ML22272A598
| ML22272A598 | |
| Person / Time | |
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| Site: | Hermes File:Kairos Power icon.png |
| Issue date: | 09/29/2022 |
| From: | Kairos Power |
| To: | Office of Nuclear Reactor Regulation |
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| References | |
| KP-NRC-2209-018 KP-TR-017-NP | |
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KP-NRC-2209-018 KP-FHR Core Design and Analysis Methodology, KP-TR-017-NP (Non-proprietary)
KPTR017NP
KairosPowerLLC
707W.TowerAve Alameda,CA94501
KP-FHR Core Design and Analysis Methodology
TechnicalReport
RevisionNo.1 DocumentDate:September2022
NonProprietary
KPFHRCoreDesignandAnalysisMethodology NonProprietary DocNumber Rev EffectiveDate KPTR017NP 1
September2022
©2022KairosPowerLLC
ii COPYRIGHTNotice ThisdocumentisthepropertyofKairosPowerLLC(KairosPower)andwaspreparedinsupportofthe developmentoftheKairosPowerFluorideSaltCooledHighTemperatureReactor(KPFHR)design.Other thanbytheNuclearRegulatoryCommission(NRC)anditscontractorsaspartofregulatoryreviewsofthe KPFHRdesign,thecontenthereinmaynotbereproduced,disclosed,orused,without priorwritten approvalofKairosPower.
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iii Rev DescriptionofChange Date 0
InitialIssuance September2021 1
RevisionupdatesSection5.3.1,SectionA.2.3,TableA4, TableA5,TableA10andFigureA7toaddressfeedback fromNRCaudit September2022
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iv EXECUTIVE
SUMMARY
Kairos Power is pursuing the design, licensing, and deployment of a Fluoride Salt Cooled, High Temperature(KPFHR)testreactor.Toenabletheseobjectives,thedevelopmentofatechnologyspecific coredesignandanalysismethodologyisrequired.Thisreportdescribesthemethodologyforcorephysics andthermalhydraulicanalysisoftheKPFHR.
The KPFHR core design methodology is comprised of the Serpent 2 nuclear design and STARCCM+
thermal,fluid,anddiscreteelementmodelingdesigncodes.Thesecodesareconnectedbyaseriesof wrappercodes.Theverificationandvalidation(V&V)methodologyforSerpent2andSTARCCM+codes is described. The methodology is informed by a Phenomena Identification and Ranking Table (PIRT) evaluation.
Serpent2andSTARCCM+andtheassociatedwrappercodesareusedtocalculatecorecompositionat variousphasesofoperationandcorrespondingparameterssuchascorereactivitycoefficients,control andshutdownelementworth,shutdownmargin,powerdistributionandthermalhydraulicparameters.
Thescopeofthisreportappliestonormaloperationandpostulatedevents.Themethodologyforusing thecodestoperformthesecalculationsandthelimitationsontheuseofthismethodologyareprovided.
In addition, a methodology for calculating the uncertainty in these calculations is provided. Sample neutronicandthermalhydraulicresultsforaKPFHRareprovidedasanappendix.
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v TABLEOFCONTENTS 1
INTRODUCTION.............................................................................................................................1 1.1 FHRDesignFeatures......................................................................................................................1 1.2 Regulatorybackground.................................................................................................................2 1.2.1 10CFRRequirements..........................................................................................................2 1.2.2 PrincipalDesignCriteria......................................................................................................2 2
COREPHYSICSANDDESIGN...........................................................................................................4 2.1 Description....................................................................................................................................4 2.2 FuelDescription.............................................................................................................................5 2.2.1 TRISOParticles....................................................................................................................5 2.2.2 KPFHRFuelPebbles...........................................................................................................5 2.3 Reactorcoredesign.......................................................................................................................5 2.4 Operationalregimes......................................................................................................................6 2.5 Phenomenaidentificationandrankingtable................................................................................7 3
COREMODELING...........................................................................................................................8 3.1 Modeling.......................................................................................................................................8 3.2 Modelingparadigm.......................................................................................................................8 3.3 Dataflow.......................................................................................................................................8 3.4 Modelingboundariesandoutputparameters..............................................................................8 4
COREDESIGNTOOLBOX...............................................................................................................11 4.1 Codes...........................................................................................................................................11 4.1.1 STARCCM+.......................................................................................................................11 4.1.2 Serpent2...........................................................................................................................12 4.2 WrapperCodes............................................................................................................................13 4.2.1 KACEGEN...........................................................................................................................13 4.2.2 KPACS................................................................................................................................14 4.2.3 KPATH...............................................................................................................................14 5
CALCULATIONMETHODOLOGY....................................................................................................15 5.1 DEMModeling.............................................................................................................................15 5.2 Neutronics...................................................................................................................................15 5.2.1 MonteCarloConvergence................................................................................................15 5.2.2 FuelCycleAnalysis............................................................................................................16 5.2.3 ReactivityCoefficients......................................................................................................16 5.2.4 ControlWorthandShutdownMargin..............................................................................17 5.2.5 KineticsParameters..........................................................................................................17 5.2.6 ReactorCoolantDepletion................................................................................................17 5.2.7 PowerDistribution............................................................................................................18 5.2.8 VesselIrradiation..............................................................................................................18
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vi 5.3 Thermalhydraulics......................................................................................................................18 5.3.1 PorousMediaModeling....................................................................................................19 5.3.2 CoreMaterialTemperatures............................................................................................20 5.4 CoreBypassModelingandReflectorTemperature....................................................................21 6
UNCERTAINTYANALYSISANDNUCLEARRELIABILITYFACTORS....................................................22 6.1 NuclearDataUAPropagationMethod.......................................................................................22 6.2 ManufacturingInputsUAPropagationMethod.........................................................................23 6.3 KineticsParametersCalculationUAMethod..............................................................................23 6.4 BurnupCalculationUAMethod..................................................................................................24 7
SUMMARY
...................................................................................................................................25
7.1 CONCLUSION
...............................................................................................................................25 7.2 Limitations...................................................................................................................................25 8
REFERENCES................................................................................................................................26 AppendixA ExampleCoreDesignModel.....................................................................................A1 AppendixB NeutronicsPIRTfortheKPFHR................................................................................B1
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vii LISTOFTABLES Table41.
Serpent2RequirementsandPlannedCodetocodeBenchmarkValidation......................27 Table42.
STARCCM+ValidationCases................................................................................................28 Table61.
ScopeofUncertaintyAnalysisforCoreSafetyParameters..................................................30 TableA1.
CoreDesignInputParameters.............................................................................................A4 TableA2.
ZonebasedPowerDensityDistribution..............................................................................A5 TableA3.
ReactivityCoefficientsatStartupandEquilibriumCore.....................................................A6 TableA4.
ReactivityControlSystemRequirementsforShorttermHotShutdown............................A7 TableA5.
ReactivityShutdownSystemRequirementsforSafeShutdown.........................................A8 TableA6.
KineticParametersatEquilibriumConditions.....................................................................A9 TableA7.
Groupwise Effective Delayed Neutron Fraction and Corresponding Decay ConstantatEquilibriumCoreConditions..........................................................................A10 TableA8.
KineticParametersatStartupCoreConditions.................................................................A11 TableA9.
