Uncertainty Quantification in Hypersonic Reentry Flows Due to Aleatory and Epistemic Uncertainties

Bettis, Benjamin R.; Hosder, Serhat

doi:10.2514/6.2011-252

Cited by 16 publications

(8 citation statements)

References 17 publications

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“…A complete list of the neutral species interactions, considered for this analysis, is given in Table A4 in the Appendix. The uncertainty in the binary collision integrals were implemented through the use of a single parameter A, similar to the studies by Bettis and Hosder [32] and Bose and Wright [12]:…”

Section: Description Of the Stochastic Problemmentioning

confidence: 99%

Uncertainty Analysis of Mars Entry Flows over a Hypersonic Inflatable Aerodynamic Decelerator

Brune

West

Hosder

et al. 2015

Journal of Spacecraft and Rockets

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A detailed uncertainty analysis for high-fidelity flowfield simulations over a fixed aeroshell of hypersonic inflatable aerodynamic decelerator scale for Mars entry is presented for fully laminar and turbulent flows at peak stagnationpoint heating conditions. This study implements a sparse-collocation approach based on stochastic expansions for efficient and accurate uncertainty quantification under a large number of uncertainty sources in the computational model. The convective and radiative heating and shear stress uncertainties are computed over the hypersonic inflatable aerodynamic decelerator surface and are shown to vary due to a small fraction of 65 flowfield and radiation modeling parameters considered in the uncertainty analysis. The main contributors to the convective heating uncertainty near the stagnation point are the CO 2 -CO 2 , CO 2 -O, and CO-O binary collision interactions, freestream density, and freestream velocity for both boundary-layer flows. In laminar flow, exothermic recombination reactions are more important at the shoulder. The main contributors to radiative heating at the nose and flank were the CO 2 dissociation rate and CO heavy-particle excitation rates, whereas the freestream density showed importance toward the shoulder. The CO 2 -CO 2 interaction and freestream velocity and density control the wall shear stress uncertainty. Nomenclature D = statistical variance N s = number of samples N t = number of terms in a total-order polynomial chaos expansion N TP = number of test points n = number of random dimensions p = order of polynomial expansion S e = percent absolute error S T = total Sobol index T e = test point error α = deterministic coefficient in polynomial chaos expansion α = generic uncertain function δ = truncation error μ e = mean error ξ = standard input random variable Ψ = random basis function Ω 1;1 = diffusion collision integral Ω 2;2 = viscosity collision integral

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Section: Description Of the Stochastic Problemmentioning

confidence: 99%

Uncertainty Analysis of Mars Entry Flows over a Hypersonic Inflatable Aerodynamic Decelerator

Brune

West

Hosder

et al. 2015

Journal of Spacecraft and Rockets

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“…There could have been expected a stronger e¨ect of the chemistry on the heat §ux, an explanation to this result being that the §ow considered here is at a moderate temperature and, if even the catalytic e¨ects need to be accounted to compute the heat §ux, it does not represent the biggest part of it. Moreover, γ is rather low and a smaller uncertainty is chosen than in [11]. The choice for this uncertainty is justi¦ed by a preliminary study on the uncertainty on the identi¦cation of the catalytic properties [12].…”

Section: Resultsmentioning

confidence: 99%

Uncertainty quantification for characterization of high enthalpy facilities

Villedieu

Cappaert

Galache

et al. 2013

Progress in Flight Physics

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The post §ight analysis of a space mission requires accurate determination of the free-stream conditions for the trajectory. The Mach number, temperature, and pressure conditions can be rebuilt from the heat §ux and pressure measured on the spacecraft by means of a Flush Air Data System (FADS). This instrumentation comprises a set of sensors §ush mounted in the thermal protection system to measure the static pressure (pressure taps) and heat §ux (calorimeters). Knowing that experimental data su¨er from errors, this methodology needs to integrate quanti¦cation of uncertainties. Epistemic uncertainties on the models for chemistry in the bulk and at the wall (surface catalysis) should also be taken into account. To study this problem it is necessary to solve a stochastic backward problem. This paper focuses on a preliminary sensitivity analysis of the forward problem to understand which uncertainties need to be accounted for. In section 2, the uncertainty quanti¦cation methodologies used in this work are presented. Section 3 is dedicated to the one-dimensional (1D) simulations of the shock layer to identify which chemical reactions of the mechanism need to be accounted for in the Uncertainty Quanti¦cation (UQ). After this triage procedure, the two-dimensional (2D) axisymmetric §ow around the blunt nose was simulated for two trajectory points of EXPERT (EXPErimental Reentry Test-bed) is simulated and the propagation of the uncertainties on the stagnation pressure and heat §ux has been studied.

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“…To alleviate some of the cost, surrogates can be created as a function of all variables and samples extracted according to a nested strategy. For relatively low dimensions, this strategy can be effective and, when combined with gradient-enhancement, could be applied to problems of moderate dimension [11]. However, once the number of epistemic variables increases sufficiently, surrogatebased approaches will again become prohibitively expensive as the required number of training points increases exponentially fast for an accurate surrogate model known as "curse of dimensionality".…”

Section: Introductionmentioning

confidence: 99%

Robust design under mixed aleatory/epistemic uncertainties using gradients and surrogates

Rumpfkeil

2013

J. Uncertain. Anal. Appl.

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In this paper, mixed aleatory/epistemic uncertainties in a robust design problem are propagated via the use of box-constrained optimizations and surrogate models. The assumption is that the uncertain input parameters can be divided into a set only containing aleatory uncertainties and a set with only epistemic uncertainties. Uncertainties due to the epistemic inputs can then be propagated via a box-constrained optimization approach, while the uncertainties due to aleatory inputs can be propagated via sampling. A statistics-of-intervals approach is used in which the box-constrained optimization results are treated as a random variable and multiple optimizations need to be performed to quantify the aleatory uncertainties via sampling. A Kriging surrogate is employed to model the variation of the optimization results with respect to the aleatory variables enabling exhaustive Monte-Carlo sampling to determine the desired statistics for each robust design iteration. This approach is applied to the robust design of a transonic NACA 0012 airfoil where shape design variables are assumed to have epistemic uncertainties and the angle of attack and Mach number are considered to have aleatory uncertainties. The very good scalability of the framework in the number of epistemic variables is demonstrated as well.

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Uncertainty Quantification in Hypersonic Reentry Flows Due to Aleatory and Epistemic Uncertainties

Cited by 16 publications

References 17 publications

Uncertainty Analysis of Mars Entry Flows over a Hypersonic Inflatable Aerodynamic Decelerator

Uncertainty Analysis of Mars Entry Flows over a Hypersonic Inflatable Aerodynamic Decelerator

Uncertainty quantification for characterization of high enthalpy facilities

Robust design under mixed aleatory/epistemic uncertainties using gradients and surrogates

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