Two-Stage 0D/1D Knock Model to Predict the Knock Boundary of SI Engines

SI engines are typically designed to operate at the knock boundary, as engine knock limits their efficiency and thus further reduction of CO₂ emissions. To consider this phenomenon in an engine process simulation, a precise knock model is needed. First, since auto-ignitions precede knocking events, the introduced 0D/1D knock model predicts when the unburnt mixture auto-ignites. For this, the model considers the two-stage auto-ignition of gasoline fuels, which occurs at specific boundary conditions, by calculating two Livengood-Wu-integrals. The model’s auto-ignition prediction is validated against measurement data of a single cylinder engine covering almost 3 000 knocking single working cycles at broadly varied operating conditions.

To determine the operating conditions where the knock boundary is reached, the newly developed knock criterion considers the state of pre-reactions of the unburnt mixture before the start of combustion. For its validation, simulations were performed to compare the point where 50% of the mass is burned (MFB50) of each simulated operating point to the MFB50 of the corresponding measured average working cycle at the knock boundary. Though the introduced criterion is calibrated at only two operating points, this new knock model predicts the MFB50 at the knock boundary at broad variations of operating conditions very precisely with a mean deviation of 1.55°CA, helping to improve the development of SI engines in 0D/1D simulation. Furthermore, a three-parameter-approach to model the knock frequency is introduced.