Speaker
Description
Background
NASA’s Dragonfly mission, which aims to deliver a rotorcraft to Saturn’s moon Titan, must withstand extreme
convective and radiative heating during its entry into the moon’s dense nitrogen-methane atmosphere. Because of strongly radiating species, particularly the cyanogen (CN) radical, the forebody radiative heating can be as much as 50% of the total heat flux, necessitating the inclusion of radiation analysis when modeling the heating
of the probe during its entry.
Engineering predictions of the heat flux to the spacecraft surface – both the forebody and afterbody – are subject to uncertainty resulting from unknown freestream methane content of Titan’s atmosphere, as well as uncertainties in the parameters used to model chemical kinetics, radiative emission, and solid conduction in the
heat shield. These uncertainties carry major implications for the entry system reliability and so must be quantified.
Furthermore, there is an interest in evaluating whether the uncertainty in Titan’s atmospheric freestream methane content can be reduced through afterbody radiometer measurements of the Red and Violet bands of CN – the main transitions driving radiative heating – that will be gathered during entry; however, whether this can be accomplished given the uncertainty in predicting these bands is unknown.
Methodology
Flow simulations are performed with US3D, a computational fluid dynamics (CFD) solver developed at the University
of Minnesota. Radiation calculations are performed using the Multi-Fidelity Radiation Package (MURP),
which is coupled to US3D using the PreCICE library. Within each US3D calculation, the grid is tailored –
typically 2–4 times – in order to minimize numerical errors originating from poor alignment of cell faces with
the bow shock. Coupling between US3D and MURP can be either one-way, with data flowing from US3D into
MURP only once, at the end of the calculation, or two-way, in which US3D and MURP actively exchange data
with one another throughout the calculation. Two-way coupling enables the US3D flowfield to respond to the flux of radiated power into or out of each cell. Sensitivity and uncertainty quantification for the radiative environment requires propagating a large set of
uncertain chemical-kinetic and CN electronic-excitation rate coefficients, together with the freestream methane
content, through the flow–radiation model. Because a single high-fidelity (HF) US3D–MURP evaluation costs on the order of tens of CPU-hours, direct propagation over the hundreds of samples needed for variance-based sensitivity analysis is computationally prohibitive. To retain HF accuracy at a tractable cost, a bi-fidelity (BF)
surrogate is constructed. For an initial analysis, the focus is on defining QoIs on the surface of the vehicle.
For the purpose of CH4 inference, the QoIs are defined as the CNred and CNviolet. The BF method chosen is interpolative decomposition (ID)1 due to the correlation obtained between the LF and HF models. A dense low-fidelity (LF) ensemble is generated with a Lagrangian streamline solver employing a one-dimensional tangentslab radiative transfer approximation2, which runs in minutes per sample and broadly covers the uncertain input space. A pivoted QR factorization of the LF ensemble identifies a small set of maximally informative skeleton samples and an associated interpolation matrix; the US3D–MURP model is then evaluated only at these skeleton samples, and the full HF dataset is reconstructed by applying the LF-derived interpolation weights to the sparse HF evaluations. Because the LF and HF radiance fields are strongly correlated and the data singular values decay rapidly, the HF CNred and CNviolet profiles are recovered to within roughly one percent in the Frobenius norm using only a handful of HF simulations, reducing the cost of the analysis by approximately two orders of
magnitude relative to a full HF ensemble. This surrogate forms the backbone of the present study and underlies the global, variance-based (Sobol) sensitivity analysis of the CNred and CNviolet band radiances and their ratio along the vehicle surface.
Building on the cost reduction demonstrated for the radiative quantities, the study extends to a reliability
analysis of the forebody heat shield, whose quantity of interest is the bondline temperature: an interior quantity,
defined at the interface between the thermal protection system (TPS) and the underlying structure, whose exceedance of a critical threshold would compromise the integrity of the heat shield and the survival of the payload. In contrast to the CNred and CNviolet radiances, which are surface observables, the bondline temperature is obtained by supplying the surface convective (US3D) and radiative (MURP) heating distributions to a solid thermal solver, from which a Sobol analysis identifies the kinetic, excitation, and composition parameters that
most strongly drive its variability, and a reliability assessment evaluates the heat shield against its thermal design
margin. Because the underlying coupled, mesh-refined flow–radiation simulations are as expensive as those in the radiative analysis, the same low-/high-fidelity paradigm is a natural candidate for keeping this analysis tractable, with the uncoupled US3D heating solution on a coarser forebody mesh serving as the LF model and the coupled,
refined solution as the HF model.
