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

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SIZING THE ENGINE: INSTALLED PERFORMANCE 203

IM3'

(Dlo

-D9)/ L

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0 '

0.0

Fig. 6.12

I I I I

I'~ I I I ' I ' I ' I

Eq.(6.15)

n=3

0.2 0.4 0.6 0.8 1.0

/)9 / Dl0

Influence of external nozzle contour on

IMS.

Figs. 6.8 or 6.9 and Eq. (6.12), depending upon M0, and compute the nozzle

installation penalty from

Dnozzle

qCD(Alo

A9)

M0--~-(AI0 -

A9)/Ao

~)nozzle -- -- -- =

(6.16)

F mo(F/mo) Fgc/(thoao)

The nozzle installation penalty when 0.8 < M0 < 1.2 uses Fig. 6.8 and

Mo(CDe/2)(A

10/A0)

~nozzle =

(6.17)

F gc / (rhoao )

For a typical supercruise case [e.g.,

= 0.10, (A10 - A9)/A0 = 0.8,

Fgc/(fnoao)

= 2.0 and M0 = 1.5],

~bnozzle =

0.03.

The nozzle external drag of Eqs. (6.16) and (6.17) is included in the AEDsys

Mission Analysis, Constraint, and Contour Plot computations.

6.2.4 Sizing the Inlet Area (A1)

The size of the inlet area A1 is required by Eqs. (6.6a) and (6.8) to estimate the

inlet loss

¢inlet

for subsonic and supersonic inlets, respectively. The assumption of

a constant inlet area simplifies the problem to finding the flight condition(s) that

requires the largest inlet area, thus sizing A1. Because the engine size is not fixed

at this point in the design process, the required inlet area A1 can be conveniently

referenced to the freestream area of choked flow A~ of the engine at sea level,

static conditions (designated as

Aoref),

and stating the required values in terms of

204 AIRCRAFT ENGINE DESIGN

A1/Aoref.

When the engine is resized to a new value of

Aoref,

then the new required

inlet capture area A1 can be determined directly because both the sizing flight

condition and the ratio

A a/Aoref are

constant.

During

subsonic flight,

the engine airflow is usually accelerated from the free-

stream Mach number M0 to the inlet Mach number M1. To prevent choking of the

inlet, Ml must be less than unity (usually 0.8 or less to allow for inlet boundary

layer displacement or blockage); in other words, the inlet physical area A1 must be

slightly larger than the area that would be required to choke the engine flow, A~.

For subsonic flight, the flight condition with the largest A~ therefore determines

the inlet physical area. In addition to sizing the inlet for M1 = 0.8 or less to allow

for boundary layer displacement, a safety margin of 4% is provided to account

for any aerodynamic or mechanical effects that may further restrict the flow. As

an example, an A1 is to be selected for the typical high bypass turbofan engine

running at maximum throttle setting (max Jrc

Tt4

)

as shown in Fig. 6.13. From

Fig. 6.13, the largest required A~ occurs at the flight condition of M0 = 0.9 and

altitudes greater than 20 kft where A~ = 1.055A0ref. Therefore, sizing A 1 for M1 =

0.8 plus a 1.04 safety factor gives

A~ = 1.04(A~/A*I)M,

=0.8A*o =

(1.04)(1.038)(1.055Aoref) = 1.139Aoref

During

supersonic flight,

no freestream deceleration or stream-tube contraction

is expected, so the inlet

area A1

must simply exceed the largest required A0 by

the minimum amount needed for boundary layer bleed and margin of safety. The

Ao~ef

1.06

1.05

1.04

1.03

1.02

1.01

1.00

20 - 50 k~

Fig. 6.13

Sea Level

) kR

0.99

0 0.2 0.4 0.6 0.8 1

Required engine inlet area, high bypass turbofan

(TR =

1.044).

