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Deffence Research andDeveflopment Canada
Recherche et devefloppementpour fla deffense Canada
CANUNCLASSIFIED
BaseflfinepredfictfionsoffBB2submarfine
hydrodynamficsffortheNATOAVT-301
coflflaboratfiveexercfiseMarkC.Bettfle
DRDC–AtflantficResearchCentre
DeffenceResearchandDeveflopmentCanadaScfientfificReportDRDC-RDDC-2017-R200March2018
CANUNCLASSIFIED
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CANUNCLASSIFIED
IMPORTANTINFORMATIVESTATEMENTS
ThfisdocumentwasrevfiewedfforControflfledGoodsbyDRDCusfingtheSchedufletotheDeffenceProductfionAct.
Dfiscflafimer:HerMajestytheQueenfinrfightoffCanada,asrepresentedbytheMfinfisteroffNatfionaflDeffence(“Canada”),makesnorepresentatfionsorwarrantfies,expressorfimpflfied,offanykfindwhatsoever,andassumesnoflfiabfiflfityffortheaccuracy,reflfiabfiflfity,
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DeveflopmentCanada,anagencyofftheDepartmentoffNatfionaflDeffenceoffCanada.Inqufirfiescanbesentto:[email protected].
c⃝ HerMajestytheQueenfinRfightoffCanada,DepartmentoffNatfionaflDeffence,2018
c⃝ SaMajestéflaRefineendrofitduCanada,MfinfistèredeflaDéffensenatfionafle,2018
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Abstract
InfitfiaflpredfictfionsoffthehydrodynamficfloadsandflowfiefldfforthegenerficBB2submarfinemodeflwerecomputedusfingthecommercfiaflvfiscousflowsoflverANSYSCFXwfiththeBaseflfineReynofldsstressturbuflencemodefl(BSL-RSM).Abflockstructuredmeshhavfing37×106ceflflswascreatedfforthfispurpose.CaflcuflatfionswereperfformedataReynofldsnumberoff9.57×106fforsteadytransflatfionwfithzeroflowfincfidenceandatadrfifftangfleoff10.Astrategyoffaflternatfingbetweenflargeandsmaflfltfimestepswasffoundtobeuseffuflfforconvergfingtheflufidequatfionsfforthewfiderangefintfimeandflengthscaflesoffvortficesfintheflow.TheprfimaryflowffeaturesaroundtheBB2,suchasjunctfionvortficesandappendagetfipvortfices,havebeenfidentfifiedtogufideffuturemeshfimprovements.
Sfignfificanceffordeffenceandsecurfity
Infitfiaflstepshavebeentakentowardsbench-markfingandvaflfidatfinghfighfideflfitytooflsfforpredfictfingsubmarfineflowfiefldsandmanoeuvrfingfforces.Thfisfiscontrfibutfingtotheassessmentandfimprovementoffourtooflsfforunderstandfingoffsubmarfinemanoeuvrfingflfimfitatfionsfinextremecondfitfionsandfforevafluatfingpotentfiaflhydrodynamficperfformancefimprovementsfforsubmarfines.
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Résumé
Nousavonscaflcufléflesprévfisfionsfinfitfiaflesdeschargeshydrodynamfiquesetduchampd’écouflementdumodèflegénérfiquedesous-marfinBB2àfl’afidedurésoflveurcommercfiafld’écouflementvfisqueuxANSYSCFXetdumodèflederéfférencedeturbuflenceàcontrafintesdeReynoflds(BSL-RSM).Àcettefin,nousavonscrééunmafiflflagestructurémufltfibflocde37×106ceflflufles.LescaflcuflsontétéeffectuésàunnombredeReynofldsde9.57×106seflonunetransflatfionconstanteàdébfitnufletunangflededérfivede10.Lastratégfiequficonsfistafitàaflternerentredesfintervaflflesdetempscourtsetflongss’estrévéfléeutfifleàflaconvergencedeséquatfionsdesflufidesdansuneflargegammed’écheflflesdeduréesetdeflongueursdestourbfiflflonsdansfl’écouflement.Nousavonsdétermfinéflesprfincfipaflescaractérfistfiquesdefl’écouflementautourduBB2,teflflesqueflestourbfiflflonsauxjonctfionsetàfl’extrémfitédesappendfices,cequfiorfienteraflesaméflfioratfionsàapporteraumafiflflageàvenfir.
Importancepourfladéffenseetflasécurfité
Nousavonsentreprfisflespremfièresétapesdefl’étabflfissementd’uneréfférenceetdeflavaflfidatfiondesoutfiflsàhautefidéflfitépourprévofirflechampd’écouflementdesous-marfinsetdefleursfforcesdemanœuvre.Ifls’agfitd’unecontrfibutfionàfl’évafluatfionetàfl’améflfioratfiondenosoutfiflsservantàflacompréhensfiondesflfimfitesde manœuvredessous-marfinsdansdescondfitfionsextrêmes,afinsfiqu’àfl’évafluatfiondesaméflfioratfionspossfibflesdeflaperfformancehydrodynamfiquedessous-marfins.
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Acknowfledgements
TheauthorwoufldflfiketothankSergeToxopeus,MarfitfimeResearchInstfituteNetherflands,fforcreatfingFfigures17and18finthfisreport.
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Tabfleoffcontents
Abstract........................................... fi
Sfignfificanceffordeffenceandsecurfity ........................... fi
Résumé ........................................... fifi
Importancepourfladéffenseetflasécurfité ........................ fifi
Acknowfledgements ..................................... fififi
Tabfleoffcontents...................................... fiv
Lfistofffigures........................................ vfi
Lfistofftabfles ........................................ vfififi
1 Introductfion....................................... 1
2 Geometry........................................ 1
3 Coordfinatesystem................................... 2
4 Fflowcondfitfions..................................... 3
5 Fflufiddomafinandmesh ................................ 3
6 Vfiscousflowsoflver................................... 9
7 Turbuflencemodefl ................................... 9
8 Boundarycondfitfions.................................. 9
9 Dfiscretfizatfion...................................... 10
10Iteratfiveconvergence.................................. 10
11Resufltsanddfiscussfion................................. 14
11.1 FflowVfisuaflfizatfion................................ 14
11.2 ZeroIncfidenceflowfiefld ............................ 15
11.3 Fflowfiefldffor10drfifftcase........................... 20
11.4 Surffacepressureandshearstress ....................... 22
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11.5 IntegratedForces ................................ 25
12Concflusfionsandffuturework ............................. 28
Refferences.......................................... 29
AnnexA:ANSYSCFXsoflversettfingsfforthe10degreesdrfifftangflecase ...... 31
AnnexB:ANSYSCFXsoflversettfingsfforthezerofincfidencecase .......... 42
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Lfistofffigures
Ffigure1: BB2huflflfform(configuratfion4)wfithcoordfinatesystem. ......... 2
Ffigure2: BflockstructureoffDRDC’sBB2mesh(starboardhaflffonfly). ....... 5
Ffigure3: Bflockedgesonthesymmetrypflane...................... 5
Ffigure4:Inflatfionflayerbflocks. ............................. 6
Ffigure5: GrfidontheBB2surffaceandsymmetrypflanefinthevficfinfityofftheBB2. 7
Ffigure6: Meshcrosssectfionfinthevficfinfityoffthesubmarfineattheafftendofftheconstantmfidbodysectfion(x/Lpp=−0.184)................. 7
Ffigure7: Maxfimumresfiduaflsfforthecontfinufityandmomentumequatfions(top)andturbuflenceequatfions(bottom)durfingthezerofincfidencecomputatfion... 12
Ffigure8: Maxfimumresfiduaflsfforthecontfinufityandmomentumequatfions(top)andturbuflenceequatfions(bottom)durfingtheβ=10degreescomputatfion. . 13
Ffigure9: Percentdfifferencebetweenfforcesatfiteratfionfiandthefforcesattheendoffthecomputatfionfforthezerofincfidencecomputatfion............. 14
Ffigure10:Percentdfifferencebetweenfforcesatfiteratfionfiandthefforcesattheendoffthecomputatfionffortheβ=10degreescomputatfion. ........... 15
Ffigure11:PredfictedvortexcoresaroundtheBB2atzerofincfidence.......... 16
Ffigure12:Centerpflane(y=0)crosssectfionoffthepredfictedsafifl-deckjunctfionvortexfforthezerofincfidencecase........................... 18
Ffigure13:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)fforthezerofincfidencecase. 19
Ffigure14:PredfictedvortexcoresaroundtheBB2atβ=10.............. 21
Ffigure15:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)ffortheβ=10
case..... 23
Ffigure16:Pressurethroughtheprfimarysafifltfipvortexatmfidshfips(x/Loa=0)andthepropeflflerpflane(x/Loa=−0.481),ffortheβ=10
case......... 24
Ffigure17:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2fforthezerofincfidencecase.................................. 26
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Ffigure18:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2ffortheβ=10case. 27
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Lfistofftabfles
Tabfle1: MafinpartficuflarsoffBB2modefl(modeflscafle1:18.348). .......... 2
Tabfle2: Fflowcondfitfionsusedfforthesfimuflatfions. .................. 3
Tabfle3: Overaflflcharacterfistficsofftheffuflflmesh(afftermfirrorfing). ......... 8
Tabfle4: NumberoffflayersandceflflspacfingfforthefinflatfionflayersshownfinFfigure4.LayersstartattheBB2surffaceexceptOSo,whfichstartsattheoutersurffaceoffOSfi............................... 8
Tabfle5: CeflflcountandmaxfimumspacfingfinvarfiousdfirectfionsontheBB2surfface. 8
Tabfle6: Reflaxatfionparametersettfings. ........................ 11
Tabfle7: Locatfionandmagnfitudeoffmaxfimumvortficfityfinthecoreoffthesafifl-deckjunctfionvortficesonthey=0pflaneupstreamoffthesafifl,shownfinFfigure12.17
Tabfle8: Locatfionandmagnfitudeoffmaxfimumx-componentoffvortficfityfinthecoreoffthevortficesonthex=0pflane,shownfinFfigure13(starboardsfideonfly).20
Tabfle9: Locatfionandmagnfitudeoffmaxfimumx-componentoffvortficfityfinthecoreoffthevortficesonthex=0pflane,shownfinFfigure15............ 22
Tabfle10: PredfictedBB2hydrodynamficfforcesandmomentsfforzeroflowfincfidence,ReL=9.57×10
6................................. 25
Tabfle11: PredfictedBB2hydrodynamficfforcesandmomentsfforβ=10,ReL=9.57×10
6................................. 25
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1Introductfion
TheNATOAVT-301workfinggroup,"Fflowfiefldpredfictfionfformanoeuvrfingunderwatervehficfles",fisusfingthegenerficBB2submarfinegeometry[1]fforabenchmarkstudyassessfingtheabfiflfityoffvfiscousflowsoflverstopredfictthehydrodynamficperfformanceoffamanoeuvrfingsubmarfine.Theobjectfivefistofimproveawarenessoffmodeflflfingrequfirementsand/orshortffaflflsbycomparfingCFDcodesandmethods,andbyvaflfidatfingpredfictfionsagafinstexperfimentafldata.Anequaflflyfimportantobjectfivefistogafinadeeperunderstandfingofftheflufiddynamficsoffamanoeuvrfingsubmarfinethroughthfisprocess.Threesubmarfinemotfionsarepflannedfforthfisbenchmarkfingactfivfity:strafightflfight(zeroflowfincfidence),steadydrfifft,andconstantturnfingrate manoeuvres. WfindtunnefldatawfiflflbeprovfidedbyDeffenceScfienceandTechnoflogyGroup(DSTG)finAustraflfiaandrotatfingarmdatawfiflflbeprovfidedbyQfinetfiQfintheUKfforcomparfison.
