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Analysis and Modelling of Non-Steady Flow in Pipe and Channel Networks

ISBN: 978-1-118-53688-9
544 pages
March 2013
Analysis and Modelling of Non-Steady Flow in Pipe and Channel Networks (1118536886) cover image

Description

Analysis and Modelling of Non-Steady Flow in Pipe and Channel Networks deals with flows in pipes and channel networks from the standpoints of hydraulics and modelling techniques and methods. These engineering problems occur in the course of the design and construction of hydroenergy plants, water-supply and other systems. In this book, the author presents his experience in solving these problems from the early 1970s to the present day. During this period new methods of solving hydraulic problems have evolved, due to the development of computers and numerical methods.

This book is accompanied by a website which hosts the author's software package, Simpip (an abbreviation of simulation of pipe flow) for solving non-steady pipe flow using the finite element method. The program also covers flows in channels. The book presents the numerical core of the SimpipCore program (written in Fortran).

Key features:

  • Presents the theory and practice of modelling different flows in hydraulic networks
  • Takes a systematic approach and addresses the topic from the fundamentals
  • Presents numerical solutions based on finite element analysis
  • Accompanied by a website hosting supporting material including the SimpipCore project as a standalone program

Analysis and Modelling of Non-Steady Flow in Pipe and Channel Networks is an ideal reference book for engineers, practitioners and graduate students across engineering disciplines.

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Table of Contents

Preface xiii

1 Hydraulic Networks 1

1.1 Finite element technique 1

1.2 Unified hydraulic networks 21

1.3 Equation system 23

1.4 Boundary conditions 28

1.5 Finite element matrix and vector 30

Reference 36

Further reading 36

2 Modelling of Incompressible Fluid Flow 37

2.1 Steady flow of an incompressible fluid 37

2.2 Gradually varied flow in time 59

2.3 Unsteady flow of an incompressible fluid 65

References 75

Further Reading 75

3 Natural Boundary Condition Objects 77

3.1 Tank object 77

3.2 Storage 90

3.3 Surge tank 91

3.4 Vessel 121

3.5 Air valves 128

3.6 Outlets 135

Reference 138

Further reading 138

4 Water Hammer – Classic Theory 141

4.1 Description of the phenomenon 141

4.2 Water hammer celerity 143

4.3 Water hammer phases 149

4.4 Under-pressure and column separation 164

4.5 Influence of extreme friction 167

4.6 Gradual velocity changes 171

4.7 Influence of outflow area change 176

4.8 Real closure laws 180

4.9 Water hammer propagation through branches 181

4.10 Complex pipelines 183

4.11 Wave kinematics 183

Reference 187

Further reading 187

5 Equations of Non-steady Flow in Pipes 189

5.1 Equation of state 189

5.2 Flow of an ideal fluid in a streamtube 195

5.3 The real flow velocity profile 202

5.4 Control volume 205

5.5 Mass conservation, equation of continuity 206

5.6 Energy conservation law, the dynamic equation 209

5.7 Flow models 215

5.8 Characteristic equations 220

5.9 Analytical solutions 225

Reference 229

Further reading 229

6 Modelling of Non-steady Flow of Compressible Liquid in Pipes 231

6.1 Solution by the method of characteristics 231

6.2 Subroutine UnsteadyPipeMtx 251

6.3 Comparison tests 261

Further reading 264

7 Valves and Joints 265

7.1 Valves 265

7.2 Joints 279

7.3 Test example 288

Reference 290

Further reading 290

8 Pumping Units 291

8.1 Introduction 291

8.2 Euler’s equations of turbo engines 291

8.3 Normal characteristics of the pump 295

8.4 Dimensionless pump characteristics 301

8.5 Pump specific speed 303

8.6 Complete characteristics of turbo engine 305

8.7 Drive engines 310

8.8 Numerical model of pumping units 314

8.9 Pumping element matrices 323

8.10 Examples of transient operation stage modelling 333

8.11 Analysis of operation and types of protection against pressure excesses 345

8.12 Something about protection of sewage pressure pipelines 353

8.13 Pumping units in a pressurized system with no tank 355

Reference 362

Further reading 362

9 Open Channel Flow 363

9.1 Introduction 363

9.2 Steady flow in a mildly sloping channel 363

9.3 Uniform flow in a mildly sloping channel 365

9.4 Non-uniform gradually varied flow 378

9.5 Sudden changes in cross-sections 398

9.6 Steady flow modelling 401

9.7 Wave kinematics in channels 407

9.8 Equations of non-steady flow in open channels 414

9.9 Equation of characteristics 422

9.10 Initial and boundary conditions 424

9.11 Non-steady flow modelling 425

References 434

Further reading 435

10 Numerical Modelling in Karst 437

10.1 Underground karst flows 437

10.2 Conveyance of the karst channel system 446

10.3 Modelling of karst channel flows 453

10.4 Method of catchment discretization 463

10.5 Rainfall transformation 468

10.6 Discretization of karst catchment with diffuse and channel flow 474

References 477

Further reading 477

11 Convective-dispersive Flows 479

11.1 Introduction 479

11.2 A reminder of continuum mechanics 479

11.3 Hydrodynamic dispersion 483

11.4 Equations of convective-dispersive heat transfer 485

11.5 Exact solutions of convective-dispersive equation 487

11.6 Numerical modelling in a hydraulic network 490

References 503

Further reading 503

12 Hydraulic Vibrations in Networks 505

12.1 Introduction 505

12.2 Vibration equations of a pipe element 506

12.3 Harmonic solution for the pipe element 508

12.4 Harmonic solutions in the network 509

12.5 Vibration source modelling 512

12.6 Hints to implementation in SimpipCore 512

12.7 Illustrative examples 515

Reference 518

Further reading 518

Index 519

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