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

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396 AIRCRAFT ENGINE DESIGN

Table 9.E2 Annular geometry of AAF

engine at stations 3.1 and 4

Station 3.1 Station 4

(ft 2)

0.194 0.144

(in.) 9.0 7.0

r i

(in.) 8.753 6.764

(in.) 9.247 7.235

H (in.) 0.494 0.472

annular geometry relations and definitions given in Fig. 9.36 and Eq. (9.122),

rm "-- ~(ri -}- ro), H "-- (ro - ri),

and

a = :n:(r 2 - r 2) = 7r(ro - ri)(ro + ri) = 2re rmH

the inner and outer radii and the radial heights H at stations 3.1 and 4 can be

calculated and are summarized in Table 9.E2.

9.4.1.1 Layout.

Some obvious ways to lay out the combustor are to match

the radius of the outer casing either to the outer radius at station 3.1 (Design A),

or to the outer radius at station 4 (Design B), or somewhere in between. Annular

geometry has been calculated for the two layouts A and B, and the number of

fuel nozzle assemblies calculated from Eq. (9.105). The results are summarized in

Table 9.E3, and the layouts of designs A and B are sketched in Fig. 9.E1.

Chiefly because it has fewer fuel nozzles, design B will be selected. However,

because design A has the smaller radial height H, mixing in the secondary and

dilution zones will be somewhat more effective than in design B [see Eq. (9.116)].

9.4.1.2 Diffuser.

The required diffuser area ratio is

AR = A3.2/A3.1 =

0.677/0.194 = 3.490, which is less than the maximum "sweet spot"

AR = 4

of Figs. 9.21 and 9.22. For this area ratio Eqs. (9.66) and (9.67) give the total pres-

sure loss coefficient

(APt/qr)9

and total pressure ratio

no,

respectively, for any

assumed diffusion efficiency. Using these equations, it is found that a value of r/9 as

Table 9.E3 Annular geometry of station 3.2 for

two possible combustor layouts

Design A Design B

1"o3.2 ~ ?'o3.1 ?'03.2 ~ ro4

(in.) 9.247 7.235

r i

(in.) 7.381 4.617

rm (in.) 8.314 5.926

H (in.) 1.866 2.618

N.oz

28 14

DESIGN: COMBUSTION SYSTEMS

397

10-

~',

, t

station 3.1 station 3.2

Fig. 9.El

-10

-8

Design A "~.

Design B jS 6

station 4

station 3.9 station 4

Layouts of designs A and B of Table 9.E3 (radial dimensions to scale).

low as 0D = 0.83 will satisfy the allocated total pressure loss, APt = Pt3.1

- Pt3.2.

If a higher diffusion efficiency is assumed, the "savings" in total pressure loss can

be allocated to the main burner, if required, to improve mixing.

All of the design relations for an annular flat-wall 4- dump diffuser were

presented in Sec. 9.2.3, in Eqs. (9.102-9.104). Assuming a diffusion efficiency

ODm

• TID9 ° =

0.9, and the given overall area ratio AR = 3.490, Eq. (9.103)

gives the optimal area ratio for transition from flat-wall to dump diffuser as

---- (0.194)(0.9)(3.490)

= 0.609 ft 2. However, because the AR is less than the

"sweet spot" value of four, a simple (no dump) flat-wall diffuser will be

chosen.

For a one-stream diffuser (no splitter plates), the slant-height distance along the

diffuser mean line can be calculated from Eq. (9.61),

L=Hl(rml") AR-1 _0.494(9 )3.490-1

k.rm2/ 2tan4.5deg ~ 2(0.0787) -- 11.868 in.

Because the main burner should be as short as possible, L can be reduced

by a factor of two or three, by employing one or two splitter plates. Although

two splitters plates could perhaps be mounted on the liner dome as a "snout"

(see Fig. 9.1), that may be too complex for this geometry, and so a two-stream

(one splitter plate) flat-wall annular diffuser might be a good compromise. For the

two-stream design the slant-height distance L is now L = 11.868/2 = 5.934 in.,

and the corresponding axial distance is

Ax = ~/L 2

- (r3.1 - r3.2) 2 =

~/(5.934) 2 - (9 - 5.926) z = 5.076 in.

