Aircraft Engines and Gas Turbines Aircraft Engines and Gas Turbines second edition Jack L Kerrebrock The MIT Press Cambridge, Massachusetts London, England © 1992 Massachusetts Institute of Technology All rights reserved No part of this book may be reproduced in any fonn by any electronic or mechanical means (including photocopying, recording, or infonnation storage and retrieval) without pennission in writing from the publisher Set by Asco Trade Typesetting Ltd from disks provided by the author Printed and bound in the United States of America Library of Congress Cataloging-in-Publication Data Kerrebrock Jack L Aircraft engines and gas turbines / Jack L Kerrebrock.-2nd ed p cm Includes bibliographical references and index ISBN 0-262-11162-4 Aircraft gas-turbines I Title TL709.K46 1992 91-41047 629.1 34'35-dc20 CIP 10987654 Contents Preface to the Second Edition Preface to the First Edition Acknowledgements ix x xii Introduction to Concepts 1 Thermal Efficiency 1.2 Propulsive Efficiency 1.3 Specific Impulse and Range 1.4 Ramjets 1.5 Turbojets 1.6 Turbofans 11 1.7 Turboprops and Other Shaft Engines: Regeneration 11 1.8 Stationary Gas Turbines: Topping 14 1.9 Energy Exchange, Mach Number, and Reynolds Number 15 1.10 Stresses 17 1.11 Noise 18 1.12 Thrust and Drag 18 1.13 Fuels and Propellants 21 1.14 Some Engines in Cutaway 27 Problems 27 Ideal Cycle Analysis: Trends 29 2.1 Stagnation Temperature and Pressure 30 2.2 The Ramjet 32 2.3 The Turbojet 36 2.4 The Afterburning Turbojet 43 2.5 The Turbofan 47 2.6 The Afterburning Turbofan 50 2.7 The Turboprop 54 2.8 Thrust Lapse 59 2.9 Cooling Cycles 60 2.10 The Regenerative Gas Turbine 62 2.11 Gas Turbines for Topping 66 12 The Importance of Turbine Inlet Temperature Problems 67 70 Contents vi Cycle Analysis with Losses 73 3.1 Variation in Gas Properties 73 3.2 Diffuser Pressure Recovery 74 3.3 Compressor and Turbine Efficiencies 75 3.4 Burner Efficiency and Pressure Loss 78 3.5 Imperfect Expansion Loss 79 3.6 Heat Exchanger Effectiveness and Pressure Loss 80 3.7 Turbojet with Losses 81 3.8 Turbofan with Losses 88 3.9 Regenerated Gas Turbine with Losses 94 10 Combined Gas Turbine-Steam Cycles with Losses 1 Concluding Comments 99 102 Problems 103 Nonrotating Components 105 Topics in Gas Dynamics 105 4.2 Diffusers 120 4.3 Exhaust Nozzles 139 4.4 Combustors and Afterburners 154 References 180 Problems 18 Compressors and Fans 185 Energy Exchange, Rotor to Fluid 187 5.2 Compressor Geometry and the Flow Pattern 197 5.3 Design Choices Based on Blade Section Performance 238 5.4 Details of Flow in Transonic Compressors 245 5.5 Stage Performance: Corrected Parameters 249 5.6 Multi-Stage Compressors 250 5.7 Compressor and Compression System Stability 254 5.8 Centrifugal Compressors 266 5.9 Supersonic-Throughflow Fan 273 References 278 Problems 280 Contents vii Turbines Turbine Stage Characteristics 285 6.2 Turbine Blading 290 6.3 Turbine Cooling 296 6.4 Turbine Design Systems 10 6.5 Turbine Similarity 31 References 13 Problems 313 Engine Structures 15 Centrifugal Stresses 15 7.2 Gas Bending Loads on Blades 320 7.3 Thermal Stresses 324 7.4 Critical Speeds and Vibration 326 283 7.5 Blade Flutter 333 7.6 Bearings 338 7.7 Engine Arrangement and Static Structure 34 References 345 Problems 345 Component Matching and Engine Performance 347 Compressor-Turbine Matching: The Gas Generator 347 8.2 Matching the Gas Generator and the Nozzle 349 8.3 Multi-Spool Matching 350 8.4 Engine-Inlet Matching and Distortion 35 8.5 Overall Performance 353 8.6 Control and Acceleration 357 References 363 Problems 364 Aircraft Engine Noise 365 9 Noise Sources: Unsteady Flow 369 9.2 Jet Noise 377 9.3 Turbomachinery Noise 386 Contents viii 9.4 10 Noise Measurement and Rules 395 References 399 Problems 400 Hypersonic Engines 40 10.1 Hypersonic Inlets 404 10.2 Heat Addition in High-Speed Flow 406 10.3 Heat Release Due to Chemical Reactions 409 10.4 Nozzle Flow 14 10.5 Fuel Injection and Mixing 15 10.6 Quantitative Discussion of Scramjet Performance 417 10.7 Cooling the Scramjet 429 10.8 The Air Turborocket 443 10.9 The Liquid-Air Collection Engine 448 11 References 451 Problems 452 Propulsion Systems Analysis 453 11 Takeoff 454 1.2 Climb and Acceleration 456 1.3 Cruise 464 1.4 Maneuvering 466 References 467 Problems 467 Index 469 Preface to the Second Edition Since the first edition of this text was completed, in 1977, the changes in aircraft engines have been mainly evolutionary At that time the after burning turbofan engine was firmly entrenched as the engine of choice for high-performance military aircraft, as was the high-bypass turbofan for commercial transports and military logistics aircraft These engine types continue to dominate their application sectors, with continual refinements greatly improving their performance The principal qualitative changes in emphasis in aircraft propulsion have been a revival of interest in hyper sonic air-breathing propulsion and a new interest in ultra-high-bypass engines, such as the high-speed turboprop Most of the content of the first edition remains valid The technology has continued to mature, and to a certain extent my understanding of it has also matured and improved; thus, changes in details will be found throughout this edition With the benefit of many