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TWO-DIMENSIONAL

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TWO-DIMENSIONALTwo

    TWO-DIMENSIONAL

JournalofHydrodynamics,Ser.B,5(2003),9197

    ;ChinaOceanPress,BeijingPrintedinChina

    ;91

    ;TWoDIMENSIoNALPLANEWATERFLoWANDWATERQUALITYDIS- ;TRIBUTIoNINBoSTENLAKE

    ;FengMin.quan,ZhouXiaode

    ;InstiuteofWaterResourcesandHydroelectricEngineering.Xi’anUniversityofTechnology,Xi’an

    ;710048,China,e.mail:fengminquan@sohu.com ;ZhengBang.min

    ;SchoolofwaterResourceandHydropower,WuhanUniversity,Wuhan430072,China

    ;MinTao,ZhaoKe.yu

    ;InstiuteofWaterResourcesandHydroelectricEngineering.Xi’anUniversityofTechnology,Xi’an

    ;710048,China

    ;(ReceivedDec.6,2002)

    ;ABSTRACT:Thetwodimensionalplanewaterflowandwa

    ;terqualitywasdevelopedbyusingthetechniquesofcoordinate ;transformation,alternatingdirections,staggeredgrid,linear ;recurrence,andimplicitschemeinthestudyoflargewater ;bodyinlakes.Themodelwasprovedtobesuitablefortrea

    ;ringtheirregularboundaryandpredictingquicklywaterflow ;andwaterquality.TheapplicationofthemodeltotheBosten ;LakeinXinjiangUygurAutonomousRegionofChinashows ;thatitisreasonableandpracticable.

    ;KEYWORDS:circulation,waterquality,coordinatetrans

    ;formation,aheratingdirection,staggeredgrid,implicit ;scheme

    ;1.INTR0DUCTIoNE]

    ;TheBostenLakeisthelargestfresh.water

    ;lakeofinlandinChinaandimportantwatersource ;intheXinjiangarea.Itisalsoofsignificancefor ;economydevelopmentandecologyprotectionin ;thisarea.Unfortunatelv,inordertopromoteagri

    ;cultureandincreasecerealyield,large.scaleland ;reclamationhasbeencarriedoutandthewaterdi. ;versionquantityforirrigationhasremarkablyin

    ;creasedwhichhasresultedindecreasingquantity ;ofinflowrapidly,loweringwaterlevel,increasing ;mineralizationdegreeanddecreasingthegrowing ;areaandyieldofreed.Itisalwaysacontroversial

    ;issuewhichhasdrawntheattentionofpeopleto ;managescientificallywaterresourceintheBosten ;Lake.Inthe1970s,waterconservancyauthorities ;putforwardadiversionplaninsteadoftheoriginal ;dredgingplanandconstructedthewestpumpsta. ;tionfortheLake.Buttheoutflowabilityofthe ;pumpstationcouldnotmatchoneortwobillion ;regulatingvolumeofthelake.Inordertoprevent ;thewaterqualityintheBostenLakefromfurther ;deteriorationtheeastpumpstationwasdecidedto ;beconstructedforsupplementingfreshwaterand ;pumpingoutsalinewater.Inordertoanalyzethe ;watercirculation,flowcharacters,dominative ;factorsandwaterquality,itisnecessarytosimu. ;1atewaterflowandwaterqualityfordifferenttyp

    ;icalwaterlevels,positionsofeastpumpstation, ;characteristicinflows,outflows,windpowersand ;directioninnonfreezingperiod.

