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

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1.0

0.8

Subcritical

St~

o 0.6

o 0.4

0.2

DESIGN: INLETS AND EXHAUST NOZZLES 447

~'~-- Critical

Supercritical

1.0

~,.

0 1.0

Inlet mass flow ratio

rhiffnl

Fig. 10.40 External compression inlet performance characteristics.

in Fig. 10.40 for a specific freestream Mach number. The "critical" operation point

and the "subcritical" and "supercritical" operating regimes are also shown on this

figure.

The engine mass flow ratio (rh0/rhl) can be expressed in terms of corrected

mass flow rates and the inlet recovery as

mo m~o Ptl moo

.... r/R (10.15)

?i'll ~'tel Pt0 t~tcl

where rhc0 is the corrected mass flow rate of the engine and

?~'tcl

is the corrected

mass flow rate based on the capture area, a constant for fixed capture area A1 and

flight condition. Variation in the engine corrected mass flow rate (rhc0) due to a

change in engine throttle can be presented on the inlet mass flow map of Fig 10.40

for the case where the boundary layer bleed and bypass flows are essentially

constant. A line of constant the0 is shown on Fig. 10.40 along with the direction

of change of slope due to increasing rhc0. When the engine's requirement for air

decreases below that required for "critical" inlet operation, the inlet operating point

moves into the "subcritical" region as the engine mass flow ratio decreases and the

fraction of air spilled increases. When the engine's requirement for air increases

above that required for "critical" operation, the inlet operating point moves into

the "supercritical" region as the engine mass flow ratio remains constant and the

total pressure recovery of the inlet decreases with the strengthening of the terminal

normal shock in the diffuser.

Two supersonic flow phenomena associated with the stability of the shock struc-

ture in external and mixed compression inlets require consideration at this point.

One is called inlet "buzz" and the other is associated with the location of the

terminal normal shock.

448 AIRCRAFT ENGINE DESIGN

,* ~ Spilled airflow

•

_..._._----

• f

• / • Choked flow

• J

Normal shock , ..- .t

....~ ~ Separated

boundary layer

Fig. 10.41 Condition leading to inlet "buzz"

"Buzz" is a low-frequency, high-amplitude pressure oscillation that is linked to

shock/boundary layer and/or shock/shock interaction at relatively low inlet mass

flow ratio. As an example of a flow condition leading to inlet buzz, consider

the external compression inlet of Fig. 10.41. When this inlet is operated in the

"subcriticar' regime, the terminal normal shock will impinge on the boundary

layer formed along the wall of the ramp causing the boundary layer to separate.

If the separated boundary layer produces a large enough low-velocity flow region,

the inlet will choke, reducing the inlet mass flow rate and moving the normal shock

forward along the ramp. The boundary layer at this forward location is thinner,

its separated flow region does not choke the inlet, and thus the inlet mass flow

increases, moving the normal shock back up the ramp toward its original location,

to be repeated again and again--creating buzz. When "buzz" occurs on a mixed

compression inlet, the inlet will unstart and engine flameout is possible.

The stability of the terminal normal shock in a mixed compression inlet is im-

portant when operating the inlet near its design point. Design for stability of the

terminal normal shock requires that the need for higher total pressure recovery be

compromised and the design throat Mach number be 1.2 with the normal shock

positioned downstream where the Mach number is 1.3. Thus, the mixed compres-

sion inlet is designed to operate in the "supercritical" regime. When the engine

needs less air than provided by this inlet, the excess air must bypass the engine

to maintain the terminal normal shock at its stable location and prevent the inlet

from "unstarting" (expelling the normal shock). When the engine wants more air

than the inlet can provide, the terminal normal shock is drawn downstream into

the diffuser, strengthening the shock and increasing corrected mass flow rate to

the engine. When the normal shock is drawn downstream into the diffuser, flow

separation and flow distortion become dominant design considerations. To limit

this problem, the inlet needs to be designed to provide the required engine mass

flow rate with the terminal normal shock positioned where the Mach number in

the diffuser is 1.3.

