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

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DESIGN: INLETS AND EXHAUST NOZZLES 437

Lip Shock ~ ..

~/ BypassAir i;

Normal Shock 1.If 7

i 1 o,,

Fig. 10.26 Model pitot inlet.

where

Aobp/A1

is equal to the mass flow ratio of bypassed air to total inlet airflow

(rhbp/rhl).

Equation (10.8) is plotted in Fig. 10.27 vs M0 for

= 1 and ~p = 0 deg,

the same conditions assumed in the development of Eq. (6.8).

The external compression inlet with one or more oblique shocks (Fig. 10.23)

has its inlet throat at or very near the cowl leading edge. Desired operation of

this inlet is with the normal shock positioned at or very near the cowl lip (critical

operation).

The total pressure recovery (0R) across n oblique shocks of equal strength

(same total pressure ratio) followed by a normal shock is shown by solid lines in

Fig. 10.28 (n = 0 corresponds to a normal shock wave). The total pressure recovery

of MIL-E-5008B is drawn as a dashed line. Increasing the number of oblique shocks

increases

for any given freestream Mach number. However, the ramp of the

extemal compression inlet turns the flow away from the axial direction and thus

the subsonic diffuser duct must turn back the flow to the axial direction, which

may add weight, length, and friction loss to the inlet. Figure 10.29 shows the total

turning angle of an external compression shock system that attains the total pressure

recovery of MIL-E-5008B (0R

spec

in Fig. 10.28) as a function of freestream Mach

number. As the freestream Mach number increases, the total shock turning angle

of the external ramp increases, resulting in increases in cowl angle and cowl drag

(see Sec. 6.2.2). External compression inlets can maintain acceptable total pressure

ratio and cowl drag up to a flight Mach number of about 2.5.

Fig. 10.27

0,8 I , ' ' I , , , ,

CDbp

0.6 -

AObp /A1

0.4-

0.2-

I I I I I I I I I

1.0 1.5 2.0

Bypass drag of model pitot inlet (Fig. 10.24) with Me = 1 and q~ = 0 deg.

Fig. 10.28

1.O

0.5

0.3 I I

1.0

2.0 3.0

Total pressure recovery of oblique shocks terminated by a normal shock, s,6

..=

1.0

Fig. 10.29

I I

2.0 3.0

Turning angle of external compression shock system?

438 AIRCRAFT ENGINE DESIGN

DESIGN: INLETS AND EXHAUST NOZZLES 439

Lin shock Normal shock

.......

Oblique shock~ r i ~ '

~,pluea.alrnow ~--~"~ ~// ~ "~\ Bypassed airflow

/ T //I // -/'\ \z" Throat [ --...

• I' I / / . \ L)ltruser

A1 Aoi I / / \ t x )-

I t" /

~ ~ Ramp ",~Bleedair

Fig. 10.30 Two-dimensional mixed compression inlet.

Mixed compression inlet.

At flight Mach numbers above 2.5, the mixed com-

pression inlet is used to obtain an acceptable total pressure ratio (utilizing the

required number of oblique shocks) while obtaining acceptable cowl drag. The

mixed compression inlet is more complex, heavier, and costlier than the external

compression inlet. The typical mixed compression inlet (Figs. 10.30 and 10.31)

achieves compression through the external oblique shocks, the internal reflected

oblique shocks, and the terminal normal shock. The ideal location of the nor-

mal shock is just downstream of the inlet throat to minimize total pressure loss

while maintaining a stable operating location of this shock. Similar to the internal

compression inlet, the mixed compression inlet requires both fast reacting bypass

doors (to maintain the normal shock in a stable location) and variable throat area

(to allow the inlet to start by swallowing the normal shock). However, the variation

in inlet throat area of the mixed compression inlet is considerably less than that of

the internal compression inlet because of the mixed compression inlet's external

oblique shock system.

Supersonic inlets can also be classified further as two-dimensional (rectangular)

and axisymmetric (circular or a portion of a circle). Figure 10.31 shows a typi-

cal axisymmetric mixed compression inlet, whereas Fig. 10.30 shows a typical

two-dimensional mixed compression inlet. Axisymmetric inlets have a slight ad-

vantage over two-dimensional inlets with respect to weight and total pressure ratio.

However, the two-dimensional inlets have an advantage in design simplicity and

in providing a larger variation in inlet airflow. Furthermore, axisymmetric inlets

have the added design problem of getting sufficient boundary layer bleed air out

from the centerbody through the support struts.

Lin

shock Normal shock

.......

