Mattingly J.D., Heiser W.H., Pratt D.T. Aircraft Engine Design
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Chapter 4. Engine Selection: Parametric Cycle Analysis ......... 95
4.1 Concept ........................................ 95
4.2 Design Tools ..................................... 96
4.3 Finding Promising Solutions .......................... 117
4.4 Example Engine Selection: Parametric Cycle Analysis ........ 126
References ...................................... 137
Chapter 5. Engine Selection: Performance Cycle Analysis ........ 139
5.1 Concept ........................................ 139
5.2 Design Tools ..................................... 140
5.3 Component Behavior ............................... 163
5.4 Example Engine Selection: Performance Cycle Analysis ....... 172
References ..................................... 187
Chapter 6. Sizing the Engine: Installed Performance ............ 189
6.1 Concept ........................................ 189
6.2 Design Tools ..................................... 192
6.3 AEDsys Software Implementation of Installation Losses ....... 206
6.4 Example Installed Performance and Final Engine Sizing ....... 207
6.5 AAF Engine Performance ............................ 220
References ...................................... 229
Part II Engine Component Design
Chapter 7. Engine Component Design: Global and Interface
Quantities .......................................... 233
7.1 Concept ........................................ 233
7.2 Design Tools ..................................... 234
7.3 Engine Systems Design ............................. 238
7.4 Example Engine Global and Interface Quantities ............ 241
Reference ....................................... 251
Chapter 8. Engine Component Design: Rotating
Turbomachinery ..................................... 253
8.1 Concept ........................................ 253
8.2 Design Tools ..................................... 254
8.3 Example AAF Engine Component Design: Rotating
Turbomachinery .................................. 299
References ...................................... 323
Chapter 9. Engine Component Design: Combustion Systems ...... 325
9.1 Concept ........................................ 325
9.2 Design Tools--Main Burner .......................... 368
9.3 Design Tools--Afterburners .......................... 384
9.4 Example Engine Component Design: Combustion Systems ..... 394
References ...................................... 416
Chapter
10
.
Engine Component Design: Inlets and Exhaust
Nozzles
........................................
419
........................................
10.1 Concept 419
..........................................
10.2 Inlets 419
10.3 Exhaust Nozzles
.................................. 461
10.4 Example Engine Component Design: Inlet and Exhaust Nozzle
.
.
483
......................................
References 504
Epilogue
........................................
507
Appendix A: Units and Conversion Factors
...................
509
Appendix B: Altitude Tables
.............................
511
Appendix C: Gas lbrbine Engine Data
......................
519
Appendix D: Engine Performance: Theta Break and Throttle
Ratio
.............................................
523
Appendix E: Aircraft Engine Efficiency and Thrust Measures
.....
537
Appendix F:
Compressible Flow Functions for Gas with Variable
Specific Heats
.......................................
547
..................
Appendix G: Constant-Area Mixer Analysis
551
Appendix H: Mixed Flow Turbofan Engine Parametric
Cycle Analysis Equations
...............................
557
Appendix I:
Mixed Flow Turbofan Engine Performance
Cycle Analysis Equations
...............................
563
Appendix
J:
High Bypass Ratio lbrbofan Engine Cycle Analysis
...
569
Appendix
K:
lbrboprop Engine Cycle Analysis
................
589
Appendix
L:
Propeller Design Tools
........................
609
Appendix
M:
Example Material Properties
...................
623
Appendix
N:
lbrbine Engine Life Management
................
635
Appendix
0:
Engine Controls
.............................
663
Appendix P: Global Range Airlifter (GRA) RFP
...............
679
Index
...............................................
681
Acknowledgments
The writing of the second edition of Aircraft Engine Design began as soon as the
first edition was published in 1987. The ensuing 15 years of evolutionary changes
have created an altogether new work. This could hardly have been done without
the help of many people and organizations, the most important of which will be
noted here.
