. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Declaration of originality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Intellectual property statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1 Justifying Nuclear Space Power Generation . . . . . . . . . . . . . . . . . . . . 11 1.1 PowerRequirementsforElectricityandPropulsion . . . . . . . . . . . . . . . 11 1.2 StateoftheArtofSpacecraftSolarPowerandThermalSystems . . . . . . . 12 1.3 ComparingNuclearwithSolar . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 PotentialApplicationsofNuclearPowerReactorsinSpace . . . . . . . . . . . 15 1.5 KeyChallenges: Technical,EconomicandPolitical . . . . . . . . . . . . . . . 16 2 Reactor Materials for Nuclear Space Power Reactors . . . . . . . . . . . . . . . 18 2.1 NuclearFuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 FuelCladdingandStructuralMaterials . . . . . . . . . . . . . . . . . . . . . . 20 2.3 ANoteaboutModerators,Reflectors,AbsorbersandRadiatorMaterials . . . 21 3 Heat Engines for Power Conversion in Space . . . . . . . . . . . . . . . . . . . 23 3.1 ChoiceofHeatCyclesandReactorCoolants. . . . . . . . . . . . . . . . . . . 23 3.2 HeXeGasThermalHydraulicsModel . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 SodiumIsothermalThermalHydraulicsModel . . . . . . . . . . . . . . . . . . 33 3.4 SimpleModelsofBraytonandRankineCyclesOperatinginSpace . . . . . . 34 3.5 SummaryofTrendsinPresentedModels . . . . . . . . . . . . . . . . . . . . . 45 4 Selecting Moderators for Nuclear Space Power Reactors . . . . . . . . . . . . 48 4.1 PotentialModeratorMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 ChoiceofSimulationCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3 MethodologyofModeratorNeutronicsAnalysis . . . . . . . . . . . . . . . . . 53 4.4 ParametersforComparingModerators . . . . . . . . . . . . . . . . . . . . . . 55 4.5 ReferenceDataforSimulationModelandLimitationsofStudy . . . . . . . . . 56 5 KinfAnalysis of Moderator Options – Variable UN Fuel Enrichment . . . . . . . 58 5.1 VariableUraniumEnrichmentResults . . . . . . . . . . . . . . . . . . . . . . . 58 5.2 VariableNitrogenEnrichmentResults . . . . . . . . . . . . . . . . . . . . . . . 65 2 5.3 SelectionofOptimumFuelIsotopicComposition . . . . . . . . . . . . . . . . . 69 6 In-DepthAnalysis of Moderator Options . . . . . . . . . . . . . . . . . . . . . . . 71 6.1 Depletionand3DCoreAnalysisfor19.75%EnrichedUNFuel . . . . . . . . 71 6.2 Depletionand3DCoreAnalysisfor14.75%EnrichedUNFuel . . . . . . . . 81 6.3 InterpretationofResultsandTrends . . . . . . . . . . . . . . . . . . . . . . . . 85 7 Synthesis of Results and Lessons Learnt . . . . . . . . . . . . . . . . . . . . . . 87 7.1 MostProbableChoicesforReactorMaterialsandSpecifications . . . . . . . . 87 7.2 InterplayofReactorMaterials,LifetimeandThermodynamics . . . . . . . . . 87 7.3 NuclearSpacePowerSystemDesignWorkflow . . . . . . . . . . . . . . . . . 89 7.4 FurtherWorkandScopeforImprovements . . . . . . . . . . . . . . . . . . . . 89 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 AppendixA: OpenMC Environment Setup and Python Scripts . . . . . . . . . . . 96 Appendix B : Heat Engine Mathematics and GNU Octave Scripts . . . . . . . . . 97 Word count : 16503 3 List of tables 1 ComparisonofHighPowerGenerationSystemsinSpace . . . . . . . . . . . . 15 2 TargetedSpecificationsforNSPSystemPoweredCommunicationsRelay . . . 17 3 ThermophysicalPropertiesofUraniumCeramicFuels . . . . . . . . . . . . . . 19 4 CommerciallyAvailableHigh-TemperatureStructuralAlloysforNSPReactors . 21 5 LimitingMassFluxforPin-in-CellFuelElementwith40g/molHeXeandPure HeliumCoolant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6 HeatCycleAnalysisScriptInputParametersforBraytonandRankineCycle . . 36 7 ThermophysicalPropertiesDataRelevanttoSodiumRankineCycles . . . . . . 40 8 SummaryofRudimentaryBraytonandRankineHeatCycleAnalysisforNSP SystemsinGeostationaryOrbit . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 9 DehydridingTemperaturesofHigh-TemperatureMetalDihydridesat2MPa . . 48 10 High-TemperatureModeratorsforNSPReactors . . . . . . . . . . . . . . . . . 52 11 OpenMCParametricStudyInputParametersandParameterLimits . . . . . . . 54 12 SummaryofPin-in-CellFuelElementModelforParametricSimulationswith OpenMC0.13.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4 List of figures 1 CurrentandFutureApplicationsofSPVandNSPGenerationinSpace . . . . . 13 2 Pin-in-CellFuelElementwithaModeratortoFuelVolumeRatioof5 . . . . . . 25 3 CalculatedHeatTransferCoefficientValuesusingtheSimplifiedTaylorHTC Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4 LimitingLinearPowerCurvesfor40g/molHeXeCooledFuelElement . . . . . 32 5 LimitingLinearPowerCurvesforSodiumVapourisationCooledFuelElement . 33 6 SimpleBraytonHeatEngineCoupledtoaRadiator . . . . . . . . . . . . . . . . 34 7 ReactorInletTemperatureforaSimpleBraytonCycle . . . . . . . . . . . . . . . 36 8 40g/molHeXeMassFlowRatesforaSimpleBraytonCycle . . . . . . . . . . . 37 9 ThermaltoElectricalConversionEfficiencyforaSimpleBraytonCycle . . . . . 38 10 SimpleRankineHeatEngineCoupledtoaRadiator . . . . . . . . . . . . . . . . 41 11 ReactorInletTemperatureforaSimpleSodiumRankineCycle . . . . . . . . . . 43 12 TurbineInletPressureforaSimpleSodiumRankineCycle . . . . . . . . . . . . 43 13 RadiatorAreaforaSimpleSodiumRankineCycleNormalisedtotheBrayton CycleRadiatorArea. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 14 ThermaltoElectricalConversionEfficiencyforaSimpleSodiumRankineCycle 45 15 High-TemperatureChemicalCompatibilityChartforMonolithicandComposite ModeratorMaterialsforNSPReactors . . . . . . . . . . . . . . . . . . . . . . . 49 16 ThermophysicalandMechanicalPropertiesDataAvailabilityofHigh-Temperature ModeratorandMatrixMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 17 BeginningofLifeInfiniteNeutronMultiplicationFactorforPin-in-CellFuelEl- ementwith19.75%EnrichedUNFueland99.5%EnrichedNitrogen(Error BarsnotVisible) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 18 BeginningofLifeOptimumModeratortoFuelVolumeRatioswith19.75%En- richedUNFueland99.5%EnrichedNitrogen . . . . . . . . . . . . . . . . . . . 60 19 BeginningofLifeOptimumModeratortoFuelMassRatioswith19.75%En- richedUNFueland99.5%EnrichedNitrogen . . . . . . . . . . . . . . . . . . . 61 20 PerCentDifferenceofBeginningofLifeInfiniteNeutronMultiplicationFactor Between19.75%and14.75%EnrichedUNFuelwith99.5%EnrichedNitrogen 62 21 PerCentDifferenceofBeginningofLifeOptimumModeratortoFuelRatios Between19.75%and14.75%EnrichedUNFuelwith99.5%EnrichedNitrogen 63 22 PerCentDifferenceofBeginningofLifeInfiniteNeutronMultiplicationFactor Between19.75%and24.75%EnrichedUNFuelwith99.5%EnrichedNitrogen 64 23 PerCentDifferenceofBeginningofLifeOptimumModeratortoFuelRatios Between19.75%and24.75%EnrichedUNFuelwith99.5%EnrichedNitrogen 65 24 PerCentDifferenceofBeginningofLifeInfiniteNeutronMultiplicationFactor for19.75%EnrichedUNFuelBetweenNaturalNitrogenand99.5%Enriched Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5 25 PerCentDifferenceofBeginningofLifeOptimumModeratortoFuelRatios for19.75%EnrichedUNFuelBetweenNaturalNitrogenand99.5%Enriched Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 26 PerCentDifferenceofBeginningofLifeInfiniteNeutronMultiplicationFactor for14.75%EnrichedUNFuelBetweenNaturalNitrogenand99.5%Enriched Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 27 PerCentDifferenceofBeginningofLifeInfiniteNeutronMultiplicationFactor for24.75%EnrichedUNFuelBetweenNaturalNitrogenand99.5%Enriched Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 28 EndofLifeInfiniteNeutronMultiplicationFactorforPin-in-CellFuelElement with19.75%EnrichedUNFueland99.5%EnrichedNitrogen(ErrorBarsnot Visible) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 29 DifferenceinInfiniteNeutronMultiplicationFactorforPin-in-CellFuelElement with19.75%EnrichedUNFueland99.5%EnrichedNitrogen . . . . . . . . . . 73 30 UraniumAtom%BurnupattheEndofLifeforPin-in-CellFuelElementwith 19.75%EnrichedUNFueland99.5%EnrichedNitrogen . . . . . . . . . . . . 74 31 XYSliceofa7-Ringed3DNSPReactorCorewithMFVolumeRatioof3.57 andYH 1.8MonolithicModerator . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 32 3DNSPReactorCoreRadiusversusNumberofFuelElementRingsfor19.75 %EnrichedUNFuelwith99.5%EnrichedNitrogen . . . . . . . . . . . . . . . . 77 33 3DNSPReactorCoreHeightversusNumberofFuelElementRingsfor19.75 %EnrichedUNFuelwith99.5%EnrichedNitrogen . . . . . . . . . . . . . . . . 78 34 Minimum3DNSPReactorCoreMassversusNumberofFuelElementRings for19.75%EnrichedUNFuelwith99.5%EnrichedNitrogen . . . . . . . . . . 79 35 3DNSPReactorCoreK effversusNumberofFuelElementRingsfor19.75% EnrichedUNFuelwith99.5%EnrichedNitrogen(ErrorBarsnotVisible) . . . . 80 36 DifferenceinInfiniteNeutronMultiplicationFactorforPin-in-CellFuelElement with14.75%EnrichedUNFueland99.5%EnrichedNitrogen . . . . . . . . . . 81 37 UraniumAtom%BurnupattheEndofLifeforPin-in-CellFuelElementwith 14.75%EnrichedUNFueland99.5%EnrichedNitrogen . . . . . . . . . . . . 82 38 3DNSPReactorCoreK effDifferenceversusNumberofFuelElementRings Between19.75%and14.75%EnrichedUNFuelwith99.5%EnrichedNitrogen 83 39 DifferenceinMinimum3DNSPReactorCoreMassversusNumberofFuel ElementRingsBetween14.75%and19.75%EnrichedUNFuelwith99.5% EnrichedNitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 40 3DNSPReactorCoreK effDifferenceversusNumberofFuelElementRings for14.75%EnrichedUNFuelwithNaturalNitrogenfromtheReferenceFuel Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6 Abstract This thesis aims to set forth the fundamental differences in the design methodology and systemengineeringofNuclearSpacePower(NSP)reactorandelectricalgenerationsystems versusterrestrialdesigns. WebeginbycomparingNSPwithSolarPhoto-Voltaic(SPV)systemsandtheirevolution inspace,intendingtoidentifyandjustifyurgentandnecessaryapplicationsofNSPgenera- tion. Then, we brieflyreview dataon fuel forms andreactor materials, eliminatingmaterials unsuitable for thermal spectrum reactors. Noting that heavy-duty materials may serve as fuelcladding,wediscussthereactorcosts,mass,longevityandeaseofmanufacture. After that,wedevelopsimplethermalhydraulicsmodelsofaPin-in-Cellfuelelementanddiscuss reactor coolant selection. Introducing our rudimentary heat engine models of the Brayton and Rankine cycles, we derive the mathematics describing the system-wide behaviour of a Brayton and Rankine cycle coupled to a radiator. Our insights from thermodynamic and thermal hydraulic analysis lead to nuclear engineering concepts that assist with building a workingreactor. WedesignparametricsimulationmodelsusingOpenMC’sPythonAPI,pro- viding us with the optimum Moderator to Fuel (MF) volume ratios, MF mass ratios, and 3D reactorcoredataforhigh-temperaturemonolithicandcompositehydridemoderators. Herein,wealsodemonstrateanovelNSPsystemdesignapproachwhereregulatoryjus- tification, logistics and spacecraft thermal design principles are exploited to enforce funda- mental constraints on the NSPsystem design. The NSPsystem design workflow we adopt relies on open-source, easy-to-use and computationally inexpensive software. Ultimately, weaimtoprovideasolidintroductiontothesubtletiesofdesigninganuclearpowersystem tooperateforlongperiodsinspacewhilebeingcompact,lightweightandrelativelyinexpen- sive. 7 Declaration of originality Iherebyconfirmthatthisdissertationismyownoriginalworkunlessreferencedclearlyto thecontrary,andthatnoportionoftheworkreferredtointhedissertationhasbeensub- mittedinsupportofanapplicationforanotherdegreeorqualificationofthisoranyother universityorotherinstituteoflearning. 