doctoral thesis final

23/11/201123/11/2011

Doctoral Doctoral ThesisThesis

““UNSTEADY ROTORUNSTEADY ROTOR--STATOR STATOR INTERACTION IN AN AXIAL INTERACTION IN AN AXIAL

TURBOMACHINETURBOMACHINE””

D. JesD. Jesúús Manuel Ferns Manuel Fernáández Orondez Oro

DtorDtor: Prof. Carlos : Prof. Carlos SantolariaSantolaria MorrosMorros

22/64/64““Unsteady RotorUnsteady Rotor--Stator Interaction in an Axial TurbomachineStator Interaction in an Axial Turbomachine””. .

Doctoral Thesis Doctoral Thesis -- GijGijóón. n. AprilApril, 7th, 2005. University of Oviedo., 7th, 2005. University of Oviedo.

TableTable ofof ContentsContents



1.1.-- IntroductionIntroduction

3.3.-- Experimental Experimental WorkWork

FacilitiesFacilities

2.2.-- Axial Axial TurbomachineTurbomachine

ResultsResults

5.5.-- DeterministicDeterministicAnalysisAnalysis

4.4.-- NumericalNumerical WorkWork

MethodologyMethodology ResultsResults

TableTable ofof ContentsContents

6.6.-- ConclussionsConclussions & & FutureFuture WorkWork




0Dh P T v f v qDt t

WhyWhy UnsteadyUnsteadyFlowFlow AnalysisAnalysis??

ThisThis unsteadyunsteady pressurepressure fieldfield isisa a consequenceconsequence ofof thethe bladesblades

motionmotion ofof thethe rotor.rotor.

UNSTEADY UNSTEADY TURBOMACHINERY TURBOMACHINERY

FLOWFLOW

1.1.-- Even, an Even, an inviscidinviscid, adiabatic flow (reversible) is exchanging enthalpy , adiabatic flow (reversible) is exchanging enthalpy (work) due to the existence of an unsteady pressure field.(work) due to the existence of an unsteady pressure field.

2.2.-- Mechanical vibrations and unsteady forces also appear due to thMechanical vibrations and unsteady forces also appear due to the e time variations of the pressure field.time variations of the pressure field.

3.3.-- Aerodynamically generated noise is associated to the pressure Aerodynamically generated noise is associated to the pressure fluctuations inside the fluctuations inside the turbomachineturbomachine. .




TURBOMACHINERY TURBOMACHINERY UNSTEADY UNSTEADY

MECHANISMSMECHANISMS

TIME PERIODIC TIME PERIODIC PHENOMENAPHENOMENA

StableStableOperationOperation

ROTORROTOR--STATOR STATOR INTERACTIONINTERACTION

PotentialPotential OriginOrigin

BoundaryBoundary LayerLayer

ShockShock WavesWaves

VortexVortexsheddingshedding

RotatingRotatingStallStall

UnstableUnstableOperationOperation

ChaoticChaotic, , aperiodicaperiodicphenomenaphenomena

RelatedRelated toto SpeedSpeedRotationRotation

Non Non relatedrelated totoSpeedSpeed RotationRotation

TransitionalTransitionalOperationOperation ––

Speed Range Speed Range VariationsVariations

TurbulenceTurbulence

ROTORROTOR--STATOR INTERACTIONSTATOR INTERACTION

TurbomachineryTurbomachinery flows are highly flows are highly unsteady because of the relative unsteady because of the relative motion of rotor and stator stages.motion of rotor and stator stages. In general, unsteadiness may be viewed as a combination of two processes: the INVISCID POTENTIAL EFFECTINVISCID POTENTIAL EFFECTand the PERIODIC PASSING OF PERIODIC PASSING OF WAKESWAKES generated by the upstream blade rows. The former is due to the relative motion of the rotors with relative motion of the rotors with respect to the statorsrespect to the stators, and this effect becomes stronger when the gap between rotor and stator is small. The latter arises from the interaction interaction of the blade boundary layers with the of the blade boundary layers with the vortices shedvortices shed from the blunt trailing edge of upstream blade rows, and from the variation of the angle of attack at the leading edge due to the wake velocity deficit. All these All these unsteady features and the unsteady features and the interaction between them make the interaction between them make the simulation of unsteady simulation of unsteady turbomachineryturbomachinery flows a highly flows a highly challenging task. (C.HIRSCH)challenging task. (C.HIRSCH)

WhichWhich UnsteadyUnsteadyFlowFlow AnalysisAnalysis??




