Predicting the Distribution of Combustion Timing Ensemble in an HCCI Engine

Control of Homogeneous Charge Compression Ignition (HCCI) engines to obtain the desirable operation requires understanding of how different charge variables influence the cyclic variations in HCCI combustion. Combustion timing for consecutive cycles at each operating point makes an ensemble of combustion timing which can exhibit different shapes of probability distributions depending on the random and physical patterns existing in the data. In this paper, a combined physical-statistical control-oriented model is developed to predict the distribution of HCCI combustion timing (CA50, crank angle of 50% fuel mass fraction burnt) for a range of operating conditions. The statistical model is based on the Generalized Extreme Value (GEV) distribution and the physical model embodies a modified knock integral model, a fuel burn rate model, a semi-empirical model for the gas exchange process and an empirical model to estimate the combustion timing dispersion. The resulting model is parameterized for the combustion of Primary Reference Fuel (PRF) blends using over 5000 simulations from a detailed thermo-kinetic model. Empirical correlations in the model are parameterized using the experimental data obtained from a single-cylinder engine. Once the model is parameterized it only needs five inputs: intake pressure, intake temperature, Exhaust Gas Recirculation (EGR) rate, equivalence ratio and engine speed. The main outputs of the model are CA50 and the Probability Density Function (PDF) metrics of CA50 distribution. Experimental CA50 is compared with predicted CA50 from the model and the results show a total average error of less than 1.5 degrees of crank angle for 213 steady-state operating points with four different PRF fuels at diversified operating conditions. Predicted PDF of the CA50 ensemble is compared with that of the experiments for PRF fuels at different running conditions. The results indicate a good agreement between simulation and the experiment.