Mattingly J.D., Heiser W.H., Pratt D.T. Aircraft Engine Design
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316 AIRCRAFT ENGINE DESIGN
Table 8.Ell
AAF Engine high-pressure compressor rim and disk results
Quantity/stage no. 1 9
ar, ~ra, ksi 25.0 25.0
p, slug/ft 3 9.08 9.08
O'r/p, ksi/(slug/ft 3) 2.75 2.75
#blades~at 0.10 0.10
h, in. (= r, - rh) 3.15 0.81
rh, in. 6.72 7.89
hr,
in. (selected) a 1 0.5
rr, in. (=
r h -- hr)
5.72 7.39
hr/rr
0.175 0.067
wry, ft/s (wheel speed) 939 1213
p(wrr)2/2aa (disk shape factor) 1.145 1.866
War/Wr (rim web thickness) 0.411 0.308
aSelected
hr can be obtained in COMPR program by entering appropriate value of hr / Wr
in stage sketch data window.
seemingly small, is similar to those found in many contemporary machines and
therefore quite practical to manufacture.
8.3.3.5 Rim web thickness~allowable wheel speed. An advanced tita-
nium material is selected for the disk (see Table 8.5 and Fig. 8.15). Thus, if the
material properties 0rr, p) [or specific strength (Crr/p)], #bta&s/Crr, hr, and rh
are as given in Table 8.Ell for stages 1 and 9, the listed values of rr, hr/rr,
wheel speed COrr (Fig. 8.23), disk shape factor (Fig. 8.22), and rim web thickness
[Eq. (8.66)] are obtained.
The wheel speed, disk shape factor, and the ratio Wdr/Wr remain in reasonable
ranges (see Figs. 8.22 and 8.23) throughout the compressor, indicating that modest
disks are required. This can also be confirmed by examining cross-sectional views
of existing engines.
8.3.3.6 Radial variation. The high-pressure compressor blades of the first
three stages have hub/tip radius ratios from 0.68 to 0.78 that indicate moderate
radial variations in both airflow and blade shape. Based on free vortex swirl distri-
bution, the COMPR program calculations for the hub of the first, second, and third
compressor stages give a degree of reaction of 0.28, 0.33, and 0.37, respectively,
and diffusion factors less than 0.56. All are within reason. As anticipated, the latter
stages of the high-pressure compressor experience smaller radial variations as a
result of their higher hub/tip radius ratios.
8.3.3. 7 High-pressure compressor design summary.
The AAF engine
high-pressure compressor design found here is sufficiently capable and sound as to
constitute a confident starting point for more detailed studies. The results obtained
are certainly very encouraging and suggest that a high-pressure compressor capable
of doing the required job can be built with modern technology. The next step would
DESIGN: ROTATING TURBOMACHINERY 317
Fig. 8.E6
ture).
AAF Engine high-pressure compressor cross section (COMPR screen cap-
be to use the results of the repeating stage/repeating row design as a starting point
in COMPR for a final design having a constant tip radius in order to maximize
the value of the rotational speed and minimize the possibility of rubbing between
rotor blade tips and air seals during axial shifting.
The design status may be conveniently captured in the pictorial form of Fig. 8.E6
(from the cross-section sketch results of the COMPR program) in order to reveal
the proportions of the selected nine-stage high-pressure compressor. The pictured
high-pressure compressor design includes inlet guide vanes with an entry Mach
number of 0.35, solidity a of 0.5, and chord-to-height ratio
c/h
-- 0.5. A chord-
to-height ratio
c/h
-- 0.6 was used for both the rotor and stator blades and a rim
width-to-blade axial chord ratio
Wr/cx
= 1.1 was used. In addition, the value of
the rim height-to-width ratio
hr/Wr
varied from 0.625 for stage one to 1.36 for
stage nine in order to obtain the assumed rim height
hr
of 1 in. for stage one and
1/2 in. for stage nine. The overall length of the nine-stage compressor is estimated
to be 17.0 in.
Once again, it is pleasing, but no longer surprising, to discover that the design
"looks like" a compressor.
