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Fluid Mechanics and Thermodynamics of Turbomachinery is the leading turbomachinery book due to its balanced coverage of theory and application. Starting with background principles in fluid mechanics and thermodynamics, the authors go on to discuss axial flow turbines and compressors, centrifugal pumps, fans, and compressors, and radial flow gas turbines, hydraulic turbines, and wind turbines.

In this new edition,more coverage is devoted to modern approaches to analysis and design, including CFD and FEA techniques. Used as a core text in senior undergraduate and graduate level courses this book will also appeal to professional engineers in the aerospace, global power, oil & gas and other industries who are involved in the design and operation of turbomachines.

Key Features – Fluid Mechanics and Thermodynamics of Turbomachinery

  • More coverage of a variety of types of turbomachinery, including centrifugal pumps and gas turbines
  • Addition of numerical and computational tools, including more discussion of CFD and FEA techniques to reflect modern practice in the area
  • More end of chapter exercises and in-chapter worked examples


Professional mechanical, civil, automotive, aeronautical, and control engineers; advanced undergraduate and graduate students in mechanical, civil, automotive and aeronautical engineering

Preface – Fluid Mechanics and Thermodynamics of Turbomachinery

This book was originally conceived as a text for students in their final year reading for an honors degree in engineering that included turbomachinery as a main subject. It was also found to be a useful support for students embarking on postgraduate courses at masters level. The book was written for engineers rather than for mathematicians, although some knowledge of mathematics will prove most useful. Also, it is assumed from the start that readers will have completed preliminary courses in fluid mechanics.

The stress is placed on the actual physics of the flows and the use of specialized mathematical methods is kept to a minimum. Compared to the sixth edition, this new edition has had a large number of changes made in terms of presentation of ideas, new material, and additional examples. In Chapter 1, following the definition of a turbomachine, the fundamental laws of flow continuity, the energy and entropy equations are introduced as well as the all-important Euler work equation. In addition, the properties of working fluids other than perfect gases are covered and a steam chart is included in the appendices. In Chapter 2, the main emphasis is given to the application of the “similarity laws,” to dimensional analysis of all types of turbomachine and their performance characteristics.

Additional types of turbomachine are considered and examples of high-speed characteristics are presented. The important ideas of specific speed and specific diameter emerge from these concepts and their application is illustrated in the Cordier Diagram, which shows how to select the machine that will give the highest efficiency for a given duty. Also, in this chapter the basics of cavitation are examined for pumps and hydraulic turbines. The measurement and understanding of cascade aerodynamics is the basis of modern axial turbomachine design and analysis. In Chapter 3, the subject of cascade aerodynamics is presented in preparation for the following chapters on axial turbines and compressors. This chapter was completely reorganized in the previous edition. In this edition, further emphasis is given to compressible flow and on understanding the physics that constrain the design of turbomachine blades and determine cascade performance. In addition, a completely new section on computational methods for cascade design and analysis has been added, which presents the details of different numerical approaches and their capabilities. Chapters 4 and 5 cover axial turbines and axial compressors, respectively. In Chapter 4, new material has been added to give better coverage of steam turbines.

Sections explaining the numerous sources of loss within a turbine have been added and the relationships between loss and efficiency are further detailed. The examples and end-of-chapter problems have also been updated. Within this chapter, the merits of different styles of turbine design are considered including the implications for mechanical design such as centrifugal stress levels and cooling in high-speed and high temperature turbines. Through the use of some relatively simple correlations, the trends in turbine efficiency with the main turbine parameters are presented. In Chapter 5, the analysis and preliminary design of all types of axial compressors are covered. Several new figures, examples, and end-of-chapter problems have been added. There is new coverage of compressor loss sources and, in particular, shock wave losses within high-speed rotors are explored in detail. New material on off-design operation and stage matching in multistage compressors has been added, which enables the performance of large compressors to be quantified.

