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

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

4.6 Flow through Liner Holes

The ow through a liner hole depends not only on its size and the pres-

sure drop across it, but also on the duct geometry and ow conditions in the

vicinity of the hole, which can strongly inuence its effective ow area.

4.6.1 Discharge Coefficient

The basic equation for ow through a hole may be expressed as



mCAPp

hDhgeomj

=[−

()],2

(4.14)

where P

is the total pressure upstream of the hole and p

is the static pres-

sure downstream of the hole.

It has been observed that some deection of the ow streamlines occurs in

the vicinity of the liner holes, to an extent that depends on the geometry of

the system, the approach velocity, and the pressure drop across the liner [3].

Thus, in practice, the coefcient of discharge of liner holes is affected by

Type (e.g., plain or plunged)•

Shape (e.g., circular or rectangular)•

Ratio of hole spacing to annulus height•

Liner pressure drop•

Splitter

plate

Dilution

hole

Dam

Figure 4.1

Flow control through dilution holes.

Aerodynamics 121

Distribution of static pressure around the hole inside the liner•

Presence of swirl in the upstream ow•

Local annulus air velocity•

From a detailed analysis of the factors governing the ow of a jet through a

liner wall, Kaddah [4] concluded that, for incompressible, nonswirling ow,

the coefcient of discharge for plain circular, oval, and rectangular holes is

given by

−

−−

1251

2205

.( )

[()]

(4.15)

where α is the ratio of hole mass ow rate to annulus mass ow rate

(/ )



han

, and Κ is the ratio of the jet dynamic pressure to the annulus

dynamic pressure upstream of the holes.

The very satisfactory level of agreement between the predictions of

Equation 4.15 and experimental data are illustrated in Figure 4.2.

In subsequent experimental measurements of the discharge coefcients

of plunged holes, Freeman [5] found that Equation 4.15 still gave very satis-

factory correlation of the data, provided that the value of the constant was

raised from 1.25 to 1.65, as shown in Figure 4.3. Thus, for plunged holes

−

−−

1651

2205

.( )

[()]

(4.16)

Oval holes

Rectangular slots

Round holes

Eq. (4.15) (α = 0.25)

Hole pressure drop coefficient, K

Discharge coefficient, C

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

23468102030406080

Figure 4.2

Inuence of hole shape on discharge coefcient. (From Kaddah, K.S., College of Aeronautics

MSc Thesis, Craneld, UK, 1964.)

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

The ow through scoops and louvers has not yet been subjected to theoreti-

cal analyses of the type conducted for plain and plunged holes. Experimental

data for these and other types of hole congurations are contained in

References [6–10].

It is apparent in Figure 4.3 that a high value of K not only provides a

high value of C

, but also ensures that C

is fairly insensitive to small

changes in K. This is an important asset because, in practice, local values of

K can change appreciably around the liner annuli due to a number of factors,

including:

Circumferential variations in combustor inlet velocity prole•

Manufacturing tolerances•

Small changes in airow distribution during combustor •

development

Ideally, the value of K just upstream of the primary holes should not be less

than six, corresponding to a velocity ratio, U

of just over two. A higher

value of K would yield even higher and more stable values of C

, but at the

expense of an increase in diffuser area ratio.

Downstream of the primary holes, ow conditions in the annuli improve

as air is drawn off through the various apertures in the liner wall. This

means that if the annular feed passages are sized to provide a satisfactory

value for K at the primary holes, then, for all the holes further downstream,

higher values of K and C

are virtually assured.

1.0

Plunged holes

Plain holes

0.9

Discharge coefficient, C

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

21346 10820

Hole pressure-loss factor, K

30 40 60 80

100

Figure 4.3

Inuence of hole type and pressure-drop coefcient on discharge coefcient. (From

Freeman, B.C., College of Aeronautics MSc Thesis, Craneld, UK, 1965.)

Aerodynamics 123

4.6.2 initial Jet Angle

It is clear from Figure 4.4 that any reduction in initial jet angle must reduce

the effective hole area. Thus, one would expect the initial angle θ to be related

to C

, and such a relationship has been established [11] as follows:

sin/,

θ=

∞

(4.17)

where C

D∞

is the asymptotic value of C

as K tends to innity. This relation-

ship is plotted alongside Kaddah’s [4] experimental data in Figure 4.5.

Figure 4.4

Representation of ow through liner hole.

Oval holes

Rectangular slots

Round holes

Equation 4.17 (C

= 0.625)

Hole pressure drop coeﬃcient, K

Initial jet angle, θ, degrees

23468102030406080 100

Figure 4.5

Variation in initial jet angle with pressure-drop coefcient for various hole shapes. (From

Kaddah, K.S., College of Aeronautics MSc Thesis, Craneld, UK, 1964.)

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

In practice, if the value of K for any row of holes is too small to provide the

desired initial jet angle, some steepening of this angle can be achieved by

attaching short chutes to each hole. Such chutes were tted to Rolls Royce

Spey combustors some 30 years ago as a means of improving primary air

recirculation and reducing smoke. This company now uses chutes on its

more modern RB211 and Trent combustors for both primary and intermedi-

ate holes.

