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

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SIZING THE ENGINE: INSTALLED PERFORMANCE 213

air intake

area

Alaux

equal to the inlet area A1 is selected for the AAF for M0 up

to 0.3. (See data used in revised engine search of Table 6.El.)

5) Determine the required thrust loading

(TsL/WT"o)req

for the revised mission

and constraint performance with this improved installation loss model. This was

done for the 20 engines under consideration and summarized in Table 6.El under

required thrust loading.

6) Change the available thrust loading

(TsL/WTO)avail

in the Mission Analysis

window of AEDsys to a value slightly larger than the required value

(TsL/WT"o)req

in order to resize the engine and have the program automatically scale the inlet

and afterbody data.

7) Based on the Thrust Scale Factor

(TSF),

resize engine mass flow rate (rh0)

in the parametric program for the engine design. Check that the engine(s) produce

the required power

(ProL

and/or

P'roH ).

If not, adjust the respective design values

of power takeoff coefficient

(CT-oL

and/or

Cron).

Generate a new reference engine

data file (*.ref) and input it into the AEDsys program. Check that the

TSF

is one

and that the engine(s) meet the required performance.

8) As required, repeat steps 6 and 7 until satisfactory convergence is obtained.

6.4.4 Selecting the Number of Engines

The choice of a one- or two-engine installation for the AAF is a design study

all its own and involves many tradeoffs between safety, performance, and cost.

The airframe design team is normally responsible for these studies in cooperation

with the propulsion design group. For engine designers, the purpose here is only

to verify that the engine size for either a single-or a twin-engine fighter is feasible

from the point of view of engine manufacturing and testing capabilities.

As was seen in Table 6.E2, the subsonic 5g tum sizes the Engine 15 with a

required thrust loading of 1.31 based on inlet and nozzle losses for one engine.

We therefore proceed with an available thrust loading

(TsL/WTO)avail

of 1.32 for

the AAF in order to provide some safety margin. With an available thrust loading

(TsL/WTO)avail

of 1.32, the

TSF

for one engine is 1.0323. The engine size for a

one- or two-engine installation can now be established and the feasibility of each

determined. Assuming the approximate installation losses included in Table 6.E2,

an engine design mass flow rate of either 200 x 1.0323 = 206.5 lbm/s for a single-

engine airplane or 103.3 lbm/s for a two-engine airplane is required. The sea level

static performance of each of these engines is shown in Table 6.E3.

Table 6.E3 Sea level static performance of four engines

Sea level static performance

Engine design mass

Type of aircraft flow rate, lbm/s a th0, lbm/s F, lbf

One engine 206.5 284.8 31,680

Two engine 103.3 142.4 15,840

F100-PW-229 engine b 248 29,000

F404-GE-400 engine b 142 16,000

a 1.451 M/36 kft.

bAppendix C.

214 AIRCRAFT ENGINE DESIGN

The engine size for the one-engine installation has a static sea level mass flow rate

that is about 15% higher than the F100-PW-229 engine (used in both the Air Force

F-15 and F-16) and a considerably higher maximum thrust, whereas the engine for

the two-engine installation has about the same mass flow rate as the F404-GE-400

engine (used in the U.S. Navy F- 18) and a slightly lower maximum thrust. The size

of each engine is therefore within current manufacturing and testing capabilities for

afterburning turbofan engines and either a single- or twin-engine AAF is feasible.

We have chosen a twin-engine installation for the AAF to provide you with the

experience of using this information in the computations. Thus, the Air-to-Air

Fighter for the RFP of Chapter 1 is configured to be a

two-enginefighter.

With the number of engines for the AAF now specified as two, the final sizing

of Engine 15 starts with an available system thrust loading

(TsL/WTo)av,~il

of 1.32

and the Chapter 6 installation loss. The resultant

TSF

is 0.5161. This corresponds

to an engine having sea level static thrust of 15,840 lb and a design mass flow rate

of 103.3 lbm/s.

6.4.5 Final Engine Sizing of Engine 15 for ( TsL/ WTO)avail --

1.32

AAF Engine 15 will be sized using these procedures by finding the values

of the required-to-available thrust loading

{(TsL/Wro)req/(Tsj Wro)avait}

at the

critical mission points. To determine this ratio, preliminary estimates of the inlet

and exhaust nozzle design parameters must first be established. Then, the instal-

lation losses are found using the design tools of Sec. 6.2. Next,

(TsL/Wro)req/

(TsL/WTO)avail

is determined following the procedure diagrammed in Fig. 6.E2.

