Analysis on ignition kernel formation in a quiescent mixture: Different characteristic time scales and critical heating powers

Abstract

Flame ignition is one of the most fundamental and ubiquitous problems in the field of combustion. Flame ignition in a quiescent flammable mixture consists of two phases: ignition kernel formation and subsequent transition to self-sustained expanding spherical flame. Most of previous studies focused on the second phase while little attention was paid to the first phase. In this work, theoretical analysis is conducted for ignition kernel formation induced by external heating within finite domain and finite duration. The ignition kernel formation consists of three stages, i.e., onset of thermal runaway, generation of reaction front at the center, and arrival of reaction front at the edge of heating domain. The characteristic time scales for these three stages are evaluated. Good agreement between theoretical analysis and transient simulation has been obtained. The delay times for the generation of reaction front at the center and its propagation to the edge of heating domain decrease rapidly with the external heating power density; and the delay time for thermal runaway is the primary component in the total time for ignition kernel formation. Moreover, a minimum power density for external heating below which thermal runaway cannot occur is determined. Since chemical reaction is self-sustained by releasing heat, two additional threshold values of external heating power densities are determined respectively corresponding to spontaneous generation of reaction front at the center and its subsequent propagation across the edge of heating domain. This study provides useful insights into ignition kernel formation occurring in premixed flame ignition.