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MECH 6111 Gas Dynamics
Project Report:
Numerical investigation of inviscid and viscous supersonic flow over a diamond head airfoil
Submitted to: Dr. Wahid Ghaly
November 30, 2015
Name Student ID Email address Jay Adhvaryu 40002804 [email protected] Nishant Patel 27853378 [email protected]
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ConcordiaUniversity GasDynamics November30,2015
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Abstract In this project we have simulated a steady-state supersonic flow over a diamond head airfoil for two types of fluids – (i) viscous and (ii) inviscid. The angle of attack is zero. We have compared the results and explain the reasons for the differences observed in simulation results. At first we considered the case of inviscid flow and got the results that includes coefficient of drag and lift. Then viscous flow is taken into consideration for the same airfoil. It includes the study of flow behavior, drag characteristics and variation of velocity along the airfoil. The simulation is carried out on commercial CFD code. The outcomes of both the viscous and inviscid flow are compared in the end.
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ConcordiaUniversity GasDynamics November30,2015
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TableofContents1. Introduction………………………………….………………………………………….….6
1.1. Supersonic Airfoils………………………………………………………………....….6 1.2. Airfoil Terminology…………………………………………………………………….6
2. Simulation…………………………………………………….….…………………………7 2.1. Introduction 2.2. Pre-processing…………………………………………………………………………..7
2.2.1. GeometryofAirfoil……………………………………………………………….7 2.2.2. Meshing…………………………………………………………………………..8 2.2.3. Selectionofsolver………………………………………………………………..9 2.2.4. BoundaryConditions………………………………………….………………….9 2.2.5. TurbulenceModel…………………………………………….…………………10
2.3. Post-processing……………………………………………………….………………..10 3. Results and Discussion…………………………………………………………………11
3.1. Mach Number………………………………………………………....………………11 3.1.1. Inviscid Flow…………………………………………..………..………………11 3.1.2. Viscous Flow……………………………………………………...……………13
3.2. Drag and Lift Coefficients……………………………………………………………14 3.2.1. Inviscid Flow…………………………………………………..………..………14 3.2.2. Viscous Flow…………………………………………………….………..……15
4. Conclusion………………………………………………………………………...………16 References…………………………………………………………………………………….18
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ConcordiaUniversity GasDynamics November30,2015
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ListofFigures2.1AirfoilGeometry……………………………………………………………………………...72.2Meshgeneratedoncontrolsurface…………………………………………………………82.3MeshandAirfoil(zoomed) ………………………………………………………………….93.1Machnumbervariationoverdiamondheadairfoil……………………………………….113.2Machnumbervariationalongthechordlength…………………………………………..123.3Machnumbervariationoverdiamondheadairfoil…………………………………….…133.4Machnumbervariationalongthechordlength………………………………………...…14 4.1Totalpressurevariationalongthechordlengthoftheairfoil(InviscidFlow) ……………164.2Totalpressurevariationalongthechordlengthoftheairfoil(ViscousFlow) ……………17
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ConcordiaUniversity GasDynamics November30,2015
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ListofAcronyms𝑐"-Coefficientoflift
𝑐$ -Coefficientofdrag𝑐%-skinfrictioncoefficient
Pa–Pascal
m–Meter
M–MachK–Kelvin
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ConcordiaUniversity GasDynamics November30,2015
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Chapter1Introduction
1.1SupersonicAirfoilsAnairfoilisbasicallytheshapeofawingthatcreatesanaerodynamicforcewhichhelpstheplanetogettherequiredlift.Theairfoilsdesignedfortheexposuretosupersonicflowsarecalledsupersonicairfoils.Supersonicairfoilshavesharpedgeinthefronttoavoidformationofdetachedbowshocksinfrontoftheairfoilasitmovesintheair[1]whereasthesubsonicairfoilsaregenerallyroundedinthefrontpart.Thesharpedgeinthesupersonicairfoilsmakesitmoresensitivetotheangleofattack.1.2AirfoilTerminologySomeofthetermsassociatedwiththeairfoilsanddefinedasfollows:
• LeadingEdge:Itisthepointatthefrontoftheairfoilwhichhasmaximumcurvatureorminimumradius.[2]
• TrailingEdge:Itisdefinedsimilarlyasleadingedgeattherearendoftheairfoil.• ChordLength:Thelengthofthelineconnectingtheleadingedgeandtrailingedgeis
knownaschordlengthoftheairfoil.• MeanCamberLine:Itisthelinemidwaybetweentheupperandthelowersurfaces.• AngleofAttack:Theanglebetweentheflowdirectionandchordlineisknownasthe
angleofattack.
