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Flow-InducedVibrationHandbook forNuclearandProcessEquipment

MichelJ.Pettigrew,ColetteE.Taylor,NigelJ.Fisher

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Contents

Preface xv Acknowledgments xvii

Contributors xix

1IntroductionandTypicalVibrationProblems 1 MichelJ.Pettigrew

1.1Introduction 1

1.2SomeTypicalComponentFailures 2

1.3DynamicsofProcessSystemComponents 9

1.3.1Multi-SpanHeatExchangerTubes 9

1.3.2OtherNuclearandProcessComponents 10

Notes 10

References 10

2Flow-InducedVibrationofNuclearandProcessEquipment:AnOverview 13 MichelJ.PettigrewandColetteE.Taylor

2.1Introduction 13

2.1.1Flow-InducedVibrationOverview 13

2.1.2ScopeofaVibrationAnalysis 14

2.2FlowCalculations 14

2.2.1FlowParameterDefinition 14

2.2.2SimpleFlowPathApproach 15

2.2.3Comprehensive3-DApproach 16

2.2.4Two-PhaseFlowRegime 18

2.3DynamicParameters 18

2.3.1HydrodynamicMass 18

2.3.2Damping 19

2.4VibrationExcitationMechanisms 25

2.4.1FluidelasticInstability 25

2.4.2RandomTurbulenceExcitation 27

2.4.3PeriodicWakeShedding 31

2.4.4AcousticResonance 34

2.4.5SusceptibilitytoResonance 35

2.5VibrationResponsePrediction 36

2.5.1FluidelasticInstability 37

2.5.2RandomTurbulenceExcitation 38

2.5.3PeriodicWakeShedding 38

2.5.4AcousticResonance 38

2.5.5ExampleofVibrationAnalysis 38

2.6Fretting-WearDamageConsiderations 40

2.6.1Fretting-WearAssessment 40

2.6.2Fretting-WearCoefficients 41

2.6.3WearDepthCalculations 42

2.7AcceptanceCriteria 42

2.7.1FluidelasticInstability 42

2.7.2RandomTurbulenceExcitation 43

2.7.3PeriodicWakeShedding 43

2.7.4Tube-to-SupportClearance 43

2.7.5AcousticResonance 43

2.7.6Two-PhaseFlowRegimes 43 Note 43 References 44

3FlowConsiderations 47

JohnM.Pietralik,LiberatN.Carlucci,ColetteE.Taylor,andMichelJ.Pettigrew

3.1DefinitionoftheProblem 47

3.2NatureoftheFlow 48

3.2.1Introduction 48

3.2.2FlowParameterDefinitions 50

3.2.3VerticalBubblyFlow 54

3.2.4FlowAroundBluffBodies 55

3.2.5Shell-SideFlowinTubeBundles 56

3.2.6Air-WaterversusSteam-WaterFlows 63

3.2.7EffectofNucleateBoilingNoise 63

3.2.8Summary 67

3.3SimplifiedFlowCalculation 67

3.4Multi-DimensionalThermalhydraulicAnalysis 74

3.4.1SteamGenerator 74

3.4.2OtherHeatExchangers 78 Acronyms 81 Nomenclature 81 Subscripts 82 Notes 83 References 83

4HydrodynamicMass,NaturalFrequenciesandModeShapes 87

DanielJ.Gorman,ColetteE.Taylor,andMichelJ.Pettigrew

4.1Introduction 87

4.2TotalTubeMass 88

4.2.1Single-PhaseFlow 89

4.2.2Two-PhaseFlow 90

4.3FreeVibrationAnalysisofStraightTubes 93

4.3.1FreeVibrationAnalysisofaSingle-SpanTube 94

4.3.2FreeVibrationAnalysisofaTwo-SpanTube 97

4.3.3FreeVibrationAnalysisofaMulti-SpanTube 99

4.4BasicTheoryforCurvedTubes 100

4.4.1TheoryofCurvedTubeIn-PlaneFreeVibration 102

4.4.2TheoryofCurvedTubeOut-of-PlaneFreeVibration 104

4.5FreeVibrationAnalysisofU-Tubes 105

4.5.1SettingBoundaryConditionsfortheIn-PlaneFreeVibrationAnalysisofU-Tubes PossessingGeometricSymmetry 106

