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

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406 AIRCRAFT ENGINE DESIGN

Table 9.E5 AAF engine afterburner core and bypass flow areas and radii

Stations

Station Station Station Station Station 6.1 and 7

5 (core) 6 (core) 13 (bypass) 16 (bypass) 6A (mixed) (mixed)

ro (in.) 11.0 14.6 13.4 15.7 15.7 15.7

ri (in.) 7.0 11.9 12.0 14.6 11.8 0.0

A (ft 2) 1.571 a 1.549 0.798 0.719 2.338 5.378

aArea at station 5 from low-pressure turbine design (see Sec. 8.3.4).

9.4.2.1 Mixer. As shown in Sec. 9.3.2, it is not feasible to design the mixer

from first principles. However, some calculations can be performed that illus-

trate the magnitude of the mixing problem, and some possible solutions can be

suggested. From Table 9.El, the areas, mass flow rates and thermodynamic prop-

erties of the mixer inlet flows at stations 6 and 16 are available. Substituting these

numbers into the mixing layer Eqs. (9.52-9.58), the velocity ratio r and density

ratio s for the shear/mixing layer can be calculated,

U16

677.21 P16 Tt6 1983.04

r ..... 0.8785 and s = -- ~ .... 2.220

U6 770.87 P6

Ttl6

893.29

from which the maximum possible rate of growth of the mixing layer (imbedded

in the shear layer) is

-- = C8 (0.0332) = 0.0150, for (CDmax = 0.45

From the geometry of Fig. 9.35 in Sec. 9.3.2,

would have to be over 12 ft,

for just the bypass stream to mix out! This is obviously not acceptable. What is

wrong, and what is to be done about it?

The problem is that in order to pressure-match the two streams prior to mixer

entry the bypass stream is slightly accelerated from station 13 to 16, while the

core stream remains at essentially constant area and velocity from station 5

to 6 (see Sec. 8.3.4.) This results in a velocity difference between the two streams

at mixer entry AU

= (U 6 - U16) =

(770.87 - 677.21) = 93.66 ft/s, which

appears to be large enough to strongly drive the shear layer. However, as can be

seen by inspection of Eq. (9.54), it is the velocity ratio, not the difference, that

determines the axial rate of growth of the shear layer, and the ratio of two large

velocities, r = 0.8785, is too close to 1.0 for the shear/mixing layer to grow at

an adequate rate. Even though a ~94 ft/s velocity difference produces a strongly

driven shear/mixing layer, the mean convective velocity of 724 ft/s convects the

developing shear/mixing layer downstream so rapidly that the axial growth rate is

small.

What is to be done about it? Noting that the component immediately downstream

of the mixer is the diffuser, it will be recalled from Secs. 9.1.5 and 9.2.3 that the

best, "sweet spot" diffuser design operates within the mild transitory stall regime,

labeled "some stall" in Figs. 9.21 and 9.22. The flow in this regime periodically

Table 9.E6

DESIGN: COMBUSTION SYSTEMS

Dimensions of AAF engine afterburner mixer + diffuser

shown in Fig. 9.E9 a

407

Station 1 (6A) Station m Station 2 (6.1)

(in.) 15.7 15.7 15.7

(in.) 11.8 5.0 0.0

rm (in.) 13.75 10.35 7.85

H (in.) 3.9 10.7 15.7

A (ft 2) 2.338 4.840 5.378

aLto =

35.2 in. Ld = 5.0 in.

separates from both walls, which causes stirring, which in turn enhances the mixing

of the co-flowing streams. This suggests that a combined mixer + diffuser might

be a good idea. However, if design data for such a combined mixer -t- diffuser

exists, it must be proprietary to the engine manufacturers, as no references could

be found in the open literature.

Consequently, for preliminary design purposes, the total pressure losses caused

by mixing and flow diffusion must be calculated individually, as if the processes of

mixing and diffusion occurred in axially separate components, whereas in actual

fact, the mixing and diffusion processes will be combined into a single component.