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ConcordiaUniversity GasDynamics November30,2015
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Chapter2Simulation
2.1IntroductionIntheessenceofthetechnology,anewtool,computationalfluiddynamics(CFD)isveryusefultoanalyzethefluidsystem.Thedifferentialandintegralformsofequationsarefirstdiscretizedsothatthecomputercanunderstandthemandthenvariousschemesaredeveloped(numericalmethods)tosolvetheproblemandoutputismadeavailablebythesoftwareisvariouswayssuchasgraphsandanimation.ComputationalFluidDynamics’simulationprocessisdividedintotwoparts-(i)Pre-processingand(ii)Post-processing.HerewehaveusedICEMCFD16.2Academic,Fluent16.2AcademicandCFDPost16.2.2.2Pre-processingPre-processingisthephaseofsimulationinwhichwedefinethegeometryofasobject,controlvolumeorcontrolsurface,mesh,etc. 2.2.1GeometryofAirfoil
Wehaveconsideredadouble-wedge(diamond-head)airfoilasshowninFig3.1.Ithasachordlengthof20mandthicknessof2m.Consequently,thethicknesstochordratiois1:10.
Fig2.1AirfoilGeometry
TheairfoilgeometryismadeinICEMCFD16.2Academic.ThefigureshownabovewasmadeinCatiav5r19.
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ConcordiaUniversity GasDynamics November30,2015
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2.2.2MeshingForthesoftwaretocarryoutcalculationsbynumericalmethods,weneedtodefinethesmallareawhichwillbeconsideredaselementalareaforcalculationpurpose.Thistaskisaccomplishedbycreatingmeshinthecontrolvolumeor,asinthiscase,oncontrolsurface.ThisprocessisknownasMeshing.Here2-Dmono-blockstructuredmeshisgeneratedusingICEMCFD16.2Academic.Inordertogetagoodmeshqualityandhencebetterflowvisualization,H-gridisused.
Fig2.2Meshgeneratedoncontrolsurface
Thefigureaboveshowstheairfoilonthecontrolsurfaceandthemeshgenerated.Theorthogonalmeshqualityattainedhereis0.98.
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ConcordiaUniversity GasDynamics November30,2015
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Fig2.3MeshandAirfoil(zoomed)Thisfigureshowsclearlythatthemeshdensityishigherneartheairfoilforbetterandpreciseresults.2.2.3SelectionofsolverTherearetwotypesofsolveravailableinFluent16.2Academic,(i)PressureBasedSolverand(ii)DensityBasedSolver.Inoursimulation,DensityBasedSolverischosendueit’shigheraccuracyincalculationsofsupersonicflow.ThePressureBasedSolverontheotherhandgivesbetterresultsforincompressibleandsubsonicflows.2.2.4BoundaryConditionsTheflowoverairfoilhasbeenanalyzedat10kmaltitudewheretheambientpressureis26500Paandtemperatureis223.5K.[3]TheairfoilisexposedtothesupersonicflowatM=3.5.Angleofattackistakentobezero.
Forthefirstpart,theflowisconsideredtobeinviscidandinthesecondpartitisviscouswhereviscosityiscalculatedbytheSutherlandLaw(ThreeCoefficientMethod).
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ConcordiaUniversity GasDynamics November30,2015
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2.2.5TurbulenceModelTurbulencemodelisimportanttoanalyzeviscousflowfield.Inthisproject,wehaveusedK-ωSSTmodelforthepurposeasitishighlyaccurateforboundarylayersimulationandhighpressuregradient.
2.3Post-processingThesolutiondatagatheredafteriterationsareconvergedandrepresentedingraphicalform.Inthisproject,CFDPostisusedforthispurpose.
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ConcordiaUniversity GasDynamics November30,2015
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Chapter3
ResultandDiscussionInthissection,resultsfromFluentandCFDPostlikeMachnumber,CoefficientofpressureandTotalpressureareshownforinviscidandviscousflows.3.1Machnumber 3.1.1InviscidFlow
Fig3.1showsthevariationofmachnumberasthesupersonicflow(M=3.5)flowsoverthediamondheadairfoil.
Fig3.1Machnumbervariationoverdiamondheadairfoil
TheFig3.2showsthevariationofmachnumberalongthechordlengthoftheairfoil.Astheangleofattackiszero,thevariationpatternissymmetricalongthechordline.Theincidenceofflowontheairfoil’sleadingedgeseesasharpdropinmachnumber.Thisisdueagenerationofanattachedobliqueshockwaveattheapexoftheairfoil.Theflowisstillsupersonic.
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ConcordiaUniversity GasDynamics November30,2015
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Fromtheapexoftheairfoiltothepointofmaximumthickness,machnumberremainsalmostconstant.Theflowdirectionisparalleltothesurfaceoftheairfoilnow.Afterthepointofmaximumthickness,theflowpassesovertherearpartofthefoilwhereitsthicknessstartsdecreasing.Duethisabruptchangeinflowdirection,expansionoftheflowtakesplaceandastheflowissupersonic,thereisagreataccelerationwhichresultsinaveryhighmachnumberintheflowoverthesecondhalfoftheairfoilandtheflowisagainparalleltoitssurface.Atthetrailingedgeoftheairfoil,theflowathighmachnumberfromtheupperandlowerportionoftheairfoilencounterseachotherandthereisagainanobliqueshockwavegenerated.Thisneutralizestheraiseinmachnumberandthemachnumberagaingoesbackto3.5.