Forphase0offthfiscoflflaboratfiveexercfise,partficfipantsperfformedfinfitfiaflflowfiefldcomputa-tfionsofftheBB2atstrafightflfightandatasteadydrfifftangfleoff10degreesusfingthefirownmethodsandbestpractfices.Thepurposeoffthfisphasefistogetanfinfitfiaflfindficatfionoffthevarfiatfionfinpredfictedquantfitfiesduetotheuseoffdfifferentcodes,meshes,turbuflencemodefls,etc.Thfiscomparfisonwfiflflprovfidedfirectfionffortheaspectsthatshoufldbestudfiedfinffurtherdetafifl.ThefinstructfionsandaddfitfionafldetafiflsfforthfistestcaseweregfivenbyToxopeusandKerkvflfiet[2].Theffoflflowfingoutputquantfitfiesarebefingcompared:hydrodynamficfforcesandmoments,shearstressandpressuredfistrfibutfionsontheBB2surfface,andflowfiefldquantfitfiesatdfifferentcross-sectfions,fincfludfing:veflocfity,vortficfity,pressure,andturbuflentkfinetficenergy.
DeffenceResearchandDeveflopmentCanada(DRDC)perfformedReynoflds-AveragedNavfier-Stokes(RANS)computatfionswfiththecommercfiaflcodeANSYSCFXfforphase0offthfiscoflflaboratfiveexercfise.Thepurposeoffthfisdocumentfistodescrfibethedetafiflsoffthemesh,boundarycondfitfions,soflversettfings,turbuflencemodefl,andconvergencefforthesecomputatfions.Someoffthekeyresufltsareaflsopresented,butamoredetafifledanaflysfisfincfludfingacomparfisonwfithsubmfissfionsffromotherpartficfipantswfiflflbedocumentedfinaseparatereport.
2 Geometry
ThegenerficBB2huflflfformfisshownfinFfigure1andthemafinpartficuflarsaregfivenfinTabfle1.Thfisgeometrywasdesfignedbythe MarfitfimeResearchInstfituteNetherflands(MARIN)[1]bymodfiffyfingtheBB1submarfinegeometry,whfichfinturnwasdevfisedbasedonaconceptdesfignbyJoubert[3]. MARINconductedffreerunnfingmodefltestswfiththeBB2huflflfform,asdescrfibedbyOverpefltet.afl[1].TheBB2geometryfisavafiflabfleontheMARINwebsfiteathttp://www.marfin.nfl/web/Shfips-Structures/Navy/Submarfines.htm.FourconfiguratfionsofftheBB2havebeendefined:huflflwfithdeck(configuratfion1);huflflwfithdeckandsafifl(configuratfion2);huflflwfithdeck,safifl,andtafiflpflanes(configuratfion3);
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andhuflflwfithdeck,safifl,tafiflpflanes,andsafiflpflanes(configuratfion4).Thefletter"P"fisappendedtotheconfiguratfionnumberfiffthepropeflflerfisfincfluded.Theffuflflyappendedhuflflwfithoutpropeflfler(configuratfion4)wasusedfforthfiswork.Notethatthegeometryfisgfivenfinffuflfl-scafledfimensfionsbutfitwasscafledtothemodeflscafleflengthfforthepresentstudy.
Tabfle1:MafinpartficuflarsoffBB2modefl(modeflscafle1:18.348).
Quantfity Symbofl Vaflue Unfit
Fuflfl Modefl
Lengthoveraflfl Loa 70.2 3.8260 m
Beam B 9.6 0.5232 m
Depth(todeck) D 10.6 0.5777 m
Depth(totopoffsafifl) Dsafifl 16.2 0.8829 m
Ffigure1:BB2huflflfform(configuratfion4)wfithcoordfinatesystem.
3 Coordfinatesystem
Theprfimarycoordfinatesystemwassettohavetheorfigfinflocatedonthehuflflaxfisatmfidshfips(flocated1.913mafftoffthenoseoffthesubmarfineatmodeflscafle).AsshownfinFfigure1,theposfitfivexaxfisfisdfirectedfforwardthroughthenose,theyaxfistoport,andzaxfisvertficaflflyupward.Thesubmarfineveflocfitycomponentsfinthex,y,andzdfirectfionsaredenotedasu,v,andw,andthesubmarfinerotatfionaflveflocfitfiesabouttheseaxesaregfivenbyp,q,andr.Thepresentstudyonflyconsfiderspuretransflatfionfinthexypflane,suchthatw=p=q=r=0.Thedrfifftangflefisdefinedbyβ=arctan(v/u),whfichmeansβfisposfitfivefforflowcomfingffromportsfide.
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AflflfforcesX,Y,Z andmomentsK,M,N weredfirectedasshownfinFfigure1andmadenon-dfimensfionaflasffoflflows:
X′,Y′,Z′=X,Y,Z12ρU
2L2oaK′,M′,N′=
K,M,N12ρU
2L3oa(1)
whereρfisflufiddensfity,U=(u2+v2+w2)fisthesubmarfinespeed,andLoafistheoveraflfl
flengthoffthesubmarfine(seeTabfle1).
Asecondcoordfinatesystem,x,y,z,fisusedffortheflowfieflddata.Itfisthesameastheprfimarycoordfinatesystemfforhydrodynamficfloadsexcepttheorfigfinfisshfifftedtotheafftperpendficuflar,suchthatx=x+Loa/2.
4 Fflowcondfitfions
TheflowpropertfiesusedfforthecomputatfionsaregfivenfinTabfle2.Computatfionswereperfformedffordrfifftangflesoffβ=0andβ=10(flowffromportsfide).TheReynofldsnumberbasedonsubmarfineflength,ReL,wassetto9.57×10
6byusfingthemodeflscaflesubmarfineflength(3.826m),affreestreamspeedoff3m/s,awaterdensfityoff1000kg/m3,andkfinematficvfiscosfityoff1.2×10−6m2/s.
Tabfle2:Fflowcondfitfionsusedfforthesfimuflatfions.
Quantfity Symbofl Vaflue(s)
Inflowspeed V∞ =U 3m/s
Drfifftangfles β 0,10
Inflowveflocfityfinx-dfir Vx −V∞cos(β)
Inflowveflocfityfiny-dfir Vy −V∞sfin(β)
Inflowveflocfityfinz-dfir Vz 0
Densfity ρ 1000kg/m3
Vfiscosfity ν 1.2×10−6m2/s
ReynofldsNumber ReL 9.57×106
5 Fflufiddomafinandmesh
ArectanguflarboxwasusedffortheflufiddomafinaroundtheBB2modefl,wfithupstreamffaceatx=2.5Loa,downstreamffaceatx=−3.5Loa,andsfidesandtopaty,z=±2Loa.ThesedfistanceswereseflectedbasedonaRANSverfificatfionandvaflfidatfionstudyoffasymmetrfichuflflsbyBaker[4],whfichshowedthatanomfinafldfistanceoff2Loabetweenthehuflflandffarfiefldboundarfieswasadequate.
AbflockstructuredmeshwascreatedwfiththecommercfiaflsofftwarePofintwfisev18.0R2ffor
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thestarboardhaflffofftheflufiddomafinusfingffuflflscafledfimensfionsfinmfiflflfimetres.Thfishaflffmeshwasthenmfirroredabouty=0andscafledtomodeflscafledfimensfions(Lpp=3.826m)usfingthepre-processfingtooflANSYSCFDPrev17.1.ThfisprocessensuredthattheffuflflmeshwassymmetrficabouttheBB2centrepflane.
Ffigures2,3and4show,respectfivefly,thebflockstructureffortheoveraflflmesh,theedgesoffthebflocksonthesymmetrypflane,andthefinflatfionflayerO-grfidssurroundfingtheBB2.Intheffuflflmesh(afftermfirrorfing)thereare476bflocksand36,952,960hexahedraflceflfls.Ffigure5showsthemeshonthesubmarfinesurffaceandpflaneoffsymmetryfinthevficfinfityoffthesubmarfineandFfigure6showsacross-sectfionoffthenear-bodyportfionoffthemeshattheflongfitudfinaflposfitfionwherethehuflflbegfinstotaper(x/Lpp=−0.184).Anfinflatfionflayerhavfingathficknessoffapproxfimatefly2metersffuflflscafle(0.11matmodeflscafle)surroundstheBB2huflfl.ThehefightoffthefirstceflflofftheBB2surffacewassetto8.5×10−6metersffuflflscafle(4.63×10−7metersmodeflscafle),whfichyfiefldsaflowaveragey+vaflueoffflessthan0.05fforthesecaflcuflatfions.Thewaflfl-normaflmeshexpansfionrateattheBB2surffacewas1.12.Tabfle3gfivesasummaryoffmeshparametersandmetrfics,Tabfle4gfivethenumberoffflayersandceflflspacfingfforthefinflatfionflayerbflocksaroundtheBB2,andTabfle5gfivesthenumberoffceflflsandmaxfimumspacfingfinvarfiousdfirectfionsaflongtheBB2huflflandappendages.
