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

Подождите немного. Документ загружается.

376 AIRCRAFT ENGINE DESIGN

(L/nl)(rm2/rml)

= 18/3 = 6, and

Am/A1

= 4, as shown in Fig. 9.27. The

attached dump diffuser requires a tailpipe of length Ld ~ (H2 -

Hm)

so that the

separated flow at dump diffuser entry (station m in Fig. 9.27) has sufficient axial

distance to reattach to the upper and lower walls. The diffusion efficiency of the

combined flat-wall + dump diffuser shown in Fig. 9.27 can be shown to be

riomAR2(1 - [A1/Am] 2) + 2 (AR[Al/Am] -

riD = (AR 2 -

1) (9.102)

where

riOm

is the diffusion efficiency of the fiat-wall diffuser. A derivation of

Eq. (9.102) is given in an appendix included in the AEDsys software CD-ROM.

Even when

is less than four, a combined fiat-wall + dump diffuser can give

somewhat better performance than an optimal or "sweet-spot" fiat-wall diffuser

alone, especially when the diffuser entry boundary layers are very thick. By taking

the derivative of rio in Eq. (9.102) with respect to

[Am/AI]

and setting it equal to

zero, there results an optimal area ratio that gives the greatest value of diffusion

efficiency for the combined diffuser

[A-~-I =riDmAR,

1.5 <AR<4 (9.103)

LIllj

opt

and a corresponding optimum diffusion efficiency

I--2riDm-F(riDmAR)2 [ am ]

riOow = rlDm (AR 2 -

1) for

~ opt = riDmAR,

1.5 <

AR < 4

(9.104)

where

riDm

should of course be riD9' of Eq. (9.68).

For example, consider a case with

= 3.5 with very thick boundary lay-

ers, so that

OD9 o "~

0.64 from Eq. (9.68). From the geometry of Fig. 9.20 and

Eq. (9.61), the three-stream diffuser alone would have a length

rm2L/rmlH 1 m

15.88/3 = 5.29. For a combined diffuser Eq. (9.103) gives an optimal flat-wall

diffuser area ratio

[Am/A1]opt

= 2.24, and Eq. (9.104) gives the correspond-

ing optimal diffusion efficiency

riDopt

= 0.658. The length of the shortened

flat-wall diffuser is

rm2Lm/rml

H1 = 7.88/3 = 2.63, and the tailpipe length is

Ld/H1

= (/-/2

Hm)/H1

= (3.5 -

2.24) = 1.26, for a combined diffuser length

(Lm + Ld)/H1

= 1.26 + 2.63 = 3.79. Although the combined diffuser efficiency

is only a modest 2.8% better than the flat-wall diffuser alone, the combined diffuser

length is 28% shorter, which is a significant improvement.

Figure 9.28 shows a combined flat-wall + dump diffuser used in practice. Note

that the inlet airflow in Fig. 9.28 is split into two streams, each of which appears

to have an area ratio of about 1.8 and length to inlet height ratio of about 6.

From Fig. 9.22, with

Am~A1 "~

1.8 and

Lm/H1

~ 5, it appears that the curved-

wall diffuser is very conservatively designed, well within the "no stall" region of

Fig. 9.22, and as a single diffuser would have a diffuser efficiency riD "~ 0.80--0.90.

(The boundary layer thickness is of course not known.) Again from inspection of

Fig. 9.28, the dump area ratio appears to be

A2/Am "~

4.7, and the overall area

ratio

AR = H2/H1 ~

8.5. With these values substituted into Eq. (9.102), the

combined diffuser efficiency is about 0.66-0.73, which seems to be rather low.

DESIGN: COMBUSTION SYSTEMS 377

Fig. 9.28 Double-annular main burner. 27

However, if an all-dump diffuser were used instead, the diffuser efficiency from

Eq. (9.70) would be a disappointingly low 0.21. The geometric and manufacturing

complexity of the curved, two-stream flat-wall diffuser in Fig. 9.28 is clearly well

worth the cost.

