Elements of
`Gas Turbine
`Propuls" ion Jack D. Mattingly
`
`Foreword by
`Hans yon Ohain
`German Inventor of the Jet Engine
`
`GE-1014.001
`
`

`
`GE-1014.002
`
`

`
`ELEMENTS OF GAS TURBINE PROPULSION
`ELEMENTS OF GAS TURBKNE PROPULSION
`
`GE-1014.003
`
`

`
`McGraw-Hill series in Aeronautical and Aerospace Engineering
`
`Consulting Editor
`
`John D. Anderson, Jr., university of Maryland
`
`Anderson: Comp~ztational Fluid Dynamics: The Basics with Applicationk
`Anderson: Fundamentals of Aerodynamics
`Anderson: Hypersonic and High Temperature Gas Dynamics
`Anderson: Introduction to Flight
`Anderson: Modern Compressible Flow: With. Historical Perspective
`Burton: Introduction to Dynamic Systems Analysis
`D’Azzo and Houpis: Linear Control System Analysis and Design
`Donaldsoni Analysis Of Aircraft Structures: An Introduction
`Gibsoni Principles of Composite Material Mechanics
`Kane, Likins, and Levinson: Spacecraft Dynam!cs
`Katz and PhJtkin: Low-Speed Aerodynamics: From Wing Theory to Panel Methods
`Matfingly: Elements of, Gas Turbine Propulsion
`Nelson: Flight Stability and Automatic Control
`Peery and Azar: Aircraft Structures
`Rivello: Theory and Analysis of Flight Structures
`Schlichting: Boundary Layer Theory
`white: Viscous Fluid Flow
`Wieseh Spaceflight Dynamics
`
`GE-1014.004
`
`

`
`McGraw-Hill Series in Mechanical Engineering
`
`Consulting Editors
`
`Jack P. Holman, Southern Methodist University
`John R. Lloyd, Michigan State University
`
`Anderson: Computational Fluid
`Dynamics: The Basics with Applications
`Anderson: Modern Compressible Flow:
`With Historical Perspective
`Arora: Introduction to Optimum Design
`Bray and Stanley: Nondestructive
`Evaluation: A Tool for Design,
`Manufacturing, and Service
`Burton: Introduction to Dynamic Systems
`Analysis
`Culp: Principles of Energy Conversion
`Dally: Packaging of Electronic Systems: A
`Mechanical Engineering Approach
`Dieter:. Engineering Design: A Materials
`and Processing Approach
`Doebelin: Engineering Experimentation:
`Planning, Execution, Reporting
`Driels: Linear Control Systems
`Engineering ’
`Eckert and Drake: Analysis of Heat and
`Mass Transfer
`Edwards and McKee: Fundamentals of
`Mechanical Component Design
`Gebhart: Heat Conduction and Mass
`Diffusion
`Gibson: Principles of Composite Material
`Mechanics
`Hamrock: Fundamentals of Fluid Film.
`Lubrication
`Heywood: lnternal Combustion Engine
`Fundamentals
`Hinze: Turbulence
`Holman: Experimental Methods for
`Engineers
`Howell and Buckius: Fundamentals of
`Engineering Thermodynamics
`Hutlon: Applied Mechanical Vibrations
`Juvinalh Engineering Considerations of
`Stress, Strain, and Strength
`Kane and Levinson: Dynamics: Theory
`and Applications
`¯ Kays and Crawford: Convective Heat and
`Mass Transfer ..
`
`Kelly: Fundamentals of Mechanical
`Vibrations
`Kimbrelh Kinematics Analysis and
`Synthesis
`Kreider and Rabh Heating and Cooling of
`Buildings
`Martin: Kinematics and Dynamics of
`Machines
`Mattingly: Elements of Gas Turbine
`Propulsion
`Modest: Radiative Heat Transfer
`Norton: Design of Machinery
`Phelan: Fundamentals of Mechanical
`Design
`Raven: Automatic Control Engineering
`Reddy: An Introduction to the Finite
`Element Method
`Rosenberg and Karnopp: Introductioh to
`Physical Systems Dynamics
`Schlichting: Boundary-Layer Theory
`Shames: Mechanics of Fluids
`Sherman: Viscous Flow
`Shigley: Kinematic Analysis of
`Mechanisms
`Shigley and Mischke: Mechanical
`Engineering Design
`Shigley and Uicker: Theory of Machines
`and Mechanisms
`Stiffier: Design with Microprocessors for
`Mechanical Engineers
`Stoecker and Jones: Refrigeration and Air
`Conditioning
`Turns: An Introduction to Combustion:
`Concepts and Applications
`Ullman: The Mechanical Design Process
`Vanderplaats: Numerical Optimization:
`Techniques for Engineering Design,
`with Applications
`Wark: Advanced Thermodynamics for
`Engineers
`White: Viscous Fluid Flow
`Zeid: CAD/CAM Theory and Practice
`
`GE-1014.005
`
`

