Fluid Mechanics and Its Applications

Volume 109

Series Editor André Thess, German Aerospace Center, Institute of Engineering Thermodynam-ics, Stuttgart, Germany

Founding EditorRené Moreau, Ecole Nationale Supérieure d’Hydraulique de Grenoble, Saint Martin d’Hères Cedex, France

The purpose of this series is to focus on subjects in which fluid mechanics plays a fundamental role. As well as the more traditional applications of aeronautics, hy-draulics, heat and mass transfer etc., books will be published dealing with topics which are currently in a state of rapid development, such as turbulence, suspen-sions and multiphase fluids, super and hypersonic flows and numerical modelling techniques. It is a widely held view that it is the interdisciplinary subjects that will receive intense scientific attention, bringing them to the forefront of technological advancement. Fluids have the ability to transport matter and its properties as well as transmit force, therefore fluid mechanics is a subject that is particulary open to cross fertilisation with other sciences and disciplines of engineering. The subject of fluid mechanics will be highly relevant in such domains as chemical, metallurgical, biological and ecological engineering. This series is particularly open to such new multidisciplinary domains. The median level of presentation is the first year gradu-ate student. Some texts are monographs defining the current state of a field; others are accessible to final year undergraduates; but essentially the emphasis is on read-ability and clarity.

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More information about this series at http://www.springer.com/series/5980

Erik Dick

Fundamentals of Turbomachines

ISSN 0926-5112 ISSN 2215-0056 (electronic)Fluid Mechanics and Its ApplicationsISBN 978-94-017-9626-2 ISBN 978-94-017-9627-9 (eBook)DOI 10.1007/978-94-017-9627-9

Library of Congress Control Number: 2014954750

Springer Dordrecht Heidelberg New York London© Springer Science+Business Media Dordrecht 2015This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, 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 publisher, 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 publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Erik DickDepartment of Flow, Heat and Combustion MechanicsGhent UniversityGentBelgium

v

Preface

This book is the English language version of a course on turbomachines, taught in Dutch by the author at Ghent University from 1992 to 2013. It was composed at the occasion of the change to English as teaching language in master programmes in engineering, starting with the academic year 2013–2014. Meanwhile, the text was adapted to include some modern evolutions in the field of turbomachinery, however avoiding advanced topics, since the objective of the book is to teach fundamentals of turbomachines.

In the first chapter, the basic equations of fluid mechanics and thermodynam-ics are derived from first principles, formulated for application to turbomachines. With this chapter, the necessary prior knowledge for the study of turbomachines is refreshed. The prior knowledge needed is basic fluid mechanics and basic technical thermodynamics. For fluid mechanics, this comprises topics such as mechanical properties of fluids, fluid statics, equations of flow in integral and differential form, dimensional analysis and internal laminar and turbulent flow of constant density

vi Preface

fluids. For technical thermodynamics, the supposed prior knowledge encompasses thermal properties of fluids, first law and second law of thermodynamics, basic heat engine cycles, gas mixtures, combustion and detailed analysis of steam cycles.

The course on turbomachines is taught at Ghent University in two parts. Chapters 1–10 form a first part, taught to all master students in electromechanical engineer-ing. This part requires basic knowledge of flow past profiles, boundary layer flow and high speed flow of compressible fluids, which are topics often covered in an advanced fluid mechanics course. The necessary fundamentals of these topics are explained in the beginning of Chap. 2 and in Chap. 4. The second part is Chaps. 11–15, taught to students with specialisation in mechanical energy engineering. This part requires somewhat more advanced knowledge of fluid mechanics. Relevant topics are transition, turbulence and heat transfer in boundary layer flows and shock and expansion phenomena in high speed flows of compressible fluids. However, care has been taken not to rely too much on prior knowledge of these topics.

The objective of the book is, as already said, study of the fundamentals of tur-bomachines. The approach is analysis of all kinds of turbomachines with the same theoretical framework. Basic equations are formulated for a general equation of state of a fluid. Specification of constant density or ideal gas is only done when ana-lysing particular machines. The building up of theory is mixed in the sense that first derivations are general, but that elaboration of the theoretical concepts is done on a particular machine, however taking into account the possibility for reuse on other machines or generalisation from constant density formulation to variable density formulation. The analysis starts with radial and axial fans, because these machines are the simplest ones. The next machines are steam turbines. The order of treating the different types of turbomachines is governed by the possibility of gradually building up the theoretical concepts. For each of the machine types, a balance is sought between fundamental understanding and acquiring knowledge of practical aspects. The main concern is always fundamental understanding and bringing the reader to independent reasoning. The point of view taken by the author is that read-ers should be able to understand what they see when a turbomachine is opened. They should also be able to make a reasoned choice of a turbomachine for a specific application and understand its operation. Design is not a primary objective. Design requires a more specialised study, although basic design of the simplest turboma-chines such as a centrifugal fan, an axial steam turbine or a centrifugal pump is possible with the topics covered in the book.

Erik DickGhent, September 2014

vii

Acknowledgements

The following companies kindly provided figures.

For fans: ebm-papst; Fläkt Woods; TLT-Turbo.

