In SI engines, the initial stages of flame kernel formation play an important role in determining the overall thermal efficiency and in reducing the cycle-to-cycle variability. Introducing a cross-flow within the spark gap has shown to reduce the combustion fluctuations by shortening this initial ignition period and activating a larger volume of the fuel-air mixture. This work presents a computational study of spark discharges in high cross-flow ignition environments using a high-fidelity, multi-physics equilibrium plasma solver. The numerical framework is designed to simultaneously model chemically reacting fluid flow coupled with electromagnetics, surface ablation physics and external circuit dynamics in a fully coupled manner. The spark channel is simulated in a constant volume combustion chamber under different operating conditions and cross flow velocities. The simulation model is validated by comparing several key parameters associated with the discharge such as the breakdown voltage, dwell current, restrike timing, and spark stretch against experimental measurements.

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