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TribologyInternationalVol.29,No.4,pp.291-297,1996Copyright01996EkvierScienceLtdPrintedinGreatBritain.Allrightsreserved0301-679X/96/$15.00+O.OOELSEVIERSCIENCEi0301-679X(95)00043-7LeakagefromlabyrinthsealsunderstationaryandrotatingconditionsH.A.El-Gamal*,T.H.AwadandE.SaberAlthoughtheleakageflowthroughlabyrinthsealsunderstationaryconditionshasbeenexaminedbymanyinvestigatorsareliablepredictionoftheeffectofvariouslabyrinthparametersonleakageratehasnotbeenreportedsofar.Thetheoreticalmodelsforthesealsproposedinmostofthepreviousliteratureprovidedresultswithconsiderabledifferencesandcontradictionsinsomecases.Thestructureofthelaminarincompressibleflowandtheperformanceofanumberofsealsofvariousshapesforbothstationaryandrotatingconditionsareinvestigatedinthispaper.Thetheoreticaltreatmentisbasedontheformulationofthree-dimensionalaxisymmetricmomentumandcontinuityequationsforlabyrinthshapeshavingsmallheighttoradiusratioasisalwaysthecaseinturbomachinery,rotodynamicpumpsandmanyhydraulicdevices.Itisfoundinthispaperthatshaftrotationisonlybeneficialfortheup-the-stepseal,hasnoeffectongroovedshaftandgroovedcasingsealsandhasanadverseeffectonthedown-the-stepseal.Itisalsofoundthattheuseofasmallerclearancesizeattheentrancemakessomeimprovementintheperformanceofthegroovedshaftanddown-the-stepsealsdependingonthevalueoftheheighttowidthratiooftheseal.Copyright01996ElsevierScienceLtdKeywords:turbomachinery,seals,labyrinthseals,contactlessseals,lubricationIntroductionManyinvestigationstackledtheproblemofleakagethroughlabyrinthsealsforturbomachinery.VariousshapeshavebeendevisedandstudiedexperimentallybyStocker?inordertoreducetheleakagerates.ManyearlytheoreticaltreatmentstotheproblemwerecarriedoutandarefoundpresentedandcomparedbyBenvenutiet~1.~.Suchtreatmentsprovidedresultswithconsiderabledifferencesandcontradictions.Insomeworksconclusionsweredrawnshowingthatshaft*DepartmentofMechanicalEngineering,AlexandriaUniversity,Alexandria,EgyptReceived19December1994;revised2February1995;accepted27March1995rotationisofnoimportance2.8.ThefirstreliablepredictionmethodwasduetoStofPwhotreatedthecaseofturbulentflowthroughalabyrinthsealofthegroovedshafttype.Hewasabletoshowhowmuchtheflowpatterninthelabyrinthisaffectedbytheratiooftheaxialleakagevelocitytotheshaftperipheralspeed.ForthelaminarcaseEl-Gamalet~l.~-~wereabletoexaminethepressuredropandhowpatternforanumberofgeometricalconfigurationsofseals.Theirresultsshowedhowimportanttheeffectofshaftrotationisontheperformanceoftheseals.References3and4-6however,werenotabletodivorcetheeffectofshaftrotationfromthemutualeffectofgeometricalconfigurationandclearancesizeontheperformanceofthesealwhentheshaftwasatrest.AlthoughtheflowthroughthesealunderstationaryTribologyInternationalVolume29Number41996291Leakagefromlabyrinthseals:H.A.El-Gamaletal.Notationwi,w.inletandoutletleakagevelocities(m/s)alabyrinthwidth(m)w:,w*,inletandoutletdimensionlessblabyrinthheight(m)leakagevelocities,W:=WiRIv,mlabyrinthheighttoradiusratio,W*,=W,RIvm=b/RYlabyrinthheighttowidthratiop_pressure(Pa)07r),5dimensionlesscoordinatesinPdimensionlesspressure,jj=pb2/v2ptangential,radialandaxialr,zradialandaxialcoordinates(m)directionsrespectively,Rshaftradius(m)q=(r-R)lb,5=zlaRerotationalReynoldsnumber,I*,vfluidviscosity(Pas)andkinematicRe=wRblvviscosity(m2/s)u,v,wvelocitycomponentsin8,randzfluiddensity(kg/m3)directions...