helpful comments from both students and professionals, a considerable number of errors have been corrected Though it would be foolish to assert that all errors have been eliminated, it is probably true that this edition will suffer less from errors than the first edition did One frequent comment has been that more expansive treat ment of certain difficult points would be helpful, that the presentation was too terse With hindsight, I agree; thus, more extensive discussions will be found at many places in the text, although I remain firmly of the view that it is better to state a logical proposition once correctly than many times imprecisely Extensive changes have been made in the chapter on compressors, to better reflect the state of the art of compressor design and to provide a guide to the vigorous ongoing research in this area A section on the stability of compression systems has been added, as has a discussion of numerical techniques for computing the flow in compressors In view of the current interest in and the potential importance of hypersonic air breathing engines, the discussion of this topic has been greatly expanded and updated The general structure of the book has not been changed It focuses on the aircraft engine as a system, rather than on the disciplines important to aircraft engines Thus, after the brief introduction in chapter 1, chapter deals with the engine as a whole from the viewpoint of thermodynamics, or cycle analysis; chapter repeats this treatment in more quantitative form Chapters 4-6 discuss the behavior of the individual components that make up the engine, showing how the thermodynamic characteristics are real- Preface x ized through the fluid-dynamic behavior of the components Chapter discusses some aspects of structures peculiar to engines, and chapter shows how the behavior of a complete engine can be deduced from the behavior of the components Noise continues to be an important consider ation for commercial aircraft engines; chapter is essentially unchanged from the first edition, except that the rules for certification and the discus sion of the takeoff noise of supersonic transports have been updated Chapter 10 has been expanded to reflect the current interest in super sonic combustion ramjets Some readers may feel it is now out of balance with the remainder of the text, considering the tentative nature of this technology and its applications The scramjet is, however, a useful vehicle for discussion of the physical aspects of high-speed flow with heat addition, and of heat transfer and film cooling Preface to the First Edition (1977) This book is intended to provide an introduction to the engineering of aircraft propulsion systems with the emphasis on the engine, rather than on the disciplines involved in engine design Because of the remarkable advances that have occurred since the large-scale introduction of gas tur bine power plants into military aircraft in the 1950s and into commercial aircraft in the 196Os, a clear understanding of the characteristics of these devices is needed at the undergraduate or early graduate level Such an understanding is essential both for entrance into professional work in the industry and for graduate study in the field The understanding of a sophis ticated engineering system that involves the sciences of fluid mechanics, solid mechanics, chemistry, automatic control, and even psychology (be cause of the problem of aircraft noise) has intrinsic value apart from its practical applications At present, the fundamental information required for such an understanding is widely dispersed in the technical literature and subliterature The aim of this book is to draw the information together in a unified form, so that the student can appreciate why aircraft propul sion systems have evolved to their present form and can thus be better prepared to contribute to their further evolution Automotive and stationary applications of gas turbines are growing rap idly The engines used in these applications s.hare much of their technology with aircraft gas turbines; indeed, they have benefited greatly from the Preface xi aircraft-engine developments of the last two decades While this book is concerned primarily with aircraft engines, the discussions of component technology are equally applicable to these other applications The discus sion of cycles in chapters and gives some attention to automotive and stationary engines The approach taken in this book is to treat the propulsion system at increasing levels of sophistication, beginning in chapter with a phenom enological discussion of the processes by which energy is converted from heat to mechanical energy to thrust In chapter 2, several types of engines are discussed in the framework of ideal cycle analysis, where the components of an actual engine are repre sented parametrically without quantitative reference to the engine struc ture Here the dependence of the engine's performance on the compressor pressure ratio and the turbine inlet temperature is established, as well as the trends of thrust and specific impulse with flight Mach number The arguments are repeated more quantitatively in chapter for a narrower spectrum of engines to convey the influence of nonidealities in the engine cycles Chapters 4-7 