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

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162 AIRCRAFT ENGINE DESIGN

Sample Printout C

Turbofan with AB--Dual Spool

AEDsys (Ver. 3.00)

Engine File: C:\Program Files\AEDsys\AAF Base Line Engine.ref

Date: 10/01/2002 6:00:00 AM

Input Constants

Pidmax = 0.9600 Pi b = 0.9500 Eta b = 0.9990

cp c = 0.2400 cp t = 0.2950 Gam c ---- 1.4000

Pi AB = 0.9500 Eta AB ---- 0.9900 cp AB = 0.2950

EtacL = 0.8674 EtacH ---- 0.8751 EtatH = 0.8995

Eta mL = 0.9950 Eta mH ----- 0.9950 Eta PL = 1.0000

Eta f = 0.8674 PTO L = 0.0KW PTO H = 281.9KW

Bleed = 1.00% Cool 1 = 5.00% Cool 2 = 5.00%

Control Limits: Tt4 = 3200.0 Pi c = 20.00

** Thrust Scale Factor = 0.9372

Parameter Reference**

Mach Number @ 0 1.4510

Temperature @ 0 390.50

Pressure @ 0 3.3063

Altitude @ 0 36000

Total Temp @ 4 3200.00

Total Temp @ 7 3600.00

Pi r/Tau r 3.4211/1.4211

Pi d 0.9354

Pi f/Tau f 3.9000/1.5479

Pi cL/Tau cL 3.9000/1.5479

Pi cH/Tau cH 5.1282/1.6803

Tau ml 0.9673

Pi tH/Tau tH 0.4231/0.8381

Tau m2 0.9731

Pi tL/Tau tL 0.4831/0.8598

Control Limit

LP Spool RPM (% of Reference Pt) 100.00

HP Spool RPM (% of Reference Pt) 100.00

Mach Number @ 6 0.4000

Mach Number @ 16 0.3940

Mach Number @ 6A 0.4188

Gamma @ 6A 1.3250

cp @ 6A 0.2782

Pt 16/Pt6 1.0042

Pi M/Tan M 0.9637/0.8404

Alpha 0.449

Pt9/P9 11.0362

P0/P9 1.0000

Mach Number @ 9 2.2217

Mass Flow Rate @ 0 187.45

Corr Mass Flow @ 0 251.91

Flow Area @ 0 5.836

Flow Area* @ 0 5.099

Flow Area @ 9 9.481

MB--Fuel/Air Ratio (f) 0.03070

AB--Fuel/Air Ratio (fAB) 0.03353

Overall Fuel/Air Ratio (fo) 0.05216

Specific Thrust (F/m0) 110.83

Thrust Spec Fuel Consumption (S) 1.6941

Thrust (F) 20775

Fuel Flow Rate 35195

Propulsive Efficiency (%) 46.26

Thermal Efficiency (%) 45.25

Overall Efficiency (%) 20.93

Pi n = 0.9700

Gam t = 1.3000

Gam AB = 1.3000

Eta tL = 0.9074

Eta PH = 1.0000

hPR = 18400

Test**

1.9000

390.00

2.4806

42000

2277.00

1269.42

1.6913/1.1620

0.9600

2.8692/1.4051

4.5285/1.9197

0.9673

0.4231/0.8381

0.9731

0.5023/0.8705

Tt4 Set

77.70

81.97

0.3748

0.4814

0.4185

1.3302

0.2750

1.0706

0.9779/0.8119

0.576

4.0243

1.0000

1.5814

59.80

195.80

3.999

3.964

3.553

0.01975

0.00000

0.01115

43.50

0.9228

2601

2400

55.78

43.25

24.12

ENGINE SELECTION: PERFORMANCE CYCLE ANALYSIS 163

5.3 Component Behavior

Off-design cycle analysis requires a model for the behavior of each engine

component over its actual range of operation. The more accurately and completely

this is done, the more reliable the computed results. Even though the approach

(constant efficiency of rotating components and constant total pressure ratio of the

other components) used in this textbook gives answers that are perfectly adequate

for this type of preliminary design, it is important to know that the usual industrial

practice is to use data or correlations having more accuracy and definition in the

form of component "maps." The material in this section will explain the role and

usefulness of these maps and will demonstrate that the approach of this textbook

is essentially correct. Indeed, the principal values of the maps are to improve the

understanding of component behavior and to slightly increase the accuracy of the

results.

5.3.1 Dimensionless and Corrected Performance Parameters

The first step is to use dimensional analysis to identify correlating parameters

that allow data taken under one set of conditions to be extended to other conditions.