8 Intellectual property statement iTheauthorofthisthesis(includinganyappendicesand/orschedulestothisthesis) ownscertaincopyrightorrelatedrightsinit(the“Copyright”)ands/hehasgivenThe UniversityofManchestercertainrightstousesuchCopyright,includingforadminis- trativepurposes. iiCopiesofthisthesis,eitherinfullorinextractsandwhetherinhardorelectroniccopy, maybemade onlyinaccordancewiththeCopyright,DesignsandPatentsAct1988 (asamended)andregulationsissuedunderitor,whereappropriate,inaccordance withlicensingagreementswhichtheUniversityhasfromtimetotime. Thispagemust formpartofanysuchcopiesmade. iiiTheownershipofcertainCopyright,patents,designs,trademarksandotherintellec- tualproperty(the“IntellectualProperty”)andanyreproductionsofcopyrightworksin thethesis,forexamplegraphsandtables(“Reproductions”),whichmaybedescribed inthisthesis,maynotbeownedbytheauthorandmaybeownedbythirdparties. SuchIntellectualPropertyandReproductionscannotandmustnotbemadeavailable forusewithoutthepriorwrittenpermissionoftheowner(s)oftherelevantIntellectual Propertyand/orReproductions. ivFurtherinformationontheconditionsunderwhichdisclosure,publicationandcom- mercialisationofthisthesis,theCopyrightandanyIntellectualPropertyand/orRe- productionsdescribedinitmaytakeplaceisavailableintheUniversityIPPolicy(see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=24420 ),inanyrelevant DissertationrestrictiondeclarationsdepositedintheUniversityLibrary,andTheUni- versityLibrary’sregulations(see http://www.library.manchester.ac.uk/about/ regulations/_files/Library-regulations.pdf ). 9 Acknowledgements The niche nature of this topic meant that I required specific guidance on a vast array of unrelated technological and scientific fields. I am very grateful to DrAiden Peakman for proposingandsupportingthisprojectandindulgingmycuriosityonthemanytopicscovered inthiswork. Iuse‘we’inthisthesistoacknowledgethatthisisourwork. Several lengthy discussions with Abhishek Avadhanam have contributed to this thesis. His background in spacecraft design and thermal management, as well as his experience workingintheaerospaceindustry,hasshapedmuchofthecontextofthediscussioninthis thesis. Hehasmysinceregratitude. IamindebtedtoNickSeibt,whotookthetimetoproofthisthesisandprovideamassive amount of feedback, which has undoubtedly improved my work to the point you see in this document. ThisworkwouldnothavebeenpossiblewithouttheassistancegivenbyResearchITand theuseoftheComputationalSharedFacility(CSF)3attheUniversityofManchester. Lastly, I would also like to thank DanielAbraham, Ty Frank and Naren Shanker for their artisticandliterarywork,whichinspiredmetoundertakethisjourneythathasculminatedin thisdegree. 10 1Justifying Nuclear Space Power Generation Before we begin discussing and analysing what a Nuclear Space Power (NSP) system should be and how it should function, it is instructive to look outside the field of nuclear engineering and peer into the competition. There is little debate in the literature that high electricalpowergenerationinspaceisthedomainoftwotechnologies: SolarPhoto-Voltaics (SPV) and nuclear fission reactors [1]. Currently, SPV dominates the market, and there is a growing push in the aerospace community to phase out radioisotope thermal generators (RTG)[2]. TheJunomissiontotheJoviansystemutilisedsolarpanelsasaproof-of-concept todeliver400We(wattelectric)[2]. FuturemissionstoJupiter,suchasthe2024EuropaClip- per, continue that trend, marking an end of nuclear-powered platforms to explore the outer solarsystem. Shortagesof238-Puandregulatoryhurdleshaveledtomissioncancellations whereRTGsweremissioncritical[3]. NSPsystemsfortheArtemisprogramhavebeenqualifiedforflight,thoughnotlaunched [4]. They are sub-10 KWe Sterling cycle fast reactors and are meant to be lightweight and deployedintoa10-unitredundantnetworktopowertheplannedlunaroutpostneartheLunar South Pole [4]. So far, space platforms have required sub-KWe power levels, which SPV systemsprovideefficiently,evenwhileoperatinginJupiterorSaturnorbit[2]. Atthesepower levels, NSP systems are impractical. The International Space Station (ISS) has the most extensive SPV system built in space, generating 117 KWe. Life support systems, battery arrays, and computing and communications infrastructure [5] consume most of this power. If one assumes that the ISS is the limit of SPV systems engineering, NSP systems should deliver more than 100 KWe to be competitive. However, we can refine that estimate by consideringthepower-intensivesubsystemsusedinspaceplatforms. Inthecomingchapter, we briefly review the factors that inform power system design in space, namely, the power- consuming subsystems, the SPV power generation technology and the expectations of the aerospacecommunity. Afterthisreview,weselectandjustifyanichewhereNSPsystemsfit and conclude with a set of challenges which need to be accounted for when designing any NSPsystem. 1.1Power Requirements for Electricity and Propulsion The International Space Station (ISS) generates a maximum of 117 KWe [5]. Astronauts utilisethiselectricalgenerationtosurviveandconductscientificstudies. AnequivalentNSP systemwouldpresentaradiationhazardtoastronautsunlessitusesheavyradiationshield- ing. Generally, an NSPsystem designed for servicing crewed missions shall face stringent radiationshieldingrequirements. ThissituationincludessystemsdesignedforLunarorMar- tiancolonies. Giventhosedisadvantagesandrisksoflocalsitecontaminationincaseofan accident,thereisnoclearconsensusrulingoutSPVsystemswithlightweightlithiumbatter- 11 iesinexchangeforamasspenalty[1]. On the other hand, high-power orbital systems which operate autonomously stand to benefitfromNSPsystems. Intheabsenceofhumans,spacecraftpowerconsumptioncom- prises communications systems, thermal management and, more recently, electric propul- sion systems. Electric propulsion systems would represent a significant power-consuming subsysteminthefuture. [6]performsadetailedanalysisofelectricpropulsionthrusterswhile considering power, system mass and system redundancy requirements. In the near future, low-power thruster subunits of 5 to 8 kilowatt electric (KWe) assembled in groups of 4 or 5 would result in a single fault-tolerant propulsion system consuming less than 50 KWe [6]. These power and redundancy specifications are meant for uncrewed spacecraft capable of cargo hauling or deep space exploration. Crewed missions require double redundancy, pushingupcostsandmass. [6]presenteda400KWesystemwith13to18KWesubunitsfor crewed deep space exploration. NSP reactors are uniquely suited to such missions due to theirlongdurationandresistancetoenvironmentaldamageduetospacedebrisorambient radiation. Considering the ISS, the Artemis colony and future electrically powered and propelled spacecraft, there seems to be a demand for 100 KWe class power generation systems for theforeseeablefuture. 1.2State of theArt of Spacecraft Solar Power and Thermal Systems SolarPhotoVoltaic(SPV)panelshavebeenusedinspacecraftsincethedawnofthesemi- conductor age in the late 1960s. They are lightweight, affordable, and commercially avail- able, and advances in semiconductor science have enabled them to grow more efficient at producing electricity. Currently, spacecraft utilise multi-junction silicon SPV panels [2] with a typical conversion efficiency of 33 %. A100 KWe system would only weigh 2000 Kg [2]. Advancesintechnologywouldincreaseefficienciesto36%andreducea100KWesystem’s massto500Kginthenearterm. Thesespecificationshavepromptedmissiondesignersto favour SPV systems even for deep space missions where the solar intensity approaches 4 %ofthevalueinEarthorbit[2]. Further,SPVsystemsdonotintrinsicallygeneratewasteheatandhavenomovingparts, reducingcomponent-levelfailures. TheaerospacecommunitystronglyprefersSPVsystems because of those characteristics. Figure 1 shows a recent SPV development roadmap re- leased by NASA. Note that NSP systems for scientific missions are not considered. Only missionstotheouterplanetsbeyondSaturnareslatedtorequireanRTG.Figure1provides contexttotheNSPsystemdesignerofSPVsystems’impressiveandgrowingcapabilities. 12 Fig. 1.CurrentandFutureApplicationsofSPVandNSPGenerationinSpace[7] 13 However,anSPVarraytogenerate100KWewouldhavesomeissueswithdeployment and space debris impacts due to its large surface area [8]. Further, SPV systems require a powerstoragesystemonboardtoprovidecontinuouspower[1]. Unexpectedly,sunlightand illumination are not SPV systems’ only environmental hurdles. Every celestial body in the solar system has a unique chemical and plasmonic environment in its orbit, and spacecraft utilising SPV panels must ensure that radiation damage, plasma sputtering and corrosion, andextremeoperationaltemperaturedonotrenderthemunusable[2]. Therefore,itseems thatthecostofdevelopingcustomSPVtechnologieswouldnotbereasonableonceinterplan- etary traffic density exceeds its current limit of 2 spacecraft per decade. NSP systems are independentoftheenvironment,enablingthemtobemodularisedandfittedintoanyspace- craftregardlessofdestination,enablingacargospacecrafttohaulgoodstotheMoon,Mars or Jupiter and survive in their varied space environments. Radioisotope thermal generator designssuccessfullyexploitthatopportunity. However,NSPdesignsinthepasthavetaken adifferentapproach,designingaspacecraftaroundthereactorconceptandthenassigning missionstoit,forfeitingthemodularityadvantage. Additionally,thereislittleknowledgeofrejectinglargeheatloadsathightemperaturesin space. The state-of-the-art thermal management is geostationary communication satellites that reject around 12 KW of thermal energy (KWth) at around 400 K [9]. Dynamic heat pump systems with single and two-phase coolant have recently been considered but have notyetseendeployment[9]. Thisstate-of-the-artisincompatiblewitha100KWeclassNSP system. Past NSP systems servicing spacecraft have required vast 100 m2class radiator arrays to reject the waste heat [10]. These radiators face similar environmental damage comparedtoSPVpanels. TodesignanNSPsystemthatplaystothetechnology’sstrengths, radiatormass,cost,andareashouldbelessthantheequivalentSPVsystem’spanels. While spacecraft thermal engineers are familiar with heat pipe radiators [11], few studies survey their cost and mass in relation to an equivalent SPV array. Furthermore, there is very little work on radiator materials and alloys used for rejecting heat at high temperatures, which hinders the development of practical NSP systems that provide a reasonable alternative to SPVsystems. 