Influence of inlet and outlet placement on the hydrodynamics of culture tanks for Atlantic salmon

InternationalJournalofMechanicalSciences188(2020)105944

ContentslistsavailableatScienceDirect

International Journal of Mechanical Sciences

journalhomepage:www.elsevier.com/locate/ijmecsci

Influence of inlet and outlet placement on the hydrodynamics of culture tanks for Atlantic salmon

JMR Gorle

, BF Terjesen

, ST Summerfelt

aNofima AS, Sunndalsøra 6600, Norway

bThe Conservation Fund Freshwater Institute, 1098 Turner Road, Shepherdstown, WV 25443, USA

a r t i c le i n f o

Keywords:

Recirculation aquaculture system (RAS) Hydrodynamics

Inlet and outlet location Eulerian-lagrangian approach Self-cleaning

a b s t r a ct

Thesalmonfarmingindustryhasrecentlyshiftedtolargerculturetankswithgreaterwaterflowstooptimize theland-basedproduction,buttanksapproaching1000m³involumecreatechallenginghydrodynamics.This paperpresentsacomputationalstudyoffourcombinationsofinletandoutletdesignsofacommercialland- basedaquaculturetank.Windows-basedOpenFOAMsolversareusedtosolvetheconservationequationsfor tankhydrodynamicswithanimplicitunsteadysecond-orderEulerian(finitevolume)techniqueonunstructured hybridmeshes. Themodelisvalidatedbythevelocitymeasurementsatdiscretelocationsinthetankusing acousticdopplervelocimetry.Tounderstandthedispersionofbiosolidsinthetank,500particleswithauniform sizeof200μmaretrackedintheLagrangianframe.Whilethetank’sReynoldsnumbervariesbetween2E6-3.5E6 dependingontheflowexchangerate,thelocalReynoldsnumberattheinletpipeisabout2E5whichdiscovers thedrag-crisisphenomenon.Theeffectofinletandoutletplacementonthevelocity,vorticityandturbulenceis addressed.Theexistingtankdesigncouldbeimprovedusingthebottom-drainandcorner-inletoptions,which strengthensrotationalflowwithbetteruniformity.Suchdesignchangeisalsoprovedtoprovidebetterparticle removalandthusensuretheimprovedself-cleaningabilityofthetank.

1. Introduction

WithRecirculatingAquacultureSystems(RAS),theaimistocreate controlledrearingconditionssothatdiseaseoutbreaksareprevented, fishperformanceisimproved,wastestreamsaremanagedsothatnutri- entscanbereclaimed,andwaterconsumptionisminimized[12,53,55]. TheNorwegiansalmonindustryhasbeenexperiencingasteadyincrease intheimplementationofRAStechnologyforthepastthreedecades,pri- marilyforproductionofapproximately100gsmoltthatissubsequently stockedintooceanpensforculturetogenerally4–5kgatharvest.More recently,however,theNorwegianMinistryofFisherieshasallowedthe productionofevenlargersmoltorpost-smoltup to1000gin tanks, beforestockinginthesea,whichhascreatedanopportunityforNorwe- gianindustrytoincreasetheinvestmentinsuchfacilities[29].Today, bycontributingabout30%totheNorwegiansalmonsmoltproduction, RASfacilitiesexperienceincreasedreliabilityandproductionefficiency, versusolderflow-throughsystemsinwhichthewaterisonlyusedonce.

Abbreviations:ADV,acousticdopplervelocimetry;CFD,computationalfluiddynamics;DNS,directnumericalsimulation;GAMG,geometricagglomeratedal- gebraicmultigrid;HRT,hydraulicretentiontime;RAS,recirculatingaquaculturesystem;RANS,ReynoldsaveragedNavier-Stokes;RNG,Re-normalisationgroup;

SIMPLE,semi-implicitmethodforpressurelinkedequations;TKE,turbulentkineticenergy;TSS,totalsuspendedsolids(ppm).

∗Correspondingauthor.

E-mailaddress:[email protected](J.Gorle).

†Currentaddress:CermaqGroupAS,DronningEufemiasgt16,N-0102,Oslo,Norway

‡Currentaddress:SuperiorFreshLLC,W15506SuperiorFreshDrive,Hixton,WI54,635USA

Increasingly,therearealsoinitiativesinseveralcountriestouseRASto culturesalmonallthewaytoharvestsize.However,RASisstillanew technologyandmuchresearcheffortisneededtoensureacceptablere- liabilityandefficiency.Forinstance,thecurrentlackofarational-based designapproachesandcharacterizationofpertinentflowphysicsresults in anuncertain hydraulicsystem ofthe culturetanks, wherein fact thefishresides.Thegeneralinformationonwatervelocityandpres- surefields isnotsufficienttoexploretheopportunitiesof improving thelargeconstructionsofRASculturetanks,whichtodaycanbe1000 m³andlarger[51].ThebenefitsofincreasedbiosecuritythroughRAS technologycanonlybeexploitedwhentheproperhydraulicsettingis implemented;otherwisefishperformance(growth,feedutilization,sur- vival),welfare,andhealth willsuffer.Correcthydrodynamics inthe culturetankiscrucialtoachievingthedesiredrotationalvelocityinthe tankforimprovedfishexerciseandhealth[23,26,60],optimummixing characteristicsforbetterwaterquality[2,57,59]anduniformflowpat- terntoavoidquiescentzonesandrapidlyflushsettleablesolidsfromthe culturetank[15].

https://doi.org/10.1016/j.ijmecsci.2020.105944

Received31March2020;Receivedinrevisedform12July2020;Accepted13July2020 Availableonline15July2020

0020-7403/© 2020TheConservationFund.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBYlicense.

(http://creativecommons.org/licenses/by/4.0/)

Nomenclature

A area(m²)

C₁,C_1𝜀,C₂,C_3𝜀,C_𝜇 modelconstantsofRealizablek–𝜀model

C_d dragcoefficient

C_f skin-frictioncoefficient

d particlediameter(m)

D meandiameterofthetank(m)

 stretchingtensor

f_p forceexertedonparticle(N) g accelerationduetogravity(m/s²) h watercolumnheightinthetank(m)

I identitymatrix

T_i turbulenceintensity

k turbulentkineticenergy(m²/s²)

m particlemass(kg)

p pressure(pa)

G_k,G_b productiontermsofTKE

R tankradius(m)

Re reynoldsnumber

R_h hydraulicradiusofthetank(m)

S_ij deformationtensor

S_k,S_𝜀 user-definedsourcetermsofkand𝜀

St stokesnumber

t time(s)

t_e eddylifetime(s)

t_int particle-eddyinteractiontime(s) t_p particlerelaxationtime(s)

t_tr transittimeoftheparticlethroughtheeddy (s)

v velocity(m/s)

̄𝑣andv′ meanandfluctuatingvelocitycomponents

ϑ particlevolume(m³)

v₀ inletnozzlevelocity(m/s) v_p particlevelocity(m/s) x_p particledisplacement(m) y+ non-dimensionalwalldistance Greeksymbols

𝛾 flowuniformityindex Γ vortexstrength(J) 𝛿 kroneckerDelta

𝜀 dissipationrateofturbulentkineticenergy(m²/s³) 𝜇 dynamicviscosity(Pa.s)

𝜇t turbulentviscosity(Pa.s) 𝜈 kinematicviscosity(m²/s) 𝜌 waterdensity(kg/m³) 𝜌p particlemassdensity(kg/m³)

𝜎k,𝜎𝜀 modelconstantsofRealizablek–𝜀model 𝜏 viscousstresstensor

𝜏w wall-shearstress(Pa) 𝜔 angularvelocity(rad/s) Ω_ij rotationtensor

Inpractice,eachplugofflowinjectedintoalargeculturetankhasits ownresidencetime,whichdependsoninflowandoutflowmomentum, flowturbulence,andinternaldesignofthetankincludingtheplacement ofinletandoutletstructures.Theresultisanon-uniformflowdomain includinglow-momentumzonesinthetank.Considerableeffectofin- letandoutletcharacteristicsontheglobalflowfieldhasbeenfoundin manybioresourcesystemssuchasbioreactors[35],biofilters[8],and flowcolumns[1].However,theexistingliterature inaquaculturere- searchfailstoaddresstheeffectofsuchdesignparametersonthetank hydrodynamics,letaloneimprovethem.

