Adapting Dimensionless Numbers Developed for Knock Prediction Under Homogeneous Conditions to Ultra-Lean Spark Ignition Conditions

Knock in spark-ignition (SI) engines has been a subject of many research efforts and its relationship with high efficiency operating conditions keeps it a contemporary issue as engine technologies push classical limits. Despite this long history of research, literature is lacking coherent and generalized descriptions of how knock is affected by changes in the full cylinder temperature field, residence time (engine speed), and air/fuel ratio. In this work, two dimensionless numbers are applied to fully 3D SI conditions. First, the characteristic time of autoignition (ignition delay) is compared against the characteristic time of end-gas deflagration, which was used to predict knocking propensity. Second, the temperature gradient of the end-gas is compared against a critical detonation-based temperature gradient, which predicts the knock intensity. These dimensionless numbers’ relationship to knocking propensity and intensity of specific cylinder conditions is investigated via 3D computational fluid dynamics (CFD) simulations utilizing a large eddy simulation (LES) framework. Simulations of a light-duty SI engine fueled with a gasoline surrogate are performed at various engine speeds (1400 rpm and 2000 rpm) and air/fuel ratios (λ =1 and 2), and end-gas temperature stratifications. The dimensionless numbers’ ability to predict knocking propensity and intensity magnitudes while being invariant to other phenomenon across these various operating conditions is validated.