8.3.4 Low-Pressure Turbine DesignmAAF Engine
Because this process parallels that of the high-pressure turbine, other than the
fact that the mechanical rotational speed is known in advance, only the outline
will be repeated here. The process begins with the selection of the turbine design
point and the turbine disk material. An initial estimate of the mean wheel speed
is made based on the allowable wheel speed calculated for a disk shape factor
(DSF)
value of two. The number of stages are chosen and their temperature ratios
determined. Design choices are then made for the stage parameters M2 and Man
318 AIRCRAFT ENGINE DESIGN
and the aerodynamic definition of each stage fixed. Next, rotating airfoil material
and taper choices are selected, the rotational speed of the high-speed spool is
found from centrifugal stress considerations, and the airfoil radii are calculated.
Finally the wheel parameters hr and #btades/Crr are estimated; and the wheel speed,
disk shape factor, and rim web thickness are determined by rim and disk stresses
considerations.
8.3.4. 1 Design point.
From Table 7.E3 and Fig. 8.E2, the low-pressure
turbine design point parameters (0.612M/sea level) are as follows:
rt,q = 0.8366 Pt4.5 = 149.1 psia Yt = 1.300
rrt/4 = 0.4236 Tt45 = 2380°R gcCpt = 7378 ft2/s2-°R
th,q = 0.9087 m4.5 = 102.441bm/s Rt = 53.0 ft-lbf/lbm-°R
and
wL = 1160 rad/s, NL = 11,070 rpm
8.3.4.2 Disk consideration. Because of lower temperatures and lower ro-
tational speeds that are found in low-pressure turbines, disk design is never a
fundamental limitation. However, the same care for durability and safety must be
applied as in the high-pressure turbine. Since rr will probably be less than 8 in., it
follows that the rim speed
O)Lr r
will not exceed 780 ft/s, well within the capability
of existing disk materials (cf. Fig. 8.23).
8.3.4.3 Number of stages. It is particularly important in the slowly ro-
tating low-pressure turbine to reduce the number of stages as much as humanly
possible. Referring to the AEDsys Engine Pictures file, you can easily find engines
with as many as six low-pressure turbine stages. These are bound to be heavy and
expensive machines.
A first guess is that the turbine will have only one stage with a mean radius of
9 in., whence
O~rm
75ts = 75tL =
Tt5/Tt4.5 =
0.8366 f2 -- 0.2075
greeCe, r,4 5
The story is quite similar to that of the high-pressure turbine. Placing this point on
Fig. 8.8 reveals that a single-stage design of this type would require values of a2
and M2 so large that high aerodynamic efficiency could not be achieved. However,
a two-stage design with each rts between 0.85 and 0.90 falls well within the "safe"
region and thus will be attempted next.
8.3.4.4 Stage temperature ratios.
A reasonable approach to efficient
stage design is to have the inlet flow angle ot2 and exit relative Mach number MaR
the same for both stages. However the Mach number leaving the first stage turbine
nozzles needs to be supersonic (M2 > 1), whereas that leaving the second stage
needs to be subsonic (M2 < 1). For the first stage,
~'~stage
1 ~
0.208 and assuming
DESIGN: ROTATING TURBOMACHINERY
Table 8.E12 AAF Engine low-pressure turbin aerodynamic results
319
Quantity/stage no. 1 2
Tt2 , °R
2380 2105
Mz,\M3R 1.05\0.8 0.7\0.6
= 09rm/~cCpt Tt2
0.2075
0.2594
a2, deg (selected) 60.0 47.8
/72, deg, Eq. (8.43) 43.63 12.16
Tt2R, °R, Eq. (8.44) 2203 2029
/33, deg, Eq. (8.45) 48.59 37.73
/32 + /33, deg
92.22 49.89
or3, deg, Eq. (8.48) 19.55 -6.49
rts, Eq. (8.50) 0.8847 0.9458
°R, Eq. (8.51) 0.1160 0.3145
zrts, Eq. (8.53) 0.5543 0.7646
7t, Eq. (8.57) 2.694 1.132
0(2 = 60 deg, M2 = 1.1, and M3R = 0.9, then Fig. 8.8 gives
(rts)stage
1 = 0.87. For
the second stage, assuming 0(2 = 60 deg, ME = 0.9, and M3R = 0.9 with
oJrm ~"~stage 1
~'2stage 2 = ~/gcCpt(.~ts)stag e 1Tt4.1
~ 0.223,
then
Fig.
8.8
gives
('(ts)stage
2 = 0.88. Because
(Tts)stag e 1 (72ts)stage
2 =
0.766, a two-
stage low-pressure turbine with the required total temperature ratio of 0.8366 is
easily obtainable. The assumed stage data just noted will be used as a starting point
in the design of the high-pressure turbine using Eqs. (8.37-8.52) or the TURBN
program (unknown:
0(3,
known: 0(2, M2, and
M3R).