We are especially indebted to Richard J. Hill and William E. Koop of the
Turbine Engine Division of the Propulsion Directorate of the U.S. Air Force Wright
Laboratories for their financial support and enduring dedication to and guidance
for this project. We hope and trust that this textbook fulfills their vision of a fitting
contribution of the Wright Laboratories to the celebration of the 100th anniversary
of the Wright Brothers' first flight. Our debt in this matter extends to Dr. Aaron
R. Byerley of the Department of Aeronautics of the U.S. Air Force Academy for
his impressive personal innovative persistence that made it possible to execute an
effective contract.
The contributions of uniquely qualified experts provide a valuable new dimen-
sion to the Second Edition. These include Appendix N on Turbine Engine Life
Management by Dr. William D. Cowie and Appendix O on Engine Controls by
Charles A. Skira (with Timothy J. Lewis and Zane D. Gastineau). It is our pleasure
to have worked with them and to be able to share their knowledge with the reader.
Many of our insights were generated by and our solutions tested by the hundreds
of students that have withstood the infliction of our constantly changing material
over the decades. It has been our special privilege to share the classroom with
them, many of whom have assumed mythic proportions over time. The second
edition is enormously better because of them, and so are we.
The generous Preface was provided by our dear friend and mentor, and coauthor
of the first edition, retired U.S. Air Force Brig. Gen. Daniel H. Daley. His inquiring
spirit, as well as his love of thermodynamics, still inhabit these pages.
The AIAA Education Series and editorial staff provided essential support to the
publication of the second edition. Dr. John S. Przemieniecki, Editor-in-Chief of
the AIAA Education Series, who accepted the project, and Rodger S. Williams,
publications development, and Jennifer L. Stover, managing editor, who took care
of the legal, financial, and production arrangements, are especially deserving of
mention. We have been blessed with the steady and comforting support of our
constant friend and comrade Norma J. Brennan, publications director.
Finally, we believe it is very important that we record our gratitude to our wives
Sheila Mattingly, Leilani Heiser, and Marilyn Pratt. By combining faith, love,
patience, and a sense of humor, they have unflaggingly supported us throughout
this endeavor and we are eternally in their debt.
xvii
A
AB
AOA
AR
a
a
b
BCA
BCM
CD
c;
CDR
CDRC
CDO
Cc
c*~
Cj
C2
C
D
d
e
exp
f~
g
gc
go
h
K1
K2
K'
K"
kobs
kTD
kTo
L
In
M
M*
N
Nomenclature (Chapters 1-3)
= area
= afterburner
= angle of attack, Fig. 2.4
= aspect ratio
= speed of sound
= quantity in quadratic equation
= quantity in quadratic equation
= best cruise altitude
= best cruise Mach number
= coefficient of drag, Eq. (2.9)
= coefficient of drag at maximum
L/D,
Eq. (3.27a)
= coefficient of additional drags
= coefficient of drag for drag chute
= coefficient of drag at zero lift
= coefficient of lift, Eq. (2.8)
= coefficient of lift at maximum
L/D,
Eq. (3.27b)
