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DESIGNOFMETALLICFOAMSASINSULATIONINTHERMALPROTECTION SYSTEMS By HUADONG ZHU ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2004 Copyright2004 by HUADONG ZHU TomyparentsandtomywifeQingxinMeng. ACKNOWLEDGMENTS FirstIwouldliketoexpressmysinceregratitudetomyadvisor,Dr.Bhavani Sankar,whoisakeyinfluenceinmygraduatestudies.Ithankhimforacceptingmeas oneofhisdoctoralstudents.Hisunwaveringsupportandfeedbackguidedmethroughmy wholePh.Dresearch.Iwouldalsoliketogivemysincereappreciationtomyadvisory committeecochair,Dr.RaphaelHaftka,forhisguidanceandsupport,withoutwhichit wouldneverhavebeenpossibletocompletethiswork. Iamblessedwithadoctoralcommitteeofcompassionateandsupportivescholars.I wouldliketoexpressmygratitudetoDrWilliamHager,andDr.MalisaSamtinoranont forservingonmysupervisorycommitteeandfortheirvaluablecommentsand suggestions.ThanksalsogotoDr.MaxBlosserfromNASALangleyresearchcenter.Dr. JacobChungandDr.AndrewJ.RapofffromMAE,Dr.SatchiVenkataramanfromSan DiegoStateUniversity,whoprovidemanyconstructivequestionsandsuggestionsonmy researchwork. Also,Iappreciatethefriendshipandencouragementofallthecolleaguesatthe CenterofAdvancedComposites(CAC)whileworkingandstudyingtogetherinthelab. Iowegreatlovetomyparentswhohavealwayssupportedandcaredforme.Last, butnotleast,Iwouldliketothankmywife,QingxinMeng,forherloveandpatience throughoutmydoctorateprogram. IV TABLEOFCONTENTS page ACKNOWLEDGMENTS iv LISTOFTABLES viii LISTOFFIGURES ix NOMENCLATURE xiii ABSTRACT xv CHAPTER INTRODUCTION 1 1 ReusableLaunchVehicles..... 1 ThermalProtectionSystems 2 FunctionallyGradedMetallicFoamMaterial 4 GoalofDissertationResearch 5 Objectives 5 Scope 5 2 THERMALPROTECTIONSYSTEMSFORREUSABLELAUNCHVEHICLES..6 ThermalProtectionApproaches 7 CurrentPassiveThermalProtectionDesigns 9 ReinforcedCarbon-CarbonTPS 9 FlexibleBlanketTPS 10 RigidCeramicTilesTPS 11 MetallicTPSPanels 12 ThermalandStructuralAnalysisofSandwichStructure 20 HeatTransferinInsulationMaterials 20 StructuralandThermalAnalysisofSandwichStructure 22 DesignOptimizationofSandwichStructure 26 3 HEATTRANSFERINFUNCTIONALLYGRADEDMETALLICFOAMS 29 ModelofMetallicFoams 32 EffectiveThermalConductivity 34 v GasConduction 34 SolidConduction 36 Radiation 37 FabricationofMetallicFoams 39 4 OPTIMUMDESIGNOFMETALLICFOAMINSULATIONUNDERSTEADY STATEHEATTRANSFERCONDITION 41 TemperatureOptimization 42 OptimalityCriteriaforMinimumHeatTransfer 42 NumericalEvaluationofDesigns 44 OptimumTemperatureandDensityDistribution 46 MassOptimization 50 CriterionforMinimumMassDesign 50 NumericalEvaluationofDesignsThatSatisfytheOptimalityCriterion 52 5 OPTIMUMDESIGNOFMETALLICFOAMINSULATIONUNDER TRANSIENTHEATTRANSFERCONDITION 59 Analysis 59 OptimalTwo-LayerDesigntoMinimizetheMaximumStructuralTemperature 62 NumericalDiscretization 62 PerformanceofSteadyStateOptimalDesign 64 Two-layerDesignwithTransientAnalysis 68 OptimalTwo-layerDesigntoMinimizetheMaximumStructuralTemperaturewith ThicknessPenalty 74 WithoutThicknessPenalty 75 EffectofThicknessPenalty 77 6 RESPONSEOFFUNCTIONALLYGRADEDMETALLICFOAMSTO MECHANICALLOADS 80 AnalysisofFunctionallyGradedBeams 80 Analysis 81 ResultsandDiscussion 86 7 ANALYSISOFSANDWICHTPSPANELSWITHFOAMCOREUNDER THERMALLOAD 90 StructuralAnalysisoftheTPSPanel 92 AnalysisofaSingleLayer 92 AnalysisoftheWholePanel 99 NumericalResults 100 EvaluationofIntegratedSandwichTPSDesignwithMetalFoamCoreforLaunch Vehicles 105 IntegratedSandwichTPSDesignandSafillDesign 105 MinimumWeightDesignduringReentry 107 vi 51 OptimumDesignConsideringStructuralTemperatureConstraint 107 OptimumIntegratedSandwichDesignforaGivenStructureThickness ConsideringTemperatureConstraintonly 11 FailureAnalysisoftheTPSStructureduetoLaunchLoads 112 8 CONCLUDINGREMARKS 11 APPENDIX A TEMPERATUREDEPENDENTMATERIALPROPERTIESOFTITANIUMAND ALUMNIUM 119 B REUSABLELAUNCHVEHICLEHEATINGPROFILE 123 LISTOFREFERENCES 128 BIOGRAPHICALSKETCH 137 vii 4- LISTOFTABLES T5-able page 