Fundamentals of Jet Propulsion With Applications by Flack. R.D

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 Engi­ neering, 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 Air­ craft. 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

RONALD D. FLACK University of Virginia

r

II

,

~lN CAMBRIDGE ~:~

UNIVERSITY PRf:SS

CAMBRIDGE UNIVERSITY PRESS 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 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 ofCongress Cataloging in Publication Data Flack, Ronald D., 1947­ Fundamentals ofjet propulsion with applications / Ronald D. Flack, Jr. p.

cm. - (Cambridge aerospace series; 17)

Includes bibliographical references and index.

ISBN 0-521-81983-0 (hardback)

I. Jet engines.

I. Title.

II. Series.

TL 709.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-IO 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

Contents

Preface Foreword

Part I

page xv

xix

Cycle Analysis

Introduction 1.1 1.2

3

History of Propulsion Devices and Turbomachines Cycles 1.2.1 Brayton Cycle 1.2.2 Brayton Cycle with Regeneration 1.2.3 Intercooling 1.2.4 Steam-Topping Cycle Classification of Engines 1:3.1 Ramjet 1.3.2 Turbojet 1.3.3 Turbojet with Afterburner 1.3.4 Turbofan . 1.3.5 Turbofan with Afterburner 1.3.6 Turboprop Unducted Fan (UDF) 1.3.7 1.3.8 Turboshaft 1.3.9 Power-Generation Gas Turbines 1.3.10 Comparison of Engine Types Engine Thrust Turbojet 1.4.1 Turbofan with a Fan Exhaust 1.4.2 1.4.3 Turboprop Performance Measures 1.5.1 Propulsion Measures Power-Generation Measures 1.5.2 Summary,

,

1.3

1.4

1.5

1.6 2

3

10

10

13 14

15

16

16

17

19

20

25

27

29

29

30

32

34

35

38

40

41

41

42

42

Ideal Cycle Analysis

46

2;1 Introduction

46

47

48

51

53

2.2

Components

2.2.1

I)i~ser

Compressor 2.2.2 2.2.3 .. Fan ..2 .2.4 Turbine 2.2.5 Propeller vii

55

56

ix

Contents

4.2.4 Combined Area Changes and Friction 4.3 Supersonic 4.3.1 Shocks 4.3.2 Internal Area Considerations 4.3.3 Additive Drag 4.3.4 "Starting" an Inlet 4.4 Performance Map 4.5 Summary

215

216

216

225

229

232

235

236

244

5 Nozzles 5.1 Introduction 5.2 Nonideal Equations' 5.2.1 Primary Nozzle 5.2.2 Fan Nozzle 5.2.3 Effects of Efficiency on Nozzle Performance 5.3 Converging Nozzle 5.4 Converging-Diverging Nozzle 5.5 Effects of Pressure Ratios on Engine Performance 5.6 Variabl~N ozzle 5.7 Performance Maps 5.7.1 Dimensional Analysis 5.7.2 TrenQs 5.8 Thrust Reversers and Vectoring 5.8.1 Reversers 5.8.2 Vectoring 5.9 Summary 6 Axial Flow Compressors and Fans 6.1 6.2 6.3 6.4

Introduction Geometry Velocity Polygons or Triangles Single-Stage Energy Analysis 6.4.1 Total Pressure Ratio 6.4.2 Percent Reaction 6.4.3 Incompressible Flow 6.4.4 Relationships of Velocity Polygons.to Percent Reaction and

Pressure Ratio 6.5 Performance Maps 6.5.1 Dimensional Analysis 6.5.2 Trends 6.5.3 Experimental Data 6.5.4 Mapping Conventions 6.5.5 Surge Control 6.6 Limits on Stage Pressure Ratio 6.7 Variable Stators 6.7.1 Theoretical Reasons' 6.7.2 Turning Mechanism 6.8 "Twin Spools 6.8.1' Theoretical Reasons

o

244

244

244

245

245

246

247

256

258

260

260

261

265

265

267

270

276

276

277

283

286

287

287

288

289

299

299

300

301

302

303

303

307

307

312

312

312

Contents

x

6.9

6.10

6.11

6.12

6.8.2 Mechanical Implementation 6.8.3 Three Spools Radial Equilibrium 6.9.1. Differential Analysis 6.9.2 Free Vortex 6.9.3 Constant Reaction Streamline Analysis Method 6.10.1 Flow Geometry 6.10.2 Working Equations Performance of a Compressor Stage 6.11.1 Velocity Polygons 6.11.2 Lift and Drag Coefficients 6.11.3 Forces 6.11.4 Relationship of Blade Loading and Performance 6.11.5 Effects of Parameters 6.11.6 Empiricism Using Cascade Data 6.11.7 Further Empiricism 6.11.8 Implementation of General Method Summary

7 Centrifugal Compressors 7.1 7.2 7.3 7.4

7.5

7.6

7.7 7.8

Introduction Geometry Velocity Polygons or Triangles Single-Stage Energy Analysis 7.4.1 Total Pressure Ratio 7.4.2 Incompressible Flow (Hydraulic pumps) 7.4.3 Slip 7.4.4 Relationships of Velocity Polygons to Pressure Ratio Performance Maps 7.5.1 Dimensional Analysis 7.5.2 Mapping Conventions Impeller Design Geometries 7.6.1 Eye Diameter 7.6.2 Basic Blade Shapes 7.6.3 Blade Stresses 7.6.4 Number of Blades 7.6.5 Blade Design Vaned Diffusers Summary