The layout for the two diffuser designs is shown in Fig. 9.E2.

9.4.1.3 Air partitioning.

From Table 9.El and Eq. (9.90), the equivalence

ratio at station 4 is calculated to be ~b4 = thfMB/fstrh3.1 = 2.7017/(0.0685 x

104.24) = 0.3784.

The liner material will be assumed to be capable of withstanding a temperature

Tm = 2110°R, by using thermal barrier coatings. The cooling gas temperature is

T¢ = Tt3.a = 1660°R, and a decision to use film cooling or transpiration/effusion

cooling is deferred for the moment.

398 AIRCRAFT ENGINE DESIGN

10 Z

two-stream one-stream

.... I .... I .... I .... I .... I .... I .... I .... I .... I .... I .... I .... P .... I'

0 2 4 6 8 10 12

-10

Fig. 9.E2 Annular flat-wall diffusers for none or one splitter plate (to scale).

Using Eqs. (9.88) through (9.101), the air mass fractions/z for primary and

secondary zones can be calculated, as well as the cooling mass fraction/Zc for any

assumed liner gas temperature Tg. For example, for assumed

= 3200°R, from

Eq. (9.89), ATmax =

(Tt4 -

Ts.1)/q~4 = (3138.8 - 1660.0)/0.3784 = 3909°R.

From Eq. (9.97), Csz = (3200 - 1660)/3909 = 0.394, and for assumed

Sez =

0.7, Eq. (9.92) gives Cez = Csz/0.7 = 0.563. The resulting mass flow fractions

are given by Eq. (9.93), /Zez = ¢4/¢ez = 0.3784/0.563 = 0.672, and from

Eq. (9.99),

lZsz

= (¢4/¢sz) - (¢4/¢ez) = (0.3784/0.394) - (0.3784/0.563) =

0.288.

The primary and secondary air flow fractions added together equal 96% of the

total airflow, leaving only 4% available for cooling and dilution. Even without

dilution, there is not enough air available for liner cooling.

To understand and find a solution to this problem, the preceding calculations

were repeated for assumed liner gas temperatures

ranging from 3000 to 4000°R,

and assumed primary zone combustion efficiency

Spz

= 0.7. The results of

these calculations, together with the corresponding cooling mass fractions from

Eqs. (9.95) and (9.96), are presented in Fig. 9.E3.

The lack of cooling air available stems from the fact that Tt4 = 3138.8°R

happens to be right in the mid-range of target liner gas temperatures that minimize

Fig. 9.E3

1.0

.~.6

~.4

e~ . Spz

= 0.7

Trn

= 2110°R

:~.2

T c

= 1660°R

0 ,P .... I,,,I .... I .... I .... I .... I .... P .... I,,,

3000 3200 3400 3600 3800 4000

Design Gas Temperature

(°R)

Variation of air mass flow fractions with design gas temperature.

DESIGN: COMBUSTION SYSTEMS

399

the production of pollutant species CO and NOx, as shown in Fig. 9.24. If

Tg =

Tt4

= 3138.8°R were assumed, exactly

all

of the air would be required for primary

and secondary air combustion, and there would be not only no dilution air required,

but also none available for liner cooling. However, if transpiration/effusion cooling

were employed, the required air fraction is so modest that

Tg ..~

3500°R would

probably work. If for some reason (probably manufacturing cost), film cooling

were to be specified,

would have to be raised to well beyond 4000°R, and there

still would be no requirement for dilution air.

Because the AAF engine being designed is a warplane, and not a global range

airlifter, commercial passenger, or transport jet, minimizing pollutant emissions is

not a principal design objective. Rather, what is required is a very wide tumdown

ratio, or in other words, a very wide range of flame stability and thus freedom

from flameout from maneuvers or high altitude. It is therefore desirable to have a

primary zone equivalence ratio above 0.8, well above the lean blowout limit q~8o

0.4 - 0.5.

