Fluent Tutorial for Wing

APROCEDUREFORNUMERICALLYANALYZINGAIRFOILSAND WINGSECTIONS AThesis PresentedTo TheFacultyoftheDepartmentofMechanical& TheFacultyoftheDep artmentofMechanical&AerospaceEngineering AerospaceEngineering UniversityofMissouriColumbia By NathanLogsdon Dr.GarySolbrekkenThesisAdvisor December2006

December2006 TheundersignedhavereadandapprovedthisHo Theundersignedhaver eadandapprovedthisHonorsProjectentitled: norsProjectentitled: APROCEDUREFORNUMERICALLYANALYZINGAIRFOILSAND WINGSECTIONS PresentedbyNathanLogsdon Writteninfulfillmentoftherequirements forsixcredithoursinMAE4995 Dr.GarySolbrekkenDr.CraigKluever AssistantProfessorProfessor HonorsAdvisorSecondReader DateDate

Acknowledgements IwouldliketothankDr.GarySolbrekkenfor Iwouldliketothank Dr.GarySolbrekkenforhisinfinitepatience,gu hisinfinitepatience,guidancean idancean dsupport withoutwhichthisprojectwouldneverhavebe withoutwhichthispro jectwouldneverhavebeencompleted.Also,myfa encompleted.Also,myfatherand therand motherandtherestofmyfamilywhohavealwa motherandtherestof myfamilywhohavealwayssupportedmeineveryt yssupportedmeineverythingIha hingIha ve chosentopartake.

Abstract Thepurposeofthisprojectistodevelopapr Thepurposeofthispr ojectistodevelopaproceduretonumericallymo oceduretonumericallymodelairfl delairfl owover airfoilsusingGambitandFLUENT.Theprocedur airfoilsusingGambit andFLUENT.Theprocedureistobeusedasanint eistobeusedasanintroduction roduction to numericalanalysistoolsbystudentswhowill numericalanalysistoo lsbystudentswhowilltakeMAE4440/7440,Aerod takeMAE4440/7440,Aerodynamics. ynamics. Twoandthreedimensionalmodelsfortheairfo Twoandthreedimensio nalmodelsfortheairfoil0012werecreated,dra il0012werecreated,drawnandme wnandme shed inGambitusinggeometrydatagatheredbythe inGambitusinggeomet rydatagatheredbytheNationalAdvisoryCommitt NationalAdvisoryCommitteefor eefor Aeronautics.ThosemodelswerereadintoFLUEN Aeronautics.Thosemod elswerereadintoFLUENTwhereflowboundarycon Twhereflowboundaryconditions ditions wereappliedandthediscretizedNavier-Stokes wereappliedandthed iscretizedNavier-Stokesequationsweresolvednu equationsweresolvednumerically merically .The airfoilsectionliftcoefficientfromthenume airfoilsectionliftc oefficientfromthenumericsimulationwascompar ricsimulationwascomparedwith edwith experimentaldatafromtheliteratureandshow experimentaldatafrom theliteratureandshowntoagreewithin10%for ntoagreewithin10%forangleso angleso fattack below10°.Accurateliftcoefficientscouldno below10°.Accurateli ftcoefficientscouldnotbegeneratedforangles tbegeneratedforanglesofattack ofattack greater than10°.Anattemptwasmadetodemonstratew than10°.Anattemptw asmadetodemonstratewingtipvorticesfroma3ingtipvorticesfroma3-Dmodel. Dmodel. Unfortunately,dototheinabilitytodevelop Unfortunately,dotot heinabilitytodevelopareliablemeshthistask areliablemeshthistaskwasnot wasnot successfully completed.

TABLEOFCONTENTS Acknowledgement3 Abstract...................................... Abstract.............. ................................................. .................................. ......... ................................................4 1.Introduction........................................................ 1.Introduction............................... .................................. ......... ...........................................6 2.Four-digitAirfoils..7 3.Gambit9 3.1CoordinateFormat...10 3.2CreatingtheAirfoilGeometry.12 3.3CreatingMeshBoundary.15 3.4Meshing2D.........22 3.5Creating3DWing..............31 3.6Meshing3D.........33 4.FLUENTProcedure..36 5.Conclusion.43 5.1Comparisonof2-Dand3-DFLUENTModels..43 5.2Comparisonof2-DNumericalResultstoNACAEmpiricalData..43 5.3WingtipVorticesModel.46 6.References..49 Appendix:Four-digitAirfoilCalculatorM-file.......50

1.Introduction Flighthasbeenamajorpartoftheworldsinc Flighthasbeenamajo rpartoftheworldsinceitwasfirstdemonstrat eitwasfirstdemonstratedbythe edbythe Wright brothersin1902.However,indepthstudiesin brothersin1902.Howe ver,indepthstudiesintotheeffectsofairflow totheeffectsofairflowoverwin overwin gsdidnt occuruntilWorldWarI(Anderson).Inanatte occuruntilWorldWar I(Anderson).Inanattempttobetterunderstand mpttobetterunderstandwhatmade whatmade a goodwing,theNationalAdvisoryCommitteefor goodwing,theNationa lAdvisoryCommitteeforAeronautics,henceforth Aeronautics,henceforthreferred referred toas theNACA,wasfounded.In1933theNACAtested theNACA,wasfounded. In1933theNACAtested78airfoilshapesinthe 78airfoilshapesintheirwind irwind tunnelswiththedatabeingpublishedinTechn tunnelswiththedata beingpublishedinTechnicalReportNo.460,"The icalReportNo.460,"TheCharacte Characte ristics of78RelatedAirfoilSectionsfromTestsint of78RelatedAirfoil SectionsfromTestsintheVariable-DensityWind heVariable-DensityWindTunnel." Tunnel." This reportalsoresultedinthecreationofthefo reportalsoresultedi nthecreationofthefour-digitschemefordefin ur-digitschemefordefiningtheb ingtheb asic geometryoftheairfoil.Thissamenamingsche geometryoftheairfoi l.Thissamenamingschemewasthenusedtodefin mewasthenusedtodefinetheoth etheoth er airfoilfamilies,suchasthefive-digitairfo airfoilfamilies,such asthefive-digitairfoils.In1939alow-turbul ils.In1939alow-turbulencetwoencetwodimensional windtunnelwasconstructedforthesolepurpo windtunnelwasconstr uctedforthesolepurposeofairfoiltesting(U. seofairfoiltesting(U.S.Centen S.Centen nial). ThisreportoutlinesthenumericproceduretoanalyzetheNACAairfoil Thisreportoutlinesthenumericprocedureto analyzetheNACAairfoil0012with 0012with a chordlengthofonemeterandtheReynoldsnum chordlengthofoneme terandtheReynoldsnumbersof3x106,6x106,and bersof3x106,6x106,and9x106.B 9x106.B otha twoandthreedimensionalmodelwerecreatedt twoandthreedimensio nalmodelwerecreatedtocompareFLUENT'saccura ocompareFLUENT'saccuracyinthe cyinthe twodimensionalanalysisandanactualsealedwingsectionthreedimens twodimensionalanalysisandanactualsealed wingsectionthreedimensionalana ionalana lysis. Thenumericalprocessusedforthisairfoilwi Thenumericalprocess usedforthisairfoilwillbeusedasatutorial llbeusedasatutorialforstude forstude ntstaking MAE4440/7440,Aerodynamics,wheretheywillb MAE4440/7440,Aerodyn amics,wheretheywillberequiredtonumerically erequiredtonumericallyanalyze analyze an airfoiloftheirowndesign.Onceaprocedure airfoiloftheirownd esign.OnceaproceduretoreplicatetheNACAemp toreplicatetheNACAempiricalda iricalda tawas found,anattempttomakeamodelshowingthe found,anattempttom akeamodelshowingthewingtipvorticesphenomen wingtipvorticesphenomenonwas onwas

constructed.Unfortunately,asuitablemeshco constructed.Unfortuna tely,asuitablemeshcouldnotbefoundforthe uldnotbefoundforthecomplicat complicat ed airfoilgeometry. 2.Four-digitAirfoils AlltheairfoilsintheNACAfour-digitairfoi Alltheairfoilsinth eNACAfour-digitairfoilfamilyaredefinedbya lfamilyaredefinedbyaserieso serieso ffour numericaldigits,i.e.2412.Thefirstdigiti numericaldigits,i.e. 2412.Thefirstdigitisthemaximumvalueofth sthemaximumvalueofthemeanli emeanli nein hundredthsofthechordandisrepresentedin hundredthsofthechor dandisrepresentedinthefollowingequationsw thefollowingequationswiththel iththel etterm. Thesecondnumberrepresentsthepositionont Thesecondnumberrepr esentsthepositiononthechordofthemaximumm hechordofthemaximummeanline eanline in tenthsofthechordandisrepresentedwithth tenthsofthechordan disrepresentedwiththeletterp.Thelasttwo eletterp.Thelasttwonumbersd numbersd esignate themaximumthicknessoftheairfoilinhundre themaximumthickness oftheairfoilinhundredthsofthechordandis dthsofthechordandisrepresent represent edbyt. Therefore,theairfoil2412tellsusthatthe Therefore,theairfoil 2412tellsusthattheairfoilhasamaximummea airfoilhasamaximummeanlineva nlineva lueoftwo hundredthsofthechordlengthatapositionf hundredthsofthechor dlengthatapositionfourtenthsthechordfrom ourtenthsthechordfromthefron thefron tofthe airfoilandamaximumthicknessoftwelvehund airfoilandamaximum thicknessoftwelvehundredthsthechordlength, redthsthechordlength,seefigur seefigur e1. Fig.1.Diagramdisplayingthechordlength,m Fig.1.Diagramdispla yingthechordlength,maximumchamber,position aximumchamber,positionofmaxch ofmaxch amberandmax thicknessoftheairfoilgeometry. TheNACAfour-digitwingsectionsarebaseduponasetofgeometricequ TheNACAfour-digitwingsectionsarebasedup onasetofgeometricequationswh ationswh ich makesthisfamilyofairfoilseasytoderiveb makesthisfamilyofa irfoilseasytoderivebyfindingasetofcoordi yfindingasetofcoordinatestha natestha tdefinethe upperandlowersurfacesoftheairfoil.These upperandlowersurfac esoftheairfoil.Theseequationswilldefineth equationswilldefinethecoordin ecoordin atesofthe

