technical note 3823
TRANSCRIPT
.
TECHNICAL NOTE 3823
IIWZESTIGATIONOF ROTATING STALL IN A
SINGLE-STAGE AXi21LCOMPRESSOR -
By S. R. Montgomery andJ. J. Braun
MassachusettsInstitute of Technology
WashhwtonJanuary1957
.
.
TECHLIBRARYKAFB,NM
NATIONALADVISORYCOMMITTEEFORAERONAU I:lllllllllllllllllull!llTECHNICALNOTE3823
INVESTIGATIONOFRO!13%TINGSWULIN
SINGLE-STAGEAXIALCompressor
OClbb715
A
By S.R.Montgomeryand
SUMMARY
J.J.Braun
Therotating-stallcharacteristicsofa single-stageaxial-flowcompressorwereinvestigated.Thenumberof stallcelJ.sandtheirpropa-gationvelocitieswerefoundwithandwithoutstatorblades.Themeas-uredvelocitieswerecomparedwiththosepredictedby Stenning’stheory(seeNACATN 358o), assumingthedownstreampressurefluctuationstobenegligible,andcorrelationwithin10percentwasobtainedat theonsetof stall.Itwasfoundthatthepressurefluctuationscausedby rotatingstallwerelessdownstreamoftherotorthanupstream;theminimumreduc-tionacrosstherotorwas40 percentwithwithoutstatorblades.Itwasalsofoundthestatorbladesdecreasedthenumberofrotatingstallat largermassflowrates.
statorbladesand75 percentthat,forthecompressortested,stallcellsandtendedto induce
INTRODUCTION
Rotatingstallmaybe definedasa regionof separatedflowmovingalonga bladerow. Ithasbeena continuingprobleminaxial-compressordevelopmentbecausetheresultingvibrationscauseseverebladestressestobe imposedat low-mass-flowoperation.If stallfrequencieswerepredictable,bladescouldbe designedhavingcriticalfrequenciesdif-ferentfromthestallfrequency.
Severaltheorieshavebeenputforwardforpredictingthepropa-gationvelocityofa stallcell(refs.1 to 3). Thesearealllinearizedanalyses,withSearsandMarbleconsideringthecascadeasan actuatordiskandStenning,asa cascadeoffinitewidth.A furtherdifferenceinthetheoriesoccursinconnectionwiththeassumptionofthedownstreamflowfield;SearsandMarbleconsideredthewakestomixin zerolength,sothattheflowfieldisa continuum,whileStenningalsoconsideredthealternativeassumptionofa seriesoffreejetsdischargingintoa regionof constantpressure.
2 NACATN 3823 Z—
Experimentalworkhasalreadybeenconductedoncompressors,in.
particularbyHarvardUniversity,theCaliforniaInstituteofTechnology, —andtheNationalAdvisoryCommitteeforAeronautics(refs.h’to6). How- a–ever,ineachinstancetheworkhasbeencarriedoutonmultirowmachines,anditappears:thatconsiderableinterferenceresultsfromthedownstreambladerows. ,—
Sincethetheoriesareinvarianceandtheinterferencedueto otherbladerowshasanunknowneffect,thepresentinvestigationhasbeencon-ductedona single-stagemachine,withandtithoutdownstreamstatorblades,inan efforttoverifythepredictedresultswitha minimumofinterference;however,Itwasnotfoundpossibletoremovetheinletguidevanes.Thedataobtainedpermita readycomparisonbetweenpre-dictedandactualstall-propagationvelocitiesand,inaddition,allow”thetheoreticalmodelsforthedownstreamflowfieldtobe checkedbymeasurementofthepressurefluctuations.
—..—
——
—
ThisinvestigationwasconductedattheMassachusettsInstituteof —TechnologyunderthesponsorshipandwiththefinancialassistanceoftheNACA.
.
A
b
c
CP
Cx
Cy
f
F
L
N
SYMBOLS
effectivebladepassagearea
totalbladepassagearea
halfwavelengthof stallcell _.
resultantvelocity
pressurecoefficient
axialvelocity
tsmgentialvelocity
stall-propagationfrequency
frequencyoftimingpulseonphotographs
bladechordlength
numberof stallcells
—
.
—— . ....
.
—
—
——---
*
.
NACATN3823.
.
P
Ps
r
rt
u
v
T?
X>Y
a
al
Cf4
P~
132
?
