toLeen
Contents
Preface xi
Acknowledgements xiii
ListofSymbols xv
1Introduction 1
1.1ApplicationofCentrifugalCompressors 2
1.2AchievableEfficiency 5
1.3DiabaticFlows 14
1.4TransformationofEnergyinRadialCompressors 19
1.5PerformanceMap 25
1.5.1TheoreticalPerformanceCurve 25
1.5.2FiniteNumberofBlades 26
1.5.3RealPerformanceCurve 28
1.6DegreeofReaction 29
1.7OperatingConditions 32
2CompressorInlets 37
2.1InletGuideVanes 37
2.1.1InfluenceofPrerotationonPressureRatio 40
2.1.2DesignofIGVs 41
2.2TheInducer 49
2.2.1CalculationoftheInlet 50
2.2.1.1DeterminationoftheInducerShroudRadius 51
2.2.2OptimumIncidenceAngle 53
2.2.3InducerChokingMassFlow 56
3RadialImpellerFlowCalculation 61
3.1InviscidImpellerFlowCalculation 63
3.1.1MeridionalVelocityCalculation 63
3.1.2BladetoBladeVelocityCalculation 66
3.1.3OptimalVelocityDistribution 68
3.23DImpellerFlow 73
3.2.13DInviscidFlow 73
3.2.2BoundaryLayers 76
3.2.3SecondaryFlows 78
3.2.3.1Shrouded–unshrouded 82
3.2.4Full3DGeometries 84
3.3PerformancePredictions 88
3.3.1FlowinDivergentChannels 88
3.3.2ImpellerDiffusionModel 90
3.3.3Two-zoneFlowModel 94
3.3.4CalculationofAverageFlowConditions 101
3.3.5InfluenceoftheWake/JetVelocityRatio �� onImpellerPerformance 102
3.4SlipFactor 104
3.5DiskFriction 108
4TheDiffuser 113
4.1VanelessDiffusers 116
4.1.1One-dimensionalCalculation 117
4.1.2CircumferentialDistortion 122
4.1.3Three-dimensionalFlowCalculation 125
4.2VanedDiffusers 131
4.2.1CurvedVaneDiffusers 131
4.2.2ChannelDiffusers 135
4.2.3TheVanelessandSemi-vanelessSpace 136
4.2.4TheDiffuserChannel 143
5DetailedGeometryDesign 147
5.1InverseDesignMethods 147
5.1.1AnalyticalInverseDesignMethods 148
5.1.2InverseDesignbyCFD 152
5.2OptimizationSystems 156
5.2.1ParameterizedDefinitionoftheImpellerGeometry 157
5.2.2SearchMechanisms 159
5.2.2.1GradientMethods 160
5.2.2.2Zero-orderSearchMechanisms 161
5.2.2.3EvolutionaryMethods 161
5.2.3MetamodelAssistedOptimization 164
5.2.4MultiobjectiveandConstraintOptimization 170
5.2.4.1MultiobjectiveRanking 170
5.2.4.2Constraints 172
5.2.4.3MultiobjectiveDesignofCentrifugalImpellers 173
5.2.5MultipointOptimization 175
5.2.5.1DesignofaLowSolidityDiffuser 175
5.2.5.2MultipointImpellerDesign 177
5.2.6RobustOptimization 181
6Volutes 185
6.1InletVolutes 185
6.1.1InletBends 186
6.1.2InletVolutes 190
6.1.3VanedInletVolutes 193
6.1.4TangentialInletVolute 194
6.2OutletVolutes 196
6.2.1VoluteFlowModel 196
6.2.2MainGeometricalParameters 197
6.2.3Detailed3DFlowStructureinVolutes 200
6.2.3.1DesignMassFlowOperation 201
6.2.3.2LowerthanDesignMassFlow 204
6.2.3.3HigherthanDesignMassFlow 205
6.2.4CentralEllipticVolutes 208
6.2.4.1HighMassFlowMeasurements 210
6.2.4.2MediumandLowMassFlowMeasurements 215
6.2.4.3VoluteOutletMeasurements 215
6.2.5InternalRectangularVolutes 215
6.2.5.1HighMassFlowMeasurements 216
6.2.5.2MediumMassFlowMeasurements 218
6.2.5.3LowMassFlowMeasurements 219
6.2.6VoluteCrossSectionalShape 221
6.2.7VolutePerformance 222
6.2.7.1ExperimentalResults 224
6.2.7.2PerformancePredictions 225
6.2.7.3DetailedEvaluationofVoluteLossModel 228
6.2.83DanalysisofVoluteFlow 230
6.3Volute-diffuserOptimization 231
6.3.1Non-axisymmetricDiffuser 233