surfacesforagivenairfoilaspercentagesof surfacesforagivena irfoilaspercentagesofthechord.Whenananaly thechord.Whenananalysisisto sisisto be conductedonanairfoilwithachordlengthsn conductedonanairfoi lwithachordlengthsnotequaltoone,thecoor otequaltoone,thecoordinatesf dinatesf orthe airfoilmustfirstbefoundforachordlength airfoilmustfirstbe foundforachordlengthofoneandthenmultiply ofoneandthenmultiplythecoor thecoor dinates, bothxandy,bythedesiredchordlength.The bothxandy,bythed esiredchordlength.Thecoordinatesfortheuppe coordinatesfortheuppersurface rsurface canbe foundwiththefollowingequations: xu=x-ytsin. (1) y=y+ycos. uct Likewisethelowersurfacecoordinatescanbefoundusingtheequations Likewisethelowersurfacecoordinatescanbe foundusingtheequationsbelow: below: x=x+ysin. lt(2) y=y-ycos. lct wherexisthepositionalongthechord,ytis wherexisthepositio nalongthechord,ytisthecorrespondingthickn thecorrespondingthicknessdistr essdistr ibutionand .istheanglebetweenthepreviouspointand .istheanglebetween thepreviouspointandthecurrentpoint.WhenN thecurrentpoint.WhenNACAfirst ACAfirst began tryingtodeterminethebestgeometryforwing tryingtodetermineth ebestgeometryforwings,theylookedattheCla s,theylookedattheClarkYand rkYand Göttingen398whichweretwoofthemostsucce Göttingen398whichwe retwoofthemostsuccessfulwingdesignsatthe ssfulwingdesignsatthetime.They time.They foundthatwhenthechamberwasremoved,thattheeffectivethicknessd foundthatwhenthechamberwasremoved,that theeffectivethicknessdistributi istributi onofthe twowingswasnearlythesame.Therefore,the twowingswasnearlyt hesame.Therefore,thethicknessdistributionfo thicknessdistributionforthefou rthefou r-digit wingsectionswasdefinedoffthegeometryof wingsectionswasdefi nedoffthegeometryofthosecurrentwingsectio thosecurrentwingsectionsandis nsandis defined bytheequation: 234 ±yt=t(0.29690x-0.12600x-0.35160x+0.2 ±yt=t(0.29690x-0 .12600x-0.35160x+0.28430x-0.10150x)(3) 8430x-0.10150x)(3) 0.20 Theleadingedgeradiusofthefour-digitairf Theleadingedgeradiu softhefour-digitairfoilsisdefinedbytheeq oilsisdefinedbytheequation: uation: rt=1.1019t2(4) wherethecenterofthecirclethisradiusdef wherethecenterofth ecirclethisradiusdefinesislocatedat0.05p inesislocatedat0.05percentof ercentof thechordon themeanline,seefigure2.

Fig.2.Visualdefinitionoffourdigitairfoi Fig.2.Visualdefinit ionoffourdigitairfoilgeometry.(Aerospaceweb lgeometry.(Aerospaceweb.org) .org) Thechamberofanairfoilisdefinedbytheam Thechamberofanairf oilisdefinedbytheamountofcurveinthemean ountofcurveinthemeanline.Th line.Th emean lineisdefinedbytwoparabolicarcstangent lineisdefinedbytwo parabolicarcstangenttothepositionofthema tothepositionofthemaximummea ximummea n-line ordinate.Theequationsthatdefinethemeanlineare: m yc=2(2px-x2)forwardofmaximumordinate(5) p m yc=2[(1-2p)+2px-x2]aftofmaximumordinate(6) (1-p) Throughtheuseofequations1-6anynumberof Throughtheuseofequ ations1-6anynumberoffour-digitairfoilcoord four-digitairfoilcoordinatesfo inatesfo rthe upperandlowersurfacescanbedefined. 3.Gambit Gambitisamodelingsoftwarethatiscapable Gambitisamodelings oftwarethatiscapableofcreatingmeshedgeomet ofcreatingmeshedgeometriesthat riesthat canbe readintoFLUENTandotheranalysissoftware. readintoFLUENTando theranalysissoftware.AnoutlinefortheGambit AnoutlinefortheGambitgeometry geometry creationprocesscanbeseeninfigure3.

Fig.3.Gambitoverviewdiagram. 3.1CoordinateFormat Sincetheairfoilgeometryisdefinedbysets Sincetheairfoilgeom etryisdefinedbysetsofcoordinatepoints,the ofcoordinatepoints,themorepoi morepoi ntsdefined willincreasetheaccuracyofthemodel.Anai willincreasetheaccu racyofthemodel.Anairfoilgeometrydefinedby rfoilgeometrydefinedbyonehund onehund red pointsforboththetopandbottomsurfacewil pointsforboththeto pandbottomsurfacewillresultinagooddefini lresultinagooddefinition.The tion.The listof coordinatesseeninfigure2werederivedbys coordinatesseeninfi gure2werederivedbyscriptingequations1-6in criptingequations1-6intoaMatl toaMatl abM-file, whichcanbefoundintheAppendix,whichthen whichcanbefoundin theAppendix,whichthensuppliedthecorrespondi suppliedthecorrespondingx,y, ngx,y, andz coordinateforeachofthehundredpointsalon coordinateforeachof thehundredpointsalongtheupperandlowersur gtheupperandlowersurfaceoft faceoft heairfoil. Withthecoordinatesdefined,theymustbelis Withthecoordinatesd efined,theymustbelistedinatextdocumentin tedinatextdocumentinthefoll thefoll owing format:

Fig.4.Propercoordinateformatforreadingc Fig.4.Propercoordin ateformatforreadingcoordinatesintoGambit. oordinatesintoGambit. Thetoptwonumbers,100and2,tellGambitth Thetoptwonumbers,1 00and2,tellGambitthatitisgoingtoreadin atitisgoingtoreadintwosets twosets ofone hundredcoordinatesonerightaftertheother. hundredcoordinateson erightaftertheother.Thecolumnonthelefti Thecolumnontheleftisthexsthexcoordinates.Thecentralcolumnisthey-coord coordinates.Thecentr alcolumnisthey-coordinatesandtherightcolu inatesandtherightcolumnisthe mnisthe zcoordinates.Theremustbenoemptylinesbetw coordinates.Theremus tbenoemptylinesbetweentherowsofcoordinat eentherowsofcoordinatesandat esandat least onespaceseparatingthecolumnsofcoordinate onespaceseparatingt hecolumnsofcoordinatesfromoneanother.Thec sfromoneanother.Thecoordinate oordinate s shouldalsobelistedverticallymovingfromt shouldalsobelisted verticallymovingfromthenoseoftheairfoilto henoseoftheairfoiltowardthe wardthe tailforthe uppersurfacefirstandthenthelowersurface uppersurfacefirstan dthenthelowersurface.Anoteofinterest,by .Anoteofinterest,byusingequ usingequ ations1-6, thetwocoordinatesthatdefinethetailofth thetwocoordinatesth atdefinethetailoftheairfoildonotbringth eairfoildonotbringthegeometr egeometr ytoasingle point,seefigure5. Fig.5.Airfoiltailgapcreatedbyequations1-6.

Thisminorgapinthetailoftheairfoilisu Thisminorgapinthe tailoftheairfoilisusefulwhen3-Dgeometries sefulwhen3-Dgeometriesarebein arebein gdefined inGambitsothegapwillbemaintained.Once inGambitsothegapw illbemaintained.Onceproperlyformattedthedo properlyformattedthedocumentsh cumentsh ould besavedasa*.txtdocument. 3.2CreatingtheAirfoilGeometry LaunchGambit.OnceGambitisopenmakecertai LaunchGambit.OnceGa mbitisopenmakecertainthesolverissetfort nthesolverissetfortheapprop heapprop riate output,i.e.FLUENT5/6,byselectingSolver. output,i.e.FLUENT5/ 6,byselectingSolver.FLUENT5/6.Thecoordina FLUENT5/6.Thecoordinate te documentmustnowbeimportedintoGambit.Thi documentmustnowbei mportedintoGambit.ThisisdonebyselectingFi sisdonebyselectingFile.Impo le.Impo rt .ICEMInputs Fig.6.Gambitcoordinateimportprocess.

ThiswillopentheICEMimportwindow.Makece ThiswillopentheICE Mimportwindow.Makecertaintheedgecommandis rtaintheedgecommandisselected selected andthatthefacecommandisdeselected,asca andthatthefacecomm andisdeselected,ascanbeseeninfigure7. nbeseeninfigure7. Fig.7.ICEMimportwindow. Oncethedesiredcoordinatefiletobeimporte Oncethedesiredcoord inatefiletobeimportedislistedintheFileN dislistedintheFileNametext ametext box,accept thesettings.SincethetextfiletoldGambit thesettings.Sinceth etextfiletoldGambittoreadintwosetsofon toreadintwosetsofonehundred ehundred coordinates,eachsetofonehundredcoordinateswillbedefinedbyone coordinates,eachsetofonehundredcoordinat eswillbedefinedbyoneedgeres edgeres ultingin Gambitwindownowdisplayingtheupperandlow Gambitwindownowdisp layingtheupperandlowersurfaceoftheairfoil ersurfaceoftheairfoil. .