Groupwise Effective Delayed Neutron Fraction and Corresponding Decay ConstantatStartupCoreConditions.................................................................................A12 TableA10. CoolantTemperatureReactivityCoefficientsforFlibeofDifferentCompositions...........A13 TableA11. keffwithandwithoutTHFeedback.................................................................................A14 TableB1.
NeutronicsPIRTResultsfortheKPFHR..............................................................................B2
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viii LISTOFFIGURES Figure21. ThermalEnergyTransferPhenomenainKPFHR.................................................................31 Figure22. KPFHRFuelPebbleandParticleDesign...............................................................................32 Figure23. AxialSectionoftheHermesCore.........................................................................................33 Figure24. ReactorCoreOperationalRegimesoftheKPFHR...............................................................34 Figure31. CoreDesignModules............................................................................................................35 Figure32. CoreAnalysisBoundaries.....................................................................................................36 Figure41. HighlevelDataFlowofKACEGEN........................................................................................37 Figure42. KPATHFramework................................................................................................................38 Figure51. ExampleIllustrationofAlgorithmforPebbleCirculationfortheCore................................39 Figure52. SpectralZonesUsedfortheHermesCore............................................................................40 Figure53. LocalHeatTransferPhenomenainPebbleBedReactorConfiguration...............................41 Figure54. PebbleandTRISOLayersTemperature................................................................................42 Figure61. SCALEworkflowforanExampleDemonstrationInvolvingPerturbedParameters (inyellow).............................................................................................................................43 Figure62. DepletionMethodologyFlowDiagramforBurnupCalculationsofFuelPebbles................44 FigureA1. CoreDesignCalculationDiagram......................................................................................A15 FigureA2. KPFHRCoreGeometry......................................................................................................A16 FigureA3. CrosssectionalViewsofNormalizedInstantaneousPebbleResidenceTime..................A17 FigureA4.
SpectralZonesusedfortheHermesCore.........................................................................A18 FigureA5. Fast (> 0.1 MeV) (left), Intermediate (middle), and Thermal (< 1.86 eV) (right)
NeutronFluxinHermesEquilibriumCore.........................................................................A19 FigureA6. DifferentialWorthofaSingleElementWithdrawal,fromAllIn(RCSonly)......................A20 FigureA7. ReactivityShutdownSystemWorthCurves,N1..............................................................A21 FigureA8. Power density (left), Flibe temperature (center), and Fuel Kernel Centerline Temperature(right)...........................................................................................................A22 FigureA9. AxialBinnedPowerDensityProfileinthecore,excludingConvergingandDiverging Regions(left),andtheRelativeDifferenceofAxialPowerShapebetweenConstant TemperatureandKPATHResults(right)............................................................................A23 FigureA10. RadialBinnedPowerDensityProfileintheCore(left),andRelativeDifferenceof RadialPowerShapebetweenConstantTemperatureandKPATHResults(right)............A24
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ix NOMENCLATURE
Abbreviations/Acronyms ACE ACompactENDF AHTR AdvancedHighTemperatureReactor AOO AnticipatedOperationalOccurrence CE ContinuousEnergy CFD ComputationalFluidDynamics CSAS CriticalitySafetyAnalysisSequence DEM DiscreteElementsMethod DHRS DecayHeatRemovalSystem ENDF EvaluatedNuclearDataFiles FHR FluoridecooledHighTemperatureReactor FOM FigureofMerit HTGR HighTemperatureGasReactor IET IntegralEffectTest IPyC InnerPyrolyticCarbonLayer KP KairosPower KPACS KairosPowerAdvancedCoreSimulator KPATH KairosPowerAdvancedThermalHydraulics MG Multigroup NRC NuclearRegulatoryCommission OPyC OuterPyroliticCarbonLayer PDC PrincipalDesignCriteria PIRT PhenomenaIdentificationandRankingTable QA QualityAssurance RSS ReactivityShutdownSystem SARRDL SpecifiedAcceptableSystemRadiologicalReleaseLimit SET SeparateEffectTest SiC SiliconCarbide TH ThermalHydraulics TRISO TristructuralIsotropic TSL ThermalScatteringLaw UA UncertaintyAnalysis V&V VerificationandValidation
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1 1
INTRODUCTION Kairos Power is pursuing the design, licensing, and deployment of a Fluoride Salt Cooled, High Temperature Reactor (KPFHR). This report is being submitted in support of a construction permit applicationbeingsubmittedinaccordancewith10CFR50.34(a),PreliminarySafetyAnalysisReport,for a nonpower test reactor known as Hermes. This report describes the core design and analysis methodology for the KPFHR test reactor at the beginning of life, startup, power ascension and at equilibriumconditions.Thismethodologyisusesasanappropriatemeanstodevelopandanalyzethe coredesignfornormaloperationanddownstreamuseinnuclearsafetyanalysisfortheKairosPowertest reactor.
1.1 FHRDESIGNFEATURES TheKPFHRtestreactorisagraphitemoderated,randomlypackedpebblebedreactorwithmolten fluoridesaltcoolantoperatingathightemperatureandnearatmosphericpressure(Reference1).The fuelintheKPFHRisbasedontheTriStructuralIsotropic(TRISO)carbonaceousmatrixcoatedparticle design.Thefuelkernelandsomeofthecoatingsontheparticlefuelprovideretentionoffission products.TRISOparticlesaredispersedwithinthegraphitematrixoffuelpebblesfuellayer.TheKPFHR fuelpebblesarebuoyantinreactorcoolantundersteadystateandpostulatedevents.Thereactor coolantisachemicallystablemoltenfluoridesaltmixture,2LiF:BeF2(Flibe)enrichedinLi7,whichalso providesretentionoffissionproductsthatescapefromanyfueldefects.Apebblehandlingandstorage system(PHSS)continuouslyinsertspebblesatthebottomofthereactorcoreandextractsthemfrom thetopofthereactorvesselduringnormaloperations.Pebblesareexaminedforburnupanddamage andareeitherreturnedtothevesselordirectedtostorage.
Aprimarycoolantloopcirculatesthereactorcoolantusingpumpsandtransferstheheattoan intermediatecoolantloopviaaheatexchangerfordirectrejectiontotheatmosphere.Thedesign includesadecayheatremovalsystem(DHRS)operatingpassivelyaboveathresholdpower.TheDHRS reliesonnaturalcirculationwithinthevesseltotransferheatfromthecoretotheDHRSthrough thermalradiationandconvectionheattransferfromtheoutervesselwalltotheDHRS.Asetinventory ofwaterintheDHRSispassivelyboiledoffoverthedurationofapostulatedeventinwhichtheprimary heattransfersystemisunavailable.
FissionproductcontrolintheKPFHRtestreactorreliesprimarilyonthemultiplebarrierswithintheTRISO fuelparticlesandfuelpebbletoensurethatthedoseatthesiteboundaryasaconsequenceofpostulated eventsmeetsregulatorylimits.Additionally,themoltensaltreactorcoolantservesasadistinctsecondary barrierprovidingretentionofsolidfissionproductsthatescapethefuelparticleandfuelpebblebarriers.
ThisadditionalretentionisakeyfeatureoftheenhancedsafetyandreducedsourcetermintheKPFHR.
