Appendix

Nomenclature*

Total pressure and total temperature are the most important quantities in thermo-dynamic cycle calculations; seldom are static pressure and temperature needed. Weuse the letters P and T for total pressure and temperature with a number as indexwhich designates the thermodynamic station.

We insert the index s before the station number for marking static pressurerespectively temperature when static pressure and temperature show up in anequation.

Parameter names

Symbol SI unit Stands for Comment, example

a m/s Velocity of sound

A m2 Area

alt m, km Altitude also expressed in ft or kft

b m Width @ radial compressor rotor exit

B Burner part-load constant

BPR Bypass ratio

cs kg/s Core size

C Coefficient

CD Discharge coefficient

CFG Thrust coefficient

CP J/(kg K) Specific heat @ constantpressure

D m Diameter

e – Efficiency e2-3 = compressor efficiencyefficiency between stations 2 and 3

EAS knot Equivalent air speed

EGT K Exhaust gas temperature often quoted in °C(continued)

© Springer International Publishing AG, part of Springer Nature 2018J. Kurzke and I. Halliwell, Propulsion and Power,https://doi.org/10.1007/978-3-319-75979-1

739

(continued)

Symbol SI unit Stands for Comment, example

f A factor

h J/kg Enthalpy

F N, kN Force, thrust

FHV MJ/kg (Lower) fuel heating value valid for 25 °C

far – Fuel-air-ratio by mass

h m Blade height

h (T) J/kg Enthalpy at a temperature H4 = h(T4)

H J/kg, m2/s2 Specific work HC = enthalpy change in the compr.H2-3 = h(T3) − h(T2)

i deg Incidence

I kg m2 Polar moment of inertia

IGV – Inlet guide vane

ISA International standardatmosphere

k various A constant value

L m Length

M – Mach number

n – Exponent in losscorrelations withReynolds number

N rpm Absolute spool speed mechanical spool speed

N – Relative spool speed absolute spool speed related to areference value

OPR – Overall pressure ratio P3/P2

P kPa Total pressure

Ps kPa Static pressure static pressure = the true pressure

PR – Pressure ratio

PSFC kg/(kW s) Power specific fuelconsumption

PW kW Shaft power

PWX kW Shaft power extracted for customer purposes

q kPa Dynamic head

Q kW Heat flow

r m Radius

rr – Radius ratio rhub/rtipR J/(kg*K) Gas constant

Re – Reynolds number

RH % Relative humidity

RNI – Reynolds number index Reynolds number relative toReynolds number at standard dayconditions

(continued)

740 Appendix

(continued)

Symbol SI unit Stands for Comment, example

rpm 1/min Revolutions per minute

s J/(kg K) Specific entropy

SFC kg/(kN s) Specific fuel consumption

SLS Sea level static

t sec Time

T K Total temperature

Ts K Static temperature static temperature = the true temp.

Trq Nm Torque

TSFC kg/(kN s) Thrust specific fuelconsumption

U m/s Circumferential velocity

V m/s Velocity absolute velocity in velocity triangles

VGV – Variable guide vane

Vol m3 Volume

W m/s Relative velocity relative velocity in velocity triangles

W kg/s Mass flow rate

war – Water-air-ratio by mass

Y DP/q describes a cascade loss

a deg Absolute flow angle

a deg Nozzle cone angle

ß deg Relative flow angle used in velocity diagrams

ß – Auxiliary coordinate used in component maps

d – P/101.325 kPa

D – A difference DH = enthalpy difference

e – A very small value

K – Stage reaction

U – Flow coefficient Vax/U

U – Burner loading parameter

c – Isentropic exponent

η – Efficiency

l kg/(m s) Dynamic viscosity

m – Blade-jet speed ratio

m m2/s Kinematic viscosity

q kg/m3 Density

r Standard deviation

r Solidity chord/pitch

W(T) – Entropy function @ atemp.

