Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications

FLOW MEASUREMENT HANDBOOK Flow Measurement Handbook is an information-packed reference for engineers on flow-measuring techniques and instruments. Striking a balance between laboratory ideal and the realities of field experience, it provides a wealth of practical advice on the design, operation, and performance of a broad range of flowmeters. The book begins with a brief review of essentials of accuracy and flow, how to select a flowmeter, and various calibration methods. Following this, each chapter is devoted to a class of flowmeter and includes detailed information on design, application, installation, calibration, operation, advantages, and disadvantages. Among the flowmeters discussed are orifice plates, venturi meters, standard nozzles, critical flow venturi nozzles, variable area and other devices depending on momentum of the flow, volumetric flowmeters such as positive displacement, turbine, vortex shedding, swirl, fluidic, electromagnetic and ultrasonic meters, and mass flowmeters including thermal and Coriolis. More than 80 different types and 250 applications are listed in the index. There are also chapters covering probes, a brief introduction to modern control, and manufacturing implications. For those readers who want more background information, many chapters conclude with an appendix on the mathematical theory behind the techniques discussed. The final chapter takes a look at directions in which the technology is likely to go in the future. Engineers will use this practical handbook to solve problems in flowmeter design and application and to improve performance. Roger C. Baker is a Visiting Industrial Fellow in the Manufacturing and Management Division of the Department of Engineering, University of Cambridge; Visiting Professor, Cranfield University; and Director of Technical Programmes, the Gatsby Charitable Foundation.

Flow Measurement Handbook INDUSTRIAL DESIGNS, OPERATING PRINCIPLES, PERFORMANCE, AND APPLICATIONS

ROGER C. BAKER

CAMBRIDGE

UNIVERSITY PRESS

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www. Cambridge. org Information on this title: www.cambridge.org/9780521480109 © Cambridge University Press 2000 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2000 This digitally printed first paperback version 2005 A catalogue recordfor this publication is available from the British Library Library of Congress Cataloguing in Publication data Baker, R. C. Flow measurement handbook : industrial designs, operating principles, performance, and applications / Roger C. Baker. p. cm. Includes bibliographical references. ISBN 0-521-48010-8 1. Flow meters - Handbooks, manuals, etc. I. Title. TA357.5.M43B35 2000 681'.28-dc21 99-14190 CIP ISBN-13 978-0-521-48010-9 hardback ISBN-10 0-521-48010-8 hardback ISBN-13 978-0-521-01765-7 paperback ISBN-10 0-521-01765-3 paperback DISCLAIMER Every effort has been made in preparing this book to provide accurate and up-to-date data and information that is in accord with accepted standards and practice at the time of publication and has been included in good faith. Nevertheless, the author, editors, and publisher can make no warranties that the data and information contained herein is totally free from error, not least because industrial design and performance is constantly changing through research, development, and regulation. Data, discussion, and conclusions developed by the author are for information only and are not intended for use without independent substantiating investigation on the part of the potential users. The author, editors, and publisher therefore disclaim all liability or responsibility for direct or consequential damages resulting from the use of data, designs, or constructions based on any of the information supplied or materials described in this book. Readers are strongly advised to pay careful attention to information provided by the manufacturer of any equipment that they plan to use and should refer to the most recent standards documents relating to their application. The author, editors, and publisher wish to point out that the inclusion or omission of a particular device, design, application, or other material in no way implies anything about its performance with respect to other devices, etc.

To Liz, Sarah and Paul, Mark, John and Rachel

Contents

Preface

page xix

Acknowledgments Nomenclature CHAPTER 1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Introduction

Initial Considerations Do We Need a Flowmeter? How Accurate? A Brief Review of the Evaluation of Standard Uncertainty Sensitivity Coefficients What Is a Flowmeter? Chapter Conclusions (for those who plan to skip the mathematics!) Mathematical Postscript i.A Statistics of Flow Measurement Introduction The Normal Distribution The Student t Distribution Practical Application of Confidence Level Types of Error Combination of Uncertainties Uncertainty Range Bars, Transfer Standards, and Youden Analysis

APPENDIX

l.A.l 1.A.2 1.A.3 1.A.4 I.A.5 1.A.6 I.A.7

xxi xxiii l

1 2 4 7 9 9 13 15 15 15 16 17 19 20 21 21

CHAPTER 2 Fluid Mechanics Essentials

24

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

24 24 24 27 30 32 34 36 38 39

Introduction Essential Property Values Flow in a Circular Cross-Section Pipe Flow Straighteners and Conditioners Essential Equations Unsteady Flow and Pulsation Compressible Flow Multiphase Flow Cavitation, Humidity, Droplets, and Particles Gas Entrapment

CONTENTS

2.11 2.12

Steam Chapter Conclusions

CHAPTER 3 Specification, Selection, and Audit 3.1 Introduction 3.2 Specifying the Application 3.3 Notes on the Specification Form 3.4 Flowmeter Selection Summary Tables 3.5 Other Guides to Selection and Specific Applications 3.6 Draft Questionnaire for Flowmeter Audit 3.7 Final Comments APPENDIX 3.A Specification and Audit Questionnaires 3.A.1 Specification Questionnaire 3.A.2 Supplementary Audit Questionnaire CHAPTER 4

