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Consulting Editors
Jack P. Holman, Southern Methodist University John R. Lloyd, Michigan State University
Anderson: Computational Fluid Dynamics: The Basics with Applications
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Evaluation: A Tool for Design, Manufacturing, and Service
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ELEMENTS OF GAS TURBINE
Manufacturing Engineering Seattle University
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This book wa., sci in Times Roman. The editors were John J. CorTigan and James W. 8 radl ey; the product ion supervisor was Leroy A . Young. The cover wa, designed by MerTill Haber. Drawings were done by ECL An . R. R. Donne lley & Sons Company was printer and hinder.
lffll Tata McGraw-Hill
ELEMENTS OF GAS TURBINE PROPULSION
Copyri ght © 1996 by The McGraw-Hill Companie,, Inc . A ll rights resen ed. No pan ot' th is publi cat ion may be reproduced or di stributed in any form or by any mean,. or stored 111 a database or retrieval , ystem. without the prior written permiss ion o t' the publisher
Tata McGraw-llill Edition 2005
Sixth reprint 2013 RLQZRRDODLCXL
Reprinted in India by arTangcment with The McGraw-Hill Companie,. Inc .. New York
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Library of Congress Cataloging-in-Publication Data
Matt ingly, Jack D. Elements or gas turbine propulsion/Jack D. Mallingly: with a foreword
by Hans von O hain . p. cm.- (McGraw-Hill series in mechanical engineering)
(McHraw-Hill ,eries in aeronautical and aerospace engineering) Includes bibliographical references and index. ISBN 0-07-9 I 2 196-9 (sell I. Airp lanes- Jet propulsion. I. Title. II. Series. Ill. Series: McGraw-Hill series in aero nauti cal and aerospace engineering. L 709.MJ8 1996 29. I 34. J5J-dc20
ISBN-13: 978-0-07 -060628-9 ISBN-JO: 0-07-060628-5
Published by Tata McGraw Hill Education Private Limited. 7 West Patel Nagar. New Delhi I JO 008. "nd printed at Sai Printo Pack Pvt. Ltd .. Delhi I 10 020
95-897
ABOUT THE AUTHOR
Jack D. Mattingly received his B.S. and M.S. in Mechanical Engineering from the Uni·:ersity of Notre Dame, and his Ph.D. in Aeronautics and Astronautics at the University of Washington. While studying for his doctorate under Gordon C. Oates, he pioneered research in the mixing of coannular swirling flows and developed a major new test facility. During his 28 years of experience in analysis and design of propulsion and thermodynamic systems, he has developed aerothermodynamic cycle analysis models and created engineering software for air-breathing propulsion systems. Dr. Mattingly has more than 23 years of experience in Engineering Education, previously as a senior member of the Department of Aeronautics at the United States Air Force Academy, where he established a top undergraduate propulsion program. He retired from active duty with the U.S. Air Force in 1989 and joined the faculty of Seattle University. In addition, he has taught and done research in propulsion and thermal energy systems at the Aeropropulsion and Power Laboratory, Air Force Institute of Technology, University of Washing­ ton, University of Notre Dame, University of Wisconsin, and IBM Corp. He was also founder of the AIAA/ Air Breathing Propulsion Team Aircraft Engine Design Competition for undergraduate students. Among his many distinguished teaching awards is Outstanding Educator for 1992 from Seattle University. Having published more than 20 technical papers, articles, and textbooks in his field , Dr. Mattingly was the principal author of Aircraft Engine Design (1987), an unprecedented conceptual design textbook for air breathing engines. He is currently Chair, Department of Mechanical and Manufacturing Engineering at Seattle University.
I have been blessed to share my life with Sheila, my best friend and wife. She has been my inspiration and helper, and the one who sacrificed the most to make this work possible. I dedicate this book and accompanying software to Sheila.
I would like to share with all the following passage I received from a very close friend over 18 years ago. This passage provides guidance and focus to my life. I hope it can be as much help to you.
FABRIC OF LIFE
I want to say something to all of you Who have become a part Of the fabric of my life The color and texture Which you have brought into My being Have become a song And I want to sing it forever. There is an energy in us Which makes things happen When the paths of other persons Touch ours And we have to be there And let it happen. When the time of our particular sunset comes Our thing, our accomplishment Won't really matter A great deal. But the clarity and care With which we have loved others Will speak with vitality Of the great gift of life We have been for each other.