Several new examples and end-of-chapter problems have also been added that reflect the new material on design, off-design operation, and compressible flow analysis of high-speed compressors. Chapter 6 covers three-dimensional effects in axial turbomachinery and it possibly has the most new features relative to the sixth edition. There are extensive new sections on three-dimensional flows, three-dimensional design features, and three-dimensional computational methods. The section on through-flow methods has also been reworked and updated. Numerous explanatory figures have been added and there are new worked examples on vortex design and additional endof-chapter problems. Radial turbomachinery remains hugely important for a vast number of applications, such as turbocharging for internal combustion engines, oil and gas transportation, and air liquefaction. As jet engine cores become more compact there is also the possibility of radial machines finding new uses within aerospace applications. Fluid Mechanics and Thermodynamics of Turbomachinery

The analysis and design principles for centrifugal compressors and radial inflow turbines are covered in Chapters 7 and 8. Improvements have been made relative to the fifth edition, including new examples, corrections to the material, and reorganization of some sections. Renewable energy topics were first added to the fourth edition of this book by way of the Wells turbine and a new chapter on hydraulic turbines. In the fifth edition, a new chapter on wind turbines was added. Both of these chapters have been retained in this edition as the world remains increasingly concerned with the very major issues surrounding the use of various forms of energy. There is continuous pressure to obtain more power from renewable energy sources and hydroelectricity and wind power have a significant role to play. In this edition, hydraulic turbines are covered in Chapter 9, which includes coverage of the Wells turbine, a new section on tidal power generators, and several new example problems. Fluid Mechanics and Thermodynamics of Turbomachinery

Chapter 10 covers the essential fluid mechanics of wind turbines, together with numerous worked examples at various levels of difficulty. In this edition, the range of coverage of the wind itself has been increased in terms of probability theory. This allows for a better understanding of how much energy a given size of wind turbine can capture from a normally gusting wind. Instantaneous measurements of wind speeds made with anemometers are used to determine average velocities and the average wind power. Important aspects concerning the criteria of blade selection and blade manufacture, control methods for regulating power output and rotor speed, and performance testing are touched upon. Also included are some very brief notes concerning public and environmental issues, which are becoming increasingly important as they, ultimately, can affect the development of wind turbines. To develop the understanding of students as they progress through the book, the expounded theories are illustrated by a selection of worked examples. As well as these examples, each chapter contains problems for solution, some easy, some hard. See what you make of them—answers are provided in Appendix F!


The authors are indebted to a large number of people in publishing, teaching, research, and manufacturing organizations for their help and support in the preparation of this volume. In particular, thanks are given for the kind permission to use photographs and line diagrams appearing in this edition, as listed below: ABB (Brown Boveri, Ltd.) American Wind Energy Association Bergey Windpower Company Dyson Ltd. Elsevier Science Hodder Education Institution of Mechanical Engineers Kvaener Energy, Norway Marine Current Turbines Ltd., UK National Aeronautics and Space Administration (NASA) NREL Rolls-Royce plc The Royal Aeronautical Society and its Aeronautical Journal Siemens (Steam Division) Sirona Dental Sulzer Hydro of Zurich Sussex Steam Co., UK US Department of Energy Voith Hydro Inc., Pennsylvania The Whittle Laboratory, Cambridge, UK I would like to give my belated thanks to the late Professor W.J. Kearton of the University of Liverpool and his influential book Steam Turbine Theory and Practice, who spent a great deal of time and effort teaching us about engineering and instilled in me an increasing and life-long interest in turbomachinery. This would not have been possible without the University of Liverpool’s award of the W.R. Pickup Foundation Scholarship supporting me as a university student, opening doors of opportunity that changed my life. Also, I give my most grateful thanks to Professor (now Sir) John H. Horlock for nurturing my interest in the wealth of mysteries concerning the flows through compressors and turbine blades during his tenure of the Harrison Chair of Mechanical Engineering at the University of Liverpool. At an early stage of the sixth edition some deep and helpful discussions of possible additions to the new edition took place with Emeritus Professor John P. Gostelow (a former undergraduate student of mine). There are also many members of staff in the Department of Mechanical Engineering during my career who helped and instructed me for which I am grateful. Also, I am most grateful for the help given to me by the staff of the Harold Cohen Library, University of Liverpool, in my frequent searches for new material needed for the seventh edition.