Fig.8.Importedairfoilgeometry. Nexttheupperandlowersurfaceoftheairfoi Nexttheupperandlow ersurfaceoftheairfoilmustbesplitatthree lmustbesplitatthreetenthsof tenthsof thechord lengthsincethefirstthirtypercentofthea lengthsincethefirst thirtypercentoftheairfoilwillbemeshedwit irfoilwillbemeshedwithanon-u hanon-u niformgrid andthelastseventypercentoftheairfoilwi andthelastseventyp ercentoftheairfoilwithauniformgrid.Thisi thauniformgrid.Thisisdoneby sdoneby selecting theGeometryCommandunderoperation. EdgeCommand. Split/mergeEdges. Startbyselectingtheuppersurfaceoftheai Startbyselectingthe uppersurfaceoftheairfoil.Thisedgecaneith rfoil.Thisedgecaneitherbesel erbesel ectedfrom thepopupmenubyselectingtheuparrownext thepopupmenubysele ctingtheuparrownexttotheedgeboxorbyshi totheedgeboxorbyshiftleft-c ftleft-c licking thedesirededge.SinceGambitcreatedthetwo thedesirededge.Sinc eGambitcreatedthetwocurrentedgesinexisten currentedgesinexistencetheyw cetheyw illbe representedbytherandomnamesedge.1andedg representedbytheran domnamesedge.1andedge.2.Thefirstsurfaceim e.2.Thefirstsurfaceimportedis portedis definedasedge.1,whichistheuppersurface, definedasedge.1,whi chistheuppersurface,andedge.2isthelower andedge.2isthelowersurface. surface. Also, anytimeanentityisselectedinGambitthatp anytimeanentityiss electedinGambitthatpartofthemodelwillbe artofthemodelwillbedisplayed displayed ina differentcolor.Oncetheedgeisselected,en differentcolor.Once theedgeisselected,enteravalueof0.3c,wher teravalueof0.3c,wherecisth ecisth echord

length,fortheglobalx-coordinate.Thiswill length,fortheglobal x-coordinate.Thiswillplaceamarkerontheed placeamarkerontheedgewhere gewhere thesplit isgoingtooccur.Thisprocesscanbeseenfo isgoingtooccur.Thi sprocesscanbeseenfora0012airfoilinthef ra0012airfoilinthefigure9. igure9. Fig.9.Edgesplitprocess. Repeatthisprocessforthelowersurface. 3.3CreatingMeshBoundary Theoutermeshgeometrymustnowbecreated.T Theoutermeshgeometr ymustnowbecreated.Thisisdonebyselecting hisisdonebyselectingtheVerte theVerte x CommandbuttonundertheGeometryOperation.B Commandbuttonundert heGeometryOperation.ByselectingtheCreateVe yselectingtheCreateVertex rtex buttonanotherwindowwithbothglobalandloc buttonanotherwindow withbothglobalandlocalcoordinateoptionsis alcoordinateoptionsisopened,s opened,s ee figure10. 15

Fig.10.VertexwindowwithvaluesforpointA. Usingtheglobalcoordinates,itispossiblet Usingtheglobalcoord inates,itispossibletocreatetheoutlinefor ocreatetheoutlineforaC-mesh aC-mesh profile aroundtheairfoilgeometry.Thiswillallowf aroundtheairfoilgeo metry.Thiswillallowforagoodquickmeshtob oragoodquickmeshtobecreated ecreated .By fillingintheglobalcoordinatepositionswit fillingintheglobal coordinatepositionswiththevaluesinTable1, hthevaluesinTable1,theoutli theoutli neofthe meshboundarywillbedefinedbyninevertices meshboundarywillbe definedbyninevertices.Namingallgeometriesc .Namingallgeometriescreatedis reatedis highly recommendedtoeasetheprocessoffindingpoi recommendedtoeaseth eprocessoffindingpointslaterinthepopupme ntslaterinthepopupmenu. nu. Table1.Globalcoordinatesofverticestocreateouterboundaryofmes Table1.Globalcoordinatesofverticestocre ateouterboundaryofmeshwherec hwherec isthechordlength oftheairfoil.Allplottedpointscanbeseeninfigure11. Labelx-coordinatey-coordinatez-coordinate Ac9*c0 B14.4*c9*c0 C14.4*cUT0 D14.4*c00 E14.4*cLT0 F14.4-9*c0 GC-9*c0 HC00 I-8*c00 They-coordinatesUTandLTcorrespondtothey-coordinatesfortheupp They-coordinatesUTandLTcorrespondtothe y-coordinatesfortheupperandlo erandlo wer surfacetailsoftheairfoil,refertofigures surfacetailsofthea irfoil,refertofigures5and11.Thesevaluesa 5and11.Thesevaluesareeasies reeasies tfoundby

referringtotheairfoilcoordinatetextfile. referringtotheairfo ilcoordinatetextfile.Oncetheseverticeshave Oncetheseverticeshavebeencre beencre atedthe workframeshouldappearasfollows: Fig.11.Resultingverticeslocations. Thisdisconnectedtailisimportantfortheprocessinwhich3Dgeometr Thisdisconnectedtailisimportantforthepr ocessinwhich3Dgeometriesarec iesarec reatedin Gambitsodon'thavetheairfoilcometoapoi Gambitsodon'thavet heairfoilcometoapointatthetail.Thesever ntatthetail.Theseverticesmus ticesmus tnowbe connectedtocreateaframeforthefacesthat connectedtocreatea frameforthefacesthataretobemeshed.Fora aretobemeshed.Forafacetob facetob ecreated later,alltheframesmustbecompletelyenclo later,alltheframes mustbecompletelyenclosed.Startbyselectingt sed.StartbyselectingtheGeomet heGeomet ry Operation.EdgeCommand.CreateEdgeCommand Operation.EdgeComma nd.CreateEdgeCommand.Thecreateedgecommand .Thecreateedgecommand mustbesettocreateastraightedge.Nowsel mustbesettocreate astraightedge.Nowselecttwoverticesbetween ecttwoverticesbetweenwhichan whichan edge needstobecreated.Straightedgesneedtobe needstobecreated.S traightedgesneedtobecreatedbetweenalloft createdbetweenallofthefollow hefollow ingpoint pairs:AB,BC,CD,DE,EF,FG,GLT,LTH,HUT, pairs:AB,BC,CD,DE, EF,FG,GLT,LTH,HUT,UTAandDH,ascanbesee UTAandDH,ascanbeseenin nin figure12.

Fig.12.Straightedgeconnections. Twoarcedgesaregoingtobecreatedforthe Twoarcedgesaregoin gtobecreatedforthefrontofthemeshboundar frontofthemeshboundary.Thisi y.Thisi sdone byright-clickingtheCreateEdgeiconwhicho byright-clickingthe CreateEdgeiconwhichopensadropdownmenu.Se pensadropdownmenu.Selectthe lectthe Arc Edgebutton,seefigure13.

Fig.13.Edgecreationdropdownlist. Thefirstthingthatmustbedoneistoselect Thefirstthingthatm ustbedoneistoselectthecenterpointofthe thecenterpointofthearc.For arc.For botharcsthis isgoingtobepointH,seefigure14andrefe isgoingtobepointH ,seefigure14andrefertofigure11forvertex rtofigure11forvertexdefiniti definiti on.

Fig.14.Arcdefinitionwindow.

TheendpointsaregoingtobeAandIandGa Theendpointsaregoi ngtobeAandIandGandI.Thefinalmeshoute ndI.Thefinalmeshouterboundar rboundar y shouldappearasfollows: Fig.15.Outermeshboundary. Eachenclosedareawillnowbeturnedintoafacewhichcanbemeshed. Eachenclosedareawillnowbeturnedintoaf acewhichcanbemeshed.Startby Startby selectingGeometryOperations.FaceCommand. selectingGeometryOpe rations.FaceCommand.FormFaceWireframe.In FormFaceWireframe.In totaltherewillbefourfacescreated.Fromf totaltherewillbefo urfacescreated.Fromfigure15thetoprightre igure15thetoprightrectanglew ctanglew illbeface ABCDH.Thelowerrightrectanglewillbeface ABCDH.Thelowerright rectanglewillbefaceDEFGHandthelefthalfc DEFGHandthelefthalfcirclewil irclewil lbe faceAIGH.Thelastfacewillbetheareaoft faceAIGH.Thelastfa cewillbetheareaoftheairfoil.Thefirstfac heairfoil.Thefirstfacemention emention edis createdbypickingtheedgesAB,BC,CD,DH,H createdbypickingthe edgesAB,BC,CD,DH,HUT,andUTA,seefigure1 UT,andUTA,seefigure16. 6.

Fig.16.FaceABCDHdefinition. Thesecondrectangularfaceiscreatedwithth Thesecondrectangular faceiscreatedwiththeedgesDE,EF,FG,GLT, eedgesDE,EF,FG,GLT,LTH,and LTH,and HD. Theairfoilismadeintoafacebyselectingt Theairfoilismadein toafacebyselectingtheimportededges,these heimportededges,thesemostlike mostlike lyhavethe genericnamesedge.1,edge.2,edge.3,andedge genericnamesedge.1, edge.2,edge.3,andedge.4,andtheedgesHUTand .4,andtheedgesHUTandLTH.The LTH.The finalfaceiscreatedbyselectingtheedgesUTA,AI,GI,GLT,LTH,and finalfaceiscreatedbyselectingtheedgesU TA,AI,GI,GLT,LTH,andHUT.In HUT.In order tosaveprocessingtimetheairfoilfacedoesn tosaveprocessingtim etheairfoilfacedoesn'tneedtobemeshed.The 'tneedtobemeshed.Therefore,t refore,t heairfoil canbesubtractedfromthehalfcirclefaceAI canbesubtractedfrom thehalfcirclefaceAIGHbyselectingGeometry GHbyselectingGeometryOperation Operation . FaceCommand. rightclickBooleanOperation.Subtract,seefigure17.

