Laminar Pipe Flow.docx
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Laminar Pipe Flow.docx
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LaminarPipeFlow
LaminarPipeFlow
ProblemSpecification
Considerfluidflowingthroughacircularpipeofcontantcross-section.ThepipediameterD=0.2mandlengthL=8m.TheinletvelocityVin=1m/s.Considerthevelocitytobeconstantovertheinletcross-section.Thefluidexhaustsintotheambientatmospherewhichisatapressureof1atm.Takedensityρ=1kg/m3andcoefficientofviscosityµ=2x10-3kg/(ms).TheReynoldsnumberRebasedonthepipediameteris
whereVavgistheaveragevelocityattheinlet,whichis1m/sinthiscase.
SolvethisproblemusingFLUENT.Plotthecenterlinevelocity,wallskin-frictioncoefficient,andvelocityprofileattheoutlet.Validateyourresults.
Note:
Thevaluesusedfortheinletvelocityandflowpropertiesarechosenforconvenienceratherthantoreflectreality.ThekeyparametervaluetofocusonistheReynoldsno.
PreliminaryAnalysis
Weexpecttheviscousboundarylayertogrowalongthepipestartingattheinlet.Itwilleventuallygrowtofillthepipecompletely(providedthatthepipeislongenough).Whenthishappens,theflowbecomesfully-developedandthereisnovariationofthevelocityprofileintheaxialdirection,x(seefigurebelow).Onecanobtainaclosed-formsolutiontothegoverningequationsinthefully-developedregion.YoushouldhaveseenthisintheIntroductiontoFluidMechanicscourse.Wewillcomparethenumericalresultsinthefully-developedregionwiththecorrespondinganalyticalresults.Soit'sagoodideaforyoutogobacktoyourtextbookintheIntrocourseandreviewthefully-developedflowanalysis.Whatarethevaluesofcenterlinevelocityandfrictionfactoryouexpectinthefully-developedregionbasedontheanalyticalsolution?
Whatisthesolutionforthevelocityprofile?
We'llcreatethegeometryandmeshinGAMBITwhichisthepreprocessorforFLUENT,andthenreadthemeshintoFLUENTandsolvefortheflowsolution.
Step1:
CreateGeometryinGAMBIT
Ifyouwouldprefertoskipthemeshgenerationsteps,youcancreateaworkingdirectory(seebelow),downloadthemeshfromhere(rightclickandsaveaspipe.msh)intotheworkingdirectoryandgostraighttostep4.
StrategyforCreatingGeometry
Inordertocreatetherectangle,wewillfirstcreatetheverticesatthefourcorners.We'llthenjoinadjacentverticesbystraightlinestoformthe"edges"oftherectangle.Lastly,we'llcreatea"face"correspondingtotheareaenclosedbytheedges.InStep2,we'llmeshthefacei.e.therectangle.Notethatin3Dproblems,you'llhavetoforma"volume"fromfaces.SothehierarchyofgeometricobjectsinGAMBITisvertices->edges->faces->volumes.
CreateaWorkingDirectory
Createafoldercalledpipeinaconvenientlocation.We'llusethisastheworkingfolderinwhichfilescreatedduringthesessionwillbestored.
NoteforACCELcomputerlabusers:
Eachusergetshis/herown100MBofdiskspaceunderS:
atACCEL.YoucanputyourfilesinS:
andit'llbeaccessiblefromanycomputer.Thisiswhereyoushouldputfilesthatyouwanttokeepandaccesslateron.
StartGAMBIT
Startyourcommandprompt.
Start>Programs>LabApps>FluentIncProducts>Gambit2.3.16>Gambit2.3.16
ThisbringsuptheGAMBITstartupwindow.ClickBrowseandselectthefolderthatyoujustcreated.Enter-idpipeintheoptionsboxtotellGAMBITtousepipeasthedefaultfileprefix,thenclickRun.
InWindows,theExceedX-serverstartsupbeforetheGAMBITinterfacecomesup.Exceedisathird-partyapplicationneededtorendertheinterfaceinWindows(GAMBITwasoriginallydevelopedunderUnix).Tomakebestuseofscreenrealestate,movethewindowsandresizethemsothatyouapproximatethisscreenarrangement.ThiswayyoucanreadinstructionsinthebrowserwindowandimplementtheminGAMBIT.
Youcanresizethetextinthebrowserwindowtoyourtasteandcomfort:
InInternetExplorer:
Menubar>View>TextSize,thenchoosetheappropriatefontsize.
InNetscape:
Menubar>View>IncreaseFontorMenubar>View>DecreaseFont.
TheGAMBITInterfaceconsistsofthefollowing:
∙MainMenuBar:
NotethatthejobnamepipeappearsafterID:
inthetitlebaroftheUtilityMenu.
∙OperationToolpad:
We'llmoreorlessworkourwayacrosstheOperationToolpadaswegothroughthesolutionsteps.Noticethataseachofthetopbuttonsisselected,adifferent"sub-pad"appears.TheGeometrysub-padisshownintheabovesnaphot.
∙GlobalControlToolpad:
TheGlobalControlToolpadhasoptionssuchasFittoScreen
andUndo
thatareveryhandyduringthecourseofgeometryandmeshcreation.
∙GAMBITGraphics:
Thisisthewindowwherethegraphicalresultsofoperationsaredisplayed.