4.1

4.2 4.3

4.4

4.5 4.6 4.7 4.8 4.9

Introduction 4.1.1 Calibration Considerations 4.1.2 Typical Calibration Laboratory Facilities 4.1.3 Calibration from the Manufacturer's Viewpoint Approaches to Calibration Liquid Calibration Facilities 4.3.1 Flying Start and Stop 4.3.2 Standing Start and Stop 4.3.3 Large Pipe Provers 4.3.4 Compact Provers Gas Calibration Facilities 4.4.1 Volumetric Measurement 4.4.2 Mass Measurement 4.4.3 Gas/Liquid Displacement 4.4.4 pvT Method 4.4.5 Critical Nozzles 4.4.6 Soap Film Burette Method Transfer Standards and Master Meters In Situ Calibration Calibration Uncertainty Traceability and Accuracy of Calibration Facilities Chapter Conclusions

CHAPTER

5.1 5.2 5.3 5.4 5.5

Calibration

5 Orifice Plate Meters

Introduction Essential Background Equations Design Details Installation Constraints Other Orifice Plates

39 41 42 42 42 43 46 53 55 55 56 56 58 61

61 61 64 65 66 69 69 72 74 74 77 77 79 80 80 81 81 82 84 91 92 93 95 95 97 100 102 106

CONTENTS

5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17

Deflection of Orifice Plate at High Pressure Effect of Pulsation Effects of More Than One Flow Component Accuracy Under Normal Operation Industrially Constructed Designs Pressure Connections Pressure Measurement Temperature and Density Measurement Flow Computers Detailed Studies of Flow Through the Orifice Plate, Both Experimental and Computational Application, Advantages, and Disadvantages Chapter Conclusions

106 109 113 117 118 119 122 124 124

APPENDIX 5.A Orifice Discharge Coefficient

128

CHAPTER

6.1 6.2 6.3 6.4 6.5 6.6 6.7

Introduction Essential Background Equations Design Details Commercially Available Devices Installation Effects Applications, Advantages, and Disadvantages Chapter Conclusions

CHAPTER

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11

6 Venturi Meter and Standard Nozzles

7 Critical Flow Venturi Nozzle

Introduction Design Details of a Practical Flowmeter Installation Practical Equations Discharge Coefficient C Critical Flow Function C* Design Considerations Measurement Uncertainty Example Industrial and Other Experience Advantages, Disadvantages, and Applications Chapter Conclusions

124 127 127

130 130 131 134 135 135 137 138 140 140 141 143 145 146 147 148 149 151 152 152

CHAPTER 8 Other Momentum-Sensing Meters

153

8.1 8.2

153 153 154 154 155 156 157

Introduction Variable Area Meter 8.2.1 Operating Principle and Background 8.2.2 Design Variations 8.2.3 Remote Readout Methods 8.2.4 Design Features 8.2.5 Calibration and Sources of Error

CONTENTS

8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14

8.2.6 Installation 8.2.7 Unsteady and Pulsating Flows 8.2.8 Industrial Types, Ranges, and Performance 8.2.9 Computational Analysis of the Variable Area Flowmeter 8.2.10 Applications Spring-Loaded Diaphragm (Variable Area) Meters Target (Drag Plate) Meter Integral Orifice Meters Dall Tubes and Devices that Approximate to Venturis and Nozzles Wedge and V-Cone Designs Differential Devices with a Flow Measurement Mechanism in the Bypass Slotted Orifice Plate Pipework Features - Inlets Pipework Features - Bend or Elbow Used as a Meter Averaging Pitot Laminar or Viscous Flowmeters Chapter Conclusions APPENDIX 8.A History, Equations, and Accuracy Classes for the VA Meter 8.A.1 Some History 8.A.2 Equations 8.A.3 Accuracy Classes

157 158 158 159 159 159 162 163 163 165 167 168 168 169 170 173 176 177 177 178 180

CHAPTER 9 Positive Displacement Flowmeters

182

9.1

182 182 183 184 184 184 185 185 187 189 190 190

9.2

9.3

Introduction 9.1.1 Background 9.1.2 Qualitative Description of Operation Principal Designs of Liquid Meters 9.2.1 Nutating Disk Meter 9.2.2 Oscillating Circular Piston Meter 9.2.3 Multirotor Meters 9.2.4 Oval Gear Meter 9.2.5 Sliding Vane Meters 9.2.6 Helical Rotor Meter 9.2.7 Reciprocating Piston Meters 9.2.8 Precision Gear Flowmeters Calibration, Environmental Compensation, and Other Factors Relating to the Accuracy of Liquid Flowmeters 9.3.1 Calibration Systems 9.3.2 Clearances 9.3.3 Leakage Through the Clearance Gap Between Vane and Wall 9.3.4 Slippage Tests 9.3.5 The Effects of Temperature and Pressure Changes 9.3.6 The Effects of Gas in Solution

191 192 194 194 196 197 197

CONTENTS

9.4 9.5

9.6 9.7 9.8 9.9

Accuracy and Calibration Principal Designs of Gas Meters 9.5.1 Wet Gas Meter 9.5.2 Diaphragm Meter 9.5.3 Rotary Positive Displacement Gas Meter Positive Displacement Meters for Multiphase Flows Meter Using Liquid Plugs to Measure Low Flows Applications, Advantages, and Disadvantages Chapter Conclusions

