A Statistical Analysis of the Influence of Cyclic Variation on the Formation of Nitric Oxide in Spark Ignition Engines

Abstract

A statistical method is presented to study the influence of cyclic variation of the combustion process on the formation of nitric oxide in spark ignition engines. In the analysis which was done for this paper, each engine cycle was treated as a realization of a random experiment. Specifically, the cylinder pressure as a function of crank angle was considered a stochastic process, and the nitric oxide concentration frozen in the expansion stroke was considered a random variable associated with the random experiment.

A set of consecutive cylinder pressure-crank angle data furnished the statistical properties of the cylinder pressure of a spark ignition engine at a normal running condition. The stochastic process of cylinder pressure was first approximated by one degree of randomness expression with peak combustion pressure as the characterizing random variable. Secondly, a combustion and nitric oxide kinetics model was used to establish the functional relationship of frozen nitric oxide concentration to cylinder pressure, particularly to the peak combustion pressure. Finally, the probability density function of the nitric oxide concentration was calculated by using the fundamental theorem of functions of random variables.