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

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DESIGN: INLETS AND EXHAUST NOZZLES 457

Table 10.2 Example 10.2 inlet performance

Mo Aoi/AI Mo Aoi/A|

0.9 0.7749 1.5 0.8895

1.0 0.7681 1.6 0.9151

1.1 0.7885 1.7 0.9378

1.2 0.7688 1.8 0.9592

1.3 0.8125 1.9 0.9798

1.4 0.8267 2.0 1.0

from Eq. (10.20) sets the size of this fixed geometry inlet. Comparison of

Figs. 10.50 and 10.51 indicates that the two most demanding operating points

will most likely be at M0 = 1.23 and M0 = 1.42. Sizing calculations at these

two Mach numbers are presented in Table 10.3. The flight condition at M0 = 1.42

determines the inlet size as A1 :

1.425

A~ref.

The resulting flow ratios of the sized inlet and its required performance are

plotted for altitudes of between 36 and 60 kft in Fig. 10.52. This plot shows the

difference in flow behavior of the inlet between actual and required flows. As the

flight Mach number increases above 1.5, the inlet mass flow rate

Aoi/A1

increases

while the required inlet mass flow rate

(Aoi/A1)req

decreases. The difference be-

tween these mass flow rates is airflow that is either accepted by the inlet and then

bypassed about the engine back to the atmosphere, or spilled about the inlet, or a

combination of bypassed and spilled. At high Mach numbers, the large quantity

of excess air for this example inlet will correspond to a high inlet installation loss.

Nevertheless, over the required Mach range (M0 < 1.7), the example inlet has

good total pressure performance (OR

rlRspec)

and moderate excess air.

An inlet size based on the model variable geometry inlet of Chapter 6 would

have an inlet capture area (A 1) of 1.24

A~ ref

(horizontal dashed line on Fig. 10.50)

vs the capture area of 1.425

A~ref

required for this example fixed geometry inlet.

Also, the excess air for this example inlet is considerably larger than for the model

inlet of Chapter 6. A better match of inlet and engine is needed, which requires a

variable geometry inlet.

Variable geometry inlet.

The INLET program included with this textbook

allows analysis of external compression inlets with variable ramps. The user can

input the desired schedule into the program and the inlet's performance is calculated

for that schedule.

As an example of a variable geometry inlet, consider our example double-ramp,

external compression inlet of Fig 10.35 with ramp angles of 5 deg that becomes a

Table 10.3 Example 10.2 inlet sizing

Mo Ao/A~ref Aoireq/A~ref Aoi/A1 A1 req/ oref

1.23 1.0290 1.0854 0.7681 1.413

1.42 1.1004 1.1803 0.8283 1.425

458

1.05

1.00

0.95

0.90

"~ 0.85

0.80

0.75

0.70

Fig. 10.52

throttle.

A* 0 . I

Aoi /A 1

Aoi

AIRCRAFT ENGINE DESIGN

req]A l

I I I I I

0.4 0.8 1.2 1.6 2

Mass flow performance of sized Example 10.2 inlet at altitude and full

single ramp, external compression inlet with ramp angle of 5 deg for flight Mach

numbers less than 1.42. This variable geometry inlet is shown in Fig. 10.53a. Since

AI = A0 at Mach 2 for the double-ramp inlet and A~ is constant, basic geometry

gives As, = 1.131As. If the inlet sizing flight condition is at a Mach number

below 1.42, the variable ramp inlet will reduce the excess airflow about 13% for

flight Mach numbers above 1.42. The actual and required inlet mass flow ratios

for this example variable geometry inlet are plotted in Fig. 10.53b. Comparison of

Fig. 10.53b with Fig. 10.52 shows that variable geometry has reduced the excess air

that must be bypassed at high Mach numbers which will result in a corresponding

reduction in installation losses.

10.2.3. 10 Inlet-airframe interference effects on inlet distortion. Both

the location of the inlet and the aircraft attitude (angle of attack and angle of

sideslip) influence the flow into the inlet and the resulting distortion of the flow

to the compressor/fan. Figure 10.54 shows three typical inlet locations. The wing-

shielded inlet and the fuselage-shielded inlet use the wing and fuselage, respec-

tively, to help turn the air into the inlet at high angle of attack. The upwash flow

around the fuselage increases the flow angularity for the side-mounted inlet. Both

the fuselage- and wing-shielded inlets experience a significant reduction in angle of

attack. However, the wing-shielded inlet can experience a higher angle of sideslip

than the fuselage-shielded inlet.

