On the (in)validation of a thermochemical model with EAST shock tube radiation measurements

Abstract

The PECOS Center is devoted to the development of a systematic methodology for the (in)validation of physical models under uncertainty. The methodology involves a statistical-based approach for the calibration of uncertain model parameters, the validation of the model itself, and the quantification of uncertainty associated with specific model predictions. It requires the use of experimental data for parameter calibration and model validation, and one ultimatelyappeals to expert opinion for correct interpretation of the results; i.e. a model is considered (in)valid if with the benefit of the above-mentioned statistical insight one, considers it (un)able to provide reliable predictions of specific quantities of interest at specific prediction scenarios. The investigation described in this paper considers the first step of the methodology described above - i.e. uncertain model parameter calibration - as well as the quantification of uncertainty in that calibration. A physicomathematical model used to simulate atomic radiation in shock-heated air plasmas was developed and a stochastic system based Bayesian approach 1, 2 was applied for the quantification of model and model parameter uncertainties. In particular, spectrally and spatially resolved absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST), located at the NASA Ames Research Center (ARC), were used to simultaneously calibrate a total of twenty-three random parameters by solving a statistical inverse problem. The parameters include a stochastic form of several Arrhenius reaction coefficients, Einstein coefficients, line broadening parameters, and shock tube operational parameters. The results indicate that there is a sufficient amount of experimental data to characterize the value of each model parameter. Obviously, these predicted values are conditional on the physical model and experimental data utilized. After statisitically calibrating the parameters we propagate their uncertainties through the solution of a statistical forward problem where the quantity of interest and the scenario of interest are those specified by the experimental setting. These forward calculations allow us to perform a basic and important verification of our computations.