4.5.2DevelopmentoftheIn-PlaneEigenvalueMatrixforaSymmetricU-Tube 109

4.5.3GenerationofEigenvalueMatricesforOut-of-PlaneFreeVibrationAnalysis ofU-TubesPossessingGeometricSymmetry 109

4.5.4FreeVibrationAnalysisofU-TubesWhichDoNotPossessGeometric Similarity 112

4.6ConcludingRemarks 114

Nomenclature 115 References 116

5DampingofCylindricalStructuresinSingle-PhaseFluids 119

MichelJ.Pettigrew

5.1Introduction 119

5.2EnergyDissipationMechanisms 119

5.3Approach 123

5.4DampinginGases 124

5.4.1EffectofNumberofSupports 127

5.4.2EffectofFrequency 128

5.4.3VibrationAmplitude 128

5.4.4EffectofDiameterorMass 128

5.4.5EffectofSideLoads 128

5.4.6EffectofHigherModes 129

5.4.7EffectofSupportThickness 129

5.4.8EffectofClearance 132

5.5DesignRecommendationsforDampinginGases 132

5.6DampinginLiquids 133

5.6.1Tube-to-FluidViscousDamping 133

5.6.2DampingattheSupports 136

5.6.3Squeeze-FilmDamping 138

5.6.4DampingduetoSliding 141

5.6.5Semi-EmpiricalFormulationofTube-SupportDamping 143

5.7Discussion 147

5.8DesignRecommendationsforDampinginLiquids 148

5.8.1SimpleCriterionBasedonAvailableData 148

5.8.2CriterionBasedontheFormulationofEnergyDissipationMechanisms 148

Nomenclature 149

Subscripts 150 References 151

6DampingofCylindricalStructuresinTwo-PhaseFlow 155

MichelJ.PettigrewandColetteE.Taylor

6.1Introduction 155

6.2SourcesofInformation 155

6.3Approach 157

6.4Two-PhaseFlowConditions 158

6.4.1DefinitionofTwo-PhaseFlowParameters 158

6.4.2FlowRegime 161

6.5ParametricDependenceStudy 162

6.5.1EffectofFlowVelocity 163

6.5.2EffectofVoidFraction 163

6.5.3EffectofConfinement 168

6.5.4EffectofTubeMass 168

6.5.5EffectofTubeVibrationFrequency 168

6.5.6EffectofTubeBundleConfiguration 169

6.5.7EffectofMotionofSurroundingTubes 169

6.5.8EffectofFlowRegime 170

6.5.9EffectofFluidProperties 171

6.6DevelopmentofDesignGuidelines 172

6.7Discussion 177

6.7.1DampingFormulation 177

6.7.2Two-PhaseDampingMechanisms 177

6.8SummaryRemarks 178

Nomenclature 178 Subscripts 179 Note 179 References 180

7FluidelasticInstabilityofTubeBundlesinSingle-PhaseFlow 183

MichelJ.PettigrewandColetteE.Taylor

7.1Introduction 183

7.2NatureofFluidelasticInstability 183

7.3FluidelasticInstability:AnalyticalModelling 185

7.4FluidelasticInstability:Semi-EmpiricalModels 186

7.5Approach 191

7.6ImportantDefinitions 191

7.6.1TubeBundleConfigurations 191

7.6.2FlowVelocityDefinition 191

7.6.3CriticalVelocityforFluidelasticInstability 196

7.6.4Damping 197

7.6.5TubeFrequency 198

7.7ParametricDependenceStudy 198

7.7.1FlexibleversusRigidTubeBundles 198

7.7.2Damping 201

7.7.3Pitch-to-DiameterRatio, P/D 201

7.7.4FluidelasticInstabilityFormulation 204

7.8DevelopmentofDesignGuidelines 206

7.9In-PlaneFluidelasticInstability 209

7.10AxialFlowFluidelasticInstability 212

7.11ConcludingRemarks 213

Nomenclature 214

Subscript 214 References 215

8FluidelasticInstabilityofTubeBundlesinTwo-PhaseFlow 219