9.2.3.2 Burner types. A wide variety of liner and casing configurations

have been used in various gas turbine engines. Three of the most widely used

configurations are illustrated in Fig. 9.29.

In early turbojet engines, and still used today in some auxiliary power units, is

the "can" configuration, in which the liner and casing are wrapped concentrically

around the symmetry axis of a single fuel nozzle. This burner type was and is easy

to fabricate and to modify for experimental development.

CAN

CANNULAR

ANNULAR

Fig. 9.29 Basic configurations of main burner liners and casings.

378 AIRCRAFT ENGINE DESIGN

As engines became bigger, it was recognized that because the combustion pro-

cess does not scale up, but rather remains optimized for one size scale, it is logical

to simply replicate the entire burner can whenever more mass flow was required.

As the geometric layout of a turbojet engine is dictated by the axial symmetry of the

rotating components, the additional cans were arranged side by side in an annular

ring. Two major problems of this "can-annular" configuration (not illustrated) are

1) that each burner is a stand-alone pressure vessel and 2) that each burner has to

have its own igniter. Consequently, the next developmental step was to retain the

cylindrical liners in annular array, but to encase them in a common, single annular

casing. This configuration was termed "cannular." Next, it was found that also fab-

ricating the liners as concentric annuli led to further performance improvements,

and so the modern "annular" burner evolved.

Attention will be focused on the design of an annular burner. For simplicity,

it will be assumed that the liner and casing walls are parallel, as shown in the

schematic Fig. 9.1, even though there are good reasons to have divergent walls, as

shown in Fig. 9.29.

9.2.3.3 Inner and outer casing.

The first step is to establish inner and

outer radii at reference station 3.2 and at station 3.9, as illustrated in Fig. 9.30.

These radii depend on the reference area A3.2, which is listed on the Engine Station

Test Results sheet (but which may be altered in the course of design iteration), and

design choices for the engine envelope, such as whether the outer casing wall

is to be in line with the tip of the last-stage high-pressure compressor stage or

high-pressure turbine first-stage nozzle, or the inner wall is to be an extension of

the root radius of either the high-pressure compressor or turbine, or someplace

in between. The required radii are not listed on the Engine Station Test Results

sheet, but must have been determined previously from the design of the high-

pressure compressor and turbine. After these radii have been determined, the radial

"heights"

Hr = (to

ri)3.2

and H4 =

(to

- ri)4

may be calculated, as shown in

Fig. 9.30.

The liner and casing have widely different structural and thermal requirements.

The inner and outer casings have negligible thermal loads, as they are convectively

cooled by the annulus air. However, they are the walls of a pressure vessel that

must withstand the full pressure difference between the interior total pressure Pt3.2

and the ambient static pressure. In marked contrast to the casing, the liner has

a negligible mechanical load, as it has to support only the small total pressure

difference APt

Pt3.2 - Pt4,

but it is subject to a severe thermal load resulting

from combustion, and therefore requires a rather elaborate system of slots and bleed

station 3.2 ("reference") ~,,.-'~--~'~,~

Fig. 9.30 Annular geometry of liner and casing radii and heights.

DESIGN: COMBUSTION SYSTEMS

379

holes for the flow of cooling air to protect it. Determining the largest mechanical and

thermal loads and designing for them separately is a critical step in the successful

design of jet engines.

9.2.3.4 Fuel nozzles. Historically, a great number of different ways have

been tried to atomize and vaporize the kerosene-type liquid fuels pumped under

pressure into fuel nozzles. Until the 1970s, the simplex spray nozzle was most

commonly used. In this nozzle the liquid fuel is pumped tangentially into a small

swirl chamber, then flows out into the primary zone through a constriction or throat,

which concentrates the vorticity in the swirling fuel so that when the fuel emerges it

is as a radial sheet, which then stretches and breaks up into a widely size-distributed

spray of small droplets. 3° These droplets are then entrained and vaporized by the

hot recirculating gases in the primary zone. Because of the distribution of droplet

sizes, many of the large droplets support heterogeneous or two-phase combustion,

with resulting smoke caused by incomplete vaporization and combustion, and

correspondingly high concentrations of all of the air pollutants already mentioned.