Unless

(TsL/WTO)req/(ZsL/WTO)avail

1.0, the engine is resized as indicated in

Fig. 6.E2.

The following series of calculations is presented here to show the methods and

procedures implemented in the AEDsys software. You may either carry out the

hand calculations for the installation loss as follows or use the AEDsys software

to do these calculations.

Inlet and exhaust nozzle design parameters--( TsL/ WTO)avail

1.32

Inlet size.

Based on the discussion in Sec. 6.2.4, the flight conditions requiring

the largest inlet area A1 can be determined by developing a plot of

A~/Aoref

and

Ao/Aoref

as in Fig. 6.14 for a low bypass ratio turbofan engine cycle. From this

plot, the limiting flight conditions can be identified and the inlet area determined.

Figure 6.E3 is such a plot of

A~/Aoref

(for M0 < 1) and

Ao/Aoref

(for M0 _> 1) vs

flight Mach number and altitude for this engine at full throttle. Note that the high

altitude, high Mach number flight conditions on a cold day are the most demanding

for the inlet area size. For this engine, the value of

Aoref

(A~ @ SLS) is 2.882 fte.

(The required inlet

A~/Ao

is listed in Table 6.E5 for the critical mission points.)

The most demanding flight condition for sizing this inlet is at 1.56M/40 kft on

a cold day where the

Ao/Aoref

equals 1.174. Thus, allowing for a 4% margin of

safety, the inlet area is selected to be

A1 = 1.04 x

Ao/Aoref× Aoref=

1.04 x 1.174 × 2.882 = 3.519ft e.

Exhaust nozzle size.

The value of A10 is selected to be at least 10% greater

than the largest value of A9 for critical operational mission points. Figure 6.E4

shows the exit area required at maximum and military power. For this engine, the

SIZING THE ENGINE: INSTALLED PERFORMANCE 215

1.20 , ,

1.15

1.10

1.05 -

1.00

0.95

0.90

0.85 ' '

0.0

Fig. 6.E3

' ' I ' ' ' '

,4£ <

A~r~

i i i i I i i i i

40 kft, Cold Day

StdDay~,

I i

I i I i ~1 i ! i I

i I i I

0.5 1.0 1.5

Required engine inlet area at maximum throttle, Engine 15.

2.0

value of

A9ref(=A9@SLS)

is 3.047 ft 2. Although the largest A9 required occurs

at 1.8M/40 kft on a cold day with maximum power (see Fig. 6.E4), this condition

will not determine the size of A10 because maximum power is not required for this

performance point.

Table 6.E4 contains the values of A9 for the critical mission and performance

points. The exit area A9 corresponding to maximum power have been computed

for each critical point except Supersonic Turn (1.6M/30 kft, 5g) and Maximum

Mach (1.8M/40 kft). The exit areas A9 computed for these two flight conditions

are those corresponding to the engine producing the required thrust because the

exit areas corresponding to maximum power are much larger than required at

any other flight condition and the required engine performance can be obtained at

partial power. As can be seen in Fig. 6.E5 (calculated using AEDsys), the reduction

in exit area A9 decreases

Po/P9

with a corresponding decrease in uninstalled thrust

F. The results pictured here are consistent with our basic understanding that ideal

expansion produces the maximum uninstalled thrust, but that performance does

not change rapidly in the neighborhood of perfect expansion (Refs. 2, 3, and 5).

For the Supersonic Turn with maximum power, an exit area of 5.150 ft 2 is obtained

Po/P9

of 0.927 with a reduction in thrust less than 0.04%. Similar results are

obtained for the Maximum Mach flight condition.

Based on the data of Table 6.E4, Al0 is selected to be 5.153 ft 2. Thus D10 and

L for this engine are 2.561 ft and, choosing L = 1.8 × D10, 4.611 ft, respectively.

216 AIRCRAFT ENGINE DESIGN

2.5 ',''1

I''''1''''

]t 9

A9ref

2.0

1.5

1.0

0.5

0.0

d Day "

Sea Level, Standard Day J

~ Afterburner Off

, , , , I , , , , I , , , , [ , , , ,

0.5 1.0 1.5 2.0

Fig. 6.E4 Required engine exit area at maximum throttle, Engine 15.

