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 of oI Paper Poper Presented Before The Third Midwestern Conference on Fluid Mechanics Mechcnics 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 in in a guide vane bend is divided into a abasic basic or primaryprj-nary two-dimensionaltso-dinensional flow wi. nlttr th superimposedsuperinposed secondarysecsndary flow. TheS:e two-dimensionaltwo-d:inensional flowflon is ls reviewedreviesed. briefly first. It is then shownshorrn from exex- perimentalperfunental data that, for practical purposes, the secondary flow has negligible influence on the two-dimensional two-disrcnsional deflection,defleetion, but the two-dimensionaltrno-dircnsional head loss loes isi-s increased materially by the secondary flow. Thethe effect of the secondarysecondar;r flow on head loss can ean 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 sec see- 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 Channel Channe1 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 Vane Yane Profiles Used in the E:rperimental-Experimental Work ffork •" . . . . . , 20 0 9 Stagger Angle Required Requinbd to Produce hoduce 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$chenatic Streamlines Streanli-nes in a Guide VaneYane Bend 24211
11r ComparisonConparison of Total Excess Head Loss and ComputedCornputed Loss AttributableAttributabletoWallShear to Wall Shear • • •., • • • •,. • • • •., • •.. • .. 25
ivav rgSg&r1!geIMPORTANCE grOF SECONDARYggg9gg4gr FLOWFI,OS IfN N GGUfDE U IDE VVAI,IE A NEBBEFDS END S
Ioru INTRODUCTIONmla0DucmoN
ResearchReseareh on diversion diyersion of incompressibleiFeonpressible fluid flows has }:as been concon- ducteddueted at thettre St. Anthony AntJrony Falls Hydraulic Laboratory over a periodperi-od of seven years. A general conclusionconcl-uslon from the research is that the streamlinesstrearnlines in flow diversiondiverslon problems tend to followfolIow thet*re potential flow pattern which is uniquelyuniqueLy associated with Tetth thetLre boundaries. If thet}e velocity profile at the beginning of the diversion wereprere irrotational,irrotationaS-, the flow would be nearly potential (allowing(a11ow'ing for boundary layer development)developrnent)" 0 BecauseBeeause the entrance entranee velocityveloeity profile is generallygenerirlly rotational,rotatj-onal, the potential streamlinesstream'lines have superimposed superi-urposed upon them a secondary flow whichrrhich sometimessometirnes entirelyenti.rely masksnasks the primary, nearly potential flow.f1ow, The potential flow may be looked upon as a first approximation and thettre potential flow plus approximateapp:roximate secondaryseeondarSr flowflolr as a secondseeond approximationapproxi-mation to thet'he real flowflos in a flow diversion di-version problem.problea"
Thisthis paper presentspresenis a demonstration and application of thet}re concept of separable primaryprinary flowflos and superimposedsuperinposed secondary flow to incompressible ineompressible flow in a guide vane bend. Thettre paper is based on research sponsoredsponsered by the Office of Naval$ava1 ResearchBeseareh and is condensed from a technical.. report prepared for that organization organization,[f]*..[l]*o Squire and Winterllinter I)],[a], among"*oog others, have considered the same subjectsubjeet in ln 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 comple complete te role of the secondary currentscunents and theirttreir influence on the primary flow.flowo
Thisthis paper is specifically concernedconeerned wi wlth 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 in in- 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 total tstal head and flowflorr direction behind the vanes is in progress usinguslng a pitot cylinder.eylinder.
Figure 3 contains typical experimental erc.perimental results.resul-ts" PlottedPlottcd in Fig. 3b are total head distribution di-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 in in a straight straight 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 a att a station designated M-MM-H and located just over 4h hydraulicnyarauti-e diameters dihmeters downstream downstreaei of thethe miter&:iter line of the ttre bend; beadS it is seen thatttrat the ttre total head distrdtstri-butionibution here is roughly simisini- lar to that in the tlre straight duct. FromFron this and other evidence, evidenceo it was concon-
cluded that thethe infl'ijenceinflgence of the ttre bend was completecourpleteu9 for practicalpractieal- purposes, inln thetlre present experimentsexperinents at Station etation 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 only onJ-y by the wakes of the vanes. There isls another region reglon 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 clearly elearly thetlie nearly potential charehar- acteraeter of the two-dimensional flow. flos. (Figure(Fi$rre 4h is for a type of vane different fromfron ~hatthat shown in Fig. 3,J, but thettre results are typical.)
Theseltrese experimentalexperinental results led naturally to the question,questi-ono howhor muchrnach different would Fig.Flg" 3cJe appear if a purely two-dimensionalt'sro*dinensional flow through thettre vanes were considered? That is,J-su whatufuat differencedlfference is therettrere between the real flow and the two-dimensional two-di-nensional flow used as a first approximation? approximat{on?'"
II.II" TWO-DIMENSIONAL mO-grlrilE$SI0[IAI, fl-flfFLOW
To answeransver the questionsquestioas just posed,posed, itii j-sis neeessarynecessary totp look at the two-dimensional flow flowfirst. 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 'nork, into acsountaccount separately [?]t5]. . In the preseatpresent work, ttrethe two-dinensi.onaltwo-dimensional fIowflow raswas sbtainedobtained experineatally.experimentally.
