Numerical Study on the Effects of Oscillation Frequency and Amplitude on Flow around Flapping Airfoil via an Improved Immersed Boundary Method

Transcription

1 mme.modares.ac.ir * ashrafizadeh@kntu.ac.ir *..... /77.. 2/80 0/ 22 0/4 0/3 0/7 0/ : : : NumericalStudyontheEffectsofOscillationFrequencyandAmplitude onflowaroundflappingairfoilviaanimprovedimmersedboundary Method AliAkbarHosseinjani AliAshrafizadeh * -DepartmentofMechanicalEngineering,KhajeNasirToosiUniversityofTechnology,Tehran,Iran. *P.O.B Tehran,Iran,ashrafizadeh@kntu.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper Received08April204 Accepted09June204 AvailableOnline5November204 Keywords: Immersedboundarymethod Vorticitycontours Flappingairfoil Kineticenergycontours Inthispaperanimprovedimmersedboundarymethodisusedforsimulatingsinusoidalpitching oscillations of symmetric airfoil. Immersed boundary methods which employ fixed Cartesian gridsarewellsuitedforsuchmovingboundaryproblems.twotestcasesareusedtovalidatethe proposedmethodandtheeffectsofoscillationfrequencyandamplitudeontheflowfieldare investigated.flowfieldvorticityandkineticenergycontoursarereportedinthispaper. It is found that the deflected wake appears at a Strouhal number around 0.4 for a fixed pitching amplitude equal to 0.7.chaoticlowcanbeobservedatoscillationamplitudeequalto2.80,forSt=0.22.Kinetic energycontoursatst=0.showthattheairfoiltransfersmomentumtothelowbutthedragforce alsoincreasesduetotheenergylossassociatedwiththeenlargementofseparationzonebehind theairfoil.byincreasingtheoscillationfrequencyandamplitude,momentumtransfertotheflow increasesandthedragforceis,therefore,reduced PurePlunging 2-PurePitching - : Pleasecitethisarticleusing: : A.A.Hosseinjani,A.Ashrafizadeh,NumericalStudyontheEffectsofOscillationFrequencyandAmplitudeonFlowaroundFlappingAirfoilviaanImprovedImmersed BoundaryMethod,ModaresMechanicalEngineeringVol.4,No.5,pp.29-30,205(InPersian)

2 NACA002.[] 0/4 0/ [2] 0/4 0/ [3]..[4. 9.[5] [6]. 0.[7]...[8]. NACA002.[9] [20] Chaotic 0-Wingvortexinteraction 3 2.[]...[2] [3]..[4].[6].[7].[8].[6] /.. -.[9].[0 -Powerderivation 2-Powerextraction 3-Feathering 4-Naturalflying 5-lift 6-Thrust 7-Marinemammals 8-Hovering 292

3 [23] f( xt, ) F( st, ) d( xx( st, )) ds b.(). () (2) () U( X( s, t )) u( x, t) d( x X( s, t)) dx xg. ((, )). ) ) -. - (2). [6].. [6]255...[4] [22] [2] Thrustengine

4 = ( ) (3) [30] u-u n t =-3 2 (uu)n + 2 (uu)n- + 2Re 2 (u+u n ) ( ) = () ( ) = ( ) () = ( ). (0) (4) () () = () (8) = (9) () () = n+ (0) Bi-CGSTAB [29] [3]. 6. ( ) Nearsingular 7-Fractionalstep 8-Biconjugategradientstabilizermethod (4) (5) (6) (7). () ).[23] [24] - 3 ( ). ().. 4 [26] [25]. 5 [27].... [29] [28] [28] [29]...[29] (3) -Continuousforcingmethod 2-Directforcingmethod 3-Forcingpoints 4-Ghostcell 5-Cutcell 294