Drawbacks to the use of chutes include additional cost and weight. Also,

some form of cooling is usually required in order to protect them from over-

heating by the hot combustion gases in which they are immersed.

4.7 Jet Trajectories

To establish a ow eld within a liner and ensure the proper distribution

of air to all zones, some knowledge is needed of the factors that govern the

trajectory and penetration of air jets in crossow. Of prime importance is the

jet mixing that occurs in the dilution zone in which relatively cold air jets

penetrate and mix with hot combustion products to achieve an outlet tem-

perature distribution acceptable to the turbine.

Detailed measurements of velocity and turbulence carried out by

Carrotte and Stevens [12] have indicated the structure of a dilution jet and

the mixing processes that develop as the jet interacts with the surround-

ing gas stream. As each air jet penetrates into the main stream, it creates

a blockage that produces an increase in pressure on the upstream side of

the jet and a reduction in pressure on the downstream side. This pressure

difference provides the force that deforms the jet and contributes to the

development of the “kidney-shaped” prole, as illustrated in Figure 4.6.

The ow eld downstream of the dilution holes is dominated by vortex

systems, which control the entrainment and mixing of dilution air and

mainstream gas.

4.7.1 experiments on Single Jets

Many workers have attempted to trace the paths of round jets injected at

various angles (usually 90°) into owing airstreams. Among the earliest was

Norster [13], who took temperature traverses in line with the jet at various

distances downstream of its origin. The point of lowest temperature in the

traverse was used to dene the center of the jet, and the maximum pen-

etration was equated to the depth at which the centerline of the jet became

asymptotic to the mainstream ow.

Norster’s data are especially relevant to gas turbine combustors, because

his test conditions were chosen to simulate those in an actual dilution

Aerodynamics 125

zone. From analysis of these and other data, Lefebvre [14] concluded that

the trajectory of a jet in crossow, as illustrated in Figure 4.4, is adequately

described by the expression

Yd JXd/.(/),

= 082

05 033

(4.18)

where

JU U= ()/( ).ρρ

jj gg

If a single jet is injected into a crossow at an angle θ, where θ is less than

90°, its trajectory is readily obtained by multiplying the value of Y/d

for 90°

by sin θ.

Equation 4.18 implies that jet penetration increases continually with an

increase in downstream distance. In practice, the jet may attain its maximum

penetration within a fairly short distance downstream of its origin. Thus,

Equation 4.18 and other similar equations found in the literature, are useful

only for describing the initial portion of the jet trajectory and lose their valid-

ity as the jet centerline becomes asymptotic to the crossow.

Of more practical interest is the maximum penetration achieved by the jet.

For a single round jet injected into a circular duct, Norster [13] found that the

maximum penetration is given by

YdJ

max

.sin= 115

.θ

(4.19)

The data on which this equation is based are shown in Figure 4.7.

Local

entrainment

Velocity

trajector

Deflected jet

Hot-gas

mainstream

Figure 4.6

Representation of a jet in crossow.

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

4.7.2 Penetration of Multiple Jets

The rst systematic study of the penetration of multiple jet congurations

was carried out by Sridhara and Norster [15,16]. For a circular duct, Sridhara

[15] found that the penetration of multiple jets was lower than that for a sin-

gle jet. He attributed this to the blockage effect of the jets in producing a local

increase in mainstream velocity. From analysis of these data, Norster [16]

recommended the following equation for estimating the maximum penetra-

tion of round air jets into a tubular liner:

YdJm mm

max

./().=+125

jggj



(4.20)

1234 6810

51° injection

71° injection

90° injection

Nozzle diameter, cm

max

Momentum flux ratio, ρ

/ ρ

Jet penetration

max

1.0

0.76

0.50

0.375

20 30 40 70

Figure 4.7

Maximum jet penetration data. (From Norster, E.R., unpublished work at College of Aeronautics,

Craneld, UK, 1964.)

Aerodynamics 127

The level of agreement between the predictions of this equation and mea-

sured values of Y

max

is shown in Figure 4.8.

Sridhara’s investigation was conned to circular ducts, but a consid-

erable amount of numerical and experimental work on the penetration

of multiple jets has been carried out using rectangular ducts to simulate

ow conditions in annular combustors. Most annular combustors feature

two rows of dilution holes in the same axial plane, one row on the inner

liner and the other on the outer liner. Usually, the number of holes in each

row is the same. In most designs, the opposing holes are arranged to be

“in-line” so that the jets impinge on each other, but in other designs, the

holes are staggered circumferentially to allow the jets to penetrate past

each other.