9.4.2.2 Diffuser.

All of the design relations for an annular flat-wall + dump

diffuser were presented in Sec. 9.3.2, in Eqs. (9.122-9.128). Assuming a flat-wall

diffusion efficiency

rio,.

= riD9 o = 0.90 and an overall area ratio

A6.1/A6A

5.378/2.338 = 2.30, Eq. (9.127) gives the optimal area ratio for transition from

flat-wall to dump diffuser

A,.op t

(2.338)(0.90)(2.30) = 4.840 ft 2.

From the annular geometry relations Eqs. (9.122) and (9.123), all of the dimen-

sions for the diffuser can be calculated, and are summarized in Table 9.E6. The

resulting combined mixer + diffuser is drawn to scale in Fig. 9.E9.

From Eq. (9.128), the combined or overall diffusion efficiency is 0D = 0.903,

essentially equal to that assumed for the flat-wall section alone.

A few comments about this design are in order. First, it may seem optimistic to

assume a diffusion efficiency as high as 0D ---- 0.9, but it must be borne in mind

that the combined mixer + diffuser has already been assessed a total pressure loss

station 6A station 6.1

Fig. 9.E9 Combined mixer + diffuser with dimensions given in Table 9.E6 (to scale).

408 AIRCRAFT ENGINE DESIGN

for mixing alone. Secondly, the centerbody length

3 ft may seem somewhat

long, but one design goal is to provide adequate length for mixing of the core

gas and bypass air streams, as well as efficient diffusion. Finally, if a worst-case

diffusion efficiency of OD = 0.6 were to be assumed, the centerbody length would

be reduced to

"~ 1 ft, just one-third of the design value! It appears that there

are some interesting trade-offs to be considered here.

All properties at station 6.1 can now be calculated, as follows:

1) At diffuser entry station 1, using values from Table 9.El for station 6A,

= Ptl

P1 = 76.859 - 68.248 = 8.611 psia,

ql = ~yP1M~

= 0.5 (1.336) (68.248) (0.4249) 2 = 8.231 psia

To be conservative, the larger value ql = 8.611 psia will be utilized.

2) The total pressure loss coefficient, from Eq. (9.66), is

\ ql / O ql

( II

= 1 (2.50) 2 (1-0.903) = 0.0787

from which the total pressure at station 6.1 is

Pt2 = etl- (Aet~

ql =

76.859- 0.0787(8.611) = 76.181 psia,

\ ql /D

and the static pressure, from Eqs. (9.62-9.64), is

( 1

P2 =- PI -k- 1 -- ~ rlDql

= 68.248 + 1 (2.30)z, /

= 74.538 psia

and the dynamic pressure is q2

Pt2

- P2 =

76.181 - 74.538 = 1.643 psia.

3) The Mach number at station 6.1 is determined by

_/2q2 ~1.336(74.538)2(1.643) - 0.1817,

M2 = V~2 =

for which the corresponding velocity is

gcP2A2M 2

32.174(74.538)(5.378)(144)(0.1817) 2

U2 - - = 268.19 ft/s

rn 228.63

and the stream thrust function at station 6.1 is

I2 = PzA2(1 + yM 2) = 74.538(5.378)(144)[1 + 1.336(0.1817) 2] = 60,270.7 lbf

All of these values are summarized on a new line to be added to the Engine

Station Test Results sheet of Table 9.El for station 6.1, given in Table 9.E7.

(1) ~0 ~

.... "'~ "~-~ ~ ~ ~' ~'~ ~--b ~'~

-~'~ *'--' ~ ~" ..-~ ~ ~'~

~ ....

o~.~

~ ~o ~ ~ ~.~ -

~-~ ~o~'--~ ~ o

II C~ {'~ ~" ~ ~

__~ ~-- II ~"

-t-

~,,,°

o~o

~.~

• ::i~

~.~~

I1"

-t-

0 0

N.~"

~Na

• ~

=,o~ I

bJ IxJ

.~.oo

~,~ oo

.w.~

.~.oo

tn hJ

~000

.~.o

.u,.~

-q b~

~o oo

/-x

o- 0

.~" 0

~" O0

~" .<

rll

410 AIRCRAFT ENGINE DESIGN

and the corresponding total pressure at station 7 is

Pt2

= Ptl-ql

(APt ~ =

76.178- 1.643(1.822)= 73.184 psia

\ ql ~lAB

which is above the target value of

Pt7

= 73.016 psia.

