Cambridge University Press
0521819830 - Fundamentals of Jet Propulsion with Applications - by Ronald D. Flack
Frontmatter/Prelims

Fundamentals of Jet Propulsion with Applications

This introductory text on air-breathing jet propulsion focuses on the basic operating principles of jet engines and gas turbines. Previous coursework in fluid mechanics and thermodynamics is elucidated and applied to help the student understand and predict the characteristics of engine components and various types of engines and power gas turbines. Numerous examples help the reader appreciate the methods and differing, representative physical parameters. A capstone chapter integrates the text material in a portion of the book devoted to system matching and analysis so that engine performance can be predicted for both on- and off-design conditions. The book is designed for advanced undergraduate and first-year graduate students in aerospace and mechanical engineering. A basic understanding of fluid dynamics and thermodynamics is presumed. Although aircraft propulsion is the focus, the material can also be used to study ground- and marine-based gas turbines and turbomachinery and some advanced topics in compressors and turbines.

Ronald D. Flack is a Professor, former Chair of Mechanical and Aerospace Engineering, and former Director of the Rotating Machinery and Controls (ROMAC) Industrial Research Program at the University of Virginia. Professor Flack began his career as an analytical compressor design engineer at Pratt & Whitney Aircraft. He is an ASME Fellow and is actively involved in research on experimental internal flows in turbomachines and fluid film bearings.

Fundamentals of Jet Propulsion with Applications

RONALD D. FLACK
University of Virginia

CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press
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This book is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2005

Printed in the United States of America

A catalog record for this publication is available from the British Library.

Library of Congress Cataloging in Publication Data

Flack, Ronald D., 1947–
Fundamentals of jet propulsion with applications / Ronald D. Flack, Jr.
p. cm. – (Cambridge aerospace series ; 17)
Includes bibliographical references and index.
ISBN 0-521-81983-0 (hardback)
1. Jet engines. I. Title. II. Series.
TL709.F5953 2005
621.43′52 – dc22 2004020358

On the cover is the PW 4000 Series – 112-inch fan (courtesy of Pratt & Whitney)

ISBN-13 978-0-521-81983-1 hardback
ISBN-10 0-521-81983-0 hardback

Cambridge University Press has no responsibility for
the persistence or accuracy of URLs for external or
third-party Internet Web sites referred to in this book
and does not guarantee that any content on such
Web sites is, or will remain, accurate or appropriate.

Dedicated to Harry K. Herr, Jr.

(Uncle Pete)

