chew packwood n turner

7/28/2019 Chew Packwood N Turner

http://slidepdf.com/reader/full/chew-packwood-n-turner 1/343

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votJJ'**1-11,

- University of Surrey -

Modelling of' Buoyant Flow I leat Transfer for

Turboinachinery Rotating Disc Caiiiies

AI IIFSIS

FNGINI-I-RINO

OFTI IF ( JNIVF'RSITY OFSI IRRFY

FORT111-1

DOCTOR OF PI III, OSOPI IY

Alistair S. R. KIII'Oll

2008

Stll)Cl-vlsc(i hy: Prof. l. W. ('IIC\%.

Co-stipci-vised by: Dr A. R. Packwood

Collaborative Supcr\ isor M. T. Turner



DECLARATION

I theundersigncdcrcbydcclarehat hework containcdn thisthcsissmyown originalwork andhis notprcviouslyn itscntirctyor in partbccnsubmitted t anyunivcrsity oradcgrce.

Signed: A. /. k

Alistair S. R. Kilfbil

Datc: March2008

-ii-



ACKNOWLEDGMENTS

My researchas akenalmostseven earso complete napart-time,Universityof Surrcy-Rolls-

Roycccollaborative asis.During hisperiodor researchhavebeen upportedyanumber f

people othat theUniversityof SurreyandatRolls-Roycend would ike to acknowledgeheircontributions.

Firstly I would like to thankall my colleaguesat Rolls-Roycefor their support, n particular Dr.

EddieWilliams, JohnMylemans, Jcff Dixon, Dr. Colin Young, Guy Snows,Dr. Tim Scanlonand

Chris Barnes rom R-R Derby, andAndy Rose,RichardBeasleyandJohn Ingle from R-R Bristol,

%kho ll helped o secure unding for my researchover the five year periodorthe mainwork.

I wish to give a thankyou to my supervisors,especiallyPror.JohnChewas my university

supervisorandto Dr. Alan Packwood,my co-supcrvisorat the university andto my industrial

supervisorMike Turner for their support, guidanccand invaluableadvicethroughoutmy research.

Also from the Surrey I`hcrmo-Fluid SystemsUniversity TechnologyCentre would like thankboth

Dr. Nick I fills andDr. Zixiang Sunfor their backgroundwork in this field orrescarch of rotating

cavity flows andheat ransfer,especiallyfor their LargeEddy SimulationComputationalFluid

Dynamicswork.

I xvouldalso like to give my thanks o theThcrmo-nuid MechanicsResearchCentreat the

University or Sussex or their experimentalandnumericalwork with the Multiple Cavity Rig. In

particular I thank Prof. PeterChilds, Dr. Chris Long andDr. Alex Alexiou.

I would like to give my full appreciation o Adam Andersonand David Mann from FluentEurope

Ltd. for all their helpwith my FLUENT User DefinedFunctionsprogramcoding problems.

I would also expressmy gratitude o Dr. PeterSmoutfor die proorrcading my thesis.

Finally. would ike to thankmyfamily,especiallymylate ather,RoyandElsieKilroil for without

theirencouragementndbackinghecompletion f myPhDwouldnothavebeenpossible.

I dedicatehisgiesisn thememory f my latemother,hlargarctKilfbil.

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ABSTRACT

In thedesignora gas urbineengine it is importantto havea good prediction of thetemperaturedistribution for componentsof theengine.This researchwork looksat the methodof predicting air

andmct3l temperatures rthc I IP compressordisc drum. It is a commonpractice o supply cooling

air for the turbinedisc andbladesby passing heair axially betweendie boresof adjacentdiscs n

die I IP compressor.some ordic central axial througliflow is known to enterthecompressornter-

disc cavitiesanda parasitictemperature ise occurs n the througliflow air as a resultor the

convectiveheat ransfer.It is importantthat the heat ransfermechanismwithin a compressornter-

disccavity is understood,asthe enginedesignerneeds o know die temperatureof the cooling air

andthedisc temperaturesn order to predict the stressandthe iiie orthe compressor,and alsoto

predict the scal andblade ip running clearances.

In this thesis,computational luid dynamics(CFD) is used o studythe flow andheatmechanism

experiencedby a gas urbine IIP compressor otor. A review of previous researchwork andknowledge n the field of rotational buoyancy-drivcn low hasshownthat die flow within the

compressorntcr-disccavities is highly three-dimensionalandtime dependentn nature.Two

approachesn thenumericalmodelling of the flow canbeconsidered;one is to useCFD as a tool to

model a single inter-disccavity with axial througliflow in full threedimensionswith unsteady low.

Usingthis approach equiresa hugeamount of computationalmemoryandtime to run the CFD

models.A secondapproach s to breakdown this complex flow processnto separate hysical

mechanisms nd introduceapproximatebut computationallycfficicnt modelsfor theseprocesses.Thesecondapproachhas been aken n this thesis,with theaim of producinga method hat canbe

incorporatednto currentdesignpractice.Two underlying flow mechanismsmay be identified for

thiscomplex flow; the first associatedwith the flow within the inter-disccavities andthesecond

associatedwith theaxial througliflow underthecompressordisc bores.

UsingthecommercialCFD codeFLUENT, modelling of thetwo underlying flow mechanisms as

beencombined and a steadyaxis),mmctric modelling methodhasbeendeveloped.This CFD

modellingmethod allows for enhancedmixing of the flow within the intcr-disccavity. The

enhancedmixing model is added o the CFD codeby usingthe User Defined Function (UDF)

functionality within FLUENT. The techniquehasbeenappliedto botha research ompressor ig

andto anactualgas urbine IIP compressor otor. CFD resultsfor both testcaseshave been

compared o measureddatacoveringa wide mngeor buoyancyconditions.For theCFD simulationsof the research ompressor ig good agreementwas achieved or thecavity shroudbeat ransfer

with a maximum error or 9% and for thedisc metaltemperatureswhere heerror was3%. The

cavity shroudheat ransrerpredictedby theCFD agreed easonablewell with theestimatedbeat

transrer or theengine compressor,however herewaspooragreementwith die disc metal

temperatures.Some nstability in the CFD solution hasbeenshown o occur with theapplicationordie enhancedmixing model.These nstability problemsarestill to be fully resolved.



NOMENCLATURE

AH

Aw [m21

Bo H

a [M]

b Iml

Cp [J kg" K*11

CP

D

DL4)'ER [m)

Dla)Con [M]

d [nl)

dh Im]

it, Im)

dy Im]

facix 1-1

E [m

Ec 1-1

F MI]G

GrGr# M

[m s21

[M fl]

11 [m)

h [W rn*2K71]

K Fl

k [W m" Kýlj

k# [W m-' K7'1

I [m]

enhanced ixing modelparameter

interiorsurface rea

Buoyancy umber Ro (PATa, 1/2

disc borc,adius

outcrradiusof cavity

specificicat

pressureocMcient QY-p.1(V.,u.,2)(Chapter Equ.5.1)

outcrdiameter r diecompressorotor

enhanced ixing modelayer hickness way romdienearest all

enhanced ixing modelconstantluid propertyayer hickness exttodiewall

depthor water

hydraulicdiameter

distance erpendicularo verticalwall (Chapter )

distance erpendicularo horizontalwall (Chapter )

cavityshroud earwall licat ransrcractorusedn theenhancedmixing model

shapeunctionusedn theenhanced ixing model

totalenergy

Eckertnumber (cor)2/(2p.&T)

licatflux

gap atio - s/b

Grashornumbcr AT L3/V2

rotationalGrashor umberr co'AT 0 p' / (T tO)

gravitational cceleration

appropriatecceleration g,gravityor - f12 , rotation

cavityheight r.- ri, cavitydepthn Chapter

licat ransfer ocfl'icicnt

cavity core actorusedn theenhanced ixingmodel

thermal onductivity

modiricd hermal onductivityn theenhanced ixingmodel

enhanced ixingmodelayer hickness



L Iml characteristicength

m [kg s7l] compressorxial hrougliflow

n [RPNI) compressorhall speed

is enhanced ixing modelparameterNu Nusscltnumber hLIk-qL /(AT k) Q/ (A,.AT)

Nub H verticalNusselt umber ased n cavityheight,h

Nul 1-1 horizontalNusscltnumber ased n cavity ength,

P [Pal staticpressure

P [Pal reduced ressurein Equation .8)

PO [Pal SussexNICRcavity pressure

Pr 1-1 Prandtlnumber p Cp kQ [W] heat low

4 [W M-1) heat lux

4A [W m"I heat ransfer yconduction lone

Ra Rayleigh umber Gr Pr

Rai localRayleighnumber

RN rotationalRayleighnumber Gr#Pr

Rah verticalRayleighnumber ased n cavityheigh4hg AThP va

M4 horizontalRayleighnumber ased n cavity ength, -g0 ATI11va

Re# Reynoldsnumber, otational fl bý v

Re, Reynoldsnumber, xial hroughilowW dh v

R.h.j (m) shaftouter adius Ch3ptcrs to9)

Ro F) Rossbynumber-W/ El a

r Iml radial distanceof cavity

ri Iml innerdiscradius

rM Iml cavity Mean adius- (r.+ rj/2

ro [m] outerdisc radius

ro (m) shaft adius

r, 0, Z [m, rad,m] cylindrical co-ordinatcs radial, circumferentialandaxial directions)

R 1-1 CFD mesh geometricalexpansion atio

SIml

cavity widthT JKI appropriateemperature

To [K] gas emperature

T, [K] innerradiusCavityW311emperaturc

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TO [K] outer adiuscavity wall temperature

T. JK] wall temperature

Tb [K] bulk fluid temperature

U,[M ell friction

velocityvW [m $'I] velocity n thecircumfcrcnti,1 ircction

w [m S*11 relativevelocity n thecircumrcrcntial irection

W [m S'11 bulkaverageelocityof dieaxial hrougliflow

X 1-1 radius atioof cavity-r/b

x Iml strcamwiscistance imcnsionChapter Figure5.1)

y nearwall distance

y nornialdistance imensionCh3ptcrFigure5.1)y non-dimcnsionalearwall distance arameter pu, Wp

yp [m) distancerompointPto thewall

Greek

a [m2S'11 thermaldifTusivityk/ (pcp)

a 101 cavitysectorangle0 101 thermal olumeexpansionoefficienta Iml boundary-layerhickness

distanceof fluid ccll centre rom thenearestwall in theenhancedmixing model

AT (K] appropriate emperaturedifference

(D [kg m*1S, jviscousdissipationterm

0 [radians] coneor

disc halfangle

(0-

90' fora

disc)

P [N SM,2j dynamicviscosity

/10 [Ns M-2j modified viscosity in the enhanced mixing model

V [M2S* 1 kinematic viscosity

P Jkgm'31 density

Tw lkg m*1S*2] wallsheartress

CO [radianss"I angularflow velocity

ri[radians

s"'I angularvelocity

-VII.



S,I 1-te'savg appropriateverage

b basic luid property alue

C,N, E, S,Wmesh ells

(cellccntrcdvalues) amed

Centre,North, East,Southand

West

core intcr-disccavitycore

corrcl corrl heat ransfer orrelation alue

Exp experiment

9 gas

I/ inner innerradius

inlet air inlet

I local

m metal

NWP nearwall point

o/ outer outer adius

W/W wall

00 frce-strcam

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CONTENTS

DECLARATION

ACKNOWLEDGMENTSABSTRACT

NOMENCLATURE

CONTENTS

LISTOFFIGURES

LIST OF TABLES

ii

iiiiv

v

ix

xv

xxii

CHAPTER INTRODUCTION I1.1An Introductiono theResearch roblem 1

1.2Outlineof theThesis 5

CIIAPTER2 REVIEWOF PREVIOUSWORK 8

2.1 Introduction 8

2.2NaturalConvection uoyancyDrivenFlowswithin aStationaryCavity 9

2.2.1Raylcigh-Binardconvection 92.2.2Naturalconvcctionwith heated idewalls 13

2.2.3Mixed horizontalandverticalconvcction 14

2.2.3.11eat ransfermeasurements 16

2.2.3.2Flowpatterns 18

2.2.3.3Temperatureistribution 19

2.2.3.4Conclusions 20

2.3Convection

lowwithin aRotatingEnclosed avity20

2.4 RotatingCavitywith Axial 71irougliflow 24

2.4.1Singlecavity nvestigations 24

2.4.1.1sothermallow 24

2.4.1.2Nonisothcrmallow 27

2.4.2Multiplecavity nvestigations 31

2.4.2.1Sussex TCmultiplecavityrig build I experimental 31investigations

2.4.2.2Sussex TCmultiplecavityrig builds2and3 33

cxpcrimcntalnvcstigations2.5Stationary ndRotatingCavities- NumericalStudies 36

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2.6 CrossFlowOvcraStationaryCavity 37

2.7A NumcricalAxisymmctricModclorthc BuoyancyEffcctsn Rotating 38CavityFlows

2.8 Conclusions 41

CHAPTER3 COMPUTATIONALFLUID DYNAMICSSIMULATIONOF 44NATURAL CONVECTION N A CUBE

Summary 44

3.1 Introduction 44

3.2 Descriptionof the Experiment 45

3.3 Test I Icat Transfer Measurements 46

3.4 Numerical Investigation 47

3.5 Numerical Simulation Results 51

3.5.1 Steady low CFD solutions 51

3.5.2 Unsteady low CFD solutionsfor dic I IC configuration 53

3.5.2.1Flow structure 53

3.5.2.21 cat transrcr 57

3.5.2.3Mcsh dependency 59

3.5.2.4Temperature ield 60

3.5.2.5Scaling 65

3.6 Conclusions 67

CIIAPTER4 COMPUTATIONAL FLUID DYNAMICS SIMULATION FOR 68

CONVECTION IN AN ENCLOSED ROTATING ANNULARSECTOR CAVITY

Summary 68

4.1 Introduction 68

4.2 Description of the Experiment 69

431 Icat Transfer Measurements 70

4.4 Numerical Modcl of Convection in a Scalcd Rotating Sector 71

4.4.1 Basic modelling assumptions and the numerical procedure 71

4.4.2 7lic governing equations 72

4.5 Numerical Simulation Results for the 4511Enclosed Rotating SectorCase

73

4.5.1 Unsteady flow FLUENT CFD solutions 73

4.5.1.1 Mean heat transrcr 73

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4.5.1.2Flowstructure nd emperatureield 76

4.5.1.3Meshdcpcndcncy 78

4.5.2Solidbody otationCFD nvestigation 79

4.6NumericalnvestigationrConvcction

na

ScaledAnnulus so

4.6.1CFDI lydrasolutionsor the ull rotatingannulus 80

4.6.2CFDFLUENTsealed otatingannulus olution 85

4.7 Conclusions 86

CIIAPTER5 COMPUTATIONALFLUID DYNAMICSSIMULATIONOF 88FLOWPASTA RECTANGULARCAVITY

Summary

5.1 Introduction

5.2 Descriptionor ti,c Experiment

5.3 Numerical Investigation

5.4 Results

5.5 Conclusions

88

88

88

89

91

97

CIIAPTER6 SUSSEXMULTI-CAVITY RIG BUILD 2THERMAL MATCHING 99

Summary 99

6.1Introduction 99

6.2 Nicthods ndAssumptions 101

6.2.1Operating onditions 103

6.2.2Tbcrmalboundary onditions 103

6.2.3Tbcrmalboundary efinitions 106

6.3Results 108

6.3.1Compressorrotoroutersurface III

6.3.2Stage discsurface III

6.3.3Stage .3shroud 112

6.3.4Stage discsurface 112

6.3.5Stationary haft 113

6.3.6Discsstages and3 axial emperatureifferences 113

6.3.7Discsstages and3 radial emperatureifTcrcnccs 113

6.3.8Best-matchedodel 130

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6.4 DiscussionandFurtherAnalysis 131

6.4.1Best-matchedmodel- modelling assumptions 131

6.4.2Heat ransfercoefficientsonthediscsurfaceand cavity shroud 133

6.4.3Cavity flow regimes 135

6.4.4Eckertnumbereffects 137

6.4.5Axial heat low calculations 137

6.4.6Theeffectof internalradiationwithin theMCR build 2 rig 143

6.5 Conclusions 145

CHAPTER7 STEADY FLOW 2-DIMENSIONAL MODELLING METHODOLOGY 147

7.1 Introduction 147

7.2 A 2D AxisymmetricModel of theBuoyancyEffects n RotatingCavity 147Flows

7.3 A Numerical2D Model of theBuoyancyEffects n aStationaryCube 152EnclosedCavity

7.3.12D steadyaminar low CFD 153

7.3.22D unsteadyaminar low CFD 154

7.3.32D unsteadyaminar low CFDwith modifiedfluid properties 156

7.4 A Numerical2D AxisymmetricModel of theBuoyancyEffects n aRotating 158SealedCavity

7.5 Final Implementationof theEnhancedMixing Model 162

7.5.1Cavityshroudheat ransfer ormulationcodedn theUDF 162

7.5.2Cavitycoreenhancedmixing model ormulationcodedn theUDF 163

7.6 User Guide or theEnhancedMixing ModelUDF and heusewithin the 1662D AxisymmetricCFDModel

7.7 Conclusions 167

CHAPTER 8 2D AXISYMMETRIC COMPUTATIONAL FLUID DYNAMICS 168

SIMULATION OF THE SUSSEX MULTI-CAVITY RIG BUILD 2

WITH THE APPLICATION OF THE ENHANCED MIXING MODEL

Summary 168


8.2 Description of the Experiment 169

8.3 Test Heat Transfer Measurements 171

8.4 Numerical Investigations of Convection in a 2D Axisymmetric Enclosed 171Rotating Cavity with Axial Throughflow



8.4.1 Basicmodelling assumptions nd henumericalprocedure 171

8.4.2Thegoverningequations 172

8.4.3Enhancedmixing model 173

8.5 Numerical SimulationResults 176

8.5.1 Singlecavity, SussexUTC MCRB2cavity no.3 176

8.5.1.1Flow structureand emperatureesults 177

8.5.1.2Heat ransfer esults 183

8.5.2SussexMCRB2- two cavities,cavity2 andcavity3, surrounding 185disc2



8.5.3 SussexMCRB2- two cavities,cavity2 andcavity3 with a 193

conjugateheatingsolution or disc2



8.6 CFD FLUENT LES Solution 206

8.7 Conclusions 208

CHAPTER 9 2D AXISYMMETRIC COMPUTATIONAL FLUID DYNAMICS 210SIMULATION OF A TYPICAL GAS TURBINE HP COMPRESSOR

ROTOR DRUM WITH THE APPLICATION OF THE ENHANCED

MIXING MODEL

Summary 210


9.2 Description of the Engine Test 210

9.3 Test Heat Transfer Measurements 212

9.4 Numerical Investigations of Convection in a 2D Axisymmetric 213HP CompressorRotor Drum with Axial Throughflow

9.4.1 Basic modelling assumptionsand the numerical procedure 213

9.4.2 The governing equations 215

9.4.3 Enhancedmixing model 215

9.5 Numerical Simulation Results 216

9.5.1 Flow structure and temperatureresults 216

9.5.2 Heattransfer results

222

9.6 Conclusions 228



CHAPTER 10CONCLUSIONSAND RECOMMENDATIONSFOR 230FURTHERWORK

10.1Conclusions 230

10.2Recommendationsor Further Work 23510.2.1cavity anddiscconjugateheatingwith theenhancedmixing 236

model or transientoperation

10.2.2CoupledCFD- thermal ransientmodel 239

10.2.3Otherrecommendations 241

REFERENCES 242

APPENDICIES 252

Appendix 1 252

Al. 1TheStandard -c TurbulenceModelas used n theFLUENT 252CFDcode

Al. 2 NearWall TurbulenceModelsused n theFLUENT CFDcode 255

A 1.2.1Standardwall functions 255

Al. 2.2Two-layermodel or enhanced all treatment 258

A 1.2.3Enhancedwall functions 260

Appendix 2 ThermalAnalysis(SC03)of theSussexUTC MCR Build 2,266

ThermalBoundaryConditionDefinition for the 'Best-Matched'Model

Appendix3 ThermalAnalysis (SC03)of theSussexUTC MCR Build 2,285Thermal Best-Matched'ModelBoundaryConditionsValuesatthe 'near' StabilisedMaximumSpeedCondition

Appendix 4 EnhancedMixing ModelFLUENT UserDefinedFunction UDF) 293

Listing of theSourceCode comp__enhanced_mixing.'

Programmedn the 'C' LanguageAppendix 5 Listing of theSchemeile 'wall-viscosity.scm' SourceCode o 318

beusedwith theEnhancedMixing ModelUserDefinedFunction(UDF)

Appendix6 UserGuide or theEnhanceMixing ModelUDF and heuse 321

within the2D AxisymmetricCFDModel

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LIST OF FIGURES

Figure1.1 Cut awaysectionof atypical civil gas urbineaero-engine. 2

Figure 1.2 Crosssection hroughatypical civil gas urbineaero-engine howing he 3HP compressor,ombustionchamberandHPturbinealong with theinternalsecondary ir systemcoolingflows.

Figure2.1 Schematicof the testcell used n theKirkpatrick andBohnexperiments 15

and hefour experimentalestconfigurations.

Figure2.2 Dimensionsof theannularcavities or threeexperimentalest 21

configurations.

Figure2.3 Schematic iagramof computedlow in a sealed45*segment f a rotating 23

cavitywith a radialheat low (in ther-a plane).

Figure 2.4 Nomenclature for axial throughflow and isothermal flow structure. 25

Figure2.5 Visual impressionsof smokepatternsn an sothermalrotatingcavitywith 26

axial throughflow:Re,,= 5000.

Figure 2.6 Schematicdiagram of the heated flow structure in r-<pplane. 28

Figure 2.7 SussexUTC Multiple Cavity Rig (Build 1). 33

Figure 2.8 SussexUTC Multiple Cavity Rig (Build 3) showing the two LDA 34

instruments.

Figure 3.1 Geometry and surface mesh (I 00x I 00x100) for the water-filled cube. 48

Figure 3.2 Contours of vertical velocity, HC case,AT= I OK. 52

Figure 3.3 Contours of vertical velocity, HC case,unsteady, aminar flow, 55

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Ra = 5.83xlO9 (AT=IOK).

Contours of temperature,HC case, unsteady,Jaminar low, Ra = 5.83xlO9 56

(AT= I OK).

Calculatedvariationof heat ransferonthetopandbottomsurfacesor 57Ra= 2.3xI010AT=40K).

Heat transfer Numerical (CFD) datacompared with Kirkpatrick and Bohn 58

empirical correlation for the HC configuration.

Heat transfer numerical (CFD) resultscompared with Kirkpatrick and 60

Bohn empirical correlation for various mesh sizes.



Figure3.8a Computationalanalysis temperatureecord or HC configurationwith 61AT = 40K for the I 00-cubedmesh.

Figure3.8b Computationalanalysis temperatureecord or HC configurationwith 61AT= I OKfor the I 00-cubedmesh.

Figure3.9 Computationalanalysis mean emperature rofile (timeaveraged)or 62HC configurationwith AT = 40K for the I 00-cubedmesh.

Figure 3.10 Computationalanalysis temperatureluctuationprofile for HC 63

configurationwith AT = 40K for the I 00-cubedmesh.

Figure 3.11 Temperature fluctuation s ectrurn from referencepoint 8mm above 64

bottom plate, Ra = 2.3x 10 0(AT = 40K).

Figure4.1 Geometryof Aachen otatingannulus. 71

Figure4.2 Meshfor Aachenannulus. 71

Figure4.3 Comparisonof thepredictedheat ransferwith experimental orrelations 75for theAachen otating sealed ector,configurationC.

Figure4.4 Wall heat ransfer rom theCFDsolutionand heAachen otating sealed 76

sectorexperimentor R4 = 3.781x109.

Figure4.5 CFDpredicted nstantaneousemperatureontoursor Ra+= 3.78 xIO9.77

Figure4.6 CFDpredictednstantaneousradialvelocitycontours or Ra#= 3.781x109.77

Figure4.7 CFDpredicted emperature lot at thecavity centre or Ra4= 3.781x101.78

Figure4.8 Comparisonof thepredictedheat ransferwith experimental orrelations 79

- CFDmeshsensitivity.

Figure4.9 Comparisonof thepredictedheat ransferwith theAachensealed otating 81

annulusexperimental orrelations.

Figure4.10 Variationsof surfaceheat ransferwith time for cases&4,82

Raý= 2.76x109.

Figure4.11 Instantaneousemperatureontoursor cases&4, Ra#= 2.76x109.83

Figure4.12 Instantaneousemperaturend ts spectrumor cases&4,83Ra,#= 2.76x109.

Figure4.13 Instantaneousvelocity and ts spectrumor case4, Ra4= 2.76x109.84

Figure4.14 Comparisonof temperaturepectra .6mm rom theoutercylinder wall 84

betweenhe wo meshes, "-4= 2.76x109.

Figure4.15 Comparisonof heat ransferbetweenFLUENTandHydracalculations, 85Ra4

=2.76x109.

-Xvi-



Figure5.1 A typical CFDmeshused n thesimulation. 90

Figure5.2 Comparisonof CFDandexperimental -velocity profiles takenat three 92

positionsacrosshe testcavity (fVs=1.5).

Figure5.3 CFDpredictedy-velocity profile acrosshetestcavity at various vertical 92distancesn

to and out of thecavity (Ws=1.5).Figure5.4 CFDpredictedand estmeasured ressure istributions Cp)along he 93

testcavitywalls (Ws=1.5),(a)upstrearnanddownstreamwalls.(b)bottornsurface.

Figure5.5 CFDpredicted low patternwith in thetestcavity- contoursof stream 95function.

Figure5.6 HaugenandDhanak low visualizationexperiment water) low patterns 95

within the testcavity.

Figure5.7 CFDpredicted low patternwith in thetestcavity (H/s= 2) using water 96

- contoursof streamunction.

Figure6.1 Extentof theSussexMCRB2geometryn thethermalmodel. 102

Figure6.2 ' Materialsused n theSussexMCR132hermalmodel. 102

Figure6.3 HP shaftspeedused n the SussexMCR132hermalmodel. 103

Figure6.4 Measuredmetal emperaturesnthecompressor rumrotor outersurface 104duringthe transientcycle.

Figure6.5 Locationof thermalboundaryconditions. 105

Figure6.6 Locationof thermocouples. 109

Figure6.7 Temperaturecontoursat stabilised,maximumspeed ondition or the 109datummodel.

Figure6.8 Disc2 bore emperatureTC7). 114

Figure6.9 Disc2 rear surfaceemperature, isccob(TC8). 115

Figure6.10 Disc2 rear surfaceemperature,nnerradii (TC9). 116

Figure6.11 Disc2 rearsurfaceemperature,mid radii (TC 10). 117

Figure6.12 Disc2 rear surfaceemperature,uter adii (TC 11). 118

Figure6.13 Disc2-3 shroudsurfaceemperatureTC12). 119

Figure6.14 Disc 3 front surfaceemperature,uter adii (TC 13). 120

Figure6.15 Disc 3 rear surfaceemperature,mid radii (TC14). 121

Figure 6.16 Disc 3 rearsurfaceemperature,nnerradii (TC 15). 122

Figure6.17 Disc 3 rearsurfaceemperature,isccob(TC 16). 123

Figure6.18 Disc 3 bore emperatureTC17). 124Figure 6.19 IP shaftsurfaceemperature,isc 2 bore(TC27). 125

Figure6.20 IP shaftsurfaceemperature,etween isc 2 and3 (TC28). 126

-Xvii-



Figure6.21 IP shaftsurface emperature, isc3 bore(TC29). 127

Figure6.22 Axial temperature ifferencesacross tage2 and stage3 discsat three 128

radial locationscomparing hedatummodeland hebestmatchedmodelwith measurements.

Figure6.23 Radial emperature ifferences discouter radius o cob) for stage2 and 129stage3 discscomparing hebestmatched, atummodel and heCONE

model with measurements.

Figure6.24 Locationof BoundaryConditions or theBest MatchedModel. 130

Figure6.25 Temperaturecontoursat StabilisedMaximumCondition or theBest 131MatchedModel.

Figure6.26 Comparisonof the thermalmodellingapproach sed n thedatummodel 133to thatused n thebest-matchedhermalmodel.

Figure6.27 Comparisonof theheat ransfercoefficientson stages and3 discsand 134

thecavity shroud or the three hermalmodels.

Figure6.28 Timehistoryof Rossbynumber Ro) for MCR build 2 stage2-3 135inter-disccavity.

Figure6.29 SussexMCR build 2 transientaccel decelcycleheat low Nyithindisc 2 140diaphragm- conductioncalculationusingmeasuredest emperatures.

Figure6.30 SussexMCR build 2 transientaccel decelcycleheat low within disc 3 141diaphragm- conductioncalculationusingmeasuredest emperatures.

Figure6.31 SussexMCR build 2 effectof internal adiationwithin thecompressor 144

inter-disccavities emissivity= 1)on metal emperatures.

Figure 7.1 Illustration of the simplified model. 148

Figure 7.2 Stream function contours. 153

Figure 7.3 Velocity vectors coloured by velocity magnitude. 153

Figure 7.4 Vertical temperature distribution through the centre of the cavity for the 154

steady laminar solution.



Figure 7.7 Vertical temperature distribution through the centre of the cavity for the 155

unsteady laminar solution.

Figure 7.8 Enhancedmixing fluid viscosity distribution. 156

Figure 7.9 Enhancedmixing fluid thermal conductivity contours. 156



Figure 7.12 Vertical temperaturedistribution through the centre of the cavity for the 157unsteady aminar flow with modified fluid properties.

-Xviii-



Figure7.13

Figure7.14

Figure7.15

Figure7.16

Figure7.17

Figure8.1

Figure8.2

Figure8.3

Figure8.4

Figure8.5

Figure8.6

Figure8.7

Figure8.8

Figure8.9

Figure8.10

Figure8.11

Figure8.12

Figure8.13

Figure8.14

Figure8.15

Figure8.16

Figure8.17

Figure8.18

Figure8.19

Figure8.20

Figure8.21

Figure8.22

Figure8.23

Figure8.24

Figure8.25

Figure8.26

Figure 8.27

Stream unctioncontours. 161

Swirl velocity contours. 161

Mixing factorcontours. 161

Vertical temperature istributionthrough hecentreof thecavity. 161

SussexUTC MCRB2 streamunctioncontours. 166

SussexMCRB2- showing hepositionsof the thermocouples. 170

Stream unctioncontourswith UDF boundaryconditions test 33). 175

A part of the2D CFDgrid. 175

CFDmeshand geometryof theSussexMCRB2 cavity 3.176

Test 33temperaturesfor n=O. ). 177

Test 33 swirl velocities. 178

Test 33discandcavitytemperatures. 178

Test34Temperaturesfor n=O. ). 179

Test34 swirl velocities. 180

Test34 discandcavity temperatures. 180

Test50temperaturesfor n=O. ). 181

Test50 swirl velocities. 181

Test50discandcavity temperatures. 182

Test 33 disc2 rear surfaceheat ransfer. 183

Test 33 disc3 front surfaceheat ransfer. 184

Test 33cavity3 shroudanddiscboresurfaceheat ransfer. 184

CFDmeshand geometryof theSussexMCRB2cavities2 and3.186

CFD Test33 streamunctioncontours. 188

CFDtest33mixing factorcontours. 188

CFDtest33temperatureontours. 189

CFDtest33 swirl velocitycontours. 189

CFDtest33cavity2 (disc I anddisc 2) temperatures. 190

CFDtest33cavity3 (disc2 anddisc3) temperatures. 190

Test33cavity2 (discs and2) surface eat ransfer. 191

Test33cavity3 (discs2 and3) surface eat ransfer. 192

Test 33cavity2 and cavity3 (discs1,2 and3) shroudanddiscbore 192

surfaceheat ransfer.

CFDmeshand geometryof theSussexMCRB2cavities2 and3 and 195

of disc2 with conjugate eating.



Figure8.28 CFDtest33 streamunctioncontours. 196

Figure8.29 CFDtest33mixing factorcontours. 196

Figure8.30 Test33 temperature ontours disc 2 modelledwith conjugateheating) 197for a) with andb) without theenhancedmixing model.

Figure8.31 Test 33 cavity2 temperaturesdisc 2 modelledwith conjugateheating) 198for a)with andb) without theenhancedmixing model.

Figure8.32 Test33cavity 3 temperaturesdisc 2 modelledwith conjugateheating) 199for a)with andb) without theenhancedmixing model.

Figure8.33 Test 33disc2 temperaturesconjugate eatingsolution)- with and 200

without theenhancedmixing model.

Figure8.34 Test34 and est50disc2 temperaturesconjugateheatingsolution) 200

- with theenhancedmixing model.

Figure8.35 Test 33 CFDcavity2 (disc I and2) with disc 2 conjugateheating 203- discsurfaceheat ransfer.

Figure8.36 Test33 CFDcavity3 (disc2 and3) with disc 2 conjugateheating 203

- discsurfaceheat ransfer.

Figure8.37 Test33 CFDcavity2 (disc I and2) and cavity 3 (disc 2 anddisc3) with 204disc2 conjugateheating- shroudanddisc boresurfaceheat ransfer.

Figure8.38 Cavity3 shroudheat ransferversesGrashofnumber CFDpredictions 205

comparedo theexperiment.

Figure8.39 Cavity3shroud

heat ransferverses

buoyancynumber

CFDpredictions

205

comparedo theexperiment.

Figure 8.40 LES 120* sector model -instantaneous emperature at the mid-axial 208

plane for the SussexMCRB2 cavity 3 simulations.

Figure 9.1 HP compressorrotor drum (rear stages)geometry. 211

Figure 9.2 HP compressor (rear stages) showing the positions of the thermocouples 212

for the engine test.

Figure 9.3 CFD mesh and geometry of the rear sectionof a HP compressor rotor 214

drum.

Figure 9.4 Engine HP compressorat steady state 1070/oNL- contours of stream 217

function with enhancedmixing.

Figure 9.5 Engine condition 1070/oNL ontoursof mixing factor -for the CFD 218

enhancedmixing model.

Figure 9.6 Engine condition 107VoNLcontours of molecular/laminar viscosity 219

- for the CFD enhancedmixing model.

Figure 9.7 Engine condition 1070/oNL ontours of turbulent/eddy viscosity 219- for the CFD enhancedmixing model.



Figure9.8 Enginecondition 1070/oNLontoursof swirl velocity - for theCFD 220


Figure9.9 Enginecondition 107VoNLcontoursof swirl velocity ratio - for theCFD 221


Figure9.10 Engine estcondition 1070/oNLemperature ontours or a) with and 223b) without theenhancedmixing model.

Figure9.11 Engine est 1070/oNLcavity 2 temperaturesor a) with andb) without the 224


Figure9.12 Engine est 1070/oNLavity3 temperaturesor a) with andb) without the 225


Figure9.13 Engine est 1070/oNL riveconecavity temperaturesor a) with and 226b) without theenhancedmixing model.

Figure9.14 Engineest

1070/oNL PCdisctemperatures

conjugateheatingsolution)

227


Figure9.15 Engine est 1070/oNL PC disctemperaturesconjugateheatingsolution) 227

- without theenhancedmixing model.

Figure9.16 Engine est I 00%NL HPC disctemperaturesconjugate eatingsolution) 228


Figure 10.1 SussexMCRB2 (cavities 2 and 3 and disc 2) extendedgeometry and the 237

position of the boundary conditions required by the CFD model.Figure 10.2 SussexMCRB2 full geometry and the position of the boundary 237

conditions required by the CFD model.

Figure 10.3 Engine HP compressor full geometry and the position of the boundary 238

conditions required by the CFD model.

Figure 10.4 SussexMCRB2 (cavities 2 and 3) SC89 coupled CFD - thermal analysis 240

transient model.

-)(xi.



LIST OF TABLES

Table3.1 Comparisonsof steadyaminarand urbulentCFDresultswith measured 51heat ransfer or theHC case.

Table3.2 Comparisonsof steadyaminarand urbulentCFDresultswith measured 53heat ransfer or theHHCC case.

Table3.3 Comparisonsof unsteadyaminar CFDresultswith measured eat 58transfer or theHC case.

Table 4.1 Comparison of the CFD results (unsteady laminar flow) with measured 74Heat transfer for the Aachen 45" enclosed rotating sector, configuration C

case.

Table4.2 Comparisonof theHydra CFDresultswith measured eat ransfer or the 80Aachensealedotating annulus,configurationB.

Table6.1 Results egend or eachSC03model. 110

Table6.2 Buoyancyparameter aluesa nearsteady tatemaximumconditionand 136duringthedeceleration.

Table6.3 Comparisonof MCRB2Discs2 and3 diaphragmaxialheat low 142

calculations,SC03predicted,CFDpredictedand a simpleconduction

calculationor

steadystateand ransient accelerationdle to maximum)testpoints.

Table 8.1 SussexMCRB2 single cavity model, cavity 3 shroud surfaceheat 185

transfer.

Table 8.2 Two-cavity CFD solution cavity temperatureresults. 187

Table 8.3 SussexMCRB2 two cavity and disc 2 model, cavity 3 temperaturesand 202

shroud surfaceheat transfer.

Table 8.4 Summaryof

CFD-LESresults

forthe calculated test casesof the

Sussex 207MCRB2.

Table 9.1 Engine HP compressorrotor 2D axisymmetric CFD with the enhanced 215

mixing model - cavity 3 temperaturesand shroud surfaceheat transfer.

. )Cxii-



CHAPTER1

INTRODUCTION

1.1An Introduction to the Research Problem.

For a typical civil aero-engine, the main gasstream annulus air temperaturescan be of the order of

1800K at entry to the turbine, where combined with high rotational speeds,of typically 10,000

rev/min on a 0.6m diameter, significant rotational stressesare created.The centrifugal loads

combined with thermal stressescreatedeflections in componentsthat can causea loss in efficiency,

or worse, compromise safety.

The performance of an aero gas turbine engine is characterisedby the thermal efficiency, propulsive

efficiency, specific thrust and specific fuel consumption. Improved engine performance may be

achievedby increasing the overall pressureratio of the cycle and by increasing the turbine entry

temperature.The gastemperaturesexperiencedby the turbine exceedthe melting point temperature

usedfor the turbine components,such asrotor blades,nozzle guide vanesand discs. Having an

effective and efficient cooling systemreducesthesehigh component temperature evels. To achieve

this, cooling air is drawn from the compressorand is passed o the turbine via an internal secondary

air system.On its route, this throughflow of air may be heatedby both convection and viscous

dissipation, and through 'windage' from bolts and other components.Sinceair is bled from the

compressorwhere work hasbeendone to raise its pressure,use of this air usually representsa

parasitic loss to the main cycle. The internal air system asa whole may use20% of the mainstream

airflow and cost up to 5% of the specific fuel consumption in a modem turbofan engine.

The objective of an efficient cooling system s to maintain acceptable component temperatureswith

minimum cost. This involves conveying the air with as little unnecessarypressure oss, temperature

rise and coolant flow loss aspossible. The internal air systemsalso perform other functions, namely

to pressurise he turbine cavities and seals o prevent hot gasingestion from the main gasstream, o

control the radial temperaturegradients in the compressorand turbine discsto reducestressesand

tip clearances, o balancebearing loads on eachspool and to pressurise he bearing chambers o

prevent oil leakageand the possibility of oil fires. In the designof a gasturbine engine it is

important to have a good prediction of the temperaturedistribution for all componentsof the

engine,especially critical rotating componentssuchasdiscs.The researchdescribedhere focuses

I



on one parlicular aspeci ofilie cooling sysicill. %%hich %lle fleal iran%f'Cr t) the compressor tinim

and til%cs.

III

IT LIlT iii, 'Itilt

I- gurt. 1.1 ( '111 (of a 1ýpical ON l g-. % til-bille

p1c. )



111'tomprc%wrdri%cconc andIIP %lul1

1111(1 tist

.I It

IIVI II ill],and Wad,

I-igurt. 1.2 Cros% %ectioll 1111-ough11'Npical ci%il g. 1%

ill-billeacro-cilgille %hol%illg

Ow III,

comprc%%or. combiwi(m chamber and III, along %%ithfic iniernal %ccomlarý air

%N%IclllCooling flfl%%%.( ollf-tv%% Rolls-RoNct. p1c)

A cul a%kaNection ofa typical c1%t gas turbine cngine I% ho%%III I igtire III lie comprevor

%rux)lcompri%c.%an outer drum and a series okh%cs. which carry and stipporl file blades. Between

cacti pair ot'disc% ofthe compressor. %caledat file periphery by I %hroud. here is an inier-disc

cavity. A cro%%ection through I typical 111'comprcs%orol'a gas turbine engine I-,shown m Figure

1.2. The diagram -, io%k%I typical I III -,pool internal %ccondaryair %ysicm here if is comillon

practice to extracted air from file inam gas slivaill tipstream ofthe 111) ompres%otenwy (region

marked yellow in life diagram). This compressed ; II passesaxially (indicated by black trro%%sn the

diagram) hcmcen I ie bores ofadjacem (11%csit tile 1111compressor and I%ised to condition t ie

turbine tfi%cs.File diagram also shows that ; II- I-, extracted from file rear offlic IIP compressor

(region marked red) and fill,, stjpplieý,cooling air to tile 111'loillc guldc %;ile%and to life 111)urbine

rotor bladcs. As file cooling air from all file %cconclary ir svs1cillssotlrcc%lll\c% back into tile

mainstream in file turbinc stages there I% loss ol'siagnafion prcsstirc III the main gas %Ircamduc it)

%I-killingcI1,Cc1%.I IIN combined with lossesIllrotigh file Cooling system liscli'decreasc-, file o\crall



thermalefficiency. I lcnce,the internalair systemmustbedesignedn sucha way to keep he

coolingair flow rateto a minimum but to retaina pressureevel that is sufficicrit to provide the

required low rate andtemperatureor turbinecooling and rim scaling pressurization.

Unfortunately, hebcncijts gainedfrom increasing heoverall pressure atio reduce hecooling

potential of the internalsystemair (higher inlet temperature) nd ncreasehebcaring oadsandscal

leakage lows. As a consequence,he internalsystem low needs o be increased.n ordcr to balance

theseconflicting requirementsandoptimize the internalair system,detailed designrules and

reliablepredictivedesignmethods or the fluid flow andtheheat ransfer n thegas urbine

components rc required.

This researchwork looksat the methodof predictingair andmetaltemperatures f the I IP

compressor.As mentionedpreviously in thedesignora gas urbineengine t is importantto havea

goodpredictionof the temperaturedistribution for all componentsof theengine,especiallycritical

rotating components uchasdiscs.11is is bcc3uscemperatureevelsandgradientshavea very

strongeffect uponcomponent ife. As cooling air flows throughtheborc of thecompressort

interactswith theair insidethe compressordisccavities.Someof this centralaxial throughflow is

known to cnterthe intcr-disccavity and a parasitic emperatureiseoccurs n thethrougliflow air as

a result of theconvectiveheat ransrer rom thedisc surraccsandtheshroudand also, as mentioned

aboveadditionalheatingmay occurdueto viscousdissipationand windage'. During changesn

cngine conditions, he temperatureat therim of thecompressor isc respondsmorequickly to

changesn thetemperature f the main gas stream low thandoes hetemperature t thehub.Ilic

resultingradial temperature radientproduceshigh stresses ndreduceddisc life. Also with the

wholecompressor rum respondingmuchslower than thecompressor asing o changesn tile

annulusair temperaturehe resultingdiffcrcntial expansions nd contractions ead o changesn the

blade ip and scalclc3ranccsaffecting thesurge imit andthecompressor filicicricy. It is important

that theheat ransrcrmechanismn thecompressor avity is understood.astheenginedesigner

needso know the temperature f thecooling air andthedisc temperaturesor both transientand

steadystateoperation.

Sensitivitystudies aveshownhat, n ordcr opredicthestrcss nd he atigueireof the

compressorswell as he otorandcasing learances,omponentemperatureredictions rc

requiredo haveanaccuracy f 5K forsteady tate nd30Kduring ransients.naccurate

prediction f metalcmpcraturcs ayallowthedesignerouseessexpcnsivematerialsor the IP

compressorotorwithconfidcncc ndalso educeheoverallengine roductionycle imeandcost.

4



Today'scomputationalmethod of usingthermalanalysis o predictcomponentmetaltemperatures

is supportedby expensive otatingmetaltemperaturemeasurementsn an engine ate in to the

enginedevelopmentprogramme costingup to L2 million per test). It is importantthat thedesign

engineerhas

an understandingof theheat ransrcr

processnsidethe

compressor avities early on

in

theenginedesign,soany changesn designcanbemadebefore heenginevalidation and

certification tests.

I'lic flow in the intcr-disc cavities becomes highly complex when the shroud or the discs arc heated,

with the flow becoming three dimensional and time dependent. Experimental tests have been

pcrrorincd to investigate the flow inside a simple rectangular rotating cavity with a central axial

throughflow, seefor

exampleFarthing. Long, Owen

andPincombe [ 1992a, 1992b]

and

Long

[19941. Also attempts have been made to model numerically the flow within the same rotating

cavity used in the cxpcrimcntal test (Tucker 1993]. An observation from the tests, also captured by

the numerical model, is that some of the central through-flow does enter the cavity. which is the

result orthe buoyancy cfrccts in the centripetal acceleration ficld. As will be discussed later, such

previous research has given insight into this complex fluid dynamics problem. but has had limited

impact on design methods. A major objective or the current study is to develop an improved

predictive capabilityfor

usein

design calculations.

1.2 Outline of theThesis

It has been established that the flow within the inter-disc cavities of aII Pcomprcssor is three

dimensional in nature and time dependent. One approach in the numerical modelling of the flow is

to use computational fluid dynamics (CFD) as a numerical tool and model a singleintcr-disc

cavity

with axial throught'low in full three dimensions with unsteady flow. Using this approach requires a

huge amount of computational memory and computational time to run the CFD models. A second

approach is to break down this complex flow process into separatephysical mechanisms and

introduce approximate but computationally ciTicicnt models for theseprocesses.The second

approach has been taken for this research, with the aim of producing a method that can be

incorporated into current design practice. Full CFD models are used to aid understanding of the

physical mechanisms.

5



Two underlying flow mechanismsmay be identified for this complex flow; the first associatedwith

the flow within the intcr-disccavitiesandthesecondassociatedwith theaxial throughflow under

dic compressordisc bores.Both of these low mechanismswill be discussedn thereview of

previouswork in Chapter2. The flow within the inicr-disccavity is a naturalconvection,buoyancy

dominatedmechanism esulting from thedifferential heatingbetween hetwo compressordiscsand

theconnectingshroudat theouter radiusof thecavity. In anengine he temperature f thecavity

shroud s usuallyhottestwith the temperaturedecreasingmoving radially inwardsto thedisc cobs,

whichare cooledby theaxial flow of air underthedisccobs.A small amountof theaxial through-

flow is known to enterthe intcr-disccavity at distinct circumferential positions hatdo vary with

time, but how much flow andat what circumferential locationsstill needs o be fully investigated.

With somegas urbineengines hecompressorntcr-disccavitiesarcscaledwith no flow entering

thecavity. Chapter2 presentsa review of existing work andknowledge n the field of rotational

buoyancy-drivcn low. Both scaledcavity flow and flow in an enclosedcavity with an axial cross

flow arc considered.

In anattempt o understandhe licat transferprocesshesimpicrcaseora completelycncloscd

cavity will beconsidered irst. In thestudythe flow insidethecavity might beassumedo have

solid bodyrotation, rotatingat thesamespeedasthecompressor iscsandhcncc ile relative

velocity of the fluid to thewalls is near zero.As a precursor o therotating flow studies,Chapter3

describesa CFD studyof the flow dueto gravity-drivcn naturalconvection n a stationary hree-

dimensionalcube. lic CFD resultsare comparedwith experimentaldata from Kirkpatrick and

Bohn [ 1986].Tlicseworkersperformedexperimentson high Rayleighnumber naturalconvection n

a cubewith variousconfigurationsof heatedandcooledvcrtical andhorizontalsurfaces.All the

configurationswere variationsof the 'licating from below' case.The CFD resultsare compared

with theexperimentalmeasurementsor heat ransfer, low patternsandtemperature istribution.

A CFD studyof buoyancy-induccd low in a centrifugal force field is prcscntedn Chapter4. This

ch3ptcrdescribesBohnct al's (1993,1994]cncloscd otatingsectorexperimentsandthe three

dimensionalCFD modclling usedof these.With rcrcrcnccalsoto otherworkers' results,similarities

anddiffcrcnccsto naturalconvectionundcrgravity arcnotcd.

The secondunderlying flow mcchanisms associatedwith die axial througliflow under he

compressor isc cobs. n theabsence f buoyancyefTectshis would bea dominantflow

mechanism.Thequestionaddresseds what cffcct theaxial cross low hason the flow within the

6



inter-disccavity. A shcar ayerexistsbetween hecross low passingover thecavity andtheair

within thecavity. 11crc is a need o know the levelsor heatand momentum ransrcracross his

shear ayer rrornthecross low to thecavity air and n termsora compressorhe transrcrof heat

andmomentumrom

theaxial througliflow underthedisc

cobs o theintcr-disc

cavities. In Chapter5a relatively simple flow, relevant o axial througliflow mechanisms considered.Comparison s

madewith I laugcnandDhanak's (1966]measurements.bcseworkerscarriedout an analyticaland

experimentalnvestigationaimedat describing he turbulentmomentum ransfermechanismn the

separationlow regionof a rectangularcavity racinganoncoming urbulentboundary ayer.The

chapterdescribes laugcnandDhanakexperimentsandthecomputationalCFD modelsused o

simulate heexperiments.The CFD resultshave beencompared o theexperimentalmeasurements

forcross

lowvelocity, pressures long thecavity walls andffic

flowpatternswithin thecavity.

Relevanceo thecompressor isccavity problemis thendiscussed nd mplications ror modelling

orthe cavity flow are considered.

Chapter looksattraditionaliniteelement asedhermalmodellingechniques.bcscarc applied

toa fully instrumentedesearchig attheUniversityof Sussex2001.Temperatureredictions

obtainedrom he hermalmodelusingCSt3blishcdorkingpracticesrccompared ithmeasured

temperatures.newnatural onvection eat ransrcr orrelationsalsocvaluitcd. 'lie rig testconsisted f an acccleration-dcccierationycleand hcrcrorche ransientemperaturesavebeen

measurednd he hermalmodels ttemptosimulateransientemperaturesswell as hesteady

stateemperatures.

In Chapter7a newtwo-dimensional 21))axisymnictricCFD-basedmodel is proposed or

buoyancy-drivcn lows. I'his is appliedto Kirkpatrick andBolin's [ 19861 tationaryenclosedcavity

experiment.The 2D axisymmetricCFD modelling approachs extended o rotatingcavities withaxial througliflow in Chapter8, and evaluatedusingtheUniversity or susscx estrig data.

Application of the2D axisymmctricCFD modelappliedto an enginecompressors thendescribed

in Chapter9.

In the final chapter,Chapter10,conclusions rom thework carried out to dateandfurther research

work will be discussed. his chapterwill describe he futurethinking of how thenew2D

axisyminctricCFD technique,modelling the two underlying flow mechanisms, anbeapplied

successfullyo link with a transient2D axisyminctric thennalmodel.7lic modelling will need o be

computationallyeconomicand easy o apply.

7



CHAPTER 2

REVIEW OFPREVIOUSWORK

2.1 Introduction

To gain anunderstandingof the fundamentalphysicsof thecomplexflow mechanismwithin the

inter-disccavities,the literaturereview will look at two flow mechanisms.Firstly thebuoyancy-

driven flow within an cncloscd otating disccavity and secondly hecffcct of axial throughflow or

thecross-flow through the borc or thecompressor n the flow within the intcr-disccavity.

Buoyancycflects, relevant o the intcr-disccavity flow. canbe brokendown into two further

categories,a stationarycncloscdcavity anda rotating encloscdcavity. Thesearcdiscussedn

sections2.2 and2.3 below. For thestationarycavity thedriving mechanismor the flow is

buoyancyunderthegravitational forcc.To achievc variousdegrees rbuoyancy differential heating

between hesurraccsor theenclosedcavity havc beenused.Naturalconvection n a rotatingcavity

is achievedby rotating thecavity about anoffset longitudinalaxis.At high rotationalspeeds,

centrifugal force dominatesover gravity andtemperature ifferences ead o ccntrirugally driven

natural convection.This is expected o show similarities to thegravitationaldriven convectionbut

will be modified by theCoriolis force in the rotatingcavity. Section2.4 reviewsthework carried

out investigating hecffcct thataxial througliflow hason the flow within thedisccavities.Different

numericalapproaches singComputationalFluid Dynamics CFD) to solvethese ypesof flows arc

discussedn section2.5. In section2.6 thework on thecross-flowovera stationarycavity is

reviewed.The chapter s completed n section2.7 by discussingpossiblemethodsof numerically

simulating these low typesby usinga steady low two-dimensionalaxisymnictricCFD model

modificd to capture he3D unsteady low cffccts.

S



2.2Natural ConvectionBuoyancyDriven Flowsmithin aStatlonaryCosity

2.2.1 lla)lclgh-llknard convection

Rayleigh-Bdnard onvection[Rayleigh 1916,Nnard 19011s thenaturalconvectionof hcat

between wo parallel horizontal platcsplaced n a gravitationalficId where he lower plate s heated

andtheupperplatecooled.For natural convection under gravity the Rayleighnumber s an

appropriatecharactcrisingparamctcr.Rayleighnumber,Ra, s dcrinedas

Ra- PrGr (2.1)

whcrePr s thePrandtlnumbcrdefinedas

Pr-pCpk

andGr isdicGrashof umbcrdcrincdas

IXT9Gr w2

(2.2)

(2.3)

I lolland ct al. [ 1975]rcportcdon theexperimentalmeasurementsor naturalconvectiveheat

transport hrougha horizontal layerof air, betweena heatedplateandanuppercooled plate,

coveringthe Rayleighnumberrangefrom sub-critical to 4x 106.Chandrasckhar1961 derivedthe

critical Rayleighnumber o be 1708.At Rayleighnumbersbelow this die fluid layer is stagnantand

theNusscltnumber s unity. r-orair a Nusseltnumberdependencehat is asymptotic o a 1/3power

on the Rayleighnumberasthe Rayleighnumberapproachesnfinity canbecorrelated rom the

combinedexperimentaldata from this testandfrom dataobtained rom GoldsteinandChu

(Rayleighnumberrange5x 103o Ix 10').

I folland ct al's experimentapparatus onsistedof two parallelcopperplates 560mmby 610mm

and I Omm hick) with theupperone cooledandthe lower oneheated o give a Icniperaturc

differenceof die orderof IOKbetween heplates. 'lic plateswere nserted nto a vacuum or

pressure) essel n which thepressure ould bevaried from 10 Pa o 700kPa.7lic plates%%,rc

spacedat 10mm,25mmand38mmapart.Measurementsf fluid tenipcraturcprorilc at high

9



Rayleighnumber showboundary-laycr ypestructures,with a nearly isothermal nnercore andhigh

temperature radientsclose o theboundarysurraccs.n their paper lolland ct al. useda conduction

laycr model to model the layeror stagnant luid next to theplatcs.Between heconducting ayers,

theinner core or the fluid was assumedo beperfectly mixed,dueto eddydiffusion, with the

temperature rofile beingapproximately hatobserved rom thedata.The following Nusseltnumber

correlationwas obtainedror air.

Air Nu - 1+ 1.44 1_1708

+Ra

Ra

] [(5830)1'3(2.4)

I lollandct al. cxtcndcdheEquation .4 oobtain he ollowingcorrclationornatural onvcction

in watcrby

%Vatcr. Nu = 1+ 1.44 1-1708

+Ra 1/3

-I +2.0[Rall'II401 (2.5)1

Ra

[(5830) 1"

In theaboveequations heexpressionsn brackets: J* ndicates hat irthe argument nsidethe

bracket s negative, hequantity is to betakenas zero.

Many otherauthorsgivc furthercorrelationsandror high Rayleighnumbers heproportionality of

Nusseltnumber o Ra'13s a good fit to cxpcrimcntaldata. For example,experimental

measurementsn the range3x 103< Ra< 7x 109arc well correlatedby anexpressionderivedby

GlobeandDropkin [19591, or theaverageNusscltnumber,

müdvm0.069Rall) Pro, 74 (2.6)

Grossmannand Lobse 2000] havederiveda systematic heory ror thescalingof tile Nussch

numberandor the Reynoldsnumber n strongRaylcigh.Wnard convection.Grossmann ndLobse

idcntiricd several egimes n the RayleighnumberversusPrandtlnumberphascspace,dcrinedby

whether heboundary ayersor thecorebulk flow dominate heglobal kinetic andthermal

dissipation,andby whether he thermalor thekinetic boundary ayer is thicker. I'lic theoryassumes

large-scaleconvection oll; Grossmann ndLolisecall this the 'wind of turbulence'and it is based

on thedynamicequationsboth in thebulk and n theboundary ayer. The theory is not applicable

ror very large lrandtl numbers or which theccll velocity 'wind' Reynoldsnumber s :550,where

10



thewhole flow is viscosity dominated.Also for very small Prandtlnumber n which tile Nusselt

numberattainsa valueor i, the theoryno longer holds. For large Rayleighnumber ile kinetic

boundary ayer becomesurbulent.BcyondtheturbulenceonsetGrossmannandLohscsaythe flow

is bulk dominated.7be theorydoesnot makeany statement bouthow the icat is transported rom

thebottomto tile top. i.e. Whethert is mainly through arge-scale onvective ransportor Mainly

transport hroughplumesrising from theheatedbottom. Both processesMay Contribute,asboth

create hermaland viscousdissipation.

Extending hework by FostcrandWallcr [1985],Asacd3andWatanabe1989] reportedon tile

small-scalestructureof freeconvectionat high llaylcigh number.which was nvestigatedby flow

visualization andtemperaturemeasurement.I'lic experimentalapparatus onsistedof a square

section ank.with sides900mm, n theplan view and700mindeep. 'lic sidcwalls andthe top wall

were nsulated,whilst thebottomwall could be heated.The top wall (or lid) wasplacedon the

surfaceof thewater.I'lic cxpcdmcnts werecarried out usingwaterwith depths angingfrom

I00mmto 150mm.The licat flux through thebottomwaskeptconstant hroughoutall testing.

Changing hewaterdepthaltcrcd the flux Rayleighnumber,Rar,dcrincdas,

Ra. - j7Fgd'1pCj) a2V (2.7)

whereF is theheatflux (W/m2)at time 1-1. which was obtained rom recordsof the temperature t

four different depthpositionswithin thewater,dcrincdasfollows,

F- pCp[T. (t.