For pumps: ANDRITZ; Flygt (a Xylem company); Grundfos; Johnson Pump (SPX Flow Technology); Klaus Union; Sulzer; Sundyne; Wilo.

For steam turbines: Alstom; MAN Diesel &Turbo; Siemens Energy.

For hydraulic turbines: ANDRITZ HYDRO.

For wind turbines: ENERCON; Vestas.

For power gas turbines: Mitsubishi-Hitachi Power Systems; Siemens Energy.

For aero gas turbines: GE Aviation; Rolls-Royce.

For radial compressors, radial turbines and turbochargers: ABB Turbo Systems; Dresser-Rand; KBB Kompressorenbau Bannewitz; MAN Diesel &Turbo.

The following publishers gave permission to reprint figures.

ASME; SAGE Publications; Springer Verlag; Vogel Buchverlag.

ix

Author Biography

Erik Dick was born on December 10, 1950 in Torhout, Belgium. He obtained a M.Sc. in electromechanical engineering from Ghent University in 1973 and a Ph.D. in computational fluid dynamics in 1980. From 1973 he worked as researcher and became full professor of mechanical engineering at Ghent University in 1995, where he teaches turbomachines and computational fluid dynamics. His area of research is computational methods and turbulence and transition models for flow problems in mechanical engineering. He is author or co-author of about 125 papers in international scientific

journals and about 250 papers at international conferences. He is the recipient of the 1990 Iwan Akerman award for fluid machinery of the Belgian National Science Foundation.

xi

List of Symbols

a acceleration m/s2

or axial interference factor –A through-flow section area m2

b rotor width in axial direction mor tangential interference factor –or bypass ratio –

c chord mor velocity of sound m/s

ca axial chord m

CD drag coefficient –

cf friction coefficient –

Cf centrifugal force by rotor rotation N/kgCFu tangential force coefficient –CL lift coefficientCM Pfleiderer moment coefficient (3.30) –Co Coriolis force by rotor rotation N/kgcp differential specific heat at constant pressure J/kgK

Cp pressure coefficient –

or integral specific heat at constant pressure J/kgKCP power coefficient –CT thrust coefficient –

Cu centrifugal force by curvature N/kgd diameter mD drag per unit of span N/mDF diffusion factor –Dloc local diffusion factor –Ds specific diameter (7.7) –e internal energy per unit of mass J/kgEk kinetic energy per unit of mass J/kg

xii List of Symbols

Em mechanical energy per unit of mass J/kgEp pressure energy per unit of mass J/kgf force per unit of mass N/kg

or friction factor (2.30) –or fuel-air ratio –

fR curvature factor (3.26) –g gravitational force per unit of mass N/kgh enthalpy J/kg

or blade height or scroll height mHm manometric head mI rothalpy J/kgk equivalent sand-grain roughness mL lift per unit of span N/m

�m mass flow rate kg/s

M rotor moment NmMd disc or wheel friction moment NmMshaft shaft moment Nm

Mst static moment of meridional section m3

NPSH net positive suction head (8.5) –n polytropic exponent�n unit normal –

p pressure PaP power WPf Pfleiderer factor (3.23) m3

q heat transferred per unit of mass J/kgor dynamic pressure Pa

qirr heat by dissipation inside flow path J/kg

qirr0 heat by dissipation outside flow path J/kg

Q volume flow rate m3/sor heat transferred per unit of time J/s=W

r radius mor pressure ratio –

R kinematic degree of reaction –or radius of curvature mor gas constant J/kgK

Re Reynolds number –Rp pressure degree of reaction (3.1) –

Rs isentropic degree of reaction (6.16) –s entropy J/kgK

or spacing of blades m

xiiiList of Symbols

S surface area m2

t time sor thickness of blades m

T temperature K or °Cor thrust force N

u blade speed (radius x rotational speed) m/sU gravitational potential energy m/s

v0inflow velocity m/s

ve energy reference velocity m/s

w flow velocity in relative frame m/sW work per unit of time J/s = Wx coordinate along streamline m

or coordinate in axial direction my coordinate perpendicular to streamline m

or coordinate in circumferential direction mz coordinate in vertical direction m

or coordinate in radial direction mZ number of blades –α angle of absolute velocity w.r.t. meridional plane °

β angle of relative velocity w.r.t. meridional plane °

Γ circulation along a contour m2/s

δ boundary layer thickness m

W∆ rotor work per unit of mass J/kg

ε Pfleiderer work reduction factor (3.23) –

ηi internal efficiency –

ηmmechanical efficiency –

η p polytropic efficiency –or propulsive efficiency (12.7)

ηs isentropic efficiency –

ηsreisentropic re-expansion efficiency (11.7) –

ηt thermal efficiency (12.9) –ηtd thermodynamic efficiency (12.9) –ηtt total-to-total isentropic efficiency –ηv volumetric efficiencyη∞ infinitesimal efficiency –