fheThe terusterms asedused in defining a trc-dinensioaaltwo-dimensional cascade of guid.eguide r€neavanes are illustnatedillustrated in Fig. 5"5. Each vane lnin the aascadecascade develops a reactLonreaction or lift which changes tlrethe momenturnmomentum of the flow from theth; old dlrectiondirection to the new direction. The coefficients of lift and~d drag C,C and C6r~ j) and the line of L acti-onaction of the 1i-ftlift rnakingmaking the angle yY witJ:with theleascadethe cascade L""axes .ruare relatcdrelated to 33 the deflection the deflection angleangle 6.A, 9 t t*:ehe velocityvelocity ratratioi o vVr/V1,21vp t ilrehe entranceentrance angleangle /31'p* ttre exlt the exi tangleangle /32'B* andand' the the spacspaeing-chord.i ng- chord :-ratioa t i o slsfe c throughttrrough thettre equationsequations of eontinuity, of continuity, momentumnomentum,~ aand nd energy. energy" These ?hese.relations "*l*tioo* areare given given byby the the equationsequations
t- v2 q'' !A "irrA = c =E% - tan ;/a- vl cos / El6 7 (1)(1)
11 tantan Y / == '2 (cot(cot i /392*2 + ccotp.,1ot (31) (2)(2)
andand areare plotted in plotted in Fig.Fi.g" 6"#-'d wiw.ith th CD = 0 (C and CD are based L "il" on the entrance velocivelocity ty headhead V12/2g)rr; 0 This figure irT. rH'"jl*",shows ~ for e3J;:,til::xample jl that each:"f:ffi"; vane in a two-disrensional 0 two-dimensional cascadecascade installed1nsta1led inin aa 90 mitera:iter 0 90o benbendd (~=(A= 9090o,, v2/vlVZIV\= = 100)1.0) mustnust be eapable be capable ofof developingdeveloping aa liftlift coefficiencoefficj_en!t of 2 of Z sis/c"c. WhetherShether oror notnot aa vane will vane will developdevelop suchsuch aa coefficienteoefficient dependsd,epends on on itsits shapeohape (principally cambercanrber), ), lts i ts staggerstagger angle 8,g, its spacing-chordspaeing-ehord ratio inin thettre cascadeeascade sic,s/c, and the entrance aad the entrance angle /3 or exit angle /3pZ"• 4 1 2 Itft is shownshorrn in tthehe basic technical technical reporeportrt [lJp] thattr.at given a cascade defined defined by the profiles of its vanes,vanes" their the5.r staggestaggerr angle 8,e, and spacing- chord ratio s/e, the sic, the approximate relatlonrelation ~
cot B,f3 = ,tr1A cot f3 *- B 2 8.,1 B t3)(3)
exists where exists where AA andand BB areare constantsconstants forfor ttrethe g:lvengive n ceascadeoascade . F,quatlonEquation (3)(3 ) plotsplots asa astrai'ghtline s a straight line onon Fig"Fig. 5"6. rnIn Fig;Figo 7~ severalseveral such 7, sucb eagcadecascade lineslines areare takentaken from experi:nental from experimental datadata byby DavisDavis [6J andand Harri s and t6] l{a*is and trairthorneFairthorne [7J andand areare plottedpl to the t?l otted to the saraesame eoordinatcscoordinates asas Fig.Fig. 6,6. The Harris · the Harris andand FairtroraeFairthorne datadata areare all for the all for the se*esame vanevane profile,profile, 08 andand s/csic bei ng vari being varied..edo theThe cascadecascade lineslines areare of li&ited length of limited length becausebecause thethe vanesvanes stallstall shenwhen the entrance tire entranee angleangle i-sis tootoo s'a1lsmall or too ]-arge or too large andand thenthen gq"Eq . {3}(3) nono longerlonger holds. If hor-ds" rf oaeheach vanevane couldcould bebe operated as ope r ated as aa singlesingle airfoil,airfoil, wittroutwithout stallingustallin g it would 9 J"t would havehave anan angleangle ofof at-at~ tacktack atat serozero lift of lift of oooa 0 rtIt isis alsoalso sho$'shown inin t he basic a the basj-c refereneereference [lJ thatthat aa cascade line tl] cascade line shoaldshould passpass throughthrough thethe valuevalue = Bo 9;= Bz=g* oo (b)(4) ...
4
0 Harris and Fairthorne neasuredmeasured ttrelrtheir value of ooa as *11.50,=11.5 , and the cascade Harris and Fairthorne o lines in Fig. 7 representing their data have been drawadrawn to paospass fhroughthrough tbethe corresponding value of ~ • corresponding value of Bo"o If caseade.cascade lireslines were ava11ab1eavailable to eovercover the entire Fig. 7, together withwi th drag eoefficientcoefficient values, two-d:lmensionaltwo-dimensional data could be taken fronfrom that
figure without reeortresort to theoretiealtheoretical conputatloncomputation or experinentoexperiment 0 SachSuch lines are not available, howe'crer.however.
theThe present experfunentplexperimentpl work was eonfinedconfined to three vane profiles 0 wirlchwhich were used in cascade to produce A6. = 90o,90 , VZ/VIv2/vl = 1.0.l-"0" 1\no-d:inensionaLTwo-dimensional data were obtained in the nidspanmidspan region of vanes of 9-in. span and 2.02-in. to h,25-in"4.25-in. ehord"chord. theThe vane profiles are shorrnshown in Fig"Fig. B,8. Figure I9 shows the
stagger angle requlredrequired for eaeheach eascadecascade and Fig"Fig 0 10alOa t'hethe corespondlngcorresponding head
loss coefficient eZ~2 wheresirere
Head Loss = (5) I, At
Theltre head loss was measured experimentallyexperi.menta3-1y by determiningdeteruining the averageaverege total he head-ad behind thettre vanes and at the ttre corresponding eorrespondlng posi-tionposition in ae straight duct. The&e lossJ-oss is the tire difference between these values. Infn Fig. 10b, 10bri' the drag coefficicbefflei- ent for each cascadeeaseade is shown. shosn. For the present conditionsconditj-ons
%, = f t i (6)
5 Ththee Reynolds Beynolds number nupber for all data is VIYrc/v clv = 105!"5 x 10 :-05 wherethere v is the kine-kine mnaticatic viscosity. viseosity" The vanesvane6 are smooth smoottr brass or aluminum. aluninum. Therelhere was some inin- didieationcation of change in head loss coeffiCient,coeffieient, but there was no measurable change in deflectiondeflectlon inln the range of Reynolds numberaumber fromfrou about 0.5A"5 to 400l+.0 x 1010).5• ((S:.neeSince Cf" = 2 s/e for the present experimentsexperiments,j FigoFig" 9p corresponds to the angle L sic of attack versusrrersus liftlj-ft coefficient,eoeffielent, Fig. lOal0a to to the lift-drag ratio versus lift ccoefficient,oeffiCient, and Fig. lOb1Ob to the coefficientcoeffieient of drag versus lift coeffiCientcoefficient ccurvesurves of single airfoil theory.) ttreory. ) 5
III.rlr" SECONDARYgEco$DA3y FLOWm.fir