The reader is directed to Chapter 13 of Ref. 1 for a thorough coverage of inlet-

airframe interference at incidence. This reference also provides the reader with a

good list of references on this topic.

DESIGN: INLETS AND EXHAUST NOZZLES 459

/ /

ii I ;s

Aoi • I I ",

I I

l / I ;

• Diffuser

High Mach Operation, M o > 1.42

i °

/ _.____--~ ~ s'

Aoi ~ I ~,

i ,

....t

i ~ °

Fig. 10.53a

Diffuser

Low Mach Operation, M 0 < 1.42

Example 10.2 variable geometry inlet.

1.05 -

1.00

0.95

0.90

0.85

0.80

A*O

I ~

Aoi /A1

Oi req /A 1

I I I I I

0.4 0.8 1.2 1.6 2

Fig. 10.53b Mass flow performance of Example 10.2 variable geometry inlet at

40 kft and full

throttle.

460 AIRCRAFT ENGINE DESIGN

SIDE-MOUNTED WING-SHIELDED

FUSELAGE-SHIELDED

Fig. 10.54 Three typical inlet locations? °

10.2.3.11 Subsonic diffuser.

The subsonic diffuser portion of a subsonic

or supersonic inlet must provide a smooth transition from the conditions at the

inlet throat to those required at the face of the fan or compressor with minimal

flow distortion and total pressure loss. In addition to a smooth variation in flow

velocity, the diffuser may be required to transition from a rectangular cross-section

to a circular one and/or to offset the flow when the inlet and engine are not aligned.

The front and side views for a fighter aircraft diffuser are shown in Fig. 10.55.

When this serpentine shape is combined with radar absorbing material (RAM),

the inlet can effectively reduce the radar cross section of the aircraft (see Fig 10.18

in Sec. 10.2.3 and Ref. 12).

The most commonly used measure for the pressure recovery of a diffuser is the

diffuser efficiency (r/D) which can be written as

h2~ - hi

r/D -- (9.65)

h2 -hi

A2/AI =

2.0

L/O--

3.5

v/o r ,is

Fig. 10.55 Typical diffuser portion of supersonic inlet, u

DESIGN: INLETS AND EXHAUST NOZZLES 461

where the subscript 1 denotes the entry of the diffuser and 2 denotes the exit. A

typical range of values for 7o is 0.80-0.95 which corresponds to total pressure

ratios

(Pte/Pti)

of 0.92-0.98 for

= 0.8.

Although the flow through the diffuser is very complex with possible flow

separation (see Fig. 9.21) in the regions of adverse pressure gradients, basic one-

dimensional gas dynamic analysis will yield useful and meaningful results. When

these results are incorporated with the diffuser efficiency, the overall performance

of a diffuser design can be estimated.

10.2.3.12 Examples of existing inlet designs.

Two examples of super-

sonic inlet designs are shown in Figs. 10.56 and 10.57. Figure 10.56a shows the

fixed, double-ramp (6 deg ramp followed by a 6.67 deg isentropic ramp 1), external

compression inlet with a throat slot bleed system developed for the J79 engine

installation in the F-16 aircraft. The total pressure recovery of this inlet is shown

in Fig. 10.56b.

The variable, triple-ramp, external compression inlet of the F-15 aircraft is

shown in Fig. 10.57. This side view of the inlet shows the ramps as they would be

positioned when operating at the supersonic design point (ramp angles of 7 deg,

8 deg, and 8 deg for the first, second, and third ramps, respectively). The first ramp

angle is fixed and the second and third ramp angles are variable. The inlet capture

area of this inlet is variable with movement of the first ramp/top of inlet assembly

from -4 deg to 4-11 deg (this assembly is shown at 0 deg).

