Measurement Science and Technology in Nuclear Engineering (Nuclear Science and Technology) 9819912792, 9789819912797

Table of contents :
Preface
Contents
1 Basics of Testing
1.1 Measurement and Methods of Measurement
1.1.1 The Concept of Measurement
1.1.2 Methods of Measurement
1.2 Components of the Measurement System
1.2.1 Composition of the Measurement System
1.2.2 Role and Requirements of the Measurement Elements
1.3 Basic Concepts of Error
1.3.1 Representation of Measurement Errors
1.3.2 Classification and Treatment of Errors
1.4 Quality Indicators for Measuring Instruments
1.4.1 Static Characteristics of the Instrument
1.4.2 Dynamic Characteristics of the Instrument
2 Temperature Detection
2.1 Overview
2.1.1 Temperature Scale
2.1.2 Classification of Temperature Measuring Instruments
2.2 Thermocouple Thermometers
2.2.1 Thermocouple Temperature Measurement Principle
2.2.2 The Circuit Nature of Thermocouples
2.2.3 Structure of Commonly Used Thermocouple Materials
2.2.4 The Cold End of the Thermocouple Compensation
2.3 Expansion Thermometers
2.3.1 Solid Expansion Thermometer
2.3.2 Liquid Expansion-Type Thermometer
2.3.3 Pressure Thermometer
2.4 Resistance Thermometers
2.4.1 Principle of Resistance Thermometer
2.4.2 Commonly Used Thermometric Resistance Elements
2.4.3 The Structure of the Thermometric Resistance Temperature Measurement Element
2.5 Temperature Measurement and Display Instruments
2.5.1 Displaying Instrument with Thermocouple Measuring Temperature
2.5.2 Mating Thermometric Resistance Temperature Measurement Display Instrument
2.6 Temperature Transmitters
2.6.1 ITE-Type Thermocouple Temperature Transmitter
2.6.2 ITE-Type Thermometric Resistance Temperature Transmitter
2.7 Contact Temperature Measurement Techniques
2.7.1 Various Factors Affecting Contact Temperature Measurement
2.7.2 High-Speed Airflow Temperature Measurement, Velocity Error Analysis
2.7.3 High-Temperature Airflow Temperature Measurement, Radiation Error Analysis
2.7.4 Dynamic Temperature Measurement, Dynamic Error Analysis
2.7.5 Measurement of Wall Temperature
2.8 Non-contact Thermometers
2.8.1 Monochromatic Radiation-Type Optical Pyrometer
2.8.2 Full Radiation Pyrometer
2.8.3 Colorimetric Pyrometer
2.8.4 Infrared Thermometer
2.9 Application of Temperature Detection Instrumentation in Pressurized Water Reactor Nuclear Power Plants
2.9.1 Application of Thermocouples in Core Temperature Measurement
2.9.2 Application of Thermometric Resistance in Nuclear Island Temperature Measurement in Nuclear Power Plants
2.9.3 Application of Thermometric Resistance in Conventional Island of Nuclear Power Plant
3 Pressure Testing
3.1 Overview
3.2 Liquid Column Manometers
3.3 Flexible Manometers
3.4 Electrical Manometers
3.4.1 Resistance Strain Gauge Pressure Sensor
3.4.2 Inductive Pressure Sensors
3.4.3 Hall-Type Pressure Sensor
3.4.4 Capacitive Pressure Sensor
3.4.5 Piezoelectric Pressure Sensors
3.5 Selection, Installation and Calibration of Pressure Measuring Instruments
3.5.1 Selection of Pressure Gauge
3.5.2 Installation of Pressure Gauge
3.5.3 Calibration of the Pressure Gauge
3.6 Airflow Pressure Measurement
3.6.1 Total Pressure Measurement
3.6.2 Hydrostatic Pressure Measurement
3.7 Reactor Coolant Circuit Pressure Measurement
4 Flow Testing
4.1 Differential Pressure Flowmeter
4.1.1 Standard Throttling Device
4.1.2 Rotameter
4.1.3 Three, Bend Pipe Flowmeter
4.2 Velocity Flow Meters
4.2.1 Overview of Velocity Flow Measurement Methods
4.2.2 Turbine Flow Meter
4.2.3 Three, Vortex Flowmeter
4.2.4 Electromagnetic Flowmeter
4.2.5 Ultrasonic Flow Meter
4.3 Mass Flow Meters
4.3.1 Direct Mass Flow Meter
4.3.2 Indirect Mass Flow Meter
4.4 Main Coolant Flow Measurement
4.4.1 Measurement with a Bent Pipe Flowmeter
4.4.2 Relevant Statistical Measures
4.5 Calibration and Indexing of Flow Measurement Instruments
4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid
4.6.1 Basic Properties of Two-Phase Flow
4.6.2 Basic Parameters Related to Gas-Liquid Two-Phase Flow
4.6.3 Basic Principles of Two-Phase Flow Measurement
4.6.4 Several Instruments for Two-Phase Flow Measurement
5 The Level Measurement
5.1 Hydrostatic Level Meter
5.1.1 Pressure-Type Level Meter
5.1.2 Differential Pressure Level Juice
5.2 Electrical Level Meters
5.3 Ultrasonic Level Meter
5.3.1 Characteristics and Basic Methods of Ultrasonic Level Measurement
5.3.2 Ultrasonic Pulse-Echo Level Measurement
5.3.3 The Gas-Mediated Ultrasonic Level Meter Example
5.4 Radar Level Meter
5.5 Nuclear Radiation-Type Level Meter
5.5.1 Principle of Nuclear Radiation-Type Liquid Level Meter
5.5.2 The Characteristics of Nuclear Radiation-Type Level Meter
5.6 Level Measurement in Nuclear Engineering
5.6.1 Reactor Pressure Vessel Level Measurement
5.6.2 Level Measurement of Pressure Regulators in Nuclear Power Plants
6 Mechanical Measurement Instruments
6.1 Displacement Detection Instruments
6.1.1 Differential Transformer-Type Displacement Detection Instrument
6.1.2 Inductive Displacement Detection Instrument
6.1.3 Eddy Current-Type Displacement Detection Instrument
6.2 Speed Measuring Instruments
6.2.1 Overview
6.2.2 Hall Speed Sensor
6.2.3 Centrifugal Tachograph
6.2.4 Magnetic Tachograph
6.2.5 Capacitive Tachograph
6.2.6 Eddy Current-Type Speed Sensor
6.2.7 Steam Engine Speed Measurement
6.3 Vibration Measurement Sensors
6.3.1 Magnetoelectric Induction Vibration Speed Sensor
6.3.2 Piezoelectric Vibration Sensors
6.3.3 Eddy Current-Type Vibration Displacement Sensor
7 Reactor Nuclear Measurements and Radiation Monitoring
7.1 Principles of Operation of Nuclear Instruments
7.1.1 Overview
7.1.2 Gas Detectors
7.1.3 Solid-State Detectors
7.1.4 Special Issues in Nuclear Measurements
7.2 Nuclear Measurement Systems for Nuclear Reactors
7.2.1 Nuclear Measurements Outside the Nuclear Reactor
7.2.2 Nuclear Reactor Core Measurements
7.3 Radiation Monitoring System
7.3.1 Radiation Monitoring of Processes
7.3.2 Radiation Monitoring in the Plant
7.3.3 Other Radiation Monitoring Systems
8 Computerized Testing Techniques and Systems
8.1 Intelligent Sensors
8.1.1 Characteristics of Smart Sensors
8.1.2 The Basic Components and Classification of Intelligent Sensors
8.1.3 Examples of Intelligent Sensor Functions
8.1.4 Intelligent Sensor Networks and Applications
8.2 Automated Data Acquisition and Processing Systems
8.2.1 Basic Components and Functions of the Automatic Data Acquisition System
8.2.2 Structural Form of the Automatic Data Acquisition System
8.2.3 Main Technical Indicators of the Automatic Data Acquisition System
8.3 Computer-Aided Test Systems
8.3.1 Typical Components of a CAT System
8.3.2 CAT System Architecture
8.3.3 Trends in CAT
8.4 Virtual Instruments and Systems
8.4.1 Structural Components of Virtual Instruments
8.4.2 Characteristics of Virtual Instruments
8.4.3 Development Platform for Virtual Instruments
8.5 Trends in Modern Testing Techniques
Appendix
Afterwords
Bibliography

Citation preview

Nuclear Science and Technology

Hong Xia Yongkuo Liu

Measurement Science and Technology in Nuclear Engineering

HFLAS S CARD E INSID

Nuclear Science and Technology Series Editors Yongping Li, Shanghai Institute of Applied Physics, Shanghai, China Hong Xia, Nuclear Science and Technology, Harbin Engineering University, Harbin, China

This interdisciplinary book series publishes monographs and edited volumes in all areas of nuclear science and technology, covering developments in theoretical research, experiments, technology and applications. The series attempts to bring together experts and professionals from all over the world, to provide readers with a library on a wide range of topics in physics, engineering, medicine and environmental sciences. Topics include but are not limited to: Nuclear physics and interdisciplinary research; Nuclear energy science and engineering; Nuclear fusion and high temperature plasmas; Synchrotron radiation applications, beamline technology; Accelerator, ray technology and applications; Nuclear chemistry, radiochemistry, radiopharmaceuticals, nuclear medicine; and Nuclear electronics and instrumentation. The books are intended for researchers, professionals, and students in the field, as well as those interested in staying current with the latest advances.

Hong Xia · Yongkuo Liu

Measurement Science and Technology in Nuclear Engineering

Hong Xia Nuclear Science and Technology Harbin Engineering University Harbin, China

Yongkuo Liu Nuclear Science and Technology Harbin Engineering University Harbin, China

ISSN 2948-1856 ISSN 2948-1864 (electronic) Nuclear Science and Technology ISBN 978-981-99-1279-7 ISBN 978-981-99-1280-3 (eBook) https://doi.org/10.1007/978-981-99-1280-3 Jointly published with Harbin Engineering University Press The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: Harbin Engineering University Press. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content. Translation from the Chinese Simplified language edition: “He Gong Cheng Jian Ce Ji Shu” by Hong Xia and Yongkuo Liu, © Harbin Engineering University Press 2023. Published by Harbin Engineering University Press. All Rights Reserved. © Harbin Engineering University Press 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

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Preface

The rapid developments in computer science, sensors, and lasers have boosted the advances in measurement science and technology in nuclear engineering, which requires a significant increase in the content of the college course of this subject in higher-education institutions. This textbook not only includes the basic theories and widely used technologies in measurement science and technology in nuclear engineering but also presents latest innovations, progresses, and trends. In particular, it highlights the test technology of process parameters in nuclear power plants. The textbook is translated from its Chinese version. Its eight chapters cover measurement and test technologies of major parameters in nuclear power engineering, including thermal parameters (temperature, pressure, flow, and liquid level), mechanical quantities (displacement, speed, and vibration), and nuclear parameters (neutron flux and radiation dose). The book also introduces the rapid development of related computer technology. Reflective questions and exercises are provided at the end of each chapter for learners to test their learning. Due to the limitation of the authors’ knowledge, the textbook may have inadequacy. We welcome your comments and suggestions. Harbin, China

Hong Xia Yongkuo Liu

vii

Contents

1 Basics of Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Measurement and Methods of Measurement . . . . . . . . . . . . . . . . . . . . 1.1.1 The Concept of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Methods of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Components of the Measurement System . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Composition of the Measurement System . . . . . . . . . . . . . . . . 1.2.2 Role and Requirements of the Measurement Elements . . . . . 1.3 Basic Concepts of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Representation of Measurement Errors . . . . . . . . . . . . . . . . . . 1.3.2 Classification and Treatment of Errors . . . . . . . . . . . . . . . . . . 1.4 Quality Indicators for Measuring Instruments . . . . . . . . . . . . . . . . . . . 1.4.1 Static Characteristics of the Instrument . . . . . . . . . . . . . . . . . . 1.4.2 Dynamic Characteristics of the Instrument . . . . . . . . . . . . . . .

1 2 2 3 4 4 5 7 7 9 9 9 11

2 Temperature Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Temperature Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Classification of Temperature Measuring Instruments . . . . . 2.2 Thermocouple Thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Thermocouple Temperature Measurement Principle . . . . . . . 2.2.2 The Circuit Nature of Thermocouples . . . . . . . . . . . . . . . . . . . 2.2.3 Structure of Commonly Used Thermocouple Materials . . . . 2.2.4 The Cold End of the Thermocouple Compensation . . . . . . . . 2.3 Expansion Thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Solid Expansion Thermometer . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Liquid Expansion-Type Thermometer . . . . . . . . . . . . . . . . . . . 2.3.3 Pressure Thermometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19 19 19 21 22 22 28 31 37 41 41 44 47

ix

x

Contents

2.4 Resistance Thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.4.1 Principle of Resistance Thermometer . . . . . . . . . . . . . . . . . . . 49 2.4.2 Commonly Used Thermometric Resistance Elements . . . . . 50 2.4.3 The Structure of the Thermometric Resistance Temperature Measurement Element . . . . . . . . . . . . . . . . . . . . . 53 2.5 Temperature Measurement and Display Instruments . . . . . . . . . . . . . 56 2.5.1 Displaying Instrument with Thermocouple Measuring Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.5.2 Mating Thermometric Resistance Temperature Measurement Display Instrument . . . . . . . . . . . . . . . . . . . . . . . 65 2.6 Temperature Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.6.1 ITE-Type Thermocouple Temperature Transmitter . . . . . . . . 70 2.6.2 ITE-Type Thermometric Resistance Temperature Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.7 Contact Temperature Measurement Techniques . . . . . . . . . . . . . . . . . 74 2.7.1 Various Factors Affecting Contact Temperature Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.7.2 High-Speed Airflow Temperature Measurement, Velocity Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.7.3 High-Temperature Airflow Temperature Measurement, Radiation Error Analysis . . . . . . . . . . . . . . . . . 81 2.7.4 Dynamic Temperature Measurement, Dynamic Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.7.5 Measurement of Wall Temperature . . . . . . . . . . . . . . . . . . . . . 88 2.8 Non-contact Thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2.8.1 Monochromatic Radiation-Type Optical Pyrometer . . . . . . . 91 2.8.2 Full Radiation Pyrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 2.8.3 Colorimetric Pyrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.8.4 Infrared Thermometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.9 Application of Temperature Detection Instrumentation in Pressurized Water Reactor Nuclear Power Plants . . . . . . . . . . . . . . 99 2.9.1 Application of Thermocouples in Core Temperature Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 2.9.2 Application of Thermometric Resistance in Nuclear Island Temperature Measurement in Nuclear Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 2.9.3 Application of Thermometric Resistance in Conventional Island of Nuclear Power Plant . . . . . . . . . . . 104 3 Pressure Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Liquid Column Manometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Flexible Manometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

107 107 109 114

Contents

xi

3.4 Electrical Manometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Resistance Strain Gauge Pressure Sensor . . . . . . . . . . . . . . . . 3.4.2 Inductive Pressure Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Hall-Type Pressure Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Capacitive Pressure Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.5 Piezoelectric Pressure Sensors . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Selection, Installation and Calibration of Pressure Measuring Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Selection of Pressure Gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Installation of Pressure Gauge . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Calibration of the Pressure Gauge . . . . . . . . . . . . . . . . . . . . . . 3.6 Airflow Pressure Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Total Pressure Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Hydrostatic Pressure Measurement . . . . . . . . . . . . . . . . . . . . . 3.7 Reactor Coolant Circuit Pressure Measurement . . . . . . . . . . . . . . . . .

121 122 127 131 133 135

4 Flow Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Differential Pressure Flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Standard Throttling Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Rotameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Three, Bend Pipe Flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Velocity Flow Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Overview of Velocity Flow Measurement Methods . . . . . . . . 4.2.2 Turbine Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Three, Vortex Flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Electromagnetic Flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Ultrasonic Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Mass Flow Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Direct Mass Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Indirect Mass Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Main Coolant Flow Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Measurement with a Bent Pipe Flowmeter . . . . . . . . . . . . . . . 4.4.2 Relevant Statistical Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Calibration and Indexing of Flow Measurement Instruments . . . . . . 4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid . . . . . . . . . . . . . 4.6.1 Basic Properties of Two-Phase Flow . . . . . . . . . . . . . . . . . . . . 4.6.2 Basic Parameters Related to Gas-Liquid Two-Phase Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Basic Principles of Two-Phase Flow Measurement . . . . . . . . 4.6.4 Several Instruments for Two-Phase Flow Measurement . . . .

159 160 160 187 192 195 195 196 202 207 213 220 220 226 233 233 234 235 238 238

5 The Level Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Hydrostatic Level Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Pressure-Type Level Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Differential Pressure Level Juice . . . . . . . . . . . . . . . . . . . . . . .

257 258 258 259

138 138 141 144 147 148 152 156

240 243 244

xii

Contents

5.2 Electrical Level Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Ultrasonic Level Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Characteristics and Basic Methods of Ultrasonic Level Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Ultrasonic Pulse-Echo Level Measurement . . . . . . . . . . . . . . 5.3.3 The Gas-Mediated Ultrasonic Level Meter Example . . . . . . 5.4 Radar Level Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Nuclear Radiation-Type Level Meter . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Principle of Nuclear Radiation-Type Liquid Level Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 The Characteristics of Nuclear Radiation-Type Level Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Level Measurement in Nuclear Engineering . . . . . . . . . . . . . . . . . . . . 5.6.1 Reactor Pressure Vessel Level Measurement . . . . . . . . . . . . . 5.6.2 Level Measurement of Pressure Regulators in Nuclear Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

262 268

6 Mechanical Measurement Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Displacement Detection Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Differential Transformer-Type Displacement Detection Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Inductive Displacement Detection Instrument . . . . . . . . . . . . 6.1.3 Eddy Current-Type Displacement Detection Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Speed Measuring Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Hall Speed Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Centrifugal Tachograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Magnetic Tachograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Capacitive Tachograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.6 Eddy Current-Type Speed Sensor . . . . . . . . . . . . . . . . . . . . . . . 6.2.7 Steam Engine Speed Measurement . . . . . . . . . . . . . . . . . . . . . 6.3 Vibration Measurement Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Magnetoelectric Induction Vibration Speed Sensor . . . . . . . . 6.3.2 Piezoelectric Vibration Sensors . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Eddy Current-Type Vibration Displacement Sensor . . . . . . .

287 287

7 Reactor Nuclear Measurements and Radiation Monitoring . . . . . . . . . 7.1 Principles of Operation of Nuclear Instruments . . . . . . . . . . . . . . . . . 7.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Gas Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Solid-State Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.4 Special Issues in Nuclear Measurements . . . . . . . . . . . . . . . . . 7.2 Nuclear Measurement Systems for Nuclear Reactors . . . . . . . . . . . . 7.2.1 Nuclear Measurements Outside the Nuclear Reactor . . . . . . 7.2.2 Nuclear Reactor Core Measurements . . . . . . . . . . . . . . . . . . .

315 315 315 318 322 331 334 334 342

268 269 273 275 277 277 278 279 279 282

288 293 296 301 301 302 304 305 305 306 307 308 309 310 311

Contents

xiii

7.3 Radiation Monitoring System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Radiation Monitoring of Processes . . . . . . . . . . . . . . . . . . . . . 7.3.2 Radiation Monitoring in the Plant . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Other Radiation Monitoring Systems . . . . . . . . . . . . . . . . . . .

349 349 355 362

8 Computerized Testing Techniques and Systems . . . . . . . . . . . . . . . . . . . 8.1 Intelligent Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Characteristics of Smart Sensors . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 The Basic Components and Classification of Intelligent Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 Examples of Intelligent Sensor Functions . . . . . . . . . . . . . . . . 8.1.4 Intelligent Sensor Networks and Applications . . . . . . . . . . . . 8.2 Automated Data Acquisition and Processing Systems . . . . . . . . . . . . 8.2.1 Basic Components and Functions of the Automatic Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Structural Form of the Automatic Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Main Technical Indicators of the Automatic Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Computer-Aided Test Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Typical Components of a CAT System . . . . . . . . . . . . . . . . . . 8.3.2 CAT System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3 Trends in CAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Virtual Instruments and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Structural Components of Virtual Instruments . . . . . . . . . . . . 8.4.2 Characteristics of Virtual Instruments . . . . . . . . . . . . . . . . . . . 8.4.3 Development Platform for Virtual Instruments . . . . . . . . . . . 8.5 Trends in Modern Testing Techniques . . . . . . . . . . . . . . . . . . . . . . . . .

369 369 370 370 371 374 376 377 379 382 383 384 385 388 389 389 390 391 392

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 Afterwords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

Chapter 1

Basics of Testing

With the purchase of this book, you can use our “SN Flashcards” app to access questions free of charge in order to test your learning and check your understanding of the contents of the book. To use the app, please follow the instructions below: 1. Go to https://flashcards.springernature.com/login. 2. Create a user account by entering your e-mail address and assigning a password. 3. Use the following link to access your SN Flashcards set: https://sn.pub/ QEyQX4. If the link is missing or does not work, please send an e-mail with the subject “SN Flashcards” and the book title to [email protected]. Nuclear engineering testing and measurement instruments are used to detect nuclear and conventional island parameters. The instruments are essential for nuclear equipment’s safe, reliable, and economic operation. The main function of these instruments is to detect various parameters such as temperature, pressure, flow, liquid level, neutron flux, radiation dose, and mechanical quantity during the start-up, shutdown, and normal operation of nuclear power plants. The instruments also provide accurate and reliable information for automatic adjustment and control of these parameters and even the whole system operation process, thus ensuring nuclear power plants’ safe, reliable, and normal operation. The signals of the detected parameters are sent to each of the indicators, the recording system, the alarm system, the control system, the protection systems, and the computer system for monitoring. Most conventional instruments can detect reactor parameters, but they should meet the unique environment and nuclear power plant detection requirements. The following main issues should be noted:

© Harbin Engineering University Press 2023 H. Xia and Y. Liu, Measurement Science and Technology in Nuclear Engineering, Nuclear Science and Technology, https://doi.org/10.1007/978-981-99-1280-3_1

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1 Basics of Testing

(1) The range and accuracy of the instrument must meet the specific requirements of the parameter being measured and take into account the need for extreme accident conditions. The protective equipment must have a response rate that meets the requirements of the protection system. (2) Those instruments that must continue to perform their specified tasks in an accident situation must be adapted to the harsh environment of the accident situation, including resistance to high pressure, high temperature, high irradiation, and the duration of operation that must be maintained. (3) Any detector element placed in the coolant piping should not impede access to the piping, and the material used shall be compatible with the fuel element and coolant. (4) Measuring the main coolant flow should be the most straightforward procedure that can give and display reliable indicators over the entire operating range. The measurement location should be selected to reflect the flow changes caused by pump speed and valve position changes. (5) The measurement of the thermal parameters that initiate the protective action should conform to the principles of system design protection, such as repeatability, diversity, independence, testability, and serviceability.

1.1 Measurement and Methods of Measurement 1.1.1 The Concept of Measurement A measurement is the acquisition, by experimental methods and specialized equipment, of the ratio of a parameter (called the quantity to be measured) whose quantitative concept needs to be determined to a similar parameter that defines its value as 1 (called the unit), and it can be expressed by the following equation: a≈

A U

(1.1)

where A is the measured; U is the chosen unit; a is the ratio. The value A of the measurement is the ratio times the unit, i.e., a.U . Equation (1.1) is taken to be approximately equal because any measurement is necessarily subject to error since neither the measurement method nor the equipment used can be perfect. Measurement includes the choice of measurement methods and equipment and measurement data processing (determining the limits of error and the reliability of measurement results).

1.1 Measurement and Methods of Measurement

3

1.1.2 Methods of Measurement The choice of method is very important for measurement work. The desired results cannot be obtained even with sophisticated measuring instruments and equipment if the method is inappropriate. There are many classifications of measurement methods, and different classifications are used depending on the research problem. The following classifications describe how the measurement results are obtained include: 1. Direct measurement methods The measuring instrument measures a value to determine the reference value. The measured value is directly obtained, such as measuring the gas pressure in the container by the pressure gauge. This type of method is simple and rapid. 2. Indirect measurement methods Since the measured quantity has a definite functional relationship with certain quantities, the value of the measured quantity is measured by direct measurement and substituted into the known functional relationship to calculate the value of the measured quantity. For example, in the case of steady flow, the flow rate is measured accurately by measuring the weight and time of the fluid flowing through a certain cross-section since both weighing and timing can be achieved with a high degree of accuracy. 3. Combined measurement methods When the measured and some directly measured quantities do not have a simple, functional relationship, there is a need to solve a system of equations to obtain the measured value. This method is referred to as the combination measurement method. For example, to measure the temperature coefficient of a resistor, the resistance value has a relationship with the temperature: Rt = R0 (1 + at + bt 2 ),

(1.2)

where Rt is the value of resistance when the temperature is t °C and can be measured directly. Similarly, the temperature can also be measured directly. To obtain the coefficients a and b, a system of quadratic equations is solved. The above classification is applied when calculating errors. From the perspective of comprehensive performance of the measurement, the determination of the measurement scheme or the design scheme of the instrumentation is classified as follows: 1. Deflection method of measurement This method uses the magnitude of the displacement of the pointer of the measuring instrument to indicate the measured value. This method is simple and quick, but not easy to achieve high accuracy. Measuring pressure with a spring-tube pressure gauge is an example of this measurement method.

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1 Basics of Testing

2. Null method of measurement (the complementary method of measurement) This method compares the known value of the standard gauge and the directly measured quantity, adjusts the standard gauge value, and uses the zero-pointing instrument to determine whether the two achieve complete balance (complete compensation). Then the value of the standard gauge is the value of the measured quantity. Weighing with a balance is a null method of measurement. This method can obtain high measurement accuracy, but the operation is costly and time-consuming. 3. Differential method of measurement It is a combination of the deflection method and the null method. A standard gauge with a value close to the measured value is compared with the measured value. A deflection-measuring instrument indicates the difference between the two values. The measured value is the sum of the standard gauge and the deflection value. This method is highly accurate, fast, and easy to operate because the standard gauge does not need to be adjusted frequently. Since the deflection is small, the accuracy is higher than the deflection method. The X-ray thickness gauge is an example of the application of this method. The gauge is zeroed with a standard thickness steel plate before measurement, and the gauge indicates the deflection value of the measured plate thickness. This method is used in the steel plate thickness measurement in the steel rolling process, which needs to be quick and highly accurate. In addition, it can also be classified according to the state of the measured in the measurement process: static measurement, dynamic measurement, according to the same measurement conditions or not: equal precision measurement, unequal precision measurement.

1.2 Components of the Measurement System 1.2.1 Composition of the Measurement System Generally, to measure a value, a number of measuring devices (including instruments, devices, components, and auxiliary equipment) are always combined in a certain way. That is, it constitutes a measurement system. For example, in the measurement of steam, the standard orifice plate is commonly used to obtain the differential pressure signal related to the flow. Then it will be sent to the differential pressure transmitter and turned into an electrical signal after conversion and operation. The connecting wire then sends the electrical signal to the display instrument and finally displays the measured flow value. This system can be represented in Fig. 1.1. Measurement systems can vary greatly due to differences in measurement principles or the accuracy required for measurement. Some may be as simple as a simple measurement system consisting of only one measurement instrument, while others may be as complex as an extremely complex measurement system with many devices. For example, using a microcomputer to collect and process the operating parameters

1.2 Components of the Measurement System

5

Fig. 1.1 Block diagram of steam flow measurement system

Fig. 1.2 Block diagram of the measurement system

of each measurement point in a nuclear or thermal power plant is a relatively complex measurement system. The measurement system can generally be represented as the system block diagram shown in Fig. 1.2. This means that the measurement system comprises elements that are the basic components for establishing some functional relationship between the two quantities of input and output.

1.2.2 Role and Requirements of the Measurement Elements 1. The sensitive component The sensitive component is directly connected to the object to be measured, in accordance with the energy from the medium to be measured. It causes it to produce an output signal that is in some way related to the measurement being made. For example, when a standard orifice plate is used to measure the flow of steam in a pipeline as described above, the differential pressure signal from the standard orifice plate ΔP is proportional to the square of the flow rate being measured qv , i.e., ΔP ∝ qv2 . The ability of the sensitive components to produce a precise and fast signal corresponding to the measured signal has a decisive influence on the measurement quality of the measuring system. Therefore, strictly speaking, the following requirements are imposed on the sensitive components: (a) The inputs and outputs of sensitive components shall have a defined singlevalued function relationship. (b) The sensitive component shall be sensitive only to the measured change and insensitive to all other signals not measured (including interference noise signals). (c) Sensitive components should not affect, or as little as possible, the condition of the medium being measured. But sensitive components that fully meet the three requirements mentioned above do not exist. For example, the second requirement can only be solved by limiting the

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component of the unwanted non-detected signal in the total signal and eliminating it using experimental methods or theoretical calculations. The third requirement can only be solved by improving the structure and principle performance of the sensitive components. All of these fall within the scope of research in sensing technology. 2. The transform component The signal output by the sensitive component is generally different, even significantly different, from the signal received by the display component because the signal output by the former and the signal received by the latter often belong to two different physical quantities; it is, therefore, necessary to transform the signal output by the sensitive component before sending it to the display component, and this is the role played by the transforming component. The signal transformation consists of the following possible forms: (a) The transformation of the physical properties of a signal, i.e., the transformation of one physical quantity into another physical quantity of a completely different nature, e.g., from a non-electric quantity to an electric quantity. (b) A numerical transformation of a signal, i.e., a numerical change in a physical quantity based on a particular law, but whose physical properties remain unchanged. (c) Both of the above. The standard orifice plate for the steam flow measurement system described above is still used as an example. The differential pressure transmitter is the transformer component of the measurement system. When it receives the signal value from the sensitive component (the upper and lower orifice of the standard orifice plate), it converts it into an electrical signal proportional to the square of the measured flow rate, then squares the electrical signal numerically, and finally transmits it to the display component through the transmission cable. This is the role of the conversion component in the standard orifice plate for the steam flow measurement system. 3. The transmission component Simply put, the transfer component is the channel that transmits signals. The elements of a measurement system are generally separated, which requires a transmission component to be used to connect them. The transmission component may be conduits, wires, optical fibers, and radio communications, depending on the signal’s physical nature, which may sometimes be simple and sometimes quite complex. For example, in a standard orifice plate system for measuring steam flow, the differential pressure signal from the standard orifice plate is transmitted by a conduit to a differential pressure transmitter, and a wire transmits the electrical signal from the differential pressure transmitter to a display component. 4. The display component The display component is the interface between the measurement system and the observer. It plays the role of displaying or regulating the measured signal in some form that complies with the observer’s record display. Among the electrical display

1.3 Basic Concepts of Error

7

components, there is analog display (instrument that reflects the continuous change of the measured value in the form of a pointer, liquid level, cursor, or graph), digital display (instruments show the measured value in digital quantity), and screen display (instruments show the measured value in various forms such as graph and number through LCD or CRT display).

1.3 Basic Concepts of Error The purpose of measurement is to obtain the true value of the measured parameter. However, various causes, e.g., poor instrument performance, imperfect measurement method, and external interference, can lead to inconsistency between the measured and true values. The inconsistency is described with the term measurement error. The measurement error is the difference between the measured and true values. It reflects the quality of the measurement. The reliability of the measurement is crucial, and the requirements for the reliability of the measurement results vary from occasion to occasion. For example, in the case of value transfer, economic accounting, product inspection, etc., the measurement results should be guaranteed to be sufficiently accurate. When the measured value is used as a control signal, attention should be paid to the stability and reliability of the measurement. Therefore, the accuracy of the measurement results should depend on and be adapted to the purpose and requirements of the measurement. It’s not realistic to pursue accuracy regardless of occasions and costs. One should have a sense of balance between technical and economic feasibility.

1.3.1 Representation of Measurement Errors There are various ways of representing measurement errors with different meanings. (i) Absolute error The following equation defines the absolute error: Δ = x − x0 ,

(1.3)

where Δ is the absolute error, x is the measured value, and x 0 is the true value. An absolute error is used when making corrections to measured values. The correction is a value of equal magnitude and opposite sign to the absolute error, and the actual value is equal to the measured value plus the correction. (ii) Relative error The use of absolute errors to express measurement errors does not indicate the quality of the measurement. For example, in temperature measurement, an absolute error

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1 Basics of Testing

Δ = l °C is not allowed for body temperature measurement, but it is an excellent result for measuring the temperature of molten steel. The following equation defines relative error: δ=

Δ × 100%, x0

(1.4)

where δ is the relative error, usually given as a percentage, Δ is the absolute error, and x 0 is the true value. Since the true value of the measurement x 0 is unknown, the actual measurement is calculated by substituting the measured value x for the true value x 0 . This relative error is called the nominal relative error, i.e., δ=

Δ × 100%. x

(1.5)

(iii) Cited error Cited error is a common method of error representation in the instrument. It is an error relative to the full range of the instrument and is generally expressed in percentage form as: γ =

Δ × 100%, U pper measur ement range − Lower measur ement range (1.6)

where γ is the citation error and Δ is the absolute error. When working with meters, it is common also to encounter the concepts of fundamental and additional errors. (iv) Fundamental error The basic error is the maximum quoted error of the instrument under the specified standard conditions. For example, the meter is calibrated under the conditions of the supply voltage (220 ± 5) V, grid frequency (50 ± 2) Hz, ambient temperature (20 ± 5) °C, and humidity 65 ± 5%. If this meter operates under this condition, the maximum quoted error that the meter has is the fundamental error. The fundamental error determines the accuracy class of the measuring instrument. (v) Additional error Additional error is the error that occurs when the instrument’s operating conditions deviate from the rated conditions, for example, temperature additional error, frequency additional error, power supply voltage fluctuations additional error, etc.

1.4 Quality Indicators for Measuring Instruments

9

1.3.2 Classification and Treatment of Errors The errors are classified into three types according to the pattern presented by the errors in the measurement data, i.e., systematic, random, and gross errors. This classification facilitates measurement data processing. (i) Gross error The error corresponding to a significant deviation of the measurement result from the actual value being measured is called gross error. Since this error seriously distorts the measurement results, it should be found and discarded by theoretical analysis or statistical methods. (ii) Random error Multiple equal precision measurements of a measured object, as long as the sensitivity of the measuring instrument is high enough, will certainly find a certain dispersion of these measurement results, which is caused by random error. After eliminating the coarse error and correcting the systematic error, each measurement result’s random error generally obeys the law of normal distribution. The application of statistical methods to deal with random error; that is, the arithmetic means of the measurement results as the best estimate of the actual value being measured, 2–3 times the root mean square deviation of the arithmetic mean as the confidence interval of the random error. The corresponding probability as the confidence probability can improve the measurement accuracy. The random error determines the precision of the measurement results. (iii) Systematic error Several equal precision measurements, such as the size and sign of each measurement’s error, remain the same or change according to a definite law. Statistical methods cannot eliminate systematic error, and it is not always possible to find it by statistical methods, so it is important to find the systematic error. It can be found by calibration comparison, changing measurement conditions, theoretical analysis and calculation, etc., and weakened by corrected values. The systematic error determines the accuracy of the measurement results.

1.4 Quality Indicators for Measuring Instruments 1.4.1 Static Characteristics of the Instrument (i) Accuracy (referred to as accuracy) Accuracy is the sum of precision and accuracy of the instrument, expressed in terms of relative error.

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Full range r elati ve err or =

Maximum absolute err or o f all values shown × 100% I nstr ument range

The accuracy level of the automatic detection instrument is graded according to a column of standard values of the specified fullness relative error (0.001, 0.005, 0.02, 0.05, 0.1, 0.2, 0.35, 0.5, 1.0, 1.5, 2.5, 4.0). Instrument accuracy class specifies the maximum quoted error of the instrument underrated use conditions shall not exceed the value. This value is called the allowable error, and the allowable error after removing the percentage sign is the accuracy class of the instrument. (ii) Stability Stability refers to the performance of the instrument value that does not change with time and use conditions. Time stability is expressed in terms of stability, that is, the amount of random change in the value over a period of time. The impact of changes in the use of conditions with the impact of error, such as the impact of the ambient temperature, shows how much change in value per degree of temperature change to indicate. (iii) Sensitivity Sensitivity is the ratio of the small change in output to the small change in input of the instrument at a steady state, i.e., S=

dy , dx

(1.7)

where dy is the small change in the value of the meter; dx is the small change in the measured value. Sensitivity is the slope of each point on the meter’s output–input characteristic curve. (iv) Variation (hysteresis) Variation is the degree of inconsistency between the forward and reverse characteristics of the instrument, expressed as a percentage of the ratio of the maximum of the difference between the forward and reverse characteristics to the range of the instrument, i.e., Eb =

Δmax × 100%, xmax − xmin

(1.8)

where Δmax is the maximum value of the difference between the forward and reverse characteristics, x max is the upper limit of the meter scale; x min is the lower limit of the meter scale. (v) Resolution Resolution is an indicator of the ability of the instrument to respond to small changes in the input quantity; i.e., it cannot cause a change in the output of the input amplitude and the ratio of the range of the instrument percentage. The resolution of the good or

1.4 Quality Indicators for Measuring Instruments

11

bad corresponds to the size of the resolution. Resolution error in the regulation of the instrument is often called a dead zone (or insensitive area). It has a very large impact on the quality of regulation. In analog instruments, the resolution is also known as the discrimination domain or sensitivity domain; in digital instruments, the resolution is also defined as the last digit of the display number change “1” represented by the measured increment. (vi) Reproducibility Reproducibility is the degree of inconsistency of the indicated value of the same measurement repeatedly under the same conditions. That is Ef =

Δ f max × 100%, xmax − xmin

(1.9)

where Δ f max is the largest repeat measurement difference in the full range.

1.4.2 Dynamic Characteristics of the Instrument The dynamic characteristics of an instrument are the response characteristics of its output to an input quantity that varies with time. When the measured quantity varies with time as a function of time, the instrument’s output is also a function of time, and the relationship is expressed in terms of dynamic characteristics. An instrument with good dynamic characteristics will have an output that reproduces the law of change of the input quantity; i.e., it has the same function of time. In fact, except for the ideal proportional characteristics, the output signal will not have the same function of time as the input signal. This difference between the output and the input is the so-called dynamic error. The dynamic characteristics are related to the form of variation of the instrument inputs in addition to the inherent factors of the instrument. In other words, when studying the dynamic characteristics of an instrument, the instrument’s response is usually examined according to different input variation laws. Although many types and forms of meters can generally be reduced to first-order or second-order systems (the higher-order can be decomposed into several lowerorder links), so first-order and second-order meters are the most basic. The input quantity of the meter varies with time in a variety of ways. In the following analysis of the dynamic characteristics of the meter, the most typical, simple, and easy-toimplement sine and step signals are used as standard input signals. For a sinusoidal input signal, the instrument’s response is called the frequency response or steady-state response; for a step input signal, it is called the step response or transient response of the instrument. 1. Transient response characteristics The transient response of an instrument is the time response. When studying the dynamic characteristics of an instrument, it is sometimes necessary to analyze the

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response of the instrument and the transition process from the time domain. This analysis method is the time domain analysis method, in the time domain, the instrument response to the added excitation signal is called transient response. The commonly used excitation signals are step function, ramp function, pulse function, etc. In the following subsection, the dynamic performance of the instrument is evaluated in terms of the unit step response of the instrument. (i) Unit step response of a first-order instrument In engineering, the following equation is considered the general formula of the unit step response of the first-order instrument: τ

dy(t) + y(t) = x(t) dt

(1.10)

where x(t) and y(t) are the input and output of the instrument, respectively, both as a function of time, and τ is the time constant of the instrument, with a time scale of “seconds”. The transfer function of a first-order instrument is H (s) =

1 Y (s) = X (s) τs + 1

(1.11)

For a meter with an initial state of zero, when a unit step signal is input; ( x(t) =

0t ≤0 1t >0

Since x(t) = 1(t) X (s) = 1s , the Rasch transform of the meter output is: Y (s) = H (s)X (s) =

1 1 · τs + 1 s

(1.12)

The unit step response signal of the first-order meter is: y(t) = 1 − e− τ . t

(1.13)

The corresponding response curve is shown in Fig. 1.3. The meter has inertia, and its output does not immediately reproduce the input signal, but starts from zero, rises exponentially, and eventually reaches the steady-state value. Theoretically, the response of the meter only reaches the steady-state value when t tends to infinity, but in practice, when t = 4τ its output reaches 98.2% of the steady-state value, it can be considered to have reached a steady state. The smaller the response curve, the closer it is to the input step curve, so the value of τ is an important performance parameter for first-order meters.

1.4 Quality Indicators for Measuring Instruments

13

x(t)

Fig. 1.3 First-order instrument unit step response

y (t)

2τ

3τ

4τ

0.993

0.950

τ

0.982

0.865

0

0.632

1

5τ t

(ii) Unit step response of second-order instruments The expression below gives the general formula for the unit step response of a second-order instrument: d 2 y(t) dy(t) + ωn2 y(t) = ωn2 x(t), + 2ξ ωn dt 2 dt

(1.14)

where ωn is the intrinsic frequency of the instrument, and ξ is the damping ratio. The transfer functions for second-order instruments are: H (s) =

s2

ωn2 . + 2ξ ωn s + ωn2

(1.15)

The Rasch transform of the meter output is: Y (s) = H (s)X (s) =

ωn2 . s(s 2 + 2ξ ωn s + ωn2 )

(1.16)

The response of a second-order instrument to a step signal is largely dependent on the damping ratio ξ and the intrinsic frequency ωn . The intrinsic frequency ωn is determined by the main structural parameters of the instrument and the higher the ωn , the faster the response of the instrument. When ωn is a constant, the response of the instrument depends on the damping ratio ξ. Figure 1.4 shows the unit step response curve of a second-order instrument. The damping ratio ξ directly affects the amount of overshoot and the number of oscillations. ξ = 0, for no damping, the overshoot is 100% and produces equal amplitude oscillations that do not reach a steady state. ξ = l, critical damping, no overshoot, and no oscillations, but longer time to reach steady state. ξ < l, underdamped, decaying oscillations, time to reach steady state increases with decreasing ξ. ξ > l, overdamped, has the shortest response time. However, in practice, it is often adjusted to be slightly underdamped. ξ is best to take 0.7~0.8 (Fig. 1.5).

14

1 Basics of Testing

y(t) 2

ξ=0 0.1 0.3 0.5

0.7 1

1 2 ωnt

0 Fig. 1.4 Second-order instrument unit step response

Fig. 1.5 Response characteristic curve

(iii) Transient response characteristics index 1. This response is characterized by the following: (1) Time Constant τ : The smaller the first-order instrument time constant τ, the faster the response. (2) Delay Time t d : The time it takes for the meter output to reach 50% of the steady-state value. (3) Rise Time t r : The time required for the meter output to reach 90% of the steadystate value. (4) Maximum Overshoot M p : The maximum value at which the meter output exceeds the steady-state value, Mp =

y(t p ) − y(∞) × 100%. y(∞)

(1.17)

1.4 Quality Indicators for Measuring Instruments

15

(5) Stabilization time t s : The time it takes for the response curve of a measurement system to reach and remain within a certain allowable error range around its final value. 2. Transient response characteristics The response characteristics of an instrument to a sinusoidal input signal are called frequency response characteristics. The frequency response method is a study of the instrument’s dynamic characteristics from the instrument’s frequency characteristics. (i) Frequency response of the first-order instrument By replacing s, in the transfer function of the first-order instrument, with jω, the frequency characteristic expression is obtained as: H ( j ω) =

1 . τ ( j ω) + 1

(1.18)

The amplitude-frequency characteristic A(ω) is given by the expression: A(ω) = √

1

.

(1.19)

Φ(ω) = − arctan(ωτ )

(1.20)

1 + (ωτ )2

Phase-frequency characteristics

The frequency response characteristic curve of the first-order instrument is shown in Fig. 1.6. From Eqs. (1.19), (1.20), and Fig. 1.6, it is clear that the smaller the time constant τ, the better the frequency response characteristics. When ωτ > ω, A(ω) ≈ 1, Φ(ω) is very small, then the output y(t) of the instrument reproduces the waveform of the input x(t). Normally, the intrinsic frequency ωn should be at least 3–5 times greater than the measured signal frequency ω, i.e., ωn ≥ (3–5)ω. In order to reduce dynamic errors and extend the frequency response range, it is common to increase the instrument’s intrinsic frequency ωn . The inherent frequency ωn is related to the mass of the instrument’s moving parts m and the stiffness of the elastic sensitive elements k, i.e., ωn = (k/m)1/2 . Increasing the stiffness k and reducing 0°

ξ=0.1 0.2

0.3 0.2

0.6 1.0 0.8

0.1 0.07 0.05

ξ=0.1 0.2 0.4 0.6 0.8 1.0

-40°

0.4

1.0 0.7 0.5

Φ(ω)

A(ω)

10 7 5 4 3 2

-80° -120°

0.03 0.02 0.01

-160° 0.1

0.2

0.5

1.0

2

5

10

0.1

0.2

0.5

1.0

ω/ωn

ω/ωn

(a)

(b)

2

5

10

Fig. 1.7 Second-order instrument frequency response characteristics. a Amplitude-frequency characteristics; b phase-frequency characteristics

1.4 Quality Indicators for Measuring Instruments

17

the mass m can increase the inherent frequency, but increasing the stiffness k will make the instrument less sensitive. Therefore, in practice, various factors should be combined to determine each characteristic parameter of the instrument. (iii) Frequency response characteristics index (a) Frequency band. The frequency range in which the instrument gain is maintained within a certain value is the instrument frequency band or passband, corresponding to having upper and lower cutoff frequencies. (b) Time Constant, τ. The time constant τ is used to characterize the dynamic characteristics of the first-order instrument. The smaller the τ, the wider the frequency band. (c) Inherent Frequency, ωn . The inherent frequency of a second-order instrument characterizes its dynamic characteristics. (d) Cutoff frequency, ωc . The frequency corresponds to the time when the amplitude ratio of a measurement system drops to the zero frequency amplitude ratio. ωc is an indicator that describes the dynamic performance of a measurement system in the frequency domain. Reflective Questions and Exercises 1.1 What are the main aspects of nuclear engineering test instrumentation that should be considered to meet the special environmental requirements of nuclear power plants? 1.2 How are measurement methods classified depending on the research question? What measurement methods are included in each classification? 1.3 What are the parts of a measuring instrument? What is the function of each part? 1.4 What are absolute error, relative error, quoted error, and additional error of a measurement? Why is the absolute error of measurement sometimes inappropriate as a measure of measurement accuracy? 1.5 What are the dynamic characteristics of a meter? What are the static characteristics of an instrument? What are transient response characteristics and frequency response characteristics, and what are the characteristics of each? 1.6 What is the response time of a meter? What is the linearity of a meter? 1.7 What are instrument stability and reproducibility? 1.8 What is the accuracy class of a meter and the sensitivity of a meter? What performance of the meter will be affected by excessive sensitivity? 1.9 What are the measuring range, upper limit, lower limit, and range of an instrument? Why is the range ratio used as an indicator of the meter’s performance? 1.10 A temperature measuring instrument has an accuracy class of 1.0, an absolute error of plus or minus l °C, and a negative lower measurement limit (the absolute value of the lower limit is 10% of the measurement range); try to determine the upper and lower measurement limits and the range of the meter.

18

1 Basics of Testing

1.11 A spring tube pressure gauge ranges from 0 to 1.6 MPa and has an accuracy class of 2.5. The maximum absolute error that occurs at a point during calibration is 0.05 MPa. Why? 1.12 A pressure gauge measures up to 0.6 MPa in the positive direction and -0.1 MPa in the negative direction. Now, only the positive part is calibrated, and its maximum error occurs at 0.3 MPa; i.e., the standard gauge indicates 0.305 MPa and 0.295 MPa in the upward and downward directions, respectively. Explain whether the gauge meets the requirement of accuracy class 1.5.

Chapter 2

Temperature Detection

2.1 Overview Temperature is a physical parameter that reflects an object’s degree of hotness and coldness. From the point of view of molecular motion theory, temperature indicates the average amount of kinetic energy of molecular motion within an object. In this sense, temperature cannot be measured directly but only indirectly with the help of heat exchange between hot and cold objects. Thus, it is an object’s physical property that varies with the degree of hotness and coldness. Various temperature sensors are used to form a variety of temperature measuring instruments.

2.1.1 Temperature Scale If two objects have different temperatures, the object with higher temperature transfers heat to the object with lower temperature. This phenomenon establishes “high” or “low” temperature. The scale used to measure temperature is called the temperature scale. It defines the starting point of temperature reading and the basic unit. The most commonly used temperature scales are the thermodynamic scale, the international practical scale, the Celsius scale, and the Fahrenheit scale. (i) Thermodynamic temperature scale The thermodynamic temperature scale, also known as the absolute temperature scale, is a theoretical temperature scale based on thermodynamics. It stipulates that the temperature at which molecular motion ceases is absolute zero. It is a temperature scale independent of any physical properties of the substance being measured. It has been adopted by the International Conference on Weights and Measures as the basic international uniform temperature scale.

© Harbin Engineering University Press 2023 H. Xia and Y. Liu, Measurement Science and Technology in Nuclear Engineering, Nuclear Science and Technology, https://doi.org/10.1007/978-981-99-1280-3_2

19

20

2 Temperature Detection

According to the Carnot theorem in thermodynamics, if there is a reversible heat engine between an infinite heat source at a temperature of T 1 and an infinite cold source at a temperature of T 2 that achieves a Carnot cycle, the heat given to the heat engine by the heat source is Q1 and the heat transferred from the heat engine to the cold source is Q2 , then the following relationship exists T1 Q1 = T2 Q2

(2.1)

Suppose a further value is specified in Eq. (2.1) to describe the temperature value at a certain point. In that case, the temperature scale can be fully determined by the heat transfer in the Carnot cycle. The 1954 International Conference on Weights and Measures determined the temperature value of the three-phase point of water, set at 273.16, and set the ratio of 1/273.16 as one degree. In this way, this temperature scale can be determined: that is, the temperature value T = 273.16(Q1 /Q2 ) and the temperature unit is set in Kelvin, abbreviated as K. In the standard unit of measurement, the use of thermodynamic temperature and Celsius temperature is specified; that is, the three-phase point of water is specified as 273.16 K and 0.01 °C, and thus the relationship between thermodynamic temperature and Celsius temperature is: t = T − 273.15 (◦ C)

(2.2)

(ii) International practical temperature scale Because the Carnot cycle cannot be realized, so the thermodynamic temperature scale is a theoretical temperature scale that cannot be put into practice and reproduction, which requires the establishment of a kind of both easy to use, but also has a certain level of science and technology of the temperature scale. After efforts in the 1920s, scientists from various countries established a kind of thermodynamic temperature scale of high accuracy, easy to use, practical temperature scale, which is the international practical temperature scale. The basic elements of a temperature scale are: the specification of reference instruments in different temperature ranges; the selection of the equilibrium temperature of some pure substance as the reference point for the temperature scale; and the establishment of an interpolation formula that allows the calculation of the temperature value between any two adjacent reference points. These are called the “three elements” of the temperature scale. The first international practical temperature standard was established in 1927 as ITS-27 and has been significantly revised approximately every 20 years since then, with a new international temperature standard (ITS-90) coming into effect in 1990. The basic elements of this temperature standard are.