TheTlre data of Fig. 9 are not truly two-dimensional two-dj-nensional ." In obtaining these ttrese dataudata~ the stagger angle was wae adjustedadJusted for eacheaeh cascadeeaseade until it appeared appeared. thattlrat the cascadeeascade alonealone'was was turning the fluid (without(wittrout assistance from fron thettre walls).ral1s)" CorrectCorreet stagger angle was obtained whenqhen the pressure was ras uniformuniforu across the duct upstream of the vanes and thettre pressures at correspondingco*esponding points in the two-dimensional region on several several- vane surfaces sr:rfaees wereurere equaLequa1" DeterminationsDetermi-natj-ons of stagger angle were made over a range of chord aspect ratios (ARc{AR. = spanstrt over chord) from about 1 to and of space aspect ratios (AR(AR" = span over 4.5h,5 space s = span over space) fromfron about 2 tota 9).. Thefhe Tangerange of aspect ratios was obtainedobtaj-ned by using uslng vanes of different dl-fferent chord ehord. length at constant span and spacing-chord ratio, and vanes of two differentdiffe:"ent spans at constant chord length and spacing~chordspacing-ehord ratio. ratio"
Therethere wassas no measurable change ini-n r~quiredrqqeired stagger angle due to these variavarj.a- tions, whereas there was a change inln head loss.loss" Itft was thereforetlrerefore concludedconeluded thatttrat the thie average deflections were independentladependent of aspect ratio and must have been identical with thettre two-dimensional two*dimensional deflectiondeflestion for each cascade.caseade.
Infn Fig. Flg. ll~110 three ttrree-dirrcns*onal -dimensional head loss coefficientscoefflcients are plotted against spacing-chordspacing-ehord ratio. Threetrree groups of data are shown.shos'n. Thettre lower pairpai-r of curves on each graph represent tWJ-dimensionaltrc*dfuceneional valuesval-ues taken from Fig. lOa.10a" ~ Ththee curves are obtained by integrating the two=dimensional two:dimensiorial head loss over thetl:e approach velocity profile,profJ-1ei oneoae over o.rer thet'he vane spansparl and one vane space, and the othotherer over the tlre entire entj-re duct cross section.sectdofi" If there werexrere no secondaryseeondary flowfLow in in- flufluenceence on thetlre two-dimensionaltwo-diraensional drag,dragr these curveseurves shouldshoul-d also represent representthe the experimental three-dimensional three*dimensional head loss.
Thethe remaremain:i-ng.ining curves and data-points showghow thet"tre trend of the three= three- dimdi-mensionalensional experimentale:peri-mental data. TheTtre SJgj curve represents the head loss data obobtainedtained fro~frop measurementsaeasurements at 0.5 chord c'trord length behind the vane trailingtrajli.ng edges and taken over one orre vane span span.and· and Qneone vane space.space" The?he nearby points marked Sb(, are similarsimi-lar but are obtained from measurementsmeasurernents taken over the entire duct crocrossss section. These data lie,1ie, on thetbe average,aserage, some 30 per cent above the cor cor- rerespondingsponding integrated two-dimensional two-&lmensional curves. The increase in 1n loss is not veryrrery large,arge , but doesd.oes exist.exist" The differences betueenbetween thettre ~gb band and SE3 3 pointspoints,repre: repre= sent the experimental effecteffeet of the lateral duct duet walls. Thethe differences are 2 seen to be very small smal1 ~orfor the data shownshorm (of thettre order of 0.01 0,01 or cr 0.02 0.0? VIV-rz/Zd, /2g), but wwhenhen thettre numbernr:sber of vanes in ia the duct was reduced to 4l+ or 5~5o Sg.,^ b . increasedinlreased gregreatJ.y"atly. 6
The upper group of curves ardand data-polntsdata- points lnin Fig. 11,11, marked ~ , the upper of f*,m represeat,represent the head loss coefficientecoefficients obtained from measarement'smeasurements further down- stneamostream. fheseTheBe were taken at station tr$-MM-M rdrerewhere the rate of loss was approxi-approxi natelymately the satnesame as in the straight duci"duct. theThe data-points fall 100 per cent and more above the integrated tsro-di-menslonaltwo-dimensional curves and alssalso well above t'hethe g. '3't and e'b-D - cttnvesocurves 0 theThe data scatter, batbut nuchmu~ of tJ:ethe scatter is eli&inatedeliminated was of with by grouping the :pointspointsnoints by bv chor,chord length {ttrere(there was no variationvari-atlon of C^'2- /. with ehordchord length). TtreThe remaining scatter naymay be attributed to experinentalexperimental €rrorerror (the estinatedestimated accuracy of tirothe neasrlrearcntsmea.~urements of average total head leis 2 per cent of ttrethe dyaaniedynamic head, and since tbethe headhe'ad l-ossloss ieis ttrethe &i:fferencedifference betreenbetween trrotwo everageaverage total heads, the possible error is l+4 per cent) and to the use of three different shapes of duct rittrwith sonedatsomewhat dlfferentdifferent entrance veloclt'yvelocity profiles. TtreThe head loss representedbytherepresented by the difference in 'mE* and Eb'b points must occ'uroccur downstream of ttlethe vanes 0
Since$ince ltit appears that the excess exeess head loss in a guide vane bend isi-s associatedaesoeiated with the secondary eecondary flow, it is ie desirable to relate r.elate the two b;rby comcon- putation. Squiregquire and "WinterTl,nter [2][Z] andana the basic referencereferenee [I.]p] srto*show that Justjust beyond the beginning of curvature, the tbe vorticityvortlcity componentconponent (.e para11elparallel to thetJre two-dimensionaltwo-djsensi-onal streamlines strea^m"llnes is givenglven by
€ :2 eqo (7)
where Ee is the smallemall angle throught"trrough whichshich each streamlinestrearal-ine has turnedturaed and 'rJrla 0 is the vorticity vortieity component normalnornal to the streamlines stil'selnlinss and vane spans apans at the be be- ginninggirrniag of curvature.curvature" Squire . and WinterElntcr have extended Eq.Sq. (1){?) to the entire bend by taking E€ as the total turning angle of thetbe two-dimensitso-dlnensional onal streamstream- lines and 'rJn as constanteonstant both along thetrhe streamlinesstrea$]j-nes and parallel to the ttrre vane spans.spansr This?his ignoreslgnores any influencelrrfluenee of the secondary flow on the basiebasic twotwo- dimensionaldirnensional motion.motiono Having computedeonputed thettre resulremlting ting secondarysecondar;r flowflsw on this basis, theyttrey arbitrarily take the energyenerry lossl-oss as half the kinetic energye:lerry of the second second- aryarXr flow. It is believed that tJ:at the Squire and WinterTlinter assumptions beyond Eq.Eq" (7) cannotcarrnot be used to obtain sbtein quantitativequantitatlve data and that ihat the true nature of the the secondary flowfLow is obscured obseured by those assumptions. assumptions" ...