Fig.17.Booleanoperationsubtractwindow. IntheupperFaceboxselectthehalfcirclef IntheupperFacebox selectthehalfcirclefaceAIGH.IntheSubtract aceAIGH.IntheSubtractFacebox Facebox select theairfoilfaceandthenselectapply.Donot theairfoilfaceandt henselectapply.Donotselecttheretainoption selecttheretainoptionsorelse sorelse multiple edgeswillexistontopofeachother.(Fora edgeswillexistonto pofeachother.(Fora3Dairfoilanalysesgoto 3Dairfoilanalysesgotosection section 3.5atthis point.) 3.4Meshing2D Theprocesstomeshthefacescannowbegin.S Theprocesstomeshth efacescannowbegin.Sincetheareaofinterest incetheareaofinterestisaroun isaroun dthe airfoil,thisistheregionthatthemeshshou airfoil,thisisther egionthatthemeshshouldbethedensest.Start ldbethedensest.Startbyselect byselect ingMesh

Operation.EdgeCommand.MeshEdge.Thiswillallowthedefiningoft Operation.EdgeCommand.MeshEdge.Thiswil lallowthedefiningoftheface heface meshthroughdefinededgemeshes.Tomeshane meshthroughdefinede dgemeshes.Tomeshanedge,selecttheedgebye dge,selecttheedgebyeitherthe itherthe popup menuorbyshiftleft-clickingtheedge.Start menuorbyshiftleftclickingtheedge.StartbyselectingedgeAB,ma byselectingedgeAB,makingcert kingcert ainthe arrowispointingfromlefttoright,seefigure18. Fig.18.Edgemeshlabelsandarrowindication. Thearrowdirectioncanbechangedbyselectin Thearrowdirectionca nbechangedbyselectingReverseatthetopoft gReverseatthetopoftheedgem heedgem esh window.Forthisedge,aFirstLengthtypemes window.Forthisedge, aFirstLengthtypemeshisdesired,seefigure hisdesired,seefigure19.This 19.This will placemoreelementsclosertothetailofthe placemoreelementscl osertothetailoftheairfoil,whichisanarea airfoil,whichisanareaofinter ofinter est,andfewer elementstothefarrightwheretheflowwill elementstothefarri ghtwheretheflowwillonceagainbeuniform.Se onceagainbeuniform.SetLength tLength to0.1 andtheIntervalCountoptioninthespacebox andtheIntervalCount optioninthespaceboxtofortyfortheinitial tofortyfortheinitialmesh,se mesh,se efigure

19.Whendecidingonthedensityofthemesh, 19.Whendecidingont hedensityofthemesh,weighthecostandbenefi weighthecostandbenefitsofcal tsofcal culation timeversusaccuracy.Startingoutwithaless timeversusaccuracy. Startingoutwithalessdensemeshisusuallybe densemeshisusuallybestsince stsince the densitycanalwaysbeincreasedinFLUENTand densitycanalwaysbe increasedinFLUENTandthiswillreducecalculat thiswillreducecalculationtimes iontimes for preliminaryresults.Thisprocesswillberepe preliminaryresults.T hisprocesswillberepeatedforedgesDHandFG, atedforedgesDHandFG,againwi againwi ththe arrowpointingfromlefttoright,refertofigure18. Fig.19.MeshEdgesoptions. TheverticaledgesUTA,BC,EF,andGLTwillb TheverticaledgesUTA ,BC,EF,andGLTwillbemeshedwithaSuccessiv emeshedwithaSuccessiveRatioo eRatioo f ratio1.15andanIntervalCountof30,refer ratio1.15andanInte rvalCountof30,refertofigure19foredges.E tofigure19foredges.EdgesUTA dgesUTA andBC shouldhavetheirarrowspointingupandedges shouldhavetheirarro wspointingupandedgesGLTandEFwiththeirar GLTandEFwiththeirarrowspoin rowspoin ting downinordertoplacethedensestmesharound downinordertoplace thedensestmesharoundtheairfoil.Thesmalle theairfoil.ThesmalledgesLTH, dgesLTH, HUT, CD,andDEwillallbemeshedwithaSuccessiv CD,andDEwillallbe meshedwithaSuccessiveRatioofratio1andan eRatioofratio1andanInterval Interval Size of0.02cwiththeirarrowspointingawayfrom of0.02cwiththeirar rowspointingawayfromthecenter.Therewon thecenter.Therewon tbeanynotab le

changealongthesesmalledges.Duetotheear changealongthesesma lledges.Duetotheearlierlinesplitconducted lierlinesplitconductedonthet onthet opand bottomsurfaces,theairfoilgeometryisnowr bottomsurfaces,thea irfoilgeometryisnowrepresentedbyfoursepara epresentedbyfourseparatelines. telines. When theseedgesaremeshedtheirarrowsshouldpoi theseedgesaremeshed theirarrowsshouldpointtowardsthetailofth nttowardsthetailoftheairfoil eairfoil ,seefigure 20. Fig.20.Airfoilarrowdirection. Thefrontedgesoftheairfoilwillbemeshed Thefrontedgesofthe airfoilwillbemeshedwithaLastLengthtypea withaLastLengthtypeataLengt taLengt hof 0.02c,wherecisthechordlength,andInterv 0.02c,wherecisthe chordlength,andIntervalCountofforty.There alCountofforty.Therearedges aredges ofthe airfoilwillbemeshedwithaSuccessiveRatio airfoilwillbemeshed withaSuccessiveRatioofoneandIntervalSize ofoneandIntervalSizeof0.02c of0.02c .These smallintervalswillcreateadensemeshright smallintervalswillc reateadensemeshrightaroundtheairfoilgeome aroundtheairfoilgeometry.Tod try.Tod etermine thenumberofmeshelementsontherearedges thenumberofmeshele mentsontherearedgesoftheairfoilselectMes oftheairfoilselectMeshOperati hOperati on. EdgeCommand.SummarizeEdgeMeshesandchoos EdgeCommand.Summari zeEdgeMeshesandchooseeithertheupperorlow eeithertheupperorlowerrear errear edge.Selecttheelementsoptionandclickapp edge.Selecttheeleme ntsoptionandclickapply.Thenumberofelement ly.Thenumberofelementsonthe sonthe line willbeprintedintheGambittranscriptwindo willbeprintedinthe Gambittranscriptwindow,seefigure21. w,seefigure21.

Fig.21.SummarizeEdgeCommand(right)andresults(bottom). Knowingthenumberofelementsonthetopand Knowingthenumberof elementsonthetopandbottomsurfacesoftheai bottomsurfacesoftheairfoil,an rfoil,an edge meshcannowbegeneratedforthearcsAIand meshcannowbegenera tedforthearcsAIandGIwiththeirarrowspoin GIwiththeirarrowspointingtowa tingtowa rd vertexI,seefigures18.Theselineswillbe vertexI,seefigures 18.TheselineswillbemeshedwithaFirstLengt meshedwithaFirstLengthtypeme htypeme sh, Length0.02cwithanIntervalCountequivalent Length0.02cwithanI ntervalCountequivalenttothenumberofelement tothenumberofelementsonthe sonthe correspondingtopandbottomsurfacesofthew correspondingtopand bottomsurfacesofthewingsectiongeometry.The ingsectiongeometry.Theinterval interval count forthe0012airfoilinthisprocedureis75. forthe0012airfoili nthisprocedureis75.Seefigure22foraview Seefigure22foraviewofallth ofallth emeshed edges.

Fig.22.Alledgesmeshed. ThefacescannowbemeshedbyselectingtheM Thefacescannowbem eshedbyselectingtheMeshOperation.MeshFace eshOperation.MeshFace Command.MeshFace.Allthefacescanbemesh Command.MeshFace.A llthefacescanbemeshedatoncebyselectingt edatoncebyselectingthethree hethree previouslydefinedfacegeometriesfromthepo previouslydefinedfac egeometriesfromthepopupwindoworshiftleftpupwindoworshiftleft-clicking clicking the facesedges.Theelementsopt sedges.TheelementsoptionshouldbesettoQua ionshouldbesettoQuad,typetoMap,andsmoot d,typetoMap,andsmoother her to None.Allotherdefaultvaluescanbekeptand None.Allotherdefaul tvaluescanbekeptandtheapplybuttonselecte theapplybuttonselected.Theco d.Theco mpleted facemeshcanbeseeninfigure23.(For3Dmo facemeshcanbeseen infigure23.(For3Dmodelsgotosection3.6to delsgotosection3.6tocontinue continue .)

Fig.23.CompletedMesh. Theboundarytypescannowbedefinedsinceth Theboundarytypescan nowbedefinedsincethemeshingiscomplete.Th emeshingiscomplete.Thisisdon isisdon eby selectingZoneOperation.SpecifyBoundaryTy selectingZoneOperati on.SpecifyBoundaryTypes.Thetypeoptionis pes.Thetypeoptionis automaticallysettoWallsodefinetheairfoi automaticallysettoW allsodefinetheairfoil'sboundaryfirst.Thee l'sboundaryfirst.Theentityopt ntityopt ionshould besettoEdgesandthenselectallsixedges besettoEdgesandth enselectallsixedgesthatdefinetheairfoilg thatdefinetheairfoilgeometry, eometry, seefigure 24.Itisagoodideatogiveallzonesandboundaryconditionsuseful 24.Itisagoodideatogiveallzonesandbo undaryconditionsusefulnamesso namesso when importedintoFLUENTlocatingthedesiredzone importedintoFLUENTl ocatingthedesiredzoneswillbeeasier. swillbeeasier.