examine the mechanical characteristics required of each major engine component to achieve the parametric behavior assumed in the cycle analysis At this step the enormous literature of the field must be abstracted and interpreted to clarify the important physical limitations and trends without submerging the reader in vast analyses and data corre lations Naturally, the presentation is strongly influenced by my own view point If it errs in detail or by omission at some points, I hope that the overview will help the serious student to correct these inadequacies Chapter synthesizes from the component characteristics evolved in chapters 4-6, a complete gas generator and a complete propulsion system An attempt is made to treat in a reasonably uniform way the problems of engine control, inlet-to-engine and engine-to-nozzle matching, and inlet distortion, which so strongly dictate the ultimate performance of the system The mechanisms by which aircraft engines produce noise are discussed in chapter At its present state of development, this subject is both highly mathematical and highly empirical Although the mathematics in this chapter is somewhat more advanced than that in other chapters, it should be understandable to a well-prepared college junior or senior In any case, 463 Propulsion Systems Analysis (11.11) Since lsp can be given only numerically, the integration along the trajectory must be performed numerically This is usua]]y done using a technique such as the Runge-Kutta method In this case a standard fourth-order Runge-Kutta procedure available in Mathematica has been used Suppose that the quantity of primary interest is the ratio of final mass to initial mass required to attain orbital energy To obtain an estimate of this quantity, we can integrate equation 11.11 along some trajectory As a first guess, we might take the trajectory for which the lIP is maximized Alterna tively, we might take the trajectory defined by the maximum dynamic pres sure the vehicle can stand for structural or thermal reasons These two cases have been carried out using the corresponding specific-impulse esti mates given in figure 10.16 The flight velocity is plotted in figure 11.4 as a function of the fraction of mass consumed in accelerating from 6000 ftjsec to the indicated velocity for the case of M4 chosen for maximum specific impulse, and for two nozzle flow assumptions treated in figure 10.16 (that where the flow freezes in the nozzle at 1.0 atm and that where it freezes at 0.1 atm) The dynamic pres sure corresponding to this trajectory is also shown It becomes quite large at the high flight velocities, making such a trajectory quite problematic � flight velocity ft/sec nozzle freezing pressure o at� 1.0 atm 250'00 20000 /v/� 1500 1000 °v 500 ��\ " ' v / 0.1 :::-f. - 0.2 1\ L free-stream dynamic pressure atm ,/ 0.3 0.4 0.5 o fraction of mass consumed Figure 11.4 Flight velocity as a function of mass ratio for the trajectory that maximizes l.p and for the dynamic pressure implied by this trajectory For discussion of specific impulse see subsection 10.6.5 464 Chapter 11 nozzle freezing pressure 0.1 atm 1.0 atm TI =0.97 KI! 25000+ -. -. �����_ flight velocity ft/sec 20000 15000+ ;d= + -+ -+_ -1 Ol� + -� -+ �� o 0.2 0.6 0.8 0.4 fraction of mass consumed FigureU.5 Flight velocity as a function of mass ratio for trajectories with qo specific impulse see subsection 10.6.5 = 0.5 For discussion of If the trajectory is limited to a dynamic pressure of 0.5 atm, the results shown in figure 11.5 are found We see that the propellant consumption is significantly greater for this case 11.3 Cruise Here the objective may be to attain the maximum range for a given fuel consumption, or it may be to achieve a given range in minimum time Consider the case of minimum fuel consumption As before, d(Ejm) = but dm = d( Ejm) = [(F - - - D)jm]uodt, (FjgI)dt; so this can be written Uo m D m gJ -dm - -uodt The range increment dR dR = = uodt, so gmdm m -luo - d(Ejm) Dna Jj If we neglect the change in Ejm, and put gm classical Breguet range equation: = W = L, this integrates to the 465 Propulsion Systems Analysis R = IUo L m(O) In m; d(Elm) Jj = 0, which was discussed in section 1.3 However, for high-speed flight the change in Elm may be quite important Furthermore, as the flight speed becomes large, the required lift is reduced by centrifugal force, so that z L mg - muo ir where r is the radius to the earth's center In this more general situation, = R = - 1mm,2 luo - LID dm z (uo Irg) m f(Elmh (Elm), L d(Elm) gD - (Uo2Irg) (11.12) In the classical Breguet case, the first integral is maximized by maximizing IUoLID; at hypersonic speeds the optimum Uo will be larger because the centrifugal lift term increases R An idea of the magnitude of this effect and of the Elm correction can be had by assuming uo, LID, and luo constant; then R = (ml) - IUo(LID) In mz (uoZlrg) _ - LID (Elm}z - (Elm)1 (uoZlrg) (11.13) In order to maintain constant LID, h must increase from point to point so that (Po }z/(Po)1 mzlml• Taking Po oc e-rth gives = (Elm}z - (Elm)1 = hz _ hI = ! In IX ( ) ml mz Finally, R = � IUo(LID) In(mt/mz) - (LID) In(mI/mz)]/IX - Uo Irg (11.14) From this result we can compute R versus Uo, for any mt/mz , using the dependence of figure 10.1 and estimates