1.3Comparing Nuclear with Solar Table 1 summarises the discussion so far. SPV systems have a range of advantages and are already mature technology. They are well suited to the sub-KWe spacecraft currently being designed and developed. One can also see that there is no sense of urgency in the market;forexample,ifascientificmissiontoNeptuneisonlypossiblewithanNSPsystem,it islikelytobescrappedasscientificmissionsareneitherurgentnornecessary. However,the situation is due to change with the introduction of crewed colonies on the Moon and Mars. NSPsystems that outperform equivalent SPV systems intended to service human colonies 14 Table 1.ComparisonofHighPowerGenerationSystemsinSpace Nuclear Solar Nascent Mature Unknownscopeforfundamentaltechnologydevelopment Amplescopeforsolarcellimprovement Requiresdenseandexpensivematerials Siliconislightandinexpensive Volumetricallycompact Largepanelarraysarecommon Independentofspaceenvironmentandmodular Sensitivetoambientradiation,plasma,debrisandtemperature Requiresheatrejection Radiatorfree Ultra-longlife Panelsdegradeyearonyear shall be developed to maturity once astronauts rely on them for survival. Fortunately, as theISSshows[5],crewedspacecraftrequire100KWeclasspowergeneration,whereSPV systems struggle without constant maintenance. SPV panels are also vulnerable to space debrisanddust[8],makingtheLunarsurface[2]achallengingenvironmentwithouthuman maintenance. One can see a clear trend. NSP systems that require minimal maintenance andareautonomouscancompetewithSPVsystemsinthe100KWeclassrange. After discussing the state-of-the-art, it seems clear that NSP system designs should be compactandlightweight. AnequivalentSPVsystemdesignshouldbereferredtowhenever possible during design so that radiator masses and sizes are kept in check. Finally, NSP systems should press their advantage of modularity and robustness, anticipating operation inadiverserangeofspaceenvironmentsthatnosingleSPVpaneldesigncanmanage[2]. The designer can maximise this advantage by developing a design workflow which creates anNSPreactordesignstartingfromagivenspacecraftdesignandapresetmission. Finally,thedesignermustconsiderthelogisticsandregulationsoftransportingthereac- tor core to the launch site and space as they are non-trivial [12]. Here, we suggest that the reactor core radius is less than 60 cm so that the core can be transported inside spent fuel casks used for terrestrial PWR plant radioactive waste storage [13]. The mass of the NSP system should be well below 8000 Kg, the typical payload limit of modern heavy-lift rock- ets [14]. The situation where an equivalent SPV system would have foregone the multiple launches,on-orbitassemblyandspecialisedtransporttothelaunchsiterequiredbyanNSP systemshouldnotarise. 1.4PotentialApplications of Nuclear Power Reactors in Space Thefinalstepinjustifyingnuclearpowerreactorsinspaceconcernsthequestionofurgency and necessity. Public perception against nuclear reactors does not spare those designs that would never be operated on Earth [15]. The expansive costs of nuclear hardware and 15 radiation safety issues make it challenging to justify NSP systems, especially for crewed missions,wheretheirpowergenerationcapabilitiesaremosthelpful. Privatecommunication withexpertsintheaerospacecommunityhasledtothefollowingpossibleapplicationsofNSP systemsthatareadequatelyjustified. Nuclear communications infrastructure in deep space is not a novel concept [16]. How- ever,uptothispoint,ithasfailedtopassthelitmustestofurgencyandnecessity. Ifsizeable colonies are established on the Moon or Mars in the coming decades, they would require high bandwidth communications to support astronauts’ basic quality of life. Thus, space- craft in geostationary orbit fitted with NSP generation capable of terabit scale transmission would support essential operations on off-planet colonies. The cost of establishing a high- bandwidthdeepspacenetworkandtherequirednetworkreliabilityjustifiesnucleardatare- laysdesignedtooperatecontinuouslyandautonomouslyforatleast10years. Thereisalso interest in developing high-powered electric propulsion systems for space tugs for cargo hauling[17]. Again,thisinfrastructureisonlyhelpfulifcoloniesrequiringreliableandfastin- terplanetarytransportofgoodsareestablished. NSPsystemsaresuitedtothisworkasthey canoperateindependentlyofthespaceenvironmentandproducetherequiredpowerlevels forredundantelectricpropulsionsystems[6]. Itseemsthatwhilenecessary,thisapplication is not urgent. Other concepts may deserve study to understand if they are necessary and urgent. Given that nuclear data relays seem to be the most urgent and necessary application of NSPsystems, we can complete a set of specifications typical of a geostationary data relay satellitedesignedtoprovidehigh-speedinternettocoloniesontheMoonorMars[18]. Note thatthestate-of-the-arttelecomsatelliteingeostationaryorbitoperatesatthe10KWeclass [9]. An NSP system would be economical if the satellite could utilise 100 KWe of constant electrical output. Here, we assume the planar radiators are non-deployable and mounted on the four lateral faces of a cuboidal geostationary satellite bus [18]. Table 2 provides the specifications used throughout the remaining chapters to illustrate the applications of the data and insight presented to a practical problem. The mass and size of the reactor are definedsomewhatarbitrarilytostaywithinthelimitsofcurrentheavyliftlaunchvehicles[14] andtheoptimumgeostationaryorbitsatellitebus[18]. 1.5Key Challenges: Technical, Economic and Political ThisintroductiontoourworkintendedtocompareandcontrastNSPsystemswiththeirSPV counterpartstofindanicheofapplicationswherethedeploymentofNSPsystemswasade- quatelyjustified. Thereviewconcludedthat100KWeclasspowergenerationsystemsarein currentdemand. Further,NSPsystemsarewellsuitedtouncrewedmissionsrequiringlong- term,autonomousoperationinvariousspaceenvironments. Weidentifiedvarioustechnical challenges: 16 Table 2.TargetedSpecificationsforNSPSystemPoweredCommunicationsRelay NSP System Parameter Target Specification RadiatorHeight 3.5m RadiatorWidth 1.5m NumberofRadiators 2 NumberofRedundantRadiators 2 SystemLifetime 10years PowerOutput 100KWe MaximumReactorCoreMass 2500Kg MaximumReactorCoreRadius 0.6m •Hardlimitof8000KgontheNSPsystemmass •Softlimitof60cmontheNSPreactorcoreradius •Lack of adequate knowledge and testing of high heat rejection systems operating at hightemperature In addition to those constraints, we selected nuclear data relay telecom satellites as a po- tentiallyurgentandnecessaryapplicationofNSPsystems. Weusedthatpremisetosetup target specifications for the NSP system, chiefly the available radiator area on the satellite busandthespacecraft’slifetime. Unlike SPV systems, NSPsystems carry significant economic and political implications. From a technical perspective, the 100 KWe class is the minimum where NSP systems be- gintocompetewithSPVsystems. However,adetailedmass-costanalysisandconsistently improving solar cell technology may push that higher. NASAhas published [12] extensive nuclear reactor design and operational guidelines to ensure compliance with safety regula- tionsthatwerecommendNSPsystemdesignersstudy. Thereisalegislativeandregulatory vacuumconcerningnuclearreactorsinspace,anditisdifficulttopredicthowthelegalframe- work would evolve in the coming decades. Similarly, the economics of NSPsystems are in fluxduetothispowergenerationoption’shighuncertaintyandlowtechnicalmaturity. Inthe end, however, there is no debate that humanity shall come to rely on nuclear technology to spreadacrossthesolarsystemwhilepreservingaconnectionwithEarthandahighquality oflife. 17 2Reactor Materials for Nuclear Space Power Reactors In this chapter, we take our first steps toward designing an NSPreactor. Chapter 1 pre- sented justification for deploying NSPsystems for nuclear data relays and practical consid- erationsthathadledtoconstraintsonreactorpoweroutput,lifetimeandsize. Therefore,we nowknowwhattheNSPsystemmustdoandwhatsortofmissionitmustsupport. Thischap- ter briefly reviews materials a designer could use to build a reactor. For a thorough review, thereaderisdirectedto[19]and[20]. Thisexercisewouldcreateanothersetofperformance constraints: materialtemperaturelimits,availabilityandcosts. Thereviewmustalsoaccount forthethermalneutronabsorptioncharacteristicsoftheselectedmaterials. Thisworkassumesathermalneutronspectrumforthecomingdiscussion,asneutronab- sorptionismostsubstantialinthethermalandepi-thermalneutronenergyrange. Simultane- ously,reactordesignersshouldnotethatharderneutronspectrumswouldrequirematerials moreresistanttoradiationdamage, whichwedonotconsiderfurtherinthisthesis. Initially, welookedthroughtheIAEAThermophysicalPropertiesofMaterialsforNuclearEngineering handbook[21]andNSPsystemsliterature[20]tocreateatentativelistofmaterials. Thislist included nuclear fuel, fuel cladding and general structural materials. There is a significant overlap between the fuel cladding materials and the general structural materials. As noted before,thereisverysparseknowledgeofhigh-temperatureradiatormaterials. However,[22] providesastartingpoint. Once we compiled the preliminary list of materials, the study moved to investigate ba- sic materials compatibility in the expected operational environment. Operating pressures of gas-cooled NSP systems in the literature are around 2 MPa [23], but temperatures vary widelybetweenparticulardesigns. Weassumedthatamaximumtemperatureof2000Kwas conservative. Giventhisreferenceoperationalenvironment, onecanusechemicalthermo- dynamicequilibriumsoftwaretopredictifachemicalreactionbetweentwomaterialsisther- modynamically favourable. This method has significant drawbacks, chiefly that it does not considerchemicalkineticsandreactionrates. Giventhescopeofthisthesis,detailedchem- ical kinetics simulations or experimental characterisation was not possible. Therefore, we usedthefreelyavailableonlinesoftwareFact-Web[24]tocreatearoughpictureofmaterials compatibilityat2MPaand2000K.Interactionsofinterestincludedthefuel-cladinteraction, clad-coolant interaction and the fuel-moderator interaction; only the first two are presented here. 2.1Nuclear Fuel The IAEAhandbook [21] provides a rich set of properties data to compare and contrast