`
`ELEMENTS OF
`GAS TURBINE
`PROPULSION
`
`Jack D. Mattingly
`
`Department of Mechanical and
`Manufacturing Engineering
`Seattle University
`
`With a Foreword By
`Hans von Ohain
`
`McGraw-Hill, Inc.
`New York St. Louis San Francisco Auckland Bogot~i Caracas
`Lisbon London Madrid Mexico City Milan Montreal
`New Delhi San Juan Singapore Sydney Tokyo Toronto
`
`GE-1014.006
`
`

`
`ENTS.O ~ ~ZSI:T B EPROPULSION
`
`2 ,?,;C~[5~i’ight @’]996 by’M~Graw2Hill, Inc. All rights reserved. Printed in the United States
`r? " : . ~-~.~f:Americm-Ex~p[ as-p~mitiedunder the United StatesCopyfigfit ’Act of-1976, ho part
`
`.",- .-, ’.’: of this. pubhcatlon,may be,reproduced or d~stnbuted m any form or by any. means or ¯
`--, " store~.~n a data base,or retrieval system;w~thout the prior written permission of the -
`
`GE-1014.007
`
`

`
`CONTENTS
`
`Foreword
`Preface
`List of Symbols
`
`1
`
`Introduction
`1-1
`Propulsion
`1-2 Units and Dimensions
`1-3 Operational Envelopes and Standard Atmosphere
`1-4 Air-Breathing Engines
`1-5 Aircraft Performance
`1-6 Rocket Engines
`Problems
`
`2 Thermodynamics Review
`2-1
`Introduction
`2-2
`Definitions
`2-3
`Simple Compressible System
`2-4
`Equations of State
`2-5
`Basic Laws for a Control Mass System
`Relations between the System and Control Volume
`2-6
`2-7
`Conservation of Mass Equation
`2-8
`Steady Flow Energy Equation
`2-9
`Steady Flow Entropy Equation,
`2-10
`Momentum Equation
`2-11
`Summary of Laws for Fluid Flow
`2-12
`Perfect Gas
`Problems
`
`XV
`
`lv
`
`lix
`
`1
`1
`2
`4
`6
`33
`53
`60
`
`67
`67
`68
`73
`74
`76
`78
`81
`81
`89
`90
`95
`96
`108
`
`xi
`
`GE-1014.008
`
`

`
`xii CONTENTS
`
`3 Compressible Flow
`Introduction
`3-1
`3-2 Compressible Flow Properties
`3-3 Normal Shock Wave
`3-4 Oblique Shock Wave
`Steady One-Dimensional Gas Dynamics
`3-5
`Simple Flows
`¯ 3-6
`3-7
`Simple Area Flow--Nozzle Flow
`3-8
`Simple Heating Flow--Rayleigh Line
`Simple Frictional Flow--Fanno Line
`3-9
`3-10 Summary of Simple Flows
`Problems
`
`4 Aircraft Gas Turbine Engine
`4-1 Introduction
`4-2 " Thrust Equation
`4-3 Note on Propulsive Efficiency
`4-4 Gas Turbine Engine Components
`4-5 Brayton Cycle
`4-6 Aircraft Engine Design
`Problems
`
`5 Parametric¯ Cycle Analysis of Ideal Engines
`Introduction
`5-1
`5-2 Notation
`5-3 Design Inputs
`5-4
`Steps of Engine Parametric Cycle Analysis
`5-5 Assumptions of Ideal Cycle Analysis
`Ideal Ramjet
`5-6
`Ideal Turbojet
`5-7
`5-8
`Ideal Turbojet with Afterburner
`Ideal Turbofan
`5-9
`5-10
`Ideal Turbofan with Optimum Bypass Ratio
`Ideal Turbofan with Optimum Fan Pressure Ratio
`5-11
`5-12
`Ideal Mixed-Flow Turbofan with Afterburning
`5-13 Ideal Turboprop Engine
`5-14
`Ideal Turboshaft Engine with Regeneration
`Problems
`
`6 Component Performance
`6-1
`Introduction
`6-2 Variation in Gas Properties
`6-3 Component Performance
`Inlet and Diffuser Pressure Recovery
`6-4
`6-5
`Compressor and Turbine Efficiencies
`6-6 Burner Efficiency and Pressure Loss
`
`114
`114
`114
`138
`145
`156
`159
`161
`174
`189
`203
`206
`
`213
`213
`213
`223
`224
`233
`236
`237
`
`240
`240
`241
`243
`244
`246
`246
`256
`266
`275
`299
`305
`313
`322
`332
`337
`
`346
`346
`346
`349
`349
`351
`360
`
`GE-1014.009
`
`

