Meinhard T. Schobeiri Gas Turbine Design,

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Meinhard T. Schobeiri

Gas Turbine Design, Components and System Design Integration

Meinhard T. Schobeiri


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Meinhard T. Schobeiri Texas A&M University College Station, TX USA

ISBN 978-3-319-58376-1 ISBN 978-3-319-58378-5 (eBook)DOI 10.1007/978-3-319-58378-5

Library of Congress Control Number: 2017943214

© Springer International Publishing AG 2018This 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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This Springer imprint is published by Springer NatureThe registered company is Springer International Publishing AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface to the First Edition

Gas turbines today are the integral parts of power generation, transportation,petrochemical and diverse industrial processing systems. Although the design andapplication of gas turbines in any of the above areas and their operationalrequirements are different, they share the same underlying physics. The physics ofturbomachinery components and systems was discussed in details in the first and thesecond enhanced edition of my textbook, Turbomachinery Flow Physics andDynamic Performance. The book found a world-wide positive echo among theturbomachinery community including industry and academia. This motivated me towrite the current textbook about the gas turbine design, where I spent more than fortyyears on almost all aspects of gas turbine design R&D in the industry, NASA G.R.C,DOE, and academia. While in the book Turbomchinery Flow Physics the aero-thermodynamics, heat transfer and performance aspects of almost all thermalturbomachines were discussed in very detail, the current book deals with the aero-thermodynamics design of gas turbine components and their integration into acomplete gas turbine system.

Designing a gas turbine requires a team work of several groups that arespecialized in aero-thermodynamics, heat transfer, computational fluid dynamics,combustion, solid mechanics, vibration, rotordynamics and system control to namejust a few. It is beyond the scope of any text book to treat the above areas in adetailed fashion. Available gas turbine handbooks do not treat the above areas in debtand breath, so that they do cannot be considered a working platform for gas turbinedesigner. They may, however, be able to provide the reader an overview of thesubject. Considering the above, the current book is concentrated on a detailed aero-thermodynamics, design and off-deign performance aspects of individual componentsas well as the system integration and its dynamic operation.

Design of gas turbines was from very beginning based on sound physics ratherthan empiricism. The first gas turbine manufactured around 1900 was not even ableto rotate, because the turbine power was much less than the required compressorpower. The reason was the poor efficiencies of both the turbine and the compressorcomponent. The failed tests showed that the prerequisite for a successful gas turbinedesign is the full understanding of its underlying viscous flow physics and itsmathematical description. The mathematical structure that describes the threedimensional viscous flow in very details was already derived by C.L.M.H. Navier in1821 and twenty years later by G.G. Stokes . However, the solution of the Navier-Stokes partial differential equations was at that time out of reach. It was due toL.Prandl’s 1904 groundbreaking boundary layer theory that provided an approximatesolution to Navier-Stokes equations. The simplification of the Navier-Stokesequations through boundary layer theory made possible to calculate total pressure loss

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specialization is the use of “black boxes” in engineering in general and inturbomachinery in particular. During my 40 years of turbomachinery R&Dexperience, I have been encountering engineers who can use commercial codes forcalculating the complex turbomachinery flow field without knowing the underlyingphysics of the code they use. This circumstance constituted one of the factors indefining the framework of the book Turbomachinery Flow Physics mentionedpreviously, which aims at providing the students and practicing turbomachinerydesign engineers with a solid background in turbomachinery flow physics andperformance. Built upon a physical basis that contains a minimum of empiricalcorrelations, I have been teaching turbomachinery courses in the past thirty years andeducated several generations of highly qualified turbomachinery engineers that areworking in US gas turbine manufacturing companies. The current book provides theinterested students and the young engineers working in the industry with a materialthey can use for preliminary design of gas turbines. It is also intended to helpinstructors of turbomachinery courses around the world to assign gas turbinecomponents as project modules that can be integrated into a complete system.

The current book consists of 18 Chapters that are grouped into three parts. PartI encompassing Chapters 1 through 6 deals with aero-thermodynamics of gas turbinedesign.

Part II of this book include Chapters 7 through 10 starts with the treatment ofcascade and stage efficiency and loss determination from a physically plausible pointof view. I refrained from presenting recipe-types of empirical formulas that have nophysical foundation. Chapter 8 deals with the calculation of incidence and deviation.Chapter 9 treats in detail the compressor and turbine blade design procedures. Radialequilibrium is discussed in Chapter 10, which concludes Part II.

Part III of the book is entirely dedicated to design, off-deign and dynamicperformance of turbomachinery components and systems. Particular attention is paidto gas turbine components, their individual modeling, and integration into the gasturbine system. It includes Chapters 11 to 16. Chapter 11 introduces the basic physicsof non-linear dynamic simulation of turbomachinery systems and its theoreticalbackground. Starting from a set of general four dimensional partial differentialequations in temporal-spatial domain, two-dimensional equation sets are derived thatconstitute the basis for component modeling. The following Chapters 12, 13 and 14deal with generic modeling of turbomachinery components and systems in whichindividual components ranging from the inlet nozzle to the compressor, combustionchamber, turbine, and exhaust diffuser are modeled. In modeling compressor andturbine components, non-linear adiabatic and diabatic expansion and compressioncalculation methods are presented.

Gas turbine design requires several preliminary steps. These steps were discussedin Chapter 17. Chapter 18 deals with the dynamic simulation of different gas turbinetypes that are subject to adverse dynamic operations. Seven representative casestudies conclude this chapter. In preparing Part III, I tried to be as concrete as

coefficient of compressor and turbine blades, define the rotating stall and surge limitof compressors, define the range of the laminar separation of the boundary layer inlow pressure turbines and many other aerodynamic aspects of gas turbine operation.In the meantime, the introduction of high speed computers and advancedcomputational methods has significantly contributed to an exponential growth ofinformation covering almost all aspects of turbomachinery design. This situation haslead to a growing tendency in technical specialization. A factor in the context of

Preface

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by readers. In this case, I sincerely appreciate the reader notifying me of any mistakesfound; the electronic address is given below. I also welcome any comments orsuggestions regarding the improvement of future editions of the book.