Using these assumptions, a good choice for target liner gas temperature can

be obtained by solving Eq. (9.92) for

Tg = Tt3.1 + q)PzepzATmax

= 1660 +

0.8(0.7)(3909) = 3849°R.

With

= 3849°R as the design target gas temperature, and still assum-

ing

epz

= 0.7 and ~Pz --- 0.80, Eq. (9.93) gives the primary zone air mass

fraction as

#ez = q~4/~pz

= 0.3784/0.80 = 0.473. From Eq. (9.97),

(bsz =

(3849 - 1660)/3909 = 0.560, and Eq. (9.99) gives the secondary zone air mass

fraction,

IZsz = (494/qbsz)-

(~b4/~pz) -- (0.3784/0.560)- (0.3784/0.80) = 0.203.

The remaining mass flow fraction (1 -

~ez -

#sz) = 1 - 0.473 - 0.203 = 0.324

is available for film cooling, or for transpiration/effusion cooling and dilution.

For

= 3849°R the required cooling effectiveness is, from Eq. (9.94), ~ =

(Tg - Tm)/(Tg - Tc)

= (3849- 2110)/(3849- 1660) ---- 0.794. From Eqs. (9.95)

and (9.96), the corresponding requirements for cooling air mass fraction are/zc =

0.644 for film cooling, and/zc = 0.155 for transpiration/effusion cooling. Because

there is not enough air available for film cooling, transpiration/effusion cooling

must be selected. With transpiration/effusion chosen for liner cooling, the required

dilution air fraction from Eq. (9.101) is

[,£DZ

1 - (#ez + #sz + IZc) = 1 -

(0.473 + 0.203 + 0.155) = 0.169. The results of the air partitioning are summa-

rized in Table 9.E4.

9.4.1.4 Dome and liner.

With the radial height of the outer casing

fixed, and air partitioning determined, it is now possible to determine the liner

height HL and corresponding dome diameter. From Eq. (9.109), the optimal

Table 9.E4 Air partitioning for AAF engine main burner, for assumed

=3849°R and

eez =

0.7

Primary Secondary Transpiration Dilution

Total zone zone cooling zone

Air flow (lbm/s) 104.24 49.306 21.161 16.157 17.616

Mass fractions 1.00 0.473 0.203 0.155 0.169

400 AIRCRAFT ENGINE DESIGN

l~ser

~~do ~terSplitter

~'~dcme

easing : : :

~. liner ~. :

4 inner

casing

.... I .... I .... I .... I .... I .... I .... I .... I .... I'"~1 .... I .... I .... I'

0 2 4 6 8 10 12

Fig. 9.E4 Layout of AAF engine combustor dome, liner, inner and outer casing

(to scale).

liner-to-reference height ratio for maximum secondary jet penetration is

Ctopt=l-

(/~t~A ~2'3 (

APt~ -1'3

\ #lr

\ qr .']MB

From Table 9.El, APt/qr = (Pt3.2 - Pt4)/(Pt3.2 - P3.2) = (579.263 -

555.859)/(579.263 - 576.537) = 8.585, and the ratio of annulus to reference flow

rate rnA/mr = tZsz + #Dz = 0.203 + 0.169 = 0.372. With these values, Oeopt =

1 - (0.372)2/3/(8.585)1/3 = 0.747,and HL = O~opeHr =0.747(2.618) = 1.957in.

The current state of the main burner layout is shown in Fig. 9.E4.

