Bayesian uncertainty quantification of recent shock tube determinations of the rate coefficient of reaction H + O<inf>2</inf>→ OH + O

Abstract

We analyze the ignition delay in hydrogen-oxygen combustion and the important chain -branching reaction H + O2→ OH + O that occurs behind the shock waves in shock tube experiments. We apply a stochastic Bayesian approach to quantify uncertainties in the theoretical model and experimental data. The approach involves a statistical inverse problem, which has four "components" as input information: (a) model, (b) prior joint probability density function (PDF) of the uncertain parameters, (c) experimental data, and (d) uncertainties in the scenario parameters. The solution of this statistical inverse problem is a posterior joint PDF of the uncertain parameters from which we can easily extract statistical information. We first perform a parametric study to investigate how the level of the total uncertainty (which we define as the sum of model uncertainty and experimental uncertainty) affects the uncertainty in the rate coefficient k1 of the reaction H + O 2→ OH + O, which is "most likely" expressed by k1=1.73×1023T-2.5exp(-11550/T) cm3 mol-1 s-1 over the experimental temperature range 1100-1472 K. We also introduce the idea of "irreducible" uncertainty when considering other parameters in the system. After statistically calibrating the parameters modeling the rate coefficient k1, we predict its 95% confidence interval (CI) for different temperature regimes and compare the CI against the values of k1 obtained deterministically. Our results show that a small uncertainty in gas temperature (±5 K) introduces appreciable uncertainty in k1. © 2012 Wiley Periodicals, Inc.