nu- clearfuelmaterials. Italsoeliminatesnovelfuelformsthatarelessstudiedfromconsidera- tion in this thesis as we did not perform a further literature study on novel fuel forms with a 18 Table 3.ThermophysicalPropertiesofUraniumCeramicFuels Property UN UCUO2 TotalDensityat273K(Kg/m3) 144201363010963 UraniumDensityat273K(Kg/m3)13619129709664 MeltingPoint(K) 312327933120 ThermalConductivityat2000K(W/mK) 27.2022.762.24 HeatCapacityat2000K(J/KgK) 305297542 lowerprobabilityofnear-termapplication. Table3summarisesthedatapresentedin[21]on UO2,UC,andUN. At a glance, we can see that UN and UO 2stand out. UO 2is well-studied, with decades ofcommercialexperienceandhasahighmeltingpoint[19]. However,ithastwosignificant drawbacks. One,ithasathermalconductivityequaltoatenthoftheotherfuelformsat2000 K.Next,UO 2incorporatesalesseramountofuraniumpercubicmeterthanitscounterparts. Its high melting point and higher heat capacity partially ameliorate the first disadvantage. However,therearenosolutionstothelowuraniumdensity,whichleadstoagreaterreactor mass. NSPreactordesignersmaystillconsiderUO 2fornuclearfuelbecauseitiscommer- ciallyavailableandhasavastapplicationlegacy. Comparing UN and UC, UC seems like a weaker contender. A review of UC thermo- physicalpropertiesstatesthatitishardertomanufactureandoffersfeweradvantagesover UO2than UN [25]. While UO 2does not interact with most materials at 2 MPa and 2000 K, UC has been known to carburise cladding materials, leading to cladding embrittlement failures [26]. Fact-Web calculations show that UC decomposes to molten U carbonising ti- tanium, chromium, zirconium, and niobium, common elements of nuclear reactor structural alloys. [25] also talks about the variable stoichiometry of UC and the difficulty of obtaining pure UC in a given sample. This chemical behaviour means UC is also unstable in contact with graphite, a common nuclear material. For these reasons, UC is less studied for future terrestrial reactor systems and past NSP systems. We conclude that UC is not a practical fuelformforNSPreactorscomparedtoUN. Past NSPconcepts, such as the SP-100 [27], have worked with UO 2and UN.The find- ings presented here reinforce those fuel form choices, and there is a strong consensus in the literature which prefers UN fuel. However, engineering materials decisions are rarely straightforward. UN is an excellent fuel form, but our Fact-Web calculations showed that it is unstable when in contact with zirconium and titanium, vital components of high-strength structural alloys. Metal nitriding is a surface process, and nitride moieties are not as mo- 19 bileascarboninalloys. Theimmobilityofnitridemeansembrittlementislessprobablewith UNthanwithUC[26]. Long-termtestingforNASA’sSP-100nuclearelectricpropulsionpro- gramrevealedthatrefractorymetalssuchasniobium,tungstenandrheniumarecompatible with UN [27]. Fact-Web calculations suggest standard steels are also compatible, which is supportedbytheliterature[26]. However, UN brings its own set of engineering problems. At higher temperatures, UN tendstodecomposeintoliquiduraniumandnitrogenifanappropriatelevelofnitrogenpartial pressure is not present [21]. This behaviour puts additional stress on the fuel cladding as it must contain gaseous fission products and nitrogen under pressure. The high melting point of UN is also somewhat misleading. When irradiated in a reactor, UN pellets undergo extensive swelling at temperatures above 1600 K, limiting nominal operational temperature compared to UO 2[28]. Finally, there is substantial debate in the literature concerning the thermal neutron absorption of natural nitrogen, which produces long-lived radioactive 14-C in situ [29]. The neutronic impact of natural nitrogen compared with enriched nitrogen is well known but not well studied quantitatively. The economic case for nitrogen enrichment is unclear, with no consistent supply nor demand, and so far, all UN fuel testing campaigns have considered only natural nitrogen [19]. In later chapters of this thesis, we shall further investigatetheeffectsofnitrogenenrichmentinUNfuel. 2.2Fuel Cladding and Structural Materials Thenuclearfuelcladdingisstructuralinnature. Itholdsvolatilefissionproductsunderpres- sure and supports the fuel pellet stack. Further, the coolant subjects the fuel cladding to corrosion under extreme irradiation. It is reasonable to assume that if a structural mate- rial can fulfil the role of cladding the nuclear fuel pellets, it would be adequate elsewhere. Widespreaduseofsuchheavy-dutymaterialsintheNSPsystemwouldincreasecostsand mass, leaving the door open to design optimisation, a process unique to each NSP sys- tem’sdesign. Thissectionexploresheavy-dutyalloyscompatiblewithcommonNSPsystem coolantsandfuelforms. Structural alloys are generally divided into alloy steels and refractory alloys [21]. The IAEAhandbook provides many thermophysical properties data on pearlitic, martensitic and austeniticsteelsbutnotesthattheirmaximumoperatingtemperatureisaround1073K[21]. TheSP-100programusedrheniumandNb-1ZralloystolinetheUNfuelpellets[27]. Some designers have also considered Mo-14Re [20]. One can see that there is no strong prefer- enceorconsensusintheliteratureonwhichmaterialsarebestsuitedtoNSPsystems. Fact-Web calculations show that standard steels and high-temperature heavy metals, also known as refractory alloys, are primarily compatible with UN and UO 2. NSP systems designersmaynotselectrefractoryalloysoversteelsbecausetheyaredenserandheavier. 20 Table 4.CommerciallyAvailableHigh-TemperatureStructuralAlloysforNSPReactors Property MA956 ODS Mo-TZM Densityat298K(Kg/m3) 7250 10160 MeltingPoint(K) 1755 2896 ThermalNeutronAbsorption(b) 2.56 2.48 AllowableStressat1400K(MPa) 15 50 AllowableStressat1600K(MPa) - 25 However,refractoryalloystypicallyalsohavehigherultimateandtensileyieldstrengths[20], allowing components to reduce alloy usage. Another issue with refractory alloys contain- ing tungsten, tantalum, hafnium or rhenium is that heavy metals absorb thermal neutrons effectively,whichisnotaproblemwithsteels. Theseinterdependentconsiderationscompli- catestructuralmaterialselection. Therefore,weeliminatedcladdingandstructuralmaterials using a combination of neutronics and availability criteria. Table 4 illustrates commercially mass-produced structural alloys which can operate beyond 1100 K, weakly absorb thermal neutronsandbehavewellincontactwithsodiumorhelium-basedreactorcoolants[20]. Table 4 does not contain some common materials encountered in the NSP systems lit- erature [20]. We excluded hafnium, rhenium, tantalum and tungsten containing alloys be- cause they strongly absorb thermal neutrons [30]. Further, Nb alloys fail to operate beyond 1100 K, while oxide dispersion strengthened (ODS) steels can operate at 1400 K [20]. Of theremainingalloychoices,searchingforvendorsyieldedonlysellersforMA956ODSand Mo-TZMalloys,indicatingthattheotheralloysarenotasreadilyavailableontheopencom- mercial market. Although our demanding elimination criteria have eliminated most of the materials under consideration, they have also illustrated the legacy NSPsystem designer’s dependence on speciality, non-commercial alloys, contributing to the costs and technical risksassociatedwithdevelopingandtestinganNSPsystem. 2.3ANote about Moderators, Reflectors,Absorbers and Radiator Materials As we wrap up this brief review of reactor materials, let us discuss the other materials in a nuclearreactorcore. Sofar,wearetargetingathermalneutronspectrumintheNSPreactor core. Therefore,neutronmoderatormaterials,whichreducethekineticenergyoffissionneu- trons, areintegral to thereactor design. Ourframework for eliminatingmaterials eliminated nearly all moderator materials currently used in the nuclear industry [21]. Pressurised wa- ter systems cannot operate beyond 1100 K without extremely bulky plumbing, and graphite has poor neutron stopping power, resulting in large reactor core volumes [21]. Moderating 21 materials which survive high temperatures and have a high neutron stopping power have onlyrecentlybeensubjectedtostudy[31]. Theconceptofcompositemoderatorsisalsoun- der study for terrestrial nuclear microreactors [32]. For these reasons, we shall investigate moderatorsintheirowndedicatedchapterslater. BerylliumandBeOhaveahistoryofpreferencebythenuclearengineeringcommunityfor fabricatingneutronreflectors. Berylliumanditsalloyshavepoorirradiationresistancedueto heliumbubbleformationandsufferfromlowoperationaltemperaturesandlowductility[33]. Hence, beryllium alloys are not suited to NSPsystems. However, BeO has the appropriate propertiesforareflector. TheNSPreactordesignerislefttodecideiftheyrequireareflector fortheirdesignandwhichmaterialtheyuse. Wedonothaveanygenericrecommendations, aseveryspecificdesignwouldhaveitsowntradeoffs. Forsimilarreasons, thisthesisdoes notcoverreactorcontrolsystemabsorberssuchasboroncarbideorHfalloy. Finally, there is the issue of turbomachinery and radiator materials. As noted in Chapter 1 and this chapter, there has been little study in this area. Generally, NSPsystem turbines, compressors and radiators can also use reactor cladding and structural alloys selected for NSPfuelcladding. Radiatorswouldbesubjectedtoawiderangeofspaceenvironments,and more study is required to determine if reactor structural alloys could survive the plasmonic environmentsaroundvariouscelestialbodies. Again,weleavetheNSPreactordesignerto decide if more common and less heavy-duty materials such as SS 316, Ti 4Al1V or others suittheirdesignandsaveoncosts. In the next chapter, we take a final detour before heading into NSP reactor engineering todiscussheatengines, operationalthermallimits, andheatrejectioninspace. Ourreview of reactor materials has left us with a list of potential materials and their operational limits. Thecomingchaptershallfurtherrefineourmaterialchoicesand,intheprocess,provideus withourfirstrealinsightintoNSPsystemsengineeringasadiscipline. 22 3Heat Engines for Power Conversion in Space In this chapter, we get on to thermal engineering. Chapters 1 and 2 covered what the basicNSPsystemspecificationsmightbeandwhatmaterialscouldbeusedforthedesign. Here,wecombinethatknowledgewiththefundamentalthermalandthermalhydraulicscon- ceptstoobtainaclear,high-levelpictureofNSPsystems. Westudythepossibleoptionsfor converting and rejecting large heat loads into space given the constraints of the spacecraft anditsmission. ThischapterprovidesthefirstvaluableinsightsintoNSPsystemsengineer- ing as a standalone discipline as we cover how one can design a simple, redundant and robustNSPsystem. Asareminder,weselectedthenucleardatacommunicationrelayasapotentiallyurgent and necessary application of NSP systems. We determined that a 100 KWe class system would fit the application. The mission determined the optimum size of the spacecraft bus [18]andtheareaavailabletomountstaticradiators. Weassumespaceisavailablefortwo planarhigh-temperatureradiatorsonthelateralsidesofthecuboidalspacecraftbus. There- mainingtwosidesfeaturebackupradiatorsforsingle-faultredundancyexpectedofuncrewed missions [6]. Surprisingly, this level of information is enough to analyse and compare heat enginesfortheNSPsystem. 