Table 6.E4 Engine 15 exhaust nozzle

A 9

and

IMS

for

(TsL/WTO)avail

1.32

Performance

M0/Alt,

requirement kft

Treq,

lbf a

Fr~q,

lbf b

% Favai!

A9, ft 2

IMS ~

Takeoff (100°F) 0.1/2 23,940 Max

Supercruise 1.5/30 10,700 5,640

Supersonic 5g turn 1.6/30 18,470 9,510

Subsonic 5g turn 0.9/30 15,220 7,740

Acceleration 1.2/30 16,780 8,470

Maximum Mach 1.8/40 9,740 4,970

7-8K Part 3 of 1.465/30 Max Max

mission accel

100.0 2.930 d 0.0604

43.24 3.065 0.0479

70.00 4.203 0.0054

99.38 4.003 d

79.33 4.608 d

46.80 3.854 0.0230

100.0 5.153 d 0.0000

aFrom Table 6.E2 for single engine.

bWwo

engines (installation loss based on single-engine results in Table 6.E2).

~A10 = 5.153 ft 2.

dMaximum throttle.

SIZING THE ENGINE: INSTALLED PERFORMANCE 217

1.005

1.002

S/S f

1.000

0.997

0.995

0.8

.... I''''1''''1''''1'~

F F

0.9 1.0 1.1 1.2 1.3

6.5

6.0

A 9

5.5

(N)

5.0

4.5

Po/P9

ref -

values at

Po/P9 = 1.0

Fig. 6.E5 Effect of exit

area

(A9) on Engine 15 performance (supersonic turn).

With these approximate nozzle design parameters determined, the integral mean

slope

(IMS)

of the nozzle can be found by using

IMS

= {1 -

(D9/Dlo)} 2

= {1 - ~}2

which follows from Eq. (6.15) with L = 1.8 x Din. The values of the exhaust

nozzle

IMS are

also given in Table 6.E6 for legs with Me > 1.2 and Me < 0.8.

Installation losses--( TsL /WTO ) avail

-- 1.32

Inlet loss coefficient.

The inlet loss coefficients are given in Sec. 6.2 as follows:

Subsonic flight:

[Mo~. (al)]/

q~i,,l~t = ~ (1 + yM~) - ~oo + yM2° [(Fg¢/rho)(yMo/ao)]

(6.6)

Supersonic flight:

~binlet= /ml - l"~lM°- /-~-~

~00 )/ ~ y- 1 2 1/2 .

2 +~_~__~M0)

}/[Fgc/(moao)]

(6.8)

218 AIRCRAFT ENGINE DESIGN

Table 6.E5 Engine 15 inlet loss coefficients for

(TsL/WTO)avail

= 1.32

Performance Mo/Alt,

Freq, a

% A~

F/rn o, Fgc A1/A~

requirement

kft lbf

Favail a

Ao, ft 2 lbf/lbm/s

rhoao A l/Ao b M1

q~inlet

Takeoff 0.1/2 Max 100.0 2.842 107.5 2.981 2.476

(100°F)

Supercruise

1.5/30 5,640 43.24 3.066 46.10 1.491 1.148

Supersonic

1.6/30 9,510 70.00 2.930 71.21 2.304 1.201

turn

Subsonic

0.9/30 7,740 99.38 2.878 103.9 3.361 1.223

turn

Acceleration

1.2/30 8,470 79.33 2.943 84.17 2.723 1.196

Maximum 1.8/40 4,970 46.90 3.154 47.88 1.592 1.116

Mach

0.242

0.572

0.0137

0.0384

0.0386

0.0114

0.0184

0.0420

aFrom Table 6.E4.

bA 1 = 7.038 ft 2 at takeoff and 3.519 ft 2

elsewhere due to

Ala,x.

where TI is related to To and A1 is related to A0 by the usual adiabatic and isentropic

flow relationships (see Sec. 1.9).

Once A1 has been selected, Eqs. (6.6) and (6.8) can be directly evaluated at

any given flight condition (M0 and ao or To) and engine power setting (A; or

A0 and

Fgc/rho).

