baseline predictions of bb2 submarine hydrodynamics for ... · title: baseline predictions of bb2...
TRANSCRIPT
Deffence Research andDeveflopment Canada
Recherche et devefloppementpour fla deffense Canada
CANUNCLASSIFIED
BaseflfinepredfictfionsoffBB2submarfine
hydrodynamficsffortheNATOAVT-301
coflflaboratfiveexercfiseMarkC.Bettfle
DRDC–AtflantficResearchCentre
DeffenceResearchandDeveflopmentCanadaScfientfificReportDRDC-RDDC-2017-R200March2018
CANUNCLASSIFIED
CANUNCLASSIFIED
IMPORTANTINFORMATIVESTATEMENTS
ThfisdocumentwasrevfiewedfforControflfledGoodsbyDRDCusfingtheSchedufletotheDeffenceProductfionAct.
Dfiscflafimer:HerMajestytheQueenfinrfightoffCanada,asrepresentedbytheMfinfisteroffNatfionaflDeffence(“Canada”),makesnorepresentatfionsorwarrantfies,expressorfimpflfied,offanykfindwhatsoever,andassumesnoflfiabfiflfityffortheaccuracy,reflfiabfiflfity,
compfleteness,currencyoruseffuflnessoffanyfinfformatfion,product,processormaterfiaflfincfludedfinthfisdocument.Nothfingfinthfisdocumentshoufldbefinterpretedasanendorsementfforthespecfificuseoffanytoofl,technfiqueorprocessexamfinedfinfit.Any
reflfianceon,oruseoff,anyfinfformatfion,product,processormaterfiaflfincfludedfinthfisdocumentfisatthesoflerfiskoffthepersonsousfingfitorreflyfingonfit.Canadadoesnotassumeanyflfiabfiflfityfinrespectoffanydamagesorflossesarfisfingoutofforfinconnectfion
wfiththeuseoff,orreflfianceon,anyfinfformatfion,product,processormaterfiaflfincfludedfinthfisdocument.
Endorsementstatement:Thfispubflficatfionhasbeenpeer-revfiewedandpubflfishedbytheEdfitorfiaflOffficeoffDeffenceResearchand
DeveflopmentCanada,anagencyofftheDepartmentoffNatfionaflDeffenceoffCanada.Inqufirfiescanbesentto:[email protected].
c⃝ HerMajestytheQueenfinRfightoffCanada,DepartmentoffNatfionaflDeffence,2018
c⃝ SaMajestéflaRefineendrofitduCanada,MfinfistèredeflaDéffensenatfionafle,2018
CANUNCLASSIFIED
Abstract
InfitfiaflpredfictfionsoffthehydrodynamficfloadsandflowfiefldfforthegenerficBB2submarfinemodeflwerecomputedusfingthecommercfiaflvfiscousflowsoflverANSYSCFXwfiththeBaseflfineReynofldsstressturbuflencemodefl(BSL-RSM).Abflockstructuredmeshhavfing37×106ceflflswascreatedfforthfispurpose.CaflcuflatfionswereperfformedataReynofldsnumberoff9.57×106fforsteadytransflatfionwfithzeroflowfincfidenceandatadrfifftangfleoff10.Astrategyoffaflternatfingbetweenflargeandsmaflfltfimestepswasffoundtobeuseffuflfforconvergfingtheflufidequatfionsfforthewfiderangefintfimeandflengthscaflesoffvortficesfintheflow.TheprfimaryflowffeaturesaroundtheBB2,suchasjunctfionvortficesandappendagetfipvortfices,havebeenfidentfifiedtogufideffuturemeshfimprovements.
Sfignfificanceffordeffenceandsecurfity
Infitfiaflstepshavebeentakentowardsbench-markfingandvaflfidatfinghfighfideflfitytooflsfforpredfictfingsubmarfineflowfiefldsandmanoeuvrfingfforces.Thfisfiscontrfibutfingtotheassessmentandfimprovementoffourtooflsfforunderstandfingoffsubmarfinemanoeuvrfingflfimfitatfionsfinextremecondfitfionsandfforevafluatfingpotentfiaflhydrodynamficperfformancefimprovementsfforsubmarfines.
DRDC-RDDC-2017-R200 fi
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.
DRDC-RDDC-2017-R200 fififi
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
DRDC-RDDC-2017-R200 vfifi
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
DRDC-RDDC-2017-R200 3
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.
4 DRDC-RDDC-2017-R200
Ffigure2:BflockstructureoffDRDC’sBB2mesh(starboardhaflffonfly).
Ffigure3:Bflockedgesonthesymmetrypflane.
DRDC-RDDC-2017-R200 5
Ffigure4:Inflatfionflayerbflocks.
6DRDC-RDDC-2017-R200
Ffigure5:GrfidontheBB2surffaceandsymmetrypflanefinthevficfinfityofftheBB2.
Ffigure6:Meshcrosssectfionfinthevficfinfityoffthesubmarfineattheafftendofftheconstantmfidbodysectfion(x/Lpp=−0.184).