W – Power coefficient DH/U2 also known as work coefficient, stageloading coefficient and aerodynamicloading

H – T/288.15 K

X – Burner loading

Appendix 741

Indices

a Air

ad Adiabatic

amb Ambient

ax Axial

B Burner (main combustion chamber)

corr Corrected

C Compressor

cl Cooling

ds Design

D Discharge

eff Effective

eq Equivalent

equi (Chemical) equilibrium

ex Exit

F Fuel

FG Gross thrust

FN Net thrust

g Gas

G Gross

h Hub

H High pressure spool

HPC High pressure compressor

HPT High pressure turbine

i Inner annulus

id Ideal

in Inlet

inj Injected

is Isentropic

IPC Intermediate pressure compressor

IPT Intermediate pressure turbine

L Low pressure spool

LPC Low pressure compressor

LPT Low pressure turbine

m Mean

mea Measured

mech Mechanical

mix Mixing

N Net

o Outer annulus

P Pressure

pol Polytropic

prop Propulsive(continued)

742 Appendix

Station numbering

0 Free stream air conditions

1 First station of interest to the engine manufacturer, e.g. propulsion system entrance,external/internal interface or vehicle/engine interface

22x

First compressor front faceIntermediate compressor stations

33x

Last compressor discharge or burner entranceIntermediate burner stations

44x

Burner discharge or first turbine entranceIntermediate turbine stations

5 Last turbine discharge

6 Available for mixer, afterburner etc.

7 Engine/exhaust nozzle interface

8 Exhaust nozzle throat

9 Exhaust nozzle discharge

(continued)

PT Power turbine

R Reduced (=corrected)

Re Reynolds

ref Reference

rel Relative

RH Reheat (= afterburner, augmentor)

sat Saturation

SD Shaft (power) delivered

std Standard day conditions

Stg Stage

t Tip

T Turbine

therm Thermal

thermo Thermodynamical

u In circumferential direction

V Volume

x In axial direction

Appendix 743

Special terms

AEDC Arnold Engineering Development Complex

Backbone A line which connects the highest efficiency points on all speedlines in a compressor or turbine map

Corrected flow,Corrected speed

WpH=d ¼ W

pðT=288:15KÞ=ðP=101:325 kPaÞN=

pH ¼ N

pðT=288:15KÞGasTurb A publicly available gas turbine performance program for

Windows

Cycle design point The operating condition which defines the geometry of theengine by means of a cycle design calculation

Incidence Flow angle with minimum lossesFlow angle measured against the minimum loss flow angle

ISA International standard atmosphere

MBTO Mean Time Between Overhaul

OEM Original equipment manufacturerGas turbine engine manufacturer

Peak efficiency line Same as backbone

Pitch-line radius Mean radius, based on equal areas rm ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r2t � r2h� �

=2q

Reduced flow,Reduced speed

W√T/PN/√T

Smooth C A program for generating compressor map tables from measuredor calculated data

Smooth T A program for generating turbine map tables from measured orcalculated data

Uninstalled No power offtake or bleed for aircraft purposesSubsonic flight: no intake pressure lossSupersonic flight: intake pressure loss as defined in MIL-E-5007

* This is not a complete nomenclature, as sparsely used terminology is described in the text

744 Appendix

Index

AAcceleration, 269Acceptance test, 167Accessories, 304Active Clearance Control (ACC), 172, 173,

215, 239, 483Adaptive random search, 718, 720Advanced map scaling, 499Aerodynamic design point, 116, 306, 307Aerodynamic Interface Plane (AIP), 252, 442Aerodynamic limits, 301Aerodynamic loading, 60Aerodynamic spool speed, 108Aerospace Standard AS755, 3Afterburner (Augmenter, Reheat)

Afterburner efficiency, 33, 546Afterburner operation, 544Afterburner simulation, 542Afterburner, 23, 30, 48, 104, 211, 421, 529,

541, 542, 649Efficiency at part load, 549Flame-holders, 545Reheat pipe, 105Temperature rise due to combustion, 616

AIA Standard, 441, 445Airbus A340, 530Aircraft

Airbus A340, 530Blackbird SR-71, 100, 112Business jets, 116, 537Concorde, 445Eurofighter Typhoon, 550Eurofighter, 446European Fighter Aircraft (EFA), 446F-4, 445F-14, 445F-15, 445F-16, 445F-104, 445

F-111, 445Fighter aircraft, 48, 95Helicopter propulsion, 56

Aircraft drag, 447Aircraft mission, 298, 309Aircraft mission requirements, 303Aircraft speeds, 617Air inlet house, 448Air intake, 439Altitude test facility, 230AM350, 431AN2, 82, 309, 396AnSyn

Analysis by Synthesis (AnSyn), 214, 235AnSyn factors, 216, 218, 219, 221, 232,

234Interpretation of the AnSyn factors, 237

Area ratio, 54Augmented turbofan, 56, 106Augmenter, see AfterburnerAuxiliary coordinate ß, 120Average new production engine, 132Average stage pressure ratio, 622Axial Mach number, 453