+A' At-' + q, (2.8)21)

(t"

%%,ere T. is thetemperatureat waterdepth z. is the thicknessof the layerwhoseaverage

tcmpcraturc s represented y T., andqj is theconductionheat ossperunit time, which was found

to be less han0.5% of theheat nput.

77heranScof the flux Rayleighnumber n thecxpcrimcntswasfrom Ix 101-1xIOl . 111C

temperature istribution near hebottomwas measured singthreehorizontalsensors ositionedat

heightsof 2mm, 4mm and7mm from thebottomplateandanotherat tile Illid. depth.*ThCluid

motionnearthebottomwas visualized with suspended luminiuni particles lluminated by a vertical

or horizontal ight sheetandphotographed. lic velocity field was obtained rom the lengthof the

particlestreaksandtheexposure ime of thephotographs.n sonicexperiments ile temperaturewas

measured t mid depthusing a sensorattachedo theendof an L-sh3pcd od thatwasmoved

horizontally at 8.3mm/s.

II



Ile aim of AsacdaandWatanabe'sresearchwasto investigate hecharacteristicsof the thermal

behaviourandthento estimate heheat ransport ate from theconductionboundary ayer to the

interior core. licy determined hat thedominant rcaturcof the flow field was manyconvection

linesor 'shcct-likc plumes' consistingof several hermals,which transportbeat from theconduction

boundary ayer to thecoreregion.Ile authors oundthat theboundaryheatflux andthe fluid's

propertiesdetermined heaveragecharacteristics rthe tiicnnais, namciy.

* Ilic distance rom theboundarywhere he thermalsaregenerated ct

,f<1013) (2.9), d - 27.1Ra,, 0'3 (for 104< Ra

Theestimate fthe amountorheatransportedway rom heboundary ythermals

20-1112 flFg)V4

cx1.2 Y)2] 1.21 2

p _(1.2x

2

_(1.2lATg = 2.08(a(XI)

/2)

]cx

D/2cxp (772)

](2.10)

[

7- -

whereAT is the temperature xcessat theccntre of the thermalsover theaverageemperature

measuredar above hedescendinglow region.L is the longitudinal lengthscale,B is the

transverseengthscale,P is the time periodduring which thethermalwassupplied with theheated

nuid from theconductionboundary ayerand wherethecoefricicntsorx, y, andt arcdetermined

from thedefinitions orL, B andP, respectively,given below.

LId- 33.ORa..1/4

(ror 107< Raf< 1011)

B/d- 16.ORa., 114 (for 10' < Rq(< 1012) (2.12)

Pald2 -9. M., '112 (ror 10' <,Ra (2.13)y< 10")

Itis intercstingtonotc, FosterandWallcr[19851 andfrom tlicircxperimcntal rcsultscstimated he

thermal ime period in dimensionless orm to beMa,, "". only a small difference n theconstant

whencompared o Equation2.13.

* Theupward elocityof the luid in athcrtnal w,(mls)

IVI=,,2

Ra,, III I 2x 2

cx _(1.2y)2 cx _(1.2t

TO(X),

Cxp[-(L12)] P[ i-/d2-)

]

P[112

71icestimate f licat ransportedy the hcrmalswasalmostequal96%)orthat suppliedrom he

bottom. Icatsuppliedrom hebottom s firststoredn theconductionoundaryaycr,and hen

12



mostof it is transported o theupperregionby thermalsgenerated long convection ines in the

form of plumes. t is therefore mportantto modelthe thermalsaccurately.The remainingbeat

transfer allowing for losses n theexperimentapparatus)s through theviscous nteractionof the

core with die conductionboundary ayer.

2.2.2 Natural convection with healed side%valls

As for Rayleigh-136nardonvection.a bodyor i tcrature s availablefor convection n cavities with

heatedsidewalls.Examplesor this researcharcdescribedbelow.

PcngandDavidson[20011carried out a numerical nvestigationof turbulentnaturalconvection

flow (Ra- 1.58x Cý,a relatively low Rayleighnumber) n a confincdcavity with two diffcrcntially

heatedsidewallsby meansof largeeddy simulation(LES). The flow was cxpcrimcnt: lly idcntirjcd

by Tian [19971asbeingcharacterized y a relatively low turbulence evel andthcrtnal stratification.

No visible transitionwasdetectedn theboundary ayeralongthe hcatcd/coolcdvertical walls.A

dynamicsub-grid-scale SGS)model modificd for buoyancy low wasused n the simulation.Pcng

andDavidsoncompared heir numericalpredictions

with Tian's testdata.

The naturalconvection low experimentcarried out by Tian usedanair-fillcd cavity with relative

dimensionsof W- D/2, If - D/2 andD in thex, y andz (spanwisc)directions.The two opposite

vertical walls, locatedat x-0 (hot wall) and x-W (cold wall) were maintainedat constant

temperaturewith a temperature ifferenceorAT - 40 K, hot wall to cold wall. The Rayleigh

numberRa- (g 0 AT 113Pr)/v2was 1.58x109.7lic flow wascxpcrimcnt, 1ly dentificd asbeing

charactcriscdby low

turbulenceand no visible transitionwasdetectedn theboundary ayeralong

the icated/coolcdvertical walls. Thebottom (y - 0) andtop (y - 11)walls werehighly conducting

boundaries.Througha well controlled experimentalsct-up,Tian claimedthat thecavity producesa

2D mean low in themiddle sectionof thespanwisedirection(at z- D/2), whcrc themeasurements

hadbeenmade.Thermocouplemeasurements ere obtained or theair temperaturen thecavity.

Two-dimensional LDA wasusedror velocity measurements.

In flic LESsimulationa

finemeshwas usedclose o

thehot/coldvertical walls andnear o the top

andbottomwith 12-13nodesclusteredwithin thenearwall distance,Y"(-Puty/p) < 10.No-slip and

adiabaticwall conditionswere used or thespanwisewalls. The time stepused n thecomputation

13



wasAt - 0.0 131o,whereto-II/ q(g 0 AT 11).The resultsfrom the LES simulationwith tile

dynamicSGSmodel(mean low streamlinesn thex-y plane)showthatwithin thecavity several

circulating flow regions exist away from thencar-wall boundary ayer flows. Therecxist several

smallercirculations(orrolls) next

to thewall

flows thatarccomparativelystrong.

With increasing

Rayleighnumbers, heboundary ayer flow maybemore ntensiveandthencighbouring rolls could

beexpected o mergewith eachother to ronn a largecirculating motion around ile core.Pcngand

Davidsonconcluded hat tile LES simulation is ableto reasonablyeproduceheglobal mean low

andthermalficld, as validated in theexperiment.ThedynamicSGSmodel is ableto yield mean

flow quantities hatagreewith the measured ata,however herearc somediscrepanciesn the

prediction of turbulence,particularly in theouter regionof thencar-wall flow where heboundary

layer interactswith thecirculating core region.Pcngand

Davidsonshowed hat the timc-avcragcd

contribution of theSGSshcar stresss significantly smaller han ts resolvablecounterpart,which

illustrates hat thesub-gdd scale urbulenttransport s a secondary ffcct. The mostvisible SGS

contribution is not in thevicinity of thewall but in the regionabout hemaximum velocity in the

boundarylaycr. In theviscous/conductivcsub-laycrorthc boundary aycrclosc to the

licated1cooledertical walls the flow tends o form strcak-likc structures,which do not however

emergen the ncar-wall flow alongthe horizontal top andbottomwalls, whereflow tends o be rc-

laminarizcd.

2.2.3Nllycd horizontal and vertIcal convecilon

Obviously, practical problems may include both vertical and horizontal thermal gradicnts,

combining the types or flows discussed in sections 2.2.1 and 2.2.2 above. I lerc the results from

Kirkpatrick and Bohn's [ 19861studies which include a varicty of heating configurations (and is

particular relevant to the present work) arc discussed.

14



Mixedcavity naturalconvoction

Lucits and wall,2 oach

Cooling/healing

plaie, 4 each

Test cell welt 4 each

L-11CM8119O(Iod Coll

$I

I kpMnwfoTow ConlIguivoitons

rýlir

-ýcj-cIf

rc

If 11 if

lic 1111cc Ilcxr 111111C

Figure 2.1Schematicor file test cell usedIn tile Kirkpatrick and Bolln experiments and tilefour experimental test configurations 119861

KirkpatrickandBohnperformedncxpcrimentil nvestigationn high Rayleigh umber atural

convection ithin acubewith four difTercntonfigurationsrdiffercritiallyheated ndcooled

verticalandhorizontal urfaces. schematicrthe testca and he estconfigurationsreshownn

Figure2.1.All theconfigurations erevariations r theheatingrom belowcase. heexperiments

conducted ere odetermine ussclt-llaylcigh umber orrelationsnd odeterminehe low

patternsnd emperatureistributions. he ourconfigurationsestedwere:

" Heatedbottomandcooled op and conductingsidewalls, IIC case

" licatcd bottomand cooledtop with oneheatedandonecooledside wall, 1111CCase

" Heatedbottomand cooling from abovewith two cooledside walls, IICCC case

"I lot andcold sidewallwithaheatcd ottomandhcatcdop, II If ICcase

Ilie cubicalenclosurehadan interior dimensionof 305mm.Theworking fluid used n testswas

dcioniscdwater. lic temperature ifTercntialchosenn thedefinition of theRayleighnumberwasdic temperature ifferencebetween hehot andcold walls. Temperaturemeasurementsn the

enclosurecoreweremadeusinga thcrmocoupIcprobe.which couldbe moved vertically androtatcd

is



aboutheccntrc ineof thecubicalenclosure.'lic probe ouldnotbeplaced loserhan8mm rom

the opandbottomsurfaces.he engthscaleusedwas he nteriordimension rthc cube,305mm.

Theheat ransfermeasurementsill beexaminedirst,rollowcdbyadescriptionof tile flow

patternsobserved or the four testcasesand finally the fluid temperature istributionswill be

discussed.

2.23.1 Heat transfer measurements

It mustbenotedthat thetemperatureused n thedcrinition orthe Nusseltnumber s thedifference

bctwccn hewall temperature ndthebulk fluid temperature. be experimentallyderivedaverage

Nussclt-Raylcighnumber icat transrcrcorrelations or each estconfiguration were:

HCcase

Nu-0.09861ta"3 forTopandBottomwalls (2.15)

HHCCcase

Nu - 1.10Rai0.236 for Top andBottomwalls (2.16)

Nu - 0.141Raho-313or Sidewalls (2.17)

HCCCcase

Nu-0.3461tao, 285 for Top, BottomandSidewalls (2.18)

HHHCcase

Nu - 0.223 Ra, " for Top wall (2.19)

Nu - 2.54 ltalo,212 for Bottom wall (2.20)

Nu - 0.233 RahO,86 for Side walls (2.21)

71c I ICcase howedhat hecxpcrimcntallyerived icat ransfer orrelation, quation .13,

compares ell with I follandct al.s [ 1975] onduction-laycrodelequation, amcly

Nu- 0.103 ta113

(2.22)

At this point it is worth comparingKirkpatrick andBohn'shcat ransrcrcorrclationswith those

corrcl3tionsdcrivcd by othcr authors.Thecorrclationscanbecornp3rcdo thestandardand

16



gcncrally scdmcanicat ransfcr orrclationsor natural onvcctionromahorizontal latcand

froma vcrlical platc.

Forahorizontalplateof lengthL, Fislicndcn ndSaundcrs19501orrelation's rc;

NULm0.54 Rk 1/4 105< Ra< 2x 107 (2.23)

NUL- 0.14 ROL3 2x 107< Ra< 3x 1010 (2.24)

andfor a vcrtical piate or licight L, Wcisc [19351andSaundcrs1936] corrclation's are;

NUL 0.59Rk 114104 Ra< 109 (2.25)

NULm0.13ROL 113 109 < Ita< 10 (2.26)

Also Jakob[19491dcrivcd the following corrclations or naturalconvcction n an cncloscd

horizontal irspacc;

Nux - 0.21 Ra 1/4 104< Ra< 3.2x101 (2.27)

Nux - 0.075Ra113

3.2x103< Ra< 107(2.28)

and oran cnclosedcrticalair spacc;

Nux - 0.2 (Ux)*"v Ra." 2x104< Ita < 2.1x 105 (2.29)

Nux - 0.071(Ux)*"9 Ra113 2.1x 105< Ra< 1.1 W (2.30)

wherc x is the clearancc bctwccn the platcs, L is the platc Icngth, and the imperaiurc diffcrcnce isdefincd as the diffcrcncc in the metal tenipcraturcs orthe two plaics.

FislicndcnandSaunders orrelationshavemultiplying factors hatare approximately wice the

factors or theJakob'scorrelations or botha horizontalplateanda vertical plate in freespace,but

thedefinition of the temperature ifference s not thesame.For die enclosed avitiesthe

temperature ifference between he two walls is used,whilst thewall to bulk air temperatures used

for theplate correlations, his will account or most of thechange n themultiplying factors.The

Kirkpatrick andBolin correlations or an enclosedcavity showtheRayleighnumberpower to lay

between lic values0.25and0.333which appear n theabovecorrelations.No disccmabicpattern

17



for themultiplying actorcanbeobserved hencomparingheenclosed avitycorrelationso the

freespace erticalandhorizontal latecorrelations.

2.2.3.2Flow patterns

KirkpatrickandBolinuseda shadowgraphoshow he lowpatternwithinIlic cube.Tbcir

observationsrcsuminariscdelow.

HC case

Thermals osefrom thebottom surfaceandfall from thetop surf3cc.The thermalswere of varying

characteristicsizes,averagingabout I Onim n heightand5mm in width. No overall flow pattern

wasdisccmablc,other thanthe mixing motion of thethcrinals.The thermalsappearedo bereleased

periodicaly from the top of a boundary ayerabout Inini away from the surfaceand propagateat

about50mm/s.Only the largethermalswere ableto penetrateo theoppositesideortic cavity. nc

thermalsusuallymoved at sonic randomangle, ess han45* to thevertical.

HHCCcase

Tbcrewasan nteraction roic thcmialsand heboundaryayer,with tile thermalshinedbytile

sidcwallboundary 3ycrsntotriangularegionsn theupper oldwall tocoldwall comerand o the

lowerhotwall tohotwall comeror tilecavity.KirkpatrickandBohn eport hat ileoverall low

pattern nd heconvection f the hermalswerealong heperimeter r tileenclosuren a clockwise

direction,wlicnviewedwith thehotsidewallontheMI. I'licrmalscausedheboundaryayer o

separatetsomepointalong hehorizontalraverse. irkpatrickandBolmnotedhat hevertical

andhorizontalNussclt

numbers erevery closeo the imitingcases, nd nferredhat he hcrmil

interactionsaveonly asmalleffectontheoverallheat ransrcrrom hesurfaces.

HCCCcase

*nIeoverall flow patternwasa centralplurne rising from thehot lower surracc,which divergedat

the top of thecavity and returnedalongthecold sidewalls.The rising thennalswere ocatednear

thecentrcorthc tankandthe falling thmnals wcrc locatednear hecold sidcwalls.77he atureor

thethennalconvectionon the sidewalls wasa rnixcd freeandrorcedconvection ype,which

18



explainedwhytheNusscltnumbers erehigher or thiscasehan or theothercases. hesidcwallheatransfersapproximatelyqualo thevcnicalheat ransfer.

HHHCcase

KirkpatrickandBolinobservedhat hcrcwasvery ittle activity n thecoreof thecavity,especially

nearhe opsurface.'lic motionof the hermalswasconfinedowithin I Ornm f theheated ottom

plate.Boundaryayerswerepresent nthesidcwalls, utnotalong hctopsurface. emperature

stratificationn thecoreoccurred ue otheheatedopplate. 'lic low licat ransferrom he op

surfacesdue o thestable tratificationn thecore.whichalso educeshesidcwallheat ransfer.

2.2.3.3Temperature distribution

I'lic temperature istributionsmeasured y Kirkpatrick andBolin showed he thermals ising from

thehot bottomandfailing from the top of the testcell. The I IC configuration showed hemost

regular hermaldisturbanceorthe fluid from a baseline emperature,with otherconfigurations

beingmore rregular.For the I IC case hemagnitudeof thetemperature isturbancewas of the

orderor IK andperiodor theorderof 4s. hican temperature istributions n thevertical mid-planc

orthe cavity for the IIC, 111CC andI ICCC configurations showed hecorefluid temperatureo be

within 0.5K of thebulk temperature bulk temperature- arcweightedaverageemperature f the

heatedandcooledwall temperatures). or the 11111C casewhere hetop is heatedhecore fluid

temperaturewas within 4K,of thebulk temperature.The resultsof the I fill IC caseshowed hata

nonzerovertical Rayleighnumber,Rah or temperature ifferencebetween op andbottom)was

required o producea &-stratified coreandthe thermalsdid not act as a mixing mechanismor the

core n this case.Both the I IC andIII [CC mean emperature rofiles showa small temperature

reversal,near he top andbottomsurfaces,attributed o thepersistence f the thermals raversing

across hc enclosure.

Resultsrom nvestigatinghe nfluenceof differentverticalRayleigh umbersnthecore

temperatureistributionshowcdhat or the if ICCcase, s hcverticalRayleigh umber%vas

increased,he evelorcorctemperaturetratificationwasdccrcascd. irkpatrickandBohnalso

showcdhat heonsetof stratificationwassudden, t a Rai, rabout0.65x1010.s the einpcrature

19



of die bottomwas ncreasedhe ormation f thermals ecameigorous nougho causemixing n

thecoreof thecavity.

2.23.4 Conclusions

Kirkpatrick andBolin concluded hatgenerallytheheated loor promote$mixing in thecavity and

tends o eliminatethe stratificationseen n the limiting caseof a horizontaltemperature ifference

alone.Although the temperature isturbances ssociatedwith thermalsappearedo persist or only a

smalldistance rom thehorizontalsurfaces,he thcrtnalsarccffcctivc in mixing tile core fluid. For

thevertical temperature ifferencecase heonly fluid motion in tile cavity wasthatdueto tile

thermals.17he eat ransfer rom theheated loor compared avourablyto a conduction-laycrmodel.

For thehorizontal temperature ifferencecase herewas rotationof the fluid core with a horizontal

velocity component o the thermals.The heat ransferfrom thehorizontalsurfaceswasnot strongly

affectedby thepresence f a horizontaltemperature ifTcrcncc;however he thermalsdid affect the

heat ransfer rom tile vertical surfaces. [cat transferfrom thevertical surfaceswas reduced f the

top washeated,dueto thestablestratification in the top portion of thecavity core.

I'lic KirkpatrickandBohnexperiment ill berevisitedn Chapter where3DCFDan3lyscs ill be

comparedo theexperimentalata.

2.3Convection Flow %illhin a Rotating Enclosed Cas-Ify

I ligh Rayleighnumbernaturalconvectionundercentrifugalaccelerationhas beenstudied

cxperimentally andcomputationallyat AachenUniversity. Bohnct al [1993,1994] reported

experimentalnvestigations or threerotatingcavity geometries.To achievea centripetalor radial

beat lux insidetheannularcavitiestheouter radii cylindrical wall washeatedandthe inner radii

cylindrical wall cooled.Both end surraccsor theannulus discs)werethermally insulated.Two or

theconfigurations, abelledA and11, Figure2.2) wcrc for closedannuli rotatingaround heir

horizontalaxis.The radius of the innercylindrical wall (ri- I25mm)andthewidth (s- I 20mm)or

theannularcavity was

thesame

or both theseconfigurations.

ForgeometryA theouter cylindrical

wall radius was rý-335rnm,and for geometryB rrMmm. The third cavity configuration,C, had

thesamedimensionsasfor 11, ut 8 radialwalls (all thermally insulated)divided theannulus nto

20



45*segments.he est ig hada maximumotorspeed f 3500 cvhninandamaximum avity

pressurer4 bar.The cnipcraturcf theoutercylindricalwall couldbevariedupto I00"C,whilst

the nnercylindricalwall couldbecooledo 15*C n thesununcr nd o 8*C n thewinter.

11

A

C

Cavity

A

11

C

ri

ri ro r. H Hirm a0

(mm) (mm) (mm) (mm) (-) (mm) (-)

125 355 240 230 0.96 120

125 240 182.5 115 0.63 120

125 240 182.5 115 0.63 120 45"

Figure 2.2 Dimcnilons of the annular cas, 11csor three experimental test configurations.

Usingthemeasured verall heat ransferBohnct al wereableto derivea Nusscltnumber

correlationfor each estconfiguration.71c temperature ifTcrcncc,AT. used n thedcrinition orGrashofnumber s thetemperature etween hehot andcoldcylindrical walls. The resultsmaybe

summariscdasfollows.

21



ConfigurationA, (I I/r,. - 0.96ands/r. - 0-5)

Nu - 0.246 Ra+ .221 1xI Ol< Ra#< x 1012 (2.31)

Configuration 11,11 r. - 0.63ands/r. - 0.66)

Nu - 0.317Ra#0*211 IxI 0'? Ra#< x 1012 (2.32)

Configuration C, (I I/r., - 0.96,s/r,,, - 0.5and45* scctor)

Nu- 0.365 la#'O-13 1x 107< Ra4< IXIO12 (2.33)

where herotationalRayleighnumber,Ra#- Gr Pr,andtherotationalGrashofnumber,Gr#- r. w2

ATL3P2/(T. p2) with L- 11,r. -(ri+ r.)12andtheNusscltnumbcris dcrincdas NU-414A

where 4 is theheat lux and4, is thc licat transferby conductionalone.

Comparing the results for configuration A widi configuration 1)shows that the change in geometry

hasonly a weak influence on the licat transfer in the rotating annulus. 11c insertion orthc

separation walls, as for configuration C, attenuates the relative circumfcrcntial velocity inside the

cavity, resulting in a decreaseorthe radial component ortim Coriolis force. The natural convection

flow inside the cavity is strcngtlicncd so the heat transfcr is increased. Comparing the results from

Configuration C to those from B confirmed the increase in licat transfer for the separatedwall sector

cavity.

In addition to theexperimentalwork, Bohnct al also carriedout a numerical simulation(CFD

analysis) or thesectoredannulusgeometry,configurationC. Both steadyandunsteadyhree.

dimensionalanalyseswereperfornicd usinga coarsemesh.All computations%%-crcarriedout with

thedensitycalculatedby the idealgas aw andthe flow wasassumedo be laminar, .e. Direct

NumericalSimulation(DNS) - like solutionswhcrethe full Navicr-Stokcsequationsarc solved

directly. Ilicir steadysolutionsshowcd hat the flow insidethesegmentwas confincd to the

boundary ayerson thecylindrical and radial walls with virtually no relative motion in thecore.The

corewasvirtually isothcrmal(with T z:1/2(TI+Tc))with noconductionoccurringin theradialor

22



circumrcrcntialdirection. I lcat transrcrwas confincd to theboundary ayers.77he redicted low is

illustratedschematically n Figure2.3.77hehot fluid that flows radially inwardcreatesa large

Nusseltnumber near ct - 0' on thecold surface,andthecold fluid that flows radially outwards

createsa

largeNusscltnumbernear ct -

45'on the

hotsurface.

Thcrcrorc. there sa

large

circurnrcrcntialvariation in the local Nusscltnumberson thecylindrical surfaces.Results rom the

steadycomputationalanalysisor thesectoredcavity showed heconvectiveheat ransrcr o be

consistentwith, but slightly greater han theexperimental esultswith differencesoraround 8 %.

Theauthorsattributedmostorthc differenceto heat ossesn theexperimentwith the losses

through he insulateddiscsestimated o be between10%and20%of theheatsupplied.711c

unsteady omputationalanalysisshowed he flow to beunstablewith the Nusscltnumbersshowing

a stochasticbehaviour.

FurtherCFD studieshavebeenmade or these ypesof caviticsandwill be discussed ater in

section2.4.

I ot outcrcylindricalsurface, i,

Adiabatic

radialwall45*)

..

of

0000

IsothennaloreT -- V2(Til+Tc)

Adiibatic

(ctradiit wall

%1(a - 0)

%«...

- M.,«b

1

%, 0wo

Ni

V001-INCold nner

cylindrical surfacc,TC

rigure 2.3Schematic dIagram or computed flow In a scaled45' segmentof a rotating cavity

%%khradial heat flow (in the r-a planc) lCouricsy O"cn and Rogers119951

Bohnct al. [1994] alsoused heAachen ig to investigate hepureaxially directedheatflux case,

whereonedisc side wall is hot andtheoppositedisc is cold andall other walls thmnally insulated.

Only configuration11was consideredn the investigation. n addition to theexperimentalwork

r

23



numcricalalculations crealsoconductcd.hederivcd icat ransfcr orrclationrom he cstdata

for thisconfigurationwas,

Nu - 0.364 Rz40.124 2x)0%< Ra< 5x 1010 (2.34)

Conclusions drawn frorn the axial heat flux work were th3t the numerical and experimental data

were in quite good agreement, with exception of high Ita-riumbers, %%,ere the numerical analysis

predicted higher heat transfer than the experiments showed. 77heheat transrcr ror the axial heat flux

case is much smaller than that ror the radial directed heat flux case.Comparison of the level orhcat

transfer between the pure radial and pure axial directed heat flux cases shows that the radial heat

transrcr is the important mechanism for cavities with the combination oraxial and radial

temperature distributions that occur in gas turbine compressor disc cavities.

Bohnct al's experiment ill berevisitedn Chapter %%,ere urther3D CFDanalyses, ith various

Rayleigh umbers, ill becomparedotheexperimentalata.

2.4 Rotating Ca%ty%s

th Axial Througitnow

2.4.1 SingIc ca%ly Investigations

As noted in Ch3pler 1. the flow in the inter-disc cavities becomes highly complex when the discs

arc heated with the flow becoming three-dimensional and time dependent.71is complexity of the

flow has been revealed by a number orcxpcrimcntal studies. much orthe published work originates

from the University orSusscx. For example, Farthing ct al [19921 pcrrormcd an experiment to

investigate the flow inside a simple rectangular rotating cavity with a central axial througliflow.

2.4.1.1hotlicrnial flow

Farthingct al. s [19921simplemodel ora rotatingcavity with axial throughtlow is shown n Figure

2.4.Two discsoroutcr radius,b, and inner radius,a, areseparated y anaxial gap,S.17herotational

speedor thecavity is n, the flow rotational speeds toandthebulk averageaxial velocity orthc

axial throughtlow is W. Fora fluid kinematicviscosityv, therotationalReynoldsnumber s dermcd

asRe. -0 b2 v, andtheaxial ReynoldsnumberasRe,-W di, v, wheredh s thehydraulic

24



diameteror oic inlct. For a cavity with an innerdrive shail or radius, r. dh- 2(a. r') and for one

without an inner drive shaft,dh- 2a.

I Stroud I

I Down*"ancisC

rigure 2.4 Nomenclature for axial throughtlow and Isothermal flow structurc. (I'arthing ct al)

A further non-dimcnsional parameter, the Rossby number, Ro links the effects of rotation and

inertia of the axial througliflow. This is defined as the ratio or the incan velocity of the throughflow

to the tangential velocity at the borc radius;

ROM

V/04M

PRc.

,1

(2.35)j2a(a-rjRc

Laser llumination flow visualisationandLaser Doppler Ancmomctry(LDA) wereusedby Farthing

ct al. [19921 o studythe flow structure n unheatedor isothermal)andheatedcavitieswith a/b

0.1. A seriesof schematicdiagramsof the isothcrmal low structure s shown n Figure2.5. I'lic

principal parameters fTccting he resultingflow arc the Rossbynumber,Ro,andthegapratio, G

Vb. For no rotation,Ro- co, he througliflow generates neor more(dependingon gapratio)

axisymmctrictoroidal vortices.Rotation has hecffcct or suppressinghe toroidal vortexand

dcstabilising hecentralthrougliflow, creatinga changen behaviourof thecentral et. This is

charactcriscdby a numberorrcgimcs oraxisyrnnictric andnon-axisymmctricvortex breakdown.

25



Gm0.533

(1) (1) (ill)Ga0.267

(IV) (V)

(1) (9) Pv)(d) Go 0.133

(v)

(1) (il) (iii) (iv) MRo (stationary) 25 421

(Shadedareas representregionsIntowhichsmokeIsconvectedrapidly.

11-1gure.5 Visual Impressionsof smokepatterns In an Isothermal rotating mity %%khxialthrougliflow: Re. - 5000(I'arthing ct al. 119921)

26



For urbulentlow (Rc,> 2000)and ora constant ap atio ourscparatecgimcsof voricx

brcakdownwere dentifiedas heRossby umbers decreasedfromaround100 oa valueof less

than1).Theseweregiven lic followingnamesin orderof decreasingossby umber):Modc Ia

(21:5Ro:5 100),Nfodc2a(2.6:5 Ro:52 1).Modc Ib (1.5:5 Ro:52.6)andModc 2b(Ro:5 1.5).Fora

gap atioof G-0.533, thercspcctivc oundariesf theseegimes ccuratRo= 21-23,2.6and1.5.

TheMode regimes rcassociatedith anon-axisymmctricchaviour f thecentralhrougliflow;

Modc2 behavioursassociatedithaxisymmetricehaviour. ecreasinghegap atioappearso

suppresshe ormationof Modc a behaviour. urther ctailsorthe testsanddescription f the

modes f instabilityaregivenbyOwenandPincombe1979]andby OwenandRogcrs1995).

2.4.1.2Nonisothernial flow

When the cavity is heated, the Sussex research has indicated that significantly more of the

throughflow penetrates into the outer part of the cavity. Most observations of tile heated now

structure were made with gap ratios of G-0.124 and 0.267, and a surface temperature distribution

that decreaseswith radius. It was found that this gave a clearly defincd flow structure. Long and

Tuckcr [I 994a] found that the flow structure inside the cavity is heavily influenced by the radial

distribution or surface temperature imposed on the discs. Flow entered the cavity in one or more

radial arms, bifurcated near the outer radius forming one or more pairs orcirculations in the radial-

circumferential, r-O plane. A schematic diagram, in the r-O plane, of the heated flow structure is

shown in Figure 2.6. One circulation rotated in the samedirection as the discs, called the cyclonic

region; the other circulation rotated in the opposite direction, which is called the anticyclonic

region. Under most conditions the regions orcirculations did not merge but were separatedby a

region in which the fluid did not appear to enter. The cyclonic region has a lower pressure than that

of the anticyclonic region. In the experiment with a surrace temperature distribution that increases

with radius it was not possible to obtain clear visual or photographic evidence of the flow structure

in the cavity. I Iowcvcr the overall impression was that significantly more of the central througliflow

penetrated the cavity, the higher velocities leading to an ill-defined flow structure especially in the

region adjacent to the peripheral shroud. These difTercnccs in flow structure may be qualitatively

explained from consideration of thermal stratification in a centrifugal rorce field. A fluid

temperature that decreases

with radiushas

a stable stratification,whilst a fluid temperature that

increaseswith radius has an unstable stratification. resulting in incrcaicd radial mixing. It appears

that heating the cavity introduces buoyancy forces that act to dcstabilise the central througliflow.

27



Farthing 1988] found that whenonly theshroud washeatedasimilar flow structure o one

mentionedaboveoccurs, cxccpt therewere multiple radial arms and multiple separation ones.

When both theshroudandthediscswereheated, hesame low structureas for theheatedshroud

wasobserved.T`hcseadial arms appear o exchange luid with thestrong cyclonic flow adj3cent o

theshroud.The cntirc flow within thecavity routes at an averageangularvelocity, w, which is

foundto vary with thedisc gap ratio (axial distancebct%%,cn thediscsto thecavity outer radius).

and s different from (1, theangularspeedorthc cavity. Carcrulexaminationof high-speed ideo

recordingswas used o determine heratio co/fl, and t was found that0.9 < (,A) <I for the Rossby

number,Ro-%V/fla,regionof 0.57< Ro < 9.2.

I

rigurc 2.6Schematic diagram of llic heated flow structurc In r4 plane

Farthingct al (1992)measuredheheat ransrcrrroin thediscsora cavity with a/b- 0.1 andG -s/b

- 0.138. 'licy roundthat for symmetricallyheadeddiscs,where he level andradialdistribution or

temperatures the same, heheat ransferwasthesameon eachdisc, implying symmetryorthe

flow in themidaxial plane.For asyninictricallyheateddiscs, heheat ransferon thecold disc was

round o be lower thantheheat ransferon thehot disc.The radial temperature istributionalsohad

a significantcffcct on the local heat ransfer.The radial variationorthe heat ransferrallowcd the

28



discsurfaceemperatureistribution.Forasurfaceemperaturehat ncreasedwith radius,heat

transfcr lso ncreasedndvice versa.From heheat ransrcrestdata,Farthing ta].derivedhe

followingheat ransfcr orrelationor adiscsurfaceemperatureistributionwherehe cmpcraturc

increases

withdisc

radius:Nis 0.0054Rc*,3Gr*-'s

%%-hcrcr = 112rl7(T,- T,,,Xb- r)' v2 ,

T, is thc disc tempcraturcand Ti. is thc inIct fluid

tcmperaturc.

xr.._q(b-

A.T,- TOT94

Theabovc orrclationEquation .36a analsobcexprcsscds,

(2.36a)

Nu - 0.0054Rclo" Rco'12PAT)" (rl bX(bl r) - 1)"" (2.36b)

%%,crc heNusscltnumbcr,Nu=qr

!-AT

Thesignificanceof Equation2.36 is that it suggestshe flow and icat transfer n the(narrowG-

0.138)cavity occursas

aresultof rotationally

induced aminarrrccconvection.71is is supportedby

thework or Long andTucker [1992,1994b], who reportedon licat transrcrmeasurementsrom the

Shroudtscir(ror a/b - 0.1 and s/b- 0.13). Tlicy notedthat thedisc surface emperature istribution

appearso have ittle cffcct on theshroud icat transrcr,providing thecavity air temperatures used

asthercrcrcncctemperature o define theNusscltandGrastiornumbers.The measured hroud icat

transrcr s then in reasonable greementwith the licat transrcrpredictedusingan established

correlationror natural convectionrroin a horizontalsurracc.Tlicse findingsarcalsoconfirmcd in

themultiple cavity

investigationsof

Longct al.

(2003]and

Long ct al. [2006]. The licat transfer

from a cavity with a wider gap ratio (G - 0.36,alb = 0.1) was nvestigatedby Long (19941.

Increasinghegap ratio wasroundto increasehelicat transrcr. n the range4< Ro< 5, therewas a

significant increaseby a factoror 3; ror Ro < 4, theresultswereapproximately heSallie; or Ro>

5. therewas a smaller ncreaseby a factoror2 in Nusscltnumberwith gapratio.Two mechanisms

were dentified asbeingresponsible or the licat transrer, otationally inducedbuoyancyanddirect

influenceor thecentralthrougliflow.

TuckerandLong (1998]carriedout furthercxpcrimcntalwork, aiming to measurehe temperature

field insidea rotating cavity. Tlic cavity used n theexperimentconsistedof two steel lat faced

29



discswithan nnerradiusa-48.5mmandouter adius, -484.5mm ndseparatedyadistance,

s-65mm.Tlicscdimensionscorrespondogap atio,G-s/b,of 0.13andan nlct radius atioa/bof

0.1.Theperipheralhroudwasmaderomacarbon-fibre poxy esincomposite. ach avitydisc

was ittedwith5 separatennular .8kW heaters,nabling ontrolof

theadial

distributionr

temperature.heshroud ouldalsobe heated ia anelectrical eater ystem. he nner acesorthe

discswerecoveredwith Imm hickglassibre nstrumentationatsowhichapproximately0

thermocoupleseremounted.lic cavityair temperatureasmeasuredsingaprobe onsisting f

threehermocouplesositioned tthenon-dimcnsionaladial ocations,/b-0.37,0.6and0.87and

theprobewasplaced alfwayalong hecavity at s/2.Tbrccdiscsurraccemperatureonditions

wereconsidered;isc emperaturencrc3singwith radiusandunheatedhroud, isc emperature

decreasingith radiusandunheatedhroud, ndunheated

iscswitha

heatedshroud.

`hcschree

conditionsepresent ngine onditions,ollowingan acceleration,ollowingadecelerationand

during heengine cceleration,espectively.uckerandLong'sexperimentalnvestigationhowed

againhat hecavityradialandcircumrcrcntialemperatureistributions erebothstrongly

influenced ycavitysurfaceemperatures.henhediscswereheated, ignificant ircumferential

cavityair temperatureariationswereobserved,howinghe low tobe hree-dimensional.Vhcn

theshrouds heated nd hediscsunheated,ocircumrcrcntialemperatureariationswere

observed.ests

wereconductedoveringarange f rotationalReynolds

umbers401:

5Rc#:

8x 105 ndaxialReynolds umbersx101: Rc,:S4x 104 nd mportantly howedhatboth he

rotational ndaxialReynolds umbersad ittle cffcct onthecavityair temperatureistributions.

Temperatureime raceswereusedo infcr that heangular elocity atio WO0, w arc hecavity

and luidangular elocities,espectively)s inverselyproportionalo theparameter AT., which

isconsistent ithprevious IDAmeasurementsy Farthing tal [1992].1 cre0 is tile fluid thermal

expansionactor -I /Ti.,Ti. is the nlctair temperature)ndAT.,, - Tn.. - TI.whereT.., is the

maximum avitysurfaceemperature.

Results rom a numericalCFD 31),unsteady low analysisby Tuckcr [19931showcdqualitativc

agreementwith thevisualisationresults n predictionorthe flow structures cfcffcd to earlier.For

thediscand shroud icat transferTuckcr showed hat thederived ocal Nusscltnumbers Nu -qL

AT k) agreed easonablewell with themeasured eat ransferdataand with theFarthingct al.

correlation.

OwenandPowell 20041made elocityand icat ransfermeasurementsn a singlecavity esearch

rig with centralnletandexit,a/b-0.4, s/b-0.2 with ust thedownstreamischeated. ests

30



were carried out for 4xIO5< Re#<3.2x 106and lAx I 01<11c, <5404.7lictimc-average LDA

measurements of tangential velocity showed that near to solid body rotation occurs in the cavity.

0.96 <w/ 11r< 0.99, when the downstream disc was heated to 75K above the inlet air temperature,

for the range of dinicnsionlcss radii 0.67 < r/b < 0.97. The radial velocity was found to be

approxinutcly two orders of magnitude smaller than the tangential velocity. 71c timc-avcrage

tangential velocity was also found to increase above w/ 11r-I when the temperature between the

disc surfaces and the inlet air was reduced to below approximatcly 40K. A spectral analysis of the

velocity measurements revealed behaviour that was consistent with one, two or three pairs or

cyclonic and anticyclonic vortices in the flow ficid.

2.4.2,%Iultlplccavity Investigations

An earlier studycarried out on an enginerepresentative eometrywasreportedby Burkhardtct al.

[ 1994). 'licir experimental ig comprised ive cavities with all thediscshavinga commonbore

radii with G-0.256 anda/b -0.286, andtestswere carriedout for rotationaland axial Reynolds

numbers1.9x106: Rc#:55.6x106and2.7x104: Rc,:59.5x104.1cat transrcrresultswereobtained

using measured urracc cinpcraturcsanda conductionsolutionmethod.'lic

testrig also carried acentraldrive shafý which could bc made o rotate n eitherdirection.The licat transrcr roin the

discswasroundto increasewhcn therotational speedor ti,c shaftapproachedhator thediscs.For

thecentraland outer part of thediscstherewasreasonable greement etween hemeasuredocal

Nusscltnumbersandthosepredictedby the Farthingct al correlation,Equation.2.36.

2.4.2.1SussexUTC multiple ca%-I(yig build I ciperlinental Invest gnIons

Furtherexperimentalwork wascarriedout by Alcxiou [2000], to investigate he[teat ransferand

flow physicswithin the intcr-disccavitiesOra gas urbinecompressorwith axial througliflow.

Alcxiou derived icat transfercorrelations rom cxpcrimcnial testdatafrom theSussexUTC

Multiple Cavity Rig (NICR)Build 1. A generalassemblydrawing for this rig is shown n Figure

2.7.The rotor and nner si,an or therig represent artOro 11 compressornternalair systemand

werescaleddown from a Rolls-RoyceTrent acro-cnginc, o a ratio orO.7:1. Temperaturemeasurements ere obtained rom thedrive concanddiscsurfaces.A conductionsolutionmethod

usingthemeasured urface emperatures sboundaryconditionswasthenused o estirnatc heheat

31



transfer rom both thesurfaceorthc rig coneandrrom thesurraccortlic disc. Alcxiou roundthat

themeasurementsrom theoutcr surraccor thecone were n reasonable greementwith the

theoreticalpredictionsror theheat ransrer rom a rrcccone n turbulent flow. I [cat transrcr

measurementsrom the inner surraceof thecone revealed wo regimesof heat ransrcr.Depending

on thevaluesor Ro/(pAT,,j)"2, theheat ransrcrwould eitherbedominatedby rotation at a low

value,Ro/(PAT.,&)"2<6 or by through-flow effects at a high value,Ro/(PAT.,, 112 6. In the

rotationallydominated egime, heshaft senseor rotationwasfound to influencetheheat ransrcr

rromthe innersurfaceof thecone.A co-rotatingshaft gavchigherheat ransrcr hana contra-

rotatingshaft. 'lic rollowing correlationswerederivedror beat ransrcrrrom the innerconcsurracc.

Ro<3.5, Nu - 0.0243Rc,O'OK6ro, 2x"," [r (al (2.37)

Ro>3.5, Nu - 8.93x 10" Rc,"341x'3-921 (2.38)

wherc,Gr - fl2r sinOPAT(r/sinO)l/v2s theGrashofnumbcr,and0 is thc conchairang1c.

17he cattransrcr rom thedisc was ower than that rromthe innercone,however heaverage

Nusscltnumbersshowedsimilar behaviour o that from the innerconesurraccandsuggcstcdhe

samenfluencefrom the two regimes.Fromtheheat ransrcr esults n thedisc-conecavity, Alcxiou

suggestedhatat thehigher Rossbynumbers Ro) the througliflow 'drives' a largevortex that rills

thecavity. At lower Rossbynumbcrs hemechanismorccntrifugal buoyancycausesadialoutflow

towards heccntrc of thecavity with radial inflow next to thediscandcone surfaces,which is

consistentwith Farthingct al. s findings.

OwenandPowell [2004] from their single cavity work alsoobscrvcd hat theheat ransfer

measurements avesupport o theexistenceortwo different flow regimes,a buoyancy nduced

rcgime at high rotationalspeedsandsmall axial througliflow, and a througliflow dominated egime

at the lower rotationalspeedsand largervaluesoraxial througliflow.

32



HOT AIR OUTP. efý^

rý--- -

COOUNGCD

AIR 1*4

6 mm

42.9 mmaý- 70.1 mm

a, - 66.55 mm

D- 491.3 mm

b- 220.0 mm

Iß 59.75 mm

,Mo: Isc

/r II.

1-igurc 2.7 Sti%%cx" VC %Itj IIi I) e Ca%il.N Rig (Build I) lAle%iou 20001

Q

2.4.2.2 Su%%t-xAV multiple can jý rig huild% 2 und 3 c%perimem.il im e%ligution%

I ong cl al. 12000al canictl otil I 1),, Illcil"Mcillents (111\%o additional 111111(kof 111C tv%,,\ \Itlllllllc

Cw ity Rig. btidd-, 2 and 3. As shown In Figure IS. the rotor has three internal di%c%and together

with the mo end plate th%cs l'our cylindrical cavities are fornied. the disc bores are ol'Iden(ical inner

radius and the central dri\c shall Is stationary. The main dillerence IvIween Build 2 and Build 3 is

the diameter ol'the central dri\c shall, and therefore the annular gap between the shah and disc

bores. The central dri\ c shall has a diameter of' I 20mm in Build 2 with in annular gap I Onim and a

diameter of' I 04mm in Build 3 with ; n I Xmin annular gap. Both builds were itimnimemed with

stationary and rotating thermocouples. For litilld 2 and Build.1

IDA measurements ofaxial and

tangential flo\k \ clocitics within the inter-disc ca\ itics ha%c been obtained. Additional

measurements of"langcmial and radial velocity components %%ere btained in Build.1.

E-1'

I. Iui aATue

IaI Pa f -,ur IICDI MA-, S FýCW

.1.1



1 1. It.0 ". 111*1 S0

Figure 2.8 Istj%%t-xW Multiple ( 'a%f.ý Rig( Build 3) %hossing the I-) 1 1) % ll--I I'll Ille'll

11.ong et al. 2000al

I lie taligcIltial N locity of file caN11%1(mdid nol appeal io\ al-Nacloss tile ;mal width of tile C. \ It\.

The axial velocities Inside the cm ily were close to /cro. For lWild 3. with file wider disc bore

annular gap. tile maximurn \; title of'm 'Llr occurred close to (lie inner radius ol'the ca\ ity ; ll(] its

magnitude Increased \\ iih Increasing Ro 1111111her.lie 11011-dilliclislonalangential velocltý

decreased1'rom his maximum it) solul body rotation, m ill I. ; % 1) - 0,0. I-or Iluild 2. smaller

it Ise bore gap, I ie non-d I riens I ona I tallgc Itt I; h clocities (II I not show a Illa\ I ll it Ill till II ISO I(I bo dy

rotiffloll was achieved near to tile Outer railitis ol'ilic cavity. The difference III radial \arlalloll of'

tangential velocity has beell attributed to I dillci-crice ill tile Influence ofilie axial througliflo\% oil

the flo\% Inside the rotating ca\ ities. A narrow armular gap appeared to allentiale Ill's "Itcractioll It

doe-, appear likely that tile behaviour ofilic. 1cl and hence tile mode of'\ orle\ breakdown %%s

affected by the change ill diNc hore geometry. Mcasuremen1% ofilie instantaneous \; Illjc of'radial

\elocilies did show some periodicity ill tile flo\\ %\ ich could be title to cyclone aliticycloric pairs.

I lie radia I \c Ioci I es ýkcrc Iypica I V two orders 01,11m gll It title IO\%cr111.11111 tallgentia I Coll I pollen I's

and comparab Ie to relat I\ e iangentia I \c Iocity. consisicrit will II c ( hwn and 1'()\%cI ob%cr\ aI Ions.

An anaIy%is oft lie frequency spec II-till 10fI lie tan genlia I \e Ioc IIy shO\%CdcI car C\ I(IC[ICCof'

14



periodicity in the flow structure.This was inked to theexistenceof pairs orcontra-rotating

vortices,which is consistentwith thecurrent understanding r theheated low structures.

TheSussexMultiple Cavity Rig shroudheat ransferresults rom Build 2 andBuild 3 have been

reportedby Long ct al. [2006b].The heat ransferfrom theshroudwasshownto begovernedby

rotationally induced reeconvectionand wasmainly affcctedby the shroudGrashofnumber.The

axial througliflow ratehad little or no cffcct on the shroudheat ransfer. lic heat ransfcrappeared

also o bevirtually insensitive o thesenseorshall rotation.Earlierwork hasdemonstratedhe

principle that theshroudheat ransfermaybepredicted rom modified cst3blishcdcorrelations or

freeconvectionfrom a horizontalplate in a gravitationalfield. Gravitationalaccelerations replaced

with thecentripetal erm andthecavity core air temperatures usedand not the inlet temperature.

I'lic rig temperaturedatawas consistentwith this approach.T'hercwasa diffcrcncc in theshroud

heat ransferbetweenBuild 2 andBuild 3, with values rom Build 3 beinggreater hanfrom Build

2.This differencewas attributedto thegreater nfluenceof theaxial throughtlow on thecavity air

whentheannulargapwas ncreased.The heat ransfer rom the insideora rotatingconicalsurface

exposedo axial througliflow could alsobepredictedusingthe frcc convcctions,providing the

Rossbynumber,Ro,was small enough.

Disc beat ransfer esultsfrom Build 2 andBuild 3 have been eportedby Longct al. 12006c].71c

discheat ransfershoweda strongerdependenceon axial Reynoldsnumber,Res han the rotational

Reynoldsnumber,Reo. ncreasingRe, cndcdto increaseheaveragedisc heat ransrcr.This was

attributed o thestabilisingcfTcctof theCoriolis acceleration.Wideningthedisc borcgapappeared

to increasehedisc heat ransrcr.Unlike theearlierwork by Farthingct al. andLong using a single

cavity with axial througliflow where hedisc heat ransrcrwas nfluencedby both forcedandrrcc

convectioncffccts, Long ct al's laterwork showed ittle cvidence o suggesthatdisc heat ransfer

wasaffectedby the buoyancydriven flow. It is clear frorn Long ct al's work that theshrouddoes

havean influenceon the flow in thecavity. As mentionedearlier for anunheated hroudand a

narrowcavity and a small radial inlct (aswith the Farthingct al. experiment)heating hedisc

createdbuoyancy orces hatdcstabilisc heaxial througliflow, andthenarrowgap ratio suppresses

rorcedconvectioncffccts. For a wider gapratio (Long [ 19941),orcedconvectioneffectswould be

cxpected o havean cffcct on the flow in thecavity. In bothnarrowandwide gap ratio cases,he

maximumdisc surface emperaturewas comparableo theshroud emperature,with valuesof the

buoyancyparameterbasedon theaveragediscsurface emperature f PAT.q - 0.25. Soeven n the

wider gap ratio cavity. buoyancydriven cffccts occurred owards heouter radiusor thediscs.71c

3S



disc icating patternon theSussexMultiple Cavity Rig was quite different to thaton tile earlier

singlecavities.The maximumdisc temperaturewas around25K less hanthe shroud emperature

and ypical valuesof [fie buoyancyparameterwere in tile range0.02< PAT.,j < 0.1.The gapratio

G-0.2 wasalso significantly largerthan in theearliersinglecavity work. Taking into consideration

all these 3ctors,andthepresence f a shaftat a relatively largeradius ratio, it is perhapsnot

surprising hat therewas little evidenceof buoyancydriven heat ransrcrbehaviouron tile disc

surfacesn OleLong experiments.

2.5Stationary and Rotating Cavities - Numerical Studies

LongandTucker 1994a) ttemptedo numericallymodelhe low withinthesame otating avity

withaxial hrougliflowusedn OwenandPowell'sexperimentalest.Thenumericalmodel

reproducedheexperimentalbservationhatsome r thecentralhrougliflowdoesenterhecavity

as he esultof thebuoyancyffccts,nduced y rotation.

Othernumerical tudies avebeencarriedout,forexample y Long,Nforse ndTucker 19971,

TuckerandLong 19951,uckerandLong 1996],Wong 20021 ndbyTian,Too,DingandXu

[2004).n general,heseCFDstudies avegiven esultshatarcqualitatively imilar o

experimentalbservationsndgiveacceptablegreement ithbeat ransfer ndLDA

measurements.he hree-dimensionalumerical tudyby Tianctal. [2004)supportsheearlier

qualitativelow visualisation orkof Farthing t al.The sothermallowstructuresseeno be

axisymmctricndstable, nd otationdecreaseshe nfluence rthc centraloroidalvortex.Fora

heatedcavity he low maybecomenstable ue o the nfluence rrotationallynduced uoyancy.

An instability hatdevelopsloseo theshroudwasseenoaffect he estor thecavityas he

Rayleighnumberwas ncreased.redictedeat ransfer ppearsobeconsistent ith previous

experimental easurementsndshowshedifferentafTcctsr the wo flow regimes r rorced nd

freeconvective eat ransrcr.

Johnsonct al. [2004)developed stabilityanalysis ndappliedhis o thecase f rotating avity

flowwith axial hrougliflow.71canalysis howedhat oraRossby umber,to < 0.1 he low in

thecavitymaybestabilised yadensitygradienthat ncreasesith increasingadius,but his

behaviourceasestRo> 1).For ntcrnictliatealues f Ito,achieving tability nvolvesamore

complexelationship f velocityand emperatureroflics.

36



As partof thestudy in to the flow and icat transrerwithin both stationaryand rotating scaled

cavitiesnumericalwork hasbeendoneusing Large Eddy Simulations LES) Cr-D. LES methods

mayhavedistinct advantages ver theunsteadyReynolds-avcragcd avicr-Stokcs(RANS)

methods or this typeof buoyancydriven problem, which is know to give rise to largescale

unsteady low structures. n LES the largerturbulenteddiesarc simulated,with smaller(sub-grid

scale)eddiesbeingmodcllcd. 7he sub-gridscalemodelling is dependentup on the mcshsizeand

unlike RANS is designed o allow developmentof the largerresolvededdies hat interactwith the

mean low.

Concurrentwork by Sun,Kilfbil, ChewandI lills [2004] andby SunandChew [2004] comparing

die useof LES with standardk-c RANS CFD for bothstationaryandrotating cavitieswith and

without axial througliflow will be describedandtheresultsdiscussedn laterchapters.

2.6 Cross Flow Over a Stationary Cavl(y.

As notedabove, or an unheated avity rotating at low speed heaxial througliflow generates neor

moretoroidal vortices in thecavity. Similar cffccts havebeenobserved or planartwo-dimcnsional

flow over a stationaryplanar2D cavity. I fence t is alsoappropriate o consider his simplerplanar

flow. The literaturereview hasrevealeda limited amountof researchwork hasbeencompletedon

this subject. t wasdecided o focusmainly on thestudyby I laugenandDhanak 1966).Ilicsc

workerscarriedout an analyticalandexperimental nvestigationaimedat describing he turbulent

momentum ransfermechanismn the separation low regionora rectangularcavity racingan

oncoming urbulentboundary ayer.

I laugcnandDhanak'sexperimentalapparatus onsistedoran adjustable engthflow channeland a

rectangularcavity with adjustabledepths.The channelwas2.5 in. (63.5mm)wide andhadan aspect

ratio of 10,ensuringa substantially2D flow. I'lic cavity width wasfixed at 2.5 in. (63.5mm)and ts

depthwasvaried up to 4.5 in (I 14.3min).7lic freestrcamair velocity was estimated o be 100 ft/s

(30.48m/s). lic boundary ayer thicknessust upstreamof thecavity could bevaried up to I in.

(25.4mm)andwas found to beturbulent.Staticpressuresweremeasured long thecavity walls by

meansof a micromanonictcr.The staticpressurewas alsomeasured cross heshearayerby a

probeheld normally to thecross-flowdirection. Tcrnporal-incan elocity andturbulent ntensities

weremeasured y meansof a constant-currcnthot-wire anemometer. variablc-position raverse

37



mechanismwasdeveloped o move a hot-wirc probe ongitudinally, parallel to the mean low, and

transvcrselyacross hemixing region.The hot-wirc probemeasurements cre used o dctcrminc the

distributionsof the timc-mcan ongitudinal velocity, turbulence ntensity,andturbulcnt shcarstrcss

acrosshemixing rcgion. For flow-visualization studiesa secondexperimental ig with thesame

dimensionswas used.This rig was subjcctcd o flow of waterapproximatelysimulatingthe

dynamicconditions in termsof flow Reynoldsnumberandrelativeboundary-laycr hickness.

Analytical flow models werepostulated or tile threezones,namely,for the flow outside he mixing

processwithin theshear aycr, for the flow within theshcarmixing layerand ror tile now outside

tile mixing zone, nsidethechannel. le velocity profiles calculatcd rom theanalysiswcrc in

agreementwith thehot wire experimentaldata n the rcgion of themixing process.

A conclusiondrawn from this work wasthat the relativesizeor the turbulentboundary ayerat the

upstreamedgeora rectangularcavity appearedo havesignificantcffects on thedragandtile

velocity profiles in theslot. This could be importantto the rotatingcavity problembecause f the

need o know the levelsof heatandmomentum ransferacross heshcar ayer from tile crossflow to

diecavity, or (in termsof a compressor)he transferof heatandmomentum rom theaxial

througliflow undertile disc bores o the intcr-disc:cavities.

Investigationsusing similar typeof cavity geometrieshavebeencarriedout at die University of

Surrey.Experimentalstudieswerepc6ornied by Disimile ct al. (2000]andby Savoryct al. (20001

whilst Czechct al. carriedout both experimentaland numericalstudies.Both theexperimentaland

numericalstudies usingthe RANS standardk-c model)showedsimilar results o the 1[3ugcnand

Dhan3kexperiments.'lic CFD modelpredicted he flow reasonablywc1land t wasconcluded hat

CFD could beusedas a cost-effective ool in thedesignprocess oncerning low overcavities.

This I laugenandDhanakexperimentwill be revisited n Chapter5 where a 2D CFD analysis,with

variouscavity depths.will becompared o the cxpcrimcntaldata.

2.7A NumericalAxisymnictricAlodelor me Buoyancy1,.fccts n RotatingCa%ty llom.

Toconclude

hereviewof previouswork,a

lookat a possible

umericalmohod o modelhe

unsteadyhrcc-dimcnsionallow buoyancy ffcctswithina rotating avitywitha simplesteady

flow two-dimensionalxisymmctricmodelscxamincd. hew 20001n adiscussionnoteon

38



axisymmctricmodellingorbuoyancy cffccts in rotating cavity flows postulateda simplificd model.

In this simplemodel flow bctwccntwo coaxial, corotiting, infinite cylindersat difrcrcnt unironn

temperatures asconsidered.Averagingover time, it is expectedhat the flow variableswill not

varywith z or 0 in thenaturalcylindrical co-ordinatesystcm(rO, ). Fromanalogywith turbulent

diffusion, simpledimensionalarguments,andconsiderationortlic stability of rotating flows, Chew

postulatedhat in the interior flow theheat lux (4) is given(in termsortimc averaged ariables)

by the rollowing cquation,

-, 4Ra,kdr dr

dr dr

whcrc he localrotationalRayleighnumbcr'Rai s dermcd s ollows

Ra,= Pr max[(I-)'_r dp,

o22c11 cp dr

(2.39)

(2.40)

I IcreA and n are non-dimcnsional constants, Listhe representative length scale and, P, /1.Pr

(-pC, A). v., CF.T. k and c denote the fluid density, viscosity, Prand(I number, swirl velocity,

specific beat at constant pressure, static temperature, thennal conductivity and the speedorsound,

respectively. In the low Mach number limit this model will promote beat transrer if the radial

temperature gradient is positive. Eckhoff and Storcslcttcn [ 1978,1980] round this necessary low

Mach nurnbcr criterion for the linear stability ora rotating, compressible and inviscid fluid.

ror theconditionsof interest hecontributionorconvcntional thennalconduction o heat ransrcr s

cxpccied o benegligible.T'lien hecoreheat flux is givcn by:

-ARal*kdT

gir(2.41)

For tile limiting conditionorsmall valuesorAp/p, AT/T andEckertnumber IY/2ATCp whereAp

andAT arerepresentative aluesof pressureandtemperature ifferences,solution or tile above

equationor Ole

coreheat

lux, elgives;

39



4r [In(r.r,)]

prploTAir-

kAF, PI(2.42)

wherc.JT, is the inncr-to-outcr temperature ise across he interior regionand 7 s a cocfricient orthcnnalexpansion,which canbe takenas I divided by the gas cinpcrature.

