Stochastic calibration of a carbon nitridation model from plasma wind tunnel experiments using a Bayesian formulation

Abstract

In this work, we calibrate a carbon nitridation model for a broad span of surface temperatures from existing plasma wind tunnel measurements by accounting for experimental and parametric uncertainties. A chemical non-equilibrium stagnation line model is proposed to simulate the experiments and obtain recession rates and CN densities, the measured model outputs. First, we establish the influence of the experimental boundary conditions and nitridation parameters on the simulated observations through a sensitivity analysis. Results show that such quantities are mostly affected by the efficiency of nitridation reactions at the gas-surface interface. We then perform model calibrations for each experimental condition and compare them based on the experimental data used. This allows us to check the consistency of the experimental dataset. Using only the trustworthy experimental data, we perform a calibration of Arrhenius law parameters for nitridation efficiencies considering all available experimental conditions jointly, allowing us to compute nitridation efficiencies even for surface temperatures for which there are no reliable experimental data available. The stochastic Arrhenius law agrees well with most of the data in the literature. This result constitutes the first nitridation model extracted from plasma wind tunnel experiments with accurate uncertainty estimates.