The total pressure recovery vs mass flow ratio of a typical mixed compression

inlet is shown in Fig. 10.42. Note that this inlet has a much smaller allowable

variation in mass flow ratio before onset of buzz than does the external compression

inlet of Fig. 10.40. This reduction in the range for inlet mass flow ratio

(rhi/rhl)

corresponds to a larger change in the amount of inlet air that is required to be

bypassed

(r~lbp)

to prevent buzz (maintain

#/i//#/1

above stability limit), with a

corresponding smaller variation in the amount of air that is spilled (Ref. 1).

DESIGN: INLETS AND EXHAUST NOZZLES 449

1.0

0.9

0.8

0.7

06-

Fig. 10.42

Stability

limit (buzz)

Subcritical

~-~'~"----- Critical

Supercritical

I I I

0.8 0.9 1.0

Inlet mass flow ratio

Yhi#h 1

Mixed compression inlet performance characteristics.

10.2.3.4 Boundary layer controL

Boundarylayercontrolisamajordesign

consideration in the design of supersonic inlets. The boundary layer will build up

on the external compression surfaces of external and mixed compression inlets as

well as on the internal duct surfaces. Since there is an adverse pressure gradient

in a supersonic inlet (static pressure rises in the direction of flow), the boundary

layer is susceptible to separation when this pressure gradient is too severe, as can

be the case when the inlet is made very short or when a shock wave interacts with

a boundary layer. Figure 10.43 shows normal shock/boundary layer interaction

without and with wall suction. If the boundary layer is thick where the shock

interacts, then separation of the boundary layer will occur with a resulting degra-

dation in the uniformity of flow to the engine. For a mixed compression inlet,

shock/boundary layer interaction can lead to inlet "unstarting." To prevent these

problems, active boundary layer bleed systems are used to remove most of the

boundary layer just prior to the region(s) where interaction(s) with shocks will

occur. Both slot and porous plate bleed methods are used, as shown in Fig. 10.44.

The porous plate method is used for regions where the interaction area can move

about, as can be the case for the terminal normal shock for both external and mixed

compression inlets and shock wave reflection in mixed compression inlets.

The boundary layer bleed air requirement is mainly a function of the type of

inlet and its design Mach number. Figure 10.45 shows the typical bleed mass flow

ratio

(rhbl/~nl = Aobt/A1)

requirements. This figure is very useful in preliminary

design of an inlet. Note that the mixed compression inlet requires about twice

the bleed air as that needed for an external compression inlet due mainly to the

increased number of bleeds required for the mixed compression inlet.

10.2.3.5 Inlet design and sizing.

The design and sizing of a supersonic

inlet is considerably more difficult than that of the subsonic inlet (see Sec. 10.2.2)

due mainly to the differences in the nature of supersonic and subsonic flows.

450 AIRCRAFT ENGINE DESIGN

~ Wall Boundary ~ Boundary Layer

S.ction

,, ~ Layer ~.~

~ ",~, ~ Supersonic ",,~~n~ ~

Obh'qu e__._.~$¢ ~, "~'~,,~

Shock t " , - ~ Boundary Layer

t -'~, Bleed-back e Normal

a a

Shock

Normal ¢

Shock #

a) Without Wall Suction b) With Wall

Suction

Fig. 10.43 Shock/boundary layer interaction: a) without wall suction; b) with wall

suction.

• • 00:00000

000

0000000000 O0

000000000 • •

000000 • •

Shock --...~•

Bleed Airflow "~

Shock --....~•

Airflow • • • Airflow

l~ i 1 1 ml 1 ~ i

Bleed Airflow

a) Slot Bleed b) Porous Bleed

Fig. 10.44 Boundary layer bleed methods: a) slot bleed; b) porous bleed.

A ob I/.41

0.16

0.12

0.08

0.04 -

0.8

Mixed Compression Inlets

mro.s ~...

I | i I I I I I

1.2 1.6 2 0 2.4 2.8 3.2 3.6 4.0

Fig. 10.45 Typical boundary layer bleed mass flow ratio?