Because neither of these stages is very highly loaded, remarks similar to those
made about the high-pressure turbine apply. There appears, in fact, to be an op-
portunity to reduce the total number of turbine stages from four to three, but that
would require a complete engine cycle iteration.
8.3.4.5 Aerodynamic definition.
Directly applying the methods of Sec.
8.2.2 on constant axial velocity, selected Mach number, mean-line stage design
to the proposed two-stage design for a mean rotor speed
(Ogrm)
of 870 ft/s, and
polytropic efficiency of 0.90 (used in all cycle calculations) leads to the results of
Table 8.E12.
Thus
and
rtL = 0.8366
zrt/~ = 0.4236
(same as cycle calculations)
(same as cycle calculations)
rhL = 0.9087 (same as cycle calculations) (4.9e-CPG)
The resulting stage loading ~ is consistent with the data of Table 8.4b. Can you
explain how and why the stage loading of low-pressure turbines is so high?
320 AIRCRAFT ENGINE DESIGN
Table 8.E13 AAF Engine low-pressure turbine airfoil centrifugal stresses
Stage no. One Two
Stage station 1 2 3/1 2 3
Engine station 4.5 5
Quantity
rn, lbm/s 102.44 102.44 102.44 102.44 102.44
Tt, °R 2380 2380 2105 2105 1991
TtR, °R 2203 2203 2029 2029
M 0.30 1.05 0.56 0.7 0.48
p,, psia 149.1 82.6 63.1
~, deg 0 60.0 19.55 47.80 -6.49
A, in. 2 132.59 130.48 144.45 179.66 195.24
AN 2,
x 10 j° in.2-rpm 2 1.68/--- 2.30
8.3.4.6 Airfoil centrifugal stress.
Aconservativeanalysisisperformedand
the results presented in Table 8.E13, by using both the average rotor annulus area
for the first stage and that of
At/Ah
= 1.0. The annulus area at inlet and exit of
each stage is calculated using Eq. (8.20) where the
MFP
is given by Eq. (1.3).
Employing Eq. (8.64) at the average rotor annulus area for each stage with
At/Ah
= 1.0 and p = 17.00 slug/ft 3 yields the stresses given in Table 8.E14,
which is well within current capabilities (cf. Table 8.5 and Fig. 8.15). Assuming
that the airfoils have a common
rm,
the results of Table 8.E14 follow.
Airfoils of these dimensions are common in modem gas turbines. The present
design is, therefore, perfectly adequate and will be pursued further.
8.3.4.7 Rim web thickness~allowable wheel speed.
Because the rim is
part of the disk, the same type of material properties are used. Thus, if the material
properties (err, p) [or specific strength (err/p)],
#bt,aes/Crr, hr,
and
rh are
as given
in Table 8.E15, then the listed values of
rr, hr/rr,
wheel speed wrr (Fig. 8.23),
disk shape factor (Fig. 8.22), and rim web thickness [Eq. (8.66)] are obtained.
Table 8.E14 AAF Engine low-pressure turbine airfoil results
Stage no. One Two
Stage station 1 2 3/1 2 3
Engine station 4.5 5.0
Quantity
rr, in. 10.17 10.15 10.28 10.59 10.73
rm, in. 9.00 9.00 9.00 9.00 9.00
rh, in. 7.83 7.85 7.72 7.41 7.27
h = rt - rh, in. 2.34 2.30 2.56 3.18 3.46
o,./p
[ksi/(slug/ft3)] 1.42/--- 1.94
cr,.,
kpsi 24.1/--- 32.9
DESIGN: ROTATING TURBOMACHINERY 321
Table 8.E15 AAF Engine low-pressure turbine rim and disk results
Quantity/stage no. 1 2
T,2R, °R 2203 2029
at, ad,
ksi 32.0 32.0
p, slug/ft 3 17.0 17.0
err~p,
ksi/(slug/ft 3) 1.88 1.88
~blades/(~r
0.20 0.20
rh, in. 7.85 7.41
hr, in. (selected) a 1.0 1.0
rr, in. (=
rh - hRi,,)
6.85 6.41
hr/rr
0.146 0.156
tort, ft/s (wheel speed) 660 620
p(~Orr)2/2ad
(disk shape factor) 0.808 0.748
War~ Wr
(rim web thickness) 0.356 0.341
aSelected
hr
can be obtained in TURBN program by entering the appropriate value
of
hr/Wr in stage sketch data window.
