Statistical calibration of thermocouple gauges used for inferring heat flux

During a test campaign at the Arnold Engineering Development Center Tunnel 9 hyper-sonic wind tunnel facility to study the NASA Crew Exploration Vehicle, a data reduction model was used to infer incident heat flux from temperature measurements using type-E coaxial thermocouples. A mismatch between the inferred heat flux values and pre-test computations motivated the need to better understand the uncertainty. In this work, the data reduction model is calibrated with a Bayesian approach using experimental data gathered during an effort at AEDC to better understand the data reduction model. The experimental data are brie y summarized. The data reduction model and statistical inverse problem are formulated. The appropriate choice of parameters for the inverse problem is shown through an analogy to self-similar solutions of the heat equation and numerical experiments. Results are shown for the calibrated material parameters and the ensuing forward propagation of uncertainty to the final, inferred heat flux value.