Therotationalvelocityinaculturetank,whichimplicitlydepends oninletflowrateandhencetheimpulseforceplaysanimportantrole increatingahealthyrearingenvironment[14,26,42,44].Flowpattern andturbulenceinthetankareprimarilyinfluencedbytheinletandout- letcharacteristics[25,27,28,34,39].Otherthantheseauthors,different inletandoutletconfigurationsinRAStankshavebeenusedinpaststud- iesbutmostofithasbeenad-hocresearch.Inthedevelopmentofan integratedrecirculatingaquacultureandolericultureplant,McMurtry etal.[36]usedafree-fallinflowmodel,andthewaterwasdrawnby meansofapumpfromthebottomofthetankusingapipe.Inarecircu- lationsystemforoysterlarvalculture,Qiuetal.[45]usedasuspended inletandcentralelevatedoutlet.However,atangentialinletflowand centralbottomdrainhavebeenthemostcommonflowboundariesin severalstudies[46,49,50].ThephysiologicalstudiesofDavidsonetal.

[16]andGoodetal.[22]deployedcircularRAStankswithtangential inletandCornelltypedual-drainsystem.Indeed,thecombinationofa centralbottomoutletandanelevatedwalldrainisoftenusedincircular RAStankstoachieveacontrolledflowpattern.However,thelocationof theinletandoutletstructuresaffectthehydrodynamicsoflargeculture tanks.

Anempiricalinvestigationonthewatervelocitiesinlargecircular andoctagonalRAStankswithtangentialinletnozzles wasperformed byGorleetal.[26].Theauthorsfoundthatcirculartanks,whichhad acentralbottomoutlet,experiencedapproximately50%lesser varia- tioninwatervelocityatthecentre,comparedtooctagonaltanksthat hadacentraltopoutlet.Also,both tanksappearedtohavedifferent velocityprofilesacrossthetank.Theoctagonaltanksusedinthefish performancestudiesofEspmarketal.[19]hadtheinletpipenearthe cornerwall.Suchdesignaspectsofflowboundariesconsiderablyinflu- encetheoverallhydrodynamicsofthetank,whichcannotbeignored whentryingtoimprovetheenvironmentalconditionsforthefish.

Theusualplacementoftheinletpipesinland-basedRASfacilities is nearthetank’speripherytoensurethat astrongerrotationalflow occurs,butthiswill,inturn,causeaflowresistanceduetothestruc- turalobstructioninthehighestvelocityregion.Thenetdragforceon theinletpipeis thesumoffrictiondragandformdrag.Formdrag, characterised byvortexsheddingandflowseparation, isa dominant componentinsuchbluff bodieslikeacircularcylinderathighReynold numbers.InRASculturetanks,themeanhydraulicretentiontimeof 30-55min.isthepreferredwaterexchangerateforsufficientwater qualityforthefish.Therotationalflowpasttheinletpipesattheseop- eratingconditionsresultsinaReynoldsnumberofapproximately2E5.

AtthiscriticalReynoldsnumber,thedragforceonasmoothcylinder abruptlydrops.Thepresentexplanatoryanalysisoftheinletpipeloca- tionexcludesthephysicsofthe‘drag-crisisphenomenon’,asnamedby Schlichting[47].Outofnumerousflowcontroltechniques,‘blowing’is anactivemethodwheretheflowseparationzoneontheleewardside ofthecylinderisreenergizedbystreamingajetthroughanorifice.The bluff bodyhydrodynamicsassociatedwiththeflowpastaninletpipe ischaracterizedbyalow-pressurewakeregionontherearsideofthe cylinder.Thepressuredragisadominantcomponent,whichcanbere- ducedupto65%bymodifyingthegeometryofbase flow[3,7].‘Jet blowing’hasbeenwidelystudiedindifferentapplicationstoenergize therecirculationzone[31,56],andthusreducethedragforce ofthe body.Representationofthesedynamicfeaturesaroundtheinletpipe andtheeffectofitslocationwasnotmadebypreviousstudiesinthe caseofculturetanks.

Acircularflowpatternwithdominanttangentialvelocityincircu- lar oroctagonal culturetanks translatesthelinearwater inflowinto arotatingvortexflow[39,40].Oneofthemostcriticalfeaturesofa centraloutletinaconfinedflowdomainistheevolutionoflocallyor- ganizedcoherentstructuresatawiderangeoflengthscales[27,28], whichdominatetheturbulencetransportmechanismslikeskinfriction, mixing,etc.Theexperimentalobservationsofsuchphenomenainvolve hugecostsandeffortsandoftendeliveruncertainoutcomes[37].Onthe otherhand,asimulation-drivendevelopmentprovidesaless-costlyvir-

J. Gorle, B. Terjesen and S. Summerfelt International Journal of Mechanical Sciences 188 (2020) 105944

Fig.1. Tankdesignsforcomputationalflowanalysis.(a)Basedesignwiththeinletpipesatsidewalls,and(b)Redesign1withtheinletpipesnearthecornerwalls ofthetank.Inbothdesigns,theflowinthetankreachestheelevatedcentraloutlet(inbluecolour)throughfourverticalpipes;thebasicdimensionsofthisoutlet systemaregiveninthetop-rightdrawing.(c)and(d)showtheredesigns2and3,whichhaveidenticalinletsystemsasinBasedesignandRedesign1,respectively, buttheelevatedoutletisreplacedbytheconventionalslottedoutletatthebottomofthetank.Thedesignspecificationsofthecentralbottomoutletareshownin zoomedviewontheright-bottomcorner.

tualenvironmenttounderstandphysicsandimprovethedesign,thanks tohigh-performancecomputing.Inthisstudy,anoctagonalshapedcom- mercialRAStankof788m³sizewasinvestigatedusingturbulencemod- elling.InadditiontotheBasedesign,threedesignvariantsintermsof inletandoutletlocationsareconsideredinthisstudytoexaminethe qualitativeandquantitativeparametersofAtlanticpost-smolttankhy- drodynamics.Thenoveltyofthestudyisthattheflowphysicsbehind therotatingturbulentflowassociatedwiththeculturetanksisexplored.

Thecombinedvortical-streamlined-vectorialrepresentationexplainsthe flowfieldstructureneardifferentoutlets.Betterinletplacementinthe tankisstudiedbasedontheforceestimates.Thisresearchalsoquanti- fiestheeffectofinlet/outletlocationsonthefieldvariablesincluding flowvelocity,uniformity,circulation,andthemotionofthebiosolidsin thetank.Inthelong-term,suchstudiescanimproveRASenergy,biore- sourceuse,andfishperformance,health,andwelfareinaquaculture.

