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

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

value of 1.75, as obtained by Greenhough and Lefebvre [2] from analysis of

combustion efciency data.)

Inspection of Equations 5.6 and 5.8 shows that there is little difference

between them. This is because the temperature dependence derived for

Equation 5.6 has been assigned to Equation 5.8. For practical purposes, e.g.,

the correlation of experimental combustion efciency data obtained from

a given combustion system or from geometrically similar systems, the two

parameters are effectively the same. It is in the comparison of combustion

systems of basically different design that points of variance between the two

parameters emerge. In the burning velocity model, the importance of the

cross-sectional area of the burning zone is emphasized, as opposed to volume

in the reaction rate analysis. This could be a useful advantage because it

ensures that any new combustor designed on the basis of the θ parameter

not only meets combustion efciency requirements, but also has adequate

combustion stability.

5.4 Mixing-Controlled Systems

If evaporation and chemical reaction rates are both innitely fast, Equation 5.1

becomes

(mixingrate/airflowrate).= f

(5.9)

The mixing rate between a turbulent air jet and the surrounding gas is

given by the product of the eddy diffusivity, the mixing area, and the density

gradient. If it is assumed that the eddy diffusivity is proportional to the prod-

uct of a mixing length, l, and the turbulent velocity in the air jet, then

mixing rate (eddy diffusivity)(mixingarea)(de= nnsitygradient)

(

)

(

)

(

)

lU ll

(5.10)

Substituting in Equation 5.10 for U

α(ΔP

/ρ)

yields

mixing rate

∝

(

)

∆

(

)

Pl TPP

//.

(5.11)

Where mixing limits performance, combustion efciency depends on

the ratio of the mixing rate to the airow rate. Thus, if one assumes that

turbulence scale is proportional to combustor size, Equation 5.11 becomes

Combustion Performance 161

mref AL

(

)

∆

(

)

fPAmTPP

//.



(5.12)

One important example of a system where mixing rates (and, under

certain conditions, evaporation rates as well) limit performance is the com-

bustion chamber of an industrial gas turbine. Such systems are not normally

required to operate at subatmospheric pressures, thus the θ parameter and

design charts based on it have no practical signicance.

5.5 Evaporation-Controlled Systems

Consider the case in which the mixing and reaction rates are fast enough for

fuel evaporation to be the rate-controlling step. In Chapter 2, the average rate

of evaporation of a fuel spray is given as:



mVqD

FArefc o

=ρ λ /,

(5.13)

where V

is the combustion volume, q is the fuel/air ratio by mass, D

is the initial

Sauter mean diameter of the spray, and λ

eff

is the effective evaporation constant.

It is assumed that as the fuel evaporates, it instantly mixes and burns with the

surrounding air. Thus, combustion efciency is obtained as the ratio of the rate

of fuel evaporation within the combustion zone to the rate of fuel supply, i.e.,

eFov AFcc A



mqmmfqm//,

(5.14)

where f

is the fraction of the total combustor airow

()



employed in com-

bustion, and q

is the fuel/air ratio in the combustion zone. Substituting for



from Equation 5.13 into Equation 5.14 gives

ηλρ

eeff gc cAo

()

VfmD/.



(5.15)

Equation 5.15 may be used for calculating or correlating combustion

efciencies in situations where fuel evaporation is known to be the rate-

controlling step. For these conditions, it shows that combustion efciency

is improved by increases in fuel volatility, turbulence intensity, combustion

volume, and gas pressure, and is impaired by increases in air mass ow rate

and mean drop size.

It should be noted that the form of Equation 5.15 allows η

to exceed unity.

When this occurs, it simply means that the time required for fuel evapora-

tion is less than the time available, so the fuel is fully vaporized within the

primary recirculation zone. In these circumstances, η

should be assigned a

value of unity.