The wheel speed is less than 700 ft/s, the disk shape factor less than 2.0, and the
rim web thickness ratio less than 1.0. All are satisfactory values.
8.3.4.8 Radial variation.
The low-pressure turbine blades have low hub/tip
radius ratios that indicate large radial variations in both airflow and blade shape.
Based on free vortex swirl distribution, the TURBN program calculations for the
degree of reaction at the hub of the first- and second-stage turbine give -0.16 and
-0.01, respectively, which are undesirable. Sophisticated CFD methods would be
employed to design these blades and alleviate this problem (Chapter 4 of Ref. 1).
8.3.4.9 Low-pressure turbine design summary.
This AAF Engine low-
pressure turbine design is sufficiently sound and balanced so that it represents an
entirely satisfactory starting point. Thus, no other iteration will be carried out. The
TURBN cross section results displayed in Fig. 8.E7 reveal the basic configuration
of the two-stage low-pressure turbine. The fact that the rotor airfoils have an almost
constant tip radius is an advantage from the standpoint of sealing against tip leakage
because unavoidable axial motion has little effect on clearance. The two-stage
low-pressure turbine has exit guide vanes with exit Mach number of 0.4 and an
approximate overall length of 10.3 in. Comparison with examples in the AEDsys
Engine Pictures file will convince you that it looks like many of its brethren.
The low-pressure turbines' mean radius is 2 in. larger that that of the high-
pressure turbine and will require a transition duct. The TURBN program could be
used to better align these two turbines.
8.3.5 AAF Engine Turbomachinery Design Closure
The present design status is summarized by Fig. 8.E8a, which combines the fan
and high-pressure compressor, and Fig. 8.E8b, which combines the high-pressure
and low-pressure turbines. Although this is a satisfactory start and no important
technological or geometrical barriers to a successful design have been encountered,
further iteration would focus on the following points: 1) redistributing the stage
322 AIRCRAFT ENGINE DESIGN
Fig. 8.E7 AAF Engine two-stage low-pressure turbine cross section (TURBN screen
capture).
20
.a,iu'?t
.... I .... I .... I .... I,,,,
Fan :" Bypass Duct
- sure
o I
, , , , i , , , , i , , , , i , , , , i
0 10 20 30 40
Axial Location (in)
50
Fig. 8.E8a General arrangement of the AAF Engine fan and high-pressure com-
pressor.
DESIGN: ROTATING TURBOMACHINERY 323
12
10
8
Radius
6
(in)
4
, , , , I , , , , I ,
High-Pressure
Turbine
I .... I , ,
Low-Pressure Turbine
0 .... I .... I .... I ' ' ' ' I ' ' '
0 5 10 15 20 25
Axial Location (in)
Fig. 8.E8b
turbines.
General arrangement of the AAF Engine high-pressure and low-pressure
temperature rise in the high-pressure compressor (more in the rear stages and less
in the front) in order to raise r m at the rear (approach a constant tip radius) and
possibly reduce the number of stages; 2) exploring aerodynamic and/or materials
approaches that can increase rm for the high-pressure turbine in order to straighten
out the main burner and the aft transition duct; and 3) evaluating different work
splits between the low- and high-pressure compressors in order to remove one
turbine stage.
It is our intention and hope that this exercise carries lessons far beyond the actual
design of these components. For one thing, it should convince you that a success-
ful design rests upon the simultaneous solution of interdependent aerodynamic,
thermodynamic, materials, and structural problems. For another, it should clearly
demonstrate the importance of advanced technology to the solution of these prob-
lems. Finally, it should show that judgment and iteration are necessary partners in
the search for the best answer.
References
1Oates, G. C. (ed.), Aerothermodynamics of Aircraft Engine Components, AIAA Educa-
tion Series, AIAA, Reston, VA, 1985.
2Wilson, D. G., The Design of High Efficiency Turbomachinery and Gas Turbines, 2nd
ed., MIT Press, Cambridge, MA, 1998.
3Horlock, J. H., Axial Flow Compressors, Krieger, Malabar, FL, 1973.
4johnsen, I. A., and Bullock, R. O. (eds.), Aerodynamic Design of Axial-Flow Compres-
sors, NASA SP-36, 1965.
