ContentslistsavailableatScienceDirect
Fusion
Engineering
and
Design
j ou rn a l h o m epa g e : w w w . e l s e v i e r . c o m / l o c a t e / f u s e n g d e s
Dynamic
thermal-hydraulic
modelling
of
the
EU
DEMO
WCLL
breeding
blanket
cooling
loops
A.
Froio
a,
F.
Casella
b,
F.
Cismondi
c,
A.
Del
Nevo
d,
L.
Savoldi
a,
R.
Zanino
d,∗aNEMOGroup,DipartimentoEnergia,PolitecnicodiTorino,10129Torino,Italy,Italy
bDipartimentodiElettronica,InformazioneeBioingegneria,PolitecnicodiMilano,20133Milano,Italy cPPPTDepartment,EUROfusionConsortium,85748GarchingbeiMünchen,Germany
dENEACRBrasimone,40032Camugnano,BO,Italy
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g
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g
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t
s
•System-levelthermal-hydraulicmodeloftheWCLLBreedingBlanketcoolingloopdeveloped.
•HighlymodularitythankstotheModelicalanguage.
•SimplifiedmodelabletosimulatethewholeWCLLcoolingsysteminfaster-than-realtime.
•ModelbenchmarkedagainstCFDcalculations.
•Firstapplicationtosteady-statenominalscenario.
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Articlehistory:Received30September2016
Receivedinrevisedform9January2017 Accepted19January2017
Availableonline16February2017 Keywords: DEMO Breedingblanket WCLL Coolingcircuit Thermal-hydraulics Modelling
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Aglobalthermal-hydraulicmodeloftheEUDEMOtokamak,basedonanobject-orientedapproachusing
theModelicalanguage,iscurrentlyunderdevelopmentatPolitecnicodiTorino.Thefirstmoduleofthe
globalmodelwillsimulatethedynamicsoftheblanketcoolingsystemanditwillbeabletoinvestigate
dif-ferentcoolantoptionsanddifferentcoolingschemes,adaptedtothedifferentblanketsystemscurrently
underdevelopmentintheBreedingBlanketproject.Followingthedevelopmentofthemodulerelated
totheHelium-CooledPebbleBedblanket,thispaperpresentsthedynamicmodeloftheWater-Cooled
LithiumLead(WCLL)blanket,designedatENEABrasimone,togetherwiththefirstresultsobtainedin
steady-stateconditions.
©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND
license(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
The development of a conceptual design of the European DemonstrationFusionPowerReactor(EUDEMO)isoneofthegoals definedintheEUfusionroadmapHorizon2020[1].Startingfrom theresultsobtainedbyITER,thisdevicewillprovethefeasibility ofaclosed fuelcycle,achievingtritiumself-sufficiency,andthe productionofnetelectricity.
Withinthisframework,theEUROfusionProjectManagement Unit(PMU)issupportingthedevelopmentofa global thermal-hydraulicmodelof thewholetokamakat PolitecnicodiTorino, aimedatthesimulationofthecoolingloopsofthemainin-vessel
∗ Correspondingauthor.
E-mailaddress:roberto.zanino@polito.it(R.Zanino).
components,includingtheex-tokamakparts.Themodelshallbe developedinamodularfashion,accordingtoanobject-oriented approach, and willeventually allowtoperformfast parametric analysesofthewholetokamakcoolingsystem.
Thefirstmoduleoftheglobalmodelisdevotedtothesimulation oftheBreedingBlanket(BB)coolingsystem,whichinDEMOwill beatthesametimethecoreelementofthepowergeneration.The developmentofthismodulestartedin2015,withthedevelopment ofthemodelfortheHelium-CooledPebbleBed(HCPB)BBconcept
[2].Inthispaperwepresentthedevelopmentandfirstapplication ofthesecondpartoftheBBmodule,devotedtothemodellingof theWater-CooledLithium-Lead(WCLL)BBconcept.
http://dx.doi.org/10.1016/j.fusengdes.2017.01.062
0920-3796/©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4. 0/).
Fig.1.Blanketsegmentation,showingthenumberingconventionoftheIB1-7and OB1-7BMs(reproducedfrom[5]).
Fig.2.CADoftherearsideoftheWCLLOB4BM,showingthecoolantI/Omanifolds.
2. WCLLcoolingcircuit
Forthedevelopmentofthismodelthe2015designoftheWCLL BB[3,4]hasbeenconsidered.Thetokamakisdividedin18equal toroidalsectors:eachsectorismadeofthreeidenticalOutboard (OB)andtwoidenticalInboard(IB)blanketsegments;each seg-mentcontains7BreedingModules(BMs)[5],seeFig.1.EachBM, showninFig.2,comprisesaportionoftheFirstWall(FW)anda BreedingZone(BZ),containingtheliquid(PbLi)breedermaterial. Thecoolingcircuitissplitwhenenteringthevessel,withtwo dif-ferentsetsofmanifoldsdeliveringthewatercoolanttotheFWand theBZinparallel,asvisibleinFig.2.
