A consistent model of the initiation, early expansion, and possible extinction of a spark-ignited flame kernel

Modelling the establishment and growth of spark-ignited (SI) flame kernels has always been a topic of great interest, especially due to their key role in affecting the performance of SI engines. A major issue is that the unsteady conditions and the small kernel size hinder the application of the typical (both linear and non-linear) flame stretch correlations, valid only long after the ignition stage. Overcoming such limitations, this work presents a novel, mathematically consistent, and compact model that enables prediction of flame kernel initiation and early expansion, including its possible extinction. Firstly, spark-driven initiation models from literature are discussed, and an effective flame kernel initiation method is proposed. Then, the expansion model is defined complementing the mass, energy, and species conservation equations for the spherical kernel with the reactant and temperature profiles outside of it using the theory of transient thermodiffusive flames. After accounting for the convective flow caused by the combustion-induced density reduction and the variable thermodynamic properties of the reacting fuel/air mixture, the result is a two-equation model that predicts the kernel expansion even up to its possible extinction due to flame stretch. After calibration of the expansion model, successful validation is achieved against literature data on lean propane/air flames, and the influence of the model parameters is examined in detail. The proposed expansion model is formulated also aiming for inclusion into the simulation of combustion in SI engines, enabling more accurate predictions at part loads, as well as more effective estimation of the cycle-to-cycle variation thanks to the good model sensitivity to the parameters most affecting the ignition.