1、大气绕山体的运动及其输移特性的研究第 24 卷第 4 期2007 年 8 月计算力学ChineseJournalofComputationalMechanicsVo1.24,No.4August2007文章编号:1007-4708(2007)04 047705NumericalmodelingofatmosphericflowanddispersionaroundamountainLILing,KIMURAShigeo(1.DepartmentofHydraulicEngineering,TsinghuaUniversity,Beijing100084,China2.InstituteofNa
2、tureandEnvironmentalTechnology,KanazawaUniversityKanazawa9208667,Japan)Abstract:Aseriesofnumericalexperimentshadbeenconductedtoinvestigatetheflowpatternsanddispersioncharacteristicsaroundamountainunderstablystratifiedflow.Thetwo-dimensionalmodelequations,basedonthetime-dependentReynoldsaveragedNavie
3、r-Stokesequations,weresolvednumericallyusinganimplicittimeintegrationinbody?fittedgridarrangement.Thebehavioroftheflowisclarifiedtoascertaintheeffectsofchangesinthestratification,whichischaracterizedbytheFroudenumberFU/NH(WhereUisspeedoftheapproachingwind,NistheBruntVaisalafrequency,andHisthemountai
4、nheight).ThenumericalresultssuggestthattheflowstructureisindependentofstratificationwhenF4.0.ThemodelpredictsleewavegenerationastheFroudenumberisdecreasedfrom4to1,thenflowsplitting,wavebreakingphenomenahappenasFisfurtherdecreasedtolessthan1.0.Further,themode1.predictedconcentrationfieldswhentheconta
5、minantiscomingwiththeapproachingwindshowthatthestratificationofatmosphericflowhassignificanteffectsonthedispersionpattern.Keywords:numericalmodeling;stratifiedflow;atmosphericflowaroundamountain;pollutantdispersion1IntroductionFlowstructurearoundamountainchangesdrasticallywithstratification,.Afundam
6、entalcharacteristicoftheflowistheproductionofleewaves,whichcanpersistforlongdistancedownstream.Whentheamplitudesofleewavearelarge,wavebreakingcanoccur,andunderthesecircumstancesstreamlinereversalleadstoalocalregionofstaticallyunstableflowwheremixingoccurs.Itisalsowellknownthatatmosphericstabilityhas
7、significanteffectsonflowanddispersionpatternsovertopography.Underunstablecondition,flowovermountainmaybeexpectedtobemoreturbulent,causinganycontaminanttodispersemorerapidly.Ontheotherhand,stablestratificationtendstodampenturbulentmixing,especiallyintheverticaldirection.Itinhibitspollutantdispersion引
8、.DespitetheirpracticalimporReceivedby:2005-0630;Revisedby:20060320.PmjectsupportedbySRFforROGS,SEM.Correspondingauthors:LILing(1970 一),Female,Dr,AssociateProfessor.1ancetoaeronauticsandairpollutiondispersion,thedistinctionsamongthesephenomenaarestilllittleknown.Moreover,theeffectsofstratificationonf
9、lowanddispersionpatternarealsofarfromclear.Verylittleresearchhasbeenconductedusingnumericalsimulationtodeterminetheeffectsofatmosphericstablestratificationontheflowovertopography.Thepresentworktriestoinvestigatethesignificanceofthestratificationeffectontheflowanddispersionpatternsbyusinganumericalmo
10、de】.2Numericalmethod2.1ModelequationsThegoverningequationsforunknownvariables“f 一(,), D,PandCconsistoftheContinuity,NavierStokes,DensityandConcentrationequations.Theequationsarewritteninthegradientformasfollows:一0(1)478 计算力学第 24 卷一a(pui)8t+8x一8xg+III6I去(,dau,+auj)8t+型 3xi 一一 (3)+一去(DaC8t8x8x8x)(4)if
11、,WheredandP|istheperturbationdensityandpressuredefinedasID=ID 一,P 一 PPB,xi=(z,y)arethephysicalcoordinatecomponents,f 一(,)arethecorrespondingphysicalvelocitycomponents,c|istheeffectiveviscositycoefficient(sumofthemolecularandturbulentviscosity),一+f.Thek-modelprovidesclosureforturbulence.gistheacceler
12、ationduetogravity.Deffistheeffectivediffusioncoefficient,DeffD+,DisthediffusiVity,SstheturbulentSchmidtnumber.Areferenceatmosphericstateisdefined,whichcorrespondstoanatmosphereinhydrostaticequilibrium.StartingfromarealtemperatureprofileTB(),dTB()/dy 一一 0.006“C,thehydrostaticpressureprofilePBisobtain
13、edbynumericallyintegratingdpB 一一gdy,assumingtheprefectgaslawpBpB/RTBisverifiedforeachaltitudey.Thecompletesetofequationsissolvedonastructuredgridbymeansofafinite-volumeapproach.PressureandvelocityarecoupledthroughtheiterativeSIMPLEalgorithm引.2.2ComputationaldomainandboundaryconditionsNumericalcalcul
14、ationisperformedonthedomainofwhichlateralboundariesarelocatedat22.5kminzdirection,whilethetopboundaryislocatedaty 一 17km.Allnumericalsimulationsusethesamemountainshape(z)一再 h0wherehoistheheightofthemountain,andaishalfwidthofthemountaincenteredatzo.Inthesenumericalsimulations,wechoseho 一 900mand一】000