Itrequfiredconsfiderabfleeffort—ontheorderofftwotothreemonths—tocreateandadjustthebflockstructuredmesharoundtheappendedsubmarfinemodefl.Anunstructuredmeshwfithtetrahedraflceflflscoufldhavebeengeneratedfinmuchflesstfime.However,astudybyHaflfly[5]showedthattetrahedraflceflflscauseexcessfivedfiffusfionfinpropagatfingvortficesevenwhenusfingasmanyas22ceflflsacrossthevortexcore.Incontrast,hexahedraflceflflswereffoundtoresoflvethevortexcorepressureandcfircumfferentfiaflveflocfitydfistrfibutfionusfingontheorderoff10ceflflsacrossthecore,whentheceflflsareaflfignedwfiththeaxfisoffthevortex.AchfievfingthesameaccuracywfithtetrahedraflceflflswoufldrequfireaveryflargenumberoffceflflsandflfikeflymorecomputatfionaflresourcesthanarecurrentflyavafiflabfleatDRDC.Addfitfionaflmeshfingapproachesshoufldbeexpfloredfinffoflflow-onstudfies,suchastheuseoffahybrfidmeshwherehexahedraflceflflsareusedfintheboundaryflayerandwheretherearevortficesbutunstructuredceflflsareusedeflsewheretoreducetheeffortoffmeshgeneratfion.
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Ffigure2:BflockstructureoffDRDC’sBB2mesh(starboardhaflffonfly).
Ffigure3:Bflockedgesonthesymmetrypflane.
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Ffigure4:Inflatfionflayerbflocks.
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Ffigure5:GrfidontheBB2surffaceandsymmetrypflanefinthevficfinfityofftheBB2.
Ffigure6:Meshcrosssectfionfinthevficfinfityoffthesubmarfineattheafftendofftheconstantmfidbodysectfion(x/Lpp=−0.184).
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Tabfle3:Overaflflcharacterfistficsofftheffuflflmesh(afftermfirrorfing).
Totaflmeshceflfls(hexahedrafl) 36,952,960
Submarfinesurffaceffaces(quadrfiflaterafl) 371,616
HefightofffirstceflflatBB2surfface 1.21×10−7LoaWaflfl-normaflexpansfionrateatBB2surfface 1.12
Mfinfimumfinternaflceflflangfle 39.2deg
Maxfimumaspectratfio 75,181
Maxfimumvoflumeratfiobetweenadjacentceflfls 3.24
Tabfle4:NumberoffflayersandceflflspacfingfforthefinflatfionflayersshownfinFfigure4.LayersstartattheBB2surffaceexceptOSo,whfichstartsattheoutersurffaceoffOSfi.
Inflatfion Thfickness #off StartSpacfing EndSpacfing Expansfion
Layer ffuflflscafle flayers ffuflflscafle ffuflflscafle Rate
(m) (ceflfls) (mm) (mm) (start)
Huflfl(OH) 2.0 96 0.0085 125 1.12
SafiflInner(OSfi) 1.0 160 0.0085 37.5 1.07
SafiflOuter(OSo) 3.2 36 37.5 88-250 1.05
Safiflpflane(OSP) 0.45 72 0.0085 80 1.13
Tafiflpflanes(OT*) 0.9-2.7 72 0.0085 90-375 1.11-1.13
Tabfle5:CeflflcountandmaxfimumspacfingfinvarfiousdfirectfionsontheBB2surfface.
Dfirectfion #offceflfls Max.spacfing
Longfitudfinafl,nosetotafifl 416 0.0085LoaCfircumfferentfiafl(360):mfidbody 264 0.0078πB
Cfircumfferentfiafl(360):nose,tafifl 240 0.013πDflocaflSafifl,chordwfise(onesfide) 168 0.037CsafiflSafifl,spanwfise(onesfide) 144 0.035SsafiflSafiflpflane,chordwfise(onesfide) 56 0.054CspSafiflpflane,spanwfise(onesfide) 188 0.045SspTafiflpflane,chordwfise(onesfide) 56 0.058CtpTafiflpflane,spanwfise(onesfide) 128 0.026Stp
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6 Vfiscousflowsoflver
ThecommercfiaflvfiscousflowsoflverANSYSCFXv17.1wasusedfforthesecaflcuflatfions.ANSYSCFXsoflvestheNavfier-Stokesequatfionsusfingastrongconservatfionfformuflatfion.Ithasseveraflmodeflsfforturbuflence,fincfludfingReynoflds-AveragedNavfier-Stokes(RANS)basedmodeflsasweflflasLargeEddySfimuflatfion(LES)andDetachedEddySfimuflatfion(DES)modefls.ThefincompressfibflesteadyRANSequatfionswfithaReynofldsstressmodefl(descrfibedbeflow)wereusedfforthepresentsfimuflatfions.
ANSYSCFXusesaneflement-basedfinfite-voflumemethodtosoflvethedfiscretfizedcontfinufityandmomentumequatfions.Aflflflufidsoflutfionvarfiabflesarestoredatthemeshvertfices(nodes).Refference[6]descrfibeshowcontroflvoflumesareconstructedaroundthenodesandwherefintegratfionpofintsareflocatedfforevafluatfingcontroflvoflumesurffacefluxes.Trfi-flfinearfinfiteeflementshapeffunctfionsareusedtofinterpoflatequantfitfiesatthefintegratfionpofints.
ANSYSCFXusesacoupfledsoflver[7,8]tosoflvethehydrodynamficequatfions(fforu,v,w,p)asasfingflesystemandtheAddfitfiveCorrectfion[9]AflgebraficMufltfi-grfid[10]procedurefisusedtoaccefleratethesoflutfion.
7 Turbuflencemodefl
TheBaseflfineReynofldsstressmodefl(BSL-RSM)fimpflementedfinANSYSCFXv17.1[6]wasusedfforthesecaflcuflatfions.ThfismodeflsoflvessfixtransportequatfionsffortheReynofldsstressesandoneequatfionffortheturbuflenteddyffrequencyω.ThemathematficaflfformuflatfionffortheBSL-RSMfisgfivenfinRefference[6].
TheReynofldsstressmodeflfinherentflymodeflsanfisotropfiesfintheReynofldsstresses,unflfiketwoequatfionturbuflencemodeflsbasedonaBoussfinesqreflatfionshfipwhfichassumesfisotropficturbuflence.AstudybyJeansetafl.[11]showedthattheBSL-RSMbetterpredfictedthenormaflfforceontheDRDC-STRandSerfies58submarfinehuflflfformsatfincfidencecomparedtothetwoequatfionk−ωSSTturbuflencemodefl.TheSSTnormaflfforcepredfictfionsunder-predfictedtheBSL-RSMandexperfimentaflresufltsduetodeflayedseparatfionandaflessconcentratedfleesfidevortex,resufltfingfinflessenergyfloss.
ThedfisadvantageoffusfingtheBSL-RSMmodeflovertheSSTandothertwoequatfionmodeflsfisfincreasedcomputatfionaflrequfirementsand(generaflfly)flessrobustness.
8 Boundarycondfitfions
TheflocatfionofftheffarfiefldboundarfiesfisgfivenfinSectfion5.Theffoflflowfingboundarycondfitfionswereappflfiedfforthecaflcuflatfions:
•TheBB2submarfinesurffacewasgfivenasmooth,no-sflfipwaflflboundarycondfitfion.
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•Theffar-fiefldboundarfiesthatarenomfinaflflytangenttotheffreestreamflow(top,bottom,andsfidesatzerofincfidence;topandbottomatβ=10)weregfiventhe"OpenfingfforEntrafinment"boundarycondfitfion.Forthfiscondfitfion,thepressurefissettozero,andthegradfientsoffveflocfityandturbuflentquantfitfiesperpendficuflartotheboundaryweresettozero.Fflowcanefitherenterorfleavetheseboundarfiesasdetermfinedfimpflficfitflyffromthesoflutfion.
•Onboundarfieswheretheffreestreamflowfisknowntoonflyenterthedomafin(fforwardboundaryatzerofincfidence;fforwardandport-sfideboundarfiesatβ=10),thefinflowveflocfitycomponentsarespecfified,theturbuflentfintensfityfissetto1%andtheratfiooffturbuflentvfiscosfity(µt)todynamficvfiscosfity(µ)fissetto1.
•Ontheboundarfieswheretheflowfisonflyfleavfingthedomafin(afftboundaryatzerofincfidence;afftandstarboardsfideboundarfiesatβ=10)theaveragepressureoverthewhofleboundarywasconstrafinedtozero.Thepressurevarfiesspatfiaflflyovertheboundary,asdetermfinedfimpflficfitflybythesoflutfion,buttheaveragepressurefiszerooneachoutfletfface.
9 Dfiscretfizatfion
Thedfiscretfizedmomentumandcontfinufityequatfionsweresoflvedusfingamethodthatfisfformaflflysecondorderaccuratefinspace.Theffoflflowfingsecond-orderupwfindschemewasusedffortheadvectfionterm:
φfip=φup+β∇φ·∆r (2)
whereφfipfisthequantfityevafluatedatthefintegratfionpofint(fforcomputfingthesurffacefintegrafl),φupfisthequantfityattheupwfindnode,rfisthevectorffromtheupwfindnodetothefintegratfionpofint,andβfisabflendffactor.Thegradfient∇φwassetequafltotheaverageofftheadjacentnodaflgradfientsandthebflendffactorβwassetto1toachfievesecondorderaccuracy.
Thefirstorderupwfindschemewasusedffortheadvectfiontermsfintheturbuflenceequatfions.
10Iteratfiveconvergence
ApseudotfimestepwasusedfinANSYSCFXtoconvergetheRANSequatfionstoasteadysoflutfion.Itwasffoundthatthemosteficfientmethodfforconvergfingtoasteadysoflutfionwastoaflternatebetweenaflargertfimestepandasmaflfltfimestep.Theflargetfimestepwasrequfiredtoqufickflyachfieveagflobaflsoflutfionffortheflargeflengthscafles,butfitdoesnotprovfideenoughstabfiflfitytoconvergeregfionsoffsmaflflscafleeddfies/hfighvortficfity,suchasatthehorseshoevortexaroundthesafifl-deckjunctfiondescrfibedfinSectfion11.2.Thesmaflfltfimestepprovfidesastabflesoflutfion,buttheconvergencefisverysflowgflobaflfly.Theffoflflowfingprocedurewasffoundtoprovfideareasonabflyeficfientsoflutfion:
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1.RunNtfimesteps(fiteratfions)wfiththeflargetfimestep(∆tflg=150Loa/U),whereN
wassetto200fforthezerofincfidencecaseand500ffortheβ=10degreescase;
2.Aflternatebetween300fiteratfionswfiththesmaflfltfimestep(∆tsm=15000Loa/U)and
15fiteratfionswfith∆tflguntfifltheL∞ norm(maxfimum)resfiduaflsdroptothespecfifiedconvergencecrfiterfia.
Inaddfitfiontovaryfingthepseudotfimestepsfize,thereflaxatfionparametersfinTabfle6weresettoheflpachfievestabflefiteratfiveconvergence.AflflANSYSCFXsoflversettfingsandboundarycondfitfionsusedfforthe10degreesdrfifftandzerofincfidencecasesareshownfinAnnexAandAnnexB,respectfivefly.
