AIAA SciTech Forum 2015 A Probabilistic Sizing .
National Aeronautics andSpace AdministrationAIAA SciTech Forum 2015A Probabilistic Sizing Demonstration of aFlexible Thermal Protection System for aHypersonic Inflatable AerodynamicDeceleratorPresented by:Steven TobinJanuary 08, 2015www.nasa.gov/hiad
Outline HIAD & Flexible TPS BackgroundMargin Policy and Probabilistic Sizing OverviewSensitivity AnalysisThermal Model CorrelationUncertainty Analysis and SizingConclusionsFuture WorkAIAA SciTech Forum January 08, 20152
HIAD & Flexible TPS Background Potential missions have been identified that will require aplanetary entry system to have an aeroshell much larger indiameter than the diameter of any feasible launch vehicle. The inflatable aeroshell of a HIAD entry system relies on aflexible thermal protection system (TPS) to prevent theunderlying structure from exceeding its thermal limits. Candidate flexible TPS materials and layups have undergoneextensive aerothermal arc jet testing in a stagnationconfiguration to evaluate thermal performance and provideboundary condition and in-depth temperature measurementdata for thermal model correlation and validation. Outer fabric protects the underlying insulation layers frombeing directly exposed to the incident convective heat fluxand the aerodynamic shear forces. The insulator layers reduce thermal soak back. Gas barrier prevents hot gas impingement on to theunderlying structure.AIAA SciTech Forum January 08, 2015outer fabricouter fabricinsulationinsulationinsulationinsulationgas barrierTC-1TC-2TC-3TC-4TC-5TC-6 (BonTC-7LI-9003
HIAD F-TPS Margin Policy Goals Given uncertainties in material properties, environments, etc.Prevent bondline over temperature of the F-TPS Use probabilistic tools to enhance F-TPSperformance and increase survivabilityduring off nominal entry conditions,while reducing F-TPS margined mass Provide more knowledge and insightabout the F-TPS design and itsperformanceAIAA SciTech Forum January 08, 20154
End-to-End Monte Carlo Simulation Uncertainties captured without stacking worst cases together Decoupled approach two separate Monte Carlo simulations are run Trajectory Output is a set of dispersed trajectories Thermal model Each resulting trajectory from the trajectory Monte Carlo is used as input to thethermal model Monte CarloAIAA SciTech Forum January 08, 20155
Monte Carlo Simulation - Implementation Margin Process Thermal Monte Carlo simulation run using several layups, each timeincreasing the number of insulation layers Peak bondline temperature tracked and presented as a bondlinetemperature distribution Margined thickness found by selecting the layup which satisfies missionreliability requirement for the F-TPS3 500 CLayup #1AIAA SciTech Forum January 08, 20153 375 CLayup #23 216 CLayup #N6
Probabilistic Sizing Process OverviewAIAA SciTech Forum January 08, 20157
Probabilistic Sizing OverviewSizing Objective Bondline Temperature Limit: 400 C Margin Policy Dictates: 97% chance Bondline temperature will be maintained below400 C (Predicted 2σ bondline temperature must be less than 400 C)Bondline Temperature Prediction RequirementsAerothermal Environment(CFD)Trajectory Dispersions(POST)Material Thermal Response(COMSOL)Thickness Margin Material Response Uncertainty –Parametric, Stochastic, & Structural Trajectory Dispersions – heat flux andheat load Aerothermal Uncertainty – heat fluxOuter FabricGas BarrierAIAA SciTech Forum January 08, 2015InsulatorNominal Thickness(Zero Margin)Bondline1st Gen Flexible TPS8
Sensitivity Analysis(Monte Carlo #1)AIAA SciTech Forum January 08, 20159
Sensitivity AnalysisThermal Response Model OverviewArc Jet Test ConfigurationType R TCs (Al2O3 coated)FlowTC 12 x Outer FabricTC 2Type K TCsTC 3FlowTest SpecimenTest SpecimenTC 44 x InsulatorTC 5Stagnation TestFlexible TPS SampleInside Model Holder1 x Gas BarrierBondline TCTC 6TC 7Instrumented Flexible TPS Test SpecimenThermal Response Model LayoutAIAA SciTech Forum January 08, 201510