Table 6.E4 gives the flight conditions and

Tre q

for each critical

mission point. When the engine is operated at the appropriate power setting for

each mission leg, the data of Table 6.E5 are obtained.

Exhaust nozzle loss coefficient.

The nozzle coefficients are given in Sec. 6.2.3

as follows:

Mo < 0.8:

CD(Alo-A9)/(Fgc~

(6.16)

~)nozzle = MO ~'- \ -Ao \ rhoao /

where

a function

oflMS

as given

by Fig. 6.8.

0.8 < M0 < 1.2:

~nozzle

m°2

\ Ao ] / \ moao /

(6.17)

Table 6.E6 Engine 15 exhaust nozzle loss coefficients for

(rsL/Wro)avai I =

1.32

Performance Mo/Alt, Freq, Fgc

requirement

kft lbf a A0, ft 2

A9, ft 2a

rhoa0

IMS a CD dpnozzte b

Takeoff(100°F) 0.1/2 Max 16.55 2.930 2.981 0.0604 0.000 0

Supercruise

1.5/30 5,640 3.066 3.065 1.491 0.0479 0.009 0.0031

Supersonic

turn 1.6/30 9,510 2.930 4.203 2.304 0.0054 0 0

Subsonic

turn 0.9/30 7,740 2.904 4.003 3.361 0.017 c 0.0040

Acceleration

1.2/30 8,470 2.943 4.608 2.723 0 0

MaximumMach 1.8/40 4,970 3.154 3.854 1.592 0.0230 0 0

aFrom Table 6.E3. hA10 = 5.153 ft 2.

cCDp.

SIZING THE ENGINE: INSTALLED PERFORMANCE

Table 6.E7 Engine 15 required thrust loading

(TsL/Wro)

for

(TsL/Wro)avail

= 1.32

219

Performance

Mo/ Alt, Favail, Treq, ~inlet "~ Freq, ( Ts L ~c (ZsL / WTO)re q

requirement kft lbP lbP

(~nozzle

lbfb

\-~OTO]req

(TsL/WTO)avail

Takeoff(100°F) 0.1/2 13,580 11,970 0.0137 12,140 1.179 0.8932

Supercruise a 1.5/30 6,030 5,350 0.0415 5,580 1.236 0.9364

Supersonic turn 1.6/30 13,590 9,240 0.0386 9,610 0.9241 0.7001

Subsonic turn 0.9/30 7,790 7,619 0.0154 7,740 1.311 0.9932

Acceleration 1.2/30 10,680 8,390 0.0184 8,550 1.047 0.7932

Maximum Mach 1.8/40 10,620 4,870 0.0420 5,080 0.6184 0.4685

aFor each engine,

b Freq = Treq /(1 - ~in!et - ~nozzle).

CConstraint analysis of AEDsys for

WT-o/S

= 64 lbf/ft 2. dAfterbumer off.

where Cop is a function of M0 as given by Fig. 6.10.

M0 > 1.2:

Equation (6.16) applies where CD at M0 = 1.2 is a function oflMS as shown

in Fig. 6.9, and Co at M0 > 1.2 is found from

Co(Mo) 1- 1.4exp(-M 2)

= r--- (6.12)

Co(1.2)

./M 2 - 1

Table 6.E6 presents the data for and the results of the nozzle loss coefficient

computation for each critical mission point.

Required thrust loading. The total installation effects on the required unin-

stalled thrust of this engine and the resulting required-to-available thrust ratio may

now be computed, and the results are summarized in Table 6.E7. The 0.9M/30 kft,

5g turn requirement has the highest required-to-available thrust loading and as such

determines the engine size. Because (TsL/WTO)req/(TsL/WTO)avail at that point is

0.9932, (Tsr/WTO)avail

"~-

1.32 will meet all of the AAF RFP requirements within

the limits of this analysis, and no further iteration will be necessary. This confirms

the earlier assertion that the engine cycle selection process is, fortunately, highly

convergent.

6.4.6 Evaluation of AAF Engine 15 for

( TsL / WTO)avail

1.32

We may safely conclude that an available thrust loading (TsL/WTO)avail of 1.320

will permit Engine 15 to meet the AAF RFP requirements. Increasing the thrust

loading from 1.25 to 1.32 changes the thrust scale factor, a measure of the engine

size, from 0.4888 to 0.5161. The results are tabulated in Table 6.E8.

