Visualization Tools for Vorticity Transport Analysis in Incompressible Flow_图文_百度文库
Visualization Tools for Vorticity Transport Analysis in Incompressible Flow
AppearedinIEEETRANSACTIONSONVISUALIZATIONANDCOMPUTERGRAPHICS,VOL.12,NO.5,SEPTEMBER/OCTOBER2006
VisualizationToolsforVorticityTransportAnalysisin
IncompressibleFlow
FilipSadlo,RonaldPeikert,Member,IEEE,andMirjamSick
Abstract—Vorticesareundesirableinmanyapplicationswhileindispensableinothers.Itisthereforeofcommoninteresttounder-standtheirmechanismsofcreation.Thispaperaimsatanalyzingthetransportofvorticityinsideincompressibleflow.Theanalysisisbasedonthevorticityequationandisperformedalongpathlineswhicharetypicallystartedinupstreamdirectionfromvortexregions.DifferentmethodsforthequantitativeandexplorativeanalysisofvorticitytransportarepresentedandappliedtoCFDsimulationsofwaterturbines.Simulationqualityisaccountedforbyincludingtheerrorsofmeshingandconvergenceintoanalysisandvisualization.Theobtainedresultsarediscussedandinterpretationswithrespecttoengineeringquestionsaregiven.
IndexTerms—Flowvisualization,vorticitytransport,unsteadyflow,linkedviews.?
1INTRODUCTION
ity.Toourknowledgevorticityhasalwaysbeenvisualizedasawhole.Butwebelievethatadeeperunderstandingofthedifferentmecha-nismsinvolvedinthedynamicsofvorticitycanbeobtainedonlybyvisualizingtheindividualtermsofthevorticity(transport)equation.Themaincontributionofthispaperisasetoftoolsfortheexplo-rationofvorticitydistributionandvorticitytransport.Thelatterisdescribedbythevorticityequationcontainingseveraltermsthatcanbeseparatedbytheirphysicalmeaning.Additionaltermsoccuriftheviscosityisnotuniforme.g.becauseatwo-equationturbulencemodelisused.Fortheinteractivestudyofsuchmultimodaldataitisbenefi-cialtohavemultiplelinkedviewsavailable[4],combiningtechniquesfromscientificandinformationvisualization.Section2givessomebackgroundonvorticitytransportandtheex-tensionofthevorticityequationtothecaseofnon-uniformviscosityandhencetwo-equationturbulencemodels.MethodsforthevisualanalysisofvorticitytransportinincompressibleflowaredevelopedinSection3.InSection4thesemethodsareappliedtoindustrialCFDsimulationsinhydromechanicalprojectsandinterpretationsofthere-sultsaregiven.
2VORTICITYTRANSPORT
Inthissectiontwoversionsofthevorticityequationaredescribed.ThefirstversionisapplicabletoCFDsimulationswithknownuniformviscosity,orinareducedmannertosimulationswithunknownviscos-ity.Thesecondversionisapplicabletosimulationswhereaspatiallyvaryingviscosityisgivenandknown.Thisisoftenthecasebecauseturbulencemodelsleadtospatiallyvarying(modified)viscosityevenforfluidswithuniformviscosity.Scalarquantitieswhichwillbeusedfortheanalysisarederivedforbothversionsofthevorticityequation.
2.1VorticityEquationforIncompressibleFlow
TheflowsimulationstobevisualizedarebasedontheNavier-Stokesmomentumequationfordivergence-freeflowwithuniformdensityandviscosity:?p?u+u·?u=-+ν?2u,(1)?tρ
withpressurep,densityρ,kinematicviscosityν,divergence?·,and
Laplacian?2.TakingthecurlofEquation1andapplyingseveralvectoridentitiesleadstothevorticityequation(thereaderisreferredtoe.g.[3]forafullderivation):Flowqualitymostlydeterminestheoperationofturbomachinery.Es-peciallyvorticesareknowntoaffectitsoperation.Itisthereforeofcommoninteresttounderstandandtolocatethemechanismsofvor-texdevelopment.Themethodstobepresentedarebasedonthecurlofvelocitycalledvorticityandusuallywrittenasω=?×uwhenuisthevelocity.Vorticityrepresentstheorientationandangularvelocityoflocalrotationandthereforeitisoftenusedasacriterionfortheex-istenceofvortices.Dependingontheapplication,thestudyofvorticescanbeaccomplishedbyfindinghighvorticitymagnitudes.SilverandWang[12]identifiedvorticesbyconnectedisosurfacecomponentsofvorticitymagnitudeanddevelopedanalgorithmfortrackingthemovertime.Strawnetal.[13]computedvortexcorelinesasheightridges[5]ofvorticitymagnitude.Alsothedirectionalinformationofthevor-ticityfieldhasbeenusedinthecontextofvortexvisualization.BanksandSinger[2]basetheirdefinitiononvorticityandpressure,whileLevyetal.