Characteristics of cycle-to-cycle combustion variability at partial-burn limited and misfire limited spark timing under highly diluted conditions

Diluted combustion with exhaust gas recirculation (EGR) has been widely employed to improve the fuel economy of spark ignition engines. The combustion kinetics, however, are affected and the flame propagation speed is decreased. In order to compensate for this adverse effect, the spark timing needs to be re-calibrated to achieve maximum brake torque (MBT). At high levels of EGR dilution, the spark timing is constrained by two ignition limits: 1) the partial-burn limit where the spark timing is retarded from MBT and 2) the misfire limit where the spark timing is too advanced. This work uses a probabilistic framework to capture the differences between both ignition limits. In particular, it introduces the concept of a nominal indicated mean effective pressure (IMEP) distribution based on the stochastic properties of the cycle-to-cycle variability (CCV) at nominal stable conditions. By defining a nominal band where fully burned cycles occur with high probability, we introduce a cycle classification method that can be used to 1) determine the level of randomness of misfire and partial-burn events, and 2) measure CCV. The new CCV metric based on the density of the nominal band is compared with the traditional coefficient of variation of IMEP (CoV_IMEP). It is shown that the nominal band concept, together with the CoV_IMEP, can help to discern between partial-burn limited and misfire limited conditions. Furthermore, the Kullback-Leibler divergence is used to demonstrate that the IMEP distribution is significantly different between nominal and partial-burn/misfire limited conditions. Experiments are carried at various EGR levels and spark timings while recoding in-cylinder pressure at steady state. Although the emphasis of this work is to characterize the differences of both ignition limits from a probabilistic point of view, similarities between partial-burn cycles at either limiting conditions are also discussed.