Development and validation of a semi-empirical model for the estimation of particulate matter in diesel engines

A semi-empirical correlation for the estimation of PM (particulate matter) emissions in diesel engines, as a function of significant engine operating variables, has been developed and validated on a GM (General Motors) Euro 5 diesel engine. The experimental data used in the present study have been acquired at the dynamic test bench of ICEAL-PT (Internal Combustion Engine Advanced Laboratory at the Politecnico di Torino), in the frame of a research activity with GMPT-E (General Motors PowerTrain-Europe) for the calibration of a Euro 5 prototype 2.0 liter diesel engine equipped with a twin-stage turbine and a piezo-driven Common Rail injection system. The experimental data were acquired for six key-points representative of the engine working conditions over a NEDC (New European Driving Cycle). The experimental tests have been carried out according to the Design of Experiment approach and for each point several variation lists of the main engine variables have been considered. As a first step, the main engine variables which are expected to be related to the formation and oxidation of PM have been identified. An exponential mathematical model has then been introduced and a detailed statistical analysis has been carried out for each key-point in order to identify the most robust combination of the input variables among all the possible ones. It was verified that PM emissions are correlated to a great extent to the value of the chemical heat release at the end of the injection of the main pulse. This quantity is in fact related to the mass of burned gases which is generated by the oxidation of the pilot pulses that precede the main injection. Such a mass can have a large impact on the local oxygen concentration and temperature of the charge in which the fuel of the main pulse is injected, with a consequent effect on PM formation. Additional quantities have also been considered in the investigation: the relative air-to-fuel ratio k, the intake charge oxygen concentration, the accumulated fuel mass, the equivalence ratio of the spray at the main pulse start of combustion and some combustion metrics related to the heat release rate. At the end of the statistical analysis, the most influencing parameters have been selected and a semiempirical model to predict the in-cylinder formed PM mass has been developed. The model has hence been tested under both steady-state and transient conditions.