198 199 199 200 202 203 205 205 206

APPENDIX 9.A Theory for a Sliding Vane Meter 9.A.I Flowmeter Equation 9.A.2 Expansion of the Flowmeter Due to Temperature 9.A.3 Pressure Effects 9.A.4 Meter Orientation 9.A.5 Analysis of Calibrators 9.A.6 Application of Equations to a Typical Meter

207 207 209 210 210 211 213

10 Turbine and Related Flowmeters

21^

Introduction 10.1.1 Background 10.1.2 Qualitative Description of Operation 10.1.3 Basic Theory Precision Liquid Meters 10.2.1 Principal Design Components 10.2.2 Bearing Design Materials 10.2.3 Strainers 10.2.4 Materials 10.2.5 Size Ranges 10.2.6 Other Mechanical Design Features 10.2.7 Cavitation 10.2.8 Sensor Design and Performance 10.2.9 Characteristics 10.2.10 Accuracy 10.2.11 Installation 10.2.12 Maintenance 10.2.13 Viscosity, Temperature, and Pressure 10.2.14 Unsteady Flow 10.2.15 Multiphase Flow 10.2.16 Signal Processing 10.2.17 Applications 10.2.18 Advantages and Disadvantages Precision Gas Meters 10.3.1 Principal Design Components 10.3.2 Bearing Design 10.3.3 Materials 10.3.4 Size Range 10.3.5 Accuracy

215 215 215 216 221 221 223 224 224 225 225 226 227 228 228 229 231 232 232 232 233 233 234 234 234 235 236 236 236

CHAPTER

10.1

10.2

10.3

CONTENTS

10.4

10.5

10.6

10.3.6 Installation 10.3.7 Sensing 10.3.8 Unsteady Flow 10.3.9 Applications 10.3.10 Advantages and Disadvantages Water Meters 10.4.1 Principal Design Components 10.4.2 Bearing Design 10.4.3 Materials 10.4.4 Size Range 10.4.5 Sensing 10.4.6 Characteristics and Accuracy 10.4.7 Installation 10.4.8 Special Designs Other Propeller and Turbine Meters 10.5.1 Quantum Dynamics Flowmeter 10.5.2 Pelton Wheel Flowmeters 10.5.3 Bearingless Flowmeter 10.5.4 Vane-Type Flowmeters Chapter Conclusions 10.A Turbine Flowmeter Theory Derivation of Turbine Flowmeter Torque Equations Transient Analysis of Gas Turbine Flowmeter

APPENDIX

10.A.1 10.A.2

237 238 238 240 241 241 241 242 243 243 243 243 244 244 244 244 244 245

245 245 246 246 251

CHAPTER 11 1Cortex-Shedding, Swirl, and Fluidic Flowmeters

253

11.1 11.2 11.3

253 253 254 255 257 259 260 263 264 264 264 267 267

11.4

Introduction Vortex Shedding Industrial Developments of Vortex-Shedding Flowmeters 11.3.1 Experimental Evidence of Performance 11.3.2 Bluff Body Shape 11.3.3 Standardization of Bluff Body Shape 11.3.4 Sensing Options 11.3.5 Cross Correlation and Signal Interrogation Methods 11.3.6 Other Aspects Relating to Design and Manufacture 11.3.7 Accuracy 11.3.8 Installation Effects 11.3.9 Effect of Pulsation and Pipeline Vibration 11.3.10 Two-Phase Flows 11.3.11 Size and Performance Ranges and Materials in Industrial Designs 11.3.12 Computation of Flow Around Bluff Bodies 11.3.13 Applications, Advantages, and Disadvantages 11.3.14 Future Developments Swirl Meter - Industrial Design 11.4.1 Design and Operation 11.4.2 Accuracv and Ranges

268 269 270

271 272 272 273

CONTENTS

11.5

11.6 11.7

11.4.3 Materials 11.4.4 Installation Effects 11.4.5 Applications, Advantages, and Disadvantages Fluidic Flowmeter 11.5.1 Design 11.5.2 Accuracy 11.5.3 Installation Effects 11.5.4 Applications, Advantages, and Disadvantages Other Proposed Designs Chapter Conclusions li.A Vortex-Shedding Frequency Vortex Shedding from Cylinders Order of Magnitude Calculation of Shedding Frequency

APPENDIX

11.A.I 11.A.2

273 273 273 274 274 275 276 276 276 276 278 278 279

CHAPTER 12 Electromagnetic Flowmeters

282

12.1 12.2 12.3 12.4

Introduction Operating Principle Limitations of the Theory Design Details 12.4.1 Sensor or Primary Element 12.4.2 Transmitter or Secondary Element Calibration and Operation Industrial and Other Designs Installation Constraints - Environmental 12.7.1 Surrounding Pipe 12.7.2 Temperature and Pressure Installation Constraints - Flow Profile Caused by Upstream Pipework 12.8.1 Introduction 12.8.2 Theoretical Comparison of Meter Performance Due to Upstream Flow Distortion 12.8.3 Experimental Comparison of Meter Performance Due to Upstream Flow Distortion 12.8.4 Conclusions on Installation Requirements Installation Constraints - Fluid Effects 12.9.1 Slurries 12.9.2 Change of Fluid 12.9.3 Nonuniform Conductivity Multiphase Flow Accuracy Under Normal Operation Applications, Advantages, and Disadvantages 12.12.1 Applications 12.12.2 Advantages 12.12.3 Disadvantages Chapter Conclusions

