Lefebvre A.H., Ballal D.R. Gas Turbine Combustion: Alternative Fuels and Emissions

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140 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

can still be used at low combustion pressures provided that L

is replaced by

–L

). This substitution enables these equations to be used for predicting

pattern factors at all levels of combustion pressure, including those at maxi-

mum power, from measurements carried out at low combustion pressures.

4.12 Rig Testing for Pattern Factor

The assessment of combustor pattern factor is usually both expensive and

time consuming. It is vitally important, therefore, that rig testing be carried

out as rigorously as possible, to reduce costs and achieve maximum cred-

ibility for the results obtained. The following general guidelines should be

observed:

Rig testing should be carried out at the maximum power conditions •

of inlet temperature, outlet temperature, and chamber reference

velocity.

The test rig should closely simulate the chamber entry velocity pro-•

le and angle of swirl.

Uncontrolled air leaks, which often occur at the rear end of the •

chamber, must be eliminated.

The ow quantities through the cooling slots must be closely con-•

trolled. This is most important because tooling changes during pro-

duction can have a profound effect.

Tests should be carried out on a number of liners to ascertain the •

degree of random scatter. If this is impossible, the chamber should

be stripped and rebuilt a few times, and the pattern factor measured

after each reassembly.

The fuel injectors should be checked for ow number and spray •

patternation.

4.13 Swirler Aerodynamics

The primary-zone airow pattern is of prime importance to ame stabil-

ity. Many different types of airow patterns are employed, but one feature

common to all is the creation of a toroidal ow reversal that entrains and

recirculates a portion of the hot combustion products to mix with the incom-

ing air and fuel. These vortices are continually refreshed by air admitted

through holes pierced in the liner walls, supplemented in most cases by air

Aerodynamics 141

owing through swirlers and are-cooling slots, and by air employed in

atomization.

One of the most effective ways of inducing ow recirculation in the

primary zone is to t a swirler in the dome around the fuel injector. Vortex

breakdown is a well-known phenomenon in swirling ows; it causes recir-

culation in the core region when the amount of rotation imparted to the ow

is high, as illustrated in Figure 4.13 [42]. This type of recirculation provides

better mixing than is normally obtained by other means, such as bluff bod-

ies, because swirl components produce strong shear regions, high turbu-

lence, and rapid mixing rates. These characteristics of swirling ows have

long been recognized and have been used in many practical combustion

devices to control the stability and intensity of combustion and the size and

shape of the ame region.

A comprehensive review of swirling ows and their practical applica-

tions is contained in the volume Swirl Flows by Gupta et al. [42]. Others have

studied the ow characteristics of air swirlers, notably Beer and Chigier [43],

Mathur and Maccallum [44], and Kilik [45]. The work of Kilik is of special

interest because it directly addresses the types of swirlers of most relevance

to the gas turbine. These and other experimental studies have provided valu-

able information on the ow characteristics and aerodynamic performance

of swirlers. The manner in which this knowledge is employed in the design

of swirlers for gas turbine combustors has been described by Dodds and

Bahr [40].

Air swirlers are widely used in both tubular and annular combustors. The

two main types of swirlers are axial and radial, as illustrated in Figure 4.14

[40]. They are often tted as single swirlers, but sometimes as double swirlers

Figure 4.13

Flow recirculation induced by strong swirl. (From Gupta, A.K., Lilley, D.G., and Syred, N., Swirl

Flows, Abacus Press, Tunbridge Wells, UK, 1984. With permission.)

142 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

that are mounted concentrically and arranged to supply either co-rotating or

counter-rotating airows. Examples of modern combustors tted with axial,

radial, and double swirlers may be found in Chapter 9.

4.14 Axial Swirlers

The conventional notation for axial swirlers is indicated in Figure 4.15. This

gure shows a at-vaned swirler whose vane angle is constant and equal

to θ. With curved-vane swirlers, the inlet blade angle is zero and the outlet

angle is θ.

