G-equation based ignition model for direct injection spark ignition engines

To accurately model the Direct Injection Spark Ignition (DISI) combustion process, it is important to account for the effects of the spark energy discharge process. The proximity of the injected fuel spray and spark electrodes leads to steep gradients in local velocities and equivalence ratios, particularly under cold-start conditions when multiple injection strategies are employed. The variations in the local properties at the spark plug location play a significant role in the growth of the initial flame kernel established by the spark and its subsequent evolution into a turbulent flame. In the present work, an ignition model is presented that is compatible with the G-Equation combustion model, which responds to the effects of spark energy discharge and the associated plasma expansion effects. The model is referred to as the Plasma Velocity on G-surface (PVG) model, and it uses the G-surface to capture the early kernel growth. The model derives its theory from the Discrete Particle Ignition (DPIK) model, which accounts for the effects of electrode heat transfer, spark energy, and chemical heat release from the fuel on the early flame kernel growth. The local turbulent flame speed has been calculated based on the instantaneous location of the flame kernel on the Borghi-Peters regime diagram. The model has been validated against the experimental measurements given by Maly and Vogel,(1) and the constant volume flame growth measurements provided by Nwagwe et al.(2) Multi-cycle simulations were performed in CONVERGE(3) using the PVG ignition model in combination with the G-Equation-based GLR(4) model in a RANS framework to capture the combustion characteristics of a DISI engine. Good agreements with the experimental pressure trace and apparent heat-release rates were obtained. Additionally, the PVG ignition model was observed to substantially reduce the sensitivity of the default G-sourcing ignition method employed by CONVERGE.