5 [6] o [6] A = St = A Re =. (2) () () (2). 255 [6]. St = A = 0.36, ,.77,2.80. (3).() -. ) 4-2 ) ) (). 6-4 ) [32] 8. max [28] [29] [28] [6]

6 . = + sin(2) (3). St = 0.,0.22,0.3,0.4 A =.07.. [22]4 (3). C (num). [22]C ([22]) Tecplot A = 2.80 [22] 3 Error 0/57 0/2 /46 /82 /74 /4 0/2 0/49 0/4 [2] C ([22]) /392 /394 /567 /592 /547 /395 /429 /427 /433 C (num) /4 /397 /544 /563 /52 /4 /432 /434 /43 / 0/5 0/75 /07 /4 /2 -Deflectedvortex /5 / [2]. 2 Error = C (num) C ([2]) 00 C ([2]) C ([2]). (4) (4) C (num) Error [2]... 4 [22] 255 0/40/3 0/220/ 0/360/7/07/772/8 = kg/m = m/s kg = 5. 0 ms [2] Error /8 /8 0/56 /08 2 [2] C ([2]) 2/2 /54 /4 /37 C (num) 2/24 /522 /408 /385 Re

7 6.[6] (5) 7. C = () (5) 2 (6) C = () 2. 8 (6). [33] 6 ( ) Leadingedgevortex 2-Trailingedgevortex

8 8 9.A = 0.7 C = 0.86 C 8 St = A = St = 0.4. (St = 0.3 St = 0.22 St = 0.)

