Text

Enclosure 4: KP-TR-017-NP, Rev. 1, KP-FHR Core Design and Analysis Methodology
	ML22272A598
Person / Time
Site:	Hermes File:Kairos Power icon.png
Issue date:	09/29/2022
From:	; Kairos Power
To:	; Office of Nuclear Reactor Regulation
Shared Package
ML22272A593	List: ML22272A594; ML22272A595; ML22272A598; ML22272A599;
References
	KP-NRC-2209-018 KP-TR-017-NP
	Download: ML22272A598 (81)
	v • d • e

KP-NRC-2209- 018

Enclosure 4 KP-FHR Core Design and Analysis Methodology, KP-TR-017-NP (Non-proprietary)

KPTR 017NP

Kairos PowerLLC

707 W.Tower Ave Alameda, CA94501

KP-FHR Core Design and Analysis Methodology

Technical Report

RevisionNo.1 DocumentDate:September2022

NonProprietary

KPFHRCoreDesign andAnalysis Methodology

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

COPYRIGHTNotice This document is the property of Kairos Power LLC (Kairos Power) and was prepared in support of the developmentoftheKairos PowerFluorideSaltCooled HighTemperatureReactor(KPFHR) design.Other thanbytheNuclearRegulatoryCommission(NRC)anditscontractorsas partofregulatory reviews ofthe KPFHR design, the content herein may not be reproduced, disclosed, or used, without prior written approvalofKairos Power.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Rev Description ofChange Date

0 InitialIssuance September2021

1 RevisionupdatesSection5.3.1, SectionA.2.3, TableA4,September2022 TableA5, TableA10 andFigure A7 toaddressfeedback fromNRCaudit

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

EXECUTIVE

SUMMARY

Kairos Power is pursuing the design, licensing, and deployment of a Fluoride Salt Cooled, High Temperature (KPFHR) testreactor.Toenablethese objectives,thedevelopmentofatechnologyspecific coredesignandanalysismethodologyisrequired.Thisreportdescribesthemethodology for corephysics andthermalhydraulicanalysisoftheKPFHR.

The KPFHR core design methodology is comprised of the Serpent 2 nuclear design and STARCCM+

thermal, fluid, and discrete element modeling design codes. These codes are connected by a series of wrapper codes. The verification and validation (V&V) methodology for Serpent 2 and STARCCM+ codes is described. The methodology is informed by a Phenomena Identification and Ranking Table (PIRT) evaluation.

Serpent 2 and STARCCM+ and the associated wrapper codes are used to calculate core composition at various phases of operation and corresponding parameters such as core reactivity coefficients, control and shutdown element worth, shutdown margin, power distribution and thermal hydraulic parameters.

The scope of this report applies to normal operation and postulated events. The methodology for using thecodestoperformthesecalculationsandthelimitationsontheuseofthismethodologyareprovided.

In addition, a methodology for calculating the uncertainty in these calculations is provided. Sample neutronic andthermalhydraulic results for aKPFHR areprovidedas anappendix.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TABLEOFCONTENTS 1 INTRODUCTION............................................................................................................................. 1 1.1 FHRDesign Features......................................................................................................................1 1.2 Regulatory background.................................................................................................................2 1.2.1 10 CFRRequirements..........................................................................................................2 1.2.2 PrincipalDesign Criteria......................................................................................................2 2 COREPHYSICSANDDESIGN........................................................................................................... 4 2.1 Description....................................................................................................................................4 2.2 FuelDescription.............................................................................................................................5 2.2.1 TRISO Particles....................................................................................................................5 2.2.2 KPFHR FuelPebbles...........................................................................................................5 2.3 Reactorcoredesign.......................................................................................................................5 2.4 Operationalregimes......................................................................................................................6 2.5 Phenomenaidentificationandrankingtable................................................................................7 3 COREMODELING........................................................................................................................... 8 3.1 Modeling.......................................................................................................................................8 3.2 Modeling paradigm.......................................................................................................................8 3.3 Dataflow.......................................................................................................................................8 3.4 Modeling boundariesandoutputparameters..............................................................................8 4 COREDESIGN TOOLBOX............................................................................................................... 11 4.1 Codes...........................................................................................................................................11 4.1.1 STARCCM+.......................................................................................................................11 4.1.2 Serpent2...........................................................................................................................12 4.2 Wrapper Codes............................................................................................................................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 Control WorthandShutdown Margin..............................................................................17 5.2.5 KineticsParameters..........................................................................................................17 5.2.6 ReactorCoolantDepletion................................................................................................17 5.2.7 PowerDistribution............................................................................................................18 5.2.8 VesselIrradiation..............................................................................................................18

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

5.3 Thermal hydraulics......................................................................................................................18 5.3.1 PorousMediaModeling....................................................................................................19 5.3.2 CoreMaterialTemperatures............................................................................................20 5.4 CoreBypass Modeling andReflectorTemperature....................................................................21 6 UNCERTAINTYANALYSIS ANDNUCLEARRELIABILITYFACTORS....................................................22 6.1 NuclearDataUAPropagationMethod.......................................................................................22 6.2 ManufacturingInputsUAPropagationMethod.........................................................................23 6.3 KineticsParametersCalculationUAMethod..............................................................................23 6.4 BurnupCalculation UAMethod..................................................................................................24 7

SUMMARY

................................................................................................................................... 25

7.1 CONCLUSION

...............................................................................................................................25 7.2 Limitations...................................................................................................................................25 8 REFERENCES................................................................................................................................26 AppendixA ExampleCoreDesignModel..................................................................................... A1 AppendixB NeutronicsPIRTfortheKPFHR................................................................................ B1

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

LISTOFTABLES Table41. Serpent2RequirementsandPlannedCodeto code BenchmarkValidation......................27 Table42. STARCCM+ ValidationCases................................................................................................28 Table61. ScopeofUncertaintyAnalysisfor CoreSafetyParameters..................................................30 TableA1. CoreDesign InputParameters.............................................................................................A4 TableA2. Zonebased PowerDensityDistribution..............................................................................A5 TableA3. ReactivityCoefficientsatStartup andEquilibriumCore.....................................................A6 TableA4. ReactivityControlSystemRequirementsfor Shortterm HotShutdown............................A7 TableA5. ReactivityShutdownSystemRequirementsfor SafeShutdown.........................................A 8 TableA6. Kinetic ParametersatEquilibriumConditions.....................................................................A9 TableA7. Groupwise Effective Delayed Neutron Fraction and Corresponding Decay Constant atEquilibriumCoreConditions..........................................................................A10 TableA8. Kinetic ParametersatStartupCoreConditions.................................................................A11 TableA9. Groupwise Effective Delayed Neutron Fraction and Corresponding Decay Constant atStartup CoreConditions.................................................................................A12 TableA10. CoolantTemperatureReactivityCoefficientsforFlibeofDifferentCompositions...........A13 TableA11. keff withandwithoutTHFeedback.................................................................................A14 TableB1. NeutronicsPIRT Resultsfor theKPFHR..............................................................................B2