The concern with pollutants starting in the late 1960s led to the development

of the "airblast" atomizer, shown in Fig. 9.31, in which a sheet of air driven by

the same pressure drop as all of the liner airflows are "blasted" into the liquid

fuel sheet emerging from a simplex nozzle, further shattering the fuel sheet and

droplets. This development effectively eliminated the problem of heterogeneous

combustion around individual fuel droplets and enabled the development of the

first "smokeless" (low unburned hydrocarbons) combustors of the 1970s, and in the

1980s and 1990s the "prevaporized, premixed" combustor of the type in universal

use today.

An airblast atomizer typically requires about 3 Ibm of primary air per Ibm of

fuel. 2 Note that this is not a separate demand on air partitioning. The airblast

atomizer airflow is just a part of the primary airflow, which passes through the

nozzle/atomizer rather than through the primary air swirler, as shown in Fig. 9.16.

If the reference radial height Hr in Fig. 9.30 is relatively small, the fuel nozzles

and their associated air swirlers can be distributed in a "single-annular" array, as

illustrated in Fig. 9.32. For a single array the number of fuel nozzles required

can be calculated by dividing the annular flow passage into square segments (in

rotating machinery terminology, a "solidity" of one), so that

:rr(ro + ri)3.2 A3.2 (47r 2~

N.oz "~ _ _ 2 rounded off (9.105)

nr ~

\ A 3.2 J

Fm3"2

Liquid ~//JJ///'~

fuel

Air =- ~--~------~----J~

Fig. 9.31 Schematic of a generic airblast atomizer. The radial sheet of fuel emerging

from the on-axis, simplex swirl-spray nozzle is blasted by a circular jet of air flowing

into it.

380 AIRCRAFT ENGINE DESIGN

(

Fig. 9.32 Single- and double-annular arrays of fuel nozzles and air swirlers.

If the reference radial height Hr is very great, the fuel nozzles and swirlers can

be distributed in a "double-annular" array, as shown in Figs. 9.28 and 9.32.

9.2.3.5 Dome and liner. The next step is to determine the optimal dome

and liner height HL, or equivalently the liner-to-casing area ratio ot = AL/Ar =

HL/Hr. For clarity, only the single-annular burner will be considered.

It is not immediately apparent what criteria should be used for finding the op-

timal area ratio e. Clearly, small ot would cause reduced residence times in all

three liner zones, and large e would cause high annular velocities, with corre-

spondingly increased viscous shear on the casing and high axial momentum flux

entering through the secondary and dilution holes, which would in turn reduce jet

penetration.

Figure 9.15 illustrates annulus-to-liner jet flow, when both annulus and liner

flows have finite axial velocities. Equation (9.44) estimates the maximum jet

penetration for the jet shown in Fig. 9.15:

"max ,l, JqXll

dj (9.106)

In Eq. (9.106) the jet dynamic pressure qj is fixed by the prescribed total pressure

loss, as determined by Eq. (9.36), but the annulus and liner dynamic pressures qA

and qL may vary, depending on the choice for areas AA and AL. Inspection of

Eq. (9.106) reveals that independently increasing either qL or qA will cause a

decrease in jet penetration, and so it appears that there may be an optimal liner-

to-reference area ratio c~

AL/Ar

that will maximize the jet penetration

Ymax.

However, as air flows from the annulus into the liner, qa decreases in the axial

direction as a result of mass outflow, while qL increases correspondingly because

of the same air mass inflow, so that a choice must be made as to the axial location

at which the jet penetration will be maximized.

Because of the importance of the secondary zone process, it is logical to maxi-

mize the jet penetration for the secondary jets. Thus qA in Eq. (9.106) will be taken

DESIGN: COMBUSTION SYSTEMS 381

,~ ~?_2-- ~-_- - .........

H r > UPZ ~ - - ~:-

.==:~_5_55

........

l Lpz ~ < Lsz

Fig. 9.33 Secondary zone air jet trajectories and nomenclature.

to be the airflow at annulus entry, and

will be taken to be

qPz

for the liner flow

at primary zone exit, as shown in Fig. 9.33.

