Uncertainty quantification of aerothermal flow-material simulations of low-density ablative thermal protection systems

Essential to space missions involving an atmospheric entry, the thermal protection system (TPS) shields the spacecraft and its payload from the severe aerothermal loads. Low-density carbon/phenolic composite materials have gained renewed interest to serve as ablative thermal protection materials (TPMs). These materials can accommodate the high heating rates and heat loads encountered during the atmospheric entry, at hypersonic velocities, by absorbing part of the incoming heat through physico-chemical transformations. One of the main endothermic processes is the pyrolysis of the resin compound, whereby volatile products are released, leaving a carbonaceous residue is left on the fibers.

Whereas new experimental data have already been published to characterize the decomposition of these low-density carbon/phenolic materials, they are yet to be exploited for the inversion of physico-chemical models. In addition, the issue of uncertainty quantification, required to assess the reliability of the numerical model and the physico-chemical models, is yet to be addressed. Therefore, the overarching objective of this thesis is to contribute to the development of an uncertainty-quantified numerical modeling of the ablation of new porous composite materials and to the analysis of the impact of uncertainty on TPS design. To that aim, we first address the development and the uncertainty characterization of physico-chemical models for resin pyrolysis on the basis of new experimental data relevant to the pyrolytic decomposition of the phenolic resin used in carbon/phenolic composite TPMs. Then, we analyze the impact of the uncertainty in the physico-chemical models on the numerical modeling of ablation of TPS by means of non-intrusive stochastic methods.

The central contribution of this thesis is to infer from these new experimental data an uncertainty-quantified pyrolysis model. We adopt a Bayesian probabilistic approach to account for uncertainties in the model identification. We use an approximate likelihood function involving a weighted distance between the model predictions and the time-dependent experimental data. To sample from the posterior, we use gradient-informed Markov chain Monte Carlo methods with an adaptive selection of the numerical parameters. We develop a versatile code for performing uncertainty characterization using Bayesian inference tools on engineering problems in which the proposed methods are implemented. To select the decomposition mechanisms to be represented in the pyrolysis model, we proceed by progressively increasing the complexity of the pyrolysis model until a satisfactory fit to the data is ultimately obtained. To improve the computational time, we derive a fast semi-analytical solution for the resin pyrolysis using multicomponent parallel reactions both for the case of a constant temperature and the case of a linear heating rate. The pyrolysis model thus obtained involves six reactions and has 48 parameters.

A second contribution is the assessment of the impact of uncertainties on the material response of an ablating TPS relevant to in-flight performance prediction. Using the six-reaction pyrolysis model, we demonstrate its use in a numerical simulation of heat shield surface recession in a Martian entry. We provide probabilistic projections of the recession of the surface, the production of gaseous species at the surface, and the temperature.

In addition to the aforementioned contributions, we also provide three supplementary pieces of research. For the first one, we contribute to the development of a model for representing the process of ablation from resin pyrolysis to char ablation in a unified flow-material approach where the Volume-Averaged Navier-Stokes equations are solved. This model is implemented in the high-fidelity numerical code Argo from the research center Cenaero and verified by a code-to-code comparison. The second one pertains to the development of an uncertainty-quantified pyrolysis model including competitive mechanisms for the pyrolytic decomposition of the PICA material. Finally, the third one concerns the calibration of material properties and environmental conditions in a Bayesian inference framework using post-flight data of the Mars Science Laboratory mission.