= coefficient in specific fuel consumption model, Eq. (3.12)
= coefficient in specific fuel consumption model, Eq. (3.12)
= quantity in quadratic equation
= drag
= infinitesimal change
= planform efficiency factor
= exponential of
= fuel specific work, Eq. (3.8)
= acceleration
= Newton's gravitational constant
= acceleration of gravity
= height
= coefficient in lift-drag polar equation, Eq. (2.9)
= coefficient in lift-drag polar equation, Eq. (2.9)
= inviscid drag coefficient in lift-drag polar equation, Eq. (2.9)
= viscous drag coefficient in lift-drag polar equation, Eq. (2.9)
= velocity ratio over obstacle, Eq. (2.36)
= velocity ratio at touchdown,
(VTD = kTD VSTALL)
= velocity ratio at takeoff, Eq. (2.20)
= lift
= natural logarithm of
= Mach number
= best cruise Mach number
= number of turns
xix
XX
n ~
P =
P~ =
P~ =
q =
R =
r ~-
S =
S ~
T =
TR =
TSFC =
t
u
V =
W =
Ze
~ =
F =
y =
A =
~ =
c ~
0 =
OCL =
oo =
00break =
A
tz =
1-I
=
if
p =
E =
~o =
f2 =
Subscripts
avg =
B =
BCA =
CAP =
load factor, Eq. (2.6)
pressure
total pressure, Eq. (1.2)
weight specific excess power, Eq. (2.2b)
dynamic pressure, Eq. (1.6)
additional drags; gas constant
radius
wing planform area
distance
installed thrust; temperature
total temperature, Eq. (1.1)
throttle ratio, Eq. (D.6)
installed thrust specific fuel consumption, Eq. (3.10)
time
total drag-to-thrust ratio, Eq. (3.5)
velocity
weight
energy height, Eq. (2.2a)
installed thrust lapse, Eq. (2.3)
instantaneous weight fraction, Eq. (2.4)
empty aircraft weight fraction (=
WE/WTO)
ratio of specific heats
finite change
dimensionless static pressure (see Appendix B)
dimensionless total pressure, Eq. (2.52b)
infinitesimal quantity
dimensionless static temperature (see Appendix B)
angle of climb
dimensionless total temperature, Eq. (2.52a)
theta break, 00 where engine control system sets simultaneous maxima
of
Tt4
and zrc. (see Appendix D)
wing sweep angle
coefficient of friction
drag coefficient for landing, Eq. (2.32)
drag coefficient for takeoff, Eq. (2.24)
mission leg weight fraction, Eq. (3.46)
density
summation
dimensionless static density (see Appendix B)
angle of thrust vector to wing chord line, Fig. 2.4
angular velocity
average
braking
best cruise altitude
combat air patrol
xxi
CL
CRIT
c/4
D
dry
E
F
FR
f
G
i
L
max
mid
min
obs
P
PE
PP
R
SL
STALL
std
TD
TO
TR
wet
A--+ J
a---~C
1--+14
= climb
= critical
= quarter chord
= drag
= without aflerburning
= empty
= fuel
= free roll
= final
= ground roll
= initial
= landing; lift
= maximum
= mid point
= minimum
= obstacle
= payload
= expended payload
= permanent payload
= rotation
= sea level static
--- corresponding to stall
= standard day
= touchdown
= takeoff
= transition
= with afterburning
= mission segments
= integration intervals
= mission phases
Nomenclature (Chapters 4-10 and Appendices)
A = area; pre-exponential factor, Eq. (9.25)
AR
= aspect ratio; area ratio, Eq. (9.61)
a = speed of sound; axial interference factor, Fig. L.4
a = constant in swirl velocity equation, Eq. (8.24)
ai
= speed of sound at station i
a' = rotational interference factor, Fig. L.4
B = ratio of Prandtl mixing length to shear later width, Eq. (9.53);
afterburner blockage
