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.