Last, but by no means least, to my wife Rosaleen, whose patient support and occasional suggestions enabled me to find the energy to complete this new edition. S. Larry Dixon I would like to thank the University of Cambridge, Department of Engineering, where I have been a student, researcher, and now lecturer. Many people there have contributed to my development as an academic and engineer. Of particular importance is Professor John Young who initiated my enthusiasm for thermofluids through his excellent teaching of the subject. I am also very grateful to Rolls-Royce plc, where I worked for several years. I learned a huge amount about compressor and turbine aerodynamics from my colleagues there and they continue to support me in my research activities. Almost all the contributions I made to this new edition were written in my office at King’s College, Cambridge, during a sabbatical. As well as providing accommodation and food, King’s is full of exceptional and friendly people who I would like to thank for their companionship and help during the preparation of this book. Fluid Mechanics and Thermodynamics of Turbomachinery

As a lecturer in turbomachinery, there is no better place to be based than the Whittle Laboratory. I would like to thank the members of the laboratory, past and present, for their support and all they have taught me. I would like to make a special mention of Dr. Tom Hynes, my Ph.D. supervisor, for encouraging my return to academia from industry and for handing over the teaching of a turbomachinery course to me when I started as a lecturer. During my time in the laboratory, Dr. Rob Miller has been a great friend and colleague and I would like to thank him for the sound advice he has given on many technical, professional, and personal matters. Several laboratory members have also helped in the preparation of suitable figures for this book. These include Dr. Graham Pullan, Dr. Liping Xu, Dr Martin Goodhand, Vicente Jerez-Fidalgo, Ewan Gunn, and Peter O’Brien. Finally, special personal thanks go to my parents, Hazel and Alan, for all they have done for me. I would like to dedicate my work on this book to my wife Gisella and my son Sebastian. Cesare A. Hall