10.2.3.13 Flow separation from sharp lip inlets.

Airflow may separate

from either the inside surface or outside surface of the sharp lip present on most

supersonic inlets when operated at subsonic flight Mach numbers. Separation from

the outside surface increases inlet drag and separation from the inside surface

creates inlet flow distortion and reduces the total pressure recovery of the inlet

(see Fig. 10.58), both of which reduce the installed engine performance. Auxiliary

air inlets (also called blow-in doors) that reduce additive drag also reduce the flow

separation from the inside surface of sharp lip inlets when operated at takeoff

conditions.

10.3 Exhaust Nozzles

The purpose of the exhaust nozzle is to increase the velocity of the exhaust gas

before discharge from the nozzle and to collect and straighten the gas flow. For

large values of thrust, the kinetic energy of the exhaust gas must be high, which

implies a high exhaust velocity. The pressure ratio across the nozzle controls the

expansion process and the maximum uninstalled thrust for a given engine is ob-

tained when the exit pressure

(Pe)

equals the ambient pressure (P0).

The functions of the nozzle may be summarized by the following list:

1) Accelerate the flow to a high velocity with minimum total pressure loss.

2) Match exit and atmospheric pressure as closely as desired.

3) Permit afterburner operation without affecting main engine operation--

requires variable throat area nozzle.

4) Allow for cooling of walls if necessary.

5) Mix core and bypass streams of turbofan if necessary.

6) Allow for thrust reversing if desired.

462 AIRCRAFT ENGINE DESIGN

~ ~ " LO

vers

Isometric Views Air Bleed

SlOt

(incoming AIr)

1.00

0.96

.~ 0.92

0.88 1

0.84

m_--

6/79 inlet

F-16 inlel i

i \

I I I I I, ,

0 0.4 0.8 1.2 1.6 2.0

M o

Fig. 10.56 F-16/J79 inlet, la

7) Suppress jet noise, radar reflection, and infrared radiation (IR) if desired.

8) Two-dimensional and axi-symmetfic nozzles, thrust vector control if desired.

9) Do all of the above with minimal cost, weight, and boattail drag while meeting

life and reliability goals.

The nozzle may be thought of as a device that converts enthalpy into kinetic

energy with no moving parts. The perfect (no loss) nozzle would thus correspond

to an isentropic (frictionless adiabatic) process. The nozzle adiabatic efficiency

(r/n) is defined as

Ti -Te V 2- Vi 2

~n -- -- --

Ti -res V 2 - Vi 2

DESIGN: INLETS AND EXHAUST NOZZLES 463

P f Second lind Third Ramp Bleed Exits

f f',o-o=,

~~ ~ Diffuser Ramp

~-- Thr~t Slot Bypl~s

L Cowl Rotation

Pivot

~ ~Third Ramp

Note:

$ideplate bleed not ,hown ~ Fi nSet CR°:d: amp

Fig. 10.57 F-15 inlet system.

where the subscripts i, e, and

refer to the nozzle inlet, exit, and ideal exit condi-

tions, respectively. For most cases, the inlet kinetic energy is small in comparison

to the exit and can be neglected. Thus

Tti - re

1 - Te/ Tti Ve 2

r/,, _ -- -- (10.22)

Tti- Tes

-- Tes/ Tti Ve2s

This expression can be recast in terms of a nozzle polytropic (en) efficiency by

using

Te/ Ta = ( Pe/ Pti) e"(y-1)/× and Tes/ Tti = ( Pd Pti) (v-l)~×.

Thus

y ln{1-rl,[1-(Pe/Pti)(×-l)/r]}

en = --

(10.23)

y - 1 In

(Pe/Pti)

The ratio of the actual exit velocity to the ideal exit velocity is the traditional nozzle

1.00 I I I I

th =

0.3

0.95 - 0.4

0.90 -

M0=0'3!~0'5

0.85- 0.237 ~ 0.115

0.166

0.80

Ao/Ath

Fig. 10.58 Total pressure recovery characteristics of sharp lip axisymmetric pitot

inlets.:

464 AIRCRAFT ENGINE DESIGN

1.00

0.95

0.90

0.85

0.80

''''1

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

C v

= 0.98

= 0.95

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

[

.... I

....