INVISCID INVISCID POTENTIAL EFFECTPOTENTIAL EFFECT

PERIODIC PASSING PERIODIC PASSING OF WAKESOF WAKES


•• WakeWake DecayDecay ((MixingMixing LossLoss))•• WakeWake TransportTransport ((ChoppingChopping effectseffects, , RedistributionRedistribution ofof MomentMoment, , Hot Hot SpotsSpots))•• WakeWake RecoveryRecovery ((WakeWake StretchingStretching))

Rotor 1

Rotor 2

Stator 2

Stator wakes

Vortex shedding




INVISCID INVISCID POTENTIAL EFFECTPOTENTIAL EFFECT

PERIODIC PASSING PERIODIC PASSING OF WAKESOF WAKES


•• Axial Axial gapgap variationsvariations. . PitchPitch effecteffect..•• CircunferentialCircunferential variationsvariations in total in total pressurepressure duedue toto thethe bladesbladesdownstreamdownstream response.response.•• Time Time circunferentialcircunferential variationsvariations andand response response toto anan uniformuniform inletinletconditionsconditions..

t t

““A steady flow pattern in a relative frame of A steady flow pattern in a relative frame of

reference with a velocity gradient in the reference with a velocity gradient in the tangential direction generates an unsteady tangential direction generates an unsteady

absolute flow patternabsolute flow pattern””. . (Lyman, 1993)(Lyman, 1993)

The static pressure field upstream and downstream of a blade rowis varying circumferentiallyvarying circumferentially (and radially) due to the blade loaddue to the blade load.

This causes a flow defect, which is felt as unsteady pressure waves felt as unsteady pressure waves by the relative moving blade rows. (by the relative moving blade rows. (JJööckercker, 2002), 2002)



1.1.-- IntroductionIntroduction HowHow UnsteadyUnsteady FlowFlow??En

ergy

Frequency

Turbulencescales

Blade-passingfrequencies

TURBOMACHINERY TURBOMACHINERY FLOW SCALESFLOW SCALES

MathematicalMathematical ModelsModels ForForTurbomachineryTurbomachinery FlowsFlows

AveragingAveraging TechniqueTechniqueSegregationSegregation

EnsembleEnsemble AverageAverage

Time AverageTime Average

PassagePassage AverageAverage

SpectralSpectral GapGap




1

1lim , , ,Me

M mf f r z

M

1 12 1 ;t m t t T t

0

1 , , , , , ,Tt e

Gf H r z t f r z t dtT

0

1 , , ,T

GH r z t dtT

1

0

1 2 2, , , ,N

ap t

n

n nf G r z f r zN N N

2

10

1 , ,2

Ll ll j

g r z d

1, , , ,L

llG r z g r z

1. 1. EnsembleEnsemble--averageaverage

2. Time2. Time--averageaverage

3. 3. PassagePassage--toto--passagepassage averageaverage

ˆ ˆ ˆ ˆij i j i j i jR u u u u u u

DETERMINISTIC FLOW INSIDE A DETERMINISTIC FLOW INSIDE A TURBOMACHINE (TURBOMACHINE (AdamzcykAdamzcyk, 1986), 1986)

PANS PANS EquationsEquations + + ClosureClosure requirementsrequirements

URANS URANS EquationsEquations

•• AperiodicAperiodic TermTerm: : IndexingIndexing contributioncontribution ofof differentdifferent bladeblade rowrow stagesstages..•• DETERMINISTIC TERM: DETERMINISTIC TERM: RotorRotor--Stator Stator InteractionInteraction atat oneone stagestage..•• ReynoldsReynolds StressesStresses:: StochasticStochastic unresolvedunresolved flowflow--fieldfield..