Sensitivity AnalysisParameters Dispersed in Monte Carlo Sensitivity AnalysisParameterInsulator Virgin Conductivity (kvrg) SF 1(Low Temperature Range)Insulator Virgin Conductivity (kvrg) SF 2(High Temperature Range)Insulator Char Conductivity (kchr) SF 1(LowTemperature Range)Insulator Char Conductivity (kchr) SF 2(High Temperature Range)Insulator Specific Heat (Cps) SFΔρ (Virgin Density – Char Density) SFGas Specific Heat (Cpg) SFGas Viscosity (µg) SFLatent Heat of Reaction 1(hR1), SFInsulator Porosity (φ ) SFInsulator Permeability (kx) SFOuter Fabric Conductivity SFBacking Material Conductivity SFAIAA SciTech Forum January 08, 2015DistributionTypeMean orNominalValueStandardDeviationor NormalNormal1.01.01.01.01.01.01.01.01.00.150.8 to 1.20.1 to 1.01.0 to 2.0-30 to 300.575 to1.090.20.20.211
Sensitivity AnalysisSensitivity Analysis ResultsTime Evolution of Input Parameter Contributions to Bondline Temperature UncertaintyUncertainty Breakdown: Temperature BL100Nextel ConductivityBacking MaterialConductivityLatent Heat ofDecomp Reaction90Uncertaintyto BL Temp% Contribution% Contributionto UncertaintyINvrg cond f1INvrg cond f2INchrdec cond f1INchrdec cond f2IN spechtdelta INdensspecht g80viscogGas Specific Heat70HR1IN porIN permOF condBack cond6050Insulator Specific Heat403020Decomposed ConductivityInsulatorVirgin Conductivity10020406080100Time (sec)120140160Time (seconds)Insertion(Beginning of Heat Pulse)AIAA SciTech Forum January 08, 2015Retraction (End of Heat Pulse)Point of Maximum Bondline Temperature12
Thermal Model CorrelationAIAA SciTech Forum January 08, 201513
Thermal Model CorrelationCorrelation ParametersCorrelated Model PredictionsParameterImposed Temperature Boundary ConditionsArc Jet Test ResultsConstant Heat FluxMarkers Arc Jet DataSolid Lines Model PredictionsTC 1RTC 2RInsulator Virgin Conductivity (kvrg) SF 1Insulator Virgin Conductivity (kvrg) SF 2Insulator Char Conductivity (kchr) SF 1Insulator Char Conductivity (kchr) SF 2Backing Material Conductivity SFOuter Fabric Conductivity SFScaledValue0.8851.090.971.011.751.70Modeled Gen 1 LayupTC 3RTC 4KTC 5KTC 6KAIAA SciTech Forum January 08, 2015Bondline Temperature14
Thermal Model CorrelationCorrelated Model PredictionsMarkers Arc Jet DataSolid Lines Model PredictionsConstant Heat FluxModeled LayupLowerConstant Heat FluxUncorrelatedAIAA SciTech Forum January 08, 2015Correlated15
Thermal Model CorrelationCorrelated Model PredictionsMarkers Arc Jet DataSolid Lines Model PredictionsLowerConstant Heat Flux2 Insulator Layers*Modeled LayupProfile Heat FluxModeled LayupUncorrelatedAIAA SciTech Forum January 08, 2015.Correlated16
Thermal Model CorrelationError Analysis Results – 12 Arc Jet Cases Compared to Predictions (4 profile and 8 constant HF)Error IndicatorUncorrelatedCorrelatedAverage Max BLTemperature Difference C16530Average Normalize BLTemperature RMS %275Max Bondline Temperature Difference (Predicted – Measured) C-50-40-30-20-1001020304050Bondline Temperature Bias RangeAIAA SciTech Forum January 08, 201517
Uncertainty Analysis and Sizing(Monte Carlo #2, #3, & #4)AIAA SciTech Forum January 08, 201518
Uncertainty Analysis & SizingMonte Carlo Input Parameters and Uncertainty QuantificationParameterDistributionTypeMean orNominal ValueInsulator Virgin Conductivity (kvrg) SF 1Insulator Virgin Conductivity (kvrg) SF 2Insulator Char Conductivity (kchr) SF 1Insulator Char Conductivity (kchr) SF 2Insulator Specific Heat (Cps) SFLatent Heat of Reaction 1( hR1) SFHeat Flux (qcw) SFBondline Temperature BiasInsulator Thickness SFInsulator Density rmNormalNormal0.8851.090.971.011.001.001.000 C1.001.00AIAA SciTech Forum January 08, 2015StandardDeviation (1σ)or Range0.1060.1060.1310.1310.07380 to 20.070 to 500.0840.08319
Uncertainty Analysis & SizingMonte Carlo Input Parameters: Trajectory Dispersions1201008060402000.96 0.970.980.9911.011.021.031.041.05Normalized Heat Load HistogramTwo thousand (2000) off-nominal trajectories were provided from a separate Monte Carlo simulation run using POSTwhere initial orbital conditions, vehicle aerodynamic parameters, atmospheric conditions, and other parametersaffecting the reentry trajectory were dispersed.The boundary condition parameters derived from each of the 2000 trajectory dispersions as inputs into each of thecorresponding 2000 thermal model Monte Carlo samples.AIAA SciTech Forum January 08, 201520
Uncertainty Analysis & SizingSizing: Nominal Case, Four Insulator LayersModeled LayupMaximum Bondline Temperature Histogram with Lognormal PDF FitAIAA SciTech Forum January 08, 201521
Uncertainty Analysis & SizingSizing: Four and a Half Insulator LayersModeled LayupMaximum Bondline Temperature Histogram with Lognormal PDF FitAIAA SciTech Forum January 08, 201522
