Cavitation of hydraulic machinery

Cavitatio n o f

Hydrauli c Machiner y

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HYDRAULI C MACHINER Y BOO K SERIES

- Hydraulic Design of Hydraulic Machinery

Editor: Prof H Radha Krishna

- Mechanical Design and Manuíacturing of Hydraulic

Machinery

Editor: ProỊ Mei z Y

- Transỉent Phenomena of Hydraulic Machinery

Editors: Prof s Pejovic, Dr A p Boldy

- Cavitation of Hydraulic Machinery

Editor: Proị Li s c

- Erosion and Corrosion of Hydraulic Machinery

Editors: ProỊ Duan c G, ProỊ V Karelin

- Vibration and Oscillation of Hydraulic Machinery

Editor: PTOỊ H Ohashi

- Control of Hydraulic Machinery

Editor: ProỊ H Brekke

The International Editorial Committee (IECBSHM):

Chairman: ProỊ Duan c G

Treasurer: Dr R K Turton

Committee Members:

ProỊ H Brekke (Norway)

ProỊ E Egusquiza (Spain)

Dr H R Graze (Australia)

ProỊ p Henry (Switzerland).

ProỊ V Kareíin (USS)

ProỊ Li Sheng-cai (China)

ProỊ M Tadeu de Almeida (Brazil)

ProỊ M Matsumura (Japan)

ProỊ Ả Mobarak (Egypt)

ProỊ H Netsch (Canada)

Prof s Peịovic (Yugoslavia)

ProỊ H Petermann (Germany)

ProỊ c s Song (USA)

ProỊ Hans Ingo Weber (Brazil)

Honorary Members:

Prof B Chaiz (Switzerland)

Secretary: ProỊ Li s c

DĩÁP Boldy

Proị V p Chebaevski (USS)

ProỊ M Fanelli (Italy)

ProỊ R Guarga (Uruguay)

Dr H B Horlacher (Germany)

ProỊ G Krịvchenko (USS)

ProỊ Liu ỏ K (China)

PTOỊ c s Marùn (USA)

ProỊ Mei Zu-yan (China)

ProỊ H Murai (Japan)

ProỊ H Ohashi (Japan)

ProỊ D Perez-Franco (Cuba)

ProỊ H c Radha Krishna (India)

ProỊ c Thirriot (Prance)

ProỊ G Ziegler (Austria)

PTOỊ J Raabe (Germany)

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^ ị p SERIES ÔN HYDRAULIC MACHINERY - VOL.1

Committee Chairman: c. G. Duan Series Editor: s. c. Li

Cavitation of

Hydraulic Machinery

Edito r

s. c. Li

University oi Warwick, U.K.

Imperial College Press

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Published by

Imperial College Press

57 Shelton Strèet

Covent Garden

London WC2H 9HE

Distributed by

World Scìentific Publishing Co. Pte. Ltd.

p o Box 128, Farrer Road, Singapore 912805

USAọỊpce: Suite 1B, 1060 Main Street, RiverEdge, NJ 07661

UK offìce: 57 Shelton Strcet, Covent Ganíen, London WC2H 9HE

British Library Cataloguing-in-Publication Data

A cataloguerccorđforthis book is avaìlable from the British Library.

CAVITATION OF HYDRAULIC MACHINERY

Copyright © 2000 by Imperial College Press

AU rìghts reserved. This book, ÓT parts thereo/. may noi be reproduced in anyform or hy any means.

elecíronic ÓT mechanicaỉ, including photocopying, recordìng ÓT any in/ormation storage and retrievaì

system now known or to be invented, without writĩen permissionfrom the Publisher.

For photocopying of material in this volume, please pay a copying fee ihrough the Copyright

Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to

photocopy ìs nót required from the publisher.