The new reference point mass flow rate for each of the two engines is simply the

original value of 200 lbm/s multiplied by the thrust scale factor (TSF) of 0.5161 or

thOnew = TSF × rh0 = 0.5161 x 200 = 103.22 lbm/s

The value of the power takeoff (Pro) produced by the engine must be adjusted

from its current value of 155.2 kW to 150 kW (300/2). This is done by adjusting

220 AIRCRAFT ENGINE DESIGN

Table 6.E8 Engine 15 sizing data

Thrust loading

(TsL/WTo)avait

1.25 1.32

Thrust scale factor

TSF

0.4888 0.5161

Thrust

FsL,

lbf 15,000 15,840

Power takeoff

Pro,

kW 146.9 155.2

Inlet area A1, ft 2 3.332 3.519

Afterbody area Al0, ft 2 4.880 5.153

Afterbody length L, ft 4.487 4.611

Required thrust loading

(TsL/WTo)req

1.311 1.311

(TsL/WTO)req/(TsL/WTO)avail

1.0488 0.9932

the power takeoff coefficient

(Cro)

as follows:

PTOHnew

150.0

Cron new -- ProHref CT"oHref

= 1-~.2(0.0152). =

0.0147

This change is too minor to warrant further iteration.

The reference point data for the properly scaled Engine 15 are summarized as

follows:

Engine 15 Reference Data

M0 = 1.451 7/f = 3.5

Tt4

= 3200°R

Crow

= 0.0147

h = 36kft a = 0.7571 Tt7 = 3600°R

Po/P9 = 1

Zrc = 28 M6 = 0.4 rh0 = 103.22 lbm/s

Hereinafter, this engine is simply known as the AAF Engine.

6.5 AAF Engine Performance

6.5.1 Installed Performance of the AAF Engine

In the mission analysis of Chapter 5, the installation losses were estimated at

about 5%. By flying the AAF Engine, the Mission Analysis portion of the AEDsys

software makes the final estimates of installation penalties. For Type A (Ps > 0)

mission legs, the calculation of the installation losses requires no iteration. For

Type B (Ps = 0) mission legs, the engine is throttled back in increments and

the corresponding installation losses calculated until installed thrust equals drag.

The installation losses of the AAF Engine at the start of each mission leg are

summarized in Table 6.E9. Note that the installation losses of the Subsonic Cruise

Climb 3-4 and Combat Air Patrol 5-6 phases are about 12%; the Supersonic

Penetration 6-7, Escape Dash 8-9, and Warm-up 1-2 A phases are about 6%; and

the Loiter phase is about 8%. The net change in fuel consumed was small because

the remainder of the mission phases and segments has installation penalties less

than 5%. The decrease in fuel used WF for legs where Ps > 0 is mainly caused

by the increase in thrust loading

Tsj Wro

from 1.25 to 1.32. The changes in fuel

used

for legs where Ps = 0 are mainly caused by the changes in installation

losses from the initial estimate of 5%.