2. Numericalmethodology 2.1. Designsunderstudy

Optimizationoflargeflowdomains,suchasculturetanksofclose to1000m³involume,isnotstraightforwardbecausetheoptimalsolu- tions,asfunctionsofdesignandoperatingconditions,cannotbefound bysimplenumericalprogramming.Anexhaustivesearchforaperfectly optimizedtankdesignoverafullsetofcontinuousvariablesinvolves rigorouscomputationaleffortandthusoffersanimpracticalmethod.A comparativestudybetweenafewselectedsolutionsisinsteadamore effectiveandtime-savingmethod.Ourearlierresearchonanoctagonal RAStankof788m³sizeinvestigatedtheeffectoftheinletnozzleangle onthetank’sperformance[28].Whilethesamedesignwastakenas referencei.ebasedesign,thisstudyconsideredthreeadditionalcombi- nationsofinlet-outletlocationsaspresentedinFig.1.

• Basedesign(Fig.1a),whichiscurrentlyinoperationataNorwe- giansmoltproducer,hastwoinletpipesnearthesidewalls.Each

inletpipehas11nozzlesthatdischargethewaterintothetankpar- alleltothesidewallssothataclockwiseflowpatterndevelopswhen viewedfromthetop.Thetankhasanelevatedoutletatthecentre, whichcollectsthewaternearthefloorofthetankthroughfourver- ticalpipesaroundit.Theeffectiveinletandoutletsurfaceareasare 0.0226m²and2.95m²,respectively.

• Redesign1(Fig.1b)hasthesameoutletastheBasedesignbutthe inletpipesweremovedclosetothenearthecornerwalls.Thedis- tancefromthecornerwalltothepipe’scentreis1.49mandthatto thetank’scentreis8.2m.Thus,theredesignfollowstheinletpipe locationat1/5thofradialdistancefromthecornerwallinNCRA’s RAStankinNorway[19,55].Thenozzleconfigurationonthepipes andinflowdirectionarethesameastheBasedesign.

• Redesign2(Fig.1c)hastheinletpipesnearthesidewalls,asinBase design,butherethecomplexcentralelevatedoutletwasreplacedby asimplebottomdrain,asusedbySummerfeltetal.[52]andDavid- sonandSummerfelt[14].Theoutletconsistsof47exitnozzlesof 15mmdiametereach,surroundedbytworadiallypatternedrectan- gularslots.Theeffectiveoutletsurfaceareawasreducedfrom2.95 m²intheelevateddraintoone-fourthinthebottomdrain.

• Redesign3(Fig.1d)hastheinletpipesnearthecornerwallsanda centralbottomdrain.

Theaforementionedtankdesignsweretestedforpracticalflowcon- ditions,asobtainedfromthecommercialsalmonsite,usingthecom- putationalfluiddynamics.Thisresearchconsideredthetankswithno biomassandhencetheanalysisofbiosolidswasnotinthescopeofthe study.Throughflowblockage,thefishresponsetovelocityandvorticity increasestheoverallturbulence.However,therelativecomparisonbe- tweenthetankdesignscanbeequallyvalidforthetankswithbiomass.

2.2. CFDmodelling

A cost-effective computationalframeworkwas developedfor the high-fidelityCFDsimulations.Thetankgeometriesweredevelopedus- ingCATIAV5R21(DassaultSystèmes,Vélizy-Villacoublay,France).The

fluiddomainwasextractedintheSTEPformattoeffectivelytransferthe CADmetadatastructuresforrobustinteroperabilitybetweendifferent softwareplatforms.3D-ToolV12(3D-ToolGmbH&Co.KG,Weinheim, Germany)wasusedtotranslatetheSTEPfileintoaParasolidformat tomakeitcompatiblewiththemeshingtool.Anautomatedmeshing tool,Castnet(DHCAEToolsGmbH,Krefeld,Germany),wasemployed forfinitevolume-baseddomaindiscretization.Afterathoroughchecked fordifferentqualityparameters,themeshwasimportedintotheCFD tool,BlueCFD(BlueCAPE,CasaisdaSerra,Portugal),whichoffersWin- dowsversionofOpenFOAMsolversalongwithagraphicalinterface, calledRunGui.TheresultsofcoupledEulerian-Lagrangiansimulations forthehydrodynamicsandparticledispersionintheculturetankwere thenpost-processedinParaview5(Kitware,NewYork,USA)andMat- labR17(MathWorks,Natick,Massachusetts,USA).Thedetailsofmodel equationsandproblemsetuparepresentedinthissection.

2.2.1. Continuousphase

ThemodellingoftheflowdomainintheRAStankwasperformedina three-dimensionalunsteadyincompressibleframeworkwiththeRANS- basedturbulencemodel.Themassandmomentumconservationequa- tionsare

∇.𝑣=0 (1)

𝐷𝑣𝐷𝑡 =−1

𝜌∇𝑝+ν ∇²𝑣 (2)

wherevisthevelocityfield,𝜌,pand𝜈representthedensity,pressure andkineticviscosityofthefluid,respectively.UsingtheReynoldsde- compositionofinstantaneousvelocityvintoaverage(̄𝑣)andfluctuating (v′)components,theEq.(2)becomes

𝐷𝑣_𝑗 𝐷𝑡 =−1

𝜌 𝜕̄𝑝

𝜕𝑥_𝑗 +ν ∇²𝑣_𝑗−𝜕𝑣_𝑖𝑣_𝑗

𝜕𝑥_𝑖 (3)

where𝜏(=𝑣_𝑖𝑣_𝑗)istheReynoldsstressterm.Theclosureapproximation inRANSmodellingtoeliminatefluctuatingvelocityv′yields

𝜏= 2

3𝑘I−𝜈_𝑡 (4)

where𝑘(= ¹

2|𝑣^′|²)istheturbulentkineticenergy,Iistheidentityma- trix,𝜈tistheeddyviscosityandistheaveragedstretchingtensor, definedby¹

2(grad̄𝑣+^𝑡grad̄𝑣).Usingthehypothesesofgradientdiffusion andeddyviscosity,themomentumequationbecomes

̇̄𝑣=−1 𝜌grad

(̄𝑝+2 3𝜌𝑘)

+( ν +ν_𝑡)

Δ̄𝑣 (5)

Althoughnumerous modelsexist tosolvethetransport equations forkandrelevantscalarvariables,eachhassomeadvantagesandlim- itationsdepending on theapplication.For industrialcases, thetwo- equationmodelsthatsolvetheequationsforkanditsdissipationrate𝜀 aremorepopularduetotheirrobustness,computationalfeasibility,and reasonableaccuracy.Inthisstudy,therealizablek−𝜀modelisused whichenforcestherealizabilityontheformulationof𝜇_𝜏byrelatingthe modelconstanttothestraintensor.Themodelrespectsthebindingcon- straintsofReynoldsstressesandrealizesthephysicsofturbulentflows.