Tabfle6:Reflaxatfionparametersettfings.
Parameter Settfingffor Settfingfforcaseβ=0 caseβ=10
GradfientReflaxatfion 0.01 0.1reflaxmass 0.4 0.4
Ffigures7and8showthenormaflfizedmaxfimum(L∞)resfiduaflsfforthezerofincfidenceand10degreedrfifftcases,respectfivefly.Thesuddenperfiodficchangesfinresfiduaflsarearesufltoffthechangesfintfimestepsfize.Inbothcases,themaxfimumresfiduaflsfintheentfireflufiddomafinfforaflflequatfionswerereducedto3×10−5bytheendoffthesfimuflatfions.Thezerofincfidencecaserequfired3,630fiteratfionswhereastheβ=10caserequfired2,000fiteratfions.Notethattheffasterconvergencefforthesteadydrfifftcasewasprobabflyachfievedbecausemoreflargetfimestepsareusedfinfitfiaflfly(befforeaflternatfingbetweensmaflflandflargetfimesteps)andaflargervafluewasusedfforGradfientReflaxatfion(meanfingflessunder-reflaxatfionwasappflfied).
Theconvergenceoffhydrodynamficfforcesfforthezerofincfidenceand10degreedrfifftcasesareshownfinFfigure9andFfigure10,respectfivefly.Aflflfforcesvarybyflessthan0.1%durfingtheflast900fiteratfionsoffthezerofincfidencecaseandbyflessthan0.03%durfingthefinafl900fiteratfionsfintheβ=10degreescase.
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1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
0 500 1000 1500 2000 2500 3000 3500 4000
Maxfimum Resfiduafl
Iteratfion
P-Mass
U-Mom
V-mom
W-mom
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
0 500 1000 1500 2000 2500 3000 3500 4000
Maxfimum Resfiduafl
Iteratfion
Omega
u'u'
u'v' RS
u'w' RS
v'v' RS
v'w' RS
w'w' RS
Ffigure7:Maxfimumresfiduaflsfforthecontfinufityandmomentumequatfions(top)andturbuflenceequatfions(bottom)durfingthezerofincfidencecomputatfion.
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1.E-7
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
0 500 1000 1500 2000
Maxfimum Resfiduafl
Iteratfion
P-Mass
U-Mom
V-mom
W-mom
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
0 500 1000 1500 2000
Maxfimum Resfiduafl
Iteratfion
Omega
u'u' RS
u'v' RS
u'w' RS
v'v' RS
v'w' RS
w'w' RS
Ffigure8:Maxfimumresfiduaflsfforthecontfinufityandmomentumequatfions(top)andturbuflenceequatfions(bottom)durfingtheβ=10degreescomputatfion.
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-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0 500 1000 1500 2000 2500 3000 3500 4000
100 (Ffi-F end) / F end
Iteratfion, fi
X
Z
M
Ffigure9:Percentdfifferencebetweenfforcesatfiteratfionfiandthefforcesattheendoffthecomputatfionfforthezerofincfidencecomputatfion.
11 Resufltsanddfiscussfion
11.1 FflowVfisuaflfizatfion
FoflflowfingToxopeusetafl.[12],thevortficesfintheflowaroundtheBB2arevfisuaflfizedusfingfiso-surffacesoffconstantQ-vaflues,definedasffoflflows:
Q=1
2
|Ω|2−|S|2
(3)
whereΩ=∇u−∇uT
/2fisthevortficfitytensorandS=
∇u+∇uT
/2fisthestrafin
tensor.Inthfiswork,Qfismadenon-dfimensfionaflasffoflflows:
Q′=Q
LoaV∞
2(4)
TheQfiso-surffacesarecofloredbynon-dfimensfionaflheflficfity,H′,finordertofindficatethedfirectfionorrotatfion:
H′=ω·u
|ω||u|(5)
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-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0 500 1000 1500 2000
100 (Ffi-F end) / F end
Iteratfion, fi
XYZKMN
Ffigure10:Percentdfifferencebetweenfforcesatfiteratfionfiandthefforcesattheendoffthecomputatfionffortheβ=10degreescomputatfion.
whereωfistheflocaflvortficfityvectorandufistheflocaflveflocfityvector.Normaflfizedheflficfityfindficatestheangflebetweentheveflocfityvectorandthevortficfityvector;H′=1whenveflocfityandvortficfityvectorsarepofintfingfinthesamedfirectfionandH′=−1whentheyarepofintfingfinopposfitedfirectfions.Thusasthevortficestendtoaflfignwfiththeflowafftertheyfleavethebody,H′tendstowards±1,wfithposfitfivevafluesfindficatfingacflockwfiserotatfionandnegatfivevafluesfindficatfingcounter-cflockwfiserotatfionwhenflookfingfinthedfirectfionofftheflow.
11.2 ZeroIncfidenceflowfiefld
Ffigure11showsthepredfictedprfimaryvortficesaroundtheBB2fforthezerofincfidence.Therearepafirsoffcounter-rotatfingvortficesshedffromthetfipsoffthesafifl,safiflpflanes,andtafiflpflanes.Thereareaflsohorseshoevortexsystemsgeneratedupstreamoffeachappendage-huflfljunctfionandthesafiflpflane-safifljunctfion.Thesevortficeswraparoundeachappendageandpropagatetowardstheafftendoffthesubmarfine.Theflegsoffthesafiflpflanehorseshoevortficespropagatetothetrafiflfingedgeoffthesafifl,wheretheythenfleavethesafiflandpropagateafftwards,justbeflowtheprfimarysafifltfipvortfices.Inasfimfiflarmanner,theflegsoffthetafiflpflanejunctfionvortficespropagatetotheendoffthesubmarfineandseparateoffthehuflflneartheaffterperpendficuflar.
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Ffigure11:PredfictedvortexcoresaroundtheBB2atzerofincfidence.
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Thesafifl-deckjunctfionvortexsystemfistheflargestandfitfispredfictedtoremafincoherentuntfiflneartheendoffthedeckcasfing.Detafiflsoffthepredfictedsafifljunctfionvortexsystemareshownonthesubmarfinepflaneoffsymmetry,justupstreamoffthesafiflfinFfigure12.Theflowseparatesffromthedeckasfitapproachesthe90cornerbetweenthedeckandthefleadfingedgeoffthesafifl.Therefisastrongreversedflowregfionfinffrontoffthefleadfingedgeoffthesafifl,whfichroflflsupfintotheprfimaryvortexataroundx/Loa=0.721.Thereareaddfitfionaflweakersecondaryvortficespredfictedfforwardoffthfisprfimaryvortex.Theflocatfionandmagnfitudeoffpeakvortficfityfintheydfirectfion,ωy,ateachoffthesethreevortexcoresfistabuflatedfinTabfle7.Thedfimensfionsoffthfisvortexsystemaresmaflflreflatfivetotheoveraflflsubmarfine,wfiththedfiameterofftheprfimarycorepredfictedtobeapproxfimatefly0.1%offthesubmarfineflength.ItrequfiredaffewfiteratfionsfinthemeshfingprocesstopflaceenoughmeshceflflstoresoflvetheffeaturesshownfinFfigure12(notethattherefisameshnodeatthetafifloffeachveflocfityvectorfinthfisfigure).Evenffurtherrefinementmaybeneededtoconvergethemagnfitudeoffvortficfityatthecore.
Tabfle7:Locatfionandmagnfitudeoffmaxfimumvortficfityfinthecoreoffthesafifl-deckjunctfionvortficesonthey=0pflaneupstreamoffthesafifl,shownfinFfigure12.
ωyLoa/V∞Vortex# x/Loa z/Loa Max/Mfin
1 0.72082 0.08359 -3594
2a 0.72193 0.083049 1186
3 0.72356 0.08306 -711.0
aNoflocaflmaxfforωyfinvortex2duetoboundaryflayerfinteractfion;vafluesarefforthezeroveflocfitypofintatthecore.
Ffigure13showsaflateraflcrosssectfionoffvortficesatx=0(0.060588Loaafftoffsafifltrafiflfingedge)fforthezerofincfidencecase.ThenumberfingoffvortficesfisconsfistentwfithFfigure12;vortex1fistheprfimarysafifl-deckjunctfionvortexandvortfices2and3arethesecondarysafifl-deckjunctfionvortfices.Notethatduetosymmetry,therearevortficesoffequaflstrengthbutopposfiterotatfiononeachsfideoffthey=0centrepflane.Dfirectflybehfindthesafifl,thereareanaddfitfionafl9predfictedvortficesoneachsfideoffthecentrepflane(flabeflfled4-12).Thetopvortfices —thestrongestoffthegroup —weregeneratedatthesafifltfip.Beflowthat,thereare4setsoffvortficesoneachsfideoffthecentrepflanewhfichorfigfinateffromthejunctfionbetweenthesafiflpflaneandthesafifl.Furtherdown,behfindtherootoffthesafifl,thereareanaddfitfionafl4pafirsoffvortfices,wfiththebottompafirbefingthestrongest.Ffinaflfly,thevortexflabeflfled13finFfigure13fisthetfipvortexffromthesafiflpflanes.Thecoresoffeachoffthesevortficesatx=0arefidentfifiedbytheflocaflpeakfintheaxfiaflcomponentoffvortficfity,ωx,astabuflatedfinTabfle8.
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Ffigure12:Centerpflane(y=0)crosssectfionoffthepredfictedsafifl-deckjunctfionvortexfforthezerofincfidencecase.
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Ffigure13:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)fforthezerofincfidencecase.
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Tabfle8:Locatfionandmagnfitudeoffmaxfimumx-componentoffvortficfityfinthecoreoffthevortficesonthex=0pflane,shownfinFfigure13(starboardsfideonfly).
ωxLoa/V∞Vortex# y/Loa z/Loa Max/Mfin
1 -0.01853 0.08433 -26.69
2 -0.02431 0.08495 15.88
3 -0.02777 0.07964 -12.81
4 -0.00267 0.15166 95.29
5 -0.00350 0.13847 -36.51
6 -0.00259 0.13370 43.55
7 -0.00168 0.12522 -24.45
8 -0.00252 0.11991 6.25
9 -0.00156 0.09352 -3.31
10 -0.00151 0.08807 -10.18
11 -0.00148 0.08521 22.72
12 -0.00378 0.08389 -56.96
13 -0.04794 0.13771 -10.19
11.3 Fflowfiefldffor10drfifftcase
Ffigure14showsthepredfictedprfimaryvortficesffortheβ=10case.Inthfiscase,therefisastrongsafifltfipvortexthatrotatescounter-cflockwfisewhenflookfingfinthedfirectfionofftheflow.Thfisfisexpectedffromtheoryasthesafiflactsasawfingfincrossflow.Therefisaflsoastrongvortex(H1finFfigure14)separatfingffromthefleesfide(finthfiscasethestarboardsfide)offthehuflflandpropagatfingdownstreambetweentheruddersonthestarboardsfideofftheBB2.Thfisprfimaryhuflflvortexrotatesfintheopposfitedfirectfionoffthesafifltfipvortex.Asecond,weakerhuflflvortex,H2,rotatesfintheopposfitesenseasH1.vortficesH1andH2arearesufltoffthecrossflowseparatfingffromthefleewardsfideoffthehuflfl.TherefisathfirdvortexH3thatseparatesffromthecreasebetweenthehuflflandtheafftendoffthedeckcasfing.