282 282 284 286 286 289 292 293 295 296 296 297 297

APPENDIX 12.A Brief Review of Theory 12. A.I Introduction

305 305

12.5 12.6 12.7

12.8

12.9

12.10 12.11 12.12

12.13

297 298 299 300 300 300 300 301 301 302 302 303 303 304

CONTENTS

12.A.2 12.A.3 12.A.4 12.A.5 12.A.6 12.A.7

Electric Potential Theory Development of the Weight Vector Theory Rectilinear Weight Function Axisymmetric Weight Function Performance Prediction Further Extensions to the Theory

307 307 308 310 310 311

CHAPTER 13 Ultrasonic Flowmeters

312

13.1 13.2

312 315 315

13.3 13.4 13.5 13.6

13.7

13.8

13.9 13.10

13.11

13.12 13.13

Introduction Transit-Time Flowmeters 13.2.1 Simple Explanation 13.2.2 Flowmeter Equation and the Measurement of Sound Speed 13.2.3 Effect of Flow Profile and Use of Multiple Paths Transducers Size Ranges and Limitations Signal Processing and Transmission Accuracy 13.6.1 Reported Accuracy - Liquids 13.6.2 Reported Accuracy - Gases 13.6.3 Manufacturers' Accuracy Claims 13.6.4 Special Considerations for Clamp-On Transducers Installation Effects 13.7.1 Effects of Distorted Profile by Upstream Fittings 13.7.2 Unsteady and Pulsating Flows 13.7.3 Multiphase Flows General Published Experience in Transit-Time Meters 13.8.1 Experience with Liquid Meters 13.8.2 Gas Meter Developments Applications, Advantages, and Disadvantages Doppler Flowmeter 13.10.1 Simple Explanation of Operation 13.10.2 Operational Information 13.10.3 Applications, Advantages, and Disadvantages Correlation Flowmeter 13.11.1 Operation of the Correlation Flowmeter 13.11.2 Installation Effects 13.11.3 Other Published Work 13.11.4 Applications, Advantages, and Disadvantages Other Ultrasonic Applications Chapter Conclusions APPENDIX 13.A Simple Mathematical Methods and Weight Function Analysis Applied to Ultrasonic Flowmeters 13.A.1 Simple Path Theory 13.A.2 Use of Multiple Paths to Integrate Flow Profile 13.A.3 Weight Vector Analysis 13.A.4 Doppler Theory

316 319 322 325 325 327 327 327 328 328 330 330 334 335 335 335 338 344 345 345 346 346 346 346 347 348 349 349 350 351 351 353 355 355

CONTENTS CHAPTER 14 Mass Flow Measurement Using Multiple Sensors for Single- and Multiphase Flows

14.1 14.2

14.3 14.4

14.5

Introduction Multiple Differential Pressure Meters 14.2.1 Hydraulic Wheatstone Bridge Method 14.2.2 Theory of Operation 14.2.3 Industrial Experience 14.2.4 Applications Multiple Sensor Methods Multiple Sensor Meters for Multiphase Flows 14.4.1 Background 14.4.2 Categorization of Multiphase Flowmeters 14.4.3 Multiphase Metering for Oil Production Chapter Conclusions 14.5.1 What to Measure If the Flow Is Mixed 14.5.2 Usable Physical Effects for Density Measurement 14.5.3 Separation or Multicomponent Metering 14.5.4 Calibration 14.5.5 Accuracy

CHAPTER

15.1 15.2

15.3 15.4

15.5

15.6

15 Thermal Flowmeters

357 357 357 359 359 360 361 361 362 362 363 365 367 367 368 369 369 370 371

Introduction Capillary Thermal Mass Flowmeter - Gases 15.2.1 Description of Operation 15.2.2 Operating Ranges and Materials for Industrial Designs 15.2.3 Accuracy 15.2.4 Response Time 15.2.5 Installation 15.2.6 Applications Calibration of Very Low Flow Rates Thermal Mass Flowmeter - Liquids 15.4.1 Operation 15.4.2 Typical Operating Ranges and Materials for Industrial Designs 15.4.3 Installation 15.4.4 Applications Insertion and In-Line Thermal Mass Flowmeters 15.5.1 Insertion Thermal Mass Flowmeter 15.5.2 In-Line Thermal Mass Flowmeter 15.5.3 Range and Accuracy 15.5.4 Materials 15.5.5 Installation 15.5.6 Applications Chapter Conclusions

371 371 371 374 374 374 375 376 376 376 376 377 378 378 378 379 381 381 381 381 382 383

15.A Mathematical Background to the Thermal Mass Flowmeters 15.A.I Dimensional Analysis Applied to Heat Transfer 15.A.2 Basic Theory of ITMFs

384 384 385

APPENDIX

CONTENTS

15.A.3 General Vector Equation 15.A.4 Hastings Flowmeter Theory 15.A.5 Weight Vector Theory for Thermal Flowmeters 16 Angular Momentum Devices

391.