who quietly helped me find the right career direction

Preface			page xv
Foreword			xix
Part I Cycle Analysis
1		Introduction	3
		1.1 History of Propulsion Devices and Turbomachines	3
		1.2 Cycles	10
		1.2.1 Brayton Cycle	10
		1.2.2 Brayton Cycle with Regeneration	13
		1.2.3 Intercooling	14
		1.2.4 Steam-Topping Cycle	15
		1.3 Classification of Engines	16
		1.3.1 Ramjet	16
		1.3.2 Turbojet	17
		1.3.3 Turbojet with Afterburner	19
		1.3.4 Turbofan	20
		1.3.5 Turbofan with Afterburner	25
		1.3.6 Turboprop	27
		1.3.7 Unducted Fan (UDF)	29
		1.3.8 Turboshaft	29
		1.3.9 Power-Generation Gas Turbines	30
		1.3.10 Comparison of Engine Types	32
		1.4 Engine Thrust	34
		1.4.1 Turbojet	35
		1.4.2 Turbofan with a Fan Exhaust	38
		1.4.3 Turboprop	40
		1.5 Performance Measures	41
		1.5.1 Propulsion Measures	41
		1.5.2 Power-Generation Measures	42
		1.6 Summary	42
2		Ideal Cycle Analysis	46
		2.1 Introduction	46
		2.2 Components	47
		2.2.1 Diffuser	48
		2.2.2 Compressor	51
		2.2.3 Fan	53
		2.2.4 Turbine	55
		2.2.5 Propeller	56
		2.2.6 Shaft	59
		2.2.7 Combustor	59
		2.2.8 Afterburner	61
		2.2.9 Primary Nozzle	63
		2.2.10 Fan Nozzle	65
		2.2.11 Bypass Duct	66
		2.2.12 Bypass Mixer	67
		2.2.13 Exhaust for a Power-Generation Gas Turbine	68
		2.3 Cycle Analysis	70
		2.3.1 Ramjet	71
		2.3.2 Turbojet	78
		2.3.3 Turbofan	91
		2.3.4 Turboprop	113
		2.3.5 Power-Generation Gas Turbine	119
		2.4 Summary	124
3		Non-ideal Cycle Analysis	134
		3.1 Introduction	134
		3.1.1 Variable Specific Heats	134
		3.2 Component Losses	135
		3.2.1 Diffuser	135
		3.2.2 Compressor	137
		3.2.3 Fan	141
		3.2.4 Turbine	141
		3.2.5 Propeller	143
		3.2.6 Shaft	144
		3.2.7 Combustor	145
		3.2.8 Afterburner	146
		3.2.9 Primary Nozzle	147
		3.2.10 Fan Nozzle	150
		3.2.11 Bypass Duct	151
		3.2.12 Bypass Mixer	152
		3.2.13 Power Turbine Exhaust	153
		3.2.14 Summary of Nonideal Effects and Simple Parameter Models in Components	154
		3.3 Cycle Analysis	155
		3.3.1 General Approach	155
		3.3.2 Examples	156
		3.4 Use of Cycle Analysis in Preliminary Design	182
		3.5 Summary	182
Part II Component Analysis
4		Diffusers	209
		4.1 Introduction	209
		4.2 Subsonic	210
		4.2.1 External Flow Patterns	210
		4.2.2 Limits on Pressure Rise	211
		4.2.3 Fanno Line Flow	214
		4.2.4 Combined Area Changes and Friction	215
		4.3 Supersonic	216
		4.3.1 Shocks	216
		4.3.2 Internal Area Considerations	225
		4.3.3 Additive Drag	229
		4.3.4 “Starting” an Inlet	232
		4.4 Performance Map	235
		4.5 Summary	236
5		Nozzles	244
		5.1 Introduction	244
		5.2 Nonideal Equations	244
		5.2.1 Primary Nozzle	244
		5.2.2 Fan Nozzle	245
		5.2.3 Effects of Efficiency on Nozzle Performance	245
		5.3 Converging Nozzle	246
		5.4 Converging–Diverging Nozzle	247
		5.5 Effects of Pressure Ratios on Engine Performance	256
		5.6 Variable Nozzle	258
		5.7 Performance Maps	260
		5.7.1 Dimensional Analysis	260
		5.7.2 Trends	261
		5.8 Thrust Reversers and Vectoring	265
		5.8.1 Reversers	265
		5.8.2 Vectoring	267
		5.9 Summary	270
6		Axial Flow Compressors and Fans	276
		6.1 Introduction	276
		6.2 Geometry	277
		6.3 Velocity Polygons or Triangles	283
		6.4 Single-Stage Energy Analysis	286
		6.4.1 Total Pressure Ratio	287
		6.4.2 Percent Reaction	287
		6.4.3 Incompressible Flow	288
		6.4.4 Relationships of Velocity Polygons to Percent Reaction and Pressure Ratio	289
		6.5 Performance Maps	299
		6.5.1 Dimensional Analysis	299
		6.5.2 Trends	300
		6.5.3 Experimental Data	301
		6.5.4 Mapping Conventions	302
		6.5.5 Surge Control	303
		6.6 Limits on Stage Pressure Ratio	303
		6.7 Variable Stators	307
		6.7.1 Theoretical Reasons	307
		6.7.2 Turning Mechanism	312
		6.8 Twin Spools	312
		6.8.1 Theoretical Reasons	312
		6.8.2 Mechanical Implementation	314
		6.8.3 Three Spools	315
		6.9 Radial Equilibrium	316
		6.9.1 Differential Analysis	316
		6.9.2 Free Vortex	317
		6.9.3 Constant Reaction	318
		6.10 Streamline Analysis Method	320
		6.10.1 Flow Geometry	321
		6.10.2 Working Equations	322
		6.11 Performance of a Compressor Stage	331
		6.11.1 Velocity Polygons	332
		6.11.2 Lift and Drag Coefficients	335
		6.11.3 Forces	340
		6.11.4 Relationship of Blade Loading and Performance	341
		6.11.5 Effects of Parameters	342
