Uncertainty quantification and model reduction of combustion kinetics using sparse polynomial chaos and the method waypoint sensitivities - Dalisay, Jon Dewitt E.
Quantification of prediction uncertainties is requisite for the development of truly predictive combustion models. Parameter uncertainties, such as those associated with reaction rate coefficients, give to combustion quantities of interest, such as ignition delay, that are uncertain. Without uncertainty quantification (UQ), numerical simulations can be trusted only qualitatively at best. Additionally, detailed chemical kinetic simulations are computationally expensive by themselves, more so when transport phenomena are involved. Numerous efforts in chemical kinetic model reduction (MR) have been made by the combustion community in order to curb the cost, but only a few studies incorporate UQ in the assessment of accuracy of reduced models. Even fewer are studies that combine the two in a single framework. This work hard two contributions: first, we used and assessed the applicability of polynomial chaos expansion based on least angle regression (LAR PCE) for the UQ and global sensitivity analysis (SA) of a high-dimensional methane combustion kinetic model. We demonstrated its effectiveness associated with its ability to construct accurate sparse PCEs. Second, we proposed and tested a novel uncertainty- aware MR scheme. Indices used to rank reactions according to importance were calculated from the global SA of "waypoint times", i.e. elapsed times of interest, using a risk based measure. The performance of the proposed scheme was compared against that improved path flux analysis (IMPFA), a recent directed relation graph (DRG) variant. The proposed scheme yielded predictive reduced models at very low species and reaction counts, i.e. high levels of reduction, while IMPFA failed to even produce models at lower levels of reduction. In line with these discoveries, we anticipated that LAR PCE and the proposed scheme will be used in the future for the UQ and MR of every large combustion kinetic models involving complex fuels. While using detailed models for combustion simulations of such fuels is quite intractable due to the associated prohibitive computational cost, the new promises a way to circumvent this significant hurdle in combustion research.