Closeo theboundaryylinders,hin layersarcassumedn which heheatconductionsgivenby

modifiedexperimentalorrelationsorconvectionromaheated orizontal latplate n gravity.

I IcretheFislicndcnandSaunders 1950]correlationsareadaptedo includecentrifugal acceleration

radicrthangravity;

Nu - 0.54 Itaoý23 for 101< Ra< 2x 107 (2.23)

Nu - 0.14 Ra0.33) for 2x 107< Ra< 3x 1010 (2.24)

%%,ereheNusselt umberNu-L4 /(k AT)and herotationalRayleigh umberta - PrWr P20AT

L3 p2andL, AT, Pr,0 (- I/Ts)denotesepresentativeengthscales,luid towal temperature

difference, randtl umber ndcoefficicritof thennalexpansion,espectively.j isOlegas

temperaturet theedgeof the ayer.Choiceof therepresentativeengthscale, issomewhat

arbitrary, s he reeconvectionorrelations based nexperimentalonfigurationsuitedifferent

from hatconsideredere. or a finitecavity hehaircavitywidthwouldbea reasonablehoice.

(Note hat hecharacteristicengthscale, will cancel ut f the low is in thehigh Ra ange s he

Oterm in theRayleigh umbersraisedoa poweror 1/3and heresulting iscancelledut when

theNusscltsconvertedoabeat ransfer ocfficicnt).

Chewsuggestshat oreachpointonthewall surracc nair temperatureouldbeestimatedinternallywithintheCFDcalculation. hismaybedonebyassociatingurface ointswith internal

mesh ointsa specified istance way rom hewall,or (moregenerally) y includinganestimate

orthethermal oundaryayerextentn the terative rocedure. sing hisvalueorair temperature,

the ocalwall temperaturend luid properties,heappropriateatural onvectionicat ransrcr

correlation quationhorizontal late)maybeappliedoestimatehe reeconvectionicat ransrer.

4,,say.The ollowingequationsmight henbeusedoestimateheadditional eat lux, 4. say,due

to buoyancyeffects.

40



-, 4Ra,k"T

in the low 'core'dr

(2.43)

r4. - r.4" in thenear-wall egion (2.44)

Sucha methodmight be incorporatedwithin the iterative CFD solution andextended o include the

effectsof cxtra mixing in themomentumconservationcquations.Forconditions in which the frcc

convectionhcattransfcrwasrelatively small thesemodificationsshouldhave ittle cffect on the

CFD solution.

In conclusionCliewrcports the following points thatcnicrSc rrom comparing he 'mixing model'

with experimentaldata rrom Bolinct al's closedannualcavity, and

the innerconecavity on

the

SussexNICR Build 1.

Frccconvcction n thecloscdrotating annulus s supprcssedclativc to thatexpectcd n an

cquivalcnt gravitational ficld. Assumingthis is duc to a uniform 'thcrm3l rcsistancc'across

thecorc flow docsnot Icadto inconsistcncywith mcasurcmcntsor difrcrcnt radius ratios.

The 'rcal' flow appcarso bc morecomplcx thanthis.

Iligh Rayleighnumber icat transfer n the innerconecavity for theSussexrig is quite

different from thatorthe closedannulus.The axial througliflow is thoughtto play a major

role in promoting mixing in thecavity.

'Mis work will be further developed nto a modelling technique n Chapter 7 andaic applicationor

themethod o rig andengine otatingcavities n chapters8 and9, respectively.

2.8 Conclusions.

This chapterhasreviewed heresearchwork carriedout in the ficid or flow within intcr-disc

cavities.Two flow mechanisms,hebuoyancydriven flow within anenclosed otatingdisc cavity

andtheaxial flow throughtheboreof thecompressor, avebeen dentirlcd. Studies n to the

buoyancydriven flowcfTects

or bothstationaryand rotatingenclosedcavities

havebeendiscussed.

ror a stationarycavity casewith a vertical temperature ifTcrenccheheated loor promotesmixing

within thecavity and eliminates hetemperature tratificationwhich occurs or thehorizontal

41



temperatureifTcrcnccase.For hevertical emperatureifference aseheonly fluidmotion n

thecavity wasthatdueto the thermals.The heat ransferfrom tile heated loor compared avourably

to a conduction-layermodel.For thehorizontal temperature ifferencecase licre was rotationof

thefluid corewith a horizontalvelocity component o thethermals. [cat transrcrcorrelationshave

beenderived from experiments or thevariousheatingconfigurations,all variations of thebeating

frombelow case,by a number of researchers.1cre is a goodagreementbetween heseheat ransfer

correlations.For the rotatingencloscdcavity, studieshaveshown hat for high rotationalspeeds,

centrifugalforcesdominategravity andtemperature ifferences eadto centrifugally driven natural

convection. Icat transfercorrelationshave beenderivedfrom experiments or pureradial

temperature ifferenceand for pure axial temperature ifferencecases.Heattransferresults

obtained rom thenumerical

studiesorthe experiments

haveshowngoodPgrccmcn4except or the

high Ra-numbcrregionwith axial temperature ifference,%%,ere henumericalanalysispredicted

higherheat ransfer han theexperimentsshowed. lic heat ransfer or theaxial heat flux case s

much smaller hanthat for theradialdirected heatflux case.Comparisonor tile level of beat

transferbetween hepure radial and pure axial directedheat lux casesshows hat the radial heat

transfer s the importantmechanismor cavitieswith thecombinationof axial and radial

temperature istributionsthatoccur in gas urbinecompressor isccavities.Bothexperimentaland

numericalstudiescarried outfor

rotatingcavitieswith axialthrougliflow haveshownthat the

physicsof flow mechanisms re complex,being3D andunsteady.For low rotationalspeedcases

3D unsteadynumericalstudieshave beenableto capture he flow physicsreasonablewell, with the

LESCFD out performingk-c RANS modelling.Fromthesestudies wo flow regimes or heat

transferwere identified,a buoyancy nducedregimeat high speeds nd small axial througliflow,

and a throughflow dominatedregime at the lower rotationalspeeds nd argevaluesof axial

throughflow.Ilic heat ransfer rom thecavity shroudhasbeenshownto begovernedby

rotation3llyinduced ree

convectionandtheaxial througliflowratehad ittle or no efTecton the

shroudheat ransfer.Shroud heat ransferhasshown o havea greater nfluenceon the flow within

tile rotatinginter-disccavity thandoes hedisc heat ransfer.7lic experimentalandnumerical

studiesshowedwith increasingrotational speed he flow within the inter-disccavitiesbecome

increasingcomplicated.To model tile now at thehigherrotationalspeedswill require ncreased

computingmemory andspeed o adequately apture he now physics o achieveanacceptable

accuracywithin a satisfactory ime scale.An alternativeapproachs model thesecomplex flow

processeswith approximatebut

computationallycfficicnt models.As

a partofthis

alternativeapproacht wasnecessaryo review tile research n cross-flowover a cavity, to studytile

interactionof thecross-flowwith the flow within thecavity.7lic mainconclusiondrawn from the

42



studies,n termsof a compressorntcr-disccavity, wasthat the relative size of the turbulent

boundaryayerat theupstreamedgeof a rectangularcavity appearedo havesignificant cffccts on

thedragandthevelocity profilcs in theslot. I'his could be importantto the rotatingcavity problem

becauseorthc need o know the levelsof licat and momentum ransferacross heshear ayer from

thecross low to thecavity. To conclude hech3ptera simple2D axisymmctricsteadynow

approach ombining the two flow processes,hecavity flow with theaxial throughflow,hasbeen

postulated,which if achievedwill beableto adequatelymodelthecomplexflow in a computational

efficicrit andtimely way.

43



CHAPTER3

COMPUTATIONAL FLUID DYNAMICS SIMULATION OF NATURAL CONVECTIONIN A CUBE

Summary

Thischapter resents FDresults or naturalconvectionn a cube.Two licatingconfigurations

wcrcconsidered,othbeingheatedromthebottomsurface. hecomputations ereperformed

assumingothunsteady ndsteadylow and esultshavebeen ompared ith otherworker's

experimentalmeasurementsor licattransfer,low patterns, nd hemeanand luctuating

temperatureistribution.

Calculated eat ransrcresults ompared ell with theexperimentalderivedicattransrcr orrelationat low Rayleighnumber5.Ox10')with asmalldifferenceat the

higherRayleighnumber3.Ox1010).heunsteadylow computationalnalysis ccuracywasbetter

than hat or thesteadylow analysis,

3.1 Introduction

Publishedresearchn this areaof naturalconvection in anenclosedcavity appears o havebeen

limited to experimental nvestigations.whilst very little computationalmodelling hasbeen

published.The majority of theexperimental researchhas beenperformedfor the limiting casesor

vertical enclosuresheated rom below and cooled from above,andhorizontalenclosures

diffcrcntially heated rom the side.A smaller amountof cxpcrimcrital work has beenperformed for

the mixed cavity natural convection,wheretheenclosure s both heatedand cooled top andbottom

andon the sides.This chaptercornparcs he CFD resultsfor naturalconvection n a cubewith test

data from the Kirkpatrick and Bohn's ( 1986]cxpcrimentst. First, a descriptionorthe experiment

will bepresented ollowed by the licat transrcrresults n section3.2. In section3.3 thenumerical

investigationusing the FLUENT [1998) CFD code will bediscussed.CFD resultswill be presented

in section3.4, firstly for the steady low and secondlyfor the unsteady low solutions.Summary

andconclusions or thechapterwill be in presentedn section3.5.

tAWof thisrescamh orkhasbeenpublithed n PaperNo.OT2004-53528.resentedtdieASNICTurboExpo,

Vienna.Austria.2004 Sun,Kilroil. Chewand fill*. 2004).

44



3.2Descriptionor the Experiment.

At Ilia Colorado StateUniversity Kirkpatrick and Bolin conducted wo separateexperiments, he

first to determinethe overall Nussclt-Raylcigh number correlationsand ilia second o determine he

flow patternsand temperaturedistributions. A brief descriptionof ilia experimentsandthe four test

licating configurations weregiven in Chapter2, section2.2.3. All the configurations havea heated

bottom plate.The experimentswerepcrronncd using the testcell shown in Figure 2.1.The cubical

enclosurehadan interior dimensionof 305mm,which wasconstructedorcight 12.7mm hick

aluminium plates. 'lic four inner plates overlapone anotherand were screwed ogetherwith a

neoprenegasketbetween hem to form the enclosure.T'he our outer plates provide heatingand

cooling to the four enclosurewalls via milled channels hroughwhich hot andcold water was

pumped.The outcr plateswere scalcdandboltcd to the inner plates.7lic remaining two vertical

surfaceswere 19mmLucite plates hat allow for flow visualization.The testcell was instrumented

with the top and two sidcwalls having centrally located hermocouplesbored to within 3mm orthe

enclosure's nner surface.The top wall also hadeight additional thermocouples ocatedas shown in

Figure2.1. The purposeor thesecoppcr-constantanhermocoupleswasto determine heaverage

wall temperaturesand spatialvariations in the wall temperatureacross heplate.The spatial

variation was lessthan 10%and typically 5% of theoverall hot-to-cold surricc temperature

difference.The hot and cold surraccswere thercroreconsidered sothermal.For the I IC case, he

two vertical metal walls were considered o beperfectly conductinggiving a linear temperature

distribution along the wall. I'lic overall licat transfermeasurementswere expected o be within: f:5%

of ilia actualconvectivelicat transfer rrom each surface.The working fluid in the testcell was

dcioniscd water. Propertiesorthe water in the testcell wcrc calculated at a tenipcraturcequal to the

averageof the heatedand cooled wall temperatures,crcrrcd to asthe bulk temperature.

Temperaturemeasurementswithin theenclosurecore weremade with a coppcr-constantan

thermocoupleprobe inserted hrough the top plate.The L-shapedprobewas movedvertically ror

vertical scansandrotatcd ror horizontal scans.The probecould not be placedcloserthan 8mm frorn

the top and bottornsurraccsor the testcell, due to the dimensionsor theprobe.The thcrtnocouple

output was sampledby a microvoltinctcr at a 101z rate for a period of 120s. 'lic time constantof

the probe is calculated o be0. Is, anorder ormagnitude smaller than thecharacteristic ime or

thermals.The temperaturemeasurementwasrepeatableo 0.1 K.

45



3.3Test I lent Transfer Measurements

Fromthe experimentalresults,Kirkpatrick andBohn wereable to derive heattransfercorrelations

for thevarious heatingconfigurations. in each of the testconfigurations, the bottom surface of the

enclosurewas heated.For thecalculation orthe Nusscltnumber,wall-to-bulk temperature

diff'ercricewas used.

Nu - h.,o

L/k (3.1)

h.,l - Q/( A. I Tw-Tb (3.2)

wherch.,g

s theavcrageicattransfcr odricica

In thedefinitionof theRayleighnumber,Ra, he emperatureifferentialusedwas hedi(Tercncen

temperatureetweenhehotandcoldwalls.

Ra- (g 0 AT L3 / V2) pr

for vcriical Rayleighnumber, Rahg0 AThh' / vabasedon enclosure icight. h

for horizontal Rayleighnumber, Rai -gPATI 11 vabasedon enclosure ength, I

(3.3)

(3.4)

(3.5)

As previouslymentionedn Chapter , section2.2.3.1,or the imiting conrigurationIC me the

Nusscit-Rayleighumber orrelation f the estdatacanbegivenby,

Nu- 0.0986Ra"j (2.14)

The I If ICC case nvolves simultaneousheat ransferrrom the surfaceand vertical sidewall to the

top surraccand opposite vertical sidcwall. Also asnicntioncd previously in Ch3pter2, for the

111CC case he Nusselt-Ray1cighnumbercorrcl3tionsof lite testdataaregiven below:

For the top andbottom surfaces, Nu - 1.10V'216 (2.15)

and for the side walls, Nu - 0.141 RP 1) (2.16)

46



Thebottomand opsurfaceNusschnumberswereapproximately5% higher han hesidewallNusscltnumbers.'lic test esultsshowedhat hcdominantmodeof heat ransrcrwas henatural

convectionromthebottom o the opof theenclosureatherhan he aminarboundary-laycreat

transrcrromoneverticalwall toanother.


Forthe numerical investigation,CFD was used o model the I IC and I If [CC conrigurationsorthe

naturalconvectionexperiments.Comparisonsorthe CFD resultshave beenmadewith the

cxpcrimcntal measurements. he interior gconictry of theexperimental estcavity wasused n the

CFD analysis.Thus, ilia geometricalsize was305mmcubcd.A typical calculation mashror the

geometry s shownin Figure 3.1. Various CFD mesheswcre used n theanalyscs.The base ine

mashwas 106ccils; 100mash ines in cachdirection. This mashhadan expansion atio, R or 1.1

away rrorneach edgeor thecavity. For a study of mashdcpcndency wo further masheswcrc used,

aI 50-cubcdmash(R-1.058) anda 200 cubed mash(R-1.039). Ilia uppcr wall temperaturewas set

to 300K for all cases,with ilia hotter, lower wall icnipcraturevaricd from 301K up to 340K to give

a rangeof Rayleighnumbers rom 5.83 x 10' to 2.33 x 1010. or the I IC test two metallic sidcwalls

were insulated(the inner conductingplate was insulated from a secondoutcr plate) and the Lucita

front andrcar surraccshada low conductivity. All the sidewalls were thcrcrorcassumedadiabatic

in die CFD analysis.For the I If [CC case. he same ncshwas used n ilia CFD. The uppcrwall and

onesidewall temperaturewereset to 300K ror all cases,with the hotter, lower wall and theopposite

sidewall temperaturesetto 31OK(Ra - 5.83 x 101)and330K (Ra - 1.75x 1010).

47



I

I

4

A

I( peollit'll-N aild %III-lact. lilt-01 ( 1110% 00% 100ý 1411.IIv ý%;lvu-filllvd cubc.

I)It*

k (1111pill. 111oll k 'Iff wd m1f 111k.owwl %'ItIon C(P1.111lill"till 111.1ý . . Mollicillull)

.111dwl 1. III

tile Ntationarv eference tame (co-ordillate .yocill defilled III 1.1glife I

I-( ollsen al oll ot

I-

I

( '1

2. CollNcr%Allollof %lollICIIIIIIII

\ threcilon

threct ion

direciion

4%ý/NI(I

( I/ V,ý-I-Iý

A

(A (1)

"\(ji\

i)

4 V. ('(I) 4 '. (11V, ) ('. ))

V

4 1/411 1

( 1'

)47.

( 7h)

(1 7o

49



3. Conservationof Energy

whcreE-h- 'pf+ ulp2

P, P.V+p

g(p. -P)

Of+V- (pEU)

w-pV-U +V-(kVT)+ (1) (3.8)

ris the otalcncrgyandscnsible nthalpy,h- fCpdT. T,,r is298.15Kr,,

and D s theviscousdissipationcnn(sccEquationAI- 10)

isarcduccdprcssurc

is thebuoyancycnn,whcrepo sthe(constant) cnsityorttic now.

Ilic fluid used n the simulationswaswater, to matchKirkpatrick and Bolin's experimental

conditions.The Pranddnumber(Pr) for water was takenas7.0. with specific heatCp- 4200 J/kgK,

thermalconductivity k-0.6 W/mK, dynamic viscosity ti - 0.001kg/msand thermalexpansion

cocfricicnt P-0.0003 K*1.As this is a natural convection problem involving small changes n

temperaturehe Boussincsqapproximation [Vcrsiccg andNfalalasckcra,19951was used o treat the

fluid density (p):

P-POO -PAT) (3.9)

whereAT -T- To,operatingemperature,o- 300 K andoperating ensity,po 1000 g/m)

In theCFDsolver FLUENT 19981,heBoussincsqmodel reatsdensityas a constant alue n all

solvedequations xceptor thebuoyancyerni(bodyrorce erm) n themomentum quation.

(p

-pa)g *I

-poP(T -To) g

The accelerationdue to gravity, g was set as-9.81 nils*2n the vertical downwards direction (i.e.

towardsthe hot bottom surface).

Modelswere un assumingothsteady ndunsteadylow. For hesteadylow models, oth

laminarand urbulent low assumptions ereusedwhilst for theunsteadylow models nly laminar

flow ("pscudo"DNSsolution)wasassumed.orthe urbulent low calculations.hestandard-c

modeland he2-laycrk-c/W nearwall turbulencemodelwereused.Thestandard-cmodelturbulencequationsnd henearwall turbulencemodels sedn theFLUENTCFDcodoarc given

in Appendix1.

49



To solvethe systemorcouplcd differential equationsa rinite volume schemewasused.For both tile

steadyand unsteadyflow models, hesegregated olver methodwasused,where ilia governing

equationsare solved sequentially.In ilia segregated olution method, eachdiscrete,non-lincar

equation s linearized implicitly with respect o thatequation'sdependentvariable. Becauselia

equationsarc non-lincar, an iterative solution loop mustbeperformedbeforea convergedsolution

is obtained.Each teration consistsorupdating the fluid properties. he u, v and w momentum

equationsare eachsolved in turn using tile current values orprcssurcs and facemass luxes (update

(fievelocity field), solve the prcssurc-corrcction continuity) equation(updatepressure,acemass

fluxes),solve energy, turbulenceandotherscalarequationsandcompletethe iteration loop by

checkingfor convergence.Temperatures,pressures, ndu, v and w velocities are calculatedand

storedat thecall centrcs.The methodchosenror discrctizationof the scalarand momentum

equationswas the sccond-ordcrupwind scheme.A secondorder schemewasusedror ilia pressure

interpolationand for the prcssurc-vclocitycoupling (prcssurc-corrcction) he SIMPLE algorithm

wasused.

ror theunsteadylow, the emporal iscrctization onnulation hosenwas hesecond rder mplicit

scheme. timesteporO.2 secondsnd20 iterationsper imestepwasusedn theunsteadylow

analysis.Rcrcrringback o thework orAsacdaandWatanabe1989]work in Ch3p1cr , they

derived onnulac o estimate timeconstantor thistypeof flow problem

Timeconstant,- LIU - L'(Pr Rtj)"" la

=LI(gflATL) II

whcrc U is thevelocityscalern/sjandL is the engthscalem)

Fora temperaturedifTercncchot to cold surface,AT or40K. U-0.191m/s and with L -0.305m

the time constantý -L/U-1.6s. For the time step heCFD codeprovider [rLUE- NTý 19951

recommendsaking a time step,At - T/4 -0.4s. Thetinic step usedrorcach or dicManalyscs

was0.2s,clearly within the time stepcalculatedabove.77hercforc. time steporO.2sshouldensure

that die majority of the thermalactivity within thecavity would becaptured.With time stepof 0.2s

die Courant.Friedrichs-Lcwy, CFL number w 13ror theaveragedistanceacrossa cell on. 05nim

that is only acceptablewhenusing the implicit solver.The CFL number s high andcould be

loweredby reducingthe time step,which may help to capture he smallerscaleflow rcaturcsand

die possible he onsetora thermalplume rising rrom theconductionlayer. Furtherscaling

calculationsarc presentedater in section3.5.2.5.

so



3.5NumericalSimulation Results

3.5.1Steady low CFD solutions

Steadylow CFDanalyseswerecarriedout rorboth the ICand II [CCheatingconfigurations.Analyseswereperrormcd ssuming oth aminar low and urbulent low models.Two temperature

differences,otto coldsurraccs, eremodelled OKand30Kandall thesimulationswere

pcrrorrncd ith aI 00-cubcdmesh.with agridexpansionatioor i. t rrorneachwall.Table3.1

belowpresents eat ransrcr esultsobtainedromthesteadylow CFDanalyseserformedor the

I ICconfiguration. heCFD icattransfer esultsarecomparedwith KirkpatrickandBohn'sheat

tmnsrcr orrelation. teat ransrcresultsareexpressedn theronnoran areaaveraged usselt

number,Nu,dcrinedby Equations .1and3.2.Thebulk temperature,bwas akenas hemeanor

thehotandcoldsurfaceemperatures.

Table 3.1 Comp2risons of steady laminar and turbulent CFD results %%1111easured licattransfer for the I IC case.

Case AT(K)

,

Pressure(Bar)

Ra Nu

(Exp.)Nu

(CFD)ANuV/0)

NotesAll ror StcatlX Flow

1 _0 1 5.833xlO^ 177 172.2.8 Laminar, 100'incsh. R-1.1

2 10 1 5.833xlO9 177 144 . 18.6 Turbulent. 100' inesh.R- 1.1

3 30 1 1 1.75xlOlo 256 222 . 13.31Laminar, 100' mcsti. R- 1.1H41 30 1 1 1.75xlO" 256 187 .27.0 1

_Turbulent100' inesh.R- I

Table3.1 clearly showsthat the heattransfercomputedby thesteady aminar flow model was

closerto the measurementshan for the turbulent flow model.Tlic steady low turbulencemodel

appearso dampdown the tlicnnal activity within ilia cavity. However, for ilia steady aminar flow

model therearc largediscrepanciesn the licat transteron the hot and cold surraccs.71is error in

thesteadystatecalculationsmay beexpected,asthe flow widiin thecavity is clearly unstableand

thcrcrorc time dcpcndcnLConvergenceof the steady low solutionswere also a problem making the

solutionsdoubtful andunsatisfactory.1 cncc the need o run ilia unsteady low solutions.

Table 3.2 showsthe steady low CFD licat transfcrrcsults rorthe 1111CConriguration.The CFD

heat ransfercompareswell with the measurementsor the top andbottom surraccsbut not for the

sidewalls.Overall, the I If ICC steady low licat transrcrresultsarc closer to the measurementshan

for the I IC configuration

51



Kirkpatrick and Bohn Natural Convection in a Box

I R, case Delta TI OK.Velocity in Ilic Y direction (bottom it) (op) - in s

M/S

0.0110

0.0 1B

0.0 160.0 140.0 12

0.0 1a

0.008

OAH

0.004

0.002

a.aoaAA02

-OA04-0.006

-0-aaB-0.0 0-aA 12-0.0 14

-0.0 16

.0.0 A

0.020

Figure 3.2 Contours of vertical velocity, IfC case, AT=IOK.

Furbulent. Sleudý

Laminar. Stead)

Laminar, I'micad)

52



Table3.2Comparisonsor s(cady aminar and turbulent CFD results t HISmeasuredheattransrer or the IIIICC case.

Case AT PressureRa Ton& ottomWalls SideWalls Notes

(K) (Bar)

I

Nu Nu ý1ANu Nu Nu ANu All ror Steady

(Exp. ýCFD) M (Expj (CFD (%) Flow

5 10 1 222 215 -3.2 161 143 -11.2 Larnmar,100, Mesh,

6 to 1 5.833404 222 210 -5.4 161 142 -11.8 Turbulent,

1003mcsil,

7 30 1 T 7-5 288 284 . 1.4 227 190 -16.3 Laminar,

1001mcsh.

8 30 1 1.754010- U8 267 7 5 -18.5 Turbulent,I

1:

1001incsh

I,

R-1.1

3.5.2UnsteadynowCFD solutions or (lie I IC conlIguration.

3.5.2.1Flowstructure

Figure3.2 showscontour plots of vertical velocity, andcompares hesteadystatecasesof laminar

andturbulent flow with theunsteady aminar flow case or aI OKtemperaturedifference.The figure

shows hat therewas lessactivity within thecube for the steadycasescompared o theunsteady

case. lic plot of the steady low turbulencemodel showstheapparentdampingor tile thermal

activity mentionedabove.This allowed a nearsteadysolution to beobtained.Overall, the unsteady

laminarmodel produced hebestresultsby capturing the main flow structureswithin thecube.As

will beshownlater, resultsfrorn theunsteady aminarmodelcompareswell with the experimental

results.The unsteady low predictions arc illustrated by a time seriesorinstantancousvcrtical

vclocity componentand temperaturecontourson tile mid-plancof thecube,shown in Figures 3.3

and3.4 respectively.Picturesarc shownat 4-sccond ntervalsover a period lasting 28 seconds.

T`hcscresults were producedon aI 00-cubcdmeshwith the bottom surraccat 31OKand tile top

surfaceat 300K, giving a Rayleigh numberor5.8x 109.Laminar flow was assumed or this

simulation.The range of the temperaturecontours s from 304K (blue) to 306K (red). During the

simulation period, two plumes canbeseen o be released rom the hot bottom surface,migrate

towardsa sideof thecubebcrorc deaching rrorn the surfaceand rising up to the cold top surracc,A

53



coldplumeappearso bereleasedromtheuppcrsurrace nd allsdowna sidcwall.but iscurtailed

beforereachingmiddistanceof theenclosure. hevelocityrangeor thecontourss from-0.02mls

to-+0.02m/s.hevelocityplots show luid risingfromthehot bottomplatenear hesidcwallsand

acceleratings t movesupwards.Notshownclearly n thepicturess thehigh evcioractivity in

thedirectlyopposite omer rormcdbetweenhe wosidcwalls)whereplumes irornhecold surracc

appearo flow down heopposite dgeof cnclosurcthebackedgesobscuredn thepictures).lic

generallow patterns thendiagonallyacrosshecoldsurracc.Much essactivity occursn the

other wocorncrs,butagain heplumes ise n onecomerandrail in thediagonallyopposite omcr.

11crcappearso be essmovementn thecentralcore.Thecore emperatures rairly uniformand

constant,hemixed emperatureeing hemeanof thehotandcoldsurfaceemperatures.ome

large-scalestructures f theflow arcevident,with upward low in thecomcrviewed.Thefindings

from hecomputationalnalysis, omparewell with theobservations aderomtheexperimental

work.Allowing for thechangen the emperatureiffcrcnccbetweenhecxperimcntalwork

(approx. 0K)and hecomputation10K),thesize, hespeed rpropagation nd heperiodof

releasef theplumesromthehot bottomsurracc rcconsistentetweenheexperiment nd he

computational ork.Time historyplotswereonly producedorthe IOKunsteadylow solutions

and heonly experimentalatawasgiven or the30Kconditions. 'hevclocity magnitudeompares

well with a valueof -0.02 m/s cstimatcdromtheadapted sacda ndWatanabe's19891

cxprcssionor theupwardvelocityscaleat theedgeof the hermalboundaryayer,Equation .13.

Thiscquationwasdeducedromexperimentsn wateraboveaheatedlat plateandwhenadiptcd o

thecurrentnotationgivesa maximumvelocityof -8.5%1(OATgd)a*"6.

Two movie clips of theCFDrcsults rorthcunstcadylaminar, I OKtcrnpcraturcdifrcrcncc I IC case

showing the vertical velocity andtcnipcraturecontoursarc includedon theCD disc attached o the

thesis.Figures3.3 and3.4 were taken rrom these wo movic clips. Filcimmesarc 'vclmovicdtlO' for

thevertical velocities and 'tcnipmovicdt 10' ror the temperatureplots.

54



Figure 3.3 Contours of vertical velocitv, IfC case. unsteady, laminar flow. Ra = 5.83%10'

(AT= 10K).

A 11911 h. Time #4 sec- 0.0 18

a. a Iý

0.006

0.004

0.002

IL^,

bm-9w

0.000 41 450.002

-0.004llqýk

-O.oa6 I'llile 412 ,cc

-0.008-0.0 10

-0.0 1.1

-0.0

14

-a.a 16

0.0 is -7-0-020 4f-j040.

55



a. Tinie 0 scc

c. Time ý8 scc

3O1

305.9

305.8

305.6

I

305.2

10 S.1

305.0

104.9

304.8

304.7

304.8

304.5

304.4

304.3

104.2

304.1

104.0

Figure 3.4 Conlours of temperature, 11Ccase, unsteady, laminar flo'A. Ra ý 5.83%109

(A'I'=IOK).

56



3.5.2.2 ficat trati%1'er

Figure I. SShows dic calculated licat transfer rales I'Mill the 101) nd bottom stuflicc'. as .1unction of'

hine for a Rayleigh number of'2.3x 101(l.Since these fluxes are averaged o%crthe walls. the

variation withtime

is perhaps surprising. and musthe due to the time dependent large-scale flow

structures. In an experiment some %ariation ofthe top and NIton, surface temperatures might also

he expected. but cannot occur mvith he houndary conditions specified in these calculations. Such

eflects might danip out some ofthe variations in the lical flux seen here. Obviously, with adiabatic

sidewalls, the t1me-averagcd licat input from the bottom plate should equal the output from the top

plate. 'rhe numerical results are seen to satisfy this condition.

11000

Figure 3.5 Calculated %arialion of hem tran%ler on the lop md hollom -. jrf. ice% for 14.1

2..1%10"'(%T 40K).

\ýciagc Ntissclt numhas 161.ach casc \%Cl. ohlamed h\ 11111C\ c1liging the smLik., 11C.1111,111,4ci

rates over a period of' I minute. As previously tiowd the Nu%seltnumber is del ined us,,,, lie

ho(-to-cold plate temperature difference, while thc Ravleigh number definition uses (lie full

temperature differcrice. Unsteady laininar flow CFD heal transfer result-, for four Rayleigh numhers

-ire presented in Table 3.3. The table shows that (lie lical transt'cr is most accurale at the lower end

17



of* he Ray eigh number range. I-or ilic I OK temperature (I 'lerence case. Case 10. a time averaged

heat transfer Nusselt Number within .1"o ol'the experimcn(al test derived Nusselt nuintwr was

achieved. At the highest Rayleigh number condition (40K). Case 12, the error is 13"..

Table 3.3 Comparisons of mWea(IN laminar CIA) resufts "ith nica%ured heat (ran%fer for the

11Ccase.

Case

12

1.1

14

10000

AT

(K)

40

40

40

PressureBar)

I

I

Ra

s.833 10.ý5.8,

ý1.1Io"

1.167x 10

2.333xI()

2.33 3,10

2.3.1.1,10

Nu

(1.,Xp.,

177

224

292

282

282

Nil %Nil

82

17.1

206

245

261

265

-2.1

-8.0

-

1.1.1

-6.7

-00

No1c..NAll fOr t Lanlinar Flow

501 IZ 1256

1001 IICNII, Z 11

1o01 lllcili, IZ 11

1001iiieNli, IZ 11

150, nics11.Z I'(M

2()()'tnic%h,[Z 1ýO

l)

Kirkpatrick and Bohn Natural Convection with In a Stationary Box - HC Case (with Water) - Mash 100

cube

K, ti,; ),2tr, c,k & Bohn. HC oonfiguration. Nu

, wolat. on

Nu -0 0986 Ra ^ (113)

Equ r from

Raf Int J Heat Mass Transfer Vol 29 No I pp 69.

82.1986

1000

1001Of -08

MI .". ^3

Celh

I

I OE 09

1(1k

Rayi*igh No. Ra

%I "(I

9 Nw (. 1 D foJI'vulla, -

40 Nu CFO "tom SurfWA

- Nu CornW (K A 13)

fI Nu CFO Top 200 cubed Mesh

0 Nu CFO Bottom 200 Cubed MOO

I OE#IO

Figure 3.6 Ifeal traiisfer numerical (111t.compared "ith Kirkpatrick and Rohn

empirical correhilion for the IfC configuration.

Al, IK

I OE-11

ss



The results obtaincd from using the 100-cubcdmcshhave beencomparedwith theexperimental

derivedhcat transferNu-Ra correlation in Figure3.6. The CFD heattransfercompareswell with the

experimentalcorrelation with a small deviation at the higher Rayleigh numbers(13% crror). As can

beseen rom the graphicalplot therewas a small imbalancebetween he heattransferson the two

surfaces.

3.5.2.3Xlesh dependency

To investigatemeshdependency,solutionswerealsoobtained n twoother incrmeshes. 50-

cubedand200-cubcd.n these asesheexpansionactors way romthewalls were educedn

order o keep heratioof maximumo minimumgridspacinghesame sfor the 100-cubcdmesh.CFDheat ransrcr esultsobtained orthehighestRayleigh umber40K)usingaI 50-cubcdmesh

(Case13)and200-cubcdmesh Case14)havebeenpresentedn Table3.3. Theresultshavealso

comparedo theexperimentalorrelation,n graphicalorni, n Figure3.7.Comparinghe

numerical eat ransrcrwith theexperimentalorrelation howshatwith mesh efinementhe

disparitybetweenhenumericalesultsand heexperimentalatacorrelationwas educedrorna

13%difrcrcnccwith the 100-cubcdmesho within6%difrcrcnceorthe correlationwith the200.

cubedmcsh. n addition, hedifferencen theNusselt umber etweenhehotandcold surfaces

was educed. his isduedirectlyto thereduced rror n the imeaveragedicatflow balance

betweenhesurraccs. rom heplot it is reasonableoassumehatnosignificantncreasen

accuracyanbegainedby increasinghenumber f mesh ellsabove200-cubcd.Numericalests

werealsoconductedo show hatsensitivityo the imc-stcp sedwassmall.Considering ossible

differences etweenexperimental ndmodelled onditions ndexperimental ncertainty.he

agreementf thesimulationswith measuredeat ransferatessexcellent.

59



Kirkpatrick and Bohn Natural Conv*ction with In a Stationary Son - HC caso O*Ita T- 40 dog (with Water)

zw u

2900

2?0 0

2600

250 o

2400

8 Nu CFO Top Surfam

Nu CFO Botlom Surlacci

Nu Coffel (K & 0)( lIs

2(k)- I

( c1l,

I(X)* I

CCII,

.

a

A

Kw"nck OMM141%0bol

Nu -0 00" ma , (113)

Equ I from

l4of I," i H" Mvas Tt anow Val 29 No I pp

1U06

230 o

0 OF 00 1OE-06 2 OF Oki I OF 0(1 4 OF 06 5 OF 06 n Of -00 Of .06 AOC (14% 9Of -06

CFD Moth Numberof Co*o

Figure 3.7 Ileat transfer numerical (CFD) re%ults compared %OlhKirkpalrick and Bohn

empirical correlation for %arious niesh sii.e, .

3.5.2.4 Temperature lield

Figure.1

Xa sho%%s ;I time series record ot'llic let npcra I tire calctilated at tile inter Im Otm l1k)"It Im"'.

gnim above the bottom surface and Sinin below (lie top surface for the IW configuration. I'liese two

posltl Ions correspond to the thermocouple probe locations Ili the experimental test. Flus particular

lime series is flor the temperal tire diflerence of'40K oil the I W-cubed inesh. The (line step used in

the computation was 0.2 seconds. The plo( shows thermals rising firom the bottom surface and

falling From the top surt'ace Crom the spike-., Ili the temp,erature. The magnitude of'the temperature

disturbance is ol'the order ot'2K. Thc period ot'llie thermals is of* the order of'6 to Ss. Comparing

with the ineasured temperat tire data (temperat tire difference 30K). the magnitudes of* the

calculated temperature fluctuations are similar (IK Ili the test). but the period ol'the thennals is

greater (4s Ili the test). III addition. the number ot'dierinals released over a set time is less Ili the case

of*1he computational analysis compared to (lie experiment. The choice of'the Mile step and Illesil In

the computational analysis may have Ili influence oil the temperature magnitude. the perrod and tile

1'requency of'the release ol'tlic thermals.

4

0

60



Temperature record for HC configuration - top and bottom of the enclosure

Temperature difference a 40 degrees

Omm bobw cold top surlace

6mm aWvo hot bottom sudeco

9

4

1'' I,Tinbe (s)

1,

100

Figure 3.8a Computational analysis -- temperature record for IW configuration %%ilh%F

40K for the 100-cubed inesh.

Temperature record for HC configuration - top and bottom of lh* enclosure

Temperature difference - 10 degrees

- Aetwnmk mý iid top eingon

elmm abow0 hat botbwn aufface

4

IK

C) 20 40 60Tinw (*I

so 1w

Figure 3.8h, Computational anulý, sis - lemperal tire record for Ifc configuration "ith NU

IOK for the 100-cubed mesh.

IA)

120

ol



To compare the temperature magnitude and (lie period of'release ol'the thernials tor a diflerent

surflace emperature differential, Figure 3.9h shows the unic series record ot'llie temperature again

for the IfC configuration but for the temperature difference of' IOK. also on the I(K)-cuhcd mesh.

The plot shows the magnitude ot'llie temperature disturhance is of' the order of' IK and the 1wriod of'

the themial is ol'the order of' 12s. Also lor the IOK temperature difference the 1requency of*(hernial

releasewas reduced. showing that there is much lessactivity in the cavity with the smaller dri%ing

temperature diflerential.

The computational time averaged temperature (over 60s) distribution along the vertical centreline of'

the chamber flor the I R' configuration with a temperature dillerence of'40K (Ra 2.11 - 10"') Is

sho%knn Figure 3.9. The tune averaged vertical centreline temperature is plotted relailve to the bulk

lemperattire, the bulk temperattire heing the average ofthe heated and cooled wall temperattires.

Mean Temperature Profile (Ra - 2.33 sIO) for HC configuration - Delta Tm 40 dog.

11-------------4

mc C4)nf4px~

Smm abovo "om

Hmm holow lop

012

T-T Bulk ( C)

09

os

oI

06

S

04

() 3

()2

0I

Figure 3.9 Computational analysis - mean lemperature profile (time averaged) for IfC

configuration with AT ý 40K for the 100-cubed mc%h.



The plot shows that the core ofthe fluid is within IK ofilie bulk Iempera ire. The experimental test

results showed the core temperature it) be %ýthin 0.5K ofthe bulk temperature. *['lie experimental

results also showed a slight temperature reversal near the top and Nmom stjrf*ace%.ue to the

thernials traversing across the enclosure. The computati.onal results %how he diflerence in (fie nican

temperature and bulk temperature is slightly sinaller than the unilonn core temperature near (fie top

surface but there is no temperature reversal. The mean core icnipera I ire is less than the bulk

temperature except close to the hot bottom stirtace. The uniforin centreline lemperature Is the result

of (fie formation ofthermals that are vigorous enough it) cause mixing within the fluid core.

, he computed non-cliniciisional temperature fluciuations along the vertical centreline llor I R'

configuration with a temperature difference ol'40K. averaged over a period of 60 seconds are

shown in Figure 3.10. The magnitudes of' the flucitiations are computed by (hviding the standard

deviation ofthe temperaitire by the hot-cold wall temperature difference. I'lic largest Iluctuanolls

are near to the top and bottom surfaces. and the smallest values ofahout 0. (9)2 in the middle ofthe

chamber. The level and distribution o I'll tict uat ions 1rom the compulational analysis compared well

" ith the fluctuations calculated lor the experimental test.

Tomp*rature Fluctuadw Prordo (Ra m2.33 *10) for HC connguration - Do*a Ta 40 d*g.

bi- I. V

Ill,Sld D*v I (Thot -Tctpldl

I'.

"1

09

04

01

41

cN

t 11

03

ol

01

Figure 3.14)Computalional analysis temperalure fluctuation profile for IfC configuration

%ith AT = 40K for the 100-cubed mesh.

63



Variation of'point values oftemperat tire with time shows randoin fluctuations and is,smular to Ille

thennocotiple measurements. Fhepredicted temperai tire fluctuation spectnim F(m) obtained from

(lie temperature variation with time at a position Smin above the heated plate is showi ill Figure

3.11. qualilit"', is dchiled Such that

T'T' f E((,))(I(,

where (t) is the frequency of the temperature fluctuations J- and the overhar denoles a tune avera...

These results were obtained 1rom simulations on the I 00-culwd mesh for Ra 2.1- 10"'. The Ii me

Step used was 0.2 s and [lie Fourier analvsIs used data from a period of' 120 seconds. The figure

includes a --5/1" trend line to allow comparison with dependency expected for isotropic turbulence

in (lie inertial subrange and observed in many experiments. Qualitatively. the spectrum has (he

properties expected ofa turbulent llo%k,.with numerical effects m the higher 1requencies.

I. E+01

1-E-01

1.E-03

1.E-05

1 E-07

1 E-09

1 E-11

0.01 0.1 1 10

Frequency Hz

Figure 3.11 Femperature fluctualion %pectruin from reference pohil Xmin abo%cbo(lom plate.

Ra 2..1% o", (.%-I- 40K).

Further to Iliesc calculations for the waler-filled cube. additional calculations %%crcerformed for in

air-Mcd cuk A Sun and Clew INNNI also using FLUENT. I-lie 1wrlect gas Ia%%was used in the

(A



CFDanda Rayleighnumberof 0.542x108wasachieved ysettingg-9.81 m/s2with a temperature

differenceof 20Kat apressure f 1.013405Pa.A 50-cubcdmcshwasuscd.TheavcragcNussclt

numberwasover 10%higher han hatgivenby KirkpatrickandBolin'scorrelationwhich is ror-

I.OxIO9<Ra<- 1.45x1010), ut in goodogrccmcntwitlithercsultsgivcnby I lollandsct41(19751

for rrccconvectionwith air ror theRayleighnumber ange I. Ox101 Ra<- I. Ox101. n the

present otationhiscorrelationgivesNu - 2.88+0.111 al/3.

3.5.2.5Scallng

Asacda ndWatanabe1989] ound hatfromtheboundary eat lux and he luid properties

averageharacteristicsuchas he hermalplumedimensions,hevcrticalvelocityof theplume, he

frequencyandperiodof the hermalplumes ouldbedetermined.llickncss of theconduction

boundaryayeraway romthewall canalsobecalculated.

As mentioned n Chapter2 AsacdaandWatanabedefineda flux Rayleighnumber,Rafas,

Raf-go Fd 4 /(pCpCtIV) (2.7)

Avcragc rcqucncyof thmnal plumcsgcncratcd crunit arcaandunit timc,f was hcndeterinincd

as,

(d4 f)/a-5.6x 10'511ar ( 107< Raf< 1011 (3.13)

Pcriod,P,during which the thm-nal was suppliedwith the licatcd fluid rrom theconduction

boundary aycr, wasdetcrrnincdas,

(Pa)/ d' - 9.9 Rar*112 ( 107< Ra(< 1011 (3.14)

Thicknessof theconductionboundary aycr, 8,

8,; d- 27.1 Ilar'" ( 103< Ra(< 1013 (2.8)

I lorizontal longitudinal scale of the thcnnal, L wasdctcmiincd as,

L/d- 33.0 Ra(*"4 ( 107< Ra(< 1011 10)

I lorizontal transverse caleof the thcrmal, B wasdctcrinincd as,

B/d- 16.0Raf 1/4 ( 10' < Ra(< 1012)

65



Vcrticalvclocity,w wasgivcnbycquation,

(Raftv,= 8.0(PATgy ý.

L_(2401<ltat<24010)

d'

)(2.13)

and PAT g-2.08 (ct2v)'1112PFg/p pp)114 (2.90)

Timestcp,At At-1/w

where -3.05inm average istance cross cell

(3.15)

Using heaboveequations,or a tcinpcraturc ifference, ottocoldsurface,ATor40K

I [catFlow- 930.628W and Icatflux. F- 10004.1Wm*'. Ra(- 2.972x 1011

f- 2747.92M,2s"' - 255.621 z, (one hermalevery0.004s).P-3.74s L-7.67mm B-3.72mm 8, - 1.4971nm -0.0 1361ns*At - 0.225swhichgivesaCFL- I comparcdoCFLft 0.9for a timesteporO.2s roranaveragedistanceacross ccitor3.05mm.

and ror aAT of I OK

I featFlow- 156.434W and [cat flux, F- 1681.63Wni*', Ra(- 4.997x 1011

f- 461.91M,2g*l- 42.971 z, (one licnnalevery0.023 ).

P-9.12s L- 11.97mmB-5.80mrn 8, - 2.557ininw-0.0087m:Cl

At - 0.351swhichgivesaCFL- I comparcdo Cr-L ms.6 for a timestepof 0.2s oran averagedistance cross ccli or3.05nim.

Both the numerical and the Kirkpatrick and Bolin cxpcrinicnt3I rcsults comparewcll with tile

Asacdaand Watanabecalculationsror theplunic dimcnsionsand tile thicknessof tile thermal

conductionboundary ayer. With theCFD mcshrcrincd nearto the wall. the near wall cell

distribution falls within theAsacdaand Watanabedcrivcd conducting layer thickness. hus

capturing the thermalactivity nearto the walls. With the 100-cubcdmcsheight cells rail within the

conducting layer thickness.The calculatedperiodof plume releasecompareswcll with the

experimentbut the CFD produccd25%-50%longerpcriod. The plume releasevclocity for tile CFD

resultsare in line with thecalculatedvelocity or-o. oinvs.

66



3.6Conclusions

In thischapter,esults romnumericalCFDsimulations f ilia experimentalestspcrronncdby

KirkpatrickandBolin for thenaturalconvectionn acubicalenclosurewith diffcrcntiallyheated

andcooledhorizontalandverticalwallshavebeenpresented.articular ttentionhasbeengiven o

theconfigurationIC casewherelia bottomsurfaces heated nd he opsurface ooled.with all

othersurfacesonsidereddiabatic. henumericalesultshavebeencomparedo theexperimental

resultshroughout.

TheCFDderivedheat ransrer ompares ell with theexperimentalorrelationwithonlya small

deviationat thehigherRayleighnumbers. heCFDsimulations lsoshow hat heheat ransrcr

computedy theunsteadyaminar low model tinic-avcrage usschnumber)was hemost

accuratetthe owerendor theRayleighnumberange.'lic steadylow modelassuming

turbulencek-cwith thek-c/W nearwall model) aircd heworst.11c useof this turbulence

modelappearso dampdown he hermalactivity within thecavity.

Comparinghenumerical eat ransferwith ilia experimentalorrelation howshatby refining hemcshhedisparitybetweenhenumericalesultsand heexperimentalatacorrelationwas educed.

Inaddition,hedifferencen theNusscltnumberbetweenhehotandcold surfaces as educed.

I'his isduedirectly o thereduced rror n ilia timeaveragedeat low balance etweenlia

surfaces.

The findings frorn the numericalanalysescomparewell with theobservationsmade rom the

experimentalwork with thesize, the speedorpropagation and the period of releaseperiod orthe

plumesbeingsimilar. The numericalanalysesalso agreewith theexperimental indings that the

heated loor appears o promotemixing in thecavity andeliminatestemperaturestratification.

67



CHAPTER 4

COMPUTATIONAL FLUID DYNAMICS SIMULATION FORCONVECTION IN ANENCLOSEDROTATING ANNULAR SECTOR CAVITY

Summary

This chapterextends he CFD simulation of naturalconvection in a stationaryheatedcube

discussedn thepreviouschapterto the modelling orconvection in a rotating enclosedannular

sectorcavity. The computationswerepcrroancdassumingunsteady low andthe resultshavebeen

comparedwith otherworker's experimentalmeasurements ndnumerical predictions for heat

transrcrand other flow ficid parameters.Somegoodagreementwith experimentalvaluesfor mean

surface icat transferhas beenshown for Rayleighnumbersof theorder 1010.1owcvcr therearc

alsosomepoor resultsfroin the CFD simulationsof the scaledrotating sector.The reasonsor the

discrepanciesn the hcat transferresultsbetween heexperimentalandCFD predictionsarc

discussed.

4.1 In(roduction

Both experimental nvestigationsand numericalsimulationswerecarried out by Bohnct al [ 19931

to analyse heconvectiveheat transrcr n a closed,gas-fillcd annulusrotating aroundits horizontal

axis using a rig in the Institute orStcam andGas Turbinesat theTechnicalUniversity orAnclicn. A

brief descriptionor the experimentsandthe threetestconfigurationswere given in Chapter 2,

section2.3. The configurations tested n theAachenexperimentareshownin Figure 2.2. It is to be

notedthat theradial distancebetween he innercylindrical wall and outercylindrical wall ror

configuration A wastwice the distanceorthat for configuration 11.lic axial lengthwaskept

constantfor both of theseconfigurations.Results rorn theexperimentand numerical simulation

werepresentedor thepure radial or centripetal icat flux situation, wherenaturalconvectionradial

licat transrcrfrom the heatedouterwall to thecooled inner wall occurs(with the side wall thermally

insulated),driven by thebuoyancycffect underrotation. Furtherwork to investigate he effect or

dividing theannulus nto sections,by insertingeight radial separationwalls to rorm a 45*sector,

configurationC (configuration 11with a 451sector)wasalso pcrrormcdon theAachenrig. In the

cxperimcntal investigations he range of rotational Raylcigh numberencounteredwasbetween1.0x

68



107and 1.0x 1012. steadystatenumerical investigationwas performedby Bohn ct al. assuming

isothermalcylindrical walls and adiabatic sidcwalls for the45* sectoredannularcavity. Bohn ct al.

[ 19941also used heAachen rig to investigate heaxially directed licat flux case,where one disc

sidcwall washot and the oppositedisc was cold with all the other walls thermally insulated.Only

configuration B wasconsidered n that investigation. In addition to theexperimentalwork, Bolin ct

al alsoconductednumerical calculations for thepurely axial heat ransfercase.

UnsteadyD CFDmodellingof convectionn a rotatingenclosed nnular ector avityhasbeen

undertakenn thepresent tudy.Only the450annular ector ase, onfigurationC,with radial icat

flow hasbeen onsideredn thiscurrentwork.Fortheradialheat low condition,heatwasapplied

to theouter adialcylindricalsurface nd he nner adialcylindricalsurfacewascooledwith all the

othersurfaces ssumedo beadiabatic. Icatflow is thcrcroren a radially nwarddirection,similar

to the IC case onsideredor thestationary ubc.Further oncurrentworkbySunandChcw

[2004]usedunsteady D CFDto model heflow andheat ransrcrwithin thesame nclosed

rotatingannulus singboththeconventional -c turbulencemodelandby LES.

4.2 Description or me Experlment

The dimensionsof theenclosuresare given in Figure 2.2. For theradial beatflux tests.an electrical

heaterplaced at the outcr radius of theannuluswasused o input heat nto thecavity. I feat is

removed rom thecavity by a water-cooled rotor shaft at the inner radiusof thecavity. Both thedisc

surracesof thecavity were thcrnially insulated.The cavity could bepressurized.lic rotor shaft was

driven by a DC motor. The test fluid contained n theenclosureswas air. I feat fluxes from theouter

cylindrical wall to theworking fluid and rrom theworking fluid to the inner cylindrical wall were

determinedby measuring he temperaturedifferencesacross hermally resistant ayers. During the

experiments he rotor speed, hecavity pressure,electriccurrent to theheaterandthe mass low rate

of (hecooling waterwere kept at constantfor each estcondition. For the radial heat flow tests he

maximum rotor speed estedwas 3500 RPNLThe maximumpressuren thecavity could be set up

to 4 bar.I'lic temperatureat the outer heatedcylindrical wall could be increasedup to IOOOC.7hc

minimum temperatureat the cooled surfacewas fixcd by thecooling water,which wastaken from a

water tap,with a temperaturebetween80Cand 15*C.For the purc axially heattransfertests here

wasnine thin-film resistancehermometersocatedacross he lengthof the inner andacross he

outer surfaces.Therewere also 18thin-film thermometersdistributedacross he rotor disc surraccs.

The accuracy n theabsolute emperaturemeasurements as0.01K.

69



The emperatureifferenceused n dcrivingtheRayleighnumbers thediffcrcncen temperatures

of thehotandcoldwalls:

Rotating Raylcigh numbcr, Ra, =(r.

w3XTL3 lv2)Pr

RotatingReynoldsnumber,Reo=par. Llp

Nusseltnumbcr,Nit - -2.qA

Eckcrtnumbcr,Ec2c,AT

4.3 Test I Icat Transfer Alcasurenien(s

(4.1)

(4.2)

(4.3)

(4.4)

As mcntioncdcarlicr in Chaptcr2, scction2.3, from the licat tr3nsrernicasurcmcnts,Bohn ct al.

dcrivcd both Nussclt-Raylcighnumbcr and Rcynold-Raylcighnumbcr corrclations or the Icst data

for configurationsA, B andC assurning adial dirccled licat flow:

ConfigurationA: Alit- 0.246Rao.2.11(2.31a) Re= 0.733Rao.173 (2.31b)

ConfigurationB: Alit= 0.3Maoo 111 (2.32a) Re- 1.441Ra.015' (2.32b)

ConrigurationC: Nu = 0.36SRa,.21) (2.33a) Re- 1.615Ra#15% (2.33b)

Ilic Aachen measurements obtained from the radial directed heat flow tests showed that changing

the inner radius to give I Ur,,,- 0.96 (Config. A) and to I I/rn- 0.63 (Conrig. 11)had only a small

influence on the Nu number. At the higher Ila number the heat transrcr was reduced by 11%

moving between configurations A and B. With the annulus divided into sections. by inserting radial

separation walls, the influence or the Coriolis rorccs is reduced resulting in an increase in the heat

transrcr. At the higher Ra number the heat transrcr was increased by 20% moving between

conrigurations B and C. Insertion orthe separation walls attenuates the rclitivc circumrcrcntial

vclocity inside the cavity, resulting in a decreaseof the radial component of the Coriolis force.

Coriolis forces have a damping crfect on the flow, thus by attenuating the Coriolis forces flow

70



Insidc Ific C; \ If\ is "lrcllý4111cllcdo Illat llic Iloat liall"k. -I In,. rcaw-, Vot the tadialk ditcctcd licai

flo%%ase heat transfer depends strongly on the Ra number bw onINI %%caklNn the Re number,

4.4 Numerical Model of('olj%t. cIioll ill.1

scaled 14411.11ing Sector

4.4.1 Ba%ic modelikig awimptiol1% and IIIc 1111111crical roct-dul. t.

ii

111111111

4

mill

I 1111.11Ii

II,, mm

I i'ý. Il It,

.4.1 ( 'collicl I'.N of % clicil I olatilig 1111111111% 1.2 Nli-%Il ill %.dIvil

lol. 11111",,ck II It' III. It HIII(IJ1,11111

1

will" 'indOw

Ine"ll used 1,01-ile calc 11it ions I., it III I igmv .421t 1" .1noll t1ill for III Ille"ll %%ilt I

cells I ()()x I ()()x 100 1t ax lal. ladial and cit-cunifei-ent tal dit cc[ Ions. respect I% ly I. ( 'onipai lilt! it)

earlier- %koik. tile inesh iesoltition maý he regai-ded as icasonable for file prewni case. %%lilta

slifficlently fille mesh it) k'apiul-c file 11(m near, lo tile li)l; l(lllg %%aIk A'.-colding to Bolin Ct A

I 1101)1. fllcý obial lied good (TI) ,()lilt Ions %%it ;I mc,, h %%ilt 1(o)(4) cel 1%\%ihin I \% ile range of

Raý leigh minihm AI I&I to M I" kw Ow 45 wool I "o briller "inlies We !well

coII,. Ie ret IIe re. ýIctw;I, cIII to II %%iI1 125AHWceHs150\qI\s ()); IIIti. I t- II IeiIIIIe-, II %kII1.1.17S. o(

cells ( 150% 50\ 1SO)\%cregencrawd (4)check 111c"llicimidelice

Sc%era I lem cases were winianhoed "ah We 6dlo"mg pmamoo% n ANN"wn QIM 40 ads).

I MOK and c; \ itv pressuic, 1',, lbal I, \kas \a II Cd to gI ie a lange tIf Cond II It ns I' mI lie

ina, tinium 1,. considewd ( 140K) gi\ Ing aA F( 1- IJ -10K. the rolanonal Raý Icigh nninher I%

Ra (VPr 33H 109, and Ockert iminhei I,. I-c () () I S*ý.%%ere (lie Icngth scale used in defining Ra

(1 45 dc.t, I.

Aro-*-ýP,11,111,111

I



is L-r. - ri.Thetemperatureradient,due o thepressureradientacrosshevortex n tilecavity, s

expectedo benegligible or thissmallvalueor r.c.TheNusscltnumberusedn thissection ollows

thedcrinitiongivenby Bolinct al, andnormaliscsheradialheat lux by thevaluegivenby pure

heatconduction,oNu - 40 . n(r. rj)/kAT.Three urthershroudemperaturesivingAT equal o

IK, IOKand30Kwerealsoconsidered, ith correspondingayleighnumbers,Ra 1.141 8,

1.092E9and2.973139,ndEckertnumbers,Ec- 0.7275,0.0727 nd0.0242respectively. he

working luid wasair for all the estcases. hegridexpands way romeachwall with an

expansionatio or i. i ror tile I 00-cubcdmesh. or the50-cubcdmcshand150-cubcdmcsh ile

expansionatiowassetsothat hefirst ccil distance way romtile wall was hesame sfor the

I00-cubcdmcsh.

