Stochastic model for the investigation of the influence of turbulent mixing on engine knock

A stochastic model based on a probability density function (PDF) was developed for the investigation of different conditions that determine knock in spark ignition (SI) engine, with focus on the turbulent mixing. The model used is based on a two-zone approach, where the burned and unburned gases are described as stochastic reactors. By using a stochastic ensemble to represent the PDF of the scalar variables associated with the burned and the unburned gases it is possible to investigate phenomena that are neglected by the regular existing models (as gas non-uniformity, turbulence mixing, or the variable gas-wall interaction). Two mixing models are implemented for describing the turbulent mixing: the deterministic interaction by exchange with the mean (IEM) model and the stochastic coalescence/ dispersal (C/D) model. Also, a stochastic jump process is employed for modeling the irregularities in the heat transfer. Parameter studies are carried out in order to assess the influence of the turbulence intensity and of the fluctuations in the gas - wall interactions.