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Cycle-To-Cycle Variability (CCV) must be properly considered when modeling the ignition process in SI engines operating with ultra-lean mixtures. In this work, a strategy to model the impact of the ignition type on the CCV was developed using the RANS approach for turbulence modelling, performing multi-cycle simulations for the power-cycle only. The spark-discharge was modelled through a set of Lagrangian particles, introduced along the sparkgap and interacting with the surrounding Eulerian gas flow. Then, at each discharge event, the velocity of each particle was modified with a zero-divergence perturbation of the velocity field with respect to average conditions. Finally, the particles velocity was evolved according to the Simplified Langevin Model (SLM), which keeps memory of the initial perturbation and applies a Wiener process to simulate the stochastic interaction of each channel particle with the surrounding gas flow.

A correct prediction of the initial stages of the combustion process in SI engines is of great importance to understand how local flow conditions, fuel properties, mixture stratification and ignition affect the in-cylinder pressure development and pollutant formation. However, flame kernel growth is governed by many interacting processes including energy transfer from the electrical circuit to the gas phase, interaction between the plasma channel and the flow field, transition between different combustion regimes and gas expansion at very high temperatures. In this work, the authors intend to present a comprehensive, multi-dimensional model that can be used to predict the initial combustion stages in SI engines. In particular, the spark channel is represented by a set of Lagrangian particles where each one of them acts as a single flame kernel.