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

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DESIGN: INLETS AND EXHAUST NOZZLES 467

10.3.2 Nozzle Functions

One can also think of the exhaust nozzle as dividing the power available from the

main burner exit gas between the requirements of the turbine and the jet power. 15

Thus, the nozzle serves as a back-pressure control for the engine and an acceleration

device converting gas thermal energy into kinetic energy. A secondary function

of the nozzle is providing required thrust reversing and/or thrust vectoring. The

nozzle design can also reduce the infrared signature of the engine.

10.3.2. 1 Engine back-pressure control

The throat area of the nozzle

is one of the main means available to control the thrust and fuel consumption

characteristics of an existing engine. In preliminary engine cycle analysis, the

selection of specific values for the engine design parameters and the design mass

flow rate fixes the throat area of the nozzle. The off-design performance methods

of Chapter 5 assume that the nozzle throat area and the other internal flow areas

of the engine remain constant. This assumption of constant areas establishes the

off-design operating characteristics of the engine and the resulting operating lines

for each major component. It is important to realize, however, that changing the

nozzle throat area from its original design value will change the engine design

and the operating characteristics of the engine at both on- and off-design (see

Appendix D). This is equivalent to displacing the operating line of the engine.

At times, it is necessary to change the off-design operation of an engine in

only a few operating regions and variation of the throat area of the exhaust nozzle

may provide the needed change. At reduced engine corrected mass flow rates

(normally corresponding to reduced engine throttle settings), the operating line of

a multistage compressor moves closer to the stall or surge line (see Fig. 10.63).

Steady-state operation close to the stall or surge line is not desirable since transient

operation may cause the compressor to stall or surge. The operating line can

be moved away from the stall or surge line by increasing the exhaust nozzle

throat area as shown in Fig. 10.6l. This increase in nozzle throat area reduces

the engine back-pressure and increases the corrected mass flow rate through the

compressor.

Large changes in exhaust nozzle throat area are required for afterburning engines

to compensate for the large changes in total temperature leaving the afterburner.

The variable-area nozzle required for an afterburning engine can also be used for

back-pressure control at its non-afterburning settings.

One advantage of the variable-area exhaust nozzle is that it improves the starting

of the engine. Opening the nozzle throat area to its maximum value reduces the

back-pressure on the turbine and increases its expansion ratio. Thus, the necessary

turbine power for starting operation may be produced at a lower turbine inlet

temperature. Also, since the back-pressure on the gas generator is reduced, the

compressor may be started at a lower engine speed, which reduces the required

size of the engine starter.

10.3.2.2 Exhaust nozzle area ratio. Maximum uninstalled engine thrust

is realized for ideal flow when the exhaust nozzle flow is expanded to ambient

pressure (Pe = P0). When the nozzle pressure ratio is above choking, the super-

sonic expansion occurs between aft-facing surfaces. A small amount of under-

expansion is less harmful to aircraft/engine performance than over-expansion.

468 AIRCRAFT ENGINE DESIGN

150

100

Eft =

0 t

20 40

Fig. 10.63

I I

60 80

% design

~nc2

I I

100 120

Compressor map ~6 with exhaust nozzle area change.

Over-expansion can produce regions of separated flow in the nozzle and on the aft

end of the aircraft, reducing the aircraft performance.

The exhaust nozzle pressure ratio is a strong function of flight Mach num-

ber as is shown by Fig. 10.64. Whereas convergent nozzles are usually used on

subsonic aircraft, convergent-divergent nozzles are usually used for supersonic air-

craft. When afterburning engine operation is required, complex variable geometry

nozzles must be used (see Fig. 10.65). Most of the nozzles shown in Fig. 10.64 are

convergent-divergent nozzles with variable throat and exit areas. The throat area

of the nozzle is controlled to satisfy engine back-pressure requirements and the

exit area is scheduled with the throat area. The sophisticated nozzles of the F-15

and B-1 aircraft have two schedules, a low-speed mode and a high-speed mode) 5

10.3.2.3 Thrust reversing and thrust vectoring.

The need for thrust re-

versing and thrust vectoring is normally determined by the required aircraft/engine

system performance. Thrust reversers are used on commercial transports to sup-

plement the brakes. In-flight thrust reversal has been shown to enhance combat

effectiveness of fighter aircraft.15 Thrust vectoring has been shown to enhance both

takeoff and combat effectiveness of fighter aircraft. 15

Two basic types of thrust reversers are used: the cascade-blocker type and the

clam-shell type (Fig. 10.66). In the cascade-blocker type, the primary nozzle exit

