Flow-Induced Vibration Handbook for Nuclear and Process Equipment

Explains the mechanisms governing flow-induced vibrations and helps engineers prevent fatigue and fretting-wear damage at the design stage 

Fatigue or fretting-wear damage in process and plant equipment caused by flow-induced vibration can lead to operational disruptions, lost production, and expensive repairs. Mechanical engineers can help prevent or mitigate these problems during the design phase of high capital cost plants such as nuclear power stations and petroleum refineries by performing thorough flow-induced vibration analysis. Accordingly, it is critical for mechanical engineers to have a firm understanding of the dynamic parameters and the vibration excitation mechanisms that govern flow-induced vibration. 

Flow-Induced Vibration Handbook for Nuclear and Process Equipment provides the knowledge required to prevent failures due to flow-induced vibration at the design stage. The product of more than 40 years of research and development at the Canadian Nuclear Laboratories, this authoritative reference covers all relevant aspects of flow-induced vibration technology, including vibration failures, flow velocity analysis, vibration excitation mechanisms, fluidelastic instability, periodic wake shedding, acoustic resonance, random turbulence, damping mechanisms, and fretting-wear predictions. Each in-depth chapter contains the latest available lab data, a parametric analysis, design guidelines, sample calculations, and a brief review of modelling and theoretical considerations. Written by a group of leading experts in the field, this comprehensive single-volume resource: 

• Helps readers understand and apply techniques for preventing fatigue and fretting-wear damage due to flow-induced vibration at the design stage 
• Covers components including nuclear reactor internals, nuclear fuels, piping systems, and various types of heat exchangers 
• Features examples of vibration-related failures caused by fatigue or fretting-wear in nuclear and process equipment 
• Includes a detailed overview of state-of-the-art flow-induced vibration technology with an emphasis on two-phase flow-induced vibration 

Covering all relevant aspects of flow-induced vibration technology, Flow-Induced Vibration Handbook for Nuclear and Process Equipment is required reading for professional mechanical engineers and researchers working in the nuclear, petrochemical, aerospace, and process industries, as well as graduate students in mechanical engineering courses on flow-induced vibration.  

Michel J. Pettigrew is a specialist consultant on flow-induced vibration and related damage, an Adjunct Professor at Ecole Polytechnique in Montreal, and Principal Research Engineer (Emeritus) at the Chalk River Laboratories of Atomic Energy of Canada. He has conducted specialist courses for the nuclear, petrochemical, and mining industries in Canada and internationally. He holds five patents, authored over 300 publications and technical reports, and is a Fellow of both the American Society of Engineers and the Canadian Academy of Engineering.

Colette E. Taylor has served as the General Manager of Engineering and Chief Engineer at Canadian Nuclear Laboratories.

Nigel J. Fisher is an engineer at Canadian Nuclear Laboratories.

Preface xiii

Acknowledgments xv

Contributors xvii

1 Introduction and Typical Vibration Problems 1

Michel J. Pettigrew

1.1 Introduction 1

1.2 Some Typical Component Failures 2

1.3 Dynamics of Process System components 9

1.3.1 Multi-Span Heat Exchanger Tubes 9

1.3.2 Other Nuclear and Process Components 10

Note 10

References 10

2 Flow-Induced Vibration of Nuclear and Process Equipment: An Overview 13

Michel J. Pettigrew and Colette E. Taylor

2.1 Introduction 13

2.1.1 Flow-Induced Vibration Overview 13

2.1.2 Scope of a Vibration Analysis 14

2.2 Flow Calculations 14

2.2.1 Flow Parameter Definition 14

2.2.2 Simple Flow Path Approach 15

2.2.3 Comprehensive 3-D Approach 16

2.2.4 Two-Phase Flow Regime 18

2.3 Dynamic Parameters 18

2.3.1 Hydrodynamic Mass 18

2.3.2 Damping 19

2.4 Vibration Excitation Mechanisms 25

2.4.1 Fluidelastic Instability 25

2.4.2 Random Turbulence Excitation 27

2.4.3 Periodic Wake Shedding 31

2.4.4 Acoustic Resonance 34

2.4.5 Susceptibility to Resonance 35

2.5 Vibration Response Prediction 36

2.5.1 Fluidelastic Instability 37

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2.5.2 Random Turbulence Excitation 38