BBackbone, 464, 467Batch of engines, 736Bellmouth, 139, 167Bernoulli equation, 342ß line, 218, 463, 516Bias, 727Blackbird SR-71, 100, 112Blade aspect ratios, 73Blade incidence, 325, 370Blade metal angles, 323Blade metal temperature, 62Blade root stress, 60, 309Blade speed/jet speed ratio, 509

© Springer International Publishing AG, part of Springer Nature 2018J. Kurzke and I. Halliwell, Propulsion and Power,https://doi.org/10.1007/978-3-319-75979-1

745

Blade untwist, 231, 483, 485Bleed schedule, 321, 483Blisk, 414, 425Blockage, 336, 340Bodie, 286Booster

Booster, 416Booster map, 190Booster operating line, 593, 597

Bore radius, 84Bottoming cycle, 19Boundary layer, 226, 325, 334, 337, 340Brayton, 3Brayton cycle, 6, 313, 357Burner, see CombustorBusiness jets, 116, 537Bypass duct, 74Bypass ratio, 35, 37, 70, 192, 229, 728

CCalibrated Airspeed (CAS), 617Camber line, 370Carnot cycle, 12Central limit theorem, 733Centrifugal compressors, 203, 651CF6, 115CFD, 334CFM56, 115, 166, 238CFM56-3, 241, 403CFM56-5C2, 530Chargeable cooling air, 664, 670, 679, 693Chemical composition, 616Chemical equilibrium, 18Chemical Equilibrium with Applications

(CEA), 613, 615Choking, 452Circumferential Mach number, 453Clearance changes of seals, 281Close-coupled, 262Closed loop control, 542Coarse Filter, 227Cogeneration, 19Combined cycle, 19Combined cycle efficiency, 22Combustor (Burner)

Burner efficiency, 159Burner loading, 159Burner outlet temperature, 663Burner part-load constant, 159Combustion Chamber, 308, 525, 647Combustion efficiency, 32Combustor, 304, 418Dilution air, 666

Flame tube, 281Overall Temperature Distribution Factor

(OTDF), 529Pattern factor, 529Pressure loss, 525Radial Temperature Distribution Factor

(RTDF), 529Stoichiometric combustion, 18Temperature rise due to combustion, 616

Commercial airliner, 44 See also AircraftCommercial subsonic aircraft, 94 See also

AircraftCommon core, 70, 115Component

Degradation, 238Design, 297, 311Design points, 306Hierarchy, 304Models, 299Performance map, 713Performance, 297Synergy, 582

Component maps, 713Compressor

AnSyn factors, 218, 219Compressor, 313Coupling, 261, 267Design envelopes, 347Deviation, 325Efficiency correction, 659HP compressor, 304, 307, 416Incidence, 325Number of compressor stages, 622Overall compressor performance, 454Peak efficiency line, 464, 467, 480Pressure ratio of 1, 713Rig, 451Through-flow model, 333Velocity diagram, 323

Compressor mapsAuxiliary coordinate ß line, 120, 218, 463,

516Efficiency contours, 452Mach number scale for compressor maps,

491, 495Map coordinates, 461Parabolic b-lines, 463, 516Performance maps, 451, 644Pressure ratio scaling, 498Re-engineering compressor maps, 451Simple map scaling, 498Spacing between map speed lines, 495Split map, 474

746 Index

Compressor map scaling, 487Conceptual design, 346Concorde, 445Condensation, 138, 179, 233, 235Condenser, 19, 21Confidence level, 726Configuration design, 299Confluent mixers, 537Constant pressure combustion, 10Constant volume combustion, 10Constraints, 720, 721Continuity characteristic, 358Contractual performance, 134, 135Control system, 266, 708Control volume, 662, 663Convergence problems, 711Convergent-divergent nozzles, 53, 102, 563Convergent nozzles, 53, 559Cooled Turbines

Chargeable cooling air, 664, 670, 679, 693Cooled turbines, 661Cooling air, 393Cooling air bookkeeping, 682Cooling effectiveness, 61, 63Cooling loss, 393NGV cooling air, 666Non-chargeable cooling air, 664, 670, 674,

679Core compressor, 68Core driven fan stage, 355Core efficiency, 26Core flow analysis, 728Core size, 68, 93Corrected parameters

Circumferential speed, 453Correction exponents, 646Flow, 452, 505Flow per area, 44, 93Fuel flow, 647Mass flow, 503Parameter correction procedure, 136Specific fuel consumption, 646Specific power, 507Speed, 307Spool speed, 94, 452, 507Thrust, 646