Oblique shock~ *',. ~ \

~pmea almow ~--------------~'-~// "~ ~'\ Bypassed airflow

[ t ) -/-2: /

[ ' , .--// // // \ )( Throat i Diffuser

A0i ~. ~" / / X / \ =

"*- Centerbody

Fig. 10.31 Axisymmetric mixed compression inlet.

440 AIRCRAFT ENGINE DESIGN

1.00 - F- 14 State-of-the-art

~t ~ ~ _ potential

~-~.,.~-~ ~ (extemal and

• O~ ,'7 --k'~ -- ~ ~ mixed compression)

// r-13 F-4D v \~ ~ //

0"95-111/

~~~:-111

0.90j F-:041 \~~~\i~~l ~

_~ 05 \

\ \ I \ TailOrmate

(fuselage shielded)

0.80- F-16 r'l 6 \

F-104 ~5 Tailor mate

-- (side mounted

two dimensional)

0.75 I I I I I I I

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Fig. 10.32 Total pressure ratio

survey. 7

The improved performance of variable geometry mixed compression inlets and

external compression inlets at high Mach numbers comes with some reduced

performance at low supersonic Mach numbers due to the increased frictional losses.

Figures 10.32 and 10.33 show the inlet total pressure ratios of past and current

aircraft and the Supersonic Transport (SST) model. Note in Fig. 10.33, the reduced

total pressure ratio of the complex SST mixed compression inlet at subsonic and

low supersonic Mach numbers when compared to the simple pitot intake. The

message of these two figures is that a supersonic inlet can be designed for good

performance at supersonic or subsonic flight Mach numbers, but not at both.

10.2.3.2 Totalpressure recovery(~lR). In the engine cycle analysis of this

textbook, the total pressure recovery of the shock system for the supersonic inlet

was estimated by

rlespec = 1 - 0.075 (M0 - 1) 1'35 for 1 < Mo < 5 (4.12c)

800

TIRspec

M~ + 935 for 5 < M0 (4.12d)

the ram recovery of military specification MIL-E-5008B. This design inlet total

pressure recovery has been added to Fig. 10.28 to give Fig. 10.34, a very useful

design tool for selection of inlet type and preliminary number of oblique shocks

required. As an example, consider an inlet for flight at a Mach number of 2.5.

Equation (4.12c) or Fig. 10.34 gives an allowable total pressure recovery for the

shock system of 0.87. Figure 10.34 shows that more than two oblique shocks of

DESIGN: INLETS AND EXHAUST NOZZLES 441

1.0

~,,,~ Pitot intake

0.95

0.90

I I

1 2

Fig. 10.33 Total pressure ratio---SST model. 7

1.0

0.9

0.8

1.0

....,,~ ,.

~.3

\ \ ~\2 \

' , 1 ~ \

"lRspec

\ \ ." ~ \/ MIL-E-5008B

-\ \ N \.

I. "\ -\ NN~\

2.0 3.0

Fig. 10.34 Total pressure recovery.

442 AIRCRAFT ENGINE DESIGN

Al =Aoi

Oblique shocks

/.#

Normal shock

//,~¢~ ~. c ~

Diffuser

/ / b

a) On-design operation

Oblique shocks

/ /

/ / •

/ / ~ ~

Normal shock

/ / ' ~

Diffuser

/ / ........-.--~ ~

1, / /~ •

ao; / / " "N

Fig. 10.35

operation.

Off-design operation

Example external compression inlet: a) on-design operation; b) off-design

equal strength followed by a normal shock are required. The required total pressure

recovery can be obtained by an external compression inlet with three oblique shocks

or a mixed compression inlet.

The total pressure recovery of the general external compression inlet shown in

Fig. 10.35 can be determined using the normal and oblique shock equations/tables 9.

The total pressure ratio across a normal shock can be calculated using

~--,-x / 2?/

y- 1 -U(×-l)

E2x - 1 2 ~:s--u2 / × + 1 x ~T ~ (10.9~

-- 2 *'*x

where

is the upstream Mach number and the downstream Mach number

(My)

is calculated using

I M~+ r-2_ 1

My = ~-~_~M~ - 1

(10.10~

For oblique shocks, the total pressure ratio is calculated using Eq. (10.9) with

replaced by M1 sin fl, where M1 is the upstream Mach number and fl is the

angle of the oblique shock with respect to the upstream velocity (see Fig. 10.35).

The downstream Mach number (M2) is calculated using Eq. (10.10) with My