9.4. 1.5 Total pressure loss. With the liner-to-reference area determined,

Eq. (9.79) can be used to see whether or not the allocated total pressure loss is

sufficient for adequate stirring by the primary zone swirler. For fez = Tu/Tt3a =

3849/1660 = 2.319, this minimum required total pressure loss coefficient is

APt = (thP__~z)2(ar~ 2

qr /min

rnr I \--~L) rpz(2rez- 1)

= (0.473] 2

\0.747) (2.319)[2(2.319)- 1] = 3.383

which is less than 40% of the allocated value of (APt/qr)MB = 8.585, a comfort-

able margin.

9.4. 1.6 Primary zone. With the reference velocity Ur = 163.90 ft/s from

Table. 9.El, the velocity for all jets is determined from Eq. (9.110),

Vj =

Urv \ qr ) MB 163.9084'-~5~.585 = 480.23 ft/s,

The air swirler annular area is determined by first assuming a hub radius of

rh = 0.5 in. to accommodate the airblast atomizer, a sharp-edge hole discharge

coefficient of CD = 0.64 from Eq. (9.33), and a swirl blade angle ofasw = 45 deg.

DESIGN: COMBUSTION SYSTEMS 401

outer casing

swirl

outer liner vanes

inner liner

annulus

inner casing

Fig. 9.E5 Layout of primary air swirlers and atomizers (to scale).

With these values as inputs, Eq. (9.111) can be solved for the swifter blade tip

radius,

rt=~r2+ (lhPZ--3thfMB) (Ar)(APt~ -1/2

NnozZrCD9o~COSOtsw ~rr \ qr /MB

49.306- 3(2.7017) (0.677(144)) ( 1 )

= (0"5)2+ 14rr(0.64) cos45deg \ ~ J ~ =0.954in.

Fortunately, this swifter tip radius is less than

HL/2

= 0.9595, sO the swifter

just fits within the envelope of the liner. The pitch of the

Nnoz

= 14 swifter +

atomizer assemblies at mean radius is

2rcrm/N~oz

= 2rr(5.926)/14 = 2.66 in.

The layout of the swifter + atomizer assembly is shown in Fig. 9.E5.

The swift number for this design is obtained from Eq. (9.48),

S ,2 II-(rh/rt)31

2 tan 45 deg I 1 - (0.5/0.954)31

= -~tane~sw 1 (rh/rt)ZJ

= 3 l~~j =0.787,

which is satisfactory. The swifter area is

Asw

= zr(r 2 - r 2) = rr[(0.954) 2 -

(0.5) 2] = 2.073 in. 2 per nozzle.

The axial length of the primary zone, measured from the "nose" of the dome, can

be laid out according to the estimate Eq. (9.50),

Lpz ~ 2S'rt

= 2(0.787)(0.954) =

1.501 in. ~ 1.5 in.

If the calculated swifter tip radius had been greater than HL/2, some adjustments

would have been necessary. These could have been any or all of the following:

a) smooth the edges of the flow passage at entry to the swifter annulus and/or make

the swifter blades airfoils instead of flat plates or slats, which would increase

perhaps 0.8, even though experience shows that flat-plate blades provide slightly

better mixing than airfoils; b) reduce the swifter blade angle to 40°--but that would

reduce the swift number S' too close to the minimum value of 0.6; c) decrease

the reference Mach number Mr by slightly increasing the reference area

Ar, and

recalculate everything; or d) increase

Nnoz

from 14 to 16, 18 or 20--although

402 AIRCRAFT ENGINE DESIGN

this would have necessarily reduced the spacing or pitch between adjacent fuel

nozzle/air swirler assemblies.

The design of the primary zone can be validated by using the AEDsys pro-

gram KINETX to model the primary zone as a single WSR. For a single noz-

zle/swirler, the inputs to KINETX are as follows:

= 1660°R;

= 540°R; P =

579.263 psia;

l~VtA

thpz/Nno z

49.306/14 = 3.522 Ibm/s;/~t F

2.7017/14 =

0.1930 lbm/s; Lpz = 1.5 in.;