[8]defineavortexcoreasaregionwherenormalizedhe-licityiscloseto-1or+1.Helicityisthescalarproductofvelocityandvorticity,andnormalizedhelicityisobtainedbynormalizingbothvectorspriortotakingtheproduct.Itwasshown[10]thatfromthisdefinitionofacoreregionacorelinecriterioncanbederivedbylocat-ingthepointswherevelocityandvorticityareparallel(orantiparallel)vectors.Therearealsovortexcoredetectionmethodsthatarenotex-plicitlybasedonvorticity,inparticulartheλ2methodbyJeongandHussain[6]andthemethodbySujudiandHaimes[14].Bothofthesemethodsarebasedonthevelocitygradientandhencemakeimplicituseofvorticity.Ontheotherhandvorticityisalsopresentinshearflowthatdoesnotexhibitswirlingmotionatall.AnexampleisthePoiseuilleflowthroughacylindricalpipe.Ithasaquadraticvelocityprofileandthere-forevorticitymagnitudeincreaseslinearlytowardsthewall.Inmorecomplexflowfields,suchasthoseoffluidmachines,theshearflowcanseparatefromtheboundary,thiswaytransportingvorticityintothein-terioroftheflow,andpossiblydevelopingintoavortex.Becausethevorticityfieldisdivergence-free,itcanbevisualizedbyvortexlines(integralcurvesofvorticity)suchthattheirdensityisproportionaltothemagnitudeofthefield[11].Larameeetal.[7]useatextureadvec-tionmethodforexploringtherelationshipbetweenvelocityandvortic-oF.SadloandR.PeikertarewiththeComputerGraphicsLaboratory,ComputerScienceDepartment,ETHZurich,Switzerland.E-mail:{sadlo,peikert}@inf.ethz.ch.oM.SickiswithVATechHydro,Zurich,Switzerland.E-mail:mirjam.sick@vatech-hydro.ch.
Manuscriptreceived31March2006;accepted1August2006;postedonline6
November2006.
Forinformationonobtainingreprintsofthisarticle,pleasesende-mailto:
tvcg@computer.org.?ω+u·?ω=ω·?u+ν?2ω.(2)Thefirsttermontherighthandsidecanbedecomposedintovortexstretchingandvortextiltingbycomputingitscomponentsparalleland
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喜欢此文档的还喜欢A STUDY ON MESOSCALE VORTICITY PROPAGATIONS IN A TYPHOON-LIKE VORTEX--《Acta Meteorologica Sinica》2003年04期
A STUDY ON MESOSCALE VORTICITY PROPAGATIONS IN A TYPHOON-LIKE VORTEX
Luo Zhexian (Nanjing Institute of Meteorology, Nanjing 210044)
By using an f-plane barotropic quasigeopotential model in the rectangular coordinate with the grid space of 5 km, ten experiments whose integration times are 36 hours are performed in order to study the interaction between a mesoscale vortex and a typhoon vortex, the initial position of the center of the mesoscale vortex is located in northwest direction to the typhoon center, with the distance between two centers being 2 rm, where rm is the radius of maximum wind of the typhoon vortex.
Results show that the interaction can creat a pair of smaller scale vortices or lumps, which extend from the outside region of the typhoon to near its center, resulting in the mesoscale vortcity propagation into the inside region. In this process, the vorticity concentration of the mesoscale vortex may appear. The coexistence of the propagation and the concentration makes the increase of vorticity in the inside region and more intensive typhoon. Meanwhile, the intensity of the lump with positive vorticity changes with time, with the oscillation period being several hours, the change of distance from the typhoon center to the lump center has a similar oscillation period, which reduces the oscillation of typhoon intensity. In the case of stronger circular basic current, the interaction can make the intensification of typhoon more obviously.
In addition, in some parametric conditions, the interaction may break down the continuous vorticity zone, exhibiting a cluster of smaller vorticity lumps.
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Vorticity and vortex-core states
The origin of the vortex-core states in s-wave and d_{x^2-y^2}-wave superconductors is investigated by means of some selected numerical experiments. By relaxing the self-consistency condition in the Bogoliubov-de Gennes equations and tuning the order parameter in the core region, it is shown that the suppression of the superfluid density in the core is not a necessary condition for the core states to form. This excludes ``potential well'' types of interpretations for the core states. The topological defect in the phase of the order parameter, however, plays a crucial role. This observation is explained by considering the effect of the vortex supercurrent on the Bogoliubov quasiparticles, and illustrated by comparing conventional vortices with multiply-quantized vortices and vortex-antivortex pairs. The core states are also found to be extremely robust against random phase disorder.
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