Fig.24.Airfoilboundarydefinition. Forthisproceduretheairfoilboundarywillb Forthisprocedurethe airfoilboundarywillbenamedairfoil.Next,th enamedairfoil.Next,thetypene etypene edstobe changedtoPressure-far-field.Theedgesthat changedtoPressure-fa r-field.Theedgesthatmakeupthisboundarycon makeupthisboundaryconditionar ditionar eall theouteredgesofthemesh.Thisconsistsof theouteredgesofthe mesh.ThisconsistsofedgesAB,BC,CD,DE,EF, edgesAB,BC,CD,DE,EF,FG,GI, FG,GI, and AI,refertofigure18.Thisboundaryconditio AI,refertofigure18 .Thisboundaryconditionwillbelabeledfarfiel nwillbelabeledfarfield.Thela d.Thela stentity thatmustbedefinedistheairflowregion.T thatmustbedefinedi stheairflowregion.Thisisdonebyselecting hisisdonebyselectingZoneOper ZoneOper ation.

ContinuumType.Thetypewillbefluidandall ContinuumType.Thety pewillbefluidandallthreefacesshouldbese threefacesshouldbeselectedfo lectedfo rentity. Thiscontinuumwillbecalledair,seefigure25. Fig.25.Continuumboundarydefinition. ThemeshcannowbeexportedtoaformatFLUEN Themeshcannowbeex portedtoaformatFLUENTcanread.Thisisdone Tcanread.Thisisdonebyselect byselect ing File.Export.Mesh.Thisopenstheexportwi File.Export.Mesh. Thisopenstheexportwindow,seefigure26. ndow,seefigure26.

Fig.26.Meshexportwindow. Makecertaintheexport2-Dmeshoptionissel Makecertaintheexpor t2-Dmeshoptionisselectedandthatthemeshf ectedandthatthemeshfileisgo ileisgo ingwhere desiredbycheckingwiththebrowsebutton.Th desiredbycheckingwi ththebrowsebutton.Thenselectacceptandthe enselectacceptandthe2Dmeshi 2Dmeshi sready tobereadintoFLUENT. 3.5Creating3DWing Thissectioncontinuesfromtheendofsection Thissectioncontinues fromtheendofsection3.3.Inordertocreate 3.3.Inordertocreatethewing thewing sectionthe threefacesthatwerepreviouslycreatedhave threefacesthatwere previouslycreatedhavetobeextruded.Thisisd tobeextruded.Thisisdonebyse onebyse lecting GeometryOperation.VolumeCommand. right-clickFormVolume.Sweep Face.Theextrusionwillconsistofextruding Face.Theextrusionwi llconsistofextrudingallthefacesintheposi allthefacesinthepositivez-di tivez-di rectionbya magnitudeofone.Selectthefacesthrougheit magnitudeofone.Sele ctthefacesthrougheithershiftleft-clickingt hershiftleft-clickingthemorel hemorel sethrough thepopupwindow.Theextrusionpathwillbev thepopupwindow.The extrusionpathwillbeviaavectorsoselectthe iaavectorsoselectthevectorp vectorp ath option.Tochangethemagnitudeoftheextrusi option.Tochangethe magnitudeoftheextrusionclickthedefinebutto onclickthedefinebuttonunderp nunderp athand setthemagnitudetothedesiredvalue.Leave setthemagnitudetot hedesiredvalue.Leavethevalueatoneinthep thevalueatoneinthepositivez ositivez -direction forthisprocedure,seefigure27.

Fig.27.Sweepfacesetupandvectordefinition. Sweptvolumescanbelabelediftheyareextru Sweptvolumescanbel abelediftheyareextrudedseparately.Oncethe dedseparately.Oncethevector vector magnitudeanddirectionaresetclickapplyto magnitudeanddirectio naresetclickapplytoextrudethefaces.Atth extrudethefaces.Atthispoint ispoint alarge numberoffaceswillhavebeencreatedwithge numberoffaceswillh avebeencreatedwithgenericlabelssincevolume nericlabelssincevolumesaredef saredef inedby faceswhichGambithascreatedthroughtheswe faceswhichGambithas createdthroughthesweepingprocess.Theeasies epingprocess.Theeasiestmethod tmethod to selectadesiredfaceistocontinuallyshift selectadesiredface istocontinuallyshiftleft-clickanedgeofthe left-clickanedgeofthefaceunt faceunt ilthedesired faceishighlightedandthenthroughthepopup faceishighlightedan dthenthroughthepopupwindowremovethefaces windowremovethefacesthatshou thatshou ldnot havebeenselected.The3Dwinggeometryisno havebeenselected.Th e3Dwinggeometryisnowcreatedandameshfor wcreatedandameshforthevolum thevolum es canbecreated.

3.6Meshing3D Allthefacesthatexistedinthe2Dmeshproc Allthefacesthatexi stedinthe2Dmeshprocessandtheirreplicaswi essandtheirreplicaswillbemes llbemes hedinthe samefashionasdescribedinsection3.4.Ther samefashionasdescri bedinsection3.4.Thereforerefertosection3. eforerefertosection3.4forthe 4forthe face meshingofthe3Dgeometry.Refertofigure28 meshingofthe3Dgeom etry.Refertofigure28forwhatafacemeshedg forwhatafacemeshedgeometrys eometrys hould looklikeatthecompletionofsection3.4.Fo looklikeatthecompl etionofsection3.4.Foreachvolumetwoopposit reachvolumetwooppositefacess efacess hould nowbeidenticallymeshed. Fig.28.Allfacesandtheirreplicasthatwerepresentinsection3.4aremeshed . InordertomeshthevolumesaCoopermeshwil Inordertomeshthev olumesaCoopermeshwillbeused.Thisisdoneb lbeused.Thisisdonebyselecti yselecti ng MeshOperation.VolumeCommand.MeshVolume. MeshOperation.Volum eCommand.MeshVolume.Thisopensthevolume Thisopensthevolume meshwindow.Thevolumemeshwillbeahexele meshwindow.Thevolum emeshwillbeahexelementmeshandtypeCooper mentmeshandtypeCooper.The .The Coopermeshwilltaketwofacespre-meshedfac Coopermeshwilltake twofacespre-meshedfaces,theSources,andthen es,theSources,andthenreplicat replicat ethe meshonthosefacesatadesiredintervalspac meshonthosefacesat adesiredintervalspacingforthevolumebetwee ingforthevolumebetweenthefac nthefac es.The Coopermeshwillnotworktryingtomeshalong Coopermeshwillnotw orktryingtomeshalongasinglelineconnecting asinglelineconnectingtwopoin twopoin tsof anyonevolumetogether.Thisiswhythegapa anyonevolumetogethe r.Thisiswhythegapattheendoftheairfoil ttheendoftheairfoilisnecess isnecess ary.Also,

fortheCoopermeshtosucceed,bothoftheen fortheCoopermeshto succeed,bothoftheendfacesmustbeidentical dfacesmustbeidentical.Theset .Theset tings usedforthevolumemeshinthisprocedureare usedforthevolumeme shinthisprocedureareseeninfigure29. seeninfigure29. Fig.29.Volumemeshsettings. Thus,usingtheCoopermeshprocess,meshall Thus,usingtheCooper meshprocess,meshallthevolumes.Thespacing thevolumes.Thespacingvaluewil valuewil l determinethedensityofthevolumesmesh.Thespacingvaluewillbe0.1forthis procedure.Thesmallerthespacingvaluethedenserthemesh.Remember procedure.Thesmallerthespacingvaluethed enserthemesh.Rememberthatwhil thatwhil ea densermeshgivesbetterresults,thecomputat densermeshgivesbett erresults,thecomputationtimeisalsoincrease iontimeisalsoincreased.Nowth d.Nowth e boundaryconditionsforthewingsectioncanb boundaryconditionsfo rthewingsectioncanbecreated.Thisisdoneb ecreated.Thisisdonebyselecti yselecti ngZone Operation.SpecifyBoundaryType.Sincetheb Operation.SpecifyBo undaryType.Sincetheboundarytypeofwallisd oundarytypeofwallisdefaultth efaultth e wingssurfacescanbedefinedfirst,seefigure30.Dontforgetthetwothinfaces atthe tailofthewingsection.

Fig.30.Thefacesthatdefinethewingsection. Thewingsectionisthenon-meshedportionof Thewingsectionisth enon-meshedportionofthevolumeandisdefined thevolumeandisdefinedbysixf bysixf ace entities.Thenextboundarytodefineistheo entities.Thenextbou ndarytodefineistheouterverticalfacesthat uterverticalfacesthatwillbed willbed efinedas symmetry,seefigure31.Thiswillpreventflo symmetry,seefigure3 1.Thiswillpreventflowdistortionsalongthee wdistortionsalongtheedgesoft dgesoft he volume. Fig.31.Facestobedefinedassymmetry.