My sincere thanks are due to many fine individuals and institutions. First andforemost, I would like to thank the faculty of the Technische Universität Darmstadt,from whom I received my entire engineering education. I finalized major chapters ofthis book during my sabbatical in Germany where I received the Alexander vonHumboldt Prize. I am indebted to the Alexander von Humboldt Foundation for thisPrize and the material support for my research sabbatical in Germany. My thanks areextended to Prof. Bernd Stoffel, Prof. Ditmar Hennecke, Professor Pelz and Dipl. Ing.Bernd Matyschok for providing me with a very congenial working environment. Itruly enjoyed interacting with these fine individuals. NASA Glenn Research Centersponsored the development of the nonlinear dynamic code GETRAN which I usedto simulate cases in Part III. I wish to extend my thanks to Mr. Carl Lorenzo, Chiefof Control Division, Dr. D. Paxson, and the administration of the NASA GlennResearch Center. I also thank Dr. Richard Hearsey for providing me with a three-dimensional compressor blade design. I also would like to extend my thanks to Dr.Arthur Wennerstom for providing me with the updated theory on the streamlinecurvature method.

I am also indebted to the TAMU administration for partially supporting mysabbatical that helped me in finalizing the book.

Last but not least, my special thanks go to my family, Susan and Wilfried fortheir support throughout this endeavor.

M.T. Schobeiri

September 2016College Station, [email protected]

possible by providing detailed simulation of existing gas turbine engines and theirindividual component.

In typing several thousand equations, errors may occur. I tried hard to eliminatetyping, spelling and other errors, but I have no doubt that some remain to be found

Preface

1 Introduction, Gas Turbines, Applications, Types . . . . . . . . . . . . . . 11.1 Power Generation Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Compressed Air Energy Storage Gas Turbines, CAES . . . . . . . . 61.3 Power Generation Gas Turbine Process . . . . . . . . . . . . . . . . . . . 81.4 Significant Efficiency Improvement of Gas Turbines . . . . . . . . . 101.5 Ultra High Efficiency Gas Turbine . . . . . . . . . . . . . . . . . . . . . . . 141.6 Aircraft Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.7 Aircraft-Derivative Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . 191.8 Gas Turbines Turbocharging Diesel Engines . . . . . . . . . . . . . . . 221.9 Gas Turbine Components, Functions . . . . . . . . . . . . . . . . . . . . . 24

1.9.1 Group 1: Inlet, Exhaust, Pipe . . . . . . . . . . . . . . . . . . . . . . 251.9.2 Group 2: Heat Exchangers, Combustion Chamber . . . . . . 261.9.3 Group 3: Compressor, Turbine Components . . . . . . . . . . 29

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2 Gas Turbine Thermodynamic Process2.1 Gas Turbine Cycles, Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1.1 Gas Turbine Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.1 Minor Improvement of Gas Turbine Thermal Efficiency . 402.2.2 Major Improvement of Gas Turbine Thermal Efficiency . 41

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3 Thermo-Fluid Essentials for Gas Turbine Design . . . . . . . . . . . . . 493.1 Mass Flow Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2 Balance of Linear Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . 513.3 Balance of Moment of Momentum . . . . . . . . . . . . . . . . . . . . . . . 533.4 Balance of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.4.1 Energy Balance Special Case 1: Steady Flow . . . . . . . . . 573.4.2 Energy Balance Special Case 2: Steady Flow . . . . . . . . . 58

3.5 Application of Energy Balance to Gas Turbines Components . 583.5.1 Application: Accelerated, Decelerated Flows . . . . . . . . . 593.5.2 Application: Combustion Chamber, Heat Exchanger . . . . 60

2.2 Improvement of Gas Turbine Thermal Efficiency . . . . . . . . . . . 39

2.1.3 Compressed Air Energy Storage Gas Turbine . . . . . . . . . 45

Table of Content

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Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVIITable of Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IXPreface to the First Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

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4 Theory of Turbomachinery Stages . . . . . . . . . . . . . . . . . . . . . . . . 1074.1 Energy Transfer in Turbomachinery Stages . . . . . . . . . . . . . . . 1074.2 Energy Transfer in Relative Systems . . . . . . . . . . . . . . . . . . . . 1084.3 General Treatment of Turbine and Compressor Stages . . . . . . . 1094.4 Dimensionless Stage Parameters . . . . . . . . . . . . . . . . . . . . . . . . 1134.5 Relation Between Stage parameter, Radial Equilibrium . . . . . . 1154.6 Effect of Degree of Reaction on the Stage Configuration . . . . . 1184.7 Effect of Stage Load Coefficient on Stage Power . . . . . . . . . . 1204.8 Unified Description of a Turbomachinery Stage . . . . . . . . . . . . 121

4.8.1 Unified Description of Stage with Constant Mean

4.8.2 Generalized Dimensionless Stage Parameters . . . . . . . . 1224.9 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.9.1 Case 1, Constant Mean Diameter . . . . . . . . . . . . . . . . . . 1254.9.2 Case 2, Constant Meridional Velocity Ratio . . . . . . . . . 125

4.10 Increase of Stage Load Coefficient, Discussion . . . . . . . . . . . . 126References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5 Turbine and Compressor Cascade Flow Forces . . . . . . . . . . . . . . 1295.1 Blade Force in an Inviscid Flow Field . . . . . . . . . . . . . . . . . . . . 1295.2 Blade Forces in a Viscous Flow Field . . . . . . . . . . . . . . . . . . . . 1345.3 The Effect of Solidity on Blade Profile Losses . . . . . . . . . . . . . 140

5.5 Optimum Solidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1425.5.1 Optimum Solidity, by Pfeil . . . . . . . . . . . . . . . . . . . . . . . 1435.5.2 Optimum Solidity by Zweifel . . . . . . . . . . . . . . . . . . . . . 144

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.4 Relationship Between Profile Loss Coefficient and Drag . . . . . 140

3.7.5 The Oblique Shock Wave Relations . . . . . . . . . . . . . . . 983.7.4 The Normal Shock Wave Relations . . . . . . . . . . . . . . . . 92

3.7.7 Prandtl-Meyer Expansion . . . . . . . . . . . . . . . . . . . . . . . . 1023.7.6 Detached Shock Wave. . . . . . . . . . . . . . . . . . . . . . . . . . . 102