OBJECTIVES OVERVIEWOBJECTIVES OVERVIEW

1.1.-- AnalysisAnalysis ofof thethe unsteadyunsteady scenarioscenario insideinside anan axial axial turbomachineturbomachine

2.2.-- BothBoth numericalnumerical andand experimental experimental characterizationcharacterization ofof thethe flowflowpatternspatterns

3.3.-- SegregationSegregation ofof instantaneousinstantaneous turbulentturbulent phenomenaphenomena throughthrough a a time average time average forfor everyevery rotor rotor phasephase

4.4.-- IdentificationIdentification ofof dynamicdynamic unsteadinessunsteadiness sourcessources, , eithereither generatedgeneratedby rotor by rotor bladesblades oror generatedgenerated by stator by stator vanesvanes

5.5.-- AnalysisAnalysis ofof thesethese dynamicsdynamics phenomenaphenomena (axial (axial gapgap influenceinfluence, , massmassflowflow raterate variationsvariations) ) associatedassociated toto bladeblade passingpassing frequencyfrequency (BPF)(BPF)

6.6.-- DeterministicDeterministic analysisanalysis ofof thethe flowflow: : wakewake transporttransport, , wakewakeconvectionconvection andand wakewake recoveryrecovery




11--STAGE STAGE AXIAL AXIAL

BLOWERBLOWER

STATOR STATOR characteristicscharacteristics::•• 13 13 InletInlet GuideGuide VanesVanes (IGV(IGV’’s)s)•• BritishBritish Circular Circular ProfileProfile C1C1

ROTOR ROTOR characteristicscharacteristics::•• 9 9 BladesBlades (127 (127 mmmm –– chord)chord)•• NACA 65 NACA 65 ProfileProfile

FAN FAN characteristicscharacteristics::•• TipTip diameterdiameter: 820 : 820 mmmm•• HubHub diameterdiameter: 380 : 380 mmmm•• RotationRotation SpeedSpeed: 2400 : 2400 rpmrpm•• DesignDesign FlowFlow RateRate: 18 m: 18 m33/s/s•• DesignDesign PressurePressure: 1200 : 1200 PaPa•• StatorStator--Rotor Rotor ConfigurationConfiguration

FrontFront ViewView

RearRear ViewView




STATOR STATOR GeometricalGeometricalParametersParameters

•• 13 13 InletInlet GuideGuide VanesVanes•• BritishBritish Circular Circular ProfileProfile C1C1

ROTOR ROTOR GeometricalGeometricalParametersParameters

•• 9 9 BladesBlades (127 (127 mmmm –– chord)chord)•• NACA 65 NACA 65 ProfileProfile

2,2º3,12º4,63º7,19º11,88ºβ

3,57º3,78º4,08º4,71º5,97º

66,46º63,47º59,7º54,84º48,64ºº

5,75º6,38º7,43º9,46º13,76º

2,9º3,71º5º7,17º10,96º

0,03º0,52º1,28º2,45º4,08ºi

8 %8,63 %9,43 %10,49 %12 %b/l

0,550,650,7911,35

67,16º64,06º60,07º54,82º47,73ºβ4

69,36º67,18º64,7º62,01º59,61ºβ3

820 710 600 490 380 D(mm)

15,68º17,81º20,73º24,84º31,17ºβ

6,75º6,45º6,15º5,85º5,54º

10,78º11,66º12,97º14,93º18,12ºº

23,21º25,2º27,81º31,51º37,18º

10,78º11,66º12,97º14,93º18,12º

- 0,88º- 0,93º- 0,93º- 0,82º- 0,47ºi

3 %3 %3 %3 %3 %b/l

0,860,981,141,371,71

15,68º17,81º20,73º24,84º31,17ºβ2

0º0º0º0º0ºβ1

820 710 600 490 380D (mm)



2.2.-- Axial Axial TurbomachineTurbomachine TestTest FacilityFacility

RegulationRegulation ConeCone

StabilizationStabilization DuctDuct

VenturiVenturi NozzleNozzle

BS 848 (1980) –“Methods of Testing Performance”. Fans

for General Purposes. British Standard

Institution.

L = 20 D

InletInlet

RotorRotorStatorStator

MotorMotor

HubHub



3.3.-- Experimental Experimental WorkWork MethodologyMethodology

1.1.--PressurePressure FiveFive HoleHole ProbeProbe 2.2.-- Hot Hot WireWire AnemometryAnemometry 3.3.-- PiezoelectricPiezoelectric transducertransducer

MEASUREMENT TYPESMEASUREMENT TYPES

• Steady measurements• Average velocity maps andpressure distributions• No BPF Response (0.36 KHz)

• Unsteady measurements• Instantaneous velocity maps• High Frequency Response: up to30 KHz

• Unteady measurements• Instantaneous Pressure signals• High Frequency Acquiring: up to100 KHz



