baseline predictions of bb2 submarine hydrodynamics for ... · title: baseline predictions of bb2...

Deffence Research andDeveflopment Canada

Recherche et devefloppementpour fla deffense Canada

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BaseflfinepredfictfionsoffBB2submarfine

hydrodynamficsffortheNATOAVT-301

coflflaboratfiveexercfiseMarkC.Bettfle

DRDC–AtflantficResearchCentre

DeffenceResearchandDeveflopmentCanadaScfientfificReportDRDC-RDDC-2017-R200March2018

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IMPORTANTINFORMATIVESTATEMENTS

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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.

fifi DRDC-RDDC-2017-R200

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

fiv DRDC-RDDC-2017-R200

11.5 IntegratedForces ................................ 25

12Concflusfionsandffuturework ............................. 28

Refferences.......................................... 29

AnnexA:ANSYSCFXsoflversettfingsfforthe10degreesdrfifftangflecase ...... 31

AnnexB:ANSYSCFXsoflversettfingsfforthezerofincfidencecase .......... 42

DRDC-RDDC-2017-R200 v

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

vfi DRDC-RDDC-2017-R200

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

vfififi DRDC-RDDC-2017-R200

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);

DRDC-RDDC-2017-R200 1

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.

2 DRDC-RDDC-2017-R200

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

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.

Ffigure2:BflockstructureoffDRDC’sBB2mesh(starboardhaflffonfly).

Ffigure3:Bflockedgesonthesymmetrypflane.

Ffigure4:Inflatfionflayerbflocks.

6DRDC-RDDC-2017-R200

Ffigure5:GrfidontheBB2surffaceandsymmetrypflanefinthevficfinfityofftheBB2.

Ffigure6:Meshcrosssectfionfinthevficfinfityoffthesubmarfineattheafftendofftheconstantmfidbodysectfion(x/Lpp=−0.184).

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

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.

•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:

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.

0 500 1000 1500 2000 2500 3000 3500 4000

Maxfimum Resfiduafl

Iteratfion

P-Mass

0 500 1000 1500 2000 2500 3000 3500 4000

Maxfimum Resfiduafl

Iteratfion

u'v' RS

u'w' RS

v'v' RS

v'w' RS

w'w' RS

Ffigure7:Maxfimumresfiduaflsfforthecontfinufityandmomentumequatfions(top)andturbuflenceequatfions(bottom)durfingthezerofincfidencecomputatfion.

0 500 1000 1500 2000

Maxfimum Resfiduafl

Iteratfion

P-Mass

0 500 1000 1500 2000

Maxfimum Resfiduafl

Iteratfion

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.

0 500 1000 1500 2000 2500 3000 3500 4000

100 (Ffi-F end) / F end

Iteratfion, fi

Ffigure9:Percentdfifferencebetweenfforcesatfiteratfionfiandthefforcesattheendoffthecomputatfionfforthezerofincfidencecomputatfion.

11 Resufltsanddfiscussfion

11.1 FflowVfisuaflfizatfion

FoflflowfingToxopeusetafl.[12],thevortficesfintheflowaroundtheBB2arevfisuaflfizedusfingfiso-surffacesoffconstantQ-vaflues,definedasffoflflows:

|Ω|2−|S|2

whereΩ=∇u−∇uT

/2fisthevortficfitytensorandS=

∇u+∇uT

/2fisthestrafin

tensor.Inthfiswork,Qfismadenon-dfimensfionaflasffoflflows:

Q′=Q

LoaV∞

TheQfiso-surffacesarecofloredbynon-dfimensfionaflheflficfity,H′,finordertofindficatethedfirectfionorrotatfion:

H′=ω·u

|ω||u|(5)

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.

Ffigure11:PredfictedvortexcoresaroundtheBB2atzerofincfidence.

DRDC-RDDC-2017-R200

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.

Ffigure12:Centerpflane(y=0)crosssectfionoffthepredfictedsafifl-deckjunctfionvortexfforthezerofincfidencecase.

DRDC-RDDC-2017-R200

Ffigure13:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)fforthezerofincfidencecase.

DRDC-RDDC-2017-R200

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.

Ffigure14:PredfictedvortexcoresaroundtheBB2atβ=10.

DRDC-RDDC-2017-R200

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

Ffigure15:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)ffortheβ=10

Ffigure16:Pressurethroughtheprfimarysafifltfipvortexatmfidshfips(x/Loa=0)andthepropeflflerpflane(x/Loa=−0.481),ffortheβ=10

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

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

Ffigure17:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2fforthezerofincfidencecase.

Ffigure18:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2ffortheβ=10case.

12 Concflusfionsandffuturework

Anfinfitfiafl37mfiflflfionceflflstructuredmeshwascreatedaroundthegenerficBB2submarfinemodeflffortheNATOAVT-301coflflaboratfiveproject.BaseflfineRANScaflcuflatfionsweredoneonthfismeshatzerofincfidenceand10drfifftcasesusfingthevfiscousflowsoflverANSYSCFXwfiththeBaseflfineReynofldsStressturbuflencemodefl.Goodfiteratfiveconvergencecoufldbeobtafinedbyaflternatfingbetweenflargeandsmaflfltfimestepsfizes.Affocusoffthefinfitfiaflpredfictfionswasonresoflvfingthesafiflhorseshoejunctfionvortex.Moreworkfisneededtoachfieveadequatemeshresoflutfionfinthfisandotherregfionsofftheflow.Thepresentcaflcuflatfionshavefidentfifiedtheapproxfimatesfizeandflocatfionoffvortficestogufidesubsequentmeshfimprovements.Astrategyshoufldbedeveflopedtorefineregfionswfithflargegradfientsfinflowvarfiabfles,suchasvortexcores,wfithoutfincurrfingexcessfivecomputatfionaflcost.Somepartficfipantshaveffoundautomatficmeshrefinementmethodstobeveryeficfient;thfisshoufldbefinvestfigatedbyDRDC.Asystematficgrfidrefinementstudyshoufldaflsobedonetoassessnumerficafldfiscretfizatfionerrors.

ExperfienceffromphasezerowfiflflthenbeusedtoperfformsfimuflatfionsatexperfimentaflcondfitfionsfforwfindtunneflexperfimentsrecentflyconductedbyAustraflfia.Acomparfisonwfithdfifferentturbuflencemodeflflfingapproaches,suchasahybrfidRANSflargeeddysfimuflatfionsshoufldaflsobeconsfideredfintheffuture.SfimuflatfionsoffrotatfionaflsubmarfinemotfionmatchfingcondfitfionsfforrotatfingarmexperfimentsconductedbyQfinetfiQareaflsopflannedffoflflowfingthesteadytransflatfionstudy.

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.

[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.

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

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

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

BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic

ENDMASSANDMOMENTUM:Optfion=EntrafinmentReflatfivePressure=0[Pa]

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

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

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

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

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

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

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

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

AnnexBANSYSCFXsoflversettfingsfforthezero

fincfidencecase

ThezerofincfidencecasesusedthesamesoflversettfingsasflfistedfinAnnexA,exceptffortheffoflflowfingdfifferences:

LIBRARY:CEL:EXPRESSIONS:Beta=0[deg]fiflg1=200

ENDEND

ENDFLOW:FflowAnaflysfis1

BOUNDARY:NegyBoundaryType=OPENINGLocatfion=StarboardBOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic

ENDEND

ENDBOUNDARY:PflusyBoundaryType=OPENINGLocatfion=Starboard2BOUNDARYCONDITIONS:FLOWREGIME:Optfion=Subsonfic

ENDEND

ENDENDSOLVERCONTROL:ADVECTIONSCHEME:GradfientReflaxatfion=0.01

ENDEND

DOCUMENTCONTROLDATA*Securfitymarkfingsfforthetfitfle,authors,abstractandkeywordsmustbeenteredwhenthedocumentfissensfitfive

1. ORIGINATOR(Nameandaddressofftheorganfizatfionpreparfingthedocument.ADRDCCentresponsorfingacontractor’sreport,orataskfingagency,fisenteredfinSectfion8.)

POBox1012,DartmouthNSB2Y3Z7,Canada

2a. SECURITYMARKING(Overaflflsecurfitymarkfingoffthedocument,fincfludfingsuppflementaflmarkfingsfiffappflficabfle.)

CANUNCLASSIFIED

2b. CONTROLLEDGOODS

NON-CONTROLLEDGOODS

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.)

6b. NO.OFREFS(Totaflcfitedfindocument.)

7. DOCUMENTCATEGORY(e.g.,ScfientfificReport,ContractReport,ScfientfificLetter)

ScfientfificReport

8. SPONSORINGCENTRE(Thenameandaddressoffthedepartmentprojectorflaboratorysponsorfingtheresearchanddeveflopment.)

POBox1012,DartmouthNSB2Y3Z7,Canada

9a. PROJECTORGRANTNO.(Iffapproprfiate,theappflficabfleresearchanddeveflopmentprojectorgrantnumberunderwhfichthedocumentwaswrfitten.Pfleasespecfiffywhetherprojectorgrant.)

9b. CONTRACTNO.(Iffapproprfiate,theappflficabflecontractnumberunderwhfichthedocumentwaswrfitten.)

10a.DRDCDOCUMENTNUMBER

DRDC-RDDC-2017-R200

10b. OTHERDOCUMENTNO(s).(Anyothernumberswhfichmaybeassfignedthfisdocumentefitherbytheorfigfinatororbythesponsor.)

11a.FUTUREDISTRIBUTIONWITHINCANADA(Approvaflfforffurtherdfissemfinatfionoffthedocument.Securfitycflassfificatfionmustaflsobeconsfidered.)

Pubflficreflease

11b.FUTUREDISTRIBUTIONOUTSIDECANADA(Approvaflfforffurtherdfissemfinatfionoffthedocument.Securfitycflassfificatfionmustaflsobeconsfidered.)

Pubflficreflease

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

d’écouflementdu modèflegénérfiquedesous-marfinBB2àfl’afidedurésoflveurcommercfiafl

d’écouflementvfisqueuxANSYSCFXetdumodèflederéfférencedeturbuflenceàcontrafintes

deReynoflds(BSL-RSM).Àcettefin,nousavonscrééunmafiflflagestructurémufltfibflocde37×106

ceflflufles.LescaflcuflsontétéeffffectuésàunnombredeReynofldsde9.57×106seflonunetrans-flatfionconstanteàdébfitnufletunangflededérfivede10.Lastratégfiequficonsfistafitàaflternerentredesfintervaflflesdetempscourtsetflongss’estrévéfléeutfifleàflaconvergencedeséquatfions

desflufidesdansuneflargegammed’écheflflesdeduréesetdeflongueursdestourbfiflflonsdans

fl’écouflement.Nousavonsdétermfinéflesprfincfipaflescaractérfistfiquesdefl’écouflementautourdu

BB2,teflflesqueflestourbfiflflonsauxjonctfionsetàfl’extrémfitédesappendfices,cequfiorfienterafles

améflfioratfionsàapporteraumafiflflageàvenfir.

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