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

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3.5.3 Application: Turbine, Compressor . . . . . . . . . . . . . . . . . 633.5.3.1 Uncooled turbine . . . . . . . . . . . . . . . . . . . . . . . 633.5.3.2 Cooled turbine . . . . . . . . . . . . . . . . . . . . . . . . . 643.5.3.3 Uncooled compressor . . . . . . . . . . . . . . . . . . . 653.5.3.4 Cooled Compressor . . . . . . . . . . . . . . . . . . . . . 66

3.6 Irreversibility and Total Pressure Losses . . . . . . . . . . . . . . . . . 673.6.1 Application of Second Law to Turbomachinery

3.7 Flow at High Subsonic and Transonic Mach Numbers . . . . . . . 713.7.1 Density Changes with Mach Number, Critical State . . . 723.7.2 Effect of Cross-Section Change on Mach Number . . . . . 773.7.3 Compressible Flow through Channels . . . . . . . . . . . . . . . 84

5.6 Generalized Lift-Solidity Coefficient . . . . . . . . . . . . . . . . . . . . 1465.6.1 Lift-Solidity Coefficient for Turbine Stator . . . . . . . . . . 1485.6.2 Turbine Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

Components 69. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Diameter 121. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Table of Content

6.7.4 Optimum Mixing Losses. . . . . . . . . . . . . . . . . . . . . . . . . 2016.8 Stage Total Loss Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 2016.9 Diffusers, Configurations, Pressure Recovery, Losses . . . . . . . 202

6.9.1 Diffuser Configurations . . . . . . . . . . . . . . . . . . . . . . . . . 2036.9.2 Diffuser Pressure Recovery . . . . . . . . . . . . . . . . . . . . . . 2046.9.3 Design of Short Diffusers . . . . . . . . . . . . . . . . . . . . . . . . 2076.9.4 Some Guidelines for Designing High Efficiency

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

7 Efficiency of Multi-Stage Turbomachines . . . . . . . . . . . . . . . . . . . . 2137.1 Polytropic Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2137.2 Isentropic Turbine Efficiency, Recovery Factor . . . . . . . . . . . . 2167.3 Compressor Efficiency, Reheat Factor . . . . . . . . . . . . . . . . . . . 2197.4 Polytropic versus Isentropic Efficiency . . . . . . . . . . . . . . . . . . . 221References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

6.4.3 Calculation of Endwall Secondary Flow Losses . . . . . . 1826.5 Flow Losses in Shrouded Blades . . . . . . . . . . . . . . . . . . . . . . . 186

6.5.1 Losses Due to Leakage Flow in Shrouds . . . . . . . . . . . . 1866.6 Exit Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1926.7 Trailing Edge Ejection Mixing Losses of Gas Turbine Blades . 194

6.7.1 Calculation of Mixing Losses . . . . . . . . . . . . . . . . . . . . . 1946.7.2 Trailing Edge Ejection Mixing Losses . . . . . . . . . . . . . . 1996.7.3 Effect of Ejection Velocity Ratio on Mixing Loss . . . . . 199

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6 Losses in Turbine and Compressor Cascades . . . . . . . . . . . . . . . . . 1576.1 Turbine Profile Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1586.2 Viscous Flow in Compressor Cascade . . . . . . . . . . . . . . . . . . . 160

6.2.1 Calculation of Viscous Flows . . . . . . . . . . . . . . . . . . . . 1606.2.2. Boundary Layer Thicknesses . . . . . . . . . . . . . . . . . . . . . 1616.2.3 Boundary Layer Integral Equation . . . . . . . . . . . . . . . . . 1626.2.4 Application of Boundary Layer Theory to Compressor . 1646.2.5 Effect of Reynolds Number . . . . . . . . . . . . . . . . . . . . . . 1686.2.6 Stage Profile Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.3 Trailing Edge Thickness Losses . . . . . . . . . . . . . . . . . . . . . . . . 1686.4 Losses Due to Secondary Flows . . . . . . . . . . . . . . . . . . . . . . . . 174

6.4.1 Vortex Induced Velocity Field . . . . . . . . . . . . . . . . . . . . 1766.4.2 Calculation of Tip Clearance Secondary Flow Losses . . 179

Diffus ers 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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Table of Content

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8.1.1 Conformal Transformation. . . . . . . . . . . . . . . . . . . . . . . . 2258.1.2 Flow Through an Infinitely Thin Circular Arc Cascade . 234

8.1.4 Optimum Incidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2408.1.5 Effect of Compressibility . . . . . . . . . . . . . . . . . . . . . . . . 242

8.2 Deviation for High Flow Deflection . . . . . . . . . . . . . . . . . . . . . 243

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

8.1.3 Thickness Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

8.2.1 Calculation of Exit Flow Angle . . . . . . . . . . . . 245. . . . .. .

8 Incidence and Deviation...

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10.4.2 Calculation of Compound Lean Angle Distribution . . . 29710.4.3 Example: Three-Stage Turbine Design . . . . . . . . . . . . . 299

10.5 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30210.5.1 Free Vortex Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30210.5.2 Forced vortex flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30310.5.3 Flow with constant flow angle . . . . . . . . . . . . . . . . . . . 304

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

11 Nonlinear Dynamic Simulation of Components and systems . . . . 30711.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

11.3 One-Dimensional Approximation . . . . . . . . . . . . . . . . . . . . . . . 31511.3.1 Time Dependent Equation of Continuity . . . . . . . . . . . 31511.3.2 Time Dependent Equation of Motion . . . . . . . . . . . . . . 31711.3.3 Time Dependent Equation of Total Energy . . . . . . . . . . 318

11.4 Numerical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

12 Generic Modeling of Turbomachinery Components and Systems 32512.1 Generic Component, Modular Configuration . . . . . . . . . . . . . . 327

12.1.1 Plenum the Coupling Module . . . . . . . . . . . . . . . . . . . . 32712.1.2 Group1 Modules: Inlet, Exhaust, Pipe . . . . . . . . . . . . . 32912.1.3 Group 2: Heat Exchangers, Combustion Chamber . . . . 330