ReactivitycontrolintheKPFHRtestreactorisaccomplishedprimarilybyinsertablecontrolelementsand shutdownelements.Theshutdownelementsdirectlyinsertintothepackedpebblebedcoreandthe controlelementsinsertoutsidethepebblebedintothenearbysidegraphitereflector.Forplannedpower maneuversoftheKPFHRreactor,onlythecontrolelementsareused.
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2 1.2 REGULATORYBACKGROUND 1.2.1 10CFRRequirements NuclearRegulatoryCommission(NRC)regulationsin10CFR50.34(a)(4)and(b)(4)requiresananalysis andevaluationofthedesignandperformanceofstructures,systems,andcomponentsofthefacilitywith theobjectiveofassessingtherisktopublichealthandsafetyresultingfromoperationofthefacilityand including determination of the margins of safety during normal operations and transient conditions anticipated during the life of the facility, and the adequacy of structures, systems, and components providedforthepreventionofaccidentsandthemitigationoftheconsequencesofaccidents.
Themethodologydescribedinthisreportisusedtoanalyzethefuelandcoreduringnormaloperation andpostulatedevents.
1.2.2 PrincipalDesignCriteria TheprincipaldesigncriteriathatapplytoaKPFHRtestreactorarecontainedinthePrincipalDesign CriteriafortheKairosPowerFluorideSaltCooledHighTemperatureReactorTopicalReport"(Reference 2).Whiletheseprincipaldesigncriteria(PDC)donotapplydirectlytothemethodology,thecoreand analysismethodologyisusedtoperformthenecessaryanalyseswhichdemonstratecomplianceofthe designwiththefollowingPDC.ThefollowingPDCarerelevant:
PDC10,Reactordesign Thereactorcoreandassociatedheatremoval,control,andprotectionsystemsshallbedesignedwith appropriatemargintoensurethatspecifiedacceptablesystemradionuclidereleasedesignlimitsare not exceeded during any condition of normal operation, including the effects of anticipated operationaloccurrences.
PDC11,Reactorinherentprotection Thereactorcoreandassociatedsystemsthatcontributetoreactivityfeedbackshallbedesignedso that, in the power operating range, the net effect of the prompt inherent nuclear feedback characteristicstendstocompensateforarapidincreaseinreactivity.
PDC12,Suppressionofreactorpoweroscillations Thereactorcore;associatedstructures;andassociatedcoolant,control,andprotectionsystems shallbedesignedtoensurethatpoweroscillationsthatcanresultinconditionsexceedingspecified acceptablesystemradionuclidereleasedesignlimitsarenotpossibleorcanbereliablyandreadily detectedandsuppressed.
PDC16,Containmentdesign Areactorfunctionalcontainment,consistingofmultiplebarriersinternaland/orexternaltothe reactoranditscoolingsystem,shallbeprovidedtocontrolthereleaseofradioactivitytothe environmentandtoensurethatthefunctionalcontainmentdesignconditionswhicharesafety significantarenotexceededforaslongaspostulatedaccidentconditionsrequire.
PDC25,Protectionsystemrequirementsforreactivitycontrolmalfunctions Theprotectionsystemshallbedesignedtoensurethatspecifiedacceptablesystemradionuclide releasedesignlimitsarenotexceededduringanyanticipatedoperationaloccurrence,accounting forasinglemalfunctionofthereactivitycontrolsystems.
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3 PDC26,Reactivitycontrolsystems Aminimumoftworeactivitycontrolsystemsormeansshallprovide:
(1)Ameansofinsertingnegativereactivityatasufficientrateandamounttoassure,withappropriate marginformalfunctions,thatthespecifiedacceptablesystemradionuclidereleasedesignlimitsare notexceededandsafeshutdownisachievedandmaintainedduringnormaloperation,including anticipatedoperationaloccurrences.
(2)Ameanswhichisindependentanddiversefromtheother(s),shallbecapableofcontrollingthe rateofreactivitychangesresultingfromplanned,normalpowerchangestoassurethatthespecified acceptablesystemradionuclidereleasedesignlimitsarenotexceeded.
(3)Ameansofinsertingnegativereactivityatasufficientrateandamounttoassure,withappropriate marginformalfunctions,thatthecapabilitytocoolthecoreismaintainedandameansofshutting downthereactorandmaintaining,ataminimum,asafeshutdownconditionfollowingapostulated accident.
(4)Ameansforholdingthereactorshutdownunderconditionswhichallowforinterventionssuchas fuelloading,inspectionandrepairshallbeprovided.
PDC28,Reactivitylimits Thereactivitycontrolsystemsshallbedesignedwithappropriatelimitsonthepotentialamountandrate ofreactivityincreasetoensurethattheeffectsofpostulatedreactivityaccidentscanneither:
(1)resultindamagetothesafetysignificantelementsofthereactorcoolantboundarygreaterthan limitedlocalyieldingnor (2)sufficientlydisturbthecore,itssupportstructures,orotherreactorvesselinternalstoimpair significantlythecapabilitytocoolthecore.
Themethodsdescribedinthistopicalreportareusedtocalculatethepowerdistributionswhicharean input to the fuel performance calculations that assure that specified acceptable system radionuclide releasedesignlimits(SARRDLs)willbemetasdescribedinPDC10.Similarly,coredesignmethodsare usedtocalculatethereactivitycoefficientstoassurethattheneteffectofthepromptinherentnuclear feedbackcharacteristicstendstocompensateforarapidincreaseinreactivityasdescribedinPDC11.The inherentcharacteristicoftheKPFHRtestreactor(smallcoreandlongneutrondiffusionlength)ensure thatpoweroscillationsdonotresultinconditionsexceedingSARRDLsasdescribedinPDC12.TheKPFHR usesafunctionalcontainmenttoensurethatradiologicalreleasestothepublicarewithinrequiredlimits asdescribedinPDC16.Themethodsdescribedinthisreportprovidetheinputforthefuelperformance calculationthatassuresthatthebarrierstoradiologicalreleasefromthefuelarenotcompromised.PDC 25 requires that the protection system be designed to ensure that the SARRDL is not exceeded for anticipatedoperationaloccurrencesandthemethodsinthisreportareusedtosupportthatdesign.
Shutdownmargincalculationsperformedwiththemethodologyinthistopicalreportensurethatthe requirementsofPDC26,ReactivityControlSystemsaresatisfied.Finally,PDC28requiresthatreactivity systemsaredesignedsuchthattheamountandrateofreactivityadditioncannotresultindamagetothe reactorcoolantboundaryortothecore,itssupportstructure,andotherreactorvesselinternals.The nucleardesignmethodsdescribedinthistopicalreportareusedtosupporttheassessmentthattheKP FHRmeetsPDC28.
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4 2
COREPHYSICSANDDESIGN ThecoredesignandanalysismethodologyalignsverycloselywiththephysicalbehaviorofaKPFHRcore.
ThefollowingsectiondescribesthereactorcorephysicsoftheKPFHRandwillserveasreferenceforthe descriptionofthemodelingtoolsandcapabilitiesusedincoredesign.