`
`ooo
`CONTENTS Xlll
`
`Exit Nozzle Loss
`6-7
`Summary of Component Figures of Merit (Constant c~ Values)
`6-8
`6-9 Component Performance with Variable cp
`Problems
`
`7 Parametric Cycle Analysis of Real Engines
`7-1
`Introduction
`Turbojet
`7-2
`7-3
`Turbojet with Afterburner
`7-4
`Turbofan--Separate Exhaust Streams
`7-5
`Turbofan with Afterburning--Separate Exhaust Streams
`7-6
`Turbofan with Afterburning--Mixed Exhaust Stream
`7-7
`Turboprop Engine
`7-8 Variable Gas Properties
`Problems
`
`8 Engine Performance Analysis
`8-1
`Introduction
`8-2 Gas Generator
`8-3
`Turbojet Engine
`¯ 8-4
`Turbojet with Afterburning
`8-5
`Turbofan Engine--Separate Exhausts and Convergent Nozzles
`8-6
`Turbofan with Afterburning--Mixed-Flow Exhaust Stream
`8-7
`Turboprop Engine
`8-8 Variable Gas Properties
`Problems
`
`9 Turbomachinery
`9-1
`Introduction
`9-2
`Euler’s Turbomachinery Equations
`9-3 Axial-Flow Compressor Analysis
`9-4 Centrifugal-Flow Compressor Analysis
`9-5 Axial-Flow Turbine Analysis
`9-6 Centrifugal-Flow Turbine Analysis
`Problems
`
`10
`
`Inlets, Nozzles, and Combustion Systems
`10-1
`Introduction to Inlets and Nozzles
`10-2
`Inlets
`10-3 Subsonic Inlets
`10-4 Supersonic Inlets
`10-5 Exhaust Nozzles
`10-6
`Introduction to Combustion Systems
`10-7 Main Burners
`10-8 Afterburners
`Problems
`
`361
`361
`363
`369
`
`371
`371
`371
`387
`392
`411
`417
`433
`444
`453
`
`461
`461
`471
`487
`507
`518
`541
`560
`573
`605
`
`615
`615
`616
`618
`676
`683
`742
`748
`
`757
`757
`758
`758
`767
`796
`814
`827
`838
`849
`
`GE-1014.010
`
`

`
`CONTENT~
`
`Appendixes
`A U.S. Standard Atmosphere, 1976
`B Gas Turbine Engine Data
`C Data for Some Liquid Propellant Rocket Engines
`D Air and (CHz)n Properties at Low Pressure
`E Compressible Flow Functions (y = 1.4, 1.33, and 1.3)
`F Normal Shock Functions (’~ = 1.4)
`G Two-Dimensional Oblique Shock Functions (~ = 1.4)
`H Rayleigh Line Flow Functions (,/’=- 1.4)
`I
`Fanno Line Flow Functions (~ = 1.4)
`J Turbomachinery Stresses and Materials
`K About the Software
`
`References
`
`Index
`
`853
`855
`860
`865
`867
`878
`897
`902
`910
`917
`924
`938
`
`945
`
`949
`
`GE-1014.011
`
`

`
`Ix
`
`LIST OF SYMBOLS
`
`FR
`g
`gc
`go
`H
`h
`
`I
`
`K
`L
`M
`
`m
`
`M
`MFP
`MR
`N
`
`F/,b
`P
`
`Ps
`Pt
`PF
`Q
`
`q
`
`R
`R,
`
`RF
`oR
`S
`
`S~
`S
`T
`
`t
`TR
`TSFC
`
`fuel/air ratio; function
`thrust ratio [Eq. (5-56)]
`acceleration of gravity
`Newton’s constant
`acceleration of gravity at sea level
`enthalpy
`enthalpy per unit mass; height
`low heating value of fuel
`impulse function [= PA(1 + ,/M2)]
`specific impulse [Eq. (1-55)]
`constant
`length
`Mach number; momentum
`time rate of change of momentum
`mass
`mass flow rate
`molecular weight
`mass flow parameter
`vehicle mass ratio
`revolutions per minute
`load factor; burning rate exponent.
`number of blades
`pressure
`profile factor
`weight specific excess power
`total pressure
`pattern .factor
`heat interaction
`rate of heat interaction
`heat interaction per unit mass; dynamic pressure
`[=pV2/(2gc)]
`gas constant~ extensive property~ radius; additional drag
`universal gas constant
`radius; burning rate
`range factor [Eq. (1-43)]
`degree of reaction
`uninstalled thrust specific fuel consumption; entropy
`time rate of change of entropy
`wing planform area
`entropy per unit mass; blade spacing
`temperature; installed thrust
`total temperature
`time; airfoil thickness
`throttle ratio [Eq. (8-34)]
`installed thrust specific fuel consumption
`
`GE-1014.012
`
`

`
`LIST OF SYMBOLS
`
`lxi
`
`U
`
`x, y, z
`
`Ze
`Z
`
`a
`/3
`
`F
`
`’ y
`A
`3
`0
`e
`~
`0
`/x
`rl
`¢r
`p
`
`"~
`
`internal energy; blade tangential or rotor velocity
`internal energy per unit mass; velocity
`absolute velocity; volume
`volume per unit mass; velocity
`weight; width
`power
`work interaction per unit mass; velocity
`weight flow rate
`coordinate system
`energy height [Eq. (1-25)]
`Zweifel tangential force coefficient [Eq. (9-97)]
`
`Greek
`
`bypass ratio; angle; coefficient of linear thermal expansion
`angle
`
`/ { 2 ’~ ("/+ 1)1(’1’-- 1)
`: V~/~-~)
`
`; constant
`
`ratio of specific heats; angle
`change
`change; dimensionless pressure (=P/Pref); deviation
`partial differential
`nozzle area ratio; rotor turning angle
`efficiency
`angle; dimensionless temperature (= T/Tref)
`Mach angle
`product
`pressure ratio defined by Eq. (5-3)
`density (=l/v)
`
`sum
`control volume boundary; dimensionless density (=P/Pref);
`tensile stress
`temperature ratio defined by Eq. (5-4); shear stress; torque
`enthalpy ratio defined by Eq. (5=7)
`installation loss coefficient; fuel equivalence ratio; function;
`total pressure loss coefficient
`function; cooling effectiveness; flow coefficient
`angular speed
`
`Subscripts
`
`A
`
`air mass
`air; atmosphere
`
`GE-1014.013
`
`