Aez = 7rr2/8

= zr(0.954)2/8 = 0.357 in. 2 (Note

that, as explained at the end of Sec. 9.1.4.4, the micromixed portion of the pri-

mary zone volume is approximately one-eighth of the volume of the recirculation

bubble.) With these inputs, and with an assumed lower heating value of 18,400

BTU/lbm for the fuel, KINETX gives a residence time

= 3.376 x 10 -5 s,

which is an order-of-magnitude greater than the blowout residence time

tBo =

4.403 x 10 -6 s. The predicted primary zone combustion efficiency

Spz

= 78.32%

and gas temperature

Tez

= 3822°R compare favorably with the assumed design

values epz = 0.7 and Tez = 3849°R that were based on a linear approximation to

the thermochemistry [Eq. (9.23)].

9.4. I. 7 Secondary zone.

To design the number and location of the sec-

ondary zone air holes, it is necessary to first calculate the various dynamic pressure

ratios,

qj APt

-- - 8.585,

qr qr

( ~ ~ )2 (0.20_3+0.169)2

mAAr 2 .s + oz

q__~A

\mrAA,]

.... \ 1--0.747 =2.162,

and

qez .fpz (rnpz Ar "~ 2

( [.Apz,~2 [ .~ 2

- - _-09 0

qr qr \ /n r AL/I = 72PZ \Olopt/

\0.747]

The maximum penetration of the jet centerline is obtained from Eq. (9.107),

Ymax

15Jqjqr(1 qAqr)

/8.585( 2.162~

-£j --1. V qr qL qr qj

=1"15¢ 0.~-~ 1 ~]=3.022

The required single jet vena contracta area is obtained from Eq. (9.112),

(Ymax)-I 1.957 __ 0.162 in.

dj = ~HI. \ dj ] -

4(3.022~

The total number of secondary holes is obtained from Eq. (9.113),

4fnsz (4AF~ Ur

=0.20314(0.677) 1447(163.90 ~

Nhsz-prTrd2~ --IZsziTr~]

~ L

~ J\480.23] ~328

or 328/14 ~ 23 secondary holes per nozzle/swifter assembly.

DESIGN: COMBUSTION SYSTEMS 403

Fig. 9.E6

(to scale).

L L

~< Lsz LDz

- ® @

j o °

i @

®® @

o o @

0 2 4 6

.... I

Layout of secondary and dilution air holes in inner and outer liner

The secondary jets enter the liner at an angle 0, as shown in Fig. 9.15, obtained

from Eq. (9.115),

sinO= 1 q__!q~-- 1 -- --0.865, soO=59.9deg

qr qj

8.585

and the diameter of each secondary air hole, from Eq. (9.43) or (9.114), is

dj O. 162

-- = --

0.234 in.

sin 0 ~ (0.865)

There are too many secondary air holes to arrange in a single lateral line, top and

bottom of the liner, as recommended in Sec. 9.2.3, but they should be positioned as

closely as possible to the end of the primary zone. Because there are 23 holes per

nozzle/swirler, they should be divided into twelve on the outer liner, and eleven

on the inner liner, arrayed as shown in Fig. 9.E6.

Following Eq. (9.116), the length of the secondary zone is calculated as

Lsz ~--

2HL

= 2(1.957) ~ 4 in.

9.4. 1.8 Dilution zone.

The same procedure is followed as for the sec-

ondary zone, except that the design goal is Ymax =

HL/3,

rather than

He~4

for

the secondary jets, so that somewhat larger diameter jets will be required. From

Eq. (9.117),

1 ( Ymax'~ -1

dJ~-sHL\ dj J

Because the secondary zone jets have reduced the annulus airflow, only the

dilution air now flows in the annulus, so that the annulus flow dynamic pressure is

reduced to

qr \thr AA]

= \l---'~J =

1---~-.7-47 =0.446

404 AIRCRAFT ENGINE DESIGN

and because the liner flow has been increased by the inflow of the secondary air,

qr \ thr AL i] ot

(0.47_3 ___+ 0.203 ~ 2

= 2.319 \ 0.747 ,/ = 1.899

The maximum penetration of the dilution jet centerline is obtained from Eq. (9.107),

Ymax 1.15,/qjqr (1 qaqr)=l 15/8.585(

0.446~

dj v qr qL qr ~ .

