Monte Carlo Analysis for Spacecraft Thermal Protection System Design

Chen, Yih-Kanq; Squire, Thomas H.; Laub, Bernard; Wright, Michael J.

doi:10.2514/6.2006-2951

Cited by 23 publications

(8 citation statements)

References 3 publications

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“…For SA/UQ calculations involving input parameters with only aleatory uncertainty, we follow the basic procedures of Bose et al [13,14], which have been applied to a variety of problems associated with reentry flows and hypersonic aerothermodynamics [15][16][17][18][19]. We start with a rough estimate of expected input uncertainties.…”

Section: A Consideration Of Aleatory Uncertaintymentioning

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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Section: A Consideration Of Aleatory Uncertaintymentioning

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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“…Another approach uses a Monte Carlo simulation to run a large number of analyses, randomly varying material properties and other design parameters based on their nominal values and standard deviations. 36 These analyses are very effective for identifying the parameters that have the largest influence on the system performance.…”

Section: The Design Process and Property Uncertaintymentioning

confidence: 99%

Material property requirements for analysis and design of UHTC components in hypersonic applications

Squire

Marschall

2010

Journal of the European Ceramic Society

317

106

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“…For system 2, the epistemic interval was selected to be 900; 1200 W∕cm 2 . The uncertainty in this interval was extrapolated from several sources, indicating different heat load values of the Stardust mission, including CFD simulations as well as sensor data collected during flight [35][36][37].…”

Section: Performance Limitsmentioning

confidence: 99%

Quantification of Margins and Uncertainties for Integrated Spacecraft Systems Models

West

Hosder

Winter

2015

Journal of Spacecraft and Rockets

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The objective of this study was to introduce an efficient and accurate approach to the quantification of margins and uncertainties for integrated spacecraft systems models. In this study, stochastic expansions, based on nonintrusive polynomial chaos, were used for efficient representation of uncertainty both in design metrics and associated performance limits of a system. Additionally, procedures were outlined for analyzing systems that contain different uncertainty types between the performance metrics and performance limits. These methodologies were demonstrated on two model problems, each possessing mixed (epistemic and aleatory) uncertainty, which was propagated through the models using second-order probability. The first was a complex system model of highly nonlinear analytical functions. The second was a coupled multisystem, physics-based model for spacecraft reentry. The performance metrics consisted of two systems used to determine the maximum g load, the necessary bank angle correction, and maximum convective heat load along a reentry trajectory. Overall, the methodologies and examples of this work have detailed an efficient approach for measuring the reliability of complex spacecraft systems models, as well as the importance of quantifying margins and uncertainties for the design of reliable systems. Nomenclature c i = mass fraction of species i F = performance metric FL, FU = lower and upper performance limit h = enthalpy or altitude, km h D = enthalpy of diffusion, J∕kg h 0 = total enthalpy, J∕kg h 0 f = heat of formation, J∕k mol Le = Lewis number M LW , M UP = lower and upper performance gate margin m = mass, kg N s = number of samples N t = number of terms in a total-order polynomial chaos expansion n = number of random dimensions P = pressure, Pa Pr = Prandtl number p = order of polynomial expansion _ q = heat flux, W∕cm 2 r = orbital radius, km S = reference area, m 2 s = downrange distance, km T = temperature, K U = velocity, m∕s U F = performance metric uncertainty U FL , U FU = lower and upper performance limit uncertainty U LW , U UP = lower and upper performance gate uncertainty α = deterministic coefficient in the polynomial chaos expansion α = generic uncertain function β = confidence level γ = flight-path angle, deg ϵ = wall emissivity θ = longitude, deg μ = dynamic viscosity, kg∕m · s ξ = standard input random variable ρ = density, kg∕m 3 σ = Stefan-Boltzmann constant, 5.67 × 10 −8 W∕ m 2 -K 4 , or bank angle, deg ϕ = latitude, deg Ψ = random basis function or heading angle, deg ω = planetary body rotation rate, rad∕s Subscripts c = conduction d = diffusion e = boundary-layer edge condition r = radiation w = wall condition ∞ = freestream condition

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Monte Carlo Analysis for Spacecraft Thermal Protection System Design

Cited by 23 publications

References 3 publications

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

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

Material property requirements for analysis and design of UHTC components in hypersonic applications

Quantification of Margins and Uncertainties for Integrated Spacecraft Systems Models

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