		6.11.6 Empiricism Using Cascade Data	346
		6.11.7 Further Empiricism	351
		6.11.8 Implementation of General Method	354
		6.12 Summary	355
7		Centrifugal Compressors	374
		7.1 Introduction	374
		7.2 Geometry	374
		7.3 Velocity Polygons or Triangles	378
		7.4 Single-Stage Energy Analysis	380
		7.4.1 Total Pressure Ratio	381
		7.4.2 Incompressible Flow (Hydraulic pumps)	381
		7.4.3 Slip	382
		7.4.4 Relationships of Velocity Polygons to Pressure Ratio	386
		7.5 Performance Maps	390
		7.5.1 Dimensional Analysis	390
		7.5.2 Mapping Conventions	390
		7.6 Impeller Design Geometries	391
		7.6.1 Eye Diameter	392
		7.6.2 Basic Blade Shapes	392
		7.6.3 Blade Stresses	392
		7.6.4 Number of Blades	393
		7.6.5 Blade Design	394
		7.7 Vaned Diffusers	394
		7.8 Summary	397
8		Axial Flow Turbines	406
		8.1 Introduction	406
		8.2 Geometry	407
		8.2.1 Configuration	407
		8.2.2 Comparison with Axial Flow Compressors	409
		8.3 Velocity Polygons or Triangles	413
		8.4 Single-Stage Energy Analysis	416
		8.4.1 Total Pressure Ratio	417
		8.4.2 Percent Reaction	417
		8.4.3 Incompressible Flow (Hydraulic Turbines)	418
		8.4.4 Relationships of Velocity Polygons to Percent Reaction and Performance	419
		8.5 Performance Maps	425
		8.5.1 Dimensional Analysis	425
		8.5.2 Mapping Conventions	425
		8.6 Thermal Limits of Blades and Vanes	427
		8.6.1 Blade Cooling	428
		8.6.2 Blade and Vane Materials	429
		8.6.3 Blade and Vane Manufacture	430
		8.7 Streamline Analysis Method	433
		8.8 Summary	434
9		Combustors and Afterburners	440
		9.1 Introduction	440
		9.2 Geometries	441
		9.2.1 Primary Combustors	441
		9.2.2 Afterburners	445
		9.3 Flame Stability, Ignition, and Engine Starting	447
		9.3.1 Flame Stability	447
		9.3.2 Ignition and Engine Starting	448
		9.4 Adiabatic Flame Temperature	449
		9.4.1 Chemistry	450
		9.4.2 Thermodynamics	451
		9.5 Pressure Losses	456
		9.5.1 Rayleigh Line Flow	456
		9.5.2 Fanno Line Flow	457
		9.5.3 Combined Heat Addition and Friction	458
		9.5.4 Flow with a Drag Object	459
		9.6 Performance Maps	461
		9.6.1 Dimensional Analysis	461
		9.6.2 Trends	462
		9.7 Fuel Types and Properties	463
		9.8 Summary	465
10		Ducts and Mixers	471
		10.1 Introduction	471
		10.2 Total Pressure Losses	471
		10.2.1 Fanno Line Flow	471
		10.2.2 Mixing Process	473
		10.2.3 Flow with a Drag Object	475
		10.3 Summary	477
Part III System Matching and Analysis
11		Matching of Gas Turbine Components	481
		11.1 Introduction	481
		11.2 Component Matching	482
		11.2.1 Gas Generator	482
		11.2.2 Jet Engine	484
		11.2.3 Power-Generation Gas Turbine	486
		11.2.4 Component Modeling	487
		11.2.5 Solution of Matching Problem	492
		11.2.6 Other Applications	499
		11.2.7 Dynamic or Transient Response	499
		11.3 Matching of Engine and Aircraft	508
		11.4 Use of Matching and Cycle Analysis in Second-Stage Design	511
		11.5 Summary	512
Part IV Appendixes
Appendix A		Standard Atmosphere	527
Appendix B		Isentropic Flow Tables	530
Appendix C		Fanno Line Flow Tables	548
Appendix D		Rayleigh Line Flow Tables	558
Appendix E		Normal Shock Flow Tables	568
Appendix F		Common Conversions	583
Appendix G		Notes on Iteration Methods	585
		G.1 Introduction	585
		G.2 Regula Falsi	585
		G.3 Successive Substitutions	588
Appendix H		One-Dimensional Compressible Flow	591
		H.1 Introduction	591
		H.2 Ideal Gas Equations and Stagnation Properties	591
		H.3 Variable Specific Heats	593
		H.4 Isentropic Flow with Area Change	595
		H.5 Fanno Line Flow	597
		H.6 Rayleigh Line Flow	598
		H.7 Normal Shocks	600
		H.8 Oblique Planar Shocks	601
		H.9 Flow with a Drag Object	604
		H.10 Mixing Processes	605
		H.11 Generalized One-Dimensional Compressible Flow	607
		H.12 Combined Area Changes and Friction	608
		H.13 Combined Heat Addition and Friction	609
		H.14 Combined Area Changes, Heat Addition, and Friction	610
Appendix I		Turbomachinery Fundamentals	613
	I.1	Introduction	613
	I.2	Single-Stage Energy Analysis	613
		I.2.1 Total Pressure Ratio	613
		I.2.2 Percent Reaction	618
		I.2.3 Incompressible Flow	618
	I.3	Similitude	620
		I.3.1 Dimensional Analysis – Compressible Flow	620
References			623
Answers to Selected Problems			628
Index			631