ISBN 1-86094-257-1

Printed in Singapore by Ưto-Print

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CONTENTS

References

3 Bubble Dynamics

Part 1: Single Bubble

A Shima

3.1 Rayleigh Analysis

3.1.1 Besant's Problem

xui

XV

xix

Ì

Preface

Foreword of the Editor

Contributing Authors

Ì Introduction

s c Li

1.1 Cavitation Ị

1.1.1 Discovery

1.1.2 ClassiScation

1.2 Hydraulic Machinery and Cavitation

3

1.2.1 Problems Caused by Cavitation

3

1.2.2 Combating Cavitation

Reíerences

2 Cavitation and Cavitation Types

A J Acosta

2.1 Cavitation Phenomenon

2.1.1 Cavitation

2.1.2 Hydrodynamic Cavitation

2.2 Types oi Cavitation

2.2.1 Cavitation Index

2.2.2 Scale ESects and Cavitation Types 12

2.3 Cavitation Eữects

2.3.1 General Phenomena

2.3.2 InAuences ôn Machine Períormance 25

2.3.3 System Stability

2.4 Cavitation Nucleation and Inception

2.4.1 Inception

2.4.2 Nuclei Measurement

2.4.3 Concluding Remarks

3 8

40

5

24

24

28

30

30

47

47

47

47

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vi Contents

3.1.2 Rayleigh's Solution 48

3.2 Vaporous and Gaseous Bubbles 49

3.2.1 Classiíìcation 49

3.2.2 Stability 49

3.3 Viscosity and Compressibility Eíĩects 50

3.3.1 Eíĩects of Viscosity and Suríace Tension 50

3.3.2 Compressibility Eữect 50

3.4 Bubble Rebound 53

3.4.1 Introduction 53

3.4.2 Studies of Rebound 53

3.5 Nonspherical Collapse and Micro-jet Formation 54

3.5*1 Collapse near Solid Wall 54

3.5.2 Collapse in Contact with Solid Wall 55

3.6 Pressures Generated át Collapse 57

3.6.1 Impact Pressure and Their Modes 57

3.6.2 Temperature Effect 60

Reíerences 61

Part 2: Multi-Bubbles (stochastic Behaviour) 65

s c Li

3.7 Origins oi Bubble Stochasticity 65

3.7.1 Introduction 65

3.7.2 Bubble-Boundary Interaction 67

3.7.3 Bubble-Bubble iioteraction 73

3.7.4 Bubble-Flow Field Interaction 94

3.7.5 Remarks 115

3.8 Stochastic Models oi Cavitation Bubbles 117

3.8.1 Introduction 117

3.8.2 Single-Event Model 117

3.8.3 Muĩti-Event (Cluster) Model 118

3.8.4 Comprehensive Model 120

3.9 Power Spectrum 121

3.9.1 Introduction 121

3.9.2 Spectrum of Single-Bubble Collapse 121

3.9.3 Spectrum for Sequence of Single Events 127

3.9.4 Spectrum for Sequence ofClusters 137

3.9.5 Spectrum for Comprehensive Sequence 148

Reíerences 153

157

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Contents vii

4 Cavitating Plow

4.1 General Features 157

H Murai

4.1.1 Sheet Cavitation 157

4.1.2 Travelling Bubble Cavitation 160

4.1.3 Vortical Cavitation 161

4.1.4 Hydraulic Loss Caused by Cavitation 161

4.2 Hydroíoil and Hydroíoil Cascade 166

H Murai

4.2.1 Cavitation Characteristics of Hydroíoil 166

4.2.2 Cavitation Characteristics of Conventional

Airíoil Sections 170

4.2.3 Cavitation Characteristics of Ogival Hydroíoils 171

4.2.4 Cavitation Characteristics of Hydroíoil Cascade 175

4.2.5 Cavitation Characteristics of Conventional Airíoil

and Ogival Proíiles 176

4.2.6 HydroíoilProíìle Suitable for Decelerating

and Accelerating Cascades 180

4.2.7 Computer Simulation oi Partially Cavitating Foil 182

4.2.8 Supercavitating Hydroíoil 184

4.2.9 Supercavitating Hydrofoil Cascade 186

4.3 Control vâlves 187

E Outa

4.3.1 General Features oi Control Valve Cavitation 187

4.3.2 Cavitation Pictures of Globe Valve Flows 194

4.3.3 Cavitation Inception due to Vortex Growth 197

4.3.4 Cavitation Erosion and Anti-Cavitation Valves 202

References 205

5 Cavitation Phenomena in Hydraulic Machinery 211

5.1 General Features of Turbine Cavitation 211

H Tanaka

5.1.1 Cavitation in Prancis Turbines 211

5.1.2 Cavitation in Propeller Turbines 220

5.1.3 Cavitation in Pelton Turbines 225

5.1.4 Cavitation in Prancis Pump-Turbines 226

5.2 General Features of Pump Cavitation 229

R K Turton

5.2. 5.2.21 Introductio General Eíĩecn t ôn Pumps 222299

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viii Contents

5.2.3 Nét Positive Suction Head 232

5.2.4 Definition of Critical NPSHR 235

5.2.5 Implications for Pump Design 236

5.2.6 The Role of the Inducer 240

5.3 Pump Cavitation Similarity 242

V Chebaevsky and V Petrov

5.3.1 Problem Nature and Similarity Conditions 242