Multiplying and dividing by

in Eq. (9.106) and relabeling qL as

qPz,

Ymax __ l.15 ,/qj qr (1 qA qr )

dj V qr qpz qr ~j

(9.107)

From Eq. (9.36),

qj/qr

= (APt/qr)MB,

the main burner total pressure loss coef-

ficient of Eq. (9.79). This is true for all jets, including the secondary zone jets. Also

making use of Eq. (9.61), together with the Boussinesq assumption introduced in

Sec. 9.1.5, Eq. (9.107) can be rewritten

~ "¢PZ \ qr

,/MB t

\ rh~ / ,, qr ,/MB

(9.108)

where a =

AL/Ar,

(1 - oe)

AA/At,

and rpz is the design value of temperature

rise ratio in both primary and secondary zones and where fixed-value parameters

have been factored out of the square root term where possible.

By taking the derivative of the right-hand side of Eq. (9.108) with respect to oe,

setting it equal to zero and solving for a there results

/1~lA\2/3 (APt ~-'/3

= - -- (9.109)

Otopt 1 (-~rr ) \ qr / MB

Substituting values cited for the 1950s burner following Eq. (9.73) into

Eq. (9.109) gives an optimum area ratio of 0.67, compared with the stated area

ratio of 0.65, which is more than adequate agreement.

9.2.3.6 Primary zone swirlor.

With the casing, dome, and liner sized, and

the number and type of fuel nozzles determined, one of the

Nnoz

inlet air swiflers

can now be designed.

From the Engine Station Test Results sheet, the prescribed total pressure loss

across the main burner assembly

APt

= Pt4 -

Pt3.1

can be obtained. Recall

that this is the specified

AP t

necessary to provide adequate turbine blade cool-

ing and is not necessarily enough to satisfy both diffuser total pressure loss

382 AIRCRAFT ENGINE DESIGN

and that required for combustor stirring. Therefore, it is essential to verify from

Eq. (9.81) that sufficient

APt

has been allocated for main burner stirring. If not,

it may be necessary to redesign the diffuser, or to negotiate for a greater

APt

allocation.

Assuming that sufficient

APt

= Pt4 - Pt3.2

is available, then the jet velocity for

all stirring jet flows into the liner film cooling slots, primary air swider, air for

the airblast atomizer, and secondary and dilution jet holes--is determined from

Eq. (9.36):

Vj=~Prt=Ur,l(APt~

q-LJ=(APt~

V \ qr /MB qr \ qr /MB

(9.110)

The annular area of a single air swirler is given by

A=w = zr (r) - r~).

The

maximum area possible is limited by the envelope of dome/liner and fuel

nozzle dimensions. Specifically, the swirl vane tip radius

cannot exceed half

the dome height HL, and the hub radius

must be at least 1/2 in. in order to

accommodate (that is, wrap around) the airblast atomizer assembly. As a rough

guideline, the recirculation bubble should be about the size of a golf ball.

The mass flow that must pass through all

N, oz

swirlers is given by

(rhpz -

3rh¢~8)

because 3 Ibm air per Ibm fuel must be directed through each airblast atomizer,

which is of course located concentrically within each swirler assembly.

Taking into account the necessary discharge coefficient (assuming fiat blades for

vanes) and swirler vane blade angle, the inner and out vane radii must be adjusted

to satisfy mass conservation through all

N, oz

swirlers, so that mass conservation

requires

(mpz - 3&fms)

N~o~

II~lr¢lAetl l

=aj(prVj)=Tr(r2-r2)CD9° c°S°tsw Z ~ MB

(9.111)

where the discharge coefficient is obtained from Eq. (9.33) and the swirler blade

angle is determined from Eq. (9.48) for the selected design swirl number S'. An

assumed swirler blade angle

Otsw ~

45 deg can be used to start the iteration.

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.

9.2.3. 7 Secondary air holes.