7
Generally ~ thethe vort ici ty 7J i-sis veryvery l-argel arge nearnear *tethe ductduct walLswall s and Cenerally, vortieity \ o decreases rapidJ.yrapidly towardt oward tfiethe interior of thethe f,luad.fluid. A.f't'erAf ter a sna1lsmall j-:rcrementi ncrement ofof turning €E e9 the vorticityvort ici t y componentscomponents {, FiLlwil l bebe rouglrlyr oughly as sl@tshedsketched 1nin Eig"Fig. a?aE12a, the size of eacheach vortex figuref i gure indicatesindicates the relat'lverelative strengths trength of tbethe vorticit6i'.vorticity. theThe associated veloeityveloci ty patterr"rpattern sil-Lwill be l-ilselike that sketched in
Fig,Fig. 12b.12b. AtAt suceeedingsucceeding sectioassections around tl:ethe bend,bendy 7J rla 0 takest akes on differenfdifferent values and 6~ will.will vary;vary ; but,but,9 qualitativelynqualitatively ,. thesethe se sketehess ketches stj-llstill givegive a pic-pic tr:reture of what must occareoccur. theThe flow patternpat ter n of Fig.Fi g . 12 L2 hashas been eonfirrnedinconfirmed' in erperimentalexperimental observatd-onsobservations ardand photographs of yarnsyarns ard and wa1lwall eoatings.coatings. It has also been observed by othersiothers ; som€some exeellentexcellen t photographsphotogr aphs nerewere published re-re cently by the $ationalNational AdvisoryAdvi sory CommltteeCommittee for AeronautlcsAeronautics b]"li3J . At ttrethe trail-trail ing edge of each 'naRe,vaney trotwo vertical curentscurrents meetmee t and form a vortex sheet';sheet; this is identical wittrwith thet he sheetsheet which would bebe at att'ri-butedtributed to the decrease in circulation near the span ends.ends" There i-sis no furfherfurthe r vortS.eityvorticit y €~ developed beyond the trailing edges edgesojl but theth~ flLowflow in thet he borxrdaryboundary layerlayer eontinuescontinues toward
the inside wall wa11 and along that wallwal1 torvardtoward itsi t s center" center 0
The impo;rta,ntj-npoftatrt consequericeconsequenae Ofqf the preeedingpreceding d:iscussiondiscussion is not so muehmuch thattLrat a secondary flowflcm develops,developsy but rathe ratherr that thistJri-s sseeond.aryecondary flow behaveebehaves inj-n such a way that itlt carriesearuj"es low=energylow:energy fluid ffromrom th thee ductduct boundary layer downdow'n thetlre suctionsuetion surface ooff each vane into thettre interj-nterisri or oof,f th thee ffluid,luid, and high=high- energyenergr fluidflu-id from fron the interior interi-or to the ducd.uctt wwaL1.all. TTirishis 'i-$edj-stributionedi s tributionof of the streamlines is observable in the total head sursurveysveys ploplottedtted in Fig. 3b3b.. The streamlinesstrea^nlines are indicated schematically in FFi-g.i g. 113"3 . HeIlener e A$d-'A . rrepreseatsepresents the two-dimensionaltwo-dinensional streamlinesstreaplines in the interioi-nteriorur~ B tthehe s separati-oneparation region associated assoclated
wirith th the two=dimensionaltno-di-mensional boundary layerlayeru 9 CC-e=c thfitee uupst'reanpstream bobounda:Trundary layer streamstream- lines~Iines, and CCt-Cci =C ' the streamlines originally iinn the interi i-nterioro r whiilhi-ehch aarere carried to the ttre boundary by the secondary flowflow, .
TheS:e strength of thettre secondaryseeondary flow ddependsepends oon n the raraliot i o cLICr1/{slc) (sic) of
thtlree two-dimensionaltwo-dirensj.onal flow (Fig. 6)6\,9 the profprofiles:i.l e s of th thee vanesvanesu9 and the entrance vvelocityelocity profile,profile; theretfrere may be other minor fafactors.ctors . Thefne present data did d"ld not permipermit t study of these factors.,factors; a recent r€cent pubpubLi-cationlication of the NationalHatlonal Advisory CommitteeCownitt*e for Aeronautics [8J[B] ggivesi ves somesonre data.dats on the t]ie first f factor.actor. Thethe relationrel-ation betweenbetrveen the e exeessxcess heheadad lossLoss aandnd the se secondarycondary flow isie nonoww apparent. In FigFig". 11Ll,9 the tire diffd:iffereneeerence bebettreentween ~ 3 and ~ 29 tthehe exexeesscess loss e 3 E* at the vanesyanes,, isj-s associated with the ttle devel developmentopment of ththee trtrai1l-ngai l i ng vortices vortlces and alalsoso with rith the modif nodi-ficationi cation of the ttre twotwo-dirensienal=dimensi onal boboundaryundary layelayerr fl flowow at at thethe x v8 vane surfaces"surfaces. That isuis~ wherewhere separatioxlseparation occarsoccurs at the vane surfacesurface j-nin the two*dimensi-oaaltwo-dimensional region,region ~ J-tit naymay notnot oceuroccur nearnear the spans pan endsoends. lbeThe d.ifferencedifference between ~ m and ~ b' thethe excess loss dcnnnstreamdownstream of ttrethe vanes,vanes~ is associated E* 6 O, withwi th increased frictj-onfriction at thethe ductwaI-lduct wall wherewher e high*enerry,high- ener gy, high-velocity fluid nosnow fornsforms the boundary layer,layer.