9 (8) = ( + ) (8) [4] = ( + ) (7) ) (7). - Thrust engine

10 St = St = St = A = (9). = 4 (9)

11 [6] M. A. Ashraf, numerical simulation of the flow over flapping airfoils in propulsionandpowerextractionregimesph.dthesis,theuniversityof NewSouthWalesAustralianDefenceForceAcademy200 [7] J.Young,S.M.Walker,R.J.Bomphrey,G.K.Taylor,A.L.Thomas, Details of insect wing design and deformation enhance aerodynamic functionandflightefficiency,sciencevol.325,no.5947pp , [8]R.W.Blake,Fishfunctionaldesignandswimmingperformance,J.FishBiol. Vol.27,pp.65-93,2004. [9] A. Betz, Ein beitrag zur erklarung des segelfluges, Zeitschrift fur FlugtechnikundMotorluftschiffahrtVol3,pp [0]T.Weis-Fogh,Quickestimatesofflightfitnessinhoveringanimals, including novel mechanism for lift production, J.ExpBiolVol.59,pp ,973 []J.M.Anderson,K.Streitlien,D.S.Barrett,M.S.Triantafyllou,Oscillating foilsofhighpropulsiveefficiency,journaloffluidmechanicsvol.360,pp. 4-72,998. [2]G.K.TaylorandR.L.A.Nudds,Flyingandswimminganimalscruiseat strouhalnumbertunedforhighpowerefficiency,nature,vol.425,pp ,2003. [3]Z.J.Wang,Vortexsheddingandfrequencyselectioninflappingflight.J. FluidMech.Vol.40,pp ,2000. [4]D.Lentink,T.F.Muijres,J.F.Donker-Duyvis,L.J.VanLeeuwen,Vortexwake interactions of flapping foil that models animal swimming and flight,journalofexperimentalbiologyvol.2,pp ,2007. [5]G. C. Lewin, H. Haj-Hariri, Modeling thrust generation of two dimensionalheavingairfoilin viscousflow,j.fluidmech.vol.492,pp ,2003. [6]R.Godoy-Diana,J.L.Aider,J.E.Wesfreid,Transitionsinthewakeof appingfoil,physicalreviewenergyvol.77,pp ,2008 [7]M.H.DickinsonandK.G.Gotz,Unsteadyaerodynamicperformanceof model wingsatlowreynoldsnumbers,j.expbiol.,vol.74,pp.45-64, 993. [8]K. D. Jones, M. F. Platzer, Numerical computation of flapping-wing propulsion and power extraction, In35thAerospaceSciencesMeeting ExhibitRenoNevada.January [9]J.Young,J.C.S.Lai,Mechanismsinfluencingtheefficiencyofoscillating airfoilpropulsion,aiaajournalvol.45,no.7,pp [20]M.R.Visbal,High-fidelitysimulationoftransitionalflowspastplunging airfoil,aiaajournalvol.47,no.,pp ,2009. [2]C. H. K. Williamson, Vortex dynamics in the cylinder wake, Annual ReviewofFluidMechanicsVol.28,pp ,996 [22]T.T.Do,L.Chen,J.Y.Tu,NumericalSimulationsofFlowsoverForced OscillatingCylinder,6 th AustralasianFluidMechanicsConferenceCrown PlazaGoldCoast,Australia.2007 [23]C.S.Peskin,Theimmersedboundarymethod,ActaNumericaVol.,pp ,2002 [24]J. Mohd-Yusof, Combined immersed-boundary/b-spline methods for simulations of flow in complex geometries, Center for turbulence researchannualresearchbriefsvol.6no.,pp ,997 [25] Y.H.Tseng,J.H.Ferziger,ghost-cellimmersedboundarymethodfor flow in complex geometry, ComputationalPhysicsVol.92,No.2,pp [26]E.Balaras,Modelingcomplexboundariesusinganexternalforcefieldon fixedcartesiangridsinlargeeddysimulations,computersfluidsvol. 33,No.3,pp ,2004 [27]M.H.Chung,Cartesiancutcellapproachforsimulatingincompressible flows with rigid bodies of arbitrary shape, ComputersFluids Vol. 35, No.6,pp ,2006 [28]M.Uhlmann,Animmersedboundarymethodwithdirectforcingforthe simulation of particulate flows, ComputationalPhysics Vol. 209, No. 2, pp ,2005 [29]S.WeiSu,M.C.Lai,C.A.Lin,Animmersedboundarytechniquefor simulating complex ows, Computers Fluids Vol. 36, pp , [30]J. Kim, P. Moin, Application of fractional-step method to incompressiblenavier-stokesequations,computationalphysicsvol.59, pp ,985 [3]MC.Lai,C.S.Peskin,Animmersedboundarymethodwithformalsecondorderaccuracyandreducednumericalviscosity,ComputationalPhysics Vol.60No.2,pp ,2000 [32]Z.Wang,J.Fan,K.Luo,Combinedmulti-directforcingandimmersed boundarymethodforsimulatingflowswithmovingparticles,int. J. MultiphaseFlowVol.34,pp ,2008. [33]G.YiHe,Q.Wang,X.Zhang,S.G.Zhang,Numericalanalysison transitions and symmetry-breaking in the wake of apping foil, Acta MechanicaSinicaVol.28,No.6,pp , /77. 0/22. 2/80 0/30/7 0/4 0/ []T.Kinsey,G.Dumas,Parametricstudyofanoscillatingairfoilinpowerextractionregime,AIAAJournalVol.46,No.6,pp ,2008. [2]M.F.Platzer,M.A.Ashraf,J.C.S.Lai,J.Young,DevelopmentofNew Oscillating-Wing Wind and Hydropower Generator, In 47th AIAA AerospaceSciencesMeeting,Orlando,FloridaJanuary,2009. [3] W.A.Davis,Nanoairvehicletechnologyforecast,BlueHorizonsPaper, CentreforStrategandtechnologyAirWarCollege,2007. [4] G.V.Lauder,E.J.Anderson,J.TangorraandP.G.A.Madden,Fish biorobotics: kinematics and hydrodynamics of self-propulsion J. Exp. Biol.Vol.20,pp ,2007 [5] T. B. Apker, Experimental investigation and modeling of time resolved thrustofflappingwingaircraft Ph.Dthesis,UniversityofNotreDame,