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

Equation 5.15 relates combustion efciency to combustor dimensions

(via V

), combustor operating conditions (via



, λ

eff

, and ρ

), fuel nozzle

characteristics (via D

), and fuel type (via D

and λ

eff

Values of λ

eff

are shown plotted in Figures 5.5 and 5.6 for ambient pressures

of 1 and 2 MPa, respectively. The manner in which these charts are used to

2.2

1.8

1.4

P = 1000 kPa

∞

= 2000 K

∞

= 1200 K

∞

= 500 K

5000

10000

(m/s)(µm)

2000

1000

10000

5000

2000

10000

5000

2000

1000

500

200

100

1000

500

200

100

500

200

100

1.0

0.6

1.2

1.0

0.8

0.6

0.4

0.2

0.22

0.18

0.14

0.10

0.06

0.02

420 440 460 480

, K

500 520 540 560

eff

, mm

Figure 5.5

Variation of effective evaporation constant with normal boiling point for a pressure of 1 MPa.

(From Chin, J.S. and Lefebvre, A.H., Proceedings of 20th Automotive Technology Development

Contractors Meeting, P-120, 325–331, 1982.)

Combustion Performance 163

calculate values of λ

eff

for a range of liquid hydrocarbon fuels at different

levels of ambient air temperature is described in Chapter 2, which also con-

tains similar data on λ

eff

for an ambient pressure of 0.1 MPa (Figure 2.7).

A useful guide to the inuence of fuel type on combustion efciency may

be obtained by dening a dimensionless efciency parameter as the ratio of

the combustion efciency of any alternative fuel “a” to that of some baseline

2.8

P = 2000 kPa

∞

= 2000 K

∞

= 1200 K

∞

= 500 K

10000

5000

2000

10000

5000

2000

10000

5000

2000

1000

500

200

100

1000

500

200

100

1000

500

200

100

, (m/s)(µm)

2.4

2.0

1.6

1.2

0.8

1.8

1.4

1.0

eff

, mm

0.6

0.2

0.22

0.18

0.14

0.10

0.06

0.02

420 440

, K

460 480 500 520 540 560

Figure 5.6

Variation of effective evaporation constant with normal boiling point for a pressure of 2 MPa.

(From Chin, J.S. and Lefebvre, A.H., Proceedings of 20th Automotive Technology Development

Contractors Meeting, P-120, 325–331, 1982.)

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

fuel “b,” when both fuels are burned in the same combustor at the same

operating conditions. From Equation 5.15 we have

ηη λλ

ca cb effo

effo

//// .=

(

)

(

)

DDb

(5.16)

This expression provides a means of assessing the effect on combustion

efciency of replacing aviation kerosine with some alternative fuel, without

reference to any particular combustor or operating conditions. It may also be

used more generally to compare the combustion efciency characteristics of

any two liquid fuels, provided, of course, that fuel evaporation is known to

be the rate-controlling step. If the level of combustion efciency of interest

is high, say greater than 90%, it is more useful and more accurate to rewrite

Equation 5.16 as

−

(

)

−

(

)

(

)

(

)

ηηλλ

cb ca effo

effo

//// .DDb

(5.17)

For pressure-swirl atomizers, the mean drop size depends on the surface

tension and viscosity of the fuel. However, conventional fuels exhibit only

slight differences in surface-tension values, so only the inuence of viscosity

on D

need be considered.

The practical utility of Equation 5.17 for predicting the inuence on combus-

tion efciency of a change in fuel type is demonstrated in Figure 5.7, which

100

0 20 40 60 80

JP4

Jet A

DF 2

Fuel oil

Baseline fuel

Theory

100

Relative engine power, percent

Combustion efficiency, percent

Figure 5.7

Inuence of fuel type on combustion efciency. (From Moses, C.A., “Studies of Fuel Volatility

Effects on Turbine Combustor Performance,” Joint Spring Meeting of Western and Central

States Sections of the Combustion Institute, San Antonio, Texas, 1975. With permission.)

Combustion Performance 165

shows experimental data obtained by Moses [10] using a T63 combustor.