MichelJ.PettigrewandColetteE.Taylor

8.1Introduction 219

8.2PreviousResearch 219

8.2.1Flow-InducedVibrationinTwo-PhaseAxialFlow 220

8.2.2Flow-InducedVibrationinTwo-PhaseCrossFlow 221

8.2.3DampingStudies 221

8.3FluidelasticInstabilityMechanismsinTwo-PhaseCrossFlow 221

8.4FluidelasticInstabilityExperimentsinAir-WaterCrossFlow 224

8.4.1InitialExperimentsinAir-WaterCrossFlow 224

8.4.2BehaviorinIntermittentFlow 227

8.4.3EffectofBundleGeometry 229

8.4.4FlexibleversusRigidTubeBundleBehavior 230

8.4.5HydrodynamicCoupling 232

8.5AnalysisoftheFluidelasticInstabilityResults 234

8.5.1DefiningCriticalMassFluxandInstabilityConstant 234

8.5.2ComparisonwithResultsofOtherResearchers 235

8.5.3SummaryofAir-WaterTests 238

8.6TubeBundleVibrationinTwo-PhaseFreonCrossFlow 239

8.6.1IntroductoryRemarks 239

8.6.2BackgroundInformation 240

8.6.3ExperimentsinFreonCrossFlow 240

8.7FreonTestResultsandDiscussion 244

8.7.1ResultsandAnalysis 244

8.7.2ProposedExplanations 247

8.7.3ConcludingRemarks 247

8.7.4SummaryFindings 249

8.8FluidelasticInstabilityofU-TubesinAir-WaterCrossFlow 250

8.8.1ExperimentalConsiderations 250

8.8.2U-TubeDynamics 251

8.8.3VibrationResponse 251

8.8.4Out-of-PlaneVibration 251

8.8.5In-PlaneVibration 254

Contents

8.9In-Plane(In-Flow)FluidelasticInstability 255

8.9.1In-FlowExperimentsinaWindTunnel 255

8.9.2In-FlowExperimentsinTwo-PhaseCrossFlow 255

8.9.3Single-TubeFluidelasticInstabilityResults 256

8.9.4SingleFlexibleColumnandCentralClusterFluidelasticInstabilityResults 258

8.9.5TwoPartiallyFlexibleColumns 258

8.9.6In-FlowFluidelasticInstabilityResultsandDiscussion 261

8.10DesignRecommendations 261

8.10.1DesignGuidelines 261

8.10.2FluidelasticInstabilitywithIntermittentFlow 263

8.11FluidelasticInstabilityinTwo-PhaseAxialFlow 264

8.12ConcludingRemarks 265

Nomenclature 265

Subscripts 266

Note 266 References 266

9RandomTurbulenceExcitationinSingle-PhaseFlow 271

ColetteE.TaylorandMichelJ.Pettigrew

9.1Introduction 271

9.2TheoreticalBackground 271

9.2.1EquationofMotion 272

9.2.2DerivationoftheMean-SquareResponse 273

9.2.3SimplificationofTubeVibrationResponse 274

9.2.4IntegrationoftheTransferFunction 275

9.2.5UseoftheSimplifiedExpressioninDevelopingDesignGuidelines 275

9.3LiteratureSearch 277

9.4ApproachTaken 277

9.5DiscussionofParameters 279

9.5.1DirectionalDependence(LiftversusDrag) 279

9.5.2BundleOrientation 279

9.5.3Pitch-to-DiameterRatio(P/D) 279

9.5.4UpstreamTurbulence 280

9.5.5FluidDensity(GasversusLiquid) 283

9.5.6Summary 283

9.6DesignGuidelines 284

9.7RandomTurbulenceExcitationinAxialFlow 287 Nomenclature 287 References 288

10RandomTurbulenceExcitationForcesDuetoTwo-PhaseFlow 291

ColetteE.TaylorandMichelJ.Pettigrew

10.1Introduction 291

10.2Background 291

10.3ApproachTakentoDataReduction 295

10.4ScalingFactorforFrequency 296

10.4.1DefinitionofaVelocityScale 297

10.4.2DefinitionofaLengthScale 298

10.4.3DimensionlessReducedFrequency 301