2.1 DESCRIPTION
TheKPFHRcorecontainsthousandsofrandomlypackedbuoyantfuelpebblesthatslowlyascendthrough thereactorcore.Pebblesarecontinuouslyinsertedatthebottomofthereactorandextractedfromthe top. The dynamics of the reactor core is characterized by the transition from a startup core to an equilibriumcoreovertime.Thefuelpebblesmaycontainnaturaluraniumallthewayupto19.55wt%U 235toreduceeffectiveenrichmentandcorereactivityinearlystartupcoreoperations.Dependingonthe chosenstartupandoperationalschemes,thecorewillalsocontainafractionofgraphiteonlymoderator pebblestomaintainthedesiredcarbontoheavymetalatomratio.Similartothewatertofuelvolume ratioinlightwaterreactors,thecarbontoheavymetalatomratioisusedinFHRstodefinetheneutron moderationconditions(overmoderatedorundermoderated)andthemixingofdifferentpebbletypes facilitatesmaintainingthecoreinundermoderatedconditions.
Whendefiningthedesiredcarbontoheavymetalratio,itisalsoimportanttorecognizetheroleofthe reactorcoolant.Flibeisamoderatorbutalsoanabsorberduemainlytolithium6,anaturalisotopeof lithium (7.59% abundance) with a large thermal absorption cross section. Enriching lithium in Li7 is required for acceptable core performance (i.e., fuel utilization) but also to ensure negative coolant temperaturefeedbacks.
AnincreaseintemperatureofFlibeleadstoadecreaseofits densitywith twocompetingreactivity feedbacks: a positive feedback due to reduced absorption and a negative feedback due to reduced moderationbyFlibe.Thelattereffectisafunctionofthecarbontoheavymetalratio;therefore,the combinedreactivityfeedbackcanbedesignedtobenegativebycontrollingthecarbontoheavymetal ratio.Aftersomeperiodofoperation,Li6isconsumedanditsconcentrationislowerthaninfreshFlibe.
Nevertheless, lithium6 in Flibe is also produced by (n,) reactions on Be9 leading eventually to an equilibriumconcentration..SaltimpuritiespresentinfreshFlibearealsoparasiticabsorbersinaddition totheaccumulationofothercorrosionmaterial,eachofwhichhaveanimpactonthecoolantreactivity coefficients.Thepropertiesandspecificationsforthereactorcoolantaredescribedin"ReactorCoolant fortheKairosPowerFluorideSaltCooled,HighTemperatureReactor"topicalreport(Reference18).
Theabilitytocontrolthemixtureofpebbletypesinthecoreallowsexcessreactivitytobeminimized duringstartupandoperation.Corereactivityisalsocontrolledbythemovementofthecontrolelements.
Shutdown elements are also available for insertion for safe shutdown at all core states. The KPFHR thermalenergytransferphenomenainthecorearedescribedinFigure21.Duringnormaloperating conditions,thermalpowergeneratedwithinthefuelistransferredbyconductiontothepebblesurface.
Thethermalenergyismainlytransferredviaconvectionfromthepebblesurfacebythecoolantthatflows throughtherandomlypackedbed.Atthesametimeasmallerportionofthethermalenergyistransferred byamixedregimeofconductionandthermalradiation.Specifically,pebbletopebbleheatconduction throughastagnantfluid,pebbletopebbleconduction,andpebbletopebbleradiation.Figure21shows these heat transfer modes and those outside the reactor core as well. Bypass flow, core barrel, downcomer,reactorvesselanddecayheatremovalheattransfermechanismsarealsohighlightedinthis figure.
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5 Aportionofthereactorcoolantflow,referredtoasthebypassflowfraction,doesnotflowthroughthe core.Thethermalenergybalancewithinthereactorcoredeterminesthetemperaturedistributionwithin thefuel,moderatorandthecoolantthatflowsthroughthecore.Largerbypassflowfractionsresultin highercoolanttemperaturesinthecore.Thetemperaturedistributionisimportantbecausetemperature caninfluencecorereactivitylevels,burnup,andpowershapes.
2.2 FUELDESCRIPTION 2.2.1 TRISOParticles TheKPFHRTRISOparticlesincludeaUCOkernel,aporouscarbonbufferlayer,andinnerpyrolyticcarbon (IPyC), silicon carbide (SiC), and outer pyrolytic carbon (OPyC) layers, as shown in Figure 22. TRISO particlesareovercoatedwithamixtureofnaturalandsyntheticgraphite,andresinbindermaterial.The KPFHRfuelparticlekernelsarecomposedofUCO,amixtureofUO2,UC,andUC2.Theovercoatthickness isspecifiedtoproduceanominal37%particlepackingfractionafterisostaticpressingandheattreatment inthepebbleannularfuelregionresultingin~16,000particlesperKPFHRpebble.
2.2.2 KPFHRFuelPebbles TheKPFHRfuelpebbledesignis40mmindiameterandhasthreeregionswithspecificfunctionsthat complementthepebblebedFHRdesign,whichisshowninFigure22.TheinnermostregionoftheKP FHRfuelpebblecontainsalowdensitycarbonmatrixcore.Thefunctionofthisregionistomakethe pebblebuoyantintheFlibecoolant.Anannularfuelregionshellislocatedonthesurfaceoftheinner carbonmatrixcore.ThisregioniscomposedofacarbonmatrixembeddedwithTRISOfuelparticles.The factthatthefuelparticlesareclosertothepebblesurfacethaninotherdesigns(e.g.,hightemperature gasreactor)reducesthefueltemperaturesrelativetothosedesigns.Afuelfreecarbonmatrixshellis locatedonthesurfaceofthefuelregiontoprotectthefuelregionfrom mechanicaldamageduring handlingandoperation.
2.3 REACTORCOREDESIGN AnaxialsectionoftheHermesreactorcanbeseeninFigure23.InatypicalKPFHRreactorcore,there areafewdesignfeaturespresentthatneedtobecapturedintheanalysis:thecylindricalpebblebed region,theupperandlowerconicregions,thefuelingregion,thedefuelingchute,coolantinletandoutlet channelsinthereflector,bypassandengineeredchannelsinthereflector,andthereactivitycontroland shutdownsystem(RCSS).
Thecoreistheregionofthepebblebedthatproducesconsiderablefissionpowerdensity,determinedas theregionfromthetopoftheupperconicregionofthecoretothebottomofthelowerconicregionof thecore.Coregeometricalcharacteristicssuchastheconicregionsanddefuelingchutearedesignedto supporta moreuniform burnupandfuelperformancein the core,astheconicregions andrelative diametersofdefuelingchuteandcylindricalsectionimpactpebblevelocityprofileandresidencetime.
Thefunctionofthefuelingregion,locatedatthebottomofthereactorcore,istoguidethepebbles comingfromtheinsertionline(s)intothereactorcore.Thedefuelingchute,locatedatthetopofthe reactorcore,isalsodesignedtobealowpowerproducingregionwherepebbleshaveadequateamount oftimetoallowforthedecayofshortlivedfissionproducts.Thedecayheatgenerationisthenlow enoughforthepebblehandlingsystemtooperatewithindesignedtemperaturelimitstoacceptthe extractedpebble.
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6 Coolantinletandoutletchannelslocatedinthebottomandtopreflector,respectively,aredesignedto reducepressurelosseswhileachievingacceptableflowdistributionandflowratesthroughthecore.The blocktypereflectordesignischaracterizedbythepresenceofradialandaxialspokegapsbetweenblocks andattheinterfacewiththevesselcorebarrel.Thisgeometrycausesaportionofthemassflowrateto bypassthecoreregion.Engineeredchannelsinthegraphiteblocksallowforthemovementofreactivity control elements placed excore and any additional channels required to reduce temperature in the reflector.
