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.
Preface xv Acknowledgments xvii Contributors xix 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 Notes 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 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 Acronyms 81 Nomenclature 81 Subscripts 82 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 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 Nomenclature 115 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 Nomenclature 149 Subscripts 150 References 151 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 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 Nomenclature 178 Subscripts 179 Note 179 References 180 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 191 7.6.3 Critical Velocity for Fluidelastic Instability 196 7.6.4 Damping 197 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 201 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 Nomenclature 214 Subscript 214 References 215 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 Nomenclature 265 Subscripts 266 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 Nomenclature 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 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 Nomenclature 324 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 346 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 354 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 Nomenclature 367 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 12.5 Experimental Verification 384 12.6 Comparison to Time Domain Approach 385 12.7 Practical Applications: Examples 386 12.8 Concluding Remarks 392 Nomenclature 392 Note 393 References 394 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 398 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 Set-Up 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 Nomenclature 429 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 Subject Index 463
Michel J. Pettigrew is Adjunct Professor at Ecole Polytechnique in Montreal, Canada and Principal Research Engineer (Emeritus) at the Chalk River Laboratories of Atomic Energy of Canada Limited. Colette E. Taylor, now retired, served as the General Manager of Engineering and Chief Engineer at Canadian Nuclear Laboratories. Nigel J. Fisher, now retired, served as Manager of the Inspection, Monitoring and Dynamics Branch and Senior Research Engineer at the Chalk River Laboratories of Atomic Energy of Canada Limited.