@
separationbetweeninletguidevanesandrotor
staticpressure
radiu,s
rotortipradius
rotorvelocityatmeanradius
stall-propagationvelocityatmeanradiusrelativetorotor
inletvelocityrelativeto rotor
coordinatedirections
blockagecoefficient
absoluteairangleenteringrotor
absoluteairangleleavingrotor
airinletanglerelativeto rotor
airoutletanglerelativeto rotor
density
perturbationvelocitypotential
U angularfrequencyof stallpropagation‘
4 NACATN3823
EQUIPMENTANDPROCEDURE
Equipment
Thesingle-stagecompressorusedinthepresentinvestigationisshowninfigure1. Ithasthre~bladerows,theinlet-guidevanes,rotorblades,andstatorblades,eachbeingof“free-vofiex”design.me char-acteristicsofthiscompressorarepresentedinreference7.
Thecompressordimensionsare:
Outsideradius,in.. . . . . . . . . . . . . . . . . . ● ● ● c 11.625Hub-tipratio~. . . . . . . . . . . . . . . . ● s ● ● ● ● c ●
Bladechordlen@h,in.. . . . . . . ● . . 0 . ● . . . . . . .Bladeaspectratio. . . . . . . . . . . . . . . .* ● ● c ● ●
Pitch-chordratioatmeanradius. . . . . . . . . . . . . . .Approximateblade-tipclearance,in. . . . . . . . . ● ● s ● ●
Bladeanglesmeasuredfromtheaxialdirectionare:
0.751.51.9
o.~0.035
I Bladeangles,deg,for-
Radius Inletguideratio, Rotor ,Statorvanesr/rt
Inlet Outlet Inlet Outlet Inlet Outlet
0.75 0 28.5 34.8 -2.9 48.9 23.3.80 0 27.1 38.0 47.2 22.0.85 0 2597 42.9 1;:; 46.2 20.6●90 0 24.4 47.5 23.4 45.1 19.4● 95 0 23.3 51.6 29.7 44.3 18.3
1.00 0 22.2 54.6 34.4 43.3 17.2
ThebladeprofileswereNACAfour-digitseries10percentthick.Figure2 isa sectionalviewofthebladeregionwherevelocityandpres-suremeasurementsweremade. An adjustablethrottlingvalvedownstreamofthebladespermittedvariationofmassflow.
Qualitativemeasurementsofvelocityfluctuationsusedto indicatethestalledregionwereobtainedbytheuseofa constant-currenthot-wireanemometer(modelHWBmanufacturedby theF1OWCorp.). Thewire ontheprobeswastungstenof0.00035-inchdismeterand0.044inchlong.An additionalhot-wireset,locallyconstructed,wasalsousedwhensimultaneousindicationsat differenttangentialpositionswererequired.Theoperationofeachsetisidenticalandthesamesizeprobeswereusedforeach.
,
.
.
—
—
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NACATN 3823 5
Theoutputofthehot-wireanemometerswasfedintoa dual-beamcathode-rayoscilloscope(type322manufacturedbytheAllenB. DumontLaboratories,Inc.),whichpermittedvisualobservationorphotographicrecordingof thevelocityfluctuations.Photographswereobtainedwithbotha stillanda strip-filmcamera,thestrip-filmcamerabeingemployedto includea greaternumberof stallcellsona singlephotograph.Repre-sentativephotographsofeachtypeappearasfigures3 and4. Thetimetraceincludedoneachvelocity-fluctuationphotographwasobtainedbyfeedingtheoutputofanaudiooscillatorintothebean-intensitycontroloftheoscilloscope.Thephotographicandhot-wireequipmentisseeninfigure1.
Pressurefluctuationsweremeasuredwitha bariumtitanatecrystal,theoutputofwhichwasfedthroughanamplifierandthencetotheoscil-loscope.Thepressuretapswerelocatedintheoutercasingofthecom-pressorbeforeandaftereachbladerowandrepresentativephotographsofthepressurefluctuationsatvariousaxialpositionsareshowninfig-ure5.
A five-holeprobeanda sphereprobe(manufaeturedbytheFlowCorp.)wereusedtodetermineairanglesandmean-radiusstaticpressure,respec-tively.Thedescriptionoftheseprobesisgiveninreference8. Themassflowcorrespondingto eachthrottlepositionwasobtainedbymeas-uring,withaninclinedmanometer,thetotalandstaticpressureinacalibratednozzle.
Procedure
Runswereconductedat 1,500rpmbothwithandwithoutstatorblades.Thisrotationalspeedwaschosenbecause.itgavea msximumaxialvelocityof 90feetpersecond,whichsatisfiedtherequirementforincompressibleflow.A fewrunsconducted.ata speed60percenthigherindicatedsimilarstallcharacteristics,sothattheresultsobtainedarerepresentativeforthemachineovera rangeofrotationalspeeds.Thevariousstallregionswereobtainedby varyingthepositionofthethrottleandtherebythemassflow. Thechangeoverfromonestallregionto anotherwasquitesharpandeasilydetectableby soundandchangeinthevelocity-fluctuationpattern.