2.1 Overview

21

1. Definition reference points: There are 17 definition reference points in ITS-90 (see 1990 International Temperature Scale Manual). 2. Reference instruments: The entire temperature scale was divided into four temperature zones using different reference instruments. These are 3 He and 4 He vapor pressure thermometers (0.65–5.0 K), 3 He and 4 He constant volume gas thermometers (3.0–24.5561 K), platinum resistance thermometers (13.8033 K to 961.78 °C), and optical or photoelectric pyrometers (above 961.78 °C). 3. Interpolation Formula. y = y1 + (x − x1 )

y2 − y1 , x2 − x1

(2.3)

where y is the linear interpolation value, x is the independent variable, x 1 , y1 are values of the function at one point, x 2 , y2 are values of the function at another point. (iii) Celsius temperature scale The Celsius temperature scale is the most used temperature scale in engineering. It specifies the freezing point of pure water at standard atmospheric pressure as 0° and the boiling point of water as 100°. The middle equivalence is divided into 100 cells, each equivalence being 1 degree Celsius, with the symbol °C. (iv) Fahrenheit temperature scale The Fahrenheit temperature scale specifies the freezing point of pure water at standard atmospheric pressure is 32°, and the boiling point of water is 212°, with an intermediate equivalence of 180 cells, each cell being 1 degree Fahrenheit, symbolized as °F. It is related to the Celsius temperature scale as follows: 5 (F − 32) (◦ C) 9 F = 1.8C + 32 (◦ F),

C=

(2.4)

where C is the Celsius temperature value; F is the Fahrenheit temperature value.

2.1.2 Classification of Temperature Measuring Instruments Temperature cannot be measured directly but is obtained indirectly by measuring the amount of change in certain physical properties of a substance as a function of temperature. Temperature measuring instruments can be classified according to their operating principle and sometimes according to the temperature range (high, medium, low, etc.) or the accuracy of the instrument (benchmark, standard, etc.). Depending on the method of measurement, temperature measurement instruments

22

2 Temperature Detection

can be divided into two categories: contact temperature measurement instruments and non-contact temperature measurement instruments. (i) Contact temperature measuring instrument Contact temperature measurement instrument uses temperature-sensing elements directly in contact with the measured medium and senses the temperature change of the measured medium. This method of measurement is more intuitive and reliable, but in some cases, it will affect the distribution of the measured temperature field, bringing measurement errors. In some media, such as high temperature or corrosive, the life of the temperature measurement element has a great impact. (ii) Non-contact temperature measuring instrument Non-contact temperature measurement instrument is a non-contact measurement instrument that uses the correspondence between the thermal radiation characteristics of the object and the temperature to measure the temperature of the object. The non-contact temperature measurement instrument does not directly contact the object to be measured. It is through the object to be measured and feel the role of thermal radiation between the parts to achieve temperature measurement. It, therefore, will not destroy the object to be measured temperature field. In theory, the upper limit of temperature measurement is not limited, but its temperature measurement accuracy is generally poor, usually used for high-temperature measurement. Examples of non-contact temperature measuring instruments include full radiation pyrometer, colorimetric pyrometer, monochromatic pyrometer, etc. Table 2.1 gives a detailed classification and range of application of the various temperature measuring instruments.

2.2 Thermocouple Thermometers In scientific research and production processes, a thermocouple is currently the most common and widely used measuring element for temperature measurement. It works using the “thermoelectric effect” phenomenon between different conductors. It has the advantages of simple structure, convenient production, wide measuring range, wide application, high accuracy, small thermal inertia, etc., and it can directly output electric signal, which is convenient for signal transmission, automatic recording, and automatic control.

2.2.1 Thermocouple Temperature Measurement Principle Two different conductors or semiconductor materials A and B form a closed loop, as shown in Fig. 2.1. If the temperatures T and T 0 at the two joints of the loop formed by

2.2 Thermocouple Thermometers

23

Table 2.1 Classification and scope of application of temperature measuring instruments Thermometer classification Contact type

Expansion type

Bimetallic thermometer

−80~550 °C

0.5~5 °C

Liquid

Mercury thermometer

−80~600 °C

0.5~5 °C

Organic liquid

−200~200 °C

1~4 °C

Gas

−270~500 °C

0.001~1 °C

Vapor pressure

−20~350 °C

0.5~5 °C

Liquid

−30~600 °C

0.5~5 °C

Metal

Platinum resistance −260~850 °C thermometer

Thermocouple Metal

Nonmetal

0.001~5 °C

Copper resistance thermometer

−50~150 °C

0.3~0.35%t

Nickel resistance thermometer

−60~180 °C

0.4~0.7%t

Rhodium iron resistance thermometer

0.5~300 K

0.001~0.01 K

0.5~30 K

0.002~0.02 K

Carbon resistance thermometer

0.01~70 K

0.01 K

Thermistor thermometer

−50~350 °C

0.3~5 °C

Non-metal Germanium resistance thermometer

Non-contact Radiant type type

Accuracy

Solid

Pressure type

Resistance type

Scope of application

Copper–Constantan −200~400 °C

0.5~1.5%t

Platinum −0~1800 °C Rhodium–Platinum

0.2~9 °C

Nickel Chromium–Kao Copper Alloy

0~800 °C

1%t

Nickel Chromium–Nickel Silicon (Nickel Aluminum)

−200~1300 °C 1.5~10 °C

Boron Carbide–Graphite

600~2200 °C

Total radiation pyrometer

700~2000 °C

Monochrome pyrometer

800~2000 °C

0.75%t

(continued)

24

2 Temperature Detection

Table 2.1 (continued) Thermometer classification

Scope of application Colorimetric pyrometer

800~2000 °C

Infrared thermometer

100~700 °C

Accuracy

Fig. 2.1 Thermocouple schematic

T0

A

B

T

A and B are not the same, a current is generated in the loop, indicating the presence of an electric potential in the loop, a phenomenon called the thermoelectric effect. The thermoelectric effect was first discovered by Seeback in 1821 and is therefore called the Seeback effect. The electric potential resulting from this effect is often referred to as the thermoelectric potential. It is often represented by the symbol E AB (T,T 0 ). Further research revealed that the thermoelectric potential is made up of two parts of the potential the contact potential and the temperature difference potential. (i) Contact potential When two conductors or semiconductor materials with different properties come into contact as shown in Fig. 2.2, due to the different internal electron density, the electron density of the material A is greater than that of the material B and some electrons will diffuse from A to B. This process makes A lose electrons to have a positive potential while B gains electrons to a negative potential, eventually forming an electrostatic field from A to B. The electrostatic field prevents further diffusion of electrons from A to B. When the diffusion and electric field forces are balanced, a fixed electric potential is established between the materials A and B. This phenomenon of forming an electric potential at the contact of two materials due to their different densities of free electrons is called the Peltier effect. The electric potential is called the Peltier potential or contact potential. Theoretically, it has been shown that the size and direction of the contact potential depend mainly on the nature of the two materials and the temperature of the contact surface. The greater the ratio of the electron density of the two conductors, the greater the contact potential, the higher the temperature of the contact surface, and the greater the contact potential. The relationship is:

2.2 Thermocouple Thermometers

25

Fig. 2.2 Contact potential schematic

A

T

B

EAB(T)

E AB (T ) =

KT N A (T ) ln , e N B (T )

(2.5)

where e is the unit charge, 4.802 × 10–10 absolute electrostatic units, K is the Boltzmann constant, 1.38 × 10–23 J/°C., N A (T )/N B (T ) is the electron density of the materials A and B at a temperature of T. (ii) Temperature difference potential As shown in Fig. 2.3, the two ends of the electrons have a different energy because the temperature of the two ends of the material is different. The higher temperature end of the electrons has higher energy, and as a result, the electrons will move to the lower end of the temperature. With the formation of an electrostatic field between the two ends of the material from the high-temperature end to the low-temperature end, the electric field will attract electrons from the low-temperature end to the hightemperature end to finally reach dynamic equilibrium. This phenomenon of electric potential due to different temperatures at the two ends of the same conductor or semiconductor material is called the Thomson effect. The resulting electric potential is called Thomson’s electric potential or temperature difference potential. The direction of the temperature difference potential is from the low-temperature end to the high-temperature end. Its magnitude is related to the temperature at both ends of the material and the properties of the material. If T > T 0 , then the temperature difference potential is: K E(T , T0 ) = e

∫T

1 d(N · t), N

(2.6)

T0

where N is the electron density of the material, as a function of temperature, T, T 0 , is the temperature at both ends of the material, and t is the temperature distribution along the length of the material. (iii) The total thermal potential of the closed loop of the thermocouple As shown in Fig. 2.4, a thermocouple loop consisting of two materials, A and B, is set up with two end contact temperatures T and T 0 , and T > T 0 , N A > N B , the temperatures

26

2 Temperature Detection

Fig. 2.3 Temperature difference potential schematic

T0

E(T,T0)

T

Fig. 2.4 Thermal potential distribution of thermocouple circuit

EAB(T0) T0 EA(T,T0)

A

B

EB(T,T0)

T EAB(T)

at intermediate points along the materials A and B from one end temperature T to the other end temperature T 0 are arbitrarily distributed t. It is clear that there are two contact potentials E AB (T)/E AB (T 0 ); two temperature difference potentials E A (T, T 0 ) and E B (T, T 0 ) in the circuit. The direction of each thermal potential is shown in Fig. 2.4. Thus, the total thermal potential of the circuit is: E AB (T , T0 ) = E AB (T ) + E B (T , T0 ) − E AB (T0 ) − E A (T , T0 ).

(2.7)

According to Eq. (2.5), the following expression is obtained: KT N A (T ) K T0 N A (T0 ) ln − ln e N B (T ) e N B (T0 ) ) ∫T ( K NA = d t · ln e NB

E AB (T ) − E AB (T0 ) =

T0

K = e

∫T

NA K ln dt + NB e

T0

K = e

∫T T0

∫T

( ) NA td ln NB

T0

NA K ln dt + NB e

∫T T0

d NA K t − NA e

∫T t T0

d NB NB

(2.8)

2.2 Thermocouple Thermometers

27

Then, Eq. (2.6) yields: K E B (T , T0 ) − E A (T , T0 ) = e =

K e

∫T

1 K d(N B · t) − NB e

∫T

1 d(N A · t) NA

T0

T0

∫T

( ( ) ) d NB d NA K T t + dt − vT0 t · + dt NB e NA

T0

K = e

∫T

d NB K t − NB e

T0

∫T t

d NA . NA

(2.9)

T0

Substituting Eqs. (2.8) and (2.9) into Eq. (2.7) then K E AB (T , T0 ) = e

∫T ln

NA dt. NB

(2.10)

T0

If the materials A and B are known, then N A and N B simply functions of temperature and Eq. (2.10) can be expressed as: E AB (T , T0 ) = f (T ) − f (T0 ).

(2.11)

Analysis of Eqs. (2.10) and (2.11) leads to the following conclusions. 1. The magnitude of the thermocouple circuit thermal potential is only related to the material that makes up the thermocouple and the temperature at which the two ends of the material are connected and is independent of the diameter, length, and temperature distribution along the thermocouple wire. 2. A thermocouple can only be formed with two materials of different properties; a closed circuit of the same material will not produce a thermal potential. 3. Once the two materials of the thermocouple are known, the magnitude of the thermal potential is only related to the temperature of the contacts at the ends of the thermocouple. If T 0 is known and constant, then f (T 0 ) is a constant. The total thermal potential of the circuit E AB (T, T 0 ) is only a single-valued function of the temperature T. When a thermocouple is used to measure temperature, one of the two contacts is always placed in a medium at a measured temperature of T. This contact is conventionally referred to as the hot or measuring end of the thermocouple. The other contact of the thermocouple is placed at a known constant temperature T 0 and this contact is called the cold or reference end of the thermocouple. It should be noted that the above equation is a theoretical expression and is not often used for calculations in practical applications. Usually, the temperature of the

28

2 Temperature Detection

cold end of the thermocouple is held at zero degrees. The resulting experimental data are tabulated as a relationship between E AB (T, T 0 ) and T, i.e., the indexing tables for various standard thermocouples (see Appendix Tables A.1–A.6).

2.2.2 The Circuit Nature of Thermocouples The closed thermocouple circuit usually consists of a display instrument and connecting wire for measuring the thermal potential in actual temperature measurement. Apart from the basic understanding of the principle of thermocouple temperature measurement, some basic laws must be applied. (i) The law of homogeneous materials A closed circuit consisting of a homogeneous material (with the same electron density everywhere) does not generate a thermal potential in the circuit, regardless of the temperature distribution along the length of the material. Conversely, if a thermal potential is present in the circuit, the material must be inhomogeneous. This law is proved by Eq. (2.10). This law requires that the two materials that make up the thermocouple A and B must each be homogeneous; otherwise, an additional potential will be generated due to temperature gradients along the length of the thermocouple, thus introducing thermocouple material inhomogeneity errors. Therefore, it is important to test and anneal the hot electrode material for homogeneity whenever possible when making precision measurements. (ii) The law of intermediate conductors When a third (or more) homogeneous material is inserted into a thermocouple circuit, the third material inserted does not affect the thermal potential of the original circuit as long as the temperature of the connection points at both ends of the inserted material is the same. Figure 2.5 is a typical line connection diagram for accessing the third homogeneous material. Figure 2.5a shows a third material C connected at the reference end of thermocouple materials A, B. The temperature at the junction of both A–C and B–C is T 0 , and the total thermal potential of the circuit is: Fig. 2.5 Wiring diagram for accessing a third material in the thermocouple circuit

C

T0

T0

T0

A

B

C T1

A

B T (a)

T0

T1

C

A

T0

T0 B

T (b)

(c)

2.2 Thermocouple Thermometers

29

E ABC (T , T0 ) = E AB (T ) + E B (T , T0 ) + E BC (T0 ) + E C A (T0 ) + E A (T0 , T ) = E AB (T ) + E B (T , T0 ) + E BC (T0 ) + E C A (T0 ) − E A (T , T0 ). (2.12) Before analyzing Eq. (2.11) further, the special case shown in Fig. 2.5c is analyzed. Assume in Fig. 2.5c that the contact temperatures of the three materials at A, B, C are the same and set to T 0 then E ABC (T0 ) = E AB (T0 ) + E BC (T0 ) + E C A (T0 ) ( ) K T0 N A (T0 ) N B (T0 ) NC (T0 ) = ln + ln + ln = 0. e N B (T0 ) NC (T0 ) N A (T0 ) This leads to E BC (T0 ) + E C A (T0 ) = −E AB (T0 ).

(2.13)

Substituting Eq. (2.13) into Eq. (2.12), we get E ABC (T , T0 ) = E AB (T ) + E B (T , T0 ) − E AB (T0 ) − E A (T , T0 ). Comparing this equation with Eq. (2.6) gives E ABC (T, T0 ) = E AB (T , T0 ).

(2.14)

This proves the conclusion of the intermediate conductor law. The circuit reader shown in Fig. 2.5b can prove the intermediate conductor law that extends to the case where more homogeneous materials are added to the thermocouple circuit. The intermediate conductor law indicates that a thermocouple circuit can be connected to an instrument that measures the thermal potential. As long as the instrument is at a stable ambient temperature, the thermopotential of the original thermocouple circuit will not be affected by the connected measuring instrument. The law also shows that thermocouple joints can be connected by welding and borrowing a homogeneous isothermal conductor. (iii) The law of intermediate temperature A thermocouple circuit of two different materials A, B has a thermal potential E AB (T, T 0 ) at contact temperatures t and t 0 equal to the algebraic sum of the corresponding thermal potentials E AB (t, t n ) and E AB (t n , t 0 ) for thermocouples at contact temperatures (t, t n ) and (t n , t 0 ), respectively, where t n is the intermediate temperature. That is: E AB (t, t0 ) = E AB (t, tn ) + E AB (tn , t0 ).

(2.15)

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2 Temperature Detection

Fig. 2.6 Schematic diagram of thermocouple intermediate temperature law

A

t t

t0

B tn

A

A

B

t0

B

As shown in Fig. 2.6, the intermediate temperature law is easy to prove by adding one f (t n ) and subtracting one f (t n ) from Eq. (2.11). The law states that when the temperature at the cold end of the thermocouple t 0 /= 0 °C, the thermocouple indexing table can still find the measured temperature t value, provided that the thermal potential E AB (T, T 0 ) can be measured and t 0 is known. If t n is set to 0 °C, Eq. (2.15) reduces to E AB (t, t0 ) = E AB (t, 0) + E AB (0, t0 ) = E AB (t, 0) − E AB (t0 , 0) Then E AB (t, 0) = E AB (t, t0 ) + E AB (t0 , 0).

(2.16)

In a thermocouple circuit, if the electrode materials A and B of the thermocouple are connected to the connecting wires A' and B', respectively (as shown in Fig. 2.7), and the temperatures of each relevant connection point are t, t n , and t 0 , tn , then the total thermal potential of the circuit is equal to the algebraic sum of the thermal potentials E AB (t, t n ) at the ends of the thermocouple at the temperatures t and t n and the thermal potentials E A' B ' (tn , t0 ) at the ends of the connecting wires A' and B ' at the temperatures tn and t0 . The total thermal potential of the circuit shown in Fig. 2.7 becomes: E AB B ' A' (t, tn , t0 ) = E AB (t, tn ) + E A' B ' (tn , t0 ).

(2.17)

The equation is proved as follows: Owing to E B B ' (Tn ) + E A' A (Tn ) =

Fig. 2.7 Schematic diagram of thermocouple and connecting wires

K Tn n B (Tn ) n A' (Tn ) ln e n B ' (Tn ) n A (Tn ) A

tn

A'

t

t0 B

tn

B'

2.2 Thermocouple Thermometers

31

[ ] n A' (Tn ) n A (Tn ) K Tn ln − ln e n B ' (Tn ) n B (Tn ) = E A' B ' (Tn ) − E AB (Tn ), =

i.e., E B B ' (tn ) + E A' A (tn ) = E A' B ' (tn ) − E AB (tn ) also known as E B ' A' (t0 ) = −E A' B ' (t0 ). Consequently, E AB B ' A' (t, tn , t0 ) = E AB (t) + E B (t, tn ) + E B B ' (tn ) + E B ' (tn , t0 ) + E B ' A' (t0 ) + E A' (t0 , tn ) + E A' A (tn ) + E A (tn , t) = E AB (t) + E A' B ' (tn ) − E AB (tn ) − E A' B ' (t0 ) − E A (t, tn ) + E B (t, tn ) − E A' (tn , t0 ) + E B ' (tn , t0 ) = [E AB (t) − E AB (tn ) − E A (t, tn ) + E B (t, tn )] + [E A' B ' (tn ) − E A' B ' (t0 ) − E A' (tn , t0 ) + E B ' (tn , t0 )] = E AB (t, tn ) + E A' B ' (tn , t0 ). (2.18) The intermediate temperature law is the theoretical basis for the application of compensation wires in industrial thermocouple temperature measurement.

2.2.3 Structure of Commonly Used Thermocouple Materials (i) Requirements for thermocouple materials In terms of the thermoelectric effect of metals, theoretically, any two conductors can constitute a thermocouple and be used to measure temperature. However, to ensure the reliability and accuracy of actual practical measurements, not all conductors are suitable for thermocouples. Thermocouple materials should meet the following requirements: 1. The thermocouple composed of two materials should output a large thermal potential to obtain a higher sensitivity and require a linear function between the thermal potential and temperature as far as possible. 2. The thermocouple should cover a wide range of temperatures, physical and chemical properties, and stable thermoelectric properties. Moreover, the thermocouple is required to have better heat resistance, oxidation resistance, reduction resistance, corrosion resistance, and other properties. 3. High conductivity and low resistance temperature coefficient. 4. The material should be readily available, easy to produce in batches, simple to manufacture, and inexpensive.

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2 Temperature Detection

However, no material can meet all of the above requirements. Therefore, the choice of thermocouple materials depends on specific parameters such as different temperature measurement conditions and requirements to choose different materials. (ii) Standardized thermocouples Standardized thermocouples are general-purpose thermocouples of specific product. Each standardized thermocouple has a uniform indexing table. The same type of standardized thermocouple is interchangeable with a matching instrument for use. When choosing a thermocouple for temperature measurement, the three requirements of temperature measurement range, price, and accuracy should be considered. The internationally recognized thermocouples with excellent performance and the largest production are described below. 1. Platinum–rhodium10 –platinum thermocouple (Indexing number S) It is a precious metal thermocouple. The positive pole is a platinum–rhodium alloy composed of 90% platinum and 10% rhodium, and the negative pole is made of pure platinum. This thermocouple can be used for higher temperature measurements and can work for a long time between 0 and 1300 °C, and short-time measurements can reach 1600 °C. The common wire diameter is 0.35–0.5 mm. The diameter of the commonly used wire is 0.35–0.5 mm. Finer diameters can be used for special use conditions. The advantages of the thermocouple include good reproducibility, high accuracy, and it is easy to produce higher purity platinum and platinum–rhodium alloy. It is generally used for precision measurement or as a reference thermocouple in the international temperature scale. The physical and chemical properties are stable and suitable for oxidizing or neutral atmosphere media. The disadvantages are weak thermoelectric potential, low sensitivity, expensive, easy to erode, and contaminated in high temperature, reducing media and deterioration. 2. Ni–Cr–Ni–Si thermocouple (Indexing number K) It is a widely used inexpensive metal thermocouple. The positive pole is nickel– chromium, and the negative pole is nickel–silicon. Its advantages are good chemical stability and can work in oxidizing or neutral media for a long time at temperatures below 1000 °C, while short-term use can reach 1300 °C. It has higher sensitivity, better reproducibility, good linearity of thermoelectric properties, low price. The metal wire diameter range is large; i.e., in industrial applications generally range between 0.5 and 3 mm. K-type thermocouple thermal potential rate is large (4~5 times larger than S-type thermocouple), but its temperature measurement accuracy is lower than S-type thermocouple. When used in experimental research, it can be stretched to finer diameters as needed. It is a thermocouple which is widely used in large numbers in industry and the laboratory. However, it is susceptible to erosion in reducing media or sulfide-containing atmospheres, so K-type thermocouples working in such atmospheres must be equipped with protective sleeves.

2.2 Thermocouple Thermometers

33

3. Copper–constantan thermocouple (Indexing number T) This is a cheap metal thermocouple. The positive pole is copper, and the negative pole is constantan. Its temperature measurement range is −200~300 °C, and it can reach 400 °C for short-term use. The commonly used thermocouple wire diameter is within 0.2~1.6 mm. It is suitable for lower temperature measurement and high measurement accuracy. When measuring the temperature below 0 °C, the positive and negative poles need to be adjusted to each other. 4. Platinum–rhodium30 –platinum–rhodium6 thermocouple (Indexing number B) This is a precious metal thermocouple, also known as a double platinum–rhodium thermocouple. Its distinctive feature is the high upper limit of temperature measurement, which can work at 1600 °C for a long time and reach 1800 °C for a short time. The measurement accuracy is high, and the thermocouple wire diameter is 0.3~0.5 mm, suitable for use in an oxidizing or neutral atmosphere. However, it is not suitable for use in reducing atmosphere. It has low sensitivity and expensive. Since this thermocouple has a thermal potential of only 15 μv below 80 °C, there is no need to consider the influence of the cold-end temperature on the measurement. In addition to the above, there are platinum–rhodium13 –platinum (indexing number R) thermocouples, iron–constantan (indexing number J), nickel–chromium– silicon–nickel–silicon (indexing number N) and nickel–chromium–constantan (indexing number E) thermocouples, giving a total of eight standardized thermocouples. Their performance is compared as shown in Table 2.2. (iii) Non-standardized thermocouples Generally speaking, the thermocouple that has not been finalized and has no uniform indexing table is called a non-standardized thermocouple. Non-standardized thermocouples are generally used in high temperature, low temperature, ultra-low temperature, high vacuum and nuclear radiation, and other special occasions. In these situations, non-standardized thermocouples often perform well. With the development of modern science and technology, a large number of non-standardized thermocouples have also been rapidly developed to meet certain special temperature measurement requirements. For example, tungsten rhenium5 – tungsten rhenium20 can measure up to 2400~2800 °C high temperature, the thermal potential at 2000 °C is close to 30 mV, the accuracy of 1% t, but it is easy to oxidize at high temperatures and can only be used in vacuum and inert atmosphere. Iridium rhodium40 –Iridium thermocouple is currently the only thermocouple that can measure up to 2000 °C in an oxidizing atmosphere, thus becoming an important temperature measurement tool in astronautics rocket technology. NiCr–AuFe is a more ideal low-temperature thermocouple used in the (2–273) K range. There are more than 50 types of thermocouples used in various countries around the world.

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2 Temperature Detection

Table 2.2 Comparison of standardized thermocouple performance Indexing number

Thermocouple Positive pole (+ve)

Negative pole (−ve)

S

Platinum rhodium10➀

Platinum

R

Platinum rhodium13

Platinum

Grade

Temperature range (°C)

Allowable error

I

0~1100 1100~1600

±1 °C ±[1 + 0.003(t − 1100)] °C

II

0~600 600~1600

±1.5 °C ±0.25%|t|

I

0~1100 1100~1600

±1°C ±[1 + 0.003(t − 1100)] °C

II

0~600 600~1600

±1.5 °C ±0.25%|t|

II

600~1700

±0.25%|t|

III

600~800 800~1700

±4.0 °C ±0.5%|t|

Platinum rhodium30

Platinum rhodium6

K

Nickel chromium

Nickel silicon

I II III

−40~1100 −40~1300 −200~40

±1.5 °C 或±0.4%|t| ±2.5 °C 或±0.75%|t| ±2.5 °C 或±1.5%|t|

N

Nickel chromium silicon

Nickel silicon

I II III

−40~1100 −40~1300 −200~40

±1.5 °C 或±0.4%|t| ±2.5 °C 或±0.75%|t| ±2.5 °C 或±1.5%|t|

E

Nickel chromium

Copper nickel alloy (Constantan)

I II III

−40~800 −40~900 −200~40

±1.5 °C 或±0.4%|t| ±2.5 °C 或±0.75%|t| ±2.5 °C 或±1.5%|t|

J

Pure iron

Copper nickel alloy (Constantan)

I II

−40~750 −40~750

±1.5 °C 或±0.4%|t| ±2.5 °C 或±0.75%|t|

T

Pure copper

Copper nickel alloy (Constantan)

I II III

−40~350 −40~350 −200~40

±1.5 °C 或±0.4%|t| ±2.5 °C 或±0.75%|t| ±2.5 °C 或±1.5%|t|

B

Note 1 t is the measured temperature, |t| is the absolute value of t Allowable error—expressed as a percentage of the temperature deviation value or the absolute value of the measured temperature, of which the maximum value is adopted

2.2 Thermocouple Thermometers

35

(iv) Structure of thermocouples There are various types of thermocouple structures. The two main types commonly used in industry are the normal and armored and others are used in special applications. 1. Ordinary-Type thermocouple Ordinary-type thermocouple usually consists of a thermal electrode, insulating material, protective sleeve and junction box, and other major parts. It is mainly used in industry to measure the temperature of liquid, gas, steam, etc. Figure 2.8 shows the structure of a typical industrial thermocouple. The two thermal electrodes of the thermocouple are covered with insulating sleeves, most of which are aluminum oxide tubes or industrial ceramic tubes. The protective sleeve is determined according to the temperature measurement conditions. The metal sleeve is generally used for measuring the temperature below 1000 °C. On the other hand, an industrial ceramic or even alumina oxide protective sleeve is used to measure temperatures above 1000 °C. Thermocouples used in scientific research are mostly made of fine thermal electrode wires and sometimes without protective sleeves to reduce thermal inertia, improve dynamic response indicators, and increase measurement accuracy. 2. Armored thermocouples It comprises a thermal electrode, insulating material, and metal casing together by pulling fine processing and forming one, also called casing thermocouple. Figure 2.9 shows the cross-sectional structure of an armored thermocouple. It has stable performance, compact structure, firmness and vibration resistance, small thermal inertia, Fig. 2.8 Schematic diagram of industrial thermocouple structure, 1—junction box; 2—protective sleeve; 3—insulating sleeve; 4—thermocouple wire

36

2 Temperature Detection

Fig. 2.9 Armored thermocouple cross-sectional structure, 1—metal sleeve; 2—insulating material; 3—thermal electrode

1

2 3

and good dynamic characteristics because of the small heat capacity at the measuring end. The outer diameter, length, and structure type of the measuring end of this thermocouple can be selected according to the need. The outer diameter varies from 0.25 to 12 mm. 3. Thin-Film thermocouples It is a special structure thermocouple made of two metal films. It uses vacuum vapor deposition or chemical coating and other manufacturing processes to vaporize two thermocouple materials onto an insulating substrate to form a thin-film thermocouple. The thin-film thermocouple’s hot-end contact is small and thin, about 0.01–0.1 μm. Because of its small heat capacity at the measurement end, it is suitable for rapid measurement of wall temperature, and its response is fast. Its time constant can reach a microsecond level to measure transient surface temperature. The base plate is made of materials such as mica or impregnated phenolic plastic sheets. Thermal electrodes are available in NiCr–NiSi, copper–constantan, etc. The temperature measurement range is generally below 300 °C when used with a binder to adhere the substrate to the surface of the object to be measured. The shape of the thin-film thermocouple made in China is shown in Fig. 2.10. The substrate size is 60 mm × 6 mm × 0.2 mm. 4. Thermowell-Type thermocouple In order to ensure that the thermocouple temperature-sensing element works under high temperature and high pressure with high flow conditions and to ensure accurate measurement and rapid response, a thermowell-type thermocouple was made. It is used exclusively in the main steam pipeline to measure the main steam temperature. The thermowell-type thermocouple is characterized by a welded installation with a conical sleeve, triangular conical support, and thermowell preserving heat. This structure type ensures the thermocouple temperature measurement accuracy and sensitivity and improves the mechanical strength and thermal shock performance Fig. 2.10 Schematic diagram of a thin-film thermocouple, 1—thermal electrode; 2—thermal junction; 3—insulating substrate; 4—lead wire

1 2

3

4

2.2 Thermocouple Thermometers

37

Fig. 2.11 Thermowell-type thermocouple construction and installation. a Structure; b installation schematic, 1—insulation; 2—sensor; 3—thermowell; 4—mounting sleeve; 5—electrically welded interface; 6—main steam pipe wall; 7—clamping fixing

of the thermocouple protection casing, whose installation schematic is shown in Fig. 2.11.

2.2.4 The Cold End of the Thermocouple Compensation According to the thermocouple temperature measurement principle, the thermal potential generated by a thermocouple E(t, t0 ) is a function of the temperatures t and t0 at both ends. For ease of use, the thermal potential is always considered a single-valued function of the temperature t. This measurement requires the cold-end temperature t0 to be 0 °C or at a certain value such that the thermal potential only varies with the temperature t, i.e., E AB (t, t0 ) = f (t) or E AB (t, t0 ) = f (t) − C. However, since the cold-end temperature t0 is affected by the ambient temperature, it is difficult to keep it at 0 °C or a certain value by itself. Therefore, to reduce the measurement error, the cold end of the thermocouple needs to take artificial measures to make its temperature constant or use other methods for correction and compensation. (i) Ice bath method The method is one of the most accurate treatments that maintain t0 at a stable 0 °C. It is implemented by placing the ice and water mixture in a thermos. The temperature t0 = 0 °C is achieved by inserting a fine glass test tube into the ice and water mixture, filling the bottom of the test tube with the appropriate amount of oil or mercury, and inserting the reference end of the thermocouple into the bottom of the test tube as shown in Fig. 2.12.

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2 Temperature Detection

Fig. 2.12 Schematic diagram of the ice bath method, 1—ice and water mixture; 2—thermos; 3—oil or mercury; 4—distilled water; 5—test tube; 6—cap; 7—copper wire; 8—thermopotential measuring instrument

A t

8 B 7 6 5 1 2

4 3

(ii) Theoretical revision method The thermocouple is indexed with the cold end held at 0 °C. Under practical use conditions, if the cold-end temperature t0 cannot be maintained at 0 °C, the measured thermal potential is relative to the thermopotential at the temperature of t0 , i.e., E AB (t, t0 ). By placing the cold end of the thermocouple at a known constant temperature, a stable t0 temperature can be obtained according to the intermediate temperature law Eq. (2.16) E(t, 0) = E(t, t0 ) + E(t0 , 0), where E(t0 , 0) is the thermopotential obtained by checking the thermocouple indexing table against the known steady temperature at the cold end of t0 . The actual temperature to be measured is obtained by checking the thermopotential at E(t, t0 ) and the sum of the thermocouple index at E(t0 , 0) to obtain the measured actual temperature t. [Example]: The thermal potential measured with a NiCr–NiSi thermocouple at a cold-end temperature of 25 °C is 34.36 mV. Find the actual temperature measured by this thermocouple. Solution: Check the indexing table of NiCr–NiSi thermocouple and get E(25, 0) = 1.00 mV, then E(T , 0) = E(T , 25) + E(25, 0) = 34.36 + 1.00 = 35.36 mV. Checking the above indexing table again, the actual temperature measured is 851 °C. (iii) Cold-end compensator method Many industrial processes have neither the conditions to maintain 0 °C nor the conditions to maintain a constant temperature at the cold end for a long time. Thermocouples’ cold-end temperature often varies with time and their environment. In this case the cold end, a compensator is used to compensate automatically. Figure 2.13 is a schematic diagram of a thermocouple circuit connected to a compensator.

2.2 Thermocouple Thermometers Fig. 2.13 Cold end compensator into thermocouple circuit, 1—thermocouple; 2—compensating wire; 3—copper wire; 4—indicating instrument; 5—cold-end compensator

39 2

3 c

4 R1

R4 a

b R3

R2 d

B

Rg

5

A

1

4V(DC)

The cold-end compensator is an unbalanced bridge with the wiring shown in Fig. 2.13. At present, the cold-end temperature compensator has a unified design of China. The bridge arm R1 = R2 = R3 = 1 Ω has manganese copper wire non-inductance winding, with a resistance temperature coefficient that tends to zero, the resistance value does not change with temperature. The bridge arm R4 with copper wire non-inductive winding, its resistance temperature coefficient is about 4.3 × 10−3 Ω °C−1 , when at the equilibrium point temperature (specified 0 °C or 20 °C) R4 = 1 Ω. Rg ; the current limiting resistor is used to adjust the supply current of the compensator when using thermocouples with different index numbers. The bridge supply voltage is 4 V DC. The output of the cold-end temperature compensator ab is connected in series with the thermocouple during the measurement, and when the cold-end temperature is at the equilibrium point temperature (assumed to be 0 °C), the bridge is balanced and there is no output from the bridge, i.e., Uba = 0, then the total potential measured by the indicating instrument is E = E(t, t0 ) + Uba = E(t, 0). When the ambient temperature changes and leaves the equilibrium temperature, the resistance value R4 changes to break the bridge balance. Thus, the bridge has an unbalanced potential output. The voltage direction is the same as the thermocouple’s thermal potential direction when it exceeds the equilibrium temperature and the opposite of the thermocouple’s thermal potential if it is lower than the equilibrium temperature. Through an appropriate design, the current limiting resistance of the bridge Rg is calculated so that the output voltage of the bridge Uba changes to a value exactly equal to [E(t, 0) − E(t, t0 )]. The total potential measured by the indicating instrument will not change with t0 . i.e., E = E(t, t0 ) + Uba = E(t, t0 ) + [E(t, 0) − E(t, t0 )] = E(t, 0).

40

2 Temperature Detection

The equation shows that when the thermocouple cold-end temperature changes, due to the cold-end compensator access, the total potential indicated by the instrument E remain as E(t, 0), which is equivalent to the thermocouple cold end at 0 °C. Thus, the role of the cold-end temperature is the automatic compensation. In fact, this compensation can only be fully compensated at the equilibrium point temperature and the calculation point temperature. The temperature is referred to as the equilibrium point temperature; that is, the above-mentioned R1 ~R4 are equal. The 1 Ω temperature point; the so-called calculation point temperature is the temperature point selected in the design of the calculation of the bridge. At this temperature point, the output voltage of the bridge circuit compensates exactly the cold end of the thermocouple temperature deviation from the equilibrium point temperature and the amount of thermal potential change. Except for the equilibrium and calculation point temperatures, only approximate compensation is available at each cold-end temperature value. (iv) Compensating wire method A thermocouple has a certain diameter, length, and a fixed structure. During the production process, there is often a need to move the cold end of the thermocouple to the measured medium farther away and more stable temperature conditions to avoid the cold end of the temperature of the measured medium interference. But this method of installation and use is not convenient because it consumes a lot of precious metal materials. Therefore, instead of part of the thermocouple wire as an extension of the thermocouple, a special wire (called compensation wire) is generally used. The thermoelectric properties of the compensation wire in the range of 0~100 °C replaced by the thermocouple wire’s thermoelectric properties are the same and with low resistivity. For the precious metal thermocouple, it is important for the compensating wire to be cheaper than the main thermocouple wire. The connection using the compensation wire is shown in Fig. 2.14. From Fig. 2.14, it can be seen that the cold-end temperature changes from t0 to t0' due to the introduction of the compensation wires A' and B ' , the total thermal potential of the circuit is: E = E AB (t, t0 ) + E A' B ' (t0 , t0' ) + E A A' (t0 ) + E B B ' (t0 ) Since the materials A and A' and B and B ' have the same thermoelectric properties, i.e., both have zero contact potential. Then there is: Fig. 2.14 Thermocouple and compensation wire wiring diagram

A

A'

t B

t0

B' t'0

2.3 Expansion Thermometers

41

Table 2.3 Commonly used thermocouple compensation wire technical data Thermocouple name

Compensation conductor

Standard electromotive force/mV (t = 100 °C, t0 = 0 °C)

Positive electrode

Negative pole

Material

Color

Material

Color

Nickel chromium–Nickel silicon

Copper

Red

Constantan

Brown

4.10±0.15

Platinum rhodium–Platinum

Copper

Red

Copper–nickel

Green

0.64±0.03

Nickel chromium–Constantan

Nickel chromium

Purple

Constantan

Brown

6.32±0.3

Copper–Kao copper alloy

Copper

Red

Kao copper alloy

Yellow

4.76±0.15

E A A' (t0 ) = 0,

E B B ' (t0 ) = 0.

According to the intermediate temperature law, there is: E AB (t, t0 ) + E A' B ' (t0 , t0' ) = E AB (t, t0' ) or E = E AB (t, t0' ). This process is equivalent to relocating the cold end of the thermocouple to a temperature of t0' , which can then be connected to a cold-end compensator or other desired instrumentation. Table 2.3 gives the compensating wire characteristics for several commonly used thermocouples.

2.3 Expansion Thermometers Most solids and liquids expand as temperature increases. This physical effect can be used to make an expansion thermometer, which indicates temperature either by directly observing the amount of expansion or by detecting it and obtaining a temperature signal through the actuator. Expansion thermometers are divided into solid expansion, liquid expansion, and gas expansion types.

2.3.1 Solid Expansion Thermometer A typical solid expansion thermometer is a bimetal, which uses the linear expansion coefficient of the two metal materials made of double-layer sheet elements. When

42

2 Temperature Detection

Fig. 2.15 Bending of a bimetallic strip

l0 d d A

φ

B

r r+d

the temperature changes due to bending deformation, the significant displacement on the other end drives the pointer to constitute a bimetal thermometer. The change in length Δl of a solid originally of length l due to a change in temperature Δt can be expressed as follows: Δl = lαΔt,

(2.19)

where α is the coefficient of linear expansion, which is generally available as a constant over a given temperature range. A bimetallic strip is formed by bonding together two strips A and B of different expansion rates and thicknesses d. When the temperature changes, the difference in expansion rates of the two materials causes the bimetallic strip to bend, as shown in Fig. 2.15. If we let the initial length of the bimetallic strip at a temperature of 0 °C be l0 , α A and α B be the coefficients of linear expansion of materials A and B, respectively, and α A < α B . Assuming that the bimetallic strip is bent into a circular arc shape when subjected to the temperature T , then l0 (1 + α B T ) r +d = , r l0 (1 + α A T )

(2.20)

where r + d is the length of strip B after expansion and r is the length of A after expansion. This can be solved for: r=

d(1 + α A T ) T (α B − α A )

(2.21)

If the strip A is made of an iron–nickel alloy, then α A is approximately zero, and Eq. (2.21) can be written as

2.3 Expansion Thermometers

43

r=

d αB T

.

(2.22)

As shown in Eq. (2.22), d is smaller for thinner bimetallic strips, which means that the bimetallic strip will show a larger bend. Bimetallic strip thermometers are made using this principle. In order to increase the sensitivity, the bimetallic strip is sometimes wound into the shape of a spiral tube. When the temperature changes, one end of the spiral tube is displaced relative to the other end, so that the pointer can be driven to give the temperature reading directly on the dial and become a pointer-type temperature measuring instrument. As shown in Fig. 2.16, bimetal thermometer can also be made into a recording-type temperature measurement instrument or bimetal electric contact temperature meter as shown in Fig. 2.17. The bimetal thermometer detection is generally in the range (−80~600) °C, the minimum can reach −100 °C, and the accuracy is generally in 1~2.5 grade and up to 0.5 grade.

Fig. 2.16 Industrial bimetal thermometer, 1—dial; 2—pointer; 3—watchcase; 4—movable nut; 5—pointer shaft; 6—protection tube; 7—temperature-sensing element; 8—fixed end Fig. 2.17 Bimetallic electric contact thermometer, 1—temperature regulating knob; 2—leaf spring; 3—bimetallic sheet; 4—electric heating wire

44

2 Temperature Detection

2.3.2 Liquid Expansion-Type Thermometer The change in volume ΔV of a liquid of volume V due to a change in its temperature ΔT can be expressed by the following equation: ΔV = VβΔT ,

(2.23)

where β is the coefficient of expansion of the volume of the liquid, averaged over a range of temperatures. The thermometer made based on the principle of liquid volume expansion due to temperature rise is called a liquid expansion thermometer. The most common type is the glass tube liquid thermometer. Figure 2.18 is a schematic diagram of a glass tube liquid thermometer. Because the coefficient of expansion of the liquid is much greater than that of the glass, the working liquid stored in the temperature-sensitive bubble expands as the temperature increases and rises along the capillary tube. A safety bubble is usually left at the top of the capillary tube to prevent the liquid from expanding and cracking the glass tube when the temperature is too high. The glass tube liquid thermometer is commonly used because of its accurate measurement, intuitive readings, simple structure, low cost, and easy use. On the other hand, glass tube liquid thermometers are disadvantaged by being fragile and lacking remote signal and automatic recording. According to the different working liquid fill, glass tube liquid thermometers are divided into two categories of mercury thermometer and organic liquid thermometer. The former does not stick to the glass, is not easy to oxidize, easy to obtain, has higher accuracy, and operates in a fairly large range (−38~356 °C) to maintain the liquid state below 200 °C. Its expansion coefficient is almost linear with the temperature so that it can be used as a precision standard thermometer. Table 2.4 gives the common working liquid and temperature range of glass tube liquid thermometer. The following two issues should be noted with liquid glass tube thermometers: (1) Zero point drift: The thermal expansion and contraction of the glass will also affect the movement of the zero position. Thus, the use of glass tube liquid thermometer should be regularly calibrated with zero position. (2) The correction of the exposed liquid column: The use of the thermometer must be strictly controlled by the depth of insertion because the temperature scale is calibrated in the thermometer liquid column immersed in the medium. Laboratory glass thermometers are usually made into (a) full immersion and (b) partial immersion. The full immersion type is used the same way as the standard thermometer. The partial immersion type is only inserted at a certain depth when used, and the exposed part is under the specified temperature conditions. If the temperature of the exposed part is not the same as the temperature of the conditions specified in the scale, the liquid column can be used according to the following formula to find its correction value Δt: Δt = n K (t B − t A ),

(2.24)

2.3 Expansion Thermometers

45

Fig. 2.18 Glass tube liquid thermometer, 1—safety bubble; 2—capillary tube; 3—scale; 4—glass rod; 5—liquid column; 6—temperature-sensitive bubble

Table 2.4 Glass tube liquid thermometer liquid work and temperature measurement range Working fluid

Measuring range (°C)

Remarks

Mercury

−30~750

The upper limit is obtained by inflating and pressurizing

Toluene

−90~100

Ethanol

−100~75

Petroleum ether

−130~25

Pentane

−200~20

46

2 Temperature Detection

where n is the number of degrees occupied by the exposed liquid column (°C), K is the coefficient of expansion of the working liquid visible in the glass (mercury K ≈ 0.00016/°C; organic liquid K ≈ 0.00124/°C), t B is the temperature of the exposed portion of the air under indexing conditions (°C), t A is the temperature of the exposed portion of the air under operating conditions (°C). If a fully immersed thermometer is not fully immersed when in use, the following correction should be made for the systematic error introduced by the exposed portion. Δt = n K (t R − t A ),

(2.25)

where n, K , t A is same as in Eq. (2.24), t R is the column reading (°C). These two corrections can be easily calculated by from the illustration in Fig. 2.19. Figure 2.19a shows the full immersion thermometer but not fully immersed, with a value of 93 °C, the immersion part is 67 °C, and the average height of the exposed mercury column at 80 °C at air temperature of 35 °C, then according to Formula (2.25) the correction value Δ t = +0.24 °C. Figure 2.19b is a partial immersion thermometer, the insertion depth meets the requirements of use, but the exposed part of the air temperature t A = 35 °C, and according to Formula (2.24) the correction value Δt = −0.021 °C. If a wire is placed near the sensing bubble of a mercury thermometer, and another wire is placed at the line corresponding to a certain temperature scale, the mercury column will turn the circuit on when the temperature rises to that temperature scale. Conversely, a drop in temperature below that scale will again break the circuit. In this way, it becomes a bit-regulated temperature sensor with a fixed switching value. This process of sending signals forms the electric contact thermometer. The electrical contact thermometer is divided into adjustable and fixed two types. The adjustable corresponds to a temperature scale of the wire that can be magnetized to

Fig. 2.19 Temperature correction for a glass tube mercury thermometer. a Correction for full immersion thermometers when not in full immersion use; b correction for semi-immersion thermometers when the operating ambient temperature differs from the indexed ambient temperature

2.3 Expansion Thermometers

47

Fig. 2.20 Variable contact mercury thermometer, 1—slender screw; 2—oval nut; 3—thin wire; 4—magnet cap; 5—flat iron block; 6, 7—outer lead

adjust the depth of its insertion into the capillary tube and thus can be adjusted to control the temperature value. The fixed type is the upper part of the wire and during manufacturing, and it is fixed to control the temperature value and cannot be adjusted. Figure 2.20 is a schematic diagram of the adjustable electric contact thermometer.

2.3.3 Pressure Thermometer It is a temperature measuring instrument made from the principle of pressure change when a liquid or gas in a closed system is heated. Figure 2.21 is the schematic diagram of the pressure thermometer, which consists of a sensitive element temperature bubble, pressure-transmitting capillary tube, and spring tube pressure gauge. If the system is filled with gas, such as nitrogen, called an inflatable pressure thermometer, the upper limit of temperature measurement up to 500 °C, the relationship between pressure and temperature is close to linear but the temperature bubble volume, thermal inertia are large (40~200 °C). If filled with liquid, such as xylene and methanol, the temperature bubble is smaller (−40~170 °C). If it is filled with a low boiling point of the liquid, its saturation vapor pressure should change with the measured temperature, such as acetone, for 50~200 °C. However, due to the saturation vapor pressure and saturation vapor, the temperature is a nonlinear relationship. Consequently, the thermometer scale is not uniform. Figure 2.22 shows the typical structure of a pressure thermometer.

48

2 Temperature Detection

Fig. 2.21 Operation principle of a pressure thermometer, 1—pointer; 2—dial; 3—elastic element; 4—transmission mechanism; 5—pedestal; 6—capillary tube; 7—working substance; 8—temperature bubble

Fig. 2.22 Typical structure of a pressure thermometer, 1—watchcase; 2—pointer; 3—dial; 4—spring tube; 5—transmission mechanism; 6—capillary tube; 7—movable nut; 8—temperature bubble

A pressure-type thermometer must be fully immersed in the temperature bubble to be measured in the medium. The capillary tube diameter of the industry pressuretype thermometer is around 0.15~0.5 mm and the length of 20~60 m. Any ambient temperature fluctuations in the capillary tube, errors will occur, e.g., changes in atmospheric pressure or improper installation location. This instrument has low accuracy but is easy to use and resistant to vibration. It is often used on open-air transformers and vehicles, such as testing the oil or water temperature of the tractor engines.

2.4 Resistance Thermometers

49

2.4 Resistance Thermometers A resistance thermometer is a temperature measuring instrument made by using the resistance of certain conductors or semiconductor materials with the characteristics of temperature change. There are metal thermistor thermometers and semiconductor thermistor thermometers.

2.4.1 Principle of Resistance Thermometer The resistance of the vast majority of metals varies with temperature. The higher the temperature, the higher the resistance, i.e., a positive resistance temperature coefficient. The relationship between the resistance of most metallic conductors Rt and the temperature t (°C) can be expressed as: Rt = R0 (1 + At + Bt 2 + Ct 3 ),

(2.26)

where R0 is the resistance value at 0 °C, A, B, C are the constants associated with the metal material. Most semiconductor materials have a negative resistive temperature coefficient. The relationship between the resistance RT and the thermodynamic temperature T (K ) is expressed as: RT = RT 0 exp B[(1/T ) − (1/T0 )],

(2.27)

where RT 0 is the resistance value at a thermodynamic temperature of T0 (K ) and B is the constant associated with the semiconductor material. According to the ITS-90 International Temperature Scale, the standard instrument for 13.81 K to 961.78 °C is the platinum resistance thermometer. Thermometric resistances are also widely used in industry to measure temperature in the low and medium temperature range of −200 to 500 °C. In recent years, experimental research work has used carbon resistance to measure ultra-low temperatures of 1 K. A high-temperature platinum resistance thermometer upper limit of up to 1000 °C is suitable for high temperatures, but it’s rarely used in the industry. Thermometric resistance materials for temperature measurement should meet the following requirements: (1) (2) (3) (4) (5) (6)

stable chemical and physical properties in the temperature measurement range; good reproducibility; large resistance temperature coefficient to obtain high sensitivity; large resistivity to obtain small-volume components; resistance temperature characteristics as close to linear as possible; low cost.

