Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection

A spectral formalism has been developed for the "non-intrusive" analysis of parametric uncertainty in reacting-flow systems. In comparison to conventional Monte Carlo analysis, this method quantifies the extent, dependence, and propagation of uncertainty through the model system and allows the correlation of uncertainties in specific parameters to the resulting uncertainty in detailed flame structure. For the homogeneous ignition chemistry of a hydrogen oxidation mechanism in supercritical water, spectral projection enhances existing Monte Carlo methods, adding detailed sensitivity information to uncertainty analysis and relating uncertainty propagation to reaction chemistry. For 1-D premixed flame calculations, the method quantifies the effect of each uncertain parameter on total uncertainty and flame structure, and localizes the effects of specific parameters within the flame itself. In both 0-D and 1-D examples, it is clear that known empirical uncertainties in model parameters may result in large uncertainties in the final output. This has important consequences for the development and evaluation of combustion models. This spectral formalism may be extended to multidimensional systems and can be used to develop more efficient "intrusive" reformulations of the governing equations to build uncertainty analysis directly into reacting flow simulations.