Counter-rotating, see Vaneless counter-rotatingturbine

Coupling Factor (CF), 262Cradle drag, 135Critical segment angle, 258Cross section, 274CSPAN mean line code, 340, 344, 351Cycle efficiency

Core efficiency, 26Overall efficiency, 27Propulsive efficiency, 27, 29, 34, 38, 44, 70Thermal efficiency, 11, 17, 18, 23, 25, 26,

29, 38, 41, 45, 132Transmission efficiency, 26

Cycle Analysis, 297Cycle design mode, 735Cycle design point, 72, 103, 305, 308, 311Cycle design point calculation, 66, 93, 100Cycle reference point, 141, 143, 148, 179, 183,

201Cycle types

Bottoming cycle, 19Brayton, 6, 313, 357Carnot cycle, 12Constant pressure combustion, 10Constant volume combustion, 10Humphrey cycle, 10Joule cycle, 3, 6, 313Rankine Cycle, 19Sequential combustion, 8, 14, 15Topping cycle, 19

DDC60 distortion coefficient, 251Deceleration, 269, 286De Haller number, 337Derivative engines, 92, 115Design constraints, 123, 301Design envelopes, 302, 345Design margins, 432Design point, 306Design point analysis, 305Design process, 296Design space, 92, 116, 348, 716, 722Design variables, 122, 302, 350Deterioration, 99, 133Deviation, 325, 369Diffusion, 336Diffusion Factor, 338, 345Dilution air, 666Direct drive turbofans, 70, 72Discharge coefficient, 192, 559Disk

Bore diameter, 85Burst margin, 433Burst speed, 433Design, 426Dimensions, 274Stress, 430Temperature, 429Von Mises stress, 432

Dissociation, 546

Index 747

DistortionCompressor distortion, 496Coupling Factor CF, 262Critical segment angle, 258Distortion Coefficient (DC60), 251Distortion intensity, 258Full coupling, 262Inlet Distortion, 249Parallel compressor theory, 249, 253

Dry engine, 30Dry turbofan, 52Ducts, 422Dynamic head, 4DYNGEN, 709, 710

EEconomizer, 21Effective burning area, 544Effective work coefficient, 455EGT, see Exhaust Gas TemperatureEGT margin, 134, 167, 225, 237EJ200, 157, 229, 550, 565, 573Emissions, 90, 302Endless random search, 125, 720Energy balance (Heat balance), 13, 222, 229,

233, 242, 587, 614, 640, 687, 692Energy-based definition of thermal efficiency,

18Engine configuration model, 298Engines

CF6, 115CFM56, 115, 166, 238CFM56-3, 241, 403CFM56-5C2, 530EJ200, 157, 229, 550, 565, 573F107-WR-400, 201GE F101, 565GE36, 401J57-19W, 147LMS 100, 8MT30, 115MTR390, 56PW1000G Geared Turbofan, 81PW4000, 115RB199, 422SGT8000H, 694T800, 56Trent, 115V2500, 274, 434

Engine design table, 306, 309Engine Development, 309Engine family, 70, 73, 115Engine geometry, 273Engine inlet diameter, 39

Engine maintenance shops, 232Engine parts rig, 230Engine Pressure Ratio (EPR), 225Engine weight, 411, 433Enthalpy-entropy diagram, 7, 8, 23, 25, 316,

360, 530, 664, 678, 689Entropy function, 615Equivalent Airspeed (EAS), 100, 617Equivalent diffusion factor Deq, 340Equivalent exhaust jet velocity, 38Equivalent jet velocity, 30, 646Equivalent single-stage turbine, 393, 670, 677Equivalent single-stage turbine efficiency, 680,

692Equivalent tip clearance, 484Erosion, 232Euler’s method, 710Eurofighter Typhoon, 446, 550European Fighter Aircraft (EFA), 446Evaporation coolers, 448Evaporator, 21Exhaust emissions, 302Exhaust Gas Temperature (EGT), 142, 174,

189, 193, 201, 223, 233, 518Exoskeletal engine, 408External compression, 445External design limits, 302

FF-4, 445F-14, 445F-15, 445F-16, 445F-104, 445F107-WR-400, 201F-111, 445Facility modifier, 135, 166, 170Fan

AnSyn factors, 234Diameter, 44Operating line, 595Tip diameter, 73Tip relative Mach number, 88Tip speed, 78

Fan mapsBypass section, 478Core section, 475Extended fan map, 479Fan maps, 473

Fanning Friction Factor, 654FHV, see Fuel Heating ValueFighter engines, 225Figure of merit, 142, 716, 721Fine Filter, 227