Metal and semiconductor resistance thermometers used have the following characteristics: (1) higher accuracy than thermocouple thermometers in the medium- and

50

2 Temperature Detection

low-temperature range; (2) high sensitivity. When the temperature increases by 1 °C, the resistance value of most metal thermometric resistance increases by 0.4–0.6%, while the resistance value of semiconductor materials decreases by 3–6%; (3) the volume of the temperature-sensing part of the thermometric resistance is much larger than the thermal contact of the thermocouple. So it is not suitable for measuring the point temperature and dynamic temperature. While the semiconductor thermistor volume is small, its disadvantaged by poor stability and reproducibility.

2.4.2 Commonly Used Thermometric Resistance Elements (i) Platinum thermometric resistance Platinum resistance made of high-purity platinum wire winding has the advantages of high accuracy, stable performance, good reproducibility, and oxidation resistance. It is widely used in benchmarking, laboratory, and industrial platinum resistance components. However, they are easily contaminated by the reducing atmosphere at high temperatures, making the platinum wire brittle and changing its resistance temperature characteristics. Therefore, they need to be protected by sleeves before use. The purity of the platinum wire used to wind the temperature-sensing element of the platinum resistance is the key to the thermometer’s accuracy. The higher the purity of the platinum wire, the higher the stability, the better the reproducibility, and the higher the temperature measurement accuracy. The purity of the platinum wire is often expressed at R100 /R0 , and R100 and R0 to indicate the resistance values at 100 °C and 0 °C, respectively. For a standard platinum resistance thermometer, R100 /R0 is not less than 1.3925 while industrial platinum resistance thermometer R100 /R0 is 1.391. The standard or laboratory platinum resistance R0 is about 10 Ω or 30 Ω. There are three main types of domestic industrial platinum resistance thermometers, Pt50, Pt100, and Pt300. Their technical specifications are listed in Table 2.5. Pt100 indexing tables can be found in Appendix Table A.7. The platinum resistance indexing tables are based on the following relationships. [ ] −200 ◦ C ≤ t ≤ 0 ◦ C : Rt = R0 1 + At + Bt 2 + Ct 3 (t − 100) ( ) 0 ◦ C ≤ t ≤ 500 ◦ C : Rt = R0 1 + At + Bt 2 ,

(2.28) (2.29)

where A = 3.96847×10−3 (°C−1 ); B = −5.847×10−7 (°C−2 ); C = −4.22×10−12 (°C−4 ). (ii) Copper thermometric resistance Apart from platinum resistance, copper thermometric resistance is also commonly used in the industry. The advantages of copper thermometric resistance include low

2.4 Resistance Thermometers

51

Table 2.5 Industrial platinum resistance thermometer technical indicators Indexing number

R0 (Ω)

R100 /R0

Allowable error of R0

Accuracy class

Maximum allowable error (°C)

Pt50

50.00

1.3910 ± 0.0007

±0.05%

I

Class I: −200~0 °C: ±(0.15 + 4.5 × 10−3 t) 0~500 °C: ±(0.15 + 3.0 × 10−3 t) Class II: −200~0 °C: ± (0.3 + 6.0 × 10−3 t) 0~500 °C: ±(0.3 + 4.5 × 10−3 t)

cost, easy to purify and process into wire, large resistance temperature coefficient (in the temperature range of 0~100 °C). However, the relationship between the resistance value of copper resistance and temperature is almost linear, so in some measurements, accuracy requirements are not very high. Copper thermometric resistance can be used in low temperatures, but it easily oxidizes for temperatures higher than 150 °C. Thus, for optimal results, it is recommended for measurements of the temperature range −50~150 °C but not suitable for higher temperatures. There are two types of copper resistance thermometers produced in China: Cu50 and Cu100, whose technical specifications are listed in Table 2.6. Refer to Tables A.8 and A.9 in the Appendix for the scale of the copper thermometric resistance, which is based on the resistance temperature relationship expressed in the following equation. Rt = R0 (1 + αt),

(2.30)

where α is the resistance temperature coefficient of copper, a = (4.25–4.28) × 10–3 (°C−1 ). The copper resistor body is winding copper wire (including the manganese copper compensation part). It is made of high-strength enameled copper wire with a diameter of about 0.l mm wrapped around a cylindrical plastic (or glued wood). The cylindrical Table 2.6 Copper resistance thermometer technical indicators Indexing number

R0 (Ω)

Accuracy class

Allowable error of R0

R100 /R0

Maximum allowable error (°C)

Cu50

50

II III

±0.1%

Class II: 1.425 ± 0.001 Class III: 1.425 ± 0.002

Class II: ±(0.3 + 3.5 × 10–3 t) Class III: ±(0.3 + 6 × 10–3 t)

52

2 Temperature Detection

1

2

3

4

Fig. 2.23 Temperature-sensing element of copper thermometric resistance, 1—coil skeleton; 2— copper thermistor wire; 3—compensation winding; 4—copper lead wire

plastic support uses a two-wire non-inductive winding method to reduce the induced current, as shown in Fig. 2.23. The outside of the copper resistance wire is dipped in phenolic resin for protection. A 1 mm diameter silver-plated copper wire is used as the lead wire and is threaded through an insulating sleeve, with both the copper resistor body and the lead wire contained in the protective sleeve. (iii) Semiconductor thermistors The use of semiconductor thermistors as temperature-sensing elements to measure temperature is becoming increasingly widespread. The biggest advantage of a semiconductor thermometer is a large negative resistance temperature coefficient—(3– 6)%, which increases its sensitivity. Semiconductor material resistivity is much larger than metal material. Therefore, it can be made into a small volume and big resistance value of the resistance element, making it have small thermal inertia. Thus, it can measure the point temperature or dynamic temperature superiority. Disadvantages semiconductor thermistors include characteristic temperature dispersion, nonlinearity, and unstable component’s performance. These characteristics make the semiconductor thermistors have poor interchangeability and low accuracy. Moreover, these shortcomings limit the promotion of semiconductor thermistors, which are still only used in some applications with low-temperature measurement requirements. However, with the development of semiconductor materials and devices, it will become a promising temperature measurement element. The material of semiconductor thermistors is usually oxides of iron, nickel, manganese, molybdenum, titanium, magnesium, copper, etc., but there are also those made of carbonates, and nitrates or chlorides, etc. The temperature measurement range is about −100 to 300 °C. Because of the poor interchangeability of components, each semiconductor thermometer needs to be indexed individually. The indexing method is to measure the resistance values RT and RT 0 in two constant temperature sources T and T0 (generally specified T 0 = 298 K) and then calculate according to Eq. (2.31) B=

ln RT − ln RT 0 . 1/T − 1/T0

Typically B is in the 1500–5000 K range.

(2.31)

2.4 Resistance Thermometers

53

2.4.3 The Structure of the Thermometric Resistance Temperature Measurement Element The platinum thermometric resistance body is made of fine pure platinum wire wound on a quartz or mica skeleton. The structure of a platinum resistance temperaturesensing element is shown in Figs. 2.24 and 2.25. It has four main components: (1) Resistance wire: A common diameter used is about 0.03~0.07 mm of pure platinum wire single winding. For the double winding method, a non-inductive winding method is used. (2) Skeleton: The thermometric resistance wire is wound on a skeleton, which is used to wind and fix the resistance wire and is often made of mica, quartz, Fig. 2.24 Industrial thermometric resistance structure, 1—outlet seal; 2—outlet nut; 3—small chain; 4—cover; 5—terminal block; 6—seal; 7—junction box; 8—terminal block; 9—protection tube; 10—insulated tube; 11—lead wire; 12—temperature-sensing element

Fig. 2.25 Several typical structures of platinum thermometric resistance temperature-sensing elements. a, b For 3-wire elements; c for 2-wire, 1—housing or insulating sheet; 2—platinum wire; 3—skeleton; 4—lead wire

54

2 Temperature Detection

A R

A B B

R B (a)

(b)

A A B B

R (c)

Fig. 2.26 Lead forms for temperature-sensing elements. a Two-wire; b three-wire; c four-wire

ceramic, glass, and other materials. The shape of the skeleton is mostly sheet and rod-shaped. (3) Lead wire: The lead wire is the factory-supplied lead wire of the thermometric resistance, whose function is to enable the temperature-sensing element to be connected to the external measurement line. The lead wire is usually located in the protection tube. Because of the large temperature gradient inside the protection tube, the lead wire should be made of high-purity and non-thermal potential material. Silver wire is used as the lead for low and medium temperatures for industrial platinum resistors, and nickel wire is used for high temperatures. Copper and nickel wires are generally used for copper and nickel thermometric resistance leads. In order to reduce the influence of lead resistance, its diameter is often much larger than the diameter of the resistance wire. Thermometric resistance leads are available in two-wire, three-wire, and four-wire systems, as shown in Fig. 2.26. (a) Two-wire system: The thermometric resistance temperature-sensing element at each end of a wire lead from the two-wire system. This twowire thermometric resistance wiring system is simple and low cost, but the additional error of the lead resistance should be considered. (b) Three-wire system: Two leads are connected to one end of the thermometric resistance sensing element, and one lead is connected to the other end. The lead form is called a three-wire system. It can eliminate the influence of lead resistance. Due to higher measurement accuracy than the two-wire system, the three-wire system is widely used. In the case of narrow temperature range, long leads, and changes in temperature along the copper wire, the three-wire thermometric resistance is more suitable. (c) Four-wire system: Two leads attached to each end of the thermometric resistance temperature-sensing element is called a four-wire system. For high accuracy measurements, the four-wire system is more suitable for use. This lead eliminates the effect of lead resistance and the effect of connecting wire resistance when the connecting wires are of the same resistance. (4) Protection tube: It is a tube used to protect the wound temperature-sensing element from environmental damage and is made of various materials such as metal and non-metal. The thermometric resistance is inserted into a protection tube and connected to the junction box simultaneously. There are two types of initial resistance, 10 and 100 Ω.

2.4 Resistance Thermometers

55

Figures 2.27 shows a standard thermometric resistance element structure. Figure 2.27a shows a spiral quartz skeleton, where the platinum wire should be unstressed, lightly attached to the skeleton and protected by a quartz sleeve. The lead wire is a platinum wire with a diameter of 0.2 mm transition to 0.3 mm. This type of temperature-sensing elements is mainly used for standard platinum resistance thermometer. Figure 2.27b is in the jagged mica sheet around the thin platinum wire. The outer layer of mica sheet is wrapped with a silver band binding and the outermost layer of metal casing protection. The lead wire for the diameter of 1 mm is a silver wire. This form of temperature-sensing elements is mostly used in industry for temperature measurement below 500 °C. Figure 2.27c is with a diameter of 0.1 mm of high-strength and insulated enameled copper wire. A non-sensitive double wire is wrapped around a cylindrical rubber wood skeleton. An insulating solid paint is glued and installed in the metal protection sleeve, with a 1 mm copper wire diameter as the lead. In order to improve the heat exchange conditions, for the construction forms in Fig. 2.17b and c, a clamping piece made of sheet metal or a copper inner sleeve is often placed between the resistor body and the metal protection sleeve (the protection sleeve for all three construction forms is not shown in the figure). The miniature platinum resistance element is developing rapidly due to its advantages such as small size, small thermal inertia, and good gas tightness. Its temperature measurements range from −200 to 500 °C. Its support and protection sleeve are made of special glass. The platinum wire has a 0.04~0.05 mm diameter, wrapped around a cylindrical glass rod. It is engraved with a thin thread outside the glass sleeve with a sealed lead wire of a diameter of 4.5 mm and a platinum wire of a diameter of 0.5 mm. The structure of miniature platinum resistance is shown in Fig. 2.28. When used for industrial temperature measurement, a metal protective sleeve is required. Two examples of the form of construction of semiconductor thermistor thermometers are shown in Fig. 2.29. Figure 2.29a shows one with a glass protection tube;

Fig. 2.27 Thermometric resistance element structure. a Standard platinum resistance, 1—quartz skeleton; 2—platinum wire; 3—lead wire. b Platinum resistance, 1—mica sheet skeleton; 2— platinum wire; 3—silver wire lead wire; 4—mica for protection; 5—silver tape for tying. c Copper resistance, 1—plastic skeleton; 2—enameled wire; 3—lead wire

56

2 Temperature Detection

Fig. 2.28 Miniature platinum thermometric resistance element, 1—sleeve; 2—glass rod; 3—temperature-sensitive platinum wire; 4—lead wire

Fig. 2.29 Semiconductor thermistor thermometer structure. a With glass protection tube b with sealed glass column, 1—resistor body; 2—lead wire; 3—glass protection tube; 4—lead pole

3

4

2

1

(a)

3

1

2

(b)

Fig. 2.29b shows one with a sealed glass column. The resistor body is a small beadlike ball of 0.2–0.5 mm in diameter, and the platinum wire leads are 0.1 mm in diameter.

2.5 Temperature Measurement and Display Instruments The previous section describes the sensitive components for temperature measurement, for which secondary instruments need to be connected to indicate the measured temperature value, i.e., temperature display instruments. In order to visually display the measured temperature, it is necessary to use display instruments with them to form a temperature measurement system. Two types of display instruments are commonly used in industry: moving coil type and automatic balance type. The moving coil-type display instrument is a series of instrument products designed and manufactured by China. There are presently several series, such as XC, XF, and XJ. Each series is divided into indication type (Z) and indication adjustment type (T). It works with a thermocouple, thermometric resistance, or other measuring elements whose output is a DC millivolt or resistance change. It can display the temperature or other parameters of the measured medium. The model number of the moving coil instrument for thermocouple is X CF Z -101 or X CF T -101, etc. Meanwhile, the model number of the moving coil instrument for thermometric resistance is X CF Z -102 or X CF T -102, etc. The advantages of the moving coil-type display instrument are simple structure, small size, reliable performance, low cost, and easy to use and maintain. It is widely used in industrial production, especially in small- and medium-sized enterprises.

2.5 Temperature Measurement and Display Instruments

57

2.5.1 Displaying Instrument with Thermocouple Measuring Temperature According to the thermocouple temperature measurement principle, the thermopotential of the thermocouple circuit is only a single-valued function of the measured temperature when the cold-end temperature is certain. Therefore, a thermopotential measuring instrument can be added to the circuit to obtain the measured temperature value by measuring the thermopotential of the thermocouple circuit. Instruments commonly used for measuring the thermal potential are moving coil instruments, manual potentiometers, automatic electronic potentiometers, and digital voltmeters. 1. Moving Coil-Type Temperature Indicator XCZ-101 It is a direct conversion instrument with a magnetoelectric millivolt meter as the core component. The thermal potential supplies the energy required to transform the signal, and the output signal is the position of the instrument pointer relative to the scale. A typical model of a domestic moving coil temperature indicator is the XCZ-101, whose operating principle is shown in Fig. 2.30. In Fig. 2.30a, the dashed box shows the internal measurement section of the XCZ-101 instrument, where R D is a magnetoelectric indicating meter that measures microampere currents. The thermocouple is connected to the temperature indicator via a compensation wire, a cold-end compensator, and an external adjustment resistor RC . Figure 2.30b shows the basic schematic of a magnetoelectric indicating instrument. When a coil in a uniform constant magnetic field is passed with a current I , the coil will produce a rotating torque M, which, given the coil geometry and number of turns, M is only proportional to the magnitude of the current flowing through the coil, i.e., M = K I,

(2.32)

where K is the proportionality constant. The torque M rotates the coil about its central axis. As the coil rotates, the tension wire supporting the coil generates a reaction torque Mn whose magnitude is proportional to the angle of deflection of the moving coil ϕ. Fig. 2.30 XCZ-101 moving coil temperature indicator schematic, 1—thermocouple; 2—compensating wire; 3—cold-end compensator; 4—XCZ-101 internal wiring

3

RL

RC

RS

4

I

M

RT 2

RP

RB RD

1 t

(a)

φ (b)

58

2 Temperature Detection

Mn = W · ϕ,

(2.33)

where W is the proportionality constant. It corresponds to the torque generated when the wire is rotated by a unit angle. Its value is determined by the material properties and geometry of the tensor wire. When the two moments M and Mn are balanced, the moving coil stops at a position where the deflection angle of the moving coil is: ϕ=

K · I = C I, W

(2.34)

where C is the instrument sensitivity. Obviously, the angle of deflection of the moving coil has a monovalent positive relationship with the current flowing through the moving coil. From Fig. 2.30a, it can be seen that the current flowing through the instrument is: Et I =∑ , R ∑ R is the total resistance value of where E t is the thermal potential of the circuit, the circuit. Figure 2.30b shows that the moving coil ∑ deflection angle ϕ can only correctly R is certain. Therefore, keeping the reflect the thermal potential value when total resistance of the circuit constant or essentially constant is the key to ensuring ∑ R = R N + R E ,R N is the temperature measurement accuracy. In the summation internal equivalent resistance of the instrument and R E is the external resistance of the instrument. (1) Instrument external resistance R E : It includes thermocouple, compensation wire and connection wire resistance R2 , cold-end compensator equivalent resistance R L , and external adjustment resistance RC . The RC is wound with manganese copper wire and is adjusted so that the external resistance R E is equal to the value specified in the instrument design (R E = 15 Ω or 5 Ω in China). Except for RC , the other resistances in R E vary slightly with the ambient temperature, which makes it difficult to compensate effectively and therefore brings some measurement error. (2) The internal resistance of the instrument R N : Includes series of adjustment resistor R S , moving coil resistor R D , temperature compensation resistor R B and RT . The measurement range of the instrument can be changed by adjusting the size of R S . The instrument is shipped from the factory with R S as long as the thermocouple type and temperature measurement range are specified.R D the resistance of a wire frame wound with fine copper wire, and the resistance varies approximately linearly with the ambient temperature to which the instrument is exposed. To ensure that R N is as constant as possible to reduce temperature measurement errors, appropriate temperature compensation measures must be taken, for which a temperature compensation circuit is connected in series with

2.5 Temperature Measurement and Display Instruments Fig. 2.31 Curve to compensate for ambient temperature

59 R/Ω

R=RD+RK RD 80 60

RB

40

RT RK =

20 20

30

40

50

RB RT RB + RT

t/°C

and in parallel with R B and RT . R B is a non-inductive winding of manganese copper wire is used. RT is a thermistor with a negative temperature coefficient. R B is the equivalent resistor in parallel with RT is R K . Figure 2.31 shows that the equivalent resistance R of (R D + R B //RT ) varies very little with ambient temperature. Typical resistance values for domestic XCZ-101 moving coil temperature measurement instruments are: R S = 200 ∼ 1000 Ω, depending on the thermocouple type and temperature range; R D = 80 Ω; R B = 50 Ω; RT (20) = 68 Ω; R P = 600 Ω are instrument damping resistors to improve the instrument damping characteristics. The accuracy class of the instrument is one. One thermocouple can be used with one moving coil temperature measuring instrument, or several thermocouples can be used with one moving coil temperature measuring instrument by switching together. Figure 2.32 shows one of the wiring methods. 2. Moving coil-type temperature indication instrument XFZ-101 The XFZ series moving coil instrument can be used with either thermocouples or thermometric resistances. It differs from the XCZ series moving coil instrument in 2

1

3

5

t 4

t0

Fig. 2.32 Multiple thermocouples sharing a single moving coil meter, 1—thermocouple and compensation wire; 2—junction box; 3—copper wire and line resistance; 4—toggle switch; 5—moving coil temperature indicator

60

2 Temperature Detection

Fig. 2.33 Block diagram of XFZ-101 moving coil instrument composition, 1—thermocouple; 2—compensating wire; 3—linear amplifier

that the measuring circuit of the XFZ series consists mainly of a linear integrated operational amplifier, as shown in Fig. 2.33 for the block diagram of the XFZ-101type moving coil instrument mated to a thermocouple. A large-torque hairspring and a glass support moving coil are used as measuring mechanism. The amplifier amplifies the weak input signal to output a voltage-level voltage signal, and the measurement mechanism line (RS and moving coil resistor RD ) converts the signal to current. The current generates a rotational torque in the magnetic field of the permanent magnet, which drives the moving coil and pointer deflection, while causing the deformation of the balance spring to generate a reaction torque. When the rotational and reaction torque are equal, the moving coil stops rotating. The angle of deflection of the moving coil and pointer is proportional to the input current, which depends on the value of the input thermoelectric potential. Hence, the pointer of the instrument indicates the corresponding temperature value. This instrument is called strong torque moving coil-type instrument because the current through the moving coil is much higher and the rotating torque obtained by the moving coil is larger due to the use of high amplification integrated circuit from the linear amplifier. Since the strong torque moving coil is used as the balancing element, it has good stability and strong anti-vibration capability. And because the integrated operational amplifier can be set in the cold-end temperature automatic compensation, there is no need to access the cold-end temperature compensator in the thermocouple temperature measurement circuit. In addition, because the input impedance of the operational amplifier is large, the equivalent resistance of the external circuit is negligible compared with the input impedance. Thus, the XFZ-101 does not have specific requirements for the equivalent resistance of the external circuit, which brings convenience to the use. Therefore, it is also equivalent to adding a series correction link to improve the instrument’s accuracy. 3. DC potential difference meter Although it is convenient to measure the thermal potential with a moving coil-type temperature measuring instrument, the current flowing through the total circuit will bring error to the temperature measurement due to the change in circuit resistance. It is also difficult to further improve the measurement accuracy due to mechanical and electromagnetic factors. Therefore, in high-precision temperature measurement, DC potentiometers are often used to measure the thermal potential.

2.5 Temperature Measurement and Display Instruments

61

Fig. 2.34 Schematic diagram of a manual potential difference meter

Potentiometer measurement works by the following balance method. The method uses a measured and known standard quantity after comparing the difference between the adjustment to zero difference in the method of measurement. Therefore, there is no current flow when the potentiometer is in a static balance thermocouple circuit. There are also no strict requirements for the change in the resistance value of the measurement circuit. (i) Manual potential difference meter It is an instrument with an integral link and therefore has a non-differential characteristic, which shows that it has a high measurement accuracy. The operating principle is shown in Fig. 2.34. The DC operating power source in the diagram E B is a dry cell or DC regulated power source, and E N is a standard battery. There are three circuits in the diagram: (a) the operating current circuit consisting of E B , R S , R N , R ABC with a current of I ; (b) the calibration circuit consisting of E N ,R N , and the current detector G with a circuit current of i N , whose function is to adjust the operating current I to maintain the current value specified at design; (c) a measurement circuit consisting of E t , R AB , and the current detector G with a circuit current of i. When the switch K is set to the “standard” position, the calibration circuit operates with the following voltage equation: E N − I R N = i N (R N + RG + R E N ),

(2.35)

where RG is the internal resistance of the current detector, and R E N is the internal resistance of the standard cell. By adjusting R S , the operating current of the operating current loop I is changed so that the current detector G points to zero; i.e., when i N = 0, then E N = I R N , at which point I is the required operating current value for the potentiometer. When the switch K is set to the “measuring” position, the measuring circuit operates with the following voltage equation:

62

2 Temperature Detection

E t − I R AB = i (R AB + RG + R E ),

(2.36)

where R E is the resistance of the thermocouple and connecting wire. By moving the sliding point B of the resistor R ABC , the current detector G points to zero, then i = 0, E t = I R AB . Since I is already the exact operating current value and R AB is precisely known from the dial, the measured value of E t is also known quite precisely. The accuracy of a manual electronic potential difference meter is determined by the high sensitivity of the current detector, the stable and accurate value of each resistor in the meter, and the stable standard voltage. The commonly used highprecision manual electronic potential difference meters can read down to 0.01 μv. (ii) Automatic electronic potential difference meter The manual electronic potential difference meter is widely used in scientific experiments and metrology departments due to its high accuracy, which makes it superior in precision measurement. Some of the most important quality tests conducted during industrial production are the continuous measurement and recording that require both high measurement accuracy and continuous automatic recording of the measured temperature. An automatic electronic potential difference meter is an ideal measuring instrument. Its accuracy level is 0.5. In addition to automatic display and recording of the measured temperature, it can also automatically compensate for the cold-end temperature of the thermocouple. The addition of accessories can also enhance various functions such as automatic alarm for parameter overrun, multiple records, and automatic control of the measured parameter. The basic operating principle of the automatic electronic potential difference meter is shown in Fig. 2.35. Its operating current circuit and measurement circuit are analogous to that of the manual electronic potential difference meter. The difference arises because the current detector is removed, and an electronic amplifier is used to amplify a small unbalanced voltage. In addition, a reversible motor is driven to operate the voltage balance automatically through a set of mechanical devices, which eventually eliminates the presence of the unbalanced voltage. Therefore, it is also a meter with an integral link having a non-differential characteristic. Figure 2.35 shows E B as a regulated power supply with a constant value current I flowing through a resistor R P . If the voltage division on R P U AB = E t , the input deviation voltage of the electronic amplifier ΔE = E t − U AB = 0, and the position of the sliding point B on R P reflects the magnitude of the measured value E t . On the other hand, if U AB /= E t , the input deviation voltage ΔE /= 0 of the electronic amplifier is amplified to have enough power to drive the reversible motor. The motor rotates forward or backward according to ΔE > 0 or ΔE < 0 and moves the sliding point B of R P either left or right by the mechanical system until E t and U AB balance each other, i.e., ΔE = 0. 4. Digital voltmeter The basic principle of the digital voltmeter for thermocouples is to convert the measured analog voltage quantity into a digital quantity in the binary system and

2.5 Temperature Measurement and Display Instruments

63

Fig. 2.35 Schematic diagram of an automatic electronic potential difference meter

then display it in the digital display by decimal digits. The core component is the analog-to-digital converter, referred to as the A/D converter. According to the different conversion principles, the common A/D converters can be divided into two types: the successive approximation type and the double-integral type. The A/D converter is the most used type in the computer data acquisition and processing system because of its fast conversion speed. It takes about 1–100 μs per conversion time, while the most common speed is about 25 μs. On the other hand, although the conversion speed of the double-integral type is slower, i.e., 30 ms per conversion, it has a stronger anti-interference ability and low price. It is common in digital voltmeters. The double-integrating A/D converter is performed using a modulation principle that generates a pulse width proportional to the value of the input analog voltage. Firstly, the input analog voltage signal is integrated for the first time over a fixed time interval T , then the input of the integration circuit is conducted to a known reference voltage for a second integration. The number of oscillating pulses over the time interval Tx , Tx from the onset until the integrated output reaches the specified value, is proportional to the input analog voltage value. Figure 2.36 shows the block diagram and waveform schematic of a double-integrating A/D converter.

Fig. 2.36 Schematic diagram and waveform diagram of double-integral A/D converter, 1—integral amplifier; 2—analog comparator; 3—control logic circuit and counter; 4—clock; 5—digital display

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2 Temperature Detection

When the control logic unit receives the start or conversion signal, it sends out a pulse command to drive the switch K so that the input analog voltage Vin connects to the integrator amplifier to start integration. When the integrator output V0 is slightly higher than 0 V, the analog comparator output changes state and triggers the counter to accept the oscillation pulse of the clock. The integration proceeds to the specified time interval T just when the counter is fully set to “1”, then the control logic drives K to connect to the reference voltage Vr e (the polarity of Vr e is opposite to Vin ), so the integrator output voltage drops linearly to 0 V. When the voltage crosses 0 V, the comparator output changes state again and the counter stops counting. This is the second integration process, in which the time interval is Tx . From the waveform plot on Fig. 2.36, it can be seen that the end-point integrator output voltage VO T at the time of T is:

VO T

1 = RC

∫T Vin dt =

T Vin . RC

(2.37)

0

At the Tx time interval, the output of the integrator is reduced from VO T to 0: 1 RC

∫TX Vr e dt =

Tx Vr e . RC

(2.38)

0

Comparing Eqs. (2.37) and (2.38) show that: TX =

Vin T Vr e

(2.39)

Since T is the time it takes for the counter to go from full “0” to full “1”,T is a fixed quantity at a fixed clock oscillation frequency;Vr e is also a fixed value. So the time interval Tx is proportional to the analog input voltage Vin . That is, the number of clock oscillator pulses recorded by the counter during the second integration process time Tx represents the value of the input voltage under test. The digital display then displays this value. From the theoretical analysis, it is clear that this double-integrating A/D converter is not affected by the capacitance value and the clock frequency because they have the same effect on the upward and downward integration. It should be noted that the digital voltmeter described here is a very general instrument and is the basis for digital meters. The core part of the digital ammeter, resistance meter, and digital multimeter is still a digital voltmeter but when measuring current, the current first flows through a known standard resistor to convert it to a voltage value. When measuring resistance, a constant current source is attached to the meter and the constant current is first converted to a voltage value through the resistor being measured.

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65

2.5.2 Mating Thermometric Resistance Temperature Measurement Display Instrument There are many methods of measuring resistance values of resistors. It is customary to use unbalanced bridges and automatic balanced bridges for resistance measurement of thermometric resistances. (i) Moving coil-type temperature indicator XCZ-102 The unbalanced bridge schematic is shown in Fig. 2.37, where the three bridge arms R1 , R2 , R3 are fixed resistance values wound from manganese copper wire. Rt is a resistive temperature measuring elements that vary with the temperature being measured. The voltage supplied to the bridge Uab remains constant. The output unbalance voltage of the bridge Ucd is ( Ucd = Uab

R3 Rt − R1 + R3 R2 + Rt

) (2.40)

Since R1 , R2 , R3 , and Uab are fixed, then Ucd is a single-valued function of Rt . Connecting a magnetoelectric moving coil microammeter with a moving coil equivalent resistance of R M to the output of c, d and applying Davinan’s theorem, the current I M flowing through R M is: IM

Ucd Uab = = RM RM

(

R3 Rt − R1 + R3 R2 + Rt

) (2.41)

Obviously, I M is a single-valued function of Rt , i.e., the deflected position of the pointer of a moving coil microammeter reflects the magnitude of Rt . The principle circuit of the XCZ-102 moving coil temperature indicator based on the unbalanced bridge principle is shown in Fig. 2.38. The power supply is a DC regulated power supply with a voltage of Uab = 4 V added to the diagonal of the bridge. The resistance of the connection line between Fig. 2.37 Schematic diagram of an unbalanced bridge

E

RP c

R3

R1

a

RM

b

R2 d Rt

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2 Temperature Detection

Fig. 2.38 XCZ-102 moving coil temperature indicator schematic wiring diagram

the thermometric resistance Rt and the XCZ-102 temperature indicator must be strictly controlled to ensure that it is equal to the specified value. Otherwise, it will have an impact on the measurement results. The XCZ-102 temperature indicator manufactured in China specifies that the connection line resistance Re is available in two sizes, 5 and 15 Ω, which must be distinguished when in use. There are two typical wiring methods for the connection of thermometric resistance elements and XCZ-102 temperature indication instrument, two-wire and three-wire systems. 1. Two-wire wiring As shown in Fig. 2.39a, the XCZ-102 temperature indicator and the thermometric resistance Rt are connected by two copper wires with the distributed resistance of r2 and r3 , respectively. In order to meet the requirements of the instrument’s specified line resistance Re = 5 Ω or Re = 15 Ω, a manganese copper wire wound line adjustment resistance Re2 and Re3 needs to be added to make Re2 + r2 = Re3 + r3 = Re1 = Re = 5(or 15) Ω). Since r2 and r3 are added to the bc arm of the bridge, changes in r2 and r3 due to changes in ambient temperature can cause large errors in the measurement.

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67

(a)

(b) Fig. 2.39 Wiring of thermometric resistance temperature measurement system. a Two-wire system; b three-wire system

2. Three-wire wiring Figure 2.39b shows the temperature indicator and the thermometric resistance element connected with three copper conductors. The top point of the unbalanced bridge b is significantly different from the two-wire wiring so that r2 and r3 are assigned to the bc and bd arms of the bridge, respectively. In general, all three

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2 Temperature Detection

connecting wires are of the same material, diameter, and length, i.e., r2 = r3 . When the ambient temperature changes, it will cause the resistance values of the two bridge arms to change in the same direction and in the same increment. As a result, there will be a significant reduction in measurement error than in a two-wire wiring. (ii) Automatic electronic balance bridge XCZ-102-type temperature indicator accuracy is 1.0 level and cannot automatically record the measured parameters. A large number of automatic balance bridges with a 0.5 level of accuracy are important temperature measurements in the industry for thermometric resistance temperature measurement. It can automatically record the measured parameters and with an automatic adjustment function. The automatic balance bridge shape, electronic amplifier and recording system are the same as the automatic electronic potential difference meter, but the measurement line is different. Figure 2.40 is a schematic diagram of the XDD transistorized miniature automatic balancing bridge. The measurement line is drawn in some detail. The measurement line is an AC balanced bridge with an AC supply voltage of 6.3 V taken from the amplifier’s power transformer. A three-wire wiring system is used. Rt is a thermometric resistance element, which forms one arm of the upper branch of the bridge with the line resistor Re , the start resistor R6 , the trim start resistor r6 and the range resistor R5 , the trim range resistor r5 and the left half of the slip wire resistor R P and the process resistor R B in parallel, and the other arm of the upper branch consists of R5 ,r5 and R P ,R B in parallel with the right half of the current limiting resistor R4 . The two bridge arms of the lower branch are R2 + Re and R3 . The line resistance Re is specified as 15 Ω. When the thermometric resistance Rt changes with the measured temperature, the measurement bridge outputs an unbalanced voltage ΔE to the electronic amplifier. Then, the amplified signal can drive the reversible motor either forward or reverse according to the positive or negative phase, driving

Fig. 2.40 Schematic diagram of an auto-balancing bridge

2.6 Temperature Transmitters

69

the sliding point b of the sliding resistor R P until the bridge is rebalanced. At the same time, the reversible motor drives the pointer and the recorder to indicate and record the measured temperature value.

2.6 Temperature Transmitters As described in the previous sections, the sensor’s output is different from the matching display instrument. Examples include the thermocouple temperature sensor with input millivolt signal from the XCZ-101-type moving coil instrument or electronic automatic potentiometer, the thermometric resistance temperature sensor with input resistance signal XCZ-102-type moving coil instrument or automatic electronic balance bridge. The differences result into a lot of inconvenience to the manufacture and use of display instruments. If the output quantity of different types of sensors is transformed into a unified standard quantity, it can realize the generalization of display instrumentation and reduce the inconvenience of display instrumentation in manufacturing and use. A temperature transmitter is essentially such a signal conversion instrument. It can be used with a variety of standardized thermocouples or standardized thermometric resistances to convert the thermal potential or thermometric resistance into a uniform DC current or voltage as an input to the display instrument. The temperature transmitter consists of an input circuit, an amplifier circuit, and a feedback circuit, as shown in Fig. 2.41. The input circuit sends out a DC millivolt signal E t corresponding to the temperature. E t is compared with the signal from the feedback circuit U f (balanced compensation voltage), and the difference between the two is sent to the amplifier circuit and then converted into a DC current or voltage output. A temperature transmitter working according to the principle of electrical balance is shown in Fig. 2.42. The input signal of the amplifier circuit is the difference between E t and U f . E t varies with temperature, and U f is equal to the product of the output current I0 and the feedback resistor R f (I0 · R f ). The output current of the amplifier circuit I0 increases or decreases when the value of E t changes due to temperature changes. At the same time, the feedback voltage changes accordingly and is compensated with E t for electrical balance. Since the electronic amplifier circuit has a large amplification factor K, even a small change in the output signal of the amplifier circuit (E t − U f ) is sufficient to vary the output current I0 from 0 Fig. 2.41 Temperature transmitter block diagram, 1—input circuit; 2—electronic amplifier; 3—feedback link

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2 Temperature Detection

Fig. 2.42 Schematic diagram of temperature transmitter components

K RL

Et

Uf

Rf

I0

mA

to 10 mA or 4 to 20 mA. In the steady state, the input signal of the amplifier circuit can be expressed by the following equation: Et − U f = 0

(2.42)

E t ≈ U f = I0 R f

(2.43)

That is,

Equation (2.43) represents the relationship between the output quantity I0 and the input quantity E t of the instrument. From the above analysis, it is clear that this type of instrument’s electrical balance compensation process is automatic. The relationship between the input and output quantities, when K >> 1, depends on the feedback link. As long as the input and output quantities of the feedback link are linear, the linearity of the whole instrument can be ensured, and the influence of the input and output quantities of the instrument due to the nonlinear factor of the transistor itself in the amplifier is reduced. Since the feedback link mainly comprises components such as resistors, this can better meet the above requirements. The feedback link is mainly composed of resistors and other components which can better meet the above requirements. Two temperature transmitters commonly used in industry are described below.

2.6.1 ITE-Type Thermocouple Temperature Transmitter ITE-type temperature transmitter is one of the main transmission units widely used in power plants at present. It can be used with various standard temperature measuring elements (thermocouple, thermometric resistance) to continuously convert the measured temperature value linearly into 1~5 V DC or 4~20 mA DC

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71

Fig. 2.43 Block diagram of the components of an ITE-type thermocouple temperature transmitter, 1—thermocouple; 2—zero adjustment and reference compensation circuit; 3—voltage stabilizing circuit; 4—power converter; 5—voltage amplifier; 6—power amplifier; 7—isolate output problems; 8—feedback resistance; 9—linearization circuit

unified signal. The signal is sent to the indication, recording instrument, or control system to realize automatic detection or automatic control of the production process. (i) Composition and working principle of the circuit The block diagram of the general type ITE thermocouple temperature transmitter using 24 V DC power supply is shown in Fig. 2.43. It mainly consists of two major parts, the linearization input circuit and the amplification output circuit. The functions of the linearized input circuit are: (1) to convert the feedback voltage signal from the power amplifier into a voltage signal with similar nonlinear characteristics to the thermocouple’s thermoelectric characteristics; (2) to realize automatic compensation of the thermocouple’s cold-end temperature and zero adjustment of the whole machine, as well as zero migration and adjustment of the range; and (3) to perform a comprehensive operation on the feedback voltage, cold-end compensation voltage, zero migration voltage, and input thermal potential. The function of the amplifying output circuit is to amplify the integrated signal output from the linearization input circuit into a unified signal output of 4~20 mA DC or 1~5 V DC. This unified signal output supplies the load and sends a feedback voltage signal of 0.2~1.0 V to the internal linearization circuit. Simultaneously, it realizes the electrical isolation between the input circuit and the output circuit through the current transformer to enhance the anti-interference capability of the instrument. As can be seen from the block diagram, the measured temperature t is converted by the thermocouple into the corresponding thermoelectric potential E t The potential is fed into the linearization input circuit, E t and the feedback voltage U f from the linearization circuit and the voltage U Z from the zero adjustment. The temperature compensation circuit at the reference end is combined and then sent to the voltage amplifier N1 and the power amplifier and converted into a current signal I0' . The current signal is then converted into a 1–5 V DC or 4–20 mA DC signal by the isolated output circuit to the indicating and recording instrument or control system. At the same time, the I0' signal is also converted into the corresponding feedback voltage U 'f through the feedback resistor and sent to the linearization circuit for arithmetic

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2 Temperature Detection

processing. This arithmetic processing into the feedback voltage U f output with the thermocouple’s thermoelectric characteristics U f achieves the negative feedback effect of the whole machine feedback to the voltage amplifier’s inverting input. When the circuit is in balance, the transmitter output voltage U0 (or current I0 ) is linearly related to the measured temperature t. (ii) Issues to be noted in use (1) The transmitter can output both 4–20 mA DC current signal and 1–5 V DC voltage signal, but the two output terminals are different. When current output is used, its external load resistance is 100 Ω. (2) Zero and range adjustments affect each other and must be adjusted repeatedly.

2.6.2 ITE-Type Thermometric Resistance Temperature Transmitter ITE-type thermometric resistance temperature transmitter can be used with various standard thermometric resistances to continuously convert the measured temperature linearly into 4–20 mA DC or 1–5 VDC unified signal. The signal is sent to the recording and indicating instrument or control instrument to realize automatic detection or automatic control of production process. (i) Composition and working principle of the circuit The schematic block diagram of the ITE-type thermometric resistance temperature transmitter is shown in Fig. 2.44. From the block diagram, it can be seen that both the ITE-type thermometric resistance temperature transmitter and thermocouple temperature transmitter composition are the same. The similarities arise from both the linearization of the input circuit and amplification of the output circuit. In addition, the two amplification of the output part of the same, only the linearization of the input part is different. 1. ITE-type thermometric resistance temperature transmitter linearization functions of the input circuit have: (1) the input thermometric resistance Rt is linearly converted into the potential signal E t corresponding to the measured temperature t. It compensates for the measurement error caused by the resistance of the thermometric resistance connecting wire; (2) realize the zeroing of the whole machine, as well as the zero migration and range adjustment; (3) perform the integrated operation of the potential signal E t , the zeroing and zero migration voltage U Z and the feedback voltage U f . The amplification output circuit serves the same purpose as the amplification output circuit of the thermocouple temperature transmitter. As can be seen from the block diagram, the measured temperature t is converted by the thermometric resistance into the corresponding thermometric resistance value

2.6 Temperature Transmitters

73

Fig. 2.44 Block diagram of the components of an ITE-type thermometric resistance temperature transmitter, 1—thermal resistance; 2—linearization circuit; 3—zero adjustment circuit; 4—voltage stabilizing circuit; 5—voltage amplifier; 6—power amplifier; 7—power converter; 8—isolate output circuit; 9—feedback circuit

and transmitted to the linearization circuit. The value is s converted by the linearization circuit into the corresponding potential signal E t ,E t and the feedback voltage U f output from the linearization circuit and the voltage U Z output from the zero adjustment. The temperature compensation circuit at the reference end is combined and then sent to the voltage amplifier N1 , amplified by N1 and the power amplifier and converted into a current signal I0' . The current signal is then converted into a 1–5 V DC or 4–20 mA DC signal by the isolated output circuit and sent to the indicator, recording instrument or control system. At the same time, the signal is also through the feedback resistor into the corresponding feedback voltage U 'f . The signal is sent to the linearization circuit for arithmetic processing, into the feedback voltage U f output, and U f feedback to the voltage amplifier inverting input to achieve the negative feedback effect of the machine. When the whole circuit is in balance, the output voltage U0 (or current I ) of the transmitter is linearly related to the measured temperature t. (ii) Use The zero point adjustment and range adjustment of this transmitter affect each other. In the actual commissioning process, adjustments need to be made repeatedly until both meet the specified values. The transmitter must also be externally wired as follows when in use. (1) The resistance of each input wire connected to the thermometric resistance r shall conform to the following: r ≤ input range (°C) × 0.1 Ω, but its maximum resistance shall not exceed 10 Ω. (2) The transmitter can output both 4–20 mA DC current signal and 1–5 V DC voltage signal, but the output terminals of both are different. When current output is used, the maximum external load resistance is 100 Ω.

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2 Temperature Detection

2.7 Contact Temperature Measurement Techniques In contact temperature measurement, whether it is an expansion thermometer, a resistance thermometer, or a thermocouple thermometer, the temperature indicated by the thermometer is fundamentally only the temperature of the sensing part itself (e.g., the temperature of the thermocouple hot contact). Often, one takes the temperature of the sensing part as the temperature of the object to be measured, which is merely an approximation, and in some cases, the difference can be significant. Because we have learned about contact temperature measurement instruments, we can get accurate information about the temperature of the sensing part itself. Therefore, this section only addresses how to make the temperature of the sensing section reflect the true temperature of the object to be measured, or how to calculate the measurement error. There are many contact temperature measuring instruments, with thermocouples being the most commonly used. In the analysis below, thermocouples are the object of analysis, but the general principles described apply to all types of contact temperature measurement instruments.

2.7.1 Various Factors Affecting Contact Temperature Measurement Contact thermometers only approximate some temperature in a fluid or solid. Several factors make the output of the thermometer deviate from the true temperature at the measurement point (i.e., the temperature when the thermometer is not placed). First of all, the insertion of the thermometer itself changes the thermal conditions in and around the measurement point, and so the temperature distribution. For example, the flow of heat into or out of the measurement point along the thermometer due to the presence of the thermometer distorts the temperature field in and around the measurement point. In a fluid, the insertion of a thermometer changes the flow state at the measurement point, which also distorts the temperature field. The hysteresis effect of airflow in the boundary layer can subject the thermometer to aerodynamic heating. For errors caused by various factors, one naturally wants to find the appropriate correction formula to correct the output of the thermometer to obtain an accurate temperature value. In practice, however, the heat transfer and flow problems associated with thermometers are very complex, and only simplified models can be used in the analysis, and the resulting correction formulae are only approximate in nature. Of course, as long as the analytical model generally reflects the actual situation, this approximation is a big step forward than no correction. To illustrate the complexity of the heat transfer problem encountered in analyzing temperature measurement errors, let’s examine a temperature sensor placed in the air stream, as shown in Fig. 2.45. The sensor is supported by stubs or just by the wire itself. The dashed lines in the figure represent the pathways for heat exchange.

2.7 Contact Temperature Measurement Techniques

75

Fig. 2.45 Heat transfer pathways for temperature sensors in the gas stream

The sensor itself exchanges energy with its surroundings in various ways, such as heat conduction through the stanchions to the wall on which the sensor is mounted; radiative heat exchange with other visible surfaces; convective and radiative heat exchange with the air stream; and, in the case of high-speed air streams, aerodynamic heating of the sensor due to viscous dissipation in the boundary layer. The stanchions or wires are also subject to heat exchange with the gas and the wall surface by radiation and convection. This heat exchange may considerably affect the heat transfer between the sensor and the wall. If the sensor has a radiation shield or velocity hysteresis cover, etc., it may be a complex component. Even if the sensor is just an exposed thermocouple contact, for every heat transfer mechanism—conduction, convection, and radiation—the geometry of the thermal contact is not the basic shape commonly used in theoretical analysis. The above discussion illustrates that the causes of errors in contact temperature measurements can be summarized as follows: (1) Reasons for heat transfer: Heat flows between the airflow and the sensor. If there is heat flow, there must be a temperature difference. If the heat is flowing from the gas to the sensor, then the temperature of the sensor must be lower than the temperature of the gas stream. Conversely, the temperature of the sensor must be higher than the temperature of the gas. (2) Pneumatic cause: Pneumatic heating of the sensor by high-speed airflow. (3) Dynamic error: If the gas temperature is changing with time, because the sensor has a certain thermal inertia, its temperature does not immediately reflect the instantaneous temperature of the gas. (4) Chemical reasons: If there are chemical reaction conditions in the gas being measured, then the platinum precious metal will act as a catalyst, making the gas temperature around the platinum thermocouple contact significantly higher. In the burner, the thermocouple may also become a flame stabilizer, due to the heating of the flame. Consequently, the measurement produces a large error.

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2 Temperature Detection

The difficulties in measuring the temperature of liquids are generally much less than those in measuring the temperature of gases. Liquid flow velocities are generally so low that velocity errors can be disregarded. Although the same heat transfer and dynamic errors exist, the situation is far less severe than when measuring gas temperatures because of the large exothermic coefficient of the liquid. Therefore, this section takes gas temperature measurements as the subject of analysis, but the principles of analysis are equally applicable to liquid temperature measurements.

2.7.2 High-Speed Airflow Temperature Measurement, Velocity Error Analysis Temperature depicts the average kinetic energy of the disordered motion of molecules. For a gas stream, in addition to the disordered motion of molecules, there is also the directed motion of molecules. When the gas stream is disturbed, the directed motion of the molecules can easily change to disordered motion, which increases the temperature of the gas. A thermometer inserted into the gas stream is a source of the disturbance. Hence, the thermometer senses the elevated temperature. This temperature increase becomes apparent when the Mach number M of the gas stream M exceeds 0.2, and at large Mach numbers, this temperature increase has a large value. This particular problem is encountered in measuring the temperature of high-speed air streams by contact methods. Thermal conductivity errors and radiation errors are also present in high-speed airflow temperature measurements. However, the thermal conductivity and radiation errors are of secondary importance because of the high flow velocity and the large convective heat transfer coefficient. (i) Speed error and recovery factor The static temperature T0 is usually used to measure the disordered kinetic energy of the airflow and the dynamic temperature Tυ to measure the directed kinetic energy of the airflow. Thus, it is possible to write mc p Tυ =

mυ 2 . 2

Therefore, Tυ =

υ2 , 2c p

(2.44)

where m is the mass of the air mass, υ is the air velocity, c p is the constant pressure specific heat [J/kg-°C]. Equation (2.44) shows that the kinetic temperature is the equivalent temperature of the kinetic energy of the airflow; that is, the temperature

2.7 Contact Temperature Measurement Techniques

77

rise caused by the conversion of all the kinetic energy of the directional motion of the airflow into thermal energy under adiabatic conditions. The sum of the static and dynamic temperatures is the total temperature of the air stream and is represented by the symbol T ∗ υ2 . 2c p

T ∗ = T0 + Tυ = T0 +

(2.45)

Applying the mainstream Mach number, the above equation can be expressed as: T∗ k−1 2 M , =1+ T0 2

(2.46)

where k is the adiabatic index, for air k = 1.4 and for gas k = 1.33, M is the Mach number, which is defined as: M = υ/a, where a is the speed of sound in the fluid, for an ideal gas: a=

√

k RT ,

(2.47)

where R is the gas constant. From Eq. (2.45), it is clear that the temperature of a gas moving at a velocity υ is the total temperature of the gas when all of its kinetic energy is converted to internal energy without loss after it stagnates. In general, one needs to know the static temperature T0 of the gas because the physical properties of the gas depend on that temperature. A direct measurement at T0 would require the temperature sensor to move with the fluid at the same speed, which is clearly impractical. In practice, a fixed temperature sensor, such as a thermocouple or thermometric resistance, installed in a high-velocity air stream has only a certain hysteresis effect on the high-velocity air stream, not a complete adiabatic hysteresis. Therefore, the sensor can neither directly indicate the static temperature T0 nor simply measure the total temperature T ∗ . The actual indication value of the sensor is called the effective temperature, noted as Tg . Tg is above the free-flowing static temperature T0 and below the free-flowing total temperature T ∗ . Thus, the difference (T ∗ − Tg ) gives the velocity error. If the external heat loss of the temperature measuring element is not considered, the portion of the airflow that is restored to internal energy by the sensor hysteresis is denoted by (Tg − T0 ). By definition: r=

Tg − T0 T g − T0 = , υ2 T ∗ − T0 2c p

where r is the recovery factor, or coefficient of rewarming.

