Thermal Turbomachines

Second Edition

Dr. Onkar Singh

Thermal Turbomachines

Thermal Turbomachines Second Edition

Dr. Onkar Singh Formerly Founder Vice Chancellor Madan Mohan Malaviya University of Technology Gorakhpur, Uttar Pradesh Professor Department of Mechanical Engineering, School of Engineering Harcourt Butler Technical University Kanpur, Uttar Pradesh

Thermal Turbomachines

Second Edition

Copyright © 2019 by Wiley India Pvt. Ltd., 4436/7, Ansari Road, Daryaganj, New Delhi-110002. Cover Image: Edi_Eco/Getty Images All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or scanning without the written permission of the publisher. Limits of Liability: While the publisher and the author have used their best efforts in preparing this book, Wiley and the author make no representation or warranties with respect to the accuracy or completeness of the contents of this book, and specifically disclaim any implied warranties of merchantability or fitness for any particular purpose. There are no warranties which extend beyond the descriptions contained in this paragraph. No warranty may be created or extended by sales representatives or written sales materials. The accuracy and completeness of the information provided herein and the opinions stated herein are not guaranteed or warranted to produce any particular results, and the advice and strategies contained herein may not be suitable for every individual. Neither Wiley India nor the author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Disclaimer: The contents of this book have been checked for accuracy. Since deviations cannot be precluded entirely, Wiley or its author cannot guarantee full agreement. As the book is intended for educational purpose, Wiley or its author shall not be responsible for any errors, omissions or damages arising out of the use of the information contained in the book. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. Trademarks: All brand names and product names used in this book are trademarks, registered trademarks, or trade names of their respective holders. Wiley is not associated with any product or vendor mentioned in this book. Other Wiley Editorial Offices: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030, USA Wiley-VCH Verlag GmbH, Pappellaee 3, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 1 Fusionopolis Walk #07-01 Solaris, South Tower, Singapore 138628 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada, M9W 1L1 First Edition: 2014 Second Edition: 2019 ISBN: 978-81-265-7923-5 ISBN: 978-81-265-8833-6 (ebk) www.wileyindia.com Printed at:

Preface During teaching the course of turbomachines, I have felt that the students consider turbomachines as a difficult subject and this perception is primarily due to non-availability of good books on the subject. Also, the students have to refer to different books for different topics of this subject. Looking upon the present requirement of the subject and students, I have made this attempt of providing a book for clear, concise and systematic presentation of the subject matter. This book has been written in lucid style with sufficient number of illustrations and numerical problems for easy understanding of turbomachines. The subject matter has been duly covered in seven different chapters in this book listed as follows: • • • • • • •

Fundamental concepts of turbomachines. Centrifugal compressors. Axial flow compressors. Turbines. Steam turbines. Pumps. Design considerations of thermal turbomachines.

The book has been written in SI system of units. I hope that the students and teachers referring to this book will find it useful. I am greatly indebted to my family members for their continuous encouragement and cooperation ­during preparation of manuscript. I would like to place on record my gratitude and apologies to my wife Parvin and kids Sneha and Prateek who patiently endured certain neglect and hardships due to my ­preoccupation with the preparation of this manuscript. I extend my thanks to all those who supported directly or indirectly in the completion of this book. I shall be extremely grateful to all the readers of this book for their constructive criticism, indicating any errors, omissions, etc. for improving its quality and form. Dr. Onkar Singh

