Fundamentals ofjet propulsion with applications

Fundamentals ofJet Propulsion with Applications This introductory text on air-breathingjet propulsion focuses on the basic operating principles ofjet engines and gas turbines.. A capston

Fundamentals ofJet Propulsion with Applications

This introductory text on air-breathingjet propulsion focuses on the basic operating principles ofjet 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 offluid 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, a~d 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 kSME Fellow and is actively involved in research on experimental internal flows in turbomachines and fluid film bearings

Fundamentals ofJet Propulsion with Applications

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo

Cambridge University Press

40 West 20th Street, New York, NY 100 114211, USA

www.cambridge.org

Information on this title: www.caInbridge.org/9780521819831

© Cambridge University Press 2005

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

Library ofCongress Cataloging in Publication Data

Flack, Ronald D., 1947­

Fundamentals ofjet propulsion with applications / Ronald D Flack, Jr

I Jet engines I Title II Series

TL 709.F5953 2005

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

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 Foreword

Part I Cycle Analysis

1.3.9 Power-Generation Gas Turbines

1.3.10 Comparison of Engine Types

6.3 Velocity Polygons or Triangles

6.4 Single-Stage Energy Analysis

7.3 Velocity Polygons or Triangles

7.4 Single-Stage Energy Analysis

7.4.1 Total Pressure Ratio

7.4.2 Incompressible Flow (Hydraulic pumps)

8.2.2 Comparison with Axial Flow Compressors

8.3 Velocity Polygons or Triangles

8.4 Single-Stage Energy Analysis

8.4.1 Total Pressure Ratio

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Contents

8.4.2 Percent Reaction

8.4.3 Incompressible Flow (Hydraulic Turbines)

8.4.4 Relationships of Velocity Polygons to Percent Reaction

and Performance 8.5 Performance Maps

8.5.1 Dimensional Analysis

8.5.2 Mapping Conventions

8.6 Thermal Limits of Blades and Vanes

8.6.1 Blade Cooling

8.6.2 Blade and Vane Materials

8:6.3 Blade and Vane Manufacture

8.7 Streamline Analysis Method

9.5.1 Rayleigh Line Flow

9.5.3 Combined Heat Addition and Friction

10.2 Total Pressure Losses

10.2.1 Fanno Line Flow

10.2.2 Mixing Process

10.2.3 Flow with a Drag Object

Part III System Matching and Analysis

11 Matching of Gas Turbine Components

11.1 " Introduction

11.2 Component Matching

11.2.7 Dynamic or Transient Response

11.3 Matching of Engine and Aircraft

11.4 Use of Matching and Cycle Analysis in Second-Stage Design

11.5 Summary

Part IV Appendixes

Appendix A Standard Atmosphere

Appendix B Isentropic Flow Tables

Appendix C Fanno Line Flow Tables

Appendix D Rayleigh Line Flow Tables

Appendix E Normal Shock Flow Tables

Appendix F Common Conversions

Appendix G Notes on Iteration Methods

Isentropic Flow with Area Change Fanno Line Flow

Rayleigh Line Flow Normal Shocks Oblique Planar Shocks Flow with a Drag Object Mixing Processes Generalized One-Dimensional Compressible Flow Combined Area Changes and Friction

Combined Heat Addition and Friction Combined Area Changes, Heat Addition, and Friction Appendix I Turbomachinery Fundamentals

1.1 Introduction

1.2 Single-Stage Energy Analysis

1.2.1 Total Pressure Ratio 1.2.2 Percent Reaction 1.2.3 Incompressible Flow

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 offluid 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 ofjet 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-and­chug" 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 10chapters 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 ea-ch 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 i~ assumed to be known at this point in the text Trend studies and quantitative analysis methodologies are presented The effects of nonideal characteristics are

xv

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 ofthe chapter At the end ofevery 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:

Rayleigh line, isentropic, normal shock flow, or constant static temperature flows

mixing flow, and area change

turboprops

pressors and axial and radial turbines

with radial equilibrium with several specifyable boundary condition types

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 Universitiit 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 <kaft 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 Universitat Karlsruhe for their collegiality Special appreciation is due to all of my graduate students at the University of Virginia, Universitat Karlsruhe, and Ruhr Universitat Bochum, who helped keep me young through the years Portions of the proceeds of this text are going back to the University

of Virginia, Universitat 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

The book entitled Fundamentals ofJet Propulsion with Applications, by Ronald

D Flack, will satisfy the strong need for a comprehensive, modern book on the principles of propulsion - Doth 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 com~ination 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 thennofluids governing the performance of - and flow mechanisms in - propulsion com­ponents, and insight into propulsion-system matching

The text is direoted 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", hut the material can also be used for the fundamentals of ground­and 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 representingcurrent 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 one­semester 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

collegeengineering studentsand teachers,practicingengineers,and members of the general

2004

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CHAPTER 1

1.1 History of Propulsion Devices and Turbomachines

Manmade propulsion devices have existed for many centuries, and natural de­vices have developed through evolution Most modem engines and gas turbines have one common denominator: compressors and turbines or "turbomachines." Several of the early turbomachines and propulsive devices will be described in this brief introduction before modem engines are considered Included are some familiar names not usually associated with turbomachines or propulsion Many of the manmade devices were developed by trial and error and represent early attempts at design engineering, and yet some were quite so­phisticated for their time Wilson (1982), Billington (1996), ASME (1997), Engeda (1998),

St Peter (1999), and others all present very interesting introductions to some of this history

"­

supplemented by photographs

One of the earliest manmade turbomachines was the aeolipile of Heron (often called

"Hero" of Alexandria), as shown in Figure 1.1 This device was conceived around 100 B.C

It operated with aplenum chamber filled with water, which was heated to a boiling condition The steam was fed through tubes to a sphere mounted on a hollow shaft Two exhaust nozzles located on opposite sides of the sphere and pointing in opposite directions were used to direct the steam with high velocity and rotate the sphere with torque (from the moment

of momentum) around an axis - a reaction machine By attaching ropes to the axial shaft, Heron used the developed power to perform tasks such as opening temple doors

In about A.D 1232, Wan Hu developed and tested the Chinese rocket sled, which was driven by an early version of the solid propulsion rocket Fuel was burned in a closed container, and the resulting hot gases were exhausted through a nozzle, which produced high exit velocities and thus the thrust Tragically, this device resulted in one of the earliest reported deaths from propulsion devices, for Hu was killed during its testing

Leonardo da Vinci also contributed to the field of turbomachines with his chimney jack

in 1500 This device was ~ turbine within the chimney that used the free convection of hot rising gases to drive a set of vanes rotationally The rotation was redirected, using a set of gears, to tum game in the chimney above the fire Thus, the game was evenly cooked At the same time, da Vinci also contributed to turbomachinery development with his conception

of a helicopter producing lift'with a large "screw."

From the conceptions of Robert Hooke and others, windmills (Fig 1.2) - actually large wind turbines - were extensively used in the Netherlands for both water pumping and milling from the 16008 to the 1800s These huge wind turbines (more than 50 m in diameter) made use of the flat terrain and strong and steady winds and turned at low rotational speeds Through a series of wooden "bevel" gears and couplings, the torsional power was turned and directed to ground level to provide usable power Some ofthe early pumping applications

of "windmills" in the Netherlands usedan inverse of a water wheel- that is, the "buckets"

on the wheel scooped water up at a low level and dropped it over a dyke to a higher level, thus, recovering land below sea level from flooding

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I / Cycle Analysis

Figure 1.1 Hero's aeolipile, 100 B.C

Giovanni de Branca developed a gas turbine in 1629 that was an early version of an impulse turbine Branca used a boiling, pressurized vessel of steam and a nozzle to drive a set ofradial blades on a shaft with the high-velocity steam The rotation was then redirected with a set of bevel gears for a mechanical drive

In 1687, Sir Isaac Newton contributed the steam wagon, which may be viewed as an early automobile He used a tank of boiling water constantly heated by a fire onboard the wagon and a small nozzle to direct the steam to develop thrust By adjusting the fire intensity, the valve on the nozzle, and the nozzle direction, he was able to regulate the exhaust velocity and thus the thrust level as well as thrust direction Although the concept was viable, the required power exceeded that available for reasonable vehicle speeds Thus, the idea was