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

LISTOFFIGURES Figure 21. ThermalEnergyTransferPhenomenainKPFHR.................................................................31 Figure 22. KPFHR FuelPebble andParticleDesign...............................................................................32 Figure 23. Axial SectionoftheHermesCore.........................................................................................33 Figure 24. ReactorCoreOperationalRegimesoftheKPFHR...............................................................34 Figure 31. CoreDesign Modules............................................................................................................35 Figure 32. CoreAnalysisBoundaries.....................................................................................................36 Figure 41. Highlevel DataFlow ofKACEGEN........................................................................................37 Figure 42. KPATHFramework................................................................................................................38 Figure 51. ExampleIllustration ofAlgorithmforPebbleCirculation for theCore................................39 Figure 52. SpectralZonesUsed for theHermesCore............................................................................40 Figure53. Local HeatTransferPhenomenainPebbleBedReactorConfiguration...............................41 Figure 54. PebbleandTRISOLayers Temperature................................................................................42 Figure 61. SCALE workflow for an Example Demonstration Involving Perturbed Parameters (inyellow).............................................................................................................................43 Figure 62. DepletionMethodologyFlowDiagramfor BurnupCalculationsofFuelPebbles................44 Figure A1. CoreDesign CalculationDiagram......................................................................................A15 Figure A2. KPFHR CoreGeometry......................................................................................................A16 Figure A3. Crosssectional ViewsofNormalized InstantaneousPebbleResidence Time..................A17 Figure A4. SpectralZonesused for theHermesCore.........................................................................A18 Figure A5. Fast (> 0.1 MeV) (left), Intermediate (middle), and Thermal (< 1.86 eV) (right)

NeutronFlux in HermesEquilibriumCore.........................................................................A19 Figure A6. Differential WorthofaSingleElementWithdrawal,fromAll In(RCSonly)......................A20 Figure A7. ReactivityShutdownSystemWorthCurves,N1..............................................................A21 Figure A8. Power density (left), Flibe temperature (center), and Fuel Kernel Centerline Temperature(right)...........................................................................................................A22 Figure A9. Axial BinnedPowerDensityProfile in thecore, excluding ConvergingandDiverging Regions(left), andtheRelativeDifferenceofAxialPowerShapebetweenConstant TemperatureandKPATHResults(right)............................................................................A23 Figure A10. Radial Binned Power Density Profile in the Core (left), and Relative Difference of RadialPowerShape between ConstantTemperatureandKPATHResults(right)............A24

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

NOMENCLATURE

Abbreviations/Acronyms ACE A CompactENDF AHTR AdvancedHighTemperature Reactor AOO AnticipatedOperational Occurrence CE ContinuousEnergy CFD ComputationalFluidDynamics CSAS CriticalitySafetyAnalysisSequence DEM DiscreteElementsMethod DHRS DecayHeatRemovalSystem ENDF EvaluatedNuclearDataFiles FHR Fluoridecooled High TemperatureReactor FOM Figureof Merit HTGR HighTemperatureGasReactor IET IntegralEffectTest IPyC InnerPyrolytic CarbonLayer KP Kairos Power KPACS Kairos PowerAdvancedCoreSimulator KPATH Kairos PowerAdvancedThermalHydraulics MG Multigroup NRC NuclearRegulatoryCommission OPyC OuterPyroliticCarbonLayer PDC PrincipalDesign Criteria PIRT PhenomenaIdentificationandRankingTable QA QualityAssurance RSS ReactivityShutdownSystem SARRDL SpecifiedAcceptableSystemRadiological ReleaseLimit SET SeparateEffect Test SiC SiliconCarbide TH ThermalHydraulics TRISO Tristructural Isotropic TSL ThermalScatteringLaw UA UncertaintyAnalysis V&V VerificationandValidation

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

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), PreliminarySafetyAnalysis Report, 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 equilibrium conditions. This methodology is uses as an appropriate means to develop and analyze the coredesignfornormaloperationanddownstreamusein nuclearsafetyanalysisfor theKairosPowertest reactor.

1.1 FHRDESIGN FEATURES

TheKPFHR testreactorisagraphitemoderated,randomlypacked pebble bedreactor withmolten fluoridesaltcoolantoperatingathigh temperatureandnearatmospheric pressure(Reference1).The fuelintheKPFHR isbasedontheTriStructural Isotropic(TRISO)carbonaceousmatrix coatedparticle design.Thefuelkernelandsome ofthecoatingsontheparticlefuelprovideretentionoffission products.TRISOparticlesaredispersedwithinthegraphitematrixoffuelpebblesfuellayer.TheKPFHR fuelpebblesarebuoyantinreactorcoolantundersteadystateandpostulatedevents.Thereactor coolantisachemicallystable moltenfluoridesaltmixture,2LiF:BeF2(Flibe)enrichedinLi7, whichalso providesretentionoffissionproductsthatescapefromany fueldefects.A pebblehandlingandstorage system(PHSS)continuouslyinsertspebblesatthebottom ofthereactorcoreandextractsthem from thetopofthereactorvesselduring normal operations. Pebblesareexaminedfor burnupanddamage andareeitherreturnedtothevesselordirected tostorage.

A primary coolantloopcirculatesthereactorcoolantusingpumpsandtransferstheheattoan intermediatecoolantloopviaaheatexchanger for directrejectiontotheatmosphere.Thedesign includesadecayheat removalsystem(DHRS)operatingpassivelyaboveathreshold power.TheDHRS reliesonnaturalcirculationwithinthevesseltotransferheatfromthecoretotheDHRSthrough thermalradiationand convectionheattransferfromtheoutervesselwalltotheDHRS.A setinventory ofwaterintheDHRSis passively boiledoff overthedurationofapostulated eventinwhichtheprimary heattransfersystemisunavailable.

Fissionproductcontrol in theKPFHR testreactorreliesprimarilyonthemultiplebarrierswithintheTRISO fuelparticlesandfuelpebbletoensurethatthedoseatthesiteboundaryas aconsequenceofpostulated eventsmeetsregulatorylimits.Additionally,themoltensaltreactorcoolantservesas adistinctsecondary barrierprovidingretention ofsolidfissionproductsthatescape thefuelparticleandfuelpebble barriers.

Thisadditional retentionisakey featureoftheenhancedsafetyandreducedsourcetermintheKPFHR.

ReactivitycontrolintheKPFHR testreactorisaccomplishedprimarily byinsertablecontrolelementsand shutdown elements. The shutdown elements directly insert into the packed pebble bed core and the controlelementsinsertoutside thepebblebedintothenearbysidegraphitereflector.For plannedpower maneuversoftheKPFHR reactor,onlythecontrol elementsareused.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

1.2 REGULATORYBACKGROUND

1.2.1 10 CFR Requirements Nuclear Regulatory Commission (NRC) regulations in 10 CFR 50.34(a)(4) and (b)(4) requires an analysis andevaluation ofthedesign andperformanceofstructures, systems,andcomponentsofthefacilitywith theobjectiveofassessing theriskto publichealthandsafetyresultingfromoperationofthefacilityand 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 providedfor thepreventionofaccidentsandthemitigation oftheconsequencesofaccidents.

