Efficient Uncertainty Quantifcation Approach for Reentry Flows with Mixed Uncertainties

Bettis, Benjamin R.; Hosder, Serhat

doi:10.2514/1.51605

Cited by 7 publications

(7 citation statements)

References 15 publications

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“…However, as the uncertainty in the freestream velocity becomes larger, the contribution from the freestream velocity increases and becomes the dominant source at the CoV 3% case. The uncertainty in stagnation-point heat transfer due to log 10 is larger in the current study compared with the results of a similar study by Bettis and Hosder [11]. This is mainly due to the higher freestream enthalpy considered in the current study, which causes more dissociation in the flowfield.…”

Section: Results With Mixed (Aleatory-epistemic) Uncertainty Assumptioncontrasting

confidence: 67%

“…The work described in this paper builds upon the previous study by Bettis and Hosder [11]. Specifically, to present a general framework to asses the accuracy of hypersonic reentry flow analysis, this paper introduces a nonlinear global SAwith Sobol indices [13], which uses the polynomial chaos expansions already derived for uncertainty propagation.…”

mentioning

confidence: 98%

“…A recent study by Bettis and Hosder [11] investigated the propagation of mixed uncertainties through high-fidelity CFD simulations for quantifying uncertainty in the aerodynamic heating of a hypersonic reentry vehicle. In that study, the freestream velocity was modeled as an aleatory uncertain variable described with a uniform probability distribution, and the recombination efficiency at the wall () was treated as an epistemic uncertainty represented with an interval.…”

mentioning

confidence: 99%

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

Hosder¹,

Bettis²

2012

Journal of Spacecraft and Rockets

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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. Nomenclature C = mass fraction CoV = coefficient of variation, D 1=2 = D = statistical variance H = enthalpy, J h = enthalpy, J=kg h D = dissociation enthalpy, J=kg k = multiplicative factor Le = Lewis number n = number of random variables p = pressure, N=m 2 _ q = heat transfer rate, W=m 2 R N = radius of curvature, m S = Sobol index S T = total Sobol indices T = temperature, K V = velocity, m=s x = lateral direction of the flow = spectral modes = stochastic output variable = recombination efficiency h f = heat of formation, J=kg = coefficient of viscosity, kg=m s = mean = standard random variable a = standard aleatory uncertain variable e = standard epistemic uncertain variable = density, kg=m 3 = random basis function 1;1 = diffusion collision integral 2;2 = viscosity collision integral Subscripts e = boundary layer edge o = total or stagnation condition sp = stagnation point w = wall 1 = freestream

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Section: Results With Mixed (Aleatory-epistemic) Uncertainty Assumptioncontrasting

confidence: 67%

mentioning

confidence: 98%

mentioning

confidence: 99%

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

Hosder¹,

Bettis²

2012

Journal of Spacecraft and Rockets

Self Cite

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“…A box is used in the figure to distinguish postprocessing routines, which comprise a negligible fraction of the total computational expense. Attributes of the proposed procedures include a lack of simplifying approximations regarding the form of (N 1)-dimensional response functions (as would be required for a surrogate modeling approach [28][29][30]), as well as greatly reduced sample size requirements in comparison with traditional nested sampling routines for UQ involving mixed aleatory and epistemic uncertainties [21]. The assumed reduction in required sample size, relative to nested sampling, follows from the fact that only a single set of sampled values are used for each input parameter; in contrast, a nested sampling approach would employ a large number of sample sets, with each sample set typically corresponding to hundreds or thousands of simulations.…”

Section: Coupled Aleatory and Epistemic Uncertaintiesmentioning

confidence: 99%

Global Sensitivity Analysis and Uncertainty Quantification for a Hypersonic Shock Interaction Flow

