Systematic validation of non-equilibrium thermochemical models using Bayesian inference
byK. Miki, S. Prudhomme, M.Panesi
K. Miki, M. Panesi, and S. Prudhomme, Systematic validation of non-equilibrium thermochemical models using Bayesian inference, Journal of Computational Physics, Submitted (2013).
The validation process proposed by Babuˇska et al.  is applied to thermochemical models describing post-shock flow conditions. In this validation approach, experimental data is involved only in the calibration of the models, and the decision process is based on quantities of interest (QoIs) predicted on scenarios that are not necessarily amenable experimentally. Moreover, uncertainties present in the experimental data, as well as those resulting from an incomplete physical model description, are propagated to the QoIs. We investigate four commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Macheret et al. , Marrone and Treanor , and Park . Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following the solution of the inverse problems, the forward problems are solved in order to predict the radia- tive heat flux, the quantity of interest, and examine the validity of these models. Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably large uncertainties in the QoI predictions.