Thelastboundarylayerwillbedefinedasap Thelastboundarylaye rwillbedefinedasapressure-far-field.There ressure-far-field.Therewillbee willbee ightfaces aspartofthiszone,seefigure32.Dontforgetthetwosmallfacesinthemiddl ebackof themeshvolumes. Fig.32.Facestobedefinedaspressure-far-field. Thefinalzonethatmustbedefinedistheflu Thefinalzonethatmu stbedefinedisthefluidvolume.Thisisdoneb idvolume.Thisisdonebyselecti yselecti ngZone Operation.SpecifyContinuumType.Theentity Operation.SpecifyCo ntinuumType.Theentityisallthevolumesandt isallthevolumesandtheywill heywill be definedasafluidtypeandnamedair.The3D definedasafluidtyp eandnamedair.The3Dgeometryisnowreadyto geometryisnowreadytobeexport beexport edinto ameshfile.ThisisdonebyselectingFile. ameshfile.Thisisd onebyselectingFile.Export.Mesh,seefigure Export.Mesh,seefigure26.Make 26.Make certaintheexport2-D(X-Y)meshoptionisnotselected. 4.FLUENTProcedure ThedesiredmeshcannowbereadintoFLUENTw Thedesiredmeshcann owbereadintoFLUENTwhichwillthenrunthege hichwillthenrunthegeometry ometry throughthenumericalanalysis.OpenFLUENTan throughthenumerical analysis.OpenFLUENTandselectthe2Ddoublepr dselectthe2Ddoubleprecision ecision

operation(2ddp)fortwodimensionaloperation operation(2ddp)fort wodimensionaloperationsand3Ddoubleprecision sand3Ddoubleprecision(3ddp)f (3ddp)f or threedimensionaloperations.TheGambitmesh threedimensionaloper ations.TheGambitmeshisreadintoFLUENTbyse isreadintoFLUENTbyselectingF lectingF ile .Read.Caseandselectingtheappropriatemeshfile.Makecertainthe .Read.Caseandselectingtheappropriateme shfile.MakecertaintheFLUENT FLUENT windowdoesn'tdisplayanyerrormessagesafte windowdoesn'tdisplay anyerrormessagesafterreadinginthemeshfil rreadinginthemeshfile.First e.First themesh shouldbecheckedbyselectingGrid.Check.T shouldbecheckedbys electingGrid.Check.Thiswillconductathorou hiswillconductathoroughcheck ghcheck of themeshtomakecertainnoerrorsarepresent themeshtomakecerta innoerrorsarepresent.Thesolvertobeusedo .Thesolvertobeusedonthegeo nthegeo metry canbechangedbygoingtoDefine.Models.S canbechangedbygoin gtoDefine.Models.Solver.Forthisanalysis olver.Forthisanalysisasegrega asegrega ted solverwillbeusedsomakecertainthatoptio solverwillbeusedso makecertainthatoptionisselected.Next,the nisselected.Next,theviscousm viscousm odelmust besetbyselectingDefine.Models.Viscous. besetbyselectingDe fine.Models.Viscous.Twodifferentviscosity Twodifferentviscositymodelswe modelswe re tested.Thefirstistheinviscidmodelwhich tested.Thefirstist heinviscidmodelwhichassumesnoviscosity.The assumesnoviscosity.Thesecondi secondi sthe Spalart-Allmaras(SA)modelwhichisaturbule Spalart-Allmaras(SA) modelwhichisaturbulenteddyviscositymodel. nteddyviscositymodel.Insteado Insteado f solvingforthekineticenergyofturbulencet solvingforthekineti cenergyofturbulencetheSpalart-Allmarasmodel heSpalart-Allmarasmodelsolvesd solvesd irectly fortheeddyviscosityfromatransportequati fortheeddyviscosity fromatransportequation.TheSpalart-Allmaras on.TheSpalart-Allmarasmodelwas modelwas designedforaerospaceapplicationsinvolvingwall-boundedflows.After designedforaerospaceapplicationsinvolving wall-boundedflows.Afterrunning running both viscositymodelsoverarangeofanglesofatt viscositymodelsover arangeofanglesofattackof0-20°theresults ackof0-20°theresultsconcludedt concludedt hatthe inviscidmodelgaveagreateraccuracy.Theref inviscidmodelgavea greateraccuracy.Therefore,selecttheviscousm ore,selecttheviscousmodelofi odelofi nviscid. Thefollowingprocedureisthesameforbotht Thefollowingprocedur eisthesameforboththeinviscidandSpalart-A heinviscidandSpalart-Allmaras. llmaras. Maintainalldefaultvaluesandclosethewind Maintainalldefaultv aluesandclosethewindow.Thefluidmaterialth ow.Thefluidmaterialthatisto atisto beusedin thisanalysisisairandthefluidproperties thisanalysisisaira ndthefluidpropertiescanbesetbyselectingD canbesetbyselectingDefine.M efine.M aterials. Airshouldbethedefaultsetting.Thedensity Airshouldbethedefa ultsetting.Thedensityoftheairshouldbecha oftheairshouldbechangedfrom ngedfrom constant toidealgasandviscosity(appliesonlyforS toidealgasandvisco sity(appliesonlyforSAmodel)shouldbechange Amodel)shouldbechangedtothe dtothe Sutherlandthreecoefficientequation.Thedef Sutherlandthreecoeff icientequation.ThedefaultSutherlandvaluessh aultSutherlandvaluesshouldbe ouldbe maintained.Bychangingthesetwopropertiest maintained.Bychangin gthesetwopropertiesthedensityandviscosity hedensityandviscositywillnow willnow be

dependentonthetemperatureofthefluid.Bec dependentonthetempe ratureofthefluid.Becausetemperatureneedsto ausetemperatureneedstobemonit bemonit ored now,FLUENTwillautomaticallyturnontheene now,FLUENTwillautom aticallyturnontheenergyequation.Withthese rgyequation.Withthesevaluesse valuesse t clickChange/Createandclosethematerialswi clickChange/Createan dclosethematerialswindow.Theoperatingcondi ndow.Theoperatingconditionsnee tionsnee dto besetnext.ThisisdonebyselectingDefine besetnext.Thisisd onebyselectingDefine.OperatingCondition.Th .OperatingCondition.Thisopens isopens a newwindowwheretheoperatingpressurecanbe newwindowwheretheo peratingpressurecanbeset.Theoperatingpress set.Theoperatingpressureshoul ureshoul dbe keptatthedefaultstandardatmosphericpress keptatthedefaultst andardatmosphericpressure.Thenextstepisto ure.Thenextstepistosettheb settheb oundary conditionsfortheboundariesthatweredefine conditionsforthebou ndariesthatweredefinedinGambit.Thisisdone dinGambit.Thisisdonebyselec byselec ting Define.BoundaryConditions.Theonlyboundar Define.BoundaryCond itions.Theonlyboundaryconditionthatneedsto yconditionthatneedstobe be modifiedisthepressure-far-fieldcondition. modifiedisthepressu re-far-fieldcondition.Byselectingfarfield,wh Byselectingfarfield,whichisth ichisth enamethat wasgiventothisboundaryzoneinGambit,und wasgiventothisboun daryzoneinGambit,underthezonemenuandthen erthezonemenuandthenclickth clickth eset button.Thisbringsupthepressure-far-field button.Thisbringsup thepressure-far-fieldwindow.ForaReynoldsnu window.ForaReynoldsnumberof3 mberof3 x106 theMachnumbershouldbesetto0.1261,fora theMachnumbershould besetto0.1261,foraReynoldsnumberof6x106 Reynoldsnumberof6x106theMach theMach numbershouldbesetto0.2522,andforaReynoldsnumberof9x106the numbershouldbesetto0.2522,andforaReyn oldsnumberof9x106theMachnum Machnum ber shouldbesetto0.3783,asseeninfigure33. shouldbesetto0.378 3,asseeninfigure33.TheseMachnumbervalues TheseMachnumbervalueswerefou werefou nd usingtheReynoldsequation,Eq.7,foraflat usingtheReynoldsequ ation,Eq.7,foraflatplatetofindthefrees platetofindthefreestreamflo treamflo wvelocity. .V8c Re=(7)  withanassumeddensity,.,of1.225kg/m3,vi withanassumeddensit y,.,of1.225kg/m3,viscosity,,of1.789x10-5 scosity,,of1.789x10-5kg/m·s,and kg/m·s,and the chordlength,c,ofoneandV8 isthefreestreamvelocity.TheMachnumberisthen foundwiththeequation: V8 M=(8) a 8 whereMistheMachnumberanda8isthespeed whereMistheMachnu mberanda8isthespeedofsoundequalto347.51 ofsoundequalto347.51m/sat m/sat standardtemperatureandpressure.

Fig.33.Pressure-far-fieldwindowsetup. Theflowdirectionswillbeadjustedtoaccoun Theflowdirectionswi llbeadjustedtoaccountfortheangleofattack tfortheangleofattack.Ifthe .Ifthe angleof attackis10°thenthex-componentwouldbeth attackis10°thenthe x-componentwouldbethecos(10°)=0.9848andt ecos(10°)=0.9848andthey-componen hey-componen t wouldbethesin(10°)=0.17365.Fora3Dmode wouldbethesin(10°) =0.17365.Fora3Dmodelaz-componentflowdire laz-componentflowdirectioncanb ctioncanb e set,however,forthe3Dprocedureconductedh set,however,forthe 3Dprocedureconductedherethez-componentwill erethez-componentwillremainze remainze ro. Forexternalflowstheturbulentviscosityrat Forexternalflowsthe turbulentviscosityratioshouldbesetbetween ioshouldbesetbetween1and10 1and10 sothe defaultvalueoftenwillbekept.Thesolutio defaultvalueoftenw illbekept.Thesolutioncontrolscannowbeset ncontrolscannowbeset.Thisis .Thisis doneby firstselectingSolve.Control.SolutionThesolutionrelaxationforeach parametercanbechangedinthiswindow.Gener parametercanbechang edinthiswindow.Generallytheonlytimethese allytheonlytimetheserelaxatio relaxatio n parametersneedtobechangedisifrepetitive parametersneedtobe changedisifrepetitiveoscillationsbeginstoo oscillationsbeginstooccuront ccuront he coefficientofliftanddragplots.Thediscre coefficientofliftan ddragplots.Thediscretizationschemescanbem tizationschemescanbemodified. odified. Startby changingthepressurediscretizationvalueto changingthepressure discretizationvaluetoPrestoandleaveallthe Prestoandleavealltheotherval otherval uessetto theirdefaultsettings.Selectingmorecomplic theirdefaultsettings .Selectingmorecomplicateddiscretizationschem ateddiscretizationschemes,such es,such assecond orderupwindandpowerlaw,willaffecttheca orderupwindandpower law,willaffectthecalculationtimeandconver lculationtimeandconvergencesta gencesta bility. Nextthesolvermustbeinitializedbyselecti Nextthesolvermustb einitializedbyselectingSolve.Initialize.I ngSolve.Initialize.Initialize nitialize  Inthe computefromdropdownlistchoosefarfield.Th computefromdropdown listchoosefarfield.Thiswillautomaticallyins iswillautomaticallyinsertvalue ertvalue sintoall