Uncertainty Analysis & SizingSizing: Five Insulator LayersModeled LayupMaximum Bondline Temperature Histogram with Lognormal PDF FitAIAA SciTech Forum January 08, 201523
Uncertainty Analysis & SizingMaximum Bondline Temperature Uncertainty Contribution Breakdown (5 Layer Case)VirginInsulatorConductivityVirgin vityVirginInsulatorThickness38%Heat Flux18%4%InsulatorSpecificHeatAIAA SciTech Forum January 08, 201524
Conclusions The probabilistic sizing methodology prescribes one additional insulation layer on topof the nominal thickness to mitigate parametric, stochastic, and structural uncertainties. A thickness margin of one layer of insulation was shown to result in a 99.87% probabilityof maintaining the bondline below 400 C, exceeding the given margin policy. This thickness margin may shrink as knowledge is gained about the parameterswhich are contributing the significantly to the uncertainty in the maximumbondline temperature or by developing a higher fidelity thermal model, enabling ahigher quality correlation and a lower maximum bondline temperature bias. The probabilistic sizing process works well and it has enabled the opportunity to makeinformed TPS design and mission risk tradeoffs. A HIAD project may decide to decrease the TPS thickness margin to one half a layerof insulation resulting in a 5% probability of bondline over-temperature asdetermined by the second Monte Carlo simulation for uncertainty analysis.AIAA SciTech Forum January 08, 201525
Conclusions Lesson Learned: Sensitivity analysis showed that the gas specific heat (Cpg) has a largeinfluence on the maximum bondline temperature, this indicates that advection is asignificant mode of heat transfer. The specific heat of the gas, as well as other gas properties, can be better definedby introducing multi-species gas mass conservation into the thermal model anddetermining the properties of the mixture. This will reduce the thermal response model structural uncertainty and allow fora better correlation to arc jet test data which will decrease the bondlinetemperature bias applied in the uncertainty analysis Monte Carlo simulations. This probabilistic sizing process can be readily implemented on other TPS layupdesigns provided a validated thermal response model, appropriate boundary conditiondispersions, and thermal model input parameter uncertainty quantification.AIAA SciTech Forum January 08, 201526
Future Work Demonstrate this process using a higher fidelity model with multispecies-gas-mass conservation integrated in to the numericalsolution approach. Further investigate uncertainties and the correlations between thethermal response model input parameters which were dispersedor not dispersed in this study. Employ automated correlation by inverse analysis (GrantRossman work). Implement this process for sizing the TPS of the Terrestrial HIADOrbital Reentry (THOR) aeroshell (HIAD technology demonstrationflight test).AIAA SciTech Forum January 08, 201527
Back Up ChartsAIAA SciTech Forum January 08, 201528
Types of Uncertainties (1 of 3) Parametric uncertainties Uncertainty that results from errors in theunderlying physical models, or model inputparameter estimates i.e. char thermal conductivity, pyrolysis gas enthalpy,decomposition kinetics constants Properties that are difficult to measure are often estimated ortheoretically calculated This type of uncertainty can be reduced throughtesting and analysis but not eliminatedAIAA SciTech Forum January 08, 201529
Types of Uncertainties (2 of 3) Stochastic variability Uncertainty that arises from natural fluctuationsin the physical environment, or from materialproperty variability i.e. Varying atmospheric conditions, lot-to-lot propertyvariation This type of uncertainty is always present and can notbe reduced Typically accounted for in the entry trajectory simulationsusing a Monte Carlo simulation These uncertainties are what most people think of whenthey think about uncertaintiesAIAA SciTech Forum January 08, 201530
Types of Uncertainties (3 of 3) Structural uncertainties Arise in numerical simulations due to the fact thatsimulations employ mathematical models to simulatephysical phenomenon Mathematical models often make simplifyingassumptions which are sometimes only valid over alimited range of conditions Computational truncation errors i.e. Tauber-Sutton radiative heating correlation,transfer coefficient-recovery enthalpy approach forconvective heating boundary condition (FIAT/CMA),differential equation discretization methodAIAA SciTech Forum January 08, 201531