Denis Papin developed the first scientific conceptions ofthe principles ofa pump impeller

in a volute in 1689, although remains of early woodencentrifugal pumps from as early as the fifth century A.D have been found In 1754, Leonhard Euler, a well-known figure in mathematics and fluids, further developed the science of pumps and today has the ideal pump performance named after him - "Euler head." Much later, in 1818, the first centrifugal pumps were produced commercially in the United States

Garonne developed a water-driven mill in 1730 This mill was an early venture with a water (or hydraulic) turbine Water at a high hydrostatic head from a dammed river was used to direct water onto a conoid (an impeller) with a set of conical vanes and turn them The rotating shaft drove a grinding mill above the turbine for grain preparation The same concept was applied in 1882 in Wisconsin, where a radial inflow hydraulic turbine was used

to generate electricity

-Gifford was the first to use a controlled propulsion device successfully to drive an "air­craft." In 1851, he used a steam engine to power a propeller-driven dirigible The total load

5

1 / Introduction

Figure 1.2 Dutch windmill (R Flack)

required to generate power was obviously quite large because ofthe engine size, combustion fuel, and water used for boiling, making the idea impractical

In 1883, Carl de Laval developed the so-called Hero-type reaction turbine shown in

Figure 1.3 utilized for early water turbines Water flowed through hollow spokes, formed high-velocity jets normal to, and at the end of, the spokes, and was used to turn a shaft This

is the basic type of rotating sprinkler head used to convert potential energy from a static body of water to a rotating shaft with torque

As another example, in 1897 de Laval developed the impulse steam turbine (Fig 1.4)

This utilized jets of steam and turning vanes or blades mounted on a rotating shaft The high-speed steam impinged on the blades and was turned, thus imparting momentum to the blades and therefore rotating the shaft and providing torque

Over the next quarter century, rapid developments took place Gas and steam turbines came into wide use for ships and power generation For example, in 1891 the first steam

turbine was developedby Charles Parsons.This device was a predecessor to the modern gas

turbine It had two separate components: the steam generator-eombustor and the turbine

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Figure 1.3 DeLaval "Hero" reaction turbine, 1883

The generator-combustor developed a high-pressure steam, which was directed as a high­velocity jet into the steam turbine In the"early 1800s, ship propellers or "screws," which are themselves a variety of turbomachines, were invented by Richard Trevithick and others Parsons' steam turbine, rated at 2100 hp (1570 kW), was used to power such a propeller

directly on the 100-ft (30.5-m)-long ocean vessel Turbinia in 1897 and drove it at 34 kt,

which was a true feat if one considers that most seaworthy vehicles were slow-moving sail craft

In 1912, a large (64-stage) steam turbine facility was installed in Chicago and ran at

750 rpm to deliver 25 MW of electrical power In the 1920s, several General Electric 40-MW units were put in service These ran at 1800 rpm and had 19 stages Although many refinements and advancements have been made to steam-turbine technology since this installation, the same basic design is still in use in power plants throughout the world

In the 1930s, simultaneous and strictly independent research and development were performed in Great Britain and Germany on gas turbines In 1930, Sir Frank Whittle (Great Britain) patented the modem propulsion gas turbine (Fig 1.5) The engine rotated at almost 18,000 rpm and developed a thrust of 1000 lbf(4450 N) It had a centrifugal flow compressor and a reverse-flow combustion chamber; that is, the flow in the burner was opposite in direction to the net flow of air in the engine - a concept still used for small engines to conserve space This gas turbine was first installed on an aircraft in 1941 after several years

of development Meher-Homji (1997a) reviews this early effort in great detail Dunham (2000) reviews the efforts of A R Howell, also of Great Britain, which complemented the work of Whittle

In 1939, the first flight using a gas turbine took place in Germany Hans von Ohain patented the engine for this aircraft in 1936 (Fig 1.6), which developed 1100 lbf (4890 N) ofthrust This engine had a combination of axial flow and centrifugal compressor stages In general, this gas turbine and further developmental engines were superior to the British counterparts in efficiency and durability A few years later the German Junkers Jumo

Steam Jet

Figure 1.4 DeLaval impulse turbine, 1897