10.4.4EffectofFrequency 301

10.5ScalingFactorforPowerSpectralDensity 302

10.5.1EffectofFlowRegime 302

10.5.2EffectofVoidFraction 304

10.5.3EffectofMassFlux 306

10.5.4EffectofTubeDiameter 306

10.5.5EffectofCorrelationLength 306

10.5.6EffectofBundleandTube-SupportGeometry 307

10.5.7EffectofTwo-PhaseMixture 308

10.5.8EffectofNucleateBoiling 310

10.6DimensionlessPowerSpectralDensity 311

10.7UpperBoundsforTwo-PhaseCrossFlowDimensionlessSpectra 314

10.7.1BubblyFlow 314

10.7.2ChurnFlow 315

10.7.3IntermittentFlow 316

10.8AxialFlowRandomTurbulenceExcitation 318

10.9Conclusions 323 Nomenclature 324 References 325

11PeriodicWakeSheddingandAcousticResonance 329

DavidS.Weaver,ColetteE.Taylor,andMichelJ.Pettigrew

11.1Introduction 329

11.2PeriodicWakeShedding 332

11.2.1Frequency:StrouhalNumber 332

11.2.2CalculatingTubeResonanceAmplitudes 335

11.2.3FluctuatingForceCoefficientsinSingle-PhaseFlow 336

11.2.4FluctuatingForceCoefficientsinTwo-PhaseFlow 338

11.2.5TheEffectofBundleOrientationand P/D onFluctuatingForce Coefficients 346

11.2.6TheEffectofVoidFractionandFlowRegimeonFluctuatingForce Coefficients 347

11.3AcousticResonance 354

11.3.1AcousticNaturalFrequencies 354

11.3.2EquivalentSpeedofSound 355

11.3.3AcousticNaturalFrequencies (fa)n 356

11.3.4FrequencyCoincidence CriticalVelocities 356

11.3.5DampingCriteria 358

11.3.6SoundPressureLevel 361

11.3.7EliminationofAcousticResonance 364

11.4ConclusionsandRecommendations 366 Nomenclature 367 References 369

12AssessmentofFretting-WearDamageinNuclearandProcessEquipment 373

MichelJ.Pettigrew,MetinYetisir,NigelJ.Fisher,BruceA.W.Smith,andVictorP.Janzen

12.1Introduction 373

12.2DynamicCharacteristicsofNuclearStructuresandProcessEquipment 374

12.2.1HeatExchangers 374

12.2.2NuclearStructures 375

12.3Fretting-WearDamagePrediction 376

12.3.1Time-DomainApproach 376

12.3.2EnergyApproach 380

12.4Work-RateRelationships 380

12.4.1ShearWorkRateandMechanicalPower 380

12.4.2VibrationEnergyRelationship 381

12.4.3SingleDegree-of-FreedomSystem 381

12.4.4Multi-SpanBeamsUnderHarmonicExcitation 382

12.4.5ResponsetoRandomExcitation 382

12.4.6Work-RateEstimate:Summary 384

12.5ExperimentalVerification 384

12.6ComparisontoTimeDomainApproach 385

12.7PracticalApplications:Examples 386

12.8ConcludingRemarks 392 Nomenclature 392 Note 393 References 394

13Fretting-WearDamageCoefficients 397

NigelJ.FisherandFabriceM.Guérout

13.1Introduction 397

13.2Fretting-WearDamageMechanisms 397

13.2.1ImpactFrettingWear 397

13.2.2Trends 398

13.2.3Work-RateModel 402

13.3ExperimentalConsiderations 404

13.3.1ExperimentalStudies 404

13.3.2Room-TemperatureTestData 404

13.3.3High-TemperatureExperimentalFacility 407

13.3.4WearVolumeMeasurements 409

13.4FrettingWearofZirconiumAlloys 409

13.4.1Introduction 409

13.4.2ExperimentalSet-Up 410

13.4.3EffectofVibrationAmplitudeandMotionType 412

13.4.4EffectofPressure-TubePre-OxidationandSurfacePreparation 412