The reactivity control and shutdown system consist of control elements that insert directly into the reflector(neartheperipheryofthecore)andshutdownelementsthatdirectlyinsertintothepebblebed.
ThecontrolelementsarecreditedonlyforallplannedpowermaneuversoftheKPFHRreactor.Toachieve shorttermshutdown(i.e.notconsideringdelayedimpactfromxenon),onlythecontrolelementsare needed.Toachievesafeshutdownconditions,theshutdownelementsareusedassumingthehighest worthshutdownelementisfullywithdrawn(stuck).Thedesignofthereactivitycontrolandshutdown systemmustsatisfyPDC25andPDC26(Reference2).
2.4 OPERATIONALREGIMES TherearefourmainperiodsofcoreoperationinthelifeoftheKPFHRreactorwithrespecttocriticality and composition: startup, power ascension, approach to equilibrium core, and equilibrium core. An illustrationofthesestagescanbeobservedinFigure24.
((
))
Whilestillsubcritical,sourcerangecontrolelementworthtestingisperformedbymeasuringchangesin neutronmultiplicationfromastartupsource.Thedistributionoffluxisalsomonitoredandassessed againstpredictedcalculationsduringthisstage.Oncecriticalityisachievedandatzeropower,isothermal reactivitycoefficienttestingisperformedandcomparedagainstpredictedcalculations.
Onceallzeropowerphysicstestingiscompleted,theascensiontothepowerphasebegins.Theprimary saltpumprunsatreducedspeedtoprovideforcedcirculation.Asthepowerlevelincreasesfromzero power,negativereactivityfeedbacksarisefromtemperatureincreases,thebuildupofxenon,andthe depletion of fuel. To compensate for these effects, the reactivity control elements can be partially withdrawn.Thisbalanceofexcessreactivityandextractionofheatfromthecorecontinuesuntilfull powerisreached.
Atfullpower(ortheinitialpowerplateau),theapproachtoequilibriumcorebegins.Fortheinitialcore composition,theradionuclideinventoryismostlyfreshfuel,andburnuphasnotyetaccumulated.To compensateforaccumulatedburnup,freshfuelpebblesareadded,anddepletedpebblesremoved,ata ratethatmaintainscorereactivity.Aftersomeperiodofpoweroperation,theisotopicconcentrationwill belargelyunchanged,andastablerateofinsertionandextractionoffuelwillbereached(assuming
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7 constantpower).Atthispoint,theequilibriumcorehasbeenreached,whichisdesignedtostaywithin thedesignedcoolantreactivitycoefficients,powerperparticlelimits,andthedesiredexcessreactivity.
2.5 PHENOMENAIDENTIFICATIONANDRANKINGTABLE APIRTevaluationwasconductedfortheKPFHRcoredesign.AfullreviewoftheexistingGeorgiaInstitute ofTechnologyFHRneutronicsPIRT(Reference3),whichusestheAdvancedHighTemperatureReactor (AHTR)reactordesignasthebasis,wasperformedpriortobeginningtheKPFHRPIRT.Thedescriptionof FiguresofMerit(FOMs)andknowledgelevelnumberingusedinthePIRTareasfollows:
- FOM1:Multiplicationfactor(1:Lowimpact,2:Mediumimpact,and3:Highimpact)
- FOM2:Powerdistribution(1:Lowimpact,2:Mediumimpact,and3:Highimpact)
- Knowledge:Knowledgelevel(1:Low,2:Medium,and3:High)
AsummaryoftheKPFHRPIRTresultsareprovidedinAppendixBNeutronicsPIRTfortheKPFHR.
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ThepredictivecapabilitiesrequirementsfortheKPFHRcorethermalhydraulics(TH)modelingfollowthe mostrelevantcoreTHPIRTphenomena.
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COREMODELING
3.1 MODELING TheKPFHRcoreconfigurationisheterogeneousandnonstationary.Thepebblebedcontinuouslyevolves fromanearlystartupphasetoastatisticallysteadyburnupequilibriumcondition.KPFHRcorephysical characteristicssuchascoregeometry,heterogeneity,andpebblebedmotionrequireuniquemodeling approaches.ThecoredesignalsorequiresdifferentmodelingapproachesduetothelackofexistingKP FHRdata.
3.2 MODELINGPARADIGM Themethodologydevelopedforcoreanalysisanddesignalignsverycloselywiththephysicalbehaviorof thecore.TheKPFHRcoremodelparadigmincludesdiscreteelementsmethods(DEM),neutronicsand THmoduleswithseveraldegreesofexplicitcouplingbetweenthem.
((
))TheneutronicanalysesoftheKPFHRcoreaccountsforthe doubleheterogeneityofTRISOparticlesandpebbleswithoutanyneedofperformingvalidationoflower ordermethods,whichalsoincludestheuseofcontinuousenergyMonteCarlo.Theexplicitneutronic modelofthecoreisusedtoinformtheloworderthermalhydraulicmodelingpowerdistributionusedto providematerialstemperaturesfeedbackforreactivitycalculations;themodelisalsocapableofcoupling withburnupcalculations.
3.3 DATAFLOW TheKPFHRsteadystateandpseudosteadystatecoredesignmodelingworkflowanddataexchange consistsofdifferentdegreesofcouplingbetweenDEM,neutronicsandTHmodules.Figure31presents agraphicalsummaryofthedataflowandprocessingofthecoremodelingparadigm.
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3.4 MODELINGBOUNDARIESANDOUTPUTPARAMETERS Thedomainsofinterestformodelingarefirstdeterminedbeforeperformingcoreanalysisforcalculating quantitiesofinterestforreactorsafetyandforinputintodownstreamuseinsafetyanalysisandsource term calculations. Domains of interest are both the geometric and material boundaries that are considered. These domains of interest are defined for each of the DEM, neutronics, and thermal hydraulicscalculationsandareshowninFigure32.Arepresentativefigureshowingtheaxialsectionof theHermesvessel(withsimplifiedinternals)alongwithalistofthegeometricandmaterialboundaries foreachcalculationisprovidedinFigure32.
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DEMconsidersthecoreshape,reflectormaterial,thepebbles,andthecoolantflowthroughthecore when performingcalculations.The coreshape,wherethe pebblesreside,isdefined by thereflector structure, which includes the cylindrical section of the core, the upper and lower conic regions, the defuelingchute,andthefuelingregion.
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Thermalhydraulicscalculationsarealsothreedimensionalcalculations((
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Using these boundaries for core analysis, the calculated output quantities of interest from this methodologyincludethefollowing:
Reactivitycoefficients o
Fueltemperature o
Moderatortemperature o
Coolanttemperature o
Coolantvoid o
Reflectortemperature
Controlandshutdownelementworth o
Integralworth o
Differentialworth
Powerdistribution o
Peakingfactor o
Axialandradialpowerprofile
Kineticsparameters o
Effectivedelayedneutronfraction o
Effectiveneutronmeangenerationtime
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Promptneutronmeanlifetime ForpostulatedeventmodelingoftheKPFHR,thefollowingdataisused:reactivitycoefficients,kinetics parameters,shutdownmargin,differentialrodworths,andpowershape(axialandradial).Thetoolsused, themethodology,andexamplecalculationatequilibriumforeachofthesequantitiesareprovidedin Section4,Section5,andAppendixA,respectively.Thisdatawillbeprovidedasinputstosafetyanalysis atthefollowingcorecompositionalregimes(seeSection2.4):startupandtheequilibriumcore.Thiscan alsobedoneforothercorestatesbetweenstartupandequilibrium,asneeded.Conservativeselectionof theappliedassociateduncertaintiesisusedforeachofthesequantitiesforthepurposesofpostulated event analysis (upper or lower bound), and each parameters associated uncertainty analysis methodologyisdescribedinSection6.