3.1Choice of Heat Cycles and Reactor Coolants [19]and[34]reviewandcomparepowerconversionsystemsforhighpowergenerationsys- temsinalevelofdetailnotpossiblehere. Insummary,BraytonandRankinecyclesofferan efficientandscalablemeanstoconvertthermalpowertoelectricity. Othersystems,suchas direct thermoelectric conversion or the Sterling cycle, work well for 10 KWe class systems butfailtoscalefurther[34]. Directthermoelectricconversionisinefficient,andhigherpower systemsultimatelyrejectavastamountoftheheattheyproduce,requiringlargerradiators. Sterling cycles, preferred by the aerospace community for reliability and efficiency, fail to handlehighpowerflowratesduetoalackofflowingcoolant,ultimatelyrelyingonheatpipes tofunction[34]. Legacy NSP systems strongly prefer gas-cooled reactors deployed with a Brayton Cy- cle [23]. Advantages include mass savings, decoupling of reactor neutronics from thermal hydraulics and extensive aerospace engineering heritage with gas turbines and centrifugal compressors. Morefundamentally,though,Braytoncyclesseemill-suitedtothespaceenvi- ronment. LegacyNSPdesignsrarelyconsideredredundancyanddidnotconsiderthehard 8000 Kg mass limit in this work. Without heat pipe radiators, the gas coolant makes ineffi- cientuseoftheradiatorareaasitstemperaturereduceswhileitpassesthrough. Interrestrial settings,heatrejectionisalinearfunctionoftemperature,butheatrejectionisproportionalto thefourthpoweroftemperatureinspace. Furthermore,thegascoolanthasanappreciable 23 temperaturegradientfromthebulkofthefluidtotheradiatortubewall, furtherreducingthe overall radiator temperature. With its isothermal heat injection and rejection, the Rankine cycleisidealformaximisingspaceradiatorutilisationandminimisingtemperaturegradients inthereactorcoreandradiatortubing[35]. Adetailed analysis of heat cycles, including complex systems with recuperators and re- generation,ispublishedforsolarconcentratorpowersystemsinspace[35]. However,they do not use working fluids or temperatures appropriate to nuclear systems. [35] concludes thattheRankinecyclepossessesthebestthermalefficiency,followedbytheBraytonandthe Sterling cycle. However, choosing cryogenic fluids for the working fluid leads to extremely lowheatrejectiontemperaturesandimpracticallylargeradiatorareas[35]. Surprisingly,NSP systems designers rarely approach thermal management first and then design the reactor basedonthelimitationsoftheheatcycleemployedandtheavailableradiatorsurfacearea. In any case, we demonstrate the utility of the thermal first approach in this chapter with two heat cycles: a Brayton cycle with HeXe gas coolant and a Rankine cycle with sodium coolant. ThereisaconsensusintheliteratureonNSPsystemsthatusetheBraytoncyclethat dopingheliumgaswithxenonisrequiredtoreduceaerodynamicstressesontheturbineand compressor blades. The reduced stresses lead to more compact turbomachinery, which is alsolightweight[23]. Inthecomingsections,weshallinvestigatetheeffectsofxenondoping infurtherdetail. ARankinecyclewithsodiumcoolantisalsoconsideredasanalternativeto theBraytoncycle. NASAhasstudiedlegacypotassiumRankinecycles[35][19]becauseof their reduced turbine blade corrosion tendency. However, modern spacecraft thermal man- agement systems extensively use looped heat pipes for rejecting high heat loads [11], and more recently, NSP systems deploy sodium heat pipes [4]. Ultimately, we selected sodium coolantsincesodium’sthermophysicalproperties[36]andstructuralmaterialinteraction[37] aremuchmorestudiedthanpotassium’sintheaerospaceandnuclearcommunities. Looped heatpipe-likesystemsavoidissuessurroundingtwo-phaseflowandboilinginnullgentirely [11],enablingaboiling-freeRankinecyclewithanannularflowregimeinthecondensercum radiator. 24 Fig. 2.Pin-in-CellFuelElementwithaModeratortoFuelVolumeRatioof5. Theblue regionisthemoderator,theblackregionisthecoolantgas,andthefuelpelletissectioned intothreeequalvolumeregionsofdifferentcoloursinthecentre. Thefuelcladdingisnot visibleonthisscale. Thisfigureistoscalewitheachedgeequalto15cm. Now that the choice of coolants for the heat cycles is clear, we can perform a simple hot-channelthermalhydraulicsanalysisforheattransferinthereactorcore. Theseanalyses wouldprovideamathematicalframeworktoconstrainthemaximumlinearpowerofthefuel pinintheNSPreactorcore. Foraperformancecomparison,weuseanexperimentallytested fuelpinconcept[38],a15.8mmdiameterUNfuelpelletcapableofsupporting275W/cm. As NSPsystemdesignersatNASA[4]recommended,weuseasimple-to-analysefuelelement designthatisalsofunctional. Figure2showsthepin-in-celldesignconsideredinthisthesis. WebelievethattheinsightsfromourworkshouldremainlargelyvalideveniftheNSPreactor designerisconsideringmorecomplexfuelelementgeometry. Themodelisinfiniteintheaxial 25 direction. It assumes the moderator hexagonal block surrounding the fuel pin is isothermal withthecoolantflowinginthechannel. Thisassumptionignoresthepowergeneratedinthe moderatorwhenitslowsdownfissionneutrons,whichisaround1to3%ofthetotalreactor thermal power for thermal spectrum reactors [39]. Lastly, the fuel pellet cladding is 0.5 mm thickMA956ODSsteel. 3.2HeXe Gas Thermal Hydraulics Model ThepropertiesofHeXegascoolantareafunctionoftheequivalentmolarmassofthecoolant [23]. Arecent review [40] compares HeXe with pure helium regarding its heat transfer co- efficient (HTC) in similar operating conditions. That work and others in the past [23] define ‘similaroperatingconditions’asequalflowtemperature,flowareaandmolarflowrate. This definition is unusual because nuclear engineers consider mass flow rates in their designs. WecreatedasetofGNUOctave8.3.0scriptstocalculatethetransportpropertiesofHeXe asafunctionoftemperatureandmolarmassusingequationsprovidedin[41]. Then,another scriptusedthatdatatobuildG-Ttables,whicharemorefamiliartonuclearengineersinthe industryusingasimplified,steady-stateversionoftheTaylorHTCcorrelationforlowPrandtl numberfluids[40]. Thesimplifiedversion,Equation1,ignorestheeffectsofthefluidbulkto wall temperature gradient on the HTC and assumes a fully formed flow. The simplification reducestheresulting HTC;therefore, it isa conservativeassumption. AppendixB provides linkstotheGNUOctavescripts. HTC =k Dh[︁ 0.023Re0.8Pr0.65]︁ (1) Figure 3 contains the HTC data as a function of the coolant temperature and the mass flux for pure helium and 40 g/mol HeXe, popular with NSP designers in the literature [40]. Multiple studies in the literature show that 40 g/mol HeXe and pure helium have the same HTC[23][40]. 26 G (Kg/m2s)/T (K)/HTC (W/m2K) 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 400NaN 3724 5151 6484 7751 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 500NaN 3842 5314 6689 7996 9252 NaN NaN NaN NaN NaN NaN NaN NaN NaN 600NaN NaN 5458 6870 8213 9503 10750 NaN NaN NaN NaN NaN NaN NaN NaN 700NaN NaN 5585 7030 8404 9723 10999 12239 NaN NaN NaN NaN NaN NaN NaN 800NaN NaN 5697 7172 8573 9920 11222 12487 NaN NaN NaN NaN NaN NaN NaN 900NaN NaN 5799 7300 8727 10097 11422 12710 13966 NaN NaN NaN NaN NaN NaN 1000 NaN NaN NaN 7415 8865 10257 11603 12911 14187 15434 NaN NaN NaN NaN NaN 1100 NaN NaN NaN 7532 9005 10419 11786 13115 14410 15678 16920 NaN NaN NaN NaN 1200 NaN NaN NaN 7622 9112 10543 11926 13271 14582 15865 17122 18356 NaN NaN NaN 1300 NaN NaN NaN 7674 9173 10614 12007 13361 14681 15972 17237 18480 NaN NaN NaN 1400 NaN NaN NaN NaN 9250 10703 12108 13473 14804 16106 17382 18635 19867 NaN NaN 1500 NaN NaN NaN NaN 9376 10849 12272 13656 15005 16325 17618 18888 20137 21367 NaN 1600 NaN NaN NaN NaN 9496 10987 12429 13830 15196 16533 17843 19129 20394 21639 NaN 1700 NaN NaN NaN NaN 9577 11081 12535 13948 15326 16674 17995 19293 20568 21825 23063 1800 NaN NaN NaN NaN 9642 11156 12620 14043 15431 16788 18118 19424 20708 21973 23220 1900 NaN NaN NaN NaN 9707 11232 12706 14138 15535 16902 18241 19556 20849 22122 23378 2000 NaN NaN NaN NaN NaN 11303 12786 14227 15633 17008 18356 19679 20980 22262 23525 G (Kg/m2s)/T (K)/HTC (W/m2K) 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 400NaN NaN 819 1032 1233 1427 1614 NaN NaN NaN NaN NaN NaN NaN NaN 500NaN NaN 843 1061 1268 1467 1660 1847 NaN NaN NaN NaN NaN NaN NaN 600NaN NaN NaN 1085 1297 1501 1698 1890 2076 2259 NaN NaN NaN NaN NaN 700NaN NaN NaN 1107 1323 1531 1731 1927 2117 2303 2486 NaN NaN NaN NaN 800NaN NaN NaN 1125 1345 1556 1760 1959 2152 2342 2527 2709 NaN NaN NaN 900NaN NaN NaN NaN 1364 1579 1786 1987 2184 2376 2564 2749 2930 NaN NaN 1000 NaN NaN NaN NaN 1382 1599 1809 2013 2212 2407 2597 2785 2969 3150 NaN 1100 NaN NaN NaN NaN 1399 1619 1831 2038 2239 2436 2629 2818 3005 3188 3369 1200 NaN NaN NaN NaN 1415 1637 1852 2061 2264 2463 2658 2850 3039 3224 3407 1300 NaN NaN NaN NaN NaN 1654 1871 2082 2288 2489 2686 2880 3070 3258 3443 1400 NaN NaN NaN NaN NaN 1670 1889 2102 2310 2513 2712 2908 3100 3290 3476 1500 NaN NaN NaN NaN NaN 1685 1906 2121 2331 2536 2737 2934 3128 3319 3508 1600 NaN NaN NaN NaN NaN 1699 1922 2139 2351 2557 2760 2959 3154 3347 3537 1700 NaN NaN NaN NaN NaN NaN 1938 2156 2369 2577 2782 2982 3179 3373 3565 1800 NaN NaN NaN NaN NaN NaN 1952 2172 2386 2596 2802 3004 3203 3398 3591 1900 NaN NaN NaN NaN NaN NaN 1965 2187 2403 2614 2822 3025 3225 3422 3616 2000 NaN NaN NaN NaN NaN NaN 1978 2202 2419 2632 2840 3045 3246 3445 3640Simplified Taylor Heat Transfer Coefficients for Pure Helium Versus Mass Flux and Flow Temperature (D h = 2.64 mm) Simplified Taylor Heat Transfer Coefficients for 40 g/mol HeXe Versus Mass Flux and Flow Temperature (D h = 2.64 mm) Fig. 3.CalculatedHeatTransferCoefficientValuesusingtheSimplifiedTaylorHTCCorrelation 27 In contrast, our results show that the HTC coefficient of 40 g/mol HeXe for conditions of equal mass flux is nearly a tenth of pure helium. These results highlight the importance of the definition of ‘similar operating conditions’. Our script factors in the Reynolds number limitsoftheTaylorHTCcorrelation[40],leadingtoinvalidresultsforcertaincombinationsof G and T. We see that the region of the G-T table with valid results for HeXe does not have valid results for pure helium. At a given flow temperature and flow area, we can define the Reynoldsnumberoftheflowas: Re=MMN ̇Dh η(T)(2) Where Ṅis the molar flux, and MMis the molar mass of the coolant. At conditions of constantmolarflux,asassumedin[23]and[40],thereisafactorof10betweentheReynolds numbersofthetwocoolants,whichalwaysplacesoneofthemoutsidetheapplicabilitycriteria oftheTaylor’sHTCcorrelation(1.8E4<Re<6E4)[40]. Therefore,onecannotmakedirect comparisonsusingtheTaylor’sHTCcorrelation. Besides