`
`Ixii
`
`LIST OF SYMBOLS
`
`AB
`¯ add
`b
`C
`c
`DB
`d
`dr
`dry
`
`ext
`F
`f
`
`g
`H
`HP
`h
`i
`int
`
`L
`M
`m
`max
`N
`
`gtac
`0
`
`o
`opt
`P
`P
`pl
`prop
`R
`
`ref
`s
`SL
`SLS
`T
`t
`
`vac
`
`w
`
`afterburner
`additive
`burner or combustor; boattail or afterbody; blade; burning
`core stream
`compressor; corrected; centrifugal; chamber
`duct burner
`diffuser or inlet; disk
`disk/rim interface
`afterburner not operating
`exit; exhaust; earth
`external
`fan stream
`fan; fuel; final
`fan nozzle
`gearing; gas
`high-pressure
`horsepower
`hub
`initial; inside; ideal
`internal
`jet
`low-pressure
`mixer
`mechanical; mean; middle
`corresponding to maximum
`new
`nozzle
`nacelle
`overall; output
`overall; outer
`optimum
`propulsive; products
`propellant
`payload
`propeller
`reference; relative; reactants
`ram; reduced; rim; rotor
`reference condition
`stage; separation; solid; stator
`sea-level
`sea-level static
`thermal
`total; turbine; throat; tip; thermal
`vacuum
`forebody; wing
`
`,?
`
`t
`
`GE-1014.014
`
`

`
`CHAPTER
`
`INTRODUCTION
`
`1-1 PROPULSION
`
`The Random House College Dictionary (Ref. 1) defines propulsion as "the act
`of propelling, the state of being propelled, a propelling force or impulse" and
`defines the verb propel as "to drive, or cause to move, forward or onward."
`From these definitions, we can conclude that the study of propulsion includes
`the study of the propelling force, the motion caused, and the bodies involved.
`Propulsion involves an object to be propelled plus one or more additional
`bodies, called propellant.
`The study of propulsion is concerned with vehicles such as automobiles,
`trains, ships, aircraft, and spacecraft. The focus of this textbook is on the
`propulsion of aircraft and spacecraft. Methods devised to produce a thrust
`force for the propulsion of a vehicle in flight are based on the principle of jet
`propulsion (the momentum change of a fluid by the propulsion system). The
`fluid may be the gas used by the engine itself (e.g., turbojet), it may be a fluid
`available in the surrounding environment (e.g., air used by a propeller), or it
`may be stored in the vehicle and carried by it during the flight (e.g., rocket).
`Jet propulsion systems can be subdivided into two broad categories:
`air-breathing and non-air-breathing. Air-breathing propulsion systems include
`the reciprocating, turbojet, turbofan, ramjet, turboprop, and turboshaft en-
`gines. Non-air-breathing engines include rocket motors, nuclear propulsion
`systems, and electric propulsion systems. We focus on gas turbine propulsion
`systems (turbojet, turbofan, turboprop, and turboshaft engines) in this
`textbook.
`
`GE-1014.015
`
`

`
`2 GAS TURBINE
`
`The material in this textbook is divided into three parts:
`
`¯ Basi( concepts and one-dimensional gas dynamics
`¯ Analysls and performance of air-breathing propulsion systems
`¯ Analysis of gas turbine engine components
`
`This chapter introduces the types of air-breathing and rocket propulsion
`systems and the basic propulsion performance parameters. Also included is an
`introduction to aircraft and rocket performance. The material on aircraft
`performance shows the influence of the gas turbine engine performance on the
`performance of the aircraft system. This material also permits incorporation of
`a gas turbine engine design problem such as new engines for an existing
`aircraft.
`Numerous examples are included throughout this book to help students
`see the .application of a concept after it is introduced. For some students, the
`material on basic concepts and gas dynamics will be a review of material
`covered in other courses they have already taken. For other students, this may
`be their first exposure to this material, and it may require more effort to
`understand.
`
`1-2 UNITS AND DIMENSIONS
`
`Since the engineering world uses both the metric SI and English unit system,
`both will be used in this textbook. One singular distinction exists between the
`English system and SI--the unit of force is defined in the former but derived in
`the latter. Newton’s second law of motion relates force to mass, length, and
`time. It states that the sum of the forces is proportional to the rate of change of
`the momentum (M = mY). The constant of proportionality is 1/go.
`
`~ F :-1 d(mV) 1 dM
`gc dt gc dt
`
`(1-1)
`
`The units for each term in the above equation are listed in Table 1-1 for both
`SI and English units. In any unit system, only four of the five items in the table
`Can be specified, and the latter is derived from Eq. (1-1).
`As a result of selecting g~ = 1 and defining the units of mass, length,
`and time in SI units, the unit of force is derived from Eq. (1-1) as
`
`TABLE 1-1
`Units and dimensions
`
`Unit system
`
`Force
`
`gc
`
`Mass
`
`Lenglh
`
`Time
`
`SI
`Eriglish
`
`1
`Derived
`P0und-force (Ibf) Derived
`
`Kilogram (kg)
`Pound-mass (lbm)
`
`Meter (m)
`Foot (ft)
`
`Second (sec)
`Second (sec)
`
`GE-1014.016
`
`