In almost all annular combustors, the aerodynamic quality of the air

approaching the outer row of dilution holes is impaired by the presence of

various obstacles in the outer annulus, such as fuel-nozzle feed arms, liner

support pins, and igniters, with the result that the ow approaching the

outer dilution holes contains numerous small eddies and other ow pertur-

bations that have an adverse effect on the uniformity of the ow entering

Jet penetration, Y

max

123

Single jet data

Multi jet data 90°

Multi jet data 130°

(ρ

/ (ρ

)

+ m

Figure 4.8

Multiple-jet penetration correlation. (From Sridhara, K., College of Aeronautics MSc Thesis

20/187, Craneld, UK, 1967. [See also National Aeronautics Laboratory Report TN 30, Bangalore,

India, 1970].)

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

the dilution holes. For this and other reasons, several studies have been

carried out on the penetration and mixing of “single-sided” jets, i.e., jets of

air entering the crossow through a single row of holes located in one wall

of a rectangular duct.

Most of the results obtained on jets in crossow applicable to gas tur-

bine combustors have been reviewed and summarized by Holdeman [17].

Generally, they conrm the ndings of Sridhara [15] and Norster and

Lefebvre [16,18] in regard to the overriding importance of momentum-ux

ratio, initial jet diameter, and the number of jets to the penetration and mix-

ing of multiple jets in crossow.

Early studies on jet penetration and mixing were largely conned to

round holes and circular jets. Since then, much useful information has

been obtained by Holdeman et al. [17,19–23] on a wide variety of hole con-

gurations. According to Holdeman et al. [19], similar jet penetration can be

obtained over a wide range of J values, independent of orice diameter, if

the orice spacing and J

0.5

are inversely proportional. However, it should be

noted that in practical combustors the amount of air available for dilution is

usually what remains after the requirements of combustion and wall cooling

have been met. Under these conditions, where variation in dilution airow

rate is not an option available to the designer, any change in J will necessitate

a change in orice diameter if optimum penetration and mixing are to be

maintained.

Kamotani and Greber [24] used smoke photographs to investigate the

detailed features of jet interaction in single- and multiple-row jets. They

observed that when two closely spaced jets are arranged parallel to the

crossow, the rear jet, being in the wake of the front jet, remains almost

undeected until it meets the front jet, whereupon the two jets quickly com-

bine. The penetration of this combined jet is slightly greater than that of a

single jet injected from a hole having a cross-sectional area equal to the sum

of the two separate holes. Holdeman [17] also compared the penetrations of

a single row of round holes and several equal-area double-row circular hole

congurations at intermediate momentum-ux ratios (J = 26) and found the

average penetration to be nearly the same for all congurations.

In a separate series of experiments, Kamotani and Greber [24] studied the

effects of an opposite wall on the characteristics of turbulent jets injected

into a crossow. They found that an opposite wall has relatively little effect

on a single jet unless J is large enough to cause the jet to impinge on the wall.

They also conducted experiments in which two jets impinged on each other,

to compare behavior in this situation with behavior when there is interaction

with an opposite wall. Their measurements showed that the trajectories for

these two situations are virtually indistinguishable from each other. Thus,

as far as velocity trajectories are concerned, the plane of symmetry between

two opposing jets can be considered equivalent to a wall. However, for this

to be true, it is very important that the velocities of the two opposing jets be

matched quite closely.

Aerodynamics 129

4.8 Jet Mixing

Jet-mixing processes play an important role in achieving satisfactory

combustion performance. In the primary zone, good mixing promotes

efcient combustion and minimum pollutant formation. In the intermediate

zone, rapid mixing of the injected air with the hot gases from the primary

zone is needed to accelerate soot oxidation and to convert any dissociated

species into normal products of combustion. Finally, the attainment of a

satisfactory pattern factor at the combustor exit is dependent on thorough

mixing of air and combustion products in the dilution zone.

In general, the rate of mixing between the air jets and the hot gases con-

tained within the liner is mainly inuenced by the following factors:

The size and (to a much lesser extent) the shape of the hole through •

which the jet issues

The initial angle of jet penetration•

The momentum-ux ratio, • J

The presence of other jets, both adjacent and opposed•

The length of the jet mixing path•

The proximity of walls•

The inlet velocity and temperature proles of the jet and the hot •

gases.

Equal signicance should not be attached to all of these parameters. In prac-

tice, the key factors governing mixing rates are momentum-ux ratio, length

of mixing path, and the number, size, and initial angle of the jets.

Most of the early work on jet mixing was carried out in cylindrical ducts

designed to simulate tubular combustion liners. Subsequent investiga-

tions, notably those of Holdeman and co-workers [17,19–23,25–30] have been

directed toward jet mixing in rectangular ducts, using both single-sided and

double-sided air injection. The results and conclusions of these various stud-

ies carried out before 1993 have been summarized by Holdeman [17].

4.8.1 Cylindrical Ducts

Sridhara [15] investigated the mixing of air jets injected into hot gas streams

under conditions that allowed the temperature and velocity of the hot and

cold streams, the injection-hole diameter, the angle of injection, and the

mixing length to be accurately controlled and varied over a wide range.

Figure 4.9 is typical of the results obtained using a circular duct of 17 cm

diameter to contain a hot gas stream into which the air jets were injected at

an initial angle of 90°. Temperature distributions were measured at a plane