Bayesian Uncertainty Quantification of the H + O2 ! Oh + O Reaction Rate

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 (Beck et al., 1998 and Cheung et al., 2009) to quantify uncertainties in the theoretical model and experimental data. The approach involves a statistical inverse problem which has three “components” as input information: (a) the model, (b) a prior joint probability density function (PDF) of the uncertain parameters, and (c) the experimental data (Hong et al., 2010). The solution of this statistical inverse problem is a posterior joint PDF of the uncertain parameters. We consider uncertainties in reaction rates, gas temperature, experimental errors and physical modeling errors, and also perform parametric studies to investigate how the form of the total uncertainty affects these uncertainties. More importantly, we introduce the idea of “irreducible” uncertainty when considering other uncertain parameters involved in the system. We compare our estimated reaction rate with other values obtained using the deterministic approach (Pirraglia et al., 1989 and Masten et al., 1990). Our results show that a small uncertainty in gas temperature (±3 K) introduces appreciable uncertainty in this reaction rate that can be as much as the reported uncertainty (Hong et al., 2010).