(2.48)

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2 Temperature Detection

The speed error ΔTυ can be expressed in terms of the recovery factor r according to Eqs. (2.46) and (2.48). ΔTυ = T ∗ − Tg = (1 − r )

υ2 2c p [

= (1 − r )

1

k−1 M2 2 + k−1 M2 2

] T ∗.

(2.49)

Equation (2.49) shows that the velocity error ΔTυ is related to the Mach number M and the recovery factor r . To reduce the velocity error ΔTυ , we want the recovery factor r of the thermometer to be large and the Mach number of streams flowing through the thermometer M to be small. However, the M number of the measured airflow cannot usually be changed at will, so the main technique to reduce the velocity error is to increase the recovery coefficient of the thermocouple so that it is close to 1 and has a more stable value. The recovery coefficient is a very complex parameter, which is related to the Mach number M, Prandtl number pr , Reynolds number Re and the size, structure type, installation method and material of the temperature sensor. It is generally determined by experimental methods. A large number of experimental data show that pr number close to 0.7 gas, if the thermocouple wire and airflow are parallel, r = 0.86 ± 0.09; if the thermocouple wire and airflow are perpendicular, r = 0.68 ± 0.07. (ii) Methods for reducing speed errors There are two ways to deal with the speed error problem of temperature sensors, one is to experimentally measure the recovery factor r value according to the operating conditions and then calculate the correction value. From Eq. (2.46), Eq. (2.48) can be derived: T0 = Tg T ∗ = Tg

1 M2 1 + r k−1 2 1+ 1

k−1 M2 2 . k−1 + r 2 M2

(2.50)

(2.51)

Thus, if the Mach number of the airflow is known M, the sensor recovery factor r and the effective temperature of the airflow are measured T g , the static temperature of the airflow T0 and the total temperature T ∗ can be found. Another way is to try to stagnate the airflow. If the gas stream is adiabatically stagnant, its total temperature can be easily measured. If we want to measure the temperature of the airflow in the test section, and the velocity of the airflow in the test section is determined by the experimental task and does not allow the entire airflow to stagnate; we can still try to stagnate a small portion of the airflow. To do this, a hysteresis hood can be placed

2.7 Contact Temperature Measurement Techniques

79

Fig. 2.46 Thermocouple with hysteresis cover

over the temperature sensor to reduce the velocity of the airflow over the sensor to a point where the velocity error can be reduced to within the allowable range and ignored. The temperature of the airflow inside the hysteresis hood is increased by the hysteresis, but it is still lower than the total temperature of the airflow because it is losing heat to the mainstream. Alternatively, a temperature sensor fitted with a hysteresis hood can still be depicted with a temperature recovery factor. Figure 2.46 is a schematic diagram of a thermocouple with a hysteresis hood. A thermocouple with a hysteresis hood is called a total temperature thermocouple, and it has been shown that the lower the airflow velocity inside the hysteresis hood, the better. However, there is an optimum internal flow velocity because the gas inside the hood has to dissipate heat to the main flow and should be constantly replaced by fresh gas. Figure 2.47 lists two hysteresis thermocouple configurations and their r values as a function of airflow velocity. Figure 2.47a is used for subsonic airflow temperature measurements. Figure 2.47b is used for supersonic airflow temperature measurements. As seen in the figure, the r value increases to 0.95–0.99 when the hysteresis shield is installed. In summary, the use of a hysteresis hood with the measurement end parallel to the airflow to improve the recovery factor r is the main method of reducing velocity errors. By machining a chamfer at the entrance of the hysteresis hood, the insensitivity angle to the direction of the airflow can be increased. (iii) Determination of the recovery factor r The recovery coefficients of thermocouples at certain Mach numbers and mounting angles are ultimately determined experimentally. The determination of the recovery coefficient r is performed on a dedicated calibration wind tunnel. Figure 2.48 shows a schematic diagram of the calibration wind tunnel. The gas flow rate in the regulator is very low, the temperature measured by thermocouple 3 is the total temperature T ∗ , the thermocouple 2 being measured is in the high-velocity gas flow at the outlet of the adiabatic nozzle, and the effective temperature is measured Tg . The recovery coefficient r of thermocouple 2 can be seen from Eq. (2.49) as: r = 1 − ( k−1 2

Owing to

(T ∗ − Tg )/T ∗ ) ( ) M 2 / 1 + k−1 M2 2

(2.52)

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2 Temperature Detection

Fig. 2.47 Measuring stagnation temperature sensor. a At lower Mach number; b at higher Mach number (1—platinum shell; 2—stainless steel)

√

[ ∗ ] p k−1 2 ( ) k −1 k−1 p

(2.53)

T ∗ − Tg r =1− [ ] , ( ) k−1 k p 1 − p∗ T∗

(2.54)

M= Consequently

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81

7 3

2 8 6

9 1

4 5

Fig. 2.48 Recovery factor r determination device, 1—regulator box; 2—thermocouple to be measured; 3—total temperature thermocouple; 4—total pressure tube. 5—manometer; 6—ice bottle; 7—toggle switch; 8—potential difference meter; 9—nozzle

where p and p ∗ are the static and total pressures, respectively. For subsonic airflow nozzles, the static pressure at the outlet is the atmospheric pressure, which can be read by an atmospheric manometer. The total pressure can be measured by the total pressure tube 4 and pressure indicator 5. It follows that the values of r can be found by measuring T ∗ , (T ∗ − Tg ) and the total jet pressure p ∗ and static pressure p.

2.7.3 High-Temperature Airflow Temperature Measurement, Radiation Error Analysis The radiation heat exchange is proportional to the fourth power of temperature. Hence, as the measured gas temperature increases, the temperature sensor and the surrounding container wall radiation heat exchange which is relative to convection and conduction heat exchange accounts for the proportional increase. For example, radiation heat is larger when the temperature measurement element around the lowtemperature heat-absorbing surface result in the temperature measurement element to the cold wall surface. Thus, the thermometer indicates a value lower than the actual gas temperature resulting in radiation-based temperature measurement error. (i) Analytical model of radiation error The high-temperature flue gas temperature measurement error is analyzed in Fig. 2.49. Let the flue gas temperature be tq , measured with a thermocouple be tr , the cold wall surface temperature of the four walls of the flue is ts , the heat transfer analysis is as follows: 1. The high-temperature flue gas transfers heat to the thermocouple mainly by convection. by ignoring the heat conduction and radiation heat transfer from the flue gas to the thermocouple, the heat transfer is:

82

2 Temperature Detection

Fig. 2.49 Schematic diagram for measuring flue gas temperature, 1—baffle; 2—insulation

2 tr tq

1

Q α = α A(tq − tr ),

ts

(2.55)

where α is the convective heat transfer coefficient of the flue gas to the thermocouple, and A is the heat transfer surface area of the thermocouple. 2. Heat exported along the thermocouple protection sleeve is: ( Q λ = −λ f

) ∂ 2t , ∂x2

(2.56)

where λ is the thermal conductivity of the thermowell material, f is the crosssectional area of the thermowell, x is the direction of the thermocouple pivot, t is the temperature distribution of the thermocouple casing along the pivot direction. 3. Heat exchange between the thermocouple and the surrounding cold wall surface, mainly in the form of radiation; ] [ Q R = εn Aσ (tr + 273)4 − (ts + 273)4 ,

(2.57)

where εn is the emissivity of the system (blackness factor), σ is the Boltzmann constant, which is 5.67 × 10–8 W/(m2 × K4 ). 4. Dynamic heat absorption by thermocouples due to changes in measured temperature over time Q t = ρcV

∂t , ∂τ

(2.58)

where ρ, c, V are the density, specific heat, and volume of the thermocouple temperature measurement element, respectively. Combining Eqs. (2.55)–(2.58), the heat balance equation for a thermocouple can be written as: Qα = Q R + Qλ + Qt That is,

2.7 Contact Temperature Measurement Techniques

83

] [ ∂ 2t ∂t α A(tq − tr ) = εn Aσ (tr + 273)4 − (ts + 273)4 − λ f 2 + ρcV ∂x ∂τ

(2.59)

or ( tr = tq +

( ) ) ] ρcV ∂t εn σ [ λ f ∂ 2t 4 4 − (tr + 273) − (ts + 273) − a A ∂x2 a a A ∂τ

(2.60)

∂t = When the thermocouple temperature measurement reaches steady state, then ∂τ 0. If the temperature measurement element is used properly and installed correctly, its thermal conductivity error can also be neglected. Then Eq. (2.59) can be simplified as:

] [ α(tq − tr ) = εn σ (tr + 273)4 − (ts + 273)4 .

(2.61)

Then the radiometric error of the thermocouple ΔTR is: ΔTR = tq − tr =

] εn σ [ (tr + 273)4 − (ts + 273)4 . α

(2.62)

When the surface area of the cold wall around the thermocouple is much larger than the surface area of the thermocouple element, the system emissivity εn is close to that of the thermocouple ε. (ii) Measures to reduce radiation errors As can be seen from the expression for radiation error (2.62), there are three main ways to reduce the radiation error ΔTR : (1) increase the temperature of the cold wall surface around the thermocouple ts ; (2) increase the convective heat transfer coefficient α; and (3) reduce the blackness coefficient of the thermocouple ε. The following specific implementations have been used: 1. Add heat shield: generally in the thermocouple jacket 1–3 layers of a thin-walled concentric cylindrical heat shield, as shown in Fig. 2.50. After adding the heat shield, the temperature measurement thermocouple and the cold wall surface are isolated. The temperature sensor does not connect directly to Fig. 2.50 Schematic diagram of adding a heat shield

(a)

(b)

84

2 Temperature Detection

the cold wall surface for heat radiation, but to the high temperature of the heat shield for radiation heat dissipation. This improved the ts in the heat shield inner wall bright nickel plating and reduces ε. Thus, reduction in temperature measurement error. The more layers of the hood, the better the effect of reducing radiation errors. However, the more layers, the more difficult and unreliable the process. Moreover, the space between the layers has to be large enough to ensure that the gas flow achieves good convective heat transfer. A good temperature measurement can also be achieved by using an electrically heated single shield. The electric shield is equipped with an additional temperature sensor. The current added to the shield is adjusted so that the temperature of the temperature sensor and the temperature of the additional temperature sensor are the same. Therefore, the measured temperature is the true temperature of the fluid. An electric heater replaces the heat radiation from the shield to the cold wall surface. 2. Double thermocouple: It consists of two thermocouples with the same material, different wire diameters, and exposed measuring ends as shown in Fig. 2.51. The temperature of the high-temperature gas to be measured can be calculated from the measured values of the two thermocouples. Let the diameters of the two thermocouples be d1 and d2 , and d 1 > d2 . The exposed measuring ends are close to each other. The convective heat transfer coefficients of the gas flow to the measuring ends are α1 and α2 , respectively. If the temperature of the measured gas is Tq and the temperature of the surrounding cold wall surface is Ts , the emissivity of both thermocouples is the same, i.e., ε1 = ε2 . The thermocouples are installed correctly so that the thermal conductivity error is negligible. Their measured temperature indications are T1 and T2 , respectively. The radiation error according to Eq. (2.62) is: Tq − T1 =

] ε1 σ [ 4 T − Ts4 α1 1

Fig. 2.51 Schematic diagram of a dual thermocouple, 1—four-hole porcelain tube; 2—heat-resistant steel jacket

(2.63)

1

d1=0.5

10 d2=0.2

2

2.7 Contact Temperature Measurement Techniques

Tq − T2 =

] ε2 σ [ 4 T − Ts4 α2 2

85

(2.64)

If the thermocouple is installed perpendicular to the direction of airflow, the convective heat transfer coefficient is known from the principle of heat transfer at a range of flow rates α = K d m−1 , where K is a constant. So α1 /α2 = (d1 /d2 )m−1 . If the conditions T14 >> Ts4 and T24 >> Ts4 are met in use, then the gas temperature can be easily calculated from the above (2.63) and (2.64) two equations as: Tq = T1 +

T2 − T1 . 1 − (d1 /d2 )m−1 (T2 /T1 )4

(2.65)

The practical application of dual thermocouples should satisfy 4 > d 1 /d 2 > 2. For high-temperature flue gas media, m is approximately between 0.37 and 0.41, for air or light flue gas m ≈ 0.5. 3. Pumping thermocouple: From Formula (2.62), it can be seen that the increase in temperature measurement element and the measured gas between the convection heat transfer coefficient can reduce the radiation error. Hence, for industrial test, the commonly used pumping thermocouple makes the thermocouple measurement end of the local flow rate to increase. A pumping thermocouple working principle is shown in Fig. 2.52. The compressed air or steam is made to pass through the nozzle 2, causing a negative pressure at the nozzle. The high-temperature gas to be measured will be pumped away at a higher flow rate in the direction shown by the arrow, with the bare end of the armored thermocouple at that flow rate. Figure 2.53 illustrates the relationship between the pumping speed and the temperature indication of a pumping thermocouple. The lower the speed, the greater the deviation of the temperature indication. When the speed increases above 100 m/s, the temperature indication tends to stabilize. Therefore, the flow rate is generally designed to be in the range of 100–200 m/s.

Fig. 2.52 Schematic diagram of a pumped thermocouple, 1—armored thermocouple; 2—nozzle; 3—heat shield; 4—mixing chamber expansion tube; 5—outer metal sleeve

86

2 Temperature Detection

Fig. 2.53 Plot of pumping speed versus temperature indication

Fig. 2.54 Indicated temperature curves for different diameter thermocouples

4. Zero diameter extrapolation method: Several thermocouples of different diameters are applied to measure the temperature of the flue gas. According to the temperature values measured by these thermocouples, the temperature value when the thermocouple diameter is equal to zero is extrapolated as a graph method to find the true temperature of the flue gas. Figure 2.54 shows the temperature shown when the extrapolated diameter is zero and the temperature values of the pumping thermocouples.

2.7.4 Dynamic Temperature Measurement, Dynamic Error Analysis According to the previous analysis, it can be seen that for the high-speed airflow temperature measurement, the prominent problem is the velocity error, which can be neglected for the thermal conductivity error and radiation error. On the other hand, the prominent problem is the radiation error for the high-temperature airflow temperature measurement. In both of the above problems, static problems are dealt with. That

2.7 Contact Temperature Measurement Techniques

87

is, neither the airflow temperature nor the output of the temperature sensor is timevarying. Now we will discuss the problem of “dynamics”. The main characteristic of “dynamics” is that the output of the temperature sensor varies with time. There are two reasons for this variation. One reason is that the airflow temperature varies, or the sensor is used to scan an inhomogeneous temperature field to vary the temperature sensed by the sensor. The other reason is that the airflow temperature does not change. Nevertheless, the sensor suddenly goes from room temperature to high temperature, and the temperature of the sensor changes over time due to the unstable heat transfer process between the airflow and the sensor. The sensor’s temperature is not equal to the measured temperature in various dynamic processes. The difference is the dynamic response error or simply referred to as dynamic error. The dynamic error mainly comes from the thermal inertia of the temperature sensor. When the temperature changes sharply with time due to the thermal inertial of the temperature sensor, the temperature felt by the sensor must lag behind the change in medium temperature. If the effect of thermal conductivity error and radiation error is ignored, then by Eq. (2.59) there is: α A(tq − tr ) = ρcV

dtr . dτ

(2.66)

Then the dynamic error tq − tr =

dtr ρcV dtr =K , α A dτ dτ

(2.67)

is called the thermal inertia coefficient. It is also known as the time where K = ρcV αA constant. Equation (2.67) is an approximate mathematical expression for the dynamic error. The equation shows that if the time constant of the sensor K is known, the dynamic error can be calculated from the value of the measured rate of change in temperature (dtr /dτ ). If the initial condition of Eq. (2.67) is that tr = tr 0 ,tq are constants when τ = 0, then the general solution of Eq. (2.67) can be solved as: )( ( τ ) tr − tr 0 = tq − tr 0 1 − e− K .

(2.68)

If we set tr 0 = 0, then Eq. (2.68) is: ( τ ) tr = tq 1 − e− K .

(2.69)

From this, it can be calculated that tr = 0.632 tq when τ = K. Based on this result, we can experimentally determine the time constant K value. When the sensor is placed in a medium known to tq , the time corresponding to the rise of the sensor’s indicated temperature tr to 63.2% of the known temperature tq is the time constant K.

88

2 Temperature Detection

On the other hand, the slope of the temperature rise curve at the initial moment can be deduced from Eq. (2.68) as: | tq − tr 0 dtr || . = dτ |τ =0 K It follows that if a tangent line is made at the start of the temperature rise curve, the time coordinate of the point where the tangent line intersects the horizontal line at tq is the time constant K . The larger the time constant of a temperature sensor, the longer it takes for the sensor to reach thermal equilibrium with the measured airflow. Therefore, the key to reducing the dynamic error is to reduce the time constant. This can be achieved by reducing the geometry of the sensor, increasing the convective heat transfer coefficient, etc.

2.7.5 Measurement of Wall Temperature The thermocouple method is commonly used for measuring the surface temperature of certain objects in engineering and scientific experiments. This method has the advantages of a small thermal contact, less heat loss, a large temperature measurement range, a high degree of accuracy, and relative convenience. In particular, the development of thin-film thermocouples has brought convenience to measuring wall temperature. Depending on the specific conditions, stable performance of the thermistor and special sheet-shaped thermometric resistance elements can also be used to measure the wall temperature. There are four types of thermocouple contact with the surface under test, as shown in Fig. 2.55. (a) For point contact, the measuring end of the thermocouple is in direct contact with the surface being measured. (b) For surface contact, the measuring end of the thermocouple is first welded to a thin sheet of metal with good thermal conductivity and then in contact with the surface under test. (c) For isothermal contact, the measuring end of the thermocouple is fixed to the surface under test and then led out by laying a distance of at least 20 times the wire diameter along the isothermal line insulation of the surface under test. (d) For discrete contact, the two hot electrodes are in contact with the surface under test. Regardless of the contact method, the main cause of measurement error is the loss of thermal conductivity of the thermocouple wire. The thermal contact of the thermocouple absorbs heat from the surface being measured. Some of the heart escapes along the thermocouple wire into the surrounding environment, leaving the temperature of the thermal contact lower than the actual temperature of the surface being measured. The four contact methods in Fig. 2.55 have the following error characteristics: the least error in the isothermal contact (c), because the thermocouple wire is laid along the isotherm and the thermal conductivity loss at the thermal contact is minimized. The method is the second-lowest in the surface contact (b), and the

2.8 Non-contact Thermometers

89

heat loss of the thermocouple wire is supplemented by a well-conducting metal sheet. The point contact (a) method has the largest error because the thermal conductivity losses are all concentrated in one point and the heat is not fully replenished. If the thermocouple diameter is coarse under the same laying method, the thermal conductivity loss along the thermocouple wire axially is large. The measurement error also increases. The measured object and the heat capacity are large and the wall is thick while the measurement error is relatively reduced. Moreover, the airflow disturbance near the thermal contact and the convective exothermic coefficient are also large while the measurement error also increases accordingly. Thus, the greater the thermal conductivity of the measured material, the easier it is for the thermocouple wire to supplement the heat from the thermal junction, making the measurement error smaller. In summary, wall temperature measurements should give priority to the following issues: 1. Thermocouples with small diameters and low thermal conductivity should be used as far as their strength allows. 2. Preference should be given to the laying of isothermal lines. 3. The material under test is a non-good thermal conductor and can be used in face contact. 4. If the material to be measured allows, surface grooving is more beneficial for improving measurement accuracy.

2.8 Non-contact Thermometers The contact temperature method of measurements uses a temperature measurement sensor in direct contact with the object to be measured. In most cases, the temperature measurement element and the object to be measured are to be measured in thermal equilibrium. This means that the sensor must withstand corrosion, oxidation, contamination, reduction, and even vibration of the various atmospheres under measured temperature conditions. For small measured objects, the insertion of the temperature measuring element also distorts the original temperature distribution to a greater extent. For some moving objects, it is almost impossible to achieve continuous measurement of their temperature by contact. Alternative temperature method of

(a)

(b)

(c)

Fig. 2.55 Thermocouple contact with the surface to be measured

(d)

90

2 Temperature Detection

measurements must be found under high-temperature conditions that contact temperature sensors cannot withstand. Therefore, non-contact optical thermometers based on the principle of thermal radiation have been developed. When the temperature of any object is above absolute zero, energy is released. The fraction of energy emitted outward as thermal energy is called thermal radiation. A non-contact thermometer is a method of determining temperature using the measurement of the radiated energy of an object. Since it does not come into contact with the measured medium, it does not destroy the temperature field of the measured medium and has a good dynamic response. Hence, it can measure the temperature values of non-stationary thermal processes. In addition, its upper measurement limit is not affected by the nature of the material. The large temperature measurement range makes it more suitable for high-temperature measurements. Non-contact temperature measurement instruments are roughly divided into two categories: (a) the optical radiation pyrometer which includes monochromatic optical pyrometer, photoelectric pyrometer, full radiation pyrometer, colorimetric pyrometer, etc.; (b) infrared radiometer includes full infrared radiation type, monochromatic infrared radiation type, colorimetric type, etc. According to Planck’s (Planck’s) law, the intensity of monochromatic radiation from an absolute blackbody E 0λ is: [ ]−1 E 0λ = C1 λ−5 exp(C2 /λT ) − 1 ,

(2.70)

where C1 is Planck’s first radiation constant, C 1 = 37.413 W·μ m4 /cm2 , C2 is Planck’s second radiation constant, C 2 = 14388 μ m·k, λ is the wavelength of radiation, μm., T is the blackbody absolute temperature, K. The units of E 0λ after using the above units are W/(cm2 ·μm). At temperatures below 3000 K, Planck’s formula can be replaced by Vien’s (Vien) formula with an error of 1% or less. The Vien formula is: E 0λ = C1 λ−5 exp(−C2 /λT ).

(2.71)

The temperature of 1064.18 °C is internationally used as the gold solidification point of the blackbody radiation intensity and a reference used for comparison. Hence, the following formula can be used for the gold solidification point above the temperature of the scale: exp(C2 /λtg ) − 1 E 0λ , = E 0λ,g exp(C2 /λT ) − 1

(2.72)

where tg is the freezing point of gold, E 0λ,g is the radiation intensity of the blackbody at the gold solidification point, and at the wavelength λ, T is the measured temperature (K). The curve as a function of Planck’s equation is shown in Fig. 2.56. As seen by the curve, the intensity of monochromatic radiation grows as the temperature

2.8 Non-contact Thermometers

91

70 2200K 60

50

0.14

2000

650K 40

E0λ/(W·cm-2·μm-1)

E0λ/(W·cm-2·μm-1)

0.12 0.10 600

0.08 0.06

30

1800

20

1600 1400

0.04

500

1200 1000

10 0.02

400 0

2

4

6

8

10

12 14

0

1

2

3 4

λ/μm

5

6

7

8

λ/μm

Fig. 2.56 Curve of radiation intensity versus wavelength and temperature

increases, and the peak of the curve shifts in the direction of shorter wavelengths as the temperature increases.

2.8.1 Monochromatic Radiation-Type Optical Pyrometer Monochromatic radiation-type optical pyrometer uses brightness comparison instead of radiation intensity comparison for temperature measurement. Since the temperature of an object above 700 °C emits visible light significantly and has a certain brightness, its monochromatic brightness B0λ is proportional to the monochromatic radiation intensity E 0λ , i.e., B0λ = C E 0λ ,

(2.73)

where C is the scale factor. Substituting the Vine formula of Eq. (2.71) into (2.73) yields: B0λ = CC1 λ−5 e−(C2 /λTS ) ,

(2.74)

92

2 Temperature Detection

where Ts is the temperature of the blackbody. The gray body also has a similar relationship to Eq. (2.74), i.e., Bλ = Cελ C1 λ−5 e−(C2 /λT ) ,

(2.75)

where Bλ is the brightness of the gray body, E λ (a) is the intensity of monochromatic radiation of the gray body, ελ (a) is the monochromatic grayscale of the object, T is the gray body temperature. When the luminance of a black body B0λ at a temperature of Ts is equal to the luminance of a gray body Bλ at a temperature of T , Eqs. (2.74) and (2.75) give: λ 1 1 1 − = ln . TS T C2 ελ

(2.76)

Because 0 < ελ < 1,Ts < T , it follows that the temperature measured directly from the optical thermometer Ts is lower than the temperature of the actual gray body. Thus, it must be corrected for the grayness of the object’s surface ελ using Eq. (2.76). Figure 2.57 shows the optical pyrometer correction curve. (i) Filament concealment-type optical pyrometer The filament-occluded optical pyrometer is a typical monochromatic radiometric optical pyrometer. It has the highest accuracy among all radiometric thermometers. It is therefore used in many countries as a reference instrument to reproduce the international practical temperature scale above the freezing point temperature of gold. The principle of the filament-implicit optical pyrometer is shown in Fig. 2.58. It compares the brightness of the monochromatic radiation of the object under test with the brightness of a temperature lamp with an adjustable current. Each current corresponds to a known filament temperature. If the brightness of both is the same, the filament outline is concealed in the image of the object under test (as shown in Fig. 2.59c). The current reading is the brightness temperature of the object, and then the true temperature of the object is found in Fig. 2.57. (ii) Photoelectric pyrometer The filament-hidden optical pyrometer mainly uses the human eye to judge the brightness balance state. Hence, the measured temperature is discontinuous, and it is difficult to make the automatic recording of the measured temperature. Therefore, the photoelectric pyrometer, which can automatically balance the brightness and automatically and continuously record the measured temperature display value, has been developed and applied. Photoelectric pyrometer consists of a photoelectric device that acts as a sensitive element to feel the brightness of the radiation source changes. These radiation changes are converted into a proportional electrical signal with the brightness. The signal by the electronic amplifier is automatically recorded

2.8 Non-contact Thermometers

93

Fig. 2.57 Optical pyrometer correction curve

as the measured object temperature value. Figure 2.60 is a schematic diagram of the working principle of the WDL-type photoelectric pyrometer. The radiant energy emitted by the object 17 under test is gathered by the objective lens 1. It is directed through the light bar 2 and the window 3 in the light shield 6. This energy is then sent to the optoelectronic device (silicon photocell) 4 through a red filter (not shown on the figure) mounted in the light shield. The beam emitted by the object under test must cover the aperture 3, which can be observed by a sighting system consisting of a sighting lens 10, a reflector 11 and a viewing aperture 12. The radiant energy emitted from the feedback lamp 15 is projected through the window 5 in the light shield 6. It passes through the same red filter as described above, onto the same optoelectronic device 4 as well. In front of the light shield, 6 is placed

94

2 Temperature Detection 1

2

3

4

1

5

2

3

4

5

R1

6

6 R2 R1

7

R3 7

R4 R5

S

S

E E

(a)

(b)

Fig. 2.58 Schematic diagram of a hidden filament optical pyrometer. a Voltage type b bridge type, 1—objective lens; 2—absorption glass; 3—pyrometer temperature lamp; 4—eyepiece; 5—red filter; 6—measuring meter; 7—variable resistor

(a)

(b)

(c)

Fig. 2.59 Brightness adjustment of the hidden filament optical pyrometer. a Filament too dark; b filament too bright; c fidden filament (correct)

(a)

10

11

12

2

17

(b) 7 3 6

5 6

1

4

3 5 15 S 16

14

13

N

8 9

Fig. 2.60 Operating principle of optical pyrometer. a Schematic diagram of the operating principle; b light modulator, 1—objective lens; 2—light bar; 3, 5—aperture; 4—optoelectronic device; 6— light shield; 7—modulating sheet. 8—permanent magnets; 9—excitation windings; 10—lenses; 11—reflectors; 12—observation holes. 13—preamplifier; 14—main amplifier; 15—feedback lamp; 16—potential difference; 17—object to be measured

2.8 Non-contact Thermometers

95

the light modulator. The excitation winding 9 of the light modulator is energized with a 50 Hz AC current. The resulting alternating magnetic field interacts with the permanent magnet 8 and causes a 50 Hz mechanical vibration of the modulating sheet 7, which alternately opens and shades the windows 3 and 5. This causes the radiated energy of the measured object and the feedback lamp to be projected onto the silicon photocell. When the two radiated energies are not equal, the photodevice produces a pulsed photocurrent I , which is proportional to the difference between these two monochromatic radiated energies. The pulsed photocurrent is zero when the value of I is negatively fed back through the amplifier. Hence, the brightness of the feedback lamp is equal to the brightness of the object being measured. An electronic potentiometer 16 is used to automatically indicate and record the value of I , scaled to the temperature value. Due to the use of negative feedback, the instrument’s stability depends mainly on the stability of the “current-radiation intensity” characteristic relationship of the feedback lamp. Some models of photoelectric pyrometer do not use the above mechanical vibration-type light modulator. They use a synchronous motor to drive a rotating disk as a light modulator. The disk has a small window to make the measured object and the feedback lamp beam alternate through the cast to the photocell. The modulation frequency is 400 Hz, and the other parts’ principle is the same as described above. Some of the errors associated with the optical pyrometer include those caused by the blackness coefficient, the measured object, and the pyrometer between the medium of radiation absorption. The distance between the observation point and the measured object is not too large, generally, not more than 3 m, to (1~2) m is appropriate.

2.8.2 Full Radiation Pyrometer A full radiation pyrometer determines the temperature of an object with the help of measuring the entire radiant energy of the object. According to the Stefan–Boltzmann formula, ∫∞ E0 =

E 0λ dλ = σ0 T 4 ,

(2.77)

0

where σ0 is the Stefan–Boltzmann constant (5.67 × 10–12 W/(m2 ·K4 ). When the blackbody radiant energy (E 0 )1 at some reference temperature T1 is known, the blackbody radiant energy E 0 at an unknown temperature T is measured and can be derived from Eq. (2.77) (E 0 )1 T4 = 14 . E0 T

96

2 Temperature Detection 1

3

2

5

4

6

3 7 8

9

Fig. 2.61 Schematic diagram of a full radiation pyrometer, 1—objective lens; 2—light bar; 3— glass bubble; 4—thermopile; 5—gray filter; 6—eyepiece; 7—platinum rhodium; 8—mica flakes; 9—secondary instruments

If the measured object is a gray body with a grayscale of ε, its temperature can be corrected by the following equation √ T = Ts 4 1/ε.

(2.78)

Figure 2.61 shows the schematic diagram of the principle operation of a full radiation pyrometer. The wavelength of the measured object λ = 0~∞ of the full radiation energy is focused by the objective lens 1 through the light bar 2 and projected onto the heat receiver 4. This heat receiver is mostly a thermopile, and the thermopile structure (Fig. 2.62) is made up of 16 pairs or 8 pairs of nickel–chromium–constantan alloy. Thermocouples of 0.05–0.07 mm diameter are connected in series to obtain a larger thermal potential. The measuring end of each pair of thermocouples is soldered to a bull’s-eye nickel foil. The cold end is connected in series by a copper foil and the output thermal potential which is read out by a display or recording instrument. The entire inner wall surface of the pyrometer housing is painted black to reduce stray light interference and create black body conditions. Equation (2.78) shows that the measured radiation temperature is always lower than the true temperature of the actual object because ε is always less than 1.

2.8.3 Colorimetric Pyrometer A colorimetric pyrometer uses the ratio of the intensity of radiation at two different wavelengths to measure temperature, hence the name two-color pyrometer. Since the monochromatic emissivity of ελ object has a monochromatic radiant intensity of:

2.8 Non-contact Thermometers

97

Fig. 2.62 Thermopile structure, 1—thermocouple; 2—mica ring; 3—bull’s eye; 4—examining copper foil; 5—lead wire

2 1

3

4 5

) ( C2 E λ = ελ C1 λ−5 exp − λT

(2.79)

Thus, the ratio of the intensity of radiation at the same temperature for two monochromatic wavelengths of λ1 and λ2 is: E λ1 = E λ2

(

λ2 λ1

(

)5 exp

C2 ( λ12 − T

1 ) λ1

)

ελ1 . ελ2

(2.80)

That is, [( ) ] E λ1 − A−P B , T = 1/ ln E λ2

(2.81)

( ) ( ) λ1 where A = 5 ln λλ21 , B = C2 λ12 − λ11 , P = ln εελ2 . For a blackbody, there is ελ1 = ελ2 = 1, and for a gray body there is ελ1 = ελ2 , at which point both have P = 0. Therefore, when a two-color pyrometer is used to measure a gray body, the temperature measurement is equal to the temperature of a blackbody with the same radiation intensity ratio. Therefore, there is no correction needed. Figure 2.63 shows the working principle diagram of single-channel photoelectric colorimetric pyrometer. The radiated energy of the measured object is focused by the objective lens set 1 and reaches the silicon photocell receiver 5 through the through-hole imaging mirror 2. The synchronous motor 4 drives the rotation of the modulation disk 3, which is equipped with two different color filters. It alternates the passing of two wavelengths of light for the silicon photocell receiver 5 to output two corresponding electrical signals. The aiming of the object to be measured is achieved by the reflector 8, the inverted image mirror 7, and the eyepiece 6. For stable operation of the photocell, it is mounted in a thermostatic container, in which the photocell thermostatic circuit automatically controls the temperature. The temperature measurement range of the single-channel colorimetric pyrometer is 900–2000 °C, and the basic error of the instrument is ±1%. If a PbS photocell

98

2 Temperature Detection 7

8

6

5

1

2

3

4

Fig. 2.63 Single-channel photoelectric colorimetric pyrometer schematic, 1—objective lens set; 2—through-hole imaging mirror; 3—modulation disk; 4—synchronous motor; 5—silicon photocell receiver; 6—eyepiece; 7—inverted image mirror; 8—reflector Fig. 2.64 Dual-channel photoelectric colorimetric pyrometer schematic, 1—objective lens; 2—reflector; 3—inverted image mirror; 4—eyepiece; 5—human eye; 6,10—silicon photocell; 7—beamsplitter; 8—objective lens; 9—field of view light bar

2

3

4

5

1 8

7

6

9 10

is used instead of a silicon photocell as the receiver, the lower limit of temperature measurement can be up to 400 °C. Figure 2.64 shows the schematic diagram of a two-channel colorimetric pyrometer. It uses a beamsplitter to divide the radiant energy into two channels of different wavelengths. The infrared light is projected onto the silicon photocell 6 through the beamsplitter 7, and the visible light is reflected by the beamsplitter onto the other silicon photocell 10. Using the difference between the output signals of the two silicon photocells, the specific color temperature value of the object under test can be found.

2.8.4 Infrared Thermometer When the temperature of the object to be measured is below 700 °C, it does not emit visible light significantly. Therefore, it is difficult to use the above-mentioned radiation thermometer to measure temperature. Since it is all infrared radiation in this temperature range (0–700 °C), an infrared-sensitive element is needed to detect it. Figure 2.65 shows the operating principle of an infrared pyrometer, which has an analogy with the operating principle of a photoelectric pyrometer, in an optical feedback structure. The infrared radiation from the measured object S and the reference source R is modulated by a disk modulator T and fed to an infrared-sensitive detector

2.9 Application of Temperature Detection Instrumentation in Pressurized … Fig. 2.65 Infrared thermometer operating principle diagram: S—object to be measured; L—optical system; D—infrared detector; A—amplifier; K—phase-sensitive rectifier; C—control amplifier; R—reference source; M—motor; I—indicator; T—modulation disk

99

L S

A

D

K

T M C R

I

D. The disk modulator T is driven by a synchronous motor M. The output electrical signal of the detector D is sent to the control amplifier C through the amplifier A and the phase-sensitive rectifier K to control the radiation intensity of the reference source. When the radiation intensity of the reference source and the object under test are the same, the heating current of the reference source represents the measured temperature, and the temperature value of the object under test is displayed by the indicator I. A thermal imaging camera uses the infrared scanning principle to measure the surface temperature distribution of the object. It takes in the distribution of infrared radiation flux from all parts of the object under test to the instrument. Then it uses the infrared detector horizontal scanning and vertical scanning, sequential direct measurement of the infrared radiation emitted from all integrated parts of the object under test to get the distribution of the object emitted infrared radiation flux image. This image is called a thermal image or called temperature field diagram.

2.9 Application of Temperature Detection Instrumentation in Pressurized Water Reactor Nuclear Power Plants The temperature detection instrumentation of nuclear power plants is not fundamentally different from that of thermal power plants in terms of its principle. The notable differences arise from the use and the reactor type. The temperature detection instrumentation used in nuclear power plants also depends on temperature detection range and occasion.

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2 Temperature Detection

2.9.1 Application of Thermocouples in Core Temperature Measurement The thermocouple used in the nuclear island portion of the temperature detection instrumentation for pressurized water reactor nuclear power plants is a nickel–chromium–nickel–aluminum thermocouple. This thermocouple is mainly used for the detection of core temperature. In order to determine suitable thermocouples for pressurized water reactors, different types have been tested under neutron flux. The following thermocouples, NiCr–NiAl, Fe–Constantan, Cu-Constantan, Pt-PtRh, W–Ni, and W-WRhe, were irradiated for longer periods of time at a thermal neutron flux of 1 × 1024 neutrons/(cm2 s). NiCr– NiAl was the most stable while Fe–Constantan was the second most stable. The remaining four thermocouples underwent compositional changes during irradiation, which inevitably resulted in changes in thermocouple properties. Therefore, NiCr– NiAl thermocouples are commonly used for temperature detection in nuclear reactor cores. NiCr–NiAl thermocouple has a diameter of about 3 mm with stainless steel sleeve, alumina insulation, and a plug-in thermocouple connector connected at the end. The detection of the outlet coolant temperature of the fuel assembly can determine the maximum possible power output from the core. Moreover, the core neutron flux and individual heat pipe factors calculations help to verify the core design parameters. There are usually dozens of NiCr–NiAl thermocouples, which are extended to the fuel assembly outlet through guide tubes running through the upper head of the pressure shell. The signal is connected to the cold-end box inside the containment via thermocouple extensions and then sent to the recording and data processing system via the penetrations and copper conductors. The functions of the core temperature measurement are as follows: 1. Giving a map of the core temperature distribution and a continuous record of the core temperature showing the maximum core temperature and the minimum temperature margin. 2. Detection or verification of the degree of imbalance in the radial power distribution in the reactor. 3. Determine whether a control rod has been detached from its group of rods. 4. For the operator to observe the trends in core temperature and subcooling during and after an accident. The temperature detection of the core of the Daya Bay Nuclear Power Plant is realized with 40 thermocouples. The thermocouples are made of chromium–nickel– aluminum–nickel alloy with stainless steel for the cladding and aluminum oxide for insulation. The arrangement of these 40 thermocouples in the core is shown in Fig. 2.66. 40 thermocouples are divided into two channels, A and B, with 20 thermocouples in each channel. The temperature signal is led from the thermocouplelead pipe through four thermocouple posts.

2.9 Application of Temperature Detection Instrumentation in Pressurized …

101

Fig. 2.66 Reactor core thermocouple arrangement, 1—channel; 2—the number of support pole; 3—thermocouple distribution

The installation of the thermocouple in the core is shown in Fig. 2.67. The hot end of the thermocouple is fixed to the corner support plate at the coolant outlet of the fuel assembly under test, above the upper core support plate. The thermocouple wires are threaded into the wire tubes, and one thermocouple support post is threaded into each of the 10 wire tubes, for four support posts. The thermocouple support posts pass through the pressure vessel top cover. After the thermocouple support pillars have been removed, the thermocouples pass through the thermocouple-lead tube connector. The thermocouple is connected to an extension wire of the same material via a connector. The extension wire is connected to the cold-end box. The pressure vessel head connector is welded to the pressure vessel. There is a removable seal between the thermocouple support column and the pressure vessel head connector and a welded seal between the lead pipe and the thermocouple support column. The thermocouple-lead tube connector is a removable seal between the thermocouple and the lead tube. There are two cold-end boxes, located outside the containment. An extension wire consisting of a single twisted nickel and chromium wire is connected to the coldend box terminals. The adapter copper wire leads the temperature signal to the core cooling monitoring cabinet in the electrical plant. A resistance thermometer detects the temperature of the cold-end box, and the temperature signal is also fed to the core cooling monitoring cabinet for cold-end temperature compensation. The secondary instrumentation and control equipment for the fuel assembly coolant outlet temperature detection system is installed in the main control room.

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2 Temperature Detection

Fig. 2.67 Reactor core thermocouple installation diagram, 1—lower support plate; 2—hot contact; 3—upper support plate; 4—conduit wire; 5—sliding fit element; 6—thermocouple support pole; 7—thermowell and head cover sleeve gate sealing; 8—non detachable connector; 9—extension wire; 10—thermocouple and conduit joint; 11—pressure vessel head connector; 12—upper support pole; 13—connecting parts

The main characteristics of the NiCr–NiAl thermocouple used for core temperature detection at the Daya Bay Nuclear Power Plant are: φ = 3.17 mm; L = 6.0−9.2 m; range : 0−1200 ◦ C. Accuracy: ±1.5 °C, 0 °C < T < 375 °C; ±0.4%T, T > 375 °C.

2.9.2 Application of Thermometric Resistance in Nuclear Island Temperature Measurement in Nuclear Power Plants Thermometric resistances have not so far been widely used for nuclear reactor core temperature measurements because the metal resistance changes in the higher nuclear radiation field. Moreover, the value of the change is a complex function of the radiation pattern and the metal temperature during and after irradiation. In addition, ordinary resistance thermometers are much larger than thermocouples and are not easily applied to reactor cores. However, thermometric resistances are commonly used for

2.9 Application of Temperature Detection Instrumentation in Pressurized …

103

the measurement of coolant temperature at the inlet and outlet of the reactor, which is in a lower nuclear radiation field. Platinum thermometric resistances are mainly used to monitor reactor coolant loop temperature in nuclear power plants. The temperature of the reactor coolant at the reactor inlet and outlet and its temperature difference ΔT and average temperature T avg are among the most important detection parameters. T avg is the main regulation quantity of the reactor power regulation system, the overtemperature ΔT and overpower ΔT protection parameters are adjusted as a function of ΔT and T avg . The reactor coolant temperature used in the control and protection systems is measured by a resistance temperature detector submerged directly in the small bypass loop (rather than in the main reactor coolant tube). The resistance temperature detector is installed in the manifold of this bypass loop. It is relatively large enough to accommodate the resistance temperature detector. In each reactor coolant loop, there are two bypass loops: one bypass loop for the hot section temperature measurement and one for the cold section temperature measurement. The driving head that generates the flow in the hot section manifold is the difference in pressure between the inlet and outlet of the steam generator. Three inlets separated by an angle of 120° (in section) receive the sample stream from the hot section. These sample streams are mixed together before entering the manifold. The return line to the intermediate section between the steam generator and the reactor coolant pump is shared between the hot section manifold sample stream and the cold section manifold sample stream. The cold section manifold inlet line is downstream of the reactor coolant pump. Because of the mixing action of the pump, it does not require multiple inlets, and only one receiver is used. The driving head that produces water flow in the cold section manifold is the differential pressure between the pump inlet and outlet. Figure 2.68 is a schematic diagram of the resistance temperature detector manifold. These resistance temperature detectors are narrow range (277–332 °C). The average temperature of the coolant loop T avg and the temperature difference ΔT can be obtained from the hot section temperature and the cold section temperature. The measurement of temperature with platinum thermometric resistances in the bypass serves two purposes: (1) to give the hot section temperature and the cold section temperature; (2) to generate the average temperature signal T avg of the primary loop coolant and the temperature difference ΔT between the primary loop coolant in the hot and cold sections necessary for the reactor control and protection system. The platinum thermometric resistance cannot be installed directly on cold and hot pipe sections. Instead, they are commonly installed on the bypass lines to measure temperature due to: (1) More uniform fluid temperatures are obtained in the bypass line. (2) The low flow rate of the fluid in the bypass line allows the use of exposed, fast-responding platinum thermometric resistance elements without sleeves.

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2 Temperature Detection

1

2 3 TE

TE

F1

3 TE

5 7

4 TE

6

8

8 9

120°

120°

120°

10

Fig. 2.68 Typical resistance thermometer loop, 1—steam generator; 2—hot section; 3—vent; 4— bypass flow meter; 5—cold section manifold; 6—hot section manifold; 7—reactor coolant pump; 8—drain hole; 9—cold section; 10—hot section profile; TE—temperature detector; FI—flow meter

(3) The bypass system allows the platinum thermometric resistance temperature measurement element to be serviced without the need for certain measures on the primary loop. The specific measurement points for reactor inlet and outlet coolant temperature detection are six platinum thermometric resistances on each loop. Three are in the hot section, two working and one on standby, and three in the cold section, two working and one on standby. The reactor coolant loop temperature can also be measured by a wide range (−18 to 371 °C) resistance temperature detector installed in each loop reactor coolant line gauge hole. Such detectors are used to indicate the temperature during warming and cooling.

2.9.3 Application of Thermometric Resistance in Conventional Island of Nuclear Power Plant A copper thermometric resistance G53 is used for the measurement of the oil return temperature of turbine generator bearings and the temperature of the working and non-working surfaces of the turbine thrust tile. It is also used for the temperature measurement of the generator stator coil. A platinum thermometric resistance BAl is

2.9 Application of Temperature Detection Instrumentation in Pressurized …

105

used for the detection of the inlet and outlet water temperature of the return water heater and the temperature of the generator core. Reflective Questions and Exercises 2.1 What is a temperature scale? What are the three elements of a temperature scale? What are the commonly used temperature scales? What is the relationship between them? 2.2 What is the principle of thermocouple temperature measurement? What are the necessary conditions for a thermocouple circuit to produce a thermal potential? 2.3 Is it possible to intervene in the thermocouple closed circuit with wires and meters and why? 2.4 How many internationally recognized standardized thermocouples are there? What are the indexing numbers? 2.5 Why is cold-end temperature compensation necessary for thermocouple temperature measurement? What are the methods of cold-end temperature compensation? 2.6 When using compensating wires in a thermocouple temperature measurement circuit, how should they be connected? What are the issues to be noted? 2.7 A thermocouple with indexing number S is used to measure a temperature of 20 °C at its reference end, and the measured thermal potential E = (t, 20) = 11.30 mV. Try to find the measured temperature t. 2.8 A nickel–chromium–nickel–silicon thermocouple with index number K is used to measure temperature, and without taking temperature compensation at the cold end, the display meter indicates a value of 500 °C, when the cold-end temperature is 60 °C. Ask what the actual temperature should be? If the temperature at the hot end is not changed and the cold end is kept at 20 °C, what should be the indicated value of the display meter? 2.9 Try to explain the principle of thermometric resistance temperature measurement. Also state the types of thermometric resistances commonly used and what the value of R0 is. 2.10 Why do thermometric resistance temperature measurement elements use a three-wire connection? What are the commonly used temperature measurement display instruments? 2.11 Analyze the causes of temperature measurement errors from contact temperature method of measurements and what measures are used to overcome them in practical applications? 2.12 Briefly describe the working principle of a temperature transmitter. 2.13 What are the characteristics of radiometric methods of temperature measurement? What are the common types of radiometric pyrometers? 2.14 The color temperature of an object is measured to be 1358 °C using a colorimetric pyrometer with a known blackness of ελ1 = 0.36 (λ1 = 0.5 μm) and ελ2 = 0.33 (λ2 = 0.58 μm). Measure the temperature without blackness correction using a NiCr-Constantan thermocouple and a matching millimeter (0–800 °C),

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2 Temperature Detection

but without using a compensating wire and compensator in the measurement, and the mechanical zero of the millimeter is at 0 °C on the scale. Ask. (1) What is the actual object temperature when the millivolt meter indicates at 200 °C and the cold-end temperature is 25 °C? (2) If the temperature of the object has not changed, but the temperature at the cold end is 50 °C, what is the indicated value of the millivolt meter at this time? (3) The millivoltmeter remains unchanged, but the thermocouple is misused as a nickel–chromium–nickel–silicon. When the temperature at the cold end is 25 °C and the millivolt meter indicates at 200 °C, ask what the object temperature is. 2.15 When measuring the surface temperature of oxidized carbon steel with a monochromatic optical pyrometer, the meter indicates a temperature of 920 °C. Ask what the true temperature of the surface of the carbon steel is. If the error in the monochromatic radiance blackness ε of the carbon steel is ± 5%, find the resulting measurement error (assuming that the monochromatic light is red and λ = 0.65 μm). 2.16 When measuring the surface temperature of a polished steel plate with a fullradiance pyrometer, try to calculate the true temperature of the surface of the plate when the meter indicates a temperature of 1000 K and 2000 K, respectively. When there is a 10% error in the estimate of the full radiation blackness coefficient ε, ask what is the resulting measurement error. 2.17 It is known that the wavelengths of light used in the colorimetric pyrometer are λ1 = 0.8 μ m and λ2 = 1 μ m. The ratio of the blackness coefficients of the object under test at the corresponding wavelengths is ελ1 /ελ2 = 1.1 ± 5%. Try to calculate the true temperature of the measured object at 1000 K and 2000 K, respectively, and calculate the error in temperature measurement due to the error in the ratio ελ1 /ελ/ . 2.18 How are temperature detection instruments used in nuclear power plants?

Chapter 3

Pressure Testing

3.1 Overview Pressure is one of the most important thermodynamic parameters. Pressure is the force acting vertically on a unit area, i.e., the physical pressure. In nuclear power plants, pressure must be monitored and controlled for the safe and economic operation of the various equipment in the nuclear and conventional islands. The pressure distribution in specific areas is also necessary for a detailed understanding of the operation of the equipment and an in-depth study of its internal processes. Objects are subjected to pressure in different ways due to atmospheric pressure on the earth’s surface. There are different ways of expressing pressure in different situations, such as absolute pressure, gauge pressure, negative pressure or vacuum, and differential pressure. Due to the different reference points, there are three ways to express pressure in engineering: absolute pressure pa , gauge pressure p, and negative pressure or vacuum pv . Absolute pressure pa is the full pressure of the measured medium acting on an object’s surface, with a complete vacuum as the zero standard. The instrument used to measure absolute pressure is called an absolute pressure gauge. Gauge pressure p is the pressure measured with a standard pressure gauge, which uses the local atmospheric pressure as a zero standard and is equal to the difference between the absolute pressure pa and the local atmospheric pressure p0 , i.e., p = pa − p0 ,

(3.1)

where atmospheric pressure p0 is the pressure formed by the column of air at the surface of the Earth, which varies with geographical latitude, altitude, and meteorological conditions. It can be measured with a special atmospheric pressure gauge (referred to as a barometer), whose value is also obtained using the absolute pressure zero level as a reference and is therefore also an absolute pressure.