    ;Differentmethodssuchasfieldmeasurement, ;physicalmodelandnumericalmodelareoftenused ;instudyingwaterenvironmentoflakes.Field ;measurementshasshortcomingsasfollows:firstly, ;itisimpossibletoconductwithoutenoughman. ;powerandfinancialsupportbecauseofthebigare

    ;asoflakes;secondly.forthelimitationofpoint ;numberandtimesofmeasurement,measureddata ;arenotcontinuousandfullintimeandplace: ;thirdly,fieldmeasureddatasupplysomequantity ;charactersunderthepresentconditionsbutcannot ;beusedtopredictfuturesituation.Physicalmodel ;isoftenusedtostudythemixingprocessofacer

    ;tainlake.Butitisdifficulttosimulatenatural ;wind.drivencirculationandbiochemicalprocessof ;materialinalake.Thusnumericalmodelisanide. ;almethod.

    ;In1956,Hansenestablishedatwo.dimension. ;almodelfortheproblem.Atwo.dimensionalmod. ;elusedtocalculateflowstateinestuaryandseaar. ;

    ;92

    ;eawasdevelopedbyLeedertesin1967.Gallagher, ;Liggetteta1.presentedatwo-dimensionalnumeri- ;calmodelforsimulatingwind.drivencirculation. ;Multi.1ayermodelforthecirculationoflargearea

    ;lakewasputforwardbySimonin1973.Butitis ;roughandhassomeshortcomingsasdescibedbe- ;low.Increasementoflayersislimited;Frictionco. ;efficientmustbeintroducedamonglayerswhichis ;difficulttobedefined.Whenobviousupfl6wand ;downflowexist.calculationunsteadinesswould ;happenonthehypothesisofimpermeabilityamong ;layers.Three.dimensionalmodelstocalculate ;stratifiedflowweredevelopedbyDaviesinin1982 ;and1983.Three.dimensionmodelofwind.driven ;circulationwasworkedoutbySimonin1985which ;hassomeshortcomings:calculationneedsmuch ;time:themodelneedsmoredatawhicharediffi. ;culttoobtainasfaraslargearealakeisconcerned; ;turbulentdiffusioncoefficientintheverticaldirec. ;tionwasintroducedwhichisdifficulttobedeter. ;mined.

    ;Inordertofitfullywithirregularboundaryof ;thelakeandrealizerapidpredictionofwaterflow ;andwaterquality,coordinatetransformation,a1. ;ternatingdirections,staggeredgrid,linearrecur- ;renceandthetwo.dimensionalplanewaterflow ;andwaterqualitymodelofimplictschemearein. ;troducedintolargewaterbodyresearchinlakes. ;Inthispaper,theeffectofsurfacewindstressis ;alsotakenintoconsideration.Thismodelhasbeen ;appliedtostudywind..drivencirculationandminer.. ;alizationdegreedistributionintheBostenLake. ;2.MATHEMATICALMoDEL

    ;Forthelakesandshallowwaterreservoirs. ;waterbodyismixeduniformlyalongthevertical ;directionbecausewaterdepthissmal1.Itisreason. ;abletodescribetheflowandconcentrationfields ;inshallowwaterwithatwo.dimensionalmodelof ;incompressible,viscousfluidandalltheequations ;areaveragedalongtheverticaldirection. ;2.1Governingequations

    ;(1)Continuityequation

    ;at+

    ;

    ;(H”)+(.

    ;(2)Momentumequations

    ;+”+au+g笔十九一一

    ;u+2u.

;+”+av+

    ;g

    ;az++

    ;+.

    ;(2)

    ;(3)

    ;where,——waterlevel;H——waterdepth;u, ;——

    ;meanvelocitycomponentsinxandYdirections

    ;respectively;f——resistancecoefficient;n——

    ;Corioliscoefficient;——turbulentviscosity; ;——

    ;windstresscoefficient;u.,Va——wind

    ;speedinthe.andyderectionsrespectively.

    ;(3)Waterqualityequation ;3t+a

    ;x

    ;+ay

    ;ax(HEa

    ;x

    ;)+ll,’,l

    ;cHE,(4)

    ;2.2Coordinatetransformation[ ;Aftercoordinatetransformation,thehydro-

    ;dynamicequationsingeneralizedcurvecoordinates

    ;becom”withrespectto

    ;andwithrespectto.

