Gas Turbine Design, Components and System Design Integration

522 Pages·2017·30.43 MB·English

by  Meinhard T. Schobeiri

Meinhard T. Schobeiri
Gas Turbine
Design,
Components
and
System Design
Integration
123
Gas Turbine Design, Components and System
Design Integration
Meinhard T. Schobeiri
Gas Turbine Design,
Components and System
Design Integration
1 3
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
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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 and
application of gas turbines in any of the above areas and their operational
requirements are different, they share the same underlying physics. The physics of
turbomachinery components and systems was discussed in details in the first and the
second enhanced edition of my textbook, Turbomachinery Flow Physics and
Dynamic Performance. The book found a world-wide positive echo among the
turbomachinery community including industry and academia. This motivated me to
write the current textbook about the gas turbine design, where I spent more than forty
years 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 thermal
turbomachines were discussed in very detail, the current book deals with the aero-
thermodynamics design of gas turbine components and their integration into a
complete gas turbine system.
Designing a gas turbine requires a team work of several groups that are
specialized in aero-thermodynamics, heat transfer, computational fluid dynamics,
combustion, solid mechanics, vibration, rotordynamics and system control to name
just a few. It is beyond the scope of any text book to treat the above areas in a
detailed fashion. Available gas turbine handbooks do not treat the above areas in debt
and breath, so that they do cannot be considered a working platform for gas turbine
designer. They may, however, be able to provide the reader an overview of the
subject. Considering the above, the current book is concentrated on a detailed aero-
thermodynamics, design and off-deign performance aspects of individual components
as well as the system integration and its dynamic operation.
Design of gas turbines was from very beginning based on sound physics rather
than empiricism. The first gas turbine manufactured around 1900 was not even able
to rotate, because the turbine power was much less than the required compressor
power. The reason was the poor efficiencies of both the turbine and the compressor
component. The failed tests showed that the prerequisite for a successful gas turbine
design is the full understanding of its underlying viscous flow physics and its
mathematical description. The mathematical structure that describes the three
dimensional viscous flow in very details was already derived by C.L.M.H. Navier in
1821 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 to
L.Prandl’s 1904 groundbreaking boundary layer theory that provided an approximate
solution to Navier-Stokes equations. The simplification of the Navier-Stokes
equations through boundary layer theory made possible to calculate total pressure loss
V
VI Preface
coefficient of compressor and turbine blades, define the rotating stall and surge limit
of compressors, define the range of the laminar separation of the boundary layer in
low pressure turbines and many other aerodynamic aspects of gas turbine operation.
In the meantime, the introduction of high speed computers and advanced
computational methods has significantly contributed to an exponential growth of
information covering almost all aspects of turbomachinery design. This situation has
lead to a growing tendency in technical specialization. A factor in the context of
specialization is the use of “black boxes” in engineering in general and in
turbomachinery in particular. During my 40 years of turbomachinery R&D
experience, I have been encountering engineers who can use commercial codes for
calculating the complex turbomachinery flow field without knowing the underlying
physics of the code they use. This circumstance constituted one of the factors in
defining the framework of the book Turbomachinery Flow Physics mentioned
previously, which aims at providing the students and practicing turbomachinery
design engineers with a solid background in turbomachinery flow physics and
performance. Built upon a physical basis that contains a minimum of empirical
correlations, I have been teaching turbomachinery courses in the past thirty years and
educated several generations of highly qualified turbomachinery engineers that are
working in US gas turbine manufacturing companies. The current book provides the
interested students and the young engineers working in the industry with a material
they can use for preliminary design of gas turbines. It is also intended to help
instructors of turbomachinery courses around the world to assign gas turbine
components as project modules that can be integrated into a complete system.
The current book consists of 18 Chapters that are grouped into three parts. Part
I encompassing Chapters 1 through 6 deals with aero-thermodynamics of gas turbine
design.
Part II of this book include Chapters 7 through 10 starts with the treatment of
cascade and stage efficiency and loss determination from a physically plausible point
of view. I refrained from presenting recipe-types of empirical formulas that have no
physical foundation. Chapter 8 deals with the calculation of incidence and deviation.
Chapter 9 treats in detail the compressor and turbine blade design procedures. Radial
equilibrium is discussed in Chapter 10, which concludes Part II.
Part III of the book is entirely dedicated to design, off-deign and dynamic
performance of turbomachinery components and systems. Particular attention is paid
to gas turbine components, their individual modeling, and integration into the gas
turbine system. It includes Chapters 11 to 16. Chapter 11 introduces the basic physics
of non-linear dynamic simulation of turbomachinery systems and its theoretical
background. Starting from a set of general four dimensional partial differential
equations in temporal-spatial domain, two-dimensional equation sets are derived that
constitute the basis for component modeling. The following Chapters 12, 13 and 14
deal with generic modeling of turbomachinery components and systems in which
individual components ranging from the inlet nozzle to the compressor, combustion
chamber, turbine, and exhaust diffuser are modeled. In modeling compressor and
turbine components, non-linear adiabatic and diabatic expansion and compression
calculation methods are presented.
