Mattingly J.D., Heiser W.H., Pratt D.T. Aircraft Engine Design

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306 AIRCRAFT ENGINE DESIGN

8.3.1.7 Fan design summary.

The AAF engine fan 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 three-stage fan capable of doing the required job can be built with

modem technology. The next step would 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.E3

(from the cross-section sketch results of the COMPR program) in order to reveal

the proportions of the selected three-stage fan. The pictured fan design includes

inlet guide vanes with an entry Mach number of 0.5, solidity cr of 0.5, and chord-

to-height ratio

h = 0.3. A chord-to-height ratio

h = 0.4 was used for both the

rotor and stator blades. In addition, a rim width-to-blade axial chord ratio

Wr/cx =

1.1 and rim height-to-width ratio

hr/Wr

= 0.625, 0.65, and 0.6 were used for the

first, second, and third stages, respectively, in order to obtain the assumed values

of the rim height

hr.

The overall length of the three-stage fan including the inlet

guide vanes is estimated to be 16.9 in.

Cente~ Line

Fig. 8.E3 AAF Engine fan cross section (COMPR screen capture).

DESIGN: ROTATING TURBOMACHINERY 307

One is always tempted to remark at this point that the design "looks like" a fan.

This should not be the least bit surprising, but rather should be expected because

the shape of the fan is determined by the physics of the situation, and not by the

whim or fancy of the designer. You will find this to be equally true for the other

AAF Engine components.

8.3.2 High-Pressure Turbine Design--AAF Engine

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 M3R 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 wheel parameters

and 6btaae,/~rr are estimated; and the wheel speed, disk shape factor, and rim

web thickness are determined by rim and disk stresses considerations.

8.3.2.1 Design point. The highest rotor mechanical speeds and centrifugal

stresses occur at the highest value of 04 for a given turbine temperature ratio. Thus

the high-pressure turbine design will be at a flight condition where Tt4 is maximum.

The design requirements of the high-pressure compressor place its design point

at full throttle flight conditions where 00 = OObreak, and this condition at sea level

is selected for the high-pressure compressor design because it corresponds to the

largest mass flow rate and inlet pressure. Because the high-pressure turbine drives

the high-pressure compressor, the high-pressure turbine design point corresponds

to the same flight conditions.

From Table 7.E3 and Fig. 8.E2, the high-pressure turbine design point para-

meters (0.612M/sea level) are as follows:

rtH = 0.7853

Pt4,1

483.6 psia Yt = 1.300

rrt/4 = 0.3083 Tt4.1 = 3102°R gcCpt = 7378 ft2/s2-°R

th/4 = 0.9028 rh4.a = 97.39 lbm/s Rt = 53.0 ft-lbf/lbm-°R

8.3.2.2 Initial estimate of wheel speed.

Presuming that advancing tech-

nology will make disk materials available for the AAF engine that provide (see

Table 8.5 and Fig. 8.15)

~rd = 30,000 psi and p = 16.0 slug/ft 3

under the anticipated environmental conditions, and applying Eq. (8.69) with an

assumed DSF of 2 (see Fig. 8.23), then

COrr = 4~@-pd/p = 1040 ft/s

which allows the initial estimate of the mean wheel speed

wrm = 1150 ft/s

This result must be checked later.

308 AIRCRAFT ENGINE DESIGN

8.3.2.3 Aerodynamic design.

It is important, particularly in the complex,

expensive, and heavy high-pressure turbine, to reduce as much as reasonably pos-

sible the number of stages. A first guess is that the turbine will have only one stage,

whence

(DE m

rts = rtl-i

= Tt4.4/Tt4.1 ---- 0.7853 f2 -- __ -- 0.240

Placing this point on Fig. 8.8 reveals that a single-stage design of this type would

require both a large M2 and a value of or2 > 80 deg, making efficient aerodynamic

design impossible (see Sec. 8.2.2). 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.

