Numerical Modeling of Spark Path with Stretching and Short Circuit in Three-Dimensional Flow

Prediction of the discharge path behavior between electrodes on a spark plug is important for efficient energy use in internal combustion engines, especially in lean combustion. In this paper, we propose a numerical model for the prediction of the spark path behaviors based on the coupling of a flow field, a Lagrangian particle model, and an equivalent circuit model. A turbulent flow around cylinders imitating electrodes is solved using a direct numerical simulation, in which Lagrangian particles along the spark path are tracked. Electric current and inter-electrode voltage are computed based on the energy conversion rate from the circuit to the mixture gas. As a result, a discharge path is reproduced with Lagrangian tracking particles virtually aligned between the cylinders. The spark path has a complicated structure along the spanwise direction due to the complex three-dimensional vortical structure of the cylinder wake. It is also observed that the discharge path repeats elongation and shortening effect. Next, cases with electrodes of 4 different shapes and permeability are investigated aiming at suppression of the vortex shedding that disturbs the discharge path. Joule heat is used in the evaluation since it causes the spark in SI engines. It is found that discharge characteristics, such as electric current and inter-electrode voltage, are dependent on the electrode features. Also, it turns out that the case of streamlined electrodes, i.e., the NACA0015 case, has the best energy conversion rate from the circuit to the mixture gas. From the results above, optimizing the shape of electrodes will improve the energy efficiency rate and contribute to further improvement in lean combustion stability.