Note that this value of

Pt7

is for "wet" operation. For "dry" operation, for which

ZAB

= 1.0, the total pressure at station 7 is

(PtT)d,-y

= 76.178 -- 1.643(0.444) =

75.448 psia.

Corrected Engine Station Test Results values for station 7 can now be calculated.

Recall that only the mass flow rate, ratio of specific heats, and total temperature

are fixed, and that all other values are "bogeys" which must now be re-calculated

because of the larger area and slightly greater total pressure of the present design.

This is easily done by calculating the mass flow parameter at station 7,

MFP'-- th4Ttt _

237.33~ = 0.2512 lbm-~/Z-R

APt

5.378(144)(73.184) s-lbf

then, using the isentropic flow functions of the AEDsys program GASTAB, enter

the values y = 1.300, molecular weight ~28.8 lbrn/lbmol, and the just-calculated

value of

MFP

(watch the units !), select subsonic values, and obtain

A P

M = 0.2986, -- = 2.0623, and -- = 0.9441,

from which follows P = 0.9441 (73.184) = 69.093 psia, A* = 5.378/2.0623 =

2.608 ft 2,

gcyPAM 2

32.174 (1.300) (69.093) (5.378) (144) (0.2986) 2

U- -- -- = 821.13 ft/s

rh 237.33

and

I = PA(1 +

yM 2) = 69.093(5.378)(144)[1 + 1.300(0.2986) 2] = 59,710.0 lbf.

For designing the thrust nozzle and determining the total thrust of the engine,

the data for station 7 recorded in Table 9.El must be corrected, as shown by bold

text in Table 9.E8.

9.4.2.3 Flameholders.

The next step is to determine how large the vee-

gutters must be, and how many rows(rings) of vee-gutters there should be. As

recommended in Sec. 9.3.2, the vee-gutters will be designed with included angle

Table 9.E8 Corrections to Table 9.El (bold text) for station 7

Station m dot gamma Pt Tt Press Mach Velocity Area Area* I

(lbm/s) (psia) (R) (psia) fit/s) (ft 2 ) (ft 2 ) (lbf)

6A 228.63 1.3360 76.859 1513.71 68.248 0.4249 779.89 2.338 1.536 28516.0

6.1 228.63 1.3360 76.181 1513.71 74.538 0.1817 268.19 5.378 1.645 60270.7

AB fuel 8.7033

7 237.33 1.3000 73.193 3600.00

69.093 0.2986 821.29 5.378 2.608 59710.0

DESIGN: COMBUSTION SYSTEMS 411

2 0 = 30 deg. In the present design, in order to meet the goal value of total pressure

loss, a sub-optimal

W/H

= 0.4 and corresponding blockage B =

D/H

= 0.314

will be utilized, where D is the lateral dimension or height of the vee-gutters and

H is the channel height or "pitch" between vee-gutters.

Equation (9.134) states that, for

W/H

---- 0.4, H must be greater than 1.042

times the product of approach velocity

U6.1

and

tBo, the

residence time at blowout

in the mixing layer at the edge of the recirculation bubble. Because U61 has been

determined from the design of the afterburner diffuser, the sole task remaining is

to use the AEDsys chemical kinetics program KINETX to determine

tBo.