D/H,
Eq. (9.87)
BCA
= best cruise altitude
BCM
= best cruise Mach number
b = constant in swirl velocity equation, Eq. (8.24)
C = constant
CA
= nozzle angularity coefficient, Eq. (10.24)
Co
= coefficient of drag; nozzle discharge coefficient, Eq. (10.22)
Cfg
= nozzle gross thrust coefficient, Eq. (10.21)
CL ---- coefficient of lift
Cp = pressure recovery coefficient, Eq. (9.62); power correlation
parameter, Eq. (L. 18)
C~, = ideal power coefficient, Eq. (L.9)
Cr
= thrust correlation parameter, Eq. (L. 17)
C~. = ideal thrust coefficient, Eq. (L.8)
CTOH =
power takeoff shaft power coefficient for high-pressure spool,
Eq. (4.21b)
CTOL =
power takeoff shaft power coefficient for low-pressure spool,
Eq. (4.22b)
Cv
= nozzle velocity coefficient, Eq. (10.23)
C~ = shear layer growth constant, Eq. (9.54)
c = airfoil chord
cp
-- specific heat at constant pressure
D = diameter; drag; diffusion factor, Eq. (8.1)
Dadd
= additive drag, Eq. (6.5)
DSF
= disk shape factor, Eq. (8.68)
d = infinitesimal change
E = modulus of elasticity
ei =
polytropic efficiency of component i
exp = exponential of
F = uninstalled thrust, Eq. (4.1)
f = fuel-to-air mass flow ratio
g¢ = Newton's gravitational constant
go ---- acceleration of gravity
xxii
xxiii
H = height; enthalpy of a mixture of gases, Eq. (9.8)
HP = horsepower
h ---- altitude; static enthalpy
her = Heating value of fuel
hr = height of rim
hti = total enthalpy at station i
I = impulse function, Eq. (1.5); air loading, Eq. (9.31)
IMS = integral mean slope, Eq. (6.11)
J = ratio ofjet-to-crossflow momentum flux or dynamic pressure,
Eq. (9.40); advance ratio, Eq. (L.20)
k j,, k-j = forward, reverse rate constant for jth reaction, Eqs. (9.14)
and (9.15)
L = length
~. = natural logarithm of
M = Mach number; mean molecular weight
MFP = mass flow parameter, Eq. (1.3)
MFp = static pressure mass flow parameter, Eq. (1.4)
tn = mass flow rate
?:nci
=
corrected mass flow rate at station i, Eq. (5.23)
N = rotational speed (rpm); number of moles, Eq. (9.26); number
of holes, Eq. (9.113 ) and (9.118); number of nozzle
assemblies, Eq. (9.105)
NB = number of blades
Nci = corrected engine speed at station i, Eq. (5.24)
N/4 = rotational speed of high-pressure spool
NL = rotational speed of low-pressure spool
n = number; exponent
ni = mass-specific mole number of ith species
nm
=
sum of mole number in mixture
P = pressure; power
Pe = external pressure
Pi -- pressure at station i
Pr = reduced pressure, Eq. (4.3c)
PTO = shaft power takeoff
eti
=
total (or stagnation) pressure at station i
P~ = wetted perimeter of duct
Q = torque
q = dynamic pressure, Eq. (1.6)
R = gas constant
R ---- universal gas constant
Rj = forward volumetric rate of j th reaction, Eq. (9.14)
RRf = volumetric reaction rate of fuel, Eq. (9.24)
r = radius; shear layer velocity ratio, Eq. (9.52)
S = uninstalled thrust specific fuel consumption, Eq. (4.2)
S' = swirl number of primary air swirler, Eq. (9.48)
s = entropy; spacing; shear layer density ratio, Eq. (9.55)
T ---- temperature
TAFT = adiabatic flame temperature, Fig. 9.3, Eq. (9.23)
xxiv
Tact
~
TR =
TSF =
Tti =
tBO =
t~ =
U =
U
V =
g r
v
W =
W~ =
¢v, =
X =
X ~
Y =
Z =
Ol ~
Ol !