11.2 Preparation for Numerical Treatment . . . . . . . . . . . . . . . . . . . . 315

9.3.3 Alternative Calculation Method.. . . . . . . . . . . . . . . . . . . 2719.4 Assessment of Blades Aerodynamic Quality . . . . . . . . . . . . . . 272References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

10 Radial Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27710.1 Derivation of Equilibrium Equation . . . . . . . . . . . . . . . . . . . . . 278

10.2 Application of Streamline Curvature Method . . . . . . . . 28610.2.1 Step-by-step solution procedure . . . . . . . . . . 288

10.3 Compressor Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29210.4 Turbine Example, Compound Lean Design . . . . . . . . . . . . . . . 295

10.4.1 Blade Lean Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 296

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2499.1 Conformal Transformation, Basics . . . . . . . . . . . . . . . . . . . . . . 249

9.1.1 Joukowsky Transformation . . . . . . . . . . . . . . . . . . . . . . 2519.1.2 Circle-Flat Plate Transformation . . . . . . . . . . . . . . . . . . 2519.1.3 Circle-Ellipse Transformation . . . . . . . . . . . . . . . . . . . . 2529.1.4 Circle-Symmetric Airfoil Transformation . . . . . . . . . . . 2539.1.5 Circle-Cambered Airfoil Transformation . . . . . . . . . . . 255

9.2 Compressor Blade Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2569.2.1 Low Subsonic Compressor Blade Design . . . . . . . . . . . 2579.2.2 Compressors Blades for High Subsonic Mach Number . 2639.2.3 Transonic, Supersonic Compressor Blades . . . . . . . . . . 264

9.3 Turbine Blade Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2659.3.1 Steps for Designing the Camberline . . . . . . . . . . . . . . . 2669.3.2 Camberline Coordinates Using Bèzier Function . . . . . . 269

9 Blade Design

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Table of Content

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15 Modeling the Compressor Component, Design and Off-Design . 36915.1 Compressor Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

15.1.1 Profile Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37215.1.2 Diffusion Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37315.1.3 Generalized Maximum Velocity Ratio for Stator

15.1.4 Compressibility Effect . . . . . . . . . . . . . . . . . . . . . . . . . 37915.1.5 Shock Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38315.1.6 Correlations for Boundary Layer Momentum

15.1.7 Influence of Different Parameters on Profile Losses . . . 39315.1.7.1 Mach Number Effect. . . . . . . . . . . . . . . . . . . . 39315.1.7.2 Reynolds number effect . . . . . . . . . . . . . . . . . 394

15.2 Compressor and Off-Design Performance . . . . . . . . . . 395

. . 39515.2.1.2 Row-by-row adiabatic compression . . . . . . . 39715.2.1.3 Off-design efficiency calculation . . . . . . . . . 401

Compression Process . . . . . . . . . . . . . . . . . . . . . . . . . 395

14 Modeling of Recuperators, Combustion Chambers . . . . . . . . . . 35314.1 Modeling Recuperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

14.1.1 Recuperator Hot Side Transients . . . . . . . . . . . . . . . . . . 35514.1.2 Recuperator Cold Side Transients . . . . . . . . . . . . . . . . . 35514.1.3 Coupling Condition Hot, Cold Side . . . . . . . . . . . . . . . 35614.1.4 Recuperator Heat Transfer Coefficient . . . . . . . . . . . . 357

14.2 Modeling Combustion Chambers . . . . . . . . . . . . . . . . . . . . . . . 35814.2.1. Mass Flow Transients . . . . . . . . . . . . . . . . . . . . . . . . . . 35914.2.2. Temperature Transients . . . . . . . . . . . . . . . . . . . . . . . . . 36014.2.3 Combustion Chamber Heat Transfer. . . . . . . . . . . . . . . . 362

14.3 Example: Startup and Shutdown of a Combustion Chamber . . 36414.4 Modeling of Afterburners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

12.1.4 Group 3: Adiabatic Compressor, Turbine . . . . . . . . . . . 33212.1.5 Group 4: Diabatic Turbine and Compressor

12.1.6 Group 5: Control System, Valves, Shaft, Sensors . . . . . 33612.2 System Configuration, Nonlinear Dynamic Simulation . . . . . . 336

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

13 Modeling of Inlet, Exhaust, and Pipe Systems . . . . . . . . . . . . . . . . 34313.1 Unified Modular Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . 34313.2 Physical and Mathematical Modeling of Modules . . . . . . . . . . 34313.3 Example: Dynamic behavior of a Shock Tube . . . . . . . . . . . . . 345

13.3.1 Shock Tube Dynamic Behavior . . . . . . . . . . . . . . . . . . . 347References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

12.3 Configuration of Systems of Non-linear Partial DifferentialEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

Components 334. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and Rotor 377. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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15.2.1 Stage-by-stage and Row-by-Row Adiabatic

15.2.1.1 Stage-by-stage calculation of compression .

Thickness 392. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XIII Table of Content

Design

16.1.3 Off-Design Efficiency Calculation . . . . . . . . . . . . . . . . 43616.1.4 Behavior Under Extreme Low Mass Flows . . . . . . . . . 43816.1.5 Example: Steady Design and Off-Design . . . . . . . . . . . 441

16.2 Off-Design Calculation Using Global Turbine Characteristics . 44316.3 Modeling the Turbine Module for Dynamic Performance . . . . 445

16.3.1 Module Level 1: Using Turbine Performance map . . . . 44516.3.2 Module Level 2: Row-by-Row Adiabatic Expansion . . 44616.3.3 Module Level 3: Row-by-Row Diabatic Expansion . . . 447

16.3.3.1 Description of diabatic turbine module: . . . . . 44916.3.3.2 Description of diabatic turbine module, . . . . . 45116.3.3.3 Heat transfer closure equations . . . . . . . . . . . 453

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

XIV

15.4 Compressor Modeling Levels . . . . . . . . . . . . . . . . . . . . . . . . . . 40915.4.1 Module Level 1: Using Performance Maps . . . . . . . . . 410

15.4.1.1 Quasi dynamic modeling using maps: . . . . . . 41215.4.1.2 Simulation Example: . . . . . . . . . . . . . . . . . . . 413