2.5.3 Periodic Wake Shedding 38

2.5.4 Acoustic Resonance 38

2.5.5 Example of Vibration Analysis 38

2.6 Fretting-Wear Damage Considerations 40

2.6.1 Fretting-Wear Assessment 40

2.6.2 Fretting-Wear Coefficients 41

2.6.3 Wear Depth Calculations 42

2.7 Acceptance Criteria 42

2.7.1 Fluidelastic Instability 42

2.7.2 Random Turbulence Excitation 43

2.7.3 Periodic Wake Shedding 43

2.7.4 Tube-to-Support Clearance 43

2.7.5 Acoustic Resonance 43

2.7.6 Two-Phase Flow Regimes 43

Note 43

References 44

3 Flow Considerations 47

John M. Pietralik, Liberat N. Carlucci, Colette E. Taylor, and Michel J. Pettigrew

3.1 Definition of the problem 47

3.2 Nature of the Flow 48

3.2.1 Introduction 48

3.2.2 Flow Parameter Definitions 50

3.2.3 Vertical Bubbly Flow 54

3.2.4 Flow Around Bluff Bodies 55

3.2.5 Shell-Side Flow in Tube Bundles 56

3.2.6 Air-Water versus Steam-Water Flows 63

3.2.7 Effect of Nucleate Boiling Noise 63

3.2.8 Summary 67

3.3 Simplified Flow Calculation 67

3.4 Multi-Dimensional Thermalhydraulic Analysis 74

3.4.1 Steam Generator 74

3.4.2 Other Heat Exchangers 78

Notes 83

References 83

4 Hydrodynamic Mass, Natural Frequencies and Mode Shapes 87

Daniel J. Gorman, Colette E. Taylor, and Michel J. Pettigrew

4.1 Introduction 87

4.2 Total Tube Mass 88

4.2.1 Single-Phase Flow 89

4.2.2 Two-Phase Flow 90

4.3 Free Vibration Analysis of Straight Tubes 93

4.3.1 Free Vibration Analysis of a Single-Span Tube 94

4.3.2 Free Vibration Analysis of a Two-Span Tube 97

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4.3.3 Free Vibration Analysis of a Multi-Span Tube 99