Establishing inputs for KINETX requires some rather tedious calculations to

determine the composition of the mixture of core gas combustion products with

turbine cooling air and fan bypass air. The required steps are:

1) Find the composition of combustion products entering the high pressure

turbine at station 4. This can be done from stoichiometric "complete combustion"

calculations, because minor or pollutant species have a negligible effect on this

calculation, or more easily by using either of the two AEDsys programs EQL

or KINETX. Either way, the mass-specific mol numbers of major combustion

products at station 4 are found to be

no2

= 4.354 × 10 -3 lbmolsO2/lbmmixture

nN2

= 2.669 × 10 -2 lbmols N2/lbmmixture

ni42o

= 1.928 x 10 -3 lbmolsH20/lbmmixture

n¢o2

= 1.780 × 10 -3 lbmols CO2/lbmmixture

The mass-specific mole numbers at station 16 are those for air alone,

no2

= 7.098 × 10 -3 lbmols O2/lbmair

nN2

= 2.669 × 10 -2 lbmols N2/lbm air

2) From Table 9.El, the mass flow of main burner combustion products at

station 4 is 106.94 Ibm/s, and the sum of the air mass flow rates for both turbine

cooling and fan bypass is 121.69 lbm/s. The mole numbers in the combined streams

at stations 6A and 6.1 are therefore calculated to be

no2

= 5.815 × 10 -3 molsO2/lbmmixture

nN2

= 2.669 X 10 -2 molsN2/lbmmixture

ni42o

---- 9.018 x 10 -4 molsH20/lbmmixture

ncoz

= 8.326 × 10 -4 molsCO2/lbmmixture

This is the composition of the gas approaching the flameholders and being

entrained into the mixing layer at the edge of the recirculation bubble.

3) Equations (9.59) and (9.60) show that the mixing layer entrains essentially

equal amounts of cold gas and hot recirculation products, which corresponds to a

recirculation ratio

= 0.5 for input to KINETX.

4) With the mass flow rate, gas composition, temperature and pressure estab-

lished at station 6.1, with recirculation ratio

---- 0.5, and the afterburner fuel

mass flow rate as inputs to KINETX, there results

tso ~

8.5 × 10 -5 s.

It is now possible to determine the minimum channel height H from Eq. (9.134):

Hmin = 1.042 (U6.1

tBo)

= 1.042 (268.19) (8.5 × 10 -5) = 0.0238 ft x 12 "~ 0.3 in.

412 AIRCRAFT ENGINE DESIGN

Fig. 9.El0 Comparison of afterburner length using two or three rings of vee-gutters

(to scale).

For a design blockage of B = 0.314, the corresponding minimum value of

vee-gutter height is

Dmi n = Bnmin =

0.314(0.3) ~ 0.1 in. In other words, a ~0.1

in. vee-gutter would be marginal, operating near extinction or blowout. To ensure

stable flameholding, operating far away from blowout, both the vee-gutter size D

and spacing H will have to be significantly larger than the minimum values, while

maintaining the design ratio B =

D/H

= 0.314. Typically, using a factor of 10

to ensure a "significantly larger" margin, the vee-gutter dimension D should be

greater than 1.0 in.

The maximum number of vee-gutter tings is determined by dividing the height

of the total afterburner flow area, H6.1 = 15.7 in., by the minimum vee-gutter

channel height nmin, and rounding down:

[Nvee]max =

15.7/1.0 "-~ 15. As long as

there

are fewer

than 15 rings of proportionately sized (B = 0.314) vee-gutters, they

should perform their flameholding function satisfactorily. The choice of number of

rings therefore depends on other design considerations such as afterburner length,

stealth shielding, and structural and manufacturing complexity.

Figure 9.El0 shows graphically the effect on afterbumer length of two versus

three tings of afterbumers. Note that, compared to the comparison of one versus

two tings shown in Fig. 9.41, the effect of more tings of smaller vee-gutters is

diminished as the number of tings increases. This is because the axial length

scale reduction goes from 1:2 to 2:3. Bearing in mind the complexity of adding

as many spray bars and manifolds as vee-gutter tings, there does not appear to

be a compelling reason to increase the number of vee-gutter rings beyond three

or four. For the present design, three tings will be satisfactory, for which H =

15.7/3 = 5.25 in, and D = (0.314)(5.25) = 1.65 in. For this design, the distance

from the nose of the vee-gutter to where the flame strikes the wall, still assuming

flame spread at 17 deg for lack of better information, is approximately 20 in. This

dimension should probably be increased to 24 in or even 30 in, because of our

imprecise knowledge of the flame spread angle, and of course while respecting

constraints on axial length as a result of the "packaging" of the entire engine within

the airframe.