The computationscarriedout solve the conservationequations or mass,momentumandenergy

using the FLUENT CFD code. Incompressiblenow with thedensity dependenton the fluid

temperatureonly was assumed hroughoutall thesimulations.Standard luid propertiesfor air were

assumed onstant,with a spccific heat(Cp)of 1004.4J/kgK, thermalconductivity (k) 0.026 %V/mK

anddynamic viscosity (p) 1.855E-5 kg/ms.The CFD calculationswere performed assuming

unsteadyaminar flow ("pscudo" DNS solution). The FLUENT segregated olver, andsecondorder

implicit timesteppingwith the secondorder upwind schemeused

for thespatial

discrctisationwere

chosen or thecalculations.A time stepof 0.0005s CourantCFL numberto2.2 for the average

distanceacrossa cell of 1.15mmwhich is acceptableor the implicit solver) and20 iterationsorthc

pressurecorrectionschemeper time step were spccificd. The time stepwastakeasbeing

approximately 1/100'hof the time for one full rotation ortlic cavity and the numberoriterations was

basedon theknowledgethat the flow solution residuals educedandbecamesteadyafler 20

iterations. The flow wassolved in the relativevelocity reference rame.The Prestoscheme

(Patankar,19801,a secondorder pressurecorrectionmethodwas set for pressurenterpolation for

the velocity. For the pressurecoupling method(prcssure-corrccton), theSIMPLE algorithm was

chosen.

4.4.2The governIng equations

1.Conservation

ofMomentum

Vvlicnhe low equations resolved n a rotating rarne f rcrcrcnce,heaccelerationf the luid is

augmentedyadditionalcnns hatappearn themoincriturn quations.Witha rotating rame he

72



problem anbesolvedusingeither heabsolute elocity.V or therelativevelocity,V', as he

dependentvariable.Thetwo velocitiesare relatedby [fie followingequation,

V,.; -(flx; ) (4.5)

here,6 is theangular elocityvector, heangular elocityof therotating rame,andF s [fie

positionvector n therotating rame.

Fora rotating crcrcncerame,hemomentumquationsanbewritten n termsof theabsolute

velocitiesas,

+v-V, 4;) +P(cl x -Vp +v-ý, V; ) (4.6)

at

or in termsof relativevelocitiesas,

a

Lit+V- (p;,

wVw)+1)(2CI ;,, +ClxClxF) - -71) +V- UIVO (4.7)

wherep(26 x ý. ) is theCoriolisforce.

2. Conscrvationof Mass

(4.8)

3.Conservationof Energy

(pE)+ V. (ý(,Pr + P)) . V. (kVr) + (11

01

cit(4.9)

whereE=h-L+ v'and D s theviscous issipationcnn.

1) 2

4.5 Numerical Simulation Results for the 45* Enclosed Rotating Sector Case

4.5.1 Unsteady flow FLUENT CFD solutions

4.5.1.1 Ileat transfer

Table4.1showshe est/model,onditions,otational peed. nd lia temperatureifference etween

thehotandcoldsurfaces,lia cavitypressure nd herotationalRayleighandEckertnumbersor

eachest.For heunsteadylow analyseshe otalheat low intoandout or ilia cnclosurehrough

73



thehot and cold surfaces, espectively, calculated from theCFD models were time averagedover a

periodof 5 seconds.T11cime averaged otal heat flow valueswere thenused o calculatethe

Nusscltnumber,Nu. for theappropriate surface. 'lic heat ransfercalculatedfrom theCFD models

wascompared o theexperimentalheat transrcrandthedifferencepresentedas a percentageerror,

ANu - (NUCMINuc,,p.

1).

Table4.1 Comparisonor theCFD results(unsteadyaminar now) %villtmeasuredheat

transfer for the Anchen45*enclosedotating sector,configurationC case.

Case Speed AT p Ra+ Ec Nu Nu ANu Notes

(rpm) (K) (bar) (Exp.) (CFD) (%)

1 2000 1 1 1.141xl5r 07-275 19.0 21.0 10.5 100' MCS1145* model

2 2000 10 1 1.092xlO" 0.0727 30.7 45.4 47.9 100' mcsh45* model

-3 2000 30 1 0.0242 38.0 69.8 83.7 1W MCS1143* model

4 2000 40 1 3.781xlO" 0.0182 40.0 73.6 84.0 100' mesh45*model

R-1.1

5 2000 40 -1 T, .781xl5r 0.0182 40.0 63.6 59.0 50'tncsh43*model11-1.256

6 2000 40 1 3.781xlO 0.0182 40.0 81.5 10.8

150' meshI I I I I43*modelR-1.038

Figure4.3 showsa plot of theaverageNusscltnumber,Nu verses otational Ray1cighnumber.Rao

forthe 1001ccllmesh.The figure also includesan adaptatioll to the rotating annulusoftheColorado Kirkpatrick and Bohn [ 19861 orrelation basedon their cxpcrimcnI of a natural

convectioncubc.The adaptcdColoradocorrelation wasobtainedby using the tcrnpcraturc

difference.AT between hehot andcold walls and rcplacinggravitational accelerationby

centrifugal acceleration.For this configuration it may bewritten,

I/)lum0.051Ra,, (4.10)

The predictedhcat transrcr s much higher than thatgiven by Bohn ct al's corrclation.Therewas

84%difference in theCFD predictedheattransrcrcomparcd,with theexperimental estcorrelated

heat ransfcrat the higher Rayleighnumbers,shownboth from the graph,Figure 4.3 andgiven in

Table4.1.1lowevcr a muchcloser fit is obtainedwhencomparedwith theadaptedColorado

74



correlation, with a good agreement at the higher Rayleigh numbers. In a subsequent study Sun and

Cliew 120041conducted a series of*(TD analyses for (lie same geometry using both FLUENT and a

Rolls-Royce code. I lydra overa range of' Rayleigh number%.Sun and Chew found that hoth CH)

codes over predicted the surfilce heat transfer compared to the experiment. Flie over-prediction was

XF. hm less than thebout 10"ý, o 20",, flor the Hydra code and approximately 40"o for FIVE

current predictions.

Bohn at al (Aachen) Heat Transfer in a Closed Rotating Annuli 45 dog. Sector at 2000 rpm

- HC case (wwrithAir)

10000

1X) 0

a

100

I OF 08 101-011

Rayleigh No, Re"I

f-.It. - 000 bir. -OdO

I

a

I OEOIO

Figure 4.3 Comparison of the predicted lical tramfer %0h c%1wrimental corrchiliom for the

Auchen rolaling sealc(l %edor, conliguralioo ( '.

I-igure 4.4 shows a comparison of'surface heat transfer between the CI-D solution and (lie

experiment in the form of time history plot for the 45 ' rotating sector. Fhee --ýertmenta heat

transt'er values were calculated using Bohn et al's heat Iranstler correlation (Fqu. 2.33). The time

step for the CIA) calculanons was 0.0005 s. and a simulation period ofat least 5 seconds was

required before it 'converged' solution could be assumed. Fhe %arialion ot'heat transfer %kth lime

indicates the presence oflarge-scale flow structures in the CIA) soltmons. but they are not ; s

prominent as those predicied by CFD t'or the natural convection in a stimonary heated cube shown

in the last chapter.

Hohý I al HC Nu,

Nu - 0365Rn A 0213

F,g a kom

%f ASME. 93-GT-292

a 100^3 Mesh, Nu CFD inner Radii Surlace

100^3 Mash, Nu CFD Outer Radii SurlaC4

No Corrotl (Bohn at al)

Nu Slatic Box (, orrfgl (Kirkpatnck & Bohn)

75



Bohn at at Heat Transfer In a Closed Rotating Annuli 45 dog. Sector. HC case - Delta T 40 dog.. 20OOrpm.

with a Mesh 100 cube, with Viscous Heating,

Inner & Outer Radii Surface Total Heat Flow

1300

1200

1100

1000

900

8001

7 00

Outer Radii Wall

Time Avoragt. (j Total I loat

[jiuw 1102/W--

OLAWRAdo,W id

OtAmr WA Smsc Time A%g

Tom wai Hem Fk)w

-Inner Ra6l W mi

-- Innow Wal 5soc. TIrnmAvU

ý.LUA0 P177771,

Test Total Heat I

Flow - 6.0M! J

Innor Radii Wall

Tmý A, -.. q-I T

1 ILL* 1-' Výý -

600 --

00 052

T nn (s)

Figure 4.4 Wall heat transfer from the CIA) %olulion and the Auchen rotating scaled %ector

c%perimentfor Ra4 3.781

%10"

4.5.1.2 F'Imý %trticitire and teniperature fleld

13 00

-1200

. 700

li 00

E\ammmg ilie flow field, It was lotind that ilic lical iranslcl- Is dominated bý a plllmlrý ýorlc\ I()\%.

instead ofthe radial arm siructures that may he expected for a full Ioo" annultis flow as identified ill

early work oil rolating cavity with axial tlirotjglillo%%by. for example, Farthing et al I 1992a. 1992bj

and Long and Tucker 119941.The flowstructure

is Illustrated by the inslamaneous temperature and

velocity plots in Figures 4.5 and 4.6. respectively. The contour plots are shown for the nud-axial.

mid-radial and mid-circuinflerential planes through the Cavity. Most of the llow actt%ly appears to

happen next to the circtinif'erciifial wall with the hot thernial plume% eaving the outer radial surflace

and moving to a circumferential wall whilst the cold denser plumes leave the inner radial wall and

travel to the opposite circunil'erennal wall. Willi all the ac(lvIiy near to the walls a central core of'

near uniform temperature is formed, with a temperature near to the inean ol'the inner and outer

radial surface leniperal tires. The radial velocity plot shows that the flowis

radially otawards closeto one circunillerential wall and radially inwards on the opposite circumferential wall. In the relative

frame the flow appears to rotate at approximately 5.0ni/s around a s(alionary central core.

76



Rohn el A (Aschen) 44" Rolmling Sector ( m%M%.

100 ( ulwil Mesh. Rotational %pred 2000 RP%l

340 0

3380

3360

334 0

I

3320

3300

3280

3260

3240

3220

3200

3180

316 0

314 0

3120

31003080

306 0

304 0

lio-I0

Joo 0

ConfounufMalk lcmpersture(kl

14i

001.1 lempoixtuic 441K

IDimclion of R:wýw=,nil

Figure 4.5 CFD predicted instantaneous temperature confour% for Rao = 3.781%109

Rohn cI al (Amchrn)45" Rcpimdnjj%rvlor( sO I%

100 ( ubed Nfeih. Ripinikinad Slwvti Z(MX) RP%f

I

55

50

45

40

35

30

25

20

1510

os

00

-05

-1 0

A

-30

-35

-40

A5

50

-!)5

1.0(Figurc 4.6 ('Fl) pre(licted instangancotis ra(Iial . clocitý- contours for Ra# 3.781-.10'

I

onkours of kji(UW %elotil% (m/%)

[IWeL-tion

tit R

17



Figure 4.7 shows the temperature variations at a monj ortng position at (lie mid-radial point oil the

mid-axial plane. This also clearly indicates the presence ol'small-scale flow acti%ty in the central

core ofthe rotating cavity. The temperature plot shows that there is a distinct drop in temperature

(approx. 0.5K) halfway through the 5-second sampling period. This drop in temperature does [lot

appear to influence file surface heat fluxes. I lowever flor other Rayleigh number casesdismict

changes in the heat fluxes, both increasing and decreasing. have been seen to occur during the CIA)

analyses. Reasons flor these sudden changes have yet to he explained. The first step %%oulde to rull

the solution over a longer time period to see H*acyclic irend is produced or not.

Bohn at &I Heat Transfer In a Closed Rotating Annull 45 dog Seclof. HC case -Oefla T 40 dog, 200orpm.

with a Mesh 100 cube. wAth Viscous Hosting.Cavity Contra Po4nt Temperature

Gowe Pam T--pwdb"

(, w*o IN TwM %soc nu AV

32480 1

32460

32440

00 os 10 10

4

Tim* (a)

lu, ý Aý-wjj I -11mah"

- .114 914 K

40

Figure 4.7 CFD p redicled fentperit I tire plof itI Ili e cit%i ) cc t Ire for Ru# 3.78 1% 0"

4.5.1.3 Mesh dependenc)

Figure 4.9 shows the CIA) mesh sensitivity for (lie highest Ra number case using (lie three meshes.

the 125.000 (50) cell mesh. the ( I()()') cell jilesh and the 3.375,000 ( 150) cell mesh.

UFD predicted lical transfer appears to converge ;,symptotically with the adapted Kirkpatrick &

Bohn correlation with increasing mesh refinemem. I lowever in doing so the heat transfer error

CavltV Contro Point

.114 914 K

79



increasescompared with the Bohn et al's correlmion. Therefore tile mesh dependency is small

relative to (lie difference beiween tile Bohn et al. correlation Fhere is a small discrepancy in tile

heat transfer balance lbr the I 50-cubed mesh, which was due to tile solution not being fully settled.

Bohn @I al (Aachen) Heat Transfer In a Closed Rotating Annuli 45 dog Sector of 2000 rpm

-HC

case (with Air)Delta T- 40 dog.

using As50.100

and a150

cubed cell mash

900

W-0

70 () ý

600

Soo

I -Uu

2

w

:I

iýý:::: ii

.Sc30 0

H/(-.,

063 b/r- - 066

200

loo ý

Bohn et al. 14Cooftgurabon. Nu correlabonNu -0 365 Ra '0 213Fig 8 brAn

Ref ASME. 93-GT-292

F-HIII

a Nu CFD Inrww 5utla(»

o Nu CFDOLA«Surfooo

Nu CorfW (BOM of 41)

Nu Stabc Boot CorrW (KO1Kpabxýk& BohN)

00

0 OE-00 5 OE*05 1 OE-06 I 5E-06 oE -06 2 SE -06 IN -06 1 Sf - 06 40( -06

CFO Mesh Coll 14ýn*Pvl

Figure 4.8 Comparison (if (lie predided heal tran%fer isilh experimental correlation% - CFD

mesh sensithi(y

4.5.2 Solid body rotation CFD invesligaliow

An adi abatic

case %%,,, imest Iga cd to I ieIIIIfy

lit)S.,bIcC.1 IScsof IIIc 0%CI-p Cd t -I o IoIIIC. ItII

ai sCI,

noted above. Compared with the theoretical -solid body rolation". tile CFD adiabatic calcu kit lolls

gave relative velocity flucitiations of'over 0.6m, %at a rotational speed ol*2MO rpin. Fills is

significant compared to the velocity fluctuations for tile heat transfer case and is likely to contribute

to the over-prediction. In a flit-ther study Still and Chew 120041also encountered difficulties In

obtaining soltitions for the solid body rotation case %vithFLUENT. I lowever. lie had more . uccess

with the I lydra UFD code, using uniform mesh spacing in (lie circumferential direction. Sun and

Chew's results are described in section 4.6 below.

79



4.6 Numerical Investigation or Convection In a Scaled Rotallng Annulus

In complementarytudies,SunandChew 2004)andSunctal. [20041 ave nvestigated olinct

al'sconfigurationB. Forcompletenessheseesultsarc ncludedanddiscussedere.

Thegeometrysexactly hesame s or therotatingsectorabove, xcepthatno radialplaneplates

were nsertedn theannulus.To save omputationalimemostof thecalculationswereperformed

usinga450modelwith assumed ircumferential eriodicity.Twodifferentmeshes ereused.a50-

cubedmeshwith unirorm, rid spacingn thecircumferential irectionanda secondcrincdmesh

with 1,000,000ells, 100-cubcd.Mostof thecalculationswerepcrronned sing he[tolls-Royce

I ydraCFDcodeand hen c-runusingFLUENT. ydrauses second rdernumerical cheme.he

same sused or standardRANScalculations. o speed pthe lydracalculationshe ow N13ch

number rc-conditioncrwasused.Sunct al. have eported imilar resultsromI lydraandFLUENT

forconvection ndergravity n a cubeas studiedn Chapter .1 ydraandFLUENTsolutionsor

the otatingannulus rcdescribedn therollowing wo subsections.

4.6.1CFD Hydra solutions for the full rotating annulus.

Fivcdiffcrcntcascswcrerun coveringa rangeof Ranumbers, .95x 104o 1.1x 1010. summary

of therunningconditionsand heresultsor theaverage eat ransfer rc shownnTable4.2.

Tablc4.2 Comparison of the I Iydra CFD results %st h measured licat transfer for tile Anchen

scaled rotallne annulus. conflLurallon It.

Case Speed AT p Ra# Ec Nu Nu ANu Notes

(rpm) (K) (bar) (Exp) (CFD) (%)1 2000 24 1 2.76x 10' 0.038 31.2 31.5 2.0 50'mcsh

45* modcl

2 2000 24 2 1.10XIO10 0.038 41.7 42.8 3.0 501mcsit

I 1 1 45* inodcl3 500 28 t 1.95x-IOT- 0.002 17.8 18.5 4.0 50' MCA

45* modcl

4 2000 24 1 2.76x10' 0.038 31.2 32.5 4.0 5Ox5Ox4OOmesh360*model

5 2000 24 1 1-

T.76x10' 0.038

.2I. j 34.2 [ 9.0.0 100' mesh I

_

[

45* model

80



The mean Nusselt numbers given in Table 4.2 for cases I to 4 arc shown graphically in Figure 4.9.

Good agreement with Bohn et al's correlation is demonstrated. including the Rayleigh number

dependency. Sensitivity to both inesh size (see Fable 4.2) and whelliera 45" sector ora full. 360"

annulus are modelled is probably within the uncertainty ot'llie experimental correlation. Figure 4.9

also includes an a(hiptation to the rotating annulus ol'the Colorado correlation (Kirkpatrick el af.

[ 19961)basedon their experimentol'a natural convectioncube.The adapicdColoradocorrelation

wasagainderived by using the temperaturedifference. AT helween(lie hot and cold walls and

replacinggravitational accelerationby cennit'ligal accelermion. t maybe wrillen

Nit - 0.05R, i, ' (4.11)

1000

100

10

a

-1u=O 317RaIO 211.

Aachen Annulus. Air

Nu=0.05RaN 1/3).

Adapted Colorado Cor'n

Hydra. 45 deg model

Hydra, Full annulus,:160 deg model

a

i;r-T-

11

.0...... .r

b-

r-T-

11111100

H- iiniIIiIit iiiIIIIiIiiII -L.

L.Li

I -0

;I-

1 OE+08 1 oi * 09 1 OF* 10 1 01 -11

Rayleigh Number Ra,..

Figure 4.9 ComparKon of Ihe predicled lical franJer %%ilh he %-ichen wäleil rotaling annulu%

C%1)Crinientill c(brrei. Itiofl% ISIIII ei al. 20041

I lie predicted ica I ransler Ievel agices %%e%%ithI Io m cIa I's t:mtclation. Much ,I mt,N 1 %c.kcr

Rayleighnumberdependency han theadaptedKirkpatrick & Bohn(Colorado)correlation, As

mentionedearlier, it seems hat theCoriolis force suppressesheconvecil'on.andthe Rayleigh

numberdependencys closer to thatexpected n gravity at lower Rayleighnumbers Ra I(y).

This lower Rayleighnumber regime is sometimes eferredto as laminarcom ect on in the

engincering iterature. I lowever, it is to berememberedhatGrossmanandLolise's 120001results

xI



indicate that the low Ra regime is associated with significant re%imanceo heat transfer across the

central core. At high Ra, (irossman and Lolise's work indicates a regime with Nu f Ra' 'In which

heat transter is controlled by the boundary layers on (lie surfaces. 11may he that in the rotating I'low

Coriolis effects suppress heat transt'er across the central core. reducing heat transfer rates and

delaying or preventing onset ofthe RaII dependency as Rayleigh numher increases.

30

25

20

15

10

5

0

"

RAN-oVI VVAVA

-Aachen Correlation

- Hyd - 45 deg model- Hyd -

Full Annulus 360 deg model

Adok AAv---- VJA

0 i. I-a... I&--i

13 14 15 16 17 18 19 20

Flow time (s)

Figure 4.10 Variatiom of surface hea( Iramfer %0h Iline for cases I&4, Ra$ - 2.76%10" ISun

el al. 20041

Figure 4.10 gives an example ol'variation of%urface heal Iransfer %%ill time It cases I and 4 from

Fable 4.2. File linic , cl) for these calculations was 10 's. and a simulation period ofat leas( 5

seconds was require(] before it *converged* solution could lie assumed. Tile figure also %flows ile

results given by tile Aachen correlation. Hie 45" sector heal trall-ster is I X" ofthat for tile I.ill

annulus due solely to tile reduced area. Flie variation ol'heM transfer %vithmile clearly indicates tile

presence of' large-scale flow structures. Such flow structures are indicated by the instantaneous

temperature comour plots in Figure 4.11. Fliese structures , io%,.,similarities to those identified for

the rotating cavity woh axial througliflow by. for example. Farthing el A 11992a. 1992hj and Long

and Tucker 119941.Although tile imposition of'periodicity in tile 45" sector model changes tile

details ofthe flowstructure, it

isapparent

froill tile mean Nussell nuinher results presented in Figure

4.9 that this does not greatly alter the overall level of licat transl1cr.

92



I /1

4.11a- 45 (leg model

I OE#ol

I OE 01

I OE-03

I OE 05

I OE 07

1 OE-09

Figurc 4.11 lifflanlancom lemperaturc conlotin for cii%e% 4.k4. Ra# 2.70%1W IStin ei al.2()()41

310

308

306

304

302

300

298296

294

292

290

13 14

"0 45 4.9 Oft t of CP

lqrl MO -, dý T .1 Col

I. I......

15 16 17 18 19

Flow time t (a)

1

10

L'

I

I OE 01 1 OE+00 I OE+01 I OE+02 I OE +03

Frequency Hs

4.111) - .160 (leg model

IOV,4'. Ong T ai ,II

I ty, J Uvo Ong filo, *] I at ( Al

1 OE-11 '

(4.1 2a) Temperal tire history (4.12h) 1'emperal tire Spectra

Figure 4.12 Instiowancous temperature and it%%pectrum for c: %e%&4. Rus - 2.7(ix 109I.Stin

ef al. 20041

Figures 4.12 a ail(i h silow tile jelliperal tire variations oil tile mid-axial plane and their

corresponding turbulent energy spectra lor cases I and 4. In tile legend ('11denotes [lie monitoring

position being ; t a nild-radial point. Hodi 45" and 300'' models give very similar spectra. A

frequency range in which tile slope is close to tile 5.1slope can also he clearly idenlified. A

numerical tail- at high frequencies is noticeable in Figure 4.1211 ndicating that numerical effects

dominate a( tile higher frequencies.

HI



O's

04 Va at CP,360 dogrrxxJol,4w

0.3Vr at CP, 360dogmodel. vý\A at CP. 360 deq mDdel. I y, i

02

01NL.

AI

..t

w.w r. .--. I., .I

IrI TV I fy III

I-0.2 [1rn1

-0 3

-04

-0.513 14 15 16 17 Is 19 20

Flow Time I (a)

(4.13a)

4

1

.0

-3>

I Of01

1 OUGS

10647

1 ce -09

I or 1110100 I OEa

Mquoc y 041

cloci(. ý %pectrum

I or 41 i or-a2 1OF-03

Figure 4.13 Instamancous %cloci() and it%%pecirum for caw 4. Ra# 2.76%10" jSun el al. 20041

IHit: Ili ree ýe Iocitý component lustories ant. I lie ir spec Ira fOr II c cAsc 4.11ic (,() simij I;it ion, dit w%%11

in Figure 4.13 also shm% the properties expected ofitirbulent flo%% Fangential and radial %elocliN

fluctuations dominate at lower frequencies. because the axial velocity is much smaller, From the

above results, it is clear that large scale motions lor the Rao 2.76x 10" case. appear in both the 45"

and 360" model results lor the sealed rotatmg annulus case. I'licre are differences hemeen the 45"

and 360" model results. but these do not greatly affect the mcan licat Iran%1'r predictions.

1 OE#()l

1M 01

1 01 (H

I OF o')

1 OE 07

1 OF ()(;

1 OE 11

1M () I

-I

-( flfl%h T njt'r

101 oo I of -()I

Froquency Hz

1 Of+02

5

1 of -o i

Figure 4.14 Comparison of jelliperalure specira 0.6mm from the otifer cýlindvr %%all)ct%,.ccll

the [%%o e%he%, aý 2.76%10 IStIll el .11.20(141

A mesh depewlence clieck was comiucled with the refined mesh ( 100' mcsh cells) I'M Ra#2.76x 10" (case 5 in Fable 4.2). The iijode, I ed coliditions " ere exactly I ie same as flor case 1. except

I'M the greater degree ofniesh resolution. It can he seen Ili-it the difference in surface heat transfer

84



between the coarse and title meshes I'Orcases I and 5 (see Table 4.2) are probably, within the

experiment uncertainty. The comparison ol'the temperalure fluctuations spectra froin the two

meshesshown in Figure 4.14 clarifies the influence ot'numerical approximanons. In this case the

spectra are 110r point 0.6 min from (lie outer cylindrical surface. File frequency range exhibiting a

slope close to the 5/3 slope is extended oil the finer mesh. As mvilhclassic large eddy simulation. it

appears that the lower frequency furbulence is imemilive to file exact mechanism oflurbillent

energy dissipation at Iligh frequencies. In this case numerical diffusion dissipaics the turbulence

energy.

4.6.2 CFD FLUENTsealed rolating annulu% %olutioll

Sun and Chew, 120041also ran FH 1F. F lo simulate Bohn c( al's scaled [oLat'llt! annulus I lie

calculation was conducted by using second order Implicit nme stepping %vitht second order tilm Ind

scheme for spatial discretisation. The velocity and pressure coupling me(hmi %kashosen to he

Presto [ Patankar, 19801.;1second order pressure correclion melhod Case I was I. 1%st galed %kII

the coarse 50-cubed mesh. All the boundary conditions and other sellings %%erche %amcI.%hose for

Ilydra except that incompressible Ilow was assumed III FH TNT Instead ofilie comprewble tlo%%

assumed III I lydra.

1*C

UI,

t

a.

10

9

8

7

6

5

4

3

2

1

0

k-ichen Correlation. 45 dog modoll

Ftydra. 45 dog modelF uent, 45 dog model

WLI AdwwTWIM 061-UA kv

r. I.......2468 10 12 14 16 Is 20

Flow tifne (s)

igure 4.15 Comparison of licit II rik its fer heowen FLUENT an (I IIý (Ira Calcula I io n%, Ra#

2.76%109 ISun and Che%%2004, Suit et id. 20041

I.igure 4.15 shows a comparison oft lie surface heal transfer predictions ohla Illed using 1-1.1 -.NV

and I lydra as well as [lie experiment correlation. 11 all I)e ,cell Illat IT( IFN F predicts a higher heat

95



transfer, ut theoverallsolutionscomparableo the lydrasolutionand lia experimentorrelation.

Solutionof theadiabatic asewith FLUENTshowcdhigherperturbationromthecxpcctcdsolid

bodyrotation" hanwasobtainedn I lydra.

4.7 Conclusions

Aspart of thepresent tudy,CFDsolutionsor convectionn rotatingenclosed nnular ector avity

havebeenobtained. hisstudywasconductedncollaborationwith SunandChewwho considered

the ull annular avityfromthesame eriesorcxpcrimcnts.Resultswerecompared ith Bohnat

al's experimentalata

andwith convection ndergravity n a cubicenclosure. unandChcw[20041CFDresults howed omegoodagreement ithexperimentalalues ormean urrace eat

transfern therotatingannulusor Rayleighnumbers f ilia order1010,pproachingheRayleigh

numbers ccurringn gas urbinehighpressureompressorisccavities. owcvcr heresultsrom

theFLUENTCFDsimulations rthe scaled otatingsectordidnot agree o well with tile

experiment. hereasonsor thediscrepanciesetweenlia experimentalndcurrentCFDresultsare

still tobe rully understood,utareassociated ith dift"iculticsn numerical onvergencedentified

for ilia solidbodyrotation estcase.Theuseof non-unirorm ircumrcrcntial icsilspacingor tilesector,mayhaveaffectednumerical tability of ilia scheme.

It has beenshownthat in both gravity and ccntrirugally driven convection,theCFD solutions

capture he presenceof large-scaleunsteady low structuresand lower frequency urbulent

structures.The smallest Kolmogorov) turbulent lengthscale$arenot fully resolved, ndicating that

thesecalculationsshouldbeclassedaslargeeddy simulationswith numericaldiffusion contributing

to the turbulenceenergydissipation.Sensitivity to numericalerrorshas been nvestigated.Meanheattransferratesshow only slight dependence n meshdensity,with the variation probablybeing

within the range of die experimentaluncertainties.Due to thepresenceor largescale low features.

thesurfaccaveragedheat ransrcrratesvary significantly with time, introducing rurtlicr

uncertainties n judging numerical convergenceandcalculationof mean icat transrcrrates.use or

eithera 45* sectormodel. with circurnrerctilial periodicity, or a fall annulushas been ound to make

little difference to themeanheattransrcrpredictions.

Following he nvestigationreported bove,LEScalculationsor the low in a rotatingcavitywith

axial hroughflowwereundcrtakcnndreported ySunct al [2004).71mestudies ivefurther

86



insight into the flow physicsandwill be referred o in thediscussionof moreelementarymodels n

subsequenthapters.

It is of interest o compare heheat ransfer n thesealed otating annulusconsideredhere o that

from theouter shroud n rotating cavitieswith a centralaxial throughflow.Kim et al (1993]and

Long et al (1994,2003] havereportedexperimental esults or axial throughflowconfigurations. n

therangeof throughflowratescovered,Long et al found ittle sensitivity of shroudheat ransfer o

throughflowrate, andtheNusseltnumberdependencyookscloser o a Ra'13 ependencyhanto

Bohnet al's Rao21 dependency.Kim et al's shroudNusseltnumbersat high throughflowrate also

appear o vary approximatelyasRa'13, ut at low flow rates heRayleighnumberdependencys

weaker.Thus, it appearshat theRadependency trengthenssthroughflowrate ncreases,perhapstending o a Ra'13 ependencyat high flow rates. t is conjecturedhatat thehigh throughflowrates,

theturbulenceassociatedwith axial throughflowstrengthensheheat ransferacross hecentral core

region.The overall level of heat ransfermight thenprincipallydependon theboundary ayeron the

outercylinder, for which a Ra1/3 ependencymight beexpectedby analogy with convectionunder

gravity. However,themixing between heaxial throughflowandthecentral coreflow in thecavity

remains o beunderstood.

It wasconcluded rom these hat theCFD modelsshowpromiseas predictivetools for compressor

disccavity convection.However,several ssues emainedo beresolvedandthecomputing

requirements revery high,which would severely imit applicationof themethodsn design.

Hence,n theremainderof thepresentstudy, t wasdecidedo concentrate n simpler modelsof the

effectsof buoyancy.

87



CHAPTER 5

COMPUTATIONAL FLUID DYNAMICS SIMULATION OF FLOW PAST A

RECTANGULAR CAVITY

Summary

In this chaptera CFD studyof theflow passingovera rectangular avity ispresented. seriesof

differing cavity depthshavebeenmodelled.Thecomputationalesultshavebeencomparedwith

otherworkers' experimentalmeasurementsf cavitypressure nd low velocities.The

computationalmodelsimulateshe flow mechanismeasonablywell. However hemodel under

predicts hestrengthof thecirculatingflow within thecavityanddoesnot predict correctly he

shearstrengthof thecross low which drives hecirculating low in thecavity.

5.1 Introduction

As noted n Chapter1,an mportant low mechanismwithin a gas urbinecompressors the

interactionof thecoolingair flowing rearwardshrough hecentrecoreof thecompressor ith the

flow within thecompressornter-disccavities.As mentioned reviously n section2.5, for an

unheated avity rotating at low speedheaxial throughflowgeneratesne or more orodidalvortices

in thecavity.Similareffectshavebeenobservedor planar wo-dimensional21))now over a

stationaryplanar2D cavity.Hence t is appropriateo considerhis simplerplanar low. The

HaugenandDhanak 1966]experimenthasbeenchosenor theCFDstudy,as t is, in principle,a

2D flow problem.

5.2 Description of the Experiment.

HaugenandDhanak'sexperimentwasdescribedn Chapter2 section2.5,but thisdescriptions

nowbriefly repeatedor completeness. heexperimental pparatusonsisted f an adjustable

length low channelandarectangular avitywith adjustable epths.Thechannelwas63.5mm,

(2.5") wideandhadanaspectatio of 10,ensuringa substantially D now. Thecavitywidth was

fixedat63.5mm 2.5") and ts depthwasvariedup to I 14.3mm4.5"). Thefreestreamair velocity

88



wasestimatedo be30.48m/s 100 ft/s). Theboundaryayerthicknessust upstreamof thecavity

couldbe increasedup to 25.4mm (I") and,by observation,wasfoundto beturbulent.Static

pressuresweremeasured longthecavity walls by meansof a micromanometer. hestaticpressure

wasalsomeasuredcross

heshear

ayer bya probe

heldnormally

to thecross-flow

direction.

Temporal-meanvelocity andturbulent ntensitiesweremeasured y meansof a constant-current

hot-wireanemometer. variable-positionraversemechanismwasderived or movingthehot-wire

probe ongitudinally,parallelto themean low, and ransversely crosshemixing region.Thehot-

wire probemeasurements ere used o determinehedistributionsof the time-meanongitudinal

velocity, turbulencentensity,and urbulentshearstressacrosshemixing region.For theflow-

visualizationstudiesa secondexperimental ig with thesamedimensionswas used.This rig was

subjectedo flow of waterapproximatelysimulating hedynamicconditions n termsof flowReynoldsnumberandrelativeboundary-layerhickness.


CFDcalculationsmodelling he interactionof theflow passingoveran opencavity with theflow

within thecavityhavebeencompletedor a numberof differentcavitydepths.A typicalCFDmesh

used n thesimulationss shown n Figure5.1. A 2D quadrilateralmeshwas usedwith themesh

expanding wayfromboththe innerwall and alsoaway romthe threewalls within therectangular

testcavity.Thenon-dimensional earwall distance arameter; , (=pu, ýp) valuesn thecavity

were ess han1.Thismeshhasa totalof 22,800cells,with 9,600of thesecells ocatedn thecavity

section.

As in the experiment, the test cavity width, s, of 63.5mm was held constant for all the numerical

simulations whilst the test cavity depth, h, was altered to give various IN geometry ratios. The

various test cavity depth to width ratios chosenfor the simulations were 1.0,1.5,2.0 and 3.0. For

the purposeof creating a boundary layer upstreamof the cavity and also to eliminate any end

effects which may have had an influence on the CFD solution in the area of the cavity, the

dimension of flow channel external to the test cavity was chosento be 250mm in height and 635mm

in length upstreamand downstream of the test cavity which is 10 x s, the test cavity width. The

inner wall of the external flow channel and the threewalls of the test cavity were set asadiabatic,

no-slip boundaries.The velocities were specified at the inlet with a constantaxial velocity of 30.48

m/s, with a total temperatureof 300 K. Static pressurewas specified as 101.32 kPa at the

89



dowliNlream outlet. The far ficid outcr boundar\ of dic emernal flow channel \%a-,%clas a symmon

houndary type and has no influence on the fhm pa%ilic lc%tcavity.

Figure 5.1 A 1ýpical (T 1) me%limed hi the %imulation.

I 11Ccolliptitat loll Carried out solve% he coiiscr%ationequaliolls fol 111011101111111nd clicip I.,

dewribed in Chapter 3. wci ion 3.4. The fluld usctj In the simulatiom " as air %%th conmant fluld

propcrile%.%Nth Npcciflc licat ((',, ) of' 100(1.43Ag IK1, tilerinal conductiN ty (k) 0.0242 Win 'K

clý'Ilaflllc viscosily (it) 1.7894 - 10

defilled III tile model.

cow-imil fluld dclisilY (P) of' 1 22ý k9lli i%%.%

90



CFD models were run assumingsteady urbulent flow. Thestandardk-c modelandthe2-laycr k-c

/W near wall turbulencemodelswcrc used.To alter theboundary-laycr hicknessupstreamof the

testcavity the turbulence ntensityspecifiedat the inlet boundarycondition wasvariedbetween1%

and 10%.The resultingrelative boundary-laycr hickness 81s) angewas0.25to 0.5 which

correspondswith boundary-laycr hicknessesrom theI laugcnandDhanakexperiments.

As in Chapter3, themethodchosen or discrctizationof thescalarandmomentumequationswas

thesccond-orderupwind scheme.A secondorderschemewasused or thepressurenterpolation

andfor thepressurc-vclocitycoupling (prcssurc-corrcction)heSIMPLE algorithm was used.

5.4Results

For thesimulationsusingair astheworking fluid, resultsobtained rom theanalysisof tile I I/s -

1.5geometrywith a relativeboundary-laycr hickncssof 0.25havebeenrcporiedandcompared

with theequivalentcxpcrimcntalresults.The bestcxperimcntalresults n termsor themeasurement

quality wereobtained or this case.

Figure5.2 showsvelocity profilcs of x-vclocity (horizontaldirection)versusdistancey (normal

coordinate) or threex (horizontalcoordinate)positionsacross hetestcavity. Coordinatey is

positive in thedirectionout of the testcavity into themaincross low, Whilst a negativey value

givesthedistance nto the testcavity. 71ic CFD resultsarc shown alongside heexperimentalest

results.The velocity plot shows hat theCFD profilc out or [fie cavity in to themaincross low does

notquite replicate heboundary-laycr hicknessn theexperiment M-0.25 CFD, -0.3 Test) but the

profilc is reasonable. lowcvcr, insidethe testcavity thevclocity proriles indicate h3t,heCFD

modelundcr-prcdicts hestrcngthof thecirculating flow within thecavity. It appearshat thek-c A.

I turbulencemodcldoesnot correctlypredicttheslicaror ti,c cross low which drivesthecirculating

flow in thecavity. Figure5.3shows hat the fine nicshemployednear o thewalls (y* < 1)

adequatelycsolvcs he flow in theregion close o the testcavity walls (x/s -0 upstreamand -I

downstreamwalls). The plot also shows hat thevertical velocity risessteeplyat thedownstream

comerof thetestcavity (for y/s -0 at positionx/s - 1)at therecompressionomcr %%Iicrchex

velocity - 0.

91



-CFD xf.%-0 15

-CFD Wý, 0 5

-CFD fý%-0 85

x Test wý, 0 15

4 Test w, -0 5

X Test xf%.o 85

11C % "l- IN IIII

'. I

Fignre 5.2 Comparison of*CIA) and experimental %-Nlocilý profiles taken sit three po%ition%

acros% fie test caNty (I 1/.% 1.5).

f

ol

I() V, 0V, M

1 1) y/I 04

(A 0 y/ N. -O

-Cl D-yO. -O

CFD-yf%-O

UID y" 01

(My, 04

,, 4 11 (,

I.

I-igure 5.3 CIA) predicted N-%clocilNpj-()j-jlt. Icl-(,%.,fic test ca%itý sit various %erfical dkiances

in to and oul offlic cu%tý ill/% 1.5j.



0.1

L

C.-

I.

"I

03 -

16on

-(, I () (, iwtvd,, w, %tr ..... ý -011

(If D Cawy ý4wmnm all

l"%1-CRmtyd,, MýIr. nfy, w. lll

4 7.. l C.a"Iv, 4,111 V, w"ll

1412Normal 01.1filicc. ý-

(a) VpAream and do%%noreami%all%

I

'le

i

01 .

02

Q3

A

dotamc in I., the :a%ts

08 04 0;

II

01 02 ol 114 11 06 07 ol 09

Non dimommial Micam%owc Olkla"Cc. %N

(h) Bot(oll) Surface.

I-igure 5.4 CIA) p redicied III (I it, %I III cmured prevure d istribil I ioll% a oll lie I v%IC.1%I%

%sall% 1/% 1.5). (.1) upOream and domi%fream (b) bottom %urface.

-CFD-Ca, Aty bottom wall

I 7061-CaAty tXMIMI Wall

93



Figurc5.4comparcs FDprcdictcd ressurc istributions long he estcavity walls withmcasurcd

prcssurcs.igurc5.4ashows rcssurcs long heupstrcamnddownstrcarn allswhast igurc 5.4b

showshepressurc istributionalong hebottomsurracc f the cstcavity.71cprcssuresgivcnas

apressurcocfricicnt Cp) dermcd s:

cp-(P-P. )/(`/`/irl! (5.1)

wherep is thestaticpressurePa], u is ti,c x-componentor time-mcanvelocity [ms*lj and p is thc

fluid density [kgm'3]. I'lic subscript,co indicates he frcc-sircamcondition.

The CFD computedpressureprofiles alongthe testcavity walls follow tile trendof the test

measured ressureprofiles,but undcr-prcdict near hetestcavity downstrcamcomcr (yls - 0). This

is againan indicationthat theCFD k-c/k.1 urbulencemodelunderpredicts hestrengthof the

circulating flow within thecavity andtheshcarstrengthof thecross low on thecirculating flow

with in thecavity.

Figure 5.5 shows tile computed flow streamlines within the test cavity. A circulation mass flow per

unit depth (perpendicular to the flow plane) orO. 162 kg/sm is generated by the shcaring of die cross

flow in the main channel. It is interesting to note that only one circulation is generated within the

cavity. For whichever cavity dcpth was chosen, CFD predicted only one circulation. For cavities

with an I Usup to 1.5. test measurement of pressureon the cavity walls indicate that only one

circulation is fornicd. I lowcvcr, tile CFD results conflict with experimental evidence. I laugcn and

Dhanak also carried out flow visualisation experiments using water as the working fluid. Various

cavity depths were tested in the I I/s - 1.0-

3.0 range. The test conditions approximately simulated

the dynamic conditions of the experiments with air in terms of flow Reynolds number and the

relative boundary-laycr thickness (m). Figure 5.6 shows the results from the water tests in tile form

or nowvisualization flow pattern pictures. The flow pattcrns portrayed show that as cavity dcpth is

increased the number orcirculations or vortices generated within tile cavity increases. I laugcn and

Dhanak observed that for I I/s -I (see Figure 5.6 (a) - note that this picture is printed upside down)

there was a single vortex and it was stable, resembling almost a solid body rotation. Around Ills of

1.75 secondary vortices appear in transition, and at a value or I i/s -2a clear second %-orlcx

structure is formed. Transition again seemsto take place around I [Is - 2.5 %%cn the number or

vortices oscillates bctwccn two and three. Finally. for I vs on, three vortices arc fornicd. The

vortices were observed to countcr-rotatc relative to eachother.

94



112708-01

,0"0

ime-oi

a wo -cie

3 000 -cia

4000-m

3000-49

2004-02

1 000 -w

I. ION%

16. k.v , in

i

Figure 5.5 CFD predicted flom, pattern i%ilh in the ico cso%ilý confour% ofoream funclion.

Ilatipen &. Dhanak - Momcnium I't-MINICT ( 'I I)&I- \I)C 'l IVII t

(a) II"I ()

Ifs 2.0

II IS

10

1'"m ,ý'. II I-, v., It, I H. -.., ýII

1-igure 5.0 Ilaugen and Dlianak fit),, %j%jj.jj/. jjion experiment (macr) flo%%pallern% %%ilhill file

1c%lca%ilý (From flaugen and Dhanak 119061).

')S



F-111111clH) compulat lolls have been performed to simulate the flo%% ithin the test cavily u%ing

%%aicrs the fluid. Two cavity II, 2 and IIS.1. %%re considered. The (T 1)calculailions

were obtained oil Olesame ('I. D meshes u,,cd in the calculation% for air. Similm Reynolds numbers

%%ereet 'm both experiments. %kih air and %%th %%ater.he (T 1) homidary conditions and fluid

properties %%-erelicred to approximate the condmons used in the %%alcr\pcnincrils. to gi\c the

correct I'low Reynolds number and the rclamc botindary-layer thickncs% 6 %).I lie inlet amal

velocily \%as et to 2.097 in , with a iotal icmperature of'.100 K and the oudo siatic pressure \%as cl

to 101.32 kPa. Inlet flow lurbulcrice illiculsitv was set it I,,,, to give an approximale relame

houndarý-laycr lhickness, 6's, of'O.25.

The fluld used In tile simulations was %%aier%kih conmani fluid properlie%. wifli specific 11C.11 (',, ) of'

4182 Ag 'K '. Ihernia I cond tic nN ty (k) ().o \\'ill 'K 1.dynamic \isco%ily (it) OOM kgm 's ' and I

constant fluld density (p) of'998.2 kgm '.

\Iodck assumcd turbolcm flow using flic Ntandardk-c model and tile 2-laycr k--#;k-/ ncar \%aII

turbuicnce models. Steady fioý% 'Is%tilliedll 111ile models.

2400+01228"1

2160+01

2 04+0 1

1 920+01

1 00"01

I sees I

1 36"1

1440+01

1 329+01

120"01

1 Oft*O 1

980*+00a 400#W

720*+00

6,000#00

4806+00

3 OD&*00

2400+00

120*+00

0 000#00

/

I

I-igure 5.7 CIA) predicted 11(m palleni i%ilh iii the ltl%t c3l%ifý (11,%of %freall) filliclioll.

- ----Tlmý

( 'lictliallon11()%% 7.125 kg %-m

2) usilig ' aki contours

96



Figure5.7showsheCFDpredictedlow patternor thecavitydepthor i us-2 with wateras he

fluid.TheCFDmodelpredicts nlyonecirculationvortex)s ronnedwhichconflictswith tile

experiment herewovorticesarcshownocxis4asshoAmn Figure5.6(c).

5.5 Conclusions

In this chapter the results from the CFD simulations of experiments pcrrormCd by I laugcn and

Dhanak, investigating the interaction orcross-flow over a rectangular cavity will) tile flow in tile

cavity have been presented. The numerical results have been compared to the velocity and pressure

measurements for the experiments with air and flow visualisation ror tile tests with water.

Theconclusionshatcanbedrawn rom hiswork are:

The urbulent -c/W 2-layermodelundcr-prcdictshestrength f thecirculatinglow withinthe

cavity.

TheCFDmodel

doesnotpredictcorrectlyheshearorceof thecross-flow ndhencehe

momentumransfer etweenhecross-flow nd he lowwithindiecavity s incorrect.

CFD predictedpressures longthecavity walls follow the trendorthe testmeasured ressures, ut

underpredict the strengthof theeffects, especiallynear he testcavity downstreamcomer(y/s - 0).

ror cavity depths up to 3 times the cavity width the CFD predicts only one circulation. For cavities

with I I/s up to 1.5. the pressure measurements on the cavity walk indicate that only one circulation

is formed. I lowcvcr the experiments with water show that more th3n one circulation is formed for

cavity depths, with I I/s greater than 1.5, whilst CFD predicts only one circulation for all depths. 77he

reason why more than one circulation (with water) can cxist and why the CFD analyses rail to

simulate this still need to be fully explained, but could lie in the turbulence modelling.

Theexperimental esultsarc limited but little otherresearchwork hasbeenreported n theareaof

engineapplications.Withsome eservations

CFDmay

beused o model flows for this typeor

applicationand asan initial s1cpwill beapplied,with caution, o thepresentproblemorcomprcssor

inicr-disccavitieswith axial througliflow. I lo%%-cvcr,urthernumerical nvestigationsusing large

97



eddysimulationLES)of turbulence re ccommendcd.t is hopcdhatLESwill capture nd

resolvehe urbulencecncratcd ithin thecavityandalson theshearayersof thecross low.

This work is importantbecauseof theneed o know the evelsof heatand momentum ransfer

across heshear ayer from thecross-flow to thecavity and n termsora gas urbinecompressorhe

transrcror heatandmomentum rom theaxial throughlow under hedisc bores o the inter-disc

cavities.In the2D axisymmetricCFD modeldescribedn Ch3ptcr7 and applied n chapters8 and

9. thestandardk-c turbulencemodel will beemployed o model sucheffects.

98



CHAPTER 6

SUSSEXAl ULTI-CAVITY RIG BUI LD 2 TI I EICNIALMATO I 14NG

Summary

A temperature atchingexercise asbeenperformed ntheUniversityorSusscxTechnology

Centre SussexUTC)multiplecavityrig build2 using heRolls-Royceiniteelement rogram

SC03.This rig simulateshe nternalcomponentsnd low featuresora high-pressureompressor

(I IPC).Threemodelswereconstructed,irstly adatummodelusingconventionalhermalboundary

conditions.Thesecondmodelusesheboundary onditionsromthedatummodelbutreplaceshe

conventional eat ransfer ocfficicntcorrelationapplied o thediscsurraces ith a-conc

correlation,CONE"whichwasderivedby SussexUTC.The hirdmodel s the"bestmatched"

model o the hermocouplemeasurements.achmodelwas unthrough hesamedle to maximum

speed ccclcration-dcccicrationycle.Resultsromthebest-matchcd odelgave emperature

differenceerrors,measuremento modelprediction,or lesshan5K bothatsteady tateand

accelerationransient onditions. lowcvcr,a temperaturerrororsK issigniricantas he

temperatureiffercnccbetweenhehotmetal nicr-disccavity shroudand hecooleraxial

throughflowair is50Kat themaximum peed ondition.Alsoto achievehebestmatch,extreme

thermalboundaryconditionshad o beassumed,ncludingan mbalanceor licallmasslow in and

out orthe intcr-disccavities.Thisestablisheshequalityof thestatc-or-the-artonventional

methods ndprovidesabenchmarkorcomparinghenewmodellingmethodhatwill be described

in Chapter .

6.1 Introduction

Themultiplecavityrig at theSussexUTCsimulatesile internalair system f ahigh-pressure

compressor.s previouslymentionedn Chapter section .4.2 ileairnortlic Sussexrig was o

provide estdata hatcanbeusedo improve hephysicalunderstandingr tile flow and icat

transfermechanisms

n theIIPCrotatingcavitiesso

hataccurate redictionsan

bemadeofair

system elivery emperatures,rummetal emperatures,iscstressingndcriticaloperating

clearances.

99



Build I of tile SussexMultiple Cavity Rig (MCRB I) wasused o investigatetile flow andbeat

transfcrmcchanisms n the I IPC drive cone cavity at the rcarorthe II PC(Alexiou 2000. ICAS-GT

2001,Alcxiou 2002]. The inner drive shaft (rcprcscntingthe intermcdiateprcssurc, P drive shaft)

wasable to co-rotatcor contra-rotateandcontainedholes for turbine disc borc anddisc rear face

conditioning air. From the MCRB I researchat Sussexa licat transrercorrelation for the inner

surfaceof the I IPC drive conehas beenderived.This 'CONE' beattransfcr corrclation hasnow

beencodedinto tile Rolls-Royce internal thcrmal analysiscomputcr program,SC03 [Barnes2002,

Collcy 2001).

TIC SusscxCONE' hcat ransfcrcorrclations,

For Ro/(P,&T)1/2<6 Buoyancy dominated now regline.

Nu = 0.0243Rc,0'0"Gro-316x-l[r-l - 11 0022 (2.37)

For Ro/(PAT)"2 >6 Througliflow dominated flow reginic.

Nu= 8.93xI O'sRc.1.301X'3.521 (2.38)

In theabove,Nu is the local Nusscit number,x- r/b is the radius ratio, Ile, is theaxial througliflow

ReynoldsnumberandGr - C12rinOPAT(r/sinO)'M is theGrashornunibcr, where0 is tile conehalf

angle. Ro is the Rossbynumber.For build 2 orthe SussexUTC Nfulti-Cavity rig (NIC11112)ile

drive coneorMCRB I wasreplacedwith two discsto createrour cylindrical cavities all with the

same nner andouter radii anddisc spacing.asshown in Figure 6.1. A non-rotating constant adius

shaft,with a glasswindow to allow optical access, eplaced he rotating inner IP drive sh. ft. Ilic

MCRB2 provided both steadystateandtransientmetalandair temperatures.n addition, velocitymeasurements rthc flow in the intcr-disc cavitieshavebeenreported(Long et al. 2006s, 2006b,

2006c].

Initially twobase inethermalanalysesmodelswereproducedor theSussexMCRB2using he

Rolls-Royceautomaticiniteelement odeSC03;adatummodelusing heconventionalmodelling

assumptionssedn the hermalmatchingorMCRB1,anda modelwith thestandard atural

convection orrelationsor thediscsurfaceseplaced y theSussexUTC CONEcorrelation. `hcsc

twoSC03 hermalmodelswereproduced ndcomparedo thediscrotating hermocoupleest

100



measurementsor a transient cccleration-decelerationycle(Kilfbil 20031.'lic nuin objectiveor

the nitial thermalanalysiswas o achievean accurateemperature atch orMCRB2 hrougha

transient cccicration-dcccierationycleandobtainsomensight ntotheheatconvection rocess.

Thesecondmodelwasproducedn order o evaluateheuseor the"conccorrclation" or disc

cavityheat ransrcr.A third thcrtnalmodelwasproducedoachieve "bestnutchcd"'modcl o the

thennocouplemeasurements.

Detailsof themethods ndassumptionsor thedatumand conecorrelation"modelsarcgiven n

section6.2.Resultsromthe hree hermalmodels regiven n section6.3.Section6.4 isa

discussionof theresults.The hermalboundary onditionassumptionsequiredoobtain hebest-

matchedmodelarcalsodiscussedn thissection.A calculationo estimatehediscaxialheatnow

using hemeasuredemperatureshenrollows.To completehesectionastudyor thecfrcctsor

internalradiationonthecomponentss discussed. hechapterscompletedwith section6.5,

conclusions longwith rccommendatonsonthewayrorwardo model IPC nternalcomponents

and low rcaturcs.

6.2 Methods and Assumptions

SC03 Version7CO)wasused or all thermalanalyses.'lic 2Daxisymmetric eometry sedn tile

thermalanalysesrMCRB2 wassuppliedby theSussexUTCandcanbeseenn Figure6.1. 'lic

rig dimensionsin mm)arealsoshown.Materialsusedn theNICKare&flownn Figure6.2. The

compressorotordrum s titanium TDQ- Rolls-Roycematerial odes).herig casing.ile inner

shaftand hecompressorriveshaftsarc steel AZA andAIIJ). I'lic innerstationary hallhasa

glasswindow(#GLASI AFT- userdefinedmaterial)oallowopticalaccesso therotorcavitiesfor LaserDopplerAnemometerLDA) nowvelocitymeasurements.

101



sunf. 1"IC %luld-C. Mly lug Build 1

Modified vAlh Nuild I Modelling cufwfirwr

IIP Rotor DrumDiscs No. I to 4

Inter-discCavities

No. I to 4

L

400KOO

i

HI2

-0

I -)

Figure 6.1 Ex(en( of (lie Sussex NICRB2 gcomcIr. N iii the thermal model.

Figure 6.2 Nia(crials used in the Sussex NICRIQ therivial model.

1-

102



6.2.1 Operating condition%

The operating conditions (along with thermocouple test dala) ý%re supplied by the Su...'sex [A U.

The speed ofthe III) shall is shown below in Figure 6.3 for the transient acceleration-deceleratioti

(accel/decal) test cycle.

Sussex UTC MCR82

__ 111ffl3000

2000

1000

------------T-FT-Tl

Fff-

i- -T-l-1-TTI=LLZTTT-FHil

II

III III

Hi

iFT1 II LLLLLL LI-LI-I II1 1-1-"

4000

ill i 1IFT-T-T-F-FT-F-FT-T-F-F-FT-T-TiI 1 1111111 11 11 11 1 Till1. LL

F-TT

Ill III rTT11-4 -- Ill

0 600 1000 1500 2000 25W 3000 3600 4000 46W 5000

Time (s)

Figure 0.3 IIP shaft speed used in lite su....ex mcRB2 Otermal model.

6.2.2 Thermal boundary condilions

-Measuredmetal temperatureswere imposedon the rotor outer surface or the %%holeycle. I-lie

measurementsrom the threethermocouples seeFigure6.6) were linearly Interpolatedand

extrapolatedacross he kill lengili of the compre%soruter surface or each measurement ine point.

Using these emperaturedistribunmis a.

11)graphof temperaturevs.axial distance%s, ycle time

wasproduced seeFigure6.4). The temperaturegraphwasthenusedasthe temperature nput in the

convectionzone on the rotor outer surlace.The definition ol'a convection/.one is gi%enn section

103



6.2.3. A very high heat transfer coefficient %%ashen specified it) force the calculaied lemperature to

match the measured metal temperaturcs on ilic compressor outer surflice.

/-I clI*pcIaIuIt

I\,.., I ), .1, ýý

.11,111bgoftillic%-1

I )mIll I littl I

Figure 0.4 Measured mcial temperalurc% on the compre%%or drmn rolor ouler %urface during

the Iramiew eNcle.

.Fhe it Ir system daut. such as ilia ss I ow, flow InI ct iempera Itire itnd ca% t y pressures %%re dcr I% d

from the test dala provided. The mass flow rale 1'()r he axial througlillow ol'air through the inside (it'

the compressor was lield at it constant rate ol'O. 4 kg s 1hrotighoul the accel, decel le%tcycle

considered.

Fhehoundary condinons III ilie cavkv between the rotor outer surf',cc and the inner surflice of 111c

casing drum were implemented III SCO. using [lie -%old" modelling 1emure.shm%n II Figure 6.5 as

V( )24.1 and V025,1. The definition ol'a thermaI void is gi%enIII sectioil 6.2.3. Therma I voids %%ere

ý1so appl Ied Io bolh I ie fron I 1',ce (VO 17.2) and to I ie rear flice (V()27.1 ) of(he rotor (Inini.

Fhe main part of1he imer-disc cavities was again modelled using the void f*cature V03. V05. V06

and V07). The standard modelling technique is to feed each void with (lie heat from 10"o ofthe

axial throught'low air. I lem transfer on the disc surfaces was assumed to he natural convection and

used the natural vertical plate correlation 'NVII(b f s,2-y)* with the characteristic length equal to the

104



cavity outer radius. 1)plus liall'the cavity width. s minus the local radius. y. For the dattim model

(his modelling approach was used except that the heat transl.er coefficient for the disc surfaces was

set to 0.5-NVI), which was it direct read across from the Sussex MURBI therinally matched model.

Also in the datum model 0.75 ýNUS(I. ). (where NUS is the natural convection heat transler from

the tipper surface ol'a horizontal flat plate correlation). was used for (lie cavity shroud. The

characteristic length. I., was set as [lie cavity width. In the region heiween the disc cohs 10"o ofilic

axial (hroughtlow was assumed to circulate and was modelled with the thermal "stream" fleature.

For the second inter-disc cavily the thermal streanis are shown in Figure 6.5 as STI I and STI 2.

1hernial streams arc t1cf-ined n section 6.2.3.

1113

ttT*MV-

tooLl-' I

ZU-,

(ý. .."I.:

)

Sunrx I TrC%IulcJ-0MIy Rig PAdid 2

Modillrd with build I modelHagrxpnirner

ý: ýBý,

ei -

3

.dý,ft

.