1.1.-- PRESSURE FIVE PRESSURE FIVE HOLE PROBEHOLE PROBE

MeasurementMeasurement SetSet--UpUp

CalibrationCalibration SetSet--UpUpMeasurementMeasurement ChainChain




2.2.-- HOT WIRE HOT WIRE ANEMOMETRYANEMOMETRY

MeasurementMeasurement SetSet--UpUp

CalibrationCalibration SetSet--UpUp

ProbeProbe repairingrepairingequipmentequipment




3.3.-- TRANSDUCER TRANSDUCER PRESSUREPRESSURE

MeasurementMeasurement PointsPoints

MeasurementMeasurementEquipmentEquipment




MEASUREMENT MEASUREMENT LOCATIONSLOCATIONS

CircunferentialCircunferential sectorsector

• Upstream and downstream rotor measurements.• Circunferential sectors used as “Windows”.

• Tangential direction: Stator pitch = 360º/13 28º.• Spanwise: From hub to tip.

• Spatial discretization: 15x15 = 225 points/window.• Temporal discretization: 36 KHz (100 instants/passage)




AXIAL BLOWER PERFORMANCE CURVE

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12 14 16 18

Flow Rate (m3/s)

Pres

sure

(Pa)

0

10

20

30

40

50

60

Tota

l Effi

cien

cy (%

)

Static Pressure, Ps Dinamic Pressure, Pd Total Pressure, Pt Numerical Points Efficiency

MEASUREMENT MEASUREMENT STRATEGIESSTRATEGIES

1.- Working Point Variations

2.-Axial Gap Modification

N) Nominal Flow Rate (Qn): 16.5 m3/s

P) -15% Nominal Flow Rate(0.85Qn): 13.5 m3/s

S) -30% Nominal Flow Rate(0.7Qn): 11.5 m3/s

1.25G) Upper Axial Gap: 100 mm

G) Lower Axial Gap: 80 mm

Axial Axial GapGap




EXPERIMENTAL EXPERIMENTAL RESULTSRESULTS

PASSAGEPASSAGE--AVERAGED FLOWAVERAGED FLOW

PHASEPHASE--AVERAGED AVERAGED FLOWFLOW

•• AveragedAveraged ResultsResults•• Mean DHW & FHPMean DHW & FHP

STEADY STEADY CharacteristicsCharacteristics

•• InstantaneousInstantaneous ResultsResults•• DHW & DHW & TransducerTransducer

UNSTEADY UNSTEADY CharacteristicsCharacteristics

3.3.-- Experimental Experimental WorkWork ResultsResults



3.3.-- Experimental Experimental ResultsResults


FHP FHP

ADIM. AXIAL VELOCITYADIM. AXIAL VELOCITY

•• BetweenBetween thethe rowsrows (D), (D), atatnominal nominal flowflow raterate, , therethere isis a a perfectperfect homogenetationhomogenetation ofofthethe flowflow, , justjust brokenbroken by by stator stator wakeswakes. . BothBoth axial axial gapsgaps..

•• Rotor Rotor downstreamdownstream (R), (R), thethestator stator wakeswakes are are clearlyclearlypresentpresent, more , more diffuseddiffused andandadvectedadvected, , butbut perfectlyperfectlyvisible.visible.

•• BoundaryBoundary layerlayer zoneszones: : ForFor(D), (D), widewide boundaryboundary atat tiptip. . InsteadInstead, , forfor (R), (R), thethe hubhubboundaryboundary layerlayer seemsseems toto be be thickerthicker. .

•• FIRST RESULTS !!FIRST RESULTS !!




ROTOR ROTOR DownstreamDownstreamSTATOR STATOR DownstreamDownstream

DHW DHW




PASSAGEPASSAGE--AVERAGED FLOWAVERAGED FLOWADIM. AXIAL VELOCITY ADIM. AXIAL VELOCITY

DHW DHW



3.3.-- Experimental Experimental ResultsResults DHW DHW

PASSAGEPASSAGE--AVERAGED FLOWAVERAGED FLOWADIM. TANGENTIAL VELOCITY ADIM. TANGENTIAL VELOCITY




PHASEPHASE--AVERAGED FLOWAVERAGED FLOW

DHW DHW





DHW DHW





PT PT



4.4.-- NumericalNumerical WorkWork MethodologyMethodology

NUMERICAL NUMERICAL METHODOLOGYMETHODOLOGY

TWOTWO--DIMENSIONAL (2D)DIMENSIONAL (2D)

