Uncertainty and Sensitivity Analysis for Reentry Flows with Inherent and Model-Form Uncertainties

The objective of this paper is to introduce a computationally efficient methodology for the quantification of mixed (inherent and model-form) uncertainties and global sensitivity analysis (SA) in hypersonic reentry flow computations. The uncertainty-quantification (UQ) approach is based on the second-order UQ theory, using a stochastic response surface obtained with nonintrusive polynomial chaos. The global nonlinear SA is based on Sobol variance decomposition, which uses polynomial chaos expansions. The methodology was used to quantify the uncertainty and sensitivity information for surface heat flux to the spherical nonablating heat shield of a reentry vehicle at an angle of attack of 0 deg. Three uncertainty sources were treated in computational fluid dynamics simulations: inherent uncertainty in the freestream velocity, model-form uncertainty in the recombination efficiency used in partially catalytic wall-boundary condition, and model-form uncertainty in the binary-collision integrals. The SA showed that the velocity and recombination efficiency were the major contributors to the heat-flux uncertainty for the reentry case considered. The UQ and SA were performed with three different levels of input uncertainty in velocity, which revealed the importance of characterizing the velocity with well-defined uncertainty levels in the study of reentry flows because the variations in this quantity can drastically impact the accuracy of the heat-flux prediction.