QoI

LQ

Figure 6.5 Localion of thermal hotjndar. ý conditions.

loo

-..,

-W

AL

OwAt"

0

I lie amal througliflow under the disc cobs vas modelled is a series oflinked conveciing "ducts-

and "sircams". Figure 6.5 shows for the first stage disc. ducts DLJ23A and D1123131*()rhe bore

thermal duct and stream ST 15 lor the thermal stream. Thermal duct is defined in section 6.2.3. In

the disc bores full axial througliflow was applied to the thermal ducts and for [lie inter-disc region

4%%

I

I\... "--: .A

34%ft

105



0.9of theaxial througliflowwasappliedo the hermalstream.A smallamountof temperature

mixinghasbeenassumedlong he nnershaftasair fromthe ntcr-disccavitiesmixeswith tile

axialthroughflow.

In the datum model the "internal radiation" featurewas applied to thecasing walls, which surround

the rotating. drum. The cmissivity wassetto 0.5. IntcmaI radiation is dermcd in section6.2.3.

In the secondSC03 model thedisc surraceNVP hcat transrcrcorrelation was replacedby the

SussexUTC CONE correlation using theparametersof thecavity outcr radius,the disc bore radius,

the IP shaft radius, the conehalf angle(ror a disc, W2radians) and theaxial throughflow rate.Also

the factor applied to the cavity shroudhcattransrerwasalteredto 0.677xNUS which gives the

equivalentheattransfcr asthat given by a secondSussexUTC correlation ror the cavity shroudhcat

transferwhich wasderived from the multi-cavity rig experiments.

The hirdSC03modelwasanattemptoobtaina"best"match o the hermocouplemeasurements

bothat steady tateconditionsandduring he ransient ccelerationrom dleto themaximum peed

condition.The hermalboundaryconditionswithin the nter-disc avitieswerealteredo try to

achievehistemperaturematch.The

modellingor

thefinalbest

matchedmodelwillbe described

later n section6.4.

6.2.3Thermal boundary definitions

Convedlon Zone: A convectingzone s usedwherethe fluid temperaturedistribution is known.

This temperaturecould bea single value or could varyin

spaceand time.Convecting

zonesareessentiallyregionsor infinite licat capacity. husthe fluid temperaturespccificd will not change

regardlessof the heattransferbetween he fluid andthecomponent.The surfaceheat flux is given

by;

Q-hA(Tr-Ts) (6.1)

where , isthesurfaceocalmetalemperaturendhe icit transferoefficictit, maybeestimated

using numberf available ussclt umberorrelations.

Vold: A thennalvoid is a regionof negligibleheatcapacity.A thmnal void isused o represent

region hat sat a unironntemperaturetheentirevoid isata single emperature)nd sat

106



instantaneousequilibriumwith itssurroundings.n practicehishas hecffcctof providingaheat

tmnsrcrmechanismhat endsoaveragehe cmpcraturcsr thesurrounding oundariesaccording

to the ocalheat lux. Thevoid can hcrcrorcbeused o transfcrheatacross nair cavity.Additional

heatcanbeaddcdo thevoid via apower crm(gcncraly froma masslow at, for example,

temperature.,,.,,, nto thevoid).

Thc void tcmpcraturc s givcn by; TIfhd4

whcrc

(6.2)

(6.3)

Stream:The hermalstrcamsusedodcrinea portionor theboundaryhathasa finite flow of

fluid along ts length. t iscapable f absorbing nergy romone ocationonthesurracc nd

transportingt to another.A strcarn asa finite licatcapacity.The nlct air temperaturerthe strcam

isdcrincdand hevariationn fluid temperaturelong heboundaryscalculated onsidering

convection,heheatcapacityor thestrcamandanyadditionalheating. uchaswindage. hermal

streamsanbe inkedandmixed ogether.

Temperatureick upalong he cngthof a streams givenby;

dT, [Tlli(T, - Tf )] dl

+7 ;,

jJvc dv

(6.4)

where,s is therelative distancealong surface, ip. is the heatpick-up andthemixed temperature,

T. i., s calculatedfrom an cnthalpy balance:

(IP'CPT), (1;C,,T), + (1;C,,T), +... - (1;C,,T). i, (6.5)

Duct: A thmnalduct s identical oa thcnnalstrcamn all respectsxcepthat woportionsof the

boundaryarcdcrincdbetweenwhich heflow occurs.Energy anbeexchangedetweenhefluid

and he wosurfaces nd ransportedia theduct low.

fh T,d,4+ Q.

107



Internal and External Radiation:The nternal adiationheat ransfcrboundary ondition sused

todcrineportionsof theboundarywhicharecapable rtransmittingandreceiving adiation rom

dicmsclvcsandcachother.View factorsarc calculated utomatically.

I [eat low:Q6, - ý,., A,a(T, - T2') (6.6)

whcrc a is the Stcfan-Boltzmannconstant- 5.6687x10*8W/rn2K4

--a.2--a0.

I

ano tnc grcy Douy vicw iactor, ;,., -,

(I FI-3 A,-,,

(6.7)

and c is theEmissivity, heproportionof blackbodyradiationemitted romeachsurracc.F is the

shapeactor.

Externaladiationsused o accountor radiativeicattransrcrromarcinotcsourcehat snot part

of the hermalmodel.I'liespccificdvalueof thisremoteemperaturesnot influenced y theheat

transfer o (or from) t.

6.3 Results

Therig 24rotating hermocouplesTC -TC24)connectedoa slip-ringunit.Twenty-one f these

thermocouplesTC -TC21)wereconnectedothecompressoriscsand o thecavity shrouds, s

shownn Figure6.6.A further3 rotating hcrmocoupIcsTC22-TC24)werepositioned xially

along heoutcrsurface f theCompressorrum.Onthe nnerstationary riveshall7

thermocouplesTC25-TC3 )werepositioned long he engthof theshaft.Further tationary

thermocoupleserepositionedo measurehemetal emperaturer thecompressorasing.Air

temperaturehermocoupleserepositionedn theannular pace etweenheoutcrsurface f the

compressorrumand hecasingand o measureheupstreamnddownstreamemperaturef the

air flowingthroughheannularpassageetweenhe nnershaftand hecompressoriscsborcs.

Temperaturemeasurementscrctakenat time ntervals f 2.5secondshroughouthecntirctest

cycle.The SC03modelwas untransiently hroughdiecycleshownn Figure6.3toa specified

accuracy f 0.2K.Towardsheendof theperiodat maximum peedtime-- 2800s)hesolution

approachessteady tatecondition.A temperatureontourplotat thistimepoint s shownn Figure

6.7.

108



V. 0

1-ý

too

ho

Uavl(yNo. I

%Uý% I 'I (' %JUJIJ A RIX IIABIld 2

%I, wUncA . 4oh build I

II)It Iý

01, , 11 0

1,1 It ,,

Cavl1v ('. 'I% ty ('. I%týNo. ý

No. INo, ý4

Ino

Figure 6.6 1ocation of Iliermocouples.

A

Figure 6.7 Temperal tire contours a, stj, j)iji. %c(j, 11.1%illitill, -.pced condilimi for (lie datuill

Illodel.

1014



The temperature time-plots at the thermocouple positions shown in Figure 6.6 are plotted in Figures

6X to 0.21 for Ilic following models in(] will be discussed below:

" Datum model using conventional modelling ass"I"ptions th.11were used in the thermal

matched MCRIII model.

" Datum model with the standard natural comcction correlations tor the disc surfacc.1%

replaced by the Sussex UTC CONF correlation.

" Final best matched thermal model.

" 'Measured Data

Table 6.1 below gives tile notation that has been used In all the temperature tinic graphs and

temperature difference v. time graphs. Fach thennocotiple nainc/number is given in the figures and

represented in the table by the brackets !,ý.

Table 6.1 Restill% legend for each SC03 model.

Tempt-ralure PredictiII11%

Model NIIIIIC title

I Model

I Model with Sussex Cone Corrclation

lic"t Matched Model

Measured I'csl D. 11a

41 111::

ccll It.::

B111t. A If::

1,1111, + IIII!:

I C111peratureDifferences (measured - S('03 predicted)

Model \'1111c odc

Datum Model

1 Model with Sussex Cone ( 'orrclation

Best malched Model

Ruff (141::

( 11cen di.::

B111c A (11::

FI crenceigures 0.8 to 0.2 1 show the icniperature time graphs (uppcr plot) and temperature (I

time graphs (lower plot) for each thermocouple position. For the tenipcrature difference graphs,

shown as the lower graph in each figure, the temperature difference or error is defined as the

110



measuredemperature inus heSC03predictedcmpcrature. igure6.22showsheaxial

temperatureifferencesacross iscsNo.2 andNo.3 at three adial ocationsor thebcst-matchcd

SC03modelcomparedo themeasuredemperatureifferences. igure6.23showsheradial

1cmpcraturcifTcrcncc,iscrim tocobfor stage and3 discs.Results avebeenproducedor the

wholecycle,however,as hematching xercise nlyconsideredhesteady tateand he

accelerationransient, nly theseesultswill be discussed.

6.3.1Compressorrotor outer surface

As aresultof applying hemeasuredemperatureso therotor outersurface ia thegraphical

functionshownn Figure6.4, hemodel emperatureserewithin ±IK of themeasurementsor

both he ransient ndsteady tateconditionsorall models, ndsohavenotbeenplotted.

63.2 S(age2 discsurface Figures6.8(o6.12)

I'lic error (measuredminus predicted emperature)n thedisc No.2 borc temperature TC7)prediction was-1 K at steadystatefor thedatummodeland increaseso a 4K error using the

CONE correlation. Errors for the bestmatchcdmodel arc lessthan IK at steadystate Figure 6.8).

The measuredemperatures n thestage2 disc showthat the upstream left side) surfacewashottcr

than the downstream right side)surface(seeFigure6.22). Predicted emperatures singthedatum

model with naturalconvectionheat ransferon both sides of thedisc do not show this temperature

difference across hedisc, andthis will bediscussed urther in section6.3.6.This is clearly shown

in the temperaturecontour plot, Figure6.7. For thedatummodel,at the near steadystatemaximum

condition therewasanerror of -3K on thedisc diaphragmand a transienterror (on theacceleration)

of IK at the inner (TC9) andoutcr (TC 11)part of thedisc diaphragm,(Figures6.10and Figure

6.12) whilst anerror of 3K occursat the mid radial position (TC 10), Figure 6.11.

With theSussexCONE correlation replacingthenaturalconvectionheattransfercorrelationon the

disc surface, he temperatureerrorsaregreaterat the inner disc radii. I lowcvcr at themid andoutcr

radial positions theCONE correlationappears o reduce he temperatureerror during both transient

andat steadystate.For thedisc cob (TC8) the temperaturecrror was large(-7K) for theCONE

model compared o ±IK for thedatum model (Figure 6.9).

III



Forthebcst-matchcdmodel herewasa maximum rroror- IK at thenearsteady tatemaximum

condition oralI positionsalong hedisccxccptat theouter adialposition TC l) where heerror

was 3K. During he ransientollowingtheaccelerationhecrror wasbetween-2K andI K.

6.3.3Stage2-3 shroud (Figure 6.13)

All three thermal model predictions for the intcr-disc cavity shroud(TC 12)agreedwith

measurementso within IK during the transientand- 2K at the near steadystate condition.

6.3.4Stage3 discsurface Figures6.14 o 6.18)

As with thestage2 disc hemeasuredemperaturesntheupstreamleft side)surfacewcrchottcr

thanonthedownstreamrightside)surfaceseeFigure6.22).Forthedatummodel. at thenear

steady tatemaximum ondition he emperaturerror waswithin-2K onthedisc diaphragm nd

during he ransientfol owing heacceleration)hecrrorwas5K at theoutcr,TC 13 Figure6.14)

andmiddle,TC 14, Figure6.15)partsof ilia disc.At the nner adialposition,TC IS(Figure6.16)

an crrorof4K

wasshown ooccur.

As with thedownstreamsurfaceof disc 2, with theSussexCONE correlation rcplacing thenatural

convectionheattransfcrcorrelationon thedisc surface he temperaturecrrors arc greaterat the

inner disc radii. For mid andouter radial positionstheCONE correlationappears o reduce he

temperatureerror at the near steadystatecondition. During the transient heerrors arereduced

along theentire disc surface.For thedisc cob, TC 16 (Figure 6.17) the temperatureerror was-3K

for the CONE model compared o IK for thedatummodel.

Forthebest-matchcdmodel herewasa maximum rrorof IK at thenearsteady tatemaximum

condition or all positions long hediscdiaphragm.During he ransientheerrorwasbetweenK

atthe nnerradialposition TC15)and5K at theoutcr adialposition TC13).

Theerror n thediscstage borc emperaturerediction,TC 17 Figure6.18)waswithin 2K during

the ransient ndat steady tate orthedatummodel.With theCONEcorrelationmodel herewasa

-2K erroratsteady tate.The bcst-matchcdmodelerrorwas esshanIK at steady tate.

112



63.5 Staflonary shaft (Figures 6.19 to 6.21)

Generally, the temperatureerrors ncreaseslightly moving axially along the shaft.At the stage2

(TC27) and 3 (TC29) disc positionsthe nearsteadystate error waswithin -3K for both thedatum

model and the CONE correlationmodel. For the bestmatchedmodel theerror wasreduced o less

than lK.

6.3.6 Discsstages2and 3 axial temperature differences (rigure 6.22)

As mentioned reviously,or bothstage2 andstage discs hemeasuredemperaturesnthe

upstreamIcft side)discsurfacewerehottcr hanonthedownstreamrightside)discsurraccsee

Figure6.22)by upto2.5K duringboth heaccelerationndat thesteady tatemaximum ondition.

Predictedemperaturessing hedatummodelwith naturalconvection eat ransrcronbothsidesof

thediscdonotshow histemperatureifrcrcnccacrosshedisc. For hebestmatchedmodel,at the

middleandouter adialpositionsheSC03solutions howvery ittle differenceaxiallyacrosshe

disc diaphragmsonbothdiscs,whilst at the nner adialposition hediscupstreamurracc

temperatureasust IK hotter han hedownstreamurraccor both hestage and3 discsat themaximum ondition..

6.3.7 Discsstages2and 3 radial temperature differences (Figure 6.23)

Comparinghepredicted iscradial emperatureiffcrcnccs, iscoutcr radius for disc 2 mean f

TC3andTC4)to thedisccob meanof TC6,TC7andTC8). for thevarious hermalmodelso the

measuredemperaturei ffcrcnccs howshat hebestmatchcdmodelmatchcdowithin IK of the

measurementstboth henearsteady tatemaximum onditionandduring he ransicnt

(acceleration)omparedo atemperatureifTcrcnccf 3K rorthedatummodeland4K for tile

CONEmodel.

113



SusexMCRIC- MetalTmperahwes

----------------- 4------------------ , ------ ----- -- ----------------1 Im m 3m «

(3)

-------------------------

Memwed- Modd esq.DifferenceTC7

-------------------------i----------------

8 Im 30 3m

Figure 6.8 Disc 2 bore lemperat tire ('117).

TIN* 1)

M

m

114



SusexMCRECMetalTengeratwes

M,m,, i mdM,.ýd'Tmjftatwes @ TO

I 3S-

ap

320--------aIar

----------------- ---------------..........

I---------------- 4 . 'r( ---------------------

1001

D2

0.

1)3

OS

t. tJ'

315 1...............

7--,. P ---------------------------------

--------------------------------- --- ----------------

----------------- ----------------- -----------------

U

................. ----------------

zm 4w

Measwei- ModelT"q. Differeace@TCS

e- ------- ----------- ---- ------ ------------ ýdo I us

pI -------------JVhL-,

Ip*O, -

--------------------------------------- :,! I--. Aw. I KIN

ff

__________ ---

0

-21----------------- 1011 " ------------- ; -------------

31 ----------

r

eRc

4-

----------

3m

T"Wes)

or10,

......................

III----------------------------------

- -----------------

...............

-----------

-------------------------

3ý- ---------- --1

............ . --11 Im un

-4---------------- I

---------------

3W

.DILW

Figure 6.9 Disc 2 rear surface (empera(ure, disc cob (TC8).

------------------------------

115



SusexMCRB2- Meal TemMatwes

MeamwedandModel emTeratwesTC9

oiAtrro9ý

tin 1 19

1)2 I)

0-

I .-

I I- II

0

-----------------------------r------------------- ----------------................

1011.

01

3m

Tlmes)

'rMeamwedModelTaq. Differeace@TC9

1 ---------- . . -r .... ... .......

e u an i u7i

......................................

------------oa4lw--------------

:--

drrog

----------- ---------- ---------------- -- -------------- ---------------

Adgpl I IN-

ilia1*

------------------ i----------------

"cý ------------ ----------------- i-------- -------

cI -MA&W17- II -11L 4.

e-I

I------------------ I:

-V-oI

..........M-4MC I

....................I...... --------

IiýLII-- -IL)-

iII

..... ..... ------------------ ------------ ------------

-----------------J-----------------L.................

: %,, r------------------------------------------------- 4----------------- t ................................... j ----------------

3W 40

Times)

Figure 6.10 Disc 2 rear surface (emperalure, inner radii (TC9).

116



SusexMCRB2- MeldTemperdwes

're

4

Measured- ModelITewt.Difference@TCII

-- ------------------------------------

Ii MN-ý

----------------------------------L.............

MeamedmdMod'elerfastwes@TCII,

2m

----------------------------

Pdo 1101tit

,

I&dfl 10

- ---------------------- ,--------------

---- r -------------- ---------- - lý --------------

1 im !m 3m «

rme(s)

Figure 6.11 Disc 2 rear surface lemperal tire, mid radii (TC10).

im

1)2 l).

71me5)

117



Sum MCRB2- Metal eogerehm

II................. ............

MeasuredandModeleoqaalwes@TCII

I

I).

................ I 10111

Iýtfl II

ýi- 111

I

Im 20 3w

Tlmes)

M

Meamei - Model en?.Difference@TCI

------------- ---------------------- -- --- -

eap 3--

--------------- 11---------------- r, ................ I-----------------

11--------------

............... -----------------.................

:----------------------------------

I im 2w 30 m

Time(s)

Figure 6.12 Di%c2 rear surface temperature, outer radii (TCl I ).

-------------------------------------------------------------------------------------

---------------- ..........----------------............

-------------- ...........................W--4L- ýr:

------------I----------------

119



SusexMCRB.-MetalTerqeratwes

Meamuredad ModelTaipff atwes@TC .1

im

Plof I.

.............. I

1(11'

tfr 12

I

ý tilt I 1'r

I

2*

................. ------------------------------------

I 3w

I )-l

Ilme(S)

I)i

m

---------------j.................L................... ................

j-ý--------

III

i-* ::................

-------------

--------------- ---------------------------------------------------------- --

---------------- ................. ....................................

- -----------------------1-----------------

L----------------- ------------------

,---------------

8 Im 2m 3m m

TImes)

Figure 6.13 Disc 2-3 shroud surfilce (emperalure (TCl 2).

119



SusexMCRB2- MetalTengeratwes

MeaswedmdMod;elTeiVeratwes@TC13

----------------- I ----------------- -----------

I

eNk

p

D

IC

eac

----- ----------------------

I

I

Im

Im

20

D.,

0

f.

[)I

4-li

101

fk,if I'

till I

--- -1 ---------- IIII

3M

Meamed- Model esq.Difference@TC13

. 0 3m

Figure 6.14 Disc 3 front surface temperature, outer radii (TC13).

Time s)

Tbw s)

M

M

120



33s---- ----

I

I

e

p

D

I

C

rC

C

C

SusexMCRIr.- MetalTemperatwes

Meamedamd odelTengaotwes@TC14

------------- ------------ ------ -- -------- ...........

im

Measured- ModelITesq. Difference@TC14

TImes)

I)., 1);

M

------------ -------------- a:---------------------------------------

-------------------------I-----------------

im m 3W

Figure 6.15 Disc 3 rear surface (emperature, inid radii (TC14).

Ilne (s)

4m

L toH4

f,ýtff14

do'F

LKI-I 41

121



SusexMCREC- MetalTemperatwes

315----------------

I

I

II

II

II

---------- -----------------I

................. ..................................

Ion M 3m

rmw 6)

40

Meamed- ModdITewq.Differeace@TCS

I

------------- --------------------------

F

D

I

e

C

I

C

C

II

II

Ion

Ilme 0)

Figure 6.16 Disc 3 rear surface lemperal tire, inner radii

40

41dul 1 ýýVitIIsNrris

122



Susex MCRIC-MetalTemilperatwes

32S

T

-------------------------

p

C

Meamwedad Modelemeratwes-r -----------

93C

IIiml sm

D2

dT16

0 (in'l 16

. ............

3w M

TImes)

Measured-Model,aq. Difference@TC 6

----------------- I ................. I ................ 1- W777-

-----------------

----------------- -----------------

-------------------------4----------------------------------;................. I-------------- --

I Im 20

Figure 6.17 Disc 3 rear surface lemperature, disc cob

(IfF16

---------------------------------

3w

,nw s)

M

a

121



Susex MCRBI.-

MeadTeagwatwes

324-

THeasurei- ModdTmq. Differeme@TC 7

-----------------

L

IS -------------

D

..........................

-15 ---------------------------------

II--I----------------------------r-------------------------------

11"

Figure 6.18 Disc 3 bore lemperahire (TCl 7).

MeamedmA odeleo ra!Fev OTC17,---------------- 02

Tlow 1)

i, ýL................I

3m

TUe (s)

fol F

1,1F-

tfr II

tmT -,

vd -1,, -1,

LEE-.

124



Susex MCREC- MetalTewperalwes

I

T

e

Meameiad [email protected]

im SN 3w

Tlme s)

M

Memwed- ModelT". Diffezence TM.III

15 -------------------- - -------------------------

p

a

Im

Figure 6.19 111shaft surface lemperature, disc 2 hore (TC27).

30

Tue(s)

II:,

tfIrl 2",

ýL, ,

I ýs



Swwx MCRB2 MomiTeogwetwes

Memwedad Modd aVestwesQTC23313............................. .....................

I);

Itol 's

nI 2S

T

em es-

I

................................................................

Im 2m 3w

nmeI)

L)

0

m

.............

MeamwedModel mq. Difference TC23

-25 ........................................... i ..............

I im :0

.I................

im

Týw (1)

Figure 6.20 11'shaft surface temperature. between disc 2 and 3( FC28).

40

126



SusexMCR82 MetalTeiVeratwes

MeaswedmdModel nvqertdwm@T('.9 I)' 1);

J) o129

£ tfF9

ý111L-I-,0

366

I Im m Im

MeameA Model mq. Difference T".

llne (8)

M

IIIi

r

-----------------------

vII .................

-----------------2k

.31-

II

II

11---------------------

1 im...... ...... I

so

Figure 6.21 111shaft %urface temperature, di-ic 3 bore (TC29).

An

Tlw (s)

127



0

ap

is-

I

IS

k-1.5

I

Im

im

im

Oder R&AW Locatim

Disc2frCll TC3)&Diw](T(-21 -rcu)

II

2m

MW RrAol Locndom

Disc2(TCII TC4) & D6sc 3 (TC21 TC 14),

2w

Iý............. L--- --

Dim. Dcdwm

Ipl" BrorAst Mrmw rd

Dist 3 DAtmk

1h. t I Reld

La 1 1.ý 1 %l mm rd

imTlow (s)

Dimc Doom

Dist liesl

Dioc 2 Meamwrd

Pisc 3 1)., vn

Pi%t 3 Resi

4w

hý RjWWLocadm

Disc 2 (TC9 - TCS) & Disc 3 (TC 19-TC 15)

2m

Tine (8)

0

A Disc2,

Mema CAPW 3 1)tdi»

Digt 3 urbi

Is Dist 3Mraxim d

14m

Figure 6.22 Axial temperature differences across stage 2 and stage 3 discs at three radial

locations comparing (he da(unt model and the best matched model Ailh measurements.

12H



DiK 1.md 3 RsAW Tempmetwe Gradad

35......

Slýv22

Disc

----- i ---------------- --------------1

5. ýý, -------------8 Im

21M 3m

Tbw is)

Tbw (s)

DDdm

I ', own -(I Y% :

Bee Mach

It Mramed

D Am

I ý'Ofulll -((I"

A Broi Mcdch

'-It,ý%%n vý

Figure 6.23 Radial temperature differences ((Ii%couter radius to coh) for stage 2 in(] %lage3di%c%comparing the best matched, (flittlill illodel and the CONE model ýOlh nicawremen(s.

121)



0.3.8 Be%f-malched model

Figure6.24 showsthe positionsol'the SC03boundarycondition Iýatures.volds. /ones. streamsand

ducts for the bestmatchedmodel. The SC03modelwas nin Iransiently through the cycle shown ill

11gure6.3 to a specifiedaccuracyol'O.2K. Towardstheend of'(he period at maximum speed he

solution approachesa steadystate condition. A temperature ontour plot a( the nearsteadystate

maximum speedcondition time point ( 2800s) s shown in Figure6.25.

The thermal I)OLIndaryconditions used in the 'best nia(ched' model are given in Appendix 2 and tile

evaluated thennal boundary condition values at the 'near' stabillsed maximum speed condition are

given in Appendix 3.

Sussex -CAmityRig Build 2

ModI84 V41t build I Me"ling rqwfira-ýý, o

"Oo T_'

7 II

0141A"

Vý

N t4

wo ..00

. ""_ . "' .---.

"-_ . "_-

I--

IIj

1110100 .,0

I

Figure 6.24 Location of Boundary Condifions for lhe Res( Malched Model.

7 \

.+

I

ý!!!

IN



P ,ý, jrc

6.25 Tempermure con(()tjrs al Slabilised Nla%iilltjnl Condition for the Best Malched

Model.

6.4 Discussion and FurtherAnalysis

Temperature results Cromhoth the datum and the SussexCONI: correlation thermal models

indicated Illat the modelling assumptions needed to be altered in both the region under and around

tile coband

bore

of*eachdisc

and in [lie inter-disc cavity spacc.

Using the Sussex CONI:correlation

applied to the disc surface generally improved the matching in (lie outer radial region of'the disc

diaphragm but it large error remained at the inner radial region ofthe disc. The modelling of' the

ititcr-disc cavity shrouds has been silowil to be acceptable as there is it good thermal inatch in this

locatiOll.

6.4.1 flesi-matched model - modelling a%%timptions

With the standard modelling assuillptions ýIpplicd to both the dattim and CONF models. no

temperature dillerence exists axially across the discs whilst the test measurementsdo indicate it

131



temperatureifTcrcncc. heonly wayto try toobtain hemeasuredemperatureradientaxially

throughhediscswas ochangehemodellingapproach.n an attempto achievehis temperature

gradienthepenetratingengthof both he hermalstreamslowing intoandout of thecavityhad o

be ncreased.he nletstrcamlowingonto hedownstream iscpenetratedpto theradiuswhere

thedisccobnarrowso thediaphragm.Ontheupstream isc heoutletstrcam tarts rom

approximately thirdof thecavitydepthonthedisc diaphragmseeFigure6.26).Thcrcrorc,an

asymmetriclow modellingsystem asbeensetup n thecavity.A newsetof modelling

assumptionsavebeenmade,with a flow rc-circulation ssumedo occur n the nnerradial egion

or diecavity,betweenhedisccobsandavoid in theouter adial egionof thecavity.Factors

appliedo the icattransferonthecavitydownstreamisc nletstrcamhad o bereducedo 0.1of

the orce reedisccorrelation

0.1xFRD),

whilstthe actor or the

cavityoutletstrcamwasseto

0.9xFRD.Theoptimum low rate n therc-circulationn the nnercavity regionwas0.07of the

axial hroughflowand0.08of theaxialthrougliflowwasassumedo reed hevoid in thecavity

outer adial egion. lowcvcrtoachieve nykindof acceptableemperature atch o diemeasured

disc emperaturesheheatnowout or thevoid(thatmixesn with thecirculation low) washalf that

assumedoenter hevoid.So hereexistsan mbalance, ith both hemasslow andheat low not

beingconserved.heheat ransferactorsapplied o therorccdductcorrelationFCD)usedn each

disc borchad o bevaried or eachdiscalong he engthof thecompressor,or thestage discI.OxFCDhad obeused, tage2 disc0.8,stage disc0.4and orstage disc0.2xFCDwasused.

It shouldbenotedthat for an actualcnginc, unlike theNICR, there s tcmperaturc ncreasemoving

axially along thecompressordue to thecompressionof themain gasstrcarnair. For a typical

military enginean axial temperaturencreasealongthe lengthofthe I IP compressor im could beas

high as250K(5K to I OKrisc for NICR132).Also, unlikctheNICR, thcrc is a largeradial

temperaturegradient from thedisc rim to thebore,cspccially during the transients.Again in a

typical military enginethe I IP compressordisc rim to borc radial temperaturediffcrcncc could be as

high as 150K. Engineradial temperaturedifferencesfrom disc diaphragmouter radiusto cob arc

typically IOOKcompared o the30K measuredn theMCRB2 discs. If thecquivalcnt pcrccntagc

crrors that result in only small tcmpcraturecffors for theMCR arc appliedto theactualenginethe

temperatures rrors will be much largerandcould besignificant in thestressand lifing oftlic

compressor otor.

132



I hic II I'm

sircaln H'..

Mctmal Void

III"..

II

I I,,V

I)u"lllly sircam w

I emperalurcI ran%lcr

1fral rmnblef --0>

I

4.p.

u

I--,

'

I

ol

(.

--

I

1 (.1) Dattlill Model (b) Re%lMatched Model

Figure 6.26 Comparkon of the thermal modelling approach u%ed in the dalum model to that

u%cd in the hest-malched thermal model.

6.4.2 [feat transfer coefficient% oil tile (fi%c%urface and ca%'i(% hroud

I lie lical transfer cocil-mcm % rialion with linic 1hrough ilic acccl (Icccl cNcle at three position,,.

mid radius on the upstream disc (stage 2). TCI 0. on dic stage 2-3 cavity shroud. I'Cl 2 and on the

downstream disc (stage i), r(, 14 are shown in the Figure 6.27. Fhe figure shows the licat transter

for the three llicrinal models. For both discs the heat transfer coefficient% for the best matched

model are in agreement with the CONI: correlation giving a value 4 times diat giýcn by the

05, NVP natural convection correlation. For the cavity shroud heat transfer [lie damin modcl used

0.75 -NUS natural convection from a liori/ontal plate correlation compared to 0.077- NUS u...cd in

the best-mate ied model. As mentioned earlier this gives the equivalent heat transfcr coefficient to

that produced by the Sussex UFC derived shroud correlation. which .%-;s 0.9 offhat used in the

dalum model. This is shown in the grapli.

131

)f DUL.

ý1.



IIr ed Tr MAIIVWCOVfikirM 00 St MgV .2&MIK 0 MW ('A%*Y. %Wtnw

HTCgm UPWREAM DISCVTC14

I

118.14TC

li 8.

T

IM

:8. "

K 6-64

0

I im

:11. Mune -('0% 1

............................................................... ja Brei mdidcä

0

--------------------------------:................I .................

............... ! ................ I

I Im

I

2m

lf'rC na DOWNSTREAM DIS('40T('14

2m

IfTCim CAVITY SHROUD @TC12

Im

AN

A3L

................. j

Tlow (8)

..........

TIme (9)

4M

---------- ------------

................ ............

...............

10

lgvaftitsýw........................................

im IM Im

Figure 6.27 Comparison oftlie licat 1 an%l'er ci)elilcietit% on %tage%2 and I (ii%c%und ilie ca% lN.

%hroud for Ihr three fliermal niodel%.

114



0.4.3 Ca%ilý flo" regime%

According to Alexiou 120001lie Rossbyiminbcr (Ro) canbeused o detenninewhetherthe flow i's

buoyancydriven or whether the throughtlow eflectsdominate.

For

For

I-or

Ro - 3.15 buoyancy effects dominate

3.15 - Ro - .1.85 flic flow is transitional

Ro - 3.85 throughtlow effects dominate

For dic MURIQ stage 2-3 inter-disc cavity the time history plot of'Rossby number is given in

Figure 6.2X. During the majority ol'the transient and at the steady state maximurn speed condilion,

the Rossby ritimber plots show that the MCRI32 1% inning in the buoyancy dominated rcginic

Tbw Mgm ni R"sby Nh. RA

IIlifolighlitm 041111111.1111

1

4

I

a

)

I

S

0

I.Iul'. uIli UI I

ii'

Itiu tui I

.S --

A; MAM 4,NM

Z: TMAN @AKUM

C; 2Wa @jullft0. J[Mie 3x717

9: 4m48 UM

r.

Figure 6.28 Time history 44 llos%l)%-t tonher (Ro) f(or %ICR build 2 %1ge 2-3 in Ier-disc cavi I).

A further set of'criteria to determine it'huoyancy ellects are dominant has heen set hy Sussex

University from Ihere work on (lie MUR 131 drive cone cavity. I lere the Iwo flow regimes were

characterised hy:

135



Buoyancycffects dominate Bo-Ro/(PAT)1/2 <6

Throughilow cffects dominate Bo-Ro /(0 AT)" >6

Table6.2 belowshowsheBuoyancyNumber Bo)valuesat thenearsteady tatemaximum peed

conditionand or thegreatest T during hedccclcration ack o idle for the hermocoupleositions

onthediscsurfacesorming hestage .3 intcr-disccavity n MCRB2.Theseassumehrought'low

fluid temperaturesf 317K(SC03duct emperature,T24)at themaximum onditionand311K at

the dlecondition.Themetal emperaturesTm)usedn thecalculation rcfromtherig

thermocouples.heRossbynumber,Ro,saconstant alueof 0.8511at themaximum peed

conditionand3.3609at the dlecondition.

Table 6.2 Buoyancy pararne(er values a near steady state maximum condition and during (fiedeceleration.

NearSteadyStateMaximum Deceleration o Idle

ThermocouplePosition AT(K) (PAT)112 flo-Ro/(PAT)"' AT(K) (PAT)"' Bo-Rol(PAT)"

TC-9 stage disc 6.7 0.145 5.86 0.5 0.040 85.13

TC-10 11.9 0.194 4.39 2.6 0.091 36.50

TC-11 29.0 0.303 2.81 6.2 0.141 23.86

TC- 12shroud 50.2 0.398 2.14 7.2 0.152 22.01

1

TC-13stage disc 33.6 0.326 2.61 6.7 0.147 22.85

TC_14 15.0 0.218 3.91 3.1 0.100 33.57

FfC-I 51 10.2 10.179 14.75 1.1 0.059 156.64

Thissecond etof criteriaalso ndicateshat hestage2-3intcr-disc avity soperatingn the

buoyancy ominatedregimeatthenearsteady tatemaximum peed ondition,butattilesteady

statedleconditionandduringmostof the hermal ransientesponsehasesorboth ile

accelerationnddeceleration,heaxialthroughtlowdominates.7his uoyancy umber riterion s

usedodeterminewhichof the woSussexUTCCONE icattransrcr orrelationss tobeused ora

particular avityflow, being

eithern

thebuoyancy

r the hrougliflowdominant

regime.

136



6.4.4Eckert number effects

The temperaturewithin thecavitiesrisesdueto thevortex associatedwith theswirl velocity of the

air, which increaseswith radius.The expected ise in relative total temperature or a forcedvortex is

given by the following formula:

.&T,,, - 0' ( r.

2- rj2 2 Cp (6.8)

In theaboveequation,r. is thecavity outer radius(m), ri is thecavity inner radius(m), C1s the

rotationalspeed rad/s)of thevortex andCp s the spccific heatcapacity(J/kg/K).

At thenearsteady tatemaximum peed ondition,Equation .8givesa relative otal temperature

riseof 7K.whilst at thenear dleconditionshe emperatureise s less hanI K. Tlicrcforc, his

cffect sonly importantat thehighcrrotational peeds. t themaximum peed ondition, hecffcct

ontheair temperature ithin thecavity'void' outcrregion san ncreaseor5K. whichhasan cffcct

of increasinghecavity shroudemperaturey 2K. Thisvortex emperatureise wasnot modelled

in anyof the hcrmalmodels.

6.4.5Axial licat flow calculations

Inorder oextractasmuch nformationromtheexperimentalataaspossible,urthcranalysis f

the emperature easurementsasundertaken.emperatureata rom both he ransientest.

describedn thischapter, nd romthree urthersteady tateests testno.33.34and50)havebeen

usedn thisassessment.

Using temperaturesat the threeradial locationson thedisc diaphragmandneglectingaxial

temperaturegradients,equationsmay be deduced or the net axial licat loss from thedisc surraccat

thecentral thcrrnocouplc ocation.This is shownbelow where a control volume including the

ccntral thcrmocouple ocation is considercdandcnergyconservationapplied.

137



I leat Hlix (W/1112)

r,, --184.5min

4-

r, 141.75iniii

4Qll

I

IIý,

10 '1,

10 11

l<

t Iflfl1r,

121nim

+I Ica( Flo\N ,, IN to [liedisc Illatclial

-I leat Flow Pý)(!. I

111Cisc Illatclial

r,, (r,,, r,, 2

r, (r. # j/2

- (),

-Q,

T%- Tr

In(

TI.- T,

r

01 licrillocoupIc position',

Sic;,(_JN,feilt How conduction F. uation.

heal flow III heat flow out Q,, 2itI-,, 2no, (6.1)

Fran"'ICIIH ca-1-1-jowConduction F(ttlallollý

11catlow III licat flow out # raic ofincrease III ctithalpy ot'llic "'a1c,

Q,,21rr,, 2n(r,,2- r. - Q, 2mr, -a(I, I (o 10ý

whm T is lime (s).

Disc niaterial is litanium witli a density, li 4421) k-giii 'and at a lemperature of' 1MI' flierinal

conductivity, k 7.72 Win 'K 'and ii)ccit"ic lical Cj, 562 lk-g kl. 'rliick-iies% ot'tlic dic

diaphragni, 1 0.008111

I Is



Forall four steadystate ests(tests33,34,50 and for theacccVdcccIcycle maximum speedsteady

statecondition) calculations,thenet axial heat flow is out of thedisc materialto thesurrounding air.

For disc 2,74%. 79% of theheatenteringthedisc diaphragmat theouter radius leavesaxially out of

thedisc diaphragm.Similarly for disc 3,74%-82% of theheat flow leavesaxially out from thedisc

diaphragm.Figures 6.29 and6.30 showthecalculatedheattransfcr(using the testmeasured

temperaturesn Equations 6.9 and6.10) into and out of thecontrol volumeduring theacceleration

(idle to max. speed)anddeceleration max. speed o idle) phases,or the two discs,disc 2 anddisc

3, respectively. lic transientcalculationshows hatat anarbitrary time (740.959s)during the

acceleration a slow acceleration n this test) theheatflow is into thedisc materialat the mid radial

position for both discs.The thermalanalysisshows hat for thesame ime point heat flow canbe

cithcr in to or out from thedisc diaphragmdependenton theradial position. According to the

thermalmodels,at radial positions inboardorr- 0.171mall theheat flow is into thedisc andat a

radiusaround0.175mmthe heat s into thedisc on thedownstreamside of thedisc andout on the

upstreamside.At a radius above0.182mall theheatflow is out of thedisc.

Table6.3compareshe NICR112iscs2and3diaphragm xialheat low calculationswithSC03

predictionsorsteady tateand ransientaccelerationdleto maximum)estpoints.Thetable

showswosetsof handcalculations,hefirstsetusedemperatureseasuredntile rig and he

second etusedSC03 hermalmodelpredictedemperatures.heheat ransrcresults romthehand

calculationsompare easonable ell with theSC03 hermalmodel esultsor bothsteady tateand

transient perating onditions. [cat ransferesultsgainedromtheCFDmodels f theNICRB2

havebeenncluded orcompleteness.heCFDresultsalsocomparewcll with both ilehand

calculations ndwith theSC03predicted eat ransfcror thesteady tateest33casebutnotso

well for thenearsteady tatemaximum ondition rom he ransientcsLThereasonor the

differencemaybe due o therig not reachingull stabiliscd teady tateconditions t tilemaximumspeed oint.Figures .29band6.30bshow hatatthestartof [liedccclcrationhehandcalculated

heat ransferwasapproximately0Woutof thediscswhich smuchclosero theCFDheat ransrcr

results. heseCFDmodelswill be hesubjectmatterorChaptcr8.

139



Sussex MCRB2 Transient Test - Accel

Disc 2- Heat Flow In To the Disc

4,1

20

10

-H-t I" co,..I 1c, ". 1',

-04" Oul Ra, *al m 1?. (ýj,,

.10

.1,1000 "(XX)1()()

li- 1.1

Figure 6.29a - Acceleration Idle to Maximum Condition%

Sussex MCRB2 Transient Test - DecalDisc 2- Host Flow In To the Disc

2500 UýK,

-1 4" bn Ri"40 41 K. ) (0. )

-e 4" 0,9 $4»cßw a R, (Q%)

-ý t" (>A A.. al N. N. i Dm A

: lux) UNX) W, X) Ak) ww 40ou 4200 4A(X)

Tlýe (a)

Figure 6.291)- Deceleration to Maximum Condition to Idle.

Figure 6.29 Sussex NICR build 2 transient acceleralion / deceleration cycle heat 114mý%iffiindi%c 2 diaphragm

- conduction calculation using measured test temperatures.

140



Sussex MCR82 Trmnei*nt Test - Accel

Disc 3- Host Flow In To the Disc

-

t ý.. l ( )"t.. I

14ý((,

).)

HOM Out AxIM- Reduced Dal. s

10

10

10

I., ý, ýx K)11-0

K)

Ti- (IL)

Figure 0.30a Acceleration idle lo illaxiIIIIIIII collditiolls.

Sussax MCRB2 Transient Test - DocolDisc 3- Host Flow In To the Disc

-Iinm W,RALUAI At RO ((). )

I 4-M OkA RWSIAO31 Ft (04)

)"1 4". 4 R-l", -1 onla

,A,. tk)O 3000 3200 Wo 3WOvm

Time (0)

Figure 6.301) - deceleralion maximum condifion to idle.

40W 4200 44M

Figure 6.30 Sussex NICR build 2 transient acceleration / deceleration cýcle heat llový %vi(hindi%c3 diaphragni

- conduction calculation using measured test temperatures.

141



Table 6.3 Comparison of AICIII12 Discs 2 and 3 disphrognt axial beat flow calculations, SC03

predicted, CFD predicted and a simple conduction calculation for steady state and transient(acceleration Idle to maximum) test points.

SC03 CFD Results Conduction Hand

Results Calculations

Non Conjugate Test SC03

Disc 2 Conjugate Measurements Predictions

SSTest 33-28.88 -27.64 -25.72 -33.41 -35.18

TransientTest SS -20.16 -30.32 -38.89 -24.71 -28.97

Maximum

TransientTest 16.48 17.08 15.89

Acccl.CWt-615s


Acccl.C(Lt-740.969s

TransientTest 40.28 -33.57 40.82

Deccl.Ca,-3167.5s

TransientTest -14.68 -15.07 -17.37

Decci.Cat-3802.5s

Note: Heat Flow (%V) -Q Is Ilcut Flow OUT orthe disc +Q Is Heat Flow IN to the disc

Disc 3

SSTest 33 -30.02 (-31.19) (-30.40) -37.11 -37.31

TransientTest SS -19.38 (-33.26) (-36.68) -26.32 -27.92

Maximum


Acccl.Ca-615s


Acccl.a(t-740.969s

TransientTest -41.61 -33.26 -41.24

[email protected]

TransiWt-T-cst. 14.61 -13.65 -17.71

Deccl.Cdt-3802.5s

142



6.4.6The effect or Internal radiation within the AICR build 2 rig.

In thebest hermalmatchedSC03modelan nternal adiationboundary onditionwasapplied o

thecasingwalls,whichsurroundherotatingcompressorrum.Thevalueof cmissivitywassetat

0.5.1owcvcraflcrdiscussionswith theSussexUTCteamt wasdiscoveredhat heMCRbuild2

rigcompressoriscswerepaintedwith a high emperaturelackmattpaint.Thereforet is

reasonableo assumehat hecmissivitycanbesetequal o 1.Alcxiouconfirmedhat hisvaluehad

been heckedwith ahandheld hcrmonictcr nd he hermocouplesn ilia rig.To investigatehe

effectof the nternalradiationwithin theMCRrig compressorrumaSCO3hermalmodelhas

beenuntocompareemperaturesith ilia bestmatchedhermalmodel. nternal adiationhasbeen

appliedoboth

heoutside urfaces f therotatingcompressorrum

ando the nside

surraccs rthecompressorisc drumandstationary haft.Emissivityhasbeenset oa valueof I rorall the

internalradiationboundary onditions.

The wographsn Figure6.31show ile metal emperaturest three adial ocations ndiscs 1.2

and3(andalso hedisc 2.3shroud) or the best'matchedhermalmodel,Figure6.31aand or the

compressorrum nternal adiationmodel,Figure6.31b. Comparinghe emperaturest the near'

steady tatemaximum ondition or the woSC03 hermalmodels howshat he nternal adiation

boundaryondition cmissivity- 1)applied o thecompressorrumdiscsurraccs as ittle effect,

an ncreaseof less hanIK onthediscmetal emperatures,xceptor thedisc I rim where he

temperaturencreases2K,with internalradiationapplied.Alsoduring he ransientsheresno

appreciablehangen discmetal emperatureetweenhe wo thermalmodels.Thercroreor the

SussexMCRwith modestemperaturesndsmalldiscradial cnipcraturc radientst canbe

assumedhat nternalradiationhasonly a negligibleefTcct nthedisc emperaturesothduring

transient peration ndat steady tateconditions.Convection nddiscradialconduction re he

dominant eat ransrcrmechanisms ithin thecompressorrum.

143



%. - M( x MI A... 60-4 F. 9

5.1 M... j ý&khd Nuw

rw

wo

IM

I*

$if

I

- II I

Figure 6.31a Alest' matched thermal model

%1( R 21 Aaw D. W t. 0

Db.

r

170

Re

M

144

K

I'

I

$4

no

Ii

A »). q4 %1 omp i,.. ýý, d

0 3031"

4 303M 130521 Db. I (, h

v MA I" II lbwb I

303jo : 1S. 16 ;:: MphSW. mim

I-I

bwb:; 30136

11 ini.. 44 bh)_r5

m ob. 1 Rbu

13013* wbam

INM134 ww"I Dh II sb-: l

=2 34 fig.

31101,119 Majob J,

31MV3 In Db. 1('. h

311111JI, 111,09

jq*1 M130 Wj

I

Rb.

WA.9"

301 M W-4"ý

Dh. I 1%. -A

4m

0-1.1

Figure 6.3 11)Compressor drum internal radialion Ihernial model

Figure 6.31 Stmex NICR build 2 effect of interital riodiatiou %silhiu the compressor inler-disc

ca%fics (entissivity - I) mi metal lemperal tire%.

144



6.5Conclusions

A thermalmodelbasedon standardndustrialpracticehasbeenproducedor therVICRI32ig and

predictedemperaturesompared ith rig measurements.ll the emperaturerrors nvolvedarc

modest, eing ess han5K rorall positionsandat all timesduring hecycle.However,heresonly

a30Kradial emperatureifferencebetweenhediscrim and hecob andonlyaSOK iffercricc n

thecavityshroudmetal emperaturend heaxial througliflow luid temperature.he 5K crror

relates, sapercentagef the emperatureifferencebetweenheshroudandaxialthroughflowgas,

toa7%crror at thenearsteady tatemaximum peed onditionandabouta 12%crrorduring he

acceleration.hisrepresentssignificanterror.

Comparisonof theresultsobtainedroma numberof modifiedmodels howedhat heressome

merit n using henew"CONE"correlation n theupstream nddownstream iscsurfaces. verall,

theconecorrelationsseenobecffcctivc n themidandouter egions f thedisc diaphragmor

thesteady tatemaximum ondition,achievingbetter esultshan hedatummodel.Onthese

criteria, heconecorrelationwasalsouseful or modellingconvection t the nnerradiusof thedisc

diaphragm uring hedecelerationo idle. I owcvcr,using heconecorrelation asadetrimental

cffcct onthedisccob andbore emperatures.uring ransientsheconecorrelation roduces disc

temperatureesponsehat sclose o themeasuredesponseor the nnerandmid partof thedisc

diaphragm.lowcvcr n theouter adialpartof thediscthedatummodelproduces better hermal

responsehan hemodelwith theconecorrelation.

Inter-disccavity shroudtemperaturepredictionswere good for thedatummodel and for the model

using theheattransferequivalentto that correlatedby SussexUTC.

Stressesn thediscsarc driven by temperaturegradient.Comparingthe radial temperature

difference,disc outcr radiusto thedisc cob, producedby the thermalmodels o that measured,he

datummodel is shownto perform much better thanthe thermalmodel with thecone correlation,

both at thenear maximum spccd steadystatecondition andduring the transients.Modelling around

thecompressordisc cobshasprovcd to bedifficult. To achievean acccptablematch with thedisc

temperaturemeasurements,he

followingnon-standard

hcrmalboundaryconditions

hadto be

assumed

14S



0 Asymmetricnictsandoutflows.

Imbalanceof hcat/masslow in andout of the ntcr-disccavity void.

1 igh and low heattransferon the upstreamanddownstreamdisc cobs,rcspectivcly.

Variation in factorsof

the forcedduct heattransferon

disc boresalong

the

compressor.

The extraordinarymethodsused o achieve a match for this applicationarenot expected o read

across o other situations. I lowcvcr, it is worth noting that thesolution involved increasing he

circulation into the cavity from the"normal" 10%to 15%of theaxial throughilow. orthis 8% goes

into theouter cavity void andthe remainderstays n the throught'lowdominatedzone.

It is clear that traditional modelling approachesor this problemsuffer from,variousdift'icultics and

thatcare s needed n interpreting the thcrtnal analysis.Greaterunderstandingor the flows occurring

in thebuild 2 configuration is required.Build 3 of the Sussexrig will provide velocity

measurementshat will help understandhe flow within the intcr-disc cavities. CFD work will

continueto beusedfor the build 2 andbuild 3 configurationsto supplement he measurements.

Someprogresshas beenmade n themodelling of thecavities with full 3D unsteadyCFD but this is

very computationally intensive.In an attemptto overcome hecomputing time problem a 2D

axisymmctric steadyflow modelling techniquehasbeendevelopedand this method will be

discussedn detail in the chapters o follow. The modelling will need o capture he flow physics,

especiallythe interactionof theaxial througliflow with thecavity flow.

146



CHAPTER 7

STEADY FLOW 2-DINIENSIONALMODELLING METHODOLOGY

7.1 Introduction

In thischapter numericalmethodof modelling hecomplexunsteadyhree-dimensionallow

buoyancy ffectswithin a rotatingcavity with asimplesteadylow two-dimensionalxisymmctric

modelwill bepresented nddiscussed. sing heknowledge ainedromthepreviouswork onthe

numericalmodellingof buoyancylowswithin cncloscd avities,a simplesteadylow two-dimensional xisymmctricmodelhasbeendevelopedhatcanbeappliedwithin a conventional

CFDmodel or theseypesof geometries.hechapterwill dctailthedevelopmentf themethod,

followedbyadescriptionof howthemodelwill be inked o conventional FDusinga 'User

DefinedFunction'or UDFwithin theFluentCFDcomputing ode. 'lie UDFmodelwill thenbe

tested yapplication f themethodo an enclosedtationary avity."I'licchapterwill closewith the

method eingapplied o arotatingenclosedavity.Theresults rom heapplication f the

simplifiedCFDmodelwill becomparedo the estdata romtheKirkpatrick& Bohn's 1986]

experimentsor a stationary nclosed avityand romtheBohnct al's [1993,1994]experimentsor

a rotatingscaled avity.

7.2 A 2D Axisymmetric Alodel or the Buoyancy Effects In Rotating Cavity Flows.

A simpleaxisymmctric (or circumfcrcntially-avcragcd)approach o modelling buoyancy-drivcn

heattransfer n thecentrifugal force field bctwccnconcentricrotating cylindcrs has bccn

considered.With reference o Chapter2, the approachadopted s similar to the 'conduction layer

technique' that hasbeenusedby other workers to modelhigh Rayleighnumberfreeconvection

undergravity.

7be flow between wo co-axial, co-rotating. infinite cylindersat different uniform temperaturess

considered irst, and is illustrated in Figure7.1. Averagingover time, it is expected hat the flow

variableswill not vary with z or (D n the naturalcylindrical co-ordinatcsystem rOz). It is also

that the flow canbe treatedas a perturbationof solid body rotation (v. - f1r). From analogy with

147



turbulent iffusion,simpledimensional rguments.ndwith theconsideration f thestabilityof

rotatingcompressiblend nviscid luidsby EckhoffandStorcslcttcn1978,19801, hew 2000],

as eportedn Chaptcr2, section .6,postulatcdhat n the nterior low theheat lux (4) is given

(in termsof timeaveraged ariables) y the ollowingequation,

Figure 7.1 Illustration or tije simplified model.

d7* dT-A Rai*T-kT (7.1)

rrr

where he local Rayleighnumber'Rai s defincdas ollows

Ra,= Prp2

V.2V

Max[(! ",)2

_rdp,

O

JUr2cp dr

(7.2)

I lere A andn arenon-dimcnsionalconstants,L is thercprcscntativc engthscale and,p.. U.Pr

(-PcWk), v., C.. T.k andc denote he fluid density,viscosity, Prandtlnumber,swirl velocity,

specific heatat constantpressure,static temperature,hermalconductivity and the speedof sound,

respectively.In the low Mach numberlimit this modelwill promoteheattransrcr if the radial

temperaturegradient is positive. Eckhoff andStorcslcttcn'sstability criteria supporttheuse of the

term in brackets ] in Equation7.2 beingnegative, f the rotating flow is stable andpositive if the

flow is unstable.The stability criterion tcrin maybedcrivcd asdescribedbelow;

148



Assuming forcedvortexwith tangential elocityv., theradialequilibriumequations,

dpp

v.dr r

andfor iscntropic flow of a pcrfcct gas,

p= npr

whcrcn is a constant.Diffcrentiating Equation7.4 w.r. . r,

dp= nypy-1

dp

dr Tr

substitutingntoEquation .3,V2

ypF. 3

._rr

With thespccdof sound,

Fira

andusingequations .4and7.7 n Equation .6.

r dp

cdr

(

(7.3)

(7.4)

(7.5)

(7.6)

(7.7)

(7.8)

If it isassumedhat he"iscntropic orcedvortex" s ust stable,t followsfrom Equation .8, he

flow is stablef,

r dp

p dr(7.9)

Using theanalogy with turbulentmixing (Chcw 20001, he tangentialcomponentof the momentum

conservationequation n the axisymmctric model is modified by theaddition of the following term.

d ARa,p[r

ýv ARI*U.

L_ vd(ALaL,, )

7 -( Pr dr Pr rir' Pr r1 rdr p(7.10)

Note hat heaboveerm szero n thecaseof a forcedvortex v cc ). It isalsoassumedhataway

fromthewallsthecontribution f conventionalhermal onductiono theheat ransfcrsnegligible.

T`hcnheradialheat lux in thecentral core"of the low isgivenby:

149



-AR IdT

(7.11)Tr

The axisymmctric model hasbeen mplementedby modifying thecore gaspropertiesof viscosity,ju

andthermalconductivity, k (Prandtlnumber remainsconstint). Thesearc multiplied by a factor

given as a function of the local Rayleighnumber,Rai, using thecquations above.The samevalue is

used o factor both the viscosity andthe thermalconductivity, as follows,

p' - ARa, jj (7.12a)

and V-Aft, "k (7.12b)

The two constantsA andn used n the factoring equationswill be determined rom the matchingof

testcaseswith experimentaldataacross he full rangeof Rayleighnumbers.Viscosity. P'uscd in

theenhancedmixing UDF model is the augmentedmolecularor laminar viscosity. The eddy or

turbulentviscosity remains unalteredusing the valuescomputedby the k-c turbulent model within

thesolver.This is best illustratedby theenginecase n Chapter9, where a comparisonof the

enhancedmixing model augmentedaminar viscosity with the eddyviscosity is made.Figures 9.6

and9.7 on page219 which show the relative magnitudesof the two viscosities,the augmented

laminarviscosity andthe eddy viscosity, respectively.

For the limiting condition of small valuesordp/v,. J77Tand EckertnumberOV111TC.. wheredp

and,dTarc rcprcscntativcvaluesof pressureandtemperaturedifferences,solution of Equation7.11

for thecore heat flux, 4 gives,

qr Prp fl'VPAT,! A-T,

= A[In(r, /r)rIPI I"

(7.13)

whcre, T, is the nncr-to-outcremperatureiseacrosshe nterior egionandP isa coefficicntof

thcnnalexpansion, hichcan

be akenas

I dividedby thegas emperature.

Close o theboundarycylinders,hin layersarcassumedn which he icatconductionsgivenby

modifiedexperimentalorrelationsor convectionromaheated orizontal latplate n gravity.

150



I JereheFishendcnandSaunders19501orrelations rc adiptcd o includecentrifugalacceleration

ratherhangravity,

A-0.54Ra 0.25 for 105 Ra< 2407 (7.14a)

N4=

0.14RaO.33 for 2407 < Ra< M010 (7.14b)

whereheNusseltnumbcrNu L41(kV) and heRayleighnumberRa- PrS22rp2,8,TL! 1p'

andL,.dT.Pr,fi (- Mi. ) dcnoterepresentativeengthscales,luid to wall temperatureifference,

Prandtl umberandcoefficientof thermalexpansion,espectively. ,,. is thegas emperaturet the

edgeof the ayer.Choiceof therepresentativeengthscale, issomewhat rbitrary,as hefree

convectionorrelationsbased n experimental onfigurationsuitedifferent romthatconsidered

here.Fora finitecavitythehalfcavitywidthwouldbeareasonablehoice. Note hat he

characteristicengthscale, will cancclout if the low is in thehighRanumber ange.

Themodeldescribed bove or theclosedannulus asbeenextendedndapplied o thecaseorco-

rotatingdisccavitieswith axial hroughnow.n these asesheRayleighnumberwill besmallor

zero n theaxialthrougliflow egionandsotheCFDmodelwill revert oconventional

axisymnictricmodel.Equation .14bhasbeen etainedor theshroud onvective eat ransfer.

Conventional FD hasbeenusedn thenear-wall egionondiediscs.Thecorrelationor turbulent

natural onvectionromahorizontalplatehasbeenusedn thesimpleaxisymmctricmodel o

produceheheat ransferonthedisccavityshroud. "hishorizontal latecorrelation roduces heat

transfer,which sgreaterhan heheat ransferproduced y theBolinct al. [ 1993,1994)adialheat

transfer orrelation. lowcvcr,aswill beenseenn Chapter ,whencomparcdo theheat ransfer

calculatedor theSussexMCR Build 2 cavity3 experimentalata henaturalconvectionroma

horizontalplatecorrelationemainsow.