for LID as a function of Mo Some typical results for mt/m2 are,given in table 11.1 Such results have been interpreted by some to mean that hypersonic transports could be more efficient than subsonic aircraft for long-distance travel In fact, when the structural requirements are met for the high tem peratures associated with hypersonic flight, the apparent advantage prob ably more than disappears, owing to the large structural weight fraction of the hypersonic aircraft, so that unless the greatly reduced travel time or the = 466 Chapter 1 Table 11.1 Mo l(s) LID R (miles) Fuel 0.8 7000 20 2.7 3000 JP-4 12.0 2000 H2 15,300 20.0 1200 H2 16,500 JP-4 14,200 8,300 Table 11.2 Mo r(miles) 3.2 20 13 29 742 increased utilization is sufficient to outweigh this effect the hypersonic air craft is unlikely to prove efficient as a transport The situation is somewhat less clear for vehicles that accelerate to orbital velocity, as was discussed in subsection 11.2.3 11.4 Maneuvering The turning radius of a military aircraft in sustained air combat is limited by the thrust, because additional drag results from the lift required for turning If r is the turning radius, the centrifugal force that must be over come is muo2/r; thus, if the tum is in a horizontal plane, the total lift is L = J(mg) + (muo2/r)2 The ratio of total lift to weight, which is termed the number of g's, is then g's = Jl + (uo2/rg)2 Thus, the turning radius is r = uo2/g (g'S) _ Some typical values fo r g s are given in table 11.2, from which it is clear that the pilot of an hypersonic transport would have to plan ahead ' 467 Propulsion Systems Analysis References 11.1 E S Rutowski, "Energy Approach to the General Aircraft Performance Problem." Journal of the Aeronautical Sciences 21, no (1954): 187-195 11.2 A E Br yson Jr., M N Desai, and W C Hoffman, Energy State Approximation in Performance Optimization of Supersonic Aircraft." Journal of Aircraft 6, no (1969): 481, " - 488 Problems 11.1 Show that if the aerodynamic drag is small relative to the net accelerating force during the takeoff roll, equation 11.2 reduces to the simple statement that accelerating force times XT equals vehicle kinetic energy at end of takeoff roll 11.2 A transport aircraft powered by turbofan engines with 0, 7.5 has LID 15 Estimate the amount of fuel it will use in ratio to its takeoff mass in taking off, climbing to an altitude of 10 km and a speed of Mo 0.8, and cruising on a Breguet path a distance of 4000 km, as a function of bypass ratio a Use the data of figure 3.6 for the engine performance = = = A fighter aircraft powered by an afterburning turbofan engine with a 1,6 7.5, and 1, in which it maneuvers through ten fulI turns at g's Estimate the amount of fuel in ratio to the initial total mass consumed during these maneuvers Assume the aircraft's LID is 10 How far could the aircraft cruise without after burning at Mo 0.8 with this same fuel expenditure? 11.3 no = 24 engages in air combat at about Mo = = = = A transport aircraft is to be powered by either a high-bypass turbofan (a 5) or a turbojet In either case, the engine is sized by the takeoff requirement that the takeoff roll be 1500 m Using the simple cycle analysis of chapter 2, estimate the ratios of air mass f10wl takeoff mass for the two engine types Assume 0, and no 24 for both Then estimate the ratio of thrust to maximum available thrust for each engine when cruising at Mo 0.8 and h 10 km For the takeoff roll, take Coo 0.01, Cc 0.02, and m(O)/Ac � 5000 kg m-2• 11.4 = = = = = = = Index acceleration 358 launch vehicle acceleration dynamics of a two-shaft turbofan 364 acceleration margin 458 acceleration stall margin 362 acceleration time 361,363 acoustic damping cavities 393 acoustic power 372,373 acoustical admittance 393 additive drag 20 adiabatic effectiveness 326 adiabatic film effectiveness 303 adiabatic processes 32 adiabatic recovery temperature 298, 302, 307 adiabatic wall enthalpy 435 adiabatic wall temperature 436 afterburner 10,161,446 determination ofiength 163 Mach number in 162 schematic 163 afterburner light and nozzle opening 363 afterburner transients 363 afterburning and nonafterburning turbofans 52 afterburning turbofan 50,363 in military aircraft 54 schematic 51 specific impulse of ideal 51 thrust of ideal 51 afterburning turbojet 43 compression ratio for maximum thrust 44 specific impulse 43 thrust 43 air turbo rocket 444 bipropellant 445 combustion chamber 446 compressor temperature ratio 446 hydrogen expander 445,447 air turborocket (ATR) 21,401,443 air-cooled turbines 296 aircraft noise 365 airframe parameters 454 airframe variables 454 airport noise 385 angular acceleration 359 aspect ratio 454 axial velocity changes due to blades 203 axial velocity density ratio 12,227 axial wave number 389 ball bearing 339 bearing 330,338 ball 339 cross sections 340 damping 331,340 DN limit on 339 intershaft 343 loads 331 magnetic 339 roller 339 shaft diameter limit due to 339 skewing 340 skidding 340 squeeze-film damping 340 stiffness 331 support structure 342 bending flutter 335 bending stresses 323 blade bending stresses 320 blade noise 386 blade stress 317 related to blade row parameters 323 blockage 209 blow-down compressor 186 blow-in doors 122 boost performance of scramjets 460 boundary layer in