SIZING THE ENGINE: INSTALLED PERFORMANCE

Table 6.E9 AAF Engine performance

221

Mission phases and segments Ps

Alt, (])inlet "~- WF, o~OWF

114o kft

(/)nozzle 1-I

lbf change a

1-2: A--Warm-up b =0 0.0 2 0.0556 0.9911 214 5.9

1-2: B--Takeoffacceleration b >0 0.0 2 0.0134 0.9956 105 -7.1

1-2: C--Takeoffrotation b =0 0.182 2 0.0023 0.9983 40 5.3

2-3: D--Horizontal acceleration b >0 0.441 2 0.0026 0.9946 129 -6.5

2-3: E--Climb/acceleration >0 0.875 16 0.0295 0.9818 428 -7.2

3--4: Subsonic cruise climb -----0 0.900 41.6 0.1161 0.9773 524 11.3

5-6: Combat air patrol =0 0.700 30 0.1239 0.9697 683 7.7

6-7: F--Acceleration >0 1.090 30 0.0408 0.9821 391 -6.9

6-7: G--Supersonic penetration =0 1.500 30 0.0622 0.9449 1183 1.9

7-8: I--1.6M/5gtum =0 1.600 30 0.0416 0.9761 470 -5.4

7-8: J--0.9M/5gtums* =0 0.900 30 0.0164 0.9740 498 -8.8

7-8: K--Acceleration >0 1.195 30 0.0446 0.9815 346 -6.2

8-9: Escape dash =0 1.500 30 0.0638 0.9818 322 0.9

9-10: Zoom climb =0 1.326 30 0.0271 0.9974 44 -4.3

10-11: Subsonic cruise climb =0 0.900 47.6 0.1177 0.9716 491 7.4

12-13: Loiter =0 0.397 10 0.0844 0.9662 569 4.0

Total 6439 0.3

aChange from Table 5.E4. bl00°E

It is interesting and important to note that the total fuel consumed changed

only by about 0.3% from the estimate at the end of Chapter 5. The AAF engine

consumes 251 lbf of fuel less than the 6690 lbf mission fuel estimate of Chapter 3.

This process has clearly demonstrated that the general engine performance models

of Secs. 2.3.2 and 3.3.2 were more than adequate for their purpose, and that they

undoubtedly contributed to the rapid convergence.

6.5.2 Final Reprise

A comparison of the installed thrust lapse ot of the AAF Engine to that estimated

for this type of engine in Sec. 2.3.2 provides insight into the change in the mission

phases restricting the engine size from the combination of Takeoff and Combat

Turn 2 to Supercruise and Combat Turn 2. This is best accomplished by comparing

the estimated installed thrust lapses found in Fig. 2.Elb for throttle ratio

(TR)

1.07 to the computed thrust lapses of the AAF Engine, as shown in Fig. 6.E6 for

both military and maximum power settings at sea level and 30 kft on a standard day.

The estimated and computed AAF Engine thrust lapses ot agree fairly well over

the entire AAF's flight envelope. Both military and maximum predicted thrust

lapses at sea level increase more with increasing Mach number than the AAF

Engine. The estimated thrust lapse for military power decreases less with increasing

altitude than the AAF Engine. The difference in thrust lapses with Mach number

is caused mainly by the moderate bypass ratio of the AAF Engine. The estimated

and computed AAF Engine maximum thrust lapses at 30 kft have the same trend

222 AIRCRAFT ENGINE DESIGN

Thrust

Lapse

(~)

1.4

1.2

1.0

0.8

0.6

0.4

0.2

' ' ' I ' ' i i I

Sea Level

Max~um

Milita~ ,~...'~

] i i p i

-- AAF Engine"

...... Predicted

0.0

~ ~ ~ , I ~ ~ , , I ~ ~ ~ L I ~ , ~ ,

0.0 0.5 1.0 1.5 2.0

Fig. 6.E6 Comparison of installed thrust lapses ~ at maximum and military power

(standard day).

until 00 > 1.07 (TR) where the estimated thrust lapse drops off more rapidly than

the AAF Engine.

In preceding chapters, a reprise was performed when better information than

the preliminary data used to start the design process became available. The AAF

Constraint Analysis of Chapter 2 was based on estimated engine thrust lapse

and preliminary aerodynamic data. The constraints were calculated and plotted

(see Fig. 2.E3), and a preliminary choice was made of the thrust loading

(TsL/Wro

= 1.25) and wing loading

(Wro/S

= 64 lbf/ft 2) for the AAE The engine

sizing, performed in Sec. 6.4, results in a static sea level installed thrust for two

AAF Engines of 31,680 lbf (vs 30,000 lbf estimated in Chapter 3) that provides

a revised thrust loading of 1.32 for the AAE A reprise of the Constraint Analy-

sis would be most appropriate now that improved thrust lapse data are available.

Only through this analysis can the question about the influence of the new thrust

lapse and aircraft weight fraction data on wing loading be answered. Table 6.El0

presents new values of the thrust lapse and aircraft weight fraction for each con-

straint boundary of Chapter 2. Using these new values of t~ and ~, computing and

plotting the new constraint boundaries yields Fig.6.E7. Please note that AEDsys

automatically updates the thrust lapse information in Constraint Analysis and Con-

tour Plots, but that you must enter the updated weight fraction manually.

Any specific boundary will shift about the constraint diagram with changes in

thrust lapse a and aircraft weight fraction ft. Increases in thrust lapse ot will reduce

the required thrust loading

Tsc/Wro

and decreases in the thrust lapse will increase