Recently, a tendency is consolidating to produce low displacement turbocharged spark-ignition engines. This design philosophy, known as "engine downsizing", allows to reduce mechanical and pumping losses at low load as a consequence of the higher operating Brake Mean Effective Pressure (BMEP). The presence of the turbocharger allows to restore the maximum power output of the larger displacement engine. Additional advantages are a higher low-speed torque and hence a better drivability and fun-to-drive. Of course, at high loads, the spark-advance must be carefully controlled to avoid the knock occurrence and this determines a substantial penalization of the fuel consumption. The knowledge of the knock-limited spark timing is hence a key point in order to reduce the fuel consumption drop at high loads. In a previous study [1], a combined procedure for the quasi-dimensional modeling of both combustion and knock phenomena was developed and applied to a 1D thermodynamic engine model in order to find the knock-limited spark-advance at wide-open-throttle (WOT) conditions, for different engine speeds. In the present paper, indeed, the previous analysis is extended to include the cycle-by-cycle variations effects. Cyclic dispersion is characterized through the introduction of a random variation on a number of parameters controlling the rate of heat release (air/fuel ratio, initial flame kernel duration and radius, EGR rate, turbulence intensity). The intensity of the random variation is specified in order to realize an Indicated Mean Effective Pressure (IMEP) coefficient of variation similar to the experimentally observed one. A kinetic scheme is then solved within the unburned gas zone, characterized by different thermodynamic conditions occurring cycle-by-cycle. This allows, for a given spark timing, to estimate a statistical distribution of a properly defined knock indicator. To the aim of validating the developed methodology, a DFT analysis of consecutive experimental pressure cycles is carried out in different operating conditions. High frequency pressure oscillations, typical of knocking occurrence, can be recognized and the statistical distribution of knocking intensity is in this way identified. Numerical and experimental results are finally compared in terms of coefficient of variation, and a good agreement is found.