Anonymous
CONTENTS
List of Symbols lix
1 Introduction 1 1-1 Propulsion 1 1-2 Units and Dimensions 2 1-3 Operational Envelopes and Standard Atmosphere 4 1-4 Air-Breathing Engines 6 1-5 Aircraft Performance 33 1-6 Rocket Engines 53
Problems 60
2 Thermodynamics Review 67 2-1 Introduction 67 2-2 Definitions 68 2-3 Simple Compressible System 73 2-4 Equations of State 74 2-5 Basic Laws for a Control Mass System 76 2-6 Relations between the System and Control Volume 78 2-7 Conservation of Mass Equation 81 2-8 Steady Flow Energy Equation 81 2-9 Steady Flow Entropy Equation 89 2-10 Momentum Equation 90 2-11 Summary of Laws for Fluid Flow 95 2-12 Perfect Gas 96
Problems 108
xii CONTENTS
3 Compressible Flow 114 3-1 Introduction 114 3-2 Compressible Flow Properties 114 3-3 Normal Shock Wave 138 3-4 Oblique Shock Wave 145 3-5 Steady One-Dimensional Gas Dynamics 156 3-6 Simple Flows 159 3-7 Simple Area Flow-Nozzle Flow 161 3-8 Simple Heating Flow-Rayleigh Line 174 3-9 Simple Frictional Flow-Fanno Line 189 3-10 Summary of Simple Flows 203
Problems 206
4 Aircraft Gas Turbine Engine 213 4-1 Introduction 213 4-2 Thrust Equation 213 4-3 Note on Propulsive Efficiency 223 4-4 Gas Turbine Engine Components 224 4-5 Brayton Cycle 233 4-6 Aircraft Engine Design 236
Problems 237
5 Parametric Cycle Analysis of Ideal Engines 240 5-1 Introduction 240 5-2 Notation 241 5-3 Design Inputs 243 5-4 Steps of Engine Parametric Cycle Analysis 244 5-5 Assumptions of Ideal Cycle Analysis 246 5-6 Ideal Ramjet 246 5-7 Ideal Turbojet 256 5-8 Ideal Turbojet with Afterburner 266 5-9 Ideal Turbofan 275 5-10 Ideal Turbofan with Optimum Bypass Ratio 299 5-11 Ideal Turbofan with Optimum Fan Pressure Ratio 305 5-12 Ideal Mixed-Flow Turbofan with Afterburning 313 5-13 Ideal Turboprop Engine 322 5-14 Ideal Turboshaft Engine with Regeneration 332
Problems 337
6 Component Performance 346 6-1 Introduction 346 6-2 Variation in Gas Properties 346 6-3 Component Performance 349 6-4 Inlet and Diffuser Pressure Recovery 349 6-5 Compressor and Turbine Efficiencies 351 6-6 Burner Efficiency and Pressure Loss 360
CONTENTS · xiii
6-7 Exit Nozzle Loss 361 6-8 Summary of Component Figures of Merit (Constant cP Values) 361 6-9 Component Performance with Variable cP 363
Problems 369
7 Parametric Cycle Analysis of Real Engines 371 7-1 Introduction 371 7-2 Turbojet 371 7-3 Turbojet with Afterburner 387 7-4 Turbofan-Separate Exhaust Streams 392 7-5 Turbofan with Afterburning-Separate Exhaust Streams 411 7-6 Turbofan with Afterburning-Mixed Exhaust Stream 417 7-7 Turboprop Engine 433 7-8 Variable Gas Properties 444
Problems 453
8 Engine Performance Analysis 461 8-1 Introduction 461 8-2 Gas Generator 471 8-3 Turbojet Engine 487 · 8-4 Turbojet with Afterburning 507 8-5 Turbofan Engine-Separate Exhausts and Convergent Nozzles 518 8-6 Turbofan with Afterburning-Mixed-Flow Exhaust Stream 541 8-7 Turboprop Engine 560 8-8 Variable Gas Properties 573
Problems 605
9 Turbomachinery 615 9-1 Introduction 615 9-2 Euler's Turbomachinery Equations 616 9-3 Axial-Flow Compressor Analysis 618 9-4 Centrifugal-Flow Compressor Analysis 676 9-5 Axial-Flow Turbine Analysis 683 9-6 Centrifugal-Flow Turbine Analysis 742
Problems 748
10 Inlets, Nozzles, and Combustion Systems 757 10-1 Introduction to Inlets and Nozzles 757 10-2 Inlets 758 10-3 Subsonic Inlets 758 10-4 Supersonic Inlets 767 10-5 Exhaust Nozzles 796 10-6 Introduction to Combustion Systems 814 10-7 Main Burners 827 10-8 Afterburners 838
Problems 849
xiv CONTENTS
Appendixes A U.S. Standard Atmosphere, 1976 B Gas Turbine Engine Data C Data for Some Liquid Propellant Rocket Engines D Air and (CH2)" Properties at Low Pressure E Compressible Flow Functions ( y = 1.4, 1.33, and 1.3) F Nomial Shock Functions ( y = 1.4) G Two-Dimensional Oblique Shock Functions ( y = 1.4) H Rayleigh Line Flow Functions ( y = 1.4) I Fanno Line Flow Functions ( y = 1.4) J Turbomachinery Stresses and Materials K About the Software
References
Index
853 855 860 865 867 878 897 902 910 917 924 938
945
949
FOREWORD
BACKGROUND The first flight of the Wright brothers in December 1903 marked the beginning of the magnificent evolution of human-controlled, powered flight. The driving forces of this evolution are the ever-growing demands for improvements in
• Flight performance (i.e., greater flight speed, altitude, and range and better maneuverability)
• Cost (i.e., better fuel economy, lower cost of production and maintenance, increased lifetime)
• Adverse environmental effects (i.e., noise and harmful exhaust gas effects) • Safety, reliability, and endurance --• Controls anli_navigation
These strong demands continuously furthered the efforts of advancing the aircraft system.