15.4.2 Module Level 2: Row-by-Row Adiabatic Calculation . 41515.4.3 Active Surge Prevention by Adjusting the Stator

15.4.4 Module Level 3: Row-by-Row Diabatic Compression . 41715.4.4.1 Description of diabatic compressor module: . . 41815.4.4.2 Heat transfer closure equations: . . . . . . . . . . 420

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422

16 Turbine Aerodynamic Design and Off-design Performance . . . . 42716.1 Stage-by-Stage and Row-by-Row Adiabatic Design . . . . . . . . 429

16.1.1 Stage-by-Stage Calculation of Expansion Process . . . . 43016.1.2 Row-by-Row Adiabatic Expansion . . . . . . . . . . . . . . . . 431

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15.3 Generation of Steady State Performance Map . . . . . . . . . . . . . 40415.3.1 Inception of Rotating Stall . . . . . . . . . . . . . . . . . . . . . . 40615.3.2 Degeneration of Rotating Stall into Surge . . . . . . . . . . 408

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Blades 416. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table of Content

17.3.1 Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45817.3.2 Compressor Blade Aerodynamics . . . . . . . . . . . . . . . . 46217.3.3 Controlling the Leakage Flow . . . . . . . . . . . . . . . . . . . 46317.3.4 Compressor Exit Diffuser . . . . . . . . . . . . . . . . . . . . . . . 46317.3.5 Compressor Efficiency and Performance Maps . . . . . . 463

17.4 Combustion Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46617.4.1 Combustion Design Criteria . . . . . . . . . . . . . . . . . . . . . 468

17.5 Turbine Design, Boundary Conditions, Design Process . . . . . 47017.5.1 Steps of a Gas Turbine Design Process . . . . . . . . . . . . . 470

17.3.6 Stagger Angle Adjustment During Operation . . . . . . . 465

17.4.2 Combustion Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468

17 Gas Turbine Design, Preliminary Considerations . . . . . . . . . . . . 45517.1 Gas Turbine Preliminary Design Procedure . . . . . . . . . . . . . . . 45617.2 Gas Turbine Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45717.3 Compressor Design, Boundary Conditions, Design Process . . 458

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. . . . . . . . . 49818.5.4 Case Studies: Maximizing the Off-Design Efficiency

of a Gas Turbine by Varying the Turbine Stator

18.5.4.1 Dynamic Change of Stagger Angle, when. . . . . . . . . . . . . . . . . . . . . 504

18.5.5 Case Study 3: Simulation of a Multi-Spool Gas

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

XV

18 Simulation of Gas Turbine Engines . . . . . . . . . . . . . . . . . . . . . . . . 47718.1 State of Dynamic Simulation, Background . . . . . . . . . . . . . . . . 47818.2 Gas Turbine Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . 47818.3 Gas Turbine Components, Modular Concept . . . . . . . . . . . . . . 48118.4 Levels of Gas Turbine Engine Simulations . . . . . . . . . . . . . . . 486

18.4.1 Zeroth Simulation Level . . . . . . . . . . . . . . . . . . . . . . . . 48618.4.2 First Simulation Level . . . . . . . . . . . . . . . . . . . . . . . . . . 48618.4.3 Second Simulation Level . . . . . . . . . . . . . . . . . . . . . . . 48618.4.4 Third Simulation Level . . . . . . . . . . . . . . . . . . . . . . . . 486

18.5 Non-Linear Dynamic Simulation Case Studies . . . . . . . . . . . . 48718.5.1 Case Studies: Compressed Air Energy Storage Plant . . 488

18.5.1.1 Case Study: Emergency Shutdown . . . . . . . . 49118.5.1.2 Case Study 1: Grid Fluctuation Response . . . 493

18.5.2 Case Study 2: Dynamic Simulation of a Gas Turbine Under Adverse Operation condition . . . . . . . . . . . . . . 493

18.5.3 Case Studies: Dynamic Simulation of a Split-Shaft GasTurbine under Adverse Operation condition

.

Stagger Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

Engine is Running

Turbine 506. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47517.5.2 Mechanical Integrity, Components Vibrational . . . . . . 475

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Table of Content

. . . . .

Nomenclature

A acceleration, force vectorAc cold side blade surface areaAh hot side blade surface areab trailing edge thickness c blade chord lengthc complex eigenfunction, c = cr + icic speed of soundcax blade axial chord lengthCD cascade drag coefficientCf friction coefficientCi constantsCL blade lift coefficientCL

* camberline lift coefficientcp, cv specific heat capacitiesd projected trailing edge thickness d = b/sin 2D diffusion factorD dimensionless trailing edge thicknessDe equivalent diffusion factorDh hydraulic diameterDm modified diffusion factore specific total energyei orthonormal unit vectorE Planck’s spectral emissive powerf slot thickness/trailing edge thickness ratio f = s/bfC reheat factor for multistage compressors fT recovery factor for multistage turbines f recovery factor for turbines with infinite number of stages F auxiliary functionF force vectorg blade geometry functionG blade geometry parameterG circulation functionGi auxiliary functionsh heighth specific static enthalpyH specific total enthalpyH immersion ratioH12 form factor, H12 = 1/ 2

XVII

XVIII

H13 form factor, H32 = 3/ 2i incidence angleI moment of inertiak thermal conductivityK specific kinetic energyl, m coordinates introduced for radial equilibriumlm specific shaft workL stage powerm massm mass flowmc cooling mass flowM Mach numberM vector of moment of momentumMa axial vector of moment of momentum n number of stationsn polytropic exponentn normal unit vector Nu Nusselt numberp, P static, total pressureP total pressure P = p + V2/2Pr Prandtl numberPre effective Prandtl numberPrt turbulent Prandtl numberq specific thermal energy (heat per unit of mass)qc cold side specific heat rejected from stageqh hot side specific heat transferred to the stageq/ specific heat transferred to stator bladesq// specific heat transferred to rotor bladesq heat flux vectorQ thermal energy (heat)

thermal energy flow (heat flow)

thermal energy flow (heat flow), blade cold side

thermal energy flow (heat flow), blade hot side

thermal energy flow (heat flow) to/from stator blades

thermal energy flow (heat flow) to/from rotor bladesr degree of reactionri radius of stage stream surface r radius vector R radius in conformal transformation R density ratio, R = 3/ 2R radiation