Thedatarecordedineachrunwerestaticandtotalpres,sureinthecalibratednozzle,photographsofthevelocity-fluctuationpattern,andphotographsofthepressurefluctuationsbeforeandaftertherotorandstator.Thevelocityfluctuationswerenormallymeasuredat themeanradius,butradialtraversesweremadeto detectanychangefromroottotip. Thesedatapermittedtheevaluationofthefrequencyoftherotatingstall,massflow,andrelativemagnitudeofpressurefluctuationsat thevariousaxialpositions.
—
6 NACATN 3823.
Thenumberofstalledregionswasdeterminedby theuseoftwohot-wireprobes,onestationaryandonefreetotraversetangentially.Thewireswereinitiallyalinedsothattheoutputsignalswereinphaseand *onewirewasthentraversedthrougha knownarc. Therelativephasedis-placementofthestalledregionwasthencorrelatedwiththetangentialdistancetraversedto determinethenumbero-fstalledregions. —.
Therotorperformancewasobtainedbymeasuringthestaticpressureandairanglesat,themeanradiusbothbeforeandsfterthebladerow,
.
usingthesphereandfive-holeprobes.Thepressuresweremeasuredwithan inclinedmanometeranddatawereobtainedformass-flowratesvaryingfromthemaximumdowntothepointwhereth_eprobereadingsbecamemean-inglessbecauseoflargevelocityfluctuations. — .
Iw3J-Ers
Thedatawereobtainedintheformofthesteady-statecharacter-isticsofthecompressorandphotographicrecords,frmnthehot-wireequip-ment,andtheresultsarepresentedinfigures.6to 8. Frommeasuredvaluesofaxialvelocityandinletandoutletanglesfromtherotorat”themeanradius,theanglesP1 ~d ~2 oftheflowwiththerotorwerecalculated‘(seefig.6(a))usingtherel.atigns
..
tan~2 =&- tana2
0
Hence,knowingthestaticpressurerise APs measuredatthemeanradius,thepressurecoefficients .-
APsCP=
(1/2)PW12
werecalculatedandplottedversusj31(fig.6(b)).=
Finally,theblockagecoefficientu,asusedby Stenningandmonsto analyzethestabilityofa propagatingwave(refs.3 and6), wascal-culatedandplottedversusthecotangentof j31(fig.7) where
A. Cospl
aulvCos?2F_=p
.
.
.
.
NACATN 3823 7
.Fromthephotographofthehot-wiretraces,thefrequencyof stall
propagationwasfoundby usingthefrequencyofthething pulseorthe“ velocityofthefilmstrip.Thenumberofcellswasfoundfromthecom-
parisonofphasechangewiththeactualangulardisplacementofthetwoprobesused,andhencetheabsolutefrequencyofa singlecellwas’cal-
—
culated. Takingthemeanradialpositionasthepointofreference,thevelocityV ofa singlecellrelativetothatoftherotorcanbe calcu-latedandisplottednondimensionallyas v/cx versusPI infigure8.
Inaddition,thetheoreticalpropagationvelocitiescanbe calculatedusingthetheoriesofSears(ref.1)andMarble(ref.2),whichshould-applyto stallcellsoflargewavelen@hwhenthepressureriseacrossthebladerowissmall,andalsousingStenninglstheory(ref.3),whichshouldbe usefulforstallcellsof smallwavelength.SinceSears’“airfoil”theorygivesunrealisticvaluesofpropagationvelocityforcellswitha wavelengthverylargecomparedwiththebladechord(forwhichthephaselagmusttendto zero),his“channel”theorywasemployedusingthelimitingcaseof zerophaselag. Forthiscase,SearstandMarblefstheoriesgivean identicalresult:
. Ifa phaselagotherthanzeroisemployedinSeam’ channeltheory,pre-dictedvaluesof V/cx arelessthan csc2pl.
. Thethirdtheoryincludesan effectdueto thenumberof stallcellsN andgivestheresult
v—Cx
where b isthehalfwavelengbhofonecell(Circumference/2N),L isthechordlength,and ‘p istheseparationbetweentherotorandinletguidevanes;theexpressionintheparenthesesinthedenominatorisacorrectiondesignedto allowfortheeffectoftheinletguidevanesonthestall-propagationvelocity.Thesetheoreticalvelocitieswerecal-culatedfromthesteady-statecharacteristicsofthecompressorandareplottedinfigure8.
a NACATN3823
DISCUSSIONOFRESULTS●
.
