Modelling ignition probability with pairwise mixing-reaction model for flame particle tracking

Reduced order models for ignition analysis can offer insights into ignition processes and facilitate the combustor optimization. In this study, a Pairwise Mixing-Reaction (PMR) model is formulated to model the interaction between the flame particle and the surrounding cell mixture during Lagrangian flame particle tracking. Specifically, the model accounts for the two-way coupling of mass and energy between the flame particle and the surrounding shell layer by modelling the corresponding turbulent mixing, chemical reaction and evaporation process if present. The state of a flame particle, e.g., burnt, hot gas or extinguished, is determined based on particle temperature. This model can properly describe the ignition process with a spark kernel being initiated in a nonflammable region, which is of practical importance in certain turbine engines and has not been rigorously accounted for by the existing models based on the estimation of local Karlovitz number. The model is integrated into an ignition probability analysis platform and is demonstrated for a methane/air bluff-body flame with the flow and fuel/air mixing characteristics being extracted from a non-reacting simulation. The results show that for the spark location being at the extreme fuel-lean outer shear layer of the recirculation zone, PMR can yield ignition events with a significant number of active flame particles. The mechanisms for the survival of the initial flame particles and the entrainment of the survived flame particles into the recirculation zone are analyzed. The results also show that the ignition probability map from PMR agrees well with the experimental observation: a high ignition probability in the shear layer of the recirculation zone near the mean stoichiometric surface, and low ignition probabilities inside the recirculation zone and the top stagnation region of the recirculation zone. The parametric study shows that the predicted shape of the ignition progress factor and ignition probability is in general insensitive to the model parameters and the model is adequate for quantifying the regions with high ignition probabilities.