0.0 0.1 0.2 0.3 0.4 0.5

Expansion Ratio -

P,,/P,

Fig. 10.59 Nozzle polytropic efficiency ('T = 1.3).

velocity coefficient

(Cv)

defined by

Cv -- --

(10.24)

½s

From Eqs. (10.22) and (10.24), the nozzle adiabatic efficiency can be therefore

approximated as

~Tn -~ C 2 (10.25)

Using Eqs. (10.23) and (10.25), the variation of nozzle polytropic efficiency versus

nozzle expansion pressure ratio

(Pe/Pti)

is given in Fig. 10.59. It is evident there

that, for a given velocity coefficient

(Cv),

the equivalent nozzle polytropic ef-

ficiency is nearly constant with

Pe/Pti.

Also, even for rather low values of

Cv,

the equivalent nozzle polytropic efficiency is equal to or greater than that of the

turbine (see Table 4.4).

10.3.1 Nozzle Types

The two basic types of nozzles used in jet engines are the convergent and

convergent-divergent (C-D) nozzle.

10.3. 1.1 Convergent nozzle.

The convergent nozzle is a simple conver-

gent duct as shown in Fig. 10.60. When the nozzle pressure ratio

(Pte/Po)

is low

DESIGN: INLETS AND EXHAUST NOZZLES 465

Nozzle entrance Nozzle throat

Fig. 10.60 Convergent exhaust nozzle.

(less than about 4), the convergent nozzle is used. The convergent nozzle has

generally been used in engines for subsonic aircraft.

10.3. 1.2 Convergent-divergent

(C-D)

nozzle.

The convergent-divergent

nozzle is a convergent duct followed by a divergent duct as shown in Fig. 10.61.

Where the cross-sectional area of the duct is at a minimum, the nozzle is said to

have a throat. Most convergent-divergent nozzles used in aircraft are not simple

ducts, but incorporate variable geometry and other aerodynamic features. The

convergent-divergent nozzle is used if the nozzle pressure ratio is high (greater than

about four). High-performance engines in supersonic aircraft generally have some

form of a convergent-divergent nozzle. If the engine incorporates an afterburner,

the nozzle throat is usually scheduled to leave the operating conditions of the

engine upstream of the afterburner unchanged (in other words, the exit nozzle area

is varied so that the engine doesn't know that the afterburner is operating). Also, the

exit area must be varied to match the internal and external static pressures at exit for

different flow conditions in order to produce the maximum available uninstalled

thrust.

Earlier supersonic aircraft used ejector nozzles (Fig. 10.62) with their high per-

formance turbojets. Use of the ejector nozzle permitted bypassing varying amounts

of inlet air around the engine, providing engine cooling, good inlet recovery, and

reduced boattail drag. Ejector nozzles can also receive air from outside the na-

celle directly into the nozzle for better overall nozzle matching--these are called

two-stage ejector nozzles. For the modem high-performance afterbuming turbofan

engines, simple convergent-divergent nozzles are used without secondary air as

shown in Fig. 10.61 for the F100 engine.

Actuation Actuation Nozzle Outer

Rod /- Ring /-- Cavity Fairing Z Open

~----

__ /-- -- -- _ ~ [ Position

~ 5 I Roll-ers~~-~ - ~~ Position

Tailpipe ~

/ Roll2s

T.~lePripe ~mg Lrima'~ ~ "~'x- Second~

Cam Nozzle ~_ Secondary Nozzle

Nozzle Link

Fig. 10.61 Convergent-divergent (C-D) exhaust nozzle schematic, is

466 AIRCRAFT ENGINE DESIGN

2 3

4 5 6

(a) Supersonic nozzle configuration with afterburning: (1) secondary flow; (2) outer case engine;

(3) movable primary nozzle shown at maximum area; (4) primary flow, effective throat; (5) movable

secondary nozzle shown at maximum exit area; (6) mixing layer between primary and secondary

streams; and (7) supersonic primary flow

8 9

10 11 12

(b) Subsonic nozzle configuration with no afterburning: (8) primary nozzle at minimum area;

(9) separation point of external flow; (10) secondary nozzle at minimum area; (11) sonic primary

stream; and (12) region of separated flow in external flow

13 14 15 16 17

flow of ambient gas into nozzle; (14) blow-in door and inflow configuration; (15) reversible

hinge/latch; (16) movable secondary nozzle; and (17) separation point of external flow.

Fig. 10.62 Ejector nozzle configuration: 5