5.3.2 Thermodynamic Property Simulation 248

5.4 Cavitatiou Detection Techniques 251

E Egusquiza

5.4.1 Introduction 251

5.4.2 Generation of Noise and Vibration 252

5.4.3 Propagation 253

5.4.4 Background Noise 254

5.4.5 Cavitation Detection in Prequency Domain 255

5.4.6 Cavitation Detection in Time Domain 259

5.4.7 Cavitation Detection with Time-Prequency Analysis 263

Reíerences 265

6 Cavitation Damage to Hydraulic Machinery 269

6. Ì General Mechanism of Cavitation Damage 269

Y Iwai and T Okada

6.1.1 Introduction 269

6.1.2 Cavitation Bubble Collapse Pressures and Damage 269

6.1.3 Correlation between Erosion Resistance

and Mechanical Property 276

6.2 Cavitation Damage in Turbines 277

s c Li

6.2.1 Introduction 277

6.2.2 Propeller and Kaplan Turbines 285

6.2.3 Prancis Turbine 286

6.2.4 Pelton Turbine 290

6.2.5 Cavitation Guarantee 292

6.3 Cavitation Damage in Pumps 295

s c Li

6.3.1 Introduction 295

6.3.2 Axial Flow Pumps 295

6.3.3 Centriíugal Pumps 296

6.3.4 Pump-turbines 298

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Contents ix

6.3.5 Cavitation Guarantee 299

6.4 Silt-Laden Water EfFect 302

s c Li

6.4.1 Introduction 302

6.4.2 Silt Erosion 302

6.4.3 Synergism of Silt and Cavitation Erosions 307

6.5 High Resistance Materials 314

s e n

6.5.1 Introduction 314

6.5.2 Fused Materials 314

6.5.3 Non-fused Materials 330

6.6 Repair oi Machine 334

s c Li

6.6.1 Introduction 334

6.6.2 Cause of Damage 334

6.6.3 Main Concerns in Repair 336

6 6 4 Examples 343

References 353

7 Cavitation Caused Vibrations 359

7.1 Cavitation Pressure Pulsation in Turbines 359

7.1.1 Blade Cavity Pulsations 359

J Sato

7.1.2 Blade Wake Cavitation Pulsations 364

J Sato

7.1.3 Draft Tube Vortex Core Cavitation Pulsations 364

p Henry

7.2 Cavitation Induced Pulsations in Pumps 369

7.2.1 Introduction 369

R K Turton

7.2.2 Characteristics oi Cavitation Induced Pulsations 372

Y Tsujimoto

7.2.3 Mechanisms of Cavitation Induced Pulsations 376

Y Tsvýimoto

7.2.4 Cavitation Characteristics - Mass Flow Gain Factor

and Cavitation Compliance 380

Y Tsujimoto

7.3 InAuence of Operating Conditions 383

p Henry

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X Contents

7.3.1 Preliminary Discussion 383

7.3.2 Part Load Precession 383

7.3.3 80% Load Oscillations 388

7.3.4 Draft Tube Free Oscillations 388

7.3.5 Auto-oscillations 398

7.3.6 InAuence oi the Test Head 401

7.3.7 Thoma Number 403

7.4 Cavitation Resonance in Hydraulic Machinery Installations 405

p Henry

7.4.1 Introduction 405

7.4.2 Prototype Installation 405

7.4.3 Model Tests 409

7.4.4 Stability of the Prototype Installation 413

References 417

8 Unsteady Cavitation Flows Caused by Machine Transients 423

Part 1: Turbine Transients 423

c s Martin

8.1 Introduction 423

8.2 Types of Turbine Cavitation 424

8.2.1 Prancis Turbines 424

8.2.2 Kaplan Turbines 432

8.3 Draft-Tube Column Separation Incidents 433

8.4 Physical Modelling of Cavitating Transient Flows 436

8.5 Two-Phase Flow Modelling in Conduits 440

8.5.1 Acoustic Velocity 441

8.5.2 Slug Flow 444

8.6 Analytical Modelling oi Cavitating Transient Flows 444

Reíerences 445

Part 2: Pump Transients 451

H Tsukamoto

8.7 Introduction 451

8.8 Transient Cavitation in Discharge Lines 451

8.8.1 Transient Cavitation Type 451

8.8.2 Water Column Separation 453

8.9 Transient Cavitating Flow in Turbopumps 453

8.9.1 True Total Pressure Rise 453

8.9.2 Transient Behaviour of a Cavitating Pump 455

8.9.3 Transient Characteristics of Pump 457

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Contents xi

8.10 Computer Simulation of Cavitating Transient Flows

in Pump System 460

8.11 Concluding Remarks 461

Reíerences 463

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PREFACE

ít is a privilege to be asked to write a preíatory note ôn this remark￾able reíerence book, the latest in the Hydraulic Machinery book series. ít is

unusually wide in scope, ranging from basic research to engineering applica￾tions. Its publication marks the achievement of a large team of specialists

in cavitation research and in the design and operation of hydro-turbines and

storage pumps.

