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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.

For the simultaneous evaluation of the influence on engine knock of both chemical conditions and global operating parameters, a combined tool was developed. Thus, a two-zone kinetic model for SI engine combustion calculation (Ignition) was implemented into an engine cycle simulation commercial code. The combined model predictions are compared with experimental data from a single-cylinder test engine. This shows that the model can accurately predict the knock onset and in-cylinder pressure and temperature for different lambda conditions, with and without EGR. The influence of nitric oxide amount from residual gas in relation with knock is further investigated. The created numerical tool represents a useful support for experimental measurements, reducing the number of tests required to assess the proper engine control strategies.

Full cycle simulations of a spark ignition engine running on a primary reference fuel have been performed using a two-zone model. A detailed kinetic mechanism is taken into account in each of the zones, while the propagating flame front is calculated from a Wiebe function. The initial conditions for the unburned gas zone were calculated as a mixture of fresh gas and rest gas. The composition of the burned gas zone at the end of the last engine cycle, including nitric oxide emissions, was taken as rest gas. The simulations confirm that the occurrence of autoignition in the end gas is sensitive on the amount of nitric oxide in the rest gas of the spark ignition engine. The comparison of autoignition timings calculated for a single cylinder test engine are getting more accurate if the nitric oxide in the initial gases is taken into account.