THREETHREE--DIMENSIONAL (3D)DIMENSIONAL (3D)




•• SpatialSpatial DiscretizationDiscretization: : up up toto 350,000 350,000 cellscells. 12,000 . 12,000 cellscells//passagepassage. . HybridHybridmeshmesh. O. O--GridGrid aroundaround thethe bladesblades. . GridGrid accuracyaccuracy analysisanalysis..•• Temporal Temporal DiscretizationDiscretization: : 5.34*105.34*10--55 s. 468 time s. 468 time stepssteps/rotor /rotor rev.rev. ((1313xx99x4).x4).•• NumericalNumerical SchemeScheme: : SIMPLE algorithm for pressureSIMPLE algorithm for pressure--velocity coupling, upwind velocity coupling, upwind discretizationsdiscretizations and second order implicit scheme for the time dependent term.and second order implicit scheme for the time dependent term.•• TurbulenceTurbulence modelingmodeling: : LESLES--(k(k--εε))RSM RSM comparisoncomparison. .

TWOTWO--DIMENSIONAL DOMAIN (2D)DIMENSIONAL DOMAIN (2D) URANS URANS SlidingSliding MeshMesh TechniqueTechnique

17.0

17.2

17.4

17.6

17.8

18.0

18.2

18.4

0 50000 100000 150000 200000 250000 300000

Número de celdas

Cau

dal (

m3/

s)

950

1000

1050

1100

1150

1200

12500 2500 5000 7500 10000 12500

Nº de celdas por canal

AP

(Pa)

Q (ajuste)QAP (ajuste)AP

-1500

-1400

-1300

-1200

-1100

-1000

-900

-800

-700

-600

0 50000 100000 150000 200000 250000 300000

Número de celdas

Stat

Pre

s (P

a)

050100150200250300350400450500

0 2500 5000 7500 10000 12500

Nº de celdas por canal

Fluc

tuac

ión

Pres

(Pa)

Pres_med (ajuste)Pres_medPres_desv (ajuste)Pres_desv




•• SpatialSpatial DiscretizationDiscretization: : up up toto 1,800,000 1,800,000 cellscells. 3,000 . 3,000 cellscells//passagepassage 3D. 3D. HybridHybridmeshmesh. O. O--GridGrid aroundaround thethe bladesblades. [100x35x25].. [100x35x25].•• Temporal Temporal DiscretizationDiscretization: : 1.068*101.068*10--44 s. 234 time s. 234 time stepssteps/rotor /rotor rev.rev. ((1313xx99x2).x2).•• NumericalNumerical SchemeScheme: : SIMPLE algorithm for pressureSIMPLE algorithm for pressure--velocity coupling, upwind velocity coupling, upwind discretizationsdiscretizations and second order implicit scheme for the time dependent term.and second order implicit scheme for the time dependent term.•• TurbulenceTurbulence modelingmodeling: : LESLES--(k(k--εε))RSM RSM comparisoncomparison. .

THREETHREE--DIMENSIONAL DOMAIN (3D)DIMENSIONAL DOMAIN (3D) URANS URANS SlidingSliding MeshMesh TechniqueTechnique

LESLESRSMRSM ExpExp



4.4.-- NumericalNumerical WorkWork ResultsResults

NUMERICAL NUMERICAL RESULTSRESULTS


PHASEPHASE--AVERAGED AVERAGED FLOWFLOW

•• TwoTwo--dimensional dimensional AveragedAveraged ResultsResults•• ThreeThree--dimensional dimensional AveragedAveraged ResultsResults

STEADY STEADY CharacteristicsCharacteristics

UNSTEADY UNSTEADY CharacteristicsCharacteristics

•• TwoTwo--dimensional dimensional InstantaneousInstantaneous ResultsResults•• ThreeThree--dimensional dimensional InstantaneousInstantaneous ResultsResults



