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

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

17 cm downstream of the air-injection holes. The gure shows that for all

congurations, an increase in jet ow improves the level of mixing up to an

optimum value, after which any further increase causes the temperature dis-

tribution to deteriorate. Presumably, this is because under-penetrating jets

fail to reach the hot gas core at the liner axis, whereas over-penetrating jets

collide to produce a cold core at the liner axis.

The main conclusion to be drawn from the Craneld experiments [13,15]

is that jet-to-mainstream momentum-ux ratio J, and jet diameter d

, are the

most signicant factors affecting jet penetration and mixing in a cylindrical

combustion liner. The data acquired in these investigations was subsequently

used by Lefebvre and Norster [18] to derive a method for determining the

optimum number and size of air injection holes for achieving the most uni-

form mixing between the air jets and the hot gas stream.

Talpallikar et al. [30] used a CFD code to numerically analyze variations in

J and slot aspect ratio (SAR) on jet mixing in a rich quick-quench lean com-

bustor (RQL) combustor. The value of J was varied parametrically from 16 to

64 by variation in jet velocity from 120 to 240 m/s. Their results showed that

SAR has a signicant effect on jet penetration and mixing performance. It

was concluded that conventional correlations for optimum mixing effective-

ness for round holes may not be applicable for slots.

Hatch et al. [31] conducted a series of parametric studies to determine the

inuence of geometry and ow variations on mixing patterns in a cylindrical

duct. The quality of mixing was assessed from temperature measurements

8 jets, 31.8 mm (1.25 in.) DIA.

4 jets, 31.8 mm (1.25 in.) DIA.

6 jets, 31.8 mm (1.25 in.) DIA.

6 jets, 25.4 mm (1.00 in.) DIA.

6 jets, 19.1 mm (0.75 in.) DIA.

dil

lin

= 1.0

Jet to gas stream mass ratio, m

120

Standard deviation of temperature, °C

160

0.5 1.0 1.5 2.0 2.5

Figure 4.9

Inuence of dilution-hole geometry on temperature distributions. (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].)

Aerodynamics 131

carried out downstream of a row of cold jets injected into a heated cross

stream. The geometries investigated included round holes and slanted slots,

i.e., slots oriented at various angles with respect to the mainstream ow. No

attempt was made to optimize the number of orices for each value of J, and

eight equispaced holes were used throughout the test program, which covered

a range of J values from 25 to 80. The jet to mainstream mass ratio (



) was

kept constant at 2.2. These values of J and



would be considered excep-

tionally high for a conventional combustion liner, but they are appropriate for

RQL combustors, which pose formidable challenges in jet mixing in a con-

ned crossow. One important consequence of high



values is that they

necessitate the use of slots instead of round holes around the liner perimeter.

The results of Hatch et al. [31] conrmed the importance of J to penetration

and mixing in a cylindrical combustion liner. They also found that increas-

ing the aspect ratio of slanted slots reduces jet penetration to the center and

enhances mixing along the walls. At low and intermediate values of J, the 4:1

aspect ratio slots gave better mixing than the 8:1 slots at all downstream loca-

tions. At the highest value of J tested, the higher aspect ratio slots exhibited

better mixing. For slanted slots, it was found that the optimum value of J for

best mixing varied with slot angle.

Zhu et al. [32] also carried out a numerical study on the penetration and mix-

ing of radial jets in a “necked-down” cylindrical duct designed to simulate the

mixing section of an RQL combustor. Two types of jet slots were considered:

rectangular straight slots aligned in the streamwise direction, and slanted

slots. The parameters investigated included wide variations in J (2–64), n (2–12),

and SAR (1–4), while maintaining a constant value of



. Their results

conrmed that J has the most prominent effect on mixing performance and

showed that the optimum conguration changes with the number of orices

and the SAR. Another interesting conclusion from this study is that modify-

ing the ow by necking down or introducing swirl merely serves to raise the

pressure loss of the system without enhancing mixing performance.

4.8.2 rectangular Ducts

Mixing studies in rectangular ducts provide useful guidance in the design

of dilution zones for annular combustors without the complications of radius

effects. For this reason, the mixing of multiple air jets in a conned rect-

angular crossow has been extensively treated in the literature. The early

studies of Holdeman, Walker, and Kors [19,20,25] identied the main ow

and geometric variables that characterize the mixing process. More recent

studies, in particular those of Holdeman and Srinivasan et al. (see, e.g., ref-

erences [22,23,26,27,33–37]), have extended the available experimental data

and yielded useful empirical correlations on the mixing of multiple jets in

crossow. The geometric variables encompassed in these studies include

area convergence, noncircular orices, double rows of holes, and opposed

rows of jets, both in-line and staggered.