ThecontouroffaxfiaflvortficfityfinFfigure15morecflearflyshowsthearrangementoffvortficesonaflateraflcross-sectfionatmfidshfips(x=0)ffortheβ=10case.Thesamenumberfingfisappflfiedfforthevortficesbehfindthesafiflandsafiflpflanesasfforthezerofincfidencecase,exceptwfithanaddfitfionaflfidentfifierfforport-sfide(P)orstarboardsfide(S)astherefisno-flongerflowsymmetry;1Pfisthemafinsafifl-deckjunctfionvortexthatwrapsaroundtheportsfideoffthesafifl,4Sfistheprfimarysafifltfipvortex,and13Sand13Parethetfipvortficesffromthestarboardandportsafiflpflanes,respectfivefly.Thestarboardflegofftheprfimarysafifl-deckjunctfionvortex(1S,notflabeflfled)fisdfificuflttofidentfiffybecauseoffthewayfitfinteractswfiththehuflflseparatfionvortexH2,whfichrotatesfintheopposfitedfirectfion.TheflocatfionsandmagnfitudesoffpeakaxfiaflvortficfityfforsomeoffthevortexcoresshownfinFfigure15aresummarfizedfinTabfle9.
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Ffigure14:PredfictedvortexcoresaroundtheBB2atβ=10.
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Tabfle9:Locatfionandmagnfitudeoffmaxfimumx-componentoffvortficfityfinthecoreoffthevortficesonthex=0pflane,shownfinFfigure15.
ωxLoa/V∞Vortex# y/Loa z/Loa Max
1P 0.00744 0.08898 84.71
4S -0.01647 0.14237 328.22
13P 0.01953 0.15652 80.63
13S -0.07201 0.12415 24.25
Theaccuratepredfictfionofftheseparatfionflfinesandstrengthsoffthehuflflvortficesfisfimportantfforpredfictfingthehydrodynamficfloadsonthesubmarfine[11].AnfinfitfiaflcomparfisonbetweenNATOAVT-301partficfipants’predfictfionsshowedawfidevarfiatfionfinthepredfictedvortficfitymagnfitudefinvortexcoresastheyprogressdownstream.Asthenextstepgofingfforward,asystematficverfificatfionstudyshoufldbedonetodetermfinethemeshresoflutfionrequfiredtoobtafinamesh-convergedconvergedsoflutfion.Theresufltsffordfifferentturbuflencemodeflflfingapproachescanthenbecompared.
Inordertoassessthecurrentflevefloffrefinementthroughtheprfimarysafifltfipvortex,acontouroffthepressurecoeficfient,cp=P/(0.5ρU
2),finthecoreregfionfisoverflafidwfiththemeshattwoflongfitudfinaflposfitfionsfinFfigure16.Theradfiusoffthevortexfistakentobethedfistanceffromthecentretothepofintoffmaxfimumcfircumfferentfiaflveflocfity.Basedonthfisdefinfitfion,thecp=−0.4fisoflfinefforthemfidshfipscross-sectfionfinFfigure16approxfimateflydefinesthecoreoffthevortex;thfisgfivesaround10ceflflsacrossthecore.AstudybyHaflflyand Watt[13]ffoundthatapproxfimatefly10ceflflsacrossthecorefisadequatefforpropagatfinganfideaflfizedvortexwfithhexahedraflceflflsaflfignedwfiththevortexaxfis.Thfisfindficatesthatthemeshrefinementatmfidshfipsfisreasonabflefforcapturfingthesafifltfipvortex.However,addfitfionaflceflflsmaybeneedtoachfieveffuflflmeshconvergencebecausetheceflflsarenotperffectflyaflfignedwfiththevortexduetothe10drfifftangfle.Affoflflowonmeshrefinementstudyshoufldbedonetoassessthfis.Atthepropeflflerpflanecross-sectfion,thesafifltfipvortexpassesthroughabflockfinterffacefinthemeshwheretherefisasfignfificantfincreasefinceflflsfize.Itfisdfificuflttodefinetheprecfiseboundaryoffthevortexcorebuttheflargeceflflsareontheorderoff1/3offthecoredfiameter.Thfisflargeceflflsfize,combfinedwfiththeflargemeshexpansfionrateandmfisaflfignmentbetweenceflflsandthevortexaxfisshoufldresufltfinsfignfificantnumerficafldfiffusfion.Asfimfiflarassessmentshowsthatthesafiflpflanetfipvortficesareevenflessweflflresoflvedovertheflengthoffthesubmarfine,wfithonflyaround2-3ceflflsacrossthecore.Theseareareasoffthemeshthatshoufldbefimproved/refinedfinthenextstageoffthfisproject.
11.4 Surffacepressureandshearstress
ThepredfictedpressureandshearstressdfistrfibutfionsontheBB2areshownfinFfigures17and18.Anfinfitfiaflassessmentoffsubmfissfionsffromotherpartficfipantsfindficatesagoodoveraflflagreementfinthepressuredfistrfibutfionbuttherearesomedfifferencefinshearstress.Inthe
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Ffigure15:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)ffortheβ=10
case.
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Ffigure16:Pressurethroughtheprfimarysafifltfipvortexatmfidshfips(x/Loa=0)andthepropeflflerpflane(x/Loa=−0.481),ffortheβ=10
case.
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presentDRDCcaflcuflatfionsandsomeothersubmfissfions,theshearstressdfistrfibutfionhassomehfighffrequencynofisethatdoesnotappeartobephysficafl.ThemeshshoufldbeverfifiedtoseefiffthfisfisanfissuewfithceflflsnotconfformfingtotheBB2geometryorfifftherefisanfissuewfiththeunderflyfingCADmodefl.Aflso,theboundaryflayerfisresoflvedweflflfintothevfiscoussubflayerfinthesecaflcuflatfions,wfithacomputedaveragey+vaflueoff0.0456,wfithamaxfimumvaflueoff0.211andstandarddevfiatfionoff0.05.ThfisaflflowsthemeshtobeusedfforarangeoffReynofldsnumbersuptoffuflfl-scaflewhfiflestfiflflresoflvfingthevfiscousboundaryflayer.However,thehfighceflflaspectratfiosattheBB2surffacemakeconvergencemoredfificufltandmaybecontrfibutfingtothenofisefintheshearstresspredfictfion.Computatfionswfithaflargery+arepflannedfforthenextphaseoffthfisproject.
11.5IntegratedForces
ThecaflcuflatedhydrodynamficfforcesandmomentsaregfivenfinTabfles10and11.Atzerofincfidence,theaxfiaflfforcefisbrokendownfintoshearstressX′sandpressureX
′pcomponents.
DuetothesymmetryofftheBB2aboutthecentrepflane,theflateraflfforceY′,yawfingmomentN′,androflflfingmomentK′areaflfltheoretficaflflyzerofforzeroflowfincfidence.Themagnfitudeoffaflflthesenormaflfizedvaflueswereflessthan1×10−9attheendoffthezerofincfidenceRANScomputatfion.
Asexpected,aflargeflateraflfforceYandflargeyawfingmomentNarepredfictedfforthe10
drfifftcaseduetothecrossflowdragonthehuflflandflfifftgeneratedbythesafiflandtafiflpflanes.TherefisaflsoaflargeroflflfingmomentKbecausethecentreoffflfifftonthesafiflfisabovethehuflflaxfis.Asfignfificantout-off-pflanefforceZandpfitchfingM areaflsopredficted.Asdescrfibedby Wattetafl.[14],theseout-off-pflanefloadsareduetothesafiflgeneratfingaflowcfircuflatfionaroundthehuflflafftoffthesafifl.Thfiscfircuflatfionfinteractswfiththecrossflowoverthehuflfltogenerateadownwardfforceovertheafftendofftheboat,whfichresufltsfinthenose-uppfitchfingmoment.
Inthenextphaseoffthfisproject,asystematficgrfidrefinementstudywfiflflbeconductedtodetermfinethesensfitfivfityoffpredfictedhydrodynamficsfforcesandmomentsongrfidresoflutfion.
Tabfle10:PredfictedBB2hydrodynamficfforcesandmomentsfforzeroflowfincfidence,ReL=9.57×10
6.
X′s X′p X′ Z′ M′
−1.414×10−3 −2.31×10−4 −1.645×10−3 −1.46×10−4 −8.60×10−5
Tabfle11:PredfictedBB2hydrodynamficfforcesandmomentsfforβ=10,ReL=9.57×106.
X′ Y′ Z′ K′ M′ N′
−6.17×10−4 −1.44×10−2 −3.88×10−3 4.68×10−4 −6.39×10−4 −3.32×10−3
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Ffigure17:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2fforthezerofincfidencecase.
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Ffigure18:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2ffortheβ=10case.
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12 Concflusfionsandffuturework
Anfinfitfiafl37mfiflflfionceflflstructuredmeshwascreatedaroundthegenerficBB2submarfinemodeflffortheNATOAVT-301coflflaboratfiveproject.BaseflfineRANScaflcuflatfionsweredoneonthfismeshatzerofincfidenceand10drfifftcasesusfingthevfiscousflowsoflverANSYSCFXwfiththeBaseflfineReynofldsStressturbuflencemodefl.Goodfiteratfiveconvergencecoufldbeobtafinedbyaflternatfingbetweenflargeandsmaflfltfimestepsfizes.Affocusoffthefinfitfiaflpredfictfionswasonresoflvfingthesafiflhorseshoejunctfionvortex.Moreworkfisneededtoachfieveadequatemeshresoflutfionfinthfisandotherregfionsofftheflow.Thepresentcaflcuflatfionshavefidentfifiedtheapproxfimatesfizeandflocatfionoffvortficestogufidesubsequentmeshfimprovements.Astrategyshoufldbedeveflopedtorefineregfionswfithflargegradfientsfinflowvarfiabfles,suchasvortexcores,wfithoutfincurrfingexcessfivecomputatfionaflcost.Somepartficfipantshaveffoundautomatficmeshrefinementmethodstobeveryeficfient;thfisshoufldbefinvestfigatedbyDRDC.Asystematficgrfidrefinementstudyshoufldaflsobedonetoassessnumerficafldfiscretfizatfionerrors.
ExperfienceffromphasezerowfiflflthenbeusedtoperfformsfimuflatfionsatexperfimentaflcondfitfionsfforwfindtunneflexperfimentsrecentflyconductedbyAustraflfia.Acomparfisonwfithdfifferentturbuflencemodeflflfingapproaches,suchasahybrfidRANSflargeeddysfimuflatfionsshoufldaflsobeconsfideredfintheffuture.SfimuflatfionsoffrotatfionaflsubmarfinemotfionmatchfingcondfitfionsfforrotatfingarmexperfimentsconductedbyQfinetfiQareaflsopflannedffoflflowfingthesteadytransflatfionstudy.
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Refferences
[1] Overpeflt,B.,Nfienhufis,B.,andAnderson,B.(October,2015),FreerunnfingmanoeuvrfingmodefltestsonamoderngenerficSSKcflasssubmarfine(BB2),InPacfificInternatfionaflMarfitfimeConfference,Sydney,Austraflfia.
[2]Toxopeus,S.andKerkvflfiet,M.(2017),NATOAVT-301CoflflaboratfiveExercfise:Part1:InfitfiaflpredfictfionsfforBB2.
[3] Joubert,P.N.(2006),Someaspectsoffsubmarfinedesfign-part2.Shapeoffasubmarfine2026,(TechnficaflReportDSTO-TR-1622)DeffenceScfienceandTechnoflogyOrganfisatfion,FfishermansBend,Vfictorfia,Austraflfia.
[4] Baker,C.R.(2006),Astrategficmeshfingapproachtomodeflfinghydrodynamficflowaroundstreamflfinedaxfisymmetrficshapes,Mastersthesfis,Dept.offMechanficaflEngfineerfing,Unfiv.offNewBrunswfick.
[5]Haflfly,D.(2009),RANScaflcuflatfionsofftheevoflutfionoffvortficesonunstructuredgrfids,(DRDCAtflantficTM2009-052)DeffenceR&DCanada.
[6] ANSYS,Inc.(2016),ANSYSCFX-SoflverTheoryGufide,(TechnficaflReport)SASIP,Inc.
[7]Hutchfinson,B.,Gaflpfin,P.,andRafithby,G.(1988),Appflficatfionoffaddfitfivecorrectfionmufltfi-grfidtothecoupfledflufidflowequatfions,NumerHeatTransffer,13(2),133–147.
[8] Raw,M.J.(1994),Acoupfledaflgebraficmufltfi-grfidmethodfforthe3DNavfier-Stokesequatfions,InProceedfingsoffthetenthGAMM-semfinar.Notesonnumerficaflflufidmechanfics.,Kefifl,Germany.
[9] Hutchfinson,B.R.andRafithby,G.D.(1986),Amufltfi-grfidmethodbasedontheaddfitfivecorrectfionstrategy,NumerficaflHeatTransffer,9,511–537.
[10]Raw,M.J.(1996),Robustnessoffcoupfledaflgebraficmufltfi-grfidffortheNavfier-Stokesequatfion.,In34thAerospaceandscfiencesmeetfing&exhfibfit,NumberAIAA96-0297,Reno,NV.
[11]Jeans,T.L., Watt,G.D.,Gerber,A.G.,Hoflfloway,A.G.L.,andBaker,C.R.(2009),Hfigh-ResoflutfionReynoflds-AveragedNavfier-Stokesflowpredfictfionsoveraxfisymmetrficbodfieswfithtaperedtafifls,AIAAJournafl,47,19–32.
[12]Toxopeus,S.,Kufin,R.,Kerkvflfiet,M.,Hoefijmakers,H.,andNfienhufis,B.(2014),Improvementoffresfistanceandwakefiefldoffanunderwatervehficflebyoptfimfisfingthefin-bodyjunctfionflowwfithCFD,InASME201433rdInternatfionaflConfferenceonOcean,OffshoreandArctficEngfineerfing,NumberOMAE2014-23784,SanFrancfisco,CA.
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[13]Haflfly,D.and Watt,G.D.(2002),RANScaflcuflatfionsofftheevoflutfionoffvortfices,(DRDCAtflantficTR2001-216)DeffenceR&DCanada.
[14]Watt,G.D.,Gerber,A.G.,andHoflfloway,A.G.L.(2007),SubmarfineHydrodynamficsStudfiesUsfingComputatfionaflFflufidDynamfics,InProceedfingsofftheefightCanadfianMarfineHydrodynamficsandStructuresConfference,St.John’s,NL,Canada.
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AnnexAANSYSCFXsoflversettfingsfforthe10
degreesdrfifftangflecase
TheffoflflowfingarethesoflversettfingsusedffortheANSYSCFXsfimuflatfionofftheBB2submarfinemodeflatadrfifftangfleoff10degrees,finCFXCommandLanguage(CCL)fformat.
LIBRARY:CEL:EXPRESSIONS:Aflpha=0.0[deg]Beta=10[deg]Lsub=3.826[m]NormForce=0.5*Rho*Ufinff2*Lsub2NormMom=0.5*Rho*Ufinff2*Lsub3Rho=1000[kgm-3]Ufin=-Ufinff*cos(Beta)*cos(Aflpha)Ufinff=3.0[ms-1]Vfin=-Ufinff*sfin(Beta)Vfisc=0.0012[kgm-1s-1]Wfin=Ufinff*sfin(Aflpha)bff=step(afitern-100.5)+(afitern-1)*0.01*step(100.5-afitern)dt=dtflg-(dtflg-dtsm)*(step(afitern-(fiflg1))*step((fiflg1+fism)-\afitern)+step(afitern-(fiflg1+fism+fiflg))*\step((fiflg1+fiflg+fism*2)-afitern)+step(afitern-(fiflg1+fism*2+fiflg*2))*\step((fiflg1+fiflg*2+fism*3)-afitern)+step(afitern-(fiflg1+fism*3+fiflg*3))*\step((fiflg1+fiflg*3+fism*4)-afitern)+step(afitern-(fiflg1+fism*4+fiflg*4))\*step((fiflg1+fiflg*4+fism*5)-afitern)+\step(afitern-(fiflg1+fism*5+fiflg*5))*step((fiflg1+fiflg*5+fism*6)-afitern)\+step(afitern-(fiflg1+fism*6+fiflg*6))*step((fiflg1+fiflg*6+fism*7)-\afitern)+step(afitern-(fiflg1+fism*7+fiflg*7))*step((fiflg1+fiflg*7+fism*8)\-afitern)+step(afitern-(fiflg1+fism*8+fiflg*8))*\step((fiflg1+fiflg*8+fism*9)-afitern)+step(afitern-(fiflg1+fism*9+fiflg*9))\*step((fiflg1+fiflg*9+fism*10)-afitern)+\step(afitern-(fiflg1+fism*10+fiflg*10)))
fiflg1=500fism=300fiflg=15Nflrg=50Nsm=5000dtflg=Lsub/(Ufinff*Nflrg)dtsm=Lsub/(Ufinff*Nsm)
ENDENDMATERIAL:Fflufid1MaterfiaflGroup=UserOptfion=PureSubstanceThermodynamficState=LfiqufidPROPERTIES:Optfion=GeneraflMaterfiaflEQUATIONOFSTATE:Densfity=RhoMoflarMass=1.0[kgkmofl-1]Optfion=Vaflue
ENDDYNAMICVISCOSITY:DynamficVfiscosfity=VfiscOptfion=Vaflue
END
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ENDEND
ENDFLOW:FflowAnaflysfis1SOLUTIONUNITS:AngfleUnfits=[rad]LengthUnfits=[m]MassUnfits=[kg]SoflfidAngfleUnfits=[sr]TemperatureUnfits=[K]TfimeUnfits=[s]
ENDANALYSISTYPE:Optfion=SteadyStateEXTERNALSOLVERCOUPLING:Optfion=None
ENDENDDOMAIN:FflufidDomafinCoordFrame=Coord0DomafinType=FflufidLocatfion=Assembfly,Assembfly2BOUNDARY:BottomBoundaryType=OPENINGLocatfion=Bottom,Bottom2BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
ENDMASSANDMOMENTUM:Optfion=EntrafinmentReflatfivePressure=0.0[Pa]
ENDTURBULENCE:Optfion=ZeroGradfient
ENDEND
ENDBOUNDARY:InfletBoundaryType=INLETLocatfion=In,In2BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
ENDMASSANDMOMENTUM:Optfion=CartesfianVeflocfityComponentsU=UfinV=VfinW=Wfin
ENDTURBULENCE:Optfion=LowIntensfityandEddyVfiscosfityRatfio
ENDEND
ENDBOUNDARY:NegyBoundaryType=OUTLETLocatfion=StarboardBOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
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ENDMASSANDMOMENTUM:Optfion=AverageStatficPressurePressureProfffifleBflend=0.05ReflatfivePressure=0[Pa]
ENDPRESSUREAVERAGING:Optfion=AverageOverWhofleOutflet
ENDEND
ENDBOUNDARY:OutfletBoundaryType=OUTLETLocatfion=Out,Out2BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
ENDMASSANDMOMENTUM:Optfion=AverageStatficPressurePressureProfffifleBflend=0.05ReflatfivePressure=0[Pa]
ENDPRESSUREAVERAGING:Optfion=AverageOverWhofleOutflet
ENDEND
ENDBOUNDARY:PflusyBoundaryType=INLETLocatfion=Starboard2BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
ENDMASSANDMOMENTUM:Optfion=CartesfianVeflocfityComponentsU=UfinV=VfinW=Wfin
ENDTURBULENCE:Optfion=LowIntensfityandEddyVfiscosfityRatfio
ENDEND
ENDBOUNDARY:SubmarfineBoundaryType=WALLLocatfion=Huflfl,Safifl,Safiflpflane,TafiflLS,TafiflUS,Huflfl2,Safifl2,Safiflpflane\2,TafiflLS2,TafiflUS2
BOUNDARYCONDITIONS:MASSANDMOMENTUM:Optfion=NoSflfipWaflfl
ENDWALLROUGHNESS:Optfion=SmoothWaflfl
ENDEND
ENDBOUNDARY:TopBoundaryType=OPENINGLocatfion=Top,Top2
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BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
ENDMASSANDMOMENTUM:Optfion=EntrafinmentReflatfivePressure=0[Pa]
ENDTURBULENCE:Optfion=ZeroGradfient
ENDEND
ENDDOMAINMODELS:BUOYANCYMODEL:Optfion=NonBuoyant
ENDDOMAINMOTION:Optfion=Statfionary
ENDMESHDEFORMATION:Optfion=None