Thisismoresignificantinaccuratelymodellingtheflowfeaturessuchas rotationsandvortices;thecriticalaspectsofculturetankhydrodynam- ics.Theconservationequationsforkanditsdissipationrate𝜀therefore become

𝜌 𝜕𝜕𝑥_𝑗 (𝑘𝑣𝑗)

= 𝜕

𝜕𝑥_𝑗 [(

𝜇+ 𝜇_𝑡 𝜎_𝑘

)𝜕𝑘

𝜕𝑥_𝑗 ]

+𝐺𝑘+𝐺𝑏−𝜌𝜀+𝑆𝑘 (6)

𝜌 𝜕𝜕𝑥_𝑗 (𝜀𝑣_𝑗)

= 𝜕

𝜕𝑥_𝑗 [(

𝜇+𝜇_𝑡 𝜎_𝜀

)𝜕𝜀

𝜕𝑥_𝑗 ]

+𝜌𝐶1𝑆_𝜀− 𝜌𝐶2𝜀² 𝑘+√

𝜈𝜀+𝐶1𝜀𝜀

𝑘𝐶3𝜀𝐺_𝑏+𝑆_𝜀 (7)

Fig.2.Meshdependencyofaveragevelocityacrosstheplanesat17%,43%

and68%ofthewatercolumnheight.

where𝐶1=max[0.43,_𝜂+5^𝜂 ], 𝜂=^𝑘

√2𝑆𝑖𝑗𝑆𝑖𝑗

𝜀 and𝑆_𝑖𝑗=¹

2(^𝜕𝑣𝑗

𝜕𝑥𝑖 +^𝜕𝑣𝑖

𝜕𝑥𝑗).G_kand G_brepresentthegenerationofturbulentkineticenergyduetoaverage velocitygradientsandbuoyancy,respectively.S_kandS_𝜀aretheuser- definedsourceterms,andthemodelconstantsareC_1𝜀=1.44,C₂=1.9, 𝜎k=1.0and𝜎_𝜀=1.2.Althoughtheturbulentviscosity𝜇_𝑡(=𝜌𝐶_𝜇^𝑘_𝜀²)iscom- putedsameasinotherk−𝜀models,thedifferencearisesfromthecal- culationofC_𝜇.WhiletheStandardandRNGmodelsassumeC_𝜇 tobe constant,therealizablemodeldefinesitas

𝐶_𝜇= 𝜀

4.04𝜀+√

6𝑘cos𝜃√

𝑆_𝑖𝑗𝑆_𝑖𝑗+Ω̃_𝑖𝑗Ω̃_𝑖𝑗

(8)

whereΩ̃_𝑖𝑗=Ω̄_𝑖𝑗−3𝜀_𝑖𝑗𝑘𝜔_𝑘.Theinclusionofmeanrate-of-rotationtensor Ω̄_𝑖𝑗 alongwithstrainrates,angularvelocity𝜔andtheturbulencepa- rameterskand𝜀,inthedefinitionofC_𝜇 andhenceinthecomputation of 𝜇tmakes therealizable k−𝜀modelmoresuperiorthanthestan- dardandRNGmodelsinpredictingthespreading ofroundjetsfrom theinletnozzlesofaculturetank.Inaddition,thetransportequation for𝜀considersthetransportofthemean-squarevorticityfluctuation, whichmadethemodelthemeansofturbulencemodellinginthecurrent study.

2.2.2. Dispersedphase

Themotionofthebiosolidsintherearingdomainisexploredby meansofLagrangianparticletrackingmethod.Uneatenfeedpelletsand faecalmatteraretheusualcontributorsofsuspendedsolidsinthecul- turetanks.TheparticledispersioninLagrangianframeiscomputedfrom theEulerianflowfield,andtheparticlemotionisgovernedby

𝑑x_𝑝

𝑑𝑡 =v_𝑝 (9)

𝑚𝑑v_𝑝 𝑑𝑡 =∑

f_𝑝 (10)

wheref_pistheforceexperiencedbytheparticleofdiameterd,massm whenithasavelocityv_patpositionx_pandtimet.

Thepresenceoftheanyparticulatematterintheculturetanksis criticaltowaterqualityandhencethefishgrowth.However,thevol- umeratiosofthebiosolidsinthetanksarevery small.Forinstance, Davidson et al. [13]shows that thetotal suspended solids (TSS)in culture tanks can range from 2.8± 0.2 ppm to 18.2± 5.9 ppm de- pendingonthewaterexchangerateandtheuse offlow-flowozona- tion.Also,[26]reportedtheTSSaccumulationindifferentNorwegian commercialsmolttanks,rangingfrom2.1±0.5to12.1±4.0ppmin varioustanksatthetimeofsampling.Insuchdilutesuspensions,the particle-particle interaction andtheeffect of particle motion on the

J. Gorle, B. Terjesen and S. Summerfelt International Journal of Mechanical Sciences 188 (2020) 105944

Fig.3. Meshvisualizationontheselectedgeometries.(a)Unstructuredtriangularcellsonthesurface,and(b)hexahedralmeshinthecoreoftheBasedesignwith anenlargedviewofthenear-casingsurfacemesh.Similardiscretizationstrategywasadoptedforotherdesignsaswell.(c),(d)and(e)showthesurfacemeshesfor theredesigns1,2and3withthezoom-inviewoftheclusteredcellsnearthebottomoutletofRedesign3.

flowandturbulencearenegligible[18].Theinfluenceoffluidmotion ontheparticlescanbecharacterisedbytheStokesnumberaccording to

𝑆𝑡=𝜌_𝑝𝑑²𝑣

18𝜇𝐿 (11)

where𝜌p anddarethedensityanddiameteroftheparticles,visthe flow,𝜇isthedynamicviscosityofthefluidandListhecharacteristic length,whichisthemeandiameterofthetankinthepresentcase.While thesizeofparticlesinculturetanksrangesfromnanotomillimetres,this studyconsidered200μmuniformlysizedrigidsphericalparticles.These specificationscorrespondtoSt<<1whichrepresentstheinteraction betweentheflowandparticlesisone-way,i.e.,fromtheformertothe latter[10,21].

Althoughtheconsiderationoflifttermsontheparticlesofdifferent sizesinturbulentflowshaslongbeenatopicofdebate[33,58],numer- ousstudiesonLagrangianparticletrackingignoredthelifttermswhen theparticlediameterissufficientlysmall(forinstance,[4,56]).Ignor- ingthepressureandaddedmassforcesalongwiththeBassethistory termforthesakeofsimplicityforarelativecomparisonbetweenthe tankdesigns,thedominantforcesontheparticlearedragf_d,buoyancy andgravitationalforcef_gi.e.,∑f_𝑝=f_𝑑+^{(𝜌𝑝−𝜌)𝜋𝑑}

3𝑝𝑔

6 .Theparticleswere assumedtohavethedragcomponentsduetospheredragandgravity.