© Harbin Engineering University Press 2023 H. Xia and Y. Liu, Measurement Science and Technology in Nuclear Engineering, Nuclear Science and Technology, https://doi.org/10.1007/978-981-99-1280-3_3

107

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3 Pressure Testing

Vacuum degree pv is the degree of approaching vacuum. When the absolute pressure is less than the atmospheric pressure, the gauge pressure is negative and its absolute value is called the vacuum degree and the expression is pv = p0 − pa .

(3.2)

Differential pressure Δp is a pressure expressed as the difference between two pressures, a pressure with any pressure other than atmospheric pressure as the zero standard, i.e., Δp = p1 − p2 .

(3.3)

Differential pressure is widely used to measure various thermal and mechanical quantities. Differential pressure measurements are made using a differential pressure gauge. The high-pressure side of the differential pressure gauge is positive pressure, while the low-pressure side is negative pressure. The negative pressure is relative to the positive pressure and may not necessarily be lower than the local atmospheric pressure. The negative pressure is different in the vacuum. The interrelationships of absolute pressure pa , pb , gauge pressure p, vacuum or negative pressure pv , atmospheric pressure p0 , and pressure differential Δp are shown in Fig. 3.1. In the International System of Units (SI) and the legal unit of measurement, the unit of pressure is “pascals”, abbreviated as “Pa”, and the symbol is “Pa”. 1 Pa = 1 N/m2 That is, the force of 1 N (Newtons) acting vertically and uniformly on the area of 1 m2 creates a pressure value of 1 Pa. ( ) The previously used units of pressure “engineering atmosphere kgf/cm2 ”, “millimeter of mercury (mmHg),” “millimeter of water column (mmH2 O)”, “Physical atmospheric pressure (atm)” have been replaced by the legal unit of measure Pa, or megapascals (MPa)

Fig. 3.1 Relationship between various pressures

3.2 Liquid Column Manometers

109

1 MPa = 106 Pa The conversion relationship between the various pressure units and “Pa” is given in Table 3.1. Depending on the characteristics of sensitive elements and pressure measuring principles, pressure measuring instruments are generally divided into the following four categories: (1) Liquid column manometer: It is based on the principle of balance between gravity and the measured pressure. It can convert the measured pressure into the height difference of the liquid column for measurement, such as the U-tube manometer, single-tube manometer, and inclined-tube manometer. (2) Elastic manometer: It is based on the principle of elastic force and the measured pressure balance made. During the formation of elastic force, the elastic element feels the pressure to produce elastic deformation when the elastic force and the measured pressure balance. The amount of deformation of the elastic element reflects the size of the measured pressure. This principle of work has been widely used in the various elastic manometers in the industry. It includes instruments such as the spring tube manometer, bellows manometer, membrane box-type manometer, etc. (3) Electrical manometer: It uses the physical properties of some substances related to the pressure to measure pressure. After some substances are pressurized, some of their physical properties will change, and the pressure can be measured by measuring this change. According to this principle, various pressure sensors are manufactured, which often have the advantages of high accuracy, small size, and good dynamic characteristics, and have become a major development direction of pressure measurement in recent years. The commonly used pressure sensors are resistive strain gauge type, capacitive type, piezoelectric type, inductive type, Hall type, etc. (4) Piston-type manometer: It is based on the principle of pressure transmission by the hydraulic fluid and converts the measured pressure into the mass of a balance weight added to the area of the piston. It is commonly used as a standard instrument for calibrating or scaling elastic-type manometers.

3.2 Liquid Column Manometers The liquid column pressure gauge is a manometer based on the principle of hydrostatics. It uses the pressure generated by the liquid column to balance with the measured pressure and determine the measured pressure’s size according to the liquid column’s height. The liquid used is called the sealing liquid, and the commonly used are water, alcohol, mercury, etc. A liquid column manometer is mainly used to measure low pressure, negative pressure, and pressure difference. The commonly used liquid injection manometers are U-tube manometers, single-tube manometers, and inclined-tube micropressure gauges. Their structural forms are shown in Fig. 3.2.

1

1 × 10–3

0.980665 × 10–4

1.01325

0.980665

1.333224 × 10–3

0.68949 × 10–1

1 × 105

1 × 102

0.980665 × 10

1.01325 × 105

0.950665 × 105

1.333224 × 102

0.68949 × 104

bar

mbar

mmH2 O

atm

at

mmHg

1bf/in2

1

1.35951 × 10

104 1.316 × 10–3

0.9678

1

0.9678 × 10–4

0.08949 × 102 0.70307 × 103 0.6805 × 10–1

1.333224

0.950665 × 103

0.9869236

0.9869236 × 10–5

atm

1.019716 × 10 0.9869236 × 10–3

1.019716 × 104

1.019716 × 10–1

mmH2 O

1.01325 × 103 1.033227 × 104

0.980665 × 10–1

1

103

1 × 10–2

1 × 10–5

1

Pa

mbar

bar

Pa

Unit

Table 3.1 Pressure unit conversion table

0.707 × 10–1

1.35951 × 10–3

1

1.0332

1 × 10–4

1.019716 × 10–3

1.019716

1.019716 × 10–5

at

0.51715 × 102

1

0.73557 × 103

0.76 × 103

0.73556 × 10–10

0.35006

0.75006 × 103

0.75006 × 10–2

mmHg

1

1.934 × 10–2

1.422398 × 10

1.4696 × 10

1.422 × 10–3

1.450442 × 10–2

1.450442 × 10

1.450442 × 10–4

1bf/in2

110 3 Pressure Testing

3.2 Liquid Column Manometers

(a) P1

111

(b)

(c)

P2 P2

P1 F2

l 0

α

h1

0 F1

h1

h

h2

P1

h2

H

P2

Fig. 3.2 Liquid column manometer. a U-tube manometer, b single-tube manometer, c inclined-tube micropressure gauge

(a) U-tube manometers The U-tube manometer is shown in Fig. 3.2a, and the pressures p1 and p2 are connected at both ends of the U-tube manometer. There is the following relationship between p1 and p2 and the seal liquid column height h: p1 − p2 = gh(ρ − ρ1 ) + g H (ρ2 − ρ1 ),

(3.4)

where ρ1 , ρ2 , ρ are the media and sealing fluid densities on the left and right sides, respectively. H is the height of the right-hand medium. g for gravitational acceleration. When ρ1 ≈ ρ2 Eq. (3.4) can be simplified to p1 − p2 = gh(ρ − ρ1 ).

(3.5)

If ρ1 ≈ ρ2 , and ρ >> ρ1 , then we have p1 − p2 = ghρ.

(3.6)

From Eq. (3.6), it can be seen that when the density of the sealing liquid inside the U-tube is certain and known, the difference in the height of the liquid column h reflects the magnitude of the pressure. This is the basic working principle of the liquid column manometer to measure pressure. Depending on the size and requirements of the pressure to be measured, the sealing fluid can be water or mercury. To avoid capillary action in fine glass tubes, the sealing fluid can sometimes be alcohol or benzene. U-tube manometers can measure pressure up to 0.2 MPa.

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3 Pressure Testing

(b) Single-tube manometer The single-tube manometer is shown in Fig. 3.2b. The pressure difference between its two sides is given by Δp = p1 − p2 = g(ρ − ρ1 )(1 + F2 /F1 )h 2 ,

(3.7)

where F1 , F2 are the cross-sectional areas of the vessel and the single tube, respectively, h 2 is the seal liquid column height. If F1 >> F2 and ρ >> ρ1 , then p1 − p2 = gρh 2 .

(3.8)

The Bates micropressure gauge shown in Fig. 3.3 utilizes the principle of a single-tube manometer. A riser tube is inserted in the middle of the large vessel, and the measured pressure is connected to the vessel’s hose. If differential pressure is measured, the low-pressure end is connected to the pressure fitting at the upper end of the riser tube. When the pressure of the vessel is higher than the ambient atmospheric pressure, the liquid level in the riser tube rises and so does the float in the riser tube. A glass scale plate hangs from the lower end of the float. A projector displays a section of the scale after it has been magnified approximately 20 times on a woolen glass having a vernier. The difference between the two adjacent scales is 1 mm, and the pressure at 1 Pa can be read accurately using the vernier scale. (c) Inclined-tube manometer Figure 3.2c shows the inclined-tube manometer. The relationship between the pressures on both sides of the inclined-tube micropressure Gauge p1 , p2 and the length of the liquid column l can be expressed as p1 − p2 = gρl sin α,

(3.9)

where α is the angle of inclination of the inclined pipe, l is the length of the liquid column. From Eq. (3.9), it can be seen that the scale of the inclined-tube manometer is magnified 1/ sin α times than that of the U-tube manometer. If alcohol is used as the sealing fluid, it is easier to measure micropressures. Generally, this slant tube manometer is suitable for measuring pressures in the range of (2–2000) Pa. (d) Measurement error of liquid column manometer and its correction Several factors affect the measurement accuracy of liquid column manometers. For a specific measurement problem, some influences can be ignored and some must be corrected.

3.2 Liquid Column Manometers

113

Fig. 3.3 Bates micropressometer, 1—gross glass sheet; 2—eyepiece; 3—wide sectional container. 4—float; 5,8—pressure fitting; 6—lift tube. 7—hose; 9—glass scale; 10—measuring fluid; 11—projection device; 12—bulb

5

6 7 4 3 2

8 9 10 11 12

1

(i) Effects of changes in ambient temperature The seal liquid density and scale length will change when the ambient temperature deviates from the specified temperature. Since the coefficient of bulk expansion of the seal liquid is 1–2 orders of magnitude larger than the linear expansion coefficient of the scale, for general industrial measurements, the influence of the seal liquid density change on the pressure measurement caused by the temperature change is mainly considered. At the same time, the influence of the scale length change also needs to be corrected for precision measurements. The correction formula for the effect of a change in seal fluid density on the manometer reading after a 20 °C deviation from the specified ambient temperature is h 20 = h[1 − β(t − 20)], where h 20 is the height of the column of sealing liquid at 20 °C, h is the column height of the sealing liquid at t °C, β is the bulk expansion coefficient of the sealing fluid, t is the actual temperature at the time of measurement.

(3.10)

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3 Pressure Testing

(ii) Correction for changes in gravitational acceleration The acceleration of gravity at the location where the instrument is used gφ is calculated from the following equation: gφ =

g N [1 − 0.00265 cos(2φ)] , (1 + 2H/R)

(3.11)

where H is the altitude of the place of use, (m). φ is the latitude and altitude of the location used, (◦ ). g N is 9.80665 m/s2 , the standard acceleration of gravity. R is 6356766 m, the nominal radius of the Earth (at 45° latitude at sea level). The column height: h N of the sealing fluid at the standard location is given by: h N = h φ gφ /g N ,

(3.12)

where h φ is the height of the liquid column of the sealing fluid at the measurement location. (iii) Errors due to capillary phenomena The capillary phenomenon causes the surface of the sealing fluid to form a curved lunar surface, which can cause not only reading errors but also a rise or fall in the liquid column. This error is related to the surface tension of the sealing liquid, the tube diameter, the cleanliness of the inner wall of the tube and other factors, which is difficult to obtain accurately. In practical application, the effect of the capillary phenomenon is often reduced by increasing the tube diameter. The sealing fluid is alcohol, the inner diameter of the tube d ≥ 3 mm; water, mercury as sealing fluid, d ≥ 8 mm. There are also scale, reading, and installation errors in liquid column manometers. When reading, the eye should be level with the highest or lowest point of the sealing liquid bending moon surface, and read along the tangent direction. U-tube manometers and single-tube manometers require vertical installation; otherwise, it will bring large errors.

3.3 Flexible Manometers Elastic manometers are based on the elastic deformation of various forms of elastic elements under pressure as the basis for measurement. The commonly used elastic elements are spring tubes, diaphragms, and bellows. There are spring tube manometers, membrane manometers, and bellows-type differential pressure gauges. The displacement produced by the deformation of the elastic element is small. It often

3.3 Flexible Manometers

115

needs to be transformed into an angular displacement of the pointer or an electrical or pneumatic signal in order to display the magnitude of the pressure. (a) Spring Tube Manometer The spring tube is the main pressure measuring element of the spring tube manometer. The cross-section of the spring tube is an oval or flat circle. It is a hollow metal tube, one end of which is closed for the free end. The other end is fixed on the shell of the instrument and connected to the pipe joint with the measured medium, as shown in Figs. 3.4 and 3.5. When the medium with pressure enters the tube’s inner cavity, the spring tube’s cross-section is oval or flat. So it will deform under pressure. The internal surface area in the direction of the short axis is larger than that in the long axis, and thus, the force is also large. When the pressure inside the tube is larger than outside pressure, the short axis should become longer and the long axis should become shorter. The tube cross-section tends to be more circular, producing elastic deformation. The spring tube bent into a circular shape is stretched outward and displaced at the free end. This displacement by the rod system and gear mechanism drives the pointer. When the deformation caused by the elastic force and the measured pressure generated by the force balance, the deformation stops. The pointer indicates the corresponding pressure value. The displacement of the free end of this single-turn spring tube manometer cannot be too large, generally not more than 2–5 mm. In order to improve the sensitivity of the spring tube and increase the displacement of the free end, a coiled spring tube or a spiral spring tube can be used as shown in Fig. 3.6. The measurement of the single-turn spring manometer is 1–4 ordinary, precision is 0.1–0.5. The measurement ranges from vacuum to 109 Pa. In order to ensure the correct indication of the spring tube pressure gauge and long-term use, should make the instrument work in the normal allowable pressure range. For fluctuating pressure, the instrument’s indicated value should often be in the range of ½. Of

1 7

4

30

40

6

20

5 3

10

Fig. 3.4 Single-turn spring tube manometer, 1—spring tube; 2—tie rod; 3—sector gear; 4—center gear; 5—pointer 6—dial; 7—swivel; 8—adjustment screw; 9—connector

2 8

9

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3 Pressure Testing

Fig. 3.5 Construction of a single-turn spring tube

r

Δα

α

B'

2b

2a

B

R

o

Fig. 3.6 Spring tube and its cross-section

which, measured pressure fluctuation hours, the instrument indicated value can be in the range of about 2/3, but the measured pressure value should generally not be lower than the range of 1/3. In addition, attention should be paid to the instrument’s vibration, explosion-proof, anti-corrosion, and other issues, and should be regularly calibrated. In production, it is often desirable to keep the pressure within a certain range for process needs or equipment safety. When the pressure is higher or lower than the specified range, a light or sound signal can be issued to remind the operator to pay attention to. Therefore, the electric contact pressure gauge can be used, and its measurement working principle and the general spring tube pressure gauge is exactly the same. But it has a set of transmitting mechanism. In the lower part of its pointer

3.3 Flexible Manometers

117

there are two pointers, one gives high pressure and the other a low pressure. Special keys in the middle of the dial are used to rotate the pin to give the pointer control over the pressure of the upper and lower limit value. With an electrical contact on each of the high and low pressure giving value pointers and the indicating pointer, the construction and circuit of an electrical contact manometer is shown in Fig. 3.7. When the indicator pointer is located between the high- and low-pressure giving pointers, the three electrical contacts are disconnected from each other and no signal is sent. When the indicator pointer is located in the position of the low-pressure given value pointer, the low-pressure contact is on, and the low-pressure indicator lights up indicating that the pressure is too low. When the pressure reaches the upper limit, that is, the indicator pointer is located in the position of the high-pressure given pointer, the high-pressure contact is on and the highpressure indicator light is on, indicating that the pressure is too high. Electric contact pressure gauge in addition to high and low-pressure alarm can also be connected to other relays and other automatic equipment, where it plays a role in the chain and automatic manipulation. But this instrument can only indicate the pressure of the high and low, cannot be remote pressure indication. Contact control part of the power supply voltage, AC shall not exceed 380 V; DC does not exceed 220 V. The contact maximum capacity of 10 VA with the maximum current of 1 A cannot exceed the above electrical power, so as not to burn off the contact. The accuracy of the electric contact manometer is generally 1.5–2.5 grade.

Fig. 3.7 Electric contact manometer, 1—low voltage feed pointer and contact; 2—pointer and contact; 3—green light; 4—high-voltage feed pointer and contact; 5—red light

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3 Pressure Testing

(a)

(b)

(c)

Fig. 3.8 Diaphragm and cartridge. a Elastic diaphragm, b flexible diaphragm, and c diaphragm box

(b) Membrane manometers Membrane manometers are divided into two types: diaphragm and membrane cartridge manometers. The former is mainly used to measure the pressure of corrosive media (non-curing) and non-crystalline viscous media. The latter is often used to measure the micropressure or negative pressure of gases. Their sensitive elements are the diaphragm and the diaphragm cartridge, respectively, and the shapes of the diaphragm and the cartridge are shown in Fig. 3.8. (i) Diaphragm manometers The diaphragm of a diaphragm manometer can be divided into two types, namely flexible and elastic diaphragms. The diaphragm is round and generally made of metal. The commonly used elastic corrugated diaphragm is a thin circular sheet pressed with ring-shaped concentric corrugations, which is fixed around it. Through the pressure, the diaphragm will be bent to the side of the low pressure, the center of a certain displacement (i.e., deflection), through the transmission mechanism to drive the pointer rotation indicating the measured pressure. The relationship between the deflection and pressure is mainly determined by the shape, number, depth and thickness and diameter of the diaphragm, while the corrugation of the edge part basically determines the characteristics of the diaphragm. The influence of the central corrugation is very small. The flexible diaphragm only plays the role of isolation of the measured medium. It is almost no elasticity itself, which is fixed in the diaphragm of the spring to balance the measured pressure. Diaphragm manometers are suitable for pressure measurement in vacuum (0 to 6 × 106 ) Pa. (ii) Membrane cartridge manometers To increase the displacement of the diaphragm and to improve sensitivity, two metal diaphragms can be welded together at the perimeter to form a diaphragm cassette. Multiple diaphragms can also be connected in series to form a diaphragm cassette group. Figure 3.9 shows a schematic diagram of the structure of a membrane cassette manometer. Its drive mechanism and display device in principle and the spring tube manometer is basically the same. Membrane box manometer is suitable for (0 ~± 4 × 104 ) Pa pressure measurement. (c) Three, bellows-type differential pressure gauge Bellows is a thin-walled tube with deep grooved corrugated folds along the outer circumference in the axial direction, which can be expanded and contracted in the

3.3 Flexible Manometers

119

Fig. 3.9 Diagram of membrane box manometer structure, 1—zeroing screw; 2—seat; 3—scale plate; 4—membrane box; 5—pointer; 6—zeroing plate; 7—limit screw. 8—curved linkage; 9— bimetal; 10—shaft; 11—lever holder; 12—linkage. 13—pointer shaft; 14—lever; 15—swivel; 16— tube fitting; 17—pressure guide tube

axial direction and its shape is shown in Fig. 3.10. It has a larger linear output range when under pressure than when under tension, so it is often used in compression. In order to improve the performance of the instrument, improve the measurement accuracy and facilitate the change of the instrument range. The bellows is often used in combination with a spring whose stiffness is several times greater than it in practice when the performance is mainly determined by the spring. Bellows-type differential pressure meter with bellows as the pressure-sensitive element to measure the differential pressure signal, they are single bellows and double bellows mainly used for flow and level measurement of the display instrument. The following is a double bellows differential pressure meter as an example to explain the working principle of this type of differential pressure meter. Figure 3.11 shows a schematic diagram of the construction of a double bellows differential pressure gauge. The connecting shaft 1 is fixed to a rigid end cap on the end faces of the bellows, B1 B2 B1 B2 are rigidly attached to each other. B1 , B2 Fig. 3.10 Bellows

120

3 Pressure Testing

through a damping ring 11 with an annular gap between the central base 8, and a damping bypass 10 on the central base. The range spring set 7 is in the low-pressure chamber, which is fixed at each end to the connecting shaft and the central base. Upon connection to the differential pressure being measured, B1 is compressed and the filling fluid therein then flows through the annular gap and damping bypass to B2 , causing B2 to elongate and the range spring 7 to be stretched until the force created by the differential pressure on both ends of B1 and B2 is balanced by the elastic force generated by the range spring and bellows. At this point, there is a displacement of the connecting shaft system to the low-pressure side and the baffle 3 pushes the pendulum 4, driving the torsion tube 5 to turn, causing the mandrel 6, which is fixed to the torsion tube at one end, to twist, and this angle of rotation reflects the magnitude of the differential pressure being measured. The bellows B3 has a small hole connected to B1 , when the temperature change causes the volume of the filling liquid in B1 and B2 to change, the volume of B1 and B2 remains basically unchanged, and the excess or deficient part of the filling liquid flows into or out of B3 through the small hole to play the role of temperature compensation. Damping valve 9 serves to control the flow resistance of the filling fluid in damping bypass 10 to prevent system oscillations caused by excessive instrument delay or frequent differential pressure changes. One-way protection valve 2 protects the instrument from damage in the event of excessive differential pressure or one-way pressure.

(a)

(b)

Fig. 3.11 Double bellows differential pressure gauge structure diagram. a Internal structure, b torsion tube structure, 1—connecting shaft; 2—one-way pressure protected valve; 3—push plate; 4—pendulum; 5—torque tube; 6—mandrel; 7—range spring; 8—central base. 9—damping valve; 10—damping bypass; 11—damping ring; 12—filling fluid; 13—needle roller bearing; 14—agate bearing; 15—spacer; 16—balancing valve

3.4 Electrical Manometers

121

(d) Errors in flexible manometers and ways to improve them The following are the main sources of error in the flexible manometer: 1. Hysteresis error under the same pressure: The deformation of the same elastic element forwards and backwards stroke is not the same, resulting in hysteresis error. 2. After-effect error: The deformation of the elastic element lags behind the change in the measured pressure, causing elastic after-effect error. 3. Gap error: There is a gap between the various moving parts of the instrument, and the deformation of the indicated value and the elastic element may not correspond exactly, causing a gap error. 4. Frictional error: The moving parts of the instrument move with frictional force between them, resulting in frictional error. 5. Temperature error: The change in ambient temperature causes a change in the modulus of elasticity of the metal material, resulting in temperature error. The main ways to improve the accuracy of the elastic manometer are 1. The use of no hysteresis error or hysteresis error is very small “fully elastic” materials, and temperature error is very small “constant elastic” material manufacturing elastic components, such as alloy Ni42CrTi, Ni36CrTiA, these are the more widely used constant elastic materials These are the more widely used constant elastic materials, and fused silica is the more ideal fully elastic material and constant elastic material. 2. Adopt new conversion technology to reduce or eliminate intermediate drive mechanism to reduce clearance error and friction error, such as resistance strain conversion technology. 3. Limiting the displacement of the elastic element, using elastic support without dry friction or magnetic suspension support, etc. 4. Adopt suitable manufacturing process so that the excellent performance of the material can be fully utilized.

3.4 Electrical Manometers Elastomeric manometers are widely used in industrial production because of their simple structure, ease of use and maintenance, and wide range of pressure measurement. However, in the measurement of rapid changes, pulsating pressure and high vacuum, ultra-high pressure, and other occasions, its dynamic and static performance cannot meet the requirements, and most of the electrical manometers are used. Electrical manometers usually convert changes in pressure into changes in electricity such as resistance, inductance or potential to form various pressure sensors. Since it outputs electrical power, it is easy to signal remote transmission, especially to connect with computer to form automatic data acquisition system. So it has been widely used and has greatly advanced the development of test technology.

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3 Pressure Testing

There are many types of electrical manometers and different ways of classification. From the pressure into electricity path, can be divided into resistive, capacitive, inductive; and electromagnetic effect, piezoresistive effect, piezoelectric effect, photoelectric effect and so on. From the pressure on the power control can be divided into active and passive categories. Active is the pressure directly through a variety of physical effects into the output of electricity, while the passive type must be input from the outside and this electrical energy is measured by the pressure in some way to control. This section will describe in some detail several of the more widely used electrical-type manometers.

3.4.1 Resistance Strain Gauge Pressure Sensor The measured pressure acts on the elastic sensitive element to deform it, and a resistance strain gauge is attached to the deformed part, and the resistance strain gauge feels the change of the measured pressure. (i) Strain effect of resistance If the length of the resistance wire is l, the cross-sectional area is A, the resistivity is ρ, and the resistance value is R, then we have R=ρ

l . A

(3.13)

Let the change in each parameter of the resistive wire under the action of an external force be dl, d A, dρ, d R, differentiating Eq. (3.13) and dividing by R, we obtain the relative change in resistance as dR dρ dl dA = + − . R ρ l A

(3.14)

From the knowledge of material mechanics, dl/l = ε is called axial strain, or strain for short; d A/A is called transverse strain, and the relationship between the two is dA = −2με, A

(3.15)

where μ is the Poisson’s coefficient of the material. With the introduction of the above notation, Eq. (3.14) can be rewritten as [ ] dρ/ρ dR = (1 + 2μ) + ε = K 0 ε, R ε

(3.16)

3.4 Electrical Manometers

123

where K 0 is called the sensitivity coefficient of a single resistive wire and has the meaning of the relative change in resistance due to a unit strain K 0 . It is obtained experimentally, and within the elastic limit, K 0 is constant for most metals. Generally, K 0 is 2–6 for metallic materials, and K 0 values can be as high as 180 for semiconductor materials. When a metal wire is made into a resistive strain gauge, the sensitivity coefficient of the resistive strain gauge K will be different from that of a single wire K 0 and will need to be determined again experimentally. Experimentally, it has been shown that the relative change in strain gauge resistance versus strain remains linear over a wide range, i.e., dR = K ε. R

(3.17)

From Eq. (3.17), it can be seen that in the case where K is a constant, the relative change in the strain gauge resistance can be directly known by measuring the strain, and thus, the measured pressure can be found. The strain gauge consists of three parts: the strain-sensitive element, the substrate and overlay, and the lead wire. Its typical structure is shown in Fig. 3.12. The strainsensitive element is the core part of the strain gauge, generally consisting of metal wire, metal foil or semiconductor material, which converts the mechanical strain into a change in electrical resistance, while the substrate and overlay serve to fix and protect the strain-sensitive element, transfer the strain, and electrically insulate it. (ii) Structure of resistance strain gauge-type pressure sensor The resistance strain gauge-type pressure sensor generally consists of strain gauges, strain barrels, external leads and other parts. The three main structural forms are diaphragm type, cartridge type, and combination type, and their principle structures are shown in Fig. 3.13a, b, and c. We will use the cartridge type as an example to illustrate the composition of a resistive strain gauge pressure sensor. The elastic sensitive element of the sensor is a thin-walled cylinder, which is also the core part of the sensor. The strain barrel

Fig. 3.12 Resistance strain gauges. a Filament wound, b foil, and c semiconductor

124

3 Pressure Testing

Fig. 3.13 Resistance strain gauge pressure sensor. a Diaphragm type, b cartridge type, c combination type, 1—elastic element; 2—connecting rod (push or pull rod); 3—cantilever beam; R1 , R2 , R3 , R4 —strain gauges

is generally made of alloy steel and deforms under pressure. The transverse strain gauges R1 and the longitudinal strain gauges R2 attached to the outer wall simultaneously produce positive strain ε1 and negative strain ε2 as shown in Fig. 3.14, i.e., the resistive strain gauges R1 are stretched and R2 are compressed, connecting into a bridge circuit as shown in Fig. 3.15. This circuit not only increases the output of the instrument, but also allows for self-temperature compensation, and this output is connected to the bridge box of the strain gauge via cable leads. (iii) Temperature compensation and bridge circuit output As already mentioned, the resistive strain gauge-type pressure sensor is based on the principle that pressure generates strain and strain causes a change in resistance value to measure pressure. However, the resistance of the strain gauges is greatly affected by temperature, and their resistance value will change with temperature; on the other hand, the coefficient of linear expansion of the elastic element and the strain gauges are hardly the same, but they are pasted together, and additional strain will be generated when the temperature changes. Therefore, resistive strain gauge pressure sensors are subject to various temperature compensation measures, usually by means of bridge compensation. There are two types of bridges, half bridge and full bridge. πd1

Fig. 3.14 Strain relief cylinder expansion

R1

R2

3.4 Electrical Manometers

125

Fig. 3.15 Bridge circuit

One reason for using the bridge method is to provide temperature compensation, and the other is to increase the output amplitude of the signal. 1. Half-bridge circuits The half-bridge circuit is shown in Fig. 3.15. The working strain gauge R1 and the compensating strain gauge R2 are mounted on two adjacent bridge arms, resulting in ΔR1t and ΔR2t being identical, and the output voltage is independent of temperature variation as shown by the bridge theory. The bridge will produce a corresponding output voltage when the strain is felt. 2. Full-bridge circuit The full-bridge circuit is shown in Fig. 3.16. The so-called full bridge means that the four bridge arm resistors R1 , R2 , R3 , R4 are all working pieces, and when subjected to pressure, their corresponding resistance increments are ΔR1 , ΔR2 , ΔR3 , ΔR4 , respectively, and the output voltage ΔU is ΔU = U A − U B Fig. 3.16 Full-bridge circuit

A R1

R4

R2

R3

-ε

C

D -ε

B U

+ε

ΔU

+ε

126

3 Pressure Testing

=

R1 + ΔR1 R2 + ΔR2 U− U. R1 + ΔR1 + R4 + ΔR4 R2 + ΔR2 + R3 + ΔR3

(3.18)

By dividing Eq. (3.18) through and omitting the quadratic trace of ΔRi from the numerator denominator, it simplifies to U (ΔR1 − ΔR2 + ΔR3 − ΔR4 ) ). ΔU = ( 2 3 4 1 + ΔR + ΔR + ΔR 4 R + ΔR 2 2 2 2 Since

ΔRi 2

(3.19)

0.65, 0.01 D ≤ α ≤ 0.02 D For any value of β, the annular gap width α should be between 1 and 10 mm. The thickness of the annular gap f ≥ 2α; the annular cavity cross-sectional area hc ≥ 1/ 2π Dα; if the annular gap consists of intermittent n rectangular holes of area f' , hc ≥ 1/2nf'.

164

4 Flow Testing

The connecting hole between the ring cavity and the pressure guide tube should be of equal diameter cylindrical shape and its length should be greater than or equal to 2Φ. Φ is the diameter of the connecting hole and its value is 4–10 mm. The individually drilled pressure extraction port can be drilled in the flange or in the clamping ring between the flanges. The size of the borehole diameter b-value is specified in the same range as the ring chamber to take the pressure ring gap width a, but for gases and liquids that may precipitate water vapor, the b-value is in the range of 4–10 mm. If the pressure hole is located at the exit edge of the inner wall of the clamping ring, it must be flush with the inner wall of the clamping ring and should have a chamfer no larger than one tenth of the diameter of the pressure hole, with no visible burrs or protrusions. The extraction hole should be cylindrical, with a length of at least 2b from the inner wall of the clamping ring, of equal diameter and its axis should be perpendicular to the axis of the pipe as far as possible. The thickness of the gasket should be such that the a- or b-value does not exceed the specified value. (b) Flanged pressure take-off device. The flange pressure-taking device is a flange with a pressure-taking hole, the structure of which is shown in Fig. 4.4. Upstream and downstream pressure-taking holes must be perpendicular to the axis of the pipe. These holes must be of equal diameter denoted by b, whose value should not exceed 0.08D and the actual size should be 6–12 mm. Can be in the upstream and downstream side of the orifice plate specified location at the same time with several flange pressuretaking hole, but in the same side of the pressure-taking hole should be configured according to the equal angle distance. The standard orifice plate for flange pressure extraction is available for pipe diameters D from 50 to 750 mm, diameter ratios β from 0.1 to 0.75, and Reynolds numbers ReD from 8 × 103 to 1 × 107 . Fig. 4.4 Flange pressure extraction device

25.4±1

25.4±1 0.6, l y2 can range from 0.49D to 0.51D. 2. Standard nozzle: This only uses the Angle connection pressure extraction method. It applies to the pipe whose diameter D ranges from 50 to 1000 mm, with a diameter ratio β of 0.32 to 0.8 and a Reynolds number of 2 × 104 to 2 × 106 (see Appendix Table A.14 for details). The structure of a standard nozzle is shown in Fig. 4.5. Its profile consists of the inlet end surface A, the contraction of the first arc surface C 1 and the second arc surface C 2 , cylindrical throat e and exit edge protection groove H. The diameter of the cylindrical throat is the opening diameter of the throttle member, which is 0.3d. The opening diameter d shall be the arithmetic mean of not less than eight single measurements, four of which are at the beginning of the cylindrical throat and four of which are at the end of the cylindrical throat, and each measured at an angle of approximately 45° apart. The deviation between any single measurement and the average value of d shall not exceed ±0.05%. The segments should be tangent to each other and should not have any unsmooth sections. E 2/3, the diameter of the inlet end of the nozzle shrinkage (1.5d) should be greater than the inner diameter of the pipe D (see Fig. 4.5b), so the inlet end must be cut off—part of its diameter and the inner diameter of the pipe D equal, cut off the length ΔL for [ ΔL = 0.2 −

(

0.75 0.25 − 2 − 0.5225 β β

) 21 [ d

(4.1)

The main dimensional requirements of the nozzle are as follows: nozzle thickness E ≤ 0.1D; when β ≤ 0.5, the radius of surface C1 r 1 = 0.2d ± 0.02d; when β > 0.5, r1 = 0.2d ± 0.006d; the radius of surface C2 when β < 0.5, r 2 = 1/3d ± 0.03d, when β ≥ 0.5, r 2 = 1/3d ± 0.01d. The nozzle should comply with the ISO-5167 standard issued by the International Organization for Standardization, but also the long diameter nozzle as the standard nozzle. Long diameter nozzle and ISAl932 nozzle is different is that the inlet constriction part of the shape of 1/4 oval arc section, the throat that is a cylinder. It is suitable for D is 50–630 mm; β is 0.2–0.8; ReD is 2 × l04 to 107 ; pipe relative roughness k/D ≤ 10 × 10–4 . Its upstream and downstream pressure pickup distance from the nozzle inlet end face is 1D and 1/2D. 3. Venturi tube: This is composed of three parts; shrinkage section, cylindrical throat C, and conical diffuser tube. According to the shape of the constriction section, it is divided into classical venturi and venturi nozzle. (1) Classical venturi venture: This is composed of an inlet cylinder section A, a conical shrink section B, a conical throat section C, and a conical diffusion section E. Depending on the method of processing the inner surface of the conical shrink section, the profile of the intersection of the conical shrink section, and the throat cylinder, they can be divided into rough shrink section type, machined shrink section type, and rough welded iron plate shrink section type. The geometric profile of the classical venturi is shown in Fig. 4.6. The classical venturi of the rough welded iron plate shrinkage section type is illustrated as an example. Each connected line section of the inlet cylinder section A, shrink section B, and cylindrical throat should have no connecting surfaces, and the inner surface should be clean, free of hard skin, and may be plated. The internal surface welds should be flush with the surrounding surfaces and should not be near any pressure take-offs. Venturi tube applicable conditions are: when 200 mm ≤ D ≤ 1200 mm, 0.4 ≤ β ≤ 0.7, 2 × 105 ≤ ReD ≤ 2 × 106 , the outflow coefficient C = 0.985. Its expansion correction factor ε is the same as the standard nozzle. (2) Venturi nozzle: The venturi nozzle profile is shown in Fig. 4.7. It is composed of a curved shrinkage section, a cylindrical throat, and a diffusion section. The shrinkage section is the same as the ISAl932 nozzle, and the throat is composed of a section E of length 0.3d and a section E' of length 0.4d–0.45d. The angle ψ of the diffusion section should be less than or equal to 30°. When the diffusion section outlet diameter is less than the diameter D is called truncated venturi.

4.1 Differential Pressure Flowmeter

167

Fig. 4.6 Geometric profile of the venturi

Conical diffusion section E R3

R1 Inlet cylinder section A

d

Connection plane

R2 21°±1°

0.5D

Conical contraction section B

φd (0.5+0.02)d

Cylindrical throat C

Flow direction

7°~15°

φD

Fig. 4.7 Venturi nozzle

Leigh tube: if the outlet diameter of the diffusion section is equal to diameter D , it is called a non-truncated venturi. The length of the diffusion section does not affect the flow coefficient, but the angle of the diffusion section has an effect on the pressure loss. Venturi nozzle conditions apply: when 65 mm ≤ D ≤ 500 mm, d ≥ 50 mm, 0.316 ≤ β ≤ 0.775, 1.5 × 105 ≤ Re D ≤ 2 × 106 , the outflow coefficient

168

4 Flow Testing

c = 0.9858−0.196β 4.5 . The expansion correction factor ε is the same as for standard nozzles. (ii) Fluid conditions and piping conditions The relationship between flow rate and differential pressure through a throttling device is obtained experimentally under specific fluid, fluid flow conditions, and under conditions where a typical turbulent flow velocity distribution has developed on the upstream side of the throttle at 1D and there are no vortices. If the fluid and its flow conditions change or if there are vortices close to the upstream side of the throttle, the relationship between them will change. Therefore, the fluid, flow conditions, piping conditions, and installation requirements applicable to the throttling device must be in accordance with the provisions of the standard. 1. Fluid conditions: The standard throttling device is only suitable for single-phase, homogeneous fluids or highly dispersed colloidal solutions in a circular tube. It requires that the fluid must fill the pipe, the fluid does not undergo a phase change when flowing through the throttle, the flow rate is less than the speed of sound, and the flow rate should be constant or change only slightly and slowly from time to time. Before the fluid flows through the throttle, its flow beam must be parallel to the axis of the pipe and there must be no vortex. 2. Piping conditions: The straight pipe section before and after the throttling device, the straight pipe section between the first and second local resistance members on the upstream side, and the differential pressure signal line are shown in Fig. 4.8. The pipe section before and after the throttling device shall be visually straight. The diameter of the measuring circular pipe used for the throttle shall be measured

Fig. 4.8 Schematic diagram of the complete throttling device, 1—second local resistance member on the upstream side of the throttle; 2—first local resistance member on the upstream side of the throttle; 3—throttle and pressure take-off device; 4—differential pressure signal line; 5—first local resistance member on the downstream side of the throttle; 6—measuring tube before and after the throttle. l 0 —the straight pipe section between the first and second partial resistance members on the upstream side; l 1 —the straight pipe section on the upstream side of the throttling member. l 2 —straight section of pipe on downstream side of throttle

4.1 Differential Pressure Flowmeter

169

physically within a length of 2D on the upstream and downstream sides of the throttle. The method is to take four single measurements of the inner diameter at 0D, 1/2D, 1D, and 2D on the upstream side, at approximately equal angular distances from the axis of the pipe, and the average of these 16 single measurements is the inner diameter of the pipe for calculation. The same should be done for the straight section on the downstream side, but the requirement is lower, and the deviation between any single measurement and the average value should not be greater than ±2%. The inner wall of the pipe should be clean and can be smooth or rough. In a 10D long pipe on the upstream side of the throttle, a pipe is considered smooth when the relative average roughness k/D value of the inner wall of the pipe is less than the limit value specified in Table 4.1 (referred to as a light pipe). The national standard is the flow coefficient of the smooth pipe (α 0 ) obtained experimentally under that condition. If the value of k/D is greater than the limit value specified in Table 4.1, it is called a rough tube. (1) Upstream and downstream side of the throttle straight pipe section length requirements upstream and downstream side of the throttle minimum straight pipe section length with the throttle upstream and downstream side of the form of resistance and throttle opening diameter ratio β value of the relationship, as shown in Table 4.2. If one of the actual straight section lengths is greater than the value in parentheses and less than the value outside the parentheses, the limit relative error of the measured flow should be arithmetically added ±0.5%. The length of the straight pipe section between the first resistance member and the second resistance member on the upstream side l0 , in the form of the second resistance member and β = 0.7 (whatever the actual value of β is), is taken to be half of the values listed in Table 4.2. For systems used in experimental studies, the minimum straight pipe section length should be at least double the values listed in Table 4.2. If space is not available, the straight section can be shortened by adding a rectifier to the tube to adjust the flow distribution. (iii) Flow equations for standard throttling devices The flow equation, which is the relationship between the flow rate through the throttling device and the differential pressure developed, can be derived from Bernoulli’s equation and the continuity equation for the fluid. However, it is still not possible to derive the relationship between flow rate and differential pressure completely quantitatively from theory, but only by finding the flow coefficient. 1. Flow equations: Table 4.1 Limits of k/D relative average roughness of smooth tubes β2 k/D ×

0.063 0.071 0.10 0.15 0.20 0.30 0.40 0.50 0.60 0.64 104

≤ Orifice plate 55.0 nozzle

–

42.0

20.0 8.7

6.3

4.7

4.2

4.0

3.9

3.9

–

31.0 12.2 7.7

5.3

4.6

4.2

3.9

3.9

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4 Flow Testing

Table 4.2 Minimum length of straight pipe upstream and downstream of the restrictor β

The form of the local resistance part upstream of the throttle part and the length of the minimum pipe section l1 throttle device

throttle device

Throttle device

11

11

11

Throttle device

11

There are multiple 90° elbows in the same plane

Elbow or tee

2D

D

≥3D 0.5D

throttle device

throttle device

throttle device

l1

There are multiple 90° elbows in different planes

≥1.5D

l1

l1

throttle device

D

Gate valve (all open)

Ball valve (all open)

l1

Shrink or expand tube

Minimum pipe section length L2 downstream of restrictor (form of all local resistance parts on left)

1

2

3

4

5

6

7

8

≤0.2

10(6)

14(7)

34(17)

16(8)

18(9)

12(6)

4(2)

0.25

10(6)

14(7)

34(17)

16(8)

18(9)

12(6)

4(2)

0.30

10(6)

16(8)

34(17)

16(8)

18(9)

12(6)

5(2.5)

0.35

12(6)

16(8)

36(18)

16(8)

18(9)

12(6)

5(2.5)

0.40

14(7)

18(9)

36(18)

16(8)

20(10)

12(6)

6(3)

0.45

14(7)

18(9)

38(19)

18(9)

20(10)

12(6)

6(3)

0.50

14(7)

20(10)

40(20)

20(10)

22(11)

12(6)

6(3)

0.55

16(8)

22(11)

44(22)

20(10)

24(12)

14(7)

6(3)

0.60

18(9)

26(13)

48(24)

22(11)

26(13)

14(7)

7(3.5)

0.65

22(11)

32(16)

54(27)

24(12)

28(14)

16(8)

7(3.5)

0.70

28(14)

36(18)

62(31)

26(13)

32(16)

20(10)

7(3.5)

0.75

36(18)

42(21)

70(35)

28(14)

36(18)

24(12)

8(4)

0.80

46(23)

50(25)

80(40)

30(15)

44(22)

30(15)

8(4)

For all Piece of resistance β values

Minimum upstream straight pipe length is required

Abrupt symmetrical reducing pipe with diameter ratio β ≥ 0.5

30(15)

Thermometer protection sleeves with diameter ≤ 0.03D

5(3)

Thermometer sleeves with diameters between 0.03D and 0.13D

20(10)

Note (1) This table is applicable to various throttle parts specified in the standard (2) The figures quoted in this table are multiples of pipe diameter D

(1) Incompressible fluid flow equation: Let us use the example of an incompressible fluid flowing through an orifice plate to analyze the flow of fluid through a throttle, at which point there is ρ1 = ρ2 = ρ. Figure 4.9 shows a schematic of this. When the fluid flows through the orifice plate, the velocity of the flow beam increases significantly due to the change in the cross-section of the flow beam, thus increasing the kinetic energy, while the static pressure of the fluid decreases. After the fluid passes through the orifice plate, the cross-section of the flow beam gradually expands and returns to the original state, the flow velocity gradually reduced to the original flow velocity, and the static pressure also gradually back up. But because the fluid energy in the flow process has a part of the consumption in the friction, vortex,

4.1 Differential Pressure Flowmeter

171

Fig. 4.9 Variation of pressure and flow rate when fluid flows through the throttle

impact, so the pressure cannot be fully restored, and there is a pressure drop, the pressure drop is called fluid flow through the pressure loss of the throttle δ p . In addition, because the flow beam before and after the throttle is not slowly variable flow, the static pressure in the same pipe cross-section is not equal. For example, at the pipe wall immediately adjacent to the orifice plate, the pressure is rising because the flow velocity is decreasing (solid line in the static pressure p characteristic curve in Fig. 4.9), while at the axis of the pipe, the pressure is decreasing because the flow velocity is increasing (dashed line in the figure). To derive the flow equation, we take two sections of the pipe: Sects. 1.1 and 2.2 present the Burr’s effort equation for the total fluid flow in these two sections as follows: p1' + c1

ρv2 ρv12 ρv2 = p2' + c2 2 + ξ 2 2 2 2

(4.2)

where c1 , c2 is the correction factor for the kinetic energy of the total flow. ξ is the coefficient of resistance. The continuity equation for the total fluid flow is v1

π D2 π d '2 = v2 4 4

Let the diameter of the opening of the throttle be d, define

(4.3)

172

4 Flow Testing

β=

d D

(4.4)

μ=

d '2 d2

(4.5)

The shrinkage factor is

Substituting Eqs. (4.4) and (4.5) into (4.2) and (4.3), and solving for them in conjunction, we get √ v2 = √

1 c2 + ξ − c1

μ2 β 4

) 2( ' p − p2' ρ 1

(4.6)

volumetric flow π '2 d Q=√ c2 + ξ − c1 μ2 β 4 4 1

√

) 2( ' p1 − p2' ρ

(4.7)

Because the location of the minimum cross-section 4.2 of the flow beam varies with the flow velocity, and the location of the actual pressure-taking point is fixed, a pressure-taking factor has to be introduced when replacing p1' , p2' with the static pressure at the fixed pressure-taking point p1 , p2 ψ ψ=

p1' − p2' p1 − p2

(4.8)

In practice, replacing ( p1' , p2' ) with the measured pressure difference and replacing ( p1 − p2 )d ' with the opening diameter of the throttle d gives the flow equation √ π 2 2 d Q=√ ( p1 − p2 ) ρ c2 + ξ − c1 μ2 β 4 4 √ μ ψ α=√ c2 + ξ − c1 μ2 β 4 √ μ ψ

(4.9)

(4.10)

where α is the flow coefficient, which is an important parameter for various throttling devices. The flow coefficient is experimentally derived, and its value is generally between 0.6 and 1.2. Mass flow π √ M = α d 2 2ρ( p1 − p2 ) 4

(4.11)

4.1 Differential Pressure Flowmeter

173

(2) Flow equation for compressible fluids: When a compressible fluid flows through a throttle, the density changes due to the change in pressure. If you still use the flow coefficient based on the Burr’s effort equation for incompressible fluids α, the calculated flow rate is high. For this reason, the standard specifies the equation ρ with the density of the fluid before throttling ρ1 , the flow coefficient with the value of the fluid calibration, and the effect of the compressibility of the fluid is corrected with a first-class beam expansion correction factor ε. Obviously, the incompressible fluid is ε = 1, and the compressible fluid is ε < 1. The flow equation can then be written as. √ π 2 2 Q = αε d ( p1 − p2 ) (4.12) 4 ρ1 π √ M = αε d 2 2ρ1 ( p1 − p2 ) (4.13) 4 2. Properties of ε, α in the flow equation (1) Expansion coefficient ε The expansion coefficient ε of the flow bundle is a factor that takes into account the effect of compressibility. It is related to the pressure ratio P2 /P1 (or (P1 – P2 )/P1 ), β, k, etc. before and after the throttle. When P2 /P1 ≥ 0.75, 50 mm ≤ D ≤ 1000 mm and 0.22 ≤ β ≤ 0.80, the ε of a standard orifice plate using an angular connection to extract pressure can be determined by the following empirical formula. ⎡ ε = 1 − (0.3703 + 0.3184β 4 )⎣1 −

(

p2 p1

)1/ k

⎤0.935 ⎦

(4.14)

The values of ε calculated according to Eq. (4.14) in the commonly used ranges of k, P2 /P1 , and β are listed in Appendix Table A.15. Again the ε of the standard orifice plate when using flange pressure extraction can be determined by the following empirical formula. ( ) Δp 1 ε = 1 − 0.41 + 0.35β 4 ρ1 k

(4.14' )

The values of ε calculated according to equation (4.14' ) in the commonly used ranges of k, P2 /P1 , β, etc. are listed in Appendix Table A.16. (2) Flow coefficient α For both incompressible and compressible fluids, the value of α theoretically depends on μ, β, and ξ .