3. Modeldescription
AsketchofthecoolingcircuitmodelisreportedinFig.3.The FWloop,composedbyrectangularcoolingchannelsimmersedin theFWsolidstructure,isfurthersplitintwoparts,withthewater coolantrunninginonedirectioninhalfofthechannelsandin coun-terflowintheotherhalf,asshowninFig.4;thisloopisalsousedto cooltheupperandlowerwallsoftheBM.ThesolidpartoftheFW
Fig.3.SchematicoftheWCLLcoolingcircuitmodel(FW#:FirstWallobject;BZ#: BreedingZoneobject;IM:InletManifold;OM:OutletManifold;ID:InletDistributor; MIX:Mixer;HX/SG:HeateXchanger/SteamGenerator).
isincludedintheFWcoolingcircuitmodelbytreatingthechannel wallsas1Dobjectsintheflowdirection,see[2]fordetails.
TheBZpart,whosemodelisshowninFig.5,iscooledby circu-lardouble-walltubes,whichareincontactwiththePbLiflowing inthefreespaceontheirouterside.Thetubesarearrangedina modularlayout,withasetofelementarycellsof21tubes(shown inFig.6)ideallystackedinthepoloidaldirection,withinletorifices tocontrolthemassflowratedistribution.
Theprimaryheatsinkistheheatexchanger(HX),whichcanbe asteamgenerator(SG),iftheprimaryheatistobedirectlyusedto produceelectricity,orawater/moltensaltsHX,ifanintermediate energystorageloopistobeused.Finally,theoperationalpressure andtherangeofwatertemperaturearethesameasintheprimary loopsofpressurisedwaterreactors(i.e.p=15.5MPa,Tbetween285 and325◦C).
ThemodeliswrittenusingModelica,whichisanobject-oriented declarativemodellinglanguageaimedatconvenientmodellingof complex systems, see[2] and references therein.The model is 0D/1D,withthecoolingchannelsmodelledwitha1Dfinite vol-umeapproach,whiletheothercomponents(suchase.g.valves) are0D;alsothemanifoldsaretreatedas0Dobjects,forthetime being.
FortheHX/SGa0DidealHXmodelisadopted,i.e.imposing thattheoutlettemperatureisalwaysatthenominalvalue(285◦C), independentlyoftheinlettemperaturevalue.Thesecondary cir-cuitisnotmodelledforthetimebeing.Inallthecomponents,the time-dependentformofconservationofmass,energyand,forthe 1Dmodelsonly,momentum,isenforced(see[2]fordetailsonthe solvedequations).
Withinthemodel,eachchannelcanbedifferentfromallthe oth-ers,bothintermsofgeometry(e.g.crosssection)andload,making thecodeanidealtooltoperformparametricanalysesaimede.g. attheoptimizationofthecoolantdistribution,withouttheneed
Fig.4.SchematicofthegenericFW#object(FWC#:FirstWallChannelobject;IM:InletManifold;OM:OutletManifold).Theinletandoutletfluidconnectorsarerepresented byverticaldisksatthebeginningandattheendofthemodel.
Fig.5. SchematicofthegenericBZ#object(BZC#:BreedingZoneChannelobject;IM:InletManifold;OM:OutletManifold).
Fig.6. Radial-poloidal(a)andradial-toroidal(b)cutofOB4,showingthedetailsof theelementarycellintheinset;the21channelsarecircledingreenintheinset (adaptedfrom[3]).(Forinterpretationofthereferencestocolourinthisfigure legend,thereaderisreferredtothewebversionofthisarticle.)
fortime-demandingdetailedComputationalFluidDynamics(CFD) calculations.
Inviewoftheverylargenumberofchannelsneededtomodel thewholeWCLLsystem,somesimplifyingassumptionshavetobe made.Hence,anewfullystandard-compliantModelicalibraryhas beendevelopedtocomputethefluid-dynamicsofthecoolant,
sim-plifyingthecomputationofthefluidproperties.Inparticular,the waterisassumedtobealwaysliquid(singlephase),withspecific heat,densityandthederivativeoftheinternalenergywithrespect tothetemperatureatconstantpressurelinearlydependentonthe temperature;theseassumptionsallowtoperformveryfast simula-tions,whilestillbeingacceptableifthecoolantstaysinsideorclose totheoperationallimits,withtheerrorsontheabove-mentioned variablesalwaysbelow3.5%andbelow2%onaverage.Inaddition tothat,thepressuredropcharacteristicofeachchannelislinearized aroundtheoperatingpoint(i.e.thepressuredropdependslinearly onthemassflowrate).Finally,theheattransfercoefficientbetween thefluidandthesolidstructuresintheFW,aswellasthesolid specificheatanddensity,areconsideredconstant.
Inthecaseofoff-normaltransients,however,theassumptions onthethermophysicalpropertiesofthecoolantmaynotbevalid anymoreandthemodelcannotbeused;forthisreason,asecond versionhasbeendeveloped,withadetaileddescriptionofthe ther-mophysicalpropertiesofthecoolantandsimplifyinggeometrical assumptionstomaintainthecodespeed,whichcanbeusede.g.for transientanalyses(e.g.in-vesselLOCAs).