    ;Afterthetransformation,waterqualityequa.

    ;tioningeneralizedcurvecoordinatesisasfollows:

    ;

    ;

    ;+(]+1?

    ;-

    ;--sE~/(c)+z(c)]一了1?

    ;{3L-HE~L/z

    ;c)]

    ;3L-HEx(c

    ;c})]}

    ;11,3L.HEy(c

    ;c;)]

    ;3

    ;v

    ;[H

    ;J

;Ey(c;

    ;c口口)]}(8)

    ;3.NUMERICALSoLUTIoN

    ;Inordertokeepthestabilityofcalculation, ;staggeredgridwasintroducedinwhich,u,,H, ;z,Y,Cwereevaluatedatdifferentgridnodes. ;Calculationwascarriedoutwiththealterna. ;tingdirectionimplicitscheme.Eqs.(5)?(7)were ;dividedintotwogroupsalongeandr/coordinatedi. ;rections.

    ;Linearrecurrencewasusedinalternatingdi. ;rectioncalculation.Theformerhalfstepistoca1. ;culateinthedirections,,uweresolvedwithan ;implicitschemeandwithanexplicitscheme.In ;thisway,afullstepcanbeaccomplished.The ;cOncentratiOnwascalculatedsimilarly. ;4.SIMULATIoNoFFLOWFIELDANDMINER

    ;ALIZATIoNDEGREEDISTRIBUTIoNINBo

    ;STENLAKE

    ;4.1Boundaryconditions

    ;(1)Atthelakebank

    ;0,0,0,0

    ;UHo1t

    ;(2)Attheinletu,,,cweregiven.

    ;(3)Attheoutle,eregivenand

    ;0.

    ;4.2Choiceofsomecoe}}tcients

    ;(1)WindstresscoefficientE.]

    ;Asfortheatmosphericboundarylayerunder ;generalconditions,Hicksfoundthattheeffectof ;dimensionoflakescouldbeomittedandthestress ;93

    ;coefficientforasmalllakewassimilartothatused ;inoceanexperiment.Ontheotherhand,Crisa ;weakfunctionofwindspeed:

    ;C/(1.1+0.053wlo)10

    ;Whenwindspeedascendsto5m/s,Cr0.001

    ;,to15m/s,Crincreasesto0.0015linearly.When ;waterdepthislessthan2.5m,longerwavecannot ;beformedandwatersurfacemaykeepinasmooth ;state.Undersuchstate,Hicks’researchresults

    ;showedthatallC/approachto0.001.Atmospheric ;stabilityalsohaslargeinfluenceonthevalueof ;Cr.ThevalueofCfwoulddecreasebV40percent

    ;understablecondition.otherwiseitwouldincrease ;by40percent.Somepeopleclaimedthatshear ;stresscoefficientollthewatersurfacewouldin. ;creasewiththeincreaseofwindspeed.Butit ;wouldbeaconstantafterhavingincreasedtoacer. ;tainvalue.Themaximumvalueis0.0026. ;Fromapracticalviewpoint,weatherstation ;maybelocatedatacertaindistanceawayfromthe ;lake.So,theordinarymethodistoconsiderC,asa ;constant.Undermostconditons,iustasinthispa. ;per,0.013issuitable.

    ;(2)Calculationofmixingcoefficients ;Onemethodistosupposethatvelocitydistri. ;butionintheverticaldirectionaccordswiththe ;Karman?Prandtllogarithmformula.Large?dimen. ;sionturbulencemixturecoefficientEcouldcalcu. ;1ated.

    ;inanotherway,accordingtothemeasuredda. ;taofvelocityandwaterdepthincross.section. ;Fisher’sthree.scaleintegralexpressioncouldbea.

    ;doptedtoevaluateEr.Therevisionshouldbedone ;accordingtolargeeddysimulation.