DESIGN: INLETS AND EXHAUST NOZZLES 469

P te/P o

I I I I I

I I I I

1.0 ~f-_ 2.0 2.4

""0

Fig. 10.64 Typical nozzle pressure ratios.

is blocked off and cascades are opened in the upstream portion of the nozzle duct

to reverse the flow. In the clam-shell type, the exhaust jet is split and reversed by

the clam shell. As shown in Fig. 10.67, the PW4000 high-bypass turbofan engine

employs the cascade-blocker type in the bypass stream and no reverser in the core

stream (some engines also employ reversers in the core stream). Since reversers

usually provide a change in effective nozzle throat area during deployment or

when deployed, most are designed such that it increases during the brief transitory

period, thus lowering the operating line in order to prevent fan/compressor stalls.

Development of thrust vectoring nozzles for combat aircraft has increased in

the last decade. Vectoring nozzles have been used on VTOL aircraft, such as the

AV-8 Harrier, and are being used on new fighters to improve maneuvering and

augment lift in combat. Thrust vectoring at augmented power settings has been

developed for use in new fighters. However, cooling of the nozzle walls in contact

SHORT CONVERGENT

StMPL~ EJECTOR

~RiS CONOI

iRiS

:::_ ;Z

FULLY VARIABLE EJECTOR

--~DRY

MAX A/B

BLOW.iN*DOOR EJECTOR

PLUG

HiGH M

~SE NTROPIC RAMP

(Short arrows indicate the presence and flow d~rection of nozz e coo ng a~r

which is usually inlet

bleed

air, compressor bleed air, o5 fan discharge air~

Fig. 10.65 Typical nozzle concepts for afterburning engines, t5

470 AIRCRAFT ENGINE DESIGN

Deployed

Primary clam-shell7

~~) propulsion nozzle .,~ \ /

~)) Blocker

Cascade reverse Clam-shell reverser

Fig. 10.66 Thrust reversers. 15

with the hot turning or stagnating flows is very difficult and requires increased

amounts of nozzle cooling airflow. Figure 10.68 shows the schematic of a two-

dimensional convergent-divergent nozzle with thrust vectoring of 4-15 deg and

thrust reversing. The thrust vectoring is typical of the capabilities incorporated

in the F-22 Raptor. The thrust vectoring nozzle of the Joint Strike Fighter (JSF)

can turn the exhaust flow 90 deg for STOVL.

10.3.2.4 Infrared signature.

The rear of the engine is very hot and can

produce a large infrared signature. Considerable effort is being used in modern

military aircraft to reduce this signature. Most effective methods involve hiding

STOWFD

Bypass Air

Core

Air

Bypass Air

Forward

Thrust

DEPLOY

m I

Fig. 10.67 PW4000 thrust reverser in stowed and deployed positions.

DESIGN: INLETS AND EXHAUST NOZZLES 471

Normal Mode Vectored

Mode

Braking Mode Reverse Mode

Fig. 10.68 Typical two-dimensional variable-area thrust vectoring nozzle with thrust

reversing. 17

the exit of the low-pressure turbine from direct view. Shown in Fig. 10.69 is the

platypus exhaust duct used on the F-117A Nighthawk stealth fighter. This exhaust

nozzle is canted up 10 degrees (Refs. 3 and 12) to prevent line-of-sight to the

turbine face. For afterburning engines, the nozzle in concert with the devices (e.g.,

fiameholders) downstream of the turbine can hide the turbine exit and thus reduce

high temperature signatures. Generally speaking reduced performance is the cost

of stealth.

10.3.3 Design Tools--Exhaust Nozzles

10.3.3. 1 Total pressure loss.