SIZING THE ENGINE: INSTALLED PERFORMANCE 205

1.20 ,

1.15

1.10

1.05

1.00

0.95

0.90

0.85 ' '

0.0

Fig. 6.14

40 kft, Cold Day

Ao,ef Aoret

~Day

/ Sea Level,

Cold Day

~Sea Level,

0.5 1.0 1.5 2.0

Required engine inlet

area, low bypass turbofan (TR = 1.07).

amount of boundary layer bleed depends on inlet type and design (see Sec. 10.2.3),

and, for example, will be about 4% for a Mach 2 external compression inlet.

Sizing an inlet that is required to operate in both subsonic and supersonic flight

regimes rests upon an analysis that includes both of the preceding requirements for

physical inlet area. Combining the constraints of subsonic and supersonic flight

operations on inlet area A1 for a specific engine size Aoref gives a family of curves

A~/Aoref

(for M0 < 1) and

Ao/Aore f

(for M0 > 1) as shown in Fig. 6.14 for a

typical low bypass, turbofan engine running at maximum throttle setting (max :re

or T~4). In this figure, each line represents the required inlet area at one altitude.

The lines are continuous at M0 ----- 1 because A0 = A~ there. From Fig. 6.14, the

maximum inlet area occurs at the flight condition of Mach 1.55 at 40 kft altitude

on a cold day, where the required A0 = 1.17Aor@ Sizing A1 for a 1.04 safety

factor gives

A] = 1.04(1.17Aoref)= 1.217Aoref

6.2.5 Sizing the Exhaust Nozzle

(A9)

To evaluate the exhaust nozzle loss

~)nozzle,

Eqs. (6.15-6.17) require the values

of Ag, A10, and L. The nozzle exit area A9 for any flight condition is obtained

directly from the Engine Test portion (or the second summary page of the Mission

206 AIRCRAFT ENGINE DESIGN

"/19

Ag~

Fig. 6.15

2.5

2.0

1.5

1.0

0.5

0.0

,,i,,,,l~,,,i,,~

Sea

I , , i ] I I I I ] I I I I J I I I I

0.5 1.0 1.5 2.0

Required engine exit area, mixed flow afterburning turbofan

(TR =

1.07).

Analysis portion) of the AEDsys program. Figure 6.15 shows the variation of

the A9 required for a mixed flow afterburning turbofan engine to match the exit

pressure P9 to the ambient pressure Po. In this figure, A9 is referenced to its sea

level, standard day value with full afterburning, known as

A9ref.

Good judgement

is used to size Alo and L with the data for A9 available. To ensure that Alo is not

smaller than A9 for any flight condition, it should be made somewhat larger than

the greater of the largest A9 required in the flight mission or the A9 required for

the maximum Mach number flight requirement of the aircraft. With A9 and Alo

fixed, the choice of the nozzle length (L) can be based on their values, a reasonable

estimate being 1-2 times D9.

6.3 AEDsys Software Implementation of Installation Losses

The AEDsys software incorporates the installation loss models of this chapter

as well as the constant loss model used in the preceding chapter. When either

of these installation loss models is selected, all of the computations in Mission

Analysis, Constraint Analysis, and Contour Plots use that loss model. The sizing

of the engine and determining its installed performance is straightforward using

this software.

The user enters the inlet area A1, afterbody area A10, and nozzle length L into

the data fields on the Engine Data window. To reduce the inlet additive drag during

takeoff (see Fig. 6.2), the program includes an auxiliary inlet

area

(Alaux)

that will

be open from static conditions through the input cutoff Mach number (M,,~).

SIZING THE ENGINE: INSTALLED PERFORMANCE 207

The preliminary inlet and afterbody dimensions are obtained by operating the

aircraft over its mission and performance requirements using an initial estimate

of the constant installation loss over the flight envelope. With this loss estimate,

the Mission Analysis gives the required area of the engine mass flow at inlet

(A~ or A0) and the nozzle exit area (A9) for each leg. These data are used to

select the inlet area A1, afterbody

area A10,

and nozzle length L as described in

Sees. 6.2.4 and 6.2.5. The Engine Test window allows the user to determine the

required engine inlet end exit areas over the entire range of operation for the

required uninstalled engine thrust

Ere q = ( TsL // WTO )req WTO.