    ;Forlackofmeasureddata,mixingcoefficient ;cannotbedefinedwiththeabovetwomethods. ;Oneformulacanbeformedaccordingtothese ;methodsandappliedtothepresentmodel: ;Emunh.,E:munh.

    ;where,misacoefficientwhichcanoftenbetaken ;as30.00?50.0;nistheManningroughnesscoeffi. ;cient.

    ;4.3Calculationscheme

    ;Typicalcomputationalconditionsareasfo1. ;1ows:threepositionsofeastpumpstation:650m, ;

    ;94

    ;Table1Computationparametersofvariousschemes ;Scheme

    ;Locationof

    ;eastpump

    ;station(m)

    ;Water

    ;level

    ;(m)

    ;Inflow

;(m3/s)

    ;0utflowof

    ;eastor

    ;westpump

    ;station(m3/s)

    ;Wind

    ;direction,

    ;windspeed

    ;(m/s)

    ;15kmand30kmawayfromwestpumpstation;the ;highwaterlevel1047.5m(theupperlimitinflood ;seasonintheBostenLake),themedianwaterlevel ;1046.80m(meanannualwaterlevelinthebig ;lake),andthelowlevel1045.OOm(thelowestop. ;eratinglevelinreceivingbasinoftheeastpump ;stationandlowerlimitofcontrollevelintheBO. ;stenLake);threetypicalinflowsinflood,normal ;anddryperiods;threetypicaloutflows:total ;90m/s(45m/sforeachpumpstation),total ;50m/s(25m0/sforeachpumpstation),total ;20m/s(10m0/sforeachpumpstation):different ;windpowersanddirections:SW:2.1m/s,NW: ;1.95m/s,NW:2.1m/s,SW:3.5m/s,NW:3. ;5m/s,NE:3.5m/s.Accordingtothemeteorologi. ;caldata,mainwinddirectionsandmonthlymean ;windspeedinnon-freezingperiod(fromMarchto ;November)inwholeyearwereconsidered. ;17kindsofcombinationsoftypicalparameters ;(i.e.,17schemes)wereselectedasshowninTable ;1.

    ;5.CALCULATIoNRESULTSANDANALYSiS

    ;GridisshowninFig.1.Flowfieldgivenby ;Schemes15,16,17areshowninFigs.2,3.and4 ;respectively.Mineralizationdegreeobtainedwith, ;Schemes15,16,17areshowninFigs.5,6.and7 ;respectively.Thefiguresfromotherschemesare ;omittedherein.

    ;5.1Flowfield

    ;ForthewinddirectionNWandthewindspeed ;3.5m/sofScheme16,flowfromnorthesttosouth. ;eastisformed.Owingtothelargewindspeed,the ;flowiSmoreobviousandextendslo;pump ;Statlon

    ;(15km)

;The

    ;intake

    ;ofeast

    ;pump

    ;Statlon

    ;(30km)

    ;The

    ;center

    ;oflake

    ;Huangshuiwan

    ;atnorthwest

    ;ofthe

    ;lake

    ;Scheme17,thevelocityfromnortheasttosouth. ;westofanticlockwisecirculationintheeastofthe ;lakeincreasesobviously,andflowfromnorthwest ;tosoutheastisnotobvious.Itcanbeseenfromthe ;aboveanalysisthatthechangesofwindspeedand ;directionarosethechangeofflowfieldimmediat- ;ly,whichshowsthatwindspeedanddirectionplay ;animportantroleintheformofshallowcircula- ;tion.

    ;_E3

    ;2

    ;2

    ;l

    ;0

    ;Fig.1Gridgenerated

    ;l0’m

    ;46

    ;5.2Waterquality

    ;Thelocationoftheeastpumpstationis30km ;farawayfromthewestpumpstation.Thewater ;levelis1045.00m.Inflowandoutflowissinail. ;winddirectionsandwindspeedsareSW,3.5m/s; ;NW,3.5m/sandNE,3.5m/srespectivelyinthese ;threeschemes.Itcanbeknownfromtheabove ;flowfieldanalysisthatunderthewinddirection ;.

