外文翻译明渠中非恒定流和非均匀泥沙输移的二维数值模拟节选.docx
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外文翻译明渠中非恒定流和非均匀泥沙输移的二维数值模拟节选.docx
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外文翻译明渠中非恒定流和非均匀泥沙输移的二维数值模拟节选
中文2500汉字,1500单词。
8700英文字符
出处:
JournalofHydraulicEngineering,2004,130(10):
págs.1013-1024.
附录
附录一、英文原文
Depth-AveragedTwo-DimensionalNumericalModelingofUnsteadyFlowandNonuniformSedimentTransportinOpenChannels
WeimingWu,M.ASCE1
Abstract:
Adepth-averagedtwo-dimensional(2D)numericalmodelforunsteadyflowandnonuniformsedimenttransportinopenchannelsisestablishedusingthefinitevolumemethodonanonstaggered,curvilineargrid.The2DshallowwaterequationsaresolvedbytheSIMPLE(C)algorithmswiththeRhieandChow’smomentuminterpolationtechnique.Theproposedsedimenttransportmodeladoptsanonequilibriumapproachfornonuniformtotal-loadsedimenttransport.Thebedloadandsuspendedloadarecalculatedseparatelyorjointlyaccordingtosedimenttransportmode.Thesedimenttransportcapacityisdeterminedbyfourformulaswhicharecapableofaccountingforthehidingandexposureeffectsamongdifferentsizeclasses.Anempiricalformulaisproposedtoconsidertheeffectsofthegravityonthesedimenttransportcapacityandthebed-loadmovementdirectioninchannelswithsteepslopes.Flowandsedimenttransportaresimulatedinadecoupledmanner,butthesedimentmoduleadoptsacouplingprocedureforthecomputationsofsediment
transport,bedchange,andbedmaterialsorting.Themodelhasbeentestedagainstseveralexperimentalandfieldcases,showinggoodagreementbetweenthesimulatedresultsandmeasureddata.
Introduction
Becauseofthecomplexityoftheturbulentflowswithfreewatersurfaceandmovablechannelbed,thenumericalsimulationofflowandsedimenttransportinopenchannelsisverychallenging.Itsadvancementcanbeattributedtomanysuccessfulnumericaltechniquesdevelopedinthefieldofcomputationalfluiddynamics.Amongthesetechniques,thestaggeredgridapproach(HarlowandWelsh1965;Patankar1980)andRhieandChow’s(1983)momentuminterpolationmethodonanonstaggeredgridhavebeenwidelyadoptedtosolvetheNavier–Stokesequationsofincompressibleflows(Peric1985;Majumdar1988;Zhu1992;andothers).Wenka(1992)andMinhDuc(1998)appliedtheRhieandChow’smethodtothedepth-averagedsimulationofsteadyandunsteadyopen-channelflows.Inthepresentstudy,theMinhDuc’sformulationismodified,andadepth-averagedtwodimensional(2D)numericalmodelforunsteadyopen-channelflowisestablished.
Sedimenttransportmodelingstartedinthe1950sandhasbeenextensivelydevelopedandwidelyappliedtoreal-lifeengineeringsincethe1970s.Severalsuccessful1Dmodels(Han1980;Chang1982;Thomas1982;HollyandRahuel1990;WuandVieira2002)havebeen
establishedtocalculatethelong-termchanneldepositionanderosionunderquasi-steadyandunsteadyflowconditions.Inrecentyears,many2Dand3Dsedimenttransportmodels(Shimizuetal.1990;SpasojevicandHolly1990;Olsen1999;MinhDuc1998;Wuetal.2000a;andothers)havealsobeenestablishedtosimulateinmoredetailthechannelevolutionincomplexsituations.Usuallythesemodelssimulatesuspendedloadtransportusingthenonequilibriumtransportapproach,butmanyofthemadopttheassumptionoflocalequilibriumwhensimulatingbed-loadtransport.Recentstudiesonthespatialandtemporallagsofbed-loadtransportshowthatthenonequilibriumtransportmodelforbedloadisalsoneededinmanycases,suchasstrongerosionandstrongdeposition,especiallyunderunsteadyflowconditions.Inaddition,thehidingandexposurephenomenathatexistinnonuniformsedimenttransportplayanimportantroleinbedmaterialsortingandchannelbedarmoring.Thesedimenttransportmodeldescribedinthispaperadoptsthenonequilibriumtransportapproachforbothbedloadandsuspendedload,andtakesintoaccountthehidingandexposuremechanismthroughtheintroductionofcorrectionfactorsinthenonuniformsedimenttransportcapacityformulas.
Althoughinatwo-phasesystemflowandsedimentalwaysinteractwitheachother,thecalculationsofflowandsedimentwerefullydecoupledinearlydevelopmentstages.Recently,severalcoupledmodels
havebeenreported(HollyandRahuel1990;andothers).Afullycoupledmodelisusuallymorestablethanadecoupledmodel.However,establishingafullycoupledmodelrequiressolvingalltheflowandsedimenttransportequationssimultaneously.Thenonlinearityofflowproblemmayreducetheefficiencyofsedimenttransportsimulation,whichcanbemathematicallysimplifiedtoalinearproblem.Inaddition,thetimescalesofflowandchannelmorphodynamicprocessesmaybedifferent,especiallyinthecasewherebedloadisdominant.Thereforefullycouplingtheflowandsedimenttransportmaynotbecost-effective.FollowingWu(1991)andWuandVieira(2002),thepresentmodeladoptsa“semicoupling”procedure,inwhichtheflowcalculationisdecoupledfromsedimentcalculation,butthethreecomponentsofthesedimentmodule(sedimenttransport,bedchange,andbedmaterialsorting)aresolvedinacoupledfashion.Thissemicouplingprocedureisverystableandefficientcomputationally.