The methodology described in this report is used to analyze the fuel and core during normal operation andpostulatedevents.

1.2.2 PrincipalDesignCriteria The principal design criteria that apply to a KPFHR test reactor are contained in the Principal Design Criteria for the Kairos Power Fluoride SaltCooled High Temperature Reactor Topical Report" (Reference 2). While these principal design criteria (PDC) do not apply directly to the methodology, the core and analysis methodology is used to perform the necessary analyses which demonstrate compliance of the designwiththefollowingPDC.ThefollowingPDC arerelevant:

PDC10,Reactordesign Thereactorcoreandassociatedheatremoval,control,andprotectionsystemsshallbedesignedwith appropriatemargin toensurethatspecifiedacceptablesystemradionuclide releasedesign limitsare not exceeded during any condition of normal operation, including the effects of anticipated operationaloccurrences.

PDC 11, Reactorinherentprotection The reactor core and associated systems that contribute to reactivity feedback shall be designed so that, in the power operating range, the net effect of the prompt inherent nuclear feedback characteristicstendstocompensatefora rapidincreasein reactivity.

PDC 12, Suppression ofreactor poweroscillations Thereactor core;associatedstructures;andassociatedcoolant,control,and protectionsystems shallbedesigned toensurethat power oscillationsthatcanresultinconditionsexceedingspecified acceptablesystemradionuclidereleasedesignlimitsarenotpossible orcanbereliablyandreadily detectedandsuppressed.

PDC 16, Containment design A reactor functionalcontainment,consistingofmultiplebarriersinternaland/orexternaltothe reactoranditscooling system,shallbeprovidedtocontrolthereleaseofradioactivitytothe environmentandtoensure thatthefunctionalcontainmentdesign conditionswhich aresafety significantarenotexceededforaslongas postulatedaccident conditionsrequire.

PDC 25, Protectionsystemrequirementsfor reactivitycontrol malfunctions Theprotectionsystemshallbedesigned toensurethat specifiedacceptablesystemradionuclide releasedesign limits arenotexceededduring anyanticipatedoperational occurrence,accounting fora single malfunctionofthereactivitycontrolsystems.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

PDC 26, Reactivitycontrolsystems A minimumoftworeactivitycontrol systemsormeansshallprovide:

(1)A meansofinserting negativereactivityata sufficientrateandamounttoassure,withappropriate margin for malfunctions, that the specified acceptable system radionuclide release design limits are not exceeded and safe shutdown is achieved and maintained during normal operation, including anticipatedoperationaloccurrences.

(2) A means which is independent and diverse from the other(s), shall be capable of controlling the rateofreactivitychangesresultingfromplanned,normalpowerchangestoassurethatthespecified acceptablesystemradionuclidereleasedesignlimitsarenotexceeded.

(3)Ameansofinserting negativereactivityata sufficientrateandamounttoassure,withappropriate margin for malfunctions, that the capability to cool the core is maintained and a means of shutting downthereactor and maintaining,ataminimum,a safeshutdownconditionfollowinga postulated accident.

(4)A meansforholding the reactor shutdownunderconditionswhich allowforinterventionssuchas fuelloading,inspectionand repairshallbeprovided.

PDC 28, Reactivitylimits Thereactivitycontrol systemsshallbedesigned withappropriatelimitsonthepotentialamountandrate ofreactivityincreasetoensurethat theeffectsofpostulatedreactivityaccidentscanneither:

(1)resultindamagetothesafety significantelements ofthereactor coolantboundarygreaterthan limitedlocal yieldingnor (2) sufficiently disturb the core, its support structures, or other reactor vessel internals to impair significantlythecapabilitytocoolthecore.

The methods described in this topical report are used to calculate the power distributions which are an input to the fuel performance calculations that assure that specified acceptable system radionuclide release design limits (SARRDLs) will be met as described in PDC 10. Similarly, core design methods are used to calculate the reactivity coefficients to assure that the net effect of the prompt inherent nuclear feedbackcharacteristicstendstocompensateforarapidincrease inreactivityas describedinPDC 11.The inherent characteristic of the KPFHR test reactor (small core and long neutron diffusion length) ensure thatpower oscillationsdonotresultinconditionsexceedingSARRDLsas described inPDC 12.TheKPFHR usesafunctional containmenttoensurethatradiologicalreleasestothepublicarewithinrequiredlimits as describedinPDC 16.Themethodsdescribedinthisreportprovidetheinputfor thefuelperformance calculationthatassuresthatthebarrierstoradiological releasefromthefuelarenotcompromised.PDC 25 requires that the protection system be designed to ensure that the SARRDL is not exceeded for anticipated operational occurrences and the methods in this report are used to support that design.

Shutdown margin calculations performed with the methodology in this topical report ensure that the requirements of PDC 26, Reactivity Control Systems are satisfied. Finally, PDC 28 requires that reactivity systemsaredesignedsuchthattheamountandrate ofreactivityadditioncannotresultindamagetothe reactor coolant boundary or to the core, its support structure, and other reactor vessel internals. The nuclear design methods described in this topical report are used to support the assessment that the KP FHRmeetsPDC28.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

2 COREPHYSICSANDDESIGN

ThecoredesignandanalysismethodologyalignsverycloselywiththephysicalbehaviorofaKPFHR core.

ThefollowingsectiondescribesthereactorcorephysicsoftheKPFHR andwillserveas referencefor the description ofthemodelingtoolsandcapabilitiesused incoredesign.

2.1 DESCRIPTION

TheKPFHRcorecontainsthousandsofrandomlypackedbuoyantfuelpebblesthatslowlyascendthrough thereactorcore.Pebbles arecontinuouslyinserted atthebottomofthereactorandextractedfromthe top. The dynamics of the reactor core is characterized by the transition from a startup core to an equilibriumcoreovertime.The fuelpebblesmay contain naturaluraniumall thewayupto19.55wt%U 235 toreduceeffectiveenrichment andcorereactivityin earlystartup coreoperations.Dependingonthe chosen startupandoperationalschemes,thecorewillalsocontainafractionofgraphiteonly moderator pebbles to maintain the desired carbon to heavy metal atom ratio. Similar to the water to fuel volume ratio in light water reactors, the carbon to heavy metal atom ratio is used in FHRs to define the neutron moderation conditions (overmoderated or undermoderated) and the mixing of different pebble types facilitatesmaintainingthecoreinundermoderated conditions.

When defining the desired carbon to heavy metal ratio, it is also important to recognize the role of the reactor coolant. Flibe is a moderator but also an absorber due mainly to lithium6, a natural isotope of 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.

An increase in temperature of Flibe leads to a decrease of its density with two competing reactivity feedbacks: a positive feedback due to reduced absorption and a negative feedback due to reduced moderation by Flibe. The latter effect is a function of the carbon to heavy metal ratio; therefore, the combined reactivity feedback can be designed to be negative by controlling the carbon to heavy metal ratio.After someperiodofoperation,Li6 isconsumed anditsconcentration islower thanin freshFlibe.