4.4 Basic Theory for Curved Tubes 100

4.4.1 Theory of Curved Tube In-Plane Free Vibration 102

4.4.2 Theory of Curved Tube Out-of-Plane Free Vibration 104

4.5 Free Vibration Analysis of U-Tubes 105

4.5.1 Setting Boundary Conditions for the In-Plane Free Vibration Analysis of U-Tubes

Possessing Geometric Symmetry 106

4.5.2 Development of the In-Plane Eigenvalue Matrix for a Symmetric U-Tube 109

4.5.3 Generation of Eigenvalue Matrices for Out-of-Plane Free Vibration Analysis of U-Tubes

Possessing Geometric Symmetry 109

4.5.4 Free Vibration Analysis of U-Tubes Which Do Not Possess Geometric Similarity 112

4.6 Concluding Remarks 114

References 116

5 Damping of Cylindrical Structures in Single-Phase Fluids 119

Michel J. Pettigrew

5.1 Introduction 119

5.2 Energy Dissipation Mechanisms 119

5.3 Approach 123

5.4 Damping in Gases 124

5.4.1 Effect of Number of Supports 127

5.4.2 Effect of Frequency 128

5.4.3 Vibration Amplitude 128

5.4.4 Effect of Diameter or Mass 128

5.4.5 Effect of Side Loads 128

5.4.6 Effect of Higher Modes 129

5.4.7 Effect of Support Thickness 129

5.4.8 Effect of Clearance 132

5.5 Design Recommendations for Damping in Gases 132

5.6 Damping in Liquids 133

5.6.1 Tube-to-Fluid Viscous Damping 133

5.6.2 Damping at the Supports 136

5.6.3 Squeeze-Film Damping 138

5.6.4 Damping due to Sliding 141

5.6.5 Semi-Empirical Formulation of Tube-Support Damping 143

5.7 Discussion 147

5.8 Design Recommendations for Damping in Liquids 148

5.8.1 Simple Criterion Based on Available Data 148

5.8.2 Criterion Based on the Formulation of Energy Dissipation Mechanisms 148

References 150

6 Damping of Cylindrical Structures in Two-Phase Flow 155

Michel J. Pettigrew and Colette E. Taylor

6.1 Introduction 155

6.2 Sources of Information 155

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6.3 Approach 157

6.4 Two-Phase Flow Conditions 158

6.4.1 Definition of Two-Phase Flow Parameters 158

6.4.2 Flow Regime 161

6.5 Parametric Dependence Study 162

6.5.1 Effect of Flow Velocity 163

6.5.2 Effect of Void Fraction 163

6.5.3 Effect of Confinement 168

6.5.4 Effect of Tube Mass 168

6.5.5 Effect of Tube Vibration Frequency 168

6.5.6 Effect of Tube Bundle Configuration 169

6.5.7 Effect of Motion of Surrounding Tubes 169

6.5.8 Effect of Flow Regime 170

6.5.9 Effect of Fluid Properties 171

6.6 Development of Design Guidelines 172

6.7 Discussion 177

6.7.1 Damping Formulation 177

6.7.2 Two-Phase Damping Mechanisms 177

6.8 Summary Remarks 178

Note 179

References 179

7 Fluidelastic Instability of Tube Bundles in Single-Phase Flow 183

Michel J. Pettigrew and Colette E. Taylor

7.1 Introduction 183

7.2 Nature of Fluidelastic Instability 183

7.3 Fluidelastic Instability: Analytical Modelling 185

7.4 Fluidelastic Instability: Semi-Empirical Models 186

7.5 Approach 191

7.6 Important Definitions 191

7.6.1 Tube Bundle Configurations 191

7.6.2 Flow Velocity Definition 196

7.6.3 Critical Velocity for Fluidelastic Instability 197

7.6.4 Damping 198

7.6.5 Tube Frequency 198

7.7 Parametric Dependence Study 198

7.7.1 Flexible Versus Rigid Tube Bundles 198

7.7.2 Damping 201

7.7.3 Pitch-to-Diameter Ratio, P/D 202

7.7.4 Fluidelastic Instability Formulation 204

7.8 Development of Design Guidelines 206

7.9 In-Plane Fluidelastic Instability 209

7.10 Axial Flow Fluidelastic Instability 212

7.11 Concluding Remarks 213

References 215

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8 Fluidelastic Instability of Tube Bundles in Two-Phase Flow 219

