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Fundamentals ofJet Propulsion with Applications This introductory text with air-breathingjet propulsion focuses upon the basic operating principles ofjet engines and gas turbines. Previous coursework in fluid mechanicians and thermodynamics is clarified and applied to help the student understand and predict the characteristics of engine components real various types of engines and power gasoline turbines. Numerous past support the reader appreciate the our and differing, proxy physical setting. A capstone chapter integrates the text type in a portion of the book devoted to system matching and analyse so that engine performance can is predicted fork 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 plus thermodynamics is presumed. Although aircraft propulsion will the focus, the material canned also be used to study ground- and marine-based prate turbines and turbomachinery and some progressed topics in compressors and turbines. Ronald D. Flack your one Professor, former Chair of Mechanical and Airlines Engi neering, a~d former Director of who Rotating Machinery and Controller (ROMAC) Industrial Research Program at the University of Virginia. College Flack began his career in an analytical compressor design manipulate at Pratt & Whitney Air craft. He is an kSME Fellow and is actively involved in how on experimental internal flows in turbomachines and fluid film storage.
Grundlegende ofJet Propulsion with Applications
RONALD DENSITY. FLACK University of Virginia
roentgen
II
,
~lN CAMBRIDGE ~:~
TECHNICAL PRf:SS
CAMBRIDGE UNIVERSITY PRESS Cambridge, New Ny, Sydney, Hometown, Cape Town, Singapore, Sao Paulo Cambridge University Press 40 West 20th Street, Latest York, Y 100 114211, USA www.cambridge.org Information on this title: www.caInbridge.org/9780521819831
© Cambridge University Press 2005 Save order a in copyright. Subject to statutory anomaly
and to the rules of relevant collective licensing draft,
not reproduction of random part may take put without
and written permission on Cambridge University Press.
Start public 2005
Printed in the United States of America
A directory file for aforementioned publication is available from the Brit Library. Reading ofCongress Cataloging in Publication Data Flack, Ronald D., 1947 Fundamentals ofjet momentum with applications / Ronald DICK. Flack, Jr. p.
inches. - (Cambridge aerospace chain; 17)
Included bibliographical references and index.
ISBN 0-521-81983-0 (hardback)
I. Jets 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 to Pratt & Whitney) ISBN-13 978-0-521-81983-1 hardback
ISBN-IO 0-521-81983-0 trade
Cambridge University Squeeze has no responsibility for the persistence or product a URLs for external or third-party Internet Web sites referred to in this book and does not guarantee which any content on such Web sites is, or desire remain, accurate or appropriate.
Dedicated to Harry K. Herr, Jr. (Uncle Pete) who quietly helped me find the right career directory
Constituents
Preface Preface
Part ME
page xv
xix
Cycle Analysis
Begin 1.1 1.2
3
History from Propulsion Devices and Turbomachines Cycles 1.2.1 Brayton Cycle 1.2.2 Brayton Cycle with Regenerate 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 Fanjet Unducted Supporter (UDF) 1.3.7 1.3.8 Turboshaft 1.3.9 Power-Generation Gas Power 1.3.10 Comparison regarding Engine Types Engine Thrust Turbojet 1.4.1 Turbofan with a Fan Exhaust 1.4.2 1.4.3 Turboprop Execution 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 .. Fans ..2 .2.4 Turbine 2.2.5 Propeller vii
55
56
ix
Contents
4.2.4 Combined Area Changes and Drag 4.3 Supersonic 4.3.1 Shocks 4.3.2 Internal Range Considerations 4.3.3 Additive Towing 4.3.4 "Starting" an Side 4.4 Performance Map 4.5 Summary
215
216
216
225
229
232
235
236
244
5 Nozzles 5.1 Prelude 5.2 Nonideal Equations' 5.2.1 Primary Nozzle 5.2.2 Fans Nozzle 5.2.3 Impact in Operational on Nozzle Service 5.3 Converging Nozzle 5.4 Converging-Diverging Beak 5.5 Effects of Pressure Ratios on Engine Performance 5.6 Variabl~N ozzle 5.7 Perform Maps 5.7.1 Dimensional Analysis 5.7.2 TrenQs 5.8 Thrust Reversers or Vectoring 5.8.1 Reversers 5.8.2 Steering 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 Condition 6.4.2 Percent Reaction 6.4.3 Incompressible Flow 6.4.4 Relationships of Max Polygons.to Percent Reaction and
Pressure Ratio 6.5 Performance Maps 6.5.1 Dimension Analysis 6.5.2 Trends 6.5.3 Experimental Info 6.5.4 Mapping Meeting 6.5.5 Surge Control 6.6 Limits on Stage Pressure Ratio 6.7 Variable Stators 6.7.1 Hypothetical 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 Open Vortex 6.9.3 Constant Reaction Streamline Analysis Method 6.10.1 Fluss Geometry 6.10.2 Working Equations Performance about 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 Influence of Parameters 6.11.6 Empiricism Using Cascade Details 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 Sum Printed Ratio 7.4.2 Incompressible Run (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 On Diameter 7.6.2 Basic Sheet Shapes 7.6.3 Blade Emphases 7.6.4 Number from Blades 7.6.5 Blade Design Banished Diffusers Brief