θ angular coordinate rad

or flow turning angle radκ heat transfer coefficient (11.18) J/kJK

λ speed ratio (u/v0) –

xiv List of Symbols

or coefficient in Pfleiderer factor Pf –m dynamic viscosity Pas

ν kinematic viscosity Pas

ξ pressure loss coefficient –

ρ density kg/m3

σ solidity c/s –

or Stodola slip factor (3.20) –or cavitation number(8.1) –

σ a axial solidity ca/s –σM moment solidity (3.31) –τ shear stress N/m3

or obstruction factor (Fig. 3.16) –

φ flow coefficient v ua / or v ur2 2/ –

Φ flow factor (7.4) –

ψ work coefficient 22/W uD

–

Ψ head factor (7.5) –

ψ 0 rotor total pressure coefficient –ψ r rotor static pressure coefficient –

ω rotor of relative velocity m2/s

or enthalpy loss coefficient –

W rotational speed rad/s

sW specific speed (7.6) –

ssW suction specific speed (8.14) –

Subscripts

0 inlet of machine or installationor total state

1 just upstream of rotor1b just downstream of rotor inlet2 just downstream of rotor2b just upstream of rotor outlet3 outlet of machine or installation∞ far away from object

or with infinite number of blades

xvList of Symbols

or on infinitesimal flow patha in axial directionc compressor

or critical or choking valued discharge/delivery sidedef deflectiondyn dynamic value (12.6–12.7)gas gas value (12.6–12.7)id idealirr due to irreversibilitym in meridional direction

or mechanical or manometric or meanmean mean valueo optimump pressure sideprop propulsive value (12.6–12.7)r in radial direction or in relative frame

or rotor or reversibles suction side or stator

or isentropicss isentropic for statorsr isentropic for rotorsre isentropic re-expansion valuet theoretical value

or turbineT tip valuett total-to-total isentropicu in circumferential direction

Superscripts

* design valueor choking value

− average→ vector quantityb blade value

xvii

Contents

1 Working Principles ................................................................................... 11.1 Definition of a Turbomachine ............................................................ 11.2 Examples of Axial Turbomachines .................................................... 2

1.2.1 Axial Hydraulic Turbine ......................................................... 21.2.2 Axial Pump ............................................................................. 4

1.3 Mean Line Analysis ............................................................................ 51.4 Basic Laws for Stationary Duct Parts ................................................ 7

1.4.1 Conservation of Mass ............................................................. 71.4.2 Conservation of Momentum .................................................. 71.4.3 Conservation of Energy .......................................................... 91.4.4 Forms of Energy: Mechanical Energy and Head ................... 101.4.5 Energy Dissipation: Head Loss .............................................. 12

1.5 Basic Laws for Rotating Duct Parts ................................................... 141.5.1 Work and Energy Equations in a Rotating Frame

with Constant Angular Velocity ............................................. 141.5.2 Moment of Momentum in the Absolute Frame: Rotor Work ... 161.5.3 Moment of Momentum in the Relative Frame:

Forces Intervening in the Rotor Work .................................... 211.5.4 Energy Component Changes Caused By the Rotor Work ...... 231.5.5 Rotor Work in the Mean Line Representation of the Flow .... 24

1.6 Energy Analysis of Turbomachines .................................................... 251.6.1 Mechanical Efficiency and Internal Efficiency ...................... 251.6.2 Energy Analysis of an Axial Hydraulic Turbine .................... 261.6.3 Energy Analysis of an Axial Pump ........................................ 30

1.7 Examples of Radial Turbomachines ................................................... 331.8 Performance Characteristics ............................................................... 361.9 Exercises ............................................................................................ 40References ................................................................................................... 46

2 Basic Components ..................................................................................... 472.1 Aerofoils ............................................................................................. 47

2.1.1 Force Generation .................................................................... 472.1.2 Performance Parameters ......................................................... 49

xviii Contents

2.1.3 Pressure Distribution .............................................................. 512.1.4 Boundary Layer Separation .................................................... 522.1.5 Loss Mechanism Associated to Friction: Energy Dissipation 552.1.6 Profile Shapes ......................................................................... 582.1.7 Blade Rows with Low Solidity .............................................. 59

2.2 Linear Cascades ................................................................................. 602.2.1 Relation with the Real Machine ............................................. 602.2.2 Cascade Geometry ................................................................. 612.2.3 Flow in Lossless Cascades: Force Components ..................... 622.2.4 Significance of Circulation .................................................... 652.2.5 Flow in Lossless Cascades: Work .......................................... 672.2.6 Flow in Cascades with Loss: Force Components .................. 682.2.7 Flow in Cascades with Loss: Energy Dissipation

and Work by Drag Force ........................................................ 702.2.8 The Zweifel Tangential Force Coefficient ............................. 722.2.9 The Lieblein Diffusion Factor ................................................ 742.2.10 Performance Parameters of Axial Cascades ......................... 75

2.3 Channels ............................................................................................. 752.3.1 Straight Channels ................................................................... 752.3.2 Bends ...................................................................................... 77

2.4 Diffusers ............................................................................................. 792.4.1 Dump Diffusers ...................................................................... 792.4.2 Inlet Flow Distortion .............................................................. 792.4.3 Flow Separation ..................................................................... 812.4.4 Flow Improvement ................................................................. 812.4.5 Representation of Diffuser Performance ................................ 822.4.6 Equivalent Opening Angle ..................................................... 842.4.7 Diffusion in a Bend ................................................................ 85

