UNIVERSITYUNryERSITY OF MINNESOTA ST. ANTHONY FALLS HYDRAULIC LABORATORY LORENZTORENZ G. STRAUB, Director TechnicalTechnicol PaperPcper No. 14, Series B Importance of Secondary Flow in Guide Vane Bends Limited Distribution ofoI PaperPoper Presented Before The Third Midwestern Conference on Fluid MechanicsMechcnics atqt the University of Minnesota,Minnesotq, Minneapolis,Minnecpolis, Minnesota,Minnesotq, MarchMqrch 23, 24, andqnd 25, 1953 by EDWARD SILBERMANSILBENMAN January,Jcnuary, 1953 Minneapolis,Minnecrpolis, MinnesotaMinnesotc --------AagggEAg,S B S T RAe T For purposes of analysis,analysi-s, the flow inin a guide vane bend is divided into aabasic basic or primaryprj-nary two-dimensionaltso-dinensional flow wi.nlttr th superimposedsuperinposed secondarysecsndary flow. TheS:e two-dimensionaltwo-d:inensional flowflon isls reviewedreviesed. briefly first. It is then shownshorrn from ex­ex- perimentalperfunental data that, for practical purposes, the secondary flow has negligible influence on the two-dimensionaltwo-disrcnsional deflection,defleetion, but the two-dimensionaltrno-dircnsional head lossloes isi-s increased materially by the secondary flow. Thethe effect of the secondarysecondar;r flow on head loss canean be divided intolnto two parts. The firstflrst part causes a loss whichnbj-eh canean be measuredmeazured tunediatelyimmediately behind the vanes, while the second part causeseauses a loss whichntrich occursoceurs between the traili-ngtrailing edges of -thettre yanesvanes and a plane about b4 duct hydraulic diametersdiamet€rs behlndbehind the miterniter line of the bend.,bend. theThe sec­see- ond part is eonsiderablyconsiderably larger tbanthan the first and naymay be attribr:.ted.attributed to in-in­ .ralL creased wall shear downstream of ttrethe vanes. ttreThe lncreasedincreased wa1lwall shear is, in turn, attrj.butableattributable to the redistribution of streanlir€sstreamlines by the secondar;rsecondary fLow"flow. 1l_ii '. !,. F.! CONTENTSg0HfEsrs +<-r----... +sr ... _- ---- li' PageFage ,Ir Abstractlbstfact •... o..• r..... I e '... e....,.• • iili Listo!Llstof nlustrationslllBgtrations •. • • iv I.f. I~TRODUCTIONI|[m0DSCffOlf . r . •. q .' . o . •. r o . ., . .' • . ... 1I II. TWOIIIO-DIIIEFSIOIIAI ...Dnm~SIONAL FLOWFT.tr . o e t . ] ,. r . .. 3 •. 2 III.Iff. SECONDARY FLoriEf,tr o i . •. .-. o 4tl .. AcknowledgmentAelaorledgnent . | . .t. •. •. 9g LlgtofRgfergncgsList o! References ,. r,,. .. r r .. .., e . r.. 10 Appendtx*ItlguresltolkAppendix ... Figures 1 to 14 . t..., e r.. o...,.. 11 lrt111 LIS T 0 F ILL U S T RAT ION S ----!rs3 9s Mgsl3{3rggE~------------ FiElguregure Page 1 Guide Vane lnstallationInstallation in High-,VelocityHigh~Velocity ChannelChanne1 rl.t.aa 12 2? GuideOuide Vanes Installed in a Test?est Bend 13 3 Total Head li-stributionDistribution in a Guide Vane Bend ,14lL&15 & 15 4L Head LossLose BehindBehl-nd the Two-nimensional1\ o-Iiraensional- Region of a Cascade •, •. • • • • • • • 1615 5 Cascade0haracteristlcs,.Cascade Characteristics • . ... ., , ! .. 17t7 6 RelationRe'l-ation Between Entrance and Exit Angles, DeflectionSeflectlon Angle, and LiftLiJt Coefficient in a Cascade 18 7 TypicalTypicalCascadeLines Cascade Lines . • •., .,.. o i... 19L9 8B Guide VaneYane Profiles Used in the E:rperimental-Experimental Workffork •" . , 20 0 9 Stagger Angle RequiredRequinbd to Producehoduce 9090o Flow Deflection •. 202A 10l_0 Two-DimensionalTwo-Dtnenslonal Headllead Losstoss and Draggrag CoefficientsCoefficie.ts i• •. •. .,, e 212t 11tt Comparison of Two-DimensionalTwo-limensional and Three-DimensionalThree-limensionaL Head Loss CoefficientsCoefflcients • • • • • • • 22 12L2 Sketch of Secondary Flow Between the Vanes 23 13 Schematic$chenatic StreamlinesStreanli-nes in a Guide VaneYane Bend 24211 11r ComparisonConparison of Total Excess Head Loss and ComputedCornputed Loss AttributableAttributabletoWallShear to Wall Shear • • •., • • • •,. • • • •., • •.. • .. 25 ivav rgSg&r1!geIMPORTANCE grOF SECONDARYggg9gg4gr FLOWFI,OS IfN N GGUfDE U IDE VVAI,IE A NEBBEFDS END S Ioru INTRODUCTIONmla0DucmoN ResearchReseareh on diversiondiyersion of incompressibleiFeonpressible fluid flows has}:as been con­con- ducteddueted at thettre St. AnthonyAntJrony Falls Hydraulic Laboratory over a periodperi-od of seven years. A general conclusionconcl-uslon from the research is that the streamlinesstrearnlines in flow diversiondiverslon problems tend to followfolIow thet*re potential flow pattern which is uniquelyuniqueLy associated withTetth thetLre boundaries. If thet}e velocity profile at the beginning of the diversion wereprere irrotational,irrotationaS-, the flow would be nearly potential (allowing(a11ow'ing for boundary layer development)developrnent)" 0 BecauseBeeause the entranceentranee velocityveloeity