Nomenclature

XIX

R radius of the mean flow path Re Reynolds numberRw thermal resistances specific entropys slot thicknesss blade spacingSi cross section at station iSt Stanton numberStr Strouhal numbert timet thicknesst tangential unit vectorT static temperatureT tangential force componentT stress tensor, T = eiej ijTo stagnation or total temperatureTc static temperature on blade cold side Th static temperature on blade hot sideTW blade material temperatureu specific internal energyu velocity U, V, W rotational, absolute, relative velocity vectorsv specific volumeV volume

mean velocity vectorVmax maximum velocity on suction surfaceW mechanical energy

mechanical energy flow (power)

shaft power

X state vectorxi coordinatesZi individual stage loss coefficient

Greek Symbols

heat transfer coefficient, absolute and relative flow anglesst stagnation angle in conformal transformation

blade stagger angle specific circulation functionshock anglecirculation vectordeviation angle

1, 2, 3, boundary layer displacement, momentum, energy thickness

Nomenclature

XX

1, 2 dimensionless displacement, momentum thicknessloss coefficient ratioconvergence tolerance

/ dimensionless parameter for stator blades heat transfer // dimensionless parameter for rotor blades heat transfer

total pressure loss coefficientefficiencyvelocity ratiosegment angleblade flow deflection angle shock expansion angletemperature ratio isentropic exponentratio of specific heatsstage load coefficientwave lengthload functionmass flow ratioabsolute viscosity

, , velocity ratioskinematic viscosity

m straight cascade stagger angledistance ratio = x/b pressure ratio

stress tensor, = eiejdensitycascade solidity = c/stemperature ratio

o, W wall sear stressstage flow coefficientdissipation function

, potential, stream functioncomplex functionisentropic stage load coefficientstream functionangular velocityRotation tensor

Subscripts, superscripts

a, t axial, tangentialc compressiblec cold sideC compressor C, S, R cascade, stator, rotorex exit

Nomenclature

XXI

F flameF fuelFi filmG combustion gash hot sidein inletmax maximumP, S blade pressure, suction surfaces isentropics shockt turbulentw wallS time averaged

random fluctuationdeterministic fluctuation

* dimensionless+ wall functions/, // stator, rotor

Abbreviations

NACA National Advisory Committee for AeronauticsNASA National Aeronautics and Space AdministrationTPFL Turbomchinery Performance and Flow Research Laboratory at

Texas A&M University

Nomenclature

1 Introduction, Gas Turbines, Applications, Types

Gas turbines are engines within which the chemical energy of the fuel is convertedeither into mechanical energy in terms of shaft power or into kinetic energy. Gasturbines that produce shaft power are power generation gas turbines. Gas turbinesthat convert the fuel energy into kinetic energy are used for generation of thrust topropel an aircraft. The conversion of fuel energy into shaft power or propulsive force,requires interaction of several components of the engine, within each of them a chainof energy conversion takes place.

1.1 Power Generation Gas Turbines Consider a power generation gas turbine shown in Figure 1.1. Air from theenvironment enters the inlet nozzle, where its total pressure is partially converted intokinetic energy. After passing through the inlet, air enters a multi-stage compressor,where its total pressure continuously increases to reach the design pressure ratio atthe exit of the compressor. The increase of total pressure is accomplished bysupplying mechanical energy through the turbine. In this case, one is dealing with apartial conversion of mechanical energy into potential energy. Based on thecompression pressure ratio, the working medium air leaves the compressor exit at arelatively high total temperature and total pressure. It enters the combustion chamber,where fuel is added. Within the combustion chamber an intensive combustion processtakes place, where the chemical energy of the fuel is converted into thermal energy.The resulting combustion gas enters a multi-stage turbine, where its total energy is,

Figure 1.1: Alstom heavy duty power generation gas turbine GT13E2 with grossoutput of 202.7 MW and a combined cycle efficiency of 53.5%.

© Springer International Publishing AG 2018M.T. Schobeiri, Gas Turbine Design, Components and SystemDesign Integration, DOI 10.1007/978-3-319-58378-5_1

1

1 Introduction, Gas Turbines, Applications, Types2

to a great extent, converted into mechanical energy. The process of energy conversioncontinues within the exit diffuser (not visible in Figure.1.1), where the kinetic energyof the exiting gas is partially converted into potential energy. The energy conversionprocess that takes place in individual components is always associated with certaintotal pressure losses causing entropy increase that leads to efficiency decrease. Theenergy conversion process discussed above is inherent to all power generation gasturbine irrespective of their power size, types and configurations. Similar componentsare found in Figure 1.2 and all power generation gas turbines .

The gas turbine configurations shown in Figure 1.1 and 1.2 are characterized byhaving one multi-stage compressor, one multi-stage turbine and one shaft that cariesboth compressor and turbine blades. The pressure increase inside the compressor isestablished by several stages, each of which comprises a stator and a rotor blade row.Total pressure increase is established by compressor rotor row only, while the statorrow increases static pressure thus reducing velocity. The stator also provides thenecessary flow deflection for the rotor row which receives mechanical energy inputfrom the turbine. Figure 1.3 shows a Siemens SGT5-4000F gas turbine with thecompressor and turbine stages. Its annular type combustion chamber has several fuelinjectors that are distributed equidistantly in circumferential direction. The annularconfiguration of the combustion chamber serves a more uniform temperature

Figure 1.2: A General Electric heavy duty gas turbine with its majorcomponents.

1 Introduction, Gas Turbines, Applications, Types 3

distribution for the following turbine component. The multi-stage turbine that followsthe combustion chamber provides the power necessary to drive the compressor unitand the generator for producing the electricity.