8.3.2.4 Stage temperature ratios.

A reasonable approach to efficient

stage design is to have the inlet flow angle or2 and exit relative Mach number

M3R the same for both stages. However the Mach number leaving the first stage

turbine nozzles needs to be supersonic

(M2 > l),

whereas that leaving the second

stage needs to be subsonic (M2 < 1). For the first stage,

~'2stag e

1 =

0.240 and,

assuming o/2

60 deg,

M 2 =

1.0, and

M3R ----

0.9, then Fig. 8.8 gives

(rts)stage I =

0.88. For the second stage, assuming ot 2

60 deg, M2 = 0.9, and M3R = 0.9 with

O)rm ~"2stage 1

- - 0.256,

~'2stage 2 = x/gcCpt('fts)stage l Tt4.1 ~1

then Fig. 8.8 gives

(rts)stage

0.89. Because

(rts)stage l(rts)stage

2 ---- 0.783, a two-

stage high-pressure turbine with the required total temperature ratio of 0.7853 is

easily obtainable. The assumed stage data just noted will be used as the start-

ing point in the design of the two-stage high-pressure turbine either using Eqs.

(8.37-8.52) or the AEDsys TURBN program (unknown: 013; known: tx2, M2, and

M3R).

8.3.2.5 Aerodynamic definition.

Directly applying the methods of

Sec. 8.2.2 for constant axial velocity, selected Mach number, mean-line stage

design to the proposed two stage design for a mean rotor speed

(Wrm)

of 1150 ft/s,

M3R

of 0.8, and polytropic efficiency of 0.89 (used in all cycle calculations) leads

to the results in Table 8.E5.

Thus

rt/4 --= 0.7853

7rt/¢ = 0.3083

and

(same as cycle calculations)

rh, = 0.9028 (same as cycle calculations) (4.9d-CPG)

Two points are worthy of special mention here. First, because both stages are

rather lightly loaded, one is tempted to shift work either to or from the high-pressure

spool in order to make more use of the hardware or to increase rt/4 enough that a

single-stage high-pressure turbine will suffice. Second, the resulting (not imposed)

values of stage loading 7z are in line with those of Tables 8.4a and 8.4b.

DESIGN: ROTATING TURBOMACHINERY 309

Table 8.E5 AAF Engine high-pressure turbine

aerodynamic results

Quantity/stage no. 1 2

Tt2,°R 3102 2720

M2 1.0 0.9

f2 = Wrm/ g~/~pcCp, T,2 0.2400 0.2563

t~2, deg (selected) 60.0 52.9

/32, Eq. (8.43) 38.38 22.26

Tt2R, °R, Eq. (8.44) 2862 2551

f13, deg, Eq. (8.45) 50.56 46.15

/32 +/33, deg 88.94 68.41

or3, deg, Eq. (8.48) 15.43 7.30

rts, Eq. (8.50) 0.8769 0.8956

°R, Eq. (8.51) 0.2254 0.3459

rrts, Eq. (8.53) 0.5275 0.5846

gr, Eq. (8.57) 2.136 1.589

8.3.2.6 Airfoil centrifugal stress. A conservative analysis will be per-

formed here, by using both the average rotor annulus area for the first stage and

assuming that At/Ah = 1.0. The annulus area at inlet and exit of each stage is

calculated using Eq. (8.20) where the mass flow parameter (MFP) is given by

Eq. (1.3). The results are summarized in Table 8.E6.

Employing Eq. (8.El) at the average rotor annulus area of 47.56 in. 2 for stage

one

47r ~c

co : pA (1 + At/Ah)

with

Crc = 21,000 psi (advanced material, cf. Fig. 8.15)

