  This work deals with the inference of catalytic recombination parameters from
plasma wind tunnel experiments for reusable thermal protection materials. One
of the critical factors affecting the performance of such materials is the
contribution to the heat flux of the exothermic recombination reactions at the
vehicle surface. The main objective of this work is to develop a dedicated
Bayesian framework that allows us to compare uncertain measurements with model
predictions which depend on the catalytic parameter values. Our framework
accounts for uncertainties involved in the model definition and incorporates
all measured variables with their respective uncertainties. The physical model
used for the estimation consists of a 1D boundary layer solver along the
stagnation line. The chemical production term included in the surface mass
balance depends on the catalytic recombination efficiency. As not all the
different quantities needed to simulate a reacting boundary layer can be
measured or known (such as the flow enthalpy at the inlet boundary), we propose
an optimization procedure built on the construction of the likelihood function
to determine their most likely values based on the available experimental data.
This procedure avoids the need to introduce any a priori estimates on the
nuisance quantities, namely, the boundary layer edge enthalpy, wall
temperatures, static and dynamic pressures, which would entail the use of very
wide priors. We substitute the optimal likelihood of the experimental data with
a surrogate model to make the inference procedure both faster and more robust.
We show that the resulting Bayesian formulation yields meaningful and accurate
posterior distributions of the catalytic parameters with a reduction of more
than 20% of the standard deviation with respect to previous works. We also
study the implications of an extension of the experimental procedure.