turbine 283 boundary layer flow 105 boundary layers and separation in channel flow 114 on airfoils 114 boundary-layer control 131 Brayton cycle 2,7,8,403 Breguet range equation 464 burner efficiency 78 burst speed 319,345 buzz saw noise 18,369,391 bypass ratio 18,47,369,382 and number of fan stages 49 effect on specific impulse 49 effect on thrust 49 with fixed fan pressure ratio 53 calorically perfect gas 106 Campbell diagram 333 Carnot cycle Carter's rule 219 cascade nomenclature 213 cascade representation of blade row 190 casing and hub layers 232 casing and hub phenomena 233 casing layer 232 centrifugal compressor 13,187,266 diffusers 272 history of efficiency and pressure ratio 274 470 centrifugal compressor (cont.) impeller 271 impeller sweep 269 overall pressure rise 268 rotor pressure rise 267 stator Mach number 269 typical performance map 274 centrifugal force 46 centrifugal stress in blades 19 centrifugal stresses 315 certification 398 channel flow 105,106 critical mass flux 107 diffusion in 113 effect of area variation 107 effect of boundary layers and separation 13 mass flux 107 channel flow approximation 418,420 characteristic time for acceleration 360 chemical equilibrium 419 chemical reaction time 164 chemical reactions 412 chute-type mixer 385 combination tone noise effect of swirl 392 rotor imperfections 392 combustion 18 effect of turbulence 157 flammability limits for 157 in pre-mixed gases 157 combustion discontinuities 372 combustion initiation kinetics 424 combustion kinetics 422 combustion process 22 combustor 7,154 cooling 160 fuel droplets 159 heat release 155 materials 160 pollutants 155 reaction rate in 156 residence time 161 schematic 159 size relative to engine size 16 combustor inlet Mach number 420 combustor length 424 combustor pressure 424 complete enthalpy 410,446,448 component matching 347 composite velocity diagram 194 compression system stability 255 modeling and experiment 261 rotating stall and surge 260 Index the "B" parameter 260 compressor 185,444 actuator disc 197 angular momentum change in 192 axial flow 186 cascade approximation 189 compressor maps 249 corrected parameters 249 direct problem 197 effect of blade Mach number 195 energy addition by pressure rise 188 enthalpy rise 192 geometry 197 high-pressure-ratio Performance map 254 in turbojet inverse problem 197 mass flow vs pressure ratio 241 pressure ratio and efficiency vs Mach number 241 radial flow 186 research and development 185 stage temperature ratio 192 temperature ratio 195 through-flow-blade-element approximation 186 throughflow 197 compressor blading controlled diffusion 214 double circular arc 214 loss factor 214 Reynolds number 214 compressor design choices 237 compressor map 348 compressor noise 367 compressor stability related to velocity triangles 196 compressor torque 359 compressor-turbine matching 364 compressor-turbine power balance 283 conservation of energy 106 of mass 106 conservation of energy including chemical energy 10 constant dynamic pressure 428 control system 357 control variables 350,357 controlled vortex 10 convected structures 417 convective cooling 307,429,433,434,438 convective internal cooling 298 convectively cooled wall 432 cooled length 436,439 Index cooling cycles 60 thrust recovery from 61 cooling effectiveness 435 cooling mass flow ratio 304 cooling systems for turbines 307 corrected speed 349 critical speed 326, 329,330,332 cutoff 389,390 cycle analysis assumptions in ideal 30 ideal 29 parameters in 29 purposes of 29 damping 330 decibels 372,374, 395 degree of dissociation 421 degree of reaction 285,286 delta symbol 31 deviation 219 diffuser 120 axisymmetric vs two-dimensional 130 external compression 127 mixed compression 129 off-design behavior 131,134 performance with fixed geometry 126 spill, subsonic and supersonic 134 with multiple oblique shocks 128 "blow-in-doors" 122 availability averaged inlet state 118 contraction ratio for starting 126 critical Mach number 125 effect of blockage 117 internal compression 124 operating modes of internal compression 125 pressure coefficient in subsonic 117 pressure recovery 74,75 starting of internal compression 124 streamtube area variations 121 subsonic 74,121 supersonic 74 supersonic streamtube variations 123 takeoffvs cruise requirements 121 diffuser with variable geometry external compression 136 mixed compression 136 diffusion factor 218 for rotor 237,238 for stator 237,238 for turbine 294 diffusion factor including radial shift 220 diffusion factor of rotor and stator vs radius 240 471 diffusion flame 158 digital electronic control 358 dipole 374,375,376,386 directional characteristic 376 radiated power 376 disc 315,317,344 disc design 318 disc stress level 319 disc thickness 318 dissociation 402 dissociation phenomena 414 distortion 353 circumferential 352 compressor response to 352 radial 352 unsteady 352 Double Annular Burner 174 drag 18,458 base 21 inlet spillage 21 subsonic 20 supersonic 20 drum 344 drum rotor 345 duct attenuation 394 duct lining 392 duct modes attenuation length 394 duct-burning turbofan 364 dynamic pressure 424 effective drag 462 effective mass 336 Effective Perceived Noise Level (EPNL) 395,396 effectiveness 307,432 effectiveness of film cooling 303,439 efficiency Brayton cycle Breguet