theremainingtextboxesinthiswindow.These theremainingtextbox esinthiswindow.Thesevaluesshouldcorrespond valuesshouldcorrespondtothef tothef arfield boundarysettings.Selectinitandthenclose. boundarysettings.Sel ectinitandthenclose.Nexttheconvergencecri Nexttheconvergencecriterianee terianee dstobe set.ThisisdonebyselectingSolve.Monitors.ResidualIntheupperleftcorn er ofthenewwindowaretheoptionstoprintand ofthenewwindoware theoptionstoprintandplotthecurrentconverg plotthecurrentconvergencecrit encecrit eria values.Sinceweonlycarethatthemodelconv values.Sinceweonly carethatthemodelconvergesandnottheexactv ergesandnottheexactvaluesat aluesat which theconvergenceoccursselecttheplotoption theconvergenceoccurs selecttheplotoptionanddeselecttheprintop anddeselecttheprintoption.Thi tion.Thi swill keepthemainFLUENTwindowfromclutteringwi keepthemainFLUENTw indowfromclutteringwithanabundantamountof thanabundantamountof information.Theminimumconvergencecriterion information.Theminim umconvergencecriterionshouldbesetto1x10-6 shouldbesetto1x10-6foreach foreach residual.Duetothelargenumberofcellsin residual.Duetothel argenumberofcellsin3Dmodelsasmallconverg 3Dmodelsasmallconvergencecrit encecrit erion canleadtolongcomputationtimes.Inordert canleadtolongcompu tationtimes.Inordertodirectlymonitortheli odirectlymonitortheliftcoeffi ftcoeffi cientbeing experiencedbytheairfoil,selectSolve.Monitor.ForceWiththeforcemonitor s windowopenselectliftforthecoefficientto windowopenselectlif tforthecoefficienttobemonitored.Underopti bemonitored.Underoptionscheck onscheck theprint andplotboxesandforwallzonesselectthea andplotboxesandfor wallzonesselecttheairfoilprofile.Theforce irfoilprofile.Theforcevectors vectors havetobe settocorrespondtotheangleofattackforw settocorrespondtot heangleofattackforwhichthemodelisgoingt hichthemodelisgoingtobecalc obecalc ulated. Thismeansforanangleofattackof10°thex Thismeansforanangl eofattackof10°thexforcevectorshouldhave forcevectorshouldhaveavalueof avalueof 

sin(10°)=-0.17365andayforcevectorofco sin(10°)=-0.17365an dayforcevectorofcos(10°)=0.9848,seefigu s(10°)=0.9848,seefigure18. re18. Fig.34.ForceMonitorswindowsettomonitortheliftcoefficientfor Fig.34.ForceMonitorswindowsettomonitor theliftcoefficientforanangle anangle ofattackof10°.

Thedragcoefficientcanbemonitoredinasim Thedragcoefficientc anbemonitoredinasimilarfashionbutaccurate ilarfashionbutaccurateresults results forthe dragcoefficientweren'tfound.Nexttherefer dragcoefficientweren 'tfound.Nextthereferencevaluesmustbeset. encevaluesmustbeset.Allforce Allforce monitor calculationsforthemodelwillusethesevalu calculationsforthem odelwillusethesevalues.SelectReport.Refer es.SelectReport.ReferenceValu enceValu es Inthecomputefromdropdownmenuselectfarfi Inthecomputefromdr opdownmenuselectfarfieldandforreferencezon eldandforreferencezoneselect eselect the fluidzonethatwasdefinedinGambit,air.Wh fluidzonethatwasde finedinGambit,air.Whilethiswillsetmostof ilethiswillsetmostoftherefe therefe rence valuescorrectly,theactualdimensionsofthe valuescorrectly,the actualdimensionsoftheairfoilgeometryhaveto airfoilgeometryhavetobeset beset independently.Sincethechordlengthofthis independently.Sincet hechordlengthofthisprocedureisonemeteran procedureisonemeterandthedep dthedep thisone meter,thedefaultvaluesarecorrect.Nowthe meter,thedefaultval uesarecorrect.Nowthemodelisreadytobesol modelisreadytobesolved.This ved.This isdone byselectingSolve.IterateSinceconvergencecriteriaweredefined,thenumber of iterationschosenshouldberelativelylarget iterationschosenshou ldberelativelylargetomakecertainasolution omakecertainasolutionhastime hastime to converge.Thenumberofiterationswillbeset converge.Thenumbero fiterationswillbesetto10,000.Theotherval to10,000.Theothervaluesinth uesinth is windowwillbeleftattheirdefaultvalues.B windowwillbeleftat theirdefaultvalues.Begintheiterationproces egintheiterationprocessbysele sbysele cting iterate.Oncethemodelfinishesiteratingthe iterate.Oncethemode lfinishesiteratingtheaccuracyoftheresults accuracyoftheresultsshouldbe shouldbe checked. Anumberoffour-digitairfoilshavealreadyh Anumberoffour-digit airfoilshavealreadyhadcoefficientofliftpl adcoefficientofliftplotsgener otsgener atedfrom NACAempiricaldata.Theseplotscanbefound NACAempiricaldata.T heseplotscanbefoundinmanydifferentsources inmanydifferentsources.Forthi .Forthi s procedurethevalueswillbecomparedtofigur procedurethevaluesw illbecomparedtofigures35,36,and37insect es35,36,and37insection5.2f ion5.2f rom reference1.Iftheresultsarenotwithinar reference1.Ifthere sultsarenotwithinarangeofaccuracydesired angeofaccuracydesiredseverals severals tepscanbe takentotryandimprovethesolution.Thefir takentotryandimpro vethesolution.Thefirst,istochangethedisc st,istochangethediscretizatio retizatio nvalues undertheSolve.Control.Solutionwindow.Thesecondistoincreasethe densityofthemesh,throughtheadaptcommand densityofthemesh,t hroughtheadaptcommand,orreducestheconverge ,orreducestheconvergencecrite ncecrite ria.No improvementswerefounddotoconvergencecrit improvementswerefoun ddotoconvergencecriterialessthan10-10.Ta erialessthan10-10.Table2giv ble2giv esthe settingswithwhichthebestsolutionswerefo settingswithwhichth ebestsolutionswerefoundforthe0012inviscid undforthe0012inviscidmodel. model.

Table2.Settingdiscretizationandmeshadaptationsettingsfor0012i Table2.Settingdiscretizationandmeshadapt ationsettingsfor0012inviscidm nviscidm odelforbestresults. Toincreasetheaccuracyofthemodelbyincreasingthenumberofcells Toincreasetheaccuracyofthemodelbyincre asingthenumberofcellsthatexi thatexi staround theairfoilssurfaceselectAdapt.BoundaryAdaptingthecellsaroundthebounda ry oftheairfoilgeometrywillbreakeachofthe oftheairfoilgeometr ywillbreakeachoftheboundarycellsintofour boundarycellsintofourcellsre cellsre sultingina densermesh.However,byincreasingthedensit densermesh.However, byincreasingthedensityofthemeshthecalcula yofthemeshthecalculationtime tiontime is increased.Underboundaryzonesselecttheair increased.Underbound aryzonesselecttheairfoilgeometryandclickt foilgeometryandclickthemarkb hemarkb utton. AnotewillpopupinthemainFLUENTwindowin Anotewillpopupint hemainFLUENTwindowindicatingthenumberofce dicatingthenumberofcellstobe llstobe adapted.Toadaptthesecellssimplyclickthe adapted.Toadaptthes ecellssimplyclicktheadaptbuttonintheboun adaptbuttonintheboundaryadap daryadap t windowandselectokintheadaptwarningwind windowandselectoki ntheadaptwarningwindow.Aftertheadaptproce ow.Aftertheadaptprocessiscom ssiscom plete themainFLUENTwindowwillprintouttheresu themainFLUENTwindow willprintouttheresultsoftheadaptingproce ltsoftheadaptingprocess.Then ss.Then umber undertheadaptedcolumnindicatesthecurrent undertheadaptedcolu mnindicatesthecurrentnumberofcellsinthem numberofcellsinthemesh.The esh.The 7436in