The tight interdependency between the performance characteristics of aerovehicle and aeropropulsion systems plays a very important role in this evolution. Therefore, to gain better insight into the evolution of the aero­ propulsif>n system, one has to be aware of the challenges and advancements of aerovehicle technology.
The Aerovehicle
A brief review of the evolution of the aerovehicle will be given first. One can observe a continuous trend toward stronger and lighter airframe designs, structures, and materials-from wood and fabric to all-metal structures; to
xv
Xvi FOREWORD
lighter, stronger, and more heat-resistant materials; and finally to a growing use of strong and light composite materials. At the same time, the aerodynamic quality of the aerovehicle is being continuously improved. To see this development in proper historical perspective, let us keep in mind the following information.
In the early years of the 20th century, the science of aerodynamics was in its infancy. Specifically, the aerodynamic lift was not scientifically well understood. Joukowski and Kutta's model of lift by circulation around the wing and Prandtl's boundary-layer and turbulence theories were in their incipient stages. Therefore, the early pioneers could not benefit from existent scientific knowledge in aerodynamics and had to conduct their own fundamen­ tal investigations.
The most desirable major aerodynamic characterjstics of the aerovehicle are a low drag coefficient . as well as a high lift I dr~g ratio L/ D for cruise conditions, and a high maximum lift coefficient forfanding. In Fig. 1, one can see that the world's first successful glider vehicle by Lilienthal, in the early 1890s, had an LID of about 5. In comparison, birds have an LID ranging from about 5 to 20. The Wright brothers' first human-controlled, powered aircraft had an LID of about 7.5. As the LID values increased over the years, sailplanes advanced most rapidly and now are attaining the enormously high values of about 50 and greater. This was achieved by employing ultrahigh wing aspect ratios and aerodynamic profiles especially tailored for the low opera­ tional Reynolds and Mach numbers. In the late 1940s, subsonic transport aircraft advanced to LID values of about 20 by continuously improving the
50
40
30
Flyer
B-70 B-58
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
FIGURE l Progress in lift/drag ratio L/ D.
FOREWORD xvii
aerodynamic shapes, employing advanced profiles, achieving extremely smooth and accurate surfaces, and incorporating inventions such as the engine cowl and the retractable landing gear.
The continuous increase in flight speed required a corresponding reduc­ tion of the landing speed/cruise speed ratio. This was accomplished by innovative wing structures incorporating wingslots and wing flaps which, during the landing process, enlarged the wing area and increased significantly the lift coeff:cient. Today, the arrowhead-shaped wing contributes to a high lift for landing (vortex lift). Also, in the 1940s, work began to extend the high LID value from the subsonic to the transonic flight speed regime by employing the swept-back wing and later, in 1952, the area rule of Whitcomb to reduce transonic drag rise. Dr Theodore von Karman describes in his memoirs, The Wind and Beyond (Ref. 1 at the end of the Foreword), how th·e swept-back wing or simply swept wing for transonic and supersonic flight came into existence:
The fifth Volta Congress in Rome, 1935, was the first serious international scientific congress devoted to the possibilities of supersonic flight. I was one of those who had received a formal invitation to give a paper at the conference from Italy's great Gugliemo Marconi, inventor of the wireless telegraph. All of the world 's leading aerodynamicists were invited.
This meeting was historic because it marked the beginning of the supersonic age . It was the beginning in the sense that the conference opened the door to supersonics as a meaningful study in connection with superson:c flight , and, secondly, because most developments in supersonics occurred rapidly from then on, culminating in 1946-a mere 11 years later-in Captain Charles Yeager·s piercing the sound barrier with the X-1 plane in level flight. In terms of future aircraft development, the most significant paper at the conference proved to be one given by a young man, Dr. Adolf Busemann of Germany, by first publicly suggesting the swept-back wing and showing how its properties might solve many aerodynamic problems at speeds just below and above the speed of sound.