174

4 Flow Testing

The beam contraction factor μ takes into account the additional contraction of the flow beam under the influence of inertial forces after passing through the throttling device. It depends on the degree of contraction of the flow beam, i.e., on the diameter ratio β and the ratio of inertia forces to friction forces (Reynolds number Re D ), i.e., μ = f (Re D , β). Here, the inertial force is determined by the velocity and density of the fluid; the internal friction depends on the viscosity (kinematic viscosity of the fluid). When the Reynolds number increases, the inertial force increases faster than the frictional force, and it is under the influence of the inertial force over the frictional force that the flow bundle after the throttle member makes the contraction increase, i.e., μ changes. The coefficient ξ takes into account the position of the pressure take-off point on the pipe wall and the influence of its construction, etc. For standard throttles (with standard pressure take-offs), ξ has a value similar to 1. The diameter ratio β directly takes into account the effect of the inlet velocity on the flow coefficient α in addition to the effect on μ. Therefore, from the analysis of μ, β and ξ , it is clear that the flow coefficient of a certain throttling element α is related to a certain diameter ratio β and fluid Reynolds number Re D , i.e., α = f (Re D , β) where the Reynolds number is for a pipe of diameter D, Re D = υγD (γ is the kinematic viscosity). It also follows that if two geometrically similar throttling devices have equal flow coefficients as long as the Re D of the flow beams are equal. In this case, the flow coefficient only varies with the single value of the Reynolds number, i.e., α = φ(Re D ) It is therefore perfectly possible to determine the α value experimentally. The flow coefficient derived experimentally in the laboratory with a very smooth pipe, i.e., the relative roughness of the inner wall of the pipe before the throttle ks/ ≤ 0.0004, is called the light pipe flow coefficient α0 . D In the case of rough pipes, a correction should be made to α0 , i.e., the flow coefficient for rough pipes α can be expressed as α = γ Re α0

(4.15)

where γ Re is the pipe roughness correction factor. ( γRe = (γ0 − 1)

lg Re D n

)2 +1

(4.16)

4.1 Differential Pressure Flowmeter

175

/ The equation γ0 is related to β and ks D , which can be found in Table 4.3. The standard orifice plate n is 6 and the standard nozzle n is 5.5. When Re D ≥ 106 , γ Re = γ0 then α = γ0 α0

(4.17)

Equations (4.15), (4.16), and (4.17) all apply to angle-joint pressure-taking orifice plates only. Exhibit II-4 lists the values for angle-joint standard / orifice plates at α0 . Use according to β, to find out Re D α0 ; according to ks D , β 2 from Table 4.3 to find out r0 ; such as Re D ≥ 106 , then by (4.17) to calculate α value; such as Re D ≤ 105 , then by (4.16) formula to calculate γRe , and then by (4.15) formula to find α value. 3. Pressure loss of fluid flow through the throttle After the fluid flows through the throttle, the pressure does not return to its original value. This pressure loss increases as the value of β decreases. Also with the form of the throttle, the fluid flow through the orifice and nozzle pressure loss than in the venturi pressure loss is greater. This pressure loss can be obtained experimentally but can also be approximated by the following formula: ( δp =

) 1 − αβ 2 Δp 1 + αβ 2

(4.18)

4. Method for estimating the total error in flow measurement Since the parameters and coefficients in the flow equation can be considered to be independent of each other, the basic relative √ error in flow measurement can be derived from the flow equation M = αε π4 d 2 2ρ1 Δp according to the law of indirect measurement error transfer as follows: Table 4.3 γ0 of standard orifice plate 400

800

1200

1600

2000

2400

2800

3200

≥3400

0.1

1.002

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.2

1.003

1.002

1.001

1.000

1.000

1.000

1.000

1.000

1.000

0.3

1.006

1.004

1.002

1.001

1.000

1.000

1.000

1.000

1.000

0.4

1.009

1.006

1.004

1.002

1.001

1.000

1.000

1.000

1.000

0.5

1.014

1.009

1.006

1.004

1.002

1.001

1.000

1.000

1.000

0.6

1.020

1.013

1.009

1.006

1.003

1.002

1.000

1.000

1.000

0.64

1.024

1.016

1.011

1.007

1.004

1.002

1.002

1.000

1.000

D/k s γ0 β2

176

4 Flow Testing

[ [1 ( σ )2 ( σ )2 ( σ )2 ( 1 σ )2 ( 1 σ )2 2 σM Δp α ε d ρ1 =± + + 2 + + M α ε d 2 ρ1 2 Δp

(4.19)

(1) Influence of measurement errors in D and d on the flow coefficient α: When using the standard flow coefficient α, the value of β is obtained by measuring the pipe diameter D and the diameter of the throttle opening d, and then checking the table to obtain the value of the flow coefficient α. However, since there are errors in the measurement of D and d, the error in the α value must be increased. α The values have the following approximate relationship to the opening diameter ratio β: α = C + 0.5β 4

(4.20)

where C is a constant. The basic relative error in the increase in the flow coefficient due to the measurement errors at D and d is | 4 | | 4 | | 2β σd | | 2β σ D | σα |+| | (4.21) = || α α d | | α D| After considering the error in the increase in the flow coefficient α caused by the measurement errors in the two components D and d, the total error in the flow measurement is ⎡( ⎢ σM ⎢ = ±⎢ ⎣ M

⎤ 21 )2 ( 4 )2 ( ) ( σα )2 ( σε )2 σD 2 β β 4 ( σd )2 + +4 +4 1+ α ε α D α d ⎥ ⎥ ⎥ (4.22) ( ( )2 )2 ⎦ 1 σΔp 1 σρ1 + + 4 ρ1 4 Δp

(2) Calculation of each basic relative error (a) The algorithms for σαα and σεε were described earlier. (b) Estimates from σDD and σdd . σDD is the basic relative error of the pipe diameter. If D20 is the measured value at 20 °C, then σDD = ±0.1% can be used as an estimate; if D20 is the nominal value, then can be used. σDD ≈ ±0.5%∼1.5% σd is the basic relative error of the throttle opening diameter, but d20 must be d measured physically, then make σdd = ±0.05%. σΔp σΔp (c) Estimation of Δp . Δp The basic relative error of differential pressure, in principle, should include the error of differential pressure signal line, transmitter, display instrument, and the connection between them. Now mainly take the differential pressure display instrument as an example to analyze the estimation σΔp . method of Δp According to the standard, the accuracy of the differential pressure display instrument is the percentage of the maximum error of the upper limit of the

4.1 Differential Pressure Flowmeter

177

instrument, and the maximum error is considered to be equal to the value of 3σ . If the range is 0∼0.1 MPa of the class 1 m, in the common flow rate of the differential pressure of the indicated value of Δpcom = 0.05 MPa, then σΔp 1 1 0.1 − 0 ≈ × × = 0.0067 = 0.67% Δp 3 100 0.05 σ

σ

(d) Estimates from ρρ11 . ρρ11 is the basic relative error of the density before the throttle. ρ1 Values are tabulated from the measured temperature T1 and pressure σ p1 values. Therefore, the ρρ11 value should include the basic error of the tabulated σ values and the measurement errors of T and. p ρρ11 The estimation of the values is more complex and can be approximated in industrial measurements by the following table. σ

1) Liquids: ρρ11 = ±0.03% when the temperature measurement conditions σt ≤ 5% (including meter check errors). t σ σ 2) Water vapor: when σtt ≤ ±5%, PP11 ≤ ±5% ρρ11 ≤ ±3% When

σt t

≤ ±1%, σ

σ P1 P1

σ

≤ ±1% ρρ11 ≤ ±0.5%

3) Gas: ρρ11 ≤ ±1.5% when

σt t

≤ ±1%,

σ P1 P1

≤ ±1%.

(iv) Differential pressure gauges for flow meters for throttling devices The throttle device and differential pressure meter together form a throttle variable pressure drop flow meter. The main differential pressure meters used in industry are double tube, ring balance, bell-type, float, membrane, and double bellows type. As required, differential pressure meters can be equipped with indicating, recording, and flow accumulation mechanisms. Some are also equipped with remote transmitters, alarms, and automatic adjustment devices. The scale of the differential pressure gauge can be graded by differential pressure or by flow rate. The upper limit of the differential pressure rating of the differential pressure gauge Δp is equal to the series value determined by the following formula, i.e., Δp = b × 10n

(4.23)

where b is any one of 1, 1.6, 2.5, 4, and 6.3; and n is any positive or negative integer, or zero. When graded by flow, the rated upper limit Q is equal to the series value determined by the following equation: Q = a × 10n

(4.24)

where a is any one of 1, 1.25, 1.6, 2.5, 3.2, 4, 5, 6.3, and 8; and n is any positive integer or negative integer or zero.

178

4 Flow Testing

Because of the squared relationship between flow and differential pressure, the flow divisions on the differential pressure gauge scale are not uniform. The closer you get to the upper limit of the scale, the larger the graduation. If the flow rate is to be calculated to obtain the cumulative flow rate or the flow signal is to be fed into the regulation system, the flow rate scale must be linearized, that is, through the differential pressure meter structure of the open device or electronic open line on the output signal of the differential pressure meter to open the square and get a linear relationship with the flow of the signal. The differential pressure gauges used in conjunction with standard throttling devices can be double bellows-type differential pressure gauges and membranetype differential pressure gauges, whose basic operating principles are described in Chap. 3 and will not be repeated here. (v) Calculation of standard throttling devices 1. Calculation of propositions In practice, there are two main types of computational propositions for throttling devices: (1) Knowing the internal diameter of the pipe, the form of the throttle, the diameter of the opening of the throttle, the method of taking pressure, and the fluid to be measured, the corresponding flow rate is required to be calculated from the measured differential pressure value. This type of proposition is mainly used to calibrate existing throttling devices. (2) Knowing the internal diameter of the pipe, the measured fluid parameters and the expected range of flow variation, the design of the throttling device is required, i.e., it is required to: (i) select the form of the throttle, the pressure-taking method and determine the opening diameter of the throttle; (ii) select the range and type of the differential pressure gauge; (iii) calculate the measurement error, etc. 2. Practical calculation formulae Throttling devices for industrial flow measurement are still customary in this country to use the engineering unit system, when the flow formula is: √

ΔP ρ1 √ 2 2 ΔP = 0.01252εγRe α0 β D ρ1 √ h 20 = 0.01251εγRe α0 β 2 D 2 ρ1 √ M = 0.01252α0 γRe εd 2 ρ1 Δp √ = 0.01252εγRe α0 β 2 D 2 ρ1 Δp Q = 0.01252α0 γRe εd 2

(4.25)

4.1 Differential Pressure Flowmeter

√ = 0.01251εγRe α0 β 2 D 2 ρ1 h 20

179

(4.25' )

where Q is the volume flow rate, m3 /h; M is the mass flow rate, kg/h; d and D are the throttle opening diameter and pipe inner diameter, mm, respectively; Δp is the differential pressure value, kg force/m2 ; h20 is the differential pressure value expressed in 20 °C water column, mm water column. All of the above refer to the values in the operating condition. The constant term 0.01252 = 3600 × 10−6 × π4 × √ 2g0 and the acceleration of gravity g0 = 9.81 m/s2 . The constant 0.0125 l takes into account the value of h20 instead of the corrected differential pressure value of h0 at 0 °C in the standard condition. At standard gravitational acceleration, the fluid densities ρ l (kg/m3 ) and gravities γ (kg force/m3 ) and the mass flow rate M (kg/h) and weight flow rate G (kg force/ h) are numerically equal, respectively. 3. Calculation method for throttling devices When using the flow equation to complete the design of the throttling device, the task of selecting the differential pressure, determining the opening diameter, and the margin of error is accomplished. In addition, all the coefficients in the formula must be obtained, and these coefficients are related to the differential pressure and opening diameter ratio. Therefore, in practical engineering, it is often based on experience to determine the maximum differential pressure at the maximum flow rate as the upper limit of differential pressure to select differential pressure gauge. Following this, the differential pressure at the commonly used flow rate is derived, and then ε = l, γRe = 1, according to the flow rate formula (α0 β 2 )1 . Under certain conditions of ReD find the value of β 1 according to Schedule II9~11 of α0 = f (α0 β 2 , ReD, β). On this basis, the values of ε and γRe are found, and again the formula is used to find (α0 β 2 )2 , and finally, the value β 2 . It is perfectly feasible to find the required value of d in this way, under reasonable conditions of data. The design method of the flange pressure-taking standard orifice plate is simpler; it can disregard the effect of roughness as long as D/k ≥ 1000. There is also a calculation method that is less applied in China, which is to make the flow rate and d to take integers. This method is conducive to the serialization of the throttle parts to improve manufacturing accuracy, but the scale of the differential pressure meter will have to be calibrated unit by unit. In order to achieve satisfactory accuracy of the designed standard throttling device, the determination of the differential pressure, the range ratio, and the roughness of the inner wall of the pipe are subdivided as follows: (1) Selection of differential pressure: In order to improve the accuracy of the measurement, the upper limit of differential pressure should be selected as a large value, and the value of β should be selected as a small value. In the design, it is possible to make β 1 ≤ 0.5. This will make the flow coefficient α stabilize at a lower ReD ; i.e., the allowable ReDmin is smaller. In practice, it is possible to make its Re at the minimum flow rateD larger than the permissible ReDmin , thus extending the range. In addition, a small β value and a large ΔP not only improve the measurement accuracy but also

180

4 Flow Testing

make the minimum straight section required before and after the throttle shorter. But the β value is small, and the pressure loss of the throttle is also large. Therefore, the selection of the upper limit of differential pressure should be determined by combining the above factors and actual needs. There are three options for differential pressure, as follows: (a) When the pressure loss δ p , the length of the straight pipe section ll , l 2 , l 0 and the actual minimum Reynolds number are specified, the β value is found according to the recommended minimum Reynolds number ReDmin applicable to standard throttling devices (Appendix Tables A.10, A.11 and A.12). The upper limit of the differential pressure is then found according to the relevant chart. (b) When there are no special requirements for pressure loss, length of straight pipe section, etc., the upper limit of differential pressure may be determined according to the following procedure: 1) Make the actual minimum Reynolds number equal to the minimum Reynolds number recommended for use, and find the β value on Appendix Tables A.10, A.11, or A.12. 2) β = 0.5 for β ≥ 0.5; if β < 0.5, the value of β found is used as the basis for selecting the differential pressure. 3) Based on the value of β, let ReD = 106 and check Appendix Tables A.18, A.19 and A.20 to obtain α0 β2 . 4) Apply the flow equation, find the differential pressure and round the calculation to the series value ΔP. 5) When the measured medium is gas or vapor, it should be verified that p2 / pl ≥ 0.75, otherwise a larger β value should be taken until it meets the requirements. (c) When the pressure loss δ p is specifically specified, the upper limit of the differential pressure may be determined according to the following procedure. 1) For standard orifice plate ΔP = (2~2.5) δ p ; For nozzle ΔP = (3~3.5) δ p . The value of ΔP is obtained rounded to a value smaller than its value, but close to its series value ΔP. 2) For gases or water vapor, again ensure that p2 /pl ≥ 0.75. (2) Determination of the range ratio: The ratio of the maximum flow rate and the minimum flow rate allowed to be measured is called the range ratio. Measuring the flow rate within the specified range ratio guarantees the measurement accuracy. The 1 flow rate Q and the differential pressure Δp 2 are not strictly proportional, which is related to many factors such as the flow coefficient α and ReD and varies with the Reynolds number. In practice, there is no concept that the flow coefficient ceases to vary when ReD is greater than a certain so-called limiting Reynolds number. The standard gives a recommended minimum Reynolds number ReDmin for a certain value of β, under which a deviation of less than 0.5% of the value of the flow coefficient α is guaranteed for a range ratio of 4.

4.1 Differential Pressure Flowmeter

181

(3) Determination of the inner wall roughness of the pipe: According to the standard, the average relative roughness k s /D of the inner wall of the pipe should be determined by experimental methods after first measuring the value of the resistance coefficient λ of the straight pipe and then using the Colebrook formula, i.e., /√ ks −1 λ − 9.34 1√ = 3.71 × 10 D Re D λ

In practical applications where the conditions for the actual measurement of λ values are not available, the pipe k values listed in Table 4.4 for different materials can also be used. 4. Examples of calculations Only examples are given of angularly connected pressure-taking standard orifice plates in standard throttling devices that are commonly used in engineering where the necessary parameters are known, and the design is required. Table 4.4 Absolute average roughness ks value of inner walls of pipes of various commonly used materials Material

Condition

k (mm)

Brass, cuprum, aluminum, plastic, glass

Smooth, sediment-free pipe

< 0.03

Steel

New cold drawn seamless steel pipe

< 0.03

New hot drawn seamless steel pipe

< 0.03

New rolled seamless steel pipe

0.05~0.10

New longitudinal seam welded pipe

0.05~0.10

New spiral welded pipe

0.10

Slightly rusted steel pipe

0.10~0.20

Rusted steel pipe

0.20~0.30

Long hard-skinned steel pipe

0.50~2

Severely peeled steel pipe

>2

New steel pipe coated with asphalt

0.03~0.05

General asphalt-coated steel pipe

0.10~0.20

Cast iron

Galvanized steel pipe

0.13

New cast iron pipe

0.25

Rusted cast iron pipe

0.10~1.5

Peeled cast iron pipe

> 1.5

New cast iron pipe coated with asphalt 0.10~0.15 Asbestos cement

Insulated and non-insulated asbestos cement pipe

< 0.03

Non-insulated general asbestos cement pipe

0.05

182

4 Flow Testing

(i) Known conditions (or propositional computation task statement) Requirement to design a standard orifice plate with an Angle connection to take pressure in a standard throttling device. (ii) Auxiliary calculations. The upper limit of the selected flow scale is M = 63 t/h according to M max . According to Appendix Table A.21, the coefficient of linear expansion of the pipe material λD = 11.16 × 10–6 mm/(mm-°C), the inner diameter of the pipe in working condition Dt = D20 [1 + λD(t − 20)] = 100[1 + 11.16 × 10 − 6(30 − 20)] = 100.0112 (mm)

The absolute pressure of water in working condition P1 = P1 + Pa = 0.6 + 0.1 = 0.7 (Mpa). According to Appendix Table A.23, the viscosity of water η = 81.6 × 10–6 mkgf s/m2 , according to Appendix Table A.22, the density of water ρ 1 = 996.016 kg/m3 , and according to Table 4.4, the pipe roughness k s = 0.075 mm, the pipe diameter and roughness ratio D/k s = 100/0.075 = 1333. 25000 M and work out Re D min = 0.036 × 100.0112×81.6×10 Follow Re D = 0.036 × Dη −6 = 5 5 1.10 × 10 and ditto Recom = 1.98 × 10 . Determine the upper limit of differential pressure: According to ReDmin = 1.10 × 105 Record Table A.10 using any β value of β < 0.725, the additional error in the measurement range between the minimum and maximum flow rate is less than 0.5% due to the change in flow coefficient α caused by the change in ReD . Since the proposition task statement states that the magnitude of the pressure loss is not limited, take β = 0.5. and let γRe = 1, ReD = 106 , and check Appendix Table A.18 to obtain α 0 β 2 = 0.1560, then by 2 Mmax 630002 h 20 max = ( )2 = ( )2 0.01251α0 β 2 D 2 ρ1 0.01251 × 0.1560 × 100.01122 × 996.016

= 10458 (mmH2 O) Take h 20 max = 10,000 mm water column. The DBC-321 electric differential pressure transmitter is selected. The differential pressure at the common flow rate is ( h 20com =

Mcom Mmax

)2

( h 20 max =

45 63

)2 × 10000 = 5100 (mmH2 O)

Assignment for propositional calculation (Type II) The Item serial number 1

Name of the medium to be tested

Symbol

Unit

Value

Water (continued)

4.1 Differential Pressure Flowmeter

183

(continued) Item The serial number 2

3

Symbol

Unit

Value

Flow range: Normal

M com

t/h

45

Maximum

M max

t/h

63

Minimum

M min

t/h

25

Working pressure

P1

Mpa

0.6 (Gage pressure)

4

Working temperature

t1

°C

30

5

Pressure loss

δP

Mpa

Unlimited

D20

mm

6

Pipe diameter

7

Piping material

20# New seamless steel tube

8

Throttling parts and pressure-taking method

Angle connection pressure (ring chamber) standard orifice plate

100

9

Throttle material

Industrial copper

10

Type of differential pressure meter required

DBC-type electric differential pressure transmitter

11

Line diagram

l0

l1

l2

(iii) Calculation 1) Let γRe = 1 and initialize (α0 β 2 )l values. Mcom 45000 = √ √ 2 0.01251D ρ1 h 20com 0.01251 × 100.01122 996.016 × 5100 = 0.1596

(α0 β 2 )1 =

2) Find the initial value of β1 from (α β)0 2 l and ReDcom . Check Exhibit II-9 and take a value of β close to ReDcom = 1.98 × 105 , (α 0 β)2 l = 0.1596 and take β 1 = 0.505. 3) From D/k s , β 1 and ReDcom , check Table 4.3 for γ 0 = 1.001 and calculate the value of γRe as

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4 Flow Testing

( )2 ) lg Re D 2 lg 1.98 × 105 γRe = (γ0 − 1) + 1 = (1.001 − 1) + 1 = 1.00078 6 6 (

4) Recalculating (α 0 β 2 )2 values. (α0 β 2 )2 =

(α0 β 2 )1 0.1596 = = 0.1595 γRe 1.00078

5) Find the β 2 and α 0 values from (α 0 β 2 )2 , ReDcom . Checking Schedule II-9 gives. Interpolation is used to find. ReD = 1 × 105 when β2' = 0.500 +

0.505 − 0.500 × (0.1595 − 0.1564) = 0.5046 0.1598 − 0.1564

α0' = 0.6256 +

0.6266 − 0.6256 × (0.1595 − 0.1564) = 0.6265 0.1598 − 0.1564

ReD = 5 × 105 when β2' ' = 0.505 +

0.510 − 0.505 × (0.1595 − 0.1594) = 0.5051 0.1629 − 0.1594

α0' ' = 0.6251 +

0.6261 − 0.6251 × (0.1595 − 0.1594) = 0.6251 0.1629 − 0.1594

ReD =2 × 105 when β2 = 0.5046 +

0.5051 − 0.5046 × (2 − 1) × 105 = 0.5047 (5 − 1) × 105

α0 = 0.6265 −

0.6265 − 0.6251 × (2 − 1) × 105 = 0.6262 (5 − 1) × 105

6) Find the value of d. d = β2 D = 0.5047 × 100.0112 = 50.4757 (mm) 7) Validation. √ Mcom = 0.01251α0 γRe d 2 ρ1 h 20com

√ = 0.01251 × 0.6262 × 1.0008 × 50.47572 996.016 × 5100 = 45019.495 (kg/h)

δM =

45019−45000 45000

= 0.043% < 0.2% Therefore, the above calculation passes.

4.1 Differential Pressure Flowmeter

185

8) Calculate the value of d 20 for processing conditions. Check Exhibit II-12 for λd = 16.60 × 10–6 mm/(mm-°C) d 50.4757 = [1 + λd (t − 20)] [1 + 16.60 × 10−6 × (30 − 20)] = 50.47 ± 0.026 (mm)

d20 =

9) Find the actual maximum pressure loss δ p : δp =

1 − α0 β 2 1 − 0.1595 × 10,000 = 7249 (mmH2 O) × h 20 max = 1 + α0 β 2 1 + 0.1595

10) To determine the length of the straight pipe section, check Table 5.2 for l 1 = 20D = 2000 mm, l2 = 6D = 600 mm, and l0 = 18D = 1800 mm. 11) Calculate the total error in flow measurement. ⎧ [ ( 4 )2 ( ) ( 4 )2 [( ) ⎫ 21 ( σ )2 ( σ )2 2 ⎪ σd 2 ⎪ σ β β ⎪ ⎪ α ε D ⎪ ⎪ + +4 +4 1+ ⎪ ⎪ ⎨ α ε α D α d ⎬ σM =± % )2 ( )2 ( ⎪ ⎪ M ⎪ ⎪ σ σ 1 1 Δp ρ ⎪ ⎪ 1 ⎪ ⎪ + + ⎩ ⎭ 4 Δp 4 ρ1 formula [ ] σα 50 4 2 2 = ±0.25 1 + 2β + 100(γRe − 1) + β (lg Re D − 6) + % α D ⎡ ⎤ 1 + 2 × 0.50474 + 100(1.0008 − 1) ⎦% = ±0.25⎣ 50 +0.50472 (lg 2 × 105 − 6)2 + 100.0112 = 0.4585% ( σ )2 α

α

= 0.212;

σε =0 ε

)2 ( σ D )2 0.50474 =4 × 0.752 = 0.02414 D 0.6262 [ [ )2 [ ( ( 4 )2 [( ) σd 2 0.50474 β =4 1+ 4 1+ × 0.052 = 0.01011 α d 0.6262 (

β4 4 α

)2 (

) ( ) ( ( ) 1 σΔp 2 1 1 Δpmax 2 1 1 10000 2 = = = 0.1068 ξ ×1× 4 Δp 4 3 Δpcom 4 3 5100

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4 Flow Testing

) ( 1 σρ1 2 1 = × 0.032 = 0.00225 4 ρ1 4

∴

1 σM = ±(0.2102 + 0.02414 + 0.01011 + 0.1068 + 0.00225) 2 = ±0.5946% M

(iv) Additional errors of non-conformity in manufacture and installation 1) The orifice plate is not sharply edged at right angles to the entrance. The measured value of the radius of the circle γk = 0.05 mm, and the maximum deviation from the average value of any single measurement of γk does not exceed ±20%. τ When γk /d = 0.05/50.47 = 0.001, th e additional error bbkk = ±0.5% is found from Exhibit II-20 for bk = 1.005. The fundamental error for the rough tube flow coefficient α should be added to its additional error geometry. [ [ [1 [1 ( σ )2 ( 1 τ )2 2 ( σ )2 ( σ )2 2 σab α a bk bk =± + + =± ab a 2 bk α bk 1 ] [ = ± 0.45852 + 0.252 2 = ±0.5222% 2) Provide a d n = 2 mm evacuation hole at the specified orifice plate location. Checking Schedule II-21 yields bn = 1.002, which gives the orifice plate opening diameter as. [ ' d20

= d20 1 +

(

dn d20

[

)2 [ 21

= 50.47 1 +

(

2 50.47

)2 [ 21 = 50.5096 (mm)

The d n of the specified evacuation hole should be the actual measured value, then the basic relative error of the opening diameter after the orifice plate correction σd' 20 ' d20

= ±0.1%. 3) After installation the orifice plate is not centered on the pipe with eccentricity 4 = 0.04. The basic error of the flow coefficient α of ex = 4 mm, eDx = 100 the rough pipe can be disregarded without any additional error when per pipe ex ≤ 0.015( β1 − 1). D Combining these results, the flow coefficient α b for the actual rough tube should be: αb = α0 γRe bk bn = 0.6262 × 1.00078 × 1.005 × 1.002 = 0.6311 The actual flow value should be. √ ' Mcom = 0.01251α0 γRe bk bn d 2 ρ1 h 20com √ = 0.01251 × 0.6311 × 50.50962 996.016 × 5100 = 45396.42 (kg/h) The total error in the actual flow measurement is.

4.1 Differential Pressure Flowmeter

187

⎧ ⎫1 ⎡ ( ( )2 ) ⎤ ) ( ) ( ⎨( σa )2 ( σ )2 4 2 ( σ ' )2 σΔp 2 1 σρ1 2 ⎬ 2 σM' β 4 ( σ D )2 β 1 ε b d ⎦ =± + +4 + 4⎣1 + + + % ⎩ ab ⎭ M' ε α D α d' 4 Δp 4 ρ1 ⎧ ⎡ ( ( )2 )2 ⎤ ⎨ 0.50474 ⎦ 0.50474 = ± 0.67132 + 0 + 4 × 0.752 + 4⎣1 + ⎩ 0.6311 0.6311 ×0.12 +

[ ] )1 1 1 1 10000 2 + × 0.032 % ×1× 4 3 5100 4

= ±0.7898% ≈ ±0.8%

4.1.2 Rotameter In industrial production and scientific work, relatively small flow measurement problems are often encountered. Throttling devices have not been standardized for pipe diameters less than 50 mm, so rotameter is commonly used for flow measurement of smaller pipe diameters. For relatively large flow measurement problems (pipe diameters above ∅ 100), rotameter is not used because rotameter of this diameter appears bulky compared to other flow meters. Rotor flowmeter has the advantages of simple structure, reliable work, small and constant pressure loss, low Reynolds number, and can measure a smaller flow rate and scale linearity In addition, it has been widely used in gas, liquid flow measurement and automatic control system. Rotor flowmeter is divided into two categories: glass tube rotor flowmeter and metal tube rotor flowmeter. Glass tube rotameter in addition to the base type and corrosion-resistant type, insulation type, and diversion type. Metal tube rotameter in addition to the basic type and special corrosion-resistant type and insulation type. (i) Principle of operation A rotameter is a vertically mounted conical tube with a float that floats freely up and down. Therefore, a rotameter is also called a float flow meter. The float floats up and down under the action of fluid flowing from the bottom up. The principle of operation is shown in Fig. 4.10. The float in the cone tube causes an annular circulation area; it is smaller than the float on the cone tube below the circulation area and produce throttling effect, so the float on the formation of static pressure difference, the direction of this force upward. The force acting on the float is also gravity, the buoyancy of the fluid to the float, and the viscous friction of the fluid to the float. These forces are balanced when the float stays in a certain position. If the flow rate increases, the average flow velocity in the annular flow cross-section also increases, making the static pressure difference between the float above and below to increase; the float rises upwards, and the annular cross-sectional area increases at such a new position so that the differential pressure decreases until the differential pressure returns to its original

188

4 Flow Testing

Fig. 4.10 Rotor flow meter operating principle diagram

value. At which point the rotor is balanced in a new upper position, so that the flow rate can be indicated by the position of the rotor in the vertebral tube. According to the throttling principle, the differential pressure generated in front of and behind the γ 2 γ 2 υ , and the viscous friction is also proportional to 2g υ , throttle is proportional to 2g so the float is subjected to an upward pressure of p = a'

γ 2 υ 2g 2

(4.26)

where a ' is the coefficient; υ2 is the average flow velocity in the annular flow area at the II-II cross-section. g and γ are the acceleration of gravity and the gravity of the fluid being measured, respectively. The difference between the gravitational and buoyant forces of the float in the fluid, i.e., the downward force acting on the float is V (γ f − γ )

(4.27)

where V , γ f , γ are the volume and weight of the float and the weight of the fluid being measured, respectively. The float in the equilibrium position shall satisfy the following equation: V (γ f − γ ) = F f p V (γ f − γ ) = a ' F f

γ 2 υ 2g 2

where F f is the maximum cross-sectional area of the float. The volume flow rate of the measured fluid is

(4.28) (4.29)

4.1 Differential Pressure Flowmeter

189

Q = F2 v2

(4.30)

Substituting Eq. (4.29) into Eq. (4.30) yields. √ Q = α F2 √ G = α F2

2gV (γ f − γ ) γ Ff

(4.31)

2gVγ (γ f − γ ) Ff

(4.32)

where Q, G and α are the volume flow rate, weight flow rate, and flow coefficient of the fluid being measured, respectively. F2 is the annular flow area formed between the float and the conical tube at section II-II. The flow coefficient α is related to the shape of the float, the construction of the flow meter, and the viscosity of the fluid to be measured and can only be determined experimentally. The annular flow area is. F2 =

) π[ ] π( 2 d − d 2f = (d0 + nh)2 − d 2f 4 z 4

(4.33)

where d Z and d f are the inner diameter of the conical tube at section II-II and the maximum diameter of the float. d0 is the internal diameter of the conical tube at the zero point of the scale. n is the magnitude of the change in the inner diameter of the cone tube per unit height of float lift. h is the height at which the float rises from the zero point of the scale. From Eqs. (4.31) and (4.32), it can be seen that if h is used as the scale for the flow of the fluid being measured, the relationship between the flow rate Q and h is nonlinear. In a metal rotameter, this can be linearized by adjusting the first four-link mechanism scale in the drive chain. The glass rotameter is solved by controlling the nonlinear error to within the basic allowable error. As seen√ in Eq. (4.33), F2 = f (h) is a function of the float rise height. In Eq. (4.31), let K =

2gV (γ f −γ ) γ Ff

then we have

Q = α K f (h)

(4.34)

To obtain a linear scale, the following equation must be satisfied: Q = ah where a = d 2f ).

Q max , h max

substituting Eqs. (4.34) into (4.35) yields f (h) =

(4.35) a αK

h=

π (dz2 4

−

190

4 Flow Testing

dz2 = d 2f +

4a h παK

(4.36)

The linear scale is guaranteed when the relationship between the cone tube diameter and h satisfies the above equation, but since a itself does not remain constant but varies with h, the cone tube is manufactured as a cone. (ii) Conversion of the indicated value when the weight of the measured mediumγ is changed The flow Eqs. (4.31) and (4.32) for the rotameter are derived with the heaviness γ as a constant (incompressible fluid). The meter is factory calibrated with water or air, and the meter is accurate as long as the values of the quantities in the flow equation are the same in use as when calibrated. If the temperature, pressure and measured medium in use are different from the calibration, then the instrument must be corrected. [Note]: Consider the calibration as standard, i.e., temperature T = 293.16 K and pressure p = 0.1 Mpa. 1. Correction factor when measuring non-aqueous liquids Q2 α2 K = = Q1 α1

√

(γ f − γ2 )γ1 (γ f − γ1 )γ 2

(4.37)

where Q 1 and Q 2 are the flow rate values for the water calibration and the actual flow rate values for non-water measured media, respectively. γ1 and γ2 are the weight of water and the actual weight of the non-aqueous medium under test, respectively. γ f , α1 and α2 are the weight of the float, the flow coefficient when measuring water and the flow coefficient when measuring non-aqueous media, respectively; when the viscosity of the measured media is very different from that of water, it can be considered α1 = α2 . 2. Correction factor when measuring non-air gases For gases γ f >> γ1 , γ f >> γ2 , here γ f is the weight of the float, γ1 is the weight of the air in the standard state, and γ2 is the weight of the gas under test in the standard state. If the temperature and pressure of the measured gas when the instrument is operating are the same as when it is calibrated, the correction factor is obtained from Eq. (4.37). Q' K = 2 = Q1 '

√

γ1 γ2

(4.38)

If the temperature and pressure of the measured gas at the time of operation and its heaviness in the standard state are different from those at the time of calibration, the correction factor is

4.1 Differential Pressure Flowmeter

191

√ K =

p1 T2 γ1 Q2 = p2 T1 γ2 Q1

(4.39)

where Q 1 and Q '2 are the indicated values of the instrument when the air being measured is standard and the flow rate value when the gas being measured is standard. Q 2 is the actual flow value of the gas being measured. p1 and p2 are the absolute pressure of the measured gas at calibration and at operation. T1 and T2 are the absolute temperature of the measured gas at calibration and at operation. Example: A rotameter is used to measure the flow of carbon dioxide gas. The temperature of the gas being measured is 40 °C and the pressure is 0.05 MPa (gauge pressure). If the meter reads 120 m3 /h, what is the actual flow rate of carbon dioxide gas? It is known that the absolute pressure at the time of calibration of the meter p1 = 0.1 Mpa and the temperature t1 = 20 °C. Solution: first calculate each value required. T1 = 273 + 20 = 293(K) T2 = 273 + 40 = 313(K) p1 = 0.1 (MPa) p2 = 0.1 + 0.05 = 0.15 (MPa) From the table of gas properties, the weight of carbon dioxide at 20 °C and 0.1 Mpa absolute pressure is γ2 = 1.842 kg force/m3 ; the weight of air at 20 °C, and 0.1 Mpa absolute pressure is γ1 = 1.205 kg force/m3 . According to Eq. (4.39), the actual flow rate of carbon dioxide gas is √ Q2 = K Q1 = √ = 120 ×

p1 T2 γ1 Q1 p2 T2 γ2

1 × 313 × 1.205 = 81.9 (m3 /h) 1.5 × 293 × 1.842

(iii) Installation of instruments and calculation of errors 1. Installation of the instrument: The rotameter must be installed vertically, and the inlet and outlet should ensure that there is a straight section of pipe longer than 5 times the diameter of the pipe. To ensure that the lower float guide bar is not bent when disassembled, the lower part of the metal pipe rotameter should have a straight pipe section that can be disassembled at the same time as the instrument. 2. Rotameter error calculation: Take the partial derivatives of all variables on the right side of Eq. (4.31); according to the indirect measurement error synthesis method, the rotameter flow rate root mean square relative error is.

192

4 Flow Testing

[ | | γ f2 γ f2 1 1 1 1 σ Q = √σa2 + σ F22 + σV2 + σ F2 f + ( )2 σγ2f + ( ) σ2 4 4 4 γf − γ 4 γf − γ 2 γ (4.40) where root mean square relative error for σa and σ F2 flow coefficients α and root mean square relative error for annular flow area. σV is the root mean square relative error of the float volume. σ F f is the root mean square relative error of the maximum cross-sectional area of the float. σγ f is the root mean square relative error of the float weight. σγ is the root mean square relative error of the measured fluid gravity. For individual calibrations, σV , σ F f , and σγ f are determined by the calibration error of the instrument, while σ F2 , although included in the calibration, can also cause additional errors due to irregularities in the drive mechanism, etc. σa Many factors are involved; for example, σa should be no less than 1% when estimated from σa0 for throttling devices. σγ is half the unit value of the last significant digit of the gravimetric table value divided by the percentage of the γ value listed in the table, which is generally very small. If changes in γ are caused by changes in the type of fluid being measured, temperature, pressure, etc., a separate correction calculation should be made, and the synthetic error for individually calibrated rotameter is typically around 2%. If a rotameter with interchangeability is to be manufactured, each of the above root mean square relative errors needs to be considered and then the total error is calculated according to Eq. (4.40).

4.1.3 Three, Bend Pipe Flowmeter (i) Principle of the bent pipe flow meter and its flow equation The bent pipe flowmeter is an unstandardized differential pressure flowmeter that has no additional pressure loss and is easy and inexpensive to install. Stable flow of fluid through the bend, due to the role of centrifugal force in the inner and outer walls of the bend, produces a pressure difference, the radius of curvature of a certain 90º bend, the square root of the pressure difference measured in the farthest position from the center of the bend and the nearest position is proportional to the flow rate of the fluid, that is, proportional to the flow rate of the fluid, which is the basic principle of the bend flow meter. Figure 4.11 is a schematic diagram of the fluid pressure distribution on the outside and inside walls of an elbow as the fluid passes through a flat lying bend with a horizontal bending surface. The pressure difference P1 − P2 reaches a maximum near the apex of the bend. In its simplest form, an elbow flowmeter is a common pipe elbow. The pressuretaking ports are usually configured on the outer and inner surfaces of the plane defined

4.1 Differential Pressure Flowmeter

193

Fig. 4.11 Pressure distribution in the tube of the bent pipe flowmeter

Fig. 4.12 Bent pipe flowmeter

by the radius of curvature of the elbow (longitudinal section) leaving the inlet face of the elbow at 45º, as shown in Fig. 4.12. The Bernoulli equation can be used to derive the flow equation for the bent pipe flow meter ( π )√ R √ D2 qm = 2ρ(P1 − P2 ) (4.41) 4 2D √ ( π )√ R 2 D2 qV = (4.42) (P1 − P2 ) 4 2D ρ where qm is the mass flow rate of the fluid through the bend. qV is the volumetric flow of fluid through the elbow. D is the internal diameter of the bend. (a) R is the radius of curvature of the bend. ρ is the density of the fluid. P1 is the outer sidewall pressure of the bend.

194

4 Flow Testing

P2 is the inside sidewall pressure of the bend. Equations (4.41) and (4.42) are theoretical flow equations derived from forced cyclonic flow theory. For the actual situation, a correction must be made so introducing a correction factor α gives )√ R √ qm = α 2ρ(P1 − P2 ) D 4 2D ( π )√ D 2 2ρ(P1 − P2 ) =C 4 √ ( π )√ R 2 2 D qV = α (P1 − P2 ) 4 2D ρ √ (π ) 2 =C D2 (P1 − P2 ) 4 ρ (π

2

(4.43)

(4.44)

√ where C = α R/2D, called the flow coefficient. The value of α is determined by the location of the pressure port configuration. When the pressure port is located away from the 90º, elbow inlet and outlet plane are 45º of the central diameter line nearest and farthest position α = 1; if the size of R and D can be accurately determined, the elbow inner diameter is equal to the inner diameter of the straight pipe, and the straight pipe length upstream of the elbow is not less than 25D, and the distribution of α values between 0.96 and 1.04, that is, the C value is directly adopted, the error is about ±4%. (ii) Use of bent pipe flow meters Due to the good reproducibility (±0.2% to ±0.1%) of the differential pressure resulting from a given flow rate, the bent pipe flowmeter is quite satisfactorily used for the detection and control system of the pressurized water reactor coolant flow. If absolute accuracy is explicitly required, the detection system needs to be calibrated for actual flow, preferably on site with the actual working fluid. For practical applications without individual calibration, if an accuracy of ±3– 5% is required, the radius of curvature of the elbow must be determined precisely, especially the inner diameter of the elbow D. The inner diameter of the elbow and the inner diameter of the connecting pipe should be equal (within 1% deviation). The upstream and downstream of the bend flowmeter should have sufficient straight pipe sections (l 1 ≥ 28D, l 2 ≥ 7D), and the pressure-taking port should be located at the outermost and innermost side of the bend on the central diameter of the bend, and the diameter of the pressure-taking port should be greater than D/ 8, while special attention should be paid to the alignment of the two pressure-taking ports.

4.2 Velocity Flow Meters

195

4.2 Velocity Flow Meters Since velocity flow measurement methods measure the volumetric flow rate by measuring the flow rate, it is important to understand the flow rate distribution of the fluid being measured and its effect on the measurement.

4.2.1 Overview of Velocity Flow Measurement Methods The velocity flow measurement method is based on the direct measurement of the flow rate of the fluid in the pipe. If the measured flow rate is the average flow rate υ in the pipe cross-section, the volume flow rate of the fluid qv = υA, A being the cross-sectional area of the pipe. If the measured flow rate is υ at a point on the pipe cross-sectionr then the volume flow rate of fluid qv = Kυ r A, K is the ratio of the average flow rate on the cross-section to the flow rate at the point being measured, which is related to the flow rate distribution in the pipe. In the case of a typical laminar or turbulent flow distribution, the distribution of the flow velocity over the circular pipe cross-section is regular, and K is a definite value. However, after local resistance members such as valves and elbows, the flow velocity distribution becomes so irregular that the value of K is difficult to determine and is usually unstable. Thus, a common feature of velocity flow measurement methods is that the accuracy of the measurement results depends not only on the accuracy of the instrument itself, but also on the distribution of the flow velocity over the pipe cross-section. In order to make the velocity distribution during measurement consistent with the velocity distribution during instrument indexing, the instrument requires sufficient straight pipe sections before and after it or the addition of a rectifier to bring the velocity distribution to that of typical laminar and turbulent flow just before the fluid enters the instrument, as shown in Fig. 4.13. For a circular pipe of radius R, in the case of laminar flow (ReD < 2300), the flow velocity distribution along the pipe cross-section due to flow stratification is Fig. 4.13 Velocity distribution in a circular tube

196

4 Flow Testing

[ ( r )2 ] υr = υmax 1 − R

(4.45)

where υ max is the maximum flow rate at the center of the pipe. υ r is the flow rate at r from the center of the pipe. r is the distance from the center of the pipe. That is, in the case of laminar flow, the flow velocity is distributed along the pipe cross-section in a parabolic fashion. From this, it can be calculated that the average flow velocity over the pipe cross-section is at r 0 = 0.7071R. This value is half of the maximum flow velocity υ max at the center of the pipe, while the flow velocity distribution along the diameter of the pipe is a parabola, with the average velocity along the diameter being given by; υ D = 23 υmax . So the average velocity over the cross-section in the laminar flow case υ is 43 times the average velocity over the diameter υ D . In the turbulent flow case, the flow velocity distribution becomes progressively flatter with increasing ReD number due to the presence of radial flow of the fluid, and the degree of flattening is also related to the roughness of the pipe. For a smooth pipe (i.e., Ks/D < 0.0004, where D is the inner diameter of the pipe and K s is the absolute roughness of the inner wall), the flow velocity distribution under turbulent flow in a circular pipe can be expressed by the following empirical equation: ( r )1/ n υr = υmax 1 − R

(4.46)

where n is a constant related to the fluid line Reynolds number ReD r is the distance from the center of the pipe.

4.2.2 Turbine Flow Meter Turbine flowmeter has the following characteristics: High accuracy with the basic error between ±0.25 and ±1.5% Large range ratio of 10:1 Small inertia in which the time constant is milliseconds. High-pressure resistance where the static pressure of the measured medium can be as high as 10 mpa. (5) The use of a wide range of temperatures in which some models can measure the flow of low-temperature medium of −200 °C, some can measure the flow of 400 °C medium flow. (6) Small pressure loss of 0.02 MPa. (7) The output is a frequency signal: It is easy to achieve flow accumulation and quantitative control, and anti-interference and other advantages. (1) (2) (3) (4)

4.2 Velocity Flow Meters

197

The turbine flow meter can be used to measure light oil (gasoline, kerosene, diesel), low viscosity lubricating oil and acid or alkali solutions that are not very corrosive. The diameter of the instrument is φ 400 ~φ 600; plug-in type can measure the flow of pipeline diameter φ 100~φ 1000; fluid cannot be combined with impurities; otherwise, the error is large, bearing wear fast, the instrument life is low, so the instrument is best installed before the filter; not suitable for measuring the viscosity of large liquids. (i) Principle and structure The turbine flow meter is essentially a turbine with zero power output, and its structure is shown in Fig. 4.14. When the measured fluid passes through, it impacts the turbine blades, causing the turbine to rotate, and the turbine speed is proportional to the flow rate within a certain flow range and at a certain fluid velocity. When the turbine rotates, the spiral blades on the turbine made of magnetically conductive stainless steel approach the detection coil on the wall of the tube. In the process, it periodically changes the magnetoelectric circuit of the detection coil, thereby producing a magnetic flux through the coil. In turn, the detection coil produces a pulse signal proportional to the flow rate. This signal is amplified by the preamplifier and transmitted to the display meter over long distances. The input pulse is then shaped in the display meter, and the pulse signal is accumulated to display the total amount on one hand, and the pulse signal is converted to current output to indicate the instantaneous flow rate on the other. The method of converting the speed of the turbine into an electrical pulse signal, in addition to the above-mentioned magnetoresistive method, can also be used. This method is known as induction method. It is designed in such a way that the rotor is made of non-permeable material, and a small piece of magnet is buried in the inner cavity of the turbine. When the magnet is driven by the turbine rotation, the detection coil fixed in the housing causes induction of the electrical pulse signal. The magnetoresistive method is relatively simple and increases the output electrical pulse frequency, which helps to improve the measurement accuracy. The function of the deflector in Fig. 4.14 is to guide the flow beam of the fluid as well as for the bearing support of the turbine. Both the deflector and the instrument housing are made of non-conductive stainless steel. In use, the performance of the bearing is the key to the service life of the turbine flowmeter. At present, the general use of stainless steel ball bearings and polytetrafluoroethylene, graphite, tungsten carbide, and other non-metallic materials made of sliding bearings, the former is suitable for clean, lubricious liquid, and gas measurement, the fluid cannot contain solid particles; the latter appropriate choice of materials can be used for non-lubricating fluids, containing tiny particles and corrosive fluid measurement, as well as due to the sudden vaporization of liquid gas and other reasons that may cause turbine high-speed operation of the occasion. (ii) Flow formula When the impeller is in equilibrium with uniform rotation and assuming that all the resistive moments on the turbine are small, the steady-state equation for turbine motion is obtained:

198

4 Flow Testing

6

5

4

3

2

v

1

Fig. 4.14 Turbine flow meter structure, 1—turbine; 2—support; 3—permanent magnet; 4—induction coil; 5—housing; 6—deflector

ω=

υ0 tgβ r

(4.47)

where ω is the angular velocity of the turbine. υ0 is the velocity of the fluid acting on the turbine. r is the mean radius of the turbine blades. β is the inclination angle of the blades to the turbine axis. The pulse frequency output from the detection coil is f = nz = or ω =

ω z 2π

2π f z

(4.48)

where z is the number of blades on the turbine. n is the speed of the turbine. υ0 =

qv F

where qv is the volumetric flow rate of the fluid. F is the effective flow through area of the meter. Substituting Eqs. (4.47) and (4.49) into (4.48) gives

(4.49)

4.2 Velocity Flow Meters

199

f = Let ξ =

f , qv

ztgβ qv 2πr F

(4.50)

ξ be called the gauge constant, then ξ=

ztgβ 2πr F

(4.51)

In theory, the instrumentation constant ξ is only related to the instrumentation structure, but in practice, the value of ξ is influenced by many factors, for example, the effects arising from bearing friction and variations in the electromagnetic resistance moment; the effect of the viscous frictional resistance moment between the turbine and the fluid, and the effect due to the different distribution of velocities along the tube cross-section. The characteristic curve of a typical turbine flow meter is shown in Fig. 4.15, and the meter is factory calibrated by the manufacturer to give its average value over the allowable flow measurement range. Thus, the relationship between the total amount of fluid flowing through qv in a given time interval and the total number of output pulses N is qv =

N ξ

(4.52)

As can be seen from the figure, at small flow rates, the instrumentation constant ξ drops sharply because of the relatively large resistance moment present, and in the transition zone from laminar to turbulent flow, the peak value of ξ appears in the characteristic curve because the fluid viscous frictional resistance moment is smaller in laminar flow than in turbulent flow; when the flow rate increases again, the rotational moment greatly exceeds the resistance moment, so the characteristic curve rises slightly but is nearly horizontal. Usually, the instrument is allowed to be Fig. 4.15 Turbine flowmeter characteristic curve

ξ 100 99 98

0

20

40

60

80

100

qv

200

4 Flow Testing

used in the flat part of the characteristic curve so that the linearity of ξ is within ±0.5% and the reproducibility is within ±0.1%. Due to the existence of viscous resistance moment, the characteristics of the turbine flowmeter by the fluid viscosity change, especially at low flow rates, and small diameter is more significant, so the turbine flowmeter should be calibrated for real liquid. Manufacturers often give the instrument for different fluid viscosity range when the lower limit of flow measurement, to ensure that the linearity of the instrument constants within the allowable measurement range is still within ±0.5%. When measuring fuel flow with a turbine flow meter, it is important to keep the oil temperature approximately constant so that the viscosities are approximately equal. In order to reduce the effect of uneven flow velocity distribution in the pipe, it is necessary to ensure that the flow velocity distribution in front of the meter is not distorted by local resistance, with a straight pipe section of more than 15D before the meter and more than 5D after the meter, where D is the diameter of the pipe, if necessary to add a rectifier. Before the instrument should be installed with a screen to prevent impurities from entering, and the instrument should be used with special care not to exceed the maximum operating temperature, pressure, and speed specified. For example, in the use of high-temperature steam cleaning process, pipeline often make turbine flowmeter damage, so must be installed bypass, so that the flushing steam does not pass through the instrument. In addition, the flowmeter should be installed horizontally, because vertical installation will affect the characteristics of the meter. The meter should be fitted with a check valve to prevent the turbine from reversing. (iii) Display instruments The display instrument of a turbine flow meter is actually a pulse frequency measuring and counting instrument which displays the number of pulses per unit time and the total number of pulses over a period of time from the output of the turbine flow transmitter in terms of instantaneous flow and cumulative flow. There are many types of this type of display meter, and the block diagram of the operating principle of one type of display meter is shown in Fig. 4.16. It is composed of a shaping circuit, a frequency instantaneous indication circuit, a meter constant division operation circuit, an electromagnetic counter and an automatic zero return circuit, an in-unit oscillator, and a power supply. The rectification circuit is an emitter-coupled bistable circuit that shapes the pulse signal from the transmitter preamplifier into a square wave signal with a certain amplitude and satisfying the pulse front requirement. As shown in Eq. (4.52), the total amount of fluid flowing over a period of time qv equals the total number of pulses N divided by the meter constant ξ. The value of ξ is different for different turbine flow transmitters and is given by calibration at the factory, so a transformable coefficient has to be set to divide with the number of output pulses in order to convert the number of pulses into the total number of fluids, and these are done by the meter constant division operation circuit. The circuit consists of a four-digit decimal counter trigger, a coefficient setter, and a with gate. The four outputs of the four count triggers are connected to each of the four

4.2 Velocity Flow Meters

201

Fig. 4.16 Diagram showing how the meter works

levels of the four band switches to become the coefficient setters. According to the ξ value of the matching turbine flow transmitter, the corresponding ξ value between 0 and 9999 can be set on the band switch. When ξ pulses are input to the shaping circuit, the division circuit outputs a pulse signal through the with gate that drives the electromagnetic counter to go one word indicating that one unit volume of fluid has flowed. This signal pulse also triggers a return-to-zero monostable, which resets the individual counting triggers to zero, ready to continue counting next time. If ξ carries a fractional number, the constant is set to be integerized by multiplying by 10m (m is a positive integer). And the total number of flow rates noted by the counter is also multiplied by 10m , e.g., if the transmitter meter constant ξ = 16.25 [pulses/ liter] and the factor is set to 1625 and N c words are noted over a period of time, the total amount of flow over that period of time qv = Nc × 102 .