An important design requirement is that the swirler should pass the desired

airow rate for a given pressure drop ΔP

, which is usually assumed to be

equal to the liner pressure drop, ΔP

. We have [46]



KAA

sw sw L

−

[]













∆

(sec /)/

(4.33)

where ΔP

is the total pressure drop across swirler (≅ ΔP

), A

is the frontal

area of the swirler, and θ is the vane angle (see Figure 4.15).

Note that A

is simply the swirler annulus area minus the area occupied

by the vanes, i.e.,

ADDntD D

sw sw hubswhub

(

)

−

(

)

−−

(

)

υυ

/..405

(4.34)

Axial

swirler

Radial

swirler

Figure 4.14

Two main swirler types. (From Dodds, W. J. and Bahr, D. W., Design of Modern Gas Turbine Com-

bustors, Academic Press, San Diego, CA, 343–476, 1990. Copyright Elsevier. With permission.)

Aerodynamics 143

Typical ranges of values for the design variables in Equations 4.33 and 4.34

are [40,46]

Vane angle, θ 30°–60°

Vane thickness, t

0.7–1.5 mm

Number of vanes, n

8–16

ΔP

3%–4% of P

1.3 for at vanes, and 1.15 for curved vanes

The hub diameter, D

hub

, is determined by the need to provide space for a

centrally mounted fuel injector. The outer swirler diameter, D

, is then

obtained by substituting the calculated values of A

from Equation 4.33 into

Equation 4.34.

4.14.1 Swirl Number

Beer and Chigier [43] have proposed the following nondimensional criterion

to characterize the amount of rotation imparted to the axial ow:

SGDG

= 2

mswt

/( ),

(4.35)

where G

is the axial ux of angular momentum and G

is the axial thrust.

For values of swirl number less than around 0.4, no ow recirculation is

obtained, and the swirl is described as weak. Most swirlers of practical inter-

est operate under conditions of strong swirl (that is, S

> 0.6).

Expressions for calculating swirl numbers for various types of swirl gen-

erators have been derived by Beer and Chigier [43]. For an annular swirler

with constant vane angle θ, they give

−

(/)

tan

hubsw

.θ

(4.36)

Vane outlet angle

c Chord

s Space

z/c Aspect ratio

s/c Space/chord ratio

hub

Figure 4.15

Notation for axial swirlers.

144 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

Thus, for a simple axial swirler, the minimum vane angle required to obtain

strong recirculation (S

> 0.6) for a typical swirler having D

hub

= 0.5 is

calculated from Equation 4.36 as 38°.

4.14.2 Size of recirculation Zone

The recirculation region in a free swirling ow is shown in Figure 4.16. Since

the ow is assumed to be axisymmetric, only half the ow pattern is consid-

ered. The recirculation region is contained within the curve ACB. The point

Β is called the stagnation point. The ow outside ACB is the main ow, which

drives the recirculation along the solid curve AB. Conditions of zero axial

velocity are represented by the dashed curve AB.

Typical axial and swirl velocity proles are shown in Figure 4.17. All the

velocity components decay in the downstream direction. After the stagna-

tion point, the reverse axial velocities disappear, and further downstream

the peak of the axial velocity prole shifts toward the centerline as the effect

of swirl diminishes.

Factors governing the size of the recirculation zone have been studied by

several workers. The most comprehensive investigation is that of Kilik [45],

who examined the separate effects on recirculation-zone size of variations

Recirculation

region

Main flow

region

Figure 4.16

Recirculation region in a swirling ow eld.

Axial

Swirl

Radius, r

Figure 4.17

Typical proles of axial- and swirl-velocity components in a strongly swirling ow.