Thefuelcompositionatequilibriumcoreisalsousedforsourcetermanalysis.Conservativeselectionof burnup uncertainties are applied for the purposes of source term analysis (whether upper or lower bound),andtheburnupuncertaintyanalysismethodologyisdescribedinSection6.4.
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COREDESIGNTOOLBOX InordertodevelopthemodelingmethodologydescribedinSection3,aseriesofsoftwarecodesareused alongwithdifferentcodewrappersforcouplinganddataexchange(seeFigure31).Thesoftwareused byKairosPowerforcoredesignincludesSerpent2fortheneutronicmoduleandSTARCCM+forDEMand THmodeling.KACEGEN,KairosPowerAdvancedCoreSimulator(KPACS),andKairosPowerAdvanced Thermal Hydraulics (KPATH) are internally developed wrapper codes that have been developed to processandexchangedatabetweensoftwarecodesandlibraries.Thesoftwarediscussedinthisreportis developedandmaintainedundertheKairosPowerQualityAssurance(QA)program.
Theverification,validationanduncertaintyquantificationmethodologyhasbeendevelopedtoreduce andcontrolallthesourcesoferroranduncertaintybetweenSTARCCM+modelsusedincoredesignand theirFOMspredictivecapabilities.Theverificationprocessconsistsofsoftwareandnumericalsolution verificationactivities.Softwareverificationaimstoensuresthatthediscretizedmodelisanaccurate representationofthecontinuousmathematicalmodel,andthattherearenouserdefinedcodeerrors.
Validation is the process of determining the degree to which a mathematical model is an accurate representationoftherealworldfromtheperspectiveofitsintendeduse.Thisisdonebycomparingthe modeloutputs(FOMs)withexperimentalmeasurementsand/orhighordernumericalresults.
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4.1 CODES 4.1.1 STARCCM+
Description STARCCM+isusedforDEMandTHmodeling.Theverification,validationanduncertaintyquantification methodologyhasbeendevelopedtoreduceandcontrolallthesourcesoferroranduncertaintybetween STARCCM+modelsusedincoredesignandtheirFOMspredictivecapabilities.TheV&VmethodsforDEM and TH are very similar. The TH V&V methodology focuses on the prediction of the core material temperatures(fuel,moderatorandcoolant)whereastheDEMmethodologyfocusesonthepebblecenter locationsandtheirresidencetimewithinthecore.Becausedesigntoreducebypassflowisperformed independentlyduetothecomplexityofbypassflowpaths,bypassflowistreatedasadefinedfractionof totalcoolantflowwhichisaninputparametertocoredesignandanalysis.
V&VPlan
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Table42summarizesthevalidationcasesthatwillbeusedforSTARCCM+.
4.1.2 Serpent2 Description Serpent2(Reference4)isthemainneutronicstoolforreactorcoredesignandoutputtosafetyanalysis.
Serpent2hasbeenextensivelyusedacrossacademiaandindustryandhasbeenvalidatedagainstvarious benchmarks. It is used at Kairos for a variety of calculations, including multiplication factor, control element worths, reactivity coefficients, power distribution, kinetics parameters, nuclear heating, and burnupcalculations.
TheuseofSerpent2provideshighfidelitysimulation,whichisimportantduetolackofexperimentalFHR operatingexperience.TherearetwokeyfeaturesthatareavailableinSerpent2:1)theabilitytoexplicitly capturethedoubleheterogeneityofthefuelpebbleandTRISOparticles,and2)theimplementationof Woodcockdeltatracking(Reference4).Thereducedcomputationalburdenwiththeimplementationof deltatrackingalsoallowsforfull3Dcoremodeling.
V&VPlan
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4.2 WRAPPERCODES Thefollowingwrappercodesareusedtotransferinformationbetweentheneutronicand thermal/hydrauliccodes.
4.2.1 KACEGEN Description KACEGEN(KairosACEGenerator)isaninternaltoolthatNJOY21usestoproducetheACEformatnuclear datalibraries.NJOY21(Reference9)isanucleardataprocessingtoolcapableofproducingbothpointwise andmultigroupcrosssectiondatafromtheU.S.EvaluatedNuclearDataFiles(ENDF)format.KACEGEN, asanexample,currentlyhasthecapabilitytogenerateACElibrariesfromanyENDF6library,including JEFF3.3,ENDFBVII.1,andENDFBVIII.0.Bothneutroncrosssectionsandthermalscatteringlibrariesare producedforeachisotopeavailableinthelibrary,andthermalscatteringlibrariescanbediscreteor continuous in energy. ACE data has been generated at the following temperatures, tailored to the temperaturerangesintheKPFHRdesign:273.15,300,600,700,800,900,1000,1100,1200,1500,1800, and2200degreesK.
ThehighleveldataflowoftheKACEGENcanbeseeninFigure41.Tostart,libraryfieldsandpathsfora particularlibrarysetareloaded,thenthecompletelistofisotopesarerunandwrittenforneutroncross sectiongeneration.Ifthermalscatteringisalsobeinggenerated,theLEAPRsmoduleofNJOY21isrunfor eithercontinuousand/ordiscretethermalscatteringlaw(TSLs).
PointwisecrosssectionsarecomparedbetweenLANLMCNPandOECDevaluatedlibrariesandtheones evaluatedbyKACEGEN/NJOY.
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inthatthebehaviorofneutronspectrumandtemperatureaffectingpebblesinspecificallydefined regionsofthecore(i.e.,spectralzones)canbeassumedconstantduetoslowlyvaryingneutronfluxand temperature.((
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ThedifferencebetweenKPACSandothercodesisthatitreliesonthehighestfidelitytoolsavailable.
Serpent2isusedtoperformthefullcoretransportandfueldepletioncalculations,andthepebble motionandlocationsareinformedbyDEMinSTARCCM+.KPACScanalsobelooselycoupledwith KPATH,forupdateofcoretemperaturedistributionasneededthroughouttheKPFHRoperationallife.
4.2.3 KPATH Description KPATHistheinternallydevelopedsoftwareinfrastructurethatcouplesSTARCCM+toSerpent2.The computational fluid dynamic (CFD)neutronic steadystate twoway explicit coupling, is such that it providesTHfeedbacksforcriticalitycalculations,powershape,andpowerpeakingcalculations.
WithintheKPATHcomputationalframework,STARCCM+isutilizedasasteadystatesolverforheat transferandfluidflowintheformofa3Dporousmediamodel.Onlynormalsteadystateoperating conditionsareconsidered.ThecouplingmethodologythathasbeendevelopediscapableofusingKPATH duringallcorephasesfromstartuptoequilibriumcoreconditions;thismeansthatKPATHcanbeusedat differentcorephasesincombinationwithKPACS.
