Compressible Flow in a Nozzle.docx

Compressible Flow in a Nozzle.docx

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CompressibleFlowinaNozzle

CompressibleFlowinaNozzle

**Underconstruction**

ProblemSpecification

Considerairflowingathigh-speedthroughaconvergent-divergentnozzlehavingacircularcross-sectionalarea,A,thatvarieswithaxialdistancefromthethroat,x,accordingtotheformula

A=0.1+x2;-0.5

whereAisinsquaremetersandxisinmeters.Thestagnationpressurepoattheinletis101,325Pa.ThestagnationtemperatureToattheinletis300K.Thestaticpressurepattheexitis3,738.9Pa.WewillcalculatetheMachnumber,pressureandtemperaturedistributioninthenozzleusingFLUENTandcomparethesolutiontoquasi-1Dnozzleflowresults.TheReynoldsnumberforthishigh-speedflowislarge.Soweexpectviscouseffectstobeconfinedtoasmallregionclosetothewall.Soitisreasonabletomodeltheflowasinviscid.

GotoStep1:

CreateGeometryinGAMBIT

Step1:

CreateGeometryinGAMBIT

Sincethenozzlehasacircularcross-section,it'sreasonabletoassumethattheflowisaxisymmetric.Sothegeometrytobecreatedistwo-dimensional.

StartGAMBIT

CreateanewdirectorycallednozzleandstartGAMBITfromthatdirectorybytypinggambit-idnozzleatthecommandprompt.

UnderMainMenu,selectSolver>FLUENT5/6sincethemeshtobecreatedistobeusedinFLUENT6.0.

CreateAxisEdge

We'llcreatethebottomedgecorrespondingtothenozzleaxisbycreatingtheverticesAandBshownintheabovefigureandjoiningthembyastraightline.

OperationToolpad>GeometryCommandButton

>VertexCommandButton

>CreateVertex

Createthefollowingtwovertices:

Vertex1:

（-0.5,0,0）

Vertex2:

（0.5,0,0）

OperationToolpad>GeometryCommandButton

>EdgeCommandButton

>CreateEdge

Selectvertex1byholdingdowntheShiftbuttonandclickingonit.Next,selectvertex2.ClickApplyintheCreateStraightEdgewindow.

CreateWallEdge

We'llnextcreatethebottomedgecorrespondingtothenozzlewall.Thisedgeiscurved.Since

A=pir2

wherer（x）istheradiusofthecross-sectionatxand

A=0.1+x2

forthegivennozzlegeometry,weget

r（x）=[（0.1+x2）/pi]0.5;-0.5

Thisistheequationofthecurvedwall.LifewouldhavebeeneasierifGAMBITallowedforthisequationtobeentereddirectlytocreatethecurvededge.Instead,onehastocreateafilecontainingthecoordinatesofaseriesofpointsalongthecurvedlineandreadinthefile.Themorenumberofpointsusedalongthecurvededge,thesmoothertheresultantedge.

Thefilevert.datcontainsthepointdefinitionsforthenozzlewall.Takealookatthisfile.Thefirstlineis

211

whichsaysthatthereare21pointsalongtheedgeandwearedefiningonly1edge.Thisisfollowedbyx,randzcoordinatesforeachpointalongtheedge.Ther-valueforeachxwasgeneratedfromtheaboveequationforr（x）.Thez-coordinateis0forallpointssincewehavea2Dgeometry.

Right-clickonvert.datandselectSaveAs...todownloadthefiletoyourworkingdirectory.

MainMenu>File>Input>ICEMInput...

NexttoFileName:

enterthepathtothevert.datfilethatyoudownloadedorbrowsetoitbyclickingontheBrowsebutton.

Then,checktheVerticesandEdgesboxesunderGeometrytoCreateaswewanttocreatetheverticesaswellasthecurvededge.

ClickAccept.

Thisshouldcreatethecurvededge.Hereitisinrelationtotheverticeswecreatedabove:

（Clickpictureforlargerimage）

CreateInletandOutletEdges

Createtheverticaledgefortheinlet:

OperationToolpad>GeometryCommandButton

>EdgeCommandButton

>CreateEdge

Shift-clickonvertex1andthenthevertexaboveittocreatetheinletedge.

Similarly,createtheverticaledgefortheoutlet.

（Clickpictureforlargerimage）

CreateFace

Formafaceoutoftheareaenclosedbythefouredges:

OperationToolpad>GeometryCommandButton

>FaceCommandButton

>FormFace

Recallthatwehavetoshift-clickoneachoftheedgesenclosingthefaceandthenclickApplytocreatetheface.

SaveYourWork

MainMenu>File>Save

Thiswillcreatethenozzle.dbsfileinyourworkingdirectory.Checkthatithasbeencreatedsothatyouwillabletoresumefromhereifnecessary.

GotoStep2:

MeshGeometryinGAMBIT

Step2:

MeshGeometryinGAMBIT

Nowthatwehavethebasicgeometryofthenozzlecreated,weneedtomeshit.Wewouldliketocreatea50x20gridforthisgeometry.

MeshEdges

Asintheprevioustutorials,wewillfirststartbymeshingtheedges.

OperationToolpad>MeshCommandButton

>EdgeCommandButton

>MeshEdges

LiketheLaminarPipeFlowTutorial,wearegoingtouseevenspacingbetweeneachofthemeshpoints.Wewon'tbeusingtheGradingthistime,sodeselecttheboxnexttoGradingthatsaysApply.