this subtlety, HeXe at 40 g/mol has a tenth of the heat capacity of pure helium. Foragivenheatsourceandtemperaturedifference,themassflowrateinahelium-powered Braytoncycleisatenthofonepoweredby40g/molofHeXe. Thereducedmassflowwould also reduce the turbomachinery RPM and size, which was the initial argument for doping heliumwithxenon. Areductioninthe turboalternatorvoltagewouldaccompany areduction inRPM.However,previousNSPturbinedesignsoperatefrom30to50kRPM[42]. TheISS primarily uses 120 to 160 V direct current systems to reduce the cabling size and mass [5], which shows that reducing the turboalternator frequency would have a minimal impact on theresultingvoltagefromthepowerconditioningsystem. Asweshowshortly, themassflowratereducestoapointwhereitisdebatableifacen- trifugal compressor is suitable where positive displacement pumps may suffice. We would alsoliketopointoutthatsince[23],compacthigh-massflowpumpsforhydrogenhavebeen developedaspartofthepushtowardahydrogeneconomy[43],whichisnoteworthyashy- drogen is more difficult to work with than pure helium. Ultimately, we leave it to the NSP systems designer to decide if they prefer HeXe or pure helium. Here, we continue with 40 g/molHeXesothatourresultsstayrelevanttolegacyNSPdesignsusingHeXe. Now that the coolant selection is complete, we can direct our attention to thermal hy- draulics. Ourthermalhydraulicsmodelissplitintocorepressurelosscalculationsandradial heat transfer calculations. We set criteria to constrain the mass flow through the coolant channelshowninFigure2: Gmach = 0.3P√︃ γ×MM RTo(3) 28 GdP=√︄ dP fHK f 2ρoDh+ 0.5[︁1 ρo−1 ρi]︁ (4) GHTC =Re×η(Ti) Dh(5) GTH=q’H CpA(To−Ti)(6) Equation3definestheincompressibleflowlimitofthegasatthecoolantchannelexitfor 0.3Machandagivencoolantpressure. Equation4definestheflowlimitfor0.2MPapressure loss across the fuel element, accounting for flow friction using the Blasius correlation, form lossesandacceleration[44]. Finally,Equation5definestheflowlimitbysettingtheReynolds number to 6E4, the upper limit of Taylor’s HTC correlation. Table 5 compares results for a 400 K inlet and 1200 K outlet temperature with an element linear power of 275 W/cm and height of 46 cm. The channel flow area is 0.75 cm2. These numbers are arbitrary and for illustration purposes. Equation 6 provides the minimum mass flux required to remove the heatgenerated. 29 Table 5.LimitingMassFluxforPin-in-CellFuelElementwith40g/molHeXeandPure HeliumCoolant Script Input Parameter 40 g/mol HeXe Pure Helium MinimumCoolantInletTemperature 400K 400K MaximumCoolantInletTemperature 1200K 1200K MaximumElementLinearPower 275W/cm 275W/cm FuelElementHeight 46cm 46cm CoolantFlowArea 0.75cm20.75cm2 CoolantChannelHydraulicDiameter 2.64mm 2.64mm CoolantMolarMass 0.04Kg/mol 0.004Kg/mol FlowReynoldsNumber 60000 60000 CoolantPressure 2MPa 2MPa MaximumPressureDrop 0.2MPa 0.2MPa FormPressureLossFactor 1.5 1.5 IncompressibleFlowMassFluxLimit 1551Kg/m2s491Kg/m2s Taylor’sHTCMassFluxLimit 753Kg/m2s537Kg/m2s PressureDropMassFluxLimit 734Kg/m2s232Kg/m2s MinimumMassFluxLimit 406Kg/m2s41Kg/m2s Table5showsthedifferencesbetween40g/molHeXeandpurehelium. Thefirstnotable 30 parameteristherequiredcorecoolingmassflowrate. At41Kg/m2s,itisunclearifacentrifu- galcompressorforahelium-poweredBraytoncycleispreferabletoapositivedisplacement pump. Table5alsoshowsthedifferenceinpressurelossesbetweenthetwocoolants. The ratio between the required mass flux to cool the reactor and the flow pressure drop limit is about5.65comparedto1.81forHeXe,whichisequivalenttostatingthattheactualpressure lossis3.12timeslowerwithpurehelium. Thisbehaviourhasbeennotedintheliterature[40], andHeXeinducessignificantlyhigherlooppressurelossesthanpurehelium. Wealsonote thattheoptimalcoolantchannelareafor40g/molHeXeiscloseto0.75cm2asthepressure dropmassfluxlimitapproachestheHTCReynoldsnumbermassfluxlimit. Apin-in-cellfuel elementdesignedforpureheliumshouldalsoexhibitsuchbehaviourwhileensuringincom- pressible flow. However, the mass flux limit equivalence would occur for a larger flow area, furtherexacerbatingthecomparativepressurelosses. Now that we have the flow constraints, we must verify that the fuel pin can support the assumed275W/cmlinearpowerinthisconfiguration. Westartbyintegratingtheexpression forthethermalconductivityofUNbetweenthefuelpelletcentrelineandthesurface[21]: kf(T) = 1.41T0.39(7) Wehavefromfundamentalheattransferinacylindricalheat-generatingbody[44]: ∫︂Tm Tskf(T)dT=q’ 4π(8) PuttingEquation7in8andsolvingforthesurfacetemperature Tsyields: Ts=[︃ T1.39 m−1.39 1.41×q’ 4π]︃1 1.39 (9) Now,wefindtheradialheatconductionandconvectionexpressionforcalculatingthefuel pelletsurfacetemperaturefrom[44]: Ts=Tb+q’×[︃lnr2 r1 2πKc(Tb)+1 2πr2HTC (G, T b)]︃ (10) We can now equate Equations 9 and 10 to numerically find the linear power of the fuel element, given that the fuel centreline temperature Tmis constrained to 1600 K to reduce UNswelling[28]. TheexpressionforthethermalconductivityoftheMA956ODSclad, kc,is from[45]: 31 kc(T) =T–273 60+ 10 (11) Figure 4 shows the script output for various coolant temperature, Tb, and mass flux, G, values. The 1200 K coolant temperature curve passes closely above 275 W/cm for the mass flux values predicted by Table 5. As the coolant temperature increases, we expect heatrejection fromthe radiatorto improve. However, thermalhydraulic constraintsexist on the fuel element’s linear power. Note that for a linear power of 150 W/cm, the allowable maximum coolant temperature is 1400 K. We selected the coolant temperature of 1200 K andflowofareaof0.75cm2bymanualoptimisationoftheresultsofthetwoOctavescripts, ensuringthatthemassfluxconstraintsandlinearpowerrequirementsaresatisfied. Fig. 4.LimitingLinearPowerCurvesfor40g/molHeXeCooledFuelElement These results provide important insight. The space environment prefers high coolant temperature; however, thermal hydraulics prevents a high coolant temperature. Ideally, a higherfueltemperatureenableshighercoolanttemperaturesforthesamelinearpower. This behaviourseeminglyfavoursUO 2fuelpellets,whichcanoperatewellabovethe1600Klimit ofUN.Thus,thereisacomplexinterplayofNSPreactorpowerdensity,coolanttemperature andradiatorheatrejection. Oncloseranalysisoftheseconditions,wefoundthattheactual fuelpelletsurfacetemperaturewas1511K,withtheremaining311Kprimarilybeingdropped across the HeXe coolant gas due to its low HTC. Thus, one wonders how the system’s thermalhydraulicswouldperformifthecoolantwereisothermal. 32 3.3Sodium Isothermal Thermal Hydraulics Model Thissectionrepeatsthethermalhydraulicsanalysisforanisothermalcoolantevaporatingin the fuel element coolant channel. The complex annular flow behaviour is not modelled. A slightmodificationtoequation10resultsin: Ts=Tb+q’lnr2 r1 2πKc(Tb)(12) Here, the coolant temperature, Tb, is now the boiling point of sodium at the operating system pressure. We assume that the NSP system designers are flexible with the system pressureand,therefore,considerthetemperaturethedrivingvariable. Equation12assumes thatthecoolantisisothermal,andtheresultsofsolvingitarepresentedinFigure5. Fig. 5.LimitingLinearPowerCurvesforSodiumVapourisationCooledFuelElement Figure5showstheutilityandpowerofanisothermalsystem. Theallowablelinearpower foracoolanttemperatureof1400Kisnow550W/cm. Acoolanttemperatureof1200Kyields 1070W/cm. Thehighheatofvapourisationofsodiumfurtherreducestherequiredmassflow rates in the coolant loop and decouples the mass flux limits from core cooling. This system far outperforms the gas-cooled system, and we suggest second-generation NSP systems investigate isothermal cooling for NSPreactor cores using principles similar to looped heat pipesalreadyusedinspacecraft[11]. 33 3.4Simple Models of Brayton and Rankine Cycles Operating in Space OurthermalhydraulicsanalysishasputboundinglimitsontheNSPreactorcoolanttempera- ture,givenadesiredreactorpowerdensity. Inthissection,wedevelopsimplemathematical modelsfortheBraytonandRankinecyclescoupledtoaradiatorforrejectingheat. Tosimplify theanalysis,weassumetheradiatortubehasnoradialtemperaturegradient. Intheinterest ofbrevity,wedonotpresentthecompletederivationshere. AppendixBcontainslinkstothe derivationofallthemathematicsforbothheatcyclesandtheGNUOctavescriptsforsolving thederivedequations. Reactor or Heat Source QinTurbine Array WoutStatic Primary Radiator Area = L x W Compressor Array Windx ṁInlet at T Outlet at T - dTTr LW To Ti Te Fig. 6.SimpleBraytonHeatEngineCoupledtoaRadiator Figure6showstheBraytoncycleunderconsideration. WhileNSPsystemstypicallycon- tain recuperators and other components [35], we wish only to study the fundamental limits here. Usinganenergybalanceacrosstheheatsource,wewrite: ṁ =Qin Cp(To–Ti)(13) Then, consider Figure 6 again. We can write for an infinitesimal section of the radiator usingtheStefan-Boltzmannlaw: dQ=ṁCp(T)dT=ϵσbφ(T4−Ta4)dx (14) 34 In space, studies [35] [10] usually take the ambient temperature to be around 200 K, significantly less than the coolant temperatures under consideration. Ignoring the ambient temperatureandsubstitutingEquation13in14,wecanintegratetoget: [︃1 3Te3−1 3Tr3]︃[︃1 To−Ti]︃ =ϵσb Qin∫︂ φdx=ϵσbLW Qin(15) The right-hand side integral ultimately yields the radiator area because we assume the radiatorisalongcoiledtubeofapparentdiameter φ,leadingto∫︁ φdx=φNW =φL φW=LW. Weseethatequation15isindependentofthecoolantproperties,whichisunintuitive. Infact, coolant properties only determine the mass flow rate in this cycle, with the other properties of interest being solely dependent on temperature. If the compressor must compensate for thepressurelossacrosstheturbine,wegetthefollowing: CPR =TPR×Fp (16) TPRistheturbinepressurerate,CPRisthecompressorpressureratio,and Fpisafactor to account for other pressure losses in the cycle, such as frictional flow loss. We conser- vatively assume TPR to be 0.5 to ensure the turbine is simple and single-stage. Using the isentropicflowrelations[46],wecannowrelatetheturbineinlettemperaturetotheradiator inlet temperature. Similarly, the radiator outlet temperature and the compressor outlet tem- peraturearerelated. SubstitutinginEquation15,anOctavescriptcannumericallysolvefor the radiator outlet temperature if the turbine inlet temperature, TPR and Fpare known. We assume a value of Fpof 1.2. Using an energy balance across the turbine, compressor and reactorandassumingaconstantvalueofcoolantmassflowrateandheatcapacity,wecan write: ηth=ηgenTo−Tr−Ti+Te To−Ti(17) Usingtheisentropicrelations,wegetanexpressionfortheconversionefficiency: ηth=ηgenTo[︁ 1−(TPR )γ−1 γ]︁ −Te[︁(︁Fp TPR)︁γ−1 γ−1]︁ To−Te(︁Fp TPR)︁γ−1 γ(18) 35 Table 6.HeatCycleAnalysisScriptInputParametersforBraytonandRankineCycle Input Parameter Parameter Value RadiatorHeight 3.5m RadiatorWidth 1.5m NumberofRadiators 4 NumberofRedundantRadiators 0 RadiatorEmissivity 0.8 