The method of uncertainty quantification and minimization using polynomial chaos expansions

• Published in: Combustion and flame 2011-12, Vol.158 (12), p.2358-2374
• Main Authors: Sheen, David A., Wang, Hai
• Format: Article
• Language: English
• Subjects: Applied sciences; Chaos theory; Combustion; Combustion. Flame; Computer simulation; Energy; Energy. Thermal use of fuels; Exact sciences and technology; Kinetic modeling; Mathematical analysis; Mathematical models; Minimization; Model optimization; Optimization; Reaction mechanism; Theoretical studies. Data and constants. Metering; Uncertainty; Uncertainty analysis
• ISSN: 0010-2180; 1556-2921
• DOI: 10.1016/j.combustflame.2011.05.010

Reliable simulations of reacting flow systems require a well-characterized, detailed chemical model as a foundation. Accuracy of such a model can be assured, in principle, by systematic studies of individual rate coefficients. However, the inherent uncertainties in the rate data leave a model still characterized by a kinetic rate parameter space which will be persistently finite in its size. Without a careful analysis of how this uncertainty space propagates into the model predictions, those predictions can at best be trusted only semi-quantitatively. In this work, we propose the Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) to quantify and constrain these uncertainties. An as-compiled, detailed H 2/CO/C 1–C 4 kinetic model and a set of ethylene combustion data are used as an example. In this method, the uncertainty in the rate parameters of the as-compiled model is quantified. Then, the model is subjected to a rigorous mathematical analysis by constraining the rate coefficients against the combustion data, as well as a consistency-screening process. Lastly, the uncertainty of the constrained model is calculated using an inverse spectral technique, and then propagated into a range of simulation conditions to demonstrate the utilities and limitations of the method.