Therefore,theparticledragbecomes

f_𝑑= 3𝑚𝜇𝐶_𝑑𝑅𝑒_𝑝 4𝜌_𝑝𝑑²

(𝑣−v_𝑝) +𝜋𝜌_𝑝𝑑³

6 𝑔 (12)

where𝑅𝑒_𝑝(=^{𝑑|𝑣−v𝑝|}

𝜈 )istheparticleReynoldsnumber,𝜌pistheparticle density,vistheflowvelocityandg(=9.81m/s²)isthegravitationalac- celeration,respectively.Assumingtheconstantmechanicalproperties, theparticledragcoefficientC_disdefinedby

𝐶_𝑑={

24

𝑅𝑒𝑝for𝑅𝑒_𝑝≤0.5

24 𝑅𝑒_𝑝

(

1+0.15𝑅𝑒⁰_𝑝^.687)

for0.5≤𝑅𝑒𝑝≤1000 0.44for𝑅𝑒_𝑝>1000

(13)

Theparticle trajectoryis computed withintheturbulent fieldus- ingtherandom-walkalgorithm[5]wheretheparticlepositionisup- dated at everytime-stepusing theeddy-interaction model.Denoting theparticlevariableswhicharederivedfromtheinterpolationofEu- lerianfieldatadjacentcellsbythesubscriptp⁺,theeffectof eddies ontheparticle’svelocityisconsideredbyaddingthelocalfluctuating velocitycomponentv^′_𝑝+. Therefore,theeffectiveparticlevelocitybe- comes̃v_𝑝+=v_𝑝++v^′_𝑝+.Thefluctuatingvelocitycomponentiscalculated from

v^′_𝑝+=𝜑

√2

3𝑘 (14)

where𝜙isarandomnumbergeneratedfromGaussianprobabilitydistri- butionwithnullmeanandunitvariance,and√

2

3𝑘isthelocalRMSflow velocityfluctuations.ADNScorrectionfactorisusedinthestochastic modeltocounterthepresumedisotropicturbulencewithinthebound- arylayerregion.Thetransittimeoftheparticletotravelthroughthe eddy(t_tr)andtheeddylifetime(t_e)aredeterminedfrom

𝑡_𝑡𝑟=−𝑡_𝑝ln

⎛⎜

⎜⎝

1− 𝑙_𝑒 𝜏_𝑝|||̃v_𝑝+−v_𝑝|||

⎞⎟

⎟⎠

(15)

𝑡𝑒=𝐶⁰_𝜇^.63𝑘1_𝜀^.5

|||v^′_𝑝+|||

(16)

Here,𝑡_𝑝(= ⁴

3 𝜌𝑝𝑑

𝜌𝐶_𝑑|𝑣−v_𝑝|)istheparticlerelaxationtimetorespondtothe changesinthelocalflow.Theparticle-eddyinteractiontimeiscalcu- latedfromt_int=min(t_tr,t_e).Then,theparticle’spositionandvelocityat then^thLagrangiantimesteparecomputedfrom

x

𝑡+∑^𝑛 𝑡=1

Δ𝑡𝑖

𝑝 =x

𝑡+^𝑛

∑−1 𝑡=1

Δ𝑡𝑖

𝑝 +v

𝑡+^𝑛

∑−1 𝑡=1

Δ𝑡𝑖

𝑝 Δ𝑡_𝑛 (17)

Fig. 4. Comparison between thecomputationally predictedandADV-basedmeasurementsofvelocity atdifferentlocationsacrossthreeverticallocations i.e.17%,43%and68%ofwatercolumnheight.

v

𝑡+∑^𝑛 𝑡=1

Δ𝑡_𝑖

𝑝 =

v^𝑡+

∑𝑛−1 𝑡=1Δ𝑡_𝑖 𝑝 +v^𝑡_𝑝+^Δ𝑡𝑛

𝜏𝑝 +𝑔Δ𝑡_𝑛 1+^Δ_𝜏^𝑡𝑛

𝑝

(18)

2.3. Domaindiscretization

Theundesiredentitiessuchasslivers,smallfacesandopenedges wereremoved,andthegeometrywassimplifiedusingthebuilt-inutil- ities of themeshing tool. Severalmeshes werecreated by changing theglobalcellsizetoevaluatemeshdependency.Severalmeshqual- ityparameterswerethoroughlycheckedforeachmeshusingthebuilt- inmesh-checkutility.Theconvergencecriterionof1E-5wassetforthe relativeerrorinthecomputationofvelocitymagnitude.Aseriesofmesh convergencetestsontheBasedesignofthetankwasconductedbyre- finingtheglobalcellsize.Fig.2showsthemeshdependencyresultsof theBasedesignfortheaverageplanarvelocityatthreeheightsofthe watercolumnwheretheempiricalmeasurementsweretaken.Thefi- nalmeshontheBasedesignhad797,819unstructuredfinitevolumes andanyfurthersizerefinementproducedanerrorsmallerthan0.2%

relativetothelastrefinedmesh.Thishybridmeshcontainingthetetra- hedralcellson solidboundaries andhexahedralcellsin thecore,as showninFig.3(a)and3(b)respectively,offerstheadvantageofnego- tiatingthecomplexgeometricalfeatureswithhigh-qualitycelldistribu- tionatthereasonablecomputationaleffort.Fourinflationlayerswith aheightratioof1.15wereused tocapturethevelocitygradientsin thenear-wallregion.Theresultingthenon-dimensionalwalldistance y+wasabove30,andstandardwallfunctionswereusedtocompute thenear-walleffects[43].Althoughhighlyskewedcellsdon’thamper tosolutionstability,these,however,reducetheorderoffaceintegra- tion.Thefinalmeshhadthecellskewnessbelow0.5.Over95%ofthe cellshadthedihedralanglebetween70° and120°,and98%ofthedo- mainhadthecellaspectratiobelow5whichensuredadequatemesh quality.Formoredetailsonthemeshtopologyandgriddependencyre- sults,pleaserefertoourpreviouspublication[28].Similartopological settingswereusedtoproducethemeshesfortheredesigns1,2and3 whichcreatedthefinalgridswiththecell-countsof796,226,779,812 and779,991,respectively.Thesesurfacemeshvisualsarepresentedin Fig.3(c-e).

2.4. Boundaryconditionsandproblemsetup

Thenozzlesontheinletpipeswereassigned‘massflow’boundary conditions,andthetank’soutletactedas‘outflow’boundary.Allsolid surfacesofthetankweredefinedas‘no-slip’smoothstaticwallswhich takezero-gradientconditionfork,𝜀andp.Free-surfacedeformationin thetankisnegligibleduetothecontinuousreplenishmentofwaterinto thetankwiththesameflowratesthroughtheinletandoutletbound- aries[28].AssumingaturbulenceintensityT_iof5%,theinitialkand𝜀 werecalculatedfrom 𝑘=1.5(𝑇_𝑖̄𝑣)² and𝜀= c_𝜇k²/5𝜈.Time-dependant segregated viscous solverwithsecond-order Gaussian lineardiscreti- sation forboth convective anddiffusivetermswas used in thesim- ulations.Thepressure-velocityequationswerecoupledusingSIMPLE (Semi-ImplicitMethodforPressureLinkedEquations)algorithm.While thepressureequationwassolvedwithGAMG(geometricagglomerated algebraicmultigrid)formulation,allotherfieldequationsweresolved usingGauss– SeidelbasedsmoothSolver.Aconstanttime-stepof0.01s wasusedwith30inner-iterations.Simulationswereruninparallelmode ona28-coreIntelXeonE5‐2683v32.00GHzcomputer.

3. Resultsanddiscussion 3.1. CFDmodelvalidation

TheCFDmodeloftheBasedesignforvalidationwasdevelopedfor aninflowof292kg/s.TheReynoldsnumberiscalculatedfrom 𝑅𝑒=4𝑅_ℎ𝜌𝑉

𝜇 (19)

wherethehydraulicradius𝑅_ℎ(= ^𝑅ℎ

𝑅+2ℎ)isafunctionoftank’sequiva- lentradiusR(=8.15m)andhistheheightofwatercolumn(=3.9m).