Once the inlet area A1, afterbody area A10, and nozzle length L are determined

and entered into the Engine Data window of AEDsys, the installation losses are

computed using Eqs. (6.6), (6.8), (6.16), and (6.17). These models are also used

in the Mission Analysis, Constraint Analysis, and Contour Plots. As was shown in

Chapter 5, the improvements in the engine model between those of Chapter 2 and

Chapter 5 resulted in better estimates of fuel usage and thrust loading for the AAF.

The improved installation loss models further refine these estimates and allow the

final determination of the engine size.

When the available thrust loading

(TsL/Wro)avaa

or the number of engines is

changed in the AEDsys program, the Thrust Scale Factor

(TSF)

is updated and

the user is asked if they want to automatically scale the inlet area (A1), afterbody

area (A10), and nozzle length (L). Because the preceding design values are based

on the preceding thrust loading or number of engines, responding "yes" saves the

user these calculations.

The external drag for the supersonic inlet of Eq. (6.10) is not included in the

AEDsys software because the shape of the cowl is not yet known and because the

internal drag estimate of Eqs. (6.6a) and (6.8) is deliberately conservative.

Finally, the iteration process ends when the selected engine size meets all of the

thrust requirements of the aircraft as verified by Constraint Analysis and Mission

Analysis computations including the final inlet and nozzle installation losses.

6,4 Example Installed Performance and Final Engine Sizing

This phase of engine design has two objectives. First, to use the installation

loss models presented in this chapter to determine a better estimate of the installed

engine performance and its impact on the engine design choices made in Chapter 5.

It is possible that the installation effects could even change the cycle design choices.

Second, to use the installation loss models to determine the engine size that will

meet all the AAF RFP performance and mission requirements.

As noted in Sees. 4.2.8 and 5.4.4, the MSH (modified specific heat) performance

model is used in all of the ensuing AAF engine computations.

6.4.1 Critical Constraint~Mission Legs for Sizing

The process begins by selecting the legs that are most likely to require the largest

values of

TsL/Wro, A9,

or A1. If they are not evident by this point, a wide search

must be executed. In the case of the AAF, the critical constraint/mission points, as

explained next, are 1) takeoff constraint; 2) supercruise constraint; 3) 1.6M/30 kft,

5g turn constraint; 4) 1.6M/30 kft, 5g turn constraint; 5) acceleration constraint;

and 6) maximum Mach number constraint.

208 AIRCRAFT ENGINE DESIGN

In Fig. 3.E5 the constraint boundaries of legs 1, 2, 4, and 5 are all close to the

available thrust loading

{(ZsL/WTO)avail}

of 1.25 selected for the AAF. At these

flight conditions, the engine can be expected to be running near its full thrust and to

have therefore the larger values of

(Ts~./WTO)req/(TsL/WTO)avail.

Flight conditions

1, 3, 4, 5, and 6 are afterburner operating points that require the larger exhaust

nozzle settings and areas (A9). From Fig. 6.14, it is evident that the high Mach

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

the inlet area requirement (A0 for this type of aircraft.

6.4.2 AAF Engine Search Including Installed Performance

Incorporating the Chapter 5 engine performance models into the Constraint,

Mission Analysis, and Contour Plot portions of the AEDsys software makes this

search effortless. The search begins with the calculation of the Constraint and

Mission Analysis for all candidate engines with constant 5% installation loss, as

was done in Chapter 5 to obtain the results of Table 5.E3. When Mission Analysis

is based on a candidate engine, the second summary page provides the area of the

engine mass flow at inlet (A N or A0) and the nozzle exit area (A9) for each mission

leg. These data are used to select the inlet area A1, afterbody area A10, and nozzle

length L.