5Dixon, S. L., Thermodynamics ofTurbomachinery, 4th ed., Pergamon, New York, 1998.
6Cumpsty, N. A., Compressor Aerodynamics, Longman Scientific and Technical, London,
1989.
7Horlock, J. H., Axial Flow Turbines, Krieger, Malabar, FL, 1973.
8Glassmann, A. J. (ed), Turbine Design and Application, Vols. 1-3, NASA SP-290, 1972.
324 AIRCRAFT ENGINE DESIGN
9Kerrebrock, J. L.,
Aircraft Engines and Gas Turbines,
2nd ed. MIT Press, Cambridge,
MA, 1992.
l°Oates, G. C.,
The Aerothermodynamics of Gas Turbine and Rocket Propulsion,
3rd ed.,
AIAA Education Series, AIAA, Reston, VA, 1997.
11Mattingly, J. D.,
Elements of Gas Turbine Propulsion,
McGraw-Hill, New York, 1996.
lZZweifel, O., "The Spacing of Turbomachinery Blading, Especially with Large Angular
Deflection,"
Brown Boveri Review,
Vol. 32, 1945, p. 12.
13Dorrnan, T. E., Welna, H., and Lindlauf, R. W., "The Application of Controlled-Vortex
Aerodynamics to Advanced Axial Flow Turbines,"
Journal of Engineering for Power,
Ser. A, Vol. 98, Jan. 1976.
14Hiroki, T., and Katsumata, I., "Design and Experimental Studies of Turbine Cooling,"
American Society of Mechanical Engineer Paper 74-GT-30, 1974.
15Hertzberg, R. W.,
Deformation and Fracture Mechanics of Engineering Materials,
4th ed., Wiley, New York, 1996.
16Budynas, R.,
Advanced Strength and Applied Stress Analysis,
2nd ed., McGraw-Hill,
New York, 1998.
17Aerospace Structural Metals Handbook,
Battelle Memorial Inst., Columbus Lab.,
Columbus, OH, 1984.
18Sorensen, H. A.,
Gas Turbines,
Ronald, New York, 1951.
19Von K~irm(m Inst.,
Turbomachinery Blade Design Systems,
AIAA, Reston, VA, 1999.
9
Engine Component Design:
Combustion Systems
9.1
Concept
With several others, I was sent on loan from the Royal Aircraft Establishment
to lead a group on combustion at Power Jets [in 1940]. I had done my thesis on
laminar and turbulent diffusion flames and knew the importance of aerodynamics
in the combustion process. It surprised me that others did not see that as much
care was required in characterising the aerodynamic features of a combustion
chamber as in the design of a blade for a compressor or turbine.
--Sir William Hawthorne, "The Early History
of the Aircraft Gas Turbine in Britain," (Ref. 1).
The purpose of the combustion systems of aircraft gas turbine engines is to
increase the thermal energy of a flowing gas stream by combustion, which is
an exothermic chemical reaction between the onboard hydrocarbon fuel and the
oxygen in the ingested airstream. The two engine components in which this "heat
addition" is made to occur are the main burner (also called the combustor) and
the afterburner (also called the augmentor or reheater.) Both are covered in this
chapter, as they have many basic processes in common, and means are provided
for preliminary design of both.
The design of the main burner and afterbumer of an airbreathing engine differs in
many ways from that of stationary combustion devices. Space (especially length)
is at a premium in aircraft applications. The combustion intensity (rate of thermal
energy released per unit volume) is very much greater for the main bumer of a
turbojet (40,000 Btu/s-ft 3) than, for example, the fumace of a typical steam power
plant (10 Btu/s-ft3).
The following properties of the main burner or combustion chamber are desired:
1) complete combustion; 2) moderate total pressure loss; 3) stability of combustion
process (freedom from flameout); 4) in-flight relight ability; 5) proper temperature
distribution at exit with no "hot spots"; 6) short length and small cross section;
7) wide operating range of mass flow rates, pressures, and temperatures; and
8) satisfaction of established environmental limits for air pollutants.
Unfortunately, every one of these desirable characteristics is in conflict with one
or more of the others. For example, complete combustion requires a large size, but
moderate total pressure loss requires a small size. Design choices that minimize the
generation of air pollutants severely impact combustion stability and narrow the
range of stable operating parameters. As with many complex engineering systems,
the design of the main burner or afterbumer is necessarily an engineering design
compromise.
325