Equations (9.42-9.44) can be used to lay

out trajectories of the secondary air jets, immediately downstream of the primary

zone, as shown in Fig. 9.33.

A good target penetration depth of the secondary air jet trajectory is about

the dome/liner height HL. As

Yrnax/dj

is available from Eq. (9.108), the required

diameter of a single secondary jet is given by

1 (Ymax~ -1

dj=~HL\ d~ /

(9.112)

DESIGN: COMBUSTION SYSTEMS 383

Because all of the secondary air must pass through round holes with jet vena

contractas of diameter

given by Eq. (9.112), the number of secondary holes is

4r'nsz { 4Ar ~ Ur

NhSZ -- prYrd2V j -- IZsz ~k"~j : ~j

(9.113)

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

dab -- Co9oo

sin 2 0 (9.114)

where

sin20=l

qAqr 1 (mA~2( 1 )2(APt~ -1

-- - -- (9.115)

qr qj \ tJ2r ./ ~-- ~ \ qr ./ MB

The

Nhsz

secondary air holes should be spaced evenly in a single lateral line (at

right angles to the engine axis), with one-half located on the upper liner wall and

the other half, staggered and opposed, on the lower wall. The axes of the secondary

holes should be located immediately at the downstream end of the primary zone,

or, in other words, at an axial distance

Lpz

from the inside nose of the liner dome.

The axial length of the secondary zone should be long enough for the inflowing

jets to mix out with the crossflowing primary zone effluent gases. For preliminary

design purposes it can be assumed that the distance to mix out is that distance

for the micromixed cores of the opposing secondary air jets to meet. This can be

estimated from Eq. (9.37), in which the distance y is now interpreted as distance

along the jet trajectory. However, the horseshoe vortex mixing system shown in

Fig. 9.14 probably doubles the mixing and growth rate given by Eq. (9.37). Setting

8m equal to

HL/2

in Eq. (9.37) (see Fig. 9.33) and doubling the growth rate from

0.123 to 0.246, the resulting distance along the jet trajectory becomes the estimated

required length of the secondary zone

Lsz "~

2(0.246) ~

2HL

(9.116)

9.2.3.8 Dilution holes.

The same procedure will be followed as for the sec-

ondar~ zone, except that the dilution jet centerlines must be designed to penetrate

! of the distance to the opposite liner wall. 2 That is, the design goal is for dilution

jets is Ymax =

HL/3,

rather than

HL/4

for the secondary jets. This will require

somewhat larger diameter jets,

(Ymax~ -1

dj --~ ~HL \ dj ] (9.117)

and the required number of dilution holes is given by

4rhDZ

(4Ar~ Ur

NhDZ --

prgrd2 ~

--J --

I,.£DZ \rid2 ] ~

(9.118)

The actual diameter of the dilution air holes is given by Eq. (9.114). However,

the sin 2 0 term is different from the secondary zone value because the annulus

384 AIRCRAFT ENGINE DESIGN

.~UPz

i-": ...............

Lsz

Fig. 9.34 Dilution zone air jet trajectories and nomenclature and layout of dilution

zone and transition duct.

airflow has been reduced by the outflow of secondary air. This term is now

sin20 = 1 qaqr l_(lhDZ)2(1)2(Al~t) -1

-- --

(9.119)

qr qj \ rnr / ~-- ~ k qr / M8

Since, by design, combustion is complete by the time the secondary zone effluent

reaches the plane of the dilution zone, micromixing is not required; only sufficiently

good stirring or macromixing to ensure that the "hot spots" or incompletely mixed

turbulent eddies with above-average temperatures are within some specified range.

This requirement is couched in terms of the pattern factor, defined by

Tma x - Tt4

Pattern factor -- (9.120)

Tt4 -- Tt3

A rough guideline for an adequate length of the dilution zone in order to provide

a satisfactory pattern factor is Lnz ~ 1.5HL.2

The layout of the dilution zone, together with a sketch of the transition duct

between stations 3.9 and 4, is shown in Fig. 9.34.