2.5 Exercises ............................................................................................ 87References ................................................................................................... 95

3 Fans ............................................................................................................ 973.1 Fan Aplications and Fan Types .......................................................... 97

3.1.1 Fan Applications ..................................................................... 973.1.2 Large Radial Fans .................................................................. 983.1.3 Small Radial Fans .................................................................. 993.1.4 Large Axial Fans .................................................................... 993.1.5 Small Axial Fans .................................................................... 1003.1.6 Cross-Flow Fans ..................................................................... 100

3.2 Idealised Mean Line Analysis of a Radial Fan ................................... 1013.2.1 Idealised Flow Concept: Infinite Number of Blades .............. 1013.2.2 Degree of Reaction ................................................................. 1023.2.3 Relation Between Rotor Blade Shape and Perfor-

mance Parameters ................................................................... 1033.2.4 Performance Characteristics with Idealised Flow .................. 105

xixContents

3.3 Radial Fan Analysis for Lossless Two-Dimensional Flow with Finite Number of Rotor Blades ................................................ 1063.3.1 Relative Vortex in Blade Channels ....................................... 1063.3.2 Velocity Difference over a Rotating Blade .......................... 1073.3.3 Slip: Reduction of Rotor Work ............................................. 1123.3.4 Number of Blades and Solidity: Pfleiderer Moment

Coefficient ............................................................................ 1153.3.5 Number of Blades: Examples ............................................... 118

3.4 Internal Losses with Radial Fans ..................................................... 1203.4.1 Turning Loss at Rotor Entrance ........................................... 1203.4.2 Incidence Loss at Rotor Entrance ........................................ 1203.4.3 Displacement by Blade Thickness ....................................... 1223.4.4 Rotor Friction Loss and Rotor Diffusion Loss ..................... 1233.4.5 Dump Diffusion Loss at Volute Entrance ............................. 1233.4.6 Incidence Loss at Volute Entrance ....................................... 1253.4.7 Friction Loss Within the Volute ........................................... 1263.4.8 Diffusion at the Rotor Inlet .................................................. 1263.4.9 Flow separation at Rotor Inlet and Rotor Outlet .................. 1273.4.10 Applicability of the Loss Models ....................................... 1293.4.11 Optimisation of the Rotor Inlet of a Centrifugal Fan ......... 1293.4.12 Characteristics Taking Losses into Account ....................... 131

3.5 Overall Performance Evaluation ...................................................... 1343.5.1 Mechanical Loss ................................................................... 1343.5.2 Leakage Loss ........................................................................ 1353.5.3 Overall Efficiency with Power Receiving Machines ........... 1353.5.4 Overall Efficiency with Power Delivering Machines .......... 136

3.6 Rotor Shape Choices with Radial Fans ............................................ 1363.7 Axial and Mixed-Flow Fans ............................................................. 140

3.7.1 Degree of Reaction with Axial Fans .................................... 1403.7.2 Free Vortex and Non-Free Vortex Types .............................. 1413.7.3 Axial Fan Characteristics; Adjustable Rotor Blades ............ 1433.7.4 Mixed-Flow Fans ................................................................. 144

3.8 Exercises .......................................................................................... 1463.8.1 Centrifugal Pump (Idealised Flow) ...................................... 1463.8.2 Rotor of a Centrifugal Fan (Finite Number of Blades

and Internal Losses) ............................................................. 1463.8.3 Number of Blades of a Rotor of a Centrifugal Fan .............. 1473.8.4 Volute of a Centrifugal Fan .................................................. 1473.8.5 Leakage Flow Rate with Centrifugal Fan ............................ 1473.8.6 Centrifugal Pump (Finite Number of Blades and

Internal Losses) .................................................................... 1483.8.7 Axial Fan (Idealised Flow): Analysis on Average

Diameter ............................................................................... 1483.8.8 Axial Fan (Idealised Flow): Free Vortex and Non-

Free Vortex ........................................................................... 149

xx Contents

3.8.9 Inlet Guide Vane with a Centrifugal Fan .............................. 1493.8.10 Change of Rotational Speed with Centrifugal and

Axial Fans ............................................................................ 1493.8.11 Two-Stage Axial Fan ............................................................ 1503.8.12 Axial Turbine ........................................................................ 151

References ................................................................................................. 151

4 Compressible Fluids ................................................................................ 1534.1 Basic Laws ....................................................................................... 1534.2 Compressibility and Velocity of Sound ............................................ 1564.3 Compressibility Effect on the Velocity-Pressure Relation ............... 1584.4 Shape of a Nozzle ............................................................................. 1604.5 Nozzle with Initial Velocity .............................................................. 1624.6 Nozzle with Losses: Infinitesimal Efficiency .................................. 1634.7 Isentropic and Polytropic Efficiencies ............................................. 1674.8 Exercises .......................................................................................... 171References ................................................................................................. 174

5 Performance Measurement .................................................................... 1755.1 Pressure Measurement ..................................................................... 175

5.1.1 The Metal Manometer .......................................................... 1755.1.2 The Pressure Transducer ...................................................... 1755.1.3 The Digital Manometer ........................................................ 1765.1.4 Calibration of Pressure Meters ............................................. 177