Contents Prefacev Chapter 1  Fundamental Concepts of Turbomachines

1

Learning Objectives 1   1.1  Introduction and Definition of  Turbomachines 1   1.2  Classification of  Turbomachines 3   1.3  Basic Laws and Governing Equations  3 1.3.1  Continuity Equation and Principle of Mass Conservation 4 1.3.2  Laws of Thermodynamics  4 1.3.3  Entropy Change in the Processes having Ideal Gas 11   1.4  Energy Transfer in Turbomachines and Euler’s Equation 12   1.5  Efficiencies of Compressors and Preheat Factor 13 1.5.1  Static-to-Static Efficiency  14 1.5.2  Total-to-Total Efficiency  14 1.5.3  Polytropic Efficiency  15 1.5.4  Stage Efficiency  16   1.6  Efficiencies of Turbines and Reheat Factor 18 1.6.1  Total-to-Static Efficiency  19 1.6.2  Total-to-Total Efficiency  19 1.6.3  Polytropic Efficiency  19 1.6.4  Stage Efficiency  20 1.6.5  Reheat Factor  22   1.7  Blade Classification  22   1.8  Blade Terminology 24   1.9  Drag and Lift  27 1.10  Cascade Testing  30 1.11  Drag and Lift in Cascade 34 1.12  Fans and Blowers 37 1.12.1  Different Types 38 1.12.2  Fan Laws 43 1.12.3  Fan Characteristics 45 1.12.4  Design Considerations 47 1.12.5  Fan Drives 49 Solved Examples 49 Summary58 Objective-Type Questions 60 Review Questions 62 Exercises62 Answers  63

viii 

•

Chapter 2  Centrifugal Compressors

C on ten t s

65

Learning Objectives 65   2.1  Introduction  65   2.2  Construction and Working  66   2.3  Energy Transfer 67   2.4  Velocity Diagram for Centrifugal Compressors  69   2.5  Slip Factor  72 2.5.1  Stodola’s Relative Eddy Theory  73   2.6  Stage Pressure Rise and Pressure (Loading) Coefficient 75   2.7  Degree of Reaction  79   2.8  Effect of Inlet Guide Vanes and Impeller Blade Profile 80   2.9  Surging  81 2.10  Stalling  83 2.10.1  Impeller Stall  84 2.10.2  Vaned Diffuser Stall  84 2.10.3  Vaneless Diffuser Stall  84 2.11  Choking  85 2.12  Centrifugal Compressor Characteristics Curves 86 Solved Examples 88 Summary104 Objective-Type Questions 105 Review Questions 107 Exercises107 Answers  108

Chapter 3  Axial Flow Compressors Learning Objectives  3.1  Introduction   3.2  Construction and Working    3.3  Energy Transfer   3.4  Velocity Diagram for Axial Flow Compressor   3.5  Elementary Theory  3.5.1  Pressure Losses Resulting from Fluid Friction  3.5.2  Pressure Loss Causing Shaft Power Loss  3.5.3  External Energy Losses   3.6  Factors Affecting Stage Pressure Rise 3.6.1  Blade Speed  3.6.2  Effect of Axial Velocity  3.6.3  Effect of Fluid Deflection    3.7  Blockage in Compressor Annulus   3.8  Degree of Reaction  3.8.1  For Degree of Reaction Equal to 50% (R = 0.5)

109 109 109 110 112 113 116 117 117 117 119 121 123 124 126 127 129

C ontents 

• 

ix

3.8.2  For Degree of Reaction Less Than 50% (R < 0.5) 129 3.8.3  For Degree of Reaction More Than 50% (R > 0.5) 130   3.9  Design Theory for 3D Flow 130 3.10  Design Process 134 3.11  Blade Design  135 3.11.1  Free Vortex Blade  136 3.11.2  Forced Vortex Blade  136 3.11.3  Constant Reaction Blade  137 3.12  Calculation of Stage Performance  137 3.13  Axial Flow Compressor Characteristics Curves 141 Solved Examples 142 Summary169 Objective-Type Questions 170 Review Questions 172 Exercises173 Answers  174