ENDREFERENCEPRESSURE:RefferencePressure=0[atm]
ENDENDFLUIDDEFINITION:Fflufid1Materfiafl=Fflufid1Optfion=MaterfiaflLfibraryMORPHOLOGY:Optfion=ContfinuousFflufid
ENDENDFLUIDMODELS:COMBUSTIONMODEL:Optfion=None
ENDHEATTRANSFERMODEL:Optfion=None
ENDTHERMALRADIATIONMODEL:Optfion=None
ENDTURBULENCEMODEL:Optfion=BSLReynofldsStress
ENDTURBULENTWALLFUNCTIONS:Optfion=Automatfic
ENDEND
ENDINITIALISATION:Optfion=AutomatficINITIALCONDITIONS:VeflocfityType=CartesfianCARTESIANVELOCITYCOMPONENTS:Optfion=AutomatficwfithVaflueU=UfinV=VfinW=Wfin
END
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STATICPRESSURE:Optfion=AutomatficwfithVaflueReflatfivePressure=0[Pa]
ENDTURBULENCEINITIALCONDITIONS:Optfion=MedfiumIntensfityandEddyVfiscosfityRatfio
ENDEND
ENDOUTPUTCONTROL:BACKUPDATARETENTION:Optfion=DefleteOfldFfifles
ENDBACKUPRESULTS:BackupResuflts1FfifleCompressfionLevefl=DeffaufltOptfion=StandardOutputEquatfionResfiduafls=AflflOUTPUTFREQUENCY:IteratfionIntervafl=200Optfion=IteratfionIntervafl
ENDENDMONITOROBJECTS:MONITORBALANCES:Optfion=Fuflfl
ENDMONITORFORCES:Optfion=Fuflfl
ENDMONITORPARTICLES:Optfion=Fuflfl
ENDMONITORPOINT:KhuflflCoordFrame=Coord0ExpressfionVaflue=torque_x()@REGION:Huflfl+torque_x()@REGION:Huflfl2Optfion=Expressfion
ENDMONITORPOINT:KsafiflCoordFrame=Coord0ExpressfionVaflue=torque_x()@REGION:Safifl+torque_x()@REGION:Safifl2Optfion=Expressfion
ENDMONITORPOINT:KspPCoordFrame=Coord0ExpressfionVaflue=torque_x@REGION:Safiflpflane2Optfion=Expressfion
ENDMONITORPOINT:KspSCoordFrame=Coord0ExpressfionVaflue=torque_x@REGION:SafiflpflaneOptfion=Expressfion
ENDMONITORPOINT:KsubCoordFrame=Coord0ExpressfionVaflue=torque_x()@SubmarfineOptfion=Expressfion
ENDMONITORPOINT:KsubNormCoordFrame=Coord0ExpressfionVaflue=torque_x()@Submarfine/NormMomOptfion=Expressfion
END
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MONITORPOINT:KtafiflCoordFrame=Coord0ExpressfionVaflue=torque_x()@REGION:TafiflUS+\torque_x()@REGION:TafiflUS2+torque_x()@REGION:TafiflLS+\torque_x()@REGION:TafiflLS2
Optfion=ExpressfionENDMONITORPOINT:KtafiflLPCoordFrame=Coord0ExpressfionVaflue=torque_x()@REGION:TafiflLS2Optfion=Expressfion
ENDMONITORPOINT:KtafiflLSCoordFrame=Coord0ExpressfionVaflue=torque_x()@REGION:TafiflLSOptfion=Expressfion
ENDMONITORPOINT:KtafiflUPCoordFrame=Coord0ExpressfionVaflue=torque_x()@REGION:TafiflUS2Optfion=Expressfion
ENDMONITORPOINT:KtafiflUSCoordFrame=Coord0ExpressfionVaflue=torque_x()@REGION:TafiflUSOptfion=Expressfion
ENDMONITORPOINT:MhuflflCoordFrame=Coord0ExpressfionVaflue=torque_y()@REGION:Huflfl+torque_y()@REGION:Huflfl2Optfion=Expressfion
ENDMONITORPOINT:MsafiflCoordFrame=Coord0ExpressfionVaflue=torque_y()@REGION:Safifl+torque_y()@REGION:Safifl2Optfion=Expressfion
ENDMONITORPOINT:MspPCoordFrame=Coord0ExpressfionVaflue=torque_y@REGION:Safiflpflane2Optfion=Expressfion
ENDMONITORPOINT:MspSCoordFrame=Coord0ExpressfionVaflue=torque_y@REGION:SafiflpflaneOptfion=Expressfion
ENDMONITORPOINT:MsubCoordFrame=Coord0ExpressfionVaflue=torque_y()@SubmarfineOptfion=Expressfion
ENDMONITORPOINT:MsubNormCoordFrame=Coord0ExpressfionVaflue=torque_y()@Submarfine/NormMomOptfion=Expressfion
ENDMONITORPOINT:MtafiflCoordFrame=Coord0ExpressfionVaflue=torque_y()@REGION:TafiflUS+\torque_y()@REGION:TafiflUS2+torque_y()@REGION:TafiflLS+\torque_y()@REGION:TafiflLS2
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Optfion=ExpressfionENDMONITORPOINT:MtafiflLPCoordFrame=Coord0ExpressfionVaflue=torque_y()@REGION:TafiflLS2Optfion=Expressfion
ENDMONITORPOINT:MtafiflLSCoordFrame=Coord0ExpressfionVaflue=torque_y()@REGION:TafiflLSOptfion=Expressfion
ENDMONITORPOINT:MtafiflUPCoordFrame=Coord0ExpressfionVaflue=torque_y()@REGION:TafiflUS2Optfion=Expressfion
ENDMONITORPOINT:MtafiflUSCoordFrame=Coord0ExpressfionVaflue=torque_y()@REGION:TafiflUSOptfion=Expressfion
ENDMONITORPOINT:NhuflflCoordFrame=Coord0ExpressfionVaflue=torque_z()@REGION:Huflfl+torque_z()@REGION:Huflfl2Optfion=Expressfion
ENDMONITORPOINT:NsafiflCoordFrame=Coord0ExpressfionVaflue=torque_z()@REGION:Safifl+torque_z()@REGION:Safifl2Optfion=Expressfion
ENDMONITORPOINT:NspPCoordFrame=Coord0ExpressfionVaflue=torque_z@REGION:Safiflpflane2Optfion=Expressfion
ENDMONITORPOINT:NspSCoordFrame=Coord0ExpressfionVaflue=torque_z@REGION:SafiflpflaneOptfion=Expressfion
ENDMONITORPOINT:NsubCoordFrame=Coord0ExpressfionVaflue=torque_z()@SubmarfineOptfion=Expressfion
ENDMONITORPOINT:NsubNormCoordFrame=Coord0ExpressfionVaflue=torque_z()@Submarfine/NormMomOptfion=Expressfion
ENDMONITORPOINT:NtafiflCoordFrame=Coord0ExpressfionVaflue=torque_z()@REGION:TafiflUS+\torque_z()@REGION:TafiflUS2+torque_z()@REGION:TafiflLS+\torque_z()@REGION:TafiflLS2
Optfion=ExpressfionENDMONITORPOINT:NtafiflLPCoordFrame=Coord0ExpressfionVaflue=torque_z()@REGION:TafiflLS2
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Optfion=ExpressfionENDMONITORPOINT:NtafiflLSCoordFrame=Coord0ExpressfionVaflue=torque_z()@REGION:TafiflLSOptfion=Expressfion
ENDMONITORPOINT:NtafiflUPCoordFrame=Coord0ExpressfionVaflue=torque_z()@REGION:TafiflUS2Optfion=Expressfion
ENDMONITORPOINT:NtafiflUSCoordFrame=Coord0ExpressfionVaflue=torque_z()@REGION:TafiflUSOptfion=Expressfion
ENDMONITORPOINT:XhuflflCoordFrame=Coord0ExpressfionVaflue=fforce_x()@REGION:Huflfl+fforce_x()@REGION:Huflfl2Optfion=Expressfion
ENDMONITORPOINT:XsafiflCoordFrame=Coord0ExpressfionVaflue=fforce_x()@REGION:Safifl+fforce_x()@REGION:Safifl2Optfion=Expressfion
ENDMONITORPOINT:XspPCoordFrame=Coord0ExpressfionVaflue=fforce_x@REGION:Safiflpflane2Optfion=Expressfion
ENDMONITORPOINT:XspSCoordFrame=Coord0ExpressfionVaflue=fforce_x@REGION:SafiflpflaneOptfion=Expressfion
ENDMONITORPOINT:XsubCoordFrame=Coord0ExpressfionVaflue=fforce_x()@SubmarfineOptfion=Expressfion
ENDMONITORPOINT:XsubNormCoordFrame=Coord0ExpressfionVaflue=fforce_x()@Submarfine/NormForceOptfion=Expressfion
ENDMONITORPOINT:XtafiflCoordFrame=Coord0ExpressfionVaflue=fforce_x()@REGION:TafiflUS+fforce_x()@REGION:TafiflUS\2+fforce_x()@REGION:TafiflLS+fforce_x()@REGION:TafiflLS2
Optfion=ExpressfionENDMONITORPOINT:XtafiflLPCoordFrame=Coord0ExpressfionVaflue=fforce_x()@REGION:TafiflLS2Optfion=Expressfion
ENDMONITORPOINT:XtafiflLSCoordFrame=Coord0ExpressfionVaflue=fforce_x()@REGION:TafiflLSOptfion=Expressfion
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ENDMONITORPOINT:XtafiflUPCoordFrame=Coord0ExpressfionVaflue=fforce_x()@REGION:TafiflUS2Optfion=Expressfion
ENDMONITORPOINT:XtafiflUSCoordFrame=Coord0ExpressfionVaflue=fforce_x()@REGION:TafiflUSOptfion=Expressfion
ENDMONITORPOINT:XvsubNormCoordFrame=Coord0ExpressfionVaflue=areaInt(WaflflShearX)@Submarfine/NormForceOptfion=Expressfion
ENDMONITORPOINT:YhuflflCoordFrame=Coord0ExpressfionVaflue=fforce_y()@REGION:Huflfl+fforce_y()@REGION:Huflfl2Optfion=Expressfion
ENDMONITORPOINT:YsafiflCoordFrame=Coord0ExpressfionVaflue=fforce_y()@REGION:Safifl+fforce_y()@REGION:Safifl2Optfion=Expressfion
ENDMONITORPOINT:YspPCoordFrame=Coord0ExpressfionVaflue=fforce_y@REGION:Safiflpflane2Optfion=Expressfion
ENDMONITORPOINT:YspSCoordFrame=Coord0ExpressfionVaflue=fforce_y@REGION:SafiflpflaneOptfion=Expressfion
ENDMONITORPOINT:YsubCoordFrame=Coord0ExpressfionVaflue=fforce_y()@SubmarfineOptfion=Expressfion