5.2 Temperature Measurement ............................................................... 1775.2.1 The Glass Thermometer ....................................................... 1775.2.2 The Temperature Transducer ................................................ 1775.2.3 The Digital Thermometer ..................................................... 178

5.3 Flow Rate Measurement .................................................................. 1785.3.1 Reservoir .............................................................................. 1785.3.2 Flow Over a Weir ................................................................. 1785.3.3 Pressure Drop Devices ......................................................... 1795.3.4 Industrial Mass Flow Rate Meters ....................................... 1805.3.5 Positioning of Flow Rate Meters in Ducts ........................... 180

5.4 Torque Measurement ........................................................................ 1815.4.1 Swinging Suspended Motor or Brake .................................. 1815.4.2 Calibrated Motor .................................................................. 1815.4.3 The Torque Transducer ......................................................... 181

5.5 Rotational Speed Measurement ........................................................ 1825.5.1 Pulse Counters ...................................................................... 1825.5.2 The Speed Transducer .......................................................... 1825.5.3 Electric Tachometer .............................................................. 182

5.6 Laboratory Test of a Pelton Turbine ................................................. 1825.6.1 Test Rig ................................................................................ 1825.6.2 Measurements ...................................................................... 183

xxiContents

5.6.3 Measurement Procedure ....................................................... 1835.6.4 Calculations .......................................................................... 1845.6.5 Measurement Example ......................................................... 184

5.7 Laboratory Test of a Centrifugal Fan ............................................... 1845.7.1 Test Rig ................................................................................ 1845.7.2 Measurements ...................................................................... 1875.7.3 Measurement Procedure ....................................................... 1875.7.4 Calculations .......................................................................... 1885.7.5 Measurement Example ......................................................... 188

5.8 Laboratory Test of a Centrifugal Pump ............................................ 1895.8.1 Test Rig ................................................................................ 1895.8.2 Measurements ...................................................................... 1905.8.3 Measurement Procedure ....................................................... 1905.8.4 Calculations .......................................................................... 1915.8.5 Measurement Example ......................................................... 192

6 Steam Turbines ........................................................................................ 1936.1 Applications of Steam Turbines ....................................................... 1936.2 Working Principles of Steam Turbines ............................................. 1956.3 The Steam Cycle .............................................................................. 1996.4 The Single Impulse Stage or Laval Stage ........................................ 200

6.4.1 Velocity Triangles ................................................................. 2006.4.2 Work and Energy Relations .................................................. 2016.4.3 Stage Efficiency Definitions ................................................ 2046.4.4 Blade Profile Shape .............................................................. 2056.4.5 Loss Representation ............................................................. 2086.4.6 Optimisation of Total-to-Static Efficiency ........................... 209

6.5 The Pressure-Compounded Impulse Turbine or Rateau Turbine ............................................................................. 2126.5.1 Principle ............................................................................... 2126.5.2 Efficiency ............................................................................. 213

6.6 The Velocity-Compounded Impulse Turbine or Curtis Turbine ....... 2146.7 The Reaction Turbine ....................................................................... 217

6.7.1 Degree of Reaction ............................................................... 2176.7.2 Efficiency ............................................................................. 2186.7.3 Axial Inlet and Outlet ........................................................... 222

6.8 Steam Turbine Construction Forms ................................................. 2246.8.1 Large Steam Turbines for Power Stations ............................ 2246.8.2 Industrial Steam Turbines .................................................... 229

6.9 Blade Shaping .................................................................................. 2316.9.1 HP and IP Blades .................................................................. 2316.9.2 LP Blades ............................................................................. 233

6.10 Exercises ........................................................................................ 236References ................................................................................................. 246

xxii Contents

7 Dynamic Similitude ................................................................................. 2477.1 Principles of Dynamic Similitude .................................................... 247

7.1.1 Definition of Dynamic Similitude ........................................ 2477.1.2 Dimensionless Parameter Groups ........................................ 2487.1.3 Similitude Conditions ........................................................... 2487.1.4 Purpose of Similitude Analysis ............................................ 2507.1.5 Dimensional Analysis ........................................................... 2517.1.6 Independent and Dependent Parameter Groups ................... 2527.1.7 Dimensionless Parameter Groups in Turbomachines

with a Constant Density Fluid .............................................. 2527.1.8 Strong and Weak Similitude Conditions .............................. 254

7.2 Characteristic Numbers of Turbomachines ...................................... 2547.2.1 Definition of a Characteristic Number ................................. 2547.2.2 Specific Speed and Specific Diameter ................................. 2557.2.3 Relation Between Characteristic Numbers

and Machine Shape .............................................................. 2577.2.4 Design Diagrams .................................................................. 2597.2.5 Shape of Characteristic Curves ............................................ 2617.2.6 Power Specific Speed ........................................................... 262

7.3 Application Example of Similitude: Variable Rotational Speed with a Pump ........................................................................... 263