DESIGN: COMBUSTION SYSTEMS 413

station 16

]~ Lm t Ld---~_

"~ station 6.1

Fig. 9.El1 "No-mix" diffuser for alternative example afterburner design.

9.4.2.4 Spray bars.

Lacking more information or better guidance, three

rings of spray bars will also be chosen, each spray bar to be located directly

upstream of each vee-gutter, and tucked back inside the diffuser tailpipe to conserve

axial space.

9.4.2.5 Summary.

The overall length of the afterburner can now be calcu-

lated, as the sum of the calculated or estimated lengths of 1) the ducting between

stations 5 and 6 and between stations 13 and 16, [12 in.]; 2) the combined mixer ÷

diffuser + spray bars, [45 in.]; 3) the flameholding and flame spread section,

[24 in.]; for a total length

LAB

= 12 + 45 + 24 = 83 in -~7 ft.

9.4.2.6 Alternate "no-mix" afterburner design.

The difficulty of mixing

the core gas stream with the bypass fan air stream has been emphasized earlier in

this section. An alternative approach, mentioned in Sec. 9.3.2, is to not try to mix

the two streams at all, but simply allow them to co-flow through the diffuser, as

shown in Fig. 9.El 1.

In this "no-mix'approach, the vee-gutter flameholders would be located at the

entrance to the "dump" portion of the diffuser, the intermediate station m in

Fig. 9.E9. If the flameholder were to be located at the end of the tailpipe sec-

tion, station 6.1, the flow dispersion in the dump section would result in unpre-

dictable, large-scale stirring between the two streams, as described in Sec. 9.1.5,

which would defeat the design premise of a two-stage, two-stream "no-mix"

afterburner.

It will be assumed that the two streams are separated by a "slip surface" across

which no mixing occurs. As can be seen from Fig. 9.35 and related estimates

made earlier in this section, this is not a bad assumption. Because both co-flowing

streams are subsonic, the static pressure is always matched in both streams, and

so Eq. (9.64) can be used to find the areas of the two streams at station m in Fig.

9.E9, as follows:

AP= {TlDql(l--~-~)}core: {tlDql(1--A~)]fa n

The area ratios of the two streams are

ARcore : otAm/A6

and

ARyan = (1

-or) x

Am~A16,

where ot is the area fraction of the core stream at station m, and where

: 4.840 ft 2 from Table 9.E6. The dynamic pressures in the two streams

414 AIRCRAFT ENGINE DESIGN

at entry can be found from the difference between static and total pressures in

Table 9.El, ql

core = (Pt

P)6 =

78.129 - 71.533 = 6.596 psia, and

qlfan

(Pt -

P)16 = 83.391 - 71.570 = 11.821 psia. Assuming the diffusion efficiencies

in the two streams to also be equal, Eq. (9.64) can now be solved to find the core

stream area fraction u = 0.7963, and the corresponding two areas at station m

Am cor e ~-

0.7963(4.840) = 3.854 ft 2, and

Amfan ~--

(1 -

0.7963)4.840

0.9859 ft 2. From the annular geometry relations Eqs. (9.122), the radius of the

slip surface dividing the two streams at station m is found to be

rslip

-- 14.2 in.,

so the radial heights of the two streams are

Hm~ore

= (14.2 - 5.0) = 9.2 in., and

Hmfan =

(15.7 - 14.2) = 1.5 in.

Applying Eq. (9.64) to either stream, and assuming a diffusion efficiency Oi~ =

0.9, the station pressure at station m is found to be

Pm=

76.53 psia.

From mass continuity the corresponding stream velocities at station m are

1.549

Urn

core =

U6 Am

co-""~e --

(770.87) 3.854 -- 309.82 ft/s,

and

A16 0.719

Urn fan

= U16 ~n --

(677"21)0.9859 -- 493.88 ft/s

and the static temperatures in both streams are essentially equal to their respective

total temperatures, listed in Table 9.El for stations 6 and 16.