Implementationof themodel n theFLUENTCFDcodewasundertaken.oreachpointonthewall

anair temperature asestimatednternallywithin theCFDcalculation. hiswasdoneby

associatingurface ointswith internalmeshpointsaspccificddistance way romthewall. Using

thisvalueof air temperature,nd he ocalwall temperaturend luid properties quation .14bwas

appliedo estimatehefreeconvection cat ransfer.4,' say.Thefollowingcquationswere hen

usedo estimateheadditionalheat lux, 4. say,due o buoyancy ffects.

dT-, IRa,k Y- in the low 'core' (7.15a)

rr

r4, r. q,, in thencar-wall egion (7.15b)

151



Aftereachupdateof the emperatureicid in theCFDsolutiondieadditionalheat lux termwas

estimatedccordingo thefollowingalgorithm,

1. For each wall point rind an appropriate 'free strcam' air temperatureand thcrtnal laycr

thickness.

2. For each wall point calculate 4., using appropriateheattmnsrercorrelations.

3. Associate each interior calculation point with the 'nearest' wall point and use the

appropriate value of thermal layer thicknessto dctcnninc whether or not the interior point

lics in the ncar-wall region.

4. For each interior point calculate 4. from the equationsgiven above using the appropriate

value of4,,.

Thisalgorithmwas ncorporated ithin the terativeCFDsolutionandextendedo include he

effectsof extramixing in themomentumonservationquations. orconditionsn which he ree

convection eat ransfers relativelysmall hesemodifications houldhave ittle effecton theCFD

solution.

7.3A Numerical2D Modelof the BuoyancyEffects n aStationaryCubeEnclosedCavity.

An initial 2D CFDmodelwasusedocheck hatmodifying hefluid propertieswithina stationary

enclosedavity wouldproduce constantemperatureore,with therequiredheat low through he

cavity.A 2D CFDmodelof Kirkpatrick& Bohn's 1986]experimentor astationary nclosed

cavitywasused.The I IC case,witha temperatureifference f 30K wasconsideredirst. Thewall

temperaturet thebottomof thecavity wassetat330Kwhilst thewall temperaturet the opof the

cavitywassetat300K.The woverticalsidcwallswereassumedobeadiabatic.Forthe

temperatureifferenceof 30KtheRayleighnumber,Ra s 1.75x 010.s with theCFDsimulations

discussedearlier n Chapter waterwasusedas he luid andgravitywasassumedoact n a

downwards irection.ThreeCFDcalculations ereperformed sing heFLUENTsegregated

solver.The first assumed teadyaminar low and hesecond ssumednsteadyaminar low; both

of these nalyses sedheconventional FDapproach. he hirdanalysis ssumedteadyamiaar

flow butwith thefluid propertiesmodificd.Similar o the3D analyses, 100by 100-squarcd esh

withacell spacing xpansionatioof 1.1wasemployedor all threeorthcscanalyses.

152



7.3.1 21) steady laminar flow CH).

Results 11orhe converged steady larninar flow CFD model are shown in Figure 7.2 as a stream

I*unctioncontour plot, and in Figurc 7.3 as a velocity vector plot. coloured by velocity magnitude.

Both figures indicate two main flow circulations with the larger ol'the two being on the right side of'

the cavity. The flow rises Froin the hot bottom wall near to the centrc and Calls back down the

sidcwalls creating the two circulations. In I clockwise direction flor the circulation on the right and

in an anti-clockwisc direction lor the circulations on the lef). The maximum calculated flow

velocity was 0.03 1ni/s.

Figure 7.2 Stream function contours.

w

Ib 41

0

" 00. U

tn (11n (11

i

flTJl1

:1,.,.,..

aa

It I, ...,,.

__

jFigure 7.3 Velocity vectors (m/s) coloured by

velocity magnitude.

Figure 7.4 show the calculated vertical temperature distribution through the ccntre of the cavity

from the hot bottom wall to the cold top wall. The plot shows that there is a uniform corc

temperature of3 19K, 4K higher than the average ofthc hot and cold wall 1cmpcraturcs. The graph

shows steep temperature gradients near to both the top and bottom walls and shows that the CFD

mesh was sufficiently fine to capturc the flow near the walls ofthc cavity. Comparing the calculated

wall heat transt'er to the heat transfer from the Kirkpatrick & Bohn experimentally derived

correlation, CFD predicted a heat transfer Nussclt number, Nu 169 for the hot wall and 128 for

the cold wall, hence a large error between the two Nussclt number%.When compared with the

Kirkpatrick & Bohn correlation value of 256 there is an error in the average heat transfer of

approximately 42%. The overall error in the heat transt'er within the cavity was large at 365W. or

13.3% ofthe heat entering the cavity. In summary, the 21) stcady laminar flow CFD solution was a

poor simulation of the experiment.

153



_________ Bottom Tot

330"Q

325042-

3JO"W

Static 315"aTompooraue

(k)310&42

303*-W

ODR-0

0 on$

Ifv -+; i-

01 018 ei onY-Co«Mate m)

I

T-16

.

-4-3 036

Figure 7.4 Vertical tenipcraturc distribution through the centre of the cavityfor the steady laminar solution.

7.3.2 2D unsteady lsminarnowCFD.

Results or the unsteady aminar flow CFD modelarc shown in Figure 7.5, as a strcarn unction

contourplot and in Figure 7.6 as a velocity vector plot, colourcd by velocity magnitude.Both

figures ndicate that a main central flow circulation angleddiagonallyacross hecavity is set up.

The flow risesfrom the hot bottom wall andcirculates n a clockwise direction. Two smaller sized

anti-clockwisc circulations arc shownto form, onein theupper lcft comer andthesecond n the

lower right comer of thecavity. Two further anti-clockwisc circulations form in the top right and

bottom left comcrs but arc much smaller in sizecompared o the threemain circulations.The

maximumcalculatedflowvelocity was

0.041nits.

Figure7.7 showthecalculated vertical

temperaturedistribution through the ccntrc of thecavity rrom thehot bottom wall to thecold top

wall. The plot shows hat there s a uniform core temperatureof 315K. the averageof thehot and

cold wall temperatures.The graph also showsthat steep emperaturegradientsexist near o both the

top andbottom walls, andthat theCFD mcshwassufficicritly fine to capture he flow nearthewalls

of thecavity.

154



I. . Aw

M. -W

26"-w

0

Ob Al

Figure 7.5 Stream function contours. Figure 7.6 Velocih %ectors (m/s) coloured bv

%,locit% magnitude.

IW-Ll

StatlcTomporaturt,

(k)

3 20W)2

31().. Oj

3-4.

30s.. 432

3 GD. W

' 'E EEHH-i-± . p. 4 . "

ft ft ;i 0030t 013 02 olm

Y-<-ný'r, imtA (m)11

Figure 7.7 Vertical temperature distribution through the centre of the cavityfor the unsteady larninar solution.

Comparing the calculated wall heat transfer to the heat transfer 1rom the Kirkpatrick & Bohn

experimentally derived correlation, the tune-averaged heat transfer Nusselt numbers were Nu-

193

flor the hot wall and 198 flor the cold wall compared to 256 calculated 1rom the correlation giving an

average heat Iranst'er error ofapproxiniately 24"/o. It is ol'interest to note that this is a much larger

error than that produced by the equivalent 31) CFD discussed earlier in Chapter 3. The overall error

in the heat transfer within the cavity was 43AW. or 2.5% ofthe heat entering the cavity. III

summarythe

unsteadylaminar flow CFD

matchesthe

experimental results muchbetter than the

steady laminar flow CFD. However neither CI-D models produced a flow field where the flow

circulates around a central core which was shown to happen with the 31) CFD models in Chapter 3.

". 411

._ 4"

155



7.3.3 21) unsteady laminar flo%scFD %sith modified fluid properties.

In anattempt o achievea cavity flow field havinga centralcore the fluld propertieshadto be

modified to give enhancednixing within thecavity. Both theviscosity and thernial conductivity

were ncreasedin proportion to each other.The specific heatcapacityremained it the normal value.

allowing the Prandtlnumberto remain thesarne.The I'linctions (I -cos jYc/2*d,/j) and(I -co.

[x/2*d, //]) were usedto increase fie value of'the two fluid properties rorn a defined minimum

value on thewails to a defined maxinium valuemoving over a setdistance1'romeach ol'the walls.

The cosine unction waschosen o allow a smoothchange n fluid propertiesacross he layer. The

'boundary layer type distance' wasset as I Wo of* hecaviiy wall si/e. giving / 0.0305m.The same

mininiurn and maximum factorsIm both viscosity and thernial conductivity weresetas5.5 and240

respectively.To enable he useol'the enhanced luid propertieswithin the FLUENT solvera User

Defined Functionor UDF was written in the programming anguageC' and incorporatedand

'hooked' to the solver. Figures7.8 and 7.9 show graphically by contour plot how viscosity and

therinal conductivity fluid propertieswere modified in theCIA) model.Figure 7.9 shows he fluld

viscosity on a line drawn through thecentre ofthe cavity and Figure 7.9showsa contour plot of'

therinal conductivity within thecavity. Apart I,om the changesmade o the fluid properties

conventionalCFD was used n the flow analysis.

III. 1!s. I!

Figure 7.8 Enhanced mixing fluid

viscosity distribution.

IIL, I.

m1 11

Figure 7.9 Enhanced mixing fluid

thermal conducthift confours.

Resu s for the unsteady laminar flow 11joijel"it lit lie UDF enhanced inixing are shown in

Figure 7.10 as a stream flinction contour plot, and in Figure 7.11 as a velocity vector plot. coloured

by velocity magnitude. Both figures indicate that a main central flow circulation angled slightly

156



across the cavity is set tip. The flow rises From the hot bolloin wall and circulatcs in a clockwise

direction. Four small anti-clockwise circulationsare shown it) form in each comer ol'the cavity,

with the Lipper lcI't and lower right circulations being stronger than the two circulations forined in

the other two corners. The inaxiinum calculated flow velocity was 0.02 1ni/s near to each of'the

Iddex%lls.

W. -W

I Ilk -02

1 31b-02

12t. -W

864-43

G$4-03

04. -,u

% I.J. (13

1ý ol

Figure 7.10 Stream function conlours. Figure 7.11 Velocity vectors (m/s) coloured by

velocity magni(tide.

Figure 7.12 shows the calculated vertical temperature distribution through the centre ol'the cavity

from the hot bottom wall to the cold lop wall. The plot shows that there is a unillorin core

temperature of'3 15K. the average ofthe hot and cold wall temperatures. The graph also shows that

temperature gradients exist near to both the top and bottom walls over the width ol'thc enhanced

fluid property boundary layer thickness.

I_. _. __. II

3

3

3

stancsTemperature

M

I

3

2SIX-1.

aaoo&.02

005 01 ols02 023

y ., q, 10' at.. ((IIý

0, Oil

Figure 7.12 Vertical temperature distribution through the centre of the cavit)

for the unsteady laininar flow with modified fluid properties.

jor. 4W

I10-W

Iu-02

157



Theoverallerror n theheat ransferbalance or thecavity wasonly 3.OW,or0.1%or thehcat

enteringhecavity. lowcvcrwhencomparinghecalculatedwall hcat ransrcro theheat ransfer

from heKirkpatrick& Bohnexperimentallyerivedcorrelationheresultswerenot so good.CFD

predicted heat ransferNusscltnumber,Aru 74 for both hehotandcold walls comparedo 256

calculatedromthecorrelationgiving an errorof approximately 1%.This sagaina much arger

error han hatproduced y theequivalent D CFD.In conclusion,heunsteadyaminar low CFD

withenhanced ixingin thecavitymatchesheexperimentalesultsmuchbetter n obtaininga

uniform emperatureentralcorewith flow circulatingaroundhiscorebut heheat ransrcrs much

too owcomparedo theexperimentalalue.

7.4A Numerical2DAxisymmetricModelof the BuoyancyEffects n it Rotating Scaled

Cavity.

In this sectionan evaluationof theenhancedmixing model is presented.The method s applied to a

rotatingenclosedcavity and results from the2D axisymnictric CFD modelare comparedwith the

resultsfrom Bohn ct al. s (1993,1994] experiments.Rotatingcavity Configuration A (seeFigure

2.2) has beenusedfor this CFD simulation. The 2D axisymnictric model wasused o check that

modifying the fluid propertieswithin a rotating cncloscdcavity would producea constant

temperature ore,with the requiredheat flow through the cavity. The cavity was setto rotateat a

speedof 2000 rpm (209.4rad/s).For a temperaturedifferencebetweendie outer and inner

cylindrical surfaceof 30K the Rayleigh number,M4 was4.255x 1010 nd rotational Reynolds

number,Re.,was7.915x101.As with theCFD simulationsof Bohn et al. s experimentdiscussed

earlier in Chapter4, air was used asthe fluid. CFD calculationswere performed using the FLUENT

segregated olverassumingsteady urbulent flow. The standardk-c and2-laycr k-c /W nearwallturbulencemodelswere used.Similar to the3D analyses,a 100x 100meshwith a cell spacing

expansion atio of 1.1wasemployedfor theanalysis.From a convergedsolution using the

conventionalCFD approach heenhancedmixing model implementedusing a FLUENT UDF, was

appliedanda convergedCFD solution for the rotating encloscdcavity with enhancedmixing in the

corewasobtained.

158



Usingthe Bohnct al. s heattransfercorrelation for the Configuration A,

for the innerandouter radius walls, Nu, =0.246Ra0.221

Therefore or AT - 30K and a Ra+- 4.255x 10109 uk - 65.21

1

Theexpectedheatflux, 4 through the inner andouter walls are given by,

kFor he nnerwall, q, = Nu* T.

-T,I

Andfor theoutcrwall, 40=k ---NU61T.-Til

r. Inr.Ir, )

(7. 6)

(7.17)

(7.18)

where he fluid thmnal conductivity, k- 0.0242 wm*IK7', cavity inner radius, ri-0.125m and

outerradius,r. - 0.355m, T. and T,aretheouter and inner wall temperaturesespectively.

Evaluating he heatflux for the conditionsconsideredyields inner wall andoutcr wall heatfluxes or

41- 362.85W/m2and 4. - 127.77W/M2respectively.

*Tbencarwall factorf isderivcdas ollows,

Theheat lux at thewall,4. isgivenby, 4W-A

(T. T1.11r) (7.19)

n"P

whereTArirps the fluid temperaturenearto thewall (CFD cclI ccntrcd temperaturen the I" ccll

next to thewall) andnN; 'Ps thedistanceof temperatureposition away from thewall.

NowPfp

Pr- -kp .,.kom

Ucp

Pt(7.20)

cc od ihere V and p' are the modificd thermalconductivity and viscosity rcsP tively. For the m ircd

viscosity near o the wall, p'= fp but now allowing f to vary locally along thewall and

substitutingEquation7.20 into Equation7.19;

filco (T.- TV"

P (7.21)Pr nx, p

where 4c.,j

is the heat flux from the appropriateBohn ct al. s experimentcorrelation.

So for theenhancedmixing model the nearwall multiplication factor. is given by,

159



Pr n"vxpromEquation7.21,pcp (T.

- TAN.P)

(7.22)

So or theouterwall, 5279.73 n,..,. (7.23)(T.-

andfor the inner wall, 14994.45 it (7.24)(T.

- TAO.,.

Equations7.23and7.24 werecoded nto the UDF to calculatetile local nearwall factors, . andf,

along heouterand inner walls. The mean nearwall factorfwas calculatedrrom the local factors

along heouterand inner walls. The core factor, K wasassumed o havea rlxcd valueor4300. A

seriesof CFD calculationswere thenperformedfor various inner andouter walls, andsidcwall

layerthicknesses.The CFD calculatedheattransferwascompared o Bolin ct al. s experimental

data o obtain the 'best' CFD model.The bestCFD resultswere obtained with the inner andouter

wall constantboundary ayer thicknessset at 0.002mand thicknessesof 0.005m for the sidCwalls.

In this CFD model the fluid propertieswereonly modified in the inner and outer wall boundary

cellsandno nearwall, f factor was appliedto the sidcwallsallowing conventionalCFD calculations

to beapplied in the0.005mboundary ayer regionson the sidewalls.The functions(I -cos[x/2*d,,n)

and(1-cos[x/2*d/n) were used o derinethe increasen tile fluid properties of thermalconductivity

andviscositymoving away from each wall. The increasen fluid propertiesover the nearwall

boundary ayer thickness, was setequal to 10%of thecavity width (0.12m), I-0.0 12m.

Resultsor thesteadyurbulent low rotatingannulus avityCFDmodel Config.A case)with tile

enhanced ixingarcshownn Figures .13 o7.16.7lic streamlinesn Figure7.13showweak low

in the nteriorwithstrongermotionnear

hewalls

n theregionswhere

heresno enhanced ixing.Theswirl velocitycontourplot,Figure7.14showshat heCFDmodeldoesproducehecxpectcd

solidbodyrotationn thecavity.Themixingfactordistributionn Figure7.15confirms ile

successfulmplementationof themethod howinghat henon-dampedcar-wall egionsmerging

smoothlywith theenhancedmixing region n thecore.Figure7.16showsdiecalculatedadial

temperatureistributionhrough heccntrcof thecavity.Theplot showshat heCFDmodel

Producesuniform emperatureentralcorewith a core emperaturef 317.5K. llic graphalso

showshat emperatureradients xist near o the nnerandouter adiuswalls over hewidth(0-002m)of theenhancedluid propertyboundaryayer hickness.

160



L-1

Figure 7.13 Stream function contours.

: 40. m

Oeb: 0

lb7. OJ

elw. ua

301.. 03

2, b. 04

104-03

a00.. O.,

446.0.,

1. QI

Figure 7.15 Mixing factor contours.

,.0

$0. . 0:

qbalw. 0:

0 24.. o

4 00-01

lop. 01

.?.0

Da.: 0

..: W

. 31.0

4 02. . 01

3 4.1.: 01

3 u. W

3 34. . 01

Figure 7.14 SAirl %el(wil% m/%)conlotim

AI

¶2. ¶' P 'M -P- C1 P tfl PUP

V

Figure 7.16 Vertical temperature dioribulion

through the centre of the ca, t%.

Hie error in the overall heat transt'er balance for the rotating annular ca%ty %kas .4 1 AV. or 3.4",, of'

the heat entering the cavity. When comparing the calculated wall heat transfIer it) the heat transfer

from the Bohn et al. experinien(ally derived Configuration A correlation the results for the inner and

outer radius walls were poor, with the CFD predicted heat transfer Ix-Ing 35.48W for the inner and

63.M4W for the outer wall compared to 34.2W calculated from the correlation giving a prediction

error ol'approximately 4(1/,(, fior the inner and for the outer wall an error ol'approximately M7"o. Using

the Bohn et al. [ 19941experimental heat transfer correlation for axial heamig conditions gives a

hcat transfer of 34.18W for this case. I ]eat transfer CFD results were 69.72W for the cold sidewall

and 36.94W for the hot side wall. It must be noted that the Bohn et al. experiments were perflornied

%eparately or radial and axial directed heat transfer and no combined axial and radial directed heat

Ifil



transferxperiments ereperformed. herefore lic correlationswerederived or radialdirected

and oraxialdirectedheat ransfern isolation.

Inconclusionhesteadyurbulent low CFDwith enhancedmixing in thecavityresultsn a

uniformemperatureentralcorebeingproduced. owever hemodeldoesnot producehe

circulatinglow arounda centralcore hatmighthavebeenexpected.1c CFDmodelheat ransfer

resultswereacceptable or the inner radius wall but poor for the outer radius wall. Closer

examinationof the CFD solution results showed ack of convergenceof some ocal nearwall

factorscalculatedalong both the inner and outer radiuscylindrical walls. The variation in these

factors rom iteration to iteration was most notable n the two comerson thehot outer radiuswall.

Furtherdevelopmentof the model focussedon rotatingcavity with axial throughflow testcasesand

this isdescribedbelow.

7.5 Final Implementation of the Enhanced Mixing Model.

In thissectionmplementationof theenhanced ixingmodelUDFmethodology redescribednd

anexplanationsgivenonhowtheUDFhasbeenappliedo a rotatingcncloscd avity with axial

throughflow.

7.5.1Cavity shroud heat transfer formulation coded In the UDF

Fora rotating intcr-disc cavity theshroud ocal Rayleighnumber,Ra has bccn definedas follows,

Ra= Gr Pr6 (7.25)

whereGrashofnumber, Gr =

andbaseinePranddnumber,

r.(T.

- To1

,, 2 2(.YP3

Pfl, = I'S'.ka

(7.26)

(7.27)

162



I erer. is thecavityshroudadius m),s is thecavitywidth,T. is the ocalshroudwall temperature

(K), 0 is the otorspeedrad/s),T,,s thegas emperatureK) at a positionn theccntrcof the

cavityat85%of thecavityouter adius.Viscosity,4 and hcrrnalconductivity. barc hebase ine

valuesetby theuser n a FLUENT nputpanel.

Thestandardeat ransfer orrelationornaturalconvectionromahorizontalplateassuming

turbulentlowwasused o obtain he ocal heat ransfer long hecavity shroud.

Nu,,,j w0.14Ra*-Jjj (7.15b)

giving a local hcat flux,Nu,.,

jks (T.

- T,(7.28)

V2)

Now usingEquation7.21,the local near wall factorf is given by,

ßäCP(T. - TXWp1

7.5.2Cavitycoreenhancedmixing model ormulationcoded n the UDF

(7.29)

ToobtainheK multiplying actor or thecnhanccdmixingcore,Equation .2for the ocal

Rayleighnumber,RaiandEquation7.11 or theheat lux havebeen odedntotheUDF-

7be ocalRat sgivenby,

where

Ra, Pr,Ra,Raj

Pr,Acp

k,

Ra, p,2 Or,+ 14,1)2ý1, 'r

2dp

Ra, At !L

p dr)

(7.30)

(7.31)

(7.32)

(7.33)

+ W,w 13

whcrc Atli (7.34)-41-.4R-T,

163



L=r, - Rsw (7.35)

RAO m) is the outer radius of thecentral shaft forming the inner radial dimensionof the cavity.

R,,44 is specifiedby the user within theUDF. The local fluid viscosity. lit and thermalconductivity,

kiwithin thecore,uses he modificd valuesat eachcomputational teration. 71c local radial cell

Centre osition is r, (m).Thc local fluid relative circumfcrcnti3l velocity is is-1.he characteristic

Icngth,L used n the local Raj number s given by, rrRW and wasdetermined hroughCFD trials

using heUDF. Stability of the CFD computationwasbestachievedwith this definition of tile

charactcristicength. From the Eckhoff andStorcslcttcn(1978,19801stability criterion, Equ3tion

7.9, f Ra2< 0, Ra2 s setto 0 and conventionalCFD is usedwith no enhancedmixing taking place

in that ocation.

Duringengine ccelerationandatsteady tateconditions)hecompressoriscand heshroud

MCMIemperaturesrcgreaterhan hecavity air temperaturend hedisctemperaturencreases

withradius. herateof change f densitywith respecto radius,dp1dr n thecavity will beexpected

tobenegative nd o strengthen ith increasen radius. Icnce he ocalRayleighnumberRa)wil I

increasewith radius.At low radii, whereheaxialthroughflowoccurs,heN13chumberwill be

smallanddpldrwill besmallor maybepositive.n thisregion heRayleighnumberendso zero

Ra: sset ozeroandconventionalCFD sused.This salso ypicallythecaseduringan engine

deceleration.

Thecoremultiplying factor,K wasdefincd as,

Ka ARaj" (736)

This s in thestandardunctionalormexpectedornatural onvection eat ransrcr.ValuesofAandn werevaried o producehenecessarynhanced ixingwithin thecavitycore. n tilenext

ch3ptcr,Ch3ptcr8,valuesof A andn havebeendeterminedhroughCFDtrials.CFDcalculations

werepcrronnedo simulateheflow andheat ransferor theSussexUTCMultipleCavity Rig

build2(MCRD2)experimentsLonget al.2006b].The ntention romthese imulationswas o

obtainagoodagreement ith theexperimentsnd o rindthevaluesof A andn thatwouldproduce

agood it toexperimentalataover hefull rangeof buoyancy onditions. aluesor.4 andn are

hardcodedntotheUDF.Thefunction, - cos[(,/2)(5/1)]wasusedodefine hechangen fluid

Propertiesncreasingaway romthewall.The hickness f this ayer.MAYER. issetwithin the

UDF-Withinthis ayera second onstant ropertyayer s formulated ext o thewall.The

164



thicknessf thissecondayer,Dlq)-Con,s alsohardcodedntotheUDF- n thisconstant roperty

layerconventional FDcalculations reperformed ndnoenhancedmixingtakesplace. lowcvcr

inthecavityshroudwall regionenhanced ixingisassumed ith theaverage earwall factor,

I fortheshroudwall used o factor hefluid properties f viscosityand hermal onductivityover

theDIa)-Conayerregion.To estimatehe hickness f theconstant ropertyayerextending way

from hewall, the urbulent low EkmanboundaryayerequationOwenandRogers19951or

rotating avity lowswasused,

0.098A(flr- w)ý'(, r)06 Re.r I' fir

whereRaos therotationalReynolds umber.

(7.37)

FortheSussexMCRB2 experiments he Ekmanboundary13ycr hicknesswithin the rotating

cavitieswascalculatedasapproximately0.002mand wasapplied to theCFD COMPUtAtionsetting

theDIa)-Convaluewithin the UDF. Using the experience rom thepreviousCFD experiments he

DLAYER hicknesswasset to 0.005m.The full sh3pCunction equations o define the cnhanced

mixing corewhich is coded nto the UDF arc as follows,

Forviscosity, po-[f + factx(K -f

)Di# (7.38)

And for thermalconductivity, kP= [f + factr(K - f)ý'b (7.39)

whcre forJ< DL4YER (7.40)

factx -I for J.? I

factx coff (5

- DIqyCon)2

(DL4YER- Dla)Con)

J is thedistance m) of the fluid ccli ccntrc away from thenearestwall.

In summary heoverall cffcct of thenearwall factor. for thecavity shroudand for thecore

enhancedmixing factor,K arc shown in Figure 7.17 for the CFD simulation of two cavities from

theSussexMCRB2 cxpcrimcnt, in the form ora strcam unction plot. 77hesccsultsarediscussedn

Ch3pter8.

165



Thefinal versionol'the EnhancedMixing UDF hasa filenameof-comp enhanced mixing-c'. The

LAWwasprogrammedusing the computer languageC. Code listings ol'the UDFand the scheme

file 'wall viscosity.scni' are given in Appendix 4 andAppendix 5 respectively.

Shroud Mai Flux

Nall'oriv. 1fori/Illate

CorTel.,

Nu 0.14Ra""',

Chara. 1, gap 2.

,%I I, I.

I.

I Mass

Rcgsonof I'nharwcd

%ilung

Vn (A Ra" I %%A-I; (X)n 01 andRa fit (d; tit).( hara Ir

11'ressurv( )ullctl

Figure 7.17 Sussex UTC NICRI12 stream function conlour%.

7.6 V%er Cuide for the Enhanced Mixing Model UDF and the u%e Aithin the 21) Axlsýnimelric

CFD Model.

It is inirw1ant to note that the 21) axisymmetric CI- 1) model needs to be setup to use a rotating

rcfcrcnce frame. A simple user guide for the I-.nhanced Mixing Mmiel VDI- and the usc within the

21) axisymnietric CFD model is given in Appendix 6. The user guide gi%c% he order of'operations

lo scl up and run the CFD model with the enhanced mixing model (JDF.

166



7.7Conclusions.

In thischapterheenhancedmixingmodelmethodologypplied o thesteadylow 2Daxi.

symmetricCFDmodelhasbeenexplained.nitial testingof themodelwaspcrrormedor botha

stationarynclosedavityand or a rotatingsectorscaled avity.Thisshowedhat t wasrcasiblco

accountor themixingnot captured y a conventional DsteadyCFDsolutionshrough

modification f theviscouserms,and hat hencar-wall reatmentouldbemodified o use

empirical orrelationsn calculatingheheat ransrcrate.71c levelof themixingfactor hat s

requiredoobtainsatisfactorymixing n thecavitycoreand oproducehecorrectevelof licat

transferhroughhecavitywasestimated.

Themodelproposedobviously includesa numberof assumptionshat will limit its generality. It

wasthereforedecidedto concentrate urther developmentand evaluation on the most relevanttest

dataavailable.The implementationwas thereforecxtcndcd to cover rotating cavities with axial

throughflow. In thenext chapter, he enhancedmixing modelwill beapplied to enclosed otating

cavitieswith axial throughflow in the simulation of theSussexNICRB2experimentscovering a full

rangeof buoyancyconditions.

167



CHAPTER 8

2D AXISYNINIETRIC COMPUTATIONAL FLUID DYNAMICSSIMULATION OF THE

SUSSEX NIULTI-CAVITY RIG BUILD 2 WITII THE APPLICATION OF THE

ENHANCED MIXING MODEL

Summary

Asdiscussedn Chapter6 themultiplecavity rig at theUniversityof Susseximulateshe nternal

airsystem f aI ligh Pressure ompressorI [PC).11icaimof therig was oprovide estdata hat

canbeusedo improve hephysicalunderstandingf theflow andheat ransfermechanismsn the

I IPCrotating avities. n thischapterhe2DaxisymnictricCFDmodellingechnique sing ile

enhanced ixingmodel o increasehemixingin thecentralcoreof a rotatingenclosed avity s

appliedo theSussexMultipleCavity Rigbuild 2 (MCRB2).Thecomputations ereperformed

assumingteadylow and heresultshavebeen omparedwith theNICRB2 xperimental

measurementsor metal emperaturesndheat ransrcr. heseesultswerealsocomparedo results

froma3D LESCFDmodelof thesame avity.

Usingtheenhancedmixing model in theCFD simulationsof theSussexrig a good agreementwith

experimentalvaluesfor the cavity shroud surface icat transrerfor rotating Rayleighnumbersof the

order 109wasobtained.Also, therewas anacccptableagrccmcntwith themeasured ompressor

discmetal temperatures.

8.1 Introduction

Numericalsimulationsor tile SussexNICRB2o analyseheconvective eat ransfern a rotating

cavitywithaxial hroughflowaredescribedere.A 2DaxisymmctricCFDmodelof a singlecavity

wasconstructedirst.Thecavity chosenor thesimulationwascavitynumber asshownn tile

diagramof the est ig in Figure8.1.Ascanbeseenn thediagram, avity3 is instrumentedwith a

series f rotating hermocoupleshatwere ocated nthecompressoriscsurfaces. onventional

CFDwasusednitially, whichassumedhe low tobesteady, ompressiblend urbulent.Using ile

convergedolution or theconventionalCFDmodelas a starting onditionhecnimnccdmixing

168



modelusing heFLUENTUserDefinedFunctionsUDF)was henapplied.Theaim of thismodel

wasosimulatehe3D unsteadylow andheat ransfern a rotatingcavity with a2Daxisymmetric

model. oachievehis, he ncreasedmixing n thecavity centralcorewasusedwith a view to

demonstratinghat hecnhanccdmixingmodeldevelopedn Chapter7 that hecorrectheat ransfer

in thecavitywill beproduced.

ThesecondCFDmodelwith enhanced ixing was or twocavities;cavities2 and3,surrounding

onecompressorisc,disc2 (seeFigure8.1).The hirdand inal CFDmodelalsowith enhanced

mixingwas or thesamewocavitiesbutnowwithcompressorisc 2 included n themodelling. n

thisCFDmodel,disc2 wasmeshed ndconjugate eatconduction olutionswereobtainedor tile

disc.By using heconjugate eatingoption, heheat ransferredhroughhedisc byconduction nd

thedisc emperatureserecalculated. oth heheat ransferhrough hecavity shrouds nd hedisc

2 temperaturesomputed y theCFDmodelswerecomparedo themeasuredeat ransferand

thermocoupleesultsor various ests overingarangeof operating onditions. herangeof

rotatingRayleighnumbers onsideredor tileCFDsimulationswas1.3x 104o 2.7x 109.Results

from he2Daxisymmctric nhancedmixingCFDwerealsocomparedo resultsroma3D LES

CFDmodelobtained y SunandChew 2004]andSunct al. (20041 t theUniversityof Surrey.

8.2 Description or the Experiment

A detaileddescriptionof the SussexMCRB2 experimentalwork carriedout by Alexiou [2000,

2001] andby Long ct al. (2006b], was givcncarlicr in Chaptcr2 section2.3. In summary,with

referenceo Figure8.1, the rotor discsand inncrshaft ofthe rig representpart of al I Pcomprcssor

internalair systemandwere scalcd

down from a Rolls-RoyceTrent acro-cngine, o a ratio of 0.7: 1.

As shown n the figure, the rotor hadthree nternaldiscsand togetherwith the two endplatediscs

rourcylindrical cavitieswere formed.Theouter radiusof eachcavity (b) was220.Omm; he inner

radiusof eachdisc bore (a) was70.1mm (a/b - 0.32)anddisc cavity spacing s) or42.9mm (s/b

0.195).Thestationary entraldriveshaft rs)hada radiusof 60mmgivingan annular apof

10.1mm.Coolingair wassuppliedo therig byasinglestage Iowdcnscrewcompressor.he

airflowwasmeasuredy orificeplates t the nletandat theexit to therig.Theoutersurface f [lie

rotorassembly asheated y impingementf hotair fromtwo I OkWheaters. emperaturemeasurementsereobtainedrom 21rotatinghermocouplesonnectedo theCompressoriscs

(TC - TC21)mainlyondiscs2 and3.A further3 rotating hermocouplesTC22- TC24)were

169



po%flionedaxially along [fie outer surface offlie Compressor drum. All tile rotating thenii(Woupics

were led out to a Wendon slip-ring unit. On the inner stationary drive shaft 7 thermocouples (TC25

TO I) werepositionedalong tile lengthofthe shall-Furtherstationary liertnocoupleswere

positioned o measurehe metal temperatureofthe compressorcasing.Air thermocoupleswere

positionedn theannular spacebetween heoutersurfaceol'the compressordrum and the casing,

Thermocouplesmeasured he upstreamanddownstream emperatureoftlic air flo%%ng through tile

annularpassage etween he inner shall and thecompressordiscs hores.Steadystate estswere

pcrfornied or a wide rangeof'operating conditionsandalso a transientaccelcration-dcceleranon

lestwasperformed.For tile transient est, temperaturemeasurementsweretakenat time infervals of'

2.5secondshroughoutthe testcycle. in addition to (lie temperaturemeasurements. DA

measurementsfaxial and tangential flow velocitieswiflun tile cavity .1were obtained.The

accuracyof'tile thermocouplemeasurementsor the steadystatetestswas stated o he fO.02K

(standarddeviation,SI), lessthan0.14), with tile exceptionbeing for lest 31 wheretile accuracý

was ess han ±0.08K (SD lessthan0,29).

mo

SuvwxUrC Muld -Camity ujg lad" 2

I. o

11.0

Cavity

No. I

4 11Cllvilý

No. 2

Ih %c

No. 3

41tI

Ca%if)

No. 4

Th

lojmr,

-300 i-? OO

.

ILI JI

('31%lý

No. 3

0"6; r' -I

150 I** to

Figure 8.1 Sussex NICRB2- showing the position% of file thermocouplew.

a

170



83 Testfleat Transfer Measurements

I feat ransferhroughhecavityshroudswascalculated sing he temperaturesbtainedromthe

thermocouplesnthecavityshrouds ndontheoutersurface rthe compressorotor radially nlinewiththeshroudhermocouple.orcavity2 the hermocouplesC23andTO (seeFigure8.1)were

used ndTC24andTC12wereusedor theheat ransfer alculationorcavity3.Thecavityshroud

heat ransferwascalculated s ollows,

I Icat lux, qrwbln(%2b)

(8.1)

D is theouterdiameterof thecompressorotor,b is thecavity shroud adius,k.,, is [fie thermal

conductivity f themetal, itanium,and(r.,,,,

- T.., ) is thedifferencen themetal emperature

acrosshecompressorotorshroudhickness.

7becavityshroudhcat ransf: , as aNusschnumbcr.wascalculatcd s ollows,

Nfi£IW4d

ilf- Tf)

(8.2)

whereC11P -a' (8.3)

2Cp

0 is the compressor otor speed, T es rig ads the air inlet temperature o the Itna is the disc

borc radius.

8.4Numerical Investigation or Convection In a 21) AxIsymmetric Enclosed Rotating Cavity

%Ilh Axial Throughnow.

8.4.1 Basic modelling assumptions and tile numerical procedure

All thecomputationscarriedout solve theconservationequations or mass,momentumandenergy

usingthe FLUENT CFD code.The CFD calculationswere performedassuming2D axisymmetric,

171



compressible.teady,urbulent low,using hestandard-cand he2-laycrk-c/k--Inearwal

turbulence odels. heFLUENTscgrcgatcdolver,second rder mplicit timestepping nd he

secondrderupwindschemeor thespatialdiscrctisation erechosenor thecalculations. he

flowwassolvedn therelativevelocity referencerame.ThePresto cheme, second rder

pressureorrectionmethod,wasset orpressurenterpolationor thevelocity.Forthepressure

couplingmethodprcssurc-corrcction),heSIMPLEalgorithmwaschosen. ll thesimulationswere

performedsingdoubleprecision ccuracy.

8.4.2The governing equations

1.Conservationof Momentum

For a 2D axisymmetric model in a rotating reference rame, the steady flow momentumcqtmtions

aregiven by,

Axial dircction,

Ia (rpv.V. +I 'o (rpv,V, =- LIP-

+Ia2ov,

-2(V.V +1

a UN,+

ON,; Ex

r Or &r ar

[r1j(

.3))]

r&

[rlý

Or &)

Radialdirection,

(IV,+V,Or r

(rpv,v, )+!

-L(rpv, v,).

-Lll-y+!l[rjj(!! V-'+ 1ý'1

11+1

TXr Or Or r& CIX OrT

jr Or Or 3

- 2p V'+1" (M) +P

VI

r2 3rr

wherc

andv, is theswirl velocity.

Tangential irection,written n tcrrnsof relativevelocities s,

Iaa

; E(rpvgv, w)+!(rpvvw)+p(2flxvrw+flxflxr)n

r clr

(8.4a)

(8.4b)

(8.4c)

VIVI-4 (8.4d)TX' ()X r1Or Pr rr

172



%4,crc herelativeswirl velocity sgiveby v., - v, -(f1r) andp(2fl x v.,, ) is theCoriolis orce.

Forturbulent flow the Rcynolds-avcragcdapproach o turbulencemodelling is used with the

additionalReynoldsstresses- pu,uj ), due to the Navier-Stokesequationsbeing decomposednto

themean timc-avcragcd)and fluctuating components.which are addedto the momentumequations

givenabove.The additional termsrepresent hecffccts of turbulence.For thek-e turbulencemodel

themethodemployed in FLUENT to relate the Reynoldsstresseso the meanvelocity gradients s

theBoussinesqhypothesis I linze 19751,

p7111-14il,auf

+all/ -3 (/v'

+ len

ax, axj 3 Lax$

)so(8.5)

In thecaseof thek-c turbulencemodel woadditionalransport quations.or the urbulent inetic

energy.A-, nd he urbulence issipationate,c.arcsolved,and he urbulentviscosity,I, is

computedsa functionof k andc. It mustbenoted hatwith theBoussinesqypothesis, is

assumedo bean sotropicscalarquantity.Thestandard-cmodel,kineticenergy, , and

turbulenceissipationrate,c, turbulence quations longwith thenearwall turbulencemodelsused

aregiven n Appendix1.

2.Conservationof Mass

3.Conscrvationr Encrgy

v- (pr"w)-o (8.6)

v- MPE + P)) -v-(k. T) + (1) (8.7)

whercE=h-L+ v'and 1)s theviscous issipationcnn.

P2

8.43 Enhanced mixing model

Theenhancedmixingmodeland ts implementationn a FLUENTUserDefinedFunctionUDr)

weredescribedn Chapter .Thefinalversionof theUDFcodewasdescribedn Section7.4and

instructionson linkingandusing heUDFwithin theCFDsimulationsweredescribedn Section

7.5andAppendix6.Theenhanced ixingmodelwasusedo increasehemixing within thecoreoreach f thecavitiesn anattempto modelunsteadyD flow reaturcswith a2Daxisymmetric

steadylow model.Thiswasachieved y modifying he luid properties f thermal onductivityand

173



viscositywithin thecavities.Thesliccificheatcapacityemained naltered y theUDFto keephe

localPranddnumberhesame.All thebaselineluid propertiesweredcrincdas unctions rthe

localgasemperatures.he function I- cos(irS/21)'wasusedodefine hechangen fluid

propertiesncreasingawayrrom hewall.Thethickness r this layer,DL,4YER,wasset o0.005m

within heUDF.A second onstant ropertyayer,Dla)-Coir, ext o tile wall %vasetwith a

thicknessf 0.002m,whichwasalsocodednto theUDF. In thisconstant ropertyayer

conventional FDcalculations rcperformed ndno enhancedmixingtakesplace. lowevcr n tile

cavityshroudwall regionenhanced ixingisassumed ith thesurface eat ransfer onstrainedo

matchhe reeconvection orrelation.Figure8.2showsheregionswhere heenhanced ixing

modelwasapplied.Thecavityfluid temperaturehatwasusedn the ocalGrashornumber

(Equation .29)and n tile heat lux (Equation7.32)calculationswas akenat apositionof 8s%or

diecavityshroud adius.As mentionedn theconcludingemarksn Chapter7 thereweresome

instabilityandconvergenceroblems. o overcomehese roblems n under-rclaxationactor urf

normally et o 0.1) hasbeenappliedo thefactoredluid properties ndalsosmoothingnsmoollt

normally et o 10passes) asappliedacross ach, rthe CFDmesh ells within tilecomputational

fluiddomain.Flowficld ccil ccntred moothingwasappliedo thefluid properties rthe

augmented olecularor laminar)viscosityand hermal onductivity.To illustrate hesmoothing

algorithmwithin theUDFprogram,

Figure8.3belowshowsapartor

tile2D CFDgrid.

Thefigure

showsourcellsnamedN, E, SandW thatarcattachedy edgeso thecentralcell,Cwhich s to

besmoothed.hesmoothingormula or theaugmentedaminarviscosity,i is Equation .8given

below,

p, -Ui, +p,, +pf +ps +pw)/ 5 (8.8)

wherepc' is thesmoothedell ccntrcdvalueorlaminarviscosity orccll, C.

Smoothingof theaugmented hermalconductivity uses hesamerormula.71c smoothedcell

ccntredvalue is the meanof thecurrent valuesorthc centralccll plus the four connecting cells. All

thecellswithin the solution spacearc smoothedandthis is repeated tsm(wh times ror eachCFD

iteration.

174



Con%critionalCFD k-c Modcl with

2-laycr near wall nuxicl, region%

where there is little or no enhanced

mixing takesplace

Rcgionof'Enhanced Mixing

Fn(A Ra") with A 1300it 0.1 or 0.2

andRa th (dp/dr), Chant. 1. r, -Rjh, ,

Figure 8.2 Stream function con(ours "ith (lDF boundary condilion% (te%l 33).

N

w C E

S

Figure 8.3 A part of ihe 21) ('Fl) grid.

175



8.5 Numerical Simulation Restills.

8-5.1 Single Cavity, Sussex UTC NICR112 cavity no.3

Figure 9.4 shows the CFD inesh (approximately 15. X)Oquadrilateral cell%) constnicled I*orcavity

no.3 ofthe Sussex MCRB2. Mesh spacing expands away from each wall %ith ; n expansion ratio of"

1.1.Temperature prol-i es obtained from the best matched SC03 ihmial analysis. dmribcd in

Chapter 6, were applied to the disc and shroud surfaces summiding the cavity as CF`D lunindary

conditions. A mass flow boundary condition was applied to (he inlef and suific pressure applied to

the outlet. Three steady state test conditions were analysed. test 33.34 and 50. ýrahlc X. give% he

boundary conditions and (lie flowparameters.

rotational. Re, and axial Reynolds number. Re. and

Grashot'numbers, flor each ol'ilie tests.

Sussex MCRB2 Cavity 3 with Test 33 Metal Temperatures

r. a 0-06m a-0.0701m ba0.22m sa0.0429m (I a 124.5rad/s Tm Shroud m390,2K

Rell. b'= 8.47E5

Re, = 3.64E4

Ro = 1.47 in Temperature Profile

Gr,p= 1.45E8 on all Surfaces

Ra,p = 1.03E8

Inlet

Mass Flow = 0.171 Kg/s

T,, = 321 K -110.

Tu = 10% Stationary Shaft

Figure 8.4 CFD mesh and geometry of the Su%. c%NICR112 ca%t%

-I-

= 300kPa

17o



8.5.1.1 Him structure and temperature rc%tilt%

A contour plot of stream function for test 33 was shown in Figure X.2. I lie figure sho%%ng that %%it

the application ol'the enhanced mixing mmiel a central core was fonticd. In the rcgion of the disc

cobs a circulation was shown to florm between the axial throught'low and the central cavity core

region. Across the three test simulations the extent ol'ilic circulation region %,.s %cry similar. A

contour plot ol'teniperature, Figure 8.5 shows that the central core has a near uniflomi core

Imperature of'334K. compared to the inlet fluid tcmpcraturc of 320K and the shroud melal

Imperature of'390K. The swirl velocity contour plot. Figurc 8.6. shows that near solid body

rotation wasachieved in the cavity central core. (Nil to compare both ternperalure and the swirl

vcloclty within (lie cavities across all tests, the temperature contour rangc of 316K to.190K was set

-ind the swirl velocity maximum was set to 54 ins" I'm all the tests)

3.9 ae4 02

3.84 P- 02

3.8Oe4 0;1

3.76e- 0,

3.7 2e 4o.,

3.68e- 0,

3-64e 02

3.6 0m (I:

3.56e - U.

3.52e-02

1.4 Re- V

!. 4 4eo K,

3.4oe. K

i. A3o4 02

i. 32e- o"

Max. lemp. 390K

InIct lemp. 320K

Figurc 8.5 Te%t33 lemperatures (K) (for ot 0.1).

177



I

4.80e. 0I4.6of94014.40e-Ol4.20e*O 14.00640 13-80o-Ol

3. i 0r. ui3.40e-013.20oi3.002.802.6001

.4Or- 01

1.60r-1.40,ý - 11I-01IA C-o I

I U'. 00

11 l 004J (I ou

.7.1 (1,100

UJ oe. 00

%tax. %cl. 2,711L..

Figure 8.6 Test 33 s%sirl%clocifics (m/%).

Sussex MCRB2 Cavity 3 Steady State Toil 33

Temperature from CFO

400

41

380

370

350

b.

340

330

40 0 4p

310 1

000

:.

aa

a

a awa

lo.0 ur

OF

0

/"". ____l

...... "s__________a00,e0*- 40 4- -0

I

005 008 01 012 0 14016 Old

02 0172ftdial Oletance (m)

Figure 8.7 Test 33 disc and cai if.% emperalure%.

oe' -*-

*00

04, l'0

., neue

--1..-....

e .00 wo19

.(ü in

46: b,

abc 2

* b%c3 o3b

23 4hroW

W A. oWCAvft CFO A-1 300 m-0 2

W AxvO OWft CFO A-1 300 m-0 i

k4o"ured - Cbbc2

ku0sured DOC I

M-04,0. d lpwmad

I.,



Figure8.7 slowsgraphically the metal temperatureofthe disc and cavity shroudsurfaces

surrounding avity 3 and (lie fluid temperaturehrough the ccnirc ol'thc cavity all plotted against

radialdistance.The metal temperatures s mentionedearlier were takenfirointhe 'hem-inatched'

thcrinalmodel.The measured hermocouple emperatures.TC7 (o]"Cl 7. arc also plotted and show

thatthedisc surfaceand shroudtemperatureprofiles were closely matched o the testmeasurements.urvesofcalculated cavity fluid temperaturehave beenplotted for two CH)

solutions.The two CFD solutionswere flortheenhancedmixing model with the local Rayleigh

number Equation7.36) powersofn 0.1 and0.2. For NO solutionsthe multiplication factor..4

used n the local Rayleigh number equation.Equation7.36.was set to a valueof 13M for reasons

dcwribcd in Chapter7. A higher core temperature.which was closer to thedisc and shroudmetal

temperatures,was l'brinedIn thecavity centralcorewhen it 0.1 than%kitht 0.2.

Test case 34 was a higher Orashol'nuinher. Gr but lower Rossby Number. R(P 11'Qij) case (han

Icst.1.1.As flor case 33, the disc and shroud surface temperatures were derived I'min the 'he%,-

inatched' thernial model. Figures 8.8 jild X. ) show the cavity temperature and swirl %clocity

contours respectively. A temperature versus radius plot is given in Figurc 8.10 %%hichshows that IIle

cavity central core temperature is near constant it 333K compared to the inlet fluid temperature of'

320K and a shroud metal temperature of 383K. The disc and shroud surface temperature. %closely

match the test thermocouple measurements. The swirl velocity plot shows that ncarM.)Itd body

rotation ol'the fluid in (lie cavity was reached.

3.90o#02

:1.840.0 ,,3.8 00. V

3.769-0,,

3.72o4 V,

3.68e- 0

3.6 4e-0

3.60&- 0

3.56e- 02

3.526- 0: 1

14 Be 0

'1.4 4is 0

3.409,02

3-3604 OL'

3.32e, 02

"ll- ,

80+0 "1

3.24 e-0 Z'ýý-20e402

3.16&- 02

Figure 8.8'1'est 34 Temperstures (K) (for tiA. U.

179



S-4 U*4 Ll I

5.? om. 01

5.0 Oe, 01

4.80e4 01

4.60e4O4.4

0040 1

I

4.2 0a,4014.0 Oco013.8 U0,0 1

3.60e-O 13.4 oe4o I

013.0a2.8 001

2-60e, 40 I

,.4 Ue*U I

: . 20e, O1.000-011.80e, 011.60". 0 1

1.4 Oe,*O I1

. _'06401

1.000401

6.0 Oe* 00

6.0 Oe, Ou4.000-06AOL

1Aor- 00

Figure 8.9'1'es( 34 swirl velocifles On/0.

Sussex MCRB2 Cavity 3 Steady State Ted 34

Temperatur@ from CFD

380

3yo

I

300 ;

340

13U

m

-... a@0

jjwmoopomý #*.0..

#0 #00

..

Sio L-

006 008 0.1 0 12 0 14 016 Ole 02

Modlol Ololanc* (m)

Figure 8.10 Test 34 (Ilse anti cavity temperatures.

190

"-

:... "'

022

4k I ), -., "( ýJ,

4D -DOC 2

0 Oisc 3 Cob

Doc 3

Oisc 2-3 Shroud

o Mid Axial Cavty - CFD A- 1300 noO 2

* Mid Axial Cavity - CFD As 1300 nmO

" Measured - Dec 2

" Measured - 01sc 3

" Measured - Shroud



`ý9'2'

0' '

78a*02

3,74a*02

3.70e-02

3.66e-02

3.UAe

54e 01

5Oe*02

46c-02

i.4. e--02

38e402

1.30+02

i..-;Ue#02-'6e+02:-'2e*02

14 [1,

Figure 8.11 Test 50 (emperatures (K) (for it OA).

").4Dm+1)15.2or'n.0 0

F4-01

4.80e 014.60e UI4.4 0e-UI4.

-1Uý+U1

4 1) (1ý5 40

3.4 Dti -013.20p-p 13.0 De-01? An^ 4nI

1.60 D1

22.4 e 01

UU01

i tin nII.6fl 11140,, -DII .

20e 4 [11

I. 00m001

H. 0 Or to Qh. 0 Pr 00

4. UUUa;,. (IuU0

1).0D0

1]

Iax. vel. will/'s

Figure 8.12 Test 50 s%virlvelocities 00/0-

181



The final test case simulated, case 50, had the smallest (frashot'number. (It- offhe three tests. but

also had the highest axial througliflow giving tile highest Rossby number. Ro Figures 8.11 and X.12

%how ile cavity lemperature and swirl velocify contours respectively. A tcnipmaturc versus radius

Plot is give in Figure 8.13 which shows that the caviiy central core lemperalure is near consfant for

thesolution witil

local Rayleighnumber power. it 0.1.

The discand shroud surface temperatures

again derived from a thennal analysis closely match (lie test thennocouple nicasuremcnis. I lie

cavity core fluid temperature was 324K compared it) (lie inlet Icnipmatirc of'3 I OK and tile shroud

metal temperature ol'378K. The swirl velocity plot shows that near solid I-xxly rotation was reached

in the cavky core but in the area around tile disc cobs where tile high axial throughilm-6,has ; n

CITCCIil tile "\%II \ Clocity.

340

.1, ý

I3N J

150

WO

:1V,

Lý,p1 Oda

110r) (11,

Radial Distance (m)

Figure 8.13 Test 50 disc and cavi(ý temperal tirm

Sussex MCRB2 Cavity 3 Steady State Test 50

Temperature from CFD

0-40

A0,

10

o'0

008 () I () %, o 14 () 16 () 111 0.1

3 Cob

3

2-3 SNVW

M-0 Axisi CAvly - CFO A* 1300noo I

Mg-asurid Disc 2

Moclaurad- Oloc 3

%4oisutvd SIw

IN2



8.5.1.2 Heat transfer results

Figures8.14to 8.16show hediscand cavity shroudsurfaceheat flux results or theenhanced

mixingmodelCFD simulationof cavity 3 for testcase33. Thesurfaceheat lux isplottedagainst

radiusor

thedownstreamaceof disc 2 (Figure8.14)andfor theupstreamaceof disc 3 (Figure8.15).Both solutionswith Rayleighnumberpower,n=0.1 andfor n=0.2 areshown n these wo

plots.Foracomparisonheheat lux results romSC03 hermalanalysisare shownand plotsshow

that heCFD solutionwith n=0.1 produceshebettermatchespeciallyat thelower radialpositions.

Howeverat thehighestradial locations heCFD solutiondoesnot match heSC03heat lux values.

Heat lux results or thediscboreand hecavity shroud ocationsplotted againstaxialdistanceare

given n Figure8.16.Results rom both CFD solutionsare shownalong with theSC03 hermal

model esults.Also plotted s thecavity shroudsurfacemeanheat lux for theexperiment,

calculated singEquation8.1. Similar to thediscsurfaces,hecavity shroudheat lux solutionwithn=0.1 produced hebettermatch o thethermalanalysis lux valuesandto theexperimental

calculatedmeanheat lux.

Sussex MCRB2 Cavity 3 Steady State Test 33

Surface Heat Flux - SC03 to CFD Comparison

N

E

aI'

CS

Radial Clistance (m)

Figure 8.14 Test 33 disc 2 rear surface heat transfer (Wm-2).

--o. -Dsc 2 Q)b - CM A= 1300n=0.2

ý Disc 2- CFDA= 1300n=0.2

-Cksc 2 Cob- CFDA=1300n=O.

-Otsc 2- CFDA= 1300n-O,

& Drsc2- S003

183



Union MCMD Cavity 3 Steady State Tod 33

Surface Host Flux-

SC*J to CPO Companion

IKXK,

42M

4cx,

34KX

YXX

Mx,

6EXI

AW"A

3 Q* (YO A-I 3W -6

ý].,: (IDA-13M-0:

'I, CAb CPOA-1300.. Gt

aolm 11

vx,044 Ole

a

03

ftds. i Di. 1ý . (-)

Figure 8.15 'I'c%t33 disc 3 front %urface heat fran%fer

Suessix MCR82 Cavity 3 Steady State Tod 33

Surface Heat Flux - SC03 to CFO Comparison

am)

S

I2

em)

4(KX,

2m)

"w** *

-0

?m

186

.01, 016 0 14

Mist Distance (m)

4

4

aju

40 :W'M.. (I DA -1300 -, U.1

w 'Moo (JUA-11COM-0)

ýb.. ' IV-oiod CP0A-I3Wn-0Z

I bb, ýMvv LVDA-1300--01

I b. ý Ift" CMA-IJWn-01

(bb, II Shrowd-

CPO A- 1300 ft-0 I

I bb, ; ra" SM3

tb" 3 obwe SW3

Ww"As

., -j" A., j

ii'! ýw

Iigure 8.16'1'e%l 33 cavity 3 shroud jn(l (li%cbore %urface heat lran%fcr (%%t)

IS-1



Table8.1SussexAIC11112inglecavity model,cavity3 shroud surface icat transfer.

Case Test33 Test34 Test 50

N

-(RPM)

1188.9 2302.8 1482.3

hi-(Kg/s)

0.173 0,171 0.599

A (Pa) 299268 297648 238835

ReesP%VdWtt 4.41E4 4.35rA 1.5 E.

Re# pflOp 1.04E6 1.99F6 1.031:

Ro WWI 1.46 0.75 5.03

Grcgv3n2PA'rb(s/2)3/v2 2.32E8 7.41E.8

1.871'18

Bo,,.) Ro/(PAT)O-s 3.0 1.65 11.5

ShmudfeatTransfy (DeviationCF tol"xmimentExperiment tj (WM*2) 4400 5800 3350

CFD LES(I20* model) 4 (Wni-2) 3250(. 26% 4250(-27%) 355 (410

CFD 2D AxIsymmetric 4 4630(+S%l 5690(. 2%)---4230(+260,4)-

Modilled A-cwhit W layer near wall model (A-1300 11-0-1)

Table8.1 summariscs hecavity 3 shroudheattransferresults,comparing tile 2D axisyllimciricenhancedmixing modelCFD resultswith tile calculatedheat ransferWin the experiments ar the

three estcases.Also shown in the tablearc ilia licat transrcrresultsobtained rroin a 3D 120' sector

LESCFD modelof thesamecavity by Sunct al. (2004).The table shows hat (lie heat ransrer

results rom the 2D axisymmctric enhancedmixing modelcompire well with tile experimcntil

values or the first two tests,cases33 and34, within an error or so,,; onip3rcdwith 27%error for

the3D LES model. However ror thehigher axial througliflow case50 tile 2D axisymmetric

enhancedmixing model performs poorly whencompared o experimental icat transrerwith an error

or26%. For the same estcase ile 3D LES modelpcrronns muchbetterwill) an error or

approximately6%.

S.S. SussexAlcI1112. twocavities,cavity 2 andcavity3. surroundingdisc 2

Thesecond artof thework was o apply heenhanced ixingmodel o the2D axisymnictricCr-Dsimulations f two connectedavitiessurrounding singledisc. RererTingo Figure8.1,cavities2

and3 Otatsurround isc2 wereusedor thisCFDanalysis.