Michel J. Pettigrew and Colette E. Taylor

8.1 Introduction 219

8.2 Previous Research 219

8.2.1 Flow-Induced Vibration in Two-Phase Axial Flow 220

8.2.2 Flow-Induced Vibration in Two-Phase Cross Flow 221

8.2.3 Damping Studies 221

8.3 Fluidelastic Instability Mechanisms in Two-Phase Cross Flow 221

8.4 Fluidelastic Instability Experiments in Air-Water Cross Flow 224

8.4.1 Initial Experiments in Air-Water Cross Flow 224

8.4.2 Behavior in Intermittent Flow 227

8.4.3 Effect of Bundle Geometry 229

8.4.4 Flexible Versus Rigid Tube Bundle Behavior. 230

8.4.5 Hydrodynamic Coupling 232

8.5 Analysis of the Fluidelastic Instability Results 234

8.5.1 Defining Critical Mass Flux and Instability Constant 234

8.5.2 Comparison with Results of Other Researchers 235

8.5.3 Summary of Air-Water Tests 238

8.6 Tube Bundle Vibration in Two-Phase Freon Cross Flow 239

8.6.1 Introductory Remarks 239

8.6.2 Background Information 240

8.6.3 Experiments in Freon Cross Flow 240

8.7 Freon Test Results and Discussion 244

8.7.1 Results and Analysis 244

8.7.2 Proposed Explanations 247

8.7.3 Concluding Remarks 247

8.7.4 Summary Findings 249

8.8 Fluidelastic Instability of U-Tubes in Air-Water Cross Flow 250

8.8.1 Experimental Considerations 250

8.8.2 U-Tube Dynamics 251

8.8.3 Vibration Response 251

8.8.4 Out-of-Plane Vibration 251

8.8.5 In-Plane Vibration 254

8.9 In-Plane (In-Flow) Fluidelastic Instability 255

8.9.1 In-Flow Experiments in a Wind Tunnel 255

8.9.2 In-Flow Experiments in Two-Phase Cross Flow 255

8.9.3 Single-Tube Fluidelastic Instability Results 256

8.9.4 Single Flexible Column and Central Cluster Fluidelastic Instability Results 258

8.9.5 Two Partially Flexible Columns. 258

8.9.6 In-Flow Fluidelastic Instability Results and Discussion. 261

8.10 Design Recommendations 261

8.10.1 Design Guidelines 261

8.10.2 Fluidelastic Instability with Intermittent Flow 263

8.11 Fluidelastic Instability in Two-Phase Axial Flow 264

8.12 Concluding RemarkS 265

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Note 266

References 266

9 Random Turbulence Excitation in Single-Phase Flow 271

Colette E. Taylor and Michel J. Pettigrew

9.1 Introduction 271

9.2 Theoretical background 271

9.2.1 Equation of Motion 272

9.2.2 Derivation of the Mean Square Response 273

9.2.3 Simplification of Tube Vibration Response 274

9.2.4 Integration of the Transfer Function 275

9.2.5 Use of the Simplified Expression in Developing Design Guidelines 275

9.3 Literature Search 277

9.4 Approach Taken 277

9.5 Discussion of Parameters 279

9.5.1 Directional Dependence (Lift versus Drag) 279

9.5.2 Bundle Orientation 279

9.5.3 Pitch-to-Diameter Ratio (P/D) 279

9.5.4 Upstream Turbulence 280

9.5.5 Fluid Density (Gas versus Liquid) 283

9.5.6 Summary 283

9.6 Design Guidelines 284

9.7 Random Turbulence Excitation in Axial Flow 287

References 288

10 Random Turbulence Excitation Forces Due to Two-Phase Flow 291

Colette E. Taylor and Michel J. Pettigrew

10.1 Introduction 291

10.2 Background 291

10.3 Approach Taken to Data Reduction 295

10.4 Scaling Factor for Frequency 296

10.4.1 Definition of a Velocity Scale 297

10.4.2 Definition of a Length Scale 298

10.4.3 Dimensionless Reduced Frequency 301

10.4.4 Effect of Frequency 301

10.5 Scaling Factor for Power Spectral Density 302

10.5.1 Effect of Flow Regime 302

10.5.2 Effect of Void Fraction 304

10.5.3 Effect of Mass Flux 306

10.5.4 Effect of Tube Diameter 306

10.5.5 Effect of Correlation Length 306

10.5.6 Effect of Bundle and Tube-Support Geometry 307

10.5.7 Effect of Two-Phase Mixture 308

10.5.8 Effect of Nucleate Boiling 310

10.6 Dimensionless Power Spectral Density 311

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10.7 Upper Bounds for Two-Phase Cross Flow Dimensionless Spectra 314