TurbinePressureRatio 0.5 PressureFactor 1.2 GeneratorEfficiency 0.9 Fig. 7.ReactorInletTemperatureforaSimpleBraytonCycle Where ηgenis the alternator or generator efficiency, assumed to be 0.9 [47]. Figure 7 showsasurfaceplotofthereactorinlettemperatureforthescriptinputparametersdescribed in Table 6. Despite the target specifications calling for 2 radiator panels with 2 more for redundancy,weinvestigatethelimitsofthesystemsbyusingall4radiatorpanelsatonce. The black area on the plot’s surface is the region where no solutions exist because the radiatorcannotreducethetemperaturetoalevelwherethereactorinlettemperatureisless than the reactor outlet temperature. In other words, the radiator is saturated and unable to reject the heat required to sustain a cycle. Surprisingly, as the reactor outlet tempera- 36 ture increases, the reactor inlet temperature reduces for a given input thermal power level. This behaviour is because of the heat rejection process’s critical dependence on the radia- tor’slocalcoolanttemperature. Thesameradiatorareacanrejectmuchmoreheat,andthe net radiator outlet temperature decreases despite the increased inlet temperature. Conse- quently,thecompressoroutlettemperaturealsoreduces,andtheoverallmassflowrequired torunthecycledropssharply. Fig. 8.40g/molHeXeMassFlowRatesforaSimpleBraytonCycle Figure 8 shows the mass flow rates for the same system for a 40 g/mol HeXe coolant. Unfortunately, the previous thermal hydraulic analysis provided a target reactor outlet tem- peratureof1200K,withnosolutionsproducing100KWeinFigure9. Therefore,inthiscase, thedesignerwouldhavetoreducethetargetedNSPreactorpowerdensityuntilthereactor outlet temperatures are in the acceptable range for a reactor. As noted earlier, the reduced maximumlinearpowerwouldbe150W/cmat1400K.However,thatisinsufficienttogetthe systemto100KWeclass. 37 Fig. 9.ThermaltoElectricalConversionEfficiencyforaSimpleBraytonCycle Therefore, increasing the radiator area by 5 times is necessary, expanding the region of acceptable turbine inlet temperatures at the cost of redundancy. The simplicity of Equation 15meansNSPsystemengineerscanquicklypredicttheresultingsystemtemperaturesand efficiencies. A5 times increase in the radiator is required because we wish to preserve the conversionefficiencyandhaveasystemthatis20%efficientwithareactorthermalpowerof 500KWth. Aswearecurrentlygetting20%efficiencyat1400Kand100KWth,weneedto increasetheradiatorareaby5timestohandlea500KWthheatloadbecauseEquation15 islinearinreactorpowerversusradiatorarea. Overall,theconversionefficiencyisdeficient comparedtothenearly30%ofthemoresophisticatedsystemspresentedinNSPliterature [48][49]. Regardless,giventhetargetof100KWeclass,ourexamplesystemwouldfallinto the required power class even at the low efficiencies of 20 % if reactor outlet temperatures and radiator areas were dramatically increased. Unfortunately, no redundant radiator area wouldbeleftevenwithsuchallowances. Moresophisticatedsystemswouldbesignificantly moreefficientbutstillstrugglewithsingle-failureredundancyandmassbudgetingissues. This analysis shows the utility of the thermals first approach. Even though we have yet to discuss nuclear engineering in detail, thermal considerations have fully constrained the reactor design for us. These computationally inexpensive analyses provide valuable data regarding the design space in which an NSPsystem remains practical. Next, we discuss a Rankinecyclewithsodiumcoolantforcompleteness. Again,completemathematicalderiva- tionsareavailableinAppendixB.Rankinecyclesdependonmaterialspropertydata. Forour analysis,wereliedonanIAEApublication[36]forsodiumliquidandvapourthermophysical properties,suchasenthalpy,densityandpartialpressure. Theentropyandratioofspecific heat data from [50] were curve-fitted in Microsoft Excel with an R-value above 0.999. For lackofabetterandsimpleralternative,weaveragedtheratioofspecificheatsbetween900 38 and1800K,whichresultedin1.5757. Thefinalequationsforthecoolantpropertiesrequired forasodiumRankinecyclearepresentedinTable7. 39 Table 7.ThermophysicalPropertiesDataRelevanttoSodiumRankineCycles Sodium Property Equation Application Limits Reference LiquidEnthalpy(KJ/Kg) Hl=−365.77 + 1 .6582 T−4.2395E-4T2+ 1.4847E-7T3+2992.6 T380K<T<2000K [36] VapourisationEnthalpy(KJ/Kg) ∆Hg= 393 .37[︃ 1−T 2503.7]︃ + 4393 .6[︃ 1−T 2503.7]︃0.29302 380K<T<2000K [36] LiquidEntropy(KJ/KgK) Sl= 7.4402E-1+ 8.2785E-3T−9.1681E-6T2+ 6.0062E-9T3−2.0202E-12 T4+ 2.7196E-16 T5380K<T<2000K [50] VapourEntropy(KJ/KgK) Sg= 2.9487E1−6.0974E-2T+ 7.1262E-5T2−4.3225E-8T3+ 1.3147E-11 T4−1.5835E-15 T5380K<T<2000K [50] PartialPressure(Pa) Psat=exp[︃ 11.9463−12633 .73 T−0.4672lnT]︃ 900K<T<2000K [36] LiquidDensity(Kg/m3) ρl= 219 .00 + 275 .32[︃ 1−T 2503.7]︃ + 511 .58[︃ 1−T 2503.7]︃0.5 380K<T<2000K [36] RatioofSpecificHeatsofVapour γ= 3.2012−7.6516E-3T+ 1.1781E-5T2−8.5367E-9T3+ 3.0237E-12 T4−4.0740E-16 T5380K<T<2000K [50] 40 Reactor or Heat Source QinTurbine Array WoutStatic Primary Radiator Area = L x W Annular EM Pump WALIPTr , Pr LW To , Po Tr , PoTr , PrFig. 10.SimpleRankineHeatEngineCoupledtoaRadiator Figure 10 shows the structure of the Rankine cycle we analysed. Using the energy bal- ance we previously applied to the Brayton cycle, we get a new expression, Equation 19, for the cycle mass flow rate. Since the heat rejection was now at a constant temperature, themathematicsfortheradiatorwerestraightforward. Equation20providesthenormalised radiator area required to condense the wet vapour exiting the turbine. The radiator area is normalisedtotheonerequiredbytheBraytoncycleinthepastanalysis. ṁ =Qin Hl(To)−Hl(Tr) + ∆ Hg(To)(19) Anorm =ṁ ∆Hg(Tr)Xr ϵσbLWT r4(20) The turbine expands the sodium vapour isentropically, condensing a fraction of it in the process. Usingtheisentropicrelations, wecanfindtheturbineoutlettemperature. Further, 41 theentropydataprovideuswithameanstofindthevapourqualityattheturbineexit: Xr=Sg(To)−Sg(Tr) Sg(Tr)−Sl(Tr)(21) The minimum vapour quality is usually around 0.8 for test Rankine cycles to avoid cav- itation damage and turbine erosion [51]. However, we set the TPR here to 0.5 instead to compare the performance with the Brayton cycle. Now, we must find the power require- ments of the sodium pump to calculate the cycle conversion efficiency. Since liquid sodium isanincompressiblefluid,thepumpingpoweroftheannularelectromagneticlinearinduction pumpisgivenby: WALIP =FpPo(1−TPR )ṁ ρl(Tr)(22) AllothercycleinputsaredefinedsimilarlytotheBraytoncycletofacilitatecomparisonand areprovidedinTable6. Finally,wecanexpressthecycleconversionefficiencyasfollows: ηth=ηgenHg(To)−Xr∆Hg(Tr)−Hl(Tr)−FpPo(1−TPR ) ρl(Tr) Hl(To)−Hl(Tr) + ∆ Hg(To)(23) Theseequationscompletethesettodescribetheheatcycle. Figure11showsthereactor temperature plot, and Figure 12 shows the corresponding nominal system pressure. Note thatthereisnotemperaturelimitingregionherecomparedtotheBraytoncycle. Secondly,the surfaceplothasbandingparalleltothex-axis,meaningthatthereactorinlettemperaturesare independentoftheheatsourcepower. TheseresultsshowthatNSPsystemdesignershave much greater flexibility with this cycle than with a Brayton cycle. The turbine inlet pressure is0.7MPaforatemperatureof1400Kcomparedtothe2MPafortheHeXeBraytoncycle. This reduction in system pressure shall contribute to a reduction in plumbing and pressure vessel mass and cost reduction compared to the Brayton cycle. Compared to the Brayton cycle, the mass flow rates fall below 50 g/s, a hundred times less due to the impressively highheatofvapourisationofsodium. Ultimately,sodiumsurpassespureheliumorHeXein everymetricofcomparison. 42 Fig. 11.ReactorInletTemperatureforaSimpleSodiumRankineCycle Fig. 12.TurbineInletPressureforaSimpleSodiumRankineCycle Figure 13 shows the normalised radiator areas compared to the Brayton cycle. We im- mediately see a region where the required radiator area is larger than the Brayton cycle. However,at1400K,theradiatorarearequiredisroughly30%ofthatoftheBraytoncycleat 500KWth. Iftheturbineinlettemperatureis1200K,theratiooftheradiatorareasisnearly 0.55 at 500 KWth. Therefore, our hypothesis that a Brayton cycle performs poorly when coupled to a radiator was proven correct. Furthermore, the Rankine cycle does not require all four radiator panels available to produce 100 KWe, making at least one radiator panel redundant. 43 Fig. 13.RadiatorAreaforaSimpleSodiumRankineCycleNormalisedtotheBrayton CycleRadiatorArea Finally, Figure 14 shows the Rankine cycle’s conversion efficiency. At the same cycle parameters,thesimpleRankinecyclealsohasanefficiencyofnearly18%at1400K,inde- pendentoftheheatsourcepower. Notably,thecycleefficiencyat1200Kissimilar. Thereis aminimumintheefficiencyaround1400Kbecausethereisacorrespondingminimuminthe entropy difference between sodium liquid and vapour around 1400 K [50]. This property of sodiumcausesthevapourqualitytoincreaseatthosetemperaturerangesandconsequently reducesthecycleefficiency. LookingbacktoFigure9,weseethatthecycleefficiencyfora Brayton system decreases with increasing reactor power as the radiator struggles to reject theheat. However,wedidnotemployafixedradiatorareawhenanalysingtheRankinecy- cle. Regardless, as Figure 13 shows, there is a large region of the parameter space where theresultingrequiredradiatorareasaresmallerthantheBraytoncycle. 44 Fig. 14.ThermaltoElectricalConversionEfficiencyforaSimpleSodiumRankineCycle 3.5Summary of Trends in Presented Models Inthischapter,weinvestigatedthermalhydraulicandheatcyclemodelstodevelopourNSP reactorengineeringconstraintsfurther. Westudiedfundamentaltrendsthatemergeinther- mal management systems that reject large amounts of heat at high temperatures through simple and rudimentary models. The mathematical models we developed for the fuel ele- mentthermalhydraulicsandheatenginethermodynamicsweresolvedbyGNUOctave8.3.0 scriptsinAppendixB. The pin-in-cell model we used was simple enough to develop a helpful set of analytical toolstostudythethermalhydraulicperformance. ThoseeffortsculminatedinFigure4,which showsthatasthemaximumcoolanttemperatureincreased,themaximumlinearpowerden- sity of the UN fuel pellet had to decrease for a fixed centreline temperature. Given the fuel elementwechose, therewasasetoffundamentalmassfluxlimitsconcerningreactorcore pressuredrop,incompressiblecoolantflowandtheTaylorHTCcorrelationsapplicabilitythat we accounted for. Ultimately, we found that a coolant temperature of 1200 K in a coolant channel of 0.75 cm2supported the targeted linear power density of 275 W/cm. The issue was that over 300 K of the temperature drop between 1600 K and 1200 K occurred due to thelowHTCof40g/molHeXegascoolant. Themaximumlinearpowerdensityskyrocketedwhenthegascoolantwasreplacedwith evaporating sodium, providing an isothermal environment. At 1200 K, the maximum linear power density was 1070 W/cm; at 1400 K, it was 550 W/cm. Therefore, we concluded that sodiumRankinesystemsthatoperatedsimilarlytoloopedheatpipesinnullgheldpromise. 