6.3.2IncreasedDiffuserExitWidth 234
7ImpellerResponsetoOutletDistortion 237
7.1ExperimentalObservations 238
7.2TheoreticalPredictions 242
7.2.11DModel 244
7.2.2CFD:MixingPlaneApproach 245
7.2.33DUnsteadyFlowCalculations 247
7.2.3.1Impellerwith20FullBlades 248
7.2.3.2ImpellerwithSplitterVanes 249
7.2.4InletandOutletFlowDistortion 249
7.2.4.1ParametricStudy 253
7.2.5FrozenRotorApproach 254
7.3RadialForces 258
7.3.1ExperimentalObservations 258
7.3.2ComputationofRadialForces 263
7.4Off-designPerformancePrediction 267
7.4.1ImpellerResponseModel 268
7.4.2DiffuserResponseModel 269
7.4.3VoluteFlowCalculation 269
7.4.4ImpellerOutletPressureDistribution 272
7.4.5EvaluationandConclusion 273
8StabilityandRange 275
8.1DistinctionBetweenDifferentTypesofRotatingStall 276
8.2VanelessDiffuserRotatingStall 280
8.2.1TheoreticalStabilityCalculation 284
8.2.2ComparisonwithExperiments 287
8.2.3InfluenceoftheDiffuserInletShapeandPinching 289
x Contents
8.3AbruptImpellerRotatingStall 296
8.3.1TheoreticalPredictionModels 297
8.3.2ComparisonwithExperimentalResults 300
8.4ProgressiveImpellerRotatingStall 301
8.4.1ExperimentalObservations 301
8.5VanedDiffuserRotatingStall 307
8.5.1ReturnChannelRotatingStall 314
8.6Surge 314
8.6.1LumpedParameterSurgeModel 316
8.6.2MildVersusDeepSurge 321
8.6.3AnAlternativeSurgePredictionModel 325
9OperatingRange 329
9.1ActiveSurgeControl 330
9.1.1ThrottleValveControl 331
9.1.2VariablePlenumControl 333
9.1.3ActiveMagneticBearings 335
9.1.4Close-coupledResistance 336
9.2BypassValves 337
9.3IncreasedImpellerStability 340
9.3.1DualEntryCompressors 342
9.3.2CasingTreatment 344
9.4EnhancedVanedDiffuserStability 347
9.5Impeller–diffuserMatching 351
9.6EnhancedVanelessDiffuserStability 354
9.6.1LowSolidityVanedDiffusers 356
9.6.2Half-heightVanes 359
9.6.3RotatingVanelessDiffusers 359
Bibliography 363 Index 385
Preface
Thegrowingawarenessoftheneedforenergysavingsandtheincreaseofefficiencyofcentrifugalcompressorsoverthelastdecadeshasresultedinanincreasingfieldofapplications. Thecompactness,smallweightandsimplicityofthecomponentsallowanefficientreplacementofmultistageaxialcompressorsbyasinglestageradialone.Theabsenceofmechanical friction,lowerlifetimecostandhighreliabilitymakescentrifugalcompressorsalsosuperiorto reciprocalones.Allthishasleadtoarevivalofcentrifugalcompressorresearch.
Centrifugalcompressorsareverydifferentfromaxialonesandrequireaspecificapproach. Thisbookintendstorespondtothat.Extensivereferenceismadetotheexperimentalresults andanalyticalflowmodelsthathavebeendevelopedduringthelast(pre-computer)century andpublishedintheopenliterature.Thisiscomplementedbytheresearchconductedinthe contextofthePhD.thesisofDrs.PaulFrigne,GeorgeVerdonk,MariosSideris,AntoniosFatsis, ErkanAyder,KoenHillewaert,AlainDemeulenaere,OlivierLéonard,StephanePierret,Tom Verstraete,AlbertoDiSanteandtheresearchprojectsofthemanyMasterstudentsthatIhad thepleasuretosupervise.
Thebookdoesnotprovidetherecipetodesign“theoptimalcompressor”butratherinsight intotheflowstructure.Thepurposeistohelpremediatingproblems,findingacompromise betweenthedifferentdesigntargetsandrestrictionsandhelpforabetterreadingandhencea moreefficientuseofNavier-Stokesresults.
