Skin-friction-reduction-by-large-air-bubbles-in-a-

SkinfrictionreductionbylargeairbubblesinahorizontalchannelflowYuichiMuraia,*,HiroshiFukudab,YoshihikoOishia,YoshiakiKodamac,FujioYamamotobaDivisionofEnergy&EnvironmentalSystem,GraduateSchoolofEngineering,HokkaidoUniversity,Kita-ku,N13W8,Sapporo,060-8628,JapanbDivisionofFiberAmenityEngineering,GraduateSchoolofEngineering,UniversityofFukui,Bunkyo3-9-1,Fukui,910-8507,JapancNationalMaritimeResearchInstituteofJapan,Shinkawa6-38-1,Mitaka,Tokyo,181-0004,JapanReceived17October2005;receivedinrevisedform15August2006AbstractMicrobubbleandairfilmmethodsarebelievedtobeapplicabletoskinfrictionreductioninships.Smallbubblesaredispersedintotheturbulentboundarylayerintheformercase,andwideairlayerscoverthewallsurfaceinthelattercase.Previousstudiesdidnotspecificallyaddresstheintermediatecasebetweenthemicrobubbleandairfilmconditions.Thisstudyisconcernedwiththepossibilityandmechanismofdragreductionusingrelativelylargeairbubblescomparedtotheboundarylayerthicknessinahorizontalturbulentchannelflow.Therelationshipbetweenlocalskinfrictionandthebub-ble’sinterfacialstructureisinvestigatedbysynchronizingthemeasurementofwall-shearstresswiththeimageacquisitionofbubbles.Thebubblesizesrangefrom2to90mmapproximately.Asaresult,anegativecorrelationbetweenthelocalskinfrictionandthelocalvoidfractionisconfirmedbythetime-resolvedmeasurement.Anewobservationisthefactthatthelocalskinfrictiondecreasesdrasticallyintherearpartofindividuallargebubbles,andrapidlyincreasesafterthebub-ble’srearinterfacepasses.Thischaracteristicunderliesthebubble-sizedependencyoftheaverageskinfrictionintheinter-mediatebubblesizecondition.2006ElsevierLtd.Allrightsreserved.Keywords:Dragreduction;Bubbledynamics;Turbulentflow;Skinfriction;Airfilm1.IntroductionVariousmethodsforreducingskinfrictionaldraginturbulentflowshavebeenproposedinthepast.Onesuchmethod–theuseofbubbles–hasrecentlybecomeafocusforengineersintheexpectationthatitmightbeapplicabletoshipsandpipelines.Therearetwomainapproachestotheutilisationofbubbles,depending0301-9322/$-seefrontmatter2006ElsevierLtd.Allrightsreserved.doi:10.1016/j.ijmultiphaseflow.2006.08.008*Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](Y.Murai).InternationalJournalofMultiphaseFlow33(2007)147–163flowuponthebubbles’size.Oneistheso-called‘microbubble’method,firstreportedbyMcCormickandBhatta-charyya(1973).Theyemployedelectrolysistogeneratemicrobubblesinwaterandwereabletodemonstratesomedegreeofdragreductionforasubmersiblehull.Laboratoryexperimentsusingawatertunnelorchannelhavealsobeencarriedoutinanumberofhydrodynamicresearchinstitutesinordertocharacterizetheskinfrictionreductionprocessassociatedwithsmallbubblesandtodeterminetheparametersinvolved(Madavanetal.,1985;MerkleandDeutsch,1992;Katoetal.,1999;Kodamaetal.,2000;MoriguchiandKato,2002;Gabilletetal.,2002).SeveraltheoreticaldiscussionshavebeenpublishedbyLegner(1984)andMarie(1987)totrytoexplainthedragreductionmechanismsimply,byreferencetosuchaspectsasthereductionindensityofthemixtureandmodificationoftheeffectiveviscosityinsidetheboundarylayer.Inparallel,numericalresearchesmainlydealingwithsmallsphericalbubbleswerereportedbyFeltonandLoth(2002),Xuetal.(2002)andFerranteandElghobashi(2004),toelaborateonthedragreductionprocess.TestsoftheapplicationofsmallbubblestoshipsorlongflatplateswerereportedbyTakahashietal.(2003)andLatorreetal.(2003).Someoftheaboveexperimentsinvolvedrelativelylargebubblescomparedtothebound-arylayerthickness.However,theseauthorsoftenstillusetheterm‘‘microbubbles’’inaqualitativesense,becausethebubblesizeisundoubtedlysmallerthantheeffectivelengthofthedrag-reducingarea.Aftercon-sideringmanysetsofpublishedexperimentaldata,wecansaythatnotonly‘‘realmicrobubbles’’butalso‘‘a-few-millimeterbubbles’’canreduceskinfriction,asreportedbyMoriguchiandKato(2002).Theyfoundthatthereappearstobenosignificantbubblesizedependencyinconditionsofhighshearrate.Therefore,recentdiscussionhasmovedontotheroleofthebubble’sdeformabilityinhelpingtoreducethelocalRey-noldsshearstress,asreportedbyKitagawaetal.(2005)andMuraietal.(2006).Inthiscontext,thebubbleisnotrequiredtobesosmallinsizeorWebernumber.Inotherwords,amechanismofdragreductionindepen-dentofthatinvolvingsphericalbubblesmaytakeplaceafterthebubblesstarttodeform.Analternativetechniquefordragreductionisthe‘airfilm’method,whichhasbeenthesubjectofattemptstomakeitpracticableforthelasttwodecades(e.g.Katsuietal.,2003).Theairfilmmethodsimplycutsoffcontactbetweenthewaterandthewallsurface.Therefore,thetechnicalproblemisjusthowtomaintainastableairsheetonthetargetwall.Theintroductionofawater-repellentsurfaceisexaminedbyFukudaetal.(2000)andMatsumuraetal.(2002).Unfortunately,theairfilmeasilybreaksuptobecomelargebubblesdownstream,owingtoKelvin–Helmholtzinstability.Whenstreamwisepersistencyofdragreductionisdesired,thebubblesizeaftercollapseisveryimportantindeterminingthetotaldragreduction.Ifthebubblesizeisstilllargeenough,thedragreductionshouldbemaintainedtosomeextent.Ifthesizeisinaparticularrangerelativetotheboundarylayer