Introduction The Fuel Flow Transmitter 16.2.1 Qualitative Description of Operation 16.2.2 Simple Theory 16.2.3 Calibration Adjustment 16.2.4 Meter Performance and Range 16.2.5 Application Chapter Conclusions

391 392 394 394 395 396 396 397

CHAPTER

16.1 16.2

16.3

386 388 389

CHAPTER 17 Coriolis Flowmeters

398

17.1

Introduction 17.1.1 Background 17.1.2 Qualitative Description of Operation 17.1.3 Experimental Investigations Industrial Designs 17.2.1 Principal Design Components 17.2.2 Materials 17.2.3 Installation Constraints 17.2.4 Vibration Sensitivity 17.2.5 Size and Flow Ranges 17.2.6 Density Range and Accuracy 17.2.7 Pressure Loss 17.2.8 Response Time 17.2.9 Zero Drift Accuracy Under Normal Operation Performance in Two-Component Flows 17.4.1 Air-Liquid 17.4.2 Sand in Water 17.4.3 Pulverized Coal in Nitrogen 17.4.4 Water-in-Oil Measurement Industrial Experience Calibration Applications, Advantages, Disadvantages, and Cost Considerations 17.7.1 Applications 17.7.2 Advantages 17.7.3 Disadvantages 17.7.4 Cost Considerations Chapter Conclusions

398 398 400 402 402 404 407 407 408 408 409 410 410 410 412 413 414 414 414 414 415 416 416 416 418 419 419 420

17.A A Brief Note on the Theory of Coriolis Meters 17.A.I Simple Theory 17.A.2 Note on Hemp;s Weight Vector Theory 17.A.3 Theoretical Developments

421 421 423 424

17.2

17.3 17.4

17.5 17.6 17.7

17.8

APPENDIX

CONTENTS

18 Probes for Local Velocity Measurement in Liquids and Gases

CHAPTER

18.1 18.2 18.3 18.4 18.5

Introduction Differential Pressure Probes - Pitot Probes Differential Pressure Probes - Pitot-Venturi Probes Insertion Target Meter Insertion Turbine Meter 18.5.1 General Description of Industrial Design 18.5.2 Flow-Induced Oscillation and Pulsating Flow 18.5.3 Applications 18.6 Insertion Vortex Probes 18.7 Insertion Electromagnetic Probes 18.8 Insertion Ultrasonic Probes 18.9 Thermal Probes 18.10 Chapter Conclusions

CHAPTER

19 Modern Control Systems

19.1

427 427 428 430 431 431 431 433 434 435 435 436 437 437 438

Introduction 19.1.1 Analogue Versus Digital 19.1.2 Present and Future Innovations 19.1.3 Industrial Implications 19.1.4 Chapter Outline 19.2 Instrument 19.2.1 Types of Signal 19.2.2 Signal Content 19.3 Interface Box Between the Instrument and the System 19.4 Communication Protocol 19.4.1 Bus Configuration 19.4.2 Bus Protocols 19.5 Communication Medium 19.5.1 Existing Methods of Transmission 19.5.2 Present and Future Trends 19.5.3 Options 19.6 Interface Between Communication Medium and the Computer 19.7 The Computer 19.8 Control Room and Work Station 19.9 Hand-Held Interrogation Device 19.10 An Industrial Application 19.11 Future Implications of Information Technology

438 439 439 440 440 441 441 442 443 444 444 445 446 446 446 447 448 448 448 449 449 449

CHAPTER 20 Some Reflections on Flowmeter Manufacture, Production, and M a r k e t s

451.

20.1 20.2 20.3 20.4 20.5

Introduction Instrumentation Markets Making Use of the Science Base Implications for Instrument Manufacture The Special Features of the Instrumentation Industry

451 451 453 454 454

CONTENTS

20.6

20.7

20.8 20.9

Manufacturing Considerations 20.6.1 Production Line or Cell? 20.6.2 Measures of Production The Effect of Instrument Accuracy on Production Process 20.7.1 General Examples of the Effect of Precision of Construction on Instrument Quality 20.7.2 Theoretical Relationship Between Uncertainty in Manufacture and Instrument Signal Quality 20.7.3 Examples of Uncertainty in Manufacture Leading to Instrument Signal Randomness Calibration of the Finished Flowmeters Actions for a Typical Flowmeter Company

455 455 456 456 457 457 459 461 461

CHAPTER 21 Future Developments

463

21.1 21.2 21.3

463 463 465 465 467 467 469 470 470 470 470 471 471 471 471 471 471 472 472 472

21.4 21.5

21.6 21.7

21.8

Market Developments Existing and New Flow Measurement Challenges New Devices and Methods 21.3.1 Devices Proposed but Not Exploited 21.3.2 New Applications for Existing Devices 21.3.3 Microengineering Devices New Generation of Existing Devices Implications of Information Technology 21.5.1 Signal Analysis 21.5.2 Redesign Assuming Microprocessor Technology 21.5.3 Control 21.5.4 Records, Maintenance, and Calibration Changing Approaches to Manufacturing and Production The Way Ahead 21.7.1 For the User 21.7.2 For the Manufacturer 21.7.3 For the Incubator Company 21.7.4 For the R&D Department 21.7.5 For the Inventor/Researcher Closing Remarks

