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

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ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 121

These numbers will also be useful in the initial estimation of

Pro Pro F

Cro -- rhoho Fho rho

(4.33)

4.3.3 Parametric vs Performance Behavior

During this process of selecting a set of reference point parameters for each

critical flight condition, it is important to remember that the final engine will always

be running off-design and will therefore behave differently at each operating point.

Thus, it makes little sense to try to find an engine, for example, of

fixed rrc, try,

or, and

Zt4

that works reasonably well at every operating point. It is, however,

desirable to have the selected sets of reference point parameters generally follow

the natural path of a single engine running off-design. Applying this logic will

increase the probability of success of a design.

But how is this natural path established in advance? There is no simple answer

to this question, but some good approximations are available. The best would

be to run several off-design computations (see Chapter 5) for promising designs

in order to generate directly applicable guidance. This would be equivalent to

coupling parametric and performance computations in an iterative manner and,

time permitting, offers a rich design experience. A simple and direct, but less

reliable, method is to use the typical off-design parameter behavior information of

Figs. 4.5-4.11, which are generated by the performance computer program portion

' ' ' ' I ' ' ' ' I '

0.0 0.5 1.0

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

' ' ' I I I i I i I I I I

[

I i I I

1.5 2.0 2.5 3.0

Aft (kft)

Fig. 4.5 Compressor pressure ratio (~'c) performance characteristics for a turbojet

with

TR =

1.0.

22 ''''l''''l''''l''''l

Air (kft)

, , J = I , , = = I ~ , , , i .... i ....

0.0 0.5 1.0 1.5 2.0 2.5

Fig. 4.6 Compressor pressure ratio (Trc) performance characteristics for a low bypass

ratio mixed flow turbofan with TR = 1.065.

4.5

I''''1''''1'

4.0

3.5

3.0

2.5

2.0

I '

Alt (kft)

1.5 i i , I , , , , I , , , , I , , , , I , ~ , ,

0.0 0.5 1.0 1.5 2.0 2.5

Fig. 4.7 Fan pressure ratio

('/l'f)

performance characteristics for a low bypass ratio

mixed flow turbofan with TR = 1.065.

122

1.1

I , , , , I , i , , I ' ' ' ,

Alt (kft)

1.0

0.9

0.8

0.7

0.6

0.5 .... I ~ , , , I , , ~ , I , , , , I , , , ,

0.0 0.5 1.0 1.5 2.0 2.5

Fig. 4.8

Bypass ratio (c~) performance characteristics for a low bypass ratio mixed

flow turbofan with

TR =

1.065.

' I ' I

I I

40k-20k

~O]Ok

, , , I , , , I , , , I , , , I , , ,

0.0 0.2 0.4 0.6 0.8 1.0

Fig. 4.9 Compressor pressure ratio (Trc) performance characteristics for a high

bypass ratio turbofan with

TR =

1.035.

123

:~l J 120k.40 k

1.52

1.50

1.48

1.46

1.44

1.42

1.40

1.38

1.36 ,

, , I , , , I , , , I , , , I , L ,

0.0 0.2 0.4 0.6 0.8 1.0

Fig. 4.10 Fan pressure ratio

(Tif)

performance characteristics for a high bypass ratio

turbofan with TR = 1.035.

10.0

I ' I I I '

9.0

a s

8.0

20k-40k

7.5 , i , , , i , , , l , , , I , , ,

0.0 0.2 0.4 0.6 0.8 1.0

Fig.

4.11 Bypass ratio (c~)

performance characteristics for a high bypass ratio

turbofan with TR = 1.035.

124

ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 125

of the AEDsys program developed in Chapter 5. Please note that the high- and

low-pressure turbine total temperature and total pressure ratios are almost constant

[see Eqs. (4.21c) and (4.22c) and Appendix D] and that afterburner operation has

no effect on these results because it is assumed (and almost universally true)

that the nozzle throat area (As) is controlled to make the mixer and all upstream

components oblivious to the afterburner conditions by maintaining a constant value

of the pressure at the mixer exit. Also, the results shown for 40 kft represent those

for all altitudes above the tropopause. Another means to understand and predict

off-design behavior is to employ the algebraic methods found in Appendix D.

Figures 4.5-4.11 all display the unmistakable signature of performance analysis,

namely the theta break imposed by the control system at 00 =

Oooreak = TR

(see

Appendix D). We will explain in much greater detail how to integrate performance

analysis computations into the search for promising reference points in Sec. 4.4.4.

4.3.4 Influence of the Mixer

One of the things about to be encountered is the remarkable impact of the

seemingly innocuous mixer on the range of acceptable design parameters for mixed

exhaust flow engines. The main reason for this influence is that the fan and core

streams are not separately exhausting to atmosphere, where their behavior would

be uncoupled and the only physical constraint would be

Pt > Po,

but they are

brought together in pressure contact within confined quarters. For this situation,

the operating parameters are much more restricted because neither M6 nor M16 can

be less than zero (reverse flow) or greater than one (choked). In tact, it is desirable

that neither M6 nor M16 even begin to approach zero because the corresponding

flow area would increase the engine cross-sectional (or frontal) area beyond reason.