8 Axial Flow Turbines 8.1 Introduction 8.2 Geometry 8.2.1 Configuration 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

314

315

316

316

317

318

320

321

322

331

332

335

340

341

342

346

351

354

355

374

374

374

378

380

381

381

382

386

390

390

390

391

392

392

392

393

394

394

397

406

406

407

407

409

413

416

417

Contents

xi

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 8.8 Summary 9 Combustors and Afterburners 9.1 Introduction 9.2 Geometries 9.2.1 Primary Combustors 9.2.2 A2b + meUe - maUa + mb(ub - Ua ) - mtu«.

+ PaA2b -

PaA2b

4.3.33

Thus, using Eq. 4.3.27 results in

+ PeAe + PaA2 + A 2b(Pb - Pa) maU a + mb (Ub - Ua ) - mrUfx,

F == -PaAa - PaAl

+ m.u; -

4.3.34

and so using Eq. 4.3.26 yields F

== (Pe -

Pa)Ae + A 2b (Pb

-

Pa)

+ meUe -

maU a

+ mb (Ub -

Ua) -

mrUrx'

4.3.35 One can next reexamine Eq. 1.4.10 for the ideal case with no additive drag and recognize that the thrust is

F'

maua) + Ae(Pe - Pa) - mrUfx.

== (meu e -

1.4.10

From Eq. 4.3.35, it is possible to see that, for the current case, F

== F' + A2b ~ -

Pa)

+ mb (Ub - Ua ) ,

4.3.36

or by defining an additive drag as

D a == A 2b (Pa

-

Ph)

+ mb(ua -

Ub) ,

4.3.37

one finds F

== F' -Da •

4.3.38

Thus, the current analysis yields the same thrust as in the ideal case considered in Chapter I with the exception of a thrust reduction due to the additive drag. Unfortunately, evaluating the additive drag is difficult. Obtaining the data required to evaluate the drag is a time­ consuming process. Estimating these pressures and velocities for an engine on the drawing board can be accomplished by CFD. Thus, for the sake of practicality, dimensionless wind

232

II/Component Analysis

tunnel studies have been performed, correlated, and published for a variety of engines with different diffusers. The drags are then presented as drag coefficients; that is, Cda

=

Da I

2

'2y u; PaAin

'

. 4,3..39

where Ain is the frontal area of the inlet. Note that the preceding analysis was performed for a turbojet engine. However, if one were to repeat the analysis for any type of engine, the thrust would be found equal to that for the ideal case with a reduction due to additive drag. For any type of engine, the actual drag will be evaluated based on CFD predictions in conjunction with wind tunnel testing of that particular geometry. In general the additive drag coefficient for a given inlet and cowl will be the function: Cda

=J(:;. u;

8)

4.3.40

For an inlet with a spike or wedge, M; and 8 predetermine the shock structure. In general the drag coefficient decreases with increasing mass flow ratio because of reduced spillage. At a mass flow ratio of unity, spillage does not occur and the drag coefficient is near zero. Also, as would be expected, the drag is less for a diffuser with an oblique shock than for a diffuser with a normal shock. For a normal shock, the drag coefficient increases with increasing Mach number.

4.3.4.

"Starting n an Inlet

A few supersonic engines are designed to operate at least part of the time with an inlet without shocks - that is, a monotonically decelerating inlet using "internal compres­ sion" from supersonic flow to sonic to subsonic due to the converging-diverging geometry. Such an inlet has the advantage of minimal total pressure losses due to the lack of shocks. However, the idea of "starting" the diffuser becomes a problem. "Starting" can also be a problem for inlets designed to operate with oblique shocks to ensure proper sizing of the inlet and location of the shocks. For either case, the aircraft must accelerate from takeoff to the nominal flight Mach number with the inlet operating efficiently. Starting is simply defined as having the aircraft reach the desired speed and having the inlet operate at the desired design condition, including proper location of or lack of any shocks. The problem encountered is similar to starting a supersonic wind tunnel. Two methods can be used to start an inlet as described in the following paragraphs. For this concept, refer to Figure 4.16. For the following scenario the aircraft is considered to have a fixed-area diffuser and is eventually to operate supersonically at Mach number Md and without any shocks, but initially it will be at rest. The diffuser has fixed inlet, minimum, and exit areas, which are designed for one particular freestream Mach number M d so that the flow enters supersonically, decelerates to the sonic condition at the throat using internal compression. and then decelerates further in the diverging section. Hill and Peterson (1992) and Zucrow and Hoffman (1976) discuss the procedure in greater detail and with analyses. First, however, consider the aircraft to be moving very slowly (for example at takeoff)­ that is, well into the subsonic regime. For this condition, the flow enters the diffuser and accelerates into the minimum area and decelerates in the diverging area, but the flow remains subsonic throughout. Next, as the aircraft speed increases but remains subsonic,

4 / Diffusers

233

M=l

M1

(

Ml

M=l

M