748 Index

First law of thermodynamics, 222First order lag, 279Flame-holders, 545Flame tube, 281Flat-back turbine blade, 369Flat rated, 225Flat rating, 310Flight envelope, 96, 100, 298, 651Flow annulus, 66Flow capacity factor, 218Flow coefficient

Compressor, 330, 347Turbine, 375, 396, 454, 455, 560

Flow correction factor, 659Flow path, 413Flow separation, 655Fogging, 448Foreign Object Damage (FOD), 232Fouling, 238Frame of reference, 321Frames

Front frame, 422Main frame, 423Rear frame, 424Turbine center frame, 423

Free-vortex, 336Front frame, 422Fuel burn, 297Fuel flow-based thermal efficiency, 18Fuel Heating Value (FHV), 17, 38, 172, 614,

625, 626, 645Full coupling, 262Fully mixed thrust, 532Fundamental pressure loss, 50

GGas Properties

Chemical Equilibrium with Applications(CEA), 613, 615

Dissociation, 546Entropy function, 615Fuel Heating Value (FHV), 17, 38, 172,

614, 625, 626, 645Gas constant, 616Generic fuel, 616Humidity, 136, 235, 506, 616, 643Hydrocarbon, 616Ideal gas, 614Isentropic exponent, 4, 639, 647Psychrometric chart, 449Specific heat at constant pressure, 614Steam, 19Temperature rise due to combustion, 616

Gas generator, 35, 57, 69, 115, 120, 188, 271Gas generator turbines, 656Gas path analysis, 232GasTurb, 346, 351, 417, 424, 429GasTurb Details, 133GasTurb Standard maps, 116, 153, 184Gauss algorithm, 704Gaussian distribution, 244, 724 See also

StatisticsGE F101, 565GE36, 401Gear ratio, 82Gearbox, 70, 72Geared Turbofan, 81Generic fuel, 616Geometric altitude, 617Geometric model, 274Global maximum, 126Global optimum, 717, 720Gradient search, 720Gradient strategy, 717Greek Ascoloy (418), 431Gross thrust, 56GT24/26, 8 See also EnginesGuaranteed thrust, 206

HHalf-ideal gas, 613Handling bleeds, 483Heat balance, see energy balanceHeat exchanger, 11, 13, 14, 650, 707Heat rate, 132Heat Recovery Steam Generator (HRSG), 15,

19Heat soakage, 282, 288Heat storage, 273Heat transfer, 278, 281Heat transfer coefficient, 279Helicopter propulsion, 56High-Bypass-Ratio Fan, 414Hot Day Take Off, 94HP compressor, 304, 307, 416HP Shaft, 424HP spool, 304HP turbine, 304, 308, 380, 418HP turbine flow capacity, 728Hub, 309Hub/tip radius ratio, 66Humidity, 136, 235, 506, 616, 643Humidity corrections, 136Humphrey cycle, 10Hybrid measured data, 190Hybrid test data, 141, 184

Index 749

Hydrocarbon, 616

IIdeal cycle, 5Ideal gas, 614Ideal jet velocity ratio, 37, 43, 127Ideal thrust coefficient, 562Idle, 709IGV, see Inlet Guide VaneIncidence

Compressor, 325Controlling incidence, 469Turbine, 369

INCONEL, 432, 718Indicated airspeed, 617Indicated total temperature, 168Infrared signature, 529Inlet

External compression, 445Inlet, 439Inlet air chillers, 448Inlet condensation, 172Inlet cooling system, 448Inlet flow distortion, 99, 249–267, 483Inlet fogging, 449, 616Inlet isentropic efficiency, 440Inlet momentum drag, 135Inlet pressure ratio, 440Inlet pressure recovery, 100, 265, 440, 446Inlet recovery factor, 168Internal compression, 444MIL-E-5008B Standard intake recovery,

440, 445Mixed compression, 445Oblique shock waves, 445Pitot inlet, 445Ram efficiency, 440

Inlet Guide Vane (IGV), 315, 321, 469Installed SFC, 86Intake, see InletIntegration step size, 710Intercooling, 9, 14Internal compression, 444Internal design limits, 301International Standard Atmosphere (ISA), 67,

136Interpretation of the AnSyn factors, 237Inter-stage bleed, 483, 497, 691, 693ISA corrected data, 235ISA correction, 224ISA Standard Day, 136Isentropic efficiency, 59, 315, 317, 320, 362,

