Quantification of model-form uncertainties affecting the calibration of a carbon nitridation model by means of Bayesian Model Averaging

Abstract

Severe epistemic uncertainties not only can affect the prescription of parameters within a given model but also the choice of models we make to interpret and infer from experimental data. In this work, we incorporate experimental, parametric and model-form uncertainties in the calibration of a carbon nitridation model. The model-form uncertainties considered stem from the different modeling choices that are taken as valid representations of a set of plasma wind tunnel experiments. To this end, we define a Bayesian Model Averaging strategy where the marginal posteriors of the nitridation reaction efficiencies are weighted by the marginalized likelihoods of the experimental data for each proposed model. First, Bayes factors are computed to possibly discard invalid models. The baseline model, a thermal equilibrium stagnation line flow with nitridation as only surface reaction, performs as well as all the alternative models proposed, which range from adding surface recombination reactions to considering thermal non-equilibrium in the gas and gas-surface interface. The presence of nitrogen recombination reactions is shown to broaden the support of the nitridation marginal posteriors considerably, allowing it to take on larger values. Lastly, a Bayesian model averaged Arrhenius law for the nitridation efficiencies is computed for a range of surface temperatures.