`
`kilogram-meters per square second (kg. m/sec2), which is called the newton
`(N). In English units, the value of gc is derived from Eq. (1-1) as
`
`INTRODUCTION 3
`
`gc = 32.174 ft ¯ lbm/(Ibf ¯ sec2) ]
`
`Rather than adopt the convention used in many recent textbooks of developing
`material or use with only SI metric units (go = 1), we will maintain gc in all our
`equations. Thus gc will also show up in the equations for potential energy (PE)
`and kinetic energy (KE):
`
`PE - mgz
`gc
`
`KE-
`
`mV2
`
`2g~
`
`The total energy per unit mass e is the sum of the specific internal energy
`u, specific kinetic energy ke, and specific potential energy pe.
`
`-
`V2
`e u+ke+pe=u+--+gz
`2go g~
`
`There are a multitude of engineering units for the quantities of interest in
`propulsion. For example, energy can be expressed in the SI unit of joule
`(1 J = 1 N. m), in British thermal units (Btu’s), or in foot-pound force (ft- lbf).
`One must be.able to use the available data in the units provided and convert
`the, units when required. Table 1-2 is a unit conversion table provided to help
`you in your endeavors.
`
`TABLE 1-2
`Unit conversion table
`
`Length
`
`Area
`
`Volume
`
`Time
`Mass
`
`Density
`Force
`
`Energy
`
`1 m = 3.2808 ft = 39.37 in
`1 km = 0.621 mi
`1 mi = 5280 ft = 1.609 km
`1 nm = 6080 ft = 1.853 km
`i m2 = 10.764 ft2
`i cm2 = 0.155 in2
`1 gal = 0.13368 ft3 = 3.785 L
`1 L = 10-3 m3 = 61.02 in3
`1 hr = 3600 sec = 60 rain
`1 kg = 1000 g = 2.2046 lbm = 6.8521 × 10-2 slug
`1 slug = 1 Ibf. sec2]ft = 32.174 lbm
`I slug/ft3 = 512.38 kg/m3
`1N = lkg. m/sec2
`1 Ibf = 4.448 N
`1J= 1N. m = 1 kg- mZ/secz
`1 Btu = 778.16 ft ¯ lbf = 252 cal = 1055 J
`1 cal = 4.186 J
`1 kJ = 0.947813 Btu = 0.23884 kcal
`
`GE-1014.017
`
`

`
`4 GAS TURBINE
`
`Power
`
`Pressure (stress)
`
`Energy per unit mass
`Specific heat
`Temperature
`
`i
`
`Temperature change
`Specific thrust
`Specific power
`Thrust specific fuel consumption (TSFC)
`Power specific fuel consumption
`Strength/weight ratio (~r/p)
`
`1 W = 1 J/sec = i kg. m2/sec3
`1 hp = 550 ft. lbf/sec = 2545 Btu/hr = 745.7 W
`1 kW = 3412 Btu/hr = 1.341 hp
`i atm = 14.696 lb/in2 or psi = 760 torr = 101,325 Pa
`I arm = 30.0 inHg = 407.2 inH20
`i ksi = 1000 psi
`I mmHg = 0.01934 psi = 1 torr
`1 Pa = 1 N/m2
`1 inHg = 3376.8 Pa
`1 kJ/kg = 0.4299 Btu/lbm
`1 kJ/(kg ¯ °C) = 0.23884 Btu/(lbm ¯ °F)
`1 K = 1.8°R
`K = 273.15 + °C
`°R = 4~9.69 + °F
`1°C = 1.8°F
`1 lbf/(lbm/sec) = 9.8067 N/(kg/sec)
`i hp/(lbm/sec) = 1.644 kW/(kg/sec)
`1 lbm/(lbf ¯ hr) = 28.325 mg/(N - sec)
`1 lbm/(hp - hr) = 168.97 mg/(kW, sec)
`i ksi/(slug/ft3) = 144 ft2/sec~ = 13.38 m~/sec~
`
`1-3 OPERATIONAL ENVELOPES
`AND STANDARD ATMOSPHERE
`
`Each engine type will operate only within a certain range of altitudes and
`Mach numbers (velocities). Similar limitations in velocity and altitude exist for
`airframes. It is necessary, therefore, to match airframe and propulsion system
`capabilities. Figure 1-1 shows the approximate velocity and altitude limits, or.
`corridor of flight, within which airlift vehicles can operate. The corridor is
`bounded by a lift limit, a temperature limit, and an aerodynamic force limit. The
`lift limit is determined by the maximum level-flight altitude at a given velocity~
`The temperature limit is set by the structural thermal limits of the material
`used in construction of the aircraft. At any given altitude, the maximum
`velocity attained is temperature-limited by aerodynamic heating effects. At
`lower altitudes, velocity is limited by aerodynamic force loads rather than by
`temperature.
`The operating regions of all aircraft lie within the flight corridor. The
`operating region..0f a particular aircraft within the corridor is determined by.
`aircraft design, but it is a very small portion of the overall corridor.
`Superimposed on the flight corridor in Fig. 1-1 are the operational envelopes
`of various powered aircraft. The operational limits of each propulsion system
`are determined by limitations of the components of the propulsion system and
`are shown in Fig. 1-2.
`The analyses presented in this text use the properties of the atmosphere
`to determine both engine and airframe performance. Since these properties
`vary with location, season, time of day, etc., we will use the U.S. standard
`
`GE-1014.018
`
`

