a brief review of recent results in vortex-induced

JournalofWindEngineeringandIndustrialAerodynamics96(2008)713–735Abriefreviewofrecentresultsinvortex-inducedvibrationsC.H.K.Williamsona,,R.GovardhanbaFluidDynamicsResearchLaboratories,MechanicalandAerospaceEngineering,CornellUniversity,Ithaca,NY14853,USAbMechanicalEngineering,IndianInstituteofScience,Bangalore560012,IndiaAvailableonline6August2007AbstractInthisbriefreview,weshallsummarizefundamentalresultsanddiscoveriesconcerningvortex-inducedvibration,thathavebeenmadeoverthelasttwodecades,manyofwhicharerelatedtothepushtoverylowmassanddamping,andtonewcomputationalandexperimentaltechniquesthatwerehithertonotavailable.Webringtogethernewconceptsandphenomenagenerictovortex-inducedvibration(VIV)systems,andpayspecialattentiontothevortexdynamicsandenergytransferthatgiverisetomodesofvibration,theimportanceofmassanddamping,theconceptofacriticalmass,therelationshipbetweenforceandvorticity,andtheconceptof‘‘effectiveelasticity’’,amongotherpoints.Wepresentnewvortexwakemodes,generallyintheframeworkofamapofvortexmodescompiledfromforcedvibrationstudies,someofwhichcausefreevibration.Somediscussionfocusesontopicsofcurrentdebate,suchasthedecompositionofforce,therelevanceoftheparadigmflowofanelasticallymountedcylindertomorecomplexsystems,andtherelationshipbetweenforcedorfreevibration.r2007ElsevierLtd.Allrightsreserved.1.IntroductionVortex-inducedvibration(VIV)ofstructuresisofpracticalinteresttomanyfieldsofengineering.ThepracticalsignificanceofVIVhasledtoalargenumberoffundamentalstudies,manyofwhicharediscussedinthecomprehensivereviewsofSarpkaya(1979),GriffinandRamberg(1982),Bearman(1984),Parkinson(1989);inabookchapterbyARTICLEINPRESS:10.1016/j.jweia.2007.06.019Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](C.H.K.Williamson).Anagnostopoulos(2002);andinbooksbyBlevins(1990),NaudascherandRockwell(1994),andSumerandFredsfe(1997),andrecentlyintheAnnualReviewofFluidMechanicsbyWilliamsonandGovardhan(2004).Herewefocusonthemorerecentaccomplishmentsofresearchers,especiallywithinthelastdecade.OnestimulusforaresurgenceofinterestinVIVcamefromtheOceanEngineeringDivisionoftheUSOfficeofNavalResearch,whichmountedaUniversityResearchInitiativeandbroughttogethermanyinternationalresearcherstoworkoncommonground.Thisreviewfollows,andtosomeextentisanabridgedversionof,amorecomprehensivereviewcontribution,towhichthereaderisreferredformoredetails,inthemostrecentAnnualReviewofFluidMechanics(WilliamsonandGovardhan,2004).Inbothofthesereviews,weareconcernedprincipallywiththeoscillationsofanelasticallymountedrigidcylinder;withforcedvibrationsofsuchstructures;withbodiesintwodegreesoffreedom;withthedynamicsofcantilevers,pivotedcylinders,cables,andtetheredbodies.AsaparadigmforsuchVIVsystems,weshallconsiderhereanelasticallymountedcylinderrestrainedtomovetransversetotheflow.AstheflowspeedUincreases,aconditionisreachedwhenthevortexformationfrequencyfViscloseenoughtothebody’snaturalfrequencyfNsuchthattheunsteadypressuresfromthewakevorticesinducethebodytorespond.Certainwakepatternscanbeinducedbybodymotion,whetherthebodymotioniscontrolledorisfreetovibrateduetothefluidforces.WilliamsonandRoshko(1988),studiedthevortexwakepatternsforacylinder,forcedtotranslateinasinusoidaltrajectory,overawidevariationofamplitudes(A/Dupto5.0)andwavelengths(l/Dupto15.0).Theydefinedawholesetofdifferentregimesforvortexwakemodes,intheplaneof{l/D,A/D},whereadescriptiveterminologyforeachmodewasintroduced.Eachperiodicvortexwakepatterncomprisessinglevortices(S)andvortexpairs(P),givingpatternssuchasthe2S,2PandP+Smodes,whicharetheprincipalmodesnearthefundamentallock-inregioninFig.1.Visualizationofthe2Pmodeisclearlypresentedinthisfigurealso.The2PandP+Smodeshavebeenfoundincontrolledvibrationstudiesin-linewiththeflow(GriffinandRamberg,1976;OngorenandRockwell,1988b),aswellastransversetotheflow(seealsoZderaetal.,1995).TheP+SmodewasalsofoundinGriffinandRamberg’s(1974)well-knownsmokevisualizations.Thesignificanceofthesemodesfromcontrolledvibrationisthattheyprovideamapofregimeswithinwhichweobservecertainbranchesoffreevibration.OnedeductionfromtheWilliamsonandRoshkostudywasthatthejumpinthephasefofthetransverseforceinBishopandHassan’s(1964)classicalforcedvibrationpaper,andalsothejumpinphasemeasuredinFeng’s(1968)free-vibrationexperiments,werecausedbythechangeoverofmodefromthe2Stothe2Pmode.Thishassincebeenconfirmedinanumberoffree-vibrationstudies(beginningwiththepioneeringworkofBrikaandLaneville,1993),andweaddressthisinSection2.Suchvortexmodesoccurforbodiesinoneortwodegreesoffreedom,forpivotedrods,cantilevers,oscillatingcones,andotherbodies.Responsedatafromallofthesestudieshavebeencorrelatedwiththemapofregimesdescribedabove.Interestingly,aforcedvibrationcanalsoleadtoothervortexmodesincludingaP+Smode,whichisnotabletoexciteabodyintofreevibration.Inessence,anominallyperiodicvibrationensuesiftheenergytransfer,orworkdonebythefluidonthebody,overacycleispositive.Thisnetenergytransferisinfluencedsignificantl