202

4 Flow Testing

Frequency instantaneous indication circuit is the role of the shaped pulse frequency linearly converted to current output, through a microamp meter to indicate the instantaneous flow, the meter scale to the frequency (Hz) number of divisions, the indicated frequency value f divided by the matching turbine flow transmitter instrumentation constant to obtain the instantaneous volume flow qv value. The instrument can be self-calibrated by toggling the switch to the calibration position and supplying a constant frequency pulse signal from the multi-harmonic oscillator in the instrument or by using a 50 Hz frequency signal from the power grid.

4.2.3 Three, Vortex Flowmeter Due to the wide measuring range of vortex flowmeter (the larger the meter diameter, the wider the measuring range, generally up to 100: 1), resistance, with digital output, its simple structure and easy installation, maintenance, the output signal is not affected by fluid pressure, temperature, viscosity and density, and other advantages, is being widely noted. The current accuracy is about ±0.5 to l% or so. The flowmeter is more convenient for flow measurement in large diameter pipelines (such as flue exhaust and natural gas flow measurement), and this flowmeter accounts for about 3–5% of the flowmeter market. According to the measurement, principle can be divided into volumetric and mass type; according to the detection method, it is divided into thermal, pressure, capacitive, ultrasonic, vibration, photoelectric, fiber optic type, etc. (i) Principle and structure When a non-streamlined column with a symmetrical shape is placed in the fluid, vortices alternate on the downstream side of the column, rotating in opposite directions and separating from the column in turn, forming a vortex column on the downstream side, also known as a “Carmen vortex street”, as shown in Fig. 4.17. It is experimentally demonstrated that the following relationship is satisfied when the longitudinal distance between the vortices h and the lateral distance are l ( sh

πh l

) =1

(4.53)

i.e., hl = 0.281 The asymmetric “Carmen vortex street” is stable when the vortex is not in the vicinity of the column. It has been shown through extensive experiments that the frequency f of vortex generation on one side is proportional to the fluid flow velocity v near the column and inversely proportional to the characteristic size of the column d, i.e.,

4.2 Velocity Flow Meters

203

h

v d

v

l

(a)

d

h l

(b)

Fig. 4.17 Occurrence of “vortex street”. a Cylinder, b equilateral triangular column

f = St

v d

(4.54)

where St is the number of uncaused events and is called the Strohal number. St is a function of the fluid Reynolds number Re D calculated with the column characteristic size d. And it is found that when Re D is in the range of 2 × 104 ~ 7 × 106 ,St is essentially constant. St The value of is 0.2 for cylinders and 0.16 for equilateral triangular columns. So once the shape and size of the column is decided, the flow rate and flow rate can be measured by determining the unilateral vortex release frequency f . For industrial circular tubes, vortex flow meters are generally used in the range Re D = 1000 to 100,000. Let the ratio of the pipe through-flow cross-section with and without the insertion of a column in the pipe be m. For a circular pipe of diameter D, it can be shown that ⎛ √ ⎞ ( )2 d 2⎝d d m =1− 1− + sin−1 ⎠ (4.55) π D D D / When d D < 0.3 m ≈ 1 − 1.25

d D

(4.56)

204

4 Flow Testing

According to the continuity of flow, the average flow velocity in the tube with a column v and without a column v¯ is inversely proportional to the flow cross-sectional area of both, i.e., v¯ =m v

(4.57)

Substituting Eqs. (4.56) and (4.57) into (4.54) yields the frequency of vortex occurrence in a circular tube f versus the average flow velocity in the tube v¯ as f =

v¯ St × d (1 − 1.25 D ) d

(4.58)

Therefore, the relationship between volume flow rate and frequency f is qV =

( ) d fd π D2 π D2 1 − 1.25 v= 4 4 D Sr

(4.59)

Let ξ be the meter constant, then ξ=

4St − 1.25 Dd )

π D 2 d(1

(4.60)

(ii) Detection of frequency signals Vortex frequency signal f detection methods are many, can use the vortex occurs when the heat of the body heat dissipation conditions change thermal detection; also available vortex generation when the vortex generates differential pressure on both sides of the vortex generator to detect, differential pressure signal can be sent through capacitive or strain gauge variable transmission, etc. For example: triangular column vortex flowmeter, in the middle of the triangular column body of the flow surface symmetrically embedded in two thermistors, because the triangular column surface coated with ceramic coating, so the thermistors and the column body is insulated. A constant current is passed through the thermistors so that their temperature is about 10 °C higher than the fluid being measured when the fluid is stationary. When swirling does not occur on either side of the triangular column, the two thermistors have the same temperature and equal resistance. When the vortex occurs alternately on both sides of the triangular column, the vortex occurs on one side of the fluid due to the vortex energy loss, and the flow rate is lower than the other side, so the heat transfer conditions become worse, so that this side of the thermistor temperature increases, and the resistance value becomes smaller. With these two thermistors as the adjacent arm of the bridge, the bridge diagonal on the output of a series of voltage pulses corresponding to the frequency of the vortex. After amplification,

4.2 Velocity Flow Meters

205

Fig. 4.18 Block diagram of a triangular column vortex flow meter

shaping to get the corresponding pulse digital output with the flow, or use the “pulse – voltage” conversion circuit converted to analog output for indication and totalization. Triangular column vortex flowmeter principle block diagram is shown in Fig. 4.18. (iii) The use and installation of vortex flowmeter 1. Flow coefficient According to Eq. (4.59), the flow coefficient is K =

( ) d π D2d qV 1 − 1.25 = f 4St D

(4.61)

The range, linearity, and reproducibility of the flow meter depend on the characteristics of the flow coefficient K. From Eq. (4.61), it can be seen that the characteristics of the flow coefficient K depend on the Strohal number S t , while S t is determined by different ReD . Different vortex generating body types have different Strohal numbers. It generally has the following pattern. (1) For Reynolds numbers above the critical value ReD , the Strohal number S t values do not vary by more than ±1%, when the ReD values are approximately 5000 to 10,000. The reproducibility error of S t is generally less than ±0.2%. (2) Linearity deteriorates below ReD , which determines the minimum flow rate to ensure accuracy. A larger minimum flow rate for small diameter vortex flow meters.

206

4 Flow Testing

(3) The minimum flow rate should be large when the viscosity of the fluid to be measured is high; otherwise, measurements cannot be made at Reynolds numbers below ReD (4) When the viscosity changes due to fluid temperature changes, ensure that the Reynolds number at the lowest flow rate is greater than ReD . 2. Pressure loss: In the vortex flowmeter vortex generator to account for part of the flow cross-section, so there is a throttling effect, and due to the generation of vortex, all make the actual fluid flow to produce energy loss, expressed as pressure loss. Compared with some other flow meters, the pressure loss is small. Pressure loss varies with the shape of the vortex generator and the ratio of the flow cross-section. 3. Installation. (1) In order to ensure the measurement accuracy, the flowmeter installation position before and after the necessary straight pipe section. Upstream side if there is a reduction resistance pieces to have 15D straight pipe section; if there is the same plane elbow to have 20D straight pipe section; if there is a valve to have 50D straight pipe section. Straight pipe sections on the downstream side shall be 5D or more. (2) Vortex flowmeter can be installed horizontally, vertically, or in other positions, but when measuring liquids, if it is installed vertically, it should make the liquid flow from the bottom up to ensure that the pipeline is always filled with liquid. (3) To be installed on a line free of shock and vibration. For steam lines, there may be shocks and vibrations, and therefore, brackets should be installed. Although the construction of vortex flow meters is more resistant to shock and vibration than most other flow meters, they should be installed in locations where shock and vibration are as low as possible. (4) Surrounding temperature and gas conditions should also be considered. Sources of high-temperature heat radiation in the surroundings should be avoided as far as possible. Areas with large variations in ambient temperature should also be avoided. If it is difficult to avoid, insulation measures should be taken. Also try to avoid the presence of corrosive gases in the surrounding area. (5) Although the waterproof vortex flowmeter has a fairly good waterproof structure, do not use it submerged in water. 4. Calculation of the range of use of vortex flow meters. (1) Calculation of the range. The general range of flow velocity when measuring liquids is 0.38–6 m/s, and the range of flow velocity when measuring gases is 4–60 m/s. (2) Adjustment of secondary instrumentation. According to

4.2 Velocity Flow Meters

207

f =

qV = ξ qv K

(4.62)

Based on the ξ value (number of pulses/liter) obtained during the calibration of the meter and the maximum flow rate of the meter qV (l/sec), the pulse frequency to be fed to the secondary meter at the maximum flow rate can be calculated from Eq. (4.62). Use the digital frequency meter to adjust the output frequency of the audio signal generator to correspond to the number of pulses sent to the secondary meter at the maximum flow rate; when sent to the secondary meter at this frequency, the output of the secondary meter should be the maximum flow rate value.

4.2.4 Electromagnetic Flowmeter The electromagnetic flowmeter has no moving parts and no flow blockers inserted into the pipe, so the pressure loss is extremely small. Its flow rate measurement range is wide (0.5–10 m/s), the caliber from 1 mm to more than 2 m, rapid response, can be used to measure pulsating flow, bidirectional flow, and such as mortar and other liquids containing solid particles flow. (i) Structure and working principle The principle of the electromagnetic flow meter is Faraday’s law of electromagnetic induction. Figure 4.19 is a schematic diagram of its construction. There is a pair of magnetic poles on either side of the working pipe and another pair of electrodes mounted on a plane perpendicular to the magnetic lines of force and the pipe. When the conductive fluid flows at an average velocity υ¯ through a Fig. 4.19 Schematic diagram of electromagnetic flowmeter structure

208

4 Flow Testing

measuring pipe section of diameter D cutting the magnetic lines of force, an induced potential is generated at the electrodes E, and the direction of the potential can be determined by the right hand rule. If the magnetic field has a magnetic induction of, the potential B E = C1 B D υ¯

(4.63)

where C1 is a constant. Because the volumetric flow rate through the meter qv =

1 π D 2 υ¯ 4

(4.64)

Combining Eqs. (4.63) and (4.64) yields qv =

D π × E 4C1 B

or E = 4C1

B qv = K qv πD

(4.65)

where K is the meter constant of the electromagnetic flow meter; K = 4C1 πBD . When the meter aperture D and the magnetic induction strength B are constant, K has a linear relationship between the induced potential and the fluid volume flow. In order to avoid the effect of polarization and contact potential difference, industrial electromagnetic flowmeter usually uses alternating magnetic field, and the disadvantage is that the interference is larger. The use of DC magnetic field for a true reflection of the rapid changes in flow is beneficial, so it is suitable for special occasions such as laboratories or used to measure non-electrodynamic liquids that do not cause polarization phenomena, such as liquid metals. The electrode is flush with the tube liner, and the electrode material is often made of non-permeable stainless steel, but also made of platinum, gold or platinum-plated, gold-plated stainless steel. The structure of the excitation coil for generating the alternating magnetic field varies according to the diameter of the conduit, and the one shown in Fig. 4.20 is suitable for large diameter conduits (100 mm or more). When an alternating magnetic field is used, the magnetic induction strength B = Bm sin ωt, then Eq. (4.63) becomes E = C1 Bm D υ¯ sin ωt

(4.66)

where Bm is the amplitude of the magnetic induction. ω is the angular frequency of the alternating magnetic field. Since it is always possible for the alternating flux to pass through the loop formed by the conductive liquid being measured, the electrode leads and the induced potential

4.2 Velocity Flow Meters

209

Fig. 4.20 Schematic diagram of electromagnetic flowmeter receptor structure, 1—tube and flange; 2—housing; 3—saddle-shaped excitation coil; 4—yoke; 5—electrode; 6—liner

(a) 3

2

1

5

4

6

(b)

measuring instrument, etc., and produce an interference potential in this loop et , the magnitude of the interference potential is et = −C2

dB dt

(4.67)

Since B = Bm sin ωt, the above equation is ( π) et = −C2 Bm sin ωt − 2

(4.68)

It can be seen that the signal potential E and interference potential et of the same frequency and phase difference of 90°, so called this interference for orthogonal interference, serious when its value can be equivalent to the signal potential or even more, so to achieve the measurement must eliminate this interference. Eliminate the method in addition to the electrode leads, such as the formation of the plane

210

i2 i1

Φ1 Φ2 Φ2 Φ1 T2 T1

v R st

Fig. 4.21 Schematic diagram of the zeroing potentiometer

4 Flow Testing

of the circuit as far as possible and the magnetic lines of force parallel, so as to avoid the magnetic lines of force through this closed circuit, in addition, also has a zeroing potentiometer, as shown in Fig. 4.21. The two leads from one electrode form two closed loops, and the interference potential generated by the magnetic lines passing through these two loops is in opposite phase, and by adjusting the zeroing potentiometer, they can cancel each other out, thus reducing quadrature interference. (ii) Converter for electromagnetic flowmeter Generally, the output AC-induced potential signal E is passed through the conversion section and converted to a uniform DC signal output of 0~10 mA for display and recording. Due to the high internal resistance of the sensing part of the electromagnetic flowmeter, the conversion part is required to have a high input impedance and a strong anti-interference capability. For example, using the principle of negative feedback, take out the quadrature interference potential from the amplifier output signal of the conversion part, and give it deep negative feedback to the input of the amplifier to further eliminate the influence of quadrature interference. In addition, to eliminate the effect of changes in the electromagnetic induction intensity B on the output, the output-induced potential E must be multiplied by l/B so that the output signal is independent of B. The schematic block diagram of the conversion section is shown in Fig. 4.22.

Fig. 4.22 Schematic block diagram of the conversion section, 1—preamplifier 2—main amplifier 3—orthogonal interference suppression 4—phase-sensitive rectification 5—power amplifier 6— coil 7—hall multiplier 8—potentiometer divider

4.2 Velocity Flow Meters

211

The induction potential E is compared with the negative feedback voltage V f to get the difference signal, ε after preamplifier, main amplifier, phase-sensitive rectifier, and power amplifier to get 0~10 mA DC current, I0 through the coil to generate magnetic induction intensity B y ,B y = K 1 I0 on a Hall multiplier B y multiplied by the control current I y . The control current I y is taken from the same source as the excitation current I A of the alternating magnetic field in the electromagnetic flow meter and is proportional to I A , i.e., I y = K × B. The output Hall potential of the multiplier VH is the resulting product, VH = K I y B y = K H K 1 K 2 B I0 , where K H is the multiplication factor of the Hall multiplier VH . After dividing the voltage the feedback voltage is obtained and V f = K 3 VH K 3 is the dividing factor. From Fig. 4.22, the relationship between the differential signal ε and the output current I0 is I0 = A1 A2 A3 A4 ε = Aε

(4.69)

where A is the amplification factor for the forward main channel. A1 , A2 , A3, A4 is the amplification factor of each amplifier and the transfer coefficient of the phase-sensitive rectifier. In the feedback channel, the feedback voltage V f is related to the output current as V f = K H K 1 K 2 K 3 B I0 = β I0

(4.70)

where β is the transfer coefficient of the feedback channel. According to Eqs. (4.69) and (4.70), we can get I0 = Aε = A(E − V f ) = A(E − β I0 ) = AE − Aβ I0 That is, I0 /E =

A 1 + Aβ

(4.71)

When the amplification factor of the forward main channel amplifier is large, i.e., Aβ⟩⟩1, then I0 /E =

1 1 = β KH K1 K2 K3 B

(4.72)

Substituting Eq. (4.65) into the above equation, we get I0 =

1 4C1 × qV πD KH K1 K2 K3

(4.73)

212

4 Flow Testing

The resulting current signal from the conversion section I0 is proportional to the volumetric flow rate and eliminates the effect of variations in magnetic induction B due to the supply voltage on the measurement. (a) the installation and use of electromagnetic flowmeter (1) Electromagnetic flowmeter should be installed in an environment without strong electromagnetic fields, and there should be no large electrical equipment nearby. (2) The “ground” of the transmitter should be connected to the measured fluid and the “ground” of the converter with a wire and buried deep underground with a grounding wire, the grounding resistance should be small, and there should be no ground current at the grounding point. (3) In order to ensure that there is no sediment or (3) in order to ensure that no deposits or air bubbles accumulate in the transmitter, the transmitter is best installed vertically, the measured fluid flows from the bottom up. If conditions do not allow, the transmitter should also be lower than the outlet pipe to avoid the accumulation of gas. (4) In order to ensure the symmetry of the measured fluid flow, there should be a certain length of straight pipe section before the transmitter. If there are elbows, tees, reducers, etc. on the upstream side, a straight section of 5 times the diameter of the pipe should be added before the transmitter; if there are various valves, there should be a straight section of 10 times the diameter of the pipe, and the downstream side can be shorter. (5) For the convenience of servicing the transmitter and zeroing the instrument, the transmitter should be bypassed with a bypass tube, which will allow the transmitter to be filled with non-flowing measured liquid and facilitate zeroing of the instrument. (6) The signal line should be worn separately into the grounded steel pipe and never allowed to wear in a steel pipe with the power supply. Signal line must use shielded wire, the length must not be greater than 30 m. If the requirement for longer signal lines, must take certain measures, if the use of double shielded wire, shielding tends to move, etc. (7) The flow direction of the measured liquid should be the direction specified by the transmitter; otherwise, the flow signal phase shift 180°, phasesensitive wave detection cannot detect the flow signal, and the instrument will have no output. The measured liquid flow rate also has a certain limit, the minimum flow rate cannot be less than 10% of the range of the instrument, and the highest flow rate is best not to exceed l0 m/s. When measuring liquids that can severely wear the lining, the maximum flow rate should be reduced to 3 m/s. (8) The lower limit of the conductivity of the liquid under test is determined by the input impedance of the converter. If the input impedance is 100 megohms, the conductivity of the liquid under test must not be less than 10 μm ohms/cm.

4.2 Velocity Flow Meters

213

(9) Cannot measure liquids with very low conductivity, such as petroleum products, organic solutions. (10) Cannot measure gases, vapors, and liquids containing a large number of larger air bubbles.

4.2.5 Ultrasonic Flow Meter In the last decade or so, the development of electronic technology has made ultrasonic flowmeter practical applications and rapid development and increasingly perfect. Ultrasonic flowmeter can be based on different principles: such as Doppler frequency shift method, acoustic beam offset method, flow rate level method, velocity difference method, etc. Here, we only introduce the velocity difference method, the measurement principle is: in the fluid ultrasonic waves to the upstream and downstream propagation velocity due to superimposed fluid flow velocity and not the same, so you can measure the fluid velocity based on the difference between the ultrasonic waves upstream and downstream propagation velocity. (i) Speed-of-dissemination method It has more measurement methods, which can be divided into: the time difference method, the phase difference method, and the frequency difference method for measuring the ultrasonic signals received at such distances up and downstream of the ultrasonic transmitter. 1. Time difference method: let the speed of sound in a stationary fluid be c, the fluid flow velocity be υ, and the distance between the sender (T) and receiver (R) be L. The propagation time difference. L 2Lv 2Lυ L − = 2 ≈ 2 2 c-υ c+υ c −υ c (when c is much larger than υ)

Δt = t2 − t1 =

where c L- υ is the counterflow time; 2. Phase difference method

L c+υ

(4.74)

is the down-flow time (Fig. 4.23).

L

Fig. 4.23 Principle of ultrasonic flow velocity measurement

v

T1

R1

R2

T2

214

4 Flow Testing

If the generator emits a continuous sine wave, the phase difference between the waves received upstream and downstream is Δϕ = ω × Δt =

2Lv c2

(4.75)

where ω is the angular frequency of the ultrasound. From the above two methods, it can be seen that υ can be found as long as Δt or Δϕ is measured, but in both methods, the speed of sound c is included, and c is related to the composition of the fluid, temperature, etc. and needs to be compensated. For example, if the temperature coefficient of the speed of sound c in water is 0.2%/°C, the temperature coefficient of Δt or Δϕ will be 0.4%/°C when the flow rate is certain, resulting in measurement error, so temperature compensation is required. 3. Frequency difference method Let f 1 = t11 , f 2 = t12 . Then Δ f = f1 − f2 =

1 1 2v − = t1 t2 L

(4.76)

If the frequency difference Δf is measured, the flow velocity can be found, and the sound velocity c is eliminated from the measurement equation. f 1 , f 2 are obtained by the echo method and the recently developed TLL method using the phase-locking technique. (1) Echo method working process First of all, let us introduce the ultrasonic oscillator: it is made of piezoelectric materials such as lead zirconate titanate ceramics, which receives ultrasonic signals by piezoelectric effect (converting ultrasonic waves into electrical pulses) and sends ultrasonic signals by using electrostriction effect (converting electrical pulses → mechanical stretchability → ultrasonic waves). Figure 4.24 shows the schematic diagram of the echo frequency difference ultrasonic flow meter. In the figure, the transducers TR1 , TR2 are installed outside the tube and controlled by the controller to act as transmitter and receiver alternately. When TR1 acts as the transmitter, the emitted ultrasonic pulse is received by TR2 through the tube and converted into an electrical pulse, which immediately amplifies and triggers TR1 to emit another acoustic pulse, and so on in a continuous cycle, forming a downstream echo loop. The echo frequency f 1 is the reciprocal of the propagation time t 1 If the average velocity of the fluid in the pipe is υ 0 , υ D is the average flow velocity of the fluid in the path of ultrasonic wave propagation, the angle between the ultrasonic wave beam and the pipe axis is θ, the speed of sound in the stationary fluid is c, and the diameter of the pipe is D, then

4.2 Velocity Flow Meters

215

Fig. 4.24 Schematic diagram of an echo frequency difference ultrasonic flow meter, 1—transmitting/receiving switch; 2—transmitting/receiving amplification; 3—frequency doubling; 4— controller; 5—counting storage; 6—A/D; 7—indicating; 8—recording

f1 =

]−1 [ 1 D/sinθ +τ = t1 c + υ D cos θ

(4.77)

where τ is the fixed delay time, which is the sum of the propagation time of the sound wave in the sound wedge and the wall of the pipe and the circuit delay time. Similarly, when TR2 transmits and TR1 receives, a countercurrent echo loop is formed along the countercurrent direction, and the echo frequency is f2 =

]−1 [ D/sinθ 1 +τ = t2 c − υ D cos θ

(4.78)

So Δ f = f1 − f2 = υD =

υD υ0

(4.79)

[D + τ csinθ ]2 Δf Dsin2θ

(4.80)

π D2 υ0 4

(4.81)

qv = Let

sin2θ ]2 υ D [ D 1 + τDc sinθ

= k (k is the flow correction factor) then [ ] 1 π D(D + τ c sin θ )2 π 2 D υ0 = Δf qv = 4k k 4 sin 2θ

(4.82)

The actual frequency difference Δf is very small, so Δf must be multiplied to improve the measurement accuracy. From Eq. (4.87), it can be seen that the frequency difference method is used for out-of-tube installation measurements, and due to the presence of a fixed delay time

216

4 Flow Testing

Fig. 4.25 Phase-locked loop ultrasonic flowmeter schematic

τ, the measurement results are still influenced by the sound velocity c, and there is a certain amount of sound velocity temperature error. (2) Frequency difference method of phase-locking technique (time -locked loop, TLL method) θ Δτ The frequency method is used for the error caused by the variation of τ δθ = 2c sin D increases with decreasing pipe diameter. If the variation of τ Δτ = 0.2 μs, δ θ is 0.18% at θ = 23° and D = 0.3 m, and if D = 3 mm, δ θ will reach 1.8%, so the frequency difference method is difficult to achieve high accuracy at small tube diameter, while the time difference method can measure the time difference after expanding it by using the phase-locking technology or echo technology, and the speed of sound c in the measurement equation can also be compensated by the calculation circuit, and the τ in the time difference is offset. Therefore, in small diameter flow measurement, the time difference method is widely used because of its high accuracy. Figure 4.25 shows the schematic diagram of a phase-locked loop (TLL)-type ultrasonic flow meter. The basic operating process is: when the switching loop is designated in downstream, the ultrasonic pulse is emitted from the upstream side to the downstream side under the action of a start signal synchronized with the frequency f 1 of the VC0-1 voltage-controlled oscillator, while the counter starts counting the frequency signal f 1 coming from V C0-1 , and when the counter counts to the set number N, the end-of-count signal is given, and the time required for this period is N/f 1 , and then this end-of-count signal is delayed in the time delay loop is delayed by τ 01 , and then compared with the ultrasonic propagation time t 1 + τ expressed by the receiver wave in the time difference detection loop. The time signal from the receiver in addition to the liquid propagation time t 1 also has the ultrasonic wave through the tube wall and acoustic wedge time τ. If τ 01 = τ, the time difference signal of N/f 1 + τ 01 and t 1 + τ is compared to N/f 1 − t 1 , which is fed back to V C0-1 to control its frequency so that the time difference N/f 1 − t 1 = 0 ( f 1 = N/t 1 ), thus forming a closed loop. Conversely, the switching loop specifies that in the case of countercurrent, the second

4.2 Velocity Flow Meters

217

TLL makes N/f 2 − t 2 = 0 ( f 2 = N/t 2 ); the frequency difference between the two V C0 ’s is Δf . D/ sin θ D/ sin θ Because t1 = c+υ = f11 , the t2 = c−υ = f12 D cos θ D cos θ Δ f = f1 − f2 =

N N sin 2θ N υD − = t1 t2 D

(4.83)

D 1π 2 D Δf (4.84) k4 N sin 2θ √ k = υυD0 (k = 4/3 for laminar flow and k = 1+0.01 6.25 + 431Re−0.237 for turbulent flow as a function of Re.) where υ D is the average fluid flow velocity in the path of ultrasound propagation. υ 0 is the average fluid flow rate along the pipe cross-section. If further comparison of f 1 , f 2 in the circuit can also identify the direction, it follows that the essence of the working principle of the phase-locked frequency difference method is as follows: qv =

1. Working principle: Phase-locked loop is a time-synchronous loop. The role of TLL is to convert the ultrasonic wave through the liquid in the pipe propagation time t to the reciprocal 1/t (i.e., echo frequency) and then use phase-locked loop technology to control the pressure oscillator V C0 , so that the frequency f of V C0 is the echo frequency 1/t N times, in this way to form a closed loop. Because the downstream and countercurrent propagation time of ultrasonic waves are different, so the frequencies of two V of downstream and countercC0 urrent are also different, and their frequencies f 1 , f 2 are N times of the downstream and countercurrent echo frequencies (1/t 1 ,1/t 2 ) respectively, and the flow rate can be known by detecting the frequency difference Δf of f 1 and f 2 . Therefore, the TLL-type ultrasonic flowmeter measures the time difference of ultrasonic wave propagation but gives the echo frequency difference after N times the frequency, so it integrates the advantages of the fast response of the time difference method and the convenient measurement of the frequency difference method, which is less affected by the speed of sound. Therefore, after the frequency difference method and the time difference method, both use information processing technology to ensure stable operation of the circuit. To ensure reliable operation in various environments, additional circuits are used to process the received information, resulting in a qualitative leap in the stability of the instrument. (1) Receiving wave loss holding circuit: When the fluid is mixed with impurities and bubbles, the ultrasonic wave propagation is obstructed, so that the detection wave level is lower than a certain value, the receiving wave loss holding circuit composed by the comparison circuit will act to cut off the control circuit to V C0 , so that the frequency of V C0 remains at the oscillation frequency f 1 , f 2 at the moment before the cut off, so the differential frequency signal Δf = f 1 − f 2 also remains at the original value This eliminates the influence on the output caused by the ultrasonic beam being blocked, so that the instrument can work

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4 Flow Testing

stably even if the medium is sewage. When the received wavelength time is lost due to a phenomenon such as a large cavity in the pipe, an alarm signal is issued through the timing circuit. (2) AGC circuit: The AGC circuit is used to control the amplifier gain, which can maintain a certain amplitude of the received wave after receiving amplification in the occasion of sound wave attenuation change. It can be used with (1) circuit to make the output stable and improve the measurement accuracy. (3) TLL monitoring control circuit: Used to monitor the stability of all actions of the basic circuit in the TLL mode. The final output signal is given only when it is stable. When it is unstable, the original output is maintained. Unlike the simple output damping circuit, it maintains the fast response characteristics. The reliability and stability of the ultrasonic flowmeter have been greatly improved, the impact of air bubbles and particulate impurities reduced, not only to measure sewage, but also expanded to industrial media other than water, and to the development of high-temperature media (250 °C). 2. Performance and applications (1) High measurement accuracy for large pipe diameters (±1% of full scale for D > 0.8 m, ±1.5% of full scale for 0.3 < D < 0.8 m, and not guaranteed for D < 0.3 m). (2) Fast response: A continuous frequency output is obtained (2.5 ms response time at D = 1 m and 400 times/s correction of the frequency of V C0 ). (3) Wide range of applications (the instrument works stably even if there are foreign objects in the fluid because of the receive-wave loss-hold circuit). (4) Easy installation (clip-on transducer). (5) Applicable measurement pipe diameter range D = 300 ~3000 mm water flow, flow rate range 0~1 to 0~10 m/s, temperature 0~40 °C, pipe: steel pipe, cast iron pipe, stainless steel pipe can be lined, L1 ≥ 10D, L2 ≥ 50D (to meet the typical velocity distribution cross-section in order to determine the relationship coefficient between the measured fluid flow rate and the flow rate represented by the ultrasonic output signal). (ii) Ultrasonic flowmeter measurement error and correction (1) Changes in the speed of sound c due to changes in temperature (T ), composition, concentration, etc. of the measured medium, which in turn causes errors in the measurement υ. Elimination method: by choosing the measurement principle or adding information processing in the line and taking it into account in the structure. (2) Inconsistency in the parameters of the dual acoustic channel. Such as mechanical size and electrical characteristics asymmetry, the measured medium flow condition changes (inconsistent), and electronic circuit asymmetry. Or although

4.2 Velocity Flow Meters

219

mono, but the above parameters in the downstream, countercurrent inconsistency caused by the measurement error. Elimination method: Structural inconsistencies can be eliminated by precise design and processing. Due to the progress of electronic technology, the switching method of mono system is basically used now. The new TLL method reduces the measurement period to a few milliseconds, and the flow can be switched hundreds of times per second between downstream and countercurrent without significant changes in flow conditions in such a short period of time. (3) The error arising from the inconsistency between the actual flow velocity distribution on the liquid flow cross-section in the pipe and the ideal flow velocity distribution; i.e., the flow equation q = π4 D 2 υ0 in υ 0 is the average flow velocity along the pipe cross-section while the ultrasonic measurement is the line average flow velocity on its propagation path υ D , if set υυD0 = k, in laminar flow k = 4/ √ 3; turbulent flow k = 1 + 0.01 6.25 + 431Re−0.237 as a function of Re. The calculations show that if the range of variation of Re does not exceed 10 times, the value of k calculated by taking the average Re, the corresponding variation does not exceed 0.5%, and if the range of variation of Re does not exceed 25–30 times, the error in the variation of k does not exceed 1%. Therefore, it is difficult to guarantee measurement accuracy in fluids with alternating Re. (iii) Comparison of time difference method, phase difference method, and frequency difference method Time difference method: Convenient measurement, short cycle time, fast response (1 m pipe diameter, 2.5 ms) suitable for large pipe diameter measurement. Phase difference method: The measurement technique is complicated, and there is also the effect of the speed of sound, so the practical application is less. Frequency difference method: If the transducer is installed inside the tube, the effect of the speed of sound c is eliminated in principle. If the transducer is installed outside the tube, it is still influenced by the speed of sound c, but less than the time difference method. Disadvantages: Slow response, so cannot be used for real-time measurement; if the echo ring is blocked by the vapor bubbles and particles in the liquid, the sampling cycle cannot be measured AND cannot get the measurement results, so it can only be used to measure the flow of clean water. (iv) Advantages of ultrasonic flow meters (1) Non-contact, small pressure loss, can measure without any processing of the original pipeline, simple structure. (2) The measurement results are not affected by the measured liquid, viscosity, conductivity, etc., and can measure the flow of fluid in a very large diameter pipe. (3) The output signal is linear with the measured fluid flow.

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4 Flow Testing

4.3 Mass Flow Meters In order to meet the requirements of process control and cost accounting in production, it is often necessary to know exactly what the mass of the fluid flowing through is, and therefore mass flow meters that can directly determine the mass flow of the fluid are required. The flowmeters we described earlier are instruments that directly measure the volume flow rate or whose output signal is directly related to the density of the fluid (such as differential pressure flowmeters), so it is not possible to obtain an accurate value of the mass flow rate in the case of a change in the density of the parameter being measured. At present, mass flow meters in general can be divided into two categories: (1) direct mass flow meters: direct detection of the measured fluid mass flow, such as calorimetric mass flow meters, differential pressure mass flow meters, gorse force mass flow meters; (2) indirect mass flow meters: through the combination of volume flow meters and density meters to measure mass flow, or through the measurement of the measured fluid volume flow, temperature, and pressure.

4.3.1 Direct Mass Flow Meter The mass flow rate of the fluid is qm = Aρυ

(4.85)

where A is the flowmeter through-flow area;ρ is the fluid density; υ is the average flow velocity of the fluid in the cross-section. If the through-flow cross-section A is constant, measuring ρυ gives qm , and ρυ actually represents the momentum per unit volume of fluid. 1. Dual turbine mass flow meters As shown in Fig. 4.26, two turbines connected to each other by springs are in a pipe back and forth, and their blades have different inclinations, θ 1 and θ 2 , respectively. When fluid flows through the two turbines, the rotational moments applied to the turbines are M 1 and M 2 M1 = K 1 qm υ sin θ1

(4.86)

M2 = K 2 qm υ sin θ2

(4.87)

where k 1 , K 2 are device constants; qm is the mass flow rate through; υ is the fluid flow rate through. Thus, the difference in torque between the two turbines can be obtained as

4.3 Mass Flow Meters

221

Fig. 4.26 Dual turbine-type flow meter, 1—time base pulse generator; 2—gate circuit; 3—counter

ΔM = M1 − M2 = (K 1 sin θ1 − K 2 sin θ2 )qm υ

(4.88)

Since K 1 , K 2 , θ 1 , and θ 2 are constants in Eq. ΔM is proportional to qm υ. In turn, ΔM is proportional to the torsion angle α of the spring connecting the two turbines, so α ∝ qm υ. α is reflected by the relative angular displacement between the two turbines. Because the two turbines are joined as one, for which their slew velocity ω is the same in the stable case and is proportional to the flow velocity of the fluid υ, i.e., ω ∝ υ. Let the time required for the turbine to turn through the angular displacement α be t, then t=

qm υ α =K = K qm ω υ

(4.89)

where k is a constant. Therefore, the mass flow rate can be found by measuring the time t required for the two turbines to turn through the torsion angle α qm . The determination of time, t, is achieved using two electromagnetic detectors mounted on the wall of the tube. When an electrical pulse from one turbine opens the counter control gate, the counter starts counting until an electrical pulse from the other turbine closes the counter control gate. Since the time base pulse period is known, the number of time difference pulses measured by the counter during this time represents the time t, which is also the pulsed digital output signal proportional to the mass flow rate. 2. Coriolis force flow meters (Coriolis force flow meters for short) The Gauche force flow meter is a device that uses the mechanical properties of the fluid being measured as it flows to directly measure mass flow. It is a simple and universal principle that can directly measure the mass flow of liquids, gases and multiphase flows, and is independent of the temperature, pressure, density, and viscosity of the fluid being measured, with high measurement accuracy.

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4 Flow Testing

Fig. 4.27 Elbow Gaucho force meter, 1—parallel U-tube 2—detector 3—drive coil

The basic principle of the Gauche force flow meter is based on Newton’s second law of motion to establish the relationship between force, acceleration and mass. There are many types of structures of this type of meter. The structure and operating principle of the bent pipe Gauche force flow meter shown in Fig. 4.27 is introduced. Two geometric shape and material mechanical properties of the exact same U-tube firmly welded in the flowmeter between the import and export of the support seat, and in a driving coil under the action of a certain frequency around the flowmeter inlet, outlet axis (that is, Fig. 4.28 in the O–O axis) vibration, the measured fluid from the U-tube flow through, the flow direction, and vibration direction perpendicular. The two U-tubes vibrate in opposite directions, so that the flowmeter can eliminate the influence of external environmental vibrations when there is an influence of external vibrations. When an object of mass m is moving in a rotating reference system at the → speed υ , it will be subjected to a force with the value →

→

→

F k = 2m ω × υ

(4.90)

→

where F k is the Gauche force. → υ is the velocity vector of the object’s motion. → ω is the rotational angular velocity vector. The fluid motion Gauche force gives an additional action to the tube wall, so that the same U-tube flow channel in and out of the two parallel straight tube due to the opposite flow direction, and the opposite force resulting in a torque M action. This torque is generated by the vibration of the parallel straight tubes, and its magnitude is directly proportional to the fluid mass flow and vibration parameters. As shown in Fig. 4.28, if the two parallel straight tubes of the U-tube are structurally symmetrical, the torque over the length of the microelement on the straight tube is d M = 2r d Fk = 4r υωdm

(4.91)

4.3 Mass Flow Meters

223

O

B

L

θ dr

O

N

N

M r

dFk

A

r

r (b)

(a) Fig. 4.28 Illustration of vibration deformation of U-tube under force

where ω is the angular velocity. (a) As mentioned earlier, the U-tube of the actual flowmeter does not rotate but vibrates at a certain frequency, so that the angular velocity is a value that oscillates with a sinusoidal law. dF k is the absolute value of the Gauche force on the microelement dy pipe, and it is clear that dF k is also a sinusoidally varying value when the U-shaped pipe is vibrating, but the forces on the two parallel pipes are 180° out of phase. υ is the fluid flow rate and can be written as dy/dt, which is the length of the tube through which the fluid flows per unit time. So, Eq. (4.91) can again be written as: / d M = 4r ω(dy dt )dm = 4r ωqm dy

(4.92)

where dm is the mass of fluid in the dy tube; qm = dm/dt is the mass flow rate. Integrating the above equation, we get ∫ M=

∫ dM =

4r ωqm dy = 4r ωqm L

(4.93)

The frequency of the torque M change is consistent with the vibration frequency of the U-tube, and its maximum value occurs when the U-tube passes through its vibration center plane, which is the N–N plane in Fig. 4.28b, when the linear velocity of the vibration of the straight pipe section is maximum. At this time, the U-tube not only vibrates around the O–O axis but also produces torsional vibration under the action of torque M, as shown in Fig. 4.28b. The frequency of the torsional vibration is the same as the original vibration frequency of the U-tube, and the maximum torsional angle occurs at the maximum torque, which is when the U-tube vibrates through the center plane N–N.

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4 Flow Testing

Let the torsion angle produced by the U-tube under the torque M be θ (see Fig. 4.28b). Since θ is small, it is linearly proportional to the torque, M = K s θ where K s is the modulus of elasticity of the U-tube. Substituting this relationship into Eq. (4.93) gives qm =

Ks θ 4r ωL

(4.94)

That is, the mass flow rate is proportional to the torsion angle θ. If the velocity of the U-tube end in the vertical direction at the vibration center position is υ p (υ p = Lω), and the torsion angle of the torsional vibration of the U-tube due to the torque action is small compared to the amplitude of the original vibration of the U-tube, it can be assumed that the velocity of the two straight sections of the U-tube when passing through the N–N plane is υ p , then the time difference between the two straight sections of the U-tube A, B passing through the vibration center plane N–N successively is Δt =

2r θ 2r θ = υp lω

(4.95)

where r is the distance from the straight pipe to the torsional vibration centerline (shown in Fig. 4.28). Substituting θ from Eqs. (4.95) into (4.94), we have qm =

Ks Ks θ = 2 Δt 4r ωL 8r

(4.96)

where both K s and r are quantities related to the construction of the flow meter. The mass flow rate is therefore independent of the fluid properties, flow pattern, and other operating conditions in the tube. The mass flow rate of the fluid flowing through the tube can be obtained from the above equation by installing two detectors at the vibrating end of the straight tube of the U-shaped tube and measuring the time interval Δt between the vibrations of the two straight sections through the central plane N–N. In practice, the vibration case of the Gossel force mass flow meter is far more complex than the above, and the coefficients in Eq. (4.96) are generally calibrated by experiment. In addition, the technical complexity and the large measurement system of the Gauche force mass flow meter limit its application. 3. Differential pressure mass flow meters The operating principle of a differential pressure mass flow meter is shown in Fig. 4.29. The fluid flow Q from the main pipe is divided into two ways, each manifold is equipped with the same orifice plates A, C and B, D. At the midpoint of these two manifolds are connected with a pipe equipped with a dosing pump. The dosing pump feeds or sucks out a constant flow of fluid in the direction of the arrow. The volume

4.3 Mass Flow Meters

225

Fig. 4.29 Four-hole plate differential pressure mass flow meter, 1,2—differential pressure gauge

flow rate of the fluid passing through orifice plate A is I. The differential pressure before and after orifice plate A is p1 − p2 Then p1 − p2 = Kρ I 2

(4.97)

where K and ρ are the coefficients of the orifice plate and the density of the fluid being measured. The volume flow of fluid through orifice plate B is (Q − I ), and the differential pressure before and after orifice plate B is p1 − p3 then p1 − p3 = Kρ(Q − I )2

(4.98)

The flow rate through orifice plate C is (I +q), and the differential pressure before and after it is p2 − p4 , then p2 − p4 = Kρ(I + q)2

(4.99)

The flow rate through orifice plate D is (Q − I − q), and the differential pressure before and after it is p3 − p4 , then p3 − p4 = Kρ(Q − I − q)2

(4.100)

Equations (4.97) and (4.99) are added to give p1 − p4 = Kρ(2I 2 + q 2 + 2I q)

(4.101)

Equations (4.98) and (4.100) are added to give p1 − p4 = Kρ(2Q 2 − 4I Q − 2q Q + 2I 2 + q 2 + 2I q)

(4.102)

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4 Flow Testing

From Eqs. (4.101) and (4.102), we have I =

Q−q 2

(4.103)

Equations (4.98) minus (4.97) followed by Eq. (4.103) gives p2 − p3 = Kρ Qq

(4.104)

From Eq. (4.104), it can be seen that the mass flow rate can be measured by measuring the pressure difference between the dosing pump outlet and inlet, as this pressure difference is proportional to the mass flow rate in the main line ρ Q. This flow meter is used to measure liquid flow in the range of 0–0.5 kg/h to 0–250 kg/h with a range ratio of 1:20 and an accuracy of up to class 0.5.

4.3.2 Indirect Mass Flow Meter 1. Inferred mass flow meters The deduced mass flow meter is based on the measurement of two corresponding parameters. The first one being the measurement through the operator to perform certain forms of mathematical operations, indirectly deduced from the value of ρυ of the fluid, so as to find the mass flow rate. The following describes the three possible forms of composition. (1) Mass flow meter using a combination of differential pressure flow meter and density meter From the differential pressure flowmeter output signal ΔP ∝ qv υ 2 ρ can be seen, when the flowmeter flow section is a certain, then ΔP ∝ υ 2 ρ. Therefore, if the differential pressure output signal and density meter output signal ρ are multiplied, and then by opening the square to get a signal proportional to ρv, this signal represents the mass flow rate of the fluid qm . Of course, the differential pressure output signal and density output signal must be converted into a unified electrical or gas signal in order to pass through the electrical or gas operator. Figure 4.30 shows a schematic diagram of a mass flow meter with a combination of a differential pressure flow meter and a density meter. The mass flow rate is indicated and recorded by the display meter, and the total amount of fluid mass flowing through it is accumulated by the accumulator.

4.3 Mass Flow Meters

227

Fig. 4.30 Mass flow meter with combination of differential pressure flow meter and densitometer

Densitometers can be of the isotope type, ultrasonic type, or vibrating tube type for continuous measurement of fluid density. (2) Mass flow meter using a combination of a velocity flow meter and a density meter Turbine flowmeter, electromagnetic flowmeter, ultrasonic flowmeter, and other velocity flowmeter output signal represent the average flow rate υ of the fluid crosssection in the tube, the υ and densitometer output ρ multiplied, you get the ρυ signal representing the mass flow of fluid, the combination of principles shown in Fig. 4.31. (3) Mass flow meter using a combination of a differential pressure flow meter and a velocity flow meter The output of the differential pressure flow meter represents ρυ 2 , and the output of the velocity flow meter represents υ. If the two signals are divided by the operator, the ρυ signal representing the fluid mass flow rate qm is obtained, and the combination principle is shown in Fig. 4.32. Fig. 4.31 Mass flow meter with combination of velocity flow meter and density meter

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4 Flow Testing

Fig. 4.32 Mass flow meter with combination of differential pressure flow meter and velocity flow meter

2. Temperature and pressure compensated mass flow meters The basic principle of temperature and pressure compensated mass flow meter is to measure the volume flow, temperature, and pressure values of the fluid. Using the known relationship between the density, temperature and pressure of the measured fluid, the measured volume flow value is automatically converted to the volume flow value in the standard state through arithmetic. Since the density ρ 0 in its standard state is a constant value after a certain type of fluid being measured, the volume flow rate value in the standard state represents the mass flow rate value of the fluid, and it is easier to measure temperature and pressure continuously than to measure density continuously. Therefore, the current mass flow meters used in industry mostly use this principle. a. When the fluid being measured is a liquid, only the effect of temperature on the density of the fluid can be considered, and the relationship between density and temperature when the velocity does not vary over a wide range is ρ = ρ0 [1 + β(T0 − T )]

(4.105)

where ρ is the density of the fluid at operating temperature T. ρ 0 is the density of the fluid at the standard (or meter calibrated) temperature T 0 . β is the volume expansion coefficient of the fluid under test. (1) Therefore, for a liquid volume flow rate qv measured with a volumetric or velocity flow meter, the following equation can be used to apply temperature compensation: qm = ρqv = qv ρ0 [1 + β(T0 − T )] = qv ρ0 + qv ρ0 β(T0 − T )

(4.106)

If the type of fluid to be measured is known, i.e., ρ 0 and β are certain, then only the volume flow qv and the temperature change (T 0 − T ) need to be measured,

4.3 Mass Flow Meters

229

and an automatic calculation can be performed to obtain the mass flow qm . For water and oil, the accuracy of the above equation can be ± 0.2% when the temperature is varied within ± 40 °C. (2) When a differential pressure flow meter is used to measure the volume flow of a liquid, the relationship between the differential pressure signal ΔP √ output / ΔP and the volume flow rate qv is qv = K ρ (where K is a constant). At this point, the equation to achieve temperature compensation is √ √ qm = ρqV = K ΔPρ = K ΔPρ0 [1 + β(T0 − T )]

(4.107)

It can be seen that the mass flow rate can be found by adding a compensation quantity proportional to the product of the output ΔP and (T 0 − T ) to the output signal ΔP of the differential pressure flow meter and then opening the square. b. When the fluid under test is a gas in the low-pressure range, it is considered to conform to the ideal gas equation of state, i.e., ρ = ρ0

P T0 × P0 T

(4.108)

where ρ is the density of the fluid at an absolute temperature of T and an operating pressure of P. ρ 0 is the density of the fluid at an absolute temperature of T 0 pressure of P0 standard state. (1) At this point, for the volume flow meter or velocity flow meter measured, fluid volume flow qv can be temperature and pressure compensation by the following formula to obtain the mass flow qm qm = ρqv =

P P T0 × ρ0 qv = C1 qv P0 T T

(4.109)

where C 1 is a constant and C1 = TP00 ρ0 . (2) For the measurement of ρqv , differential pressure flowmeter can be compensated for temperature and pressure according to the following formula: √ qm = ρqv = ρ K

√ √ √ P ΔP T0 P = C2 ΔP = K ΔPρ = K ΔPρ0 × P0 T T ρ (4.110)

√ where C 2 is a constant, the C2 = K ρ0 TP00 From the above equation, it is clear that the mass flow rate value can be obtained by measuring the differential pressure value, the temperature, and pressure values of the differential pressure flow meter. Figure 4.33 shows the schematic

230

4 Flow Testing

_ V

IT

T

Differential pressure transmitter

Pressure transmitter

Temperature transmitter

IP

P

IΔp ΔP

pq v2

multiplier

I

pq v2P

divider

P T

-pq v

I square root extractor

2

t

∫q m d t 0

I

qm qm

Fig. 4.33 Schematic diagram of the temperature and pressure compensation system for gas mass flow measurement

diagram of the temperature and pressure compensation system for gas mass flow measurement. 3. Vibrating tube densitometer Some indirect mass flow meter need density meter. The vibration tube density meter has many advantages, such as high accuracy, stability, and repeatability, can be installed directly on the process pipeline for continuous measurement of density, can measure both liquid density and gas density, and can output pulse frequency signal, the accuracy of up to 0.1~0.5%. (1) Working Principle: These work using the principle that the intrinsic frequency of a thin-walled metal circular tube produced by excitation is related to the density of the medium inside the tube, and its structural principle is shown in Fig. 4.34. A cylindrical support is installed in a section of the metal tube, and a coil is installed on the upper and lower sides of this support. The two coils are at 90° to each other in space, one is used to detect the vibration of the metal tube, and the other is the excitation coil that amplifies the signal obtained from the detection coil and then excites the vibration of the metal tube. It is known from physics that the tube vibrates with an intrinsic frequency of 1 f0 = 2π

√

K mg

4.3 Mass Flow Meters

231 Detecting coil

amplifier

output

Field coil

Fig. 4.34 Schematic diagram of a vibrating tube densitometer

where mg and K are the mass of the vibrating tube and the elasticity coefficient of the vibrating tube. When the vibrating tube is placed in a medium of density ρ, the intrinsic frequency of its vibration is √ K 1 (4.111) f = 2π m g + m l where ml is the mass of the medium around the vibrating tube. f = f0

√

mg m g + ml

(4.112)

Let V be the volume of fluid being measured around the vibrating tube, and divide V by the numerator and denominator of the right end of Eq. (4.112) to obtain √ f = f0

√

mg V mg V

+

ml V

=

ρ0 ρ0 + ρ

(4.113)

where ρ is the density of the fluid being measured ρ = mVl . ρ 0 is the ratio of the mass of the vibrating tube to the volume of the measured m fluid passing around it, ρ0 = Vg , and is called the equivalent density of the vibrating tube. From Eq. (4.113), we have

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4 Flow Testing

T02 ρ0 = T2 ρ + ρ0

(4.114)

where T 0 and T are the self-oscillation period of the empty tube and the selfoscillation period of the fluid being passed into the measured fluid. From Eq. (4.114), we have ρ=

ρ0 2 (T − T02 ) T02

(4.115)

ρ = K2 T 2 − K0 where k 0 and k 2 are coefficients, K 0 = ρ0 , K 2 = Tρ02 . 0 Equation (4.115) is a theoretical relationship. In practice, the relationship between the vibration period of the vibrating tube and the density of the fluid being measured is ρ = K0 + K1T + K2 T 2

(4.116)

(2) Correction of the vibrating tube densitometer. Usually, the vibrating tube densitometer is calibrated in the standard state, and the coefficients K 0 , K 1 , and K 2 given at the factory correspond to the standard state. If the instrument is used at a temperature, pressure, or other conditions different from the calibration condition, the value of the instrument should be corrected. Temperature correction formula ρt = ρ[1 − K 4 (t − 20) + K 5 (t − 20)]

(4.117)

where ρ t and ρ are the temperature-corrected and uncorrected density values. K 4 , K 5 , and t are the temperature coefficients and the temperature of the medium. Pressure correction formula ρ p = ρt [1 + K 6 ( p − 1) + K 7 ( p − 1)]

(4.118)

where ρ p and p are the density corrected for temperature and pressure and the pressure of the medium. K 6 , K 7 , and ρ t are the pressure coefficients and the density corrected for temperature.