The total pressure loss of an exhaust nozzle

is primarily due to viscous effects. The fraction of total pressure loss can be

expressed for one-dimensional flow in its differential form as

dPt

Y M2Cf_e__~d X

p, 2

where

and

= Friction coefficient

Pw = Wetted perimeter of the duct

Comparison of the total pressure loss of a two-dimensional nozzle to that of an

axisymmetric nozzle can be made using the above equation. Assuming the same

axial distribution of Mach number, friction coefficient, and flow area, then the

472 AIRCRAFT ENGINE DESIGN

Side View

Top

View

(Engine)

Vertical Tension Posts

(21 per tailpipe)

A B

Installation Sketch

Section A-A

Section B-B

Fig. 10.69 Exhaust nozzle of F-117A [Originally published in Have Blue and the

F-117A: Evolution of the "Stealth Fighter," D. Aronstein and A. Piccirillo, AIAA, 1997

total pressure loss is proportional to wetted perimeter (Pw), and the ratio of the

total pressure loss of a rectangular cross-sectional nozzle to that of a circular can

be written as

1 - (Zrn)rectangular (APt / Pt

)rectangular

(Pw)rectangular

- (7rn)cireular (APt/P)circula r (Pw)cireular

where the ratio of wetted perimeters can be expressed in terms of the aspect ratio

(AR = W/H,

where W is the duct width and H is the duct height) of a rectangular

nozzle of the same flow area. The resulting relationship for total pressure loss

comparing rectangular to circular cross-sectional nozzles is

- (Tgn)rectangular __

(AR +

-- (10.26)

1 -- (TlJn)circular

Thus, the total pressure loss of a rectangular nozzle with an aspect ratio of 2 will

be 1.2 times that of a circular nozzle of the same area. Also, if

(Zrn)circular

= 0.980,

then

(Tgn)rectangular =

0.976.

10.3.3.2 Nozzle coefficients. Nozzle performance is ordinarily evaluated

by two dimensionless coefficients: the gross thrust coefficient and the discharge or

flow coefficient. Figure 10.70 shows a convergent-divergent exhaust nozzle with

the geometric parameters used in the definitions of nozzle coefficients to follow.

Only total pressure losses downstream of station 8 are included in the gross thrust

coefficient.

Gross thrust coefficient.

The

gross thrust coefficient (Cfg)

is defined as the

ratio of the actual gross thrust

(Fgactual)

the ideal gross thrust

(Fg

ideal)

C f g = Fg actual/ Fg ideal

(10.27)

DESIGN: INLETS AND EXHAUST NOZZLES 473

A8 L s ,

Station: 7

A 8 =

Primary nozzle throat area

A9=

Secondary nozzle exit area

a = Secondary nozzle half angle

0 = Primary nozzle half angle

Ls = Secondary nozzle length

Fig. 10.70 Nozzle geometric parameters.

Empirically derived coefficients are employed in Eq. (10.27) to account for

the losses and directionality of the actual nozzle flow. Each engine organization

uses somewhat different coefficients, but each of the following basic losses are

accounted for:

1) Thrust loss due to the exhaust velocity vector angularity and/or dispersion;

2) Thrust loss due to reduction in velocity magnitude caused by friction in the

boundary layers;

3) Thrust loss due to loss of mass flow between stations 7 and 9 from leakage

through the nozzle walls;

4) Thrust loss due to flow non-uniformities.

Discharge orflow coefficient.

The ratio of the actual mass flow (rn8) to the

ideal mass flow (rnsi) is called the

discharge coefficient (Co)

CD - rn8/rh8i

This coefficient can be shown to be identically equal to the ratio of the effective

one-dimensional flow area actually required to pass the total nozzle flow (A8e) to

the ideal nozzle throat area (As) of the engine cycle calculations as follows:

rhs ps V8A8 A8

CD -- rhsi psVsAse Ase

(10.28)

The variation of the discharge coefficient with nozzle pressure ratio is shown in

Fig. 10.71 a for a conic convergent nozzle. When the nozzle is choked, the discharge

coefficient reaches a maximum value (CDmax). The value of Cornax is a function

of the primary nozzle half-angle (0) as shown in Fig. 10.7lb. Figure 10.71c shows

the variation in discharge coefficient for a convergent-divergent nozzle with nozzle

pressure ratio. Note the change in behavior of

between that of the convergent-

divergent (C-D) nozzle and that of the convergent nozzle as the nozzle pressure

ratio drops below choking. This is due to the venturi behavior of the convergent-

divergent nozzle.