4.4.-- NumericalNumerical ResultsResults


3D 3D




PASSAGEPASSAGE--AVERAGED FLOWAVERAGED FLOWADIM. TANGENTIAL VELOCITY ADIM. TANGENTIAL VELOCITY

3D 3D



4.4.-- NumericalNumerical ResultsResults 3D 3D


ADIM. AXIAL VELOCITY ADIM. AXIAL VELOCITY



4.4.-- NumericalNumerical ResultsResults 3D 3D

PASSAGEPASSAGE--AVERAGED FLOWAVERAGED FLOWAZIMUT ANGLE AZIMUT ANGLE





3D 3D





2D2D





2D 2D




UNSTEADY FORCESUNSTEADY FORCES

2D 2D




PERTURBATIONS PERTURBATIONS PROPAGATIONPROPAGATION

3D 3D

INLET PLANEINLET PLANEOUTLET PLANEOUTLET PLANE

Axial Axial VelocityVelocity atatInletInlet//OutletOutlet planesplanes

Tyler and Sofrin Rule




PERTURBATIONS PROPAGATIONPERTURBATIONS PROPAGATION

3D 3D

(FIXED)(FIXED) (MOVING)(MOVING)



5.5.-- DeterministicDeterministic AnalysisAnalysis

NAVIERNAVIER--STOKESSTOKES

PASSAGEPASSAGE--TOTO--PASSAGEPASSAGEAVERAGEAVERAGE

PANS EQUATIONSPANS EQUATIONS--PassagePassage--toto--passagepassage AverageAverage

NavierNavier--StokesStokes--

RANS EQUATIONSRANS EQUATIONS--ReynoldsReynolds AverageAverage

NavierNavier--StokesStokes--

ˆ ˆ ˆ ˆij i j i j i jR u u u u u u ij i ju u

REYNOLDSREYNOLDSAVERAGEAVERAGE

SOLUTIONSOLUTION

TURBOTURBOMACHINERYMACHINERY

GENERALGENERALPURPOSEPURPOSE

CL

OSU

RE

CL

OSU

RE




ˆ ˆ ˆ ˆij i j i j i jR u u u u u u

•• AperiodicAperiodic TermTerm: : IndexingIndexing contributioncontribution ofof differentdifferent bladeblade rowrowstagesstages..•• DETERMINISTIC TERM: DETERMINISTIC TERM: RotorRotor--Stator Stator InteractionInteraction atat oneone stagestage..•• ReynoldsReynolds StressesStresses:: StochasticStochastic unresolvedunresolved flowflow--fieldfield..

1

1( , , , ) ( , , , )N

ei i

i

u r z t u r zN

( )

10

1 1( , , ) ( , , , ) ( , , , )R R

T Nt Se e e R

i i i nnR R

u r z u r z t dt u r zT N

( ) ( )( )

0

1 ( , , , ) ( , , ) ( , , , ) ( , , )RT

t S t SDet S e e e eij i i j j

R

R u r z t u r z u r z t u r z dtT

( ) ( )

1

1 ( , , , ) ( , , ) ( , , , ) ( , , )RN t S t S

e R e e R ei n i i n i

nR

u r z u r z u r z u r zN

( )

10

1 1( , , ) ( , , , ) ( , , , )S S

T Nt Re e e S

i i i nnS S

u r z u r z t dt u r zT N

( ) ( )( )

0

1 ( , , , ) ( , , ) ( , , , ) ( , , )ST

t R t RDet R e e e eij i i j j

S

R u r z t u r z u r z t u r z dtT

( ) ( )

1

1 ( , , , ) ( , , ) ( , , , ) ( , , )SN t R t R

e S e e S ei n i i n i

nS

u r z u r z u r z u r zN

1.1.-- EnsembleEnsemble Average (Average (PhasePhase))

2.2.-- PassagePassage--toto--passagepassage AverageAverage

Fixed Reference Frame Moving Reference Frame



5.5.-- DeterministicDeterministic AnalysisAnalysis –– Exp.Exp.

DETERMINISTIC STRESS TENSORDETERMINISTIC STRESS TENSOR TaxTax--axaxFixed Frame




DETERMINISTIC STRESS TENSORDETERMINISTIC STRESS TENSOR TcircTcirc--circcircFixed Frame




DETERMINISTIC STRESS TENSORDETERMINISTIC STRESS TENSOR TaxTax--circcircFixed Frame



5.5.-- DeterministicDeterministic AnalysisAnalysis –– Num.Num.