7.4 Imperfect Similitude ......................................................................... 2667.4.1 Effect of Reynolds Number with the Same Fluid ................ 2667.4.2 Effect of Relative Roughness ............................................... 2677.4.3 Effect of Viscosity ................................................................ 2687.4.4 Rotor Diameter Reduction: Impeller Trimming ................... 2707.4.5 Reduced Scale Models ......................................................... 271

7.5 Series and Parallel Connection ......................................................... 2727.5.1 Parallel Connection of Fans ................................................. 2727.5.2 Parallel Connection of Pumps .............................................. 2737.5.3 Series Connection of Fans .................................................... 274

7.6 Turbomachine Design Example: Centrifugal Fan ............................ 2767.7 Exercises .......................................................................................... 279References ................................................................................................. 282

8 Pumps ....................................................................................................... 2838.1 Cavitation ......................................................................................... 283

8.1.1 Cavitation Phenomenon and Cavitation Consequences ....... 2838.1.2 Types of Cavitation .............................................................. 2848.1.3 Cavitation Assessment: Cavitation Number and

Required Net Positive Suction Height ................................. 2868.1.4 Optimisation of the Inlet of a Centrifugal Pump Rotor ........ 2898.1.5 Net Positive Suction Head of the Installation ...................... 2918.1.6 Increasing the Acceptable Suction Height ........................... 292

xxiiiContents

8.2 Priming of Pumps: Self-Priming Types ........................................... 2938.2.1 Side Channel Pump .............................................................. 2938.2.2 Peripheral Pump (regenerative pump) ................................. 2958.2.3 Self-Priming Centrifugal Pump ............................................ 2968.2.4 Jet Pump ............................................................................... 297

8.3 Unstable Operation ........................................................................... 2978.4 Component Shaping ......................................................................... 299

8.4.1 Simply and Doubly Curved Blades in Radial Rotors ........... 2998.4.2 Mixed-Flow and Axial Pumps ............................................. 3008.4.3 Pump Inlet ............................................................................ 3008.4.4 Pump Outlet ......................................................................... 3018.4.5 Vaneless Diffuser Rings ....................................................... 3018.4.6 Vaned Diffuser Rings ........................................................... 3028.4.7 Volute ................................................................................... 3038.4.8 Return Channels ................................................................... 305

8.5 Internal Parallel and Series Connection Of Rotors .......................... 3058.5.1 Reason for Internal Parallel or Series Connection ............... 3058.5.2 Internal Parallel Connection of Rotors ................................. 3068.5.3 Internal Series Connection of Rotors: Multistage Pumps .... 306

8.6 Constructional Aspects ..................................................................... 3078.6.1 Rotor ..................................................................................... 3078.6.2 Stator .................................................................................... 3078.6.3 Shaft Sealing ........................................................................ 3078.6.4 Bearings ................................................................................ 3098.6.5 Axial Force Balancing with Single-Stage Pumps ................ 3098.6.6 Axial Force Balancing with Multistage Pumps .................... 3108.6.7 Wear Rings ........................................................................... 311

8.7 Special Pumps .................................................................................. 3118.7.1 Borehole Pumps ................................................................... 3128.7.2 High-Pressure Pumps ........................................................... 3128.7.3 Sealless Pumps: Circulation Pumps, Chemical Pumps ........ 3128.7.4 Slurry Pumps ........................................................................ 3138.7.5 Pumping of Solid Materials ................................................. 3148.7.6 Vertical Submerged Pumps .................................................. 3148.7.7 Partial Emission Pumps ........................................................ 3158.7.8 Pumps for Viscous Fluids ..................................................... 315

8.8 Exercises .......................................................................................... 3168.8.1 Looking up Pump Characteristics ........................................ 3168.8.2 Verification of an NPSH-Value ............................................ 316

References ................................................................................................. 317

9 Hydraulic Turbines ................................................................................. 3199.1 Hydraulic Energy ............................................................................. 3199.2 Hydraulic Turbine Types .................................................................. 320

9.2.1 Large Turbines (> 10 MW) ................................................... 3209.2.2 Small Turbines (< 10 MW) ................................................... 322

xxiv Contents

9.3 Pelton Turbines: Impulse Turbines ................................................... 3249.3.1 Performance Characteristics ................................................. 3249.3.2 Specific Speed ...................................................................... 3269.3.3 Determination of the Main Dimensions ............................... 3289.3.4 Flow Rate Control and Over-Speed Protection .................... 328

9.4 Francis and Kaplan Turbines: Reaction Turbines ............................ 3299.4.1 Shape of the Velocity Triangles: Kinematic Parameters ...... 3299.4.2 Optimisation of the Velocity Triangles ................................ 3309.4.3 Degree of Reaction and Speed Ratio ................................... 3319.4.4 Velocity Triangles with Varying Degree of Reaction ........... 3329.4.5 Specific Speed and Meridional Shape of Francis Turbines . 3339.4.6 Flow Rate Control with Reaction Turbines .......................... 3359.4.7 Examples (Figs. 9.16, 9.17) ................................................. 337

9.5 Bulb and Tube Turbines ................................................................... 3389.6 Reversible Pump-Turbines ............................................................... 3409.7 Exercises .......................................................................................... 342References ................................................................................................. 345