Numericaltechniquesarenotdescribedindetailbutattentionisgiventotheirapplication, inparticulartothecorrectoperatingconditionsandrestrictionsofthedifferentapproaches andtotheiruseinthemoderncomputationaldesignandoptimizationtechniquesdeveloped duringthelasttwodecades.
Thebookisbasedonthe“AdvancedCourseCentrifugalCompressors”thatistaughtbythe authorinthe“ResearchMasterProgram”atthevonKarmanInstitute.Itintendstobeareferenceforengineersinvolvedinthedesignandanalysisofcentrifugalcompressorsaswellas teachersandstudentsspecializinginthisfield.
IamindebtedtomyformercolleaguesatthevonKarmanInstitute,Profs.FransBreugelmans, ClausSieverding,TonyArtsandmysuccessorTomVerstraete.Workingwiththemhasbeena veryenrichingandmotivatingexperience.ThanksalsotoDr.Z.Alsalihiandir.J.Prinsierfor themanyyearsoffruitfullcollaborationandCFDsupportincludingthepreparationoffigures, andtotheVKIlibrariansChristelleDeBeerandEvelyneCrochardfortheirlogistichelpin preparingthisbook.
Thisbookwouldnothavebeenrealizedwithouttheunderstanding,encouragementand unlimitedsupportofLeen,mywifeandsoul-mateformorethanfiftyyears.Specialthanks forthat.
Alsemberg,February25,2018
RenéVandenBraembussche, Hon.ProfessorvonKarmanInstitute
Acknowledgements
TheauthorwishestothanktheForschungsvereinigungVerbrennungskraftmaschinen(FVV) forpermissiontoincluderesultsinthisbookandinparticularthemembersoftheworking groupVorleitschaufelnforthemanyfruitfuldiscussions.
Permissionsfromthefollowingtoreproducecopyrightedmaterialisgratefullyrecognized:
TheAmericanSocietyofMechanicalEngineersfor:figs.5and6fromAbdelhamid(1980)as fig.8.33,fig.3fromAbdelhamid(1982)asfig.9.39,figs.2and5fromAbdelhamid(1987)as fig.9.40,fig.9bfromAbdelwahab(2010)asfig.7.8,figs.4and6fromAgostinellietal.(1960) asfigs.7.25and7.26,figs.8and9fromAmannetal.(1975)asfig.9.27,figs.15and16from Arigaetal.(1987)asfig.8.43,fig.16fromArnulfietal.(1999b)asfig.9.7,figs.1and9from Baljé(1970)asfig.3.15,fig.3fromBhinderandIngham(1974)asfig.3.12,fig.6bfromBonaiuti etal.(2002)asfig.4.27,fig.11bfromBowermannandAcosta(1957)asfig.6.22,fig.1from Casey(1985)asfig.1.20,figs.2and13fromChenandLei(2013)asfig.9.23,figs.7and14from Chenetal.(1993)asfig.9.39,figs.1and2fromChildsandNoronha(1999)asfig.1.17,fig.8d fromConradetal.(1980)asfig.4.36,fig.6fromDavisandDussourd(1970)asfig.3.2,fig.7from DeanandSenoo(1960)asfig.4.13,fig.6fromDeanandYoung(1977)asfig.8.55,fig.3from Dickmannetal.(2005)asfig.9.22,fig.3fromDussourdandPutman(1960)asfig.9.20,figs.5, 11,and12fromDussourdetal.(1977)asfigs.9.10and9.9,figs.7to11fromEckardt(1976)as figs.3.34and8.60,fig.9fromElderandGill(1984)asfig.8.47,figs.10,11,13,15,and17from Ellis(1964)asfigs.3.16,4.20,and4.21,figs.7and96fromEverittandSpakovszky(2013)asfigs. 7.11and8.45,fig.8fromFinketal.(1992)asfig.8.64,figs.4,10,and11fromFlathersetal.(1996) asfigs.6.10and6.14,figs.16and17fromFlynnWeber(1979)asfig.9.16,fig.4fromFowler (1966)asfig.1.10,fig.7bfromGreitzer(1976)asfig.8.67,fig.16fromGyarmathy(1996)asfigs. 8.50and8.51,fig.3fromHayamietal.