    ;E

    ;2

    ;Fig.2FlowfieldfromScheme15

    ;E

    ;2

;Fig.3FlowfieldfromScheme16

    ;95

    ;NWandthewindspeed3.5m/sofScheme16, ;flowisformedfromnorthwesttothesoutheastof ;thelake.Thecirculationflowformedislarger ;thanthatoftheotherschemes,andthusitisinfa. ;

    ;96

    ;_

    ;2

    ;lO.m

    ;Fig,4FlowfieldfromScheme17

    ;E

    ;3

    ;2

    ;0

    ;0

    ;x710m

    ;46

    ;Fig.5MineralizationdegreefromScheme15 ;4

    ;3

    ;.

    ;2

    ;2

    ;O

    ;.Jr/1o.m

    ;Fig.6MineralizationdegreefromScheme16 ;voroftheadmixtureofthewater.Forthewind ;speed3.5m/sandthewinddirectionNEofScheme ;17,thevelocityfromnortheasttosouthwestofthe ;anticlockwisecirculationintheeastofthe1akein. ;creasesobviously.Thevelocityneartheoutletof ;thepumpstationalsoincreases.Itcanbeseen ;fromFig.7thatthedistributionofmineralization ;degreeiSeveninthewholefigure.Thecritical ;pointsofSchemes16,17arelistedinTable2area ;一盈—?l?蠡强r

    ;4

    ;E

    ;3

    ;2

    ;0O

    ;x}10Iil

;46

    ;Fig.7MineralizationdegreefromScheme17 ;littlebiggerthanthoseofScheme15,whichshows ;thatNWwindandNEwindfacilitatetheformof ;thelargecirculationflow,infavoroftheadmix

    ;tureofthewater,thereforeinfluencethewater ;qualityindirectly.

    ;6.CoNCLUSIoNS

    ;(1)Inthispaper,atwo.dimensionalmodel ;forplanewaterflowandwaterqualityisdeveloped ;byusingcoordinatetransformation,alternatingdi

    ;rections,staggeredgrid,linearrecurrenceandim

    ;plicitschemeinthestudyoflargewaterbodyin ;lakeswhichcantotallyfittheirregularlakebound

    ;ary?

    ;(2)ThismodeliSprovedtobevalidbythe ;simulationonwaterflowandqualityintheBosten ;LakeinXinjiang.

    ;(3)Researchonvariousinflowsandoutflows ;showsthatthechangeofinflowandoutflowhasno ;obviousimpactonflowfield.

    ;(4)Windspeedanddirectionhaveimpacton ;flowfieldandfurtheronwaterquality.Whenthe ;winddirectioniSSW,ananticlockwisemaincircu. ;1ationiSformedinthesoutheastofthelake.OW. ;ingtotheblockofthebank,itturnstothenoth. ;teastofthelake,thusanunclosedanticlockwise ;circulationiSformedintheeastofthelake.When ;thewinddirectioniSNW,flowfromnorthwestto ;southeastiSformedbesidesthemaincirculationin ;theeast.ofthelake.WhenthewinddirectioniS ;NE.thevelocityfromNEtoSWoftheeastanti. ;clockwisecirculationincreasesobviously. ;(5)Thechangeofwaterlevelhasnoobvious ;influenceoncircularflow:themineralizationde. ;greedecreaseswithincreasingwaterleve1.. ;(6)Thechangeofpumpstationpositiondo ;

    ;notbringaboutobviousvariationofflowfieldand ;mineralizationdegree.[2]

    ;REFERENCES

    ;[1]FENGMinquan.Twodimensionalplaneandvertical ;flowfieldandwaterqualitynumericalsimulationof ;largelakeandreservoirI,D].Xi’an:Xi’anUniversity

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