Otsw
t l/
a 6, ot 6 =
=
fib =
F =
y =
A =
Ah~ =
~ =
~c
~t =
E
E T
E l
E 2
?~i ~--
~70 =
fiR =
~7f~spec =
activation temperature, Eq. (9.24)
throttle ratio, Eq. (D.6)
thrust scale factor (Section 6.3)
total (or stagnation) temperature at station i
residence time or stay time at blowout, Eqs. (9.76) and (9.129)
residence time or stay time, Eqs. (9.76) and (9.129)
velocity component in direction of flow
axial or throughflow velocity
velocity; volume, Eq. (9.19)
turbine reference velocity, Eq. (8.38)
tangential velocity
weight; thickness; width
power absorbed by the compressor
power produced by the turbine
axial component of distance along jet trajectory, Fig. 9.14,
Eq. (9.40)
axial location
radial component of distance along jet trajectory, Fig. 9.14,
Eq. (9.40)
mole fraction of ith species, Eq. (9.25)
Zweifel coefficient
engine bypass ratio, Eq. (4.8a); angle; coefficient of thermal
expansion; area fraction, Eq. (9.108)
mixer bypass ratio, Eq. (4.8f)
off-axis turning angle of swirler blades, Eq. (9.48)
stoichiometric coefficients of ith species in j th reaction, Eq. (9.13)
bleed air fraction, Eq. (4.8b); angle
blade angle
function defined by Eq. (8.7)
ratio of specific heats; angle
finite change
enthalpy of formation of ith species, Eq. (9.7) and Table 9.1
small change in; dimensionless static pressure (see Appendix B);
time-mean width of shear layer, Figs. 9.12 and 9.19, Eq. (9.54)
exit deviation of compressor blade, Eq. (8.18)
dimensionless total pressure at station i, Eq. (5.21)
time-mean width of mixing layer, Eqs. (9.37) and (9.58)
exit deviation of turbine blade, Eq. (8.55)
combustion reaction progress variable, Eq. (9.21)
rate of dissipation of turbulence kinetic energy, Eq. (9.74)
cooling air #1 mass flow rate, Eq. (4.8c)
cooling air #2 mass flow rate, Eq. (4.8d)
adiabatic efficiency of component i
engine overall efficiency of engine, Eq. (E.3)
engine propulsive efficiency of engine, Eq. (E.4)
inlet total pressure recovery (Section 10.2.3.2)
mil spec inlet total pressure recovery, Eq. (4.12b~l)
engine thermal efficiency of engine, Eq. (E.4)
0
Oi
Oobreak
n
~r
P
(7
=
=
=
=
=
=
XXV
~blade =
ac =
(9" D
(7" R =
tTtr
~to =
a. =
ri =
rr =
~ZAB =
cb =
4) =
~inlet =
/)nozzle =
7, =
~2 =
°R c
OR t _~_
Subscripts
A =
AB =
A/C =
add =
avail =
b =
bl =
bp
=
break =
C =
C =
CC =
ce
cH =
dimensionless static temperature ratio (see Appendix B); angle
dimensionless total temperature at engine station i, Eq. (5.22)
theta break, 00 where engine control system sets simultaneous maxima of
Tt 4
and nc (see Appendix D)
weight fraction, Eq. (3.46)
total pressure ratio of component i
isentropic freestream recovery pressure ratio, Eq. (4.5b)
density
solidity; stress; static density ratio (see Appendix B); time-mean
conical half-angle of round jet, Fig. 9.12, Eq. (9.37)
average blade stress, Eq. (8.66)
rotor airfoil centrifugal stress, Eq. (8.62)
disk stress
rim stress
disk thermal differential stress in radial direction, Eq. (8.71)
disk thermal differential stress in tangential direction, Eq. (8.72)
ultimate stress
enthalpy ratio; temperature ratio
total enthalpy ratio of component i
adiabatic freestream recovery enthalpy ratio, Eq. (4.5a)
enthalpy ratio of burner, Eq. (4.6c)
enthalpy ratio of afterburner, Eq. (4.6d)
cooling effectiveness, Eq. (8.56)
entropy function, Eq. (4.3b); equivalence ratio, Eq. (9.3)
inlet external loss coefficient, Eq. (6.2a)
nozzle external loss coefficient, Eq. (6.2b)
turbine stage loading coefficient, Eq. (8.57)
dimensionless turbine rotor speed, Eq. (8.38)
angular velocity
degree of reaction for compressor stage, Eq. (8.8)
degree of reaction for turbine stage, Eq. (8.36)
air; annulus
afterburner
aircraft
additive drag
available
burner; bleed air
boundary layer bleed
bypass
location where engine control system has simultaneous
maximums of Z,4 and zrc
core flow
compressor; centrifugal; capture; corrected; chord; cooling
compressor corrected
engine corrected
high-pressure compressor