Co max

~8mo

Convergent nozzle

0.96

1.00

0.98

0.94

0.92

10 20 30

Primary nozzle half angle 0

474 AIRCRAFT ENGINE DESIGN

b) CD max versus 0

max

Pt8/Po

c) C-D nozzle

Fig. 10.71 Nozzle discharge coefficient: is a) convergent nozzle; b) convergent and

C-D nozzle CDmax VS 0; c) C-D nozzle.

DESIGN: INLETS AND EXHAUST NOZZLES 475

0.988

1.0

l O00

0.996

9 6

0.992

1 I I I

2.0 3.0 4.0

A91A8

Fig. 10.72 C-D nozzle velocity coefficient, is

The discharge coefficient is used to size the nozzle throat area to pass the desired

mass flow rate. For example, consider a nozzle with rh8 = 200 Ibm/s,

Pt8

= 30 psia,

Tt8 = 2000°R, y = 1.33, and 0 = 20 deg. From Gas Tables,

MFP(@M8

= 1) =

0.5224 and thus A8 = 570.7 in. 2 Figure 10.71b gives

Comax ~

0.96 for 0 =

20 deg and thus the required throat area

A8e

is 594.5 in. 2

Velocity coefficient.

The

velocity coefficient (Cv)

is the ratio of the actual exit

velocity (V9) to the ideal exit velocity (V9i) corresponding to

Pt9 =

et8

CV "-- V9/ V9i

(10.24)

represents the effect of frictional loss in the boundary layer of the nozzle and is a

measure of the nozzle's efficiency [Eq. (10.25)]. It is mainly a function of the length

of the nozzle, which depends on the nozzle area ratio

(A9/As)

and the half-angle

ot as shown in Fig. 10.72.

Angularity coefficient.

The

angularity coefficient (CA)

represents the axial

fraction of the nozzle momentum and thus is proportional to the thrust loss due to

the non-axial exit of the exhaust gas (see Fig. 10.73). For a differential element of

flow, this coefficient is the cosine of the local exit flow angle (aj). The local flow

/'9

axial = 1/9 COS aj

Fig. 10.73 Local angularity coefficient, is

476 AIRCRAFT ENGINE DESIGN

1.00

0.99

0.98

0.97

1.0

\ -6

.--------8

~10

Puendc~ 12x 14

Predictions

I I \ I I I

1.2 1.4 1.6 1.8

2.0

A9/A8

Fig. 10.74 C-D nozzle angularity eoemcient, is

angle (o~j)

varies from zero at the centerline to ot at the outer wall and thus the

nozzle angularity coefficient is the integral of otj across the nozzle.

CA ".2_ __

COSOlj dth

(10.29)

Figure 10.74 presents the correlation of the angularity coefficient with the noz-

zle area ratio (A9/A8) and the half-angle, or. This figure is based on analytical

evaluations of the inviscid flow field in convergent-divergent nozzles for a range

of practical nozzle geometries.

One-dimensionalflow. Many of the nozzle flow coefficients simplify to alge-

braic expressions or become unity for the special case of one-dimensional adiabatic

flow. This is a useful limit for understanding each coefficient and for preliminary

analysis of nozzle performance using engine cycle analysis data.

For one-dimensional adiabatic flow, CA = 1,

rn8 A8 Pt8

CD------

r'n8i A8e Pt7

and the velocity coefficient (Cv) is given by

Cv "..x. V9 / V9 i

(10.24)

where V9 is the exit velocity corresponding to Tt8 and A/A*I9 = (Pt9/Pts) ×

{A9/(CoA8)} and

V9i

is the ideal exit velocity corresponding to Tts and

A/A*I9i = A9/(CoA8). The discharge coefficient at station 9 has been taken

to be one.

The uninstalled gross thrust for a one-dimensional flow is defined as

Fgactual = r'n8V9/gc + (P9 - Po)A9 (10.30)