The gas compositions of the two streams have already been determined earlier in

this section. With all inputs to the AEDsys software program KINETX now fixed,

including the design afterburner exit temperature of

= 3600°R, the blowout

residence times in the two streams are found to be

tBo

core

1.49 × 10 -4 s and

tBofan

= 7.07 x 10 -5 s, and the required fuel mass flow rates in the two streams

are rhfcore

= 3.331 lbm/s and

l~lffan =

5.795 lbm/s.

Assuming the optimal wake width to channel height ratio

W/H

= 0.5,

Eq. (9.135) gives the minimum channel widths for flameholding for the two

streams,

Hcore > U6 rBOcore

= 309.82 (12) (1.49 × 10 -4) ---- 0.55 in., and

Hfa, >

U16

~'BOfan =

493.88(12)(7.07 × 10 -5) = 0.42 in. The maximum number of vee-

gutter rings in each stream is determined as before by dividing the radial pas-

sage height by a safety margin of 10 times the minimum height required for

flameholding and rounding down,

[Nvee]core =

9.2/10(0.55) ~ 1, and

[Nvee]fa n =

1.5/10(0.42) ~ 0.

For the core stream with a single vee-gutter ring, and with the optimal blockage

B = 0.417 for a 30 deg included angle vee-gutter, as given by Eq. (9.137), the

corresponding vee-gutter lateral dimensions are

Dcore

= 0.417(9.2) = 3.84 in.

This corresponds to a shear layer residence time ts

ncore/Urncore =

9.2/

(12) 309.82 = 2.48 × 10 -3 s, which is a comfortable ~16 times the minimum

residence time for flameholding,

tBocore

= 1.49 × 10 -4 s. In the fan stream,

a single vee-gutter with the same blockage would required a vee-gutter of di-

mension

Dfa,

= 0.417 (1.5) = 0.62 in. This gives a shear layer residence time

ts = Hfa,,/Umfa,

= 1.5/(12) 493.88 = 2.53 × 10 -4 s, which is less than ~3.6

times the minimum residence time for flameholding,

tsofa~

= 7.07 × 10 -5 s.

There are some problems with this alternative flame stabilization design: 1) The

required fuel mass flows to achieve the design exit temperature of Tt = 3600°R

DESIGN: COMBUSTION SYSTEMS 415

Fig. 9.E12 Alternative "no-mix" design arrangement of vee-gutter rings and spokes.

in both streams add up

to/'r/f =

3.331 + 5.795 = 9.126 Ibm/s, nearly 5% greater

than the fuel flow required for the mixed-stream design, and 2) The 9.2-in. height

of the core stream is not quite large enough to accommodate two flameholders

with good stability, so a single, D = 3.8 in. vee-gutter is required, whereas the

1.5-in. height of the fan stream can accommodate only a single D = 0.625 in.

vee-gutter, for which the residence time is only a marginal 3.6 times greater than

the minimum required for flameholding.

One workaround to the flameholder size problem, used on at least one currently

operational engine and as illustrated in Fig. 9.E12, is to attach radial spokes of vee-

gutter shape and lateral dimension great enough to give a residence time 10 times

the blowout value,

Dfa,,

= 1.76 in. The spokes can be spaced circumferentially

with appropriate solidity to maintain the desired blockage B = 0.417 in the fan

stream.

However, because the root area of the spokes is in the core stream, the ring

vee-gutter must be reduced in lateral dimension

Dcore

to, say, 3 in., to offset the

core gas blockage of the root area of the spokes. Further complicating this design

solution, additional inward-protruding spokes must be provided to add back the

needed blockage in the portion of the core gas stream inboard of the vee-gutter

ring.

A stealth variation of this design is to locate the single vee-gutter ring in such a

way as to hide the moving blades at low-pressure turbine exit, in case the turbine

blades are not already hidden by ducting as in the present design.