Although the problem of cavitation in machines is an old one, dating back

át least to the time of Galileo (16th century), Ít has nót yet been completely

solved. This is because hydraulic machines are faced with increasingly se￾vere períormance requirements demanded by economic pressures. The need

to provide cheaper designs involving smaller and more powerful machines

rotating át higher speeds continues to heighten the danger of cavitation.

Despite improved techniques thát have been developed for detecting and

measuring cavitation, and thereby assessing the damage capacity of cavitat￾ing flows, they do nót necessarily solve the problem, bút may nevertheless

provide useíul guidance for avoiding trouble.

The International Editorial Committee of the book series decided to ini￾tiate an úp to date review of the state of the art of coping with practical

cavitation problems in hydraulic machinery. An imposing team of twenty

specialists was íormed to cover topics ranging from basic cavitation research,

machine design and períormance, cavitation and abrasion damage and its

repair, and also cavitation induced machine vibration and transient oscil￾lations. A study of the chapter headings will show the particularly wide

variety of topics covered in one volume; Ít is also a welcome trend thát they

range from basic science/applied physics to engineering operations. This

has required a well conceived plan and efficient organisation by a patient

and indeíatigable Editor who has also written several of the sections. With

exemplary co-operation he and the other authors have been engaged for

twelve years in producing this comprehensive review of current knowledge.

Congratulations and thanks are thereíbre due to all concerned with launch￾ing and completing this monumental task. ì am sure thát all readers will be

most grateful to the international team's outstanding achievement in assem￾bling this treasure trove.

s.p. Hutton

Emeritus Proíessor

University of Southampton xiii

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Foreword of the Editor

The present book Cavitation of Hydraulic Machinery is a volume in the

Hydraulic Machinery book series. ít covers cavitation related subjects from

ủindamental mechanisms to practical applications in turbines and pumps1

.

Cavitation is one of the most unwanted phenomena in hydraulic machin￾ery despite the fact thát Ít does have some positive eíĩects in other íìelds. Al￾though a great advance in understanding this phenomenon has been achieved

in the last 100 years, our knowledge about cavitation is nót good enough to

precisely predict and completely solve this problem. Nowadays, most of the

cavitation related work in hydraulic machinery still, to a great extent, relies

ôn previous experience, model test and prototype observation.

After introducing cavitation and its relationship to hydraulic machines,

the rest oithis book falls naturally into two parts. The íìrst part,Chapters

2, 3 and 4, deals with the íundamental knowledge necessary for understand￾ing the cavitation involved in hydraulic machines. ít includes: cavitation

types, scale eíĩects, nucleation and inception,single bubble dynamics, multi￾bubble dynamics (bubble-bubble, bubble-boundary and bubble-flow inter￾actions), stochastic models of cavitation bubbles, noise spectra, cavitating

flows of hydro-íbil and cascade, cavitating characteristics of valves and other

hydraulic elements. The second part, Chapters 5, 6, 7 and 8, deals with

cavitation related themes in turbines and pumps such as cavitation íeatures,

similarities, cavitation detection techniques, cavitation damage mechanism

and íeatures,synergism of cavitation with silt erosion, material resistances to

cavitation damage, cavitation-damage repair, cavitation-induced pressure￾pulsations, cavitation resonance, cavitating transientflowand computersim￾ulation. As Ítisimpossible to include all relevantsubjects in a single volume,

careíul selection has been necessary. Only those basic concepts and new de￾velopments which are nót covered by existing books and review articles2

are

given in-depth treatment. Extensive lists of reíerences and íootnotes are

thus included to support the presentation and assist readers who want to

dig deeper.

A total of 17 authorsfrom 7 countries, all expertsin their chosen fields,

have made contributionsto the book. By drawing upon wide resources and

'As agreed át the Inaugural Meeting of the International Editorial Committee, the

Book Series would deal only with hydro-turbines and pumps.