Siemens gas turbines SGT5-4000F have a gross power output of 292 MW, a grossefficiency of 39.8%, a gross heat rate of 9038 kJ/kWh, a compressor pressure ratioof 18.2 by 15 stages, an exhaust temperature of 580.0 C and an exhaust mass flow688kg/s. In Combined Cycle configuration the plant produces a net power of 423MW at a net efficiency of 58.4% and a net heat rate of 6164 kJ/kWh

The gas turbines shown in Figures 1.1-1.3 share a common characteristic: thenumber of their compressor stages is three-to four times larger than the number oftheir turbine stages. This phenomenon is explained in terms of different flowcharacteristics in these two components. While the pressure inside a compressor bladechannel is continuously increasing, the one inside a turbine blade channel is

Figure 1.3: Siemens power generation gas turbine SGT5-4000F with a multi-stage compressor, an annular combustor with a set of fuel injectors and a multi-stage turbine.


decreasing. In compressor case, the blade boundary layer is exposed to a positivepressure gradient causing the fluid particles to decelerate, eventually come tostandstill and reverse the direction. This is the triggering mechanism of what is termedrotating stall. In turbine case, however, the fluid particles inside the turbine bladechannel and within its boundary layer are subject to a negative pressure environmentthat causes the particle to accelerate. As a result, turbine blades can be subject to amuch stronger pressure gradient than the compressor blades. This statement isvisualized by comparing a compressor cascade with a turbine cascade. As Figure 1.4shows, the deflection of the turbine cascade is approximately . A

quantifying parameter to describe this phenomenon is the stage load coefficientdefined as with as the specific total enthalpy of the stage and U thecircumferential velocity of the rotor blade in the mid-section. Assume a single stageturbine with has to process a pressure ratio of . For an axialcompressor to supply this pressure ratio four stages are needed, each with pressureratio of . In contrast to the axial compressors with relatively low pressureratio per stage, radial compressors can be designed with a single stage exceedingpressure ratios above 5. These type of compressors can be applied to gas turbines ofsmall power size. As an example, a small gas turbine OP16 by OPRA, is shown inFigure 1.5. The rotor carries a single stage centrifugal compressor with a pressure

VV

V

V

V

αα

V

α

Θ

α

Turbine Cascade, Flow Deflection

Compressor Cascade, Flow deflection

Θ

Θ = 4 Θ

V

Figure 1.4: Flow deflection in a compressor and a turbine cascade.


Figure 1.6: A Kawasaki small gas turbine with two centrifugalcompressors, a four stage turbine and a single combustion chamber.

ratio of . The compressor is driven by a single stage centripetal turbine thatproduces a net power of 2MW at a gross efficiency of 26%. This 2 MW class engineis suitable for oil and gas, marine, industrial and commercial power applications.

Figure 1.5: OP16 gas turbine with centrifugal compressor and centripetalturbine.


To obtain a higher pressure ratio, two or more centrifugal compressors can bearranged and operated in series. A small Kawasaki gas turbine, M1A-13/17, with 1.5MW power is shown in Figure 1.6. It has a two stage centrifugal compressor, a singlecombustion chamber and a four stage turbine. For small size engines, the centrifugalcompressor is the appropriate pressure supplier, but it cannot be used for large powergeneration gas turbines or aero-engines. As will be explained in detail in Chapter 4,the mechanism of pressure generation by a centrifugal compressor is based on thedifference in the circumferential kinetic energies from exit to inlet, . Sincethe power is directly proportional to the mass flow, large engines require large amountof mass flow. In order for a centrifugal compressor to provide the same amount ofmass flow as an axial compressor, its exit diameter must be substantially larger thanthe inlet mean diameter. This makes the use of centrifugal compressors impracticalfor installation into the large power generation gas turbines. For aero-engines, adisproportionately large outer diameter increases the drag force and thus the fuelconsumption.

1.2 Compressed Air Energy Storage Gas Turbines, CAES

The first compressed air energy storage (CAES) plant was designed andmanufactured by Brown Boveri & Cie (BBC), installed in Huntorf Germany andcommissioned 1978. It comprises of a compressor train that pumps air into a largeunderground cavern, an electric/generator and a gas turbine unit. The plant wasdesigned to cover the peak-load demand in a highly efficient manner. Its gas turbineunit distinguishes itself from all other conventional turbines. The conventional gasturbines require up to two thirds of the turbine power to drive the compressor, leavingabout one third as the net power for electricity generation. In contrast, the CAES-gasturbine uses the pre-compressed air stored in an underground cavern. During the highelectric energy demand the compressed air is directed to the combustion chamber,where fuel is added. Thus, the entire thermal energy of the combustion gas istransferred to the shaft. Figures 1.7 show the schematics of the CAES Huntorf with more detailspresented in [1]. The plant has been operating reliably since 1978 as an emergencypower generator to cover the peak electric energy demand. It consists of (1) acompressor train, (2) an electric motor/generator unit, (3) gas turbine, and (4)underground compressed air storage. During a period of eight hours of low electricenergy demand (night), the electric motor operating at 60MW drives the compressortrain that pumps air into an underground salt cavern with a storage volume of 310,000m3 more than 600 m deep below the ground at a maximum pressure of about 70 bar.The compressor train consists of an axial low pressure compressor with 20 stages anda high pressure unit with 6 radial impellers operating at 7622 rpm. The compressedair has a relatively high exit temperature and must be cooled down before entering thestorage cavern. The HPC has two inter-cooler and one after-cooler.

During the compression mode, the turbine valve VT is closed, while the


compressor valve VC is open. During the power generation mode, the compressorvalve VC is closed, while the turbine valve VT opens. During high electric energydemand, the cavern exit valves open, and air after passing through a pre-heater entersthe high pressure (HP)-combustion chamber, where fuel is added. The leancombustion gas expands in HP-turbine, and exits into the low pressure(LP)-combustion chamber, where the remaining fuel is added. The gas turbineoperates and delivers 290 MW for about two hours.

The core component of this and the more advanced Soyland CAES facility is the gasturbine shown in Figure 1.8. It consists of a high pressure (HP) combustion chamberfollowed by a multi-stage HP-turbine followed by a low pressure (LP) combustionchamber and a multi-stage LP-turbine. A detailed dynamic performance andefficiency study of this CAES-gas turbine operating in power generation modecompared to the one with only one combustion chamber and one multi-stage turbinegave a substantial increase of efficiency. Although this standard efficiencyimprovement method was used in CAES plant design, until late eighties it did notfind its way into the power generation gas turbine design. The reason for not applyingthis very effective method to gas turbines was in first place the inherent problem ofthe integration of the typical BBC-large volume silo-type combustion chambers intoa compact gas turbine engine. Adding another conventional large volume combustionchamber such as those in CAES raised a number of unforeseeable design integrityand operational reliability concerns that deterred engine manufacturer. However,

Figure 1.7: Compressed air storage facility Huntorf, Germany


taking advantage of the well known reheat concept and its successful application toCAES-Huntorf, seemed to be a viable solution for improving the BBC gas turbineefficiencies. The adoption of this concept occurred after the merger between theSwedish company Asea and Brown Boveri, Switzerland in 1988.