profile is generallygenerirlly rotational,rotatj-onal, the potential streamlinesstream'lines have superimposedsuperi-urposed upon them a secondary flow whichrrhich sometimessometirnes entirelyenti.rely masksnasks the primary, nearly potential flow.f1ow, The potential flow may be looked upon as a first approximation and thettre potential flow plus approximateapp:roximate secondaryseeondarSr flowflolr as a secondseeond approximationapproxi-mation to thet'he real flowflos in a flow diversiondi-version problem.problea" Thisthis paper presentspresenis a demonstration and application of thet}re concept of separable primaryprinary flowflos and superimposedsuperinposed secondary flow to incompressibleineompressible flow in a guide vane bend. Thettre paper is based on research sponsoredsponsered by the Office of Naval$ava1 ResearchBeseareh and is condensed from a technical.. report prepared for that organizationorganization,[f]*..[l]*o Squire and Winterllinter I)],[a], among"*oog others, have considered the same subjectsubjeet inln a similarsinilar manner; theirtJ:elr paper shows thettre theoreticalttreoretical devel­devel- opment of the secondaryseeondar;r currents using the HelmholtzHe1mholiz form of the equations of motionnotion but does not describe the complecomplete te role of the secondary currentscunents and theirttreir influence on the primary flow.flowo Thisthis paper is specifically concernedconeerned wiwlth th fixed, twotss-dimensional -dimensional guide vane structuresstruetures like those shown in the installation in Fig.Fig" 1.1" However, thetie results are at least qualitatively applicable to all types of blading in­in- stallations.stallations, FigureRlgure 2 is a photograph of a set of guide vanes installedlnstaIled in a 0 99Oo0 test bend usedused. in the present experimental work. A surveyourwey for totaltstal head and flowflorr direction behind the vanes is in progress usinguslng a pitot cylinder.eylinder. Figure 3 contains typical experimentalerc.perimental results.resul-ts" PlottedPlottcd in Fig. 3b are total head distributiondi-st'r.'ibution and flow directiondlreetlon immediatelytnrraedi.ately behind thet&e vanes, o}f,*b""" *Numbers in bracketsbraekets refer to references on pop" 10010. -t2 whileufrrile Fig. 3a shows total head distributiond:istributS"on inin a straightstraight duct underr:nder thethe samesane entranceentranee conditions asae those shown in Fig. 3b3b". FigureFig'ore 3dJd locateslocates thethe survey planes.pl-anes, Figure 3cJc showsshons the results of a survey taken aatt a station designated M-MM-H and located just over 4h hydraulicnyarauti-e diametersdihmeters downstreamdownstreaei of thethe miter&:iter line of thettre bend;beadS it is seen thatttrat thettre total head distrdtstri-butionibution here is roughly simi­sini- lar to that in thetlre straight duct. FromFron this and other evidence,evidenceo it was con­con- cluded that thethe infl'ijenceinflgence of thettre bend was completecourpleteu9 for practicalpractieal- purposes, inln thetlre present experimentsexperinents at Stationetation M-Ml[--M or before .o Examination of Fig.Fig" 3b shows thatt'hat theretirere is a largelarge, 9 two-dimensional,two-*inensional, nearly potential flow region surrounding tht}re.e horizontalhorisontal center line of the duct, marrednarred onlyonJ-y by the wakes of the vanes. There isls another regionreglon near the vane ends whichui:leh is disturbed ' by secondarysecondarXr flows.flows" Perhaps the two-dimensional region is better illustratedill-ustrated inln Fig. 4,h, whichwtrich is a ploplott of head loss iinn a plane at midspannidspan behindbehlnd thetbe vanes and showsshoss even more clearlyelearly thetlie nearly potential char­ehar- acteraeter of the two-dimensional flow.flos. (Figure(Fi$rre 4h is for a type of vane different fromfron ~hatthat shown in Fig. 3,J, but thettre results are typical.) Theseltrese experimentalexperinental results led naturally to the question,questi-ono howhor muchrnach different would Fig.Flg" 3cJe appear if a purely two-dimensionalt'sro*dinensional flow through thettre vanes were considered? That is,J-su whatufuat differencedlfference is therettrere between the real flow and the two-dimensionaltwo-di-nensional flow used as a first approximation?approximat{on?'" II.II" TWO-DIMENSIONALmO-grlrilE$SI0[IAI, fl-flfFLOW To answeransver the questionsquestioas just posed,posed, itii j-sis neeessarynecessary totp look at the two-dimensional flowflowfirst. first. Theltre two-dimensionaltnro**ineneional flow through a cascadecaseade of vanes naymay be obtained theoretically byoneby one of several methodsnethcds [3,I) , liltr] or by experimentexperinent. If ttreoreticaltheoretical nethodsmethods ac'eare :used.\)usedn thetlie boundary layers on the vanes nustmust be taken