365, 621, 625

Isentropic exponent, 4, 639, 647Iteration algorithms, 697

JJ57-19W, 147Jacobian matrix, 703, 704Jet velocity ratio, 70, 74Joule, 3, 6, 313

KKink point, 225

LLaminar separation, 654Limiter, 708Lip contraction, 442LMS 100, 8Loading coefficient

Compressor, 330Turbine, 374, 380Zweifel loading coefficient, 377, 396

Local maximum, 126Local optimum, 720Loss coefficient

Compressor, 343, 347Turbine, 361

Low-Bypass-Ratio Fan, 413Lower Fuel Heating Value FHV, 616, 626LP Compressor, 413 See also CompressorLP Shaft, 425LP spool, 304LP Turbine, 308, 381, 420, 655

MMach number scale for compressor maps, 491,

495Mach number, 4, 639Mach number similarity, 224, 642, 645Main frame, 423Maintenance shops, 166Manufacturing tolerance, 132, 735Maps, see Compressor maps, Fan maps,

Turbine mapsMap entry point, 488Map extrapolation, 713Map manipulation, 451Map preparation, 496Map scaling during off-design, 501Map scaling point, 153, 189, 194, 207, 488,

490Map-tweaking, 184

Mass flow AnSyn factor, 218Mass flow scaling, 499

750 Index

Mass storage, 281Materials

AM350, 431Greek Ascoloy (418), 431INCONEL 718, 432Material properties, 431Ti-6AL-4 V, 432

Max Climb, 73, 94Max Continuous, 225Max Dry, 225Max Reheat, 225Mean line analysis

CSPAN mean line code, 340, 344, 351Mean line analysis, 335, 382Mean line code, 385Mean line loss model, 333, 342, 388

Measured data, 133, 134Measurement error, 243Measurement uncertainty, 723Mechanical design point, 116, 307, 308, 411MIL-E-5007, 100MIL-E-5008B Standard intake recovery, 440,

445MIL-STD 210, 617Minimum afterburner rating, 541Minimum (guaranteed) performance, 132Minimum production engine, 206Mission analysis, 90, 297Mission performance, 90Mixed compression inlet, 445Mixed flow nozzles, 422Mixed flow turbofan, 44, 45Mixer

Efficiency, 533Geometry, 531Mixed cycle, 529Off design, 539Practical mixers, 536Thrust gain, 46Velocity coefficient, 534

Model-based performance analysis, 213, 215,222, 227, 312

Model fault, 239Monte Carlo, 244, 723Moody Chart, 653, 657MT30, 115MTOW, 297MTR390, 56Multi-point Design, 93Multi-spool turboshaft, 607Multi-stage compressor, 316, 354, 416Multi-stage cooled turbine, 393

NNacelle, 44Nacelle drag, 447N dot control, 271Nested loop, 704Net thrust, 56Newton algorithm, 700, 706Newton-Raphson algorithm, 702, 704NGV cooling air, 666Noise, 89, 90, 617Non-chargeable cooling air, 664, 670, 674, 679Non-dimensional parameter

Circumferential speed, 453Flow, 452, 505Flow per area, 44, 93Fuel flow, 647Mass flow, 503Specific fuel consumption, 646Specific power, 507Speed, 307Spool speed, 94, 452, 507Thrust, 646

Non-dimensional performance, 300, 639, 644,646

Non-symmetric probability distribution, 726Normal Distribution, 723Nozzles

Convergent-divergent nozzles, 53, 102, 563Convergent nozzles, 53, 559Ideal thrust coefficient, 562Mixed flow nozzles, 422Nozzle area AnSyn factor, 221Nozzle discharge coefficient, 153Nozzle pressure ratio, 53Nozzles, 421, 558Subsonic nozzles, 421, 422

Nozzle guide vane (NGV), 663Nozzle pressure ratio, 53Number of compressor stages, 622Number of turbine stages, 64Numerical analysis

Iteration algorithms, 697Nested loop, 704Newton algorithm, 700, 706Newton-Raphson algorithm, 702, 704Regula Falsi, 701, 706

Numerical optimization, 116, 124, 142, 223,715

Constraints, 720, 721Figure of merit, 142, 716, 721Global maximum, 126Global optimum, 717, 720Gradient search, 720

Index 751

Numerical optimization (cont.)Gradient strategy, 717Local maximum, 126Local optimum, 720Pareto front, 722

Nusselt number, 650

OOblique shock waves, 445Off-design analysis, 306Off-design calculations, 93Off-design matching scheme, 223Off-design performance, 305, 306Open loop, 542Open rotor, 42Operability, 484Operating lines, 97, 494, 588Optimization, see Numerical optimizationOutput shaft power, 518Overall compressor performance, 454Overall efficiency, 27Overall engine simulation, 662, 706Overall pressure ratio, 39, 141, 184, 216Overall Temperature Distribution Factor

