Application and refinement of scaling analyses for mild ignition
Thermal and compositional inhomogeneities may significantly affect outcomes in a variety of fundamental and practical systems, including shock tubes, rapid compression machines, and combustion engines. Even in idealized configurations, homogenous reactive mixtures can never be completely uniform. This can lead to premature ignition, undesired flame propagation, or even detonation. Such perturbations to reacting flows have been recently analyzed by the authors of this work using a novel scaling analysis. That analysis identified three competing processes that affect the influence of an inhomogeneity on the globally observed ignition. First, diffusive quenching of a locally perturbed hot-spot can compete with premature ignition of this reaction center. Next, the ignited flame may extinguish due to high stretch rate. Finally, compressive heating of the end-gas due to flame propagation can compete with homogeneous ignition of the unperturbed bulk gas. In the present work, this scaling analysis is applied to ignition delay measurements reported in the literature. In these experiments, ignition often occurs earlier than expected due to inhomogeneities in the mixture. The previously-developed framework is utilized to infer a representative hot-spot geometry which could lead to the observed early ignition, demonstrating the validity of the scaling analysis.