Laminar-to-turbulent flame transition and cycle-to-cycle variations in large eddy simulation of spark-ignition engines

This paper investigates the effect of laminar-to-turbulent flame transition modeling on the prediction of cycle-to-cycle variations (CCVs) in large eddy simulation (LES) of spark-ignition (SI) engines. A laminar-to-turbulent flame transition model that describes the non-equilibrium sub-filter flame speed evolution during an early stage of flame kernel growth is developed. In the present model, the flame transition is characterized by the flame kernel size at which the flame transition ends, defined here as the flame transition scale. The proposed model captures the effects that variations in a turbulent flow field have on the evolution of early-stage burning rates, through variations in the flame transition scale. The proposed flame transition model is combined with the front propagation formulation (FPF) method and a spark-ignition model to predict CCVs in a gasoline direct injection SI engine. It is found that multi-cycle LES with the proposed flame transition model reproduces experimentally-observed CCVs satisfactorily. When the transition model is not considered or when variations in the transition process are neglected, CCVs are significantly under-predicted for the case considered here. These results indicate the importance of modeling the laminar-to-turbulent flame transition and the effect of turbulence on the transition process, when predicting CCVs, under certain engine conditions. The LES results are also used to analyze sources for variations in the flame transition. It is found, for the present engine case, that the most important source is the cycle-to-cycle variation in the turbulence dissipation rate, which is used to measure the strength of turbulence in the proposed model, near a spark plug. The large-scale velocity field and the variations of the laminar flame speed due to the mixture composition and thermal stratification are also found to be important factors to contribute to the variations in the flame transition.