GoverningEquationsandBoundaryConditionsGoverningEquationsofOpen-ChannelFlow
Thedepth-integratedcontinuityandmomentumequationsofopen-channelfloware
wheret=time;xandy=horizontalCartesiancoordinates;h=flowdepth;U
andV=depth-averagedflowvelocitiesinxandydirections;
Zs=water
surfaceelevation;g=gravitationalacceleration;r=densityofflow;Txx,
Txy,Tyx,andTyy=depth-averagedturbulentstresses;
τbx
and
τby=bed
shearstressesthataredeterminedbyand
;
inwhichn=Manning’sroughnesscoefficientandw=bedanglewiththehorizontal.
TheturbulentshearstressesaredeterminedbytheBoussinesq’sassumption
whereν=kinematicviscosityofwater;
νt=eddyviscositydueto
turbulence;andk=turbulenceenergy,whichisdroppedfromEqs.(4a)and(4c)whenthezero-equationturbulencemodelsareused.
Severalturbulencemodels,includingthedepth-averagedparaboliceddyviscositymodel,themixinglengthmodel,thestandardκ-εturbulencemodel(Rodi1993),andtherenormalizationgroup(RNG)
κ-εturbulencemodel(Yakhotetal.1992)havebeenimplementedin
theproposedmodeltodeterminetheeddyviscosity
νt.Inthepresent
paper,onlythedepth-averagedparabolicmodelandthestandard
κ-εturbulencemodelareused.Inthedepth-averagedparabolicmodel,
theeddyviscosityiscalculatedby,inwhich
U*=bedshear
velocityand
0.3and1.0.
αt=empiricalcoefficientbetween
Inthestandardκ-εturbulencemodel,νtiscalculatedwith
νt.HereCμ=empiricalconstant.Theturbulenceenergykand
itsdissipationrateεaredeterminedwith
where
and
=empiricalcoefficients.Thestandardvaluesofthesecoefficientsare
and
GoverningEquationsofSedimentTransport
Thetotalloadisusuallyseparatedasbedloadandsuspendedloadregardingsedimenttransportmode,ordividedintobed-materialloadandwashloadaccordingtosedimentsource.Thereforetotalloadtransportcanbemodeledwithtwoapproaches,eitherseparatelyasbedloadandsuspendedload,orjointlyasbed-material
load(washloadusuallyisignoredinthesimulationofbedmorphologicalchanges).
Theadvection-diffusionequationofsuspended-loadtransportis
where
=depth-averagedconcentrationofthekthsizeclassofsuspendedload;
=depth-averagedsuspended-loadconcentrationunderequilibriumconditionsorthesuspended-loadtransportcapacity;
=diffusivitycoefficientofsediment;α=nonequilibriumadaptationcoefficientofsuspendedload;and
=settlingvelocityofsedimentparticles.
Themassbalanceequationinthebed-loadzoneis
whereδ=thicknessofbed-loadzone;
=averageconcentrationofbed
loadatthebed-loadzone;
αbx
and
αby=directioncosinesofbed-load
movement,whichareusuallyassumedtobealongthedirectionofbedshearstress,butareadjustedwhentakingintoaccounttheinfluenceofthesecondaryflowincurvedchannelsandtheeffectofthegravityover
steepslopes;
=actualtransportrateofthekthsizeclassofbedload;
=porosityofbedmaterial;and
=bedchangeratecorrespondingtothekthsizeclassofsediment.
Forbed-loadtransport,Wellington(1978);Phillipsand
Sutherland(1989);Thuc(1991);andWuetal.(2000a)adoptedarelation
todeterminethebedchange.Here,
=bed-loadtransportcapacity,and
=nonequilibriumadaptation
lengthofbedload.Thisrelationcanbeusedwhenbedloadisthemaintransportmode.Similarly,whenthesuspendedloadisdominant,thebed
changecanbedeterminedby
.
However,ingeneralsituationsoftotal-loadtransport,thebedchangeshouldbedeterminedby
where
=actualtotal-loadtransportrate;
=total-loadtransportcapacity;andL=nonequilibriumadaptationlengthoftotalload.
Inserting
and
inEq.(9)gives
where
and
.Usuallywecanassume
.Therefore,insertingEq.(10)inEq.(8)leadstothefollowing
nonequilibriumbed-loadtransportequation:
Thegoverningequationofbed-materialloadcanbederivedbysumming
Eqs.(7)and(11).Asanextremecase,ifsedimentsmovemainlyasbedload,thediffusionofsuspendedloadisnegligibleandtheresultinggoverningequationforbed-materialloadissimilartoEq.(11),with
and
beingreplacedbytheactualtransportrateandtransport
capacityofbed-materialload.However,ifthesuspendedloadisthedominanttransportmode,theresultinggoverningequationfor
bed-materialloadissimilartoEq.(7),with
and
being
replacedbythequantitiesofbed-material
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