Uncertainty Quantification on the High-Temperature Kinetics of Dioxygen Dissociation and Oxygen Recombination

Abstract

A stochastic system based on a Bayesian approach is applied to quantify the uncertainties in the rate constants of both the dioxygen () dissociation reaction and the O recombination reaction . The O concentration profile behind shock waves is calculated by a shock-capturing scheme and is compared with two experimental measurements by Matthews (“Interferometric Measurement in the Shock Tube of the Dissociation Rate of Oxygen,” Physics of Fluids, Vol. 2, No. 2, 1959, pp. 170–177): case 1 ( and ), and case 2 ( and ). The effect of the overall uncertainties, including the physical model errors and the experimental errors, is investigated. The estimated reaction rate of dissociation is compared with the previously reported values, and it is found that the estimated reaction rate is close to Park’s model (“Review of Chemical-Kinetic Problems of Future NASA Mission, I: Earth Entries,” Journal of Thermophysics and Heat Transfer, Vol. 7, No. 3, 1993, pp. 385–398) and the corresponding uncertainty is relatively small in the temperature range between and 5000 K. The uncertainty of the O recombination rate is as great as two orders of magnitude; as a result, many previously reported values and the experimental data are within the 95% confidence interval. Finally, it is concluded that reproducing these types of experimental data could be insufficient for the determination of the reaction rate, particularly when the statistical dependence among model parameters is taken into account. The relation of the reaction rate determination to the O concentration is strongly influenced by the inflow Mach number and the shock location, as well as these uncertainties.