The book aims to aid designers, researchers and postgraduate students of pipes conveying fluid in predicting their dynamic behaviour for various flow velocities, fluid pressures and initial tensions as well as varying geometric and material properties. It also aims to provide practically useful information of interactions between fluids and structures. Throughout,numerical results are carefully compared with experimental observations, and conclusions drawn as to the appropriateness and accuracy of the models used.

Preface

List of Principal Symbols

Chapter 1 Introduction

 1.1 Background

 1.2 Objectives

 1.3 Procedures

 1.4 Outline of book

Chapter 2 Theoretical model I: elastic tubes conveying steady fluid flow

 2.1 Introduction

 2.2 Review of previous work

 2.3 Basic assumptions and description

 2.4 Finite element model development

2.4.1 Order of magnitude analysis

2.4.2 The dynamic equilibrium equation

 2.5 Numerical solution

2.5.1 Dynamic response

2.5.2 Eigenvalues and eigenvectors

 2.6 Analytical model

 2.7 Numerical results

 2.8 Conclusions

Chapter 3 Theoretical model H: elastic tubes conveying steady fluid flow

 3.1 Introduction

 3.2 Model formulation

 3.3 A numerical example

 3.4 Conclusions

Chapter 4 Theoretical model IH: viscoelastic tubes conveying steady fluid flow

 4.1 Introduction

 4.2 Finite element model of the system

4.2.1 The e]astic finite element model

4.2.2 Viscoelastic material properties

4.2.3 Single-degree-of-freedom viscoelastic system

4.2.4 Multi-degree-of-freedom viscoelastic system

 4.3 A numerical example

 4.4 Conclusions

Chapter 5 Experimental model I: tubes conveying steady fluid flow

 5.1 Introduction

 5.2 Experimental set-up

5.2.1 Hydraulic piping system

5.2.2 Exciting system

5.2.3 Sensing system

5.2.4 Data acquisition and processing system

 5.3 Experimental procedures and analysis

5.3.1 Experimental procedures

5.3.2 Experimental analysis

 5.4 Experimental measurement range

 5.5 Experimental uncertainty

 5.6 Experimental results

 5.7 Conclusions

Chapter 6 Comparison of experiment and theory: tubes conveying steady fluid flow

 6.1 Introduction

 6.2 Experimental and theoretical investigation

6.2.1 Experiment

6.2.2 Theory

 6.3 Comparison of measured and predicted dynamic response

6.3.1 Effect of initial axial tensions

6.3.2 Effect of flow velocities

 6.4 Comparison of measured and predicted natural frequencies

6.4.1  Effect of initial axial tensions

6.4.2 Effect of flow velocities

 6.5 Conclusions

Chapter 7 Theoretical model IV: Thin cylindrical shells conveying steady inviscid fluid flow

 7.1 Introduction

 7.2 Overview of previous work

 7.3 Governing equations

7.3.1 Shell equations

7.3.2 Fluid equations

 7.4 The method of solution

 7.5 Numerical examples

7.5.1 Convergence analysis

7.5.2 Model validation

7.5.3 Effect of initial axial tensions

7.5.4 Effect of hydrostatic pressures

7.5.5 Effect of the flow velocities

7.5.6 Effect of geometric properties

7.5.7 Effect of material properties

 7.6 Conclusions

Chapter 8 Theoretical model V: thick cylindrical shells conveying steady inviscid fluid flow

 8.1 Introduction

 8.2 Overview of previous work

 8.3 Formulation of the problem

8.3.1 The shell equation

8.3.2 The fluid equation

8.3.3 Boundary conditions

 8.4 Method of solution

8.4.1 Shell domain

8.4.2 Fluid domain

8.4.3 Coupling equation

 8.5 Results and discussion

8.5.1 Convergence analysis

8.5.2 Model validation

8.5.3 Effect of flow velocities

8.5.4 Effect of supported conditions

8.5.5 Effect of material properties

 8.6 Conclusions

Chapter 9 Comparative study of axisymmetrica thin cylindrical shells containing fluid

 9.1 Introduction

 9.2 Elemental mass and stiffness matrices

9.2.1 Cylindrical frustum elements

9.2.1.1 Frustum elements based on the Sanders' shell theory

9.2.1.2 Frustum elements based on the combination of the Sanders' shell theory and FEM

9.2.2 Isoparametric axisymmetrical shell elements

 9.3 Free vibration of axisymmetrical shells containing fluid

 9.4 Numerical examples

 9.5 Conclusions

Chapter 10 Theoretical model VI: cylindrical shells conveying steady viscous fluid flow

 10.1 Introduction

 10.2 Overview of previous work

 10.3 Governing equations

10.3.1 The Navier-Stokes equations

10.3.2 Shell equation

10.3.3 Boundary conditions

 10.4 Finite element formulation

 10.5 Fluid-structure coupling

 10.6 Results and discussion

 10.7 Conclusions

Chapter 11 Theoretical model VII: tubes conveying pulsatile viscous fluid flow

 11.1 Introduction

 11.2 Model formulation

 11.3 Methods of solution

11.3.1 Numerical solution I

11.3.1.1 FDM

11.3.1.2 MOC

11.3.1.3 The combination of FDM and MOC

11.3.2 Numerical solution II

11.3.2.1 FEM

11.3.2.2 MOC

 11.4 Numerical examples

11.4.1 Large wave speeds

11.4.2 Small wave speeds

 11.5 Conclusions

11.5.1 Large wave speeds

11.5.2 Small wave speeds

Chapter 12 Experimental model II : tubes conveying pulsatile fluid flow

 12.1 Introduction

 12.2 Experimental set-up and procedures

12.2.1 Pulsatile flow system

12.2.2 Instrumentation

12.2.3 Experimental procedures

 12.3 Experimental analysis

 12.4 Comparisons of measured and predicted results

 12.5 Conclusions

Chapter 13 Analysis of transient flow in pipelines with fluid-structure interaction

 13.1 Introduction

 13.2 Physical model

 13.3 Method of solution

 13.4 Numerical results

13.4.1 Validation

13.4.2 Damping mechanisms

13.4.3 Effect of Tc

 13.5 Conclusions

Chapter 14 Transient flow in rapidly filling air-entrapped pipelines

 14.1 Introduction

 14.2 Formulation of the problem

14.2.1 Fluid domain

14.2.2 Entrapped air domain

 14.3 Coordinate transformation and scaling

 14.4 Method of solution

 14.5 Numerical results and discussion

 14.6 Conclusions

Chapter 15 Theoretical study on charging-up process in pipelines with entrapped air

 15.1 Introduction

 15.2 Mathematical model

 15.3 Method of solution

 15.4 Numerical results

 15.5 Conclusions

References

Appendix 1 Characteristic equations and the Bessel function

Appendix 2 Isoparametric elements