Preface

My goal with this project is to repay the gas turbine industry for the rewarding profession it has provided for me over the course of more than three decades. At this point in my career, student education is a real passion for me and this book is one way I can archive and share experiences with students. I have written this text thinking back to what I would have liked as an undergraduate student nearly 40 years ago. Thus, this work has been tailored to be a very student friendly text.

This book is intended to serve primarily as an introductory text in air-breathing jet propulsion. It is directed at upper-level undergraduate students in mechanical and aerospace engineering. A basic understanding of fluid mechanics, gas dynamics, and thermodynamics is presumed; however, thermodynamics is reviewed, and an appendix on gas dynamics is included for reference. Although the work is entitled Jet Propulsion, it can well be used to understand the fundamentals of “aeroderivative” ground- or marine-based gas turbines such as those used for marine propulsion, ground transportation, or power generation. Although turbomachinery is not the primary target of the text, it is the book’s secondary focus, and thus the fundamentals of, and some advanced topics in, compressors and turbines are also covered.

This text covers the basic operating principles of jet engines and gas turbines. Both the fundamental mathematics and hardware are addressed. Numerous examples based on modern engines are included so that students can grasp the methods and acquire an appreciation of different representative physical parameters. For this reason, development of “plug-and-chug” equations or “formulas” is de-emphasized, and the solutions of all examples are logically and methodically presented. The examples are an integral part of the presentation and are not intended to be side issues or optional reading. A student is expected to understand the individual steps of analyzing an entire engine or an individual component. By the use of examples and homework problems a student is also expected to develop an appreciation of trend analysis; that is, if one component is changed by a known amount, how will the overall engine performance change? Both British and SI units are used in the examples. A strong and unique feature of the book is a capstone chapter (Chapter 11) that integrates the previous 10 chapters into a section on component matching. From this integrated analysis, engine performance can be predicted for both on- and off-design conditions.