4. Asimpleapplicationofthemodel
Inordertocheckitscapabilities,thecodehasbeenusedto sim-ulateasimplescenario.Sincethedataontheex-vesselcomponents arenotavailableyet(astheirdesignisstillongoing),theloopisnot closedandonlythein-vesselcomponents(i.e.channelsand man-ifolds)aresimulated.Hence,asboundaryconditions,thenominal valuesofpressureandtemperatureareimposedattheinlet,while attheoutletthepressureisimposed accordingtotheexpected pressuredropof7.7kPa(OBmodules)or7.3kPa(IBmodules)[3]. Moreover,theorificesattheinletofthechannelsaresetinorderto havethemassflowrateuniformlydistributedamongthechannels. Followingasimilarapproachtowhatwasdonein[2]forthe HCPB,inordertocheckifallthepointsintheBZvolumeare ade-quatelycooled,i.e.ifallthecoolingchannelsinsideoneelementary cellreach(almost)thesameoutlettemperaturevalue,a steady-stateheatloadisimposed(equaltothenominalvaluesreportedin
[3]).ThepowerisgeneratedinthePbLiaccordingtoan exponen-tiallawpeakedontheplasmaside,whichisconsideredreasonable
Fig.7. Powerdistributioninoneelementarycell.
Fig.8.1Dprofilealongthechannel(a)anddistributionintheradial-toroidalplane (b)ofthecoolanttemperatureinfourselectedcoolingchannelsoutofthe21ofan elementaryunitoftheOB4module.
asthepowergeneratedisproportionaltotheneutronflux,thatis assumedtofollowanexponentiallaw[3].Asinthemodeleach channelisconsideredresponsibleforthecoolingofthevolumeof PbLiaroundit,andthesevolumesturnouttobedifferentbecause ofthedispositionofthechannels,theresultingdistributionofthe powerdepositedineachchannel,reportedinFig.7,isnot expo-nential:channelsfurtherawayfromtheplasma,buttakingcareofa largervolumeofPbLi,endupextractingmorepowerthanchannels closertotheplasma.
Fig.8 reports thetemperature distribution for fourselected channelsoutofthe21ofoneelementaryunitoftheOB4 (equa-torial)module;a similarsituationis foundinalltheIBand OB BMs.
Thetemperatureincreaseisdifferentfromchanneltochannel, withsomeofthemreachingatemperatureabovethemaximum designvalueof325◦C[4].Thisresultwasexpected,sincethemass flowratedistributionwasnotregulatedbasedontheheatload
6–18 307.5 315.2
7–10–12–19 303.2 320.1
8–20 337.9 325.7
9–11–13–21 328.5 335.6
distributionamongthechannels,andreflectswithacceptable accu-racytheresultsobtainedin[3]usingCFD,seeTable1,qualitatively confirmingthevalidity ofthemodel,particularlyifconsidering thatintheCFDmodelthedetailedtemperaturedistributioninthe PbLiwastakenintoaccount,whileinthepresentworkasimple exponentialpowerdistributionisassumed.
InordertoensureadequatecoolingofallthepointsoftheBZ andtohave(atleastinnominalconditions)thesameoutlet tem-peratureinallthechannels,itishenceneededtotunethemass flowintothechannels,usingtheorificesatthechannelinlets.This canbedoneapplyingthemodeltoperformaparametricanalysis varyingtherespectivepressuredropsinasuitablerange,which mightbeprohibitivelyexpensiveifperformedthroughCFD.
5. Conclusions
Asystem-leveltransientmodeloftheEUDEMOWCLLBBcooling systemhasbeendeveloped.BeingwrittenusingtheModelica lan-guage,itishighlymodularandcanbeeasilyadaptedtotheongoing designoftheBB.
Thankstoitsspeed,thistoolcanbeveryhelpfulinthisphase ofthedesign, torapidlylookat theeffectofthevariation of a parameter,withouttheneedforcomputationallyexpensiveCFD calculations.
ThemodelhasbeenimplementedasanewModelicalibrary, containingasimplified definitionof thecoolant thermophysical propertiesandalltheobjectsneededtomodelthecoolingloop;this libraryhasbeenspecificallywrittenforthemodeltobeextremely fastinsimulatingthewholecoolingsystem,whilestillkeepingan acceptableaccuracy.
Thenewlydevelopedtoolhasbeentestedinasimple steady-statecasetocheckitsvalidityandperformances,withtheaimof lookingatthemassflowrateunbalancesamongtheBZcooling channels;asexpected,theresultsshowedthattheflowmustbe optimizedinordertobetterredistributethetemperatureincrease inthechannelsandavoidhot-spotswithtemperaturesabovethe saturationvalue.
Acknowledgments
This work has been carried out within the framework of theEUROfusionConsortium and hasreceivedfundingfromthe Euratomresearchandtrainingprogramme2014-2018undergrant agreementNo633053.Theviewsandopinionsexpressedherein donotnecessarilyreflectthoseoftheEuropeanCommission.
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