresponding laminar burning velocity. Application of activation-energy asymptotics reveals finite-rate chemistry, among essential intermediates (with concentrations so small that associated heat release is negligible), occurring throughout the preheat zone. There is leakage of both fuel and oxygen through the thin heat-release zone, with zones of consumption of an intermediate species on each side of the heat-release zone, thicker than that zone but still thin compared with the preheat-zone thickness. Predicted laminar burning velocities are compared with recently reported measurements for n-dodecane, performed in a newly designed high-pressure droplet ignition apparatus, resulting in reasonable agreement after account is taken of the process of insertion of the droplet into the furnace and of the velocity of the buoyant plume present in the experiment.