range equation Carnot cycle compressor 75 cooled turbine 310 cooling effect in turbine 307 film cooling effect 309 in transonic compressor rotors 229 of gas turbine-steam combined cycle 101 of stage related to loss factor 223 of turbine related to solidity 293 overall overall propUlsion system polytropic 75 propulsive 1,3 radial variation of 229 Index 472 efficiency (cont.) thermal turbine 75,283 ejector nozzle 143 off-design behavior 146 primary and secondary flows 146 emission standards 166 EPA 167 FAA certification 168 leAD 167 emissions formation of nitrogen oxides 170 emissions near airports 169 energy exchange blades to fluid 15 by heat transfer 15 kinetic to thermal 15 energy exchange in engines 15 energy exchange, rotor to fluid 187 engine arrangement 341 for Energy Efficient Engine 343 engine cross section 23 engine design 453 engine dynamics 358 engine failure on takeoff 455 engine parameters 454 engine pressure ratio 349 engine structures 315 engines in cutaway 27 enhancing mixing 417 entropy 207, 209,230,308,371,422 change due to cooling 309 environmental constraints 453 equivalence ratio 164,413,449,462 equiValence ratio for cooling 430 Euler equation 189,191,198 Euler turbine equation 192,286 exhaust nozzle 139 blow-in doors 144 ejector type 144 expansion ratio 140 matching to turbojet airflow 140 off-design behavior 141 secondary air in 144 separation in 142 throat area 139 thrust 141 expansion kinetics 418 external compression 127 external compression diffuser 135 external compression inlet 128 fan 11 fan noise 367 fan stage performance maps 251 FAR 36 367 Federal Aviation Rule Part 36 (FAR-36) 365 film coefficient 303, 305 film cooling 298,301,302, 307,429,431,438 cooling effectiveness 435 heat-transfer effectiveness 437 light-gas 438 temperature effectiveness 437 with hydrogen 435 film cooling equivalence ratio 439,441 film-cooling mass flow 303 finite element method 311 fixed-nozzle engine 350 flame speed 158 flexible shaft 331 flight trajectory for a scramjet-powered vehicle 425 fluid-film bearings 339 flutter 211,333,334 clearance 337 damping work 336 effect of pressure 338 effect of temperature 338 excitation of 334 in bending 334 logarithmic decrement 336 phase shift in 335 reduced velocity 336 Reynolds number effect 338 shock induced 337 stalling 334 supersonic unstalled 337 foreign-object damage 211 freezing 420,428 freezing pressure 421 frequency spectrum 379 frozen nozzle flow 422 fuel 21 energy content of heating value 22 gas generator 23,347,349,350,353 gas generator, 10 gas turbine combined cycle 70 gas turbine-steam combined cycle 14,98 gas turbines for topping 66 gyroscopic loads 343 heat addition 406 due to chemical reactions 409 effect on stagnation pressure 408 heat addition in supersonic flow 407 Index heat exchanger effectiveness 80 heat flux 434 heat flux limits 431 heat oHonnation 409,410,449 heat transfer analogy to momentum transport 119 effects of rotation 300 gas to solid 118 internal to blades 300 Prandtl number 120 Reynolds analogy 119 Stanton number 119 heat transfer with film cooling 438 heat-transfer effectiveness 437,440 heating value 22 lower 22 upper 22 Helmholtz resonator 393 high-aspect-ratio blading 210 high-bypass turbofan 367 high-pressure turbine 343 high-speed spool 343 hub and casing layers 232 hydrazine 452 hydrogen 444 hydrogen coolant 432 hydrogen fuel 402 hydrogen fueled turbojet 402 hypersonic flow fuel injection 416 mixing 416 hypersonic inlet 404,405 hypersonic propulsion 402 hypersonic scramjet engine 403 hypersonic transport 466 473 bypass ratio effect on 382 directional characteristics 378 effect of shock structure 381 frequency distribution 379 imperfect expansion 381 Lighthill's eighth power rule 378 refraction 379 shocks 380 subsonic 377 supersonic 380 turbine inlet temperature effect on 382 jet noise suppression 382, 385 jet noise suppressors 365 jet propulsive power of turboprop 55 kinetic energy efficiency 404,415, 419, 428 kinetic phenomena 411 kinetic rates 415 ICAO 367 impingement cooling 298,299,304,305 impulse stage 285 impu�turbine 285,287 inlet 7,403 inlet distortion 352 inlet guide vanes 194 effect on axial velocity distribution 200 effect on pressure ratio and efficiency 243 potential vortex 199 solid body 200 inlet-engine matching 352 internal compression diffuser 124 internal cooling 298 internal cooling of a turbine blade 301 law of mass action 411 life-cycle cost 453 lift/drag ratio 454 light-gas film cooling 438 limiting heat flux 434 linear cascade 189 liquid air 448 liquid air collection (LACE) system 21,401 liquid-air collection engine 448,449 local chemical equilibrium 411 loss factor 214,295 as function of span and D 231 connection to wake thickness 217 correlation to diffusion factor 218 Mach number effects on efficiency 222 physical basis 216 related to efficiency 221 related to Zweifel coefficient 295 loss-factor correlation 230 losses due to leakage in turbines 291 effect on throughflow in compressor 207 estimation of in transonic rotors 230 in turbines 291 nozzle 73 sources of 73 supersonic blading 228 losses in transonic rotors 230 low-aspect-ratio blading 210 low-pressure spool 350 low-pressure turbine 343 lower heating value, 22 jet acoustic power 378, 380 jet noise 18,367,369,380,382 Mach number 15 