2

Such as Cavitation by Knapp/Daily/Hammitt (1970), Cavitation hy Young (1989),

Cavitation and Bubbỉe Dynamics hy Brennen (1995) and 'Cavìtation in Fluid Machinery

and Hydraulic Structure' (Ann. Rev. Fluid XV Mích) hy Arndt (1981) etc.

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xvi Foreword of the Editor

experiences from North America, Europe, China, Russia, Japan etc, the

book aims to give a more balanced view oi the various topics. The editor

is greatly indebted to ai! the authorsfor their valuable contributions and

eíĩective cooperation over last 12 years. Without their great efforts, the

book would nót have been possible. In particular, ì would like to say a few

words in memory of Proíessor Pierre Henry who died ôn 26th April 1994

írom cancer. We miss him very much, he was only 54 and had built úp

the Lausanne Laboratory and established a brilliant reputation in unsteady

operating conditions due to cavitating vortices. The sections of §7.1.3, §7.3

and §7.4 he wrote were mainly based ôn thát remarkable work.

The structure and content of this book was originally proposed by the

editor in 1983 as a monograph to be written in collaboration with Proíessor

Predrick G. Hammitt (University oi Michigan, USA) as an eíĩort to bridge

the existing gap between íundamental cavitation phenomena and cavitation￾related subjectsin hydraulic machines. This book, together with another

proposed joint book ôn the topic of transients in hydraulic machines, sub￾sequently provided the inspiration for the Hydraulic Machinery book series.

The International Editorial Committee (IECBSHM) was established for this

purpose in 1986 in Beijing. Unfortunately, a deterioration in his health

denied Proíessor Hammitt the opportunity to participate in the book. Nev￾ertheless, his enthusiastic response to the editor's initial motion was a vital

support and encouragement. ì would like to take this opportunity to say a

special word of thanksin memory of Fred, who passed away in 1989.

In order to provide up-todate iníormation to our readers, authors were

allovved to amend their contributions right úp to the last minute, squeez￾ing the editing and compilation into the last few months. This presented

me with a very complicated and intensive job. The support of the follow￾ing persons was invaluable in achieving this. Many experts were invited

to review manuscripts. Their constructive criticism, comments, discussion

and suggestions are highly valued by the authors and the editor. They are

Professor Peter w Carpenter (Warwick ưniversity, UK), Professors Allan

Acosta, Dr. M L Billet and Proíessor c E Brennen (Caliíornia Institute of

Technology, USA), Dr. R K Turton (Loughborough University, UK) and Mr.

Harland Topham (Water Turbine and Pump Consultant, UK). Thanks also

go to Proíessor Duan c G and Dr A p Boldy oi IECBSHM for their support:

to Proíessor H Murai for his assistance in coordinating with some authors in

the early stage; to Dr. Tony Price and Dr. Wanda Lewis (Warwick University.

UKsity) for their advice; to Mrs. Wendy Murray (ÍT Services, Warwick Univer- ) for her assistance in preparing computer-editable source íìles from some

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Foreword of the EdỉtoT xvii

manuscripts; and to Mr. Alan Hulme (the Engineering Computer Manager)

and the secretaries for their effective support.

The constant support and encouragement received from Proíessor David

Anderson (the Chairman, School of Engineering) and Proíessor Peter w Car￾penter (the Head of the Division, Civil & Mechanical Engineering), and the

advice given by Dr s p Hutton (Proíessor Emeritus, University of Southamp￾ton, UK), who also wrote the preface, were greatly appreciated.

During the publishing process, the advice received from the commission￾ing editors, Dr John Navas, Mr Anthony Doyle, and the desk editor, Mr

Yeow Hwa Quek, was vital thát made this volume eventually available to

our readers.

My work ôn the book is supported in part by the National Research

Grant No 87022190 of Water aríd Power (China), the EPSRC (Engineer￾ing and Physic Science Research Council, UK) Grants (GR/F57977 and

GR/L74729), and the internal íunds of the School of Engineering, Warwick

University (UK).

The íigures in the book have come from a variety of sources. The ac￾knowledgement appears in the caption as a parenthetical reference keyed by

the name(s) of the original author(s) and a number to the list of reíerences

át the chapter end where the source is cited in full. A particular thank you

goes to Mr. R Stahel (Sulzer Hydro Ltd, Switzerland) who kindly supplied

me with the original photos of Figures 6.14, 6.23, 6.24, 6.26 and 6.27.

Finally, the editor is in great debt to his íaraily members for their un￾derstanding, support and íorbearance during the lengthy process oi writing

and editing this book.

LI s c, Editor

University oi Warwick

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