Subjects are treated with equal emphasis, and the parts of the book are interdependent in such a way that each step builds on the previous one. The presentation is organized into three basic areas as follows:

1.	Cycle Analysis (Chapters 1 through 3) – In these chapters, different engines are defined, the fundamental thermodynamic and gas dynamic behavior of the various components are covered, and ideal and nonideal analyses are performed on each type of engine considered as a whole. Fundamental applicable thermodynamic principles are reviewed in detail. The performance of each individual component is assumed to be known at this point in the text. Trend studies and quantitative analysis methodologies are presented. The effects of nonideal characteristics are demonstrated by comparing performance results with those that would occur if the characteristics were ideal.
2.	Component Analysis (Chapters 4 through 10) – In these chapters the components are studied and analyzed individually using thermodynamic, fluid mechanical, and gas dynamic analyses. Diffusers, nozzles, axial flow compressors, centrifugal compressors, axial flow turbines, combustors and afterburners, ducts, and mixers are covered. Individual component performance can be predicted and analyzed, including on- and off-design performance and “maps,” thus expanding on the fundamentals covered in cycle analyses. The effects on component performance of different geometries for the various components are covered. Some advanced topics are included in these sections.
3.	System Analysis and Matching (Chapter 11) – This chapter serves as a capstone chapter and integrates the component analyses and characteristic “maps” into generalized cycle analyses. Individual component performance and overall engine performance are predicted and analyzed simultaneously. Both on- and off-design analyses are included, and prediction of engine parameters such as the engine operating line and compressor surge margin is possible.

Every chapter begins with an introduction providing an historical overview and outlining the objectives of the chapter. At the end of every chapter, a summary reviews the important points and specifies which analyses a student should be able to perform. In addition, appendixes are included that review or introduce compressible flow fundamentals, general concepts of turbomachinery, and general concepts of iteration methods – all of which are a common thread throughout the text.

The text is well suited to independent study by students or practicing engineers. Several topics are beyond what a one-semester undergraduate course in gas turbines can include. For this reason, the book should also be a valuable reference text.

A suite of user-friendly computer programs is available to instructors through the Cambridge Web site. The programs complement the text, but it can stand alone without the programs. I have used the programs in a variety of ways. I have found the programs (especially the cycle analysis, turbomachinery, and matching programs) to be most useful for design problems, and this approach reduces the need for repetitious calculations. In general, I provide the programs to students once they have demonstrated proficiency at making the fundamental calculations. The programs are as follows:

Atmosphere – Table for standard atmosphere.

Simple1D – Compressible one-dimensional calculations or tables for Fanno line, Rayleigh line, isentropic, normal shock flow, or constant static temperature flows.

General1D – Computations for combined Fanno line, Rayleigh line, drag object, mixing flow, and area change.

Shock – Calculations for normal, planar oblique, or conical oblique shocks.

Nozzle – Calculations for shockless nozzle flow.

JetEngineCycle – Cycle analysis of ideal and real ramjets, turbojets, turbofans, and turboprops.

PowerGTCycle – Cycle analysis of power-generation gas turbines with regenerators.

Turbomachinery – Mean-line turbomachinery calculations for axial and radial compressors and axial and radial turbines.

SLA – Three-dimensional streamline analysis of axial flow compressors or turbines with radial equilibrium with several specifyable boundary condition types.

CompressorPerf – Fundamental prediction of compressor stage efficiency due to lift and drag characteristics and incidence flow.

Kerosene – Adiabatic flame temperature of n-decane for different fuel-to-air mix ratios.

JetEngineMatch – Given diffuser, compressor, burner, turbine, and nozzle maps are matched to find overall turbojet engine performance and airframe drag maps are used to match engines with an aircraft.

PowerGTMatch – Given inlet, compressor, burner, turbine, regenerator, and exhaust maps are matched to find overall power-generation gas turbine performance.

A solutions manual (PDF) to the more than 325 end-of-chapter problems is also available to instructors. Please email Cambridge University Press at: solutions@cambridge.org.

This book was primarily written in two stages: first from 1988 to 1993 and then from 2000 to 2004 – the void being while I was Chair of our department. The bulk of the writing was done at the University of Virginia, although a portion of the book was written at Universität Karlsruhe while I was on sabbatical (twice). Some chapters were used in my jet propulsion class starting in 1989, and I began to use full draft versions of the text starting in 1992. In the course of this extended use, students have suggested many changes, which I have included; more than 300 students have been very important to the development of the text. I have also used portions of draft versions of the text in a graduate-level turbomachinery course, and graduate students have also made very useful suggestions. Over the past 15 years, I have incorporated many comments from students, and I took such suggestions very seriously. I am indebted to the numerous students who contributed in this way.