Therefore,ameanretentiontimeof45min,inthiscase,correspondsto Reof2.3E6.Thevelocitymeasurementsweretakenatpredefinedloca- tionsinthesalmonculturetankwhenoperatedwithoutfish.ANortek high-resolutionacousticDopplerprofiler,Vector,wasusedforthemea- surementsat45discretelocationsinthetankacrossthreeheights,i.e., 17% and43%and68%of the watercolumn.The validation of the CFDmodelusingthevelocitymeasurementsinFig.4showsthatthe simulationresultslargelyfallwithinthestandarddeviationbarsofthe ADVfindings.Thelatestdevelopmentsoftransducershavereducedthe

J. Gorle, B. Terjesen and S. Summerfelt International Journal of Mechanical Sciences 188 (2020) 105944

Fig.5. Flowpatternaroundtheinletpipe,whenplacednearthesidewall(left)andcornerwall(right).Streamlinedistributionisplottedatfourheightsforawater columnheight,h,of3.9m.Flowdirectionisfromlefttoright.

Fig.6. Variationofskin-frictioncoefficient,C_f,withthemeanhydraulicreten- tiontimeofdifferenttankdesigns.

blankingdistanceofmodernADVinstrumentstoaslowas5cm.How- ever,theeffectofflowdisturbances,bothduetothedomainturbulence andtheinstrumentinducement,ontheperformanceofthesetransduc- erschallengethemeasurementaccuracy[17].Also,theDopplernoiseis likelytoinfluencethepeakvelocitiesrecordedbytheADVmodule.De- spitethatlow-qualitydatawasremovedbythesignalfilteringprocess, thesignalaliasingwasexpectedtocombinewiththeDopplernoiseand velocityfluctuations,whichpossiblyinfluencetheADVmeasurements intheturbulentflowsin aRAStank.Acorrelationcoefficientabove 90%andsignal-to-noiseratioofmorethan15dBwasachievedwitha samplingfrequencyof25Hz.Theresultingcoefficientofvariationisap- proximately7%andtheaveragedifferencebetweentheADVandCFD

resultsis9%.This,alongwithourpreviousresearch[25–27],highlights thatADVandCFDmethodscomplementeachothermorethanvalidate oneanother.Formoredetailsonthemeasurementsetup,andthevali- dationofvelocitytrendsandflowanglesacrossthetank,pleasereferto Gorleetal.[28].

3.2. Flowfieldaroundtheinletpipe

Previousstudieshavedeterminedthattherotationalvelocityatthe perimeterofcirculartanksisstronglydependantupontheimpulseforce ofwaterflowinjectedtangentiallyintothecircular-typetank.Thus,the rotationalvelocitydependsuponthehydraulicexchangerateandinlet nozzlevelocityandthedirectionproducedattheflowinletstructures.

Fundamentally,theinletpipeintheculturetankconditionsfortheprob- lemofflowaroundacircularcylinder,whichisoneofthestandardcases offluidmechanics.Inoctagonaltanks,theflownearthecornerwalls turnsintoitselftonegotiateitspathwiththetankwalls.Therefore,the inletpipesinthetankredesigns1and3experienceamanoeuvringflow, representedbycurvilinearstreamlinesinFig.5(b).Thishasasignifi- canteffectonthelocationsofstagnationpoints,pressuredistribution andwakeformation,comparedtothecaseofstraightflowoverthein- let pipes,i.e.,thepipesnearthesidewallsasintheBasedesignand Redesign2.Asaresult,thepressuredistributiononthepipe(partially showninFig.5)issignificantlydifferentinbothcasesofinletpipelo- cation.

Thedistanceofthetank’scentrefromthecornerwallis13%more thanthatfromthesidewall,whichcausesthestreamlinestospreadmore alongthediagonalsofthetankthanalongthex-ory-axisinacircular patternedflow.Thismeansthattheinletpipenearthecornerwallis exposedtoalowerflowvelocity(~15%lesservelocity)thanthoseat thesidewalls.Usingtheempiricalrelationshipbetweenthedragforce andReynoldsnumber,formulatedbyCheng [9], thedragcoefficient C_dof theinletpipewithnojetfromnozzleswas foundtobe1.206, whichisconsistentwiththeclassicaldragcurveofasmoothcylinder [57].Withthejetblownatmuchhighervelocitiesthanbaseflow,Fre-

Fig.7. Quarter-wedgesectionalviewofthevortexcolumnformedinthefourselectedtankdesigns.Velocityprofileandstreamlinepatternsareshownacross mutuallyperpendicularplanes.TheflowratecorrespondstoameanHRTof45min.

undandMungal[20]achievedzerodragonthebodyofinterest.Inthe presentstudy,theinletvelocityformeanhydraulicretentiontime(HRT) inthetankof40minis2.69m/s,whichisapproximately4timeslarger thanthemeanrotationalvelocitywhentheinletpipeisplaced near thesidewall.AsdepictedinFig.5(a),thelow-pressurewakeregionwas replacedbyapressurerecoveryregion,representedbytheaccelerated flowontherearsideofthepipe.Thus,thenozzleinjectionhasgreatly cancelledthedragforceofthepipebymorethan99%.Thenozzleflow fromtheinletpipenearthecornerwallishowevernotalignedwiththe basestreamlines,resultinginanoffsetbetweenthewakezoneandpeak velocitystream,asshowninFig.5(b).HendrickandDegrez[30]high- lightedthesignificanteffectofjetlocationontheflow-inducedforces.

Consistentwiththis,arelativelyweaksuppressionofthelow-pressure regiondownstreamofthepipeisobserved.However,thelow-velocity flownearthecornerwallkeepsthedragforceofthepipelesserthan whenplacednearthesidewallsby29%whichmakesitabetterplace- mentintermsofaveragevelocityandhenceenergyuse.Anotheradvan- tageofcornerwallpositioningoftheinletpipeisthatthelow-velocity regiongainsadditionalmomentumdue tothestructural obstruction aswellasinletflow,andhenceincreasestheflowuniformity inthe tank.

Theeffectofoutletlocationisassociatedwithkeepingorremoving thecomplexcentraloutletsystem,whichispresentintheBasedesign andRedesign2.Withsuchadrainingsystem,theflowhastotravelmore distancefrominlettooutlet.Inaddition,therotationalflowaroundthe centralverticalpipescreatesadditionaldrag,comparedtoredesigns1 and3.Thecomparisonbetweenthedesignsfortheskin-frictioncoeffi- cient,whichisdefinedasC_f= ^τ𝑤

0.5𝜌𝑣²with𝜏wbeingwall-shearstress,is showninFig.6.Withanelevatedoutlet,theinletpipenearthecorner wall(Redesign1)experiences10%lesserC_fthanthatnearthesidewall (Basedesign),whereasthisdifferencebetweentheredesigns2and3 becomes20%.ThereasonforlesserC_fwithRedesign1comparedtothe Basedesignisthattheflowintheformerhaslowenergylosstothewalls fromthebaseflow,whichisalsotrueforRedesign3comparedtoRe- design2.Over30%lessC_fisobservedwiththereplacementofcomplex central-topoutletbyconventional bottomoutlet.TheReynoldseffect ontheoveralldragforceisdemonstratedbyaslightbutsteadyincrease inC_fwithHRT.