4.4 Main Coolant Flow Measurement

233

4.4 Main Coolant Flow Measurement Maintaining a normal flow of coolant in the reactor coolant circuit is an important condition for ensuring the reactor power output and safety. Therefore, the flow measurement system must ensure that a protective action signal is triggered when the reactor coolant flow falls below a defined value. This flow signal is also used for the calculation of the reactor thermal power.

4.4.1 Measurement with a Bent Pipe Flowmeter The main coolant flow is measured using an elbow flow meter. The specific measurement is carried out with three differential pressure transmitters at the bends in the middle section of each loop of the reactor. There is a common high-pressure measurement on the outside of the bend and three low-pressure measurement ports on the inside of the bend. The differential pressure between the outside and inside of the bend gives the main coolant flow rate and provides information to the reactor protection system. The method and principle of measuring the main coolant flow using a bent pipe flow meter are shown in Fig. 4.35. The basic function of this measurement device is to provide information on whether the flow rate is decreasing. One advantage of this method of flow measurement is that no parts need to be inserted into the coolant flow path. If parts were inserted into the flow path, there would be a pressure drop and as a result either a reduction in flow or an increase in pump power would be required. The kinetic effect of coolant flow shows that when coolant flows through an elbow, the pressure at the outer radius of the elbow is higher than the pressure at the inner radius of the elbow, thus creating a pressure differential. The relationship between flow rate and differential pressure can be described by the following equation: ΔP = ΔP0

(

q q0

)2 (4.119)

where ΔP0 is the differential pressure corresponding to the reference flow q0 and ΔP is the differential pressure corresponding to some different flow q. The corresponding differential pressure ΔP0 for the reference flow is the value determined at the initial start-up of the plant and then extrapolated along this correlation curve to determine the low flow protection adjustment point. The application of the bend flow meter to measure coolant flow must meet the following two conditions: (1) the upstream and downstream of the bend flow meter must be straight pipe sections, and to be no less than 28D straight pipe sections upstream and at least 7D long straight pipe sections downstream (where D is the inner diameter of the pipe); (2) the Reynolds number of the fluid in the pipe must be greater than 5 × 104 .

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4 Flow Testing

Fig. 4.35 Schematic diagram of bent pipe flow meter measurement

B B

22-1/3

Low pressure interface

High pressure interface

15° 15°

Section BB

4.4.2 Relevant Statistical Measures With the increasing cross-section of the main lines in large nuclear power plants, the unevenness of the stratification of the flow form of the medium makes it difficult to meet the measurement accuracy of the bent pipe flow meter. For this reason, another method of measuring flow using the activated 16 N in the first-loop coolant has emerged, called the correlation statistical flow measurement method. The 16 O in the first-loop coolant becomes 16 N with a half-life of 7.35 s in the presence of reactor fast neutrons, and it emits γ-rays with energies of 6.13 and 7.10 meV during the decay process. Therefore, two γ detectors A and B with the same sensitivity are installed at a known distance in the main line at the reactor outlet, as shown in Fig. 4.36. The reading of the downstream detector B should be smaller than that of the upstream detector A due to the decay of 16 N. The magnitude of the difference is related to the flux: detector A/detector B = eτ (t B −t A )

(4.120)

where t A , t B is the time for the coolant to flow from the core to detectors A and B, respectively; τ is the half-life of 16 N, which is determined by the correlation method (t A − t B ), which also enables the measurement of the flux.

4.5 Calibration and Indexing of Flow Measurement Instruments Fig. 4.36 Schematic diagram of the principle of correlation statistical measurement methods

235

L

A probe

B probe

amplifier

amplifier

correlator

Microcomputer data processing and display

Some nuclear power plants also use synchronization devices connected to the main pump shaft and pulse counting with a digital display of the glow tube to give a very accurate picture of the number of revolutions of the reactor coolant main pump, which represents the coolant flow.

4.5 Calibration and Indexing of Flow Measurement Instruments In addition to the standard throttling device and standard Pitot tube, other varieties of flow measurement instruments, in the factory before most of the need to use experiments to obtain the flow coefficient of the instrument to determine the flow scale of the instrument, that is, the flow meter indexing. While in use, there is a need to regularly calibrate to check whether the basic error of the meter exceeds the error range allowed by the meter’s accuracy class. Standard throttling device indexing relationship and errors are obtained through calculations, but it must be noted that the “standard” in the flow coefficient and other data is also obtained through a large number of tests. In addition, when high measurement accuracy is required, the complete throttling device must still be tested and calibrated. In the calibration and indexing of flow measuring instruments, the standard values of instantaneous flow are obtained by means of a standard test set using standard weights, standard volumes, and standard times (frequencies). The so-called standard test set is also a set of liquid or gas circulation system that can regulate the flow rate and make it highly stable at different values. If the flow rate in the system can be kept constant, the instantaneous volume flow rate qV or mass flow rate qm can be obtained by accurately measuring a certain period of time Δτ and the total volume

236

4 Flow Testing

ΔV or mass Δm of fluid passing through the system during this period of time by the following equation: qv =

ΔV Δm or qm = Δτ Δτ

The flow standard value and installed in the system to be calibrated against the meter indication value, you can achieve the purpose of calibration and indexing to be calibrated flowmeter. Figure 4.37 is a schematic diagram of the water flow calibration system, the system uses a high level water tank to generate the pressure head, and the method of overflow to maintain a constant pressure head, in order to achieve the purpose of stable flow; with the switching mechanism synchronized with the timer to determine the time Δ τ fluid flow into the metering tank, with a standard volume metering tank (or with weighing equipment) to determine Δ V (or Δm); before and after the calibrated flowmeter must have a long enough straight pipe section, flow Adjustment is controlled by the valve after the meter being calibrated. The Reynolds number that can be achieved by the system is limited by the height of the high level tank. In order to achieve higher Reynolds number, some test devices use pumps and multi-stage pressure stabilization tank, instead of high level overflow tank as a constant pressure water source. Volumetrically calibrated reference volume tubes and highly accurate volumetric flow meters are also often used as standards for calibration and indexing of flow measurement instruments. They are more suitable for field calibration of flowmeters because of their ease of movement and ability to be mounted on production process

3

7 8

4 2

9 10

5 12 6

1

11

1

Fig. 4.37 Water flow calibration system, 1—pool; 2—circulation pump; 3—high level tank; 4— second overflow pipe; 5—straight section; 6—movable joint; 7—switching mechanism. 8—standard volume metering tank; 9—level scale; 10—vernier; 11—bottom valve; 12—meter being calibrated

4.5 Calibration and Indexing of Flow Measurement Instruments 2

1

8

5

3

237

4

6

13

12

9 7 10 11

To the power supply

To the power supply

14 2

15 16

Receive the ball

Ball loading - Take the ball (turn 90°)

17 Send ball (turn 90°)

Fig. 4.38 Typical unidirectional return sphere-type reference volume tube system, 1—manometer; 2—vent valve; 3—breakaway tee; 4—ball; 5—ball stopper; 6—ball control valve; 7—operator; 8—thermometer; 9—pulse generator; 10—flow meter; 11—transmitter tee; 12—detection switch; 13—reference volume tube; 14—electronic counter; 15—blind; 16—plug; 17—vent valve

piping. The reference volume tube, shown in Fig. 4.38, is based on the principle of two micromovement detection switches set at a certain distance from the inner wall of an equal diameter pipe section. When the rubber ball with a diameter slightly larger than the diameter of the tube is pushed by the fluid through the former switch, an electric pulse is sent to open the counting gate of the counter and start counting the time-based pulses; when the rubber ball passes the latter switch, an electric pulse is sent to close the counting gate of the counter and stop counting, and the number of pulses counted between the two electric pulse signals represents the time Δτ. The volume of the tube section between the two switches is accurately calibrated; i.e., ΔV is determined, so the instantaneous volume flow qV can be found by measuring Δτ. The base volume tube has rubber ball input and separation charges at each end so that the rubber balls can be automatically input from the front of the base volume tube and separated from the back of the volume tube for continuous circulation through the volume tube.

238

4 Flow Testing

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid Two-phase flow is a flow system in which any two of the three phases, solid, liquid, and gas, are combined together with an interphase interface. The interface includes: gas–solid, gas–liquid, and solid–liquid two-phase flow, whose flow measurement is much more difficult than that of single-phase flow due to the complexity of the flow law. So far, no mature two-phase flow instrumentation has been produced. This section provides only an overview of the flow measurement problem for gas–liquid two-phase flows.

4.6.1 Basic Properties of Two-Phase Flow Two-phase flow phenomena are widely present in energy, petroleum, chemical, and nuclear industrial processes. The flow pattern and structure of two-phase flow are much more complex than that of single-phase flow. Take the gas–liquid two-phase flow in a vertical rise tube as an example, the basic flow structure (also known as flow pattern) has the following four types: Bubbly flow, slug flow, churn flow, churnannular flow, and annular flow). Figure 4.39 shows a schematic diagram of these four flow structures and the evolution of these four flow structures. The flow structure of a gas–liquid two-phase fluid in a horizontal tube is more complex than in a vertical tube and is mainly characterized by the fact that all flow structures are not axisymmetric, which is mainly caused by the effect of gravity biasing the heavier liquid phase toward flow along the lower part of the tube.

Fig. 4.39 Flow structure of a vertically rising gas–liquid two-phase flow, 1—bubbly flow; 2—plug flow; 3—chaotic flow; 4—chaotic-annular flow; 4—annular flow

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

239

100 Bubbly flow and diffuse flow

USL/m/s

10 1 Plug flow

0.1 0.01

Annular flow Smooth stratified flow Wavy stratified flow

0.001 0.001

0.01

0.1

1

10

100

USG/m/s Fig. 4.40 Air–water two-phase flow pattern in a horizontal pipe (0.l MPa, 24 °C, pipe diameter 4.l cm). U SL , U SG are apparent liquid, gas flow rates

Experimental studies have shown that the basic flow structure of gas–liquid twophase flow in a horizontal pipe has the following six types: bubble flow, long bubble flow, plug flow, smooth stratified flow, wave-like stratified flow, and annular flow. Figure 4.40 is a flow pattern diagram illustrating the variation of the flow structure with the gas–liquid flow rate at atmospheric pressure of air–water in a horizontal pipe. It is to be noted that the flow structure of a two-phase flow is always changing during the flow, and there is generally no fully developed flow like a single-phase flow. A rising low velocity bubbly flow in a vertical tube has to eventually change to a plug flow after a certain time evolution. And whether horizontal or vertical plug flow, the gas bullet is always getting longer. Therefore, flow measurement in two-phase flow is very difficult, and the difficulties arise from the following aspects: (1) Two-phase flow is time-nonstationary and spatially inhomogeneous. The distribution of the phases in a certain cross-section of the flow channel is both completely inhomogeneous and varies dramatically with time. An example is plug flow; when the gas bullet through, the gas occupies most of the flow channel cross-section, while the liquid plug is the liquid occupies most of the cross-section, and the gas bullet, the liquid plug alternately through a certain flow channel cross-section with a frequency that varies greatly. This makes the vast majority of volumetric, throttling, and velocity flowmeters unusable for flow measurement of such intermittent flow.

240

4 Flow Testing

(2) The phase interface is propagating at a certain velocity, and the relationship between this propagation velocity and the flow rate of each phase is still the most difficult subject for two-phase flow studies, for example, the uplift of small bubbles relative to the liquid flow within a bubbly flow, the motion of solid fluidization in a dense gas–solid two-phase flow, the propagation of fluctuations at the gas–liquid interface in a wave-like stratified or annular flow, and the propagation of air bombs in a plug flow. Therefore, the velocities obtained by two sensor measurements upstream and downstream of the general flow channel are such propagation velocities, not the velocity of each phase mixture or the flow velocity of each single phase. Thus, the intercorrelation method developed in recent years to measure the two-phase flow rate by measuring the two-phase flow velocity encounters great difficulties, because the measurement obtains the phase interface propagation velocity rather than the phase flow velocity. (3) The two-phase flow measurement has to measure the flow rate of each phase simultaneously and the number of parameters to be measured, such as the average velocity of the flow channel cross-section and the volume or mass content of each phase of the two-phase mixture to be measured simultaneously. And the numerous flow patterns as mentioned earlier make the flow pattern discrimination parameter also an additional quantity to be measured, which may be a pulsating pressure value or a pulsating velocity, etc. Due to the above difficulties, the basic existing methods for two-phase flow measurement are for steady-state flow, and this section will focus on gas (vapor) and liquid two-phase flow measurement methods.

4.6.2 Basic Parameters Related to Gas-Liquid Two-Phase Flow 1. Speed Let a gas–liquid two-phase flow in a pipe with a cross-sectional area of A and the area occupied by the i phase (i = G for the gas phase and i = L for the liquid phase, hereinafter) at a given cross-section is Ai , and the axial velocity of the i phase at any point r of Ai is υir , which is a function of r and time t, then the average axial velocity of the i phase at Ai υi =

1 Ai

∫ υir d A

(4.121)

Ai

Usually, the liquid phase velocity υ L and the gas phase velocity υG are not equal; i.e., there is a relative motion between the gas and liquid phases. Define the sliding ratio s to represent the difference in the velocities of the two phases. s=

υG υL

(4.122)

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

241

2. Volume flow and mass flow Based on the relationship between velocity and flow rate, the volume flow rate Q i and mass flow rate G i of the i phase can be obtained as ∫ Qi =

υir d A = Ai υi Ai

(4.123)

∫

Gi =

ρi υir d A

(4.124)

Ai

where ρi is the density of the i phase on Ai The total two-phase volume flow rate Q and mass flow rate are G Q = QG + Q L

(4.125)

G = GG + G L

(4.126)

Generally for subsonic two-phase flows, ρi can be considered completely constant at Ai , when ∫ qmi = ρi υir d A = ρi υi Ai = ρi qvi (4.127) Ai

Clearly,qvi ,qv ,qmi ,qm in the above equations are instantaneous flows. As with single-phase flow, the average flow over the time interval [t − T2 , t + T2 ] can be averaged to obtain the average flow over this time interval.

1 q¯vi = T

i+ T / 2

∫

qvi dt

(4.128)

i− T / 2

1 qmi ¯ = T

i+ T / 2

∫

qmi dt

(4.129)

i− T / 2

3. Gas content rate The gas content is an important parameter when analyzing the flow rate of gas–liquid two-phase flows, and the following gas content rates can be defined, as needed: (1) Time-averaged gas content at a point in the pipe r αr

242

4 Flow Testing

In the time interval [t − T2 , t + T2 ], let the total time of the gas phase flow over the point r be TG , then define αr =

TG T

(4.130)

αr Can be measured with a needle point probe. (2) Average air content of the cross-section α A αA =

AG A

(4.131)

where A G is the sum of the area occupied by the gas phase on A. (3) Volumetric gas content α Q . It is defined as the proportion of the volume of the gas phase in a given volume. α Q It can be expressed in terms of volume flow as αQ =

QG Q

(4.132)

(4) Mass gas content (dryness) x It is defined as the proportion of the mass of the gas phase within a certain mass x. It can be expressed in terms of mass flow rate as x=

GG G

(4.133)

Of the above gas content rates,αr is the time average and the rest are spatial averages. The relationship between α Q and x can be obtained from Eqs. (4.126), (4.132), and (4.133): / / α Q = Q G Q = Q G (Q G + Q L ) = =

1 1+

ρL x ρ L x + ρG (1 − x)

QL QG

=

1 1+

G L ρG G G ρL

(4.134)

From Eqs. (4.122), (4.123), (4.131), and (4.132), we have the following relationship between α A and α Q : αA =

αQ α Q + s(1 − α Q )

(4.135)

The relationship between α A and x can be obtained from Eqs. (4.127), (4.132), and (4.133)

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

αA =

ρL x ρ L x + sρG (1 − x)

243

(4.136)

4.6.3 Basic Principles of Two-Phase Flow Measurement In order to obtain the split-phase flows Q G ,Q L ,G G ,G L , there are several methods. (1) Since the tube cross-sectional area A is known, the gas content α A and the twophase velocities vG and v L can be measured separately, then A G and A L can be obtained from α A and then calculated by Eq. (4.123) for Q G and Q L , and if the two-phase densities ρG and ρ L are known, then G G and G L can be calculated by Eq. (4.127). (2) Since the relationship between the total flow rate G, Q and the fractional phase flow rate qmi , qvi and the gas content rate is satisfied as follows: Q G = αQ Q

(4.137)

Q L = Q − QG

(4.138)

GG = x G

(4.139)

G L = G − GG

(4.140)

Therefore, the split-phase flow rate qmi or qvi can be obtained by measuring G,x or Q,.α Q . In some special cases, the total flow rate is known; i.e., it can be accurately measured using the measurement technique of single-phase flow, when only the gas content rate α Q or x needs to be measured. In order to obtain the total flow rate and the gas content, the following method can be used: For the mass flow rate, two different flow meters are used to measure the two-phase flow with the values of S1 and S2 , which are both functions of G and x: S1 = f 1 (G, x)

(4.141)

S2 = f 2 (G, x)

(4.142)

The two equations can be solved by combining G and x. It is often very difficult to determine the functional relationships of Eqs. (4.141) and (4.142) by experimental calibration or rigorous theoretical analysis, and the most

244

4 Flow Testing

common method is to obtain the available functional relationships by theoretical analysis based on certain assumptions about the two-phase flow. However, when the actual flow condition differs significantly from the assumptions, it introduces a large error.

4.6.4 Several Instruments for Two-Phase Flow Measurement Two-phase flow measurement is still under development, and flow measurement methods are mainly based on the direct measurement of a number of parameters related to the flow of two-phase fluids to determine the value of each flow rate. Among the various instruments used to measure flow, the cross-sectional gas content α A or the dryness x are commonly used. Currently, the most established method of measurement is the γ-ray meter. In the following discussion, it is assumed that α A has been measured by a γ-ray meter and that, in the absence of relative motion between the gas–liquid phases, the relationship between α A and x is αA =

ρL x ρ L x + ρG (1 − x)

(4.143)

1. Target-type flowmeter The target flowmeter is used for single-phase flow measurement. The technology is more mature, but for two-phase flow, its characteristics are not yet fully understood. It is generally accepted that the total force acting on the target F consists of two parts, one for the gas phase and one for the liquid phase. Following a principle of action similar to that of single-phase fluids,F can be expressed as F=

KL KG α A ρG υG2 A0 + (1 − α A )ρ L υ L2 A0 2 2

where A0 is the area of the target. K G and K L are the drag coefficients for the gas and liquid phases. From Eqs. (4.128), (4.131), and (4.133), we have υG = υL =

xG GG = α A AρG α A AρG

GL (1 − x)G = (1 − α A )Aρ L (1 − α A )Aρ L

Substituting into Eq. (4.144) yields

(4.144)

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

x 2G2 (1 − x)2 G 2 KG KL α A ρG A 0 2 2 2 + (1 − α A )ρ L A0 2 2 α A A ρG (1 − α A )2 A2 ρ L2 ] [ A0 G 2 K G x 2 K L (1 − x)2 = + 2 A α A ρG (1 − α A )ρ L

245

F=

(4.145)

If K G = K L , then [ 2 ] x (1 − x)2 A0 K G 2 + F= 2 A2 α A ρG (1 − α A )ρ L

(4.146)

It can be seen that the force F is related to the unknown parameters G, x, α A , and if α A has been measured by the γ-ray meter, then only the unknown G; x are in Eqs. (4.145) and (4.146). Further assuming a sliding ratio of s = 1, then x can be calculated from α A according to Eq. (4.143). At this point, a very concise expression for the force F can be obtained as A0 K G 2 2 A2 ρ √ 2ρ F G=A K A0 F=

(4.147)

(4.148)

where ρ is the two-phase flow mixing density, the ρ = α A ρG + (1 − α A )ρ L

(4.149)

Thus, the combination of a γ-ray meter and a target flow meter can measure the fractional phase flow G G ,G L . It should be noted that Eq. (4.148) is derived under the assumptions that K G = K L = K and s = 1, which will result in measurement errors if they do not match. The inhomogeneity of the fluid momentum distribution over the pipe cross-section will also produce measurement errors. As with single-phase flow, when a disk-shaped target is used, some areas of higher momentum may lie outside the target, making the measured value lower than the actual value. In order to avoid this situation as much as possible, generally used as shown in Fig. 4.41 perforated circular plate-shaped target and circular screen-shaped target. Anderson et al. have conducted experiments with various targets and the structural parameters of the targets are shown in Table 4.5. / In the table, the flow area ratio = ( A − A0 ) A; the scale factor K is used for / single-phase water K = A/A0 ( 1 ρ L υ 2 ) and is determined experimentally. L 2 The experimental results show that the best error of 6.8% is achieved by using a large-hole circular plate-shaped target, and the worst error of 32% is achieved by using a disk-shaped target.

246

4 Flow Testing

Fig. 4.41 Shape of the target. a Small-hole circular plate shape; b large-hole circular plate shape; c screen shape

Table 4.5 Structural parameters of various targets Target

Circulation area ratio

Proportionality factor K

Target

Circulation area ratio

Proportionality factor K

Disk shape

0.89

–

Small hole (aperture 1.19 cm) disk shape

0.67

1.64~1.74

Screen mesh shape

0.81

–

Large hole (aperture 2.13 cm) disk shape

0.77

1.42~1.62

2. Turbine flow meters Turbine flow meters measure the velocity of a fluid and when used for two-phase flow, the relationship between the measured velocity υt and the velocity of the gas phase υG and the liquid phase υ L is not known, and there are three models representing the relationship between υt ,υG and υ L as follows: (1) Volumetric model υt = α A υG + (1 − α A )υ L

(4.150)

This is derived from the volumetric balance, i.e., think of υt as the ratio of the total volumetric flow rate Q to the cross-sectional area of the pipe A. (2) Aya model C G ρG α A (υG − υt )2 = C L ρ L (1 − α A )(υi − υ L )2

(4.151)

(3) Rouhani model C G x(υG − υt ) = C L (1 − x)(υt − υ L )

(4.152)

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

247

Equation (4.151) model and Eq. (4.152), C G , C L are the drag coefficients of the turbine flowmeter turbine assembly on the gas and liquid phases, respectively. Both the Aya and Rouhani models are derived under the assumption of momentum balance, and there is no practical difference between the two. (1−x)G G G Substituting υG = α AGAρ = α AxAρ and υ L = (1−α into Eqs. (4.148), (4.151), G G A ) Aρ L and (4.152) yields the relationships for the three model measures υt and G,x above. (1 − x)G xG + ρG A ρA ]2 [ − υt = C L (1 − α A )ρ L υt − υt =

[

xG (1 − x)G ρG α A A ρ L (1 − α A )A ] ] [ [ xG (1 − x)G − υt = C L (1 − x) υt − CG x ρG α A A ρ L (1 − α A )A

C G ρG α A

(4.153) ]2 (4.154) (4.155)

All the above three models were obtained after making certain idealized assumptions and their measurement errors depend on the actual flow conditions. Experiments on horizontal pipes show that the volumetric model is better when υG < υ L , while the Aya or Rouhani model is better when υG > υ L . Turbine flow meters can be combined with γ-ray meters and target flow meters for flow measurement. For example, with a turbine flowmeter, the Rouhani model expressed in Eq. (4.155) yields (for simplicity, take C G = C L = 1). υt =

[ 2 ] x G (1 − x)2 + A ρG α A ρ L (1 − α A )

(4.156)

Equation (4.146) is obtained with a target flow meter, and both Eqs. (4.146) and (4.156) are functions of G, x, and α A , and if α A can be measured by a γ-ray meter, then the two equations can be combined to give G=

2 AF A0 K υt

A0 K υt2 x2 (1 − x)2 = + ρG α A ρ L (1 − α A ) 2F

(4.157)

(4.158)

Thus, from the turbine flow meter reading υt and the target flow meter reading,F G and x can be calculated to obtain the split-phase mass flow rate. The application of turbine flow meters needs to further address the influence of the two-phase flow pattern, the viscosity of the fluid, and the distribution of the flow velocity on the measurement and find a model that can include more influencing factors to more accurately approximate the actual situation.

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4 Flow Testing

3. Bishop trusteeship Currently, there are two ways to handle the use of the Pitot tube for two-phase flow measurements. (1) The flow is assumed to be homogeneous; i.e., the two-phase flow is considered to be well mixed. This is equivalent to treating the two-phase fluid as a single-phase fluid and then correcting the measurement results for the actual flow conditions. Under the above assumptions, the relationship between the dynamic pressure measured by the Pitot tube Δp and the flow rate υ and density ρ is the same as in the case of single-phase flow √ υ=K

2 Δp ρ

(4.159)

where K is the experimentally determined coefficient. ρ is the two-phase flow mixing density. The total mass flow rate can be expressed as √ G = ρυ A = K A 2ρΔp

(4.160)

Since the velocity distribution of two-phase flow in the cross-section of the pipe is complex and there are many influencing factors, the actual measurement, the installation position of the Pitot tube, and the size of the Pitot tube diameter in small diameter pipes will have a large impact on the results. (2) In order to give a true picture of the velocity distribution of the fluid, several Pitot tubes may be placed at different locations in the cross-section of the pipe when conditions permit, and the results obtained averaged. This is particularly relevant when the flow conditions are very different from the homogeneous flow. For more accurate results, velocity distributions and α A can also be measured with multiple biotubes and multiple γ-ray meters. The data are also processed with a computer. Equation (4.159) can also be expressed as the relationship between Δp and G, x [ ] x G2 1−x Δp = + 2K 2 A2 ρG ρL

(4.161)

The results of x measurements with a single Biotube according to the above equation, when G is known, show that the errors are large, and it is certain that the results will be better if multiple biotubes are used. (3) The force acting on the Pitot tube probe is considered to be the sum of the forces acting on the gas–liquid phase, and its mathematical expression is A' Δp = β1

ρG υG2 ' ρ L υ L2 ' A G + β2 AL 2 2

(4.162)

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

249

where A' is the full pressure orifice area. A'G , A'L is the area occupied by the gas and liquid phases on A' . β1 , β2 are the coefficients determined experimentally. Substituting A' = A'G + A'L into the above equation and taking into account αA =

A' AG = G A A

1 − αA =

A' AL = L' A A

obtain Δp = β1

ρG υG2 ρ L υ L2 α A + β2 (1 − α A ) 2 2

(4.163)

Assuming no relative motion between the two phases, that is; vG = v L = v. Experiments show that at α A < 0.7, the gas phase becomes discrete small bubbles distributed in a continuous liquid phase at β1 = β2 = 1, whereupon √ 2Δp ρG α A + ρ L (1 − α A )

υ=

(4.164)

At α A > 0.7, the liquid phase is distributed as discrete droplets in the gas phase, at which point β1 = 1, β2 = 2, so √ υ=

2Δp ρG α A + 2ρ L (1 − α A )

(4.165)

Provided that α A has been measured with the γ radiometer, the v (vG = v L = v) can be obtained from the Biotope by measuring Δp, and then G G = ρG A G υG = α A AρG υ

(4.166)

G L = ρ L A L υ L = (1 − α A )Aρ L υ

(4.167)

This gives the split-phase mass flow rate G G and G L . To reduce the effect of the velocity distribution on the measurement results, it is also advisable to use multiple biotopes. Fincke has measured G G and G L with a combination of a comb biotope and a γ radiometer as shown in Fig. 4.42, and processed the data as described above, showing that the errors were not significant. It is important to point out that measuring two-phase flow with either a target flow meter or a Pitot tube assumes υG = υ L = υ, which is s = 1, that there is no slip between the two phases of gas (vapor) and liquid. This is only the case when the two

250

4 Flow Testing

Fig. 4.42 Comb bidet

phases do not differ greatly in density, such as when the gas is a high-pressure wet vapor, and when the two-phase mixture flows at a high velocity or when the liquid flow velocity is very high. At this point, the two-phase flow is nearly homogeneous and has properties similar to single-phase flow. 4. Orifice plate Orifice plates have been standardized for single-phase fluids, but the relationship between the differential pressure between the two sides of the orifice plate Δp and, Gx when used for two-phase fluids is not yet clear. In the last 20 years, a lot of experimental work has been done in this area, and many models have been proposed to determine the relationship between Δp and, Gx. The three main types of these models are as follows: (1) Homogeneous phase flow model The two-phase flow is considered as homogeneous flow and gravity and friction are neglected in the orifice plate, and it is assumed that no phase change occurs as the fluid flows through the orifice plate. Under these conditions, the results are similar to those when single-phase flow is Δp =

G2 2αt2 εt2 A20 ρ

where αt is the flow coefficient for two-phase flow through an orifice plate. εt is the two-phase fluid expansion coefficient. A0 is the open area of the orifice plate. ρ is the two-phase flow mixing density, see Eq. (4.149). Substituting Eq. (4.134) into Eq. (4.149) yields

(4.168)

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

251

1 + 1−x ρL

(4.169)

ρ=

x ρG

Equation (4.169) is then brought into Eq. (4.168) to express Δp as a function of G and x. This relationship, in combination with other meters, can be used to determine G and x. In two-phase flow measurements, orifice plates are often used when is known Gx. In this case, assuming a flow rate of G for single-phase water, Δp = Δp L0 can be calculated from the orifice plate equation for single-phase flow Δp L0 =

G2 2αt2L A20 ρ L

(4.170)

where αt L is the flow coefficient as the water flows through the orifice plate. Equation (4.168) is divided by Eq. (4.170) to obtain the so-called full liquid phase conversion factor of the orifice plate Φ2L0 , which, considering Eq. (4.168), gives: Φ2L0

( ) αt2L x 1−x Δp = 2 2 ρL + = Δp L0 ρG ρL αt εt

(4.171)

If you take αt L = αt , εt = 1 then ( Φ2L0

= ρL

x 1−x + ρG ρL

) (4.172)

cause ( 2 )/( ) ρL Ψ L0 = Φ L0 − 1 − 1 ρG

(4.173)

Substituting Eqs. (4.172) into (4.173) yields Ψ L0 = x

(4.174)

The above models, experimentally proven to have large errors, have led to the emergence of many modified models based on them, such as replacing Eq. (4.174) with Ψ L0 = x n (experimentally shown that n is better taken as 1.4) or multiplying the left end of Eq. (4.170) by a factor, etc. (2) Momentum flow model Neglecting the gravitational force and frictional force of the fluid passing through the orifice plate, the relationship between Δp and G,x can be obtained from the momentum balance of the two-phase flow as

252

4 Flow Testing

[ 2 ] x G2 (1 − x)2 Δp = + (1 − α A )ρ L 2αt2 εt2 A20 α A ρG

(4.175)

Divide Eqs. (4.168) and (4.170) in the case where G is known, to obtain Φ2L0

[ 2 ] αt2L x Δp (1 − x)2 = = 2 2 ρL + Δp L0 α A ρG (1 − α A )ρ L αt εt

(4.176)

If we take αt L = αt , εt = 1, then Φ2L0 = ρ L [

x2 (1 − x)2 + ] α A ρG (1 − α A )ρ L

(4.177)

If α A has been measured by a gamma ray meter, the above equation can be used to calculate x. All of the above analyses use the full liquid phase conversion factor Φ2L0 = / 2 Δp/ Δp Δp L Δp L is the differenΔp L0 , or the split-phase conversion factor (Φ L = tial pressure across the orifice plate for a single-phase flow at G L ) or the split gas / phase conversion factor Φ2G = Δp ΔpG (ΔpG is the differential pressure across the orifice plate for a single-phase flow at G G ). According to the definitions of Δp L and ΔpG , there are Δp L = ΔpG =

G 2L 2 2αt L A20 ρ L

=

G 2 (1 − x)2 2αt2L A20 ρ L

(4.178)

G 2G G2x 2 = 2αt2G A2G εG2 ρG 2αt2G εG2 A2G ρG

(4.179)

where αt G is the flow coefficient of the gas phase as it flows through the orifice plate. εG is the gas expansion coefficient. The liquid phase conversion factor can be scored from Eqs. (4.175) and (4.178) Φ2L

[ 2 ] αt2L x (1 − x)2 Δp = ρL + = Δp L α A ρG (1 − α A )ρ L (1 − x)2 αt2 εt2

(4.180)

Retrieved from αt L = αt , εt = 1 then Φ2L

[ 2 ] x ρL (1 − x)2 1 + = (1 − x)2 α A ρG 1 − αA

(4.181)

Remember the parameters Δp L = X = ΔpG 2

(

1−x x

)2

ρG ρL

(

αt G εG αt L

) (4.182)

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

253

If we take αt G εG = αt L , then ( X = 2

1−x x

)2

ρG ρL

(4.183)

From (4.136) we have αA =

1 ρL x = ρ L x + sρG (1 − x) 1 + s 1−x x

ρG ρL

=

1 x 1 + s X 2 ( 1−x )

(4.184)

Substituting this into Eq. (4.181), we get Φ2L =

1 c Δp =1+ + 2 Δp L X X

(4.185)

among others ( )1 ( ) 21 1 ρL 2 ρG c= +s s ρG ρL

(4.186)

If you take s = 1, then ( c=

ρL ρG

) 21

( +

ρG ρL

) 21 (4.187)

Equations (4.183) and (4.185) are the widely used Chisholm formula. From Eqs. (4.180), (4.187), and (4.179), the right-hand side of Eq. (4.188) is a function of x only, while the left-hand side is a function of G, x, as G is known, to find x. Likewise, the split-phase conversion factor expressed in the following equation can be obtained Φ2G =

Δp = X 2 + cX + 1 ΔpG

(4.188)

(3) Energy flow model In the case of two-phase flow through an orifice plate, if only the accelerated pressure drop is considered, the relationship between Δp and G, x can be obtained from the energy balance ] [ 3 G2 x (1 − x)3 ρ + Δp = 2αt2 εt2 A20 α 2A ρG2 (1 − α A )2 ρ L2

(4.189)

254

4 Flow Testing

where ρ is the two-phase flow mixing density as shown in Eq. (4.149) or Eq. (4.169). Substituting Eqs. (4.169) into (4.189) yields ] [ 3 1 G2 (1 − x)3 x Δp = ρ 2 2 + 2 2 2 2 x 2 2αt εt A0 α A ρG (1 − α A ) ρ L ρG + 1−x ρL

(4.190)

Then divide Eqs. (4.190) with (4.170) to obtain the full liquid phase conversion factor 2 φ L0

α2 Δp = = 2t L2 Δp L0 αt εt

ρ L2 x 3 (1−x)3 + (1−α 2 ρG2 α 2A A) ρL x + (1 − x) ρG

(4.191)

If you take αt L = αt , εt = 1 then 2 φ L0

=

ρ L2 x 3 (1−x)3 + (1−α 2 ρG2 α 2A A) ρL x + (1 − x) ρG

(4.192)

In practice, several of these measurement instruments discussed above are often used in combination, to obtain more data for analysis and comparison, for example, a combination of γ-ray meter, target flow meter, turbine flow meter, thermocouple, pressure gauge, etc. Such combinations may also include biotubes, orifice plates and others. Aya[citation] has used the above combinations to measure the flow rate G, dryness x and slosh ratio s of two-phase flows. A target flow meter has also been installed upstream and downstream of the turbine flow meter, and the signals from the two target flow meters have been correlated to obtain the velocity of the fluid and compared with the velocity signal measured by the turbine flow meter to obtain more reasonable results. When multiple instruments are used in combination, interference between instruments needs to be considered. Disturbances to the fluid from sensors installed upstream can affect the normal operation of downstream sensors. This interference is particularly severe when installing a turbine flowmeter upstream of a target-type meter. Reflective Questions and Exercises 4.1 Briefly describe which standard throttles are currently specified internationally? 4.2 Briefly describe the component parts of a standard throttling device and their function. What are the requirements for the installation of a flow measurement system? Why is it important to ensure that the measurement line has a certain length of straight pipe section before and after the throttling device? 4.3 Explain the operating principle of a throttled differential pressure flow meter. 4.4 Describe the characteristics of the signal piping to be laid when measuring liquid, steam, and gas flow with a standardized throttling device. Under what

4.6 Flow Measurement of Two-Phase Flow: Gas-Liquid

4.5

4.6 4.7 4.8 4.9 4.10

4.11

255

conditions are balancing vessels, collectors, settlers, isolators, etc., used and why? Briefly describe the components and operating principles of a turbine flow meter. A turbine flowmeter has an instrumentation constant of K = 150.4 times/L. What is the corresponding instantaneous flow rate when its output frequency during flow measurement is f = 400 Hz? How do float flow meters differ from differential pressure flow meters in terms of measurement principle? Describe the operating principles of electromagnetic flow meters and what are the requirements for the use of these meters? What is the detection principle of a vortex flow meter? What are the common types of vortex generators? What are the methods of mass flow measurement? A rotameter is used to measure the flow of carbon dioxide gas. The temperature of the gas being measured at the time of measurement is 40 °C and the pressure is 0.05 MPa (gauge pressure). If the flowmeter reads 120 m2 /h, what is the actual flow rate of carbon dioxide gas?. It is known that the absolute pressure at the time of calibration of the meter p1 = 0.1Mpa and the temperature t1 = 20 °C. Known: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Name of medium under test: boiler feedwater. Temperature of the measured medium: t = 215 °C. Pressure of the measured medium: P = 135 kgf/cm2 . Inner diameter of the tube (measured at 20 °C) D20 = 150 mm. Pipe material: 20# new seamless steel pipe. Throttle form: standard orifice plate (angular connection to take pressure). Material of the throttle: 1Cr18Ni9Ti. ' Orifice diameter of the throttle (measured at 20 °C) d20 = 95.59 mm. Form of differential pressure gauge: U-tube differential pressure gauge. Differential pressure values: ΔP = 945 mmHg. Piping systems. 6m

Find: the flow rate q at workm (kg/h).

5m

2m

256

4 Flow Testing

4.12 Briefly explain the working principle of the ultrasonic flow meter. 4.13 Briefly describe the basic principles of two-phase flow measurement. 4.14 List several commonly used instruments for measuring two-phase flow and the principles of measurement. 4.15 How do you select the form of throttle member for a throttle device? What factors should be considered in the selection? Why? 4.16 Why does a vortex flow meter have a minimum Reynolds number limit? 4.17 Briefly describe the principle of Gothic force mass flow meter measurement.

Chapter 5

The Level Measurement

As a process parameter, the liquid level can also reflect the operating status of the nuclear power plant. For example, the reactor coolant level and the liquid level of the regulator and steam generator directly reflect the operating conditions of the nuclear power system. There are many methods of liquid level measurement, and they are still evolving, but whichever one is used, it often boils down to measuring certain physical parameters such as measuring length (height), pressure (differential pressure), capacitance, ray intensity, and acoustic resistance. The main types of level measuring instruments in common use are the following: 1. Direct reading level measuring instrument: This is the most primitive yet widely applied liquid level measuring instrument. It can use the glass tube directly or glass plate connected with the measured vessel to display the level height in the vessel. 2. Float type liquid level measuring instrument: This is a kind of instrument that uses the float to reflect the liquid level by floating on the liquid surface and rising or falling with the liquid level. It is also one of the earliest and widely used liquid level measuring instruments. 3. Hydrostatic level measuring instrument: It is an instrument that indirectly measures the liquid level by using the height of the liquid column to generate pressure at a fixed point and measure the pressure at that point or measure the pressure difference between that point and another reference point. 4. Electrical level measuring instrument: It is a liquid level instrument that converts the change of liquid level into the change of some electrical quantity such as capacitive, inductive, and resistive level meter, for indirect measurement. 5. Ultrasonic level measuring instrument. 6. Nuclear radiation type liquid level measuring instrument. In addition to the above listed measuring instruments, there are optical, weighing, hammer, and rotating wing plate-type level measuring instruments. But due to

© Harbin Engineering University Press 2023 H. Xia and Y. Liu, Measurement Science and Technology in Nuclear Engineering, Nuclear Science and Technology, https://doi.org/10.1007/978-981-99-1280-3_5

257

258

5 The Level Measurement

the problems of radiation damage, sealing and corrosion in nuclear engineering, liquid level detection instruments are basically limited to 1. hydrostatic level measuring instruments; 2. electrical level measuring instruments; and 3. ultrasonic level measuring instruments. This chapter will introduce these level measuring instruments.

5.1 Hydrostatic Level Meter 5.1.1 Pressure-Type Level Meter The liquid has a certain height in the container and will exert a certain pressure on its bottom or a point on its side. The higher the liquid level, the greater the pressure on a point, so as long as the pressure at a point is measured, the height of the liquid level can be determined. By converting the level measurement into a pressure or differential pressure measurement, the level measurement is greatly simplified; for example, by using high-precision pressure gauges, single-tube manometers and differential pressure transmitters in unit combination instruments to measure the level. Figure 5.1 shows a measurement system for measuring the level of a liquid in a vessel with a pressure gauge. The reading of the pressure gauge at this point should be p = γ H + γ h,

(5.1)

where γ is the heaviness of the liquid. Since the pressure gauge is mounted in a fixed position, h is a constant. The weight of the liquid is generally considered constant in the measurement, so the scale equation of the gauge is p = γ H + C,

(5.2)

where C = γ h is a constant.

H

1

2

h

Fig. 5.1 Level measurement by pilot tube level meter, 1—liquid to be measured; 2—pressure gauge

P

5.1 Hydrostatic Level Meter

259

Fig. 5.2 System for measuring liquid level with a pressure gauge in an open vessel. a Level measurement with a pressure gauge; b pressure versus level

For open vessels connected to the atmosphere, the pressure gauge can be installed at the lowest level, as shown in Fig. 5.2.

5.1.2 Differential Pressure Level Juice Level gauges using the principle of differential static pressure also work on the basis of a relationship between the static pressure of the liquid column and the height of the liquid level in direct proportion to each other. As shown in Fig. 5.3, the high-pressure chamber of the differential pressure transmitter is connected to the lower pressuretaking point of the vessel, and the low-pressure chamber is connected to the space above the liquid level (where it is connected to the atmosphere). The differential pressure transmitter high-pressure chamber is positioned h1 + h2 lower than the lowest liquid level and h2 lower than the bottom of the vessel, and the range of levels to be measured is H. At this point, the pressure in the high and low-pressure chambers of the differential pressure transmitter are p1 = H γ + (h 1 + h 2 )γ p2 = 0 The pressure difference between the two chambers is Δp = p1 − p2 = H γ + (h 1 + h 2 )γ − 0 = H γ + Z 0 ,

(5.3)

where γ is the heaviness of the liquid in the vessel; Z 0 is the zero point migration and Z 0 = (h 1 + h 2 )γ .

260

5 The Level Measurement

Fig. 5.3 Principle of open container level detection. a Differential pressure level meter device system and b differential pressure Δp versus level height H

From Eq. (5.3), it can be seen that the presence of Z 0 shifts the H-Δ p relationship curve in the positive direction of Δ p by the position of Z 0 , as shown in Fig. 5.4b. Therefore, when the level H is equal to zero, the pneumatic differential pressure transmitter still has the air pressure signal output corresponding to Z 0 , which should make the transmitter independent of Z 0 , i.e., when H = 0, the output air pressure is 0.2 kgf/cm2 ; at the highest level, it is l kgf/cm2 . In this case, positive migration is to be performed, and the amount of zero migration is Z 0 = (h 1 + h 2 )γ . The zero migration is achieved by adjusting the internal migration spring of the transmitter. As shown in Fig. 5.4, the high- and low-pressure chambers of the differential pressure transmitter are connected to the lower and upper pressure-taking points of the vessel, respectively. If the weight of the liquid being measured is γ 1 , then the differential pressure acting on the high- and low-pressure chambers of the transmitter are Δ p = Hγ 1 . In practice, in order to prevent the liquid and gas in the container from entering the pressure-taking chamber of the transmitter and causing pipeline blockage or corrosion, as well as to maintain a constant height of the liquid column in the lowpressure chamber, the high- and low-pressure chambers of the transmitter and the pressure-taking point are equipped with isolation tanks, as shown in Fig. 5.5, which are filled with isolation fluid γ 2 , usually γ2 >> γ1 . At this time, the pressures in the high- and low-pressure chambers are Fig. 5.4 Differential pressure transmitter level measurement principle

5.1 Hydrostatic Level Meter

261

Fig. 5.5 Level measurement system with isolation tank, 1–differential pressure transmitter; 2—isolation tank

p1 = h 1 γ2 + H γ1 + p p2 = h 2 γ2 + p. The pressure difference between the high- and low-pressure chambers is Δp = p1 − p2 = H1 γ1 + h 1 γ2 − h 2 γ2 = H γ1 − C,

(5.4)

where p1 and p2 are the pressure of the high- and low-pressure chamber, respectively; γ 1 and γ 2 are the weight of the liquid to be measured and the isolation liquid, respectively; h1 and h2 are the lowest level and the highest level to the transmitter, respectively; p is the pressure of the gas in the vessel; C is a constant, C = (h 2 − h 1 )γ2 . From Eq. (5.4), it can be seen that when H = 0, Δ p = (h 1 − h 2 )γ2 , so it is a negative migration. Figure 5.6 shows a graph of the positive and negative characteristics of the transmitter. The transmitter is adjusted to the range spring prior to installation based on the migration so that I = 4 mA when H = 0 and I = 20 mA when H = H max . Fig. 5.6 Positive and negative migration characteristics

262

5 The Level Measurement

5.2 Electrical Level Meters 1. Capacitance level meter for conductive liquids When parallel plate capacitors are filled with different media between them, the magnitude of the capacitance varies, and hence, the change in capacitance can be measured to determine the level of a liquid, the level of a material or the parting of two different liquids (Fig. 5.7). Figure 5.7 shows a capacitor consisting of two coaxial cylindrical pole plates. When a dielectric with a dielectric constant ofε is filled between the two cylinders, the capacitance between the two cylinders is C=

2π εL , ln Dd

(5.5)

where d and D are the outer diameter of the inner electrode and the inner diameter of the outer electrode of the cylinder; L is the length of the two coaxial cylinder electrodes; ε is the dielectric constant, the ε = ε p · ε0 = 8.84 × 10−12 ε p ,

(5.6)

where εp is the relative dielectric constant of the medium; ε0 is the vacuum dielectric constant (dry air can be approximated by this value). From Eq. (5.5), it can be seen that for a certain cylinder electrode, i.e., for a certain D, d, the capacitance C is proportional to the product of the cylinder electrode length L and the dielectric constant ε. Figure 5.8 shows the schematic diagram of a capacitive level meter for measuring the level of a conductive medium. A copper or stainless steel electrode of diameter d is coated with a Teflon plastic sleeve or enamel as the dielectric and insulating layer. If the container 4 of diameter D0 is made of metal, the dielectric layer is air plus plastic or enamel when there is no liquid in the container, and the electrode covers the entire length L. If the conductive liquid level is at a height H, the conductive liquid is part of the other pole plate of the capacitor in the height range, the inner diameter of the part of the liquid as the

1

D

2 d

L

Fig. 5.7 Composition of capacitors, 1—inner electrode; 2—outer electrode

5.2 Electrical Level Meters

263

D d

Fig. 5.8 Schematic diagram of a capacitive level meter for measuring the level of conductive media, 1—inner electrode; 2—insulating sleeve (dielectric layer); 3—false level; 4—vessel

1 2

L

H

3 4

H

D0

D d

Fig. 5.9 Level measurement of non-conductive media, 1—inner electrode; 2—outer electrode; 3—insulating sleeve; 4—circulation orifice

1 3

L

4 2

H outer electrode of the capacitor is D, and the diameter of the inner electrode is d. Therefore, the capacitance of the whole capacitor is C=

2π ε0' (L − H ) 2π ε H + , D ln d ln Dd0

(5.7)

where ε is the dielectric constant of the insulating sleeve or coating; ε0' is the equivalent dielectric constant of the capacitor consisting of the electrode insulation and the gas inside the container. When the container is empty, i.e., when H = 0, the second term of Eq. (5.7) becomes a capacitor consisting of an electrode and a container with a capacitance of C0 = Thus, Eq. (5.7) becomes

2π ε0' L ln

D0 d

.

(5.8)

264

5 The Level Measurement

( C=

) 2π ε 2π ε0' − D0 H + C 0 . ln Dd ln d

(5.9)

The above equation can be written as H = K i C − K . where K i =

1

2πε ln D d

2πε ' − D0 ln d0

. If D0 >> d and ε0' < ε, then

Ki =

2πε0' D ln d0