Gas turbine design requires several preliminary steps. These steps were discussed
in Chapter 17. Chapter 18 deals with the dynamic simulation of different gas turbine
types that are subject to adverse dynamic operations. Seven representative case
studies conclude this chapter. In preparing Part III, I tried to be as concrete as
Preface VII
possible by providing detailed simulation of existing gas turbine engines and their
individual component.
In typing several thousand equations, errors may occur. I tried hard to eliminate
typing, spelling and other errors, but I have no doubt that some remain to be found
by readers. In this case, I sincerely appreciate the reader notifying me of any mistakes
found; the electronic address is given below. I also welcome any comments or
suggestions regarding the improvement of future editions of the book.
My sincere thanks are due to many fine individuals and institutions. First and
foremost, I would like to thank the faculty of the Technische Universität Darmstadt,
from whom I received my entire engineering education. I finalized major chapters of
this book during my sabbatical in Germany where I received the Alexander von
Humboldt Prize. I am indebted to the Alexander von Humboldt Foundation for this
Prize and the material support for my research sabbatical in Germany. My thanks are
extended to Prof. Bernd Stoffel, Prof. Ditmar Hennecke, Professor Pelz and Dipl. Ing.
Bernd Matyschok for providing me with a very congenial working environment. I
truly enjoyed interacting with these fine individuals. NASA Glenn Research Center
sponsored the development of the nonlinear dynamic code GETRAN which I used
to simulate cases in Part III. I wish to extend my thanks to Mr. Carl Lorenzo, Chief
of Control Division, Dr. D. Paxson, and the administration of the NASA Glenn
Research 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 streamline
curvature method.
I am also indebted to the TAMU administration for partially supporting my
sabbatical that helped me in finalizing the book.
Last but not least, my special thanks go to my family, Susan and Wilfried for
their support throughout this endeavor.
M.T. Schobeiri
September 2016
College Station, Texas
[email protected]
Table of Content
Preface to the First Edition ................................... . V
Table of Content ............................................ . IX
Nomenclature ............................................ XVII
1 Introduction, Gas Turbines, Applications, Types .............. . 1
1.1 Power Generation Gas Turbines ......................... . 1
1.2 Compressed Air Energy Storage Gas Turbines, CAES........ . 6
1.3 Power Generation Gas Turbine Process ................... . 8
1.4 Significan tEfficiency Improvemen tof Gas Turbines......... . 10
1.5 Ultra High Efficiency Gas Turbine ....................... . 14
1.6 Aircraft Gas Turbines ................................. . 17
1.7 Aircraft-Derivative Gas Turbines ........................ . 19
1.8 Gas Turbines Turbocharging Diesel Engines ............... . 22
1.9 Gas Turbine Components, Functions ..................... . 24
1.9.1 Group 1: Inlet, Exhaust, Pipe ...................... . 25
1.9.2 Group 2: Heat Exchangers, Combustion Chamber...... . 26
1.9.3 Group 3: Compressor, Turbine Components .......... . 29
References .............................................. . 30
2 Gas Turbine Thermodynamic Process ...................... . 31
2.1 Ga sTurbine Cycles ,Processes .......................... . 31
2.1.1 Gas Turbine Process............................. . 32
2.2 Improvemen to fGa sTurbine Therma lEfficiency ........... . 39
2.2.1 Minor Improvement of Gas Turbine Thermal Efficiency. . 40
2.2.2 Major Improvement of Gas Turbine Thermal Efficiency. . 41
2.1.3 Compressed Air Energy Storage Gas Turbine ......... . 45
References .............................................. . 47
3 Thermo-Fluid Essentials for Gas Turbine Design ............. . 49
3.1 Mass Flow Balance................................... . 49
3.2 Balance of Linear Momentum........................... . 51
3.3 Balance of Moment of Momentum....................... . 53
3.4 Balance of Energy.................................... . 56
3.4.1 Energy Balance Special Case 1: Steady Flow ......... . 57
3.4.2 Energy Balance Special Case 2: Steady Flow ......... . 58
3.5 Application of Energy Balance to Gas Turbines Components .. . 58
3.5.1 Application: Accelerated, Decelerated Flows ......... . 59
3.5.2 Application: Combustion Chamber, Heat Exchanger .... . 60
IX
Table of Content X
3.5.3 Application: Turbine, Compresso r .................. 63
3.5.3.1 Uncoole dturbine........................ 63
3.5.3.2 Cooled turbine.......................... 64
3.5.3.3 Uncooled compressor .................... 65
3.5.3.4 Cooled Compressor...................... 66
3.6 Irreversibility and Total Pressure Losses .................. 67
3.6.1 Application o fSecond Law to Turbomachinery
Components ................................... 69
3.7 Flow at High Subsonic and Transonic Mach Numbers........ 71
3.7.1 Density Changes with Mach Number, Critical State .... 72
3.7.2 Effect of Cross-Section Change on Mach Number...... 77