Finally, common sense would encourage keeping design point values of M6 and

MI6 in the range of 0.4-0.6 because they are certain to migrate away during off-

design operation and therefore should start off with some cushion.

It is challenging to balance rrc, try, or, and

Tt4

in order to make M6 and M16 behave

properly. One available life preserver is to recognize that this desired behavior

requires

Pt6

approximately equal to

Ptl6,

Pt6 Po~rT"fdYfcLYrcHYrbYrtHrftL

Ptl6 POTfr~dTg f

which reduces to

7licLJ~'c.HJ'gtHJ'CtL/Yr f

~ -- ~'~

1 (4.34)

7rb

and then to use Eqs. (4.21c) and (4.22c) to reveal how to make yrc~/, Yrtn, and

ZrtL bring

Pt6

and

Ptl6

together. For example, if Zrc~/, zra4, and

ZrtL are

too large,

Eq. (4.22c) clearly shows that rtL, and therefore rrtL, Can be reduced by increasing

o/or ygf and by decreasing rx. The physical interpretation of this is that the low

pressure turbine drives the increase of fan airflow and pressure ratio. Also, as rx and

the capacity for each pound of air to do work in the low pressure turbine decrease,

zrtL must decrease in order to maintain the same power output. A valuable feature

of the ONX computer program is its ability to calculate the fan pressure ratio (7rf)

for a given bypass ratio (or), or Vice versa, that automatically matches the total

pressures at stations 6 and 16 using the complete Eqs. (4.21a) and (4.22a). This

126 AIRCRAFT ENGINE DESIGN

feature is activated by following the directions at the bottom of the ONX input

data window for the mixed flow turbofan engine.

The final safety net is that the ONX computer program has been arranged to

override the input of M6 if M16 is out of limits in order to obtain a legitimate

solution. Even if the solution is not a useful one (i.e., M16 "~ 0), the results will

indicate the right direction. If no solution is possible, the printout will tell which

of the two mixer entry total pressures was too high.

4.3.5 The Good News

Applying the ONX parametric engine cycle computer program to a new set of

requirements is an exhilarating experience. The tedious work is done so swiftly and

the results are so comprehensive that natural curiosity simply takes over. Almost

any search procedure from almost any starting point quickly leads to the region

of most promising results. The influence of any single input parameter on all of

the output quantities can be immediately determined by changing its value only

slightly. This is the basis of sensitivity analysis (see Sec. 4.4.5). The behavior of

each component can also be clearly traced and the possibility of exceeding some

design limitation (e.g., compression ratio or temperature) easily avoided.

In addition to fun, there is also learning. Armed with computational power and

an open mind, the best solutions made possible by natural laws literally make

themselves known. Simultaneously, the payoff made possible by various tech-

nological improvements or changes in the ground rules is determined. For the

moment, each participant really is like an engine company preliminary design

group, with similar capabilities and limitations. No wonder it is exhilarating.

4.4 Example Engine Selection: Parametric Cycle Analysis

Using the methods of the preceding sections, the search begins for the best com-

binations of engine design parameters for the Air-to-Air Fighter (AAF) described

in the Request for Proposal (RFP) of Chapter 1. Of the three thermodynamic mod-

els available with the ONX program, we have chosen to use for this exercise the

modified specific heat model MSH (constant specific heats through all components

except the combustor and afterburner where variable specific heats give a more

accurate estimate of the fuel consumption). This engine model gives the best of

both worlds--quick and accurate estimates of engine parametric behavior. Possi-

ble combinations of engine design points at selected critical flight conditions will

be investigated in order to narrow the ranges of key engine design parameters.

Once the most promising ranges of these parameters have been found, off-design

or performance analysis (Chapter 5) can proceed and the selected engine sized

(Chapter 6) to produce the installed thrust required.

4.4.1 Selection of Suitable Ranges of Design Point Parameters

In the constraint analysis of Chapter 2, a preliminary choice was made of the

engine's throttle ratio

(TR),

and a value of 1.07 was selected. The AAF constraint

and mission flight conditions are plotted vs theta zero (00) in Fig. 4.El. Note that

the corresponding flight conditions bracket the 1.07 value of 00. The engine is

Tt4

limited to the right of 00 = 1.07 and zrc limited to the left (see Appendix D).

To shrink the bewilderingly large number of promising reference point choices

to a manageable size, it is not necessary to conduct an exhaustive investigation of

ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS

190 = 1.07

127

Alt

(k ft)

0.0 0.5 1.0 1.5 2.0

Critical flight conditions

vs theta

zero (00)

for standard

day.

Fig. 4.El

all possible combinations of aircraft flight conditions and engine design points.