Burt

Josyula

2015

Journal of Thermophysics and Heat Transfer

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Hypersonic gas flows over concentric double-cone configurations are commonly used to investigate shock-shock and shock wave/boundary-layer interaction phenomena, and are characterized by the formation of interacting flow structures that are highly sensitive to models used in flow simulation. The work presented here is intended to clarify the influence of several modeling parameters and approximations on simulation output quantities through a more general and systematic approach than has previously been employed for this type of flow, with the ultimate goal of improved model validation for simulation of hypersonic shock interactions. Global sensitivity analysis and uncertainty quantification techniques are integrated with a direct simulation Monte Carlo gas flow simulation code, and a large number of these Monte Carlo simulations are performed for a representative hypersonic double-cone flow. Aleatory and epistemic uncertainties are considered in sensitivity analysis/uncertainty quantification calculations, both independently and in combination, through a variety of probabilistic sampling procedures. These procedures include a novel uncertainty quantification technique that combines elements of importance sampling sensitivity analysis with Latin hypercube sampling, as an efficient surrogate-free means of simultaneously considering mixed uncertainty types. Following a strong engineering interest in surface heating augmentation due to hypersonic shock wave/boundary-layer interaction, this paper focuses on surface heat flux at a shock impingement point as an output quantity in sensitivity analysis/uncertainty quantification calculations; other output quantities of interest include impingement point pressure and the integrated force and heat transfer rate over the model surface. Nomenclature a = local speed of sound f = Gaussian probability density function K = number of postprocessing Monte Carlo samples for target input parameter distributions Kn max = maximum gradient length local Knudsen number M = sample size (or number of simulations) used for uncertainty quantification N= number of input parameters associated with uncertainty n = number density P = cumulative probability corresponding to a given output quantity value R i = Pearson product-moment correlation coefficient between quantities x i and y r = random number within specified domain for Latin hypercube sampling S = N × M matrix of input value combinations based on Latin hypercube sampling s ij = element in matrix S T = temperature V = bulk velocity magnitude x i = value for input parameter i ∈ 1; N y = output quantity value ϑ = uniformly distributed random number in [0, 1] λ = mean free path μ i = mean value for distribution of input parameter i ∈ 1; N ρ = mass density σ i = standard deviation for distribution of input parameter i ∈ 1; N

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“…Surrogate function approaches attempt to replace the actual physical models with simpler (typically polynomial) functions that relate both epistemic and aleatory input parameter uncertainties to uncertainties in the output quantities of interest [11][12][13]. The surrogate or response functions are obtained through a relatively small number of simulations, and these functions are then refined using various statistical approaches [12].…”

Section: Introductionmentioning

confidence: 99%

Uncertainties in Satellite Drag Associated with Variations in Atmospheric Conditions

Титов

Burt

Josyula

et al. 2013

5th AIAA Atmospheric and Space Environments Conference

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An uncertainty quantification (UQ) computational technique based on principles of importance sampling is applied to Space Environmental NanoSat Experiment (SENSE) satellite aerodynamic studies. Computational simulations are performed at an altitude of 100 km using a DSMC solver that is coupled with the UQ technique, allowing for automated variation of DSMC input parameters and propagation of input uncertainties through the flow solution. Satellite drag is identified as the parameter of interest because of its role in defining the trajectory and eventual lifespan of the satellite. Contributions of the ambient flow temperature and density uncertainties on the resulting satellite drag uncertainty are studied in detail. Two types of uncertainties, epistemic and aleatory, are considered and resulting probability boxes for satellite drag are presented. DSMC calculations incorporating UQ are applied to this configuration for the collisional flow at 100 km altitude. It is found that the nominal value of the computed drag guarantees reentry of a SENSE type satellite within a very small fraction of an orbit. This is an expected result for small satellites orbiting around 100 km altitude.

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Efficient Uncertainty Quantifcation Approach for Reentry Flows with Mixed Uncertainties

Cited by 7 publications

References 15 publications

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

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

Global Sensitivity Analysis and Uncertainty Quantification for a Hypersonic Shock Interaction Flow

Uncertainties in Satellite Drag Associated with Variations in Atmospheric Conditions

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