This is necessary because it is always impractical to accumulate experimental data

for the bewildering number of possible operating conditions and because it is often

impossible to reach many of them in a single, affordable facility.

The quantities of pressure and temperature are normally made dimensionless by

dividing each by their respective standard sea level static value. The dimensionless

pressure and temperature are represented by ~ and 0, respectively. When total

(stagnation) properties are nondimensionalized, a subscript is used to indicate the

station number of that property. The only static properties made dimensionless are

freestream, the symbols for which carry no subscripts. Thus,

¢~i "~ eti/ estd

(5.21)

and

Oi ~ Tti/ T~ta

(5.22)

where

Pstd

= 2116.2 lb/ft z and Tstd = 518.69°R.

Dimensional analysis of engine components yields many useful dimensionless

and/or modified component performance parameters. Some examples of these are

the compressor pressure ratio, adiabatic efficiency, Mach number at the engine face,

ratio of the blade (tip) speed to the speed of sound, and the Reynolds number. 2

The "corrected mass flow rate" at engine station i used in this analysis is defined

ITt ci ":- m i ~ii / ~ i

(5.23)

and is related to the engine face Mach number. The "corrected engine speed" is

defined as

N,.i -- N /v/-~i

(5.24)

and is related to the Mach number of the rotating airfoils.

There is another interpretation of the corrected mass flow rate that you may

find intuitively appealing. Starting from the definition of the mass flow parameter,

164 AIRCRAFT ENGINE DESIGN

substituting Eqs. (5.21-5.23), and rearranging, you will find that

• estdAi

mci = V~std MFPi

Thus,

rnci

is the amount of mass that would flow under standard conditions if

and

MFPi

(i.e., F and

Mi)

were fixed. In other words, it is the mass flow that would

be measured if a given machine were tested at standard conditions with the critical

similarity parameter

kept equal to the desired operating value.

It must be understood that this selection of parameters represents a first approx-

imation to the complete set necessary to reproduce nature. This collection would

not reflect, for example, the effects of viscosity (Reynolds number), humidity, or

gas composition. Nevertheless, it is extremely useful and has become the propul-

sion community standard. When required, the effects of the mission parameters

are supplied by "adjustment factors" also based upon experience. Please note also

the appearance, for the first time, of rotational speed (N), a quantity of obvious

significance to the structural designer•

5.3.2 Fan and Compressor Performance Maps

The performance map of a compressor or fan is normally presented using the

following performance parameters: total pressure ratio, corrected mass flow rate,

corrected engine speed, and adiabatic efficiency.

The performance of two modem high-performance fan stages is shown in this

format in Fig. 5.4. They have no inlet guide vanes. One has a low tangential

Mach number (0.96) to minimize noise. The other has supersonic tip speed and a

considerably larger pressure ratio. Both have high axial Mach numbers.

Variations in the axial flow velocity in response to changes in pressure cause

the multistage compressor to have quite different mass flow vs pressure ratio

characteristics than one of its stages. The performance map of a typical high-

pressure ratio compressor is shown in Fig. 5.5.

A limitation on fan and compressor performance of special concern is the stall

or surge line. Steady operation above the line is impossible and entering the region

even momentarily is dangerous to the engine and aircraft.

1.5-

1.4-

N1.3-

1.2-

1.1

2.0

p°int~ ~110 .~

design

°perating linerS. ~'80 ~J~., I j:~ 1.8'

stall line /,~ i "100 09

-t/,ZN°8'

N~:2

1.4-

"" " ~65 L~

Eft= 0.85 0.86

I I I I I

40 60 80 100 120

% Design Corrected Mass Flow

a. Subsonic Tangential Mach

1.2

operating line ~/~ 082

design p°int'~" ~/i "Eft = 0.80

°-84,~,',~ V; l

I I I I t

40 60 80 100 120

% Design Corrected Mass Flow

b. Supersonic Tangential Mach

Fig. 5.4 Typical fan stage maps. 3

ENGINE SELECTION: PERFORMANCE CYCLE ANALYSIS 165

150

100-

% Design

Pressure

Ratio

50-

Fig.

5.5

i I i I i I i i

design point

operating line

stall line ~.~~

~~'~o/oN'~c2~__~ ~ Eft= 0"7590

' I ' I ' I ' I

40 60 80 100

% Design Corrected Mass'Flow

Typical compressor map. 4

110

120

5.3.3 Combustor Maps

The combustor performance parameters that are most important to overall en-

gine performance are the pressure loss through the combustor and combustion

efficiency. The pressure loss performance of a combustor (rOb) is normally plotted

vs the corrected mass flow rate through the combustor (rh3x/~3/83) for different

fuel-air ratios as shown in Fig. 5.6a. The efficiency of the combustor (fib) Can be

presented as a plot vs the temperature rise in the combustor or fuel-air ratio for

various values of inlet pressure as shown in Fig. 5.6b.