DRDC-RDDC-2017-R200 7
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
8 DRDC-RDDC-2017-R200
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.
DRDC-RDDC-2017-R200 9
•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:
10 DRDC-RDDC-2017-R200
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.
DRDC-RDDC-2017-R200 11
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.
12 DRDC-RDDC-2017-R200
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.
DRDC-RDDC-2017-R200 13
-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)
14 DRDC-RDDC-2017-R200
-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.
DRDC-RDDC-2017-R200 15
Ffigure11:PredfictedvortexcoresaroundtheBB2atzerofincfidence.
16
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.
DRDC-RDDC-2017-R200 17
Ffigure12:Centerpflane(y=0)crosssectfionoffthepredfictedsafifl-deckjunctfionvortexfforthezerofincfidencecase.
18
DRDC-RDDC-2017-R200
Ffigure13:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)fforthezerofincfidencecase.
DRDC-RDDC-2017-R200
19
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.
20 DRDC-RDDC-2017-R200
Ffigure14:PredfictedvortexcoresaroundtheBB2atβ=10.
DRDC-RDDC-2017-R200
21
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
22 DRDC-RDDC-2017-R200
Ffigure15:Lookfingafftatvortficfitycontoursonthex=0cross-sectfionaflpflane(flocated0.060588Loaafftoffsafifltrafiflfingedge)ffortheβ=10
case.
DRDC-RDDC-2017-R200 23
Ffigure16:Pressurethroughtheprfimarysafifltfipvortexatmfidshfips(x/Loa=0)andthepropeflflerpflane(x/Loa=−0.481),ffortheβ=10
case.
24 DRDC-RDDC-2017-R200
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
DRDC-RDDC-2017-R200 25
Ffigure17:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2fforthezerofincfidencecase.
26 DRDC-RDDC-2017-R200
Ffigure18:Predfictedpressurecoeficfient(top)andaxfiaflcomponentoffwaflflshearstressnormaflfizedby0.5ρU2(bottom)aflongtheBB2ffortheβ=10case.
DRDC-RDDC-2017-R200 27
12 Concflusfionsandffuturework
Anfinfitfiafl37mfiflflfionceflflstructuredmeshwascreatedaroundthegenerficBB2submarfinemodeflffortheNATOAVT-301coflflaboratfiveproject.BaseflfineRANScaflcuflatfionsweredoneonthfismeshatzerofincfidenceand10drfifftcasesusfingthevfiscousflowsoflverANSYSCFXwfiththeBaseflfineReynofldsStressturbuflencemodefl.Goodfiteratfiveconvergencecoufldbeobtafinedbyaflternatfingbetweenflargeandsmaflfltfimestepsfizes.Affocusoffthefinfitfiaflpredfictfionswasonresoflvfingthesafiflhorseshoejunctfionvortex.Moreworkfisneededtoachfieveadequatemeshresoflutfionfinthfisandotherregfionsofftheflow.Thepresentcaflcuflatfionshavefidentfifiedtheapproxfimatesfizeandflocatfionoffvortficestogufidesubsequentmeshfimprovements.Astrategyshoufldbedeveflopedtorefineregfionswfithflargegradfientsfinflowvarfiabfles,suchasvortexcores,wfithoutfincurrfingexcessfivecomputatfionaflcost.Somepartficfipantshaveffoundautomatficmeshrefinementmethodstobeveryeficfient;thfisshoufldbefinvestfigatedbyDRDC.Asystematficgrfidrefinementstudyshoufldaflsobedonetoassessnumerficafldfiscretfizatfionerrors.
ExperfienceffromphasezerowfiflflthenbeusedtoperfformsfimuflatfionsatexperfimentaflcondfitfionsfforwfindtunneflexperfimentsrecentflyconductedbyAustraflfia.Acomparfisonwfithdfifferentturbuflencemodeflflfingapproaches,suchasahybrfidRANSflargeeddysfimuflatfionsshoufldaflsobeconsfideredfintheffuture.SfimuflatfionsoffrotatfionaflsubmarfinemotfionmatchfingcondfitfionsfforrotatfingarmexperfimentsconductedbyQfinetfiQareaflsopflannedffoflflowfingthesteadytransflatfionstudy.
28 DRDC-RDDC-2017-R200
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.
DRDC-RDDC-2017-R200 29
[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.
30 DRDC-RDDC-2017-R200
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
DRDC-RDDC-2017-R200 31
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
32 DRDC-RDDC-2017-R200
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
DRDC-RDDC-2017-R200 33
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
34 DRDC-RDDC-2017-R200
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
DRDC-RDDC-2017-R200 35
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
36 DRDC-RDDC-2017-R200
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
DRDC-RDDC-2017-R200 37
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
38 DRDC-RDDC-2017-R200
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
DRDC-RDDC-2017-R200 39
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
40 DRDC-RDDC-2017-R200
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
DRDC-RDDC-2017-R200 41
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
42 DRDC-RDDC-2017-R200
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
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.