Uncertainty analysis in mechanism reduction via active subspace and transition state analyses

Abstract A systematic approach is formulated for the uncertainty analysis of kinetic parameters on combustion characteristics during skeletal reduction. The active subspace method together with sensitivity analysis is first employed to identify extreme low-dimensional active subspace of input parameter space and to facilitate the construction of response surfaces with small size of samples. An intermediate transition state during reduction is then defined such that the uncertainty change arising from uncertainty parameter truncation and reaction coupling during reduction can be decoupled and quantified. The approach is demonstrated in the reduction of a 55-species, 290-reaction dimethyl ether (DME) mechanism, with the rate constants characterized by independent lognormal distribution. Three representative skeletal mechanisms are identified for the uncertainty analysis, with each of the subsequent reduction yielding significant errors in the single-stage and/or two-stage DME-air auto-ignition process. Results show that sensitivity analysis can reduce the number of kinetic parameters from 290 down to 32, and the active subspace method can further identify a dominant active direction within this 32-dimensional subspace, which greatly facilitates the polynomial fitting for constructing the response surface of the ignition delay times. The uncertainty analysis with the polynomial chaos expansion method shows that the reduction from DME42 with 42 species to DME40 with 40 species has influential effect on the high-temperature reaction pathway; while the reduction from DME55 to DME42 and from DME40 to DME30 mainly affects the low-temperature pathway. In addition, the uncertainty change associated with parameter truncation is shown to be proportional to the change in the most active direction, which could further accelerate uncertainty analysis.