`
`INTRODUCTION 5
`
`Lift (stall) limit
`
`X~Upper limit ~1
`turbojet f I
`
`turbofan/
`
`¯
`
`/
`
`*X \
`
`/ Tem erature
`/’~"’- limitp
`~, I
`~
`Helicopter
`Upper-limi~ /
`turboprop
`I
`I /
`Limited by
`[
`~/
`aerodynamic
`; f
`p~ sPtP2~ -~ ~nr~i tn ~’~’!
`force loads
`I
`I 1/
`
`FIGURE 1-1
`Flight limits.
`
`Mach number
`
`atmosphere (Ref. 2) to give a known foundation for our analyses. Appendix A
`gives the properties of the U.S. standard atmosphere, 1976, in both English
`and SI units. Values of the pressure P, temperature T, density p, and speed of
`sound a are given in dimensionless ratios of the property at altitude to its
`value at sea level (SL), (the reference value). The dimensionless ratios of
`pressure,, temperature, and density are given the symbols 6, 0, and o5
`
`-’~ Piston engine and propeller
`
`~ Turboprop
`
`Turbofan
`
`Turbojet
`
`Ramjet
`
`1 2 3 4
`Flight Mach number
`
`FIGURE 1-2
`Engine operational limits.
`
`t Piston engine and propeller
`
`~ Turboprop
`
`Turbofan
`
`Turbojet
`
`Ramjet
`
`20
`
`40
`60 80 100
`Altitude (1000 fl)
`
`GE-1014.019
`
`

`
`6 GAS TURBINE
`
`respectively. These ratios are defined as follows:
`
`P
`
`T
`
`0-~_
`
`Pref
`
`(1-2)
`
`(1-3)
`
`(1-4)
`
`The reference values of pressure, temperature, and density are given for each
`unit system.at the. end of its property table.
`For nonstandard conditions such as a hot day, the normal procedure is to
`use the standard pressure and correct the density, using the perfect gas
`relationship cr = 5/0. As an example, we consider a 100°F day at 4-kft altitude.
`From App. A, we have ~ = 0.8637 for the 4-kft altitude. We calculate 0, using
`the 100°F temperature; 0 = T/Tra= (100 + 459.7)/518.7 = 1.079. Note that
`absolute temperatures must be used in calculating 0. Then the density ratio is
`calculated using o- = 3/0 = 0.8637/1.079 = 0.8005.
`
`1-4 AIR-BREATHING ENGINES
`
`The turbojet, turbofan, turboprop, turboshaft, and ramjet engine systems are
`discussed in this part of Chap. 1. The discussion of these engines is in the
`context of providing thrust for aircraft. The listed engines are not all the
`engine types (reciprocating, rockets, combination types, etc.) that are used in
`providing propulsive thrust to aircraft, nor are they used exclusively on
`aircraft. The thrust of the turbojet and ramjet results from the action of a fluid
`jet leaving the engine; hence, the name jet engine is often applied to these
`engines. The turbofan, turboprop, and turboshaft engines are adaptations of
`the turbojet to supply thrust or power ~hrough the use of fans, propellers, and
`shafts.
`
`Gas Generator
`
`The "heart" of a gas turbine type of engine is the gas generator. A schematic
`diagram of a gas generator is shown in Fig. 1-3. The compressor, combustor,
`and turbine are the major components of the gas generator which is common
`to the turbojet, turbofan, turboprop, and turboshaft engines. The purpose of a
`gas generator is to supply high-temperature and high-pressure gas.
`
`GE-1014.020
`
`