theThe part of the loss occurring ata t the t he vanesvanes i-sis eonparatlvelycomparatively smal1,small, and not too nuchmuch attention has been given to it yet.yet . CarterCarter and Cohen [?][fl fravehave computed tliethe part of the drag coeffi-cient,coefficient attribr:tableattributabl e tot.o the'traiLingthe ' traili ng vortlcesvortices w:ithinwi thin an unknowrrunknown factorfact or representingr epresenting thet he distaneedistance between each no11ed-uprolled-up trailing vortex and the diretduct wa-llnwall. BecaueeBecause of thisthis unknorrnunknown factor, their eorn-com putation cannot be verified.verified directly using the present data.data,
AA, rough computationcomputation of the loss eoefficientcoefficien t attributableattributable to additlonaladditional shear at the wa11wall was made in the basic reference. The formula was obtained
$x^ =C tt = 0.03ow (8(8) ) whererhere tr~T is the head loss coefficientcoefficj-ent aettributablettributable to the greater ,:$hearshear at the wall,waI1, KX is a parameter dependingdependir€ onoa enentlrancetrance vvelocitt'profileeloci typrofile G(K ~* 1/3t/3 for tar the present experiments),experi-u:ents), andffid sxoz2 isls half the ratioratj-o of wall rall are areaa exper exper5-encingi encing additional additi-onal shear to frsl passage area between the vanes.
In the formula, fo::rrula, x is the distancedlstance requiredrequ5-red dodownstreauwnstream of the tlre vanes for the t'he In *a2 disdisturbed turbed velocityve1.ocity profile to retur returnn approximately to te it its s value at the entrance to the vanes. The experiments indicated that x*Z tend tendeded to increase i-ncrease withsit'h de de- the vanes. The experfuaents 2 creasing spacingspaeing betweenbetmeen the vanes for the ttre plate vanes but waswae more nearly coconstantnstant for thetbe thick tliiek vanes. AssumingAssun:ing that at the clclosestosest vane spacing in the ppresentresent experiments (about 1l- in,) in. ) thetrre boundary layerI-ayer did dld not return to normaluormal ununtiltil station M-M was reached (x ~ 30 in.);>!in")" Eq , (8)(B) yieldedyiel-ded station M-M reaehed {*qp2 30 Pq"
0"3 ft =m (8a)(8.) whfiereere ss.0 Jl. is the passage areaar€a in5-n squaresqu4ro incheslnehes ." ....
9I
Infn Fig.Fig" 14,1\, experimental values of ~mt, ~- ~EZ 2 have been plotted against j-s list3,/a!, for one of the plate vanesvanese9 and EqoEq" (8a)(Ba) for f,~T is alsoal-so shown.shown* It is - to be remembered that the values of ~mE* - ~2ep ini-neludeclude not only ~Tt, but also thet'lre coefficientscoeffieients of the losses occurring oceurring at the vanesv&,nes andarid ini.n the spaces betweenbetryeen the vanes andand. wallswal1s (of{of thet}re order of 0.05). 0"05) " Thelbe trendtrend. of the t}re data follows the formula.formula, OtherSther data show that at the ttre largest passage areas (where(wtrere there were too fewfery vanes eanes in the bend), the trend of the datad.ata was opposite to ilia*Jrat t of the formula.fornula"
Thethe thick vanes used ini-n these experiments were designed Withwith constant eonstant gap between the vanes; x wasrr&s more nearly constant than for the plate vanes, gap between vanes; *Z2 more nearly aonstant f,or the vanes, so that Eq.Iq" (8)(B) indicates that STt, should tend to remain constant. The exex-
perimentalperinental values of m =* 2 for these lhese vanes werumee also roughly constant.constant" St * S!, ' In conclusionconclusioR,j it has been shown that the secondaryseeondary flowsfl-ows increase thetlre two-dimensional loss coefficient, principally by$r increasing the wall wall- shear downstream of the vanesvanee but also by increasing lncreasing the loss at the vanes. The ?he head 16ssldss coefficient SC initt a guide vane bend maynaay be written
Ftrr ·S'!= "" S92*2 + S9i+9ri + ST (9)(ei
is the two-dimensional loss coefficient ~ vrhere lz is the two-dinenslonal loss coefflclent, 9 Ei ists the loss coefficient at the vanes, and
tt is the loss coefficientcoefficient, j due principallyprlneipally to increased wall weJ-l shear, downstreamdosnstream fromfron the vanes.vaneso
