Application of the generalized Polynomial Chaos expansion to the simulation of an internal combustion engine with uncertainties

The study of combustion associated phenomena in internal combustion engines is important for reasons that include pollutant formation control, and the heat transfer between the hot gases, the piston and combustion chamber walls. Although there are several models for the chemically reacting turbulent flow inside the combustion chamber, such models always suffer from some level of uncertainties in their formulations or in the physical parameters used for their simulation. The main objective of the present paper consists in modeling the combustion phenomena in a combustion chamber of an internal combustion engine, using a model based on the First Law of Thermodynamics, considering uncertainties in the mass fraction of burned fuel. As a result, the curve describing the in-cylinder pressure as a function of the crank angle can be obtained for different uncertainties levels. For this purpose, the generalized Polynomial Chaos (gPC) and Monte Carlo techniques were applied to a set of ordinary differential equations obtained from a First Law analysis, and the stochastic moments of the solution were obtained. Uniform and Gaussian uncertainties distributions were considered in order to obtain the stochastic solution. Results show that the gPC is more computationally efficient than the Monte Carlo simulation for the considered application . Besides, experimental engine results were also used in order to validate the implemented numerical procedure.