Chapter 4  Turbines  Learning Objectives   4.1  Introduction    4.2  Classification of Turbines    4.3  Description of Axial Flow Turbines    4.4  Energy Transfer in Axial Flow Turbines    4.5  Velocity Diagram for Axial Flow Turbines   4.6  Types of Blades in Axial Flow Turbines    4.7  Vortex Theory  4.7.1  Free Vortex Design 4.7.2  Constant Nozzle Angle Design   4.8  Choice of Blade Profile, Pitch and Chord   4.9  Estimation of Stage Performance in Axial Flow Turbines 4.10  Description of Radial Flow Turbines 4.11  Velocity Diagram and Elementary Theory for Radial Flow Turbines 4.11.1  Cantilever Blade Type Turbines  4.11.2 90° Blade Inward-Flow Radial Turbine 4.12  Estimation of Stage Performance in Outward-Flow Radial Turbines 4.13  Characteristic Curves for Turbines 4.14  Gas Turbine Starting and Control System 4.14.1  Single-Spool and Multi-Spool Systems 4.14.2  Control Systems  4.15  Combustion Systems in Gas Turbines 4.15.1  Standard Combustion System 4.16  Gas Turbine Blade Cooling 4.16.1  Convection Cooling or Internal Cooling 

175 175 175 175 176 177 180 184 186 186 187 188 191 191 193 193 195 200 203 204 204 206 207 207 209 210

x 

•

C on ten t s

4.16.2  Film Cooling  212 4.16.3  Transpiration Cooling  213 4.17  Safety Limits and Control 215 4.18  Losses in Turbine  216 4.19  Governing of Turbines 217 4.19.1  Nozzle Control Governing  218 4.19.2  Bypass Governing  219 4.19.3  Throttle Governing  219 4.19.4  Combined Governing 220 Solved Examples 220 Summary227 Objective-Type Questions 229 Review Questions 231 Answers  231 References232

Chapter 5  Steam Turbines 

233

Learning Objectives 233 5.1  Introduction  233 5.2  Classification of Steam Turbines  234 5.2.1  Direction of Flow  234 5.2.2  Cylinder Arrangement  234 5.2.3  Number of Stages  234 5.2.4  Steam Action  234 5.2.5  Speed of Rotation  235 5.2.6  Inlet Pressure  235 5.2.7  Steam Exhaust  235 5.3  Construction and Working of Steam Turbines 235 5.4  Losses in Steam Turbine  241 Summary241 Objective-Type Questions 242 Review Questions  244 Answers  244

Chapter 6  Pumps  Learning Objectives 6.1 Introduction 6.2  Classification of Pumps 6.3  Construction and Working of Pumps 6.3.1  Centrifugal Pump 6.3.2  Working  6.4  Centrifugal Pump Calculations 

245 245 245 245 247 247 251 252

C ontents 

• 

xi

6.4.1  Net Positive Suction Head 255 6.4.2  Minimum Starting Speed of Pump 255 6.5  Elementary Theory of Pumps  256 6.6  Performance Characteristic Curves  257 6.6.1  Characteristic Curves for Centrifugal Pumps  257 6.6.2  Characteristics Curves for Axial Flow Pumps  258 6.7  Cavitation and Its Control  259 6.8  Miscellaneous Types of Pumps  260 Solved Examples 264 Summary271 Objective-Type Questions 272 Review Questions 274 Exercises274 Answers  275

Chapter 7  Design Considerations of Thermal Turbomachines

277

Learning Objectives 277 7.1 Introduction 277 7.2  Overall Design Choices  277 7.2.1  Shafts  278 7.2.2  Rotor  279 7.2.3  Stator  280 7.3  Selection of Number of Stages 280 7.4  Material Selection  280 7.5  Design with Traditional Materials  281 7.5.1  Fatigue  282 7.5.2  Creep  282 7.5.3  Crack Propagation  282 7.5.4  Oxidation  283 7.5.5  Ultimate Tensile Stress  283 7.5.6  Vibration Characteristics  283 7.5.7  Thermal Stresses  283 7.6  Testing and Measurements 283 7.6.1  Unsteady Flow Considerations 287 7.6.2  Error Estimation 288 7.6.3  Test Result Presentation 288 Summary289 Objective-Type Questions 289 Review Questions 291 Answers  291