For practical purposes, the deflection produced by a guide vane systemsystena is the samesante as the two-dimensional hro-dirnensional deflection. deflection"
GiSiven ven Ct! e{ (s/tsle) c) forf,or the tire two-dimensional tso-dimenslonal flow, thetAe vane profiles, and ththee entranceentranee velocity profile, it shouldsbould be possible to compute both ~. and Ef1 ST't, " Methods for accomplishingaecomplishing this have not yet been devisedodevlsed"
ACKNOWLEDGMENTACfi}IW&ENC*ilEI{T
Thisthls paper is based on research sponsored by the Office of NavalNavalRe He- ssearchearch under Contract ONR-662040IA,-6620h and isj.s condensed from a final final- report for that ttrat oorganizationrganization [lJ.F]. The work was perforxredperformed at the St. Anthony falls!'a11s Hydraulicliydraulic LabLaboratoryoratory under the general directiondi-rection of Dro!r" Lorenz G. Straub,$traub, Director.9ireetor. 1n I\J10
!rq3LIS T gs 0 F EREFEFERENCES ERE N C E S
Silberman, E. Secondary Flows in Guide Vane Benda With Some Notes on the . Primary Two-Dimensional Flow. Universit y of Minnesota)) st. An thony Falls Hydraulic Labor atorya t ory ProjectBeportProject Repor t No"Noo 36r36J> JanuarytJanuary, 1953.;.-953. 102 pages"pages. t ] $quire,Squire, H,H. GnGo and ffinter,Winter 9 K,K" G"G. n1l:eliThe $eeondarySecondary Flow in a Cascade of A,ir-Air foils in a l{onr:niformNonuniform Stream.Str eam. irIi Journal-Journal cfvf AeronautagdAer onau ti.cal !sie399tScience, Yol'Vol. J-Bu18)) ;q6"No.4 l*r!1 pp. 271:2??"271 ~ 2 77 . f3H--**:1951 nThe t3]DJ gler,Tyler, n"R. A"A. "The Available TtreoreticalTheoretical Analyses of lko*'li-nensionalTwo~Dimensional Cas-Cas cade Elow"ffFlow." Natj-onalNational ResearehResearch eouncilCouncil of,of CanadauCanada, Aero Note, AN-4,AN-l+u Ottawa,ottawa, 1949. 58 pages. FGraphical, [4Jttr] Poritslqy,Poritsky, H"rH., Sells, B. E'E.r9 and DanforthDanfortlu9 CC.o E'Eo "Graphical, Mechanical, and ElectricalElectrisal Aids for Compress Compressiblei ble FluFlui-di d Flow.Flow"lt n Journal of AppliedAppli-ed Mechanics,Mecha_Llcso Vo1.Vol. 1212n, lrlo.No. I1,, pp"pp. J3V-h6"7 ~46 . 1950.L95O.- [5Ji5l Schlicting,Schlietlngo H. and Scholz,Schelz, N. ''Theoreticaltlfheofetical DeDebrninationtermination of Flow LossesEosses in a PlaneFlane Cascade Casoadern (ifbe{ilberr diedj.e TheoreTheoretjechetj"sche Berechnung der Stromungsverluste$tr6nungsverluste eineselnes ebenebenenen Sgehaarfelgitter).chaufel gi t t er) . IngenieurIngenieur- Archiv, Vol.VoI" 191P,, pp.pp" 42-65)+2-65". 1951 L95L0
tfA 1f [6Jt6] Davis, H. "A Method of CorrelatingCorrelatlng Axial-Fla Axial-Fl-orry-Conrpressorw-Compressor Cascade Data.!ata.q TransactionsTransaetions of the ASMEA$lffu)) Vol. Vo1. 70, pp.pp . 9957-955.51~955. 1948.191+8 mWind [7Jl-?l Harris,Harrisn R. G.G" and Fairthorne, R R,o A. "Wind TTunnelunnel Experiments &cperlments withwit'h InIn- finifinite te Cascades ofof, AAirfoils.rui rfoils. Ii BriBri-'b:i-shtish AeAerouautical r onautical Research Council))Counciln ReportsRepjg'ts and MemorandaMemglq!4q,, Nff6o.-:C2 06. 10928. r^'t tt$ff,eetof [8JLBJ Hansen, A.A" G., Costello, Costelloe G. G" ROllE.n and HerzigHerzig,, HH,". Z. Il Effec t of Geometry on Secondary FlowsflLows inin Blade Rows.fi,owso IIrt NaN'at.:-onaltional AdAdvisory vi s ory CommiConn:it'tee ttee for Aeronautics,.6,eronautics, Research M Hemorandufff,Tfl'Effiemor andu.m;-'R1T E ~ H26J October, 1952" 38 pages. "Prelim.l:i:a:'y Invtstfgation lnto the Threo- [~tfl Carter,Carter; A. D.D. S.S" an.dand. Cohen, Cohenl E.!fPrelin.:iE. .nar y I nvestigation into the Three DimensionalDlsenstonal FlowFlorE througthror:gfsh aa CCaseadeascade ooff AAercfolLs'ier of' oi ls~ BritishSrltish AeroAero- nauticalnantl caL ResearRoseareb,ch CounCounecilt l j1rReporteiReports aand.nd Mel,{emorandamoranda,No.2339.r$o, 2539. 1946.1945, '.
------AIIgIgITAPPENDIX FigureFigures s 1 to 141l+ . '
t2l2
,:\
\ :\
~GUid~ '
IJ *',*,.,
\ 1 Xnr)=) )) ~';J )) ))))))) ) r5"
•
'. ll i:.
