A simple HCCI combustion model was developed that consists of an auto-ignition expression based on the Livengood-Wu integral approach and a Wiebe heat release function. In the model, which requires short calculation times, the auto-ignition timing is calculated using an algebraic expression which is a function of mixture temperature, cylinder pressure, air/fuel ratio and Residual Gas Fraction (RGF). Furthermore, a constant was added to the expression to accounts for the effect of pre-ignition chemistry on the ignition delay time. The ignition expression, including functions representing the effect of each parameter on the ignition delay time, was derived in a structured and systematic way.
A detailed-chemistry HCCI model that previously has been extensively validated against experimental engine data was used to provide input data for the ignition expression calibration process. The input data consisted of crank angle resolved mixture temperature and composition as well as cylinder pressure during the compression stroke.
The ignition expression developed was calibrated to simulate the combustion process in gasoline HCCI engines with internal EGR trapping. It is proven that the ignition expression properly manages to predict the trends in auto-ignition timing when varying the engine speed, the temperature at IVC, the cylinder pressure at IVC, the air/fuel ratio or the RGF, when compared with results from the detailed-chemistry HCCI model. A comparison with results from HCCI engine experiments shows that HCCI modeling applying the derived ignition expression can accurately predict in-cylinder processes and global engine parameters typical for HCCI combustion.