13.4.5EffectofTemperature 412

13.4.6EffectofpHControlAdditiveandDissolvedOxygenContent 413

13.4.7Discussions 414

13.5FrettingWearofHeatExchangerMaterials 417

13.5.1Work-RateModelandWearCoefficient 417

13.5.2EffectofTestDuration 419

13.5.3EffectofTemperature 422

13.5.4EffectofWaterChemistry 424

13.5.5EffectofTube-SupportGeometryandTubeMaterials 426

13.5.6Discussion 427

13.6SummaryandRecommendations 429

Nomenclature 429

Notes 429 References 430

ComponentAnalysis 433

Introduction 433

AnalysisofaProcessHeatExchanger 435 AnalysisofaNuclearSteamGeneratorU-Bend 445

SubjectIndex 463

Preface

Excessiveflow-inducedvibrationcausingfailuresbyfatigueorfrettingwearmustbeavoidedin processandnuclearcomponents.Thatisthepurposeofthishandbook.Inthisbook,thetermprocesscomponentsisusedgenerallytodescribenuclearreactorinternals,nuclearfuels,pipingsystems,andallshell-and-tubeheatexchangers,includingnuclearsteamgenerators,powerplant condensers,boilersandcoolers.

Therearealreadyanumberofgoodbooksonflow-inducedvibration.So,whyanotherone?This handbookistohelpengineerstodesign,operate,anddiagnoseheattransferequipment.The emphasisinthishandbookisontwo-phaseflow-inducedvibration.Despitethefactthatroughly halfofallheatexchangerequipmentoperatesintwo-phaseflow,previousflow-inducedvibration textshaveprovidedlimitedguidanceregardingvibrationinducedbytwo-phaseflow.Thepredictionoffretting-weardamageisanotherimportantpriority.Thestateoftheartispresentedinthe designguidelines,figuresandtables.Theuseofthesedesignguidelinesisillustratedwithexample calculations.Toassiststudentsandnewdesignengineers,thecalculationsaresupplementedand presentedwithmoreexplanationinanappendix.

Largely,thishandbookistheoutcomeofsome40yearsofresearchanddevelopmentattheCanadianNuclearLaboratories.Theemphasisofthisbookisthepresentationofdesignguidelinesbased onextensiveanalysisoftheliteratureand,inparticular,onexperimentaldataobtainedinthefield andattheCanadianNuclearLaboratoriesinChalkRiver.

Webelievethatthisbookwillbeusefultoengineeringdesignfirmsinthenuclear,petrochemical andaerospaceindustries,graduateschoolsinmechanicalengineeringandtechnicalsupportgroups inoperatingnuclearandpetrochemicalplants.Thishandbookisnotatextbook,althoughitcould beusedasaresourceinagraduatecourse.Wealsohopethatthisbookwillhelptostimulatefurther researchintheareaoftwo-phaseflow-inducedvibration.

Acknowledgments

Theauthorswouldliketorecognizetheinstitutionsandcolleagueswhohaveprovidedpermissions,supportandinspirationtothisproject.Webeginbyrecognizingthepublisherswhohave kindlygivenpermissiontousecopyrightedtablesandfigures.Ratherthanaddtherequestedrecognitionstatementstoeachfigure,thefollowinggeneralstatementsareprovidedtoavoid repetition.

• Figuresfromthe CongressoftheEngineeringInstituteofCanada(EIC) reprintedwithpermission fromtheEIC.

• Figuresfromthe InternationalAssociationforStructu ralMechanicsinReactorTechnology (IASMiRT)conferences reprintedcourtesyofIASMiRT.

