A control-oriented real-time semi-empirical model for the prediction of NOx emissions in diesel engines

The present work describes the development of a fast control-oriented semi-empirical model that is capable of predicting NOx emissions in diesel engines under steady state and transient conditions. The model takes into account the maximum in-cylinder burned gas temperature of the main injection, the ambient gas-to-fuel ratio, the mass of injected fuel, the engine speed and the injection pressure. The evaluation of the temperature of the burned gas is based on a three-zone real-time diagnostic thermodynamic model that has recently been developed by the authors. Two correlations have also been developed in the present study, in order to evaluate the maximum burned gas temperature during the main combustion phase (derived from the three-zone diagnostic model) on the basis of significant engine parameters. The model has been tuned and applied to two diesel engines that feature different injection systems of the indirect acting piezoelectric, direct acting piezoelectric and solenoid type, respectively, over a wide range of steady-state operating conditions. The model has also been validated in transient operation conditions, over the urban and extra-urban phases of an NEDC. It has been shown that the proposed approach is capable of improving the predictive capability of NOx emissions, compared to previous approaches, and is characterized by a very low computational effort, as it is based on a single-equation correlation. It is therefore suitable for real-time applications, and could also be integrated in the engine control unit for closed-loop or feed-forward control tasks.