Engine knock is emerging as the main limiting factor for modern spark-ignition (SI) engines, facing increasing thermal loads and seeking demanding efficiency targets. To fulfill these requirements, the engine operating point must be moved as close as possible to the onset of abnormal combustion events. The turbulent regime characterizing in-cylinder flows and SI combustion leads to serious fluctuations between consecutive engine cycles. This forces the engine designer to further distance the target condition from its theoretical optimum, in order to prevent abnormal combustion to severely damage the engine components just because of few individual heavy-knocking cycles. A RANS-based model is presented in this study, which is able to predict not only the ensemble average knock occurrence but also a knock probability. This improves the knock tendency characterization, since the mean knock onset alone is a poorly meaningful indication in a stochastic event such as engine knock. The model is based on a look-up table approach from detailed chemistry, coupled with the transport of the variance of both mixture fraction and enthalpy. These perturbations around the ensemble average value are originated by the turbulent time scale. A multivariate cell-based Gaussian-PDF model is proposed for the unburnt mixture, resulting in a statistical distribution for the in-cell reaction rate. An average knock precursor and its variance are independently calculated and transported, and the earliest knock probability is always preceding the ensemble average knock onset, as confirmed by the experimental evidence. This allows to identify not only the regions where the average knock first occurs, but also where the first knock probability is more likely to be encountered. The application of the model to a RANS simulation of a modern turbocharged direct injection (DI) SI engine is presented and a small percentage of knocking cycles is predicted by the model although the average behavior is knock-free, in agreement with the experiments. The estimate of the knocking probability improves the consolidated “average knock” RANS analysis and gives an indication of the statistical knock tendency of the engine.
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