9.2.3.9 Transition ducL The shape of the transition duct is not a criti-

cal feature of the engine design. Accelerating subsonic flow creates a favorable

(decreasing) axial pressure gradient, so all that is required is to reduce the height

of the flow passage smoothly from HL to (ro

- ri) 4

within an axial length "~Hr, as

shown in Fig. 9.34. Note that the casing walls have been extended to allow cooling

air to protect the transition duct.

9.3 Design Tools--Afterburners

Procedures for preliminary design of the afterburner are the subject of the present

section. As with the design of the main burner, extensive use will be made of

concepts and equations from Sec. 9.1, and the same design philosophy will be em-

ployed as that given in the introductory paragraph of Sec. 9.2. An example design

of an afterburner, including the use of the AEDsys computational tools, principally

subprograms EQL, AFTRBRN, and KINETX, can be found in Sec. 9.4.2.

Afterburning or reheating is a method of augmenting the basic thrust of the

turbojet engine or the turbofan engine, on demand, without having to use a larger

DESIGN: COMBUSTION SYSTEMS 385

engine with increased frontal area and weight. The afterburner increases thrust by

adding thermal energy to the entering gas stream. For a turbojet engine this gas

stream corresponds to the exhaust gases of the turbine. However, for the augmented

turbofan engine, this gas stream may be a mixture of the bypass air and the turbine

exhaust gases. At the afterburner inlet there is still much unburned oxygen in the

gas stream. The higher inlet temperatures and near-stoichiometric fuel-air ratio of

the afterburners enable them to operate with a simpler configuration (see Fig. 9.2)

than the main burner. The resultant increase in temperature raises the exhaust

velocity of the exiting gases and therefore boosts engine thrust. Most afterburners

will produce about 50% increase in thrust--but at a cost of a 300% increase in

fuel flow rate!

Because the engine's specific and actual fuel consumption is considerably higher

during afterburning ("hot" or"wet") operation, as compared to the nonafterburning

("cold" or"dry") mode, afterburning is used typically where large thrust is required

for a short period of time, such as takeoff, climb, transonic acceleration, and combat

maneuvers.

For a turbofan engine augmentation can be used in both fan and core streams.

Afterburning in a separate fan stream is normally referred to as "duct burning,"

and this alone or in combination with afterburning in the core stream may be

advantageous for certain flight conditions.

The major components of an afterburner are shown in Fig. 9.2. Gas leaving

the turbine is deswirled and diffused, fuel is added by fuel spray bars (tubes) or

rings, combustion is initiated by an igniter or pilot burner and in the wake of

a number of flame stabilizing devices (flameholders), and the thermal energy of

combustion is mixed along flame surfaces spreading outward and downstream from

the flameholders. Also, a liner is used in afterburners as both a cooling liner and a

screech or antihowl liner. (Screech and howl are acoustic-combustion instabilities.)

This liner can also serve as an annular passage for the cooling air required by the

exhaust nozzle. All engines incorporating an afterburner must also be equipped

with a variable area throat exhaust nozzle, in order to provide for proper operation

in both afterburning and nonafterburning modes (see Chapter 5).

Specific design requirements and/or desiderata for an afterburner are as follows:

1) large temperature rise (The afterburner is not subject to the physical and tem-

perature limits of the turbine. The temperature rise is limited by the amount of

oxygen that is available for combustion and by the liner and nozzle cooling air

requirements.); 2) low dry loss (The engine suffers a very slight penalty in thrust

during cold operation as a result of the drag caused by the flameholders, fuel spray

bars, and the walls of the afterburner.); 3) wide temperature modulation [The abil-

ity to obtain "degrees" ("zones" or "stages) of afterburning permits more pre-

cise control of thrust.]; 4) high combustion efficiency; 5) short length and light

weight; 6) altitude light-off capability; 7) no acoustic-combustion instabilities;

8) long life, low cost, easy repair; and 9) stealth--hiding hot elements of the

engine (turbine exit). 28,29

9.3.1 Afterburner Design Parameters

Overall engine cycle considerations have already fixed the molecular compo-

sition, thermodynamic state, and mass flow rates of core gas and bypass air that