(1990)asfig.9.42,fig.11fromHunzikerandGyarmathy (1994)asfig.8.44,figs.12and13fromIshidaetal.(2000)asfig.9.38,figs.8and14fromJansen (1964b)asfig.8.11,fig.2fromKammerandRautenberg(1986)asfig.8.61,figs.4and6from KangJeong-seeketal.(2000)asfig.4.32,fig.9fromKinoshitaandSenoo(1985)asfig.8.14,figs. 5and10fromKochetal.(1995)asfigs.6.12and6.13,fig.1fromKrain(1981)asfig.4.2,fig.12 fromKrameretal.(1960)asfig.3.11,figs.4and6fromLennemannandHoward(1970)asfigs. 8.1and8.37,figs.7.1and7.2fromLüdtke(1983)asfig.9.37,figs.16and26fromLüdtke(1985) asfigs.6.16,6.8,and6.9,figs.15and16fromMishinaandGyobu(1978)asfigs.6.20and6.21, figs.6aand9fromMizukietal.(1978)asfigs.8.34and8.38,fig.5fromMorrisetal.(1972) asfig.2.3,figs.1b,2c,and3cfromMukkavillietal.(2002)asfigs.9.43,9.44,and9.45,fig.3 fromNeceandDaily(1960)asfig.3.53,fig.4fromPampreen(1989)asfig.4.25,figs.4band4d fromReneauetal.(1967)asfig.4.41,fig.10fromRodgers(1968)asfig.9.33,figs.2band5from Rodgers(1977)asfigs.2.10and9.15,figs.5and6fromRodgers(1978)asfig.8.40,fig.3from Rodgers(1962)asfig.2.23,fig.4fromRodgers(1998)asfig.2.31,fig.7fromRodgers(1991)as fig.1.15,fig.2fromRodgers(1980),asfig.1.14,figs.4,14,and17fromSapiro(1983)asfigs.
9.46and9.47,fig.1fromStrubetal.(1987)asfig.1.16,fig.1fromRotheandRunstadler(1978) asfig.8.63,figs.5,23,25,26,and27fromRunstadlerDean(1969)asfigs.4.1and4.42,figs.4 and2fromSalvage(1998)asfigs.4.39and9.35,fig.12fromSenooIshida(1975)asfig.4.12, fig.1fromSenooetal.(1977)asfig.4.16,figs.7,4a,5a,and6fromSenooandKinoshita(1977) asfigs.8.15to8.19,fig.6fromSenooandKinoshita(1978)asfig.8.18,fig.3fromSenooetal. (1983a)asfig.4.26,figs.7and13fromSimonetal.(1986)asfigs.2.6and9.34,fig.1fromSimon etal.(1993)asfig.9.5,fig.15fromSugimuraetal.(2008)asfig.5.30,fig.19fromTamakietal. (2012)asfig.9.25,figs.6and7fromToyamaetal.(1977)asfigs.8.65and8.66,fig.11from Trébinjacetal.(2008)asfig.4.31,fig.8and5bfromTsujimotoetal.1994asfigs.8.35and8.9, fig.126fromWiesner(1967)asfig.3.49,figs.3and15fromYoonetal.(2012)asfig.9.8,fig.4 fromYoshidaetal.(1991)asfig.9.29,figs.7and8fromYoshinagaetal.(1985)asfig.9.45,figs. 5band8aandcfromTsujimotoetal.(1994)asfigs.8.9and8.35,fig.7fromKosugeetal.(1982) asfig.8.41,fig.14fromMarsanetal.(2012)asfig.9.30.
ConceptsNRECfor:fig.1.7fromJapikseandBaines(1994)asfig.1.13,fig.6.9fromJapikse (1996)asfig.8.42.
Dr.Heinrichforfig.11fromHeinrichandSchwarze(2017)asfig.6.59.
GasTurbineSocietyofJapanfor:figs.2and4fromKrainatal.(2007)asfig.4.29.
InstitutionofMechanicalEngineeringfor:figs.14and15fromJapikse(1982)asfig.6.62,fig. 1fromSiderisetal.(1986)asfig.4.2.
InternationalAssociationofHydraulicResearchfor:figs.2,3,4,5,6,and7fromMatthias (1966)asfig.6.4,fig.1fromRebernik(1972)asfig.4.19.
JapanSocietyofMechanicalEngineeringfor:fig.11fromHasegawaetal.(1990)asfig.7.23, fig.13fromAokietal.(1984)asfig.7.27,figs.13,6,and7fromNishidaetal.(1991)asfigs.8.27 and9.41,figs.2and8fromNishidaetal.(1988)asfigs.8.21and8.23,figs.2,4,5,6,7,11,and 13fromKobayashietal.(1990)asfigs.8.22,8.23,8.24,8.25,and8.28.