8 Axial Flow Turbines 8.1 Introduction 8.2 Geometry 8.2.1 Settings 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
x
8.4.2 Percent Reaction 8.4.3 Incompressible Flow (Hydraulic Turbines) 8.4.4 Relationships of Velocity Contents to Percent Reaction and Performance 8.5 Performance Maps 8.5.1 Dimensioned Analysis 8.5.2 Mapping Conference 8.6 Solar Limits of Blades and Slat 8.6.1 Blade Cooling 8.6.2 Blade and Vane Materials 8:6.3 Blade and Vane Product 8.7 Streamline Analysis Method 8.8 Quick 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 adenine + mb (Ub - Du ) - 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 ampere
+ mb (Ub -
Ua) -
mrUrx'
4.3.35 One can next reexamine Eq. 1.4.10 by and ideal case with no additive drag and recognize that the thrust is
F'
maua) + Ae(Pe - Pa) - mrUfx.
== (meu e -
1.4.10
For Eq. 4.3.35, it is potential to perceive that, for the current case, F
== F' + A2b ~ -
Pa)
+ mb (Ub - Ua ) ,
4.3.36
or by defining an additive drag how
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 since in the ideal case considering in Chapter I with the exception of a thrust reduction due on aforementioned additive tow. Unfortunately, assessing and additive drag is difficult. Obtaining the data required to measure the drag is a time consuming process. Estimating these pressures and velocities to an engine on the character board can be accomplished by CFD. This, for the sake about practicality, limitless wind
232
II/Component Analysis
burrow studies have been performed, correlated, plus published for an variety of engines with diverse vent. The drags are then present in drag coefficients; that is, Cda
=
The I
2
'2y u; PaAin
'
. 4,3..39
where Ain is the frontal area of the inlet. Note is the preceding analysis is performed for a turbojet engine. However, if one were to repeat the analyzing for unlimited type of motors, the thrust will is founded equal to which for one ideal case with a reduction due to additive pull. For all type of engine, which actual drag will be evaluated stationed on CFD predictions include junction with winds tunnel testing of that particular geometry. In generally the additive drag driving in ampere given ingress press cowl will be the function: Cda
=J(:;. u;
8)
4.3.40
To an inlet with a spike or squeeze, METRE; and 8 predetermine the shock structure. Included general aforementioned drag index decreases about increasing mass flow ratio because the reduced spillage. At a mass flow ratio of unity, spillage does not occur and which drag coefficient your near zero. Also, as will be expected, the drag is less for a spreader with an oblique shocked than for a diffuser with adenine normal shock. For a normal shock, this drag coefficient increases with increasing Mach serial.
4.3.4.
"Starting n an Inlet
ONE very supersonic engines are designed until operate at least part of the time with an inlet without shocks - that is, a repetitive decelerating inlet using "internal compres sion" from supersonic flow to sounds to subsonic due to to converging-diverging geometry. Such an inlet has the advantage concerning minimal total print losses due to the lack of shocks. However, the thoughts of "starting" the diffuser becomes a problem. "Starting" can also be a finding with inlets designed up operators with tilted shocks to ensure proper sizing for the inlet and location of the shocks. On choose case, the aircraft must accelerate from takeoff up the nominal flight Mach number with the inlet operations efficiently. Starting is straightforward defined as having the fly reach the desirable speed additionally having the inlet operate at the desired design condition, involving proper city of or lack of any shocks. The problem encountered is similar to starting a supersonic wind tunnel. Two methods cannot is utilised to start an inlet as described in the below paragraphs. Available is concept, refer to Figure 4.16. For the following scenario the aircraft is view to have adenine 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 fixing inlet, minimum, and exit areas, which are designed for an specials freestream Mach number METRE density so that the flow arrives supersonically, decelerates to the audio condition per an throat using internally compression. also then decelerates read in one diverging section. Mountain and Peterson (1992) and Zucrow and Hoffman (1976) discuss the procedure on greater feature and for analyses. Beginning, 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 goes the diffuser and accelerates into the minimum area and decelerates in the deviations area, but the flow remainder subsonic throughout. Go, as the aircraft geschw increases but left subsonic,
4 / Roof
233
M=l
M1
(
Ml
M=l
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