Finesso, R. and Spessa, E., "Real-Time Predictive Modeling of Combustion and NOx Formation in Diesel Engines Under Transient Conditions," SAE Technical Paper 2012-01-0899, 2012, doi:10.4271/2012-01-0899.
The present work has the aim of developing a fast approach for the predictive calculation of in-cylinder combustion temperatures and NOx formation in diesel engines, under steady state and transient conditions. The model has been tested on a PC, and found to require very little computational time, thus suggesting it could be implemented in the ECU (Engine Control Unit) of engines for model-based control tasks. The method starts with the low-throughput predictive combustion model that was previously developed by the authors, which allows the predictive estimation of the heat-release rate and of the in-cylinder pressure trace to be made on the basis of the injection parameters and of a few quantities measured by the ECU, such as the intake manifold pressure and temperature. A three-zone thermodynamic model is used for the in-cylinder temperature evaluation: the combustion chamber is divided into a vapor fuel zone, an unburned gas zone and a stoichiometric burned gas zone, to which the energy and mass conservation equations are applied. The temperature values are calculated by means of second-order polynomial equations. The temperature evaluation allows the in-cylinder NOx concentration to be calculated by means of the prompt and Zeldovich thermal mechanisms. The procedure also takes into account the intake charge NOx concentration, and is therefore suitable for both engines equipped with traditional short-route EGR (Exhaust Gas Recirculation) systems, and engines equipped with SCR (Selective Catalytic Reduction) and long-route EGR systems. The tuning parameters of the combustion model for pressure estimation were calibrated on six NEDC (New European Driving Cycle) key-points, by means of the DoE (Design of Experiment) methodology, while the thermodynamic model did not require any specific calibration. The NOx model features a single calibration coefficient, which is mainly engine dependent. NOx prediction can be further improved, for a specific engine, by changing the model tuning coefficient as a function of the engine load. The complete model was applied to analyze steady state operating conditions and the urban and extra-urban phases of the NEDC cycle in a modern EURO V low-CR (Compression Ratio) diesel engine, equipped with piezo-driven injectors. A very good matching was found with experimental results in terms of in-cylinder pressure and NOx emissions, with very little computational effort.