J.WileyandSonsfor:figs.6.66and5.133fromBaljé(1981)asfigs.9.35and2.24,figs.2.12 and2.15fromNeumann(1991)asfigs.6.11and6.15.
NATOScienceandTechnologyOrganizationfor:fig.6afromBenvenutietal.(1980)asfig. 2.27,fig.7fromWalitt(1980)asfig.3.1,fig.3c2fromPoulainandJanssens(1980)asfig.3.33b, figs.14and15fromVavra(1970)asfigs.3.37and3.54,figs.3b,10,4,and112fromJansenetal. (1980)asfigs.9.21and9.26,fig.1afromJapikse(1980)asfig.8.48,fig.13fromVinauetal. (1987)asfig.9.31,figs.25and37fromKenny(1970)asfigs.4.33and8.46.
Prof.M.Rautenbergfor:figs.8,9,10,and11fromRautenbergetal.(1983)asfigs.1.24aand 1.24b.
SagePublicationsfor:fig.8fromCaseyandRobinson(2011)asfig.1.18,fig.22fromPeck (1951)asfig.6.57.
SolarTurbinesIncorporatedfor:figs.7,15,and16fromWhiteandKurz(2006)asfigs.9.13 and9.14.
SpringerVerlagforfig.6.16.6fromTraupel(1966)asfig.3.50,fig.381fromEckertandSchnell (1961)asfig.3.51,figs.12,15,and17fromPfau(1967)asfig.7.2.
TheAcademicComputercenterinGdanskTASCfor:fig.9fromDicketal.(2001)asfig.7.21. ToyotaCentralLaboratoryfor:fig.4fromUchidaetal.(1987)asfig.7.3. TsukasaYoshinakafor:figs.3,4,5,and9fromYoshinaka(1977)asfigs.8.68,8.69,8.70,and 8.71.
vonKarmanInstitutefor:figs.3,15,and17fromBenvenuti(1977)asfigs.1.3and1.4,fig.4 fromBreugelmans(1972)asfig.2.4,figs.2,3b,4,7,and25fromDean(1972)asfigs.1.1,2.1, 3.41,3.42,and4.43,fig.11fromSenoo(1984)asfig.4.17,figs.20and22fromStiefel(1972)as fig.6.19,fig.26fromSchmallfuss(1972)asfig.9.17.
ListofSymbols
A crosssectionarea
A(U ( ⃗ X ), ⃗ X ) performanceconstraintfunction
AIRSabruptimpellerrotatingstall
AR arearatio
AS aspectratio(b∕Oth ) a speedofsound
⃗ a acceleration
A�� realpartofgrowthrateS
b impelleroutletordiffuserwidth
B2 Greitzer B2 factor(Equation8.43)
Bf distortionfactor
bl relativeblockage
c chordlength
C impelleroutletjetflowareaatzerowakevelocity
Cd dissipationcoefficient
Cf Darcyfrictioncoefficient
CDFcumulativedensityfunction
CFDcomputationalfluiddynamics
CFLCourant-Friedrichs-Lewy
Cm momentumortorquecoefficient
CM jet-wakefrictioncoefficient
CP staticpressurerisecoefficient
Cp specificheatcoefficient
D diameter
DH hydraulicdiameter
DOEdesignofexperiment
DR diffusionratio(W1 ∕WSEP )
dS controlsurface
EL equivalentchannellength
ESDemergencyshutdown
EMemergencyshut-offvalve
f frequencyofunsteadiness
F force
FEAfiniteelementstressanalysis
g gravityacceleration
G controllergain
Gk ( ⃗ X ) geometricconstraintfunction
xvi ListofSymbols
GPMgallonsperminute
h staticenthalpy
hb bladetobladedistance
H totalenthalpy manometricheight
i incidence
J momentofinertia
ks equivalentsandgrainsizeofroughness
K radialforcecoefficient(eqn.7.14)
kb bladeblockage
L lengthofchannel
LH hydrauliclength
LSDlowsoliditydiffuser
LWRlengthoverwidthratio
m meridionaldistance
̇
m massflow
M Machnumber
Mo momentumortorque
MR radialmomentum
Mu tangentialmomentum
Mx axialmomentum
NACANationalAdvisoryCommitteeforAerodynamics
NS specificspeed
NUEL numberofcircumferentialpositions
n distanceperpendiculartoaxisymmetricstreamsurface
nD numberofdesignparameters
N numberofrotations(RPM) numberofindividualsinapopulation
NPSHRnetpositivesuctionheadrequired
O openingorthroatwidth
OF (U ( ⃗ X ), ⃗ X ) objectivefunction
P pressure amplitudeofpowerspectrum penalty
PDFprobabilitydensityfunction