Steady-StateCharacteristics .——
Thesteady-statecharacteristicswereobtainedbothwithandWith-outthestatorbladesinposition,andexcellentagreementwasobtainedbetweentheobserveddata.Inaddition,it-wasfoundthatwithoutthestatorbladesitwaspossibleto obtainreasonabledatawhenstallcellsof shortwavelengthwerepresent,sothatmeandataareavailableforpartof
Inversusforthecussion
theregionofrotatingstall.
figures6(b)and6(c)wherethepressurecoefficientisplotted@l,therangesinwhichrotatingstalloccursaremarkedbothstagewithstatorbladesandforthatwithout;a detaileddis-oftheseregionsisgivenbelow.Itwillbenotedthatthereis
—
a riseinpressure~oefficientat pl= 660-0‘lhis wu due to the onsetofrotatingstall,whichcausedtheflowthroughthestalledbladepas- :sagesto decrease,whiletheflowthroughtheunstalledbladepassages —increased.Thenetlossesacrossthebladerowareapparentlyreduced,
~
givingan increaseinthepressureriseandhencea localriseinpres-surecoefficient.Withstatorbladesinplacenoreliablemeasurement””ofanglesorstaticpressuresispossiblewhenstallbegins,sincethe
—
velocityfluctuationsarelarge. .-
Fromstability”considerationsfora wavepropagatingina cascade(refs. 3 and6)thestartofrotatingstallis predictedto coincide@th “~thepointwherea linefromtheoriginistangenttothecurveoftheblockagecoefficientu versuscotangentP1. Infigure7 it is Seen
-
thatstallpropagationdoesnotstartuntilthereis”asomewhatlarger Z—
valueof 91 thanthatpredicted.Thisisprobablyduetothefactthatfinitefluctuationsareinvolvedratherthanthesmallfluctuationsassunedinthetheoreticalmodel.
StallCharacteristicsWithStatorBlades
Thefirsttestswereconductedwiththestatorbladesinposition,andthefollowingcharacteristicswereobservedastherelativeinlet
—
anglewasincreasedby decreasingthemassrateofflow. “ —
Fourseparateregimesofrotatingstallwerefound,thefirstcon-sistingofonecellatthetipsofthebladesandtheothershavingone}two,andthreecells,respectively,coveringtheentireblade.&etweeneachregime,a transitionstateoccurredinwhichthenumberofcellsvariedbetweenthosefoundintheadjacentregimes(seefig.6(b)).The _*
velocityfluctuationsweremeasuredata numberofaxialpositions,and.
.
.
NACATN 3823
itwasfoundthatthemagnitudewithdistancebothupstreamand
Thefirstsignof stallas
9
ofthevelocityfluctuationsdecreaseddownstreamoftherotor.
~1 wasincreasedabovethedesignvaluewastheappearanceofrandmnvelocityfluctuations,whichappearedwithincreasingregularityuntiltheregimeofpropagatingtipstallwasentered.Thestalledregionextendedfromtherotortipforabout3/4inchdowntheblade,a distanceapproximatelyequalto thethicknessoftheboundarylayerenteringtherotor(ref.7). Thenumberofbladesoverwhichtheregionextendedwasgreatestat thetipanddecreasedfurther-downtheblade,butnoactualmeasurementsweremadeofthenumberofbladescoveredby thecell.As ~1 wasfurtherincreased,a singlecellwasfoundextendingovertheentirebladelength,andthenumberofbladescoveredincreasedwith ~1 untilthenextregimewithtwostallcelJswasentered.Intheregimeswheretheentirebladewasstalled,neitherthevelocity-fluctuationpatternnorthenumberofbladescoveredvariedmark-edlyfromrootto tip. As ~1 wasincreased,thenumberof cellsincreasedprogressivelyfromoneto twoto three,a largernumberbeingunobtainablethan800,as
aspurelyrandomfluctuationsappearedwhen ~1 wasgreatershownatthebottomoffigure3.
StallCharacteristicsWithoutStatorBlades
Whenthestatorbladeswereremoved,therewasa verymarkedchange .intherotating-stallcharacteristics;theonsetof stallwasdelayeduntila greatervalueof B1 wasreached;and,followingtheinitialregimewithrandomvelocityfluctuations,tworegimeswerefoundcon-sistingofa muchlargernumber(eightandnine,respectively)of smallcellsthanwereobtainedwiththestatorbladesinplace.Onfurtherincreaseof PI,thestallcharacteristicsresembledthosewiththestatorbladesinplaceandreghescontainingone, three, andfourcellswerefoundbeforerandomstallreappesxedat 131= 85o. Theregtiewithtwocellsappearedasanunstableconditionina verynarrowrangeof inletangles(fig.6(c)).
