gas dynamics project report

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]

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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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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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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ListofAcronyms𝑐"-Coefficientoflift

𝑐$ -Coefficientofdrag𝑐%-skinfrictioncoefficient

Pa–Pascal

m–Meter

M–MachK–Kelvin


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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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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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2.2.2MeshingForthesoftwaretocarryoutcalculationsbynumericalmethods,weneedtodefinethesmallareawhichwillbeconsideredaselementalareaforcalculationpurpose.Thistaskisaccomplishedbycreatingmeshinthecontrolvolumeor,asinthiscase,oncontrolsurface.ThisprocessisknownasMeshing.Here2-Dmono-blockstructuredmeshisgeneratedusingICEMCFD16.2Academic.Inordertogetagoodmeshqualityandhencebetterflowvisualization,H-gridisused.

Fig2.2Meshgeneratedoncontrolsurface

Thefigureaboveshowstheairfoilonthecontrolsurfaceandthemeshgenerated.Theorthogonalmeshqualityattainedhereis0.98.


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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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2.2.5TurbulenceModelTurbulencemodelisimportanttoanalyzeviscousflowfield.Inthisproject,wehaveusedK-ωSSTmodelforthepurposeasitishighlyaccurateforboundarylayersimulationandhighpressuregradient.

2.3Post-processingThesolutiondatagatheredafteriterationsareconvergedandrepresentedingraphicalform.Inthisproject,CFDPostisusedforthispurpose.


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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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Fromtheapexoftheairfoiltothepointofmaximumthickness,machnumberremainsalmostconstant.Theflowdirectionisparalleltothesurfaceoftheairfoilnow.Afterthepointofmaximumthickness,theflowpassesovertherearpartofthefoilwhereitsthicknessstartsdecreasing.Duethisabruptchangeinflowdirection,expansionoftheflowtakesplaceandastheflowissupersonic,thereisagreataccelerationwhichresultsinaveryhighmachnumberintheflowoverthesecondhalfoftheairfoilandtheflowisagainparalleltoitssurface.Atthetrailingedgeoftheairfoil,theflowathighmachnumberfromtheupperandlowerportionoftheairfoilencounterseachotherandthereisagainanobliqueshockwavegenerated.Thisneutralizestheraiseinmachnumberandthemachnumberagaingoesbackto3.5.

Fig3.2Machnumbervariationalongthechordlength

Heretheblackdotsindicatethemachnumbervariationalongthelowersurfaceandthoseinredshowsthesamealongtheuppersurfaceoftheairfoil.


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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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Fig3.4Machnumbervariationalongthechordlength

3.2DragandLiftCoefficients 3.2.1InviscidFlow

Astheangleofattackiszero,flowisinviscidandtheairfoilissymmetricalongchordlength,therewillbenoliftforcegenerated,sotheliftcoefficientcanbeexpectedtobezero.Belowaretheresultsderivedfromthesimulationscarriedout,whichagreeswiththeexpectation.

𝑐$ = 0.012076 c. = −4.137x1034≈0


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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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Chapter4Conclusion

Inthepresentwork,numericalstudywascarriedoutoverDiamondHeadairfoilinviscousandinviscidmediumatsupersonicMachnumberof3.5.Fromthedetailsoftheanalysiswecometothefollowingconclusion:

• Duetoviscousflowthereisalossintotalpressure.Itisclearlyseenfromthetotalpressurevariationalongthechordlengthoftheairfoil(asshownisFig4.1),thatininviscidflowthetotalpressureisconstantalongthechordlengthaftertheshockformationandaftertheexpansionoccurs.Ontheotherhand,inviscousfluid(asshowninFig4.2),duetoviscousdissipationthereisacontinuouslossintotalpressurealongthesurfaceoftheairfoilaftertheshockisformed.

Fig4.1Totalpressurevariationalongthechordlengthoftheairfoil(InviscidFlow)


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Fig4.2Totalpressurevariationalongthechordlengthoftheairfoil(ViscousFlow)

• Fromtheobservationofdragcoefficient,wecansaythatdragcontributionduetoviscousflowis𝑐% = 0.0022281101,whichisnotassignificantaswavedrag.Thatiswhyinmostof2-Dsupersoniccasesviscouseffectisneglected.

• ThereisalsoremarkabledifferenceintheMachnumbervariationalongthechordlengthininviscidandviscousflows.Thereasonforacontinuousandsteadydecrementinthemachnumberobservedinviscousflowalongtheairfoilsurfaceistheresultofviscousdissipation.


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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

gas dynamics project report

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