With Jet A designated as the baseline fuel, and using values for λ

eff

from

Figure 5.5, the combustion efciencies of the other fuels are readily calcu-

lated from Equation 5.17 by assuming that mean drop sizes are proportional

to (fuel viscosity)

0.25

for the pressure-swirl atomizer employed in the T63

combustor. The results of the calculations are shown in Figure 5.7, where

the dashed curve describes the combustion efciency of the baseline fuel

as determined experimentally. The solid curves represent the predictions

of Equation 5.17 for the other fuels. The level of agreement between the pre-

dicted and measured values is clearly satisfactory.

5.6 Reaction- and Evaporation-Controlled Systems

In some situations, for example, with fuels of low volatility burning at low

pressures, the rate of heat release may be limited by both chemical reaction

and evaporation rates. Under these conditions, the combustion efciency is

obtained as the product of the evaporation efciency, η

, and the reaction

efciency, η

, i.e.,

ηηη

θce

.=×

(5.18)

The rst term on the right hand side of Equation 5.18 represents the fraction

of the fuel that is evaporated within the combustion zone. For η

> 1, η

= η

which denotes the fraction of fuel vapor that is converted into combustion

products by chemical reaction.

From analysis of the available experimental data on combustion efciency,

the following expressions for η

and η

have been derived [11].

=−

(

)

[]

10022 400

exp. exp/ /,

PV Tfm

cc cA



(5.19)

and

ηλ

eceffcoc A

=− −×

[]

−

13610

exp/,PV TD fm



(5.20)

where P

is the combustor inlet pressure in kPa, V

is the combustion (pre-

dilution) volume in m

, T

is the combustion (predilution) temperature in

degrees Kelvin, f

is the fraction of air used in combustion,



is the total

combustor airow in kg/s, D

is the Sauter mean diameter of the fuel spray

in microns, and λ

eff

is the effective evaporation constant in mm

/s.

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

It should be noted in Equations 5.19. and 5.20 that the temperatures

are expressed in terms of T

rather than T

. Either may be used (with suitable

adjustment to the constants), but T

is the adiabatic ame temperature in the

combustion zone assuming complete combustion of the fuel. It is calculated

from the expression

TT T

∆ ,

(5.21)

where ΔT

is obtained from standard temperature rise charts for the fuel in

question, using appropriate values of P

, T

, and q

(=q

In the late 1970s, the US Air Force, Army, and Navy, along with NASA

and the engine manufacturers, initiated programs to determine the effects

of anticipated future fuels on the life and performance of existing aircraft

engines. As a result of these studies, data became available that yielded new

and useful insights into the effects of fuel properties, combustor design,

and engine operating conditions on all major aspects of combustion per-

formance, including combustion efciency [12–17]. Some of these data are

shown in Figures 5.8 and 5.9, which demonstrate the satisfactory correlation

of combustion efciency data provided by Equation 5.18. Further examples

to illustrate the application of this equation to the correlation of experimental

data on combustion efciency may be found in [11].

It should be noted that these investigations and correlations apply to

petroleum-based conventional jet fuels. For synthetic and bio-based jet

fuels, the validity of this approach and correlations are yet to be studied and

demonstrated.

100

All fuels

TF 41

= 429 K

= 0.962 kg/s

= 291 kPa

86 88 90 92 94 96 98 100

Combustion efficiency (predicted), %

Combustion efficiency (measured), %

Figure 5.8

Comparison of measured and predicted values of combustion efciency for a TF 41 combustor.

(From Lefebvre, A.H., Journal of Engineering for Gas Turbines and Power, 107, 24–37, 1985. With

permission.)

Combustion Performance 167

5.7 Flame Stabilization

One of the primary requirements of a gas turbine combustor is that

combustion must be maintained over a wide range of operating conditions.

This is especially true for the aircraft combustion chamber, which must

sometimes operate at low temperatures and pressures, and at fuel/air ratios

that lie well outside the normal limits of ammability for hydrocarbon/air

mixtures. Combustion must be initiated and sustained in highly turbulent

airstreams, owing at speeds many times greater than the normal burning

velocity of the fuels employed. Moreover, the ame must cope with the vari-

ous abnormal conditions that are sometimes encountered in ight, such as

those created by the ingestion of tropical rain or ice.