Iss



For the two-cavity CFD simulations the same enhanced mixing model parameter %alue%%ere

uscd as those used I-or the single cavity sI Intilat ions. The shape lunclion ,I cos(x, 5/21) * was used

with a thickness of the /)LA YER set to 0.005m and constant property layer. Phti-C(m. next to the

wall set to a thickness of*0.002m. The modified fluid property tinder relaxation factor. ut-/ %%;%set to

0.2 the smoothing, nsmooth was set to 10 passes. Figure X. 17 %ho%%he CIA) mesh consinicied for

the two cavities, cavity no. 2 and cavity no. 3. which surround disc no. 2 ol'iho: Sussex MCRI12. I lie

mcsh size I'M this simulation was 26,600 quadrilateral cells. Mesh spacing expands away from each

wall with an expansion ratio of' 1.1. A temperature profile obtained from the 'hcm-matched' SCOI

thcmial analysis and applied as CFD boundary conditions to the di%c and shroud %tjrf*;cc%

surrounding the two cavities. A mass flow boundary condition was applied it) the inlet and static

prcssure applied to the outlet. The saine three steady state lest condition% as for (hesingle

cavity

%%erenalysed, test 3.1,.14 and 50. Retcr to Fable S. I for the lest condilton% and flo%%pataincler-s.

NIUSSFlow

Inlet

('P'I) of the Sussex NICR Ruild 2 Ca,. ilies 2 and 3

Rotor

Disc I

011110

Figure 8.17 CFD inesh and geornclrý of the Su%%ex%1CRB2 ca%lllc%2 and 3.

196



8.5.2.1 lowstructure and tenipcratureresults

Figure8.18showsa contour plot of stream unction for test33 showing that with the application or

dieenhancedmixing model a central core was formed in each cavity. Figure 8.19 showsa contour

plotof themixing factor, formed by theenhancedmixing model.A circulation is formed betweentheaxial througliflow and thecentral cavity core region for eachcavity. Temperaturecontour plot,

Figure8.20,showsthat the central corehasa nearuniform temperatureof 331K for cavity 2 and

334Kfor cavity 3, compared o the inict fluid temperatureor320K and the shroud metal

temperaturesf 384K and390K for thecavities 2 and 3 respectively.The swirl velocity contour

plot, Figure8.21,showsthat nearsolid body rotational wasachieved n thecoreorboth cavities.

Figures8.22and8.23 show graphically the metal temperatureof thedisc and cavity shroudsurr; cCs

surroundingboth cavities andthe fluid temperature hrough theccntrc oreaci, cavity plottcd against

radialdistance.The measuredhermocouple,TC I to TC7, temperatures replotted on the Figures

8.22rorcavity 2 and thermocouple emperatures, C7 to TC 17are plotted on Figure 8.23 ror cavity

3.TheTC I measured emperatureon thedownstreamsurfaceordisc I was7K lower than theSC03

thermalprediction. Both plots show that ror all theother thcrinocouplepositions the disc surfice

andshroud emperatureprofiles wereclosely matched o the testmeasurements.Only theenhanced

mixing model local Rayleigh number(Equation7.36) powcr it - 0.1 curve orthe CFD calculated

cavity fluid temperaturehas beenplotted for the two cavities.Also, asWorc the cnhinced mixing

multiplication factor,A used n the local Rayleighnumberwassetto a value or 1300.The cnh3nccd

mixing modelUDF uses he cavity fluid temperatureat a position of 8s,.,,4orthe cavity shroud

radius o calculated he local shroudheat ransferandwall factor. I (Equation 7.29) for eachcavity

independently. t was reassuring hat the two-cavity simulation solution ror all the testcases

produced hesamecavity 3 central core temperatures s far the singlecavity solution. Table 8.2

shows heCFD temperatures or eachof the tests.

Table8.2Two-cavityCFD solutioncavity temperature esul(s.

InIct Cavity2 Cavity3

Temperature

(K)

ShroudNictal

TemperatureK)

CavityFluid

TcmpcraturcK)

ShroudNIctal

TcrnpcraturcK)

CavityFluid

TemperatureK)

Case-3 320 384 331 390 334

Case 4 320 378 332 38 334

Case 0 316 374 323 378 324

187



I \\

___T rFigure 8.18 CIA) (est 33 stream fuilclioll

I-IIý0.4 (II

9.98e4 fj'i

9.46&40

8.9 3e- 0

8.4 1f,+U-i7.8 8-ý+0

7.36o4fl

6.83e- 0

6.3 1c-to i

5.7 8,n#

5.2 5a +

4.7 3e- 0'34.2 09+(1-1,

1.68c* 0ýj

3.1 5e4 (i j,2.63e- 01

2.10 e., U

1.58cfD

I. 111ý4Iýj

. ..)4F--nI

Figure 8.19 CFD test 33 Illixing factor contoll"S.

199

/



3.66e+ 2

3.62e+ 2

3.78a#023.74a+02

3.70e+02

3.66e+023.62e+023.58e 023.54e-023.50e,02

3.46r, 0

3.42c+023.38e+023.34e+02

3.30e+02

3.26e+023.22e+023.18o-02

3.14e-02

Figure 8.20 CFD les( 33 teill peral tire (K) conlours.

I

5.40e+O 15.20

+015.0 0014.80 014.60 014

.40014.20e+O 14.00o+0 13.60 f--013.60 c, 1)13.40e+0 13.20 a -.013.000-11 12.80o+O

-60 e+02.4 0+01

2.20 +01

,.0 a-aI

1.8084.0 11.60 e, 01

1.40a4.0

11.20e+01

1.000+01

a.Doc,0P).aC+04.00e+902. D0e000.0aaa0

Max. vel. 271n/s

Figure 8.21 CIA) (est 33 swirl (m/%)con(our%.

I st)



Sussex MCR82 Cavity 2 Steady State Test 33

Temperature trom CFO

VA)

M)

170

360

0 IN,, I Cob Raw

. (N,, I Raw

" IN., I Cob V'-I

" D-sc 2 From

" DOC 12 stv-1

" Wd A.. 41 CAwly (J 0A-I UX)

" Mossuled Doc I Rý

" K4"surd Doc 2 F". q

ef;

.01_p "

I

ý so

.W

008 01

008

016

Figure 8.22 CFD test 33 cavily 2 (disc I (li%c2) temperalurc%.

Sussex MCR62 Cavity 3 Steady State Test 33

Temperature from CFO

CYI

2 C. 1, N...,

N- 2 Rew

0h"I Cýh I, 'w

IN., JFýl

IN., 2.3 Showl

M"J A-141 GOWY (J 1) AýI UX) -0 1

Mensw*d L)-.1

14-,

... wed -Disc II -I

Sh"N"I

35.0

1 0",

35.0

3.L

0061

0 14

R&dial 04slence 0"1

0 12Radial (Nollance IM)

() I

IM

016

Figure 8.23 CIA) (est 33 cavil-, 3 (disc 2 all(I (Ij%c3) temperal tirm

02

11.1.1

6

022

1W



8.5.2.2 Ifeat transfer results

Figures 9.24 to 8.20 show the disc and cavity shroud surface heat flux results lor the enhanced

mixing model CFD simulation for the test case 33. The surface heat flux is plotted againm radiu%for

the disc I downstream and disc 2 upstream surlaces in Figure 8.24 and for di%c2 downstream anddisc 3 upsiream surfaces in Figure 8.25. Comparing the licat flux results on the diso.surfitces

surrounding cavity 3 lor (lie two-cavity simulation to the single ca%ty simulation %hows he heat

transfer has reduced for (lie two-cavity model even though the disc st rl*,ce Icnipcralurc profile

remained unaltered. This is consistent with the CI: D cavity 3 core temperature being %lighthigher

than that 1'c the single cavity, The licat transtler results remai n 1)(x)r at the outer radii of*(lie di%c%

The heat flux results are also lower dian the SC03 therinal analysis value%.Heal I'lux result,, for he

disc bore and the cavity shroud locations plotted against axial distance arc given in Figure 8.20,

Also plotted are (lie cavity 2 and .1shroud surf. ce inean heat lltj\e% for the experiment. calctilated

using I'quation 8.1. Comparing the ca%ty 3 CFD heal translcr to the experimenial \altic. CI. 1)

under predicts (lie mean heat transCerby 4"o in contras( to ; n over prediclion ol'5% from file single

cavity CFD solution. The general trend was that the cavity 3 -shroudheat transtler \?.,.%ess for the

two-cavity CFD solution compared to tile single cavity solution. A large error in the cavily I shroud

heat transfer remains for Test 50 with over prediction of*24%.

Sussex MCR82 Cavlty 2 Steady State Test 33

Surface Host Flux - SCO3 to CFO Comparlacm

1000

1600

1400

1200

1000

400

1)

Ot

- Disc I Cob Rom-

CFO A- 1300 n-0 I

-Disc I Row-CFOA-13OOn-0 I

-Oisc 2Q)bFnx*-CFO

A-13OOn-0 I

-Oisc2F-)m (; FDA-1300. -Ol

Madlel Oftlance Iml

Figure 8.24'1'est 33 cavity 2 (discs I and 2) surface heat transfer (Wni I ).

191



Sussex MCRIE12Cavity 3 Steady State Test 33

Surface Hoat Flux - SC03 to CFO Comparison

45N

4000

3500

3000

2500

2000

1500

1000

500

01

006

-500

1000

- Disc 2 Cob Rear -CFD A- 13W n-0 I

- Disc 2 Rom - CFD A- 1300 n-0 I

- Disc 3 Cob Front - CFD A- 1300 n-0 I

- Disc 3 Front- CFD A- 1300 n-0 I

Disc 2 Rear- SC03

Disc 3 Front- SC03

0 12

I&a

.6

0 14 016 Ole

Radial Distanco (m)

Iigure 8.25 Tes( 33 cavity 3 (discs 2 and 3) surface heat (ran%fer 0%in

Sussex MCR82 Cavities 2&3 Steady Slat* Test 33

Surface Heat Flux -SC03

toCFD Compartsort

sooo-

4sw

4000

3500

.500

2000

14nn500

1000

SOO

a

a

a

«,-, **7v-- -- -

04)24 ()

.11, () .1

Ili Ih 14

AmI&Ioialmnce (m)

ý00a

Figure 8.26 Test.13 cavi(v 2 and c: %t%

.1((Ii%c% .2 and 3) %hroud And (11%core

%urface heal fransfer

a

0.2

£

£

£

022

('*w i Www 0 A- 1300 M-o 1

-MK I Owo Cf 0 A- 1300 n-0 I

- Oaac 3 Ikorw ýCFO A- 1300 n-O I

- Oiec 12 Shr*ud UO A- 1300 n-0 I

CNar 2.3 Stw*W.

r-FD A- 1300 n-0 I

Diec 2 Som

-

S(; 03

* (Noc 3 Gorw SOO]

* 0-oc 23 StwoW SC03

Cap Avg ShroW Doe 1-2

F op Avg ShpoW Ojec 2-3

ýI, III



8-S. Sussex kICRI12- WO Cavities, cavity 2 and cavity 3 vilth a conjugate heating solution for

disc2.

The hirdand inalpartof theCFDstudy or theMCRB2was o apply hecnhancedmixingmodel

tothe2DaxisymmctricCFDsimulations f twoconnectedavitiessurrounding singledisc forwhicha conjugateicatingsolutionwascomputed. hesamewocavitieswerechosen,avities2

and3,anddisc2 wasmeshed. hissolutionwouldallowthedisc 2 temperatureso bepredicted

from heCFDsolution.Thesame nhancedmixingmodelparameteralueswereusedhereas or

thepreviousCFDmodel.Figure8.27showsheCFDmesh onstructedor the wocavities, avity

no.2 andcavityno.3,and or thediscno.2 solidmaterial.Themeshsize or thissimulationwas

25,500quadrilateralellsfor thefluid domainand3900cellsror diesoliddomainof theno.2disc.

Meshspacing xpands way romeachwall with anexpansionatio or t. I. A temperaturerofile

obtainedromthc'bcst-matched'SC03 hermalanalysiswasappliedasCFDboundaryonditions

to thedisc I downstreamsurface nd o theupstreamurface rdisc 3,and o bothcavityshroud

surfaces. masslow boundaryconditionwasappliedo the nletand staticpressureppliedo the

outict.Thematerialorall of thediscswas itaniumandaconstant alue orthedicniial

conductivity f 7.72W/mKwasset n theFLUENTsolver.An extraboundarywas equiredor the

disc2 rim metal emperatures. temperaturerofilewasobtainedoreachostcaserontthe

thermal nalysis ndwasappliedasaboundary ondition.Inaddition o the hreesteady tateest

conditions,est33,34and50,twoextracaseswereanalysed.hesencludedest3 1,a high

rotational peed, ighGrashofnumber,ow Rossby umber aseanda maximum peed teady

condition aken romanacccicration-dccclcratontransientycle.The atercasewasahighspeed,

highGrashofnumber ndmid rangeRossby umber ondition.11crcroTable8.3rorthe est

conditions nd low parameters.

8.5.3.1Flow structure and temperature results

Figure8.28showsacontourplotof strcamunctionor test33showinghatwith theapplication r

theenhanced ixingmodela centralcorewas ormcdn eachcavitywith tile flow Pattern eing

verysimilar o the wo-cavityonlysimulation.Figure8.29showsacontourplotor tilemixing

factor, ormcdby theenhancedmixingmodel.Twotcinperatureontourplotsareshownn Figure

8.30comparinghecavitytci-npcraturcs,) with theenhanced ixingmodelappliedandb) without

themixingmodel,whereconventionalCFDusingunmodirtedluid propertieswasused.

193



Comparinghe wotemperaturelotsclearlyshowshatenhancedmixing model cduccslia radial

temperatureradientn thecavity andnearunironilcore emperature as ornied.At amidradial

positionwithincavity3 theradial emperatureradient ot theconventionalCFDwas362K/m

comparedo40 K/m, ot theenhancedmixingmodel.Comparinghecavitytemperaturesot ilia

two-cavitywith disc2 conjugate eatingmodelsolution o ilia two-cavityonly solution ot test33

therewasno significant hangen thecavitytemperaturesetweenhe womodels.lia core

temperatureas330K rot cavity2 and333K rotcavity3,comparedo thecavity emperaturesr

331Kand334K,respectivelyot theearliermodel.Figures .31and8.32showgraphically ot test

33, hemetal emperaturef thediscandcavity shroud urfacesurrounding othcavitiesand he

fluidtemperaturehroughheccntrcof cachcavityplottcdagainst adialdistanceor3)with tile

cnhanccd ixingmodelappliedandb) without hemixingmodel.Themeasuredhermocouple,

TC toTC7, emperaturesrcplottedon theFigures .31 ot cavity2 and hennocoupic

temperatures,C7toTC 17arc plottedon Figure8.32 ot cavity3. Forcavity2.Figure8.31,TCI

was heonlythcn-nocouplenthedownstreamurracc rdisc I (measurementas7K below he

thermal rediction) nd he emperaturerortleplottedwas he(hernialmodelpredictionusedasa

CFDboundarycondition.Similarly, hermocouplesC13 oTCl 7 positioned n ilia upstream

surracef disc3 (Figure8.32)havea thermalmodelpredictionemperaturerorile plottedagainst

themeasured

emperaturesndagainwasusedas he

CFDboundary ondition.The wocavity

shroudhermocouples,C2 rot cavity2 andTCl 2 rotcavity3 shown%%,rctestmcasurcmcnts;ith

predictedemperaturerofilesplottedagainsthemagainwith theprofilc beingused ot theCFD

boundaryconditions. he hermocouplesf real nterestwereoil disc 2,TO toTC6ondie

upstreamurrace ndTC8toTCII on thedownstreamurracc ndTC 7 positionedn thediscbore.

Figures .31and8.32show heCFDpredicted isc3 surraccemperature.heplotsclearlyshow

thatdieuseof thecnhancedmixingmodelsignificantlymproveshepredictionorthedisc 3

temperatures.herewasgoodagreementn thepredictedCFDdisc3 temperaturesiongmostorthediscsurraces, ith the argest rrors overprediction) ccurringat ilia middiscdiaphragm

positionsTC4andTC10)onbothsidesof thedisc.Alsoplottcdonbothfiguresarc hemidcavity

fluid temperaturesnd,asmentioned bove,heplotsclearlyshow hat hecnhanccdmixing model

reducesile radial emperatureradientanda nearunirorm emperatureorewasestablishedn both

cavities.Thefluid temperaturesot cavity3 arcpresentedn Table8.3for all tile testcases

analysed.

194



Rolor

Disc I

Mass Flms

lnle(

i talionan Shall

Rolor

Di%c.1

llre%%ure

()tlllcl

Figure 8.27 CIA) mesh and geome1r) of lhe -Sti%%c%ICRR2 caillic% 2 sind .1and of

di%c 2 Ailh conjugale licaling.

Figure 9.33 compares the CIA) predicted disc 2 metal temperatures for test.1.1.ý%th and %%lhotit tile

enhanced mixing model being used. For tile enhanced mixing model solution tile predicted di%c

Icinivratures were within 5K corresponding to in error of'9". %%-heremir 01red-WaO I-iit%c

nm-l*lnlc(). this compares to a dillerence of 19K. that is a 350oerror for the comcntional

Alw. flor comparison the crror in SC03 therinal anaksis. predicted temperatures arc gi%cii using tile

%ame rror criteria. The I gtire sho%vshat for tile majority offlic disc tenipcraturcs fileCIA)

%%thenhanced mixing predictions were more accurate than tile 1herinal analyms predictiom I tic a%cragc

error for tile (+`D predicted temperat tires was 3.06"o compared to 3.09*o for file therinal analyms

predictions. 11*11lewo ,,,(I-(Ilsc (Ijaphragin lemperat tires were not included (he a%cragecm)r would

be 1.56% compared to 3.3 PO. Hence there is a significant improvement in (he prediction ofilic

disc 2 Icinperal tires using the enimliced inixing CFD modcl compared it) tile SC03 thcrinal model

prodictions. The UFD enhanced mixing model predicted disc 2 temperatures for tc%t%.est.14 and

test 50 are shown in Figure 8.34. Good agrevincrit hem,ccii the CFD results and the tc%t

Measurements is silowil flor both tests, with (lie largest percentage error being 3.4% (1 9K) for tc%t34 and 1.5% (O.XK) for test 50. Cavity 3 CFD temperature results for the five tc%Ls rc %hown n

Table 9.3.

193



I

0

Figure 8.28 CIA) test 33 %tream filliction confoum

1. 11 -4 1,.1

IlAbc +1ý

1). 6e -8.9 3L%-8.4 17.8 8

7.36e

6.83e,

A ll.. ý

5.7ae

5.25e-4.73e-

4.20e-

-ý.jac 1.1

I 5e

". 63e

).10e

5c -

Figure 8.29 CIA) les( 33 llii%illg factor comour%.

I

196



ith [lie Enhanced Mixing Model

W.,

I

3.9

3.86e+02

3.82e+il:,

3.T8a fl,3.T4e,.0,

3.7De U2

3.66e 02

3.621-- 02

3.5Be+o,,

3.54e+11.3.50.5+ 13.4 6e-

3.4 2e-

3.36a4.]34 (1

+0

Max lemp. I'A)K

1111clCIIIII 120K

Withollf file Enhanced Mking Modd

.1. ýju, #o

,I-86e40

,3.82e,402

3.78e+02

3.74o#02

3.70e-02

3.66e- 0?

3.62e402

3.58e4 0'

3.5 4eU, ':3.50eU. '

46e, U.,

424!ý-0..,

-A 4402

"040"

:-16k-02

i.2a#02

11.18e402

i. Ae402

max. lemp. IINK

Inlet lemp. 120K

Figure 8.34)Test 33 temperature confours Wkc 2 Illodelled with conjugate healing) for a)

with and b) without (he enhanced mixing model.

l')7



:1)

390

3W

3TO

3W

350

340

IN

320

Stjs%ex MCRB2 Cavity 2& 01,,, ý1 CoIli ulpir I Tc,%I II

Tompoorature from CUD

0 14 016

Radial Didance (M)Ole

b" II, t.

Gob Ffonl (0 DI

I h" I Fford(CFT)i

(ks,-

12 Slwoud (,, 0 1,

0 WA. wiilCavity ODA IW(X),, III

0 k%ssurod Doc I How

310

1

() (Xi 00a

b)

IM)

380

VO ,

Sussex MCIRE12Cavity 2A Disc 2 (Conjugate) Sleady Stele Test 33

vAthout the Enhanced Mixing Model (No UDIF)Ternimrature from CFD

a-I b%, I CAjb fbw (sco. 1)

-Ih, I F4"r (SC03)

b, I Cob Front (CFO PA)AVi

I Front (CFD No Lirl

a12 Shroud (scO3)

"W A-WO CRv*y-

CFD PA, k4*

" Measured- (bac 1 14pa,

M-1-Iffed 08ý I,, -, I

N, ... . ýl Sh-A

0

330 -

320

310

1

006 008 OA 12 0 14 0 ifi

Radiel Ode"mce (m)Ole

02

02

022

..,2 1110(jelled%%ilhonjtiga(c healing) for a) %%ilhigure 83 11 e%(33 cavily 2 lemper-.11,11-cs(Ii.

and h) AiIII(IIII the enhanced mixing model.

JQS,



SussexMCRE12avity3& Disc2(C(mlugate)SteadyStateTest 33

TorqmrstureIrc" CFD

4(X)

390

380 -

370 ,

h)

4(M)

390 ,

380

370

340

ISO

0 hi, I Gob How ((J Di

0 b- 2 Fbar (CFD)

0 b- 3 Cob Front (sc 0 1)

*Ib. c 3 Front (SC03)

4, (Isc 23 Stwoud (sco Ii

" PM A. mWCavity-a 1) A

" Kuasufod Disc 2 14.4,

" Mermsured D%c :11, -1

a 0A."Sawed ! W-1

IVNI"ý,

0 12Radial INGUnce (M)

016 Ole

Sussex MCRB12Cavity 3& Disc 2 (Conjugate) Steady State Test 33

%vithout he Enhanced Mixing Model (No UOF)Terqmralure from CFD

-4b- 1W I Cob How (M) P*, iAv

0 (ý, - ýPaw(CFDWLO)

* (b. - I Ch Front (%,.03)

Disc 3 Front (sc03)

Orsc 2.3 Stwoud (%, 0 ti

NWAmmilGovily (II)N, tAV

k%asured-

Olac

0 12Radial EiAMCS (m)

016 1.

02 022

FiRure 8.32 Test 33 c. %i ý31 emper at ures (d i%c2 modelled A t h conjuga Ir hen in g) for a) %%Ih

and b) Ailhoul Itic enhanced inixing model.

I)()



%%ilh Enhanced Mixing

' Os)

.III

rm -. 171.4

1411(10

Icto

fifu)

C"i

.I

, 111 LL8

I -(1 1

I-I 'I

I-N II

1 4161

%%ilhoul Fnh. mccd Mixing

Im 0 'A k1ý

-IIIV,, -46, . A I romp IkI

1-1Wo. word IrmpikiI:

i( 1 1) Pred. -%I rotor MI ramp (k 11

1)4.c kim. Im-I '4k

I hrough fie" %if.

I in - 420. Ik

11)1rt- (Ilfmi Mm KTtn Tins

4)

, 10

ItsCC7o

fc?

Figure 8.33 Tesl 33 disc 2 lemperal ure%(conjugale licalilig %ld"fiOll) - -Alth and i%ilhoW dir

enhanced mixing ino(fel.

I'I'e%t34 - %%th Fithallce(I Nli,, illg

IN) A

4604

(. 41 ýj

F-11I I--I

.Tm - 374.3 K

II

I

( 11

1,10

I't-%t 50-

%%th Enhanced %li%ing

. m - 10.7 k

-\ lp I-

t 1) P, Mkl,, d 1,-. p 4k)

ete %Ira%orrd I rmp (k I

(( W Prrd. %Irasa red I emp ik ii

(I NI[-ý-

4"..1

D-e. I

T

Me

ý; -I

CFD I-war - (Prvd

".I""'LE.-rouI:h thm W. I in - 12o.,

WAS I(Im

.0

I--

Ir,

rTin i

1

I,

ý (141

o;I

AI,11LO

- --) (41i( 41 T qi"ý'j =

Figure 834 Test 34 and test 50 disc 2 lempersoluro. (conjugale healing %olution) - %%Ithhe

enhance(] mixing model.

'I II

II;

0Itt to

It 1*

2(g)



Table83 SussexNICIII12 wo cavity anddisc2 model,cavity 3 temperaturesand shroudsurfaceheat ransrcr.

Case Test 31 Test33 Test 34 Test 50 Trans.

INIAX.SS

N (RPM) 5871.6 1188.9 2302.8 1482.3 5513.0

xf-(Kg/s)

0.165 0.173 0.171 0.599 0.376

P. (Pa) 298343 298268 297(Ag 238835 240285

Re, - p%Vdh/tt 4.17E4 4.41E4 4.35 F4 1.53r-._9.49E4

Rc4 - PM24i 5.02F6 1.04F6 1.99F6 1.03E6 3.77F6_

Ro- W/a! 0.28 1.46 0.73 3.03 0.86

GEiv",= f12PATb(s/2)1/v2 3.83r.9 2.32F8 7.41EIR 1.97FR 1.951.9

jlo,,, ) - Ro/(PAT)O-s 0.7 3.0 1.65 11.5 2.24

InletTemperature K) 322 320 321 316 315

ShroudMetal TemperatureW 385 390 383 367

Cavity Fluid Temperature K) - T 3441 337 337 325 328

Shroud featTransfer(Deviation C- to Experh MY-

Experimentil (Wni-2) 8250 4400 5800

3350 6450

CFD LES(I 20* model) (Win'2) 3250

(.26%)-

4250

(.271%)

3550

(-61,

CFD 2D Ailsynimetric (%Vm'2)

1

8060

(-2'Yo) 1

4305

(. 2%)---

5300

69%)

3880

(+6%)

6820

Modliled 4--civith W layer near wall model (A-1300 it-0-1)

Tests31,33,34, So& Trans Max. with Disc 2 Conjugate Healing

202



Sussex MCRB2 Cavity 2& Disc 2 (Conjugate) Steady State Test 33

Surfaca Host Flux

1, )0

low

I

I

OW

Wx)

(X)

; NX)

700

- Disc I Cob Row-CFD

A- 1300 n-0 I

- D4sc I Row-

CFD A- 1300 n-0 I

- Disc 2 Cob Frarg - CFD A- 1300 n-0 I

-D, %c2F, ml CFDA-IW-ol

() 08 (). I 012 () 14

Radial Distance (m)

016 Ole 02 OP2

Figure 8.35 Test 33 CIA) ca%ty 2 ((Ii%c I and 2) %%ilh11%c.1conjugale healing

di-scsurface heal fran%fer ONm

Sussex MCRB2 Cavity 3& Disc 2 (Conjugate) Steady State Toot 33Surface Heat Flux

4500

3500

III

3000

2500

20(X)

Isoo

1000

Soo

I(XX)

'-Dific2CobR*or CFDA-1300-ol

Disc 2 Row-

CFD A- 1300 n-0 I

Disc 3 Cob Frr"-

CFD A- 1300 n-0 I

Disc 3 FrorA-

CFD A- 1300 n-0 I

Disc 2 Rear- SC03

a Disc 3 Frcoti4 S(, 03

RediM Distonce (m)

Figure 8.36'1'est33 CIA) cavily 3 (di%c2 and 3) Allh disc 2 conjugule heating

disc surface hem transfer (Win 2).

£

a

aa

aa

aa

203



Sussex MCRE12 Cavities 2&3 & Omc 2 (Conjugate) Steady Slat* Test 33

Surface Hrat I lux

"(KX)

4500

4000

3500

3000

2

2-, X)I

11500

IOOD

Soo

ýý'j

A£

I

I

aaa #%

a&

Diac 2 mcm cro A. 13W M.4 I

r)wc 3 Gore Cfn Aý I 3W n-Q I

2 SPWOA cro A. I= "a I

3 shrmA CFO A- I wo "-a I

Galv SC03

I Sh"A SCO3

" VWMA ow 12

K, A-j *bfý DMK 23

qw" *0-0-0

o IN

Awiel 04 ,, (094

() 14

ýaaa

Figure 8.37 Te%l 33 CIA) ca% h 2 ((Ii%c I and 2) und ca% fý.1

((Ii%C 2 211d di%c.1)

,Ailh disc 2 conjugate heating %hroud mid di%c bore %urface lit-at Iramfer 0% m

I 19111X ;S'and Figure 8.39 show graphs ofca%it ý shimid Iica I ia it%I i I,It Itct again ,I( ii-i'dit II

number. (or and agaill.st I)tI,)yjIIcy number. Ho I*Orile Sussex MCR Both plot%%ho%%xperimental

data I'M cavilies 2 and 3 Crom imids I and 2 (build I as 'Other rig Ie%Idata. When file ztvoal

1hrought1mv s do,11111.1,11ile ( Irasliof* number is lo%%,ile buoyancy number v. high. and the C; % 1ý

shroud heat transler is Im%.When tile buoyancy %%111111ile ca%ly Is dmitinant. tile Gra%hot'number

is 111911.ile bilovancy number is lo%%and tile shroud heat transfer is high. File criteria ihal is used to

d0ennine file flow regime is. O'llo -6 the llo%%s III buoyancy dominant regime and ifliti - (i the

flow is lit 1hroughtlow reginic. Flus I., shmim by tile experimental data in 11gure 9.11) I-lie

exrxi-imcnial results Fromilic 1-1%cests that 11,1%eeen %imulawd ire slumn tonthe graph-, .1% olid

diamond symbols. The corresponding CIA) heat transfer rc, 1111%iroill the conjugate heating. 21)

ax,%yrilmetric enlLinced mixing model soltmons are plotted as black rings. 1*ocomplete the plois tile

-11)120- sector I. F.S CFD model restills ; re slumn as solid squates I-lie dclinittom offfic (irashof

number and Buoyancy number are I gi%en in Fable 8; Bt)ih graph-, %ho%%lia[ 21) avitsymnictric

enhanced mixingmodcl

hem transIlerresults correlate

well with the test data. %%ill all file testIumnis

lying within the scaller of1he experimental dam, File graphs also show illat file full rangc of'

buoyancy conditions have been analysed by tile iivc 21) axisyrnmetric CIA) %imula(tom

2(m



Sussex MCR Build 2 Test & CFD Romilts

250

200z

.ol50E3z

100

50

-; ý-l G"v I

.I Mhw .0 t"l 40.

I pwwlwg T-131

*I . Pý-., A

-PW%I-A T"Iio

wits ýLmq

aIL Sý Oft. 1. T"Iso

SCJ 0 A) A,, oym

rp, II

u:

0

1.OE+10

Figure 8.38 CavifN 3 %hroud heat (ran%fer %er%e%r-i%hof number prt-diclion%

compared lo (he e%peritnent.

Sussex MCR Build 2 Test & CFD Results

1 OE+08 1 OE+09

Grashof Number Gr,h

1.5E-04

1 OE-04

NUsh/Re,1.3

5.OE-05

m

IIIII iii

111,111 .w,U. aM.

I

*

., -W ý

&

O.OE+00III SSSI

0

.

10I

A£ ALIAS

t. 'ý 1.01 3

1,0". G ftw 406

*r". -a T. 031

*r. vw-o tdW23

*I I. Mbi

to

i

05 10 15

Buoyancy Number Bosh=Ro/(IIAT)O 5

HL'ure 8.39 Ca%ilý 3 shroud lical fran%fer %ci-%e%moýancý nunihcr ( -1- ) pre(liction%

cOmPared 14) he c%perimew.

2()',



8.6CFDFLUENT LESSolution

In acomplementarystudy,SunandChew [20041carriedout CFD simulations for the Sussex

MCRB2cavity 3 using Large Eddy Simulation (LES). Forcompletenesshe results rrom the 3D

CFDLES simulationsare includedanddiscussedbelow. Simulationswerecarried for threetests.33

and34wereconductedat Surrey,whilst test50 wascomputedat Volvo Acro Corp. [Abrahamsson,

2001. Tests 33 and 34 areconsidered o be in thebuoyancydominatedflow regime whilst test50 Is

in thehigh throughilow regime.Most of the calculationswereconductedwith a 3D 120*sector

modcl,whilst for test33,45* and90* sector modelswerealsocalculated.77hemeshsizesemployed

for thesemodelswere 1.36M, 3.14NIand4.07M cells for the45%90* and 120*modcls,

respectively.I'lie mcshspacing n theaxial and radial directionsexpandedaway from die walls with

a finc mcshnext to the walls to captureand resolvethe flow adequately n the nearwall rcgion. I'lic

meshspacing n the circumrcrcntial direction wasuniform. I'lic boundaryconditions wcre set,as

theywere for the 2D axisymmctric models,accordingto theexperimentaldata.The inlet flow

turbulencentensity was set to be 20% (10% wasused n the2D axisymmetric models).as t was

consideredhat therewould bestrong mixing clTectsbetween lia axial througliflow andthe swirling

flow in thecavity. As only partial domainswere simulated,all thrcc modelswere applied with

circumrcrcntialperiodicity.

The FLUENT codewasusedfor thecalculations.The LES Smagorinsky-Lilly sub-grid scalemodel

waschosen or the calculations.The Smagorinsky-Lilly modelconstantC., which represents

relationshipbetween he mixing-Icngth, associatedwith the sub-grid scales,andthe filicring cut ofT

length,was set to 0.23. The temporalandspatialdiscrctisationswere2"Jorder implicit with the

time stcpbeing I.Omsand the 2"dordercentral differcncing scheme. cspcctively.

A summaryof the shroudheat ransrerresults from the three3D LES-CFD Inodell is I; %-cnn Table

8.4.

206



Table8.4Summary of CFD-LES results for the calculated test casesof the Sussex MC11112ISunand Chew, 20041.

_Case Model Experiment 4r,,;, Win" CFD4c-tDWM'2 A4c-rl)/4r,,

p

Tcst33 45' sectormodel 4400 2350 42%

90*sectormodel 3150 .28%

120*sectormodel 3250 -26%Test34 120*sectormodel 58DO 4250 .27%

Test501 120'sectormodel ~3350 3550 6%

TheLESshroudheat ransrcresults avealreadybeen omparcdo tile2DaxisymmetricCFD

modelesultsn

theprevious ection ndareshownnTable8.3.Tile LES

shroudheat

ransferresultsorthe120*sectormodelwerealso ncludedn Figures .38and8.39. n theseigureshe

LESresults rcgivenby thesolidsquare ymbols.Sunetal.observedhat herearc some

differencesn tile shroudheat ransrcr etweenheLEScalculations nd hecxperitnentalesults,

althoughheuncertainty f themeasurementsnd heuncertainty r theboundary onditions

specifiedortheCFDmodelmaycontributeo tiledeviations.n addition, t canbeseenroinTable

8.4 hat, ortest33,tile larger hedonla.nor tile sector.hebetterheCFDresultsare.For his

reason EScalculationswereonlyperrormcd sing ile 120'sectormodel or the woother ests.

Sunct al.wereveryencouragedy theLESresults,with tilecapture f tilebroad rendsor tileNusscltnumber ariationwith Grashof ndBuoyancy umbers.

The large-scalestructuresof the flow capturedby the LES areclearly visible in the Sectionalviews

of the instantaneousemperature,shown in Figure8.40.Cold andhot "an'W' penetrate lia cavity.

Theboundarybetweenthecold axial througliflow region and relatively hot, rutationally dominated

buoyantouterswirl flow region is clearly visible too. The existenceorthe ine-wale structuress

consistentwith ilia experimentalevidence.A sharp nicrracebetween hecold central flow

througliflow and ilia main cavity is mostapparent or test50. The 2D axisyninictric CFO modelwith theenhancedmixing also captures heboundarybetween hecold througliflow andcentralcore

cavity swirling flow, but this boundary s ilia circulation regionsetup between lia disc cobs.17here

is no evidence hat the 3D sectorCFO modelscomputea circulation region although ilia solutions

My not havebeenexaminedfor this rcaturc.

207



Stj%%e%iiiii(12 / Fluent LFS / (, mitteilt. %al eili(1-2%iill uläne

(a)Tesl 33 LES

Rolal ion

\ýf

(C) Volvo LES

Test 500

14401.1lioll (b) I'e%l 34 LES

Hgure 8.40 LES 120 sector model - insillillancous temperature at the plane for the

Su%%cx ICRI12 cavily 3 simulations IStin et al. 20041.

8.7 Conclusions

Numerical simulations 11,1veieen carried out Ilor the Susse\ NIURB2 It, analýse the co1I\CcI1%eical

transtler n a rotating cavity with axial 1hrougliflo\% A 21) amsymmetric CFD mixielling lechnique

using the enhanced inixing 111odelo increase the inmrig in (lie cenlral core ol'a rotating ;:.I\ ltý has

bccn used. The comptitat Otis were perflornied assuilling steady flow and the rcstilis ha%chccn

compared with the experinienial measurements for inetal iemperatures and licat iran.-ler. I'lic

simulations were broken down into three sections. first the simulation ofa %ingleca%fy. cavity .1.

wcondly simulations ol*(\vo colinected c;, %,tlcs. cavities 2 and 1. and thirdly %imulations for the

s3nic Iwo Connectedcavities but with the dist: 2 Iijodelled %kthin the CIA) tising conjugate licaiing,

Finally the restilts were also compared to results 1rom a .11)%cciorITS intx1cl ofthe --inic c.1%ly

L'sing the enhanced mixing model good agreement with experimental Valtics for the ca%ty shroud

%url'ace eat transfIer has been shown for rotating Rayleigh numbem of the order 10". All the steady

209



stateMCRB2ests, ovcring hefull buoyancyange,havebeensuccessrullyimulated sing he

axisymmctricFDmodelwith enhanced ixing.Themodelproducedavityshroudsurracc eat

tmnsfcrshatwerecloser o themeasuredeat ransrcrshanprcdictcdby the3D 12011ectorLES

model. herewasalsoan acceptablegreement ith themeasuredompressoriscmetal

temperaturesor eachof the tests.The modelproduceda nearsolid body rotationalcentral core

within eachcavity. Also within eachcavity thecoretemperatures nearlyunirorm. Both or these

featuresareknown from experimentsand from 3D unsteadyCFD simulationsto be present or

naturalconvection n rotating cavities.The enhancedmixing model wassuccessful n being able to

distinguish heregions in the flow field wheretheaxial througliflow dominatesand no cnhanccd

mixingwasrequiredand regions whererotationalbuoyancydominatesandenhancedmixing was

required.With the good agreementbeingachievedboth ror thecavity shroudbeattransrcrand ror

disctcmpcraturcshe CFD model appearso bepredicting thecorrectaniountormixing within the

cavities or this application.

Forall theSussexMCRB2 CFD simulationsusingcnh3nccdmixing modcl, with the local Rayleigh

numbcrpowcr, t sctcqual 0.1 andthemultiplication factor,A set equalto 1300produccd(lie best

resultsboth ror cavity shroudheat ransrcrand in obtaining a centralcavity core flow. ror other

applicationshese ocal constantsmayneed o bealtered.The useorunder-rclaxation on the

factorcd luid properties ogetherwith the flow ficId cell smoothinghelped o reduce he

instabilities n the solution andalso liclpcd theconvergence.

In Chapter9, theenhancedmixing modelwill beapplied to theCFD simulationof a real gas urbine

I IPcompressor rum that hasmany inter-disccalviticsandaxial througliflow.

1.109



CHAPTER 9

21)AXISYAINIETRIC COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A

TYPICAL GASTURBINE IIP COMPRESSORROTOR DRUM WITH THE

APPLICATION OF THE.

ENHANCEDMIXING MODE j

Summary

In thischapter he2D axisymmctric CFD modelling techniqueusing thc enhancedmixing model

hasbeenapplied to a typical gas urbine I IP compressor otor drum. The computationswere

Performed ssumingsteady low and the resultshavebeencomparedwith enginetestmeasurements

for metaltemperaturesandheat ransfer.An acceptableagreementwith enginetestmeasured

compressor iscs temperatures asbeenshown.

9.1 ntroduction

Numcricalsimulationswerecarriedout ona typicalgas urbine IP compressorotor oanalysehe

convectiveeat ransfern a series f connectingotatingcavitieswith anaxial throughflow.A 2D

Axisymmctric FDmodelof the car hreediscstages nddie driveconeof aI lp compressorotordn'mwereconstructed.hecavityusedn thesimulationssshown n Figure9.1. Figure9.2shows

thepositionof therotating hermocouplesnthediscs hatwereusedn theengineest.As in the

previous hapter, onventional FDwasusednitially. whichassumedheflow to bestc3dy,

compressiblend urbulent.Theenhancedmixingmodelusing heFLUENT UDFwas henSPPlicd-hethreecompressoriscswcrcmodelledwithin FLUENTusing heconjugate eating

$Olvcr. y usingconjugate eatinghedisctemperaturesouldbecalculated. hedisc emperatures

prcdictcd y theCFDmodelswerecomparedo themmurcd thermocouplecmpcraturcs.

91 Descriptionof the EngineTest

Incontrasto theSussexMCRB2, hegeometry f theengine III compressorotor smuch11nore

complex,with the ntcr-disccavitieshavingvaryingshroud iameters nddiffering discbore adiiforeachof the hreediscstages. lso theLPshaftdiameter ariesalong he engthof compressor.

210



Alm) di flerent tot lie M UR 112,1 ie compressor rotor rear dri ve cone cavity was mmicl led I'lic

9COMCIryofthe rear stages ofthe engine I III compressor is shown in Figurc 1) 1 In the diagram the

dirrictisions for cavity number 3 are given. The outer radius thc cavity (h) was I 73.9mm. the inticr

radius of disc 4 bore (a) was 80.5min (a/b 0.46) and disc ca% ty %pacing (s) %%-a%9 Xmm (%,

0.29). The 1-1)%hall (rj rotates in the same direction as the IIP rotor but at 0.9 ofilic IIP rotor speed

and had a radius ot'52.15iiiiii. giving in annular gap of 28.35inni. at thc disc 4 localion. I'lic airflow

axially through the compressor was predicted from a sccondary air vy%tcrn modcl offlic criginc 1cm.

Thc material of'the I IP compressor rotor was titanium. whilst the 1 1)%haft matcrial %%astccl.

Tompcrature measurcinenis were obtained from 49 rotating (licnii, wouples connected to thc 1hrCC

rotor discs and drive cone. Figure 9.2 shows the 24 locations ofthe 1hcnmx: ouplc% %%th two

thcrITIOCOuPlespositioned at each location. The thet-niocoupic% werc lahellcd a%%16214 (on the

Cavity I shroud) through to M6229 (on the curvic coupling). Fwo ncar %icady statc maximum I

rotor %pecdtests points. taken from an acceleration deccimmon irarimcni icst cycic h.i%c hccii

%imulatcd.

L%%*Il

1-1ý1n-id

% IIP ( comprrsaforRolor (Hror mor")

I INOff $me

ll, t- ( ,n, ( . %. ,

Pov~v 4kilki

-6ý -

1-11 hall

Figure 9.1 HP compressor rotor drum (rear %tage%) conidn.

I

211



FT"P,--,. &% urbine oir ( omprr%mr ihom (meet %tow"i

I

. 4.111

064

lp ý

HXure 9.2 IIP compressor (rear stages) - shiming the imiliom tol' he lhvrm(woup1v-. for the

rogine fell.

9.3 Test Ileal Transfer Measurements

Ibc heat Iransfer through (lie cavity shrouds was estimated using the 1cinpuaturc% oblamcd from

the thcrinocouples on the cavity shrouds and by using the predicted icinpcraturc% from the ouNdc

surfaceofthe shroud obtained froin the 'hest-inatchcd' SC03 thmnal analv%i% uidcl ofilic 111'

compressor rotor. The cavity shroud heat transf'cr was then calculated in the %aincway a% n the

Pirrviouschapter, using following equations.

flux.

F==TNF-.

q,.bln(1),

h)

(91)

Dlb theouter diameterofthe compressor otor. 1) s the cavity shroudradius. k_, mthe thermal

Mkluclivlty of the metal, titanium. and(T..,.,,

- 7'.,._

)is the difference in the metal temperature

Scrusshecompressor otor shroudthickness. t is ofnolc that thecalculatedheat fluxc%u%ing

k(T, i__. )

212



r-

Lquation.1comparedwell with theSC03 hermalmodel esults.

7becavityshroudheat ransfer, saNusschnumber.wascalculateds ollows,

Nurw ,dk1lT..... - T,r

hcrc TS= Tjj, +fll(b2 -A

2Cp

f) isthecompressorotor speed ndT,.wis theair inlettemperatureo the est ig.

(9.2)

(9.3)

9.4Numerical Investigation of Convection In a 21) Axisymnictric 111,Compressor Rotor

Drum %I(hAxial Throughflow.

9.4.1Basicmodelling assumptionsand the numerical procedure

All he omputationsarriedout solve

heconservationquations

ormass,momentum

ndenergy

usingheFLUENTCFDcode.TheCFDcalculationswereperformed ssumingD axisymmctric

compressible,teady,urbulent low,using hestandard -cand he2-laycrk-C W nearwall

twbuicnccmodels. heFLUENTsegregatedolver,second rder mplicit timestepping ndwith

thesecondrderupwindscheme sedor thespatialdiscrctisation erechosenor thecalculltions,

The lowwassolvedn therelativevelocity crcrcncemnle.The Presto cheme, second rder

Mssurccorrectionmethodwasset orpressurenterpolationor tile velocity.Fortilepressure

couplingmethodprcssurc-corrcction),heSIMPLEalgorithmwaschosen. ll thesimulationswerePerformedsingdoubleprecision ccuracy. oth hestandardluid properties f air and ile

M'ICTi3l roperties f the ip compressor erespecifiedasrunctions f temperature.

Figure .3showsheCFDmesh onstructedor the nternalcavitiesanddiscsof thercarsection r

the IPcompressorotordrum.The otalmesh ize or thissimulationwas$3,800qu3drilatcml

cells,72,200luid cellsand11,600 ells or thesoliddomainorthc three otordiscs.hleshspacing

expandsway romeachwall withan expansionatioof approximately. I. Temperaturerofilcsforthecompressorallswereobtainedromthe best-matchcd'SC03hermalanalysis f the IP

compressorngineest.TemperaturesereappliedasCFDboundary onditionso all thewalls

213



surroundingthe compressor apart from the three discs where tile conjugate heating solution was

applied.Predicted inetal temperatures for tile disc rinis were also applied as conjugate heating

boundaryconditions. A inass flow boundary condition was applied to each ofthe inlels and a %tatic

pressureapplied to tile two outlets. As tile CFD model was axisymnictric the R3 I inlet rotaling

holeswere modelled as a circumferential slit with the equivalent area oftlic 90 l(mini discreic

1101CS.wo near steady state niaxinlurn rotor speed test conditions were analvscd. These were at

1071,16NI.and I 00%NI-, 1.11compressor rotor speed condition%. For the flo%knlet. R.1 an estimate

of the anlount of'swirl was niade I'M each of the two test conditions. %%ich was approximalciv 600,6

thecircumferential velocity ofthe rotor. This swirl was estimated froin (tic ratio oftlic flow

residence imes ofthe holes. the time for the flow to pass through tile hole to tile rotational passing

time ofthe hole. Forthe

flowthrough tile

frontcurvic coupling. inlet

R91). ullrotor SIVcd Was

assumed.As can be seen in Figure 9.3, for the outlet at right hand side ot'thc geometry. the mesh

wasextendedbeyond the curvic coupling. This extension was included %o flat tile outlet %kouldnot

haveany influence on the flow under tile curvic coupling. The IT shall rotates at approximately 0.9

of the speedofthe 111)compressor rotor and in the same direction. A turbulent intensity of' 10"oand

the hydraulic diameter was specified to estimate the level ofturbulence in tile llo%k or tile Iwo

Inlets. Table 9.1 gives the boundary conditions and the flow parameters, rolalional. Re, and axial

Reynolds number, Re. and Orashot'numbers. Gr, for each of the test conditions. The Kilt and nuts

through the front CUrvic coupling (see tile area within tile dashed line in Figure 19.1 have not been

modelled in this current analysis.

ýPrcscrib d Metal Teinneraturcs on the 1111 olor

II PrescribedMetal FenilwFatilicsof, dic IP Sho'll llrr%,%urr hitlet

Figure 9.3 CFD mesh and geometry of the rear section of it IfP compre%,or rotor drum.

214



Table9.1Engine IP compressor otor MaxisymmetrICCIFI) A th theenhancedmixingmodel cavity3 temperaturesand shroudsurfaceheattransfer.

Case I(W%Nl, 107%Nl,

n(NJ NQ (RPM) 15142/13U)915519/14543

Nf- (Kg/s) 0.23915 0.25163

Po (Pa) 213969 224421

Re1_-!

ýPWdVp 4.457r; -4.538r.

REj=nb2/jt 2.5(AE6 2.5791'6

Ro- W/af) 0.111 0.113

soo f)2PATb(s/2)3/v2i 5.35HE9 5.824E.9

Bocoo Ro/(PAT)-s 0.205 0.201

AxialThroughflowRd. Total TemperatureK) 439 - 449ShroudMctalTcmpcratureK) (AV) 631

CavityFluidTcmpcraturcK) 509 531

Shroudicat Transfcr DcviationCFD o ExperimcnMermal Prediction)

EXPcfimcntTlicmial Prcdiction4 (Wnf2) 31140 34230

CFD21)Axisymmciric 4 (Wm'2) 31620

J+2

36570

(+7%)-

CFDderivedNusscitNumbcr,Nuh 151.7 153.7

CFDdcrivcdNu.h Rc..3 1.3 1E4 1.357134

AlodIfIcdA-swith W laver nearwall model A-1300n-0.1)

9.4.2Thegoverning equations

Tbe2D axisymmctric CFD model calculationswere performed usinga rotating reference rame.the

steadycompressible urbulent flow equations or conservationof mass,momentumand cncrgYwere

asgivenby equations n Chapter 8, Equation8.4,8.6 and 8.7, respectively.

9.4.3Enhancedmixing model

Theenhancedmixing model FLUENT UserDefincd Function (UDF) methodology formulated and

describedn Chapter7, hasagainbeenappliedto the CFD of the engineIIP compressor otor with

Axialthroughflow.The final version of theUDF codewasdescribed n Section 7.4 andhow to link

21S



anduse heUDFwithin theCFDsimulationswasdescribedn Section .5andAppendix6.The

enhanced ixingmodelUDFparameter alueswcrc,4 - 1300andn-0.1 -Thesameunction

"I- cos(,S/21)'wasusedwith a thickness f theDL4YER et o 0.005mandconstant roperty

13yer,I,7)-Con,ext o thewall set o a thickness f 0.002m.Although hesame alueof A usedn

thesimulations f SussexMCR-B2wasusedhe luid viscosityusedn thecalculation f the ocal

Rayleighnumberwasaltered romthestandardemperaturearyingviscosity alue o theenhanced

mixingvalue.This has hecffcct of reducinghe ocal Rayleighnumber ndhencereducinghe

enhanced ixingfactor.Figure9.4showsheregionswhere heenhanced ixinghadasignificant

CffCcL hecavityfluid temperaturehatwasusedn the ocalGrashof umberEquation7.26)and

in theheat lux (Equation7.28)calculationswhichwas henusedocalculatehe ocalnearwall

factor. (Equation .28) or theshroudwall)was akenatapositionof 85%of thecavityshroud

radius.To overcome tabilityandconvergenceroblemsn thesolution heundcr-rclaxationactor,

Urf.set o0.1.wasapplied o factored luid properties nd10passesf smoothingnsmoofh)was

alsoappliedacross achof theCFJDmesh ellswithin thecomputationalluid domain.Also to help

with thestabilityof theheat ransfernear hecavityshrouds moothing f the ocalnearwall factors

hasbeenapplied.

9.5NumericalSimulation Results

Table9.1 summariscshe cavity 3 shroudhcattransferresults,comparingtheconjugateheating,

enhancedmixing model resultswith thecalculated icat transfer from theexperiments or the two

engine estconditions.The tableshows hat theheattransferresultsfrom the2D axisymmctric

enhancedmixing model comparcwell with theexperimentalvalues(from the 'best matched' SC03

thermalmodel) for all the tests,with largesterror bcing7% for 1000/*NL/ 107%NLIcst condition.

9.5.1 Flow structure and temperature results

Figure9.4 showsa contour plot of strcarn unction for the steadystate107%NLtestcondition

showingthat with theapplication of theenhancedmixing modela centralcore was formed in each

cavity. In theregionof the disc cobstheplot shows hat the axial throughflow wasthedominant

flow feature.Figure9.5 showsa contour plot of the mixing factor, formcd by theenhancedmixing

model.The mixing factor plot clearly showsregionswhere the flow is buoyancydominatedand

216



enhancedmixing hasbeenapplied. In tile disc bore regions where tile axial throughtlow is

dominanttheplot showsthat no enhancedmixing was applied. The mIxIng faclor plot %hows

rippling effect in tile outer radial regionsof'the ca%fies. This is relatedto tile stabilily problem 111.11

waspresentli

tileMitial s111,111ý1tionsfthe

SussexMCR132.eported in

ChapterS.and

has

reappearedII tile enginesimulations.The stability problemsencounleredwith Stjs%c\%1('Rwere

rc.wlved by introducing multiple smoothing oftlic flow field flind properties augmented i%cosily

andthenrialconductivity), this was achievedby repeatninning of'the snux)Ihingalgorithm at each

itcration. I owever, evenwith InUltiple smoodungapplied to tile fluid propertiesfor tile engine

simulations he instability ol'the solution could not be flully resolved.As the in%tabilttýc\i-..,%.n

local regionsaway 1rom he cavity gastemperaturesampling rk)si ion used n tile ci% t\ .hroud lical

transfercalculation,tile beattranster into thecavitieswasnot directly aflectcd. llo\%ever he level

of mixing within file cavities illay beafTected y tile instabilities and hence ile ca\ itý iemperal ire',

Illay alsobe'11,1ccted.

Shroud I leat Flux Nal.Convilon/ Plate CorTcl

Nti 0.14 Ra" '" Chara. 1, gap,2AF *1',AI'm-,

Rcgion of Enhamcd Mixing

Fn(A Ra" ) with A- I YX) n

Ra- fn (di-,, r). Cham I t,

Figure 9.4 Engine fill compressor of sleady %tale 107%Nl, - conlours of %tremillfunction with enhanced mixing.

217



I

48000

46000

44000

42000

40000

38000

36000

34000

32000

30000

28000

26000

24000

22000

20000

18000

1600014000

1200 0

10000

8000

6000

4000

2000

00

Fi&,.ure 9.5 Engine condition 107%Nl, contour% of inking factor for the (11)

enhanced mixing Illodel.

Contour plots ofthe augmented laininar viscosity and eddy or turbulcnt viscosity arc shown in

Figures 9.6 and 9,7, respectively. for the 107"oNL condition. Comparing thc%.c two Plot%wIth

Figurc 9.5, the enhanced mixing coniour plot. showed that in the arcas whcrc the crillariccid mixing

was not taking place eddy viscosity was prominent. The main rcgions for eddy viscosity wcrc

around the disc cobs where the axial throughtlow was dominant. Within the micr-disc C. % 11C%

wherc enhanced mixing does takes place. laininar viscosity was augnicntcd and dommatc%over thc

oddy viscosity.

Figures 9.Mand 9.9 show tile swirl velocity and the swirl velocity ratio. rc%rwdi%CIN. predicted by

the UFD model with enhanced mixing Ipplicd for the 107"oNi. condition. The pit)(%show that near

m)hd body rotation was achieved in two ofthc three Inier-disc cavities. 2 and 3. TbC %%,irl velocity

in cavity I was influenced by tile R31 flow jillet swirl velocity which had a %wirl ratio of 0.0 File

ploLsshow that the CIA) predicted flow in tile drive cone c.1vity to he ovcr-swirled by a --mail

amount, with a swirl ratio ol'approximately 1.2. The R31 illici flow was %ho%no increase in swirl

velocity moving radially inwards to a swirl ratio ol'approxinuitely 2.0 and this %%kirlelocity was

218



maintained by the axial throught'low along the full length of the comprc%%or ruin

0 10000-0196W4 02

9 OWO 02

oboog 02

0 WO@

0:7 6000 0: ) Z

70me 07

65000 02

8000907

66000 02

6000902

4600002

40009 07

36009 02

30000 02

28000 02

70000 02

, 6000 02

1 fflos 07

e,o000 03

) ü000.00

Figure 9.6 Engine condition 107%Nl. contour% of molecular/lantinar %%co-.l) (kg m1%

for the CFD enhanced mixing model.

26000 ol

24009.01

23000 01

2200001

21000 01

20006 01

1 PWO 0118000 01

1 7000 ül

16000 oi

16000 (, ,14009 Gi

13000 ci

1 2000 01

1 1()00 C,

1 0000 ei90000 (.7

80000 ("21000407

60000 02

a 0000 0?

40006 02

30000 02

70000 o2

1 0000 07

00000. co

Figure 9.7 Engine condition 107%NT contours (of furbulent/rd(lý %wmilý (kU ns

for the CFD enhanced mixing model.

I)

'I wo temperature contour plots are shown in Figure 9.10 comparing the ca%ty IC11111craturcs.) %%

theenhanced mixing model applied and

b) without the mixing n1micl. %%hereonventional (T-D

using unmodified fluid properties was used. Comparing the two teiiipcraturc plots %ho%%hat the

enhanced mixing 111odel roduces a small reduction in the radial tciiipcraturc gradient in cacti of'thc

csvltics. At a inid radial position within the cavity 3 the radial tcniperaturc gradient for the

219



conventional (TI) was 590 K/in compared to 570 K'in t.or the enhanced inixing model. Comparing

the cavity temperatures flor the enhanced inixing niodel for the 107'. Nl. case. the core Icniperalurc

was 507K flor cavity 2 and 531 K flor ca%,iy 3, compared to the ca% ty temperatures of 497K and

514K. respect I vely flor the convcntlona I CFD inodel. Figures 9.11 and 9.12 show graphically for

Engine'rest 107"oNl., the inetal temperature ofthe disc and cavity shroud %urfaccs surrounding

both cavities and the fluid temperature through the ccnirc of each ca% ty plotted against radial

distance flora) with the enhanced mixing model applied and b) %%thout the mixing model. The

mewsurcd thermocouples l'or the disc 3 rear surl'acc and f*()r the front I'acc of di%c 4 together %%th the

cavity 2 shroud thermocouple are plotted on the Figure 9.11 for cavity 2. Thcnnocouplc

temperatures on the disc 4 cob rear surtace and on the front surface of disc 5 together A ah the

cavity 3 shroud 1herinocouple are plotted on Figure 9.12 for cavity 3. The two cavity shroud

thermocouples shown in the figures were test measurements with predicted SC03 temperature

profiles plotted against thein. The temperature profiles being used for the ('I. D boundary conditions.

The plots show that the use ol'the enhanced inixing model improves the prediction of'thc disc inctal

temperatures. There was good agreement in the predicted CFD disc cob temperature% but a large

error occurs on the disc 3 downstream diaphragm surface (in621 7) and on the upstream diaphragm

surface of'the disc 4 On6225). Also the plotted on both figures arc the mid cavity fluid temperatures

and. as mentioned above, the plots show that the enhanced mixing model reduce% the radial

temperature gradient slightly. The fluid temperatures for cavity 3 arc presented inTabic 1).1 for the

two engine test cases analysed.