3.7.3 Compressible Flow through Channels ................ 84
3.7.4 The Normal Shock Wave Relations ................. 92
3.7.5 The Oblique Shock Wav eRelations ............... 98
3.7.6 Detached Shock Wave........................... 102
3.7.7 Prandtl-Meyer Expansion......................... 102
References .............................................. 105
4 Theory of Turbomachinery Stages .......................... 107
4.1 Energy Transfer in Turbomachinery Stages ................ 107
4.2 Energy Transfer in Relative Systems ..................... 108
4.3 General Treatment of Turbine and Compressor Stages........ 109
4.4 Dimensionless Stage Parameters......................... 113
4.5 Relation Between Stage parameter, Radial Equilibrium....... 115
4.6 Effect of Degree of Reaction on the Stage Configuration...... 118
4.7 Effect of Stage Load Coefficient on Stage Power ........... 120
4.8 Unified Description of a Turbomachinery Stage............. 121
4.8.1 Unified Description of Stage with Constant Mean
Diameter .............................. ........ 121
4.8.2 Generalized Dimensionless Stage Parameters ......... 122
4.9 Special Cases........................................ 124
4.9.1 Case 1, Constant Mean Diameter ................... 125
4.9.2 Case 2, Constant Meridional Velocity Ratio .......... 125
4.10 Increase of Stage Load Coefficient ,Discussion ............. 126
References .............................................. 128
5 Turbine and Compressor Cascade Flow Forces ............... 129
5.1 Blade Force in an Inviscid Flow Field..................... 129
5.2 Blade Forces in a Viscous Flow Field..................... 134
5.3 The Effect of Solidity on Blade Profile Losses .............. 140
5.4 Relationship Between Profile Loss Coefficient and Drag ..... 140
5.5 Optimum Solidity .................................... 142
5.5.1 Optimum Solidity, by Pfeil........................ 143
5.5.2 Optimum Solidity by Zweifel...................... 144
5.6 Generalized Lift-Solidity Coefficient ..................... 146
5.6.1 Lift-Solidity Coefficient for Turbine Stator ........... 148
5.6.2 Turbine Rotor .................................. 152
References .............................................. 155
XI Table of Content
6 Losses in Turbine and Compressor Cascades ................. 157
6.1 Turbine Profile Loss ................................. 158
6.2 Viscous Flow in Compressor Cascade .................... 160
6.2.1 Calculation o fViscou sFlows ..................... 160
6.2.2. Boundary Layer Thicknesses ...................... 161
6.2.3 Boundary Laye rIntegra lEquation .................. 162
6.2.4 Application of Boundary Layer Theory to Compressor .. 164
6.2.5 Effect of Reynolds Number ....................... 168
6.2.6 Stag eProfil eLosses ............................. 168
6.3 Trailing Edge Thickness Losses ......................... 168
6.4 Losses Due to Secondary Flows ......................... 174
6.4.1 Vortex Induced Velocity Field ..................... 176
6.4.2 Calculation of Tip Clearance Secondary Flow Losses ... 179
6.4.3 Calculation of Endwall Secondary Flow Losses ....... 182
6.5 Flow Losses in Shrouded Blades ........................ 186
6.5.1 Losses Due to Leakage Flow in Shrouds ............. 186
6.6 Exi tLoss ........................................... 192
6.7 Trailing Edge Ejection Mixing Losses of Gas Turbine Blades .. 194
6.7.1 Calculation of Mixing Losses ...................... 194
6.7.2 Trailing Edge Ejection Mixing Losses ............... 199
6.7.3 Effect of Ejection Velocity Ratio on Mixing Loss ...... 199
6.7.4 Optimum Mixing Losses.......................... 201
6.8 Stage Total Loss Coefficient............................ 201
6.9 Diffusers, Configurations, Pressure Recovery, Losses ........ 202
6.9.1 Diffuser Configurations .......................... 203
6.9.2 Diffuser Pressure Recovery ....................... 204
6.9.3 Design of Short Diffusers......................... 207
6.9.4 Some Guidelines for Designing High Efficiency
Diffus ers.... ... ......... .... ......... ......... 210
References .............................................. 211
7 Efficiency of Multi-Stage Turbomachines .................... 213
7.1 Polytropic Efficiency.................................. 213
7.2 Isentropic Turbine Efficiency, Recovery Factor ............. 216
7.3 Compressor Efficiency, Reheat Factor .................... 219
7.4 Polytropic versus Isentropic Efficiency.................... 221
References .............................................. 223
8 Incidence and Deviation .................................. 225
8.1 Cascade with Low Flow Deflection ...................... 225
8.1.1 Conformal Transformation......................... 225
8.1.2 Flow Through an Infinitely Thin Circular Arc Cascade.. 234
8.1.3 Thickness Correction ............................ 240
8.1.4 Optimum Incidence.............................. 240
8.1.5 Effect of Compressibility ......................... 242
8.2 Deviation for High Flow Deflection ...................... 243
8.2.1 Calculation of Exit Flow Angle ....... ............. 245
References .............................................. 247