Results
Before proceeding with sample generation, differences in forebody radiative heating between one- and two-way
coupling are evaluated first. Results from ten sample points evaluated at the maximum convective heating trajectory point reveal a difference of approximately 1% between the radiative heating obtained from the two-way
vs. one-way US3D–MURP coupling. As a result, the first 200 high-fidelity samples are generated using one-way
radiation coupling.
Bi-fidelity surrogates constructed from the interpolative decomposition reproduce high-fidelity CNred and
CNviolet radiance profiles to within approximately 1% of the high-fidelity result using only a handful of targeted
high-fidelity evaluations, at roughly two orders of magnitude lower computational cost than a full high-fidelity ensemble. Global sensitivity analysis confirms that freestream methane concentration is the dominant driver of variability in the CNred/CNviolet radiance ratio at both trajectory points considered, providing quantitative justification for using this ratio as a single-parameter diagnostic of methane abundance. Spatially resolved Bayesian inversion shows that methane identifiability is strongest in the near-afterbody at peak radiative heating, and is comparatively weaker and more spatially confined at peak convective heating, where CN emission is less intense.
When uncertainty in the CN electronic excitation rate coefficients is additionally propagated, the region over which methane remains identifiable contracts substantially, indicating that excitation-rate uncertainty is a
first-order factor limiting the diagnostic value of afterbody radiometer measurements and should be prioritized
in future efforts to reduce Titan atmospheric composition uncertainty.
Results
Before proceeding with sample generation, differences in forebody radiative heating between one- and two-way coupling are evaluated first. Results from ten sample points evaluated at the maximum convective heating trajectory point reveal a difference of approximately 1% between the radiative heating obtained from the two-way vs. one-way US3D–MURP coupling. As a result, the first 200 high-fidelity samples are generated using one-way
radiation coupling.
Bi-fidelity surrogates constructed from the interpolative decomposition reproduce high-fidelity CNred and
CNviolet radiance profiles to within approximately 1% of the high-fidelity result using only a handful of targeted
high-fidelity evaluations, at roughly two orders of magnitude lower computational cost than a full high-fidelity
ensemble. Global sensitivity analysis confirms that freestream methane concentration is the dominant driver of
variability in the CNred/CNviolet radiance ratio at both trajectory points considered, providing quantitative justification
for using this ratio as a single-parameter diagnostic of methane abundance. Spatially resolved Bayesian
inversion shows that methane identifiability is strongest in the near-afterbody at peak radiative heating, and is comparatively weaker and more spatially confined at peak convective heating, where CN emission is less intense.
When uncertainty in the CN electronic excitation rate coefficients is additionally propagated, the region over which methane remains identifiable contracts substantially, indicating that excitation-rate uncertainty is a first-order factor limiting the diagnostic value of afterbody radiometer measurements and should be prioritized
in future efforts to reduce Titan atmospheric composition uncertainty.
Conclusion
Uncertainty quantification efforts relating to the Dragonfly mission’s entry into Titan’s atmosphere were summarized, with particular emphasis on the feasibility of inferring the freestream methane concentration and on quantifying the reliability of the forebody heat shield. Freestream methane identifiability is shown to be strongly affected by both the radiometer placement and the degree of uncertainty in rate coefficients used to model CN electronic excitation. Further results from the forebody reliability study will be given in the presentation.
References
[1] H. Cheng et al. “On the Compression of Low Rank Matrices”. In: SIAM Journal on Scientific Computing 26.4 (2005), pp. 1389–1404. doi: 10.1137/030602678; J. Hampton et al. “Practical error bounds for a non-intrusive bi-fidelity approach to parametric/
stochastic model reduction”. In: Journal of Computational Physics 368 (2018), pp. 315–332. doi:10.1016/j.jcp.2018.04.015
[2] S. Boccelli et al. “Lagrangian diffusive reactor for detailed thermochemical computations of plasma flows”. In: Plasma Sources
Science and Technology 28.6 (2019), p. 065002.
Summary
Sensitivity and uncertainty analyses of the Dragonfly capsule using CFD and radiation solvers, focusing on the inference of atmospheric CH4 concentration and on the estimation of forebody heat shield reliability.