河冰演变过程分析的一维数学模型研究

225201110JournalofWaterResources＆WaterEngineeringVol．22No．5Oct．20112011-06-131956-。3000723。、3、。、。3。、。P343．63A1672-643X201105-0078-06One－dimensionalmathematicalmodelsofrivericeevolvingprocessXUGuobinStateKeyLaboratoryofHydraulicEngineeringSimulationandSafetyTianjinUniversityTianjin300072ChinaAbstractNormallyaccordingtotheiceformationandmeltingprogressesrivericephenomenacanbedividedintothreestepsiceperiodfreeze－upperiodandfrostfreeperiod．Arivericemathematicalmodelwhichcancompletelydescribetheprocessesofthesethreestepsismadeupofthreepartialmod-elshydraulicthermo－mechanicalandfrozenmodels．Hydraulicmodelsareappliedtocalculatetheflowfieldandotherhydraulicelements．Thermo－mechanicalmodelsareusedtocalculatetheheatex-changeswater－temperaturedistributionandthecoolingprocesses．Frozenmodelsarecapableofsimu-latingfraziliceformationiceflowerandsuspendedicetransportationanchoricegrowthanddecayicecovergenerationprogressionandaccumulationthermalgrowthanddecayoficecoverthepotentialtransportabilityoficecoverleadingedgeandicejamevolutionprocesses．Thesethreemodelsinteractwitheachotherhydraulicconditionsaffectthermalexchangeandfreezingprocessesthermalconditionsdeterminefreezingprocessesfreezingprocessesinturnaffecthydraulicconditionsandthermalcondi-tions．Thestudypresentsaone－dimensionalmathematicalmodelwhichcancompletelydescribetheprocessesoficeformationfreezingupandmelting．Moreovereverypartialmodelcanalsobeusedtocalculateaspecificiceprocess．Keywordsrivericehydraulicmodelsthermo-mechanicalmodelsfrozenmodelsmathematicalmodels。3。0℃。。。。。。。。80%。。。。。。。、。1－10、。、3、。、。3。、。1。。。。。。。n=χbnb3/2+χini3/2χb+χ()i2/31χbmnbχimni111。1/d1～1011～3031～50510．080～0．0400．050～0．0200．030～0．0150．025～0．0150．100～0．0500．060～0．0300．040～0．0250．030～0．02022．1。。。1dMJ/m2·d106J/m2·d。∑S11∑S=S1+S2+S8+S9－S3+S4+S5±S6+S7+S102∑SS1S2S3S4S5S6S7S8S9S10MJ/m2·d。S1、S2、S8、S9S3、S4、S5S6、S7、S10。∑S。S1～S1011。。975。11∑Si=kiw∑S3∑SiMJ/m2·d∑SMJ/m2·d2kiw0．205～0．972。2kiwcm3581010．970．950．920．9030．960．930．880．8550．910．850．760．70100．880．800．680．60200．830．710．540．42300．810．680．490．36400．790．650．440．30500．780．630．410．26600．750．600．380．2052．2。。9tAρCPTw+xQρCPTw－xExAρCPTwx+B∑S=04Am2ρkg/m3CpCp=0．0042MJ/kg·℃Tw℃Qm3/sExm2/sBmt、xs、m∑SMJ/m2·s23。3。。3、3。。3．10℃。12Qwi=η0B∑SLiρi5Qwim3/d·mη0η0=1－CaCaBmLiLi=0．335MJ/kgρiρi=917kg/m3∑SMJ/m2·d。3．29Qi=AvCi6Qim3/sAm2vm/sCi。69tACi+Qix－xExACix+Qwi－αisωisCiB－βibv*crCiB=07Exm2/sQwim3/s·mαisωism/sωis=vzCi－EzCi/z/Civzm/sEzm2/sβibv*crm/s。3．3。08201169tAaCa+Qax－xExAaCax+αiωsCiB=08CaAam2Aa=Bδiu+1－εfδidQam3/sδiumδidmεfExm2/s。