3.3. Flowfieldneartheoutlet

Ideal axisymmetric vortices, governed by Burger’s equation, are basedontheassumptionthattheeffectsofaxisymmetricstrainingand viscositydiffusionarebalanced.Thisisnottrueinrealflows,andthere- fore thecylindricalvortices arenot perfectlyaxisymmetric. Detailed characterizationofvorticityisimperativeasitaffectstheglobalvelocity fieldofthetank[27].Fig.7showsthecut-awayviewofthevortexcol- umnprevailingatthecentreintheselectedtankdesigns.Theresultant circularflowpatternisthecombinationofstreamlinesacrosstheplane

??=constant,alarge-scalecylindricalvortexaroundtheoutlet,andthe rotationalflow,representedbyvectors.Here,theisovortexsurfacewas quantifiedbyQ-criterion,whichisdefinedbythepositivesecondinvari- antofvelocitycurl(∇xv),Mathematically,Q=|Ω_ij|²−|S_ij|²,whereΩ andSaretherotationalanddeformationcomponentsofvelocitygradi- entrespectively[24].Thesizeofthevortexcolumnwithconventional bottomoutlet,asinredesigns2and3,isapproximately22%lesserthan thecentraltopoutletduetothespaceoccupiedbythepipesinthetank’s centre(BasedesignandRedesign1).

3.4. Large-scaleandsmall-scaleturbulentstructures

Theevolutionofturbulentstructuresatdifferentlength scalesin- fluencestheglobalflowfieldthroughvortex-vortexinteraction,forex- ample.Thefine-scalecoherentstructureslikelyaffectthedynamicsof large-scaleturbulence[11,48],whichinturnaffectthedispersionofpar- ticlesinthewall-boundedflows[6].Therefore,itisnecessarytochar- acterizetheturbulentstructuresinthedifferentdesignsoftheculture tank.Inthisstudy,thesmall-scaleturbulencewasidentifiedbycoherent vorticalstructures,usingQ-criterionwhiletheturbulentkineticenergy defined by𝑘 = 0.5𝑣^′_𝑖𝑣^′_𝑖with𝑣^′_𝑖 beingthefluctuatingvelocitycompo- nent,wasusedtodefinethelarge-scaleturbulentstructures.Asseen fromFig.8,theintensityofthetime-averagedvorticityincreaseswith thehydraulicexchangerate.Thevortexringinmid-radiuslocation,by receivingtheturbulentenergyfromthebaseflow,seemstobemoving fasterandcontributestothemotionofthevortexcore.Thesizeofthe vortexringisapproximately12%lesserinthedesignswithinletpipe nearthecornerwalls,comparedtothatnearthesidewalls.

J. Gorle, B. Terjesen and S. Summerfelt International Journal of Mechanical Sciences 188 (2020) 105944

Fig.8. Coherentvorticitydistributioninthebasedesignandredesignsfordifferentoperatingconditions.Iso-surfacesofQ=0.01arecolouredonvelocityscale.

Fig.9showsthetime-averageddistributionofturbulentkineticen- ergy(TKE)inthetankdesigns.Onageneralnote,theTKEisnotuni- formlydistributedthroughoutthedomain.Mixingofinflowwiththe rotatingflowinthetankcreatesthemostintenseturbulence,butfur- therfromthismixingregion,theturbulencedecaysasthewaterspreads inthetank.Turbulencelevelsneartheoutletarereasonablyhighdue tothelocallystrainedflow.Denserturbulentkineticenergycontoursin theBasedesign,andredesigns1and2,particularlyathigherflowex- changerates,revealthehigherflowviscidityinthecoreofthetank.In particular,thehigherTKEdistributioninBasedesignexplainsthatthe flowpatternismoredisorderandrandom,whichisrelativelynegligible inredesigns2and3.Itcanbeconcludedthattheinletpipesnearthe sidewallsandcentraltopoutletconfigurationsaremoredetrimentalin termsoftheflowuniformityandenergyloss.Theviscouseffectsinthe conservationequationsbecomedominantwhenthelengthscaleofan eddyisadequatelysmall.Theturbulentkineticenergyisthenquickly dissipatedandthereforethenonuniformityoftheflowvanishes.Thus,

thedissipationrateofturbulentkineticenergy𝜀isacrucialparame- ter,whichisgovernedbythedynamicsofsmall-scaleeddies.Fig.10 comparesthedesignsintermsofthetime-averagedplanardistribution of𝜀nearthefloorandwatersurface.Concentratedprofilesof𝜀atthe watersurfaceinBasedesignandRedesign1explainshigherturbulent diffusivityandhencebettermicromixingoftheflow.Ontheotherhand, theheight-wisevariationof𝜀inRedesign2isrelativelynegligible.The lowestamountsofTKEinRedesign3leadtolowturbulentmixingand thereforelowdiffusionrate.

3.5. Performancemetrics

Theselecteddesignswerefurthercontrastedforthreeperformance metrics;normalizedrotationalvelocity(v/v₀),flowuniformityindex(𝛾) andvorticitystrength (Γ/Dv₀),wherev₀ is theinletnozzlevelocity.

These hydrodynamic indicatorswereevaluated atfourinflowcondi- tionsof328,292,263and239kg/s,representingthemeanhydraulic

Fig.9.Contoursofturbulentkineticenergy,k,inbasedesignandredesignsofthetankfordifferentoperatingconditions.

Fig.10. Planardistributionofturbulentdissipationrate,𝜀,inthefourtankdesignsforHRT=40min.

retentiontimeof 40,45,50,and55 minrespectively, andReynolds numbersrangingwithin2E6-3.5E6.RecallingthattheBasedesignand Redesign1havethecentral-topoutlet,whileredesigns2and3havethe central-bottomoutlet.AscanbeseenfromFig.11,thisclassificationwas reflectedinthevelocitydistributioninthetanks,andtheplacementof inletpipesseemsrelativelyinconsequentialinthisregard.Theflowpas- sagesatthebottomandtopoftheoutletstructure(i.e.60%and40%, respectively)intheBasecaseandRedesign1causeslocalaccelerated

regions,whichleadstothepeaksinthevelocityprofilesinFig.11(a) and11(b).Theconfinedflowgeometrycausestospreadthelowerpeak, i.e.,atthebottomoftheverticaloutletstructureandnegotiatewiththe adjacentvelocitydistributions,whichresultedinasmoothvelocitypro- file.Theanomalousbehaviourofthefree-surface,however,limitsthis scenariofortheflowthroughthecasingchannels,resultinginanear comparativelysharpervelocitypeaks.Replacingthecomplexcentral- topoutletsystemsimplybyholesontheflooratthetank’scentrehave

J. Gorle, B. Terjesen and S. Summerfelt International Journal of Mechanical Sciences 188 (2020) 105944

Fig.11. Normalizedvelocitydistributionacrossthetankwithdifferentinletandoutletconfigurations.

Fig.12. Comparisonbetweentheselecteddesignsforflowuniformityindex𝛾 forHRT=45min.

drasticallychangedthevelocitytrends,asdepictedin Fig.11(c)and 11(d).Exceptnearthefloorandwatersurfacewherestrongerflowgra- dientsexist,thevelocityismoreuniformacrossthetankheightwith thecentralbottomoutlet.Theincreaseinthevelocitymagnitudewith decreasingHRTislinearwiththebottom-outlet,whichisnottruewith top-outlet.Thetrendofvelocitychangewiththewaterexchangerateis hardtoquantifyduetothenonlinearnatureofthevelocitydistribution inthecaseofthecentral-topoutlet.