Table of Contents – Fluid Mechanics and Thermodynamics of Turbomachinery


Preface to the Seventh Edition


List of Symbols



Chapter 1. Introduction: Basic Principles

1.1 Definition of a turbomachine

1.2 Coordinate system

1.3 The fundamental laws

1.4 The equation of continuity

1.5 The first law of thermodynamics

1.6 The momentum equation

1.7 The second law of thermodynamics—entropy

1.8 Bernoulli’s equation

1.9 The thermodynamic properties of fluids

1.10 Compressible flow relations for perfect gases

1.11 Definitions of efficiency

1.12 Small stage or polytropic efficiency

1.13 The inherent unsteadiness of the flow within turbomachines


Chapter 2. Dimensional Analysis: Similitude

2.1 Dimensional analysis and performance laws

2.2 Incompressible fluid analysis

2.3 Performance characteristics for low-speed machines

2.4 Compressible flow analysis

2.5 Performance characteristics for high-speed machines

2.6 Specific speed and specific diameter

2.7 Cavitation


Chapter 3. Two-Dimensional Cascades

3.1 Introduction

3.2 Cascade geometry

3.3 Cascade flow characteristics

3.4 Analysis of cascade forces

3.5 Compressor cascade performance

3.6 Turbine cascades

3.7 Cascade computational analysis


Chapter 4. Axial-Flow Turbines: Mean-Line Analysis and Design

4.1 Introduction

4.2 Velocity diagrams of the axial turbine stage

4.3 Turbine stage design parameters

4.4 Thermodynamics of the axial turbine stage

4.5 Repeating stage turbines

4.6 Stage losses and efficiency

4.7 Preliminary axial turbine design

4.8 Styles of turbine

4.9 Effect of reaction on efficiency

4.10 Diffusion within blade rows

4.11 The efficiency correlation of Smith (1965)

4.12 Design point efficiency of a turbine stage

4.13 Stresses in turbine rotor blades

4.14 Turbine blade cooling

4.15 Turbine flow characteristics


Chapter 5. Axial-Flow Compressors and Ducted Fans

5.1 Introduction

5.2 Mean-line analysis of the compressor stage

5.3 Velocity diagrams of the compressor stage

5.4 Thermodynamics of the compressor stage

5.5 Stage loss relationships and efficiency

5.6 Mean-line calculation through a compressor rotor

5.7 Preliminary compressor stage design

5.8 Off-design performance

5.9 Multistage compressor performance

5.10 High Mach number compressor stages

5.11 Stall and surge phenomena in compressors

5.12 Low speed ducted fans


Chapter 6. Three-Dimensional Flows in Axial Turbomachines

6.1 Introduction

6.2 Theory of radial equilibrium

6.3 The indirect problem

6.4 The direct problem

6.5 Compressible flow through a fixed blade row

6.6 Constant specific mass flow

6.7 Off-design performance of a stage

6.8 Free-vortex turbine stage

6.9 Actuator disc approach

6.10 Computational through-flow methods

6.11 3D flow features

6.12 3D design

6.13 The application of 3D computational fluid dynamics


Chapter 7. Centrifugal Pumps, Fans, and Compressors

7.1 Introduction

7.2 Some definitions

7.3 Thermodynamic analysis of a centrifugal compressor

7.4 Inlet velocity limitations at the compressor eye

7.5 Design of a pump inlet

7.6 Design of a centrifugal compressor inlet

7.7 The slip factor

7.8 A unified correlation for slip factor

7.9 Head increase of a centrifugal pump

7.10 Performance of centrifugal compressors

7.11 The diffuser system

7.12 Diffuser performance parameters

7.13 Choking in a compressor stage


Chapter 8. Radial-Flow Gas Turbines

8.1 Introduction

8.2 Types of IFR turbine

8.3 Thermodynamics of the 90° IFR turbine

8.4 Basic design of the rotor

8.5 Nominal design point efficiency

8.6 Some Mach number relations

8.7 The scroll and stator blades

8.8 Optimum efficiency considerations

8.9 Criterion for minimum number of blades

8.10 Design considerations for rotor exit

8.11 Significance and application of specific speed

8.12 Optimum design selection of 90° IFR turbines

8.13 Clearance and windage losses

8.14 Cooled 90° IFR turbines


Chapter 9. Hydraulic Turbines

9.1 Introduction

9.2 Hydraulic turbines

9.3 The Pelton turbine

9.4 Reaction turbines

9.5 The Francis turbine

9.6 The Kaplan turbine

9.7 Effect of size on turbomachine efficiency

9.8 Cavitation in hydraulic turbines

9.9 Application of CFD to the design of hydraulic turbines

9.10 The Wells turbine

9.11 Tidal power


Chapter 10. Wind Turbines

10.1 Introduction

10.2 Types of wind turbine

10.3 Performance measurement of wind turbines

10.4 Annual energy output

10.5 Statistical analysis of wind data

10.6 Actuator disc approach

10.7 Blade element theory

10.8 The BEM method

10.9 Rotor configurations

10.10 The power output at optimum conditions

10.11 HAWT blade section criteria

10.12 Developments in blade manufacture

10.13 Control methods (starting, modulating, and stopping)

10.14 Blade tip shapes

10.15 Performance testing

10.16 Performance prediction codes

10.17 Environmental matters

10.18 The largest wind turbines

10.19 Final remarks


Appendix A. Preliminary Design of an Axial-Flow Turbine for a Large Turbocharger

Design requirements

Mean radius design

Determining the mean radius velocity triangles and efficiency

Determining the root and tip radii

Variation of reaction at the hub

Choosing a suitable stage geometry

Estimating the pitch/chord ratio

Blade angles and gas flow angles

Additional information concerning the design



Appendix B. Preliminary Design of a Centrifugal Compressor for a Turbocharge

Design requirements and assumptions

Determining the blade speed and impeller radius

Design of impeller inlet

Efficiency considerations for the impeller

Design of impeller exit

Flow in the vaneless space

The vaned diffuser

The volute

Determining the exit stagnation pressure, p03, and overall compressor efficiency, ηC


Appendix C. Tables for the Compressible Flow of a Perfect Gas

Appendix D. Conversion of British and American Units to SI Units

Appendix E. Mollier Chart for Steam

Appendix F. Answers to Problems

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10


Details – Fluid Mechanics and Thermodynamics of Turbomachinery

No. of pages: 556Language: EnglishCopyright: © Butterworth-Heinemann 2014Published: 30th October 2013Imprint: Butterworth-HeinemannHardcover ISBN: 9780124159549eBook ISBN: 9780123914101

About the Author

S. Larry Dixon

Dr. Dixon has published numerous scientific research papers in turbomachinery and lectured in turbomachinery at the University of Liverpool for nearly 40 years. For 25 of those years he was Chief Examiner in Mechanics for the Council of Engineering Institutions in the UK.

Affiliations and Expertise

Senior Fellow at the University of Liverpool

Cesare Hall

Dr. Hall has been University Lecturer in turbomachinery at the University of Cambridge since 2005. His current research with the university’s Silent Aircraft Initiative has led to the development of radical new ideas for aircraft engine design. Prior to teaching, he worked at Rolls-Royce as a turbomachinery aerodynamicist.

Affiliations and Expertise

University Lecturer in Turbomachinery, University of Cambridge, UK

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