10 Wind Turbines ......................................................................................... 34710.1 Wind Energy ................................................................................... 34710.2 Types of Wind Energy Conversion Systems .................................. 348

10.2.1 Drag Machines ................................................................. 348 10.2.2 High-Speed Horizontal-Axis Turbines ............................. 349 10.2.3 Technical Aspects of Horizontal-Axis Wind

Turbines for Electricity Generation .................................. 351 10.2.4 Low-Speed Horizontal-Axis Wind Turbines .................... 355 10.2.5 Vertical-Axis Wind Turbines ............................................ 356

10.3 Wind Turbine Performance Analysis ............................................. 358 10.3.1 Momentum Analysis (Single Streamtube Analysis) ........ 358 10.3.2 Multiple Streamtube Analysis .......................................... 361 10.3.3 Blade Element Analysis ................................................... 363

10.4 Adaptation to a Wind Regime ........................................................ 365References ................................................................................................. 368

11 Power Gas Turbines .............................................................................. 36911.1 General Concept and Components ................................................. 369

11.1.1 Definition of a Gas Turbine .............................................. 369 11.1.2 Comparison with Other Thermal Engines ........................ 371 11.1.3 Example of a Power Gas Turbine ..................................... 372 11.1.4 Compressor Part ............................................................... 374 11.1.5 Turbine Part ...................................................................... 377 11.1.6 Combustion Chamber ....................................................... 381

11.2 Thermodynamic Modelling ............................................................ 384 11.2.1 Isentropic Efficiency with Adiabatic Compression

or Expansion ..................................................................... 384 11.2.2 Reheat Effect .................................................................... 387

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11.2.3 Infinitesimal Efficiency; Polytropic Efficiency .................. 38911.2.4 Thermodynamic Properties of Air and Combustion Gas ... 39211.2.5 Heat Capacity Representation ............................................ 39611.2.6 Cooled Expansion .............................................................. 39611.2.7 Compression with Extraction ............................................. 401

11.3 Performance of Simple-Cycle Power Gas Turbines ......................... 40211.3.1 Idealised Simple Cycle ....................................................... 40211.3.2 Simple Cycle with Component Efficiencies and

Different Heat Capacities of Air and Combustion Gas ...... 40311.3.3 Simple Cycle with Component Efficiencies, Cooling

and Variable Gas Properties ............................................... 40511.4 Performance of Power Gas Turbines with Enhanced Cycles ........... 409

11.4.1 Compression with Intercooling .......................................... 40911.4.2 Expansion with Reheat ....................................................... 41111.4.3 Recuperator ........................................................................ 41211.4.4 Combined Gas and Steam Cycles ...................................... 41311.4.5 Steam Injection ................................................................... 416

References ................................................................................................. 417

12 Thrust Gas Turbines ............................................................................... 41912.1 Thrust Generation ............................................................................. 419

12.1.1 Screw or Propeller .............................................................. 41912.1.2 Reactor or Jet Engine ......................................................... 42312.1.3 Rocket ................................................................................ 426

12.2 Overview of Aircraft Gas Turbine Engines ...................................... 42712.2.1 Turbojet .............................................................................. 42712.2.2 Turboprop and Turbo-Shaft ................................................ 42712.2.3 Bypass Turbojet .................................................................. 42812.2.4 Turbofan ............................................................................. 42812.2.5 Prop-fan and Unducted Fan ............................................... 42912.2.6 Geared Turbofan ................................................................. 432

12.3 Performance Parameters of Aircraft Propulsion Systems ................ 43212.3.1 Specific Thrust ................................................................... 43212.3.2 Dynamic Power .................................................................. 43312.3.3 Gas Power and Dynamic Efficiency .................................. 43312.3.4 Thermal Power, Thermodynamic Efficiency and

Thermal Efficiency ............................................................. 43312.3.5 Propulsive Power and Propulsive Efficiency ..................... 43412.3.6 Overall Efficiency .............................................................. 43412.3.7 Rocket ................................................................................ 43512.3.8 Generalisation for Double-Flow Engines ........................... 43512.3.9 Specific Fuel Consumption ................................................ 437

12.4 Performance of the Gas Generator and the Single-Jet Engine ................................................................. 43812.4.1 Analysis with Loss-Free Components ................................ 43912.4.2 Analysis with Component Losses ...................................... 441

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12.5 Performance of Double-Flow Engines ............................................. 44412.5.1 Unmixed Flows (Double-Jet Engine: Turbofan,

Turboprop) ......................................................................... 44412.5.2 Mixed Flows (Bypass Engine) ........................................... 44812.5.3 Intercooling and Recuperation ........................................... 450

12.6 Technological Aspects of the Turbofan Engine ................................ 45112.6.1 Discs and Shafts ................................................................. 45112.6.2 Vanes and Blades ................................................................ 45112.6.3 Combustion Chamber ......................................................... 45212.6.4 Mixer and Thrust Reverser ................................................. 454

12.7 Exercises .......................................................................................... 45412.7.1 Single-Flow Jet Engine ...................................................... 45412.7.2 Single-Flow Jet Engine with Post-Combustion ................. 45512.7.3 Turbofan with Separate Flows ........................................... 45612.7.4 Turbofan with Mixed Flows ............................................... 45612.7.5 Optimisation of Turbine Inlet Temperature with a