δa=δiu+1－εfδid9Qa=vCaBδa93．4。。10dΔibdt=11－εibβiv*crCi+SwiρiL()i10Swi=kwiTi－TwdΔib/dtεibv*crm/sSwiMJ/m2·skwiMJ/m2·s·℃Ti0℃Tw℃。①Tw≥0℃。②v*crv*cr1v*cr2。βi=0。。。v*cr1=0v*cr2=∞。。。。10ρiLiddthsbebs1－εib=Siwebs11Siw=kiwsTw－Twi+SpzSiwMJ/m2·shsbmebsSpzMJ/m2·skiwsMJ/m2·s·℃Twi0℃。hsb＞hc。hchc=0．4dd。。101－εibVibρ－ρi＞Wb+Fb12VibmWbkg/m2FbWb。3．5、。。1。。。、5。vv013。v＜v0=∑S1130－1．1－Tw－15vf113013∑SMJ/m2·dTw℃vfm/s。。1859。ΔB=14．1∑SρLivv()0－0．93Ca1．0814ΔBv0m/s13Ca。v＞v0。2。。。。、。v9vcp=Qa－Qb*Bδ01－εj－Qa－Qb*/v15δ0mBmQam3/s9Qb*m3/s23εjεj=εp+1－εpεcεpεc。。1δ0δa。。FrpFrc。Frc9Frc=f1－δa()h·2g1－ρiρ1－εcδa[]h1/216fδa/la0．66～1．3δa、lamhmρ、ρikg/m3εc。Frc0．05～0．06。FrpFrp=v槡gh17vm/shm。2FrpFrc。。。Frp9Frp=1－δ0()h21－ρiρ1－εcδ0[]h1/218δ0m。FrpFrm。Frm0．05～0．114Frm=0．1581－ε槡c19。。0．6～1．3m/s0．08。1988Frm0．09。3、。。。92τcδ0+μlFl=τs+τg+τfB20τckN/m2μlFlkNτskN/m2τgkN/m2τfkN/m2。2τcδ0+μlFl＜τs+τg+τfB、。3．6282011。。。。。。。。、－。－Stefan15δit=kis∑tζis21δit∑tcmkisζis∑t℃。《》SL278－2002－kis、ζis。ζis=0．50～0．56kis=2．0～2．3ζis=0．50～0．56kis=2．6～3．0。12δim=8．3Φ－27822δimcmΦ36°～54°N。3．7。Frm。。。10=5．487Θ－Θc1．523=qb*/diωsqb*m3/s·mdimωsm/sωs=kwg1－ρi/ρd槡igm/s2kω1．0ΘΘ=v2i*/ω2svi*m/s24ΘcΘc=0．041。7vi*槡=gRJ24R=hiw1+nb/ni3/2J=v2n2hiw/2．04/3RmJhiwmnbnin。。qibδ0101－εuδijt+qibx=025δijmεu0．4。4、、。1PetrykSCarsonRHodgingsDetal．DevelopmentofacomprehensivenumericalrivericemodelC∥．ColdRe-gionsHydrologyandHydraulics．PublisherASCE1990739－760．2SaadeRGSarrafS．Simulationoficecovermeltingintur-bulentflowJ．InternationalJournalofNumericalMethodsforHeatandFluidFlow199557647－653．3MaXFukushimaY．Anumericalmodeloftheriverfreez-ingprocessanditsapplicationtotheLenaRiverJ．HydrologicalProcesses200216112131－2140．4ShenHT．MathematicalmodelingofrivericeprocessesJ．ColdRegionsScienceandTechnology20106213－13．8738521999－2002%1234567891011121999000000．20．20．300000．0620000000001．31．200000．2020010000000000000200200008．30．200．300000．7300008．30．41．51．800000．99120002001。199920021%。。。21999－200210%。。3、。。WRMM。。。1MckinneyDCCaiX．LinkingGISandwaterresourcemanagementmodelsanmethodanobjectorientedmethodJ．EnvironmentalModelingandSoftware2002175413－425．2PA．J．2004171－5．3．J．2008392183－188．4．J．200940160－66．5AlanAlbertaEnviromnentNaturalResourcesServiceBowRegionWaterAdministrationBranch．WaterResourcesManagementModelComputerProgramDescriptionM．Canada檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵檵1999．835．J．198920154－60．6．J．2002331040－47．7．J．2003146700－705．8．J．2009202293－297．9WasanthaLalAMShenHT．Mathematicalmodelforriv-ericeprocessesJ．JournalofHydraulicEngineering19911177851－867．10ShenHTWangSWa