V1.899 1 8.~-~] = 2.381

SO the dilution jet vena contract area of each jet is

1 (

Ymax

~-1 1.957

dj "~ -~ IlL -- -- --

0.274 in.,

\ dj ,/ 3(2.381)

and the dilution jet entry angle is

sin0 = ~1

qaqL--~l

0.446

qr qJ

~--0.974, so0=76.8deg

The diameter of each dilution air hole, from Eq. (9.43) or (9.114), is

dh -- dj _

0.274 -- 0.352 in.

sin 0 ~ (0.974)

and the required number of dilution holes is given by Eq. (9.113),

4r'nDz (4Ar~

gr = 0.169[4(0.677) 1441 (163.90~

NhDZ--pr:rgd2~--#DZ~Kd2:~J

L ~r (0--6~4-) 2 J \48~'~'23] ~95

or 95/14 "-~ 7 dilution holes per nozzle/swifter. Because their lateral location is

not essential, the total 95 holes can be spaced equally, 47 on the inner liner wall

and 48 on the outer wall, around the periphery at the end of the secondary zone,

as shown in Fig. 9.E6.

The estimate of Sec. 9.3.2 can be used for the length of the dilution zone,

LDZ ~ 1.5HL

'~ 3 in.

The total length of the main burner liner can now be summed,

LL = Lpz + Lsz +

LDZ

----

1.5 + 4 + 3 = 8.5 in.

A side view of the main burner layout is presented in Fig. 9.E7.

9.4.2 AAF Engine Afterburner Design

In Sec. 9.3.2, it was shown that the axial length of both the mixer and the

afterburner hot section can be minimized by making the outer radii as large as

possible. Happily, there are no tradeoffs to consider with this issue, and so the

afterburner will be sized with its outer diameter equal to the maximum diameter

DESIGN: COMBUSTION SYSTEMS 405

4L,,z p-- Lsz-- Loz-->t

6 : splitter~'-""" [-[~'~-econdaryholes .,~

-_: airblast~c/'L~J

dilution holes

- . atomize! .~ z

//,

4 --- primary swmer

.... = .... J .... = .... r .... = .... = .... = .... = .... = .... = .... = .... t .... = .... = .... ='"

0 2 4 6 8 10 12 14 16

Fig. 9.E7 Side view of AAF engine main burner layout (to scale).

of all of the upstream components, namely, the outer diameter at fan inlet,

ro =

15.7 in.

Ducting will be required to direct the core flow and fan bypass air outward from

their respective outlets to their pressure-matched entries to the mixer. For the core

flow, the ducting will be from station 5 to station 6, and for the bypass air flow, the

ducting will be from station 13 (bypass) to station 16.

Because station 16 is radially outboard of station 6 (see Fig. 9.2), its outer radius

will be set to the maximum afterburner design radius,

= 15.7 in, and the station

16 inner radius determined from

and the area given in Table 9.El, using the

geometric relations for annuli given by Fig. 9.36 and Eq. (9.122).

The outer radius at station 6 will be set equal to the inner radius at station 16,

and the station 6 inner radius determined from the outer radius and area from

Table 9.El, in the same manner as for station 16. After exiting the mixer, the gas

stream must then be diffused from station 6A to the afterburner hot section entry

at station 6.1. The given areas and both given and calculated radii are summarized

in Table 9.E5, and the ducting is shown in Fig. 9.E8.

Note that, because

ri6 > ro5 ,

the duct from station 5 to station 6 hides from

downstream view the motion of the last stage low-pressure turbine rotor blades, a

good stealth feature of this design.

~6q r

-1 ~ion 16

stat4on ~.~- station 6

0 2 4 6 8 10 12

Fig. 9.E8 Ducting from station 5 to 6 and from station 13 to 16

(to

scale).