TheKPATHcodewrappermanagesthethermalpowerandmaterialstemperaturesexchangebetween Serpent2spectralzonesandSTARCCM+porousregionasshowninFigure42.Convergenceisreached whenkeffandcorematerialtemperaturesdifferenceswiththepreviousiterationiswithinaspecified tolerance.
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CALCULATIONMETHODOLOGY Thissectionprovidesanoveralldescriptionofthemodelsusedwithinthecoredesignandanalysismodel.
5.1 DEMMODELING TheDiscreteElementMethod(DEM)isthemethodologyusedtogeneratethereactorcoregeometryfor theexplicitpebblemodelinginSerpent2.DEMisutilizedtosimulatethegranularflowbydescribingthe motionofmanyinteractingdiscretesolidpebbles.DEMmodelingprovidesdetailedresolutionthatother methodscannotachieve.((
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STARCCM+modelsDEMpebblesbasedonasoftparticleformulationinwhichparticlesareallowedto develop an overlap proportional to the contact force and can undergo large deformations without rupture.Thisoverlapisnotphysicallyrealisticbutisusedtoaidineaseofcomputation.Thecalculated contactforceisproportionaltotheoverlap,aswellastotheparticlematerialandgeometricproperties.
STARCCM+DEMprovidesalargeamountofdataforeverysinglepebblesuchastimehistories,velocity, position,andforces.Thedatacollectedprovideastatisticalbasisforneutroniccalculations.DEMprovides thelocationofthecentersofthefuelpebblesnecessaryforcriticalitycalculations.Burnupcalculations needmoreinformationinadditiontothelocationoftheindividualpebbles.DEMprovidesthepebble flowprofileinsidethereactorcoreandpebbleresidencetime.Themethodologytocalculateresidence timeisbasedonrecirculationofthepebblesinthecorefromtheentrytoexitpoint.
TheFOMsusedfortheDEMV&Vplanare:
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5.2 NEUTRONICS 5.2.1 MonteCarloConvergence
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5.2.2 FuelCycleAnalysis
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5.2.3 ReactivityCoefficients ThecalculationforreactivitycoefficientsisdoneusingEquation51.Wherexisthereactivitycoefficient withrespecttoquantityx,xisthechangeinquantityxwithrespecttoreferenceconditions(positiveor negative),krefistheneutronmultiplicationfactorofthecorecalculatedfromSerpent2atreference conditions,andkxistheneutronmultiplicationfactorofthecorecalculatedbySerpent2afterquantity xwaschangedbyx.
1 1
1
Equation51
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((
5.2.4 ControlWorthandShutdownMargin
))
Shutdownmarginisalsomaintainedatallcorestates.ThecontrolelementsintheRCSSareresponsible forallplanned,normalpowermaneuvers.TheworthrequirementsdependontheKPFHRdesignof interest.
ControlworthiscalculatedusingEquation52where,isthewithdrawnpositionand,isthe insertedpositionofinterest.DifferentialcontrolworthiscalculatedusingEquation53,where,is the neutron multiplication factor of the core for step position of interest,, is the neutron multiplicationfactorofthecoreforstep1positionofinterest,istheaxialpositionofthecontrol rod(s)forsteppositionofinterest,andistheaxialpositionofthecontrolrod(s)forstep1 positionofinterest.
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5.2.5 KineticsParameters In addition to reactivity coefficients, kinetics parameters such as delayed neutron fraction and their associated decay constant(s), neutron mean generation time, and neutron mean lifetime are also calculated. As discussed in Section 3.4, kinetics parameters are used for modeling timedependent behavioroftheKPFHR.Thecalculationofthesekineticsparametersiscalculatedusingtheiteratedfission probabilitymethod(Reference14).Theeffectivedelayedneutronfractionisdividedintosixgroups.
Delayedphotoneutrons,fromBe(,n)reactioninFlibe,willalsobeassessedtounderstandtheirimpact on the effective delayed neutron fraction and delayed neutron group structure (Reference 15). This impactfromdelayedphotoneutronsissmallerthanotherreactorsthathavebeenimpactedfromthis particularsourceofdelayedneutrons,suchasfromheavywater(D2O)reactors.
5.2.6 ReactorCoolantDepletion
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5.2.7 PowerDistribution
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5.2.8 VesselIrradiation
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5.3 THERMALHYDRAULICS
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5.3.1 PorousMediaModeling Packedbedsarecommonlyusedinchemicalengineeringsystemsbecausetheyhavehighlypredictable and uniform flow distributions and transport. The randomly packed pebble bed in the KPFHR core enablestheuseoflowordermathematicalmodelstopredictglobalflowdistributionsandheattransport.
TheTHmodelusedincoredesign,adoptsatwoequationporousmediamodeltodescribethemacroscale behavioroftheflowandenergytransportwithinthereactorcoreregion.Thecoreporousregioncanbe thermally coupled with other invessel solid regions, including the reflector structure, by the use of conjugate heat transfer modeling. The TH model resolved porous length scales characterize the liquid/solid phase mixture of liquid coolant and solid pebbles. The core macroscale porous model is derivedbyapplyingavolumeaveragingoperatortotheNavierStokesandtwophaseenergytransport equationsoverarepresentativeelementaryvolume.Thesolidandliquidphasesareassumedtobein nonthermal equilibrium; this allows modeling two separate temperature fields for the coolant and pebblesrespectively.Thesolidporousphaserepresentingthepebblesusesthefissionpowerdensityfrom Serpent2asanenergysourcetermandprovidesthepebbleaveragesurfacetemperaturedistribution.
Byremovinginformationaboutresolvedgeometry,thevolumeaveragingoperatorgeneratesadditional unknowntermsinthemomentumandenergyequationsthatneedamodelingmathematicalclosure correlation.Asisconventional,experimentalbasedcorrelationsareusedtomodelthelocalmomentum andheattransferinformationthatarelostduringthevolumeaveragingprocess.Figure53showsan exampleoflocalheattransferphenomenathatneedaclosurecorrelation.
Momentumclosuremodel
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ll Equation59
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Energyclosuremodels
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5.3.2 CoreMaterialTemperatures ThepebblesandcoolanttemperaturefieldsresultfromtheporousmediumvolumeaveragedNavier Stokes equations and energy equations are used as baseline for the core material temperatures evaluation.ThecorematerialtemperaturesthattheTHmodelprovidestotheneutronicmoduleare:
Flibetemperature Graphitepebbletemperature Pebblelayersmaterialtemperatures o Lowdensitycore o Fuelmatrixlayertemperature o Shelllayer TRISOlayersmaterialtemperatures o OuterPyClayer o SiCLayer o InnerSiCLayer o BufferLayer FuelKerneltemperature
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21 The spatial temperature distributions calculated for each material type that are fed back into the neutronicsmodulearevolumeaveragedbasedonzonesfortheleveloffidelitythatisrequiredforthe calculatedoutputparameterofinterest.
TheflexibilityoftheTHmoduleimplementationallowsthethermalcouplingwithanyotherreactorvessel internalsofrelevantneutronicimportance,asaconsequenceadditionalcorematerialtemperaturescan beaddedtothelistaboveforexplicitcoupling.