`
`Gas generator -
`
`INTRODUCTION
`
`T
`
`Compressor
`
`C0mbustor
`
`3
`
`FIGU~iE 1-3
`Schematic diagram of ga~ generator.
`
`The Turbojet
`
`Byadding ah inlet and a nozzle to the gas generator, a turbojet engine can be
`constructe.d. A schematic diagram of a simple turbojet is shown in Fig. 1-4a,
`and a turbbjet with afterburner is shown in Fig. 1-4b. in the aiialysis of a
`turbojet engine, the major components are treated as sections. Also shown in
`Figs. 1-4a and 1-4b are the station numbers for each section.
`
`Gasgen~rator
`
`l~let
`
`Low-pressure
`compressor
`
`Nozzle
`
`P
`T
`4 4.5 5 8
`
`HPT = High-pi’es~re turbine
`LPT = Low-pressure turbine
`
`FIGURE 1-4a
`Schematic diagram of a turbojet (dual axial compressor and turbine).
`
`GE-1014.021
`
`

`
`8 GAS TURBINE
`
`Gas generator
`
`Spray bar
`
`Flame holder
`
`j
`
`Nozzle
`
`<
`< ~
`
`Afterburner
`
`Inlet Low-
`pressure
`compressor
`
`2.5
`
`5
`
`4
`4.5
`
`8
`
`HPT = High-pressure turbine
`LPT = Low-pressure turbine
`
`FIGURE 1-4b
`Schematic diagram of a turbojet with afterburner.
`
`The turbojet was first used as a means of aircraft propulsion by von
`Ohain (first flight August 27, 1939) and Whittle (first flight May 15, 1941). As
`development proceeded, the turbojet engine became more efficient and
`replaced some of the piston engines. A photograph of the J79 turbojet with
`afterburner used in the F-4 Phantom II and B-58 Hustler is shown in Fig. 1-5.
`
`FIGURE 1-5
`General Electric J79 turbojet with afterburner. (Courtesy of,General Electric Aircraft Engines.)
`
`GE-1014.022
`
`

`
`INTRODUCTION 9
`
`The adaptations of the turbojet in the form of turbofan, turboprop, and
`turboshaft engines came with the need for more thrust at relatively low speeds.
`Some characteristics of different turbojet, turbofan, turboprop, and turboshaft
`engines are included in App. B.
`The thrust of a turbojet is developed by compressing air in the inlet and
`compressor, mixing the air with fuel and burning in the combustor, and
`expanding the gas stream through the turbine and nozzle. The expansion of
`gas through the turbine supplies the power to turn the compressor. The net
`thrust delivered by the engine is the result of converting internal energy to
`kinetic energy.
`The pressure, temperature, and velocity variations through a J79 engine
`are shown in Fig. 1-6. In the compressor section, the pressure and temperature
`increase as a result of work being done on the air. The temperature of the gas
`is further increased by burning in the combustor. In the turbine section, energy
`is being removed from the gas stream and converted to shaft power to turn the
`compressor. The energy is removed by an expansion process which results in a
`decrease of temperature and pressure, In the nozzle, the gas stream is further
`expanded to produce a high exit kinetic energy. All the sections of the engine
`must operate in such a way.as to efficiently produce the greatest amount of
`thrust for a minimum of weight.
`
`200
`
`2400 ~- 2000 r
`
`175
`
`2100b 1600].
`
`150
`
`18001- 1200~
`
`125
`
`1500b 1000~
`
`12001- 8001,
`
`75
`
`9001- 6001-
`
`50
`
`25
`
`¯ 300~ 200[
`
`0’
`
`0L
`
`0t
`
`Afterburning
`- operation
`
`-- Military
`
`\
`
`Compressor
`
`’l’ Combustorl Turbine 1"
`
`Exhaust
`
`Exhaust gases
`
`FIGURE 1-6
`Property variation thi’ough the General Electric J79 afterburning turbojet engine.
`
`GE-1014.023
`
`

`
`10 GAS TURBINE
`
`The Turbofan
`
`The turbofan engine consists of an inlet, fan, gas generator, and nozzle. A
`schematic diagram of a turbofan is shown in Fig. !-7. In the turbofan, a portion
`of the turbine work is used to supply power to the fan. Generally the ~urbofan
`engine is more economical and efficient than the turbojet engine in a limited
`realm of fiight~ The thrust specificfuel consumption (TSFC, or fuel mass flow
`rate per un!t. thrust) is lower for turbofans and indicates a more economical
`operation: The turbofan also accelerates a larger mass of air to a lower v~locity
`than a turbojet for a higher propulsive efficiencY. The frontal area of a
`turbofan is quite large compared to that of a turbojet, and for this reason more
`drag and more weight result. The fan diameter is also limited aerodynamically
`when compressibility effects Occur. Severa! of the current high-bypass-ratio
`turbofanengines used in subsonic aircraft are sl~own in Figs. 1-8a through 1-8f.
`Figures 1-9a and 1-9b show the Pratt & Whitney F100 turbofan and the
`Generai Electric Fl10 turbofan, respectively. These afterburning turbofan
`engines are used in the F15 Eagle and F16 Falcon supersonic fighter aircraft. In
`this turbofan, the bypass stream is mixed with the core stream before passing
`through a common afterburner and exhaust nozzle.
`
`The Turboprop and Turboshaft
`
`A gas generator that drives a propeller is a turboprop engine. The expansion of
`gas through the turbine SUpplies the energy required tO turn the propeller..A
`
`13
`
`17
`18
`
`Bypass
`
`Low-pressure
`
`Nozzle
`
`Inlet
`
`High-
`pressure
`compressor
`
`H
`
`L
`P
`T
`
`2.5
`
`3
`
`4 4.5
`
`5
`
`HPT = High-pressure turbine
`LPT = Low-pressure turbine
`
`FIGURE 1-7
`Schematic diagram o[ a high-bypass-ratio turbofan.
`
`GE-1014.024
`
`