As just noted, the most demanding flight condition for sizing the inlet of the

AAF occurs at 1.6M/40 kft on a cold day (similar to Fig. 6.14). To obtain this

information for any candidate engine, the Engine Test portion of AEDsys program

is used to calculate the uninstalled performance on a cold day at 40 kft over a range

of Mach numbers. The printed and plotted results give the variation of engine mass

flow inlet area (A N or A0) and nozzle exit area (A9) with flight Mach number.

We found that the largest nozzle exit area corresponds to the AAF Mission

Segment 6--7 F acceleration with full afterburner at 1.465M/30 kft. Although

a larger nozzle exit area is predicted for the maximum Mach flight constraint

(1.8M/40 kft) with full afterburner and

Po/P9

= 1, this large an engine or nozzle

is not needed to meet this flight condition [uninstalled engine thrust of 10,750 lb

(=10,210/0.95)]. You can verify this conclusion by testing the engine at

1.8M/40 kft over a range of Tt7 and noting the required nozzle exit area corre-

sponding to the required uninstalled thrust or testing the engine at the required

uninstalled thrust and noting the exit area listed on the Summary of Test Results

output of the Engine Test window.

Table 6.El shows the maximum engine areas (A N or A0 and A9) for Engines

1-20 of Table 5.E3. The selected values of the inlet area A1, afterbody area A10,

and nozzle length L are also listed. These are entered into the Chapter 6 installation

loss model data of the Engine Data window. To reduce installation loss at takeoff,

an auxiliary air intake

area

Alaux

equal to the inlet area Al was selected for the

AAF up to M0 = 0.3.

The installed performance was calculated for the 20 candidate engines at an

available thrust loading

[(TsL/WTO)avail]

of 1.25. The mission fuel usage results

are given in Table 6.El and plotted in Fig. 6.El. Comparison with Table 5.E3 and

Fig. 5E.3 shows that the overall fuel saved is now 20 to 70 lbf less than predicted

earlier. An improved estimate of the required engine thrust loading

[(TsL/WTO)req]

was obtained using Constraint Analysis with the aircraft weight fraction (fl) set

to 0.8221 (see Sec. 3.4.3) for maneuver weight and calculations performed for wing

SIZING THE ENGINE: INSTALLED PERFORMANCE 209

7.4

~1 ~ .~o

,,~ ',5 '~ ,,~

',~ ~5 ',5

,,,4 ,,'-; ' ,,,'-;

,-4

,,.4

(,q

E ,~'a

@O~x~a

210 AIRCRAFT ENGINE DESIGN

Fuel

Saved

(lbf)

300

200

100

-100

-200

' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' l ' ' ' ' I ' ' ' '

20 21 22 23 24 25 26 27 28

Compressor Pressure Ratio (~,)

Fig. 6.El Fuel saved referenced to

WF =

6690 Ibf.

loading of 64 lbffft 2. On balance, Engine 15 remains the preferred choice for the

AAE It consumes 245 lbf of fuel less than the Chapter 3 estimate of 6690 lbf

and the required thrust loading {(TsL/Wro)req} is one of the lowest available (see

Sec. 5.4.5).

The Engine 15 thrust loading required for aircraft performance at both the

5% constant installation loss and the loss model of this chapter are presented in

Table 6.E2. The large changes in required thrust loading (TsL/WTO)req between the

estimates of Chapters 5 and 6 are as a result of the improved installation loss model.

Nevertheless, the RFP performance requirement of the subsonic 5g turn at 0.9M/30

kft continues to size the AAF engine. The increase in fuel consumption (decrease

in fuel saved from Table 5.E3) is caused by the increase of the installation losses in

the Combat Air Patrol 5-6, Supersonic Penetration 6-7G, and Loiter 12-13 legs

of the AAF mission (see Table 6.E9 for final details of the sized AAF Engine).

6.4.3 AAF Engine Sizing Procedure

The design tools developed in this chapter and incorporated into the AEDsys

software are used to estimate the installed thrust loading (TsL/Wro) necessary

to meet the AAF RFP requirements. The minimum engine size necessary is that

for which the design engine mass flow gives the available installed thrust

(Tavail)

equal to the required installed thrust (Treq) for the flight condition that is the

most demanding as measured by the ratio of required-to-available thrust loading

[ ( TsL / WTO )req / ( TsL / WTO )avail] .