Nevertheless, lithium6 in Flibe is also produced by (n,) reactions on Be9 leading eventually to an equilibrium concentration.. Salt impurities present in fresh Flibe are also parasitic absorbers in addition to the accumulation of other corrosion material, each of which have an impact on the coolant reactivity coefficients. The properties and specifications for the reactor coolant are described in "Reactor Coolant for theKairos PowerFluorideSaltCooled,HighTemperatureReactor"topicalreport(Reference18).

The ability to control the mixture of pebble types in the core allows excess reactivity to be minimized duringstartupandoperation.Corereactivityisalsocontrolled bythemovementofthecontrolelements.

Shutdown elements are also available for insertion for safe shutdown at all core states. The KPFHR thermal energy transfer phenomena in the core are described in Figure 21. During normal operating conditions, thermal power generated within the fuel is transferred by conduction to the pebble surface.

Thethermalenergyismainlytransferredviaconvectionfromthepebblesurfacebythecoolantthat flows throughtherandomlypackedbed.Atthesame timeasmallerportionofthethermalenergyistransferred by a mixed regime of conduction and thermal radiation. Specifically, pebble to pebble heat conduction throughastagnant fluid,pebbletopebble conduction,andpebbletopebbleradiation.Figure21 shows these heat transfer modes and those outside the reactor core as well. Bypass flow, core barrel, downcomer,reactor vesselanddecayheatremovalheattransfermechanismsarealsohighlightedinthis figure.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

A portion of the reactor coolant flow, referred to as the bypass flow fraction, does not flow through the core.The thermal energy balance withinthereactorcoredeterminesthetemperature distributionwithin the fuel, moderator and the coolant that flows through the core. Larger bypass flow fractions result in highercoolanttemperaturesinthecore.Thetemperaturedistributionisimportantbecausetemperature caninfluencecorereactivitylevels,burnup,andpowershapes.

2.2 FUELDESCRIPTION

2.2.1 TRISOParticles TheKPFHR TRISOparticlesinclude aUCOkernel,aporouscarbonbufferlayer,andinnerpyrolyticcarbon (IPyC), silicon carbide (SiC), and outer pyrolytic carbon (OPyC) layers, as shown in Figure 22. TRISO particlesare overcoatedwitha mixture ofnatural andsyntheticgraphite,andresinbinder material. The KPFHR fuelparticle kernels arecomposed ofUCO,amixtureofUO2,UC,andUC2.Theovercoatthickness isspecified toproduceanominal37%particlepackingfractionafterisostaticpressing andheattreatment in thepebbleannular fuelregionresultingin~16,000particlesperKPFHR pebble.

2.2.2 KPFHR FuelPebbles The KPFHR fuel pebble design is 40mm in diameter and has three regions with specific functions that complement the pebblebed FHR design, which is shown in Figure 22. The innermost region of the KP FHR fuel pebble contains a lowdensity carbon matrix core. The function of this region is to make the pebble buoyant in the Flibe coolant. An annular fuel region shell is located on the surface of the inner carbonmatrixcore.Thisregioniscomposed ofacarbonmatrixembeddedwithTRISOfuelparticles.The fact that the fuel particles are closer to the pebble surface than in other designs (e.g., high temperature gas reactor) reduces the fuel temperatures relative to those designs. A fuelfree carbon matrix shell is located on the surface of the fuel region to protect the fuel region from mechanical damage during handlingandoperation.

2.3 REACTORCOREDESIGN

An axial section of the Hermes reactor can be seen in Figure 23. In a typical KPFHR reactor core, there are a few design features present that need to be captured in the analysis: the cylindrical pebble bed region,theupperandlower conicregions,thefuelingregion,thedefueling chute,coolantinlet andoutlet channelsinthereflector,bypassandengineeredchannelsinthereflector,andthereactivitycontrol and shutdownsystem(RCSS).

Thecoreistheregionofthepebble bed thatproducesconsiderablefissionpower density,determined as theregionfromthetopoftheupper conicregionofthecore to the bottomofthelower conicregionof the core. Core geometrical characteristics such as the conic regions and defueling chute are designed to support a more uniform burnup and fuel performance in the core, as the conic regions and relative diameters of defueling chute and cylindrical section impact pebble velocity profile and residence time.

The function of the fueling region, located at the bottom of the reactor core, is to guide the pebbles coming from the insertion line(s) into the reactor core. The defueling chute, located at the top of the reactor core, isalsodesignedtobe alowpower producingregionwherepebbleshaveadequateamount of time to allow for the decay of shortlived fission products. The decay heat generation is then low enough for the pebble handling system to operate within designed temperature limits to accept the extractedpebble.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Coolant inlet and outlet channels located in the bottom and top reflector, respectively, are designed to reducepressurelosseswhileachievingacceptable flowdistributionandflowratesthrough thecore.The blocktype reflector designischaracterizedbythepresence ofradial andaxial spokegapsbetweenblocks and at the interface with the vessel core barrel. This geometry causes a portion of the mass flow rate to bypass thecore region.Engineered channelsin thegraphiteblocksallowfor themovementofreactivity 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.

Thecontrol elementsarecreditedonlyfor all plannedpower maneuversoftheKPFHR reactor.Toachieve shortterm shutdown (i.e. not considering delayed impact from xenon), only the control elements are needed. To achieve safe shutdown conditions, the shutdown elements are used assuming the highest worth shutdown element is fully withdrawn (stuck). The design of the reactivity control and shutdown systemmustsatisfy PDC 25 andPDC 26(Reference2).

2.4 OPERATIONALREGIMES

There are four main periods of core operation in the life of the KPFHR reactor with respect to criticality and composition: startup, power ascension, approach to equilibrium core, and equilibrium core. An illustrationofthesestagescanbeobservedinFigure24.

((

))

Whilestillsubcritical,sourcerangecontrol element worth testingis performedbymeasuring changesin neutron multiplication from a startup source. The distribution of flux is also monitored and assessed againstpredictedcalculationsduringthisstage.Once criticalityisachievedandatzeropower, isothermal reactivitycoefficienttestingisperformedandcomparedagainstpredictedcalculations.

Onceallzeropower physicstestingiscompleted,theascensiontothepowerphasebegins.The primary salt pump runs at reduced speed to provide forced circulation.As the power level increases from zero power, negative reactivity feedbacks arise from temperature increases, the buildup of xenon, and the depletion of fuel. To compensate for these effects, the reactivity control elements can be partially withdrawn. This balance of excess reactivity and extraction of heat from the core continues until full power isreached.

At full power (or the initial power plateau), the approach to equilibrium core begins. For the initial core composition, the radionuclide inventory is mostly fresh fuel, and burnup has not yet accumulated. To compensate foraccumulatedburnup,freshfuelpebblesareadded,anddepleted pebblesremoved,ata rate thatmaintainscorereactivity.Aftersomeperiodofpower operation,theisotopic concentrationwill be largely unchanged, and a stable rate of insertion and extraction of fuel will be reached (assuming

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

constant power). At this point, the equilibrium core has been reached, which is designed to stay within thedesignedcoolantreactivitycoefficients,power perparticle limits,andthedesiredexcessreactivity.