DESIGN: INLETS AND EXHAUST NOZZLES 451

1.0

A~ ~ I ~ AO

Chapter 6

Inlet Airflow

Aoi req

0.0

I I I I

0.5 1.0 1.5 2.0

Fig. 10.46 Chapter 6 inlet airflow performance.

The supersonic inlet is designed to operate at both subsonic and supersonic flight

Mach numbers. The capture and throat areas of the inlet must be large enough not to

choke the airflow required by the engine, while providing for the bypass, boundary

layer bleed, and auxiliary air systems. For supersonic flight conditions, the inlet's

capture

area (A1)

is sized to capture the required airflow. Since this airflow varies

with both flight Mach number and engine throttle setting, variable geometry inlet

design is sometimes needed to meet the total pressure recovery goal of military

specification MIL-E-5008B and/or keep the installation losses low (spillage drag

and/or bypass air drag).

10.2.3.6 Inletpefformance model The model supersonic inlet of Fig. 6.4

consists of an external compression inlet with fixed capture area and variable

geometry such that the inlet's shocks converge at the outer lip (see Fig. 10.35a).

As a result the inlet mass flow ratio (Aoi/A1) has a constant value of unity. The

airflow performance of this variable inlet is shown in Fig. 10.46 along with the

required inlet airflow. The difference between the inlet mass flow ratio and the

inlet's required mass flow ratio is the "excess air" that enters the inlet and must

bypass the engine. The drag associated with the change in momentum of this excess

air was used in Chapter 6 to estimate the inlet installation loss

((9inlet).

This was

a conservative estimate since the installation loss can be reduced by changing the

inlet capture area and by operating with some spillage and its associated drag as

shown in Fig. 10.47.

10.2.3.7 Required inlet airflow. Therequiredvaluesofengineairflow(rh0)

and the corresponding values of freestream area (A0) calculated by the parametric

452 AIRCRAFT ENGINE DESIGN

~ntet

~ Bypass

% Bypass 100

Fig. 10.47 Spillage and bypass drag.

(on-design) and performance (off-design) analyses of this textbook and the com-

puter programs ONX and AEDsys are based on the total pressure recovery given

by military specification MIL-E-5008B where

ORspec

1 for M0 < 1 (4.12b)

ORspec

= 1 -- 0.075(M0 - 1) L35 for 1 < M0 < 5 (4.12c)

800

ORspec

M04 + 935

for 5 < M0 (4.12d)

This same reference inlet total pressure recovery is used by many others.

Note:

Since the total pressure recovery 0R of an inlet design may be different

than

ORspec,

the required values of engine airflow rh0 and the corresponding values

of freestream area A0 will be different from those calculated in the engine per-

formance analyses. Thus the values of rh0 and A0 determined by using the total

pressure recovery of Eq. (4.14) will be referred to as rn 0

spec

and

Ao spec,

respectively,

from this point on.

Inlet design and sizing begins with an analysis of its airflow requirements.

Figure 10.48 shows the variation in inlet airflow requirements from engine per-

formance analyses

Aospe c

with flight Mach number and altitude for a typical su-

personic engine. Variable boundary layer bleed (see Fig. 10.45) and safety margin

of 4% have been added to the maximum full-throttle engine airflow to obtain the

required inlet airflow

Aoispec.

The engine airflow requirements (rh0, A0) for any arbitrary inlet design 0R Can

be estimated based on the engine airflow requirements

(rhospec, Aospec)

obtained

using the original inlet total pressure recovery OR

wet.

Since the engine operates as

essentially a constant corrected mass flow device (rhc2 = constant) when throttle

and flight conditions are constant, then the required engine airflow rn0 for a specific

inlet design 0R can be determined from required engine airflow data (rno,pe¢,

Ao ~pec)

based on a reference inlet total pressure recovery OR

spec

using

rno A0 OR

..... (10.16)

/nospec Aospec ORspec

DESIGN: INLETS AND EXHAUST NOZZLES 453

5.6

5.0

4.5

~ 4.0

3.5

3.0

0.0

o15

Boundary layer

bleed air

A~= [ ~A0~

J~~L...- --~ 36-60 kft

~.~,,,., ~t 30 I- /

~30kft

Fig. 10.48 Airflow requirements.