Instead, a few critical flight conditions having significantly different characteristics

and/or large fuel usage (small FI) may be used to establish important trends. For

the AAF of the RFP, the following represent such a sample:

1) Takeoff, 100°F at 2,000 ft--High thrust is required at a flight condition

(00 > 1.07) where the engine operation is

Tt4

limited. This is not plotted in Fig. 4.E 1

because the flight condition does not occur on a standard day.

2) Subsonic Cruise Climb (BCM/BCA), 0.9M/42 kftiLow fuel consumption

is required in phases 3-4 (I-I = 0.9736) and 10-11 (FI = 0.9698).

3) Supersonic Penetration and Escape Dash, 1.5M/30 kft--High thrust is re-

quired to permit low fuel consumption without afterburning (supercruise) in phases

6-7 segment G (FI = 0.9382) and 8-9 (FI = 0.9795).

4) Supersonic Acceleration, 1.2M/30 kftiBoth high thrust and low fuel con-

sumption with afterburning are required in phases 6-7 segment F (FI = 0.9837)

and 7-8 segment K (FI = 0.9828).

4.4.2 Component Design Performance Parameters

Referring to the data of Table 4.4, and recognizing that the AAF engine will

use the most advanced engine technology available, the design will be based on

the following component performance parameters and information:

128 AIRCRAFT ENGINE DESIGN

Description Input value

Polytropic efficiency

Fan

(ef)

0.89

Low-pressure compressor

(eeL)

0.89

High-pressure compressor (ecu) 0.90

High-pressure turbine (etH) 0.89

Low-pressure turbine (etD 0.91

Total pressure ratio

Inlet (Ygd max) 0.97

Burner (zrb) 0.96

Mixer (ZrM

max)

0.97

Afterburner (ZrAB) 0.95

Nozzle (zrn) 0.98

Component efficiency

Burner

(Ob)

0.995

Afterburner 0/AS) 0.97

Mechanical

Low-pressure spool

(OmL)

0.995

High-pressure spool (0m/4) 0.995

Power takeoff LP spool

(l]meL)

0.995

Power takeoff HP spool

(tlmeu)

0.995

Fuel (JP-8) heating value

(heR)

18,400 Btu/lbm

Main burner exit (Tt4

max )

_~< 3400 ° R

Afterburner (TtT) 3600°R

Turbine cooling air

Tt4max > 2400°R 61 = 62 = (Tt4max - 2400)/16,000

Tt4max

~-~ 2400°R sl = 62 = 0

4.4.3 Analysis of Results

The ONX parametric computer program accompanying this textbook was used

to study 60 different design point combinations of the design parameters Zrc, zrf, or,

Tt4, and Tt7 for the three flight conditions selected as critical for fuel consumption

in Sec. 4.4.1. The carpet plots in Figs. 4.E2-4.E6 are the results of this study

for the most promising combinations of design choices. The results are plotted as

uninstalled specific fuel consumption vs uninstalled specific thrust. The required

uninstalled specific fuel consumption (S) is plotted in order to allow for convenient

comparison with the estimated value of the uninstalled fuel consumption. Please

note that ~ = 0 corresponds to a zero bypass turbofan, normally known as a

turbojet. Incorporation of the engine control into the parametric analysis requires

that

Tt4

be limited to values less than

Tt4ma x

for flight conditions where 00 is less

than the throttle ratio

(TR).

The value of

Tt4

for these flight conditions can be

calculated using (see Appendix D)

00 ,~ "max

(4.35)

Zt4 = ~1,4

(i/h)

1.10

1.05

1.00

0.95

0.90

0.85

0.80

Target or Goal

I I I

Fig.

4.E2

I ' I

°=05 t

, I , , , , I ,

55 60

F / rh o

(Ibf/lbm/s)

BCM/BCA,

Tt4

= 2613°R, no AB.

1.15

1.10

1.05

1.00

(l/h)

0.95

0.90

0.85

' I ' ' I '

0.3

, , , , I , , , , I ,

60 65

F / rh o

(lbf/lbm/s)

Fig. 4.E3 BCM/BCA,

Tt4

= 2776°R, no AB.

129

4.6

4.4

4.2

4.0

3.8

3.6

3.4

3.2

Tt4 = 2613°R ....

Tt4 = 2776°R --

a=0.3

r S

J a=0.4 o~= 0.3

- ~ o~= 0.4

~ ~ a=0.5

..........

10 15 20 25 30

zcc

Fig. 4.E4 BCM/BCA, fan pressure ratio vs compressor pressure ratio,

Tt4

-- 2613

and 2776°R.

(l/h)

1.45

1.40

1.35

1.30

1.25

1.20

1.15

1.10

1.05

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

a=~ 0"3

, , , ,z~,, , ,~~-

~.°

, .... , ,

60 65 70

F / rh o

(lbf/lbm/s)

Fig. 4.E5 1.5M/30 kft,

Tt4

3200°R, no AB.

I I I

130