• Figuresfrom ANLReports,copyrightbyArgonneNationalLaboratory,managedandoperatedby theUniversityofChicago,U.S.DepartmentofEnergy,reprintedwithpermission.

• Figuresfromthe NuclearPowerSafety,the JournalofFluidsandStructures,the JournalofSound andVibration,the JournalofMultiphaseFlow andthe JournalofNuclearEngineeringandDesign , reprintedwithpermissionfromElsevier.

• Figuresfrom ConvectiveBoilingandCondensation ,OxfordPublishingLimited,Oxford,GB, reproducedwithpermissionofOxford PublishingLimitedthroughPLSclear.

• Figuresfrom AEREreports reproducedwiththepermissionofUKAEAScientificPublications.

• Figuresfrom WashingtonStateUniversityReports reprintedwithpermissionfromtheWashingtonStateUniversityLibraries.

• Figuresfromthe 8 th InternationalHeatT ransferConference reprintedwithpermissionfrom BegellHouseInc.

• Figuresfromthe JournalofHeatTransferEngineering andthe JournalofNuclearScienceand Engineering ,reprintedwithpermissionofthepubli sher(Taylor&FrancisLtd,https://www. tand-fonline.com/)

• Figuresfrom AtomicEnergyofCanadaLtd.Reports,usedwithpermissionfromAECL.

Thisdocumentisbasedonsome40yearsofresearchanddevelopmentconductedatChalkRiver Laboratoriesintheareaofflow-inducedvibration.Thistechnologydevelopmenteffortwaslargely supportedbyAtomicEnergyofCanadaLimited(AECL)andbytheCANDUOwnersGroup(COG). ItalsoreceivedsupportfromtheHeatTransferandFluidFlowService(HTFS),theCentred’Etudes NucleairesdeSaclay(CEN-Saclay),thePressureVesselResearchCouncil(PVRC)andtheWashingtonPublicPowerSupplySystem(WPPSS).Thesupportofalltheseorganizationsisverygratefullyacknowledged.Manypeoplehavecontributedtothiseffortincludingcolleaguesfromindustry anduniversities.Recognizingthatwewillfailtoacknowledgeallofourpartners,wehavedecided tonamesomeofthekeyindividualsandinstitutions.

Theauthorshavebenefitedfromdiscussionswithresearchersinotherinstitutionssuchas F.AxisaandB.Villard,Centred’EtudesNucleairesdeSaclay;H.G.D.Goyder,UKAEAHarwell; R.T.Hartlen,OntarioHydro;N.W.MureithiandmanygraduatestudentsatÉcolePolytechnique, Montreal;I.G.Currie,UniversityofToronto;R.J.Rogers,UniversityofNewBrunswickand M.P.Païdoussis,McGillUniversity.

Visitingscientists,B.S.Kim,KoreaPowerEngineeringCompanyInc.,Taejon,Korea;A.Yasuo, CentralResearchInstituteofElectricPowerIndustry,Japan;andZ.L.Qiao,XianJiaotongUniversity,China,contributedtothedevelopmentoftheflow-inducedvibrationdatabase.

ThecontributorswouldalsoliketorecognizetheinputofcolleaguesfromtheCanadianNuclear Laboratoriesthroughoutthepast50years:J.Albrecht,K.M.Boucher,W.A.Cook,T.Dickinson, P.Feenstra,E.G.Hagberg,Y.Han,G.Knowles,J.Mastorakos,J.McGregor,K.Moore,J.N.Patrick, P.J.Smith,Y.Sylvestre,J.H.Tromp,M.K.Weckwerth,andT.Whan.Theseindividualsablyassisted withconstruction,instrumentationandinstallationofvariousflowloopsandtestsections,aswell ascopiousdataanalysis.

Finally,theauthorswishtoexpressourgratitudetoourunderstandingpartnersinlife,forallowingustotakethetimetowritethishandbookandfortheirmoralsupport. xviii Acknowledgments

Contributors

LiberatN.Carlucci