2.5 PHENOMENAIDENTIFICATIONANDRANKINGTABLE

A PIRTevaluationwas conducted for theKPFHR coredesign. Afullreview oftheexistingGeorgiaInstitute of Technology FHR neutronics PIRT (Reference 3), which uses the Advanced HighTemperature Reactor (AHTR)reactordesignas thebasis, was performedpriortobeginningtheKPFHR PIRT.Thedescriptionof FiguresofMerit(FOMs)andknowledgelevel numberingusedinthePIRTareas follows:

FOM1:Multiplicationfactor(1:Lowimpact,2:Medium impact,and3:Highimpact)

FOM2:Powerdistribution(1:Lowimpact,2:Medium impact,and3:Highimpact)

Knowledge:Knowledgelevel (1:Low, 2:Medium, and3:High)

A summaryoftheKPFH RPIRTresultsareprovidedinAppendixBNeutronicsPIRTfortheKPFHR.

((

))

Thepredictive capabilitiesrequirementsfor theKPFHRcorethermalhydraulics(TH)modeling followthe mostrelevantcoreTHPIRTphenomena.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

3 COREMODELING

3.1 MODELING TheKPFHR coreconfigurationisheterogeneousandnonstationary. Thepebblebedcontinuouslyevolves from an early startup phase to a statistically steady burnup equilibrium condition. KPFHR core physical characteristics such as core geometry, heterogeneity, and pebble bed motion require unique modeling approaches. The core design also requires different modeling approaches due to the lack of existing KP FHRdata.

3.2 MODELINGPARADIGM

Themethodologydevelopedfor coreanalysisanddesignalignsverycloselywiththephysicalbehaviorof the core. The KPFHR core model paradigm includes discrete elements methods (DEM), neutronics and THmoduleswithseveraldegrees ofexplicitcoupling betweenthem.

((

)) The neutronic analyses of the KPFHR core accounts for the doubleheterogeneity ofTRISOparticlesandpebbleswithout anyneed ofperforming validationoflower order methods, which also includes the use of continuousenergy Monte Carlo. The explicit neutronic model ofthecoreisusedtoinformtheloworderthermalhydraulic modelingpowerdistributionusedto providematerialstemperaturesfeedbackforreactivitycalculations;themodelisalsocapableofcoupling withburnupcalculations.

3.3 DATAFLOW

The KPFHR steady state and pseudosteady state core design modeling workflow and data exchange consists of different degrees of coupling between DEM, neutronics and TH modules. Figure 31 presents agraphicalsummaryofthedataflowandprocessingofthecoremodeling paradigm.

((

))

3.4 MODELINGBOUNDARIESANDOUTPUTPARAMETERS

Thedomainsofinterestfor modeling arefirstdetermined beforeperformingcoreanalysisfor calculating quantities of interest for reactor safety and for input into downstream use in safety analysis and source 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 hydraulics calculations and are shown in Figure 32. A representative figure showing the axial section of the Hermes vessel (with simplified internals) along with a list of the geometric and material boundaries for eachcalculationisprovidedinFigure32.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

DEM considers the core shape, reflector material, the pebbles, and the coolant flow through the core when performing calculations. The core shape, where the pebbles reside, is defined by the reflector structure, which includes the cylindrical section of the core, the upper and lower conic regions, the defueling chute,andthefueling region.

((

))

Thermal hydraulicscalculationsarealsothreedimensional calculations((

))

Using these boundaries for core analysis, the calculated output quantities of interest from this methodologyincludethefollowing:

Reactivitycoefficients o Fueltemperature o Moderator temperature o Coolanttemperature o Coolantvoid o Reflectortemperature Control andshutdownelementworth o Integralworth o Differential worth Powerdistribution o Peakingfactor o Axial andradial power profile Kineticsparameters o Effectivedelayed neutronfraction o Effectiveneutronmean generationtime

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

o Promptneutronmeanlifetime For postulated event modeling of the KPFHR, the following data is used: reactivity coefficients, kinetics parameters, shutdownmargin,differential rodworths, andpowershape(axial andradial).Thetoolsused, the methodology, and example calculation at equilibrium for each of these quantities are provided in Section 4, Section 5, and Appendix A, respectively. This data will be provided as inputs to safety analysis atthefollowingcorecompositionalregimes (see Section2.4):startupand theequilibrium core.Thiscan alsobe doneforothercorestatesbetweenstartupandequilibrium,as needed.Conservativeselectionof the applied associated uncertainties is used for each of these quantities for the purposes of postulated event analysis (upper or lower bound), and each parameters associated uncertainty analysis methodologyisdescribedinSection6.

The fuel composition at equilibrium core is also used for source term analysis. Conservative selection of burnup uncertainties are applied for the purposes of source term analysis (whether upper or lower bound),andtheburnupuncertaintyanalysismethodologyisdescribedinSection6.4.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

4 COREDESIGN TOOLBOX

In order todevelop themodelingmethodologydescribedinSection 3,aseriesofsoftwarecodesareused alongwithdifferentcodewrappersfor couplinganddataexchange (seeFigure31). Thesoftwareused byKairos Powerfor coredesignincludesSerpent2fortheneutronicmoduleandSTARCCM+ forDEMand TH modeling. KACEGEN, Kairos Power Advanced Core Simulator (KPACS), and Kairos Power Advanced Thermal Hydraulics (KPATH) are internally developed wrapper codes that have been developed to processandexchangedatabetweensoftwarecodesandlibraries.Thesoftwarediscussedin thisreportis developedandmaintainedundertheKairos PowerQualityAssurance(QA)program.

The verification, validation and uncertainty quantification methodology has been developed to reduce andcontrolallthesourcesoferroranduncertaintybetweenSTARCCM+ modelsusedincoredesignand their FOMs predictive capabilities. The verification process consists of software and numerical solution verification activities. Software verification aims to ensures that the discretized model is an accurate representation of the continuous mathematical model, and that there are no userdefined code errors.

Validation is the process of determining the degree to which a mathematical model is an accurate representationofthereal worldfromtheperspectiveofitsintended use. Thisisdonebycomparing the model outputs(FOMs)withexperimentalmeasurementsand/orhighordernumericalresults.

((

))

4.1 CODES

4.1.1 STARCCM+

Description STARCCM+ isused for DEMandTHmodeling.Theverification,validation anduncertaintyquantification methodologyhasbeendevelopedtoreduceandcontrolall thesourcesoferroranduncertaintybetween STARCCM+ modelsused incoredesign andtheirFOMspredictivecapabilities. TheV&VmethodsforDEM and TH are very similar. The TH V&V methodology focuses on the prediction of the core material temperatures(fuel,moderator andcoolant)whereas theDEMmethodology focusesonthepebble center locations and their residence time within the core. Because design to reduce bypass flow is performed independentlydue tothecomplexityofbypass flowpaths, bypass flowistreatedas adefinedfractionof total coolantflowwhichisaninputparametertocoredesign andanalysis.