5.3.4

Turbine Maps

In a turbine, the entry stationary airfoils, often called inlet guide vanes or noz-

zles, expand the entering flow and discharge it into rotating airfoils, known as

rotors or blades. The flow of gas through the turbine nozzles has much in com-

mon with the flow of a compressible fluid through an exhaust nozzle, including

choking at the minimum area when the backpressure is below the critical value.

Therefore, the flow through the turbine nozzles is a function of the turbine pressure

ratio (Trt), the turbine inlet total pressure (Pt4), and the turbine inlet total temper-

ature (Tt4) when the nozzles are operating at a subcritical pressure ratio and are

not choked. Conversely, the flow through the turbine nozzles depends only upon

the inlet total pressure (Pt4) and the inlet total temperature (Tt4), once choking

occurs.

The work extraction of modem gas turbines is usually so large, and 7rt so small,

that the nozzles are usually choked for the design point and the surrounding region.

If not, the throat Mach number is sufficiently close to one that the mass flow

166 AIRCRAFT ENGINE DESIGN

"fib

I I I I I I

I I I I I

60 70 80 90 100

%DesignCorrec~dMass Flow

I I

110 120

b) l.O0

T~b

0.95 --

I I I I I I

0.90 I I I I I

600 800 1000 1200 1400 1600

Tt4 - Tt3

(°R)

Fig. 5.6 Combustor maps.

Pt3

(psia)

1800 2000

parameter approximates that of choking (Ref. 1). The analytical convenience this

makes possible has already been capitalized upon in Chapters 4 and 5.

The parameters that are normally used to express the performance of a turbine

are total pressure ratio, corrected mass flow rate, corrected engine speed, and

adiabatic efficiency.

Figure 5.7 shows the reciprocal turbine total pressure ratio ( 1/:rrt

also known as

the expansion ratio, plotted as a function of the corrected mass flow rate (rh4 ~'04/34)

and corrected mechanical speed

(N/4~4).

The maximum flow of gas that can be

accommodated by the nozzles when choked is clearly evident.

For reasons of size, it is desirable that the turbine mass flow rate per annulus

area be as large as possible, which also points to choking and a high reciprocal

total pressure ratio (1/~rt). Because the mass flow rate is nearly independent of

ENGINE SELECTION: PERFORMANCE CYCLE ANALYSIS 167

3.5

3.0-

2.5--

2.0-

.~ 1.5-

I I

%N~4 = 80 90 100 110

1.0

I I I

70 80 90 100 110

% Design Corrected Mass Flow

Fig. 5.7 Turbine map.

speed for the pressure ratios of interest, all speed characteristics collapse onto a

single line when plotted vs the turbine expansion ratio (1/zrt) and the turbine has

the mass flow characteristics of a choked nozzle• So that only one map is required

to show the performance of a turbine, the abscissa can be taken as the corrected

mass flow rate multiplied by the corrected engine speed; thus, a separate plot for

the turbine adiabatic efficiency is not required. A map for a typical 50% reaction

(at mean radius single-stage turbine is shown in this format in Fig. 5.8.

5.0

4.5

4.0

"~ 3.5

i 3.0

x~ 2.5

2.0

1.5

1.0

I I [o I I I I

YoNc4

= 90

60 I 70~ .~'8t-- -- --I -- 10~0~ "~.~11 1 120

operating

I 0.83 / / 0.86 A 0.90 / !'*. l \ )ine

I/ I,"I ,'"T', I', I \J

I t----[4---~t-'-- 1_ - ,

\,, \.. ;-}

-- ~-'& 1--~/T I

/'L'P 4 fJ.'

Eft = 0.80 \ '~' "" ~ ~ ~ ~ /

"$.

1"'1---t--/-7 J

} ZJ/J./J

I I I I I I I

60 70 80 90 100 110 120 130

% Design Corrected Mass Flow x % Corrected RPM

Fig. 5.8 Typical turbine map.

168 AIRCRAFT ENGINE DESIGN

Because the turbine adiabatic efficiency does not vary as rapidly with off-design

variations as in a compressor, the turbine characteristic can be approximated for

preliminary design calculations by a constant adiabatic turbine efficiency (t/t) and

a choked mass flow characteristic. These are the characteristics that were used in

performance analysis.