Fig3.2Machnumbervariationalongthechordlength
Heretheblackdotsindicatethemachnumbervariationalongthelowersurfaceandthoseinredshowsthesamealongtheuppersurfaceoftheairfoil.
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ConcordiaUniversity GasDynamics November30,2015
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3.1.2ViscousFlow Fig3.3showsthevariationofmachnumberwhenaviscoussupersonicflow(M=3.5) flowsoveradiamondheadairfoil.
Fig3.3Machnumbervariationoverdiamondheadairfoil
Asseeninthefigures3.3and3.4,justlikeininviscidflow,thereisasharpdropinmachnumberwheninflowsovertheapexoftheairfoilandthereisanincreaseinitwhenitpassesoverthesecondhalfoftheairfoil.Butitcanbeclearlyseenthatwhentheviscousflowpassesovertheincreasingthicknessanddecreasingthicknessoftheairfoil,themachnumberisnotconstantbutisdecreasingallalongthepathsteadily.Eventheraiseinmachnumberwhenthethicknessstartsdecreasingisnotsohighasthatintheinviscidflow.Anotherremarkablethingobservedisasleevealongtheairfoilwithverysmallmachnumber.Thisisbecauseoftheviscosityofthefluid.Aboundarylayerisgeneratedwherethevelocityofthefirstlayerofairthatcomesincontactofthesurfacereducestozero.
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ConcordiaUniversity GasDynamics November30,2015
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Fig3.4Machnumbervariationalongthechordlength
3.2DragandLiftCoefficients 3.2.1InviscidFlow
Astheangleofattackiszero,flowisinviscidandtheairfoilissymmetricalongchordlength,therewillbenoliftforcegenerated,sotheliftcoefficientcanbeexpectedtobezero.Belowaretheresultsderivedfromthesimulationscarriedout,whichagreeswiththeexpectation.
𝑐$ = 0.012076 c. = −4.137x1034≈0
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ConcordiaUniversity GasDynamics November30,2015
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3.2.2ViscousFlow
Unlikeinviscidflow,inviscousflow,thereisananotherformofdragcalledskinfrictiondragduetoviscouseffect.Theliftforcewillstillbezeroduetosymmetryandzeroangleofattack.Theresultsofthesimulationsareshownbelow.
TotalCoefficientofDrag𝑐$ = 0.014211 c. = 1.0147x1035≈0 𝑐% =0.0022281101
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ConcordiaUniversity GasDynamics November30,2015
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Chapter4Conclusion
Inthepresentwork,numericalstudywascarriedoutoverDiamondHeadairfoilinviscousandinviscidmediumatsupersonicMachnumberof3.5.Fromthedetailsoftheanalysiswecometothefollowingconclusion:
• Duetoviscousflowthereisalossintotalpressure.Itisclearlyseenfromthetotalpressurevariationalongthechordlengthoftheairfoil(asshownisFig4.1),thatininviscidflowthetotalpressureisconstantalongthechordlengthaftertheshockformationandaftertheexpansionoccurs.Ontheotherhand,inviscousfluid(asshowninFig4.2),duetoviscousdissipationthereisacontinuouslossintotalpressurealongthesurfaceoftheairfoilaftertheshockisformed.
Fig4.1Totalpressurevariationalongthechordlengthoftheairfoil(InviscidFlow)
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ConcordiaUniversity GasDynamics November30,2015
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Fig4.2Totalpressurevariationalongthechordlengthoftheairfoil(ViscousFlow)
• Fromtheobservationofdragcoefficient,wecansaythatdragcontributionduetoviscousflowis𝑐% = 0.0022281101,whichisnotassignificantaswavedrag.Thatiswhyinmostof2-Dsupersoniccasesviscouseffectisneglected.
• ThereisalsoremarkabledifferenceintheMachnumbervariationalongthechordlengthininviscidandviscousflows.Thereasonforacontinuousandsteadydecrementinthemachnumberobservedinviscousflowalongtheairfoilsurfaceistheresultofviscousdissipation.
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ConcordiaUniversity GasDynamics November30,2015
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References [1] Courant & Friedrichs. Supersonic Flow and Shock Waves. Pages 357:366. Vol I.New York: Inter science Publishers, inc, 1948 [2] Houghton, E. L.; Carpenter, P.W. (2003). Butterworth Heinmann, ed. Aerodynamics for Engineering Students (5th ed.). ISBN 0-7506-5111-3. p.18 [3] James E. A. John and Theo G. Keith, Gas Dynamics. Page 281 Third Edition. Pearson Education, Inc., ISBN 0-13-120668-0