V&VPlan

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

Table42summarizes thevalidation casesthatwillbeusedfor STARCCM+.

4.1.2 Serpent2 Description Serpent2(Reference4)isthemainneutronicstoolfor reactor coredesignandoutputtosafetyanalysis.

Serpent2hasbeenextensively usedacrossacademiaandindustryandhasbeenvalidatedagainstvarious 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.

TheuseofSerpent2provideshighfidelity simulation,whichisimportantduetolackofexperimentalFHR operatingexperience.Therearetwokeyfeaturesthat areavailableinSerpent2:1)theabilitytoexplicitly capture the doubleheterogeneity of the fuel pebble and TRISO particles, and 2) the implementation of Woodcock deltatracking (Reference 4). The reduced computational burden with the implementation of deltatracking alsoallowsfor full3Dcoremodeling.

V&VPlan

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

4.2 WRAPPERCODES

Thefollowingwrapper codesareusedtotransferinformation between theneutronicand thermal/hydrauliccodes.

4.2.1 KACEGEN Description KACEGEN(KairosACEGenerator) isaninternaltoolthatNJOY21usestoproduce theACEformat nuclear datalibraries.NJOY21 (Reference 9)isanucleardataprocessing tool capable ofproducingbothpointwise and multigroup cross section data from the U.S. Evaluated Nuclear Data Files (ENDF) format. KACEGEN, as an example, currently has the capability to generate ACE libraries from any ENDF6 library, including JEFF3.3,ENDFB VII.1, andENDFB VIII.0. Bothneutron crosssections andthermalscattering librariesare produced for each isotope available in the library, and thermalscattering libraries can be discrete or continuous in energy. ACE data has been generated at the following temperatures, tailored to the temperaturerangesintheKPFHR design: 273.15,300,600,700,800,900,1000,1100,1200,1500,1800, and2200degreesK.

Thehighlevel dataflowoftheKACEGENcanbeseenin Figure41.Tostart,libraryfieldsandpathsfora particularlibrary setareloaded,thenthecomplete listofisotopesarerunandwrittenfor neutroncross sectiongeneration. Ifthermal scatteringisalsobeinggenerated,theLEAPRsmoduleofNJOY21 isrunfor eithercontinuousand/or discretethermalscatteringlaw (TSLs).

Pointwise crosssectionsarecomparedbetweenLANLMCNPandOECD evaluatedlibrariesandtheones evaluatedbyKACEGEN/NJOY.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

4.2.2 KPACS Description KPACSisaninternallydevelopedfuelcycleanalysiswrapper thatlooselycouplesSerpent2anddiscrete elementmodeling (DEM)inSTARCCM+ for pseudosteadystate analysis. Themajorunderlying assumptioninKPACSissharedwithpastcodessuchas VSOP(Reference10)andPEBBED(Reference11),

inthatthebehavior ofneutron spectrumandtemperature affectingpebblesinspecificallydefined regionsofthecore(i.e.,spectralzones)canbeassumedconstantduetoslowlyvarying neutronfluxand temperature.((

))

ThedifferencebetweenKPACS andothercodesisthat itreliesonthehighestfidelitytoolsavailable.

Serpent2isused toperformthefullcore transportandfueldepletion calculations,andthepebble motionandlocationsareinformedbyDEMinSTARCCM+. KPACScanalsobelooselycoupledwith KPATH,for updateofcoretemperaturedistributionas neededthroughouttheKPFHR operationallife.

4.2.3 KPATH Description KPATH is the internally developed software infrastructure that couples STARCCM+ to Serpent 2. The computational fluid dynamic (CFD)neutronic steadystate twoway explicit coupling, is such that it providesTHfeedbacksfor criticalitycalculations,power shape,andpower peakingcalculations.

Within the KPATH computational framework, STARCCM+ is utilized as a steady state solver for heat transfer and fluid flow in the form of a 3D porous media model. Only normal steady state operating conditionsareconsidered.Thecouplingmethodologythathasbeendevelopediscapable ofusing KPATH duringall corephasesfromstartuptoequilibriumcoreconditions; thismeansthatKPATHcanbeusedat differentcorephasesincombinationwithKPACS.

The KPATH code wrapper manages the thermal power and materials temperatures exchange between Serpent 2 spectral zones and STARCCM+ porous region as shown in Figure 42. Convergence is reached when keff and core material temperatures differences with the previous iteration is within a specified tolerance.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

5 CALCULATIONMETHODOLOGY

Thissectionprovidesanoverall descriptionofthemodelsusedwithinthecoredesignandanalysismodel.

5.1 DEMMODELING

TheDiscreteElementMethod(DEM)isthemethodology usedtogeneratethereactorcoregeometryfor theexplicitpebblemodelinginSerpent 2.DEMisutilizedtosimulatethegranular flowbydescribingthe motionofmanyinteractingdiscretesolidpebbles.DEMmodelingprovidesdetailedresolution thatother methods cannot achieve. ((

))

STARCCM+ models DEM pebbles based on a softparticle formulation in which particles are allowed to develop an overlap proportional to the contact force and can undergo large deformations without rupture. This overlap is not physically realistic but is used to aid in ease of computation. The calculated contactforceisproportional totheoverlap,as well astotheparticlematerialandgeometricproperties.

STARCCM+ DEMprovidesalargeamount ofdatafor everysinglepebblesuchas timehistories, velocity, position,andforces.Thedatacollectedprovideastatistical basisfor neutroniccalculations.DEM provides the location of the centers of the fuel pebbles necessary for criticality calculations. Burnup calculations need more information in addition to the location of the individual pebbles. DEM provides the pebble flow profile inside the reactor core and pebble residence time. The methodology to calculate residence timeisbasedonrecirculation ofthepebblesinthecore fromtheentrytoexitpoint.

TheFOMs usedfor theDEMV&Vplanare:

((

))

5.2 NEUTRONICS

5.2.1 MonteCarloConvergence

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

5.2.2 Fuel CycleAnalysis

((

))

5.2.3 ReactivityCoefficients Thecalculationfor reactivitycoefficientsisdoneusing Equation 51.Wherexisthereactivitycoefficient withrespecttoquantityx,xisthechangeinquantityxwithrespecttoreferenceconditions(positive or negative), kref is the neutron multiplication factor of the core calculated from Serpent 2 at reference conditions,andkx istheneutronmultiplicationfactorofthecorecalculated bySerpent2afterquantity xwas changed byx.

1 1 1 Equation51

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

5.2.4 ControlWorthandShutdownMargin

((

))

Shutdown margin is also maintained at all core states. The control elements in the RCSS are responsible for all planned, normal power maneuvers. The worth requirements depend on the KPFHR design of interest.

Control worthiscalculatedusing Equation52where, isthewithdrawnpositionand, isthe inserted position of interest. Differential control worth is calculated using Equation 53, where, is the neutron multiplication factor of the core for step position of interest,, is the neutron multiplication factor of the core for step 1 position of interest, is the axial position of the control rod(s) for step position of interest, and is the axial position of the control rod(s) for step 1 positionofinterest.

