Goldsborough, S., Smith, T., Johnson, M., and McConnell, S., "Evaluation of Ignition Timing Predictions Using Control-Oriented Models in Kinetically-Modulated Combustion Regimes," SAE Technical Paper 2012-01-1136, 2012, doi:10.4271/2012-01-1136.
Knock integrals and corresponding ignition delay (τ) correlations are often used in model-based control algorithms in order to predict ignition timing for kinetically modulated combustion regimes such as HCCI and PCCI. They can also be used to estimate knock-inception during conventional SI operation. The purpose of this study is to investigate the performance of various τ correlations proposed in the literature, including those developed based on fundamental data from shock tubes and rapid compression machines, those based on predictions from isochoric simulations using detailed chemical kinetic mechanisms, and those deduced from data of operating engines. A 0D engine simulation framework is used to compare the correlation performance where evaluations are based on the temperatures required at intake valve closure (TIVC) in order to achieve a fixed CA50 point over a range of conditions. In this study engine speeds from 500 to 4000 rpm are covered with fuel mean effective pressures (FMEP) ranging from approximately 5 to 70 bar. Two low temperature combustion schemes are utilized here, one which is fuel lean with atmospheric oxygen concentrations, and another which employs stoichiometric fuel-to-oxygen loadings but is diluted with various levels of EGR.It is noted that some features of each of the correlations follow the trends exhibited by the LLNL detailed toluene reference fuel (TRF) mechanism, however none is a good match under all conditions. The TIVC "operating maps" illustrate some similarities between the correlations, as well as some significant differences. A few correlations indicate the existence of a TIVC "fall-off" regime, especially at higher fuel loadings, i.e., boost pressures, due to the influence of low temperature/NTC chemistry. This regime however, is diminished with high EGR due primarily to the reduction in oxygen in the system. Under many conditions covered in this study a few correlations do a very inadequate job following the trends of the LLNL TRF mechanism. This study demonstrates the need for a robust correlation that includes low temperature/NTC chemistry, and is valid over a wide range of engine operating conditions, as well as various levels of fuel reactivity, i.e., octane number.