Table 8.E6 AAF Engine high-pressure turbine annulus area

Stage no. One Two

Stage station 1 2 3/1 2 3

Engine station 4.0 4.1 4.4

Quantity

th, lbm/s 92.34 97.39 97.39 97.39 97.39

Tt, °R 3200 3102 2720 2720 2436

TtR, °R 2862 2862 2551 2551

M 0.2 1.0 0.53 0.9 0.56

P, psia 483.6 255.1 149.2

or, deg 0 60.0 15.43 52.9 7.3

A, in. 2 61.25 43.54 51.58 64.58 78.02

310 AIRCRAFT ENGINE DESIGN

Table 8.E7 AAF Engine high-pressure turbine airfoil centrifugal stresses

Stage no. One Two

Stage station 1 2 3/1 2 3

Engine station 4.0 4.1 4.4

Quantity

rt,

in. 7.69 7.50 7.56 7.72 7.86

rm,

in. 7.00 7.00 7.00 7.00 7.00

rh,

in. 6.31 6.50 6.44 6.26 6.14

h = rt - rh,

in. 1.38 1.00 1.12 1.44 1.72

~rc, kpsi 21.0/--- 32.4

AN 2,

10 l° in.Z-rpm 2 1.65/--- 2.47

and

then

p = 15.00 slug/ft 3

(Table 8.5)

o~ = 1970 rad/s

N = 18,800 rpm

rm = (Wrm)/Co

= 1150/1970 = 7.00 in.

Assuming that the airfoils have a common mean radius of 7 in. the airfoil properties

are as shown in Table 8.E7.

Airfoils of such small heights are challenging from the standpoint of both effec-

tive cooling and high aerodynamic efficiency, but are certainly possible. To reduce

and thus increase their height, the foregoing calculations can be traced back

to reveal that the rotational speed N may have to increase in order to maintain

f2, thus requiring an even stronger blade material. The present design is, however,

perfectly adequate and will be pursued further.

8.3.2. 7 Rim web thickness~allowable wheel speed. Because the rim is

part of the disk, the same advanced of material properties are used. Thus, if the

material properties

(at, p)

[or specific strength

(ar/p)], Obtades/ar, hr,

and

are as given in Table 8.E8, 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.

The results of Table 8.E8 indicate that the wheel speed is less than the initial

estimate of 1040 ft/s, the disk shape factor is less than 2.0, and the rim web thickness

ratio is less than 1.0. All are satisfactory values (see Figs. 8.22 and 8.23). This is

evidently a situation where the high-pressure spool rotational speed is dictated by

the turbine airfoil centrifugal stress.

8.3.2.8 Radial variation.

The high-pressure turbine blades have high hub/

tip radius ratios that produce small radial variations in both airflow and blade

DESIGN: ROTATING TURBOMACHINERY

Table 8.E8 AAF Engine high-pressure turbine rim and disk results

311

Quantity/stage no. 1 2

Tt2R, °R 2862 2551

Or, Or, ksi 30.0 30.0

p, slug/ft 3 16.0 16.0

o'r/p, ksi/( slug/ft 3) 1.88 1.88

6blades/Or,

0.20 0.20

rh, in. 6.50 6.27

hr, in. (selected) a 1.0 1.0

rr, in. (= rh -- heim) 5.5 5.27

hr/rr 0.182 0.190

wrr, ft/s (wheel speed) 900 870

p(~orr)2/2Od (DSF) 0.678 0.668

Wdr/Wr (rim web thickness) 0.353 0.349

aSelected

hr can be obtained in TURBN program by inputting appropriate value of

hr/Wr in stage sketch data window.

shape. Based on free vortex swirl distribution, the TURBN program calculations

of the first stage give degree of reactions for the hub and tip of 0.10 and 0.32,

respectively. These are acceptable variations.

8.3.2.9 High-pressure turbine design summary. This AAF engine high-

pressure turbine design is sufficiently sound and balanced that it represents an

entirely satisfactory starting point. Thus, no other iteration will be carded out. The

TURBN cross section results displayed in Fig. 8.E4 reveal the basic configuration

of the two-stage high-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

complete turbine stage computations of TURBN could be used now, for example,

to trim this design to have an exactly constant tip radius. The turbine has an

approximate overall length of 7.0 in. Comparison with examples in the AEDsys

Engine Pictures file will convince you that it looks like many of its brethren.

8.3.2.10 Spool design speeds comment. Before proceeding with the

design of the remaining two rotating machines, the high-pressure compressor and

the low-pressure turbine, special note should be taken regarding the assumptions

about their design mechanical speeds.

