Calibration of rates parameters for multi-temperature models using Bayesian formulation

In this paper, we apply a Bayesian analysis to calibrate the parameters of a model for atomic Nitrogen ionization using experimental data from the Electric Arc Shock Tube (EAST, from NASA) wind-tunnel. We use a one-dimensional flow solver coupled with a radiation solver for the simulation of the radiative signature emitted in the shock-heated air plasma, as well as a Park's two-temperature model for the thermal and chemical nonequilibrium effects. We simultaneously quantify model parameter uncertainties and physical model inadequacies when solving the statistical inverse problem. Prior to the solution of such a problem, we perform a sensitivity analysis of the radiative heat flux in order to identify important sources of uncertainty. This analysis clearly shows the importance of the direct ionization of atomic Nitrogen as it mostly influences the radiative heating. We then solve the statistical inverse problem and compare the calibrated reaction rates against values available in the literature. Our calculations estimate the reaction rate of the atomic Nitrogen ionization to be (3:7±1:5)×10¹¹ cm³mol^-1s^-1 at 10,000 K, a range consistent with Park's estimation. Finally, in order to assess the validity of the estimated parameters, we propagate their uncertainties through a statistical forward problem defined on a prediction scenario different from the calibration scenarios and compare the model predictions against other experimental data.