Bibliography A Selection of International Standards

473 475

Conferences

479

References

483

Index

515

Main Index Flowmeter Index Flowmeter Application Index

515 518 521

Preface

This is a book about flow measurement and flowmeters written for all in the industry who specify and apply, design and manufacture, research and develop, maintain and calibrate flowmeters. It provides a source of information on the published research, design, and performance of flowmeters as well as on the claims of flowmeter manufacturers. It will be of use to engineers, particularly mechanical and process engineers, and also to instrument companies' marketing, manufacturing, and management personnel as they seek to identify future products. I have concentrated on the process, mechanical, and fluid engineering aspects and have given only as much of the electrical engineering details as are necessary for a proper understanding of how and why the meters work. I am not an electrical engineer and so have not attempted detailed explanations of modern electrical signal processing. I am also aware of the speed with which developments in signal processing would render any descriptions which I might give out of date. In the bibliography, other books dealing with flow measurement are listed, and my intention is not to retread ground covered by them, more than is necessary and unavoidable, but to bring together complementary information. I also make the assumption that the flowmeter engineer will automatically turn to the appropriate standard; therefore, I have tried to avoid reproducing information that should be obtained from those excellent documents. I include a brief list that categorizes a few of the standards according to meter or application. I also recommend that those involved in new developments keep a watchful eye on the regular conferences, which carry much of the latest developments in the business. I hope, therefore, that this book will provide a signpost to the essential information required by all involved in the development and use of flowmeters, from the field engineer to the chief executive of the entrepreneurial company that is developing its product range in this technology. In this book, following introductory chapters on accuracy, flow, selection, and calibration, I have attempted to provide a clear explanation of each type of flowmeter so that the reader can easily understand the workings of the various meters. I have then attempted to bring together a significant amount of the published information that explains the performance and applications of flowmeters. The two sources for this are the open literature and the manufacturers' brochures. I have also introduced, to a varying extent, the mathematics behind the meter operations, but to avoid disrupting the text, I have consigned this, in most cases, to the appendices at the end of many chapters. This follows the approach that I have used for technical review papers on turbine meters, Coriolis meters, and to a lesser extent earlier papers on

PREFACE

electromagnetic flowmeters, positive displacement flowmeters, and flowmeters in multiphase flows. However, when searching the appropriate databases for flowmeter papers, I quickly realized that including references to all published material was unrealistic. I have attempted to select those references that appeared to be most relevant and available to the typical reader of this book. However, the reader is referred to the list of journals and conferences that were especially valuable in writing this book. In particular, the Journal of Flow Measurement and Instrumentation has filled a gap in the market, judging by the large number and high quality of the papers published by the journal. It is likely that, owing to the problems of obtaining papers, I have omitted some that should have been included. Topics that I do not consider to be within the subject of bulk flow measurement of liquids and gases, and that are not covered in this book, are metering pumps, flow switches, flow controllers, flow measurement of solids and granular materials, open channel flow measurement, hot-wire local velocity probes or laser doppler anemometers, and subsidiary instrumentation. In two areas where I know that I am lacking in first-hand knowledge - modern control methods and manufacturing - 1 have included a brief review, which should not be taken as expert information. However, I want to provide a source of information for existing and prospective executives in instrumentation companies who might need to identify the type of products for their companies' future developments. This requires a knowledge of the market for each type of flowmeter and also an understanding of who is making each type of instrument. It requires some thought regarding the necessities of manufacturing and production and the implications for this in any particular design. I have briefly referred to future directions for development in each chapter where appropriate, and in the final chapter I have drawn these ideas together to provide a forward look at flow metering in general. The techniques for precise measurement of flow are increasingly important today when the fluids being measured, and the energy involved in their movement, may be very expensive. If we are to avoid being prodigal in the use of our natural resources, then the fluids among them should be carefully monitored. Flow measurement contributes to that monitoring and, therefore, demands high standards of precision and integrity.

Acknowledgments

My knowledge of this subject has benefited from many others with whom I have worked and talked over the years. These include colleagues from industry and academia, and students, whether in short courses or longer-term degree courses and research. I hope that the book does justice to all that they have taught me. In writing this book, I have drawn on the information from many manufacturers, and some have been particularly helpful in agreeing to the use of information and diagrams. I have acknowledged these companies in the captions to the figures. Some went out of their way to provide artwork, and I am particularly grateful to them. Unfortunately, space, in the end, prevented me from using many of the excellent diagrams and photographs with which I was provided. In the middle of already busy lives, the following people kindly read through sections of the book, of various lengths, and commented on them: Heinz Bernard (Krohne Ltd.), Reg Cooper (Bailey-Fischer & Porter), Terry Cousins (T&SK Flow Consultants), Chris Gimson (Endress & Hauser), Charles Griffiths [Flow Automation (UK) Ltd.], John Hemp (Cranfield University), Yousif Hussain (Krohne Ltd.), Peter lies-Smith (Yokagawa United Kingdom Limited), Alan Johnson (Fisher-Rosemount), David Lomas (ABB Kent-Taylor), Graham Mason (GEC-Marconi Avionics), John Napper (formerly with FMA Ltd.), Kyung-Am Park (Korea Research Institute of Standards and Science), Bob Peters (Daniel Europe Ltd.), Roger Porkess (University of Plymouth), Phil Prestbury (Fisher-Rosemount), David Probert (Cambridge University), Karl-Heinz Rackebrandt (Bailey-Fischer & Porter), Bill Pursley (NEL), Jane Sattary (NEL), Colin Scott (Krohne Ltd.), John Salusbury (Endress & Hauser), Dave Smith (NEL), Ian Sorbie (Meggitt Controls), Eddie Spearman (Daniel Europe Ltd.), J. D. Summers-Smith (formerly with I.C.I), and Ben Weager (Danfoss Flowmetering Ltd.). I am extremely grateful to them for taking time to do this and for the constructive comments they gave. Of course, I bear full responsibility for the final script, although their help and encouragement was greatly valued. I am also grateful to Dr. Michael Reader-Harris for his advice on the orifice plate discharge coefficient equation, and to Prof. Stan Hutton for his help and encourgement when Chapter 10 was essentially in the form of technical papers. I acknowledge with thanks the following organizations that have given permission to use their material: ASME for agreeing to the reproduction of Figures 5.10(a), 10.11, 10.16, 17.1, 18.2, and 18.4.