Table2underadaptisreferringtothisvalue Table2underadaptis referringtothisvalue.Nowthatthemeshisde .Nowthatthemeshisdenserthe nserthe model mustbereinitializeandthentheiterationprocessrepeated. 5.Conclusion 5.1Comparisonof2-Dand3-DFLUENTModels Byfollowingtheprocedureasdescribedabove, Byfollowingtheproce dureasdescribedabove,botha2-Dand3-Dmodel botha2-Dand3-Dmodelofthef ofthef ourdigitairfoil0012werecreated.Whenthesemo digitairfoil0012wer ecreated.WhenthesemodelswereruninFLUENTu delswereruninFLUENTunderthe nderthe same conditionsidenticalresultswereproduced.Th conditionsidenticalr esultswereproduced.Thisgoestoprovethevali isgoestoprovethevalidityofu dityofu singa simpler2-Dmodelforanalyzingairflowovera simpler2-Dmodelfor analyzingairflowoverairfoilsinsteadofthemo irfoilsinsteadofthemoretimec retimec onsuming 3-Dmodel. 5.2Comparisonof2-DNumericalResultstoNACAEmpiricalData 5.2Comparisonof2-DNumericalResultstoNAC AEmpiricalData Throughconductingthisresearch,aprocessto Throughconductingthi sresearch,aprocesstoobtainresultswithless obtainresultswithlessthana1 thana1 0%error, whencomparedtoNACAempiricaldata,usingFL whencomparedtoNACA empiricaldata,usingFLUENT,wasfoundforangle UENT,wasfoundforanglesofatta sofatta ck lessthan10°.However,astheangleofattack lessthan10°.However ,astheangleofattackoftheairfoilincreased oftheairfoilincreasedbeyond10°t beyond10°t he accuracyalsodecreased.Figure35,36,and37 accuracyalsodecrease d.Figure35,36,and37showacomparisonofthe showacomparisonoftheFLUENT FLUENT producedresultsascomparedtotheNACAempir producedresultsasco mparedtotheNACAempiricaldataaswellasthe icaldataaswellastheaccuracy accuracy ata givenangleofattackfortheReynoldsnumbers givenangleofattack fortheReynoldsnumbersof3x106,6x106,and9x1 of3x106,6x106,and9x106respec 06respec tively. Valueshavebeenplottedforboththeinviscid Valueshavebeenplott edforboththeinviscidandSpalart-Allmarasmod andSpalart-Allmarasmodel. el.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 048121620 AngleofAttack(degrees) CoefficientofLift 0 5 10 15 20 25 30 35 40 Error(%) NACA Inviscid SA InviscidError SAError 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 048121620 AngleofAttack(degrees) CoefficientofLift 0 5 10 15 20 25 30 35 40 Error(%) NACA Inviscid SA InviscidError SAError Fig.35.PlotofcoefficientofliftsversusN Fig.35.Plotofcoeff icientofliftsversusNACAempiricaldataandpe ACAempiricaldataandpercenterr rcenterr ordifferencebetween theresultsforReynoldsnumber3x106. 0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 048121620 AngleofAttack(degrees) CoefficientofLift 0 5 10 15 20 25 30 35 40 Error(%) NACA Inviscid SA InviscidError SAError Fig.36.PlotofcoefficientofliftsversusN Fig.36.Plotofcoeff icientofliftsversusNACAempiricaldataandpe ACAempiricaldataandpercenterr rcenterr ordifferencebetween theresultsforReynoldsnumber6x106.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 048121620 AngleofAttack(degrees) CoefficientofLift 0 5 10 15 20 25 30 35 40 45 Error(%) NACA Inviscid SA InviscidError SAError 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 048121620 AngleofAttack(degrees) CoefficientofLift 0 5 10 15 20 25 30 35 40 45 Error(%) NACA Inviscid SA InviscidError SAError Fig.37..Plotofcoefficientofliftsversus Fig.37..Plotofcoe fficientofliftsversusNACAempiricaldataand NACAempiricaldataandpercente percente rrordifference betweentheresultsforReynoldsnumber9x106.

Ascanbenoticedfromthesefigures,theinvi Ascanbenoticedfrom thesefigures,theinviscidmodelproducedmore scidmodelproducedmoreaccurate accurate results ateveryangleofattack.Also,theaccuracyo ateveryangleofatta ck.Also,theaccuracyofeithermodeldoesn'tne feithermodeldoesn'tnecessarily cessarily increase ordecreasecorrespondingtotheflowvelocity ordecreasecorrespond ingtotheflowvelocity.Astheangleofattack .Astheangleofattackincreases increases the accuracyofbothmodelsdropsdramatically.At accuracyofbothmodel sdropsdramatically.Attemptstoincreasethisa temptstoincreasethisaccuracyw ccuracyw ere madebybothincreasingthedensityofthemes madebybothincreasin gthedensityofthemeshandthetighteningthe handthetighteningtheconvergen convergen ce criterion.Unfortunately,neitherreducingthe criterion.Unfortunate ly,neitherreducingtheconvergencecriterionle convergencecriterionlessthan1 ssthan1 0-10nor increasingthedensityofthemeshresultedin increasingthedensity ofthemeshresultedinanincreaseofaccuracy anincreaseofaccuracyforthel forthel ift coefficient.Thislargeerrorcouldbedueto coefficient.Thislarg eerrorcouldbeduetothefactthatstatistical thefactthatstatistical(Reynold (Reynold saveraged Novier-Stokes)turbulencemodelshavedifficul Novier-Stokes)turbule ncemodelshavedifficultysolvingproblemswith tysolvingproblemswithlargeedd largeedd y turbulenceeffects(Mellen).Thus,usingFLUEN turbulenceeffects(Me llen).Thus,usingFLUENT'sinviscidmodel,lift T'sinviscidmodel,liftcoefficie coefficie ntscan befoundwithin10%oftheirempiricalvalues befoundwithin10%of theirempiricalvaluesforanglesofattackless foranglesofattacklessthan10°. than10°.

5.3WingtipVorticesModel Athreedimensionalwingmodelwascreatedusi Athreedimensionalwi ngmodelwascreatedusingthesameprocessdescr ngthesameprocessdescribedins ibedins ection 3.5.Theonlyadditionwasasecondvolumeextrusioninthepositivez3.5.Theonlyadditionwasasecondvolumeext rusioninthepositivez-direction direction ,see figure25. Fig.38.ExtrudedWingmodel. Anattemptwasthenmadetomeshhalfofthew Anattemptwasthenma detomeshhalfofthewingsectionasafluidto ingsectionasafluidtocreatet createt he conditionsnecessaryforawingtipvortextoo conditionsnecessaryf orawingtipvortextooccur.However,duetothe ccur.However,duetotheairfoils airfoils peculiar geometryaquadmeshwasnotpossible.Atrim geometryaquadmeshw asnotpossible.Atrimeshonthetwoendfaces eshonthetwoendfacesoftheai oftheai rfoil wasattemptedsothataCoopermeshcouldbep wasattemptedsothat aCoopermeshcouldbeperformedforthevolume. erformedforthevolume.Unfortuna Unfortuna tely, thefacesmeshesdidnotcomeoutidentical,seefigure26.

Fig.39.DisplayingthefailureoftheTripavemesh. Thereasonforthisisunknownsincebothgeom Thereasonforthisis unknownsincebothgeometrieswereidentical.Th etrieswereidentical.Theonlyfa eonlyfa cemesh thatresultedinidenticalfaceswasaQuad/Tr thatresultedinident icalfaceswasaQuad/Trimap.Unfortunately,thi imap.Unfortunately,thisresults sresults inan extremelyskewedmeshwhichledtoinaccuracy extremelyskewedmesh whichledtoinaccuracyintheresults,seefigur intheresults,seefigure27. e27.

Fig.40.DisplayingtheQuad/Trimapmeshgeneratedforthemeshedwing Fig.40.DisplayingtheQuad/Trimapmeshgene ratedforthemeshedwingsection. section. Resultedin skewedcellswhichgivepoorresults. AnattemptwasmadetouseFLUENTtoanalyzethemeshwiththeskewedc AnattemptwasmadetouseFLUENTtoanalyzet hemeshwiththeskewedcells, ells, however,duetotheskewedcellsnoconvergenc however,duetothesk ewedcellsnoconvergenceeveroccurred.After50 eeveroccurred.After5000iterat 00iterat ions themodelwasstoppedandanattemptwasmade themodelwasstopped andanattemptwasmadetoseeifanywingtipvor toseeifanywingtipvortexwas texwas discernable.Thisattemptresultedinthecomp discernable.Thisatte mptresultedinthecomputerrunningoutofmemor uterrunningoutofmemoryandno yandno final visualrepresentationofthemodelcouldbepl visualrepresentation ofthemodelcouldbeplotted.Whileitislikely otted.WhileitislikelyFLUENTi FLUENTi s

capableofmodelingwingtipvortices,analter capableofmodelingwi ngtipvortices,analternatemeshmethodwillhav natemeshmethodwillhavetobea etobea ttempted andamorepowerfulcomputermaybenecessary andamorepowerfulco mputermaybenecessarytosolvethemodel. tosolvethemodel.

6.References 1. Abbott,I.,andVonDoenhoff,A.,1959,Theory Abbott,I.,andVonDo enhoff,A.,1959,TheoryofWingSections,Dover, ofWingSections,Dover, Mineola,NY 2. Anderson,Jr.,J,2001,FundamentalsofAerody Anderson,Jr.,J,2001 ,FundamentalsofAerodynamics,3rdEd.,McGrawH namics,3rdEd.,McGrawHill, ill, Singapore 3. Eastman,J.,andWard,K.,1933,"Thecharacte Eastman,J.,andWard, K.,1933,"Thecharacteristicsof78relatedair risticsof78relatedairfoilsect foilsect ions fromtestsinthevariable-densitywindtunnel fromtestsinthevari able-densitywindtunnel,"NACA-report-460 ,"NACA-report-460 4. Aerospaceweb.org,"NACAAirfoilSeries," http://www.aerospaceweb.org/question/airfoils/ http://www.aerospacewe b.org/question/airfoils/q0041.shtml(2006) q0041.shtml(2006) 5. FLUENT,"studentFLUENT-TutorialLibrary-Airfoil," http://www.FLUENT.com/software/studentFLUENT/t http://www.FLUENT.com/ software/studentFLUENT/tutorial_airfoil.htm(16N utorial_airfoil.htm(16Nov ov 2006) 6. U.S.CentennialFlightCommission,"TheNation U.S.CentennialFlight Commission,"TheNationalAdvisoryCommitteefor alAdvisoryCommitteefor Aeronautics(NACA)," http://www.centennialofflight.gov/essay/Evolut http://www.centennialo fflight.gov/essay/Evolution_of_Technology/NACA/Te ion_of_Technology/NACA/Tech1 ch1 .htm(7Dec2006) 7. Mellen,C.,Fröhlich,J.,andRodi,W.,2003, Mellen,C.,Fröhlich, J.,andRodi,W.,2003,"LessonsfromLESFOILPro "LessonsfromLESFOILProjecton jecton Large-EddySimulationofFlowAroundanAirfoi Large-EddySimulation ofFlowAroundanAirfoil,"AIAAJournal,Vol.41 l,"AIAAJournal,Vol.41, , No.4.

Appendix:Four-digitAirfoilCalculatorM-file function[Upoints,Lpoints]=FourSeries(c,m,p,t) %c:thelengthofthechord %m:maxordinateofmeanlineinpercent %p:chordwisepositionofmaxordinateintenths %t:maxthicknessofairfoilaspercent x=linspace(0,1); %Calculatingthethicknessoftheairfoil i=1; whilei