PIRSprogressiveimpellerrotatingstall
Pw power(W)
Q volumetricflow
qheatfluxperunitmass
Q heatflux(W) dynamicpressure (P o P )
R radiusmeasuredfromimpelleraxis
R(U ( ⃗ X ), ⃗ X ) performanceevaluator
r radiusmeasuredfromthevolutecrosssectioncenter degreeofreaction
ℜ curvatureradius
diffuserinletround-offradius
Re Reynoldsnumber
Rf relaxationfactor
RG gasconstant
RHSrigthhandside
Ro rothalpy
RPMrotationsperminute
RV hub/shroudradiusratio(R1H ∕R1S )
s distancealongstreamline
S surface exponentialgrowthrateofperturbation entropy
Sr acousticStrouhalnumber
Sx axialgapbetweenimpellerbackplateandcasing
t time pitch
T temperature
u non-dimensionalizedmeridionallength
U peripheralvelocity
U ( ⃗ X ) outputofperformanceevaluator
v absolutevelocityintheboundarylayer
V freestreamabsolutevelocity
VDRSvanelessdiffuserrotatingstall
compressorvolume
plenumvolume
w relativevelocityintheboundarylayer
W freestreamrelativevelocity
x axialorlongitudinaldistance
⃗
X geometry
y distanceinpitchwisedirection directionperpendiculartoxandz
Z numberofbladesorvanes controllertransferfunction
Zp ,Zu parametersdefiningdiffuserinletconditions(Equations8.9and8.10)
z directionperpendiculartoxandy
�� absoluteflowanglemeasuredfrommeridionalplane
�� relativeflowanglemeasuredfrommeridionalplane
���� phaseshiftofcontroller
�� anglebetweenmeridionalstreamsurfaceandaxialdirection
�� boundarylayerthickness ratioofinletpressures(Equation1.106)
��cl impeller-shroudclearancegap
��bl bladethicknessperpendiculartocamber
�� skewnessanglebetweenwallstreamlineandmainflowdirection
�� relativewakewidth
��kb relativebladeblockage
�� isentropicefficiency
��W wheeldiffusionefficiency(Equation3.40)
�� angularcoordinate(measuredfromthetongue) halfdiffuseropeningangle ratioofinlettotaltemperatures(Equation1.103)
�� isentropicexponent
�� numberofstallcellsorrotatingwaves ratioofwakemassflow/totalmassflow
�� workreductionfactor dynamicviscosity
�� wake/jetvelocityratio kinematicviscosity �� ∕��
�� totalpressurelosscoefficient
Ω impellerrotationalspeed(rad/sec)
ΩR reducedfrequency(Equation7.1)
��m mth modalfrequencyoftheimpeller
��s streamwisevorticity
���� rotationalspeedofstallcell imaginarypartofS
�� pressureratio
�� flowcoefficient(Vm ∕U )
�� nondimensionalpressurerisecoefficient
Ψ streamfunction
�� density
�� slipfactor solidity(chord/pitch) stress(MPa)
�� timeforoneimpellerrotation periodofperturbation shearstress
vectorproduct ∇2 Laplaceoperator
Subscripts
0upstreamofIGVorinletvolute
01downstreamIGV
1impellerinlet
2impelleroutlet
3vaneddiffuserleadingedge
4diffuseroutlet
5voluteexit
6compressoroutlet-returnchannelexit
11attheinnerradiusoftheimpellerbackplate
a absoluteframeofreference ad adiabatic
b inbladetobladedirection
bl oftheblade
b2basedontheimpelleroutletwidth
C ofthecompressor
c criticalvalue
atcenterofvolutecrosssection
ce duetocentrifugalforces
ch atchoking
cl duetoclearance
Cor duetoCoriolisforces
curv duetocurvature
D ofthediffuser deterministicsolution
d downstream des designvalue
dia diabatic
EC oftheexitcone
F oftheforce
fl oftheflow
fr duetofriction
H atthehub
i, j, k indicesinmeridional,tangentialandnormaldirection
IGV inletguidevanesettingangle
inc incompressible duetoincidence
inl attheinlet
iw attheinnerwall
j inthejet
indexofcircumferentialposition