(OTDF), 529Over-tip leakage loss, 392

PParabolic b-lines, 463, 516Parallel compressor theory, 249, 253Parameter correction procedure, 136Pareto front, 722Pass-off test, 134Pattern factor, 529Peak efficiency line, 464, 467, 480Performance deck, 132Performance monitoring, 235Performance prediction, 230Performance scatter, 735Performance synthesis program, 214Pinch point, 21Pipe flow analogy, 654, 657Pitch line loading, 74Pitot inlet, 445Point performance, 100Polar moment of inertia, 269Polytropic efficiency, 59, 318, 320, 363–365,

622, 625Power control, 211Power generation, 15, 146Power off-take, 97Practical mixers, 536Preheat effect, 318Preliminary compressor design, 333

Preliminary engine design, 295, 298, 299Preliminary turbine design, 122, 380Preprocessing measured data, 183Pressure ratio AnSyn factor, 218Pressure ratio parameter, 622Pressure ratio scaling, 498Probability distribution, 726Production tolerance, 723Profile factor, 529Profile loss, turbine, 391Propulsive efficiency, 27, 29, 34, 38, 44, 70Pseudo RIT, 673Psychrometric chart, 449Pulse detonation engines, 10PW1000G Geared Turbofan, 81, 425PW4000, 115

QQuality criterion, 69

RRadial compressor, 495Radial distortion, 251Radial equilibrium, 335Radial Temperature Distribution Factor

(RTDF), 529Rake, 226Ram effect, 25Ram efficiency, 440Ramjet, 107Random errors, 727Range Check, 227 See also SensorsRankine Cycle, 19Rated Power, 225Ratings, 94Raw data, 216Rayleigh flow, 50RB199, 422Reaction, 336, 354Real cycles, 15Rear frame, 424Red line temperature, 225Reduced parameters

Flow, 380, 452, 505, 514, 515, 642Fuel flow, 645Shaft power, 644Speed, 642Thrust, 646Torque, 514

Re-engineering performance, 211Regula Falsi, 701, 706Reheat, see AfterburnerRelative humidity, 136Relative roughness, 653

752 Index

Relative velocity, 326, 371Re-slam, 289Re-stagger, 496Reynolds correction, 159Reynolds number, 229, 483, 488, 496, 499,

639, 647, 650, 651, 657Reynolds Number Index, 97, 279, 652Rim Load, 427Root Sum Squared, 725, 737Rotor blade metal temperature, 61Rotor inlet temperature, 663, 673Rotor loss coefficient, 361

SScreech damper, 421, 541Secondary air system, 221, 304, 687, 690Secondary effects, 146Secondary loss, 392Sensitivity studies, 142Sensors

Checking, 227Coarse filter, 227Fine filter, 227Sensor failure, 241Sensor readings, 223Sensor tolerances, 736

Separate flow turbofans, 43, 45Separate flow nozzle, 422Sequential combustion, 8, 14, 15SGT8000H, 694Shafts, 424Shock losses, 391Sign convention in velocity diagrams, 324, 370Simple map scaling, 498Single Point Design, 91Single spool gas turbines, 694Smith Chart, 379, 382, 397Smooth C, 186, 190, 195, 218, 463, 482, 487,

496, 502Smooth T, 512Solidity, 339Spacing between map speed lines, 495Specific fuel consumption, (SFC), 27, 297Specific heat at constant pressure, 614Specific power, 7Specific thrust, 39, 48, 100, 102, 646Specific work, 7, 458, 507Speed, 100% values, 311Speed line, 454Spillage drag, 447, 448Split map, 474Splitters, 416Spool speed, 68, 144Spray bars, 545

Spray rings, 545Stage loading coefficient, 380, 396Stage loading, 347Stage matching, 321Stage reaction, 330, 347, 375Standard Day, 617Standard deviation, 244, 723Static pressure, 4Static temperature, 4Station numbers, 3Statistics

Addition theorem for normal distributions,724

Manufacturing tolerance, 132, 735Measurement uncertainty, 723Monte Carlo, 244Non-symmetric probability distribution,

726Normal Distribution, 723Probability distribution, 726Random errors, 727Root Sum Squared, 725, 737Standard deviation, 244, 723Truncated normal distribution, 725