The fan and high-pressure compressor are initially designed to their highest

required pressure ratios. Given normal map behavior, these will also correspond to

their highest required mechanical speeds. The turbines that share their respective

shafts must be designed to perform reliably at the same mechanical speeds. It may

be safely assumed that, because turbine efficiency varies slowly around the map,

the exact choice of the turbine aerodynamic design point is not critical.

In the case of the high-speed spool, the high-pressure turbine has been designed

to operate at its almost constant design point at a structurally acceptable mechanical

312 AIRCRAFT ENGINE DESIGN

Fig. 8.E4 AAF Engine two stage high-pressure turbine cross section (TURBN screen

capture).

speed (that is, 18,800 rpm). The high-pressure compressor may therefore not

exceed this value, and logic indicates that the highest required pressure ratio should

occur at the same mechanical speed.

On the low-speed spool, similar reasoning applies. The maximum mechanical

speed of the shaft has already been determined for the fan (that is, 11,070 rpm),

and this cannot be exceeded by the low-pressure turbine. The corresponding aero-

dynamic design point of the low-pressure turbine must be chosen to be some

representative condition, the exact one being less critical because of the forgiving

nature of the turbine efficiency. To illustrate this, the low-pressure turbine will be

designed for the engine design point at the maximum allowable mechanical speed.

Other approaches are, of course, possible, but all will lead to iterations that

converge on the best answer. What is important are the means to get started and

the tools to do the work. This example has provided the first approximation and

some indications of the direction that will yield improvement. In the end, everything

must work well together. Hence

NL = 11,070 rpm

NH = 18,800 rpm

DESIGN: ROTATING TURBOMACHINERY 313

1"Cot ¢

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

Fig. 8.E5

' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' '

i i i i i i i i i i i , , i , , , ,

20 22 24 26 28

Corrected Mass Flow Rate Ihc25 (lbm/s)

AAF Engine high-pressure compressor operating line.

8.3.3 High-Pressure Compressor DesignuAAF Engine

Because this process parallels that of the fan design, other than the fact that the

mechanical rotational speed is known in advance, only the outline will be repeated

here.

8.3.3.1 Design point.

The high-pressure compressor (a.k.a. "compressor")

operating line of Fig. 7.E11, reproduced here as Fig. 8.E5, reveals that the com-

pressor must operate over a wide range of pressure ratios and corrected inlet mass

flow rates, although the variations are not as large as for the fan. The operating

point requiring the highest pressure ratio again corresponds to full throttle flight

conditions at 00 =

Oobreak,

where Zrct-/is 8.0 (see Table 7.E3). To be certain that

the high-pressure compressor can meet this most stringent condition, this will be

chosen as the design point. Of all of the possible theta break flight conditions for

design, sea level is selected because it corresponds to the largest mass flow rate

and inlet pressure. Hence, the key parameters are obtained from Fig. 8.E2, which

presents the flow properties at the most demanding operating point obtained from

the AEDsys program.

The high-pressure compressor design parameters (0.612M/sea level) are as

follows:

rh2.s = 100.91bngs

Pt2.5

= 63.51psia

Tt2.5

= 833.3°R

ATt = 780.0°R Zrc/4 _> 8.0 t/c/t _> 0.8678 (Fig. 7.1)

yc = 1.4 g~cp~

= 6006 ft2/s2-°R R = 53.34 ft-lbf/lbm-°R

314

and

AIRCRAFT ENGINE DESIGN

con = 1970 rad/s, Nu = 18,800 rpm

8.3.3.2 Number of stages.

Table 8.1 gives the ATt per stage range of

design values for high-pressure compressors as 60-90°R. To achieve an overall

ATt of 780.0°R with a compressor having n repeating stages, the following stage

total temperature increases are required:

Number of stages, n Stage AT, °R

8 97.5

9 86.7

10 78.0

An initial choice of n = 9 gives a stage ATt of 86.7°R (upper range of design

range from Table 8.1) that is slightly more conservative than the fan, thus reducing

the development risk of the system.