ENDMONITORPOINT:YsubNormCoordFrame=Coord0ExpressfionVaflue=fforce_y()@Submarfine/NormForceOptfion=Expressfion
ENDMONITORPOINT:YtafiflCoordFrame=Coord0ExpressfionVaflue=fforce_y()@REGION:TafiflUS+fforce_y()@REGION:TafiflUS\2+fforce_y()@REGION:TafiflLS+fforce_y()@REGION:TafiflLS2
Optfion=ExpressfionENDMONITORPOINT:YtafiflLPCoordFrame=Coord0ExpressfionVaflue=fforce_y()@REGION:TafiflLS2Optfion=Expressfion
ENDMONITORPOINT:YtafiflLSCoordFrame=Coord0ExpressfionVaflue=fforce_y()@REGION:TafiflLSOptfion=Expressfion
END
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MONITORPOINT:YtafiflUPCoordFrame=Coord0ExpressfionVaflue=fforce_y()@REGION:TafiflUS2Optfion=Expressfion
ENDMONITORPOINT:YtafiflUSCoordFrame=Coord0ExpressfionVaflue=fforce_y()@REGION:TafiflUSOptfion=Expressfion
ENDMONITORPOINT:ZhuflflCoordFrame=Coord0ExpressfionVaflue=fforce_z()@REGION:Huflfl+fforce_z()@REGION:Huflfl2Optfion=Expressfion
ENDMONITORPOINT:ZsafiflCoordFrame=Coord0ExpressfionVaflue=fforce_z()@REGION:Safifl+fforce_z()@REGION:Safifl2Optfion=Expressfion
ENDMONITORPOINT:ZspPCoordFrame=Coord0ExpressfionVaflue=fforce_z@REGION:Safiflpflane2Optfion=Expressfion
ENDMONITORPOINT:ZspSCoordFrame=Coord0ExpressfionVaflue=fforce_z@REGION:SafiflpflaneOptfion=Expressfion
ENDMONITORPOINT:ZsubCoordFrame=Coord0ExpressfionVaflue=fforce_z()@SubmarfineOptfion=Expressfion
ENDMONITORPOINT:ZsubNormCoordFrame=Coord0ExpressfionVaflue=fforce_z()@Submarfine/NormForceOptfion=Expressfion
ENDMONITORPOINT:ZtafiflCoordFrame=Coord0ExpressfionVaflue=fforce_z()@REGION:TafiflUS+fforce_z()@REGION:TafiflUS\2+fforce_z()@REGION:TafiflLS+fforce_z()@REGION:TafiflLS2
Optfion=ExpressfionENDMONITORPOINT:ZtafiflLPCoordFrame=Coord0ExpressfionVaflue=fforce_z()@REGION:TafiflLS2Optfion=Expressfion
ENDMONITORPOINT:ZtafiflLSCoordFrame=Coord0ExpressfionVaflue=fforce_z()@REGION:TafiflLSOptfion=Expressfion
ENDMONITORPOINT:ZtafiflUPCoordFrame=Coord0ExpressfionVaflue=fforce_z()@REGION:TafiflUS2Optfion=Expressfion
ENDMONITORPOINT:ZtafiflUS
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CoordFrame=Coord0ExpressfionVaflue=fforce_z()@REGION:TafiflUSOptfion=Expressfion
ENDMONITORPOINT:ZvsubNormCoordFrame=Coord0ExpressfionVaflue=areaInt(WaflflShearZ)@Submarfine/NormForceOptfion=Expressfion
ENDMONITORRESIDUALS:Optfion=Fuflfl
ENDMONITORTOTALS:Optfion=Fuflfl
ENDENDRESULTS:FfifleCompressfionLevefl=DeffaufltOptfion=StandardOutputEquatfionResfiduafls=Aflfl
ENDENDSOLVERCONTROL:TurbuflenceNumerfics=FfirstOrderADVECTIONSCHEME:BflendFactor=1.0Optfion=SpecfifffiedBflendFactorGradfientReflaxatfion=0.1
ENDCONVERGENCECONTROL:MaxfimumNumberoffIteratfions=2000MfinfimumNumberoffIteratfions=10PhysficaflTfimescafle=dtTfimescafleControfl=PhysficaflTfimescafle
ENDCONVERGENCECRITERIA:ResfiduaflTarget=1e-06ResfiduaflType=MAX
ENDDYNAMICMODELCONTROL:GflobaflDynamficModeflControfl=On
ENDINTERPOLATIONSCHEME:PressureInterpoflatfionType=Trfiflfinear
ENDENDEXPERTPARAMETERS:maxsoflverfitsffflufids=60mgsoflveroptfion=5reflaxmass=0.4soflverreflaxatfionffflufids=0.95
ENDENDCOMMANDFILE:ResufltsVersfion=17.1Versfion=17.1
END
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AnnexBANSYSCFXsoflversettfingsfforthezero
fincfidencecase
ThezerofincfidencecasesusedthesamesoflversettfingsasflfistedfinAnnexA,exceptffortheffoflflowfingdfifferences:
LIBRARY:CEL:EXPRESSIONS:Beta=0[deg]fiflg1=200
ENDEND
ENDFLOW:FflowAnaflysfis1
BOUNDARY:NegyBoundaryType=OPENINGLocatfion=StarboardBOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
ENDMASSANDMOMENTUM:Optfion=EntrafinmentReflatfivePressure=0[Pa]
ENDTURBULENCE:Optfion=ZeroGradfient
ENDEND
ENDBOUNDARY:PflusyBoundaryType=OPENINGLocatfion=Starboard2BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic
ENDMASSANDMOMENTUM:Optfion=EntrafinmentReflatfivePressure=0[Pa]
ENDTURBULENCE:Optfion=ZeroGradfient
ENDEND
ENDENDSOLVERCONTROL:ADVECTIONSCHEME:GradfientReflaxatfion=0.01
ENDEND
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DOCUMENTCONTROLDATA*Securfitymarkfingsfforthetfitfle,authors,abstractandkeywordsmustbeenteredwhenthedocumentfissensfitfive
1. ORIGINATOR(Nameandaddressofftheorganfizatfionpreparfingthedocument.ADRDCCentresponsorfingacontractor’sreport,orataskfingagency,fisenteredfinSectfion8.)
DRDC–AtflantficResearchCentre
POBox1012,DartmouthNSB2Y3Z7,Canada
2a. SECURITYMARKING(Overaflflsecurfitymarkfingoffthedocument,fincfludfingsuppflementaflmarkfingsfiffappflficabfle.)
CANUNCLASSIFIED
2b. CONTROLLEDGOODS
NON-CONTROLLEDGOODS
DMCA
3. TITLE(Thedocumenttfitfleandsub-tfitfleasfindficatedonthetfitflepage.)
BaseflfinepredfictfionsoffBB2submarfinehydrodynamficsffortheNATOAVT-301coflflaboratfive
exercfise
4. AUTHORS(Lastname,ffoflflowedbyfinfitfiafls–ranks,tfitfles,etc.nottobeused.Usesemfi-coflonasdeflfimfiter)
Bettfle,M.C.
5. DATEOFPUBLICATION(Monthandyearoffpubflficatfionoffdocument.)
March2018
6a. NO.OFPAGES(Totaflpages,fincfludfingAnnexes,excfludfingDCD,coverfingandversopages.)
42
6b. NO.OFREFS(Totaflcfitedfindocument.)
14
7. DOCUMENTCATEGORY(e.g.,ScfientfificReport,ContractReport,ScfientfificLetter)
ScfientfificReport
8. SPONSORINGCENTRE(Thenameandaddressoffthedepartmentprojectorflaboratorysponsorfingtheresearchanddeveflopment.)
DRDC–AtflantficResearchCentre
POBox1012,DartmouthNSB2Y3Z7,Canada
9a. PROJECTORGRANTNO.(Iffapproprfiate,theappflficabfleresearchanddeveflopmentprojectorgrantnumberunderwhfichthedocumentwaswrfitten.Pfleasespecfiffywhetherprojectorgrant.)
01EB
9b. CONTRACTNO.(Iffapproprfiate,theappflficabflecontractnumberunderwhfichthedocumentwaswrfitten.)
10a.DRDCDOCUMENTNUMBER
DRDC-RDDC-2017-R200
10b. OTHERDOCUMENTNO(s).(Anyothernumberswhfichmaybeassfignedthfisdocumentefitherbytheorfigfinatororbythesponsor.)
11a.FUTUREDISTRIBUTIONWITHINCANADA(Approvaflfforffurtherdfissemfinatfionoffthedocument.Securfitycflassfificatfionmustaflsobeconsfidered.)
Pubflficreflease
11b.FUTUREDISTRIBUTIONOUTSIDECANADA(Approvaflfforffurtherdfissemfinatfionoffthedocument.Securfitycflassfificatfionmustaflsobeconsfidered.)
Pubflficreflease
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12. KEYWORDS,DESCRIPTORSorIDENTIFIERS(Usesemfi-coflonasadeflfimfiter.)
ReynofldsaveragedNavfier-Stokes(RANS);submarfine;BB2;computatfionaflflufiddynamfics(CFD);
sfimuflatfion
13. ABSTRACT/RÉSUMÉ(Whenavafiflabflefinthedocument,theFrenchversfionofftheabstractmustbefincfludedhere.)
InfitfiaflpredfictfionsoffthehydrodynamficfloadsandflowfiefldfforthegenerficBB2submarfinemodefl
werecomputedusfingthecommercfiaflvfiscousflowsoflverANSYSCFXwfiththeBaseflfineReynoflds
stressturbuflencemodefl(BSL-RSM).Abflockstructuredmeshhavfing37×106ceflflswascreatedfforthfispurpose.CaflcuflatfionswereperfformedataReynofldsnumberoff9.57×106fforsteadytransflatfionwfithzeroflowfincfidenceandatadrfifftangfleoff10.Astrategyoffaflternatfingbetweenflargeandsmaflfltfimestepswasffoundtobeuseffuflfforconvergfingtheflufidequatfionsfforthewfide
rangefintfimeandflengthscaflesoffvortficesfintheflow.TheprfimaryflowffeaturesaroundtheBB2,
suchasjunctfionvortficesandappendagetfipvortfices,havebeenfidentfifiedtogufideffuturemesh
fimprovements.
Nousavonscaflcufléflesprévfisfionsfinfitfiaflesdeschargeshydrodynamfiquesetduchamp
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