ACKNOWLEDGMENTS

Elsevier Science Ltd. for permission to use Figures 4.18, 5.5, 5.10(b), 5.12, 8.6,11.7, 11.11,11.13,11.14,11.17,13.9, 21.1, 21.2 and for agreement to honor my right to use material from my own papers for Chapters 10 and 17. National Engineering Laboratory (NEL) for permission to reproduce Figures 4.9, 4.14-4.16, 4.19, 5.11, 11.4-11.6, and 14.5. Professional Engineering Publishing for permission to draw on material from the Introductory Guide Series of which I am Editor, and to the Council of the Institution of Mechanical Engineers for permission to reproduce material identified in the text as being from Proceedings Part C, Journal of Mechanical Engineering Science, Vol. 205, pp. 217-229, 1991. Extracts from BS EN ISO 5167-1:1997 are reproduced with the permission of BSI under licence no. PD\ 19980886. Complete editions of the standards can be obtained by mail from BSI Customer Services, 389 Chiswick High Road, London W4 4AL, United Kingdom. I am also grateful for the help and encouragement given to me by many in the preparation of this book. It would be difficult to name them, but I am grateful for each contribution. The support of my family must be mentioned. In various ways they all contributed - by offering encouragement, by undertaking some literature searches, by doing some early typing work, and by helping with some of the diagrams. I particularly thank my wife whose encouragement and help at every stage, not to mention putting up with a husband glued to the word processor through days, evenings, holidays, etc., ensured that the book was completed. My editor has been patient, first as I overran the agreed delivery date and then as I overran the agreed length. I am grateful to Florence Padgett for being willing to overlook this lack of precision!

Nomenclature

d Diameter of tube bundle straightener tubes Q Sensitivity coefficient g Acceleration due to gravity f{x) Function for Normal distribution Hodgson's number K K factor in pulses per unit flow quantity H K Pressure loss coefficient k Coverage factor M Mach number M Mean of a sample of n readings n Index as in Equation (2.4) m Index p Pressure N(/JL, a2) Normal curve po Stagnation pressure n Number of measurements, Exponent APioss Pressure loss across a pipe fitting p Probability, Index qv Volumetric flow rate q Mean of n measurements qj, Exponent qm Mass flow rate qj Test measurement R Radius of pipe qv Volumetric flow rate Reynolds n u m b e r qvo Volumetric flow rate at calibration point Re r Radial coordinate (distance from pipe r Exponent axis) s Exponent T Temperature s(q) Experimental standard deviation of To Stagnation temperature mean of group qj V Velocity in pipe, Volume of pipework s(qj) Experimental standard deviation of qj and other vessels between t h e source t Student's t of t h e pulsation a n d t h e flowmeter U Expanded uncertainty position u(xi) Standard uncertainty for the zth quantity Vb Velocity on pipe axis uc(y) Combined standard uncertainty Kms Fluctuating component of velocity x Coordinate V Mean velocity in pipe Xi Result of a meter measurement, Input z Elevation above datum quantities y Ratio of specific heats x Mean of n meter measurement li Dynamic viscosity y Output quantity y Kinematic viscosity z Normalized coordinate (x — /x)/a p Density l± Mean value of data for normal curve SUBSCRIPTS v Degrees of freedom 1,2 Pipe sections o Standard deviation (a2 variance) 4>(z) Area under Normal curve [e.g., 4>(0.5) is the area from z = -oo to z = 0.5] CHAPTER 3 (x) Function for normalized Normal Cj Sensitivity coefficient for the zth distribution quantity famin Lubrication film thickness CHAPTER 2 n Bearing rotational speed p Bearing load A Cross-section of pipe ui Standard uncertainty for the / th quantity Local speed of sound c Specific heat at constant pressure r) Friction coefficient Specific heat at constant volume k Specific film thickness Diameter of pipe ix Fluid viscosity D

CHAPTER 1

NOMENCLATURE

a

Combined roughness of the two contacting surfaces of the bearing

CHAPTER 4 Q Concentration of tracer in the main stream at the downstream sampling point Cdmean Mean concentration of tracer measured downstream during time t Q Concentration of tracer in the injected stream Cu Concentration of tracer in the main stream upstream of injection point (if the tracer material happens to be present)

cx Mn p qv qVi R T t V v p

Sensitivity coefficient Net mass of liquid collected in calibration Pressure Volumetric flow rate in the line Volumetric flow rate of injected tracer Gas constant for a particular gas Temperature Collection time during calibration, Integration period for tracer measurement Amount injected in the sudden injection (integration) method Specific volume Liquid density

f

H h K Li

h '2

M'2 n Pd

Pu Ap qm qv

Re

r t V

CHAPTER 5

A

a\ a€ b b€ C CRe Claps

c C\ C*

D D1 d E ET E* e F

Function of p and Re Expression in orifice plate bending formula Constant Constant Constant Discharge coefficient Part of discharge coefficient affected by Re Part of discharge coefficient which allows for position of taps Discharge coefficient for infinite Reynolds number Expression in orifice plate bending formula Constant Pipe diameter (ID) Orifice plate support diameter Orifice diameter Velocity of approach factor (1 - £4)~~1/2:, Thickness of the orifice plate Total error in the indicated flow rate of a flowmeter in pulsating flow Elastic modulus of plate material Thickness of the orifice Correction factors used to obtain the mass flow of a (nearly) dry steam flow

