Semi-physical mean-value NOx model for diesel engine control

A semi-physical model has been developed to predict nitrogen oxide (NO_x) emissions produced by diesel engines. This model is suitable for online NO_x estimation and for model-based engine control. It is derived from a zero-dimensional thermodynamic model which was simplified by only retaining main phenomena contributing to NO_x formation. The crank angle evolution of the burned gas temperature, which has a strong impact on NO_x formation rate, is described by a semi-empirical model whose key variable is the maximum burned gas temperature. This variable presents a good correlation with the molar fraction of NO_x at the end of combustion and can be expressed as a function of the intake burned gas ratio and the start of combustion. The maximum burned gas temperature sub-model is then coupled to an averaged NO_x formation kinetic model (based on the Zeldovich mechanism) to form a mean-value model for NO_x computation. This latter model was validated using data sets recorded in two diesel engines for steady-state operating conditions as well as for several driving cycles including parametric variations of the engine calibration.