VerticalVerticol Section Seciion
Fig.Fig. 1- l- GuideGride \kine\bne Installationkrstollolion init High-Velocity Hidr-Wlocity ChannelChonnd 1?13
:ii.:: : , ;;i.:r: ,:l*- *&
FigFiq.2. 2 -- GuideGuide VanesVones InstalledInstolled inin ao TestTest Bend Bend 141lr
".ll.'-U1J.1'---_. ____• . ______illl.WlIlill
a.O. StraightStroight Duct, Section A-A
DimensionlessDrmensionless Totol Toiol HeadHeod 0 0.3 0.3 0.7 -=IIIIllTI 0.7 0.98 0.9 =| - lOv..Over 0.98 dqA
"0 c ~ CD ~ '0 '0 ~ ~ "0 "0 ." ~" :3
bb.. Immediate lmmediotelyly DownstreamDownstreom of M tvliteriter EElbow,lbow, Section B-B-BB
Fig.3- TotalTotol HeadHeod Distribution in ao Guide VoneVane Bend $15
Wells
c.C. DownslreomDownstream ofo f Bend,Bend, SectionSection M-MM·M
- -~1------r- 1 1Y2~'6 ' 6" 8 ( f'rx --J ~--A >. (21) ' "" (20 3003OO VaneVone Shape Shope ~283 5 ReRer-c " 1.5 t.5 x* 10'Ou RedRe6.33 ~ 3.8 x t 10 ,O"5
B
M M Dimensisl€ss Totol Heod dd.. Vane Vone ArrangementAnongement
tfrTmr t07 - o98
Fig.3-Fig.3-Total Totol Head Heod Distribution Disiribution inin a o GuideGuide Vane Vone Bend Bend 16
Flow 6"
I ,
I " I I ' /1 ~O%IO" I , . ,I I '32 I I I I I J I I I 1,.,, I I t-+ I i (30)(3O) 400 VaneVone ShapeShope ReRe.=c = L5t.5 x 10to55 RedRe6= = 5.35 x 10ros5
Fig.4-HeadFig.4-Heod Loss Behind the Two-Two-DimensionolDimensional Region of ao CascadeCoscode 1717
!t o c I I
':I J o ! I (,o o o o ; c)
'l::'T' ka
DeflectionDefl€ction Erit Angle Angle Angle B 6.A e
Enfronce Anele
Fig.5-Fig.5-CascodeCoscode ChorocteristicsCharacteristics 1B18
B, cotp2 t.o
60° 0.5
° 0 ,~ o· " r: \~ '\. c.y
90090° 0.0 ""
-0.5 "I['"" 1200
135° - 1.0
- I .5
150°
-2.0-e.o
Cotcot /3 p,1 -0.5 0.00.0 0 . 5 1.0LO 1.5 2 .0
90°goo 600 450 /3p,1 45° 30°
Fig.6-RelationFig.6-Relotion BetweenBetween EntranceEntronce andond ExitExit AnglesAngles,, DeflectionDef lection Angle,Angle, andond LiftLif t CoefficientGoefficient inin ao CascadeOoscode 1910
p2 /3B,2 Cotcot {32 1r.o.0
t col a P * 60(' 0o.5. 5 ----),'_---' : 68° le'680
90°900 00.o.0 'r{>e cY =golso ----v e 90.5 ° /"E~--II-----4iI'- -- -0--o-
0--o-- -0--o- /'
~--a Va 120° -0--- e ' ll3o
-_o I e --0-_ -. -·/76126 CotDCorl 0 - ______-4 ______1t35035 - 1.0t.o ~ ~ ~~A'~/' ~824 __~ ______~
-t.5-1 . 5
15001500
'2.O- 2 .0
Ccotot p, -o.s 0 .0 0 .5 /31 -0. 5 o.o o.5 t.o1.0 r.51.5 2.O2.0
p, 900900 600600 45045° 30030° /31
- FromFrom Fig.Fig . 22 byby OovisDavis IO][6J rcpresenfin0representing erperimentolexperimental dofo data -- -o-e --- - FromFrom HorrisHarris ondand FoirthornefFairthorne [7J7]
(Slorred(Starred poinlspoints represenlrepresent slostalledllrd cqscodcscascades occordingaccording toto referereference.nce. ChccledChecked poinlrpoin ts represenlre present coscodescascades withwith obnormollyabnorma II y highhig h drog.drag.))
Fig.7-TypicolFig. 7- Typical GoscodeCascade LinesLines 20
~ 1------4.2S"------+iJ I. 2.63" I /-:\ ~1,------4.25·-----_+l11 I. 2.83" I
Trunnion Hole -\ A L----..L*rJ ,.,. ---~ Fig.Fig.8-Guide 8 - Guide VaneVone Profiles Used in the ExperimentalExperimentol Work
I 15· ----r_--,_---r--~---r_--,_---~----~ "A 2,02"2.O2' chord EIo 2.83" or 2.93"2.9J' Chord .,9 4.25"4,25" chord ,.,\ 6"e" byuy 6" bend 0 !i 6"s" by 9" bend,bsnd,g' 9" highhitl 110 \----t----+---t---t----t----i _1_ 6" by g' bend,6" high q)o -:- 6" by 9' bsr'd,6" hidl //,.t 6" by 9" bend,4,5"bcnd,4,s" hi9hhidl o!!g (21)3003OO vonevone4 (with(wl?h Splitter)Splitlcrl coCD c:c ~ CDo coCD coCD 0o ino 0 100 9~L---~~~~--~---L----~---L--~----~--~g5" 0.2o.2 0.3 0.4 0.5 0.6 00.7.7 0.80a 0.9 1.0 1.1 Spacing-ChordSpocing-Chord RatioRorio ...!..f c Fig.9-StaggerFig.9-Stogger Angle Required to Produce 90°90" Flow Deflection 212I 0..24o.24 VaneVone Chord 2.0.2"zoz" 2.83" 2.93" 4.25"4.2s" (30.)40.0.(30)4oo ~-{-F- 0.o.20.20. d - rr-{l Type II -~-- (21)300(21)3OO ----{lrrlrr \ --- . -~- -'!f-- + .,(Goscode c:c \ *Cascade axisoxis shiftedshified Q)o 0..16o.r6 :§ I ...... ; \ Q)o I peI Vo1e -o \ ,:v A o 0..12o.t2 t---'tX---=iIF"1;~'r--+-a\\\ ---+-\--+---+---j--~F-----1 /l (J)o t 3')O Vone (J)o G /Y (2t) o \ .....I) a \i I a\'-' o.o8 @@vs?o-e) "0o o -, o.0.oo. o.o.