Turbofan Engine ................................................................. 45612.7.6 Helicopter Rotor ................................................................. 45612.7.7 Ramjet ................................................................................ 457

References ................................................................................................. 457

13 Axial Compressors .................................................................................. 45913.1 Mean Line Analysis .......................................................................... 459

13.1.1 Velocity Triangles ............................................................... 46013.1.2 Fundamental Equations ...................................................... 46113.1.3 Loss Representation ........................................................... 46213.1.4 Loss Coefficients ................................................................ 46513.1.5 Force Components ............................................................. 46513.1.6 Diffusion Factor and Loss Correlations ............................. 46613.1.7 Kinematic Parameters ........................................................ 47013.1.8 Secondary Flow: Principle ................................................. 47113.1.9 Radial Variation of Flow: Principle .................................... 47313.1.10 Optimisation of a Stage .................................................... 47413.1.11 Blade Shape ...................................................................... 47613.1.12 Attainable Pressure Ratio ................................................. 478

13.2 Secondary Flow ................................................................................ 47813.2.1 Definition of Secondary Flow ............................................ 47813.2.2 Passage Vortex and Trailing Vortices ................................. 47913.2.3 Corner Vortices ................................................................... 48013.2.4 Horseshoe Vortex ............................................................... 48013.2.5 Leakage Vortex and Scraping Vortex ................................. 48013.2.6 Loss Assessment ................................................................. 481

13.3 Radial Flow Variation ....................................................................... 48113.3.1 S1-S2 Decomposition .......................................................... 48113.3.2 Radial Equilibrium ............................................................. 48213.3.3 Free Vortex Blades ............................................................. 483

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13.3.4 Forcing of the Vortex Distribution ..................................... 48513.3.5 Effect of End Wall Boundary Layers ................................. 48713.3.6 Three-dimensional Blade Design ....................................... 488

13.4 Compressor Blade Profiles ............................................................... 49113.4.1 Subsonic and Supercritical Cascades ................................. 49113.4.2 Transonic Cascades ............................................................ 49413.4.3 Supersonic Cascades and Transonic Cascades with

High Inlet Mach Number ................................................... 49613.5 Performance Characteristics and Operating Range .......................... 497

13.5.1 General Shape of a Characteristic Curve ........................... 49713.5.2 Rotating Stall ...................................................................... 49813.5.3 Choking .............................................................................. 49913.5.4 Surge .................................................................................. 50113.5.5 Operating Range ................................................................. 502

13.6 Exercises .......................................................................................... 505References ................................................................................................. 506

14 Radial Compressors ................................................................................ 50914.1 Construction Forms and Applications .............................................. 509

14.1.1 Rotor Types ........................................................................ 50914.1.2 General Shape of a Radial Compressor ............................. 51114.1.3 Comparison Between Radial and Axial Compressors ....... 51214.1.4 Examples of Radial Compressors ...................................... 513

14.2 Kinematic Parameters ...................................................................... 51614.3 Pressure Ratio ................................................................................... 51914.4 Rotor Shape ...................................................................................... 521

14.4.1 Number of Blades .............................................................. 52114.4.2 Inducer ................................................................................ 523

14.5 Diffusers ........................................................................................... 52514.5.1 Flow Non-homogeneity at Rotor Outlet ............................ 52514.5.2 Mixing Zone ....................................................................... 52614.5.3 Vaneless Diffusers .............................................................. 52714.5.4 Vaned Diffusers .................................................................. 527

14.6 Performance Characteristics ............................................................. 52814.6.1 Flow Instability .................................................................. 52814.6.2 Choking .............................................................................. 52814.6.3 Operating Characteristics and Operating Range ................ 529

14.7 Exercises .......................................................................................... 53114.7.1 Velocity Variation at Constant Radius in a Rotor ............... 53114.7.2 Variable Geometry ............................................................. 533

References ................................................................................................. 533

15 Axial and Radial Turbines for Gases ..................................................... 53515.1 Axial Turbines .................................................................................. 535

15.1.1 Kinematic Parameters ........................................................ 53515.1.2 Radial Variation of Flow Parameters ................................. 541

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15.1.3 Blade Profiles ..................................................................... 54215.1.4 Three-dimensional Blade Design ....................................... 54515.1.5 Vane and Blade Clocking ................................................... 54615.1.6 Operating Characteristic of Axial Turbines ........................ 546

15.2 Radial Turbines ................................................................................ 54915.2.1 Shape and Functioning ....................................................... 54915.2.2 Kinematic Parameters ........................................................ 55115.2.3 Operating Characteristic of Radial Turbines ...................... 55315.2.4 Radial Turbine Applications ............................................... 554

15.3 Dimensional Analysis with Compressible Fluids ............................ 55415.3.1   Independent and Dependent Π-groups  ............................... 55415.3.2 Dimensionless Compressor and Turbine Characteristics ... 55615.3.3 Corrected Quantities ........................................................... 556

15.4 Exercises .......................................................................................... 557References ................................................................................................. 558

Index ............................................................................................................... 561