V

vWs X

a

P y

Hm €1 K

Pi

°y 4>

Frequency of the pulsation Hodgson number Thickness of orifice plate Loss coefficient, Related to the criterion for Hodgson's number = h/D = l'2/D (The prime signifies that the measurement is from the downstream face of the plate) Distance of the upstream tapping from the upstream face of the plate Distance of the downstream tapping from the downstream face of the plate (The prime signifies that the measurement is from the downstream face of the plate) = 2L'2/(1 - p) Index Downstream pressure Upstream pressure Differential pressure, pressure drop between pulsation source and meter Mass flow rate Volumetric flow rate Reynolds number usually based on the pipe ID Radius of upstream edge of orifice plate Time Volume of pipework and other vessels between the source of the pulsation and the flowmeter position Mean velocity in pipe with pulsating flow Root-mean-square value of unsteady velocity fluctuation in pipe with pulsating flow Dryness fraction Flow coefficient, CE Diameter ratio, d/D Ratio of specific heats Small changes or errors in qm, etc. Expansibility (or expansion) factor Expansibility (or expansion) factor for orifice

Isentropic exponent Density at the upstream pressure tapping cross-section Yield stress for plate material Ratio of two-phase pressure drop to liquid flow pressure drop Maximum allowable percentage error in pulsating flow

CHAPTER 6

C

cRe

Coefficient of discharge Part of coefficient of discharge affected by Reynolds number

NOMENCLATURE

Ctp Coo D d E

Coefficient for wet gas flow equation Discharge coefficient for infinite Reynolds number Pipe ID Throat diameter Velocity of approach factor (l-/*4)-l/2

Frg g k n Ap qg qi qm qtp qv Re Red Vsg X £ e p pg p\

Superficial gas Froude number Gravitational acceleration Roughness Index Differential pressure Gas volumetric flow rate Liquid volumetric flow rate Mass flow rate Apparent volumetric flow rate when liquid is present in the gas stream Volume flow rate Reynolds number based on D Reynolds number based on d Superficial gas velocity Lockhart-Martinelli parameter diameter ratio d/D Expansibility (or expansion) factor Density Gas density Liquid density

CHAPTER 7

A2 A* a ac az b bc bz C CR C* c cp cv d dt d2 f M Mi M n po pi p2i p2max p*

Outlet cross-sectional area Throat cross-sectional area Constant Constant Constant Constant Constant Constant Discharge coefficient = C*^Z Critical flow function Sound speed Specific heat at constant pressure Specific heat at constant volume Throat diameter Diameter of tapping Outlet diameter Obtained from Equation (7.17) Mach number Mach number at inlet when stagnation conditions cannot be assumed Molecular weight Exponent in Equation (7.12) Stagnation pressure Pressure at inlet when stagnation conditions cannot be assumed Ideal outlet pressure Actual maximum outlet pressure Throat pressure in choked conditions

R Red To % X Z ZQ

p y K V

PO

Mass flow Universal gas constant Reynolds number based on the throat diameter Stagnation temperature Throat temperature in choked conditions Mole fraction of each component of a gas mixture Compressibility factor Compressibility factor at stagnation conditions d/D Ratio of specific heats Error Isentropic exponent Kinematic viscosity Density at stagnation conditions

CHAPTER 8

A A' Af Ax A2 a B C Cc D d E F g K L M p qv R Re V V v x /x fig /xstd p Pi

Cross-sectional area of the pipe, Constant Constant Cross-sectional area of float Cross-sectional area of tapering tube at height x Annular area around float, Annular area around target Area of target Constant Coefficient Contraction coefficient, Constants in curvefitfor target meter discharge coefficient Pipe diameter Throat diameter for pipe inlet Full-scale or upper range value of flow rate used in precision calculation Summation error in flow rate Gravity Loss coefficient, Precision class, Bend or elbow meter coefficient Length of laminar flow tube Actual flow rate used in precision calculation Pressure Volumetric flow rate Radius of bend or elbow Reynolds number Velocity, Volume of float Mean velocity in tube Specific volume of gas Height of float in tube Viscosity Viscosity of calibration gas at flowing conditions Viscosity of reference gas at standard conditions Density Density of float material

NOMENCLATURE

Viscosity Angular position of arm of calibrator

CHAPTER 9

E F g

Young's modulus of elasticity Friction force Acceleration due to gravity

L

Length of clearance gap in direction of flow Axial length of clearance gap Axial length of measuring chamber Mass of rotor Rotational speed of rotor Rotational speed of cam disk of calibrator (clutch system) Rotational speed of shaft into calibrator (epicyclic system) M a x i m u m rotational speed of rotor Rotational speed of outer ring of calibrator (clutch system) Rotational speed of shaft out of calibrator (epicyclic system) Slippage in NIN N u m b e r of teeth o n gear Downstream pressure Upstream pressure As u s e d in Equation (9.A.6) Leakage flow rate Bulk volumetric flow rate

I £ax M N N[ NIN Nmax No NOUT Ns n pa pu