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

4.8.2.1 Inﬂuence of Density Ratio

Holdeman, Walker, and Kors [19] suggested that density ratio did not need

to be considered independently from momentum-ux ratio. This was con-

rmed over a broad range of density ratios in the experiments by Srinivasan

et al. [26]. Another interesting conclusion from these experiments is that

circumferential nonuniformities mix much more rapidly with increasing

downstream distance than do radial nonuniformities.

The main results from the various numerical and experimental studies

carried out so far are summarized below. More detailed information may be

obtained from the quoted references.

Momentum-ux ratio and orice spacing [17] or size [18] are the •

main factors governing mixing performance.

Jet penetration remains largely unchanged when the product of • d

and J

0.5

is kept constant [18].

The temperature distributions obtained using square orices are •

almost identical to those observed from equal-area circular orices

at all downstream locations [17,33,34,38].

The penetration and mixing of 45• ° slanted slots are less than

for streamlined or bluff slots or equal-area circular orices.

Moreover, the temperature distributions for slanted slots are

skewed and shifted laterally with respect to the injection center-

plane [17,34].

Double rows of jets have penetrations and temperature distributions •

similar to those from a single row of equally spaced, equal-area,

circular orices [17,23,25,27].

Flow area convergence, especially injection-wall convergence, sig-•

nicantly improves mixing performance [17].

For opposed rows of jets with the orice centers in-line, the optimum •

ratio of orice spacing to duct height is one-half of the optimum

value for single-sided injection at the same momentum-ux ratio

[1 7, 2 2, 39 ] .

For opposed rows of jets with the orice centers staggered, the opti-•

mum ratio of orice spacing to duct height is double the optimum

value for single-sided injection at the same momentum-ux ratio

[1 7, 2 2, 36 ] .

In-line congurations have better initial mixing than staggered con-•

gurations at their respective optimum values of orice spacing-to-

duct height ratio [28].

Density ratio does not need to be considered independently from •

momentum-ux ratio [19,26].

Aerodynamics 133

4.8.3 Annular Ducts

Very little information is available in the open literature on jet penetration

and mixing in annular ducts, despite their enormous practical importance to

the design of annular gas turbine combustors, due mainly to the very high

cost of conducting systematic experimental research on annular congura-

tions. Holdeman [17] has reported on the results of numerical calculations

on the mixing of jets in an annular duct whose inside radius was made equal

to the duct height. The orice geometry was opposed rows of in-line holes

with J = 6.6. Similar penetration and mixing was achieved by specifying the

hole spacing for the annular duct to be equal to that in a rectangular duct at

the radius that divides the annulus into equal areas.

The results and correlations of temperature distributions obtained in the

Craneld and NASA test programs cannot be applied directly to the dilution

zones of practical combustors owing to the effects of liner-cooling airow, the

nonuniform temperature distribution of the hot gases entering the dilution

zone, and the convergence of the ow area in the dilution zone. Nevertheless,

they provide useful guidance in liner design, as discussed below.

4.9 Temperature Traverse Quality

One of the most important and, at the same time, most difcult problems

in the design and development of gas turbine combustion chambers is that

of achieving a satisfactory and consistent distribution of temperature in the

efux gases discharging into the turbine. In the past, experience has played a

major role in the determination of dilution-zone geometry, and trial-and- error

methods have, of necessity, been employed in developing the temperature

traverse quality of individual combustor designs to a satisfactory standard.

The temperature attained by an elemental volume of gas at the chamber

outlet is dependent on its history from the time it emerges from the com-

pressor. During its passage through the combustor, its temperature and

composition change rapidly under the inuence of various combustion, heat-

transfer, and mixing processes, none of which are perfectly understood. The

nal mixing process, for example, is affected in a complicated manner by

the dimensions, geometry, and pressure drop of the liner, the size, shape,

and discharge coefcients of the liner holes, the airow distribution to vari-

ous zones of the chamber, and the temperature distribution of the hot gases

entering the dilution zone. For any given combustor, the latter is strongly

inuenced by fuel spray characteristics, such as drop size, spray angle, and

spray penetration, because these control the pattern of burning and hence

the distribution of temperature in the primary-zone efux. It is known that

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

spray characteristics are strongly inuenced by pressure, especially with

atomizers of the simplex- or dual-orice type. It is to be expected, therefore,

that the temperature traverse will also vary with pressure, although the

extent of this variation varies from one chamber to another, depending on

design and, in particular, on length. Thus, it is highly desirable that rig work

on the improvement of temperature traverse quality should be carried out at

the maximum engine pressure, because this corresponds to maximum heat-

transfer rates to nozzle guide vanes and turbine blades.