Severalstrikingdifferenceswereobservedbetweencellsofshortandlongwavelen@h (highandlowfrequency).Withtheformer,itwasfoundthatthevelocityfluctuationswereverynearlydmped‘outintherootboundarylayer,whilethelattershowedfluctuationsofgreatersmplitudeinthessmeplace.Itwasalsofoundthat,forshortwavelengths,thevelocityfluctuationsmeasureddirectlydownstreamoftherotorat sectionF infigure2 wereconsiderablysmallerthsnthoseatsectionG. No satisfactoryexplanationforthishasbeensuggested. .-
Thelimitsofthevsriousregimeswerecomparativelywelldefinedwhentherewerea smallnumberofcells,sinceanychangeinnumbercaused
10 NACATN3823
anappreciablechangeinthefrequencyandinthephaseshiftbetweentwoprobes.Witheightorninecells,theproblemofdeterminingtheactualnumberbecomesmoredifficultandthereisa rangeofuncertaintybetdeenthesetworegions.Furtherdifficultiesarecausedby thenon-symnetryofthecellsaroundtheannulus(fig.4)andalsoby thefactthateachcelldoesnotcausethesamevelocityfluctuationsattheprobe.
Sincethebladepassagesareoffinitewidth,theprobemaybe atanypointacrossthepassageattheinstant.whentheadjacentbladestalls.Theprocessofstallingcausesseparationfromtheleadingedgeoftheblade,andthereisa reductionofvelocityinthisregionofseparatedflow(positionA insketch),whilethevelocityintheunseparatedpor-
—
tionofthepassagemayhavean instantaneousincreasebecauseofthereductionin-flow-area-(positionB).
/
n.———
Y——/
.
*
.l
—
.
B A
Iftheprobeisclose”tothetrailingedgeoftheblade,itmaythereforeshoweitheran increaseordecreaseinvelocitywhenstalloccurs.Furtherdownstream,mixinghasoccurredsothateachstallcellcausesa netdecreaseinvelocity,and,similarly,a probeupstreamof
—
thebladerowwillalwaysindicatea reductioninvelocityonaccountofthepartialblockageofthebladepassage._Thephenomenonwasnotedforstallcellsof shortwavelengthandwouldbe expectedwhenthereareonly
—
a smallnumberofblade
Finally,itshouldvelocityincreasesincemidpointofthecellis
passagescoveredby each-cell.
be notedthata flowreversalwilla hottireisnondirectional,and,sometimesdifficultto findonthe
be shownasahence,theOscillogram.
ComparisonofActualandPredictedPropagationVelocities _ _
As explainedaboveinthesectionentitled“Results”theexperimen-talpointsandtheoreticalcurvesofpropagationvelocitiesareplotted
.
infigure8. Theforminwhichthesefiguresarepresentedpermitsa.=
.
NACATN 3823 11
comparisonofthetheoreticalandexperimentalvaluesofthepropagationvelocitiesrelativetotherotor,andimportantconclusionscanbe drawnfromthem.
First,allthetheoriesarebasedontheassumptionof smallpertur-bationsona steadyvelocityfieldandsowouldbevalidonlyattheonsetofrotatingstall.GdodagreementisobtainedatthispointwithStenning’stheory,bothwithandwithoutstatorblades,whilethepropagationveloc-itiespredictedby theSearsandMarblelarge-wave-lengththeoriesliebelowthevaluesobservedwithstatorbladesandabovethoseobservedwith-outstatorblades.Athighvaluesoftheinletangle,thevelocityfluc-tuationscannotbe consideredas small,butalltheoriesgivethecorrectorderofmagnitude(withinabout25percent)forthepropagationveloc-itiesifthetheoreticalcurvesareextrapolated.Itwillbe notedthatthroughouttherangeofavailabledatathevelocitiespredictedby SearsandMarblecorrespondalmostexactlywiththosepredictedby StennhgforfourstalJcells.
Anotherstrikingfactorwhenno statorbladesareusedisthesuddenchangefromninecellsto a singlecell,witha verysmallchangeIn Pl(fig.8(b)).Thepropagationvelocityincreasesby 90percentwhenthishappens,whichwouldseemto confirmthepredictionof Stenninglstheorythatthepropagationvelocityisa functionofthenumberofcellsand
. increaseswithincreaseofwavelength.
A similarresultcouldbededucedfromSears’generaltheorywith. thephaselagincludedbecausethephaselagisproportionalto theratioofbladetimedelayto fieldtimedelay,andthisratiobecomessmallerasthewavelengthincreases.