Through these investigations, the myth that sonic speed is the fundamental limit of aircraft flight velocity, the sound barrier, was overcome.
In the late 1960s, the Boeing 747 with swept-back wings had, in transonic cruise speed, an LID value of nearly 20. In the supersonic flight speed regime, LID values improved from 5 in the mid-1950s (such as LID values of the B-58 Hustler and later of the Concorde) to a possible LID value of 10 and greater in the 1990s. This great improvement possibility in the aerodynamics of super­ sonic aircraft can be attributed to applications of artificial stability, to the area rule, and to advanced wing profile shapes which extend laminar flow over a larger wing portion.
The hypersonic speed regime is not fully explored. First, emphasis was placed on winged reentry vehicles and lifting bodies where a high LID value w:::., i-.Ot of greatest importance. Later investigations have shown that the LID values can be greatly improved. For example, the maximum LID for a " wave
Xviii FOREWORD
rider" is about 6 (Ref. 2). Such investigations are of importance for hypersonic programs.
The Aeropropulsion System
At the beginning of this centu'ry, steam and internal combustion engines were in existence but were far too heavy for flight application. The Wright brothers recognized the great future potential of the internal combustion engine and developed both a relatively lightweight engine suitable for flight application and an efficient propeller. Fig. 2 shows the progress of the propulsion systems over the years. The Wright brothers' first aeropropulsion system had a shaft power of 12 hp, and its power/weight ratio (ratio of power output to total propulsion system weight, including propeller and transmission) was about 0.05 hp/lb. Through the subsequent four decades of evolution, the overall efficiency and the power/weight ratio improved substantially, the latter by more than one order magnitude to about 0.8 hp/lb. This great improvement was achieved by engine design structures and materials, advanced fuel injection, advanced aerodynamic shapes of the propeller blades, variable-pitch propellers, and engine superchargers. Th_e overall efficiency ( engine and propeller) reached about 28 percent. The power output of the largest engine amounted to about 5000 hp.
In the late 1930s and early 1940s, the turbojet engine came into existence. This new propulsion system was immediately superior to the reciprocating engine with respect to the power/weight ratio (by about a factor of 3);
.~~~~~~~~~---,,,--~~~~~~~~~~---,50%
• Wright brothers 1903: -0.05 hpt1b I ,,
• End WWII: - 0.8 hp/lb I TURBO-JET AND FAN-JET -~ 20 ,.. ENGINES ~ / - 40%
PROPELLER/PISTON ENGINES I ~h~~" ,,, ,,,•' I ffe, ,,,,,,, I #c:> 1111 - 30% 15 f- # ,,,,,,
~'~ ~ ,,,, ~~,,,P:-S.T,,,,,, ,,,,,·' "'''"" l ,'' ~ hp/lb ,,,,, <,1' 11'111
,,,, ,,' I ... 11 ,, ,• 5 - ,,, l1•11
/'-, hpttb ···•··•· I - -- - -~-- -- - - I
!::.. !::.. 12 hp -400 hp
!::.. - 100,000 hp
Trends of power per weight (hp/ lb) and overall efficiency ( l'/o) of aeropropulsion systems from 1900 to 2000.
FOREWO RD xix
however, its overall efficiency was initially much lower than that of the reciprocating engine. As can be seen from Fig. 2, progress was rapid. In less than four decades, the power/weight ratio increased more than 10-fold, and the overall efficiency exceeded that of a diesel propulsion system. The power output of today's largest gas turbine engines reaches nearly 100,000 equivalent hp.
Impact Upon the Total Aircraft Performance
The previously-described truly gigantic advancements of stronger and lighter structures and greater aerodynamic quality in aerovehicles and greatly ad­ vanced overall efficiency and enormously increased power output/weight ratios in aeropropulsion systems had a tremendous impact upon flight performance, such as on flight range, economy, maneuverability, flight speed, and altitude. The increase in flight speed over the years is shown in Fig. 3. The Wright brothers began with the first human-controlled, powered flight in 1903; they continued to improve their aircraft system and, in 1906, conducted longer flights with safe takeoff, landing, and curved flight maneuvers. While the flight speed was only about 35 mi/hr, the consequences of these first flights were enormous:
• Worldwide interest in powered flight was stimulated. • The science of aerodynamics received a strong motivation.
2000 mi/hr
1500 mi/hr
1000 mi/hr
500 mi/hr
~;_;1- ?B-10
SUPERSONIC AIRCRAFf
Jets
Props
L....,o=-~-'-~L..--L..~_J__~.L----'-~--'----'_l 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
Power: 12 hp -400 hp -4000 hp -100,000 hp
FIGURE 3 Aircraft speed trends.
XX FOREWORD
• The U.S. government became interested in power flight for potential…