Aerodynamics 145

in vane type (at or curved), vane angle, vane aspect ratio, and space/chord

ratio. His experimental data show that the size of the recirculation zone is

increased by

1. An increase in vane angle

2. An increase in the number of vanes

3. A decrease in vane aspect ratio

4. Changing from at to curved vanes

4.14.3 Flow reversal

One of the primary functions of the swirler is to induce combustion prod-

ucts to ow upstream to meet and merge with the incoming fuel and air. For

weak swirl, there is little or no ow recirculation, but when the swirl number

is increased and reaches a critical value (S

> 0.4), the static pressure in the

central core just downstream of the swirler becomes low enough to create

ow recirculation, as indicated in Figure 4.13. From velocity measurements

carried out along the swirler axis for several swirler designs, Kilik [45] was

able to ascertain the inuence of the key geometric parameters on the reverse

mass ow rate. His results showed that curved-vane swirlers induce larger

reverse mass ows than the corresponding at-vane swirlers, and that the

reverse ow is increased by an increase in swirl number. The effect of swirl

number on the maximum reverse mass ow rate is illustrated in Figure 4.18.

Curved vanes

Flat vanes

0.5

1.0

/ m

1.5

2.0

Swirl number, S

Figure 4.18

Inuence of swirl number on maximum reverse mass ow.

146 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

This gure includes Kilik’s data for curved vane swirlers and Mathur and

Maccallum’s [44] results for at-vaned swirlers. It is of interest to note that

under conditions of very strong swirl, corresponding to vane angles of

around 65°, the reverse mass ow created by the swirler can actually exceed

the swirler ow.

4.14.4 influence of Swirler exit geometry

The geometry of the transition between the swirler exit and the combustor

dome can have a strong inuence on the primary-zone ow eld and can

also affect the trajectories of droplets injected into this ow eld [40]. For

example, a diverging passage downstream of the swirler exit increases both

the size of the recirculation zone and the amount of air recirculated [43].

4.15 Radial Swirlers

Radial inow swirlers are now widely used in both conventional and dry

low emissions (DLE) combustors. Their ow characteristics have not been

studied to the same extent as those of axial swirlers, but experience has

shown that the ow elds generated by the two different swirler types are

broadly the same. Thus, the design rules established for axial swirlers can

provide useful guidance in the design of radial swirlers. The notation for

conventional radial swirlers is indicated in Figure 4.19.

hub

Figure 4.19

Notation for radial swirlers. (From Dodds, W. J. and Bahr, D. W., Design of Modern Gas

Turbine Combustors, Academic Press, San Diego, CA, 343–476, 1990. Copyright Elsevier. With

permission.)

Aerodynamics 147

The airow into the swirler is determined by the effective ow area at the

trailing edge of the vane. This can be calculated as

AnswC

sw D

υυ υ

(4.37)

where n

is the number of vanes, s

is the vane gap, w

is the vane width, and

is the vane discharge coefcient (see Figure 4.19). According to Dodds and

Bahr [40], for preliminary design purposes an appropriate value for C

is 0.7.

The dimension w

can then be adjusted during combustor development to

obtain the desired swirler airow rate.

4.16 Flat Vanes Versus Curved Vanes

All the evidence presented in this section on swirling ows shows that

curved vanes are more efcient aerodynamically than at vanes. This is

because they allow the incoming axial ow to gradually turn, which inhibits

ow separation on the suction side of the vane. Thus, more complete turn-

ing and higher swirl- and radial-velocity components are generated at the

swirler exit, which results in a larger recirculation zone and a higher reverse

ow rate. However, these arguments in favor of curved vanes should not

exclude the use of at vanes in certain applications. One advantage of at

vanes is that they are cheap and easy to produce. Moreover, the ow stri-

ations associated with at-vane swirlers, which are created by the stalled

regions attached to each vane, tend to promote a more stable ame and

reduce combustion noise. Another asset of the at-vane axial swirler is that

its exit velocity prole is less peaked and less biased radially outboard than

that of the corresponding curved-vane swirler. In consequence, it provides

better aeration of the main soot-forming zone, which is normally located just

downstream of the fuel injector.

For these reasons, at-vane swirlers are still preferred in some combus-

tor congurations. However, when air swirlers are incorporated into airblast

atomizers, curved vanes should always be used because the wakes produced

downstream of at vanes could adversely affect the quality of atomization.