31 magnetic bearing 339,341 Index 474 mass flow range 211 mass fractions 411 maximum range 464 meanline design 310, 311 measuring stations 366 meridional plane 207 meridional velocity 207 minimum fuel consumption 460 minimum fuel consumption in climb 460 minimum time to climb 456,459 minimum-loss incidence 215 mission profile 453 mixed compression 129 mixer nozzle 148 analysis of 150 for afterburning turbo fan 149 for turbofan 149 mixing process 153 thrust 151 model propulsion systems 454 model vehicles 454 monopole 374,375 multi-stage compressor 250 low speed operation 252 multiple spools 252 variable stators 252 National Aerospace Plane (NASP) 401 nitrogen oxides effect of compression ratio 175 emission by SSTs 169 formation in combustion 172 in engine exhaust 165 methods for reduction 173 regulation by EPA 165 noise 1,18 at John F Kennedy Airport 396 bypass ratio 18 human response 395 jet 18 landing 365 measuring stations 365 noise effectiveness forecast (NEF) 395 noisiness 395 quantitative indices 395 sideline 365 supersonic commercial aircraft 367 takeoff 365 turbomachinery 18 "buzzsaw" 18 noise certification 366 Noise Effectiveness Forecast (NEF) 395 noise limits imposed by FAR-36 398 noise of turboprops 54 noise production 369 noise propagation in ducts 387 condition for propagation 389 cutoff 389 noise restrictions 365 noise sources 368 noise suppression 383 ejector 383 inverted-temperature-profile nozzles 385 variable-cycle engines 385 noise suppression vs thrust 383 NOY 397 nozzle 7,403 choked 82 convergent 82 imperfect expansion loss 79 turbojet with ideally expanded 83 nozzle flow 420 nozzle flow with reaction equilibrium flow 414 freezing 414 nozzle losses due to under- or overexpansion 73 nozzle pressure ratio 354 nozzle vanes 285,298 nozzle velocity coefficient 415 Nusselt number 305 oblique shocks 406 oil-damped bearings 331 operating limits 358 operating point 351 overall efficiency overexpanded nozzle 141 ozone destruction by nitrogen oxides 177 engine designs for reduction of nitrogen oxides 178 variation with altitude 177 perceived noisiness 397 performance trends specific impulse 354 thrust/weight 354 pi symbol 31 plug nozzle 143 pollutant formation 164 pollutants polytropic efficiency 76,77 related to compressor efficiency 78 related to turbine efficiency 78 power-lever 357 Prandtl number 120,298 preliminary design 453 Index pressure coefficient at stall in compressor 235 pressure drop in combustor 160 in cooling air 308 pressure loss in heat exchanger 80 in hypersonic inlets 405 pressure recovery of internal-compression diffuser 132 principal axes 323 principal moments of inertia 323 propagating modes 391 propellant 21 propulsion system 347 propulsion system efficiency propulsion systems analysis 453 propulsive efficiency 1,3,367 propulsive efficiency and thrust per unit massflow propulsive lift 461 pumping characteristics 348,350, 353,364 pure-tone sound 369 quadrupole 374,375,376,377 radial equilibrium 198,206 radial inflow turbine 313 radiated power 376 radiated sound 390 radiation cooling 429 ramjet 6,32 principle of operation specific impulse 33 supersonic combustion thermal efficiency of thrust 33 thrust variation with altitude 35 thrust variation with M 36 with stoichiometric combustion 35 range effect of centrifugal lift 465 equivalent offuel 465 reacting gases 414 reaction kinetics 428 reaction stage 285 real-gas chemistry 418 real-gas computational scheme 419 recombination 421 regenerated gas turbine with losses 97 regeneration 12, 14 regenerative Brayton cycle 12 regenerative cooling 440 regenerative gas turbine 62 475 regenerative gas turbine cycle compared to simple cycle 64 resonance 328 Reynolds analogy 298 Reynolds number 16 effect on compressor pressure rise 220 roller bearings 339 rotating stall 256,258,259,263,337 rotation elTects on impingement cooling 306 rotor 316 rotor and stator blade number elTect on noise 365 rotor stress 317 rotor structures 344 rotor wakes 391 rotor-stator interaction 391 scramjet 401,418 combustor inlet Mach number 424 cooling 429 cooling with hydrogen fuel 430 dynamic pressure 425 flight trajectory 424,425 incomplete mixing 425 performance for orbit 463 regenerative cooling 441 specific impulse along trajectories 427 scramjet combustor 434,435 scramjet performance 414,460 SCRAMJET Program 419 secondary flow 232 secondary flow losses 291 section inefficiency 224 separated flow 115 separation 114 separation in a boundary layer 116 shaft critical speed 330,346 shaft deflection 330 shaft turbine 12 shock location in divergent passage 132 stability in convergent passage 132 shock losses 291 shock noise 382 shock waves 105,108,372 deflection angle 110 oblique and normal 109 on wedges and cones 110 stagnation pressure ratio 109 static pressure ratio 109 wave angle 110 shock-boundary layer interaction 293 smoke number 166 Index 476 solid-body inlet guide vanes 206 solidity 210,292, 293,311 sorties 453 sound power level 374 sound pressure level 374,397 sound radiated 373 specific impulse 4, 33,354, 401,418,422, supersonic throughflow fan 138,273, 275, 277,369 supersonic throughflow stage 276 supersonic transports 367,368 surge 257,260,263 surge and stall-operational consequences 264 445, 447,450 specific impulse for air-turborocket engines 448 