DETERMINISTIC STRESS TENSORDETERMINISTIC STRESS TENSOR TaxTax--axaxFixed Frame




DETERMINISTIC STRESS TENSORDETERMINISTIC STRESS TENSOR TcircTcirc--circcircFixed Frame




DETERMINISTIC STRESS TENSORDETERMINISTIC STRESS TENSOR TaxTax--circcircFixed Frame




DETERMINISTIC STRESS TENSORDETERMINISTIC STRESS TENSOR 2D 2D Blade-to-blade

0

10

20

30

40

50

60

70

Hub Midspan Tip

Kdet

(m2/

s2)

1.25GG

TaxTax--axax 1.25G 1.25G -- midspanmidspan TaxTax--axax 1.25G 1.25G -- tiptip

TaxTax--circcirc 1.25G 1.25G -- hubhub TaxTax--circcirc 1.25G 1.25G -- tiptip

3

1

12Det ii

i

K T




WAKE RECOVERYWAKE RECOVERY Theory

1 2

2 2 2 21 2 0 1 1 0 1 1

1 12 2

L Lt t

x x

u u v u u v

1inK 2exK

21 2 1 2 1 1

1

1 exin ex in in

in

KK K K K RK

1 ( )D

2 ( )R

1 2 0

1 2 0

No Recovery

Recovery



5.5.-- DeterministicDeterministic AnalysisAnalysis NumericalNumerical

WAKE RECOVERYWAKE RECOVERY



6.6.-- ConclusionsConclusions & & FutureFuture WorkWork

1.1.-- BothBoth NUMERICAL NUMERICAL andand EXPERIMENTAL EXPERIMENTAL studiesstudies havehave beenbeen realizedrealized in in orderorder totoCHARACTERIZE CHARACTERIZE thethe UNSTEADY ROTORUNSTEADY ROTOR--STATOR INTERACTION in STATOR INTERACTION in anan AXIAL FLOW AXIAL FLOW BLOWER.BLOWER.

•• IntensiveIntensive DHW DHW measurementsmeasurements havehave beenbeen achievedachieved forfor thethe experimental experimental methodologymethodology..•• InstantaneousInstantaneous numericalnumerical velocityvelocity mapsmaps werewere obtainedobtained throughthrough a URANS a URANS simulationsimulation in in thethe FLUENT FLUENT codecode..

CONCLUSIONSCONCLUSIONS

2.2.-- BothBoth ROTOR ROTOR andand STATOR STATOR framesframes ofof referencereference havehave beenbeen consideredconsidered forfor a more a more comprehensivecomprehensive understandingunderstanding ofof thethe generationgeneration andand transporttransport ofof thethe unsteadyunsteady flowflowfeaturesfeatures. .

3.3.-- AnAn IDENTIFICATION METHODOLOGY IDENTIFICATION METHODOLOGY basedbased onon thethe deterministicdeterministic stressesstresses modelmodelhas has beenbeen employedemployed, so UNSTEADY SOURCES , so UNSTEADY SOURCES relatedrelated toto BLADE PASSING BLADE PASSING FREQUENCIES FREQUENCIES havehave beenbeen determinateddeterminated. . EitherEither interactioninteraction locationlocation, , oror unsteadinessunsteadinessintensityintensity havehave beenbeen properlyproperly segregatedsegregated andand estimatedestimated. .




4.4.-- CharacteristicCharacteristic POTENTIAL EFFECTS (INVISCID POTENTIAL EFFECTS (INVISCID mechanismsmechanisms) ) andand WAKE WAKE EFFECTS (BOUNDARY LAYER EFFECTS (BOUNDARY LAYER mechanismsmechanisms) ) werewere observedobserved::

•• ROTOR BLOCKAGE (ROTOR BLOCKAGE (PotentialPotential).).•• WAKEWAKE--BLADE BLADE InteractionInteraction (Radial (Radial migrationmigration ofof stator stator wakeswakes).).•• WAKEWAKE--RECOVERY RECOVERY StretchingStretching (Stator (Stator wakeswakes passingpassing throughthrough rotor rotor passagespassages).).•• WAKEWAKE--TIP TIP InteractionInteraction ((MaximumMaximum unsteadyunsteady valuesvalues atat tiptip locationslocations).).•• WAKEWAKE--WAKEWAKE InteractionInteraction (Residual stator (Residual stator wakeswakes affectingaffecting rotor rotor wakeswakes).).


5.5.-- GAP AXIAL MODIFICATIONS GAP AXIAL MODIFICATIONS andand OFFOFF--DESIGN CONDITIONS DESIGN CONDITIONS havehave beenbeen includedincludedin in thethe studystudy toto determine determine thethe influenceinfluence ofof thesethese parametersparameters. General . General conclusionsconclusionspointpoint out out thatthat::

•• BothBoth parametersparameters modifymodify WAKEWAKE--ROTOR ROTOR unsteadyunsteady patternspatterns..•• WAKEWAKE--WAKEWAKE featuresfeatures are are lessless affectedaffected by by gapgap reductionreduction andand badlybadly relatedrelated totopartialpartial load load perfomanceperfomance..