Status Model, 311Stealth, 529Steam, 19Steam turbines, 21Stoichiometric combustion, 18Streamline model, 333Stress distribution, 433Structural limit, 301Subsonic nozzles, 421, 422Super cruise, 55Supersonic flight, 54Supersonic nozzles, 421, 422Supersonic speed lines, 456Surge, 249Surge line, 97Surge margin, 69, 97, 471, 484, 495Surge pressure ratio, 494Systematic errors, 727

TT800, 56Take off, 94, 116, 225, 307, 522Taper, turbine airfoil, 387Technology level, 299Temperature-entropy diagram, 5Temperature rise due to combustion, 616Tensile strength, 431Test analysis, 213, 728Test cell, 170Test cell calibration, 232

Index 753

Thermal efficiency, 11, 17, 23, 25, 27, 29, 38,41, 45, 132

Thermal limits, 301Thermodynamic cycle model, 298Thermodynamic turbine efficiency, 678, 680Three-dimensional flow, 335Through-flow model, 333Thrust coefficient, 560, 562, 564Thrust correction, 135Thrust gain, 46, 105Thrust gain potential, 534Thrust management, 265, 310, 311Thrust per frontal area, 48, 53Thrust response times, 290Thrust/weight ratio, 48, 53Ti-6AL-4 V, 432Time constant, 279Tip clearance, 69, 145, 172, 231, 232, 269,

273, 274, 276, 277, 289, 483, 484, 497,519, 647

Top of climb, 45Topping cycle, 19Torque, 85, 460Total pressure, 3Total temperature, 3Trailing edge loss, 392Transient Performance

First order lag, 279Simulation, 269Transient control, 269Transient performance, 269

Transmission efficiency, 26Trend Monitoring, 236Trent, 115True airspeed (TAS), 617Truncated normal distribution, 725Turbines

AnSyn factors, 219Center frame, 423Cooling air, 692Design envelopes, 394Efficiency, 15, 58, 661Equivalent single-stage turbine, 393, 670,

677Equivalent single-stage turbine efficiency,

680, 692Flow capacity, 121, 219, 233, 581HP turbine, 304, 308, 380, 418HP turbine flow capacity, 728Inlet conditions, 663LP turbine, 308, 381, 420Over-tip leakage loss, 392Performance, 503Profile loss, 391

Rotor blade temperature, 229Rotor loss coefficient, 361Stage count, 679Tip clearance, 197, 200Turbine function, 357Turning, 336Two-staged cooled turbine, 668Uncovered turning, 369Vane loss coefficient, 361Velocity triangles, 61, 510Zweifel loading coefficient, 377, 396

Turbine mapsTurbine map b-lines, 516Turbine map format, 512, 515Turbine map scaling, 517Turbine map shape, 145

TurbofanAugmented turbofan, 56, 106Direct drive turbofan, 70, 72Dry turbofan, 52Mixed flow turbofan, 44, 45Separate flow turbofans, 43, 45Turbofan, 34, 66, 100Turbofan booster operating line, 597

TurbojetDry engine, 30Turbojet, 23, 100, 220, 578Wet engine, 30

TurbopropTurboprops, 146Unducted Fan (UDF), 401

Turboshaft, 5, 146, 737Two-stage cooled turbine, 668

UUltimate strength, 431Uncertainty, 223, 727Uncovered turning, 369Unducted Fan (UDF), 401Unmixed thrust, 533Untwist correction, 487US Military Standard 210, 617

VV2500, 274, 434Vane incidence, 325, 370Vaneless counter-rotating turbine, 370, 401,

520Vane loss coefficient, 361Variable area nozzles, 53, 266, 541Variable compressor geometry, 590Variable Cycle Engine (VCE), 355Variable geometry compressor, 601Variable geometry turbine, 520, 650

754 Index

Variable guide vanes (VGV), 144, 188, 195,266, 321, 469, 482

Variable inlet guide vanes, 468Velocity coefficient, 562Velocity diagram

Compressor, 321, 326Turbine, 61, 75, 367, 371, 405, 510Velocity triangles, 454, 468

Virtual NGV, 673Virtual RIT, 673, 676Virtual T4, 674, 676Volume filling, 281Von Mises stress, 432

WWater/air mass ratio, 136Water injection, 616

Wave rotor, 10Weight, 90Weight Analysis of Turbine Engines (WATE),

411Wet engine, 30Work coefficient, 380, 454Worm diagram, 683

YYield strength, 432

ZZero-D performance programs, 66Zero-speed line, 455Zweifel loading coefficient, 377, 396

Index 755