Likewise for the inlet airflow area

Aoi OR

- -- (10.17)

Aoi

spec T] R spec

10.2.3.8 Inlet mass flow.

Preliminary inlet design and sizing requires

the performance analysis of candidate designs. The previous material on total

pressure recovery presented the tools for estimating the total pressure recovery of

an inlet (OR), and the tools for estimating the inlet mass flow ratio (Aoi/A1) are

presented below.

Consider the generalized extemal compression inlet of Fig. 10.49 with capture

area A1 and area As at location s. The inlet mass flow ratio can be written as

Aoi Aoi As

-- -- (10.18a)

A1 As A1

where As/A1 is determined by the geometry of the inlet. The shock system deter-

mines the area ratio Aoi/As as follows. Conservation of mass gives

/~/i "~- /~/s or

poVoAoi = psVsAs

T / ~ I

/ I \ Diffuser

Aoi

/ Shock system I ~ 2

/ I

k___

// I

/ ~ ~

Fig. 10.49 External compression inlet.

454 AIRCRAFT ENGINE DESIGN

thus

Aoi Ps Vs

As Po Vo

and, for adiabatic flow in the inlet, the ratio of density times velocity in the above

equation can be written in terms of the total pressure ratio and the Mach numbers

using the mass flow parameter [see Eq. (1.3)] as

Aoi psVs Pt~ MFP(Ms) Pts [A/A*]M o

A~ poVo Pro MFP(Mo) Pro [A/A*]M~

(10.18b)

where

A/A*

is the isentropic area ratio defined for a calorically perfect gas as

y+l

A -- 1 {~+I(I+Y-IM2)}2(Yl) (10.19)

A* M 2

A/A*

is tabulated in many gas dynamics textbooks and is available in the gas

tables program (GASTAB) included within the AEDsys software package. Equa-

tions (10.18a) and (10.18b) provide the tools to estimate the inlet mass flow ratio

(Aoi/A1)

of an inlet. The area ratio

(As~A1)

is a geometric function of the inlet

design, whereas the area ratio

(Aoi/As)

is a function of the flow properties at

stations 0 and s.The previous section on total pressure recovery presented the an-

alytical tools for determining both Ms and

Pts/Pto

of a general inlet as is shown

in the following example. Reference 1 contains exact solutions for one and two

oblique shock inlets designed for critical operation.

10.2.3.9 Inlet sizo.

The ratio of the inlet capture area A1 to the engine's

area at state 0* (i.e., at M = 1) for the cycle reference point

A~ref

will be referred

to as the

inlet size Al/A~ref

since this ratio is the size of the inlet relative to the

engine. The required inlet size

(A 1/A~

ref)re q

a flight condition can be calculated

from the required inlet airflow

(Aoi/A~

ref)req

and the inlet mass flow ratio

Aoi/A1

using

A1) (Aoi/A~ref)req

= Aoi/A1

0 ref req

(10.20)

For a fixed inlet capture area inlet, the flight condition requiring the largest inlet

size

(A1/A~ ref)req

is used to size the inlet capture

area A1.

Care must be taken that the inlet does not choke the flow to the engine at subsonic

flight conditions. As discussed in Chapter 6, this can be assured by having the inlet

capture

area (A1)

larger than the maximum required one-dimensional inlet area

A~i

by about 4%

(A/A*

= 1.038 at M = 0.8) and/or providing additional air inlet

area for takeoff requirements.

DESIGN: INLETS AND EXHAUST NOZZLES 455

1.28

1.24

1.20

1.16

1.12

1.08

1.04

1.00

0.96

0.0

0.5

A~-~

( Aoi "~

\Ao reI'T--]req

! __

y "-u

re]

I I I

1.0 1.5 2.0

Aoi spec

Ao ref

Fig. 10.50 Inlet airflow requirement for Example 10.2 inlet.