kb duetobladeblockage
LE leadingedgevalue
m meridionalcomponent
max maximumvalue
mech mechanical
min minimumvalue
MC correspondingtoremainingswirl
MVDLduetomeridionalvelocitydumplosses
n normalcomponent
N nominalvalue
o attheoutlet
opt optimumvalue
ow attheouterwall
p ofthepipe polytropic
P duetopressure oftheplenum
PS onthepressureside
r oftherotor(relativeframe)
R radialcomponent atresonance robustsolution
ref referencevalue,referencegas
ret atreturnflow
Ro correspondingtorothalpy/correctedforrotation
s streamwisecomponent
S attheshroud swirlcomponent
SS onthesuctionside
S S statictostatic
SEP atseparationpoint
T troughflowortangentialcomponent ofthethrottledevice
TE trailingedgevalue
th atthethroatsection
T S totaltostatic
T T totaltototal
TVDL duetotangentialvelocitydumplosses
u peripheralcomponent upstream
un uncontrolled
V basedonabsolutevelocity
w inthewake onthewall
W basedonrelativevelocity
x axialcomponent
∞ freestreamvalue athighReynoldsnumber
Superscripts
i isentropic
k numberofthetimestep
nr nonrotating
o stagnationconditions
t atnexttimesteporgeneration
perturbationcomponent ∼ average
vector
∞ assuminganinfinitenumberofblades
targetvalue
Introduction
Aradialcompressorcanbedividedintodifferentparts,asshowninFigure1.1.Theflowis aspiratedfromthe inletplenum andafterbeingdeflectedbythe inletguidevanes (IGV), itentersthe inducer.Fromthereontheflowisdeceleratedandturnedintotheaxialand radialdirectionsbeforeleavingtheimpellerinthe exducer.Thepresenceofaradialvelocity componentisresponsibleforCoriolisforces,which,togetherwiththebladecurvatureeffect, tendstostabilizetheboundarylayerattheshroudandsuctionsideoftheinducer(Johnston 1974;Koyamaetal.1978).Theboundarylayerbecomeslessturbulentandwillmoreeasily separateundertheinfluenceofanadversepressuregradient.
Twodifferentflowzonescanbeobservedinsidetheimpellerresultingfromflowseparation andsecondaryflows(Carrad1923;Dean1972):
• AhighlyenergeticzonewithahighrelativeMachnumber,commonlycalledthe jet.Theflow inthiszoneisconsideredquasiisentropic.
• AlowerenergeticzonewithalowrelativeMachnumberwheretheflowishighlyinfluenced bylosses.Thiszone,commonlycalledthe wake,isfedbytheboundarylayersandinfluenced bysecondaryflows.
Afterleavingtheimpeller,rapidmixingtakesplacebetweenthetwozonesduetothedifferenceinangularmomentum(mixingregion).Thisintensiveenergyexchangeresultsinafast uniformizationoftheflow.
Theflowisfurtherdeceleratedbyanareaincreasecorrespondingtotheradiusincreaseof the vanelessdiffuser andinfluencedbyfrictiononthelateralwalls.
Incaseofa vaneddiffuser,theflow,afterashortvanelessspace,entersthe semi-vaneless space,i.e.thediffuserentryregionbetweentheleadingedgeandthethroatsectionwherea rapidadjustmentrearrangestheisobarpatternfromnearlycircumferentialtoperpendicularto themainflowdirection.IftheMachnumberishigherthanone,ashocksystemmaydecelerate theflowsuchthatthe throatsection becomessubsonic.
Afurtherdecreaseinthevelocityinthedivergent diffuserchannel downstreamofthe throatrealizesanadditionalincreaseinthestaticpressure.Dependingonthethroatflow conditions,theboundarylayersinthischannelwillthickenorevenseparate,whichlimitsthe staticpressurerise.
Theflowmayexitthecompressorbya volute orplenum,orcanbeguidedintothenextstage bya returnchannel.