1

Fundamental Concepts of Turbomachines

Learning Objectives After reading this chapter, you will be able to understand: •  Introduction and definition of  turbomachines. •  Turbine efficiency and reheat factor. •  Classification of turbomachines. •  Classification of blades and blade terminology. •  Basic laws and governing equations for   •  Phenomenon of drag and lift. turbomachines. •  Cascade testing and drag and lift in cascade •  Euler’s equation and energy transfer in •  Basic calculations related to turbomachines. ­turbomachines. •  Principle and working of fans and blowers. •  Compressor efficiency and preheat factor.

1.1

Introduction and Definition of Turbomachines

The history of turbomachines dates back to 70 BC when Romans first introduced paddle-type waterwheels for grinding grains. The literature reports about the invention of the first steam turbine of pure-reaction type (a steam-powered engine called aeolipile) in 120 BC by the Greek geometrician Hero of Alexandria. Hero’s aeolipile (Fig. 1) had a spherical vessel mounted on bearings, with oppositely placed pipes projecting from it. These pipes discharged steam tangentially out in the periphery of the vessel (steam jets), which rotated the vessel due to the thrust generated by the steam jets’. In 1629, Giovanni Branca developed the first impulse turbine (Fig. 2). Centrifugal blowers and pumps were reported to be developed by D. Papin in 1705. Waterwheels with curved blades, which were the precursor to radial-f low hydraulic turbines, were reported to be developed in 1753 by Bernard Forest de Belidor. The development of turbomachines got an impetus when the Swiss mathematician Leonhard Euler carried out the mathematical analysis of the working of Hero’s turbine and published Euler’s equation based on Newton’s laws in 1754. The word ‘turbine’ was used for the first time in 1822 by Claude Burdin of France. This word was developed from the Latin term ‘turbinis’, meaning something that spins, like a spinning top. Fourneyorn, a radial outf low-type turbine, was developed in 1843 by Elwood Morris of the US which was later modified by U. A. Boyden in 1846 for improved efficiency by putting a vaneless radial diffuser in it. Vortex turbine, having a radial-inf low turbine with a spiral inlet casing and adjustable inlet guide vanes, was developed in 1847 by James Thomson of the UK. In 1851, James B. Francis developed the Francis turbine. A number of successful steam turbines were developed at the end of the 19th century when Gustaf de Lavel designed a high-speed steam turbine built on the principle of reaction turbines in 1883.

2 

•

Cha pter 1 / Fu n dam en tal C on c ep ts o f T urb oma c h i n es

Figure 1  Aeolipile. The term ‘turbomachine’ has been derived from the Latin words ‘turbo’ and ‘machine’. The Latin word ‘turbo’ means spin, as turbomachines have a rotating element. Turbomachine refers to a device which changes the enthalpy of the f luid stream passing through it and where work interaction on the rotor shaft of the device occurs. Thus, turbomachine is a device that produces energy interaction through a rotating element called rotor ; that is, the energy of the f luid stream passing through a turbomachine either increases or decreases. In other words, turbomachine is a device which takes out or provides energy to the f luid passing through it mostly owing to the f luid dynamics of the rotor; this interaction between the rotor and the f luid appears as a change in enthalpy. This change in enthalpy may also be due to heat transfer, but it would be significantly small compared with the enthalpy change due to the interaction between the f luid and the machine. A drag also appears along with the lift, but generally, turbomachines are designed in a manner so as to keep such unwanted drag forces and other losses small or negligible. However, there are turbomachines in which most of the interaction between the f luid and the rotor is of drag type due to the viscous action of the f luid; such machines are also called viscous-action machines.

Figure 2  Branca’s turbine.