DESIGN: INLETS AND EXHAUST NOZZLES 443

replaced by Me sin (/3 - 0), where 0 is the ramp angle. The angles/3 and 0 and

upstream Mach number M1 are related by

tan(fl - 0) = ~ + ~ (M1 sin/3) 2 (M~ sin /3 cos /3)

which can be solved for the ramp angle (0) to give

tan 0 = 2ctn/3 (M2sin2/3- 1) (10.11)

2 + m~o' + 1 - 2 sin 2 13)

Two limiting values of ramp angle occur9: the ramp angle (0") leading to M2 = 1

and the maximum ramp angle (0max) for which an oblique shock solution exists.

The corresponding values of oblique shock angle (/3) are given by

(si n2/3)0

.... =

(y + 1)M12 - 4ff(y + 1){(y + 1)M 4 + 8(y - 1)M 2 + 16}

4yM~

(10.12a)

(~, + 1)M~ - (3 - y)V/(y + 1){(y+l)M 4 - 2(3 - y)M~ + y + 9}

(sin 2/3)o* = 4yMl 2

(10.12b)

and the ramp angle (0) calculated using Eq. (10.11).

The GASTAB program included with this textbook as a part of the AEDsys

software can perform these calculations for normal and oblique shocks plus many

others (e.g., multiple oblique shocks and conical shocks).

Example 10.1 External Compression Inlet (Part I)

Applying the normal and oblique shock equations to the external compression

inlet of Fig. 10.35 with Oa = Ob = 5 deg yields the results tabulated in Table 10.1

and plotted in Fig. 10.36. The total pressure recovery (OR) of the inlet is the

product of the total pressure ratio across every shock. This inlet's OR exceeds the

total pressure recovery of MIL-E-5008B (ORspec) at 1.7M (0.9654 vs 0.9537) but

not at 1.8M (0.9396 vs 0.9445). These results can also be obtained easily using

the INLET computer program included with AEDsys.

Note that for M0 between 1.26 and 1.42, the second oblique shock becomes

the terminal normal shock because its ramp angle

(Ob)

is larger than

0ma x

for Ma

between 1.238 and 1.023. Likewise, the first oblique shock becomes the terminal

normal shock for M0 between 1.23 and 1.0. Also note that the total pressure

recovery goes through local maxima and minima as these oblique shocks become

normal shocks.

10.2.3.3 Mass flow characteristics. The inlet mass flow ratio is defined

as the ratio of the actual mass flow rate of the inlet (rhi) to the mass flow rate that

444 AIRCRAFT ENGINE DESIGN

Table 10.1 Example 10.1: External compression inlet of Fig. 10.35 with

Oa = Ob = 5 deg

Mo ~° P,°/P~o

Mo ~b P,b/ P,o Mb P,o/ P,b ~R

2.00 34.30 0.9979 1.821 37.95 0.9982 1.649 0.8765 0.8731

1.95 35.23 0.9980 1.773 39.09 0.9983 1.602 0.8945 0.8912

1.90 36.23 0.9981 1.725 40.34 0.9983 1.554 0.9117 0.9084

1.85 37.30 0.9982 1.677 41.70 0.9984 1.506 0.9278 0.9246

1.80 38.44 0.9982 1.628 43.19 0.9984 1.457 0.9428 0.9396

1.75 39.68 0.9983 1.579 44.84 0.9985 1.407 0.9563 0.9533

1.70 41.03 0.9984 1.529 46.69 0.9985 1.356 0.9684 0.9654

1.65 42.50 0.9984 1.480 48.78 0.9985 1.303 0 9788 0.9758

1.60 44.11 0.9985 1.429 51.21 0.9985 1.248 0.9873 0.9842

1.55 45.89 0.9985 1.378 54.11 0.9984 1.190 0.9937 0.9906

1.50 47.89 0.9985 1.325 57.77 0.9982 1.125 0.9980 0.9947

1.45 50.16 0.9985 1.272 63.05 0 9976 1.045 0.9999 0.9960

1.44 50.65 0.9985 1.261 64.59 0.9973 1.024 1.0000 0.9958

1.43 51.16 0.9985 1.250 66.59 0.9969 0.9974 1.0000 0.9953

1.42 51.68 0.9984 1.238 90 0.9886 0.8223 1.0000 0.9870

1.41 52.22 0.9984 1.227 90 0.9899 0.8289 1.0000 0.9884

1.40 52.78 0.9984 1.216 90 0.9912 0.8357 1.0000 0.9896

1.35 55.93 0.9983 1.156 90 0.9963 0.8739 1.0000 0.9946

1.30 59.96 0.9980 1.090 90 0.9992 0.9230 1.0000 0.9972

1.29 60.95 0.9979 1.075 90 0.9995 0.9352 1.0000 0.9974

1.28 62.04 0.9977 1.059 90 0.9998 0.9486 1.0000 0.9975

1.27 63.26 0.9976 1.042 90 0.9999 0.9639 1.0000 0.9975

1.26 64.69 0.9973 1.023 90 1.0000 0.9819 1.0000 0.9973

1.25 66.50 0.9969 0.9986 0 1.0000 0.9986 1.0000 0.9969

1.24 69.90 0.9957 0.9553 0 1.0000 0.9553 1.0000 0.9957