`
`FIGURE 1-Sa
`Pratt & Whitney JT9D turbofan. (Courtesy of Pratt & Whitney.)
`
`GE-1014.025
`
`

`
`12 GAS TURBINE
`
`FAN
`
`LOW PRESS~JRE
`COMPRESSOR
`
`HIGH PRESSURE
`COMPRESSOR
`
`HIGH PRESSURE
`TURBINE
`
`COMBUSTION
`CHAMBER
`
`LOW PRESSURE
`TURBINE
`
`/
`
`/
`
`ACCESSORY
`SECTION
`
`TURBINE
`BLADES
`
`TURBINE
`EXHAUST
`CASE
`
`INLET
`CASE
`
`FIGURE 1-8b
`Pratt & Whitney PW4000 turbofan. (Courtesy of Pratt & Whitney.)
`
`GE-1014.026
`
`

`
`INTRODUCTION 13
`
`FIGURE 1-8c
`General Electric CF6 turbofan. (Courtesy of General Electric Aircraft Engines.)
`
`FIGURE 1-Sd
`Rolls-Royce RB-211-524G/H turbofan. (Courtesy of Rolls-Royce.)
`
`GE-1014.027
`
`

`
`14 GAS TURBINE
`
`FIGURE 1-8e
`General Electric GE90 turbofan. (Courtesy of General Electric Aircraft Engines.)
`
`e
`
`FIGURE 1-8f
`SNECMA CFM56 turbofan. (Courtesy of SNECMA.)
`
`GE-1014.028
`
`

`
`INTRODUCTION
`
`FIGURE 1-ga
`Pratt & Whitney F100-PW-229 afterburning turbofan. (Courtesy of Pratt & Whitney.)
`
`schematic diagram of the turboprop is shown in Fig. 1-10a. The turboshaft
`engine is similar to the turboprop except that power is supplied to a shaft
`rather than a propeller. The turboshaft engine is used quite extensively for
`supplying power for helicopters. The turboprop engine may find application in
`VTOL (vertical takeoff and landing) transporters. The limitations and advan-
`tages of the turboprop are those of the propeller. For low-speed flight and
`short-field takeoff, the propeller has a performance advantage. At speeds
`approaching the speed of sound, compressibility effects set in and the propeller
`loses its aerodynamic efficiency. Due to the rotation of the propeller, the
`propeller tip will approach the speed of sound before the vehicle approaches
`
`FIGURE 1.gb"~
`General Electric F110-GE-129 afterburning turbofan. (Courtesy of General Electric Aircraft.
`Engin es. )
`
`GE-1014.029
`
`

`
`16 GAS TURBINE
`
`Propeller - , Gas generator " ’
`
`FIGURE 1-10a
`
`Schematic diagram of a turboprop.
`
`FIGURE 1-10b
`Allison T56 turboshaft. (Courtesy of Allison Gas Turbine Division.)
`
`Diffuser
`
`Air inlet
`
`Three-stage
`axial flow
`
`Accessory
`
`drive
`
`Reduction
`gearbox
`
`Propeller
`driveshan
`
`Free (power turbine)
`
`Combustion
`chamber
`
`Compression
`turbine
`
`Centrifugal
`compressor
`
`FIGURE 1-10c
`Canadian Pratt & Whitney PT6 turboshaft. (Courtesy of Pratt & Whitney of Canada.)
`
`GE-1014.030
`
`

`
`the speed of sound. This compressibility effect when one approaches the speed
`of sound limits the design of helicopter rotors and propellers. At high subsonic
`speeds, the turbofan engine will have a better aerodynamic performance than
`the turboprop since the turbofan is essentially a ducted turboprop. Putting a
`duct or shroud around a propeller increases its aerodynamic perfgrmance.
`Examples of a turboshaft engine are the Canadian Pratt & Whitney PT6 (Fig..
`1-10c), used in many small commuter aircraft, and the Allison T56 (Fig.
`1-10b), used to power the C-130 Hercules and the P-3 Orion.
`
`The Ramjet
`
`The ramjet engine consists of aninlet, a combustion zone, and a nozzle. A
`schematic diagram of a ramjet is shown in Fig. 1-11. The ramjet does not have
`the compressor and turbine as the turbojet does. Air enters the inlet where it is
`compressed and then enters the combustion zone where it is mixed with the
`fuel and burned. The hot gases are then expelled through the nozzle,
`developing thrust. The operation of the" ramjet depends upon the inlet to
`decelerate the incoming air to raise the pressure in the combustion zone. The
`pressure rise makes it possible for the ramjet to operate. The higher the
`velocity of the incoming air, the greater the p