3200310030002900MO 02700260025002400MO 0

220021002000190018001700160015001400130012001100

. 000noo

100

1

:00boo

Figure 9.8 Engine condition 107%Nl. confours of %wirl veltwit) (m/%) for the CFD

enhanced mixing model.2

-1)



765

4i3

I

Zd212019181710151413121110090807

06050403020100

Figure 9.9 Engine condition 107%. N 1. contours of s-A rl . elocil, * ratio for I he ('1- 1)

enhanced mixing model.

Figure 9.13 shows the disc 5 rear surface anti 1111 rive cone temperatures along %%ithhe mid cavi Iy

(line drawn diagonally across the cavity) fluid temperature for the 107'oN[. case. comparing the

temperatures. a) with the enhanced mixing niMel applied and h) without the mixing rnMel.

Tllcrm()coIjplemeasurements on the rear surface of'disc 5 (rn6230 disc 5 bore. m6232 and in6233)

together with the drive cone shroud thermocouple, m6236 arc plotted on the graph. lIoth the shroud

and drive cone temperature profiles were predicted from thc. %-L,3 thermal m(Xicl and used as

boundaryconditions for the CIA) analyses. The plots show that the CFD with enhanced mixing over

PrcdicLs the disc 5 rear surl'ace temperatures by approximately I OK. The conventional CFD nuxicl

Produces a closer match to the measured tempera ttires. When comparing the dim. surface radial

temperature gradient. the enhanced mixing model proKitices a gradient comparable to the mcasuml

tempcraturc gradient.

From CFD solutions there was a predicted increase in gas iemperalurC ofthc amil 1hroughtlOWOf

45K to 50K froin the R31 rotating holes rearward down through the comprc%u.r Ix)rc to the curvic

coupling. which was lower than the approximate temperature difYcrcticc ofWK mcasurcd on thc

enginc tests.

221



Figures9.14and9.15 compares he CFD predicteddisc metal temperatures, IPC discs 3,4 and5.

for thenearsteadystate107%NL condition, with andwithout the enhancedmixing model being

used, espectively.For the enhancedmixing model solution the predicteddisc temperatureswere

within 21K or anerror of 16%wherecrror - (Prcd-Nicasy(Tdiscrim-Tinlet) compared o 28K. a

21% error for theconventionalCFD. Also for comparison hecrror in SC03thermalanalysis

predicted emperaturesarcgiven using the sameerror criteria. '17heigure shows hat for tile

n*ajorityof thedisc temperatureshe CFD with enhancedmixing predictionswere lessaccurate

than hethermalanalysispredictions.The averageerror for theCFD predicted emperatureswas

7.7%compared o 3.3% for the thermal analysispredictions.I fencetherewasno improvement n

thepredictionof thedisc temperaturesusing theenhancedmixing CFD model compared o theSC03 hermalmodelpredictions.CFD enhancedmixing model predicteddisc temperaturesor tile

nearsteadystate100%NL condition arc shownin Figure9.16.There was a small improvement n

theCFD predicteddisc temperatures or the 100%NLcasecompared o the 107%NLcasewith the

largestpercentage rror being 14% (18K).

9.5.21ent transferresufts

Table9.1summariscshecavity3 shroudheat ransrcresults, omparingheconjugate eating.2D

axisymmctric nhanced ixingmodelCFDresultswith thecalculated eat ransfer rorn he

experimentsorthe woengineests.Thetableshowshat heheat ransreresultsrom he2D

'XiSymmetricnhanced ixingmodelcomparewell with thecxpcrimcnt3i aluesor bothengine

tests,with anerrorof 7%for the 107%NLestandan erroror2% rortheMOM test.

Figure8.37andFigure8.38 n Chapter8showed raphs f cavityshroudicattransrcr lotted

againstGrashofnumber,Grandagainst uoyancy umber,Do for (lieSussexNICIL t is interesting

tonote hat orbothengineestconditionshecavity3 shroudheat ransferNusscltnumbers,

derivedromCFD, ieontheGrashornumbcrurvespread f datapointsproducedor tileSussex

MCIL Also forbothconditionshebuoyancy umberwasvery ow andhcnce ying in tile

buoyancy ominantregime.The CFDderived,Nuh/ Re, ) valuesarehighandagainie within the

curve it spread f datapointsproducedor theSussexNICR.

222



II

690068006700

66006500

6400

630062006100

6000

59005900

5700560055005400

53005200510050004900

480047004600

4500

440,0430.0

69006800670066006500

640063006200610060005900

5800570056005500

54005300520051005000

4900480047004600

450,044004300

a) With (he Enhanced Mixing Model

Mi=

b) Without the Enhanced Mixing Model

Figure 9.14)Engine test condition 107%Nl, temperature contours (K) for 2) 'Aith and h)

without the enhanced mixing model.

223



a)

620

$Do

aw i

480

M

440 ý

004

620

9

Engine HPC Cavity 2 (Disc 3 and 4 Cavity) - Steady State Man Cond IOT%W

Enhanced Mixing CFO k-e Modell

- Cavity 2 Shroud

- Disc 3 Downstream

- Disc 3 Cob Downstream

-Disc 4 Upstream

- Disc 4 Cob Upstream

- Cavity 2 Contra Line

- Disc 3 Bare Centre Line

- Disc 4 Bore Centre Line

* Cavity 2 Shroud Measured

* Disc 3 Dwn Sirm Measured

* Disc.4 Up Sinn Monsufod

b)

006 0,06 01 012RO" Coordkum (-)

014

Engine HPC Cavity 2 (Disc 3 and 4 Cavity) - Steady 840101111811Ond 10?0^4t

Conventloctal CFO k-0 Model

am CavNy2 Shroud

Disc 3 Downstream

580Disc 3 Cob Downstream

Disc4 UpstreamDisc 4 Cob Upstream

5W i- Cavity 2 Centre Line

- Disc 3 Bore Centro Line

- Mar, 4 R- r-w- I. -

Cainty 2 Shroud Measured

Disc 3 Dwn SIrm MeasuredVO Disc 4 Up Sirm Measured

6.

Soo

4au

4w i

004 006

00

006 ol 012

Radial Coordkwft (-I

e

014

le

016

Hgure 9.11 Engine test 107%NLcavity

2 temperatures for a) %ith and h) mAithoutthe


In

Ole

224



Engine HPC Cavity 3 (Disc 4 and 5 Cavity) - Steady State MEN CAWW10r%W

Enhanced Mixing CFO k-e Model

ow

640

Wo

ow

580

Sao

540

5A

5001

4440 ,

004

ow

640

- Cavity 3 Shroud

- Disc 4 DownstreamDi%(:4 Cob Downstream

D,,., 5 Upstream

- Disc 5 Cob Upstream

- Cavity 3 Contra Line

- 0116c; Bore Centre Line

- Disc 5 Bore Centre Line

* Cavity 3 Shroud Measured

* Disc 4 Dwn Sinn Measured

is Disc 5 Up Sinn Measured

h)

006 008 () 1 012

Radial CoordIns" 0")

014

Engine HPC Cavity 3 (Disc 4 and 5 Cavity) - StesdY 311810kl8m Cand 10? %ML

CA)nvervtkmW CFO k-e M04W

Cavity 3 Shroud

Disc 4 Downstream

Disc 4 Cob Downstream

-Disc 5 Upstream600

DISC5 Cob Upstream

S@DCavity 3 Contra Line

Disc 4 Ekxe Centre Line

Disc 5 Bore Centre Line

0 Cavity 3 Shroud Measured

540, Disc 4 Dwn Strm Measuf,

I

Dtac 5 Up Strm Measured

6.Wý

&W

400

004

aS

006 000 01 0 12Radid Coordkuft Im)

014

() 16

() la

Figure 9.12 Engine test 107%Nl, cavity 3 fernperatum for a) %ith and b) 'Aithout the


ký.

- ýý 4 Lmn ýtrm measufou

s utac ") up z)trm measurna

all

aI$

225



8) Engine HPC Drive Cone Cavity (Disc 5 and Drive Cone Cavity) - Steady State Man Cond 107%NL

Enhanced Mixing CIFID -e Model

7(w

Goo

660640

Drive Cone Cavity Shroud

- Disc 5 Downstream

- Disc 5 Cob Downstream

- Drive Cone

- Drive Cone Cavity Centre Line

620

g 600

560560

540

520

Soo

480

4410

- Disc 5 Bore Contra Line

* Drv Cons Cavity Shmud

* Disc 5 Dwn Strm Messumd

440 1

004

?00

aw I

640

GN

gem56D

sw

sw

sm

900

400

006 008 01 v I.,

Radial Coordinals (m)

14 0 16

Engine HPC Drive Cone Cavity (Disc 5 and Drive Cone C&v*Y) * Steady $tml* ill" Cond 107"t

Conventional CFD k-o Model

Drive Cons Cavity Shroud

DISC5 Downstream

Disc 5 Cob Downstream

Drive Cone

Drive Cone Cavity Centre Line

Disc 5 Bore Centre Line

* Drv Cone Cavity Messurod

* Disc. S Dwn St" Monmewl

ols

Ole

Filture 9.13 Engine test 107%Nl, drive cone cavity lemperature% for a) 'Aith and h) -Ailhoul

the enhanced mixing model.

226



IN.I-

IN.. I lOIn.

tIn - '4').

K

114

. 6216

kil WN R.4. -j, 1,. p11. - 410k

" II

-I II,

U.

Figure 9.14 Engine test 107%Nl, IIII(Aisc temperatures (conjugate heating %oluflon) - %ilhthe enhanced mixing, model.

J--

116.1 som1. - %4qk

I/

(

I ýMG21610,--

*" 2)

hdo Mo. Alt lrmprr Iwo",- 418k

4 '.

41W

4

-

I. "

. 4%

4-1

(. 221

too.

so25

1. - "Ok 41sk

Ift. 4

4!!ri4&1

4*1

416

(-Ito

4149,

oil

r-ýk4

9711

"S'a

I in. -

f7U

0!0710

4dL723

I."' J

'SI

/\

Figure 9.15 Engine test 107%Nl, IIP('disc lemperatures (conjugate healing %olution) -without the enhanced mixing model.

(2II'll

dis2i/ (. 22)

17-

--

I

4ý 71 I It)t'a. kd 1. P, k.

-jID I", I. -I M, ., ýI,,, I ý.

glek1. -4W&

47--ý771

1. - t64h

2-1

. 42220

I*I=

1"""'

227



41

(II

riI IWO

,4. lu, I-P

11. - 422k

I 'I

I., )

I. r., e.

SI, .... d

II)P.. 4 M.... d I. pcfl

II-r.. I '4 I...

F----71 to

Figure 9.16Engine test 100%N1. IIPC disc temperatures

(conjugate heating%olution) - %,iththe enhanced mixing model.

9.6 Conclusions

Numerical siniulat ions have been carried out on a typical gas Iurbi Ile 111) oniprc%%ort) ana ý%c ie

III axionvective heat transfer in a rotating cavity with ax'al through1lo%.

Fhe 21) *svinmctric

m(xiclling technique using the enhanced mixing model to increase (he mixing in the central core of*

a rotating cavity has been used. The computations were pcrf*()nned assuming steady flow and the

rcsults have been compared with the engine test measurements for metal temperatures. I'lic

simulations were performed on the three rear compressor disc stages that formed three inter-

connecting inter-disc cavities, which was also linked to the I IP comprcs.m)r drive shatl cone cavity.

The three compressor discs were modelled and conjugate heating solutions wcrc ob(amcd from the

combined CIA) simulations. Two near steady state maximum operating conditions wcrc chown for

the simulations.

.1y using the enhanced mixing model good agreement with Icst values l'br the cavity shmud %tjrf*, c

hcat transfer has heen shown for rotat ing Rayleigh numbers ofthe ordcr 10". Both cnginc Icst

. ý. 11

ý.4-7)

f-- I

4-

I'

---I

.ý .11;

228



conditions imulatedwere n thebuoyancy ominantegime.Although heCFDcavityshroudheat

transferwas n goodagreement,herewaspooragreement ith themeasuredompressoriscmetal

temperatures.he2DaxisymmctricCFDmodelwith theenhancedmixingUDFmodelemployed

Producesnearsolidbodyrotationalcentralcorewithin eachcavity.I owcvcr, herewasstill a

significantadial emperatureradientacross achof thecavities,whena uniformcorecavity

temperaturewasexpectedo beachievedwhen heenhancedmixing modelwasapplied.'lic

enhancedmixingmodelwassuccessfuln beingable o distinguishheregionsn dieflow field

where heaxial hrougliflowdominatesandno enhanced ixing was equired nd egionswhere

rotationalbuoyancy ominatesandenhancedmixingwas equired.Withineachof thecavities here

weresmall ocalregions,normally n theouter adialpositions,wherenstabilitiesn theCFD

solutionoccurredwhen heenhancedmixingmodelwasapplied.The

contourplot of themixingfactorshowedhesenstabilities,with theplotshowinga ripplingeffect n theouter adial egions

of thecavities.Thesestabilityproblemswerepresentn the nitial simulations f theSussex

MCRB2andwere esolved y introducingmultiplesmoothing f the luid properties.lowcvcr,

evenwith multiplesmoothing pplied o the luid propertiesor theengine imulationshe

instabilityof thesolutioncould notbe fully resolved. urtherattemptso resolveheproblemwere

to smooth ot ust the luid properties utalso o smoothhemixing factorand hedensityradial

gradient.Unfortunatelyhisdid nothelp o improvehestabilityof theCFDsolutions.Using helocalenhanced ixingvalueof fluid viscositynstead f thestandardemperaturearyingviscosity

value educedhe evelof mixing within thecavities.Thishad hecffcct of reducinghe ocal

Raylcighnumber ndhenceeducingheenhanced ixing factor. ncreasingheenhancedmixing

factor,nearero the evelsachievedn theSussexNICR132imulations, y increasinghemixing

factorUDFconstant, , increasedhemixingbutthe nstabilitiesn thesolutionalso ncreasedover

a largerareaof thecavityspace.

The CFD modelpredictionsobtainedcanbeconsidcrcdas a rcasonablc irst csti=tc to achieving a

disc temperaturematch.To achievea closermatch, ncrease n the mixing within thecavities will

be requiredbut for this to happen, urther work will be rcquircd to rcsolvc the stability problems.

Finally, adjustingthe heattransferon thedisc surfacesusing a similar method o thatapplied to the

cavity shroudscould also beconsidered.

229



CIIAPTER 10

CONCLUSIONSAND RECOMMENDATIONS FOR FURTHERWORK

10.1Conclusions

It has ongbeenestablishedhat heflow within the ntcr-disccavitiesof aI IPcompressors thrcc-

dimensionaln natureand imedcpcndcnt. o enable greaterunderstandingf thenatureorthisflow andassociatedeat ransfer, neapproachs to model heflow usingCFDrcsolving he hree-

dimensionalandunsteady ffccts. lowcvcr hisapproachcquircsa hugeamountorcomputational

memoryand ime o runtheCFDmodcls.A second pproachs to brcakdown hiscomplex low

processntoseparatehysicalmechanismsnd ntroduccapproximate utcomputationally fficient

modelsor these rocesses.hesecond pproach as aken or thisrcscarch,with theaim of

producing methodhatcanbe ncorporatedntocurrentdesignpractice.Two undcrlyingnow

mechanisms aybe dcntificd for thiscomplexlow; thefirst associated ith theflow within the

inter-disccavitiesand hesecond ssociatedith theaxialthroughflowunder hecompressorisc

bores.Bothof theselow mechanismserediscussedn thereviewof previouswork. In the nter.

disccavitiesbuoyancyn thecentripetalorce ielddominates. heaxialthroughflow esultsn a

$hear rivencirculationn the nnerpartof thecavity.

Anevaluationof the useof CFD to simulate he

flowand natural convection

ina scaledcube

has

beenpresentedKirkpatrick andBohn, 1986].Two heatingconfigurationswere considered,both

being heated rom the bottom surface.The computationswere pcrrormed assumingeither unsteady

or steady low for laminar or turbulentnow models.A range of temperaturedifference between he

hot andcold surfaces I OKto 40K) wereusedgiving a range of Rayleighnumbers,Ra- 5.83x 109

to 2.33x1010. he CFD resultswerecomparedwith other worker's experimentalmeasurementsor

hc3ttransfer.flow patterns, andthe meanandfluctuating temperaturedistribution. I'lic CFD

simulationsshowedthat the time-avcragcdhcat transfercomputedby theunsteady aminar flow

model ("pscudo" DNS solution) was the mostaccurate.Calculatedheattransrerresultscompared

well with the experimentalderived hcat transrcrcorrelation at low Rayleigh number(-3% error)

with a small difference at the higher Rayleighnumber(6% to 13%error). The steady low model

230



assumingurbulencek-c with thek-c /W nearwall model)performedheworst.Theuseof a

turbulencemodelappearso dampdown he hermalactivity within thecavity.Comparinghe

, umerical eat ransferwith theexperimentalorrelation howedhatby refining hemeshhe

disparityetweenhenumericalesultsand heexperimentalatacorrelationAas educed-13% to

-06 error) or the200-cubcdmeshat thehigherRayleighnumber).n addition,diedifferencen

theerror n theoverallheatbalance lsoreduced nthefincr mesh.Thenumerical nalyses

compared ell with otherobservationsmade romtheexperimental ork.Thecalculated ize, he

speed f propagationnd heperiodof release f theplumesromtheheated ottomsurface f the

cubeagreedwith experiment. henumerical nalyseslsoagreedwith theexperimentalindings

that heheatedloorappearso promotemixing n thecavityandeliminatesemperature

stratification.

TheCFDsimulation f naturalconvectionn astationary eated ubewasextendedo the

modelling f convectionn a rotatingenclosed nnular ector avity.CFDsimulations f convective

beat ransferwithinascaledotatingsectorandwithinascalcd otatingannulusor theBolinct al's

(1993,1994]experimentsavebeenpresented.hecomputations ereperformed ssuming

unsteadylow and heresultscompared ith

experimentalmeasurementsndnumerical redictions

forheat ransfer ndother low ficld parameters.orthescaledotatingannulus omegood

agreementetweenheCFDresultsand heexperimentalaluesor mean urface eat ransferhas

ken shownor Rayleighnumbers f theorder1010,pproachingheRayleighnumbers ccurringn

gas urbinehighpressureompressorisccavities.For hehigherRayleighnumberan error of 4%

wasshownor the ull 360"annulusCFDmodel ising o a9%errorfor the4311nnulus ectorCFD

model. Iowevcr herearc somepoor resultsromtheCFDsimulations rthc scaled otatingsector.

At the owerRayleighnumberhedifferenceromexperimentwas 10% whilstat thehigherRayleighnumberherewasan84%difference.n a subsequentFDstudybySunct al. [20041 or

thesame eometry singbothFLUENTandaRolls-Royceode, Iydraoverarangeof Rayleigh

numberst was ound hatbothCFDcodes verpredictedhesurface eat ransfer omparedo the

experiment.heovcr-prcdictionwasabout10% o20% or theI Iydracodeandhigher or

FLUENT,40%approximately, hich s less han hat ound or thecurrcntpredictions. hereasons

for thediscrepanciesetweenheexperimentalndcurrentCFDresultsarestill to befully resolved,

butare houghto beassociated ith difficultics n numerical onvergence.heCFDresults

cOnfirmheexperimentalmeasurements,hichshowed reduced eat ransferanddifferent

Rayleighnumber ependencyor therotatingannuluswhencomparedo gr:kvity-ddvcn onvection.

231



Thenextpartof thestudy ookedat thesecondlow mechanism,heaxial hroughflow nder he

compressoriscboresand nteractionof thiswith the low within the nter-disc avities.A CFD

studyof the low passing ver a rectangular avity for a seriesof differingcavitydepthswas

presented.hecomputationalesultswerecompared ith experimentalmeasurementsf cavitypressurend low velocities.Thecomputationalmodclsimulatedhe lowmechanismeasonably

well for theexperiments ith air. I lowcvcrtheCFDturbulentk-C/W 2-13yermodelunder

predictedhestrength f thecirculating low within thecavity anddid notpredictcorrectlyhe

shear trength f thecross low whichdrives hecirculating low in thecavity.For heexperiments

usingwaterCFDfailed opredict hemultiplecirculationswithin thecavity.Thercasonwhy the

CFDanalysesailsto simulatehecirculations till needso be fully explained. heworkwas

consideredo be mportantbecausef theneedo know he evelsof heatandmomentumransrer

acrossheshearayer romthecross-flowo thecavity and n termsof agas urbinecompressorhe

transrcr f heatandmomentumromtheaxialthroughflowunder hedisc boreso the ntcr-disc

cavities.

To gaugehebenefitsof anew2D axisymmctricCFDmethodo model heheat ransferwithin the

compressorntcr-disccavities t wasnecessaryo performathermalanalysis sing raditionalmodellingechniquesor the hermalboundary onditionswithin thedisccavities.For his

assessmentheSussexMCRB2wasusedandatemperature atching xercise sing heRolls.

Roycehcrmo-mcchanicaliniteelement rogramSC03wasperformed.Therig simulate$ile

internalcomponentsnd low features f ahigh-pressureompressorI IPC).Threemodelswere

constructed,he irstbeingadatummodelusingconventionalhermalboundaryonditions.A

secondmodel hatusesheboundary onditionsromthedatumbutreplacesheconventional eat

transfer ocflicicntcorrelation pplied o thediscsurfaceswith a-conecorrelation,CONH"which

wasderivedatSussex y Alcxiou (2000],using estmeasurements.he hirdmodels the"best.

matched'model o the hermocouplemeasurements.achmodelwas unthroughhesamedle to

maximum peed cccicration-dcccicrationycle.Resultsromthe best-matched'modelgave

temperatureifferenceerrorsof less han5K bothat steady tateconditionandduring he

accelerationransient.lowcvcr,an errorof 5K issignificant or therig cycleas herewasonlya

30Kradial emperatureifferencebetweenhediscrim and hecob andonly a50Ktemperature

difference etweenhehotmetal ntcr-disccavityshroudand hecooleraxial hroughnow ir atdie

Maximum peed ondition.Thereforehe5K errorrelates, sa percentagef the cnapenturc

between ieshroudandaxialthrougliflowgas,o a7%error at thesteady tatemaximum peed

conditionanda 12%errorduring heacceleration.his s a significanterrorwhenconsideringhe



larger temperaturesoccurring in engines.Comparisonof the resultsobtainedfrom both the CONE

model andthe 'bcst-matchcd'modcl with the datummodel, showedthat therewas some merit in

using the conecorrelationon the disc surfaces.Overall, theconecorrelation wasshownto be

cffcctive in the mid andouter regions of the disc diaphragmfor the steady state nuximum

condition, achievingbetterresultsthan the datummodel. I lowcvcr. using theconecorrelation hada

detrimentaleffect on thedisc cob and bore temperatures.During transients hecone correlation

Produceda disc temperature esponse hat wascloseto themeasured esponseor the inner andmid

Pall of thedisc diaphragm.But in the outer radial part of thedisc die datum modelproduceda better

thermal response han the model with theconecorrelation. Inter-disccavity shroudtemperature

Predictionswere good for the datummodel and for themodelusing the heattmnsrcrCquivalent o

that derivedat the SussexUTC [Long ct al. 2006b].Stressesn thediscsaredriven by temperature

gradient; socomparingthe radial temperaturedifferenceproducedby the thermalmodels to that

measured,he datummodel was shown to perform muchbetter than the therrnalmodelwith the

conecorrelation, both at the maximum speedsteadystatecondition andduring the transient$.

Modc1lingaroundthecompressordisc cobs proved to be difficult and to achieveanacceptable

matchwith thedisc temperaturemeasurements xtreme hcrmal boundaryconditions Ind to be

assumed, ncluding an imbalanceof hcat/rnasslow in andout of the inter-disccavities.

To increasetheunderstandingf theflowsoccurringn theNICRB2CFDwill continueo beused.

Someprogress asbeenmaden themodellingof thecavitiesWith ull 3D unsteadyCFD but this s

computationallyntensive.n anattempto overcomehecomputingimeproblema2D

axisYnlmctric teadylow modelling echnique asbeendeveloped. newCFDmodelling

techniquewas ntroducedandused o increasehemixingwithin the ntcr-disccavities.The

enhancedmixingmodelmethodologywasappliedo steadylow axisymmctricCFDmodels.nitial

testingof theenhancedmixingmodelwasperformedor bothastationwyenclosedavity and or a

rotatingsector caled avity.Goodagreementntheheat ransrcror thestationary nclosed avity

betweenheexperiment nd heCFDwith themodifiedcore luid propertieswasobtainedinner

andouterwall heat ransfer2% errorfor thehigherRayleighnumber). lowcvcr herewaspoor

agreementetweenheenhancedmixingCFDmodeland heexperimentsor dieradialheat

transferhrough hecore or therotatingannulicavity(87%error).From heseestCFDsimulations

the evelof themixingfactor hat s requiredoobtainsatisractorymixing n thecavity coreand o

producehecorrectevelof heat ransferhroughhecavitywasestimated. he estsllustratedhat

theenhancedmixingmodelhas hepotential obeusedo model hecomplexunsteadyD rotating

cavityflow with a2DaxisymmctricCFDmodel.TheFLUENTUserDefinedFunction UDF)

233



Programor theenhanced ixingmodelwas henapplied o enclosedotatingcavitieswith axial

throughflown thesimulation f theSussexNICRB2cxperimcntsoveringa full rangeof buoyancy

conditions.

Tte axisymmctricCFDmodelling echnique sing hecnhancedmixing model o increasehe

mixing n thecentralcorcof a rotatingenclosed avitywasapplied o theSussex ICRB2.711C

computations ereperformed ssuming teadylow and heresultswerecompared ith

Cxpcrimcntalmeasurementsor metal emperaturesndheat ransfer.Forthe inalsetof simulations

Of heSussexMCRB2, woconnecting avitiessurroundingnediscwereused.The discwas

modelledwithin theCFDanda combined avityandmetalconjugate eatingCFDsolutionswere

obtained.Using heenhanced ixing modelproduced goodagreement ith cxperimentalaluesfor thecavityshroud urface eat ransferor rotatingRayleighnumbers f theorderIe. For he

steady tateMCRB2 ests,he2D axisymnictricCFDwith theenhancedmixingmodelemployed

wasable o successfullyimulatehe ests themaximumheat ransfererrorwas94%).lic CFD

modelproduced avityshroud urfaceheat ransfershatwerecloser o themeasuredeat ransrcrs

thanpredicted y usinga3D 120"sectorLES-CFDmodel SunandChew,2004) aheat ransrcr

crrorof -25%). An acceptablegreement ith themeasuredompressoriscmetal emperatures

for eachof the estshasbeen hown -3% error).77hexisymnictricCFDmodelwithenhanced

mixingproduced nearsolidbodyrotationalcentralcorewithincachcavity.Alsowithin each

cavitythecore emperatureasshown o benearlyuniform.Bothof theseeaturesmknownrrom

CxPcrimcntsnd rom3DunsteadyCFDsimulationso bepresentn naturalconvectionn rotating

cavities.Theenhanced ixingmodelwassuccessfuln beingable o distinguishheregionsn the

flow fieldwhere heaxialthroughflowdominatesndnoenhancedmixingwas equired ndregions

where otationalbuoyancy ominates ndcnhancedmixingwas equired.Withthegoodagreement

beingachieved oth or thecavityshroudheat ransfer ndror disctemperaturesheCFDmodel

appearso bepredictinghecorrectamountof mixingwithin thecavities or theSussexMCRB2

application.Forall theCFDsimulations sing heenhancedmixingmodel.with die ocalRayleigh

numberpowcr,n setcqual0.1and hemultiplicationactor,A setequal o 1300producedhebest

resultsbothfor cavityshroudheat ransferand n obtainingacentralcavitycore low.Theuseor

under-rclaxationnthe actoredluid propertiesogetherwith theflow fieldccll smoothing elped

to reducehe nstabilitiesn thesolutionandalso

helpedheconvergence.

Tocompletehe estingof theaxisymmctricCFDmodelling echnique sing heenhanced ixing

model. t wasappliedo atypicalgas urbine1111ompressorotordrumwithanaxial hrougliflow.

234



Tbccomputations ereperformed ssuming teadylow and heresultswerecompared ith engine

testmeasurementsor metal emperaturesndbeat ransfer. besimulationswereperformed n the

three earcompressoriscstageshatformed hreentcr-connectingntcr-disc:cavities,whichwere

also inkedto the IP compressorriveshaftconecavity.Thethreecompressoriscsweremodelled

andacombined avityandmctal conjugate catingCFDsolutionwasobtainedor twonearsteady

statemaximumoperating onditions.By using heenhanced ixing modelUDF in theCFD

simulations oodagreement ith testvalues or thecavity shroud urfaceheat ransferheat

transfererrorof -7%) hasbeenshown or rotatingRayleighnumbers f theorder109.Bothengine

testconditions imulatedwere n thebuoyancy ominantegime.Although heCFDcavityshroudbeat ransferwas n goodagreement,herewaspooragreement ith themeasuredompressorisc

Inct3l emperatures-16% error).TbeCFDmodelproduced earsolidbodyrotationaln thecentralcore or eachcavity.Ilowcvcr,therewasstill a significant adial emperatureradient cross ach

of thecavities.Theenhancedmixingmodelwasagainsuccessfuln beingable odistinguishile

regionsn theflow fieldwhere heaxialthroughflowdominates ndno enhancedmixingwas

requiredand egionswhere otationalbuoyancy ominatesndenhancedmixing was equired.

Unfortunately,nstabilitiesn theCFDsolutionwereshownooccurwithineachcavityeven

thoughmultiplesmoothing f theflow field fluid properties,hemixing factorand hedensity adial

gradientwereappliedo thesolution.Reducinghe ocal Rayleighnumber, encereducinghe

enhancedmixing factorappearsodecreasehe evelof instabilitybutthis is to thedetriment r

beingable oobtaina uniform emperatureore low within thecavities.To achieve closerm3tch,

to themeasuredisctemperaturesn ncreasen themixingwithin thecavitieswill berequired ut

for thisto befeasible,urtherworkwill berequiredo resolvehestabilityproblems.

10.2Recommendations for Further Work

Researchcarriedout for thisthesishasshown hat heaxisymmctricCFDwith theenhanced ixing

UDFmodelappliedadequatelyaptureshe3Dtimedependent ow physicswithin thecompressor

intcr-disccavities or the low fieldandheat ransfer tsteady tateoperating onditions.Further

work is requiredodevelophemodellingprocessouse or transient ngineoperation.During

engineoperation heflow within the ntcr-disccavitieswill mainlybe n thebuoyancy ominated

regime.Duringaccelerationndat steady tatemaximum peed onditionsilecavitynowwill be

in thebuoyancyregimewhilstduring hedecelerationndat low speeddleconditionshe low

may all into theaxialthrougliflowdominant egime.Twoapproachesanbetakenomodel he

235



lltc%t:lh"i Metal I crilpetaluirl

I Pfcýflhýj Nicial

on IIIC ', 131-nan ( cnital %h. ft

Figure 10.1 Su,%%ex ICR112 (cavilles 2 and 3 and di%c 2) oilended gromon sind the po%itionof the boundary

conditions requiredh) the CIA)

model.

Immomr,

I

I t-_J

Pfrw, hýl "Icifi-I

flu. Sul"qwN %Imfl

I

\ 1.I

'..igure 10.2 Su%%ex ICRI12 full geotnews and the po%llion of lhc houndar-% conditions

required by the CIA) model.

ý.m

,117



Further testing ol'the combined cavity and disc conjugate heating 21) axisyminctric CFD WHIItile

enhanced mixing method could be applied to tile engine III, compressor geometry used I'M file

steady state CFD simulations in Chapter 9. 'rhe CFD geometry would need to he extended it)

include the compressor drurn discrim,

the front drive ann and the I ill comprcs-wr drive cone. For

the CFD model to run through a transient operating cycle, transient temperatures on the compressor

drum outer surface, on tile front drive arm. on the drive cone and along the IT central %haflwill

need to be specified. The Cullengine I IP conlprcssor geometry and the ix)silion of tile boundary

conditions f'or the CFD model are shown in Figure 10.3.

Prescnbcd Metal'rcnTwtotuirc%

on the HPC

ýrom Drive Armouter

Strfacc

I N Ih-( ww 0,11cl sm I. -

P..ý lear"alwc. ml

(AUCI

1'rc%crthctiMetal I-enipcraturcisonI ic 1111C otor I hum (hiter Stirfiocc

11elliprtnitucý tm ihr 1 ' %häft

Figure 10.3 Engine IlP compressor full geomewt and the po%ilion (of the boundsrý condition%

required by the CFD model.

During transient operation the flow field (velocities and pre%surc%)%%thin the ca, iltc%ý%ll re%l-kind

much quicker than the temperature field. especially during a deceleration. for hoth the air and (he

solid. To solve a combined conjugate heating CFD problem for a transient to required temperature

accuracy will require the time steps to be small. Also to achieve "pscudo" steady state convergence

at each time point many iterations per time step will be needed. This implies long computational

times to solve relative simple transient problems. such as an acccicration-decclerai ion cycle. To

238



Following on from the testing of the axisymmetric enhanced mixing modcl coupled with the

thermal model using the SC89 program on MCR132 two-cavity model. testing on the engine 111'

compressor geometry in Chapter 9 could be perf'Onned.

llwrnul N&vdcl%4'01Houndatv Condo am

c, ti ng Amm

Figure 10.4 Sussex MCRB2 (cavities 2 and 3) SC89 coupled CFD thermal anal) %is ranslent

model.

In conclusion the SC99 coupled CFD thermal analysis is the favourcd and the most feasible

approach flor transient analyses as it is automatic with the user specifying the solution accuracy and

the program is 101 to determine the timestep

intervals required to achieve this accuracy throughout

the solution. The combined CFD conjugate heating approach has the limitation that the houndary

temperatures need to he specified. which could he difficult. especially for transient analyses. If has

been shown that this approach produces g(x)d results for steady state analyses. where the houndary

temperatures are known flor tile steady state condilions. For transient analyses this appnmch is more

problematic. With a transient analysis the problem is to determine the rate of heat transfer through

the solid metal and thus the user. from guide lines and experience. will need to make a judgement

when an acceptable solution has been obtained for each time step and the user will alu.have

tojudge the time step intervals. This knowledge can only he gained from validating tmn%.cnt

conjugate heating CFD analyses over a wide range of applications. engine type..and operating

cycles.

240



101.3Other recommendations

Otherrecommendationsnclude hefollowing,

Forbuoyancyype lowsresearchiteratureor bothgeophysicalndmeteorologicallows

shouldbereviewed.A comparison etweenheseypesor nowsand herotatingcavity

flowspresentwithin agas urbinecompressorouldpossiblybemade.Similarly,

environmentallow literatureshouldbereviewedor cross-flowover acavity.

ThecnhanccdmixingCFDmodelneedso bevalidated cross widerrangeof applications

to determinetheenhancedmixing model ocal Rayleighnumberpower ndices,n and he

multiplyingfactor,A valueso achieveherequiredmixingwithin the ntcr-disccavities.t

is tobehopedhatsinglevaluesor the woenhanced ixing p3ramcicrswill cover he ull

rangeof applications r an algorithmcouldbederived or eachof the woparameters.

To invcstigatcheuscof othcr urbulenccmodclswithinthe2Daxisymmetricwith

cnhanccdmixingCFDmodcl.

To investigatemethods o solve the solution instability problems with the enhancedmixing

model andto improve theconvergence ateof the solution so the method canbeusedmore

CRIcientlywith the coupledCFD - thermalanalysisprogram,SC89andobtaina transient

solution within acceptable imcscalcs.

Finally,to rciinetheenhanced ixingmodel, t shouldnowbeapplied o other ig andenginecompressors,ncluding heSussexEnginePartsRig' (acivil enginecompressornd

turbinespool ig), to largecivil enginecompressorsnd o smallhelicopterengineaxial

compressors.

Theserecommendationsandthe research eported n this tlicsis are consistent with the recently

announced virtual engine" modelling at Rolls-Royce.The ultimate Aimof this initiative is to have

CFD and FEA-bascdmodels for completeengines.Limiting factors for the approacharemodelling

inaccuraciesandcomputing limitations. Useof computationallycfricicnt CFD-bascdmodels

matched o experimentaldataoffer advancesover current techniqueswith a frameworkthat canbe

extended o includeothermethods suchasLES) ascomputingpower improves.

241



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251



Appendix I

Al. l. The Standard k-c Turl)ulcncc Alodel as usedIn the FLUENT CrD code

Ilie standard-cmodel A I] isa semi-cmpiricalmodelbasedon model ransport quitions or tile

turbulenceineticenergyk) and tsdissipationate r). 11Cmodel ransport quationor k Is

derived rom heexactequation,%%ilethemodel ransportquationor c wasobtained sing

physicaleasoningndbearsittle resemblanceo itsmathematicallyxactcounterpart.

RgmMrt Ugglions

Turbulcntkincticcncrgy,k

D(fA)+ vf,/Nku)v /I +

p, Vk +G#+G,, -pe-), wdi

1(

76-)

1

Rateof dissipation,c

LIPHI+V+ W",-)Vc] + Cl, -f

(GI +C.4

Gj - Cl,dt

'Ikk

The turbulent (or eddy) viscosity./4, is computedby combining k andc as follows.

P

A-Pc, 7

%%Iicrc# saconstant.

r-orall the CFD computations he following dcrault valucs %-cre scd'

Cl,rw 1.44,C2e 1.92,C1, 0.09.cris 1.0.al, - 1.3

(A1-3)

Gi isrepresents icgeneration r turbulenceincticenergy ue o themean clocaySfadicnts,

252



Gi - -pu, u,air,

To evaluateGA n amanner onsistent ith theBoussincsqypothesis,

Gj - pS 3

%%hereis the modulusof the mean atc-of-straintensor,defincd as,

S= 42-Sv-S1

Gb s the generationof turbulencekinetic energydueto buoyancy,

(AW)

(M-5)

(A 1-6)

G* 1107" (Al-7)Pr,27,

herePri s the urbulentPrandtlnumberorenergy-0.85deraultvalue)andg, isdiecomponctit

of thegravitationalector n the thdirection.lic cocfficientof thennalcxpansion,7 sdefinedas,

(A1-8)

I'lic degreeo whichc isaffected y thebuoyancys detcnnincd y theconstantC), C), Is

calculatedo thefollowingrelation A21,

C,u n tanhý

.,

UV1(A .9)

wherev is flic componentf the low velocityparallel o thegravitationalectorandU sthecomponentf the low velocityperpendicularo diegravitationalector.Cie%kill eequal for

buoyantshearayersor %%hichiemain lowdirectionsalignedwith thedirectionorgravityand

Z,rororbuoyantshcarayershatareperpendicularo thegravitationalector.

Turbulentheat ransportsmodelled, sing heconcept r Reynolds' nalogyo turbulent

momentum. quation .8 s the-modelled"energyequation,%%here). heviscous issipationerm

is givenby,

253



where r,),ff isthedcviatoricstrcsscnsor,dcrincdas,

ail

clu,t5v(LarL,

3 ar,

(Al. 10)

1)

also he hmnal conductivity, in theenergyequation, quation .8, s replaced y diecffectiveflicrmalconductivity, ff givenby,

ke,nk+,c /1,Pr,

I'lic defaultvalueof the turbulent Prandtlnumber, 1r, s 0.83.

(Al . 12)

Forhigh-Mach-numberlows,compressibility ffectsurbulencehrough o-calleddilatation

dissipation",which snormallyneglectedn themodellingorincomprcssiblelows JA31.

Neglectingthedilatationdissipationails o predictheobservedecreasenspreadingatewith

increasingMich numberor compressible ixingandother rceshear 3ycrs.o accountor these

CfTectsn thek-cmodcls n thecode.hedilatationdissipationerm.Ym. s ncluJcdn theA

equation. 1iis erm smodelled ccordingo aproposal y SatkarJA4):

Ymw2pcilfl

%here f, s the urbulentMachnumber. efinedas

mt

-F;-s

whcrea (-4yRI) isthespccdof sound.

(AI-14)

Ilis

compressibilitymodificationalwaysakes

efrcct%henie

compressibleorm

ofthe deal

gaslaw sused.

254



A1.2. Near Wall Turl)ulcncc Models used In the FLUENT CI-'D ctxlc.

A1.2.11. tandard wall functions

I"he standardwall functions in thecodearebasedon die proposalor LaunderandSpalding AS],

andhavebeenmostwidely used or industrial flows.

Momcnitim

711caw-or-the-wallor mean elocityyields

UOn ln(Ey*)

ulicre

uo mucvAll,

r. lp

(AI-15)

(Al .16)

* pCVAkV')#Y Ir V

11

PP (AI-17)

%licreK is dic von KdrmAnconstant - 0,4187).E is an empirical wall functionconstant -9.793),Up s themeanvelocity oraic fluid at point P,Apis he turbulencekinetic energy at 11,-pis the

distance rom point P to the wall and j is thedynamicviscosityof the fluid.

1"heogarithmic law for meanvelocity is known to bevalid rbr.)ý > about30 to 60.111hecode, he

log-law is employed%%-Iicny*11.225.Wicri the mesh s such hat. ý < 11.225at thewall-adjaccnt

cells, thecodeappliesthe laminarstrcss-strainelationship hatcanbe%Titicnas,

uf my* (Al-19)

It shouldbenoted hat, n thecode,he a%%,-or-thc-%%*allor mean elocityand emperaturere

basedonthewall unity .. ratherhany* Viesequantities reapproximatelyqual n

equilibrium urbulentboundaryaycrs.

253



Encre

Reynolds'analogybetweenmomentum ndenergyransport ivesasimilar ogaridimicaw ror

meanemperature.s in the aw-or-the-wallor mean elocity, he aw-or-the-wallor temperature

employedn dic codecompriseshe ollowing wodifrcrcnt aws:

linear law for the thermalconduction sublaycr%%hereonduction s important

logarithmic law for the turbulent region%%hereffccts orturbulcncc dominateconduction

Tbe thicknessof the thermalconductionlayer is, in general,different rrom die thicknessorthe

(momentum)viscoussubl3ycr, andchanges rom fluid to fluid. For example, ile thicknessof tile

thermalsublayerfor a high-ilrandti-nunibcr fluid (e.g.. oil) Is much less hanIts momentum

subl3ycr hickness.For fluids of low Prandtlnumbers e.g.. liquid metal). on thecontrary, it Ismuch

largerthanthe momentumsublaycr hickness.

In highlycompressiblelows, he emperatureistributionn thenear-wallegioncanbe

significantlydifferent rom hatof low subsoniclows,due o the icatingbyviscous issipation.n

thecode,he emperatureall functionsncludehecontributionrom heviscous eating A61.

Ilic law-of-dic-wallmplementedn thecodebs the ollowingcompositeorm:

rv4, t V)0, .<

)'r*)

,*

(r.-Tp)lvpCv4kv3

Pr )-* + Y;tilr ur,

Tm4=Iv4kVI

Pf,A:

ln(E),O)+I']+VaPC"

4"

(Pr,U,.+ (Pr-

(A 1.19)

%%hereiscomputed y using heronnuI3givenby Jayatillckc A71:

P=9.24

r(Pr [I

+ 0.2Se*4 (A 1-20)

andp is die fluid density,cp s the spccific licat of the fluid, 4 It the%%allicat flux, TpIs the

temperatureat thecell adjacent o the wall, T. is die temperatureat Oicwall, I't is die molecular

256



Prandtlnumber(pqlk IC rM3r, is the turbulent Prandilnumber(-0.83 at die %%ill), /is th the I

conductivity of the fluid and U, is the mean velocity m3gnitudeat jo*- Yr

Note hat, or thesegregatedolver, he erms

v2ppr and VSf Pr,U; + (I)r- pr,

qUp

q

will bc includcd in EquationA1. 19only for comprcssible low calculations.

Thenon-dimensionalicrmalsublaycrthickncss.'r, in EquationA1-19 scomputeds ile Y*%, luc

atwhich he ncar awand he ogarithmic aw intersect, iven ilemolecularPrandilnumber f tile

fluid beingmodcllcd.

Tlic proceduref applyinghe aw-or-the-wallor temperaturesas ollows.Oncehephysical

propertiesf thefluid beingmodelled rc spccificd,tsmolecularPranddnumberscomputed.

11cn,given hemolecularPrandd umber.he hermal ublaycr iicknessyr, Iscomputedrom he

intcrscction

of theinear

andogarithmic

rorilcs,andstored.During he teration. cpcnding

onthe

.ývalueatdienear-wall ell, cidicrthe inearor the ogarithmic rofile n EquationAl-19 is

appliedo compute ic wall temperature. or licatflux 4(dependingnthe ypeof thed1cmial

boundaryconditions).

IV-rhulcncc

In thek-cmodels nd n theRSNI if theoption oobtainwall boundaryonditionsromdieA

equationsenabled), ie k equationssolvedn thev%holcomainncludinghe%ill-adjaccrit ells.

7110oundarycondition ork imposed tdie%%ills,

a

Oil

%here is the ocalcoordinateonnal o thewall.

(A I2 I)

Tbeproduction f kineticenergy,GA,and tsdissipationate,e,atthewall-adjuentcells,%hich

are hesourceermsn thek equation. rccomputednthebasisoraic localcquaibriwn

257



hypothesis. nder hisassumption,heproduction f k and tsdissipationateareassumedobe

equaln diewall-adjaccnt ontrolvolume.

Tlius. heproduction f k is computedmm,au r.Gi x r. j- - r.

. g(4kVIkrc"e p Yp

andcis computedrom

rV402

cp

(AI-22)

(A1.23)

The c equation s not solvedat the wall-adj3cent cells, but instead s computedusing EquationAI-

23.

Note hat,asshownhere,hewall boundary onditionsor thesolutionvariables,ncludingmean

velocity, emperature,andc arcall takencareor bytile wall functions. 7herctore,here snoneed

to beconcernedbout heboundary onditions tthewall$.

Thestandard all functionsworkreasonably ell rorabroad angeor %kall-boundedows.

I lo%%,cvcr, hey end o becomeess eliablev%hcnheflow situations epartoomuch minthe deal

conditionshatarcassumedn theirderivation.Amongothers, ieconstant-shcarnd ocal

equilibriumhypothesesarc heoneshatmost estrictdieuniversality rthe standard all

functions.Accordingly,whcn henear-walllowsarcsubjectedo severe ressure radients,nd

%%,cn the flows arc in strong non-cquilibrium, thequality orthe predictions s likely to be

compromised

A1.2.2. Two-layer model for enhanced vall treatment

Enhancedwall treatmentsa ricar-wallmodellingmediodhatcombines t"o-layer modelwith

enhanced all functions.f thenear-wallmeshsfineenougho beable o resolvetic11minar

sublaycrtypicallyy*m, y*-AyWv-v1(,.1p)), hen heenhanced%%illreatmentwill be denticalo the

traditionalwo-layer onalmodel.

In thencar-wallmodel, heviscosity-affcctcdcar-wall egion scompletelyesolved ll theWAYo

theviscous ublaycr.lic two-laycrapproachsan ntegralpartorthe enhanced%%allreatment nd

258



is used o specify bothc andthe turbulent viscosity in the near-wall cells. In this arproach,die

whole domain is subdivided nto a viscosity-afTectedegionanda rully-turbulcnt region.Ilic

demarcationoroic two regions s determinedby a wall-distancc-bascd,urbulentReynoldsnumber,

Reý,definedas,

ým,rk-Reyn,P

whcrey sthenormaldistance rom hewall at thecell centrcs,

), a mi+ - F.P.Or.

(A1-24)

(AI-25)

%%,ere F is the position vectorat the field point, and F. s the position vector on the wall boundary.

r. is the unionof all the wall

boundaries nvolved. Thisinterpretationallows).

to beuniquelydefined in flow domainsof complex shape nvolving multiple wans. rurthermorc,)-defined in this

way is independentof die mesh opology used,and is definableeven on unstructuredmeshes.

Re' -200), die A-cmodel (describedearlier In Sectionn the fully turbulent region (Re.,> Re*'I,

ALI) is employed. n theviscosity-affcctcdncar-wall region(ReP< Re'$''),

theonc-equationmodel

or Wolrstcin [A8] is employed. n die onc-cquationmodel, the momentumequationsandthek

equation s retainedasdescribed n SectionALI. However,the turbulentviscosity..u, is computed

from,

A.14, n CI.. (A1-26)

%khcreie engthscalehatappearsn EquationA 1-26 scomputcdrom A91

1'. - )TA, - C-141A.) (A 1-27)

The wo-layer ormulationor turbulent iscositydescribedbovesusedasapartordic enhanced

wall treatment,n which he wo-laycrdefinition ssmoothlyblendedwith thehigh-Rcynolds.

nurnbcrp,dcfinition fromtheouter egion,asproposedyJongenA 10):

A.,.A - AIA + (1- AdA.24.1

(Al-28)

whcrc.p, is the high-Rcynolds-numbcrdcrinition asdescribed n SectionA 1.1ror die A-cmodels.A

blendingrunction,A, is defined in sucha way that it is equalto unity rar from walls and s zero very

near o walls. I'lic blending function choscn s,

259



A, m11+ tanli21

1A(A 1-29)

Theconstant determinesile width or theblending unction.By defininga widthsuchhat ile

valueof A, will bewithin 1%of its far-fieldvaluegivena variationoraq. theresult s,

A M,

J'i Ile'l(AI-30)

tanh(O.8)

Typically, Alley would beassigneda valuethat is between5% and20% or Re" n rposc,,.

The mai pu

of the blending function A, is to prevent solution convcrgcnce rom being Impeded%%Iicnhek-c

solution in the outer layer doesnot match with the two-laycr rormulation.

Thec field iscomputcdrom,

C0AVI

11

Ile lengthscalcs hat appear n Equation A1-31 are again computed rom Chenandflatel (A91:

It - )-C,,- C.

)(A1.32)

If the%%holelow domain s inside heviscosity-affectcdegion Iter< 200).c Isnotobtained y

solving he ransport quation;t is instead btained lgebraicallyromEquationA1-31.111Code

uses procedureor thec specificationhat ssimilar o thep,blending norder oensure smooth

transition etween iealgcbraically-spcciriedin the nner egionanddiec obtainedromsolution

or the ransport quationn dieouter egion.

Ilic constantsn the lengthscale onnulas, EquationsA 1.27andA1-32.am takcn from [A91:

CJOK p-V4.40, -70. .4,-2cl (A 1.33)

A1.23. Enhancedwall functions

Tohaveamethodhatcanextendtsapplicabilityhroughouthencar-%%Illegion i.e.. aminar

sublaycr, ufferregion,and ully-turbulent uter egion) t Isnecessaryo formulatehe aw-or-the

wallasasinglewall law rortheentirewall region.7lic codeachieveshisby blendinginear

Oaminar)and ogarithmicturbulent) aws-oklic-wallusinga functionsuggestedy Kadcr A I 11:

'%606



U+. Cr, -Jew. FL (A1-34)

where heblcnding unctionsgivcnby:

cj(v* (AI-35)I

c -exE

-1.0 (A 1-36)

a-O. Olc (AI-37)

bm5c

where -9.793 andE" scqualoElf, %ýeref,sa roughnessunction.

Similarly.hegcncralqu3tionor hederivative"*

is14WOO

_dutly, dy

(AI-38)

(AI-39)

'Mis approachallows the fully turbulent law to beeasily modified and extended o take nto account

odicr effectssuchaspressuregradientsor variablepropcrtics.This formula also guarantees ie

correctasymptoticbehaviour for largeandsmall valuesor J, andrcasonable eprcscntationof

velocity Profiles in die cases%%Iicrc* falls insidedie wall bulYcrrcSion(3 < j, " < 10).

Theenhanced all functionsweredevelopedysmoothly lendinganenlunccdurbulent%vallaw

widi the aminarwall law.Thecnhanccdurbulentaw-or-thc-%vallorcompressiblelow withheat

transfer ndpressureradients asbeen erivedbycombiningheapproachesf W1111Cnd

CristophA 12]and luangctal. [Al 31:

-

-k('-'1'-(yrv' A)'

(At-40)

261



hcre somI+ay* for 0" < ).. )

(AI4 1)11

+ a),, for (), * < y, )

and amv. dp p !/ip

r. u* dx dr

,on

C... T. lvpu*T.

(A142)

(A143)

y ff,

(Ully

(AI44)2c,,T.

%%here, is the ocationat which he og-lawslopewill remainixed.By derault, 60.The

cocfficicnta in EquationA140 representshe nfluencesrpressurc radients%Oilche

cocfYicients/7ndy representhermal ffccts.EquationA140 isan ordinarydifferentialequation

and hecodewill providean appropriatenalytical olution.ra. fl andy all equal0,ananalytical

solutionwould cad o theclassicalurbulentogarithmicaw-of-the-wall.

Tbclaminaraw-of-thc-walls determinedrom he ollowingexpression:

21*k= -I+

91Y(AI-43)

Note hat heaboveexpression nly includes frcctsorpressurc radientshrougha,%%Ililcle

aects orvariablepropertiesue o licat ransfer ndcompressibilitynOle aminarwall laware

neglected.1icsecffectsareneglected ecauseheyare hought o beof minor mporunce%%en

theyoccurcloseo alewall. Integration rEquationAl 43 resultsn,

# y. +a,,,AM(2)

(A 146)

Enhancedthcnnalwall functions ollowthe same pproachc%,clopcd ortheprofile or u*. ne

unifiedwall thmnal fonnulationblendshe iminar and ogarithmic rorilesaccordingo the

method f Kadcr A I fl:

I

crTL. + tj T (A 147)

262



here r= --- (AI48)I+b I'r' Y*

wherePr s themolecularPranddnumber, ndOiccoefficients andb aredefinedas n Equations

A1-37andA1.38.Apartfromtheaboveormulationor T%ctiliancedlicniial%%,ll functions

followthesameogicaspreviouslydescribedorstandard iernial%%illunctions. bcboundary

conditionor turbulence ineticenergys diesame s or standard all functionsEquationAl -21).

1owevcr,heproduction f turbulenceineticenergyGAscomputed sing hevelocitygradients

thatareconsistent ith dieenhanced3w-or-dic-wallEquations l-34 andA 1.39).cnsuring

formulationthat svalidthroughouthencar-wallegion.

Al. REFERENCES

Al. B. E.LaunderandD. 11.Spalding.

lActuresIn AlathernaticalModelsofTurl)ulcnce.

AcademicPress, ondon,England,1972.

A2. R.A. W. hi. I lenkes,F.F.vandcrFlugt,andC.J. I loogendoom.

Natural Convection Flow In a Square Cavity Calculated "11h LOw-licYnOlds-Number

Turbulence Models.

InI. J. lkatAlass 7Miqfer, 34: 1543-1557.1991.

A3. D. C.Wilcox,

Turbulence Modelling for CFI)-

DCWIndustries,nc., La Canada, alirOmiA, 998-

M. S.Sarkar ndL. 13alakrishnan,

Applicationorm tcynolds-SircssTurbulence %ItWclo file COMPfvssll)lchearLayer.

ICASERcport90.18,NASA CR 192002,1990.

AS. B. E.Loundcr ndD. B. Spalding,

TheNumericalComputationo(Turl)ulcnt Flo"s.

ComputcrMcthodsn Applicd MechanicsndEnginccdng. :269-289.1974.

1.63



A6. J. R.Vicgas,Nf. %V. ubcsin, ndC. C. I lorstman.

On the Useof Wall Functions as Boundary Conditions for TiAo-Dimensional-ScParated

Compressible Flows.

TechnicalReportAIAA-85-0180, AlAA 23rdAcrospice Scienceshlecting, Reno.Nevada, 1985.

A7. C. Jayntillckc,

The Influence of Prandil Number anti Surface Roughnesson the Resistanceof the Laminar

Sublayer to Afoinentum and I lent Transfer.

Prog.I featMassTransrcr,1: 193-321,1969.

A8. M. Wolrstein,The Velocity and Temperature Distribution or One-DImensional tlow -Ath Turbulence

Augmentation and PressureGradient.

Int.J. I IcatMassTransfer,12:301-318,1969.

A9. If. C. ChenandV. C. Patel,

Near-Wall Turbulence Models for Complex 11ows ncluding Separation.

AIAA Journal,26(6):641-648.1988.

A 10.T. Jongcn,

Siniulation und Nlodelling of Turbulent lnconipressit)10

11)iD iesis,EPF Lausanne,Lausanne,S%vl'ucrländ,992.

A 11.13.Kader,

Ternperature und Concenimlion Proralesn Fully Turbulent Iloundäry Lii)ert.

Int. J. 1 cat NiassTransfer, 24(9): 1541-1544,1993.

A 12. F. Mite andG. Christopli,

A Simple New Analysis of CompressibleTurbulent Skin rriction Under Arbitrary

Conditions.

Tcchnical RcportAr-FDL-Tit-70-133, rebruary 1971.

264



A13. P.Iluang,P. Bradshaw,andT. CoAlcy,

Skin Friction anti VelocityProfilc Family for Compressible urbulcnt BoundaryLayers.

AIAAJournal,31(9):1600-1604,cptctnbcr 993.

265



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Appendix 6

User Guide forthe EnhanceMixingAllodel UDF and the use 141thinhe2DAxisymnictric

CFD Model

The2DaxisymmaricCFDmodelneedso besetupo usearotating cfercnccrame.

71icorderof operations o set up and run theCFD modelwith die enhancedmixing modelUDr

is as follows,

1. Pcrfon-n conventional FDanalysiswith wall temperaturesf known)usingstandard

k-c urbulencemodeluntil a converged olution

sobtained.

2. Read n dieCFDmodel.cas,caseile.File-> Read-> Case...

3. Read n theschemeile, wall_viscosity.cm. rile ->Read.> Scheme...

4. In theUDr panel. ompile,ink and oad heUDFsource ode.

Define-> Uscr-Defined->

1. Functions->Compiled...

AddSource ile"comp_cnhanced-mixing."

LibraryName usedefaultnameibudo

PressBuildbutton

Press oadbutton

Setdie UDFFunction looks.

2. Functionsilooks...

Set heUDFhooks,nitialization-> initJactor andAdjust-> adjust-factor

Set henumber r UDFNlemoryocations.

3. Mcmory...

Set heNumber r User-Defmcd emoryLocationso 10

5. In the fluid matcriMspanelset hemodified nuid propertiesUDr- parameternanics,

Define -> Niatcri3ls->

I'liennal Conductivity > uscr-derined> factorc4_conductivity

Viscosity -> user-defined> factorcd-viscosity

chew packwood n turner

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