A RANS knock model to predict the statistical occurrence of engine knock

In the recent past engine knock emerged as one of the main limiting aspects for the achievement of higher efficiency targets in modern spark-ignition (SI) engines. To attain these requirements, engine operating points must be moved as close as possible to the onset of abnormal combustions, although the turbulent nature of flow field and SI combustion leads to possibly ample fluctuations between consecutive engine cycles. This forces engine designers to distance the target condition from its theoretical optimum in order to prevent abnormal combustion, which can potentially damage engine components because of few individual heavy-knocking cycles. A statistically based RANS knock model is presented in this study, whose aim is the prediction not only of the ensemble average knock occurrence, poorly meaningful in such a stochastic event, but also of a knock probability. The model is based on look-up tables of autoignition times from detailed chemistry, coupled with transport equations for the variance of mixture fraction and enthalpy. The transported perturbations around the ensemble average value are based on variable gradients and on a local turbulent time scale. A multi-variate 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; this results in the prediction of an earliest knock probability preceding the ensemble average knock onset, as confirmed by the experimental evidence. The proposed model estimates not only the regions where the average knock is promoted, but also where and when the first knock is more likely to be encountered. The application of the model to a RANS simulation of a modern turbocharged direct injection (DI) SI engine with optical access is presented and the analysis of the knock statistical occurrence obtained by the proposed model adds an innovative contribution to overcome the limitation of consolidated "average knock" analyses typical of a RANS approach.