This project has been most fulfilling and it has been a culminating point in my own life. Through the writing and the resulting input from students, I have become a better and more patient teacher in all aspects of my life. Acknowledgments and thanks are in order starting with Mac Mellor and Sigmar Wittig, back in 1968, and then Doyle Thompson, in 1971, who triggered my interest in gas dynamics and gas turbines with projects at Purdue – the concepts have been central to my professional life since then. Certainly, thanks are due to my colleagues at both the University of Virginia and Universität Karlsruhe for their collegiality. Special appreciation is due to all of my graduate students at the University of Virginia, Universität Karlsruhe, and Ruhr Universität Bochum, who helped keep me young through the years. Portions of the proceeds of this text are going back to the University of Virginia, Universität Karlsruhe, and Purdue to help further undergraduate gas turbine education.

My family has been a timeless inspiration to me. Missy and Todd are both great kids who allowed me to forget work when needed, and now my granddaughters Mya and Maddie enable me again to see how much fun little ones can be. And then there are Zell and Dieter – one could not want better companions.

I cannot say enough about Nancy, my soul mate and best friend since 1966. This book would never have come to fruition without her positive influence. She helped me to realize the true value of life and to keep the proper perspectives.

Ron Flack
2004

Foreword

The book entitled Fundamentals of Jet Propulsion with Applications, by Ronald D. Flack, will satisfy the strong need for a comprehensive, modern book on the principles of propulsion – both as a textbook for propulsion courses and as a reference for the practicing engineer.

Professor Flack has written an exciting book for students of aerospace engineering and design. His book offers a combination of theory, practical examples, and analysis utilizing information from actual aerospace databases to motivate students; illustrate, and demonstrate physical phenomena such as the principles behind propulsion cycles, the fundamental thermofluids governing the performance of – and flow mechanisms in – propulsion components, and insight into propulsion-system matching.

The text is directed at upper-level undergraduate students in mechanical and aerospace engineering, although some topics could be taught at the graduate level. A basic understanding of fluid mechanics, gas dynamics, and thermodynamics is presumed, although most principles are thoroughly reviewed early in the book and in the appendixes. Propulsion is the primary thrust, but the material can also be used for the fundamentals of ground- and marine-based gas turbines. Turbomachinery is a secondary target, and the fundamentals and some advanced topics in compressors and turbines are covered.

The specific and unique contributions of this book and its strengths are that fundamental mathematics and modern hardware are both covered; moreover, subjects are treated with equal emphasis. Furthermore, the author uses an integrated approach to the text in which each step builds on the previous one (cycle analyses and engine design are treated first, component analysis and design are treated next, and finally and uniquely, component matching and its influence on cycle analysis are addressed to bring all of the previous subjects together). The latter feature is a very great strength of the text. In contrast to most other texts, the author incorporates many numerical examples representing current engines and components to demonstrate the main points. The examples are a major component of the text, and the author uses them to stress important points. In working through these examples, the author de-emphasizes the use of “ready-made formulas.” Numerous trend analyses are performed and presented to give students a “feel” of what can be expected if engine or component parameters are varied. The book can be used as a text for a university course or as a self-learning reference text.

At the beginning of every chapter the author presents an introduction outlining some history as well as the objectives of the chapter. At the end of every chapter he provides a summary recalling the key points of the chapter and places the chapter in the context of other chapters. The text is well suited for independent study by students or practicing engineers. Several topics are covered that are beyond those typically included in a one-semester undergraduate gas turbine course. As a result, the book should also be a valuable reference text.

As a teacher of an aerospace engineering course, I strongly recommend the book to college engineering students and teachers, practicing engineers, and members of the general public who want to think and be challenged to solve problems and learn the technical fundamentals of propulsion.

Abraham Engeda
Professor of Mechanical Engineering and
Director of Turbomachinery Laboratory
Michigan State University
2004