25--1TPSconceptsforreusablelaunchvehicle(RLV) 18 6-1DifferentVjccorrespondstodifferentinsulationthicknessforminimummassdesign understeadystateheattransfercondition 54 7- 1Two-layerdesignsforminimizingthemaximumtemperatureofstructureunder transientconditions 69 2Comparisonbetweenoptimalthree-layerdesignandtwo-layerdesignforminimizing maximumstructuraltemperature 74 1Thhe—c\o0efmfimcientsofthecubicpolynomialforE{z).E(f=10GPaandbeamthickness 86 1Minimumweightdesignwithvariableinsulationandstructuralthickness,subjectto 450Kmaximumtemperatureconstraint 108 7-2Minimumweightdesignwithvariableinsulationandstructuralthickness,subjectto 450Kmaximumtemperatureconstraintandstressconstraints 110 7-3Minimumweightdesignforintegratedsandwichwithfixedfoaminsulationthickness upperbound90mmandstructurethicknessof2.2mm 112 7-4MinimumweightdesignforbothintegratedsandwichTPSdesignandSafilldesign duringlaunch 113 B-lThermalloadandtransversepressureforreentryofreusablelaunchvehicle 123 vm LISTOFFIGURES Figure page 2- 23--1RadiativemetallicTPSpanel 13 2-2AssembledmultiwallTPStile 14 2-3PrepackagedsuperalloyhoneycombsandwichmetallicTPSpanel 16 3-4SchematicrepresentationofARMORmetallicTPSpanel 17 4- 1Photographsofclosecellandopencellaluminumfoams 31 3-2Rectangularrepresentativevolumeelementusedforheattransfermodelinopen-cell foamwithfixedstrutdiameterds 33 3-3Dependenceoftheeffectivethermalconductivityonthetemperatureandvolume fractionforafixedstrutdiameterof0.05mm 38 4Dependenceofeffectivethermalconductivityonsolidityforvarioustemperatures rangingfrom250Kto1000K.Thestrutdiameterisfixedat0.05mm. 38 1Schematicrepresentationofone-dimensionalheattransferproblem 42 4-2Optimalconductivitydependingonsolidityforminimumheatdesign 45 4-3Optimumeffectiveconductivityandsolidityasfunctionoftemperatureforminimum heatdesign.Quadraticpolynomialsfittedtodataarealsogiven 46 4-4Temperaturedistributionthroughthethicknessoftheinsulationfordifferentvalues ofincidentheatfluxthatsatisfyoptimalityconditionsformaximumoutside temperature 47 4-5Ratioofmaximumtemperaturesattainedbyfunctionallygradedanduniform insulation 48 4-6Comparisonofheattransmittedthroughthegradedanduniforminsulationof minimumheatdesign 49 4-7Optimalcellsizedistributionforgradedanduniforminsulationsofminimumheat design 49 IX 4-8ScohTemmaAtriecproefsehnetasttthreanhsefaetrriandiinastueldatbiaocnk.Qinotoisstphaeceappliedaerodynamicheatingw,and50 4-9Lociofoptimumsolidityvaluesofminimummassdesignwithvariousvaluesof thickness 53 4-10Candidatetemperaturedistributionsthroughthethicknessoftheinsulationfor differentthicknesstominimizemass,00=300,000W/m 55 4-11Optimumsolidityprofileofminimummassdesignforvariousthicknessofthe 4- insulation 55 45--12Optimumcellsizedistributionsofminimummassdesignforvariousthicknessesof theinsulation 56 4-13Comparisonofmassperunitareaforfunctionallygradedanduniformdensity insulations 57 14Temperatureattheoutsidewallforvariousdesignsstudied 58 1Schematicoftheheattransferintheinsulationonareusablelaunchvehiclestructure60 5-2Heatfluxatachosenpointonthewindwardsideduringascentandreentry 61 5-3Solidityprofilesforgradedinsulationdesignedforthesteady-stateconditionsand uniforminsulationofsamemass 65 5-4Structuraltemperaturehistoriesforgradedinsulationdesignedforsteady-state conditionsanduniforminsulationofagivenmass 66 5-5Temperatureprofilesinagradedinsulationdesignedforsteady-stateconditionsanda uniforminsulationofsamemassatdifferenttimes 67 5-6Temperaturehistoriesofagradedinsulationdesignedforthesteady-stateconditions andauniforminsulationofequalmassatdifferentlocations 67 5-7Structuraltemperaturehistoryforvarioustwo-layerdesigns 70 5-8Historyofheatfluxtoinsulationinvarioustwo-layerdesigns 70 5-9Historyofheatstoredinthewholeinsulationinthetwo-layerdesigns 71 5-10Historyofhotsidetemperaturesinvarioustwo-layerdesignsduringtheheating phase 72 5-11Effectiveconductivityoffoamasafunctionoftemperaturefordifferentdesigns...73 5-12Maximumstructuretemperaturecontoursforoptimaldesign 76 x