Efficient Uncertainty Quantification & Sensitivity Analysis for Hypersonic Flow and Material Response Simulations Under Inherent and Model-Form Uncertainties

Accurate numerical prediction of coupled hypersonic flow fields and ablative TPS material response is challenging due to the complex nature of the physics. The uncertainties associated with various physical models used in high-enthalpy hypersonic flow and material response simulations can have significant effects on the accuracy of the results including the heat-flux and temperature distributions in various layers of ablating TPS material. These uncertainties can arise from the lack of knowledge in physical modeling (model-form or epistemic uncertainty) or inherent variations in the model inputs (aleatory or probabilistic uncertainty). It is important to include both types of uncertainty in the simulations to properly assess the accuracy of the results and to design robust and reliable TPS for reentry or hypersonic cruise vehicles. In addition to the quantification of uncertainties, global sensitivity information for the output quantities of interest play an important role for the ranking of the contribution of each uncertainty source to the overall uncertainty, which may be used for the proper allocation of resources in the improvement of the physical models or reduce the number of uncertain variables to be considered in the uncertainty analysis.

The uncertainty quantification for coupled high-fidelity hypersonic flow and material response predictions can be challenging due to the computational expense of the simulations, existence of both model-form and inherent uncertainty sources, large number of uncertain variables, and highly non-linear relations between the uncertain variables and the output response variables. The objective of this talk will be to introduce a computationally efficient and accurate uncertainty quantification (UQ) and global sensitivity analysis approach for potential application to coupled aerothermodynamics and material response simulations, which is being developed to address the aforementioned challenges. The UQ approach to be described is based on the second-order uncertainty quantification theory utilizing a stochastic response surface obtained with non-intrusive polynomial chaos and is capable of efficiently propagating both the inherent and the model-form uncertainties in the physical models. The non-intrusive nature of the UQ approach requires no modification to the deterministic codes, which is a significant benefit for the complex numerical simulation considered in this problem. The global non-linear sensitivity analysis to be introduced is based on variance decomposition, which again utilizes the polynomial chaos expansions.

In addition to the description of the UQ approach, the talk will also include the presentation of UQ results from a recent demonstration of the methodology, which included the uncertainty quantification and sensitivity analysis of surface heat-flux on the spherical heat shield of a reentry vehicle (a case selected from CUBRC experimental database). This study involved the use of NASA DPLR code and the treatment of the free-stream velocity (inherent uncertainty), collision integrals for the transport coefficients (model-form uncertainty), and the surface catalysis (model-form uncertainty) as uncertain variables. The talk will also include the description of an adaptive UQ framework being developed as part of a NASA JPL STTR project to quantify the uncertainty in multi-physics spacecraft simulations with large number of uncertain variables.