The most important temperature parameters are those that affect the

power output of the engine and the life and durability of the hot sections

downstream of the combustor. As far as overall engine performance is con-

cerned, the most important temperature is the turbine inlet temperature, T

which is the mass-ow-weighted mean of all the exit temperatures recorded

for one standard of liner. Since the nozzle guide vanes are xed relative to

the combustor, they must be designed to withstand the maximum temper-

ature found in the traverse. Thus, the parameter of most relevance to the

design of nozzle guide vanes is the overall temperature distribution factor,

which highlights this maximum temperature. This pattern factor is normally

dened as

Pattern factor =

−

max

(4.21)

where T

max

is the maximum recorded temperature, T

is the inlet air tempera-

ture, and T

is the mean exit temperature.

The temperatures of most signicance to the turbine blades are those that

constitute the average radial prole. They are obtained by adding together

the temperature measurements around each radius of the liner and then

dividing by the number of locations at each radius, i.e., by calculating the

arithmetic mean at each radius. A typical radial temperature prole is shown

in Figure 4.10. The expression used to describe the radial temperature distri-

bution factor, also known as the prole factor, is

Profile factor

−

(4.22)

where T

is the maximum circumferential mean temperature.

The pattern factor and prole factor, as dened above, are best suited for

situations where a perfectly uniform exit-temperature distribution would

be considered ideal. However, in modern high-performance engines, which

employ extensive air cooling of both nozzle guide vanes and turbine blades,

the desired average radial distribution of temperature at the combustor exit

plane is far from at; instead, it usually has a prole that peaks above the

midheight of the blade, as illustrated in Figure 4.10. The objective is to provide

Aerodynamics 135

lower temperatures at the turbine blade root, where mechanical stresses are

highest, and at the tip of the blade, which is the most difcult to cool [40]. A

parameter that takes the design prole into account is the turbine prole factor,

which is dened as

Turbineprofile factor

)

rdes max

−

(

(4.23)

where (T

4.r

–T

4.des

)

max

is the maximum temperature difference between the

average temperature at any given radius around the circumference and the

design temperature for that same radius.

4.10 Dilution Zone Design

At this stage in the design process, the amount of air available for dilution

purposes will have been established, along with estimates of liner diameter

and liner pressure-loss factor. The principal dilution-zone design variables

are the number and size of the air-admission holes and the zone length. To

ensure a satisfactory temperature prole at the chamber outlet, there must

be adequate penetration of the dilution air jets, coupled with the correct

number of jets to form sufcient localized mixing regions. The penetration

of a round jet is a function of its diameter (see Equation 4.20). If the total

Design profile

Actual profile

max

- T

}

- T

}

- T

des

}

Temperature

100

Blade span, percent

max

Figure 4.10

Explanation of terms in exit-temperature prole parameters.

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

dilution-hole area is spread over a large number of small holes, penetration

will be inadequate, and a hot core will persist through the dilution zone. At

the other extreme, the use of a small number of large holes will result in a

cold core, due to overpenetration and unsatisfactory mixing. Thus, the rst

step in the design process is to determine the optimum number and size of

the dilution holes.

4.10.1 Cranfield Design Method

If a liner wall contains a row of n dilution holes, each of which has an effec-

tive diameter d

, then the total mass ow rate of air through these holes is

given by



mndU

jjj

=.(/)πρ4

(4.24)

Now

= (/).

∆ρ

(4.25)

Hence



mndP

jjL

= (/)( ),

πρ42

∆

and

nd mP PT

jjL

15 25=

−

.( /) .



∆

(4.26)

This equation may be used along with Equation 4.20 to determine opti-

mum values of n and d

for both tubular and annular combustors. For tubular

combustors, Y

max

in Equation 4.20 is made equal to 0.33D

. This allows d

be calculated from Equation 4.20 and this optimum value of d

is then substi-

tuted into Equation 4.26 to determine the optimum number of dilution holes.

The actual geometric diameter of the holes is then given by

ddC

hjD

= /,

.05

(4.27)

where C

is obtained from Figure 4.2 or 4.3, or from References [6–10].

For annular combustors, the procedure is exactly the same except that Y

max

in Equation 4.20 is made equal to 0.40D

For both tubular and annular combustors, the length of the dilution zone

should be around 1.5D

. Shorter lengths lead to inadequate mixing, whereas

longer lengths do not improve the pattern factor signicantly because

Aerodynamics 137

the additional wall-cooling air required reduces the amount available for

dilution.

4.10.2 NASA Design Method

Holdeman et al. [23,34,37] analyzed experimental and CFD data from a

number of NASA-Lewis-sponsored studies to obtain the following expres-

sion for calculating the optimum number of dilution holes for best mixing:

opt

J=π()/,

(4.28)

where C is an experimentally derived constant.