PressureFluctuations
Inthetheoreticalanalysisofrotatingstall,twosimpleassumptionscanbemadeabouttheconditionsdownstreamofthebladerow. Eitherthebladepassagescanbe consideredasnozzlesdischargingintoa regionofconstantpressure,or itcanbe assumedthatmixingoccursimmediatelydownstreamoftherow,sothatthedownstreamflowfieldisa continuum.Theseassumptionscanreadilybe checkedbymeasuringtherelativemagni-tudeoftheupstresmanddownstreampressurefluctuationsandtheresultsof suchtests,takenattheoutercasingofthecompressor,wereasfollows:
Withstatorbladesinposition,itwasfoundthatpressurefluctua-tionswerenegligibledownstreamofthestatorbladesandupstreamofthe
. inletguidevanesas comparedwiththefluctuationsupstreamoftherotor.Thefluctuationsdownstreamoftherotorwerenotgreatlyaffectedby theonsetofrotatingstall,butintheextremeconditionan appreciable
12 NACATN3823 —
.
variationsseen(fig.5(c)).Theupstreamfluctuationsduetorotatingstallwereapproximatelydoublethosedownstreamoftherotor.Itwouldappearfromthisthattheconditionofa constantdownstreampressure *.field,asassumedby Stenning,wasnotsatisfiedandthereforethecloseagreementbetweentheoreticalandobservedpr@agationvelocitiesmustBe __ ._:consideredfortuitous. —
Withoutstatorblades,a greaterreductioninpressuiefluctuationsacrosstherotorwasfound,as seen”infigures5(d)and~(e),smdthe
—
maximumdownstreamfluctuationsduetorotatingstallwerelessthan25percentofthoseupstream.
—.—— --
Inorderto confirmthemostsuitableassumptionforthedownstreamflowfieldinthetheoreticalanalyses,anexpressionforthemagnitudeof ~thepress~efluctuationsbasedonStenning’smodelofthestallprocesswiththedownstreamflowfieldconsideredas--acontinuumiscalculatedin “- “-theappendix.Theexpressionobtainedis: —.,
Fromexperimentaldataonthepropagationvelocitiesof stallcel~s_ ‘.withoutstatorblades,thepredictedrelativemagnitudeofthepressurefluctuationscanbe calculatedassuningtha~.thedownstreamflowpattern
-
iscontinuous.Representativevaluesaregf~enInthefollowingtable”.
andcanbe comparedwiththeobservedvaluesinfigure6.——.-—
Nwnberofcells. . . . . . . . .P,deg. ... . . . . . . . . . . . 67.: 73.: 74.: 78.;
....
tan~l. . . . . . . . . . . . . . 2.36 3.40 3.63 4.92—
v/cx. . . . . . . . . . . . . . . 0.862 ~ 1.24 2.32 2.54 ..
1 -tip/b
1::-~plb ““”” ”’”” ””””0”825 ‘-0”8670.151 0d413
5p~/5p2. i.. i”....... . 1.99 1.88 0.56 0.96
Fromtheobservedvaluesofpressurefluctuationswithoutstatorbladesitcanbe seenthattheactualupstreampressurefluctuationsare ___alwaysgreaterthanfourtimesthedownstrefifluctuationssothattheassumptionofa constantpressurefield.downstreticorrespondsmorecloselytotheobservedresultsthantheasstimptionof.acontinuum. -—— ..
.
NACATN 3823
CONCLUDINGREMARKS
13
Fromtheresultsobtainedfromtheinvestigationofrotatingstallina single-stageaxialcompressor,itcanbe seenthatthepropagationvelocityhasbeenpredictedwithin10percentfora singlebladerowattheonsetofrotatingstallusingtheresultsof Stenningistheory.Sears’theorycouldbemadeto agreewiththeobservedpropagationvelocityatthebeginningofrotatingstallby usinga suitablevalueofphaselag,althoughthepressureriseacrossthebladerowisstillquitehigh,so.thattheneglectofthefactor(l+mere Cp isthepressurecoef-ficient,inSeartstheorywouldleadtoan erroneousvalueofphaselag.At highinletsinglesrelativetotherotor,wherethevelocityfluctuationsbecomelargeandthepressurecoefficientissmall,theactualandpredictedvelocitiesagreereasonablywellwithStenning’stheoryandwiththeresultsof Sears’andMarble’sanalysesforcellsoflargewavelength.
It isalsoseenthattherotating-stallcharacteristicsofthecom-pressorareinfluencedverystronglybystatorbladesdownstreamoftherotor,theeffectofthisinterferencebeingto dampoutthepropagationof stallcellsathighfrequenciesandto inducestallpropagationathighermass-flowrates.