5.4 COREBYPASSMODELINGANDREFLECTORTEMPERATURE
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UNCERTAINTYANALYSISANDNUCLEARRELIABILITYFACTORS
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6.1 NUCLEARDATAUAPROPAGATIONMETHOD
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6.2 MANUFACTURINGINPUTSUAPROPAGATIONMETHOD
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6.3 KINETICSPARAMETERSCALCULATIONUAMETHOD
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SUMMARY
7.1 CONCLUSION
Thisreportdocumentsthecoredesignandanalysismethodologywhichisusedtoperformnuclear designandthermalhydrauliccalculationsfortheKPFHR,includingreactivitycoefficients,shutdown margin,powerdistribution,andreactorcorekineticsparameters.Thesemethodsapplytonormal operationandpostulatedeventsforaKPFHRtestreactor.
ThemethodologyforperformingcoredesignandanalysisisbasedprimarilyontheSerpent2andSTAR CCM+codes.Thesehighfidelityanalyticaltoolsareusedinamethodologyspecificallytailoredtothe uniquefeaturesoftheKPFHR.
V&VoftheSerpent2andSTARCCM+codesisperformedthroughcomparisonswithexperimentalresults andtoanalysesfromothercodes.Theuncertaintyintheresultsfromthesecodesisestablishedbasedon industryexperienceandwithaconservativebiasduetothelackofoperatingexperiencewithKPFHRs.
TheconservativedeterminationofuncertaintiesisconfirmedusingtheSCALEcodesystem.
ThecompletionoftheV&VofthecodesandmethodologywillbesubmittedtotheNRCaspartofafuture licensingapplicationsthatmakesuseofthismethodology.Inaddition,thevaluesoftheuncertainties usedinanyapplicationswillbedocumentedaspartofthesafetyanalysisdocumentsassociatedwiththe application.
7.2 LIMITATIONS Thiscoredesignandanalysismethodologyissubjecttothefollowinglimitations:
- 1. The pebble velocity needs to be a small fraction of the time constant of delayed neutron precursors.
- 2. Rangeofcoolantvelocityisapplicabletotherangeoftheavailableheattransfercorrelations.
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W.G.D.Bedenig,ParameterStudiesConcerningtheFlowBehaviorofaPebblewithReferenceto theFuelElementMovementintheCoreoftheTHTR300MWePrototypeReactor,Nuclear EngineeringandDesign,vol.7,pp.367378,1968.
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C.Keckler,N.Satvat,K.Johnson,B.HaughandM.Fratoni,"Photoneutronproductionand characterizationinfluoridesaltcooledhightemperaturereactors,"NuclearEngineeringand Design,vol.372,2021.
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SafetyStandardLossofpressurethroughfrictioninpebblebedcores.KTA3102.21987;Issue3/81.
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27 Table41.Serpent2RequirementsandPlannedCodetocodeBenchmarkValidation
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Table42.STARCCM+ValidationCases
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Table42.STARCCM+ValidationCases
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30 Table61.ScopeofUncertaintyAnalysisforCoreSafetyParameters
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31 Figure21. ThermalEnergyTransferPhenomenainKPFHR
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32 Figure22. KPFHRFuelPebbleandParticleDesign
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33 Figure23. AxialSectionoftheHermesCore
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34 Figure24. ReactorCoreOperationalRegimesoftheKPFHR
Note:Thexandyaxisarenotionalandarenottoscale.Belowthecriticallevelontheyaxisrepresents subcriticality,andabovethecriticallevelontheyaxisrepresentspowerlevel,buteacharenotional.
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35 Figure31. CoreDesignModules
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36 Figure32. CoreAnalysisBoundaries
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37 Figure41. HighlevelDataFlowofKACEGEN
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38 Figure42. KPATHFramework
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39 Figure51. ExampleIllustrationofAlgorithmforPebbleCirculationfortheCore
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40 Figure52. SpectralZonesUsedfortheHermesCore
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41 Figure53. LocalHeatTransferPhenomenainPebbleBedReactorConfiguration
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42 Figure54. PebbleandTRISOLayersTemperature
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43 Figure61. SCALEworkflowforanExampleDemonstrationInvolvingPerturbedParameters(in yellow)
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44 Figure62. DepletionMethodologyFlowDiagramforBurnupCalculationsofFuelPebbles
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A1 APPENDIXA EXAMPLECOREDESIGNMODEL This section presents an example of application of the core design modeling methodology for the evaluationofaKPFHRreactorwitha 35MWth powerlevel.FigureA1showsa typical sequenceof calculationsperformedbyusingthecoredesignmethodologydescribedinthisdocument.
TableA1summarizesthemainHermescore designinputparameters consideredin thisexampleof applicationofcoredesignmethodology.
FigureA2showsthecoregeometryandnomenclatureassociatedwithcoremainregions.
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TableA1.CoreDesignInputParameters
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A5 TableA2.ZonebasedPowerDensityDistribution
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A6 TableA3.ReactivityCoefficientsatStartupandEquilibriumCore
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TableA4.ReactivityControlSystemRequirementsforShorttermHotShutdown
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TableA5.ReactivityShutdownSystemRequirementsforSafeShutdown
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TableA6.KineticParametersatEquilibriumConditions
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TableA7.GroupwiseEffectiveDelayedNeutronFractionandCorrespondingDecayConstantat EquilibriumCoreConditions
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TableA8.KineticParametersatStartupCoreConditions
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TableA9.GroupwiseEffectiveDelayedNeutronFractionandCorrespondingDecayConstantat StartupCoreConditions
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TableA10.CoolantTemperatureReactivityCoefficientsforFlibeofDifferentCompositions
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TableA11.keffwithandwithoutTHFeedback
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FigureA1. CoreDesignCalculationDiagram
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FigureA2. KPFHRCoreGeometry
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FigureA3. CrosssectionalViewsofNormalizedInstantaneousPebbleResidenceTime
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FigureA4.SpectralZonesusedfortheHermesCore
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FigureA5. Fast(>0.1MeV)(left),Intermediate(middle),andThermal(<1.86eV)(right)Neutron FluxinHermesEquilibriumCore
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FigureA6. DifferentialWorthofaSingleElementWithdrawal,fromAllIn(RCSonly)
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FigureA7. ReactivityShutdownSystemWorthCurves,N1
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FigureA8. Powerdensity(left),Flibetemperature(center),andFuelKernelCenterlineTemperature (right)
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A23 FigureA9. AxialBinnedPowerDensityProfileinthecore,excludingConvergingandDiverging Regions(left),andtheRelativeDifferenceofAxialPowerShapebetweenConstantTemperatureand KPATHResults(right)
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A24 FigureA10.RadialBinnedPowerDensityProfileintheCore(left),andRelativeDifferenceofRadial PowerShapebetweenConstantTemperatureandKPATHResults(right)
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B1 APPENDIXB NEUTRONICSPIRTFORTHEKPFHR
APhenomenaIdentificationRanking(PIRT)evaluationwasconductedfortheKPFHR.Asummaryofthe resultsofthePIRTareincludedforinformationinthisAppendix.ThedescriptionofFiguresofMerit (FOMs)andknowledgelevelnumberingareasfollows:
FOM1:Multiplicationfactor(1:Lowimpact,2:Mediumimpact,and3:Highimpact)
FOM2:Powerdistribution(1:Lowimpact,2:Mediumimpact,and3:Highimpact)
Knowledge:Knowledgelevel(1:Low,2:Medium,and3:High)
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