Biases and Margin Biases are factors applied to the nominal thicknessto account for known deficiencies in themethodology used to calculate the nominal TPSthickness Biases account for structural uncertainty and are applied toboth nominal and margined thicknesses A bias should be applied if the thermal model shows a consistentdifference between prediction and test data i.e. CEV TPS applied a bias to thickness based on the calculatedrecession For HIAD we need to add a bias to account for an uncorrelatedmodel Margin is applied to the nominal thickness toaccount for the parametric and stochasticuncertainty typesAIAA SciTech Forum January 08, 201532
Random Variable Correlation Random variables are statistically correlated when the probabilitydistribution of one depends on the value of another random variable The strength of the dependence between two random variable isassessed by calculating their correlation coefficient which variesbetween -1 and 1. A values of 0 means no correlation. In semi-plain English, when a functional relationship exists betweentwo parameters, they are correlated and can not be treated asindependent random variablesDensitySample correlation coefficientn XY x y nx yi 1n xi 1i2i nxin2 yi 1i2 ny 2Where x and y are the mean valuesfor each random variableAIAA SciTech Forum January 08, 2015ThermalConductivitySpecific HeatPermeability33
Random Variable Correlation This may seem like a problem, but its not . For each sample in Monte Carlo simulation, a vector of randomnumbers are generated corresponding to the thermal modelparameters of interest, {R} If there are parameter correlations present, {R} must be modifiedbased on each parameters correlation with one another. Thecorrelation coefficients are collected in a correlation matrix [C] The correlation matrix [C] can’t be used directly, so anintermediate matrix [U] must be found such that:[U ]T [U ] [C ] Once [U] is found by using Cholesky decomposition, thecorrelated vector of random variables can be determined by:{Rc } [U ]{R}AIAA SciTech Forum January 08, 201534
Random Variable Correlation In reality there is a good chance that correlations exist betweendensity and many other thermal model parameters, however . . . In the COMSOL model, we are not able to determine whether or notcorrelations exist between density and thermal conductivity, density and specificheat, density and permeability, etc, because there is no functional relationshipestablished between these parameters in the COMSOL model The correlations can be determined experimentally, but at an expense By adding the degree of char to the COMSOL model, we may be ableto computationally determine if there are correlations, but it is not assimple as just tracking the density change over temperature sincegas conduction plays a significant role in the effective thermalconductivity of the materialAIAA SciTech Forum January 08, 201535
Current Root-Sum-SquaredApproach Currently TPS is sized using a root-sum-square(RSS) approach. Typically using three cases Case 1: size heat shield to nominal bondline temperature,apply trajectory dispersion multiplying factors to heat flux Case 2: size heat shield to nominal bondline temperature,apply trajectory dispersion and aerothermal uncertaintymultiplying factors to heat flux Case 3: size heat shield to lower than nominal bondlinetemperature, apply trajectory dispersion multiplying factorsto heat flux These three cases are RSS’ed together to arrive atthe margined thickness𝜏𝑅𝑆𝑆 1.10 [𝜏1 AIAA SciTech Forum January 08, 2015𝜏2 𝜏12 𝜏3 𝜏1236
Type Mean or Nominal Value Standard Deviation (1σ) or Range Insulator Virgin Conductivity (k vrg) SF 1 Normal 0.885 0.106 Insulator Virgin Conductivity (k vrg) SF 2 Normal 1.09 0.106 Insulator Char Conductivity (k chr) SF 1 Normal 0.97 0.131 Insulator Char Conductivity (k chr) SF 2 Normal 1.
AIAA SciTech, 52nd AIAA Aerospace Sciences Meeting, January 2014, National Harbor, AIAA 2014{0414 Hybrid feedback design for subsonic and transonic airfoils and wings M. Zhang 1, C. Wang , A. Rizzi1, R. Nangia2 1Royal Institute of Technology (KTH), 10044 Stockholm, Sweden 2Nangia Aero Research Associates, Bristol, UK A hybrid inverse/optimization
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