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Engine knock is one of the most limiting factors for modern Spark-Ignition (SI) engines to achieve high efficiency targets. The stochastic nature of knock in SI units hinders the predictive capability of RANS knock models, which are based on ensemble averaged quantities. To this aim, a knock model grounded in statistics was recently developed in the RANS formalism. The model is able to infer a presumed log-normal distribution of knocking cycles from a single RANS simulation by means of transport equations for variances and turbulence-derived probability density functions (PDFs) for physical quantities. As a main advantage, the model is able to estimate the earliest knock severity experienced when moving the operating condition into the knocking regime.

In this paper, an orifice-based lumped parameter model has been developed and tailored to predict the feeding performances of a single stage, inwardly opening, PWM controlled gas injector for automotive applications. In particular, simplifying the description of injector relevant sections, and adopting a “semi-perfect” approach to depict the gas properties dependency on pressure and temperature, the sub-sonic efflux through the injector metering section is studied involving both an isentropic and a polytropic expansion. Then, considering dry air as fluid medium, the injector feeding characteristics variations with the duty cycle, with the feeding pressure and with temperature are highlighted.