1.23 90 0.9896 0.8272 0 1.0000 0.8272 1.0000 0.9896

1.22 90 0.9907 0.8332 0 1.0000 0.8332 1.0000 0.9907

1.21 90 0.9918 0.8392 0 1.0000 0.8392 1.0000 0.9918

1.20 90 0.9928 0.8454 0 1.0000 0.8454 1.0000 0.9928

1.15 90 0.9967 0.8784 0 1.0000 0.8784 1.0000 0.9967

1.10 90 0.9989 0.9153 0 1.0000 0.9153 1.0000 0.9989

1.05 90 0.9999 0.9568 0 1.0000 0.9568 1.0000 0.9999

1.00 1.0000 1.0000 0 1.0000 1.0000 1.0000 1.0000

DESIGN: INLETS AND EXHAUST NOZZLES 445

1.00

0.95

0.90

0.85 t J i t i

1.2 1.4 1.6 1.8 2

Fig. 10.36

Total pressure

recovery of Example 10.1--external compression inlet

Fig. 10.35 with

= Ob = 5

deg.

could be captured (tn l) by the geometrical opening A1 of the inlet if the freestream

flow were undisturbed (see Fig. 10.37). From the conservation of mass equation

171i

po VoAoi Aoi

(10.13)

17t l po Vo A1 A1

which is the inlet area ratio. Thus the inlet mass flow ratio and the inlet area ratio

are used interchangeably. The difference between/~t

and/Tt i is the air that is spilled

around the inlet. The engine mass flow ratio is defined, similarly to that of the inlet,

as the ratio of the required engine mass flow rate (rh0) to the mass flow rate that

the inlet could capture (rhl) or

r'no po VoAo Ao

-- -- --

(10.14)

ml poVoA1 A1

// Bypass

/ / / Spilled airfloV

AObp

/ / ~ airflow

/ /__ ~ ///

/ / ; Diffuser

rh] / / ~ ,

) A1

Aoi A o

/ /

', ..... rn 0

l N,~ Bleeds

Aobl

Fig. 10.37 External compression inlet operating at its critical condition.

446 AIRCRAFT ENGINE DESIGN

I t

/ / •

/ / ,° ~ Spilled airflow

/ / •

/ / ,,..I- Normal shock

/ / , Diffuser

/ / :

Fig. 10.38 Subcritical inlet operation.

The difference between rhi and rh0 is the air that enters the inlet but is removed

through boundary layer bleed, the bypass system, or the secondary air system.

When the inlet can accept the mass flow rate of air required to position the

terminal shock just inside the cowl lip, as shown in Fig. 10.37 ("critical" operation),

the fraction of air spilled around the inlet is a minimum and the inlet is said to be

"matched" to the engine. When the inlet is not matched, as shown in Fig. 10.38,

the normal shock moves upstream ("subcritical" operation) and the fraction of air

spilled is increased. This increase in air spillage has associated with it an increase

in "spillage drag," drag due to the change in momentum of the spilled air and the

pressure forces on its streamtube.

When the inlet cannot capture the mass flow rate required by the engine and

the other systems, the terminal normal shock is sucked down into the diffuser

("supercritical" operation), as shown in Fig. 10.39, which strengthens the shock

and increases the

corrected

mass flow rate to the engine. At a specific operating

point on the fan or compressor map, the engine operates as a constant corrected

mass flow device. Thus, when the inlet cannot provide the required corrected mass

flow rate at "critical" operation, the engine causes "supercritical" operation and

attains the required corrected mass flow rate. Note that "supercritical" operation has

a lower inlet total pressure recovery associated with it and thus a reduction in engine

performance (lower thrust and higher specific fuel consumption). "Supercritical"

operation of the inlet is to be avoided when possible because of the poor engine

performance.

A common way of presenting the mass flow rate characteristics of an inlet is

through a map of the total pressure recovery vs the inlet mass flow ratio as shown

in Fig. 10.40. The performance of a typical external compression inlet is presented

/ /

/ / ~ Spilled airflow

/ /

/ t

/._. ~ 4-- ~ ,~......~Normal shock

/ /

/ / I Diffuser

/ /

Fig. 10.39 Supercritical inlet operation.