Speaker
Description
Background
The 2023 Planetary Science Decadal Survey has deemed a mission to the Ice Giant planets a high priority for the next NASA Flagship Mission.$^1$ In order to safely enter hydrogen-helium-methane (H$_2$/He/CH$_4$) atmospheres that are characteristic of the Ice Giants, it is important to accurately characterize the aerothermal environment around the entry vehicle to predict quantities like convective and radiative heating, which will drive the design of the thermal protection system (TPS). Computational modeling tools are used to simulate the chemical kinetics in the nonequilibrium region of the flow between the shock and the surface of the TPS. It is desirable to validate computational models with experimental data, which typically comes from shock tube and expansion tunnel facilities that generate relevant aerothermodynamic quantities, like emission spectra. There are challenges associated with generating this data, such as difficulty obtaining high enough speeds to represent an Ice Giant entry trajectory and shock position uncertainty.$^2$ Because of these challenges as well as uncertainties in existing chemical kinetics models, previous studies have identified challenges with validating computational models of Ice Giant entry systems with experimental data.$^3$
The current study aims to investigate the existing gap between simulations and experiments for predicting spectral radiance in H$_2$/He/CH$_4$ systems with an uncertainty quantification (UQ) analysis that includes the uncertainties in both the chemical kinetics models implemented in simulations and in experimental measurements. This mixed uncertainty quantification analysis is a useful tool to determine the sensitivities of key quantities of interest (QoIs). The QoI in the present study is spectral radiance, which is measured experimentally and has implications for the radiative heating the vehicle will experience upon hypersonic entry. Initial results with the mixed UQ framework show large variations in spectral radiance predictions based on current uncertainty bounds,$^4$ calling for the need for a detailed rate assessment to determine the best uncertainty bounds to use in the mixed UQ analysis. The presentation will include a detailed assessment of the chemical kinetic rate model and uncertainty bounds associated with each rate, which will be implemented into the mixed UQ framework. Results will be shown from the mixed UQ framework with the updated rates and uncertainty bounds applied to a range of experimental conditions.
Methodology
The computational model used in the present work is a general-purpose nonequilibrium chemical kinetics solver called the Toolkit for Excitation, Reactions, and Radiation with Applications (TERRA) with NASA's radiation solver, NEQAIR. One-dimensional incident shock simulations are generated, and the resulting position, temperatures (translational-rotational and vibrational-electronic), and species number densities for a 12-species H$_2$/He/CH$_4$ model are passed into NEQAIR as a line-of-sight, which is then used to compute radiance and spectral radiance. This enables direct comparison to the experimental datasets, which come from the T6 Stalker Tunnel at the University of Oxford$^5$ and the Electric Arc Shock Tube (EAST) facility at NASA Ames Research Center.$^6$
The two main categories of uncertainty in numerical modeling are aleatory uncertainty, which is due to the randomness of uncontrollable factors like instrument noise, and epistemic uncertainty, which is due to an inadequate understanding of the physics model that is represented in the numerical tool. Both aleatory and epistemic uncertainties are propagated through the model simultaneously, though they are treated separately. The mixed UQ problem is set up in a nested loop such that the outer loop varies the epistemic uncertain parameters, which are the chemical kinetic rate parameters, and the inner loop varies the aleatory uncertain parameters, which are the freestream conditions from the experiments. The mixed UQ analysis is driven by UQLab, by which a polynomial chaos expansion (PCE) and Sobol’ indices are computed.$^7$ The PCE is computed using the Ordinary Least Squares (OLS) regression method to form a surrogate model of the system. Sobol’ indices are computed from the PCE coefficients, and are a useful metric for quantifying how much the uncertainty in an input parameter affects the prediction of a QoI, which in this study is spectral radiance.
Results
The mixed UQ framework is first applied to an experimental condition from the T6 Stalker Tunnel operating in shock tube mode with a velocity of 16.3 km/s, a pressure of 13.0 Pa, and a test gas composition by volume of 80% H$_2$/15% He/5% CH$_4$, then to another experimental condition with a velocity of 16.4 km/s, a pressure of 12.8 Pa, and a test gas composition by volume of 84.5% H$_2$/15% He/0.5% CH$_4$.$^5$ Sobol' indices are computed for the QoIs integrated spectral radiance within the wavelength range of interest from 350 - 570 nm and spectral radiance at the peaks of major spectral features, which are found around 430 nm, 468 nm, and 514 nm. These spectral features are mostly caused by the CH(A-X) radiation band, C$_2$ Swan band, atomic lines for neutral and atomic carbon, and the Balmer series for atomic hydrogen.