Finally,measurementsofpressurefluctuationsupstreamanddown-streamoftherotorwhenthefollowingstatorwasremovedshowthatneitheroftheetiremeconditionsassumedinthetheoriesforthedownstreamflowfieldrepresentsthetruestateofaffairssatisfactorily,althoughforthisparticularmachinethe“freejet”assumptionseemscloserto,thetruththantheassumptionthatmixingoccursina shortdistance.
MassachusettsInstituteofTechnology,Cambridge,Mass.,June8, 1955.
14 NACATN 3823
APPENDIX.
.
PRESSUREFLUCTUATIONSINA DOWNSTREAMCONTINUUM
Thefollowinganalysisisdesignedto estimate,therelativemagni-tudeoftheupstreamanddownstreampressurefluctuationscausedbyrotatingstallwhenthedowmtresmflowfieldisconsideredasa continuum.
Theanalysisisbasedonthemodelusedby Stenning(ref.3) showninthesketch.
—
. —
m
Forincompressibleirrotationalflowupstream,a perturbationveloc-itypotential@ canbe defined,and,frcxncontinuity,
——
Iftherotatingskallisconsideredasa sine~ve propagatingalongthecascade,thesolutionis
.-— —.
()[@= Asin~-mt efix/b 1+e-fi(x+~)/b (1)
—
whichsatisfiestheconditiontht @X = o at x = -P. Thisconditionallowstheinterferenceeffectduetoupstreamguidevanestobe esti-mated,ontheassumptionthattheseguidevanesarecloselYsPacedand
>–
oflargechordlength..— .-
.
NACATN 3823
FromEuler’sequationsturbations,upstreamof“the
15
ofmotionforunsteadyflowwithsmallper-cascade(eq.(2)ofref.3)
#t+c5c+*=o -W<x<o (2)
Downstreama continuumisassumed(appendixIII,ref.3)and
5P2—=P (@t)1 (3)
By definition
C2= c# + c#
therefore
and
C5C= Cx ‘5Cx+ Cy ~cy
c15C1= (cx@x)l + (cY@Y)l
Evaluatingequation(2)atpoint1 intheprecedingsketchanddividingbyequation(3),
Substitutin~for @ fromequation(1),
16 NACATN 3823 .
.—
Comparingthemagnitudeofthesepressurefluctuations, ..
—
.-
Thisequationshowsthattheeffectof inletguidevanesisto reduce —.—theratioofupstresmto downstre~pressurefluctuations,anditcanbe– -..—usedto estimatethetheoreticalpressurefluctuationswiththedownstream -flowfieldconsideredasa continuum. ,:
“
.
RIIWRENCES
.
NACATN 3823 17
1.Sesxs,W. R.: A Theoryof “RotatingStall”inAxialFlowCompressors.ContractAF-33(038)21406,OfficeSci.Res.,U.S.AirForce,sndGraduateSchoolAero.Eng.,COrnelltbliv.,Jsn.1953.
2.Marble,FrankE.: PropagationofStallina CompressorBladeRow.Tech.Rep.4,ContractAF-18(@o)-178,U.S.AirForcesandGuggenheimJetPropulsionCentre,C.I.T.,Jan.19’34.
3. Stenning,AlanH.,ICciebel,AnthonyR.,andMontgomery,StephenR.:StallPropagationinAxial-FlowCompressors.NACATN35&),1956.
4. Emmons,H.W.,Pearson,C.E.,andGrant,H. P.: CompressorSurgeandStallPropagation.PaperNo.53-A-56,presentedat 1953annualmeeting(Nov.9-Dee.3,1953),A.S.M.E.,Dec.19.53.
5. Iura,T.,andRannie,W. D.: ExperimentalInvestigationofRotatingStallinAxial-FlowCompressors.Trans.A.S.M.E.,vol.76,no.3,Apr.1954,pp.463-471.
6. Huppert,MerlerC.,andBenser,WilliamA.: SomeStallandSurgePhenomenainAxial-FlowCompressors Jour.Aero.Sci.,vol.20,no.12,Dec.1973,pp.835-845.
7. Moore,R.W.,andSchneider,K.H.: MeasurementofFlowThroughaSingle-StageAxialCompressor.Rep.27-6,GasTurbineLab.,M.I.T.,Dec.1954.
8. Moore,‘RaymondW.,Nelson,WarrenG.,Prasad,Arun,Richardson,DavidL.,andTurner,JsmesR.: ExperimentalTechniquesforThree-DimensionalFlowResearch.Rep.27-8,GasTurbineIab.,M.I.T.,Dec.1954.