((

))

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.Thecalculationofthesekineticsparametersiscalculatedusing theiteratedfission probabilitymethod(Reference14).Theeffectivedelayedneutronfractionisdividedintosixgroups.

Delayedphotoneutrons,fromBe(,n)reactioninFlibe,willalsobeassessedtounderstand their impact on the effective delayed neutron fraction and delayed neutron group structure (Reference 15). This impact from delayed photoneutrons is smaller than other reactors that have been impacted from this particularsourceofdelayedneutrons,suchas fromheavywater (D2O)reactors.

5.2.6 ReactorCoolantDepletion

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

5.2.7 PowerDistribution

((

5.2.8 VesselIrradiation ))

((

))

5.3 THERMALHYDRAULICS

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

5.3.1 PorousMediaModeling Packed beds are commonly used in chemical engineering systems because they have highly predictable and uniform flow distributions and transport.The randomly packed pebble bed in the KPFHR core enablestheuseofloworder mathematical modelstopredictglobalflowdistributionsandheattransport.

TheTHmodelused in coredesign,adopts atwoequation porousmediamodel todescribethemacroscale behavioroftheflowandenergytransportwithinthereactorcoreregion.The coreporousregioncanbe 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 derived by applying a volume averaging operator to the Navier Stokes and two phase energy transport equations over a representative elementary volume. The solid and liquid phases are assumed to be in nonthermal equilibrium; this allows modeling two separate temperature fields for the coolant and pebblesrespectively.Thesolidporousphaserepresentingthepebblesusesthefissionpower densityfrom Serpent2as anenergy sourcetermandprovidesthepebbleaveragesurfacetemperaturedistribution.

By removing information about resolved geometry, the volume averaging operator generates additional unknown terms in the momentum and energy equations that need a modeling mathematical closure correlation. Asisconventional,experimentalbased correlationsareused tomodel thelocal momentum and heat transfer information that are lost during the volume averaging process. Figure 53 shows an exampleoflocalheattransferphenomenathat needaclosure correlation.

Momentumclosuremodel

((

))

l l Equation59

((

))

Energyclosuremodels

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

5.3.2 Core MaterialTemperatures The pebbles and coolant temperature fields result from the porous medium volume averaged Navier Stokes equations and energy equations are used as baseline for the core material temperatures evaluation. Thecorematerialtemperaturesthat theTHmodel providestotheneutronicmodule are:

Flibetemperature Graphitepebbletemperature Pebble layersmaterialtemperatures o Lowdensity core o Fuelmatrixlayer temperature o Shelllayer TRISO layers materialtemperatures o OuterPyC layer o SiCLayer o InnerSiCLayer o Buffer Layer FuelKerneltemperature

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

The spatial temperature distributions calculated for each material type that are fed back into the neutronics module are volumeaveraged based on zones for the level of fidelity that is required for the calculatedoutputparameter ofinterest.

TheflexibilityoftheTHmoduleimplementationallowsthethermal couplingwithany otherreactorvessel internalsofrelevantneutronicimportance,as aconsequenceadditional corematerialtemperaturescan be addedtothelistabovefor explicitcoupling.

5.4 COREBYPASSMODELINGANDREFLECTORTEMPERATURE

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

6 UNCERTAINTYANALYSIS ANDNUCLEARRELIABILITYFACTORS

((

))

6.1 NUCLEARDATAUAPROPAGATIONMETHOD

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

6.2 MANUFACTURING INPUTSUAPROPAGATIONMETHOD

((

))

6.3 KINETICSPARAMETERSCALCULATIONUAMETHOD

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

6.4 BURNUPCALCULATION UAMETHOD

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

7

SUMMARY

7.1 CONCLUSION

Thisreportdocumentsthecoredesignandanalysismethodologywhichisusedtoperformnuclear designandthermalhydrauliccalculations for theKPFHR, includingreactivitycoefficients,shutdown margin,power distribution,andreactorcorekineticsparameters.Thesemethodsapplytonormal operation andpostulatedeventsfor aKPFHR testreactor.

Themethodologyfor performing coredesignandanalysisisbasedprimarilyontheSerpent2andSTAR CCM+codes.Thesehighfidelityanalyticaltoolsareused inamethodologyspecificallytailoredtothe uniquefeaturesoftheKPFHR.

V&VoftheSerpent2andSTARCCM+codesisperformedthroughcomparisonswithexperimentalresults andtoanalysesfromothercodes.Theuncertaintyintheresultsfromthesecodesisestablished basedon industry experience and with a conservative bias due to the lack of operating experience with KPFHRs.

TheconservativedeterminationofuncertaintiesisconfirmedusingtheSCALEcodesystem.

Thecompletion oftheV&Vofthecodesandmethodology willbesubmittedtotheNRCas partofafuture licensing applications that makes use of this methodology. In addition, the values of the uncertainties used inanyapplicationswillbe documentedaspartofthesafetyanalysisdocumentsassociatedwiththe 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.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

8 REFERENCES

1. Kairos PowerLLC,"DesignOverview oftheKairos powerFluorideSaltCooled, HighTemperature Reactor,"KPTR001P, Revision1, February 2020.

2. Kairos PowerLLC,"PrincipalDesign Criteriafor theKairos PowerFluorideSaltCooled High TemperatureReactor,"KPTR003P A, Revision1, July2019.

3. D.Diamond,C.Edgar,M.Fratoni,H.Gougar, A.Hawari,J.Hu,N.Hudson,D.Ilas,I. Maldonado,B.

Petrovic, F. Rahnema,D.SerghiutaandD.Zhang,"PhenomenaIdentification andRankingTables (PIRT)ReportforFlouridHighTemperature Reactor(FHR)Neutronics,"Transactionsofthe AmericanNuclearSociety,2016.

4. J.Leppanen,"SerpentaContinuousenergy MonteCarloReactorPhysicsBurnupCalculation Code,"http://montecarlo.vtt.fi/download/Serpent_manual.pdf,June18,2015.

5. VTT,"SerpentOfficial Website,"VTT,18May2021.[Online]. Available:http://montecarlo.vtt.fi/.

[Accessed18 May2021].

6. VTT,"Publicationsandreports relatedtoSerpentdevelopment," VTT,18 May2021.[Online].

Available:http://montecarlo.vtt.fi/publications.htm.[Accessed18 May2021].

7. W.A.Wieselquist,R.A.Lefebvre,M.A.JesseeandEds.,"SCALECodeSystem, ORNL/TM2005/39, Version6.2.4,"OakRidgeNationalLaboratory, OakRidge,TN,2020.

8. C.J..Werner,"MCNPUserManualCode Version6.2,LAUR 17 29981,"LosAlamos, NM, 2017.

9. J.L.Conlin,A.Kahler, A.P.McCartney andD.A.Rehn,"NJOY21:Nextgenerationnucleardata processing capabilities,"International ConferenceonNuclearDatafor ScienceandTechnology, vol. 146,2017.