~-~----~----~----~----~----~----~----~--~ 0.2o.2 0..3o.3 0..4o.4 0..5o.s 0..60.6 0..7 0.7 0..80.8 0..9o.9 1.0.l.o 1.1l.l SpacingSpocing - Chord RatioRotio tI oo.. Head Heod Loss Coefficient Coefficienl 5 ReRe"=c = 1.5)(1'5t'Ou 10. 0.u.. 16tb a'" 0O t?0) 4004oo IvooVone\,\ (~O) / Ol 0..12o.t2 0o ~ 0o (T pe I VaneVorp (21)l2 30.0.300 vane)bnel (' /' 0 / - 0..0.8o.o8 ..- c:g /~ /' Q)o \ N g ~ {; .....F \ ---/' ~-.:;"" Q)(D 0.0.04.0.4 , ~ ...~ss.+. ."- t 0 ..... - ...... 0 ~----.. -7-"' 0..0.0.o.oo 0..2o.? 0..30.3 0..40.4 0..50.5 0..6 0.6 0..70.7 0..8 0..90.9 1.0.t.o 1.1 SpacingSpocing -Chord- Cho rd RatioRolio t b. Coefficient of DragDrog = 5 RR.. ec = 151.5 x 10.lO5 FigFig.lO-Two-Dimensionol.IO-Two- Dimensional HeadHeod Loss andond DragDrogCoef Coefficientsf icients 2222 o.320 .32 \4- , x 5 \ Re.=Ree = l51.5)( 1gs10 ~tlF t'a."- 0.28 \ . 6"6"by by 6"6"bend bend o.28 l\l "- t., I 6"6" byby 9"9" bend,bend, \ I l Chord= 02") \.rh \ /\fr i s"9" trign high v o.24024 t\ \ 11A \\t x' -.- 6"by6" by 9"9" bend,bend, x \ :1 \ T$ 6"6" hhigh igh 'oo 4 $. 14 BendBend wollswalls somesame ~ 0.200 . 20r-----~._--_r~~_+------r_----~~~_r----_+----~ /\ oo shopeshape osas vonevane (,<..) (Ghord= z.s3) * V> - 028,------,----,-----,------,----, , Chord= 4. lc^ / 0.241-----+---+-----+--- -+----/ "trjl \ '\+,,/'tt V. \ }F H rr->' L m (Chord=Chord' -. J 22.83").83") tV :L 020r-----r-----r-----r-----r----1 r_----~~~r---~nr---.rr-----r----1 \- f em (Chord = 293') \ t \ f cc I Q) +\v ,oo 0.16 r_~--_+_----_r-----+_9'~--r_--- 1 .9 ! o t o T T o v 'ne \b, 16.int.qt Ited over spon\ '"o 0.12 I----+_- t\ oo I'rr,aA ...J'" J rb /c" '0 !to i"N o Q) \'' l-l-- 4/ o :I \a' 5 I I bF \ l-t,^ Q\ -'!t.'..*-. I ...... -0- ·(::.. l::::::.:::: the duct 004'-----.l.....---.J...... --...J.-----J.,.--....J !e ··lni~~~~/~~:i1l eotdle o ~:er 0.3 0.4 0.50.5 06 0.6 0.7 0.2 0 .3 0.40.4 0.50.5 0.6o.6m 0.7 0.8r\Q 0.4 n - - SpacingSpocing - ChordChord RalioRotio iI SpacingSpocing - Chord Chord Ratio Rotio tE bb.. Type Type I I Vane Vone cc.. (21)(21) 300 3OO Vane Vone Fig.ll-Fig.II - ComparisonComporison ofof Two-DimensionalTwo-Dimensionol andond Three-Dimensional Three-Dimensionol HeadHeod Loss Loss CoefficientsCoefficients 232) DuctDuci Wall Woll \\\\ \\\\ )))))))) ))))))-)) ))) \\\\ \\\\ ))))) ) )) )))))J)) ))) "0 C -g)))))))))))))))))) ) ) ) ) ) Q) Q) al al -o Q) "0 ....'in o:> Vanes a - Schematic Vortex Distribution I I I I \ \ \ \ rl r J / 2 ) Jl J I -) -! -t -t -j -r -\,t -\ J -\,J -'\ t z'lJ-l -\ ..' -.i -.i -J -f -i ,,-Duct Wall )))) )._ t ! t I )))) "0 C : Q) I )) )) ) al o '0 - Q) Q) "0 "0 'in ~ .5 o:> t--L- Vane~ -...r- b-Schemoticb- Schematic SecondorySecondary FlowFlow PotfcnPattern Fig.l2-SkctchFiO,12-Sketch ofof SecondorySecondary FlowFlow BciwecnBetween lhethe VonesVanes .... 2\24 Legend - /t \ S'treomlines .at-.-- NeorWo 11 # ,'lr'r.;;--i\ - Streomlines - Duct / t: ^.l* ------_-JIc'___ - ...... - C' Y -~ c o c+4 o a Q) co oc >o A .... - -~A ElevationElevotion Fio.FigllScfranqlicl3-Sch ematic St Streomlines ream lines 10° in ao GGuideUI °d e VaneVone BBendend 251> 0.3~ 8-A 2 2.02-in..02-in. chordchord 0tr 2.S3-in.2.83-in. chordchord 0.3 0 9V 4.25-in.4.25-in. chordchord ,t.. , 6-in.6-in. xx 6-in.6-in. bendbend 0.2 8 II ii 6-ine-in.. xx 9-in.9- in. bend,bend, 99 inin.. highhigh -.- 6-in.6-in. xx 9-in9-in.. bend,bend, 66 in.in. highhigh 0.26 , 0.24 'Q 0.22 (30) 400 Vanes C\IN '-..It ~~ II 0.2 0 E If)@ O.IS "E * .9Q) "'"' :.9~ ~ -Q;o ~ o 0.16 U g ~ If)a o If)o .JJ 8- 0.14 ...~ E "0o Q)o 'Q I L' ~ • .S 0.12 .:or rt)Q) ou c ¢ oQ) l!r- 2o 0.10 A- 5 0.0 S V ~ ¢ ~ 0.0 6 ~ ~ ~ :, /s9- ~ 0.0 4 ?Oo3-4. ~ 0.0 2 , I""'" ---- 0.08.04 0.)606 0.080.08 o.to0.10 o.tz0.12 0.t40.14 0.t60.16 0,t80.18 0.200.20 0.220.22 0.24 0.26 II -I ReciprocolReciprocal ofof PossogePassage Areo, Area, 3.1SI inin unitsunits ofof (sq.(sq. in.flin.) Fig.l4-Fig.14-ComparisonCompcrison ofof TotolTotal ExcessExcess HeodHead LossLoss ondand CompufedComputed LossLoss AltributobleAttributable foto WollWall SheorShear