It is found that the Sobol' index contributions, and therefore uncertainty in spectral radiance predictions, are dominated by the CH$_3$ dissociation process that forms CH, followed by the H$_2$ dissociation process. Since CH is one of the strongest radiators in this system, and the Balmer series for atomic hydrogen also contributes to spectral features within the wavelength range of interest, it is expected that the processes that form these species would contribute most to uncertainty in spectral radiance. The spectral features that are caused by the C$_2$ Swan band also show high sensitivities to the only process that forms C$_2$ in the system, which is the CH-C exchange reaction. The sensitivities of spectral radiance are similar between the 5% methane condition and 0.5% methane condition, however, the contributions of the H$_2$ dissociation processes have higher Sobol' indices for the 0.5% methane condition than for the 5% methane condition. Although the contribution of H$_2$ dissociation is higher for the lower methane condition, the uncertainty in spectral radiance is still overall dominated by CH$_3$ dissociation, indicating that this is a key contributor to the discrepancy in spectral radiance predictions between simulations and experiments.
The presentation will show results of the mixed UQ framework applied to higher-velocity conditions from the EAST facility,$^6$ which are likely more representative of an Ice Giant entry trajectory. Comparisons of key sensitivities from the different facilities and conditions will be presented.
Conclusions
The mixed UQ framework is a powerful tool that can be used to identify the uncertain parameters that contribute most to uncertainty in spectral radiance predictions from a nonequilibrium chemical kinetics solver plus radiation solver that causes discrepancies in comparisons with experimental data. Future work includes reducing the uncertainty bounds on the largest contributors to spectral radiance uncertainty through a Bayesian inference analysis. This framework can be applied to different experimental datasets across different facilities, and can be used to identify which data is suitable for Bayesian inference and which is limited by experimental uncertainty. The framework can also be used to identify critical facility uncertainties that may limit the utility of the existing data. In general, this study investigates the existing gap between simulations and experiments for Ice Giant entry systems.
References
[1] “Origins, Worlds, and Life 2023”. In: National Academies Press (Oct. 2023).
[2] Alex T. Carroll et al. “State-Specific Kinetic Modeling for Predictions of Radiative Heating in H2/He Entry Flows”. In:AIAA SciTech 2024 Forum. American Institute of Aeronautics and Astronautics, Jan. 2024.
[3] Kaelan Hansson et al. “Analysis of Chemical Kinetic Parameters for Hydrogen Atmospheres”. In: AIAA SciTech 2021 Forum. American Institute of Aeronautics and Astronautics, Jan. 2021.
[4] Cate Leszcz, Timothy T. Aiken, and Iain D. Boyd. “Mixed Uncertainty Quantification for Hypersonic Entry into Hydrogen-Helium Atmospheres”. In: AIAA Aviation 2026 Forum. American Institute of Aeronautics and Astronautics, June 2026.
[5] Joseph Steer et al. “Commissioning of Upgrades to T6 to Study Giant Planet Entry”. In: Journal of Spacecraft and Rockets 61.6 (Nov. 2024), pp. 1545–1562. issn: 0022-4650.
[6] Brett A. Cruden and David W. Bogdanoff. “Shock Radiation Tests for Saturn and Uranus Entry Probes”. en. In: Journal of Spacecraft and Rockets 54.6 (Nov. 2017), pp. 1246–1257. issn: 0022-4650, 1533-6794.
Summary
This study investigates the gap between simulations and experiments for predicting relevant aerothermodynamic quantities, like spectral radiance, for Ice Giant entry systems. This is done through a mixed uncertainty quantification (UQ) analysis that includes epistemic uncertainties in hydrogen-helium-methane chemical kinetics models as well as aleatory uncertainties in experimental measurements to determine the sensitivity of spectral radiance predictions to these uncertain parameters.