Statistical Analysis of Knock Intensity Probability Distribution and Development of 0-D Predictive Knock Model for a SI TC Engine

Knock is a non-deterministic phenomenon and its intensity is typically defined by a non-symmetrical distribution, under fixed operating conditions. A statistical approach is therefore the correct way to study knock features. Typically, intrinsically deterministic knock models need to artificially introduce Cycle-to-Cycle Variation (CCV) of relevant combustion parameters, or of cycle initial conditions, to generate different knock intensity values for a given operating condition. Their output is limited to the percentage of knocking cycles, once the user imposes an arbitrary knock intensity threshold to define the correlation between the number of knocking events and the Spark Advance (SA). In the first part of the paper, a statistical analysis of knock intensity is carried out: for different values of SA, the probability distributions of an experimental Knock Index (KI) are self-compared, and the characteristics of some percentiles are highlighted. The innovative contribution of this work is to correlate such KI probability curves with mean combustion parameters (like maximum in-cylinder pressure or combustion phase) through an analytical function. In this way, KI distributions can be predicted by a fully deterministic combustion model, ignoring CCV. In the final part of the paper such relations are implemented in a 1-D environment and tested using a combustion model, previously calibrated via Three Pressure Analysis (TPA) for knock-free operating conditions. Validation is carried out by comparing experimental and simulated KI distributions.