1.3  Basic Laws an d G ov er n in g Eq uation s 

1.2

• 

3

Classification of Turbomachines

Turbomachines can be classified on the basis of various attributes in the following manner: 1. Type of work interaction: Turbomachines can be work-absorbing machines (or power-absorbing machines), such as compressors, pumps, etc. or work-producing machines (or power-producing machines), such as turbines. In work-absorbing machines, the enthalpy of the f luid increases from the inlet to the exit, whereas in work-producing machines, it decreases from the inlet to the exit. 2. Type of f low: On the basis of the type of f low, turbomachines can be classified as •  Axial-f low turbomachines: In these the f luid f lows in the direction parallel to the axis of the rotor. •  Radial-f low turbomachines or centrifugal turbomachines: In these the f luid moves either radially ­inwards or outwards. •  Mixed-f low turbomachines: In these the f low at the inlet and at the exit is neither in the radial nor in the axial direction. These machines include axial-f low compressors, axial-f low turbines, radial-f low compressors, radialf low turbines, mixed-f low turbines, etc. 3. Shrouding: On the basis of shrouding (enclosure of the casing), turbomachines can be classified as •  Shrouded turbomachines: In these turbomachines, the rotating elements (rotor) are enclosed in a casing so that the working f luid cannot f low around the edges of the impeller. Some examples are turbines, compressors and pumps. •  Unshrouded turbomachines: In these turbomachines, the rotating elements (rotor) are not enclosed in a casing and the f luid f lows around the edges of the impeller. Some examples are propeller and fans. 4. F luid admission: Turbomachines classified on the basis of f luid admission are •  Full-admission turbomachines: In these turbomachines, the f luid f lows through the blading during admission in an axisymmetrical manner. •  Partial-admission turbomachines: In these turbomachines, only a portion of the blading may be used for the admission of the f luid. 5. Number of stages: On the basis of the number of stages, turbomachines can be classified as •  Single-stage turbomachines. •  Multiple-stage turbomachines. The ‘stage’ generally refers to the minimum configuration of the rotor and the stator needed to obtain the required performance from the turbomachine.

1.3

Basic Laws and Governing Equations

Turbomachines can be studied and analyzed using basic laws of thermodynamics and f luid mechanics. These laws and governing equations are discussed in the following subsections.

About the Book

New in This Edition

The book Thermal Turbomachines presents a systematic account of the concepts and principles of thermal turbomachines. It covers the requirements of undergraduate course on turbomachinery including Thermal Turbomachines and Pumps for students of Mechanical and Aerospace Engineering. It is aimed at building the basics for advanced courses in turbomachines at postgraduate level. Topics are presented in simple and lucid style and provided with sufficient number of illustrations and numerical problems – both solved and unsolved – along with numerous review questions. The book is written in SI system of units.

The following sections have been supplemented in Chapter 1 and Chapter 7: Chapter 1 l Fans and Blowers v Different Types v Fan Laws v Fan Characteristics v Design Considerations v Fan Drives Chapter 7 l Testing and Measurements v Unsteady Flow Considerations v Error Estimation v Test Result Presentation

About the Author Dr. Onkar Singh, formerly Founder Vice Chancellor of Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, is the Professor of Mechanical Engineering at Harcourt Butler Technical University, Kanpur, Uttar Pradesh. He has vast teaching experience of more than 27 years at undergraduate and postgraduate level in different institutions. Dr. Singh has published large number of research papers in national/international journals and conference proceedings. His areas of interest include Thermal Engineering, CAD, and Turbomachines. He has undertaken numerous research projects funded by AICTE, New Delhi; Department of Science and Technology, Govt. of India; University Grants Commission, New Delhi; Council of Science and Technology, Uttar Pradesh; etc. He is the proud recipient of AICTE Young Teacher Career Award, possesses two records in Limca Book of Records, has received 100 Most Influential Vice Chancellors Award and Asia's Education Excellence Award, etc.

READER LEVEL Undergraduate/Graduate SHELVING CATEGORY Engineering

ISBN: 978-81-265-7923-5

9 788126 579235