SIZING THE ENGINE: INSTALLED PERFORMANCE

Table 6.E2 Required thrust loading for Engine 15"

211

Chapter 6

Performance Chapter 5

(TsL / WTO)req Ol b Treq c

lbf ~bi,le, +

requirement Mo Alt, kft

(Tsc/WTO)req ~)nozzle b

Takeoff (100°F) 0.1 2 1.223 1.179 0.8461 23,940 0.0135

Supercruise 1.5 30 1.231 1.235 0.3610 10,700 0.0520

Supersonic 5g 1.6 30 0.9436 0.9235 0.8334 18,470 0.0288

turn

Subsonic 5g 0.9 30 1.359 1.310 0.4842 15,220 0.0152

turn

Horizontal 1.2 30 1.091 1.047 0.6678 16,780 0.0093

acceleration

Maximum Mach 1.8 40 0.6367 0.6181 0.6564 9,740 0.0209

aft = 1.0 at takeoff and 0.8221 at all other flight conditions.

bBased on data in Table 6.El.

CTreq = ~(TsL/Wro)req WTO.

To find this minimum engine size for the AAF, the procedure diagrammed in

Fig. 6.E2 and listed next will be followed:

1) Select as critical RFP mission points those flight conditions having the poten-

tial to require a) the largest fraction of available thrust

{(TsL/WTO)req /

(TsL / WTO)avail},

the largest exhaust nozzle exit area (A9), or c) the largest inlet

area (A1) at engine station 1 (Figs. 4.1a and 6.4).

2) Assuming a constant installation loss of 5% and available thrust loading

(TsL / WTO)avail

of 1.25, determine

(TsL/WTO)req

for the selected engine (Engine 15)

at the critical mission points and required performance constraints. The resultant

thrust loadings

{(TsL/Wro)req}

for critical aircraft performance are summarized

in Table 6.E2 under the Chapter 5 column. This was done for each engine of

Chapter 5 and summarized in Table 5.E3 as percent increase in thrust loading.

3) Based on the largest

(TsL/Wro)req

and estimated

Wro

from Chapter 3, find

the tentative engine size

(ZSL)req.

Separately examine the feasibility of a single- or

multiengine installation and select the number of engines to be used in the AAF

(see Sec. 6.4.4 for guidance). Simply entering the selected number into its input

field on the Engine Data window of AEDsys changes the number of engines. When

the number of engines is changed, the

TSF

is updated and the user is asked if he

or she wants to automatically scale the inlet area (A1), afterbody area (Al0), and

nozzle length (L). Because the preceding design values are based on the preced-

ing thrust loading or number of engines, responding "yes" saves the user these

calculations.

4) Determine the required A1, Al0, and L for the engine with available thrust

(Tsc/WTO)avail

of 1.25. This was done in Sec. 6.4.1 for the 20 engines under

consideration and summarized in Table 6.El for a single-engine installation. Select

"Installation Loss Model of Chapter 6" in the Engine Data window of AEDsys

and input the data for A1, A10, and L. Note that area can be input for an auxiliary

air intake to be used at low Mach number to reduce installation loss. An auxiliary

212 AIRCRAFT ENGINE DESIGN

Resize

Al,

A~o,

and L

I(TsL/mTo)avai, ~'(TsL/mTo)req

~..

Done

Initial Engine rh0,

Cro's

Assume Available Thrust Loading

(TsL / Wro )avail

for Aircraft System

Estimate (¢i.,e, + Cno=le ) and

Determine (TsL

/ Wro )req

Select Number of Engines

Determine

A t , A~o,

and L

Determine

( TsL / Wro

)req

~Yes

Resize Engine

rho, Cro ' s L.

Fig. 6.E2 Flowchart for engine sizing.

Nol