10. H.Rütten,K.Haas, H.Brockmann,U.Ohlig,C.PohlandW.Scherer,"VSOP(99/09)ComputerCode SystemforReactorPhysicsandFuelCycleSimulation;Version2009,"Forschungszentrum,Jülich, 2009.

11. H.D.Gougar,A.M.Ougouag andW.K.Terry, "AdvancedCoreDesignAndFuelManagementFor PebbleBed Reactors,"IdahoNationalLab,IdahoFalls,ID,USA,Tech.Rept.INEEL/EXT0402245, 2004.

12. W.G.D.Bedenig,ParameterStudiesConcerning theFlowBehaviorofaPebble withReferenceto theFuelElementMovementintheCoreoftheTHTR300MWePrototypeReactor, Nuclear EngineeringandDesign,vol. 7, pp.367378, 1968.

13. M.R.Laufer,PhDThesis,Granular DynamicsinPebbleBedReactor Cores, UCBerkeley,2013.

14. E.Fridman,R.Rachamin,S.VanderMarck,J.Leppnen andM.Aufiero,"Calculationofeffective point kineticsparametersinSerpent2MonteCarlocode,"AnnalsofNuclearEnergy, vol.65, pp.

272279, 2014.

15. C.Keckler,N. Satvat,K.Johnson,B.HaughandM.Fratoni,"Photoneutron productionand characterizationin fluoridesalt cooled hightemperature reactors,"NuclearEngineeringand Design,vol. 372,2021.

16. D.A.NieldandA.Bejan,ConvectioninPorousMedia,New York,NY:Springer,2013.

17. L.Cheng,A.Hanson,D.Diamond,J.Xu,J.CarewandD.Rorer,"Safety AnalysisReport(SAR)for LicenseRenewalfortheNational InstituteofStandardsandTechnology ReactorNBSR,"National Institute ofStandardsandTechnology(NIST),2004.

18. Kairos PowerLLC,"ReactorCoolantfor theKairos PowerFluorideSaltCooled, HighTemperature Reactor,"KPTR005P A, Revision1, January2020.

19. Geschftsstelle des Kerntechnischen Ausschusses, Nuclear Safety Commission of Germany (KTA).

SafetyStandard Lossofpressurethroughfrictioninpebblebedcores.KTA3102.2 1987;Issue3/81.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Table41. Serpent2Requirements andPlannedCodetocode BenchmarkValidation

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Table42. STARCCM+ValidationCases

((

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Table42. STARCCM+ValidationCases

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Table61. ScopeofUncertaintyAnalysis forCoreSafetyParameters

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 21. ThermalEnergy TransferPhenomenainKPFHR

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 22. KPFHR FuelPebbleandParticleDesign

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 23. Axial SectionoftheHermesCore

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 24. Reactor CoreOperationalRegimesoftheKPFHR

Note:The xandyaxisarenotional andarenot toscale. Belowthecriticallevelontheyaxisrepresents subcriticality, andabovethecriticallevelontheyaxisrepresentspowerlevel,buteach arenotional.

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 31. Core DesignModules

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 32. Core AnalysisBoundaries

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 41. Highlevel Data FlowofKACEGEN

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 42. KPATHFramework

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 51. ExampleIllustrationofAlgorithmforPebbleCirculationfor theCore

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 52. SpectralZonesUsedfortheHermesCore

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 53. LocalHeatTransferPhenomenainPebble BedReactor Configuration

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 54. PebbleandTRISOLayers Temperature

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 61. SCALEworkflowforanExampleDemonstrationInvolvingPerturbedParameters(in yellow)

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure 62. DepletionMethodologyFlowDiagramforBurnupCalculationsofFuelPebbles

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

APPENDIX A EXAMPLECOREDESIGN MODEL This section presents an example of application of the core design modeling methodology for the evaluation of a KPFHR reactor with a 35MWth power level. Figure A1 shows a typical sequence of calculationsperformedbyusing thecoredesign methodologydescribedinthisdocument.

Table A1 summarizes the main Hermes core design input parameters considered in this example of applicationofcoredesignmethodology.

FigureA2showsthecoregeometryandnomenclatureassociatedwithcoremain regions.

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA1. Core DesignInputParameters

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA2. Zonebased PowerDensityDistribution

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA3. ReactivityCoefficientsatStartup andEquilibriumCore

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA4. ReactivityControlSystemRequirementsforShorttermHotShutdown

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA5. ReactivityShutdownSystemRequirementsforSafeShutdown

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA6. KineticParametersatEquilibriumConditions

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA7. GroupwiseEffective DelayedNeutronFractionandCorrespondingDecay Constantat EquilibriumCoreConditions

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA8. KineticParametersatStartup CoreConditions

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA9. GroupwiseEffective DelayedNeutronFractionandCorrespondingDecay Constantat Startup CoreConditions

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA10. CoolantTemperature ReactivityCoefficientsforFlibeofDifferent Compositions

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

TableA11. keff withandwithoutTHFeedback

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A1. Core DesignCalculationDiagram

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A2. KPFHR CoreGeometry

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A3. Crosssectional ViewsofNormalizedInstantaneousPebbleResidence Time

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A4. SpectralZonesusedfor theHermesCore

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A5. Fast(>0.1 MeV)(left), Intermediate(middle),andThermal(<1.86eV)(right)Neutron Flux inHermesEquilibriumCore

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A6. Differential WorthofaSingleElementWithdrawal,fromAllIn(RCSonly)

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A7. ReactivityShutdownSystemWorthCurves,N1

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A8. Powerdensity(left),Flibetemperature(center),and Fuel KernelCenterlineTemperature (right)

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A9. Axial BinnedPowerDensityProfileinthecore,excludingConvergingandDiverging Regions(left), andtheRelative DifferenceofAxialPowerShapebetween ConstantTemperature and KPATHResults(right)

((

))

Non Proprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

Figure A10.RadialBinnedPowerDensityProfile intheCore(left),and RelativeDifferenceofRadial PowerShapebetweenConstantTemperatureandKPATHResults(right)

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

APPENDIX B NEUTRONICSPIRTFOR THEKPFHR

A Phenomena IdentificationRanking(PIRT)evaluationwas conducted for theKPFHR. A summaryofthe resultsofthePIRTareincludedfor information inthisAppendix.Thedescription ofFiguresofMerit (FOMs)andknowledgelevel numberingareas follows:

FOM1:Multiplicationfactor (1:Lowimpact,2:Mediumimpact,and3:Highimpact)

FOM2:Powerdistribution(1:Lowimpact,2:Mediumimpact,and3:Highimpact)

Knowledge:Knowledge level(1:Low,2:Medium,and3:High)

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

NonProprietary DocNumber Rev EffectiveDate

KPTR017 NP 1 September2022

((

))

ML22272A598

Contents

Text

SUMMARY

SUMMARY

7.1 CONCLUSION

2.1 DESCRIPTION

SUMMARY

7.1 CONCLUSION

Navigation menu

ML22272A598

Text

SUMMARY

SUMMARY

7.1 CONCLUSION

2.1 DESCRIPTION

SUMMARY

7.1 CONCLUSION

Navigation menu

Search