Stochastic Model for the Investigation of the Effect of Inhomogeneities on Engine Knock

A stochastic model based on a probability density function (PDF) approach was developed for the investigation of spark ignition (SI) engine knock conditions. The model is based on a two zone model, where the burned and unburned gases are described as stochastic reactors, and the movement of the turbulent flame front is expressed with a Wiebe function. Using a stochastic particle ensemble to represent the PDF of the scalar variables associated with the burned and unburned gases, allows the consideration of inhomogeneities in gas composition and temperature, as well as turbulence mixing effects. The turbulent mixing is described with the interaction by exchange with the mean model. A stochastic jump process is used for modeling the heat transfer, hence accounting for the temperature fluctuations and the fluid wall interaction. Detailed chemistry is used in the calculations. A parameter study investigates the effects of end gas inhomogeneities related to residual gas composition and temperature, on the autoignition process.