According to Holdeman et al. [17,23], the optimum value of C for cylindri-

cal ducts and rectangular ducts featuring single-sided air injection is 2.5. For

rectangular ducts having opposed rows of jets, C

opt

is 1.25 for in-line injec-

tion and 5.0 for staggered injection.

Most of the data on which Equation 4.28 is based were obtained using

round dilution holes and low values of



(usually less than unity).

Srinivasan et al. [33] found that the optimum value of C for round holes in

a cylindrical duct applied equally well to square holes of the same area, a

result that was later conrmed by Zhu et al. for higher values of



[32].

However, Zhu et al. noted that the value of C

opt

for round holes needs to be

modied for rectangular or slanted slots.

Bain et al. [28] also employed a high value of



(2.0) in their study on

axially opposed rows of staggered and in-line jets injected into a rectangular

crossow. Their results generally substantiate Equation 4.28, but they rec-

ommend that C should be increased by a factor of 1.8 for two-sided, in-line

congurations.

4.10.3 Comparison of Cranfield and NASA Design Methods

The main difference between these two approaches to dilution-zone design is

that one stresses the importance of hole size, while the other places primary

emphasis on hole spacing. Thus, for any given values of J and downstream

distance, the Craneld method leads to an optimum hole size and the spacing

between adjacent holes is then chosen to provide the design value of



On the other hand, the NASA procedure rst identies the optimum hole spac-

ing and the hole size is then estimated to give the required ratio of



Unfortunately, the two different approaches do not always lead to the

same conclusions. For example, if J is increased by increasing U

, then both

methods make the same recommendations in regard to how the number,

size, and spacing of the holes should be changed in order to retain optimum

penetration and mixing. However, if J is increased by reducing U

, then the

two approaches give different results.

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

An interesting feature of the Craneld method is that it takes account in a

very direct manner (see Equation 4.20) the adverse effects on jet penetration

and mixing arising from the aerodynamic blockage created by the presence

of adjacent air jets. This could be a useful asset in situations where the ratio



is exceptionally high as, for example, in the quick-quench zone of an

RQL combustor (see Chapter 9).

4.11 Correlation of Pattern Factor Data

Two parameters of crucial importance to pattern factor are the liner length,

which controls the time and distance that are available for mixing, and the

pressure drop across the liner, which governs the penetration of the dilu-

tion jets and their rate of mixing with the products of combustion. From the

analysis of experimental data on tubular, tuboannular, and annular combus-

tors, it is found that

max

−

=×













ref

∆

(4.29)

where ΔP

ref

is the liner pressure-loss factor, L

is the total liner length, and

is the liner diameter or height.

The correlation of data obtained for tubular and annular liners is shown in

Figures 4.11 and 4.12, respectively. In connection with these gures, it should

be noted that the correlation is based not on the L/D ratio of the dilution

zone, but on that of the complete liner. This is found to provide a better t to

the data.

For tubular and tuboannular combustors, it is found that

max

exp.

−

=− −













−

10070

ref

∆

(4.30)

while for annular combustors

max

exp.

−

=− −













−

10050

ref

∆

(4.31)

Equations 4.30 and 4.31 embody the assumption that the total length of

the liner is available for mixing. This is valid for most practical purposes

because pattern factor is important to engine life only at the highest combus-

tion pressures, where evaporation rates are so fast that the time and space

Aerodynamics 139

occupied in fuel evaporation are negligibly small. However, at low combus-

tion pressures, the liner length employed in fuel evaporation constitutes a

signicant fraction of the total line length and can no longer be ignored. It

may be obtained as [41]

LmDA

eAogLeff

=⋅03310

./,



ρλ

(4.32)

where λ

eff

is a measure of fuel volatility as discussed in Chapter 2.

Equation 4.32 shows that the inuence of fuel volatility on evaporation

length (and hence on pattern factor) is relatively small at high combustion

pressures, corresponding to high values of ρ

, but becomes increasingly

important with a reduction in combustion pressure. Equations 4.30 and 4.31

Tu bo-annular combustors

Equation 4.30

0.1

0.2

0.3

Pattern factor, (T

max

–T

)/(T

–T

)

0.4

0.5

30 40 50

(L/D)

(∆P

ref

)

60 70 80 90 100

Figure 4.11

Pattern factor correlation for tubular and tuboannular combustors.

Annular combustors

Equation 4.31

0.1

0.2

0.3

Pattern factor, (T

max

–T

)/(T

–T

)

0.4

0.5

30 40 50

(L/D)

(∆P

ref

)

60 70 80 90 100

Figure 4.12

Pattern factor correlation for annular combustors.