6.6.-- PROPAGATION PROPAGATION mechanismsmechanisms alongalong DUCTED FAN DUCTED FAN havehave beenbeen alsoalso reviewedreviewed in in thethenumericalnumerical modellingmodelling. . TheThe relationshiprelationship betweenbetween INLET INLET andand OULET OULET perturbationsperturbations andandVANE VANE andand BLADE BLADE numbersnumbers waswas establishedestablished throughthrough TURBOFAN NOISE ANALYSIS. TURBOFAN NOISE ANALYSIS.




7.7.-- TheThe constructionconstruction ofof thethe DETERMINISTIC STRESS TENSOR in DETERMINISTIC STRESS TENSOR in bothboth fixedfixed andandmovingmoving referencereference framesframes has has concludedconcluded thisthis workwork. . AboutAbout thisthis issueissue, , itit can be can be saidsaidthatthat::

•• DeterministicDeterministic unsteadyunsteady featuresfeatures are more are more pronouncedpronounced atat thethe stator.stator.•• BladeBlade--toto--bladeblade tensor has tensor has revealedrevealed thatthat stator stator wakewake corecore isis unaffectedunaffected by by circumferentialcircumferential pressurepressure gradientsgradients generatedgenerated by by thethe rotor.rotor.•• BetweenBetween thethe rowsrows, similar , similar valuesvalues toto ReynoldsReynolds stressesstresses are are encounteredencountered forforDeterministicDeterministic StressesStresses ((formerformer studiesstudies).).•• DeterministicDeterministic unsteadinessunsteadiness sourcessources havehave beenbeen indentifiedindentified, so , so allall correlationscorrelationscan be can be usedused as as inputinput data data forfor a a steadysteady RANS RANS simulationsimulation..


8.8.-- WAKE RECOVERY WAKE RECOVERY processprocess has has beenbeen outlinedoutlined, , withwith thethe goalgoal ofof obtainingobtaining ananestimationestimation onon thethe residual residual deterministicdeterministic kinetickinetic energyenergy associatedassociated toto stator stator wakeswakesatat downstreamdownstream rotor rotor locationslocations..




1.1.-- ANALYSIS OF THE ROTORANALYSIS OF THE ROTOR--STATOR CONFIGURATION, as STATOR CONFIGURATION, as wellwell as as thethe formerformerstatorstator--rotor rotor stagestage..

FUTURE WORKFUTURE WORK

2.2.-- NUMERICAL SOLUTION ENHACEMENT NUMERICAL SOLUTION ENHACEMENT throughthrough RADIAL GAP RADIAL GAP modellingmodelling. . AlsoAlso, , improvementimprovement ofof 3D 3D meshesmeshes qualityquality ((mainlymainly, , highhigh dense dense zoneszones atat bladeblade passagespassages), in ), in orderorder toto improveimprove LES LES characteristicscharacteristics ((y+y+ restrictionsrestrictions criterioncriterion))

5.5.--A A fewfew HOLYDAYSHOLYDAYS

3.3.-- DEEPER DEEPER knowledgeknowledge onon DeterministicDeterministic StressesStresses TransportTransport andand DiffusionDiffusion. . AnalysisAnalysis ofofotherother physicalphysical topicstopics relatedrelated toto DST, DST, likelike radial radial andand circumferentialcircumferential redistributionredistribution ofofthethe momentummomentum, , alsoalso reportedreported in in thethe literatureliterature..

4.4.-- INTRODUCTION OF CLOCKING EFFECTS, INTRODUCTION OF CLOCKING EFFECTS, throughthrough considerationconsideration ofof largerlargermachines machines withwith more more thanthan justjust oneone single single stagestage..

23/11/201123/11/2011

Doctoral Doctoral ThesisThesis

““UNSTEADY ROTORUNSTEADY ROTOR--STATOR STATOR INTERACTION IN AN AXIAL INTERACTION IN AN AXIAL

TURBOMACHINETURBOMACHINE””

D. JesD. Jesúús Manuel Ferns Manuel Fernáández Orondez Oro

Prof. Carlos Prof. Carlos SantolariaSantolaria MorrosMorros

doctoral thesis final

Education