Systematic validation of non-equilibrium thermochemical models using Bayesian approach

The validation process proposed by Babuska et al.¹ 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 feasible 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 three commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Park2 and Macheret.³ Up to 15 uncertain parameters are statistically calibrated with a Bayesian approach and the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) located at the NASA Ames Research Center (ARC). After solving statistical inverse problems (calibration of uncertain parameters), the statistical forward problems are solved in order to predict the radiative heat flux (QoI) and examine the robustness of these models. Our results show that all three models are invalid, but for different reasons: the one-temperature model has insufficient capability to reproduce the data, while the two-temperature models exhibit unacceptable large uncertainties in the QoI predictions.