Then,changeIntervalCountto20forthesideedgesandIntervalCountto50forthetopandbottomedges.

（Clickpictureforlargerimage）

MeshFace

Nowthatwehavetheedgesmeshed,weneedtomeshtheface.

OperationToolpad>MeshCommandButton

>FaceCommandButton

>MeshFaces

Asbefore,selectthefaceandclicktheApplybutton.

（Clickpictureforlargeimage）

SaveYourWork

MainMenu>File>Save

GotoStep3:

SpecifyBoundaryTypesinGAMBIT

Step3:

SpecifyBoundaryTypesinGAMBIT

SpecifyBoundaryTypes

Nowthatwehavethemesh,wewouldliketospecifytheboundaryconditionshereinGAMBIT.

OperationToolpad>ZonesCommandButton

>SpecifyBoundaryTypesCommandButton

ThiswillbringuptheSpecifyBoundaryTypeswindowontheOperationPanel.Wewillfirstspecifythattheleftedgeistheinlet.UnderEntity:

pickEdgessothatGAMBITknowswewanttopickanedge（faceisdefault）.

NowselecttheleftedgebyShift-clickingonit.TheselectededgeshouldappearintheyellowboxnexttotheEdgesboxyoujustworkedwithaswellastheLabel/TypelistrightundertheEdgesbox.

NexttoName:

enterinlet.

ForType:

selectVELOCITY_INLET.

ClickApply.YoushouldseethenewentryappearunderName/Typeboxnearthetopofthewindow.

Createboundarytypesforeachoftheedgesasspecifiedinthechartbelow:

EdgePosition

Name

Type

Left

inlet

PRESSURE_INLET

Right

outlet

PRESSURE_OUTLET

Top

wall

WALL

Bottom

centerline

AXIS

YoushouldhavethefollowingedgesintheName/Typelistwhenfinished:

SaveandExport

MainMenu>File>Save

MainMenu>File>Export>Mesh...

Typeinnozzle.mshfortheFileName:

.SelectExport2dMeshsincethisisa2dimensionalmesh.ClickAccept.

Checknozzle.mshhasbeencreatedinyourworkingdirectory.

GotoStep4:

SetUpProbleminFLUENT

Step4:

SetUpProbleminFLUENT

LaunchFLUENT

Start>Programs>FluentInc>FLUENT6.0

Select2ddpfromthelistofoptionsandclickRun.

ImportFile

MainMenu>File>Read>Case...

Navigatetoyourworkingdirectoryandselectthenozzle.mshfile.ClickOK.

ThefollowingshouldappearintheFLUENTwindow:

Checkthatthedisplayedinformationisconsistentwithourexpectationsofthenozzlegrid.

AnalyzeGrid

Grid>Info>Size

Howmanycellsandnodesdoesthegridhave?

Display>Grid

Howmanynodesarethereintheradialdirection?

Arethenodesclusteredtowardsthewall?

Why?

DefineProperties

Define>Models>Solver...

UndertheSolverbox,selectCoupled.UnderSpace,chooseAxisymmetric.

ClickOK.

Define>Models>Viscous

SelectInviscidunderModel.

ClickOK.

Define>Models>Energy

Theenergyequationneedstobeturnedonsincethisisacompressibleflowwheretheenergyequationiscoupledtothecontinuityandmomentumequations.

MakesurethereisacheckboxnexttoEnergyEquationandclickOK.

Define>Materials

SelectairunderFluidmaterials.UnderProperties,chooseIdealGasnexttoDensity.Youshouldseethewindowexpand.ThismeansFLUENTusestheidealgasequationofstatetorelatedensitytothestaticpressureandtemperature.

ClickChange/Create.

Define>OperatingConditions

We'llworkintermsofabsoluteratherthangaugepressuresinthisexample.SosetOperatingPressureinthePressureboxto0.

ClickOK.

ItisimportantthatyousettheoperatingpressurecorrectlyincompressibleflowcalculationssinceFLUENTusesittocomputeabsolutepressuretouseintheidealgaslaw.

Define>BoundaryConditions

Setboundaryconditionsforthefollowingsurfaces:

axis,default-interior,fluid,inlet,outlet,wall.

SelectinletunderSurfaceandpickpressure-inletunderTypeasitsboundarycondition.ClickSet....ThePressureInletwindowshouldcomeup.

Setthetotal（i.e.stagnation）pressure（notedasGauageTotalPressureinFLUENT）andtemperatureattheinlet.Forasubsonicinlet,Supersonic/InitialGaugePressureistheinitialguessvalueforthestaticpressure.Calculatethisinitialguessvaluefromthe1Dsolution.Afteryouhaveenteredthevalues,clickOKtoclosethewindow.

Usingthesamestepsasabove,pickpressure-outletastheboundaryconditionfortheoutletsurface.Then,whenthePressureOutletwindowcomesup,setthepressureandtemperatureasabove.ClickOK.

GotoStep5:

Solve!

Step5:

Solve!

Nowwewillsetthesolvesettingsforthisproblemandtheniteratethroughandactuallysolveit.

Solve>Control>Solution

Takealookattheoptionsavailable.WewantSecondOrderUpwindfortheFlow（undertheDiscretizationbox）.

MakesurethatisselectedandclickOK.

Solve>Initialize

Asyoumayrecallfromtheprevioustutorials,thisiswherewesettheinitialguessvalues（thebasecase）fortheiterativesolution.Onceagain,we'llsetthesevaluestobetheonesattheinlet.SelectinletunderComputeFrom.

ClickInit.

Solve>Monitors