∙GAMBITDescriptionPanel:
TheDescriptionPanelcontainsdescriptionsofbuttonsorobjectsthatthemouseispointingto.MoveyourmouseoversomebuttonsandnoticethecorrespondingtextintheDescriptionPanel.
∙GAMBITTranscriptWindow:
ThisisthewindowtowhichoutputfromGAMBITcommandsiswrittenandwhichprovidesfeedbackontheactionstakenbyGAMBITasyouperformoperations.If,atsomepoint,youarenotsureyouclickedtherightbuttonorenteredavaluecorrectly,thisiswheretolooktofigureoutwhatyoujustdid.YoucanclickonthearrowbuttonintheupperrighthandcornertomaketheTranscriptwindowfull-sized.Youcanclickonthearrowagaintoreturnthewindowtoitsoriginalsize.Goahead,givethisatry.
SelectSolver
IfthewindowtitlebardoesnotsaythesolverisFLUENT5/6,thenyouneedtospecify:
MainMenu>Solver>FLUENT5/6
VerifythishasbeendonebylookingintheTranscriptWindowwhereyoushouldsee:
Theboundarytypesthatyou'llbeabletoselectinthethirdstepdependsonthesolverselected.
Wecanassumethattheflowisaxisymmetric.Theproblemdomainis:
whererandxaretheradialandaxialcoordinates,respectively.
Strategyforcreatinggeometry
Wewillputtheoriginofthecoordinatesystematthelowerleftcorneroftherectangle.Thecoordinatesofthecornersareshowninthefigurebelow:
Wewillfirstcreatefourverticesatthefourcornersandjoinadjacentverticestogettheedgesoftherectangle.Wewillthenformafacethatcoverstheareaoftherectangle.
CreateVertices
FindthebuttonsdescribedbelowbypointingthemouseateachofthebuttonsandreadingtheDescriptionWindow.
OperationToolpad>GeometryCommandButton
>VertexCommandButton
>CreateVertex
NoticethattheCreateVertexbuttonhasalreadybeenselectedbydefault.Afteryouselectabuttonunderasub-pad,itbecomesthedefaultwhenyougotoadifferentsub-padandthencomebacktothesub-pad.
Createthevertexatthelower-leftcorneroftherectangle:
Nexttox:
entervalue0.Nexttoy:
entervalue0.Nexttoz:
entervalue0(thesevaluesshouldbedefaults).ClickApply.Thiscreatesthevertex(0,0,0)whichisdisplayedinthegraphicswindow.
IntheTranscriptwindow,GAMBITreportsthatit"Createdvertex:
vertex.1".Theverticesarenumberedvertex.1,vertex.2etc.intheorderinwhichtheyarecreated.
Repeatthisprocesstocreatethreemorevertices:
Vertex2:
(0,0.1,0)
Vertex3:
(8,0.1,0)
Vertex4:
(8,0,0)
Notethatfora2Dproblem,thez-coordinatecanalwaysbelefttothedefaultvalueof0.
OperationToolpad>GlobalControl>FittoWindowButton
ThisfitsthefourverticesoftherectanglewehavecreatedtothesizeoftheGraphicsWindow.
CreateEdges
We'llnowconnectappropriatepairsofverticestoformedges.ToselectanyentityinGAMBIT,holddowntheShiftkeyandclickontheentity.
OperationToolpad>GeometryCommandButton
>EdgeCommandButton
>CreateEdge
SelecttwoverticesthatmakeupanedgeofthisrectanglebyholdingdowntheShiftbuttonandclickingonthecorrespondingvertices.Aseachvertexispicked,itwillappearredintheGraphicsWindow.ThenletgooftheShiftbutton.Wecanchecktheselectedverticesbyclickingontheup-arrownexttoVertices:
.
Thiswillbringupawindowcontainingtheverticesthathavebeenselected.VerticescanbemovedfromtheAvailableandPickedlistsbyselectingthemandthenpressingtheleftorrightarrowbuttons.
Afterthecorrectverticeshavebeenselected,clickClose,thenclickApplyintheCreateStraightEdgewindow.
Repeatthisprocesstocreatearectangle.
CreateFace
OperationToolpad>GeometryCommandButton
>FaceCommandButton
>FormFace
Toformafaceoutoftheareaenclosedbythefourlines,weneedtoselectthefourledgesthatenclosethisarea.ThiscanbedonebyholdingdowntheShiftkey,clickingoneachline(noticethatthecurrentlyselectedlineappearsred),andthenreleasingtheShiftkeyafterallfourlineshavebeenselected.
Alternatively,aneasierwaytodothiswouldbetoclickontheuparrownexttoedges:
ThiswillbringuptheEdgeListwindow.ClickonAll->toselectalloftheedgesatonce.ClickClose.
ClickApplytocreatetheface.
Step3:
SpecifyBoundaryTypesinGAMBIT
CreateBoundaryTypes
We'llnextsettheboundarytypesinGAMBIT.Theleftedgeistheinletofthepipe,therightedgetheoutlet,thetopedgethewall,andthebottomedgetheaxis.
OperationToolpad>ZonesCommandButton
>SpecifyBoundaryTypesCommandButton
ThiswillbringuptheSpecifyBoundaryTypeswindowontheOperationPanel.Wewillfirstspecifythattheleftedgeistheinlet.UnderEntity:
pickEdgessothatGAMBITknowswewanttopickanedge(faceisdefault).
NowselecttheleftedgebyShift-clickingonit.TheselectededgeshouldappearintheyellowboxnexttotheEdgesboxyoujustworkedwithaswellasth
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