8.3.3.3 Aerodynamic definition.

The analysis of Sec. 8.2.1 on repeating

stage, repeating row mean-line design is used with the following assumptions:

D = 0.5 (conventional technology); M1 = 0.5 (upper range of corrected mass

flow/area in Table 8.1); a = 1.0 (conventional technology); and ec = 0.90 (used

in all cycle calculations).

The required stage total temperature rise of 86.7°F can be obtained with an inlet

flow angle (or l) of 45.2 deg with the following results:

~1 = 45.2 deg assumed

F = 3.845 Eq. (8.7)

~2 = 60.85 deg Eq. (8.6)

Aa = 15.65 deg c~2 - or1

rs = 1.104 Eq. (8.12)

ATt = 86.67°F Ttl(rs - 1)

zr~ = 1.366 Eq. (8.13) - First stage

Ttl / Tsta

V1 = Mlal = Mlastd 1 + (Yc -- 1)M12/2 = 690.4 ft/s

O)rm/V 1

1.973 Eq. (8.16)

O~rm = 1362 ft/s

M]R = 0.723 Eq. (8.17)

DESIGN: ROTATING TURBOMACHINERY

Table 8.E9 AAF Engine high-pressure compressor annulus areas

315

Quantity/

stage no. 1 2 3 4 5 6 7 8 9 Exit

Tt,°R 833.3 920.0 1007 1093 1180 1267 1353 1440 1527 1613

Pt, psia 63.5 86.7 100.1 149.4 190.0 237.5 292.6 355.8 427.7 508.9

M1, 0.500 0.475 0.453 0.434 0.417 0.402 0.389 0.376 0.365 0.355

Eq. (8.13)

A, in. 2 164.0 131.0 106.9 88.8 74.8 63.9 55.1 48.0 42.2 37.3

so that

ro~/= 1.936 (vs 1.935 of cycle analysis calculation)

rrcH = 8.013 (vs 8.000 of cycle analysis calculation)

OcH = 0.8678 (vs 0.8678 of cycle analysis calculation)

These results are satisfactory, and so the annulus area at the inlet and exit from

each stage can be calculated using Eq. (8.20). The results are summarized in

Table 8.E9. The mean radius is 8.3 in.

[(Wrm)]/co

= 1362/1970]. Special note

should be taken of the fact that

Tt3

= 1613°R is close to the rule-of-thumb upper

limit for compressor discharge temperature of 1700°R (1240°F) of Table 8.1.

8.3.3.4 Airfoil centrifugal stress.

With co known, and assuming constant

mean radius and

At/A h =

1.0 and an advanced titanium (see Table 8.5 and

Fig. 8.15) having p = 9.08 slug/ft 3, the results in Table 8.El0 may be directly

calculated.

Two observations are important here. First, the diminishing area more than

compensates for the effect of increasing temperature on allowable

AN 2

or trc

through the compressor. The result is that it will be possible to manufacture all of

the rotor airfoils from titanium. Second, the exit blade height of 0.81 in., although

Table 8.El0 AAF Engine high-pressure compressor airfoil centrifugal

stresses

Quantity/

stage no. 1 2 3 4 5 6 7 8 9

A, in. z 164.0 131.0 106.9 88.8 74.8 63.9 55.1 48.0 42.2

AN 2,

× 101° 5.80 4.63 3.78 3.14 2.64 2.26 1.95 1.70 1.49

in.2-rpm z

h, in. 3.15 2.51 2.05 1.71 1.43 1.23 1.06 0.92 0.81

rt,

in. 9.87 9.55 9.32 9.15 9.01 8.91 8.83 8.76 8.70

rh,

in. 6.72 7.04 7.27 7.44 7.58 7.68 7.77 7.84 7.89

TtlR,°R 877 963 1050 1137 1223 1310 1397 1483 1570

t:rc/p,

4.89 3.90 3.18 2.64 2.22 1.91 1.64 1.43 1.26

[ksi/(slug/ft3)]

~rc, ksi 44.4 35.4 28.9 24.0 20.2 17.3 14.9 13.0 11.4