,.: ...- , W+#?”-
L-93573Figure1.-Apparatususedininvestigation.
● ✌
,! u,, ,1, ,, .
-..
>~
—-U-1
0)
Q
B
X..
I
Figure2.- Schematicdiagramofmeasurementstationsofcompressor.
3—..—Lettersrefertostationdesignatio~.
G
20
TIM E+-
NACATN 3823 —...
.
---1~1 =63.0°
F= 50 CPSN=lf = 7.85CPS
p , =67.9°
t
F= !Oocps
N=2f=15.5cps
-4~1 =73.8°
F= I()()cf)s
N=3
( f= 23.2 CPS
Figure3.- Velocityfluctuationswiths,tatorblades.Velocitiesdecreasetowardcenterofeachphotograph;probesaredoyzustreamofstatorand
.—●
1800apart..-
. . s , . ,
POSITIVE ;VELOC+TY
I(a) Eight mk; f.135 CPS; PI. IS7.O.
[b) MM c21b; f. 149 GP9; ~1, 73.6°
-t~
CcwCw
l-..cl,m+ mm(e) Fou CCI16; f.st.o CPS; B, .s4.9.
FYgure4.-Representativestripfilmrecordsofhot-wiretraceswithoutstatorblades.Rwbesarebeforerotorand450apart;clockwiseprobereceivessi@ first.CW,clockwiseprobe;CC!W,couutercloclwiseprobe. P
STATIOM ‘x ‘ALPOSITION
FSEI-IINDROTCi7
GBEHINDSTATOR
HOT-WIRETRACE
EBEFOREROTOR
(b)
NUMBER
OF CELLSo
8
,,
1
3
4
Figure5.-Staticpressure
(d)Withoutstator
s .!1 .Illl:’l
blades;beforerotor(station
fluctuations.
E).
(e)Withoutstatorblades;behindrotor(stationF).
Hot-wiretrace is added for comparison inparts(a)to (c),
. ‘
‘,
* or
60
50
40m$
.
G30
20
—
O WITH STATOR BLADES
A WITHOUT STATOR BLADES
Io45 50 55 60 65 70 75
fll , deg
(a) t3,2 against PI.
~gure6.-Rotorperforrmnce.
,5
,4
,3
Cp
.2
.1
a
P-
0 WITH STATOR BLADES
A WITHOUT STATOR BLADES
*Y
I CELL .2CELLS—
I CELL ALLTIP ONLY BLADE 3 CELLS
I I
50 55 60 65 70 75 80 ~
~l,degS’=
(b) ~ agdnst pl showingskillregionswithstatorblades. g
me G.-conttiu~.
. #1,
,50-1 I I I I
Cp
,20
r
L 0 WITH STATOR BLADES
A WITHOUT STATOR BLADES
,10
.LJJ50 55 60 65
T9C
~,, deg
(c) c-p againstPI Ehowing stallregions
Figure6.-Concluded.
n
s-
2 CELLSTRANSIENT)
-1 CELL +
I
75
.,
,
withoutstatorblades.
a
--
1.01 I I I I I / I I
.9
,8
.7
,6
.5
.4 [
/ 0
TIP STALL STAR-/ WITH STATOR
‘// ‘=ALL OVER
d
WHOLE BLADE
/WITH STATOR
/STALL STARTS
/WITHOUT STATOR
I /,31- /
1/,2
I
//
,1 /0 WITH STATOR BLADES
/ A WITHOUT STATOR BLAU/
oI I I I I I I
o 12 ,4 ,6 ,8 I 10cot#?l
= 7.-Blockagecoefficienta agairmtcOtPI.Cospl
as#@! = .COB$z~~
, ..I
, < , ,
5#c
4,0
3,0
v/cff
2!0
I ,0
0
, 1
X I S~ALL CELL’- TIP ONL+I lfJ
O ISTALL CELL - WHOLE BLADE❑ 2 STALL CELLSA 3STALL CELLS A
/
,//
/- /’B/
,+ ,Y
/,0,A
0’
/##!&?&l
<0
Go;/y SEARS’ AND MARBLE’S
THEORY
-$--
55 60 65 70 75 80 85
BI,*9
(a) Withstatorblades.
Figure8.-Stallpropagationvelocitiesv/~ agxblst131.
580
4,C
3!0
v/cx
2,0
I.c
(
. ,
—
o I STALL CELL
❑ 2 STALL CELLS
A 3 STALL CELLSx 4 STALL CELLS
P 8 STALL CELLS@ 9 STALL CELLS
/’A
I I I Ii 60 65 70 75 80
~,,deg
(b)Withoutstatorbides.
IIgure8.-concluded.
s ‘
5
, 1
r