Example 10.2 External Compression Inlet (Part

II)

As an example, consider the fixed geometry, double ramp, external compression

inlet of Fig. 10.35 with 0a = 0b = 5 deg to be used with the engine whose required

airflow is plotted as

Ao/A*oref

in Fig. 10.50. These data are based on the airflow

requirements of Fig. 10.48 at 40 kft altitude and an

A~r e

of 4 22 ft 2 at sea-level

,f •

static conditions. The inlet is to be capable of operating up to Mach 2 at 40 kft

with efficient operation at Mach numbers less than 1.7. The inlet size and mass

flow characteristics of inlet and engine are required.

Inlet airflow requirements.

From performance (off-design) cycle calculations

based on the reference inlet recovery of military specification MIL-E-5008B, the

required full throttle engine mass flow ratio is given as

A o

spec/A~

ref

in Fig. 10.50.

Inspection of Fig. 10.50 shows that the most demanding mass flow requirements of

the inlet occur at altitudes above 36 kft. Increasing these values for boundary layer

bleed (0% at 0.8M, 4% at 2.0M. and linearly in between) and for safety margin

(4%) yields the required inlet mass flow ratio

Aospec/A1

(based on the reference

inlet recovery,

rlRspec )

times the inlet

size

Al/A~ref

Aoispec/A~ref.

Correcting

these data for the total pressure recovery OR of the inlet of interest (Table 10.1)

yields the required inlet performance

(Aoi/A~ ref)req"

Inlet performance.

The total pressure recovery of this inlet

(OR)

is tabulated

in Table 10.1, is plotted in Fig. 10.36, and was found to meet the requirement for

efficient total pressure recovery at Mach numbers less than 1.7. Analysis of the

mass flow characteristics of the inlet and engine are required before this inlet can

be sized. As long as the normal shock between stations b and c touches the lip of

the inlet, either station b or c of Fig. 10.35 can be equated to station s of Fig.10.49.

456 AIRCRAFT ENGINE DESIGN

Thus

and

Aoi Ptb [A/A*]Mo Ptc [A/A*]Mo

As Pro [A/A*]M b Pto [A/A*]M~

(10.21a)

Ptc Ptb ~R

-- = ~R; -- --

(lO.21b)

P,o P,o P~c/ P~b

The area ratio

(Aoi ~As)

can be calculated using the results of Table 10.1 assuming

that

Ms = Mb

at subsonic values Of Mb (no local flow acceleration or deceleration).

For subsonic M0, a reasonable approximation is for choked flow at station s and

thus

A~i = As.

The results of the area ratio

Aoi/A s

calculations for this example inlet are plotted

in Fig. 10.51. Note that this plot has a minimum value of unity at M0 = 1. Also

note the jumps in value of

Aoi/As

corresponding to the transition between normal

and oblique shocks at each ramp. (These also correspond to the jumps in total

pressure shown in Fig. 10.36.)

The selected design point of an external compression inlet sets the value of

As~A1.

Since

Aoi

= A1

at the inlet design point, then

As~A1

= 1/(Aoi/As)

evaluated at the inlet's design point. For this example, let the inlet design point

be M0 = 2. Thus,

A,/A1

= 0.7681 and the resulting values of

Aoi/A1

using

Eq. (10.18a) are tabulated in Table 10.2.

Inlet size.

Now that the mass flow ratio of the inlet has been determined,

the inlet mass flow rate requirements must be established before it can be sized.

Using these data, the maximum calculated value of the inlet size

(A1/A~ref)req

1.35 -

1.30 -

1.25 -

1.20 -

1.15 -

1.10 -

1.05 -

1.00

1.95

0.0

Fig. 10.51

I I I

0.4 0.8 1.2

Area ratio of Example 10.2 inlet (Fig. 10.35).

I I

1.6 2.0