Nomenclature

A area, m

h.geom

hole area, geometric, m

h.eff

total effective liner hole area, m

148 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

annulus area, m

area ratio (A

geom

)

discharge coefcient

hub

swirler hub diameter, m (see Figure 4.15)

liner diameter or height, m

Sauter mean diameter of fuel spray, m

swirler diameter, m (see Figure 4.15)

d diameter, m

diameter of secondary hole, m

J momentum-ux ratio,

ρρ

jj gg

(

)

(

)

K hole pressure-drop coefcient, (1 + Δp

)

, K

constants in Equation 4.10

k ratio of liner to casing area

L length, m

evaporation length, m

M Mach number



mair mass ow rate, kg/s



entrained mass ow rate, kg/s



ratio of primary-zone airow to total chamber airow



maximum reverse mass ow rate, kg/s

ratio of air entering snout to total chamber airow

n number of holes

P total pressure, Pa

p static pressure, Pa

q dynamic pressure, Pa

R gas constant, 286.9 Nm/(kg K)

r ratio of casing area to combustor inlet area

S length of jet path, m

swirl number

T total temperature, Κ

U velocity, m/s

X distance downstream of hole, m

X downstream distance, m

Y jet penetration, m

α hole bleed ratio

(/ )



han

γ ratio of specic heats

Δ difference

θ initial jet angle, or swirler vane angle

λ diffuser pressure-loss coefcient (see Chapter 3)

eff

effective evaporation constant, m

ρ density

Subscripts

0 initial value

3 combustor inlet plane

Aerodynamics 149

4 combustor outlet plane

an annulus value

diff diffuser

g gas value

h hole value

I local value

j jet value

L liner value

max maximum value

pz primary-zone value

ref reference value

sw swirler value

References

1. Scull, W. E., and Mickelsen, W. R., “Flow and Mixing Processes in Combustion

Processes,” Chap. II, NACA Report 1300, 1957.

2. Lefebvre, A. H., and Norster, E. R., “The Design of Tubular Combustion Cham-

bers for Optimum Mixing Performance,” Technical Advances in Gas Turbine

Design,” pt. 3N, Proceedings of the Institution of Mechanical Engineers, Institution

of Mechanical Engineers, London, UK, 1969.

3. Sullivan, D. Α., “Gas Turbine Combustor Analysis,” ASME Paper 74-GT-2, 1974.

4. Kaddah, K. S., “Discharge Coefcients and Jet Deection Angles for Combustor

Liner Air Entry Holes,” College of Aeronautics MSc thesis, Craneld, UK, 1964.

5. Freeman, Β. C., “Discharge Coefcients of Combustion Chamber Dilution

Holes,” College of Aeronautics MSc thesis, Craneld, UK, 1965.

6. Callaghan, E. E., and Bowden, D. T., “Investigation of Flow Coefcients of

Circular, Square, and Elliptical Orices at High Pressure Ratios,” NACA TN

1947, 1949.

7. Dittrich, R. T., and Graves, C. C., “Discharge Coefcients for Combustor Liner

Air Entry Holes I, Circular Holes,” NACA TN 3663, 1956.

8. Dittrich, R. T., “Discharge Coefcients for Combustor Liner Air Entry Holes II,

Flush Rectangular Holes, Step Louvers, and Scoops,” NACA TN 3924, 1958.

9. Graves, C. C., and Grobman, J. S., “Theoretical Analysis of Total Pressure Loss

and Airow Distribution for Tubular Turbojet Combustors with Constant

Annulus and Liner Cross-Sectional Areas,” NACA Report 1373, 1958.

10. Grobman, J. S., “Comparison of Calculated and Experimental Total Pressure

Loss and Airow Distribution in Tubular Turbojet Combustors with Tapered

Liners,” NASA Memo 11-26-58E, 1959.

11. Fletcher, R. S., and Bastress, E.K., “The Design and Performance of Gas Turbine

Combustion Chambers,” Northern Research and Engineering Corporation,

NREC Report 1082, 1964.

12. Carrotte, J. F., and Stevens, S. J., “The Inuence of Dilution Hole Geometry on

Jet Mixing,” Journal of Engineering for Gas Turbines and Power, Vol. 112, No. 1,

pp. 73–9, 1990.