1.3 Power Generation Gas Turbine Process

Worldwide prior to 1986, the thermal efficiency of gas turbines, based on the turbineinlet temperature (TIT) ranged from . Achieving higher efficiencyrequired a substantial increase of TIT necessitating extensive cooling of the frontturbine stages. Studies in [2] and [3] show that a significant efficiency improvementcan be achieved by introducing the reheat concept used in CAES-turbine design. Thethermodynamic process in Figure 1.9 shows the thermal efficiency as a function ofpressure ratio (top) and specific gas turbine work (bottom) with TIT as a parameter.As seen, for each TIT, there is an optimum pressure ratio that increases with risingthe turbine inlet temperature. Increasing the pressure ratio beyond this optimum pointwill reduce the efficiency. Given a certain maximum compressor stage pressure ratioas a limit (1.15-1.25), any increase in overall pressure ratio requires adding morestages. In practice, the compressor is designed with a pressure ratio less than theoptimum but with . Figure 1.9 explains this process: using a temperature

Figure 1.8: CAES Soyland from [1].


3.0

Θ=6.0

3..54.0 4.5 5.0

5.5

Θ = TIT/Tref

Tref = 300 KηT=90%ηC=90%

Specific GT-Work (kJ/kg)

η th

0 100 200 300 400 5000

0.1

0.2

0.3

0.4

0.5

5.55.0

4.54.0

Θ=3.0

3.5

6.0

Θ = TIT/Tref

Tref = 300 KηT=90%ηC=90%

π

η th

0 5 10 15 20 25 30 35 400.00

0.10

0.20

0.30

0.40

0.50

Figure 1.9: Efficiency improvement of conventional gas turbines.

ratio of , its optimum pressure ratio is close to (red circle). Itsoptimum efficiency, however, is very close to the one at (circle markedgreen). To provide the difference of , at least 7 stages, each with a

are necessary to arrive at . Considering Figure 1.9 (bottom),it should be noted that the maximum efficiency and maximum specific gas turbinework are at two different pressure ratios as shown in Figure 1.10. In fact, movingtoward smaller pressure ratios as discussed above is not only saving a significantnumber of stages, but it also moves the specific GT-work to higher level which isdesirable for integrating the gas turbine into a combined cycle (CCGT).


Θ=6.0

3.0

Θ=6.0

5.5

5.0

4.5

4.0

3.5

π

Spec

ific

GT-

Wor

k(k

J/kg

)

0 10 20 30 400

100

200

300

400

500

Figure 1.10: Specific GT-work as a function of pressure ratio with TIT asparameter.

2

3

4BL BL

BLT3BL

a

2

1

BL

b

3BLT

4BL

BL3

23

5

6

Entropy s

Baseline GT (BL) GTwith reheat

Tem

pera

ture

T

Entropy s

Tem

pera

ture

T

Figure 1.11: Performance comparison of a conventional and a reheat gasturbine.

1.4 Significant Efficiency Improvement of Gas Turbines

A schematic representation of the reheat concept mentioned previously is given inFigure 1.11 in terms of T-S-diagrams for a baseline gas turbine (a) and a gas turbinewith reheat stage (b). To apply the reheat concept, first the optimum pressure ratioand the corresponding design pressure ratio must be obtained. This ratio is for the

same baseline temperature almost twice the baseline pressure ratio. Using a gasturbine with an efficiency of 36% as the baseline GT, a reheat stage was added asshown in Figure 1.11. The blue hatched area in Figure 1.11 (a) represents theperformance of the baseline GT, whereas the area hatched in blue and red represents


the performance of a GT with a reheat stage. It should be noted that the turbine inlettemperature for the baseline GT and the GT with reheat are the same. This is a veryimportant aspect that enables a gas turbine design with a high efficiency but at alower temperature; for example 1200 oC. Figure 1.12 shows quantitatively theefficiency improvement using the reheat concept. The blue curve represents theefficiency of a relatively advanced GT up to 1986. The green curve exhibits theefficiency of a generic reheat gas turbine. This curve includes the predicted efficiencyof 40.5% already reported in [4]. While the pressure ratio of this generic gas turbineand the one of ABB-GT24/26 are identical, the turbine inlet temperature is by 4oClower than the turbine inlet temperature of GT24/26 [4].

As seen, the new reheat gas turbine has an efficiency increase of 8.5% compared tothe one of GT-9 and 4.5% compared to the baseline of a more advanced gas turbinein the same period of time. The corresponding measured efficiency for GT24 reportedin [4] was 38.2%. The difference of 2.3% was attributed to numerous failuresassociated with compressor blade distress in the form of cracking [4]. The failuresoccurred at the start of the engine operation. Although the difference of 2.3% is notinsignificant, an enormous improvement of thermal efficiency was achievedcompared to the existing ones at that time. This efficiency improvement was achieveddespite the facts that: (a) The compressor pressure ratio is far greater than the one ofconventional GT one causing the compressor efficiency todecrease. The latter is because of reduced blade height associated with an increase insecondary flow losses. (b) The introduction of a second combustion chamberinherently causes additional total pressure losses.

0

GT- with reheat stageConcept realization: ABBOptimum presure ratio: π = 40Design pressure ratio π = 30Predicted ηth = 40.5%Measured ηTh= 38.2%

PredictedTIT = 1200Cfor both GTs

Baseline GTBaseline GT

GT-9:ηth=32%

Measured

π

η th

0 10 20 30 40 500.2

0.3

0.4

0.5

Figure 1.12: Efficiency comparison between a conventional (blue curve)and a reheat gas turbine (green curve).

Meinhard T. Schobeiri Gas Turbine Design,

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