Oneoftheobjectivesintheculturetankdevelopmentistoachieve themaximumpossible flowuniformityacrossthetank,whichwould resultinmoreconsistentwatervelocitiesforthefish.Becauseofnon- uniformityassociatedwiththevorticesintheformofvelocitygradients, theoverallflowuniformityisaffectedbytheincreasingvortexintensity andturbulence,whichis commonin mostfluidicsystems(forexam- ple,[38,41]).Theindex𝛾wasusedinthisstudytoquantifytheflow uniformityinthetank.Mathematically,itisdefinedby

𝛾=1− 1 2𝑛𝐴

∑𝑛 𝑖=1

√( 𝑣_𝑖−̄𝑣)2

̄𝑣 𝐴_𝑖 (20)

wherenisthenumberofcomputationalcellsinthesectionofareaA,v_iis thevelocityinthecell,whoseareaisA_iandvisthearea-weightedmean planarvelocity.Theindex𝛾iscomputedacrossthehorizontalplaneat every10%heightandinterpolatedtoconstructtheflowuniformitypro- filefortheentireheightofthewatercolumn.Thecomparisonbetween theBasedesignandtheredesignsinFig.12revealsthatthedesignshave different𝛾 profilesacrossthetank’sheight.Irrespectiveofthedesign,

theoverallflowuniformityisalwaysabove90%.Amereshiftofinlet pipesfromthesidewalllocation(Basedesign)tocornerwalllocation (Redesign1)causestheflowuniformitytodropby2%.Theoptimum flowuniformitywasachievedbyRedesign2,i.e.,withtheinletnearthe sidewallandbottomdrainwhilethelowestuniformitywasfoundwith Redesign1,i.e.,withinletnearthecornerwallandelevateddrain.

Theflowfeaturesinthetankdesignswerefurtherstudiedintermsof vortexstrength,whichisdefinedby ^Γ=(∫_𝐷^𝐴_𝑣^{𝜔𝑑𝐴)}

0 where𝜔isthevorticity magnitudeandDisthecharacteristiclength.Theconvectiveandvis- coustermsinthemomentumtransportequationdependontheReynolds number.Therefore,thevortexstrengththatdominatesthemeanflow variedwiththeinflowrateofthetank.AsobservedfromFig.13,agrad- ualdecreaseinthevortexstrengthwithincreasinghydraulicretention timeisobservedwithBasedesignandRedesign1,whereasthisdropis fairlyconstantinredesigns2and3.Thisimpliesthatthecentralbot- tomdraingivesamorepredictiveperformancethanthecentralelevated drain,asvorticitydistributionisconcerned.Lookingattheheight-wise variationin thevortexstrength,thecentralelevateddrainyetagain displaysahighlynon-lineardistribution.Thetwopeaksoftheprofiles inFig.13(a)and13(b)representincreasedvortexstrengthbecauseof flowthroughfourverticalpipesat5cmfromtank’sfloorand40%of thetotalflowthroughtheopeningsofoutletcasingnearthewatersur- face.Incontrast,thevortexstrengthismorelinearlydistributedacross thetankheightinredesigns2and3(Figs.13cand13d).Thelocation oftheoutletsurfacegrosslydeterminesthevortexstrengthofthewa- tersurface;theclosertheoutlettowatersurface,thehigherthevortex strengthwouldbe.

Thebiosolidsgeneratedintheculturetankfromthefishandbiofilms need to be flushed rapidly as their hydrolysis leads to decomposi- tionwhichdecreasesthedissolvedoxygenlevelsandreleasesorganic molecules,finesuspendedsolidsandammonia.Anotherdangerthatcan occurinRASusingseawateristhattoxicH2Scanalsoaccumulatein thetank,anditislikelythatsuchascenarioismoreprobableifsolids arenotrapidlywashedout[32].Togetridofparticleaccumulation, thetankdesignneedstobeself-cleaning sothatthefishgrowthand welfarewouldnotbenegativelyimpacted.Hence,thepracticalimpli- cationsofanincorrecttankdesignhaveprofoundeffectsonaquaculture operations.Acommonpracticeintheindustryistoemployaparticle trapneartheoutletthatreceivesapproximately1%ormoreoftheto- taloutflow.Whenaparcelof500particleswithaspecificgravityof 1.02isreleasedatthefree-surfacewithaninitialdownwardvelocityof 1cm/s,thedistancebetweenthedespatchlocationtothedomainexitin thecaseofelevatedoutletisapproximatelydoubleofthatinthebottom outlet.Tomakeavalidcomparisonforparticledynamics,onlyredesigns 2and3withthesameretentiontimeof55minwereexaminedwhere theoutletwasonthetank’sfloor,buttheinletswerenearthesidewalls andcornerwalls,respectively.Particlebreakupandsurfaceroughness

Fig.13. Time-averagedvortexstrengthinthetankdesignsfordifferenthydraulicretentiontimes.

Fig.14. Lagrangianparametersofthefeedpelletsinthetankwiththeinletsplacednearthesidewalls(Redesign2)andcornerwalls(Redesign3).Bothdesigns havethesameoutlet,whichisonthetank’sfloor.

effectswereignoredwhichdidnotaffectthemodelaccuracyasparti- cles’motionisconcerned.Fig.14presentstheintegratedinformation abouttheparticledispersioninthetankdesignsoveratimeof30min.

Withtheearlyparticleflushingwithin7min,Redesign2dominatesits counterpartforabout10minuntil10%ofparticlesareflushed.Around thistime,withasuddenfallintheparticlecount,Redesign3hasasud- denfallintheparticlecountandcontinuestoexhibitasuperiorflushing activitytoRedesign2.AsalmonculturetankwithRedesign3isthere- foresaferforthefishandgivesbetterwelfareandperformance,because thereislesstimeforparticlestodisintegrateandproducewaterqual- ityproblemsfromthebreakdownproductsoftheseparticles.Fromthe particlevisuals,itcanbeseenthatRedesign2hasmorestaticparticles (inbluecolour)onthefloorthanRedesign3.Asviewedfromthetime- historyoflinearkineticenergy,Redesign2createsamorefluctuating trendwithamean18%morethanRedesign3.Bytheendoftheconsid- eredduration,18%moreparticleswereleftinRedesign2,accounting for14%higherkineticenergythanthosein Redesign3.Thus,mov-

ingtheinletpipesfromthesidewalllocationtothecornerwallswould considerably improvetheflushingactionof biosolidsin theexisting tank.

4. Conclusions

Rapidsolidsflushingoutofsalmonculturetanksis aprerequisite foradequatefishwelfareandfishperformance.Inthisstudy,weshow that inletandoutletplacements haveaconsiderableimpactonboth solids’removalfromthetankaswellastheenergyusedtosustainthe flowinthetank.Confinedrotatingflowinalargedomainwithacen- traloutletasinthiscaseresultsin acomplexcombinationofalarge vortexcolumnatthecentreandarangeofturbulentfilamentsaround it.Bymovingtheinletpipestothecorner wallthisprovides advan- tages,suchasthereductioninthedragforceandlocalre-energization oftheflow,whencomparedtothepracticeofinletpipesplacednear thesidewall.Regardingtankoutletdesign,thestudyshowedthatthe