specific impulse with combustor inlet Mach number 423 spill 406 spools-number of in engines 342 squeeze films 330 SST engine 369 stability of compressor flow 257 stabilization of compression systems axial compressors-rotating stall 265 centrifugal compressors- surge 265 stagnation pressure 30, 188 stagnation temperature 30,188 stall 363 stall line 353 stall margin 352 Stanton number 119,298,432,438 stiff rotor 331 stoichiometric 403, 430 stoichiometric equation 411 stoichiometric ramjet 34 stoichiometric reactions 412 stratosphere effect of engine emissions 176 ozone depletion 176 streamline curvature throughflow method 207, 208 streamsurfaces 211 streamtube 198 streamtube contraction 212 streamwise vorticity 417 stress 316 stress concentrations 319 stress due to centrifugal force 17 Strouhid number 380 subcritical operation of diffuser 133 subsonic blading 212 subsonic spill 135 substantial derivative 370 supersonic blading 224 supersonic civil transports 385 supersonic combustion ramjet 8,21,401 supersonic compressor 226 supersonic diffuser 123 supersonic spill 135, 137 takeoff 454,455 takeoff gross weight 453 tangential Mach number 283 temperature rise in combustion 413 thermal choking 452 thermal coefficient of expansion 324 thermal effect 16 thermal efficiency 1, of regenerative gas turbine 63 thermal efficiency of the core 87 thermal efficiency of the ramjet thermal strain 434 thermal stress 300,302, 315,324,325,433 cooling requirements 326 scaling with engine size 326 thermal stress susceptibility 325,433 thermally perfect gas 106 thermodynamic properties stagnation 31 static 31 theta symbol 31 throttle excursions 453 throughflow 198 throughflow analysis 310 throughflow and temperature ratio 206 thrust 3,18,32,445,450 thrust and drag 18,19 thrust lapse 59 thrust reversal 456 tip clearance 235 effect on pressure rise at stall 236 tip clearance leakage 232,234 total energy 456,461,462 total enthalpy 209 transition 299,406 transonic blading 219 transonic compressor 210,224 design procedure 230 effect of unsteady flow on efficiency 246 flow alignment with suction surface 227 flow details 245 loss prediction 248 loss transport 247 performance map 231 physical description 226 relation to supersonic diffusers 226 477 Index rotor vortex shedding 247 shock losses 226 unsteady flow 246 upstream wave structure 227 transpiration cooling 302 turbine 444 blade loading 292 blading 290, 293 choked mass flow 312 compressor-drive 11 corrected parameters 311 exit vanes 290 in turbojet losses vs dilTusion factor 293 mass flow capacity 288 nozzle for maximum work 288 optimum reaction 289 radial variations in 290 seals 291 shock losses 291 similarity 311 stress calculation 311 tip leakage 291 typical performance map 312 turbine cooling 296 historical trend 297 schematic arrangement 297 turbine design systems 310 turbine efficiency 76 turbine exit flow area 284 turbine inlet stagnation temperature 287 turbine inlet temperature 10,67,296,300, 382 and bypass ratio 68 elTect on specific impulse 68 elTect on thrust 68 turbine nozzle area 348 turbine rotor temperature 287 turbine stage 285,286 turbine torque 359 turbo-ramjet engine 402 turbofan 11,47 afterburning 26 elTect of compressor pressure ratio 92 elTect of losses summarized 95 elTect of polytropic efficiency 92 elTect of pressure ratio 91 elTect of turbine efficiency 92 elTect of turbine inlet temperature 94 nacelle installation 25 single-nozzle 103 specific impulse 89 specific impulse of ideal 48 thrust 89 thrust lapse of 59 thrust of ideal 48 thrust vs altitude and M 59 typical performance 90 with losses 88 turbofan engine 11,365 cross section 24 turbojet 9,36 elTects of inefficiency and pressure losses 84 F and I at M 39 F and I for ideal 41 F vs M for ideal 42 ideal cycle analysis 36 pressure changes 37 propulsive efficiency of 10 specific impulse of ideal 39 temperature changes 37 thrust of ideal 38 turbine T for maximum F 40 typical performance 85 with constant rotational speed 46 with losses 81 turbojet engine schematic diagram turbojet with afterbuming 45 turbomachinery noise 365 blade-passing frequencies 390 rotor-stator 386 rotor-stator interaction 390 tangential Mach number 386 turboprop 11 exhaust pressure· 56 high-speed 12 jet propulsive power 55 maximum work 57 specific fuel consumption 57 temperature for maximum work 58 work coefficient 55,56 turboprop engine 54 turborocket engine 443 turboshaft engine 11 turning radius 466 two-spool engine 350 two-spool turbojet 350 = unstart 132 unsteady compression 188 unsteady flow giving rise to noise 370 upper heating value 22 upper-atmosphere emissions 168 variable cycle 385 variable cycle engine 369 variable-geometry dilTuser 136 478 variable-geometry external-compression inlet 137 variable-geometry nozzle 143 velocity change in hypersonic engines 404 velocity coefficient 420 velocity diagram 193 velocity triangles effect of inlet guide vanes 201 vibration 330 bending 333 blade-shroud modes 333 compressor blade 332 disc 332 modes 332 umbrella mode 333 viscous elTects 16 viscous losses 420 VorbixCombustor 174 vortex inlet guide vanes 206 vorticity disturbance 372 wall heat flux 436 wave angle 406 wave equation 372 wave number 378 wing loading 454 work coefficient 55 Zweifel coefficient 292,293,295,310 Index