Reduced Order Modelling and Quantification of Uncertainty in Non Equilibrium Flows

Abstract

This study investigates uncertainty propagation and sensitivity analysis of state-specific dissociation and excitation rate coefficients in the context of macroscopic quantities of interest such as species mole fraction evolution and quasi-steady-state (QSS) rate coefficient. To accomplish this, an isothermal isochoric zero-dimensional chemical reactor is solved for various bath conditions. To handle the computational complexity of the master equations, three different coarse-graining methods are utilized: a 200-bin energy-based lumping model, a 3-bin energy-based lumping model, and a 10-bin spectral clustering-based model. The results show that while the uncertainty propagation is sensitive to the type of coarse-graining, the spectral clustering method produces the least model error when compared to the other coarse-grained models employed. Moreover, when an uncertainty factor of 5 is applied to the state-specific dissociation rate coefficients, it leads to an approximate ± 10% uncertainty range around the nominal values of the QSS rate coefficient. The sensitivity analysis conducted using the 200-bin model reveals that the most influential factor affecting the QSS rate coefficient and dissociation time is the mono-quantum vibrational excitation from low-lying levels. Additionally, at low temperatures, the high-lying dissociation rate coefficients contribute significantly to the uncertainty of the studied quantities, while at high temperatures, the dissociation from low to moderate-lying vibrational energy states plays a crucial role. These findings underscore the critical role played by vibrational excitation in determining the behavior of reactive systems at different temperature regimes.