5.3.5 Component Matching

This is the time to clarify what appears to be a shortcoming or internal incon-

sistency in the off-design calculation procedure. The heart of the matter is this:

the off-design equations are silent with regard to the rotational speeds of the ro-

tating machines, despite the obvious fact that each compressor is mechanically

connected via a permanent shaft to a turbine, whence they must always share the

same rotational speed. The rotational speed will, in general, be different from the

design point speed and, for this purpose, dimensionless compressor and turbine

performance maps (e.g., Figs. 5.4 and 5.8) also contain data pertaining to rotational

speed. It would seem, then, that the off-design equation set lacks some true physical

constraints (i.e., Arc =

Nt)

and must therefore produce erroneous results. The fol-

lowing discussion will demonstrate that this appearance is, fortunately, misleading.

The business of ensuring that all of the relationships that join a compressor

and turbine are obeyed, including mass flow, power, total pressure, and rotational

speed, is known as "component matching." The off-design calculation procedure of

this textbook correctly maintains all known relationships except rotational speed.

The simplest and most frequently cited example of component matching found

in the open literature is that of developing the "pumping characteristics" for the

"gas generator" (i.e., compressor, burner, and turbine) of a nonafterburning, single-

spool turbojet (e.g., Refs. 1, 2, 5-7). Careful scrutiny of this component matching

process reveals that the compressor performance map is used to update the estimate

of compressor efficiency and to determine the shaft rotational speed; the turbine

performance map and shaft rotational speed are then used only to update the

estimate of turbine efficiency. In other words, the main use of enforcing Arc = Art

is to provide accurate values of compressor and turbine efficiency.

If suitable compressor and turbine performance maps were available, they could,

of course, be built into the off-design calculation procedure, and the iteration just

described would automatically be executed internally. When such performance

maps are not available, as is often the case early in a design study, the best approach

is to supply input values of t/c and t/t based on experience. This "open-loop" method

can also be employed later when satisfactory performance maps become available.

The principal conclusion is that accurate estimation of t/c and t/t at the off-design

conditions has the

same

result as using performance maps and setting

Nc = Nt.

Consequently, the off-design calculation procedure of this textbook is both correct

and complete. An important corollary to this conclusion is that the "operating line"

(i.e., Jr or r vs

rhv'CO/8)

of every component in the engine is a "free" byproduct of

the off-design calculations, even when the engine cycle is arbitrarily complex.

To make these conclusions even more concrete, it is useful to look more closely

at the turbine. According to the typical turbine performance map of Fig. 5.8, this

machine can provide the same work (i.e., 1 - rt) for a wide range of No =

Nt,

while t/t varies only slightly. Please recall that as long as the flow in the turbine

ENGINE SELECTION: PERFORMANCE CYCLE ANALYSIS 169

Station:

1 Stator 2 2R Rotor 3R 3

I I I I I

I ,or., : looo fps I I

I I ~

I //]v

u2 = u2R ~-~__,,r / , / I 3R

= w r~

[ rm

a ~

Fig. 5.9 Single stage impulse turbine.

inlet guide vane and some downstream flow area remains choked and rh does

not vary significantly, then Eq. (5.2) has demonstrated that ~rt and rt must be

essentially constant. The question, then, is how the turbine flow conditions can

adjust themselves in order to provide the

same

rt at

different

values of (or. If the

mechanics of adjustment are straightforward, then the entire process of component

matching should be more easily comprehended.

Consider the single-stage, impulse, maximum work (i.e., no exit swirl), is-

entropic, constant height turbine of Fig. 5.9 (see Ref. 2). At its design point, this

turbine has a choked inlet guide vane and an entirely subsonic flow relative to the

rotor. The flow angles are all representative of good practice. In short, this is a

rather standard design.

Isentropic calculations have been performed at rotational speeds ±10% from

design, which would encompass the entire operating range for most compressors.

The necessary condition for a solution was that rt have a design point value of

0.896. The results are displayed in Table 5.2.

These results confirm the message of the Euler turbine equation. Since (1 - rt)

is proportional to

(orm(1)2R --

1.'3R),

then

M2,

Men, and

M3R

must increase in order

to compensate for reductions in

(orm,

and vice versa. Nevertheless, even for such

large differences in

Wrm,

the aerodynamic results are far from disastrous. For one

thing, the inlet guide vanes remain choked (M2 > 1) and the rotor airfoils remain

subsonic

(M21¢

< 1 and M3R < 1) at all times. For another, the rotor airfoil relative

inlet flow angle (/32) and the inlet flow angle to the downstream stator airfoils (~3)

are well within the low loss operating range for typical turbine cascades. Finally,

one might expect the frictional losses to increase and the efficiency to decrease as

(orm

decreases and the blade scrubbing velocity increases, but only gradually.