10.7.1 Bubbly Flow 314

10.7.2 Churn Flow 315

10.7.3 Intermittent Flow 316

10.8 Axial Flow Random Turbulence Excitation 318

10.9 Conclusions 323

References 325

11 Periodic Wake Shedding and Acoustic Resonance 329

David S. Weaver, Colette E. Taylor, and Michel J. Pettigrew

11.1 Introduction 329

11.2 Periodic Wake Shedding 332

11.2.1 Frequency: Strouhal Number 332

11.2.2 Calculating Tube Resonance Amplitudes 335

11.2.3 Fluctuating Force Coefficients in Single-Phase Flow 336

11.2.4 Fluctuating Force Coefficients in Two-Phase Flow 338

11.2.5 The Effect of Bundle Orientation and P/D on Fluctuating Force Coefficients 347

11.2.6 The Effect of Void Fraction and Flow Regime on Fluctuating Force Coefficients 347

11.3 Acoustic Resonance 354

11.3.1 Acoustic Natural Frequencies 355

11.3.2 Equivalent Speed of Sound 355

11.3.3 Acoustic Natural Frequencies (fa )n, 356

11.3.4 Frequency Coincidence — Critical Velocities 356

11.3.5 Damping Criteria 358

11.3.6 Sound Pressure Level 361

11.3.7 Elimination of Acoustic Resonance 364

11.4 Conclusions and Recommendations 366

References 369

12 Assessment of Fretting-Wear Damage in Nuclear and Process Equipment 373

Michel J. Pettigrew, Metin Yetisir, Nigel J. Fisher, Bruce A.W. Smith, and Victor P. Janzen

12.1 Introduction 373

12.2 Dynamic Characteristics of Nuclear Structures and Process Equipment 374

12.2.1 Heat Exchangers 374

12.2.2 Nuclear Structures 375

12.3 Fretting-Wear Damage Prediction 376

12.3.1 Time Domain Approach 376

12.3.2 Energy Approach 380

12.4 Work-Rate Relationships 380

12.4.1 Shear Work Rate and Mechanical Power 380

12.4.2 Vibration Energy Relationship 381

12.4.3 Single Degree-of-Freedom System 381

12.4.4 Multi-Span Beams Under Harmonic Excitation 382

12.4.5 Response to Random Excitation 382

12.4.6 Work-Rate Estimate: Summary 384

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12.5 Experimental Verification 384

12.6 Comparison to Time Domain Approach 385

12.7 Practical Applications: Examples 386

12.8 Concluding Remarks 392

References 393

13 Fretting-Wear Damage Coefficients 397

Nigel J. Fisher and Fabrice M. Guérout

13.1 Introduction 397

13.2 Fretting-Wear Damage mechanisms 397

13.2.1 Impact Fretting Wear 397

13.2.2 Trends 399

13.2.3 Work-Rate Model 402

13.3 Experimental Considerations 404

13.3.1 Experimental Studies 404

13.3.2 Room-Temperature Test Data 404

13.3.3 High-Temperature Experimental Facility 407

13.3.4 Wear Volume Measurements 409

13.4 Fretting Wear of Zirconium Alloys 409

13.4.1 Introduction 409

13.4.2 Experimental Considerations 410

13.4.3 Effect of Vibration Amplitude and Motion Type 412

13.4.4 Effect of Pressure-Tube Pre-Oxidation and Surface Preparation 412

13.4.5 Effect of Temperature 412

13.4.6 Effect of pH Control Additive and Dissolved Oxygen Content 413

13.4.7 Discussions 414

13.5 Fretting Wear of Heat Exchanger Materials 417

13.5.1 Work-Rate Model and Wear Coefficient 417

13.5.2 Effect of Test Duration 419

13.5.3 Effect of Temperature 422

13.5.4 Effect of Water Chemistry 424

13.5.5 Effect of Tube-Support Geometry and Tube Materials 426

13.5.6 Discussion 427

13.6 Summary and Recommendations 429

13.6 Notes 429

References 430

Component Analysis 433

Introduction 433

Analysis of a process Heat Exchanger 435

Analysis of a nuclear Steam Generator U-Bend 445

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