The usual method of surmounting this problem is to create a sheltered

zone of low velocity at the upstream end of the liner, where ame speeds

are greatly enhanced by imparting a high level of turbulence to the primary

air jets and by arranging for hot combustion products to recirculate and mix

with the incoming air and fuel.

5.7.1 Definition of Stability Performance

In combustion parlance, the term “stability” is often used rather loosely to

describe either the range of fuel/air ratios over which stable combustion can

be achieved, or as a measure of the maximum air velocity the system can

tolerate before ame extinction occurs. Thus, the description “good stability

100

J 85

All fuels

= 148–445 kPa

= 336–570 K

= 4.4–12.2 kg/s

84 86 88 90 92 94 96 98 100

Combustion efficiency (predicted), %

Combustion efficiency (measured), %

Figure 5.9

Comparison of measured and predicted values of combustion efciency for a J 85 combustor.

(From Lefebvre, A.H., Journal of Engineering for Gas Turbines and Power, 107, 24–37, 1985. With

permission.)

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

performance,” when applied to a specic combustor, could mean either that

it is capable of burning over a wide range of mixture strengths or that its

blowout velocity, U

, is high. Clearly, it is important to differentiate between

these two properties, both of which contribute to the overall stability of the

system.

In general, with experimental forms of stabilizer, where the fuel is sup-

plied premixed with air, the main emphasis has been on blowout velocity,

whereas in gas turbine combustion chambers, the burning range is usually

considered of prime importance.

5.7.2 Measurement of Stability Performance

In the development of a new combustion chamber, it is customary to deter-

mine its stability performance by carrying out a series of extinction tests

at constant, predetermined levels of inlet air temperature and pressure.

After turning on the fuel and igniting the mixture, the fuel ow is gradually

reduced until ame extinction occurs. After noting the fuel and air ows at

this “weak extinction” or “lean blowout” point, combustion is re-established

and the fuel ow slowly increased until “rich extinction” occurs. This pro-

cess is repeated at increasing levels of air mass ow until the complete stabil-

ity loop can be drawn. Figure 5.10 illustrates the main features of a stability

loop obtained by this technique. The region of stable burning is bounded by

rich and weak limits that gradually converge with increasing mass ow rate

until eventually a ow rate is reached beyond which combustion is unattain-

able at any fuel/air ratio. Of special interest with such curves are the “rich”

0.03

= constant

Region of

stable burning

0.02

0.01

0 0.25 0.50 0.75 1.00

Air mass flow, kg/s

Fuel/air ratio

Figure 5.10

Typical combustion chamber stability loop.

Combustion Performance 169

and “weak” extinction points obtained at the air mass ows corresponding

to the design value of chamber reference velocity.

The complete stability performance of an aero-engine combustor is

obtained by carrying out sufcient extinction tests to allow a number of

stability loops to be drawn at different levels of pressure, as illustrated in

Figure 5.11. It is then a fairly straightforward procedure to translate these

stability loops into performance charts illustrating the range of ight condi-

tions over which stable combustion is possible, as illustrated in Figure 5.12.

In practice, the risk of overheating the liner and rig ducting tends to restrict

the number of rich extinction points that can be obtained, especially at high

pressures. Moreover, even with large-scale test facilities, it is usually impos-

sible to determine the peaks of the loops, owing to limitations on the amount

of air that can be supplied at subatmospheric pressures. Fortunately, these

are not serious drawbacks, as it is the lean blowout limit that is of primary

interest and importance. With aircraft systems, which must provide for sud-

den changes in throttle setting, it is essential that the lean blowout limit

should exceed 250 AFR at atmospheric pressure. In this context, the method

of fuel injection is of paramount importance.

In conventional combustion chambers, good stability performance is

usually attained without undue difculty. However, in chamber designs

featuring complete fuel evaporation and thorough mixing of fuel and air

prior to combustion, current views on what is acceptable in terms of stabil-

ity performance may have to be modied considerably in order to achieve

worthwhile reductions in pollutant emissions. For this reason, it is essential

Decreasing pressure

Air mass flow, kg/s

Fuel/air ratio

Figure 5.11

Inuence of pressure on stability loops.