Thefollowingchaptersdescribetheflowinthedifferentparts(IGV,impeller,diffuser,etc.) togetherwiththeequationsgoverningtheflowinthesecomponents.Afirstobjectiveis toprovideinsightintotheflowstructuretoallowabetterunderstandingofnumericaland experimentalresults.Asecondobjectiveisthecharacterizationofthecompressorcomponents basedonalimitednumberofgeometricalparameters,experimentalcorrelations,andflow DesignandAnalysisofCentrifugalCompressors, FirstEdition.RenéVandenBraembussche. ©2019,TheAmericanSocietyofMechanicalEngineers(ASME),2ParkAvenue,NewYork,NY,10016,USA(www.asme.org). Published2019byJohnWiley&SonsLtd.
MIXING REGION
CHANNEL DIFFUSER
DIFFUSER THROAT
SEMI VANELESS SPACE
IMPELLER EXIT
Figure1.1 Schematicviewoftheradialcompressorcomponentsandflow(fromDean1972).
parameterssuchasthediffusionratio(DR),thejetwakemassflowratio(��)fortheimpeller flow,thepressurerecovery(CP )forthediffuser,etc.
Theultimatepurposeistoprovideinputforthedesignofcompressorsthatbettersatisfythe designrequirementsintermsofpressureratio,efficiency,massflow,andstableoperatingrange.
1.1ApplicationofCentrifugalCompressors
Experiencehasshownthatthespecificspeed NS isavaluableparameterintheselectionofthe typeofcompressor(axial,centrifugalorvolumetric)thatisbestsuitedforagivenapplication. Thespecificspeedisdefinedby
Thisisanon-dimensionalparameteronlyifcoherentunitsareused(m3 /sforthevolumeflow ̇ Q,m2 /s2 fortheenthalpyrise ΔH ).However,acommonlyuseddefinitionofspecificspeedfor compressors
doesnotuseSIunitsandisnotnon-dimensional. Acommondefinitionforpumpsis NSP =
whereGPM = USgallon/minandthemanometricheadisinft. ThefollowingdefinitionsinSIunitsarenon-dimensional:
Previousdefinitionsarelinkedby:
Radialcompressorscanachievehighpressureratiosandtheinletvolumeflowcanbevery differentfromtheoneattheoutlet.Weshouldthereforeverifywhichoneofthetwohasbeen usedinthedefinitionof NS .Rodgers(1980)proposesusinganaveragevalueoftheinletand outletvolumetricflow:
Thevariationofefficiencyasafunctionofspecificspeedforaxial,centrifugal,andvolumetric compressorsisshowninFigure1.2.Testresultsfornumerouscompressorsliewithintheshaded areasandthefulllinesenvelopthedatacorrespondingtothedifferenttypes.Themeridional crosssectionofthecorrespondingtypeofcompressorgeometryisshownontop.Thelimiting curvesonthefigureintendonlytoshowthetrendincompressorefficiencyasafunctionof specificspeed.Theyshouldnotbeusedforpredictionpurposesbecausetheinformationdates fromaperiodwhentheflowinradialimpellerswasnotyetfullyunderstood(Baljé1961).Great improvementshavebeenmadesincethen,thankstotheinformationobtainedbyCFDand opticalmeasurementtechniques.MorerecentresultsareshowninFigure1.14.
Centrifugalcompressorscanalsobedesignedforspecificspeedvaluesawayfromthe optimumindicatedonFigure1.2butthisdoesnotfacilitatethejob.Positivedisplacement (volumetric)compressorsareoftenreplacedbylessefficientverylowspecificspeedcentrifugal compressorsforoperationalandmaintenancereasons.
Figure1.2 Variationofefficiencyandgeometrywithspecificspeed.
Figure1.3 Industrialcentrifugalimpellers(fromBenvenuti 1977).
Centrifugalcompressorsareusedatlower NS thanaxialcompressors.Thelow NS mayresult from:
• operationatlowRPM:thisisoftenthecasewithindustrialcompressors(Figure1.3)forreasonsofmaximizinglifetime
• smallvolumeflowasoccurringinlaststages(Figure1.4a)ofmulticorpsindustrialcompressors(Figure1.4b)
• ahighpressureratioperstageincombinationwithasmallvolumeflow(Figure1.5)oreven largevolumeflowincombinationwithverylargepressureratios(Figure1.6)asoccursin turbochargers
• ahighpressureratioandsmallvolumeflowasinsmallgasturbinesforautomotiveapplications(Figure1.7),inthelastcompressorstagesofsmallgasturbines,turboproporjetengines (Figure1.8),andinmicrogasturbines(Figure1.9).
Figure1.4 (a)Lastcorpsofahighpressureindustrialcentrifugalcompressorwith(b)verylowspecificspeed impeller(fromBenvenuti1977).