45 Then, we developed a simple Brayton cycle’s mathematical equations using isentropic relations and fundamental physics. First, we found that the radiator performance was inde- pendentofthegascoolant’sproperties,andthecoolant’spropertiesonlyaffectedthecycle massflowrate. Second,wefoundthatforourselectednucleardatarelayapplication,there wasnotenoughradiatorareaonthesatellitebustoprovideenoughredundancyalongwith functional heat rejection at 1200 K and 1400 K. Figure 7 showed that for a given thermal power, increasing the reactor outlet temperature would result in a decrease in the radiator exittemperature. Thus,wehadtoconsidera1400Kreactoroutlettemperaturebyreducing the maximum reactor linear power density to 150 W/cm and increasing the total available radiatorareaby5times. Finally,wefoundthatthesimpleBraytoncyclewasrelativelyinef- ficientatpowerconversion,onlymanaging20%atselectedtemperatures. Atthebeginningofthechapter,wehypothesisedthattheBraytoncyclewouldhavepoor performanceinspaceduetoissueswithheatconductioninthegascoolantandtheinefficient usage of the available radiator area. To investigate further, we developed the mathematics forasimplesodiumRankinecycle,whichacceptsandrejectsheatisothermally. Compared toagas-cooledBraytoncycle,theisothermalheattransferdramaticallyimprovedthelinear powerdensitylimitsandtherequiredradiatorareas. Figure13showsthatthesimpleRankine cyclerequiredasmallerradiatorforanampleparameterspacethantheBraytoncycle. We alsofoundthattheRankinecyclefunctionedwellataradiatortemperatureof1200K,hadat leastoneredundantradiatorpanelandhadnearly18%efficiency,independentoftheinput thermal power. This behaviour starkly contrasted with the Brayton cycle, which suffered fromadecreaseinefficiencyasthethermalpowerwasincreasedwhilekeepingtheradiator areaconstant. Overall,thischapterproducedastrongargumentforNSPsystemdesigners toresearchanddevelopRankinecycleandsodiumturbo-alternatorsforsecond-generation NSPsystems. Table8summarisesourresultsinnumbers. Avastamountoflegacyliterature deals with gas-cooled Brayton cycles; therefore, it seems likely that the first generation of NSPsystemswoulddeployaBraytoncycle. Forlaterchaptersinthisthesis,wecontinuewith a 40 g/mol HeXe-cooled Brayton system to maintain applicability with legacy NSP system designs. Thenextchapterbuildsupontheresultsofouranalysisheretoeliminatemoderator materialsanddesignaparametricneutronicsperformancestudyofNSPreactorcores. 46 Table 8.SummaryofRudimentaryBraytonandRankineHeatCycleAnalysisforNSP SystemsinGeostationaryOrbit NSP System Parameter Optimum Value for Brayton Cycle Optimum Value for Rankine Cycle RadiatorWidth 1.5m 1.5m RadiatorHeight 3.5m 3.5m RadiatorEmissivity 0.8 0.8 RadiatorTubingMaterial MA956ODS MA956ODS RequiredNumberofRadiatorPanels 10 2 AvailableRadiatorPanelsonBus 4 4 GeneratorEfficiency 0.9 0.9 TurbinePressureRatio 0.5 0.5 PressureFactor 1.2 1.2 ReactorThermalPower 500KWth 750KWth HeatCycleConversionEfficiency 0.20 0.18 ReactorOutletTemperature 1400K 1400K MaximumFuelElementLinearPower 150W/cm 550W/cm HeXeCoolantChannelArea 0.75cm2- HeXeCoolantMolarMass 40g/mol - 47 4Selecting Moderators for Nuclear Space Power Reactors Itisfinallytimetobeginnuclearengineering. Inthischapter,wesynthesisetheconstraints developedinthepreviouschapterstodevelopaframeworktostudyvariousmoderatorma- terials for NSP reactor designs. Table 8 represents the overall design constraints on the HeXe-cooled NSP system design for the nuclear data relay. The thermal power output re- quirementandthemaximumlinearpowerlimiteffectivelydecidethetotalNSPreactorcore volume. Themaximumreactoroutlettemperatureisvitalineliminatingmoderatormaterials choices. AsinChapter2,wecreateapredictableframeworktoeliminatemoderatormaterial choices. Weuse[31]asamonolithicandcompositemoderatormaterialsreference. Recently,aneedforhigh-temperatureandhighneutronstoppingpowermoderatorshas beenrecognised. Startingfromthesetofbasematerialsin[31],weusedFact-Webtopredict theboundingoperatingtemperatureofyttrium,zirconiumandcalciumhydridesatapressure of 2 MPa. There is a consensus in the literature [31] [32] that hydride moderators are nec- essary for thermal spectrum nuclear microreactors, which are neutronically similar to NSP reactors. Table 9 displays our findings. At 0.1 MPa, zirconium hydride dehydrides at 900 K whileyttriumhydrideremainsstableat1200K[52]. Fact-Websuggeststhatasthehydrogen partialpressureincreasesto2MPa,zirconiumhydrideismoreresistanttodehydridingthan yttriumhydride. Table 9.DehydridingTemperaturesofHigh-TemperatureMetalDihydridesat2MPa Metal Dihydride Maximum Operating Temperature at 2 MPa Zirconium 1300K Yttrium 1200K Calcium 1600K Hydrogen loss at high temperatures [53] is a critical issue with monolithic hydride mod- erators. The universally agreed solution is the development of composite moderators [31]. Compositemoderatorscompriseanon-moderating,weaklyneutron-absorbingmatrixcarry- ing a highly moderating metal hydride. Typically, MgO is used for a matrix with zirconium andyttriumhydridesastheentrainedmoderator[31]. MgOisimpermeabletohydrogenand thuspreventsoutgassing[52],enablingcompositemoderatorstofunctionathighertemper- aturesthantheirmonolithiccounterparts. Inthis thesis, wefocus oncomposite moderators because, as Table 9 shows, familiar monolithic moderators used by nuclear engineers un- dergo dehydriding well below the temperatures that our thermodynamic analysis of a 100 KWeclassNSPsystemcalledfor. 48 4.1Potential Moderator Materials As discussed, hydrides of zirconium, yttrium and calcium have been studied for application inmicroreactors[32]. Figure15describestheresultsofourFact-Webcompatibilitycalcula- tions. MonolithicZrH2-x YH2-xBeO 7Li2O CompositesMgO Matrix CaO MatrixBeO-MgO Matrix7Li2OBeO YH2-x7Li2O YH2-xZrH2-x CaH2-xZrH2-x 7Li2OModerators for NSP Reactors Fig. 15.High-TemperatureChemicalCompatibilityChartforMonolithicandComposite ModeratorMaterialsforNSPReactors WeselectedcompoundscontainingmoderatingelementssuchasHandLiandsubjected themto1400Kand2MPawiththesoftware. WecanseewhytheMgOmatrixisapopular 49 choice, as MgO is compatible with a range of moderating hydrides and oxides. Further- more,MgOcompositescanbesinteredbelow1000KwithLiF[31]addition,enablingthese compositestobepracticallymanufacturedwithoutsubjectingtheentrainedmoderatortode- hydriding temperatures. BeO as a matrix is enticing but suffers from a high sintering onset temperatureof1563K[54],whichmeansthathydridescannoteasilybeincorporated. After aliteraturereview,wefoundwork[55]describingaBeO-MgOeutecticceramiccomposedof 70mole%ofBeO,whichmeltsnear2133K[55]. Whiletherearenosinteringstudiesofthis ceramiceutecticmixture,weexpectthesinteringonsettemperaturetobeapproximatelyhalf themeltingtemperature,resultingin1066K.Further,thepresenceofMgOimpliesthatsinter- ingadditivessuchasLiF[31]thatcatalyseMgOsinteringcouldassistinsinteringBeO-MgO as well. Therefore, we included BeO-MgO in our study as it is potentially manufacturable andabettercompositemoderatorthansimpleMgOcomposites. Finally, we considered calcium hydride. CaH 2is incompatible with MgO at the temper- atures of interest. CaH 2is well known for having a high dehydriding temperature and low hydrogen partial pressure [56]. It has been recently studied for thermal batteries for ter- restrial solar thermal power plants [57] and as a moderator for nuclear reactors [58]. The corresponding matrix, CaO, is inexpensive and commercially available. The kinetics of sin- tering CaO are not as well studied as MgO, but they seem similar and are also catalysed by LiF [59]. Therefore, it seems that a CaH 2containing composite moderator would be an inexpensivecompetitortotherareearthhydride-containingoptions. Ultimately,wearecau- tiousaboutthismoderator’sviabilityasCaH 2beginstomeltfrom1090K,andthus,theCaO would require to contain a molten moderator, which has no precedent. Recent studies of composite phase change materials support the viability of such composites [60]. However, anexperimentalcampaignwouldbenecessarytounderstandifaCaH 2containingcomposite isamanufacturableandpracticalhigh-temperatureneutronmoderator. Asidefromchemicalcompatibility,wealsoconsideredthedepthofliteratureandexperi- encewiththemoderatormaterialsinquestion. Figure16summarisesourfindings. Wefound nodataonthethermophysicalpropertiesoflithiumoxides,whichremovedthemfromconsid- eration. Naturallithiumhasahighthermalneutronabsorptioncrosssection[30],andnuclear reactionsinthemoderatorreleaseheliumgas. Therefore,itsviabilityasahigh-temperature, long-lifeneutronmoderatorislimited,andwecansafelyeliminateit. 50 YHx ZrH x Be BeO MgO CaO CaH x S(α, β) ENDF VIII.0 ENDF VIII.0 ENDF VIII.0 ENDF VIII.0 NCRYSTAL NCRYSTAL JEFF 3.3 ρ(T) Shivaprasad-2020 Yamanaka-2002 Tomberlin-2004 Hou-2022a Hofmeister-2014 Tian-2022 Kimura-2019 Cp(T) Shivaprasad-2020 Yamanaka-1999 Tomberlin-2004 Hou-2022a Hofmeister-2014 Chase-1998 Balakrishnan-2023 CTE(T) Shivaprasad-2020 Yamanaka-1999 Tomberlin-2004 Hou-2022a k(T) Shivaprasad-2020 Tsuchiya-2001 Tomberlin-2004 Hou-2022a Hofmeister-2014 Bird-2020 Balakrishnan-2023 PIE Shivaprasad-2020 Kawamura-2004 Hou-2022b Hickman-1965 TmeltShivaprasad-2020 Shivaprasad-2022 Tomberlin-2004 Hou-2022a Jiang-2017 Tian-2022 Balakrishnan-2023Complete Data TsinterShivaprasad-2020 Snead-2022 Kurinskiy-2018 Hou-2022a Jiang-2017 Tian-2022Incomplete Data Sa(T) Shivaprasad-2020 Yamanaka-1999 Tomberlin-2004 Hou-2022a Vasilos-1964Not Readily Available Fig. 16.ThermophysicalandMechanicalPropertiesDataAvailabilityofHigh-TemperatureModeratorandMatrixMaterials 51 Table 10. High-TemperatureModeratorsforNSPReactors Moderator Name Atomic Composition Density at 298 K (Kg/m3) Graphite C:1 1710 ZirconiumHydride(H/M=1.66) Zr: 0.38,H:0.62 5653 YttriumHydride(H/M=1.8) Y:0.36,H:0.64 4293 BerylliumOxide Be: 0.5,O:0.5 3015 40vol%YH 1.8inMgO Y:0.12,H:0.21,Mg: 0.33,O:0.33 3866 40vol%YH 1.8in70mole%BeO-MgOEutectic Y:0.11,H:0.19,Be: 0.25,Mg: 0.10,O:0.35 3651 40vol%CaH 2inCaO Ca: 0.43,H:0.27,O:0.30 2684 We found similar issues with beryllium and its alloys; thus, we also removed them from furtherconsideration. Wenotedagapintheliteratureregardingpost-irradiationexamination (PIE) and density versus service temperature for zirconium hydrides. Despite having many gaps in knowledge, allowable mechanical stress (S a) and thermophysical properties data, we chose to include calcium hydride in our study because of their potential cost savings and high-temperature dehydriding resistance. We also included graphite and BeO due to theirextensiveuseinfastreactordesigns,whichallowedustocompareourresultswithfast reactorNSPsystems. Table10showsthemoderatorsweconsideredforfurtherneutronics analysis. Figure 16