The development of a semi-empirical model for rapid NO x concentration evaluation using measured in-cylinder pressure in diesel engines

Continued legislative pressure to reduce NO _x emissions from diesel engine combustion systems generates a desire for cycle-by-cycle emissions data, with a view to their use in a feedback control strategy, perhaps in conjunction with an exhaust catalytic reactor. While NOx sensors that provide fast, robust, reliable, and continuous measurements in a diesel exhaust at a reasonable price are currently the subject of much development, the present work focuses on an indirect approach. This has led to the development of a semi-empirical model that can be used to estimate NO _x emissions, based on more easily measured input data, primarily in the form of instantaneous in-cylinder pressure as a function of crank angle. The model computations are based on fundamental thermodynamic principles, but key empirical constants have been derived with the aid of statistical techniques. The approach taken relied on the availability of an extensive bank of experimental data from three different designs of direct injection diesel engine, each utilizing common rail type fuel injection systems and, in some cases, with the use of multiple injections per cycle.