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. Each particle is convected by the gas flow and its growth is governed by flame speed and thermal expansion due to the energy transfer from the electrical circuit. From particle positions and size it is then possible to reconstruct the flame surface density distribution, that is then used by the gas phase to compute the fuel reaction rate. A simplified model for the secondary electrical circuit was applied to estimate the amount of energy transferred as function of the circuit properties (equivalent resistance and inductance), discharge energy and time. To compute the flame kernel expansion velocity, the heat conduction equation was solved accounting for real gas properties in the 5000 - 50000 K temperature range. All the effects of the flame kernel growth are grouped into a single source term, that is added to the flame surface density transport equation, solved following the Extended Coherent Flamelet Model (ECFM).
The proposed model has been extensively validated with experimental data provided by Herweg et al., illustrated in [1, 2]. A computational mesh reproducing the geometrical details of the optical, pre-chamber SI engine was built, including the electrodes. Initially, cold-flow simulations were carried out to verify the validity of the computed flow-field and turbulent distribution at ignition time. Then, the combustion process was simulated accounting for the effects of different engine speeds, air/fuel ratio, ignition systems and spark-plug position. Validation was performed by comparing computed and experimental evolution of the burned gas volume. Encouraging results were achieved for a wide range of operating conditions.