15、m.Thiskind0fmol】ntainhasbe-anusedinpreviouswork.Montavon1998,LucaBonaventura2000andL.Klassen2003).Inordertovalidatethemathematicalmodelsandnumericalmethod,theschemehasbeentesttocomparetheresultswiththesametestcaseproposedinthereferenceE8,103.Uniformhorizontalvelocityandalineardensityprofilearespecif
16、iedatinflow.Theturbulentkineticenergyissetat0.001m/sandthedissipationrateissetat1.010 一 m2/s.atinflow.Thecontaminantconcentrationisset1.0inthelayerbetween900mandl100matinflow.Simpiezerogradientconditionsareappliedforallvariablesatoutflow.A“movingwallconditionisappliedatthetopofthedomain.Noslipbounda
17、ryconditionsareappliedtothemountainsurfaceandground.Inournumericalsimulations,theFroudenumber(F)isusedasaquantitativemeasureofthestablestratificationwithuniformapproachingflow.F_U/NHN 一(一 gd)V.(5)Withtheheightofthemountainhofixed(900m)andvelocityofapproachflowsUfixed(13.28m/s),Fcanbechangedonlybyvar
18、yingNanddpffdyinoursimulation.3Resultsanddiscussions3.1validationofmathematicalmodelsandnumericalmethodAtestwasperformedassuminga=1000m,ho 一 900mandinitialhorizontalvelocityUl3.28m/s.Forthistestcase,temperaturehasbeenchosensothatN 一 0.02S-andF 一 0.74.ThesametestcaseproposedinthereferenceE83wasalsope
19、rformed.Thehorizontalvelocityandpotentialtemperaturecontoursobtainedattimet:=2400sareplottedinFig.1.Theresultsagreewellwiththoseofreference8-.Itcanbeobservedthatthesteepwavepatterndownstreamoftheobstacleiswellreproduced(see,己 g,theanalyticalsolution第 4 期李玲,等:大气绕山体的运动及其输移特性的霉 479Dresentedinthereferen
20、ce(Miles,1968)forsimilarcase)andthattheflowacceleratesdowntheslopeasexpected.Inthiscase,astationYLeewaveformsinthevicinityofthemountam,andaverticallypropagatinggravitywaveISalsogeneratedandpropagatesalongwiththeinternal要Fig.1(a)Horizontalve|odtyinthetestca.O3.2Flowpatternofatmosphereflowaroundmounta
21、in0therfournumericalsimulationsusingdifferentFroudenumbers,rangingfromF=1?0toF=4.0,werecarriedout.Underneutralandslightlystablestratification(F4),nearlyhozontalflowisobservedjustaboveanddownwind0fthemountainasshowninFig.2(a).Thequasijump.ThereexistbothwaVebreakingaloftandupstreamblocking.Theflowisdy
22、namieallyunstableintheregionofwavebreaking.Ithasshownthatthenumeriealmodelcanbeusedtosimulateatmosphericflowsovercomplextopography.互Fig.1(b)Potentialtemperatureinthetestc.seOtheDeriodicstructureofthegravitywaveisalreadyformedinthedomainbetweenthemountamandupperboundaryasshowninFig.2(bc)?WhenFisdecre
23、asedto1,thestructureofleewaveiswe11reproducedasshowninFig.2(d)?TheflowacceleratesdownthemountainandthestructureofthestreamlinenearthemountamISwe11resolvedtoconfirmtheexistenceoftheleesymmetricalstructureoftheflowiswellrealized?waVes?WhenFroudenumberFisdecreasingfrom4to(a)N=O.00369,4(c)N=0.0l18,1.25(
24、b)N=0.00738,2Fig.2Isolinesofthehorizontalvelocity(d)N=0.0148,F=I.0gE25002000E15001000500暑O4Conclusions(d)N=0.0148.F=IFig.3ConcentrationcontOursAseriesofhumericalsimu1ationshadbeen.nductedin.rdert.examinetheeffects.fstabletratificationontheflowpatternanddispersionoVeramountain?Thenumericalsimulationr
25、esu1tsshowthatthefI.wfieldbecomeessentia11yindependen.fFwhenF4.Thefl.wstructureis第 4 期李玲,等:大气绕山体的运动及其输移特性的研究 481onlyweaklydependentonstratificationforF2.Strongstablestratification,ascharacterizedbyF2,ontheotherhand,haslargeeffectsontheflowstructure,inparticular,whenFislessthan1.Theconcentrationfield
26、sarealsocalculatedandtheresultsshowthatturbulentdiffusionplaysflmoreimportantroleascomparedwithmeanadvectionindispersingtheeffluentfromfllayerlocatedintheheightof900m1100m,especiallyunderstronglystratifiedcondition(F2).Itisessentialtoaccuratelysimulatetheturbulentflowfieldoverthemountainforimproving
27、theaccuracyoftheconcentrationfieldsinthemode1.Itisprovedthatk 一turbulentmodelusedinthenu-mericalsimulationcandoitwel1.References:12334BAINESPG.UpstreamblockingandairflowovermountainsJ.AnnuRevFluidMech,1987,19:7597.SMITHRB.HydrostaticairflowovermountainsJ.AdvancesinGeophysics,AcademicP55,1989,31:l 一
28、41.SNYDERWH.SomeobservationsoftheinfluenceofstratificationondiffusioninbuildingwakesA.StablyStratifiedFlows:FlowandDispersionourTopographyM.1994:301324.ClarendonPress,Oxford,England.I|AUNDERBE,SPAI,DINGDB.MathematicalModelsofTurbulenceM.AcademicPress,NewYork.1972.53VANDOORMAL,G.D.Raithby,EnhancementoftheSIMPLEmethodforpredictingincompressiblefluidflowsU.NumerHeatTransfer,1984,7:147-163.6LINYL,WANGTA.Flowregimesandtransientdynamicsoftwodimensionalstratifiedflowoveran