170 AIRCRAFT ENGINE DESIGN

Table 5.2 Turbine off-design performance

Quantity - 10% Design + 10%

Wrm,

ft/s 900 1000 1100

M2 1.22 1.10 1.02

0/2, deg 50.6 52.0 52.4

f12, deg 35.2 32.6 28.4

MzR 0.947 0.804 0.708

M3R 0.820 0.804 0.790

0/3, deg -4.2 0 3.5

rt 0.899 0.896 0.898

Tt2 = 2800°R; y = 1.33;

gcR

= 1716

ft2/(s2--¢~R).

This turbine therefore performs gracefully as expected, providing the same rt

with slight changes in Ot for a wide range of Arc =

Nt,

all of the while remaining

choked.

5.3.6 Engine Performance Program Predictions

The engine performance portion (referred to as Engine Test) of the AEDsys

program, based on the equations developed in this chapter, can determine the

performance of many types of engines at different altitudes, Mach numbers, and

throttle settings. The accuracy of the resulting computer output depends on the

validity of the assumptions specified in Sec. 5.2.2. The engine speed (N) is not

incorporated in the off-design equations and is needed only when the efficiency of

the rotating components (fan, compressor, or turbine) vary significantly over the

operating speed (N) of the engine. Thus, the assumption of constant component

efficiency (Of, 0eL, 0cH, Or/4, and OtL) removes the engine speed from the system

of equations for prediction of off-design performance. This absence of engine

speed from the off-design equations allows the determination of engine perfor-

mance without the prior knowledge of each component's design point (knowl-

edge of each component's design point and off-design performance by way of

a map is required to include engine speed in the off-design performance). As

shown in the maps of Figs. 5.4, 5.5, and 5.8, the efficiency of a rotating compo-

nent remains essentially constant along the operating line in the 70-100% engine

speed range of design

N/x/-O.

However, a significant reduction in component ef-

ficiency occurs when the engine speed exceeds 110% or drops below 60% of

design

N / v"O.

The component maps of Figs. 5.4, 5.5, and 5.8 give considerable insight into

the variation of engine speed with changes in flight conditions. High values of

fan or compressor pressure ratio correspond to high engine speed and low val-

ues of pressure ratio correspond to low engine speed. Figures 4.5, 4.6, 4.7, 4.9,

and 4. l0 show that pressure ratio increases with altitude and decreases with Mach

number with Tt4 held constant. Thus, engine speed increases with altitude and

decreases with Mach number with

Tt4

held constant. The operating regimes where

the assumption of constant component efficiency may not apply then correspond

ENGINE SELECTION: PERFORMANCE CYCLE ANALYSIS 171

to the regions of high-altitude/low Mach number and low-altitude/high Mach

number flight. Some of the high-altitude/low Mach number region is excluded

from the operational envelope of many aircraft because of its low dynamic pres-

sure and the high coefficient of lift (CL) required to sustain flight. Some of the

low-altitude/high Mach number region is excluded from the operational envelope

of many aircraft because of the structural limits of the airframe and the presence

of very high dynamic pressure in this flight region.

The effect of decreasing component efficiency is to reduce the pressure ratio,

engine air mass flow rate, and thrust and increase the thrust specific fuel consump-

tion from that predicted by the off-design computer program. The magnitude and

range of this effect depends on each component's design and design point, which

are not known at this point in the analysis.

The predicted performance of the engine over the aircraft mission is used to

select the best engine cycle, size the selected engine, and select component design

points. Output of the performance portion (Engine Test) of the AEDsys computer

program can be used to create plots of the compressor operating line at full throttle,

as shown in Fig. 5.10, and the variation of the compressor pressure ratio at full

throttle with changes in the flight condition, as shown in Fig. 5.11. However when

the maximum compressor pressure ratio that the engine control system will allow

is equal to the sea-level static value, the control system limits the fuel flow and

the compressor pressure ratio is limited as shown at low Mach/high altitude in

Fig. 5.11.

Compressor

Pressure

Ratio (n,.)

i i i i i , i , i i , i t i i i i i i

60 70 80 90 100

% Corrected Mass Flow Rate

Fig. 5.10 Predicted compressor operating llne.