It is becoming increasingly important to understand cycle-to-cycle variability (CCV) of direct-injection spark-ignition (DISI) engines in order to maximize engine efficiency and minimize pollutant formation from these engines. Direct-injection fuel sprays have a significant effect on the in-cylinder flow field and fuel-air mixing process. Shot-to-shot variability in fuel injections helps drive overall CCVs. Current computational fluid dynamics (CFD) modeling techniques used for engine simulations do not typically directly model all the sources of shot-to -shot spray variability. They are instead incorporated into the models as boundary condition terms. Thus it is necessary to implement methods to incorporate this uncertainty in boundary conditions into the simulation results.

Uncertainty Quantification (UQ) provides methods and analysis tools to incorporate and analyze the effects of uncertainty in model input parameters on simulation results. This presentation will discuss the application of two different UQ methods to analyze the effects of boundary condition uncertainty on the simulation of a typical DISI injector for automotive applications. Latin-hypercube Sampling (LHS) is a Monte-Carlo-like technique that is easily implemented and robust to any model response behavior, but is slow to converge statistically, which can be problematic for large CFD simulations. Polynomial Chaos Expansions (PCE) models uncertain variables using orthogonal polynomial basis functions of random variables. PCE can have much higher statistical convergence rates, but is limited in the number of uncertain inputs that can be considered simultaneously due to the “curse of dimensionality,” and can experience problems if the model response is non-smooth. The PCE method us ing nested grids also offers the advantage of being able to analyze the effects of sub-sets of uncertain input parameters re-using previous simulation results.

Results will be presented from UQ calculations incorporating uncertainty from 4 model input parameters: 2 numerical modeling parameters related to the break-up of the liquid fuel, and 2 physical boundary conditions. Initial simulation results showed much larger response variability than seen in experimental measurements. Further tests using input parameter sub-sets showed the large simulation response variability was primarily due to uncertainty in the numerical modeling parameters. Uncertainty in model response variables due solely to physical boundary conditions was much closer to variability in experimental measurements.