Lefebvre A.H., Ballal D.R. Gas Turbine Combustion: Alternative Fuels and Emissions
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150 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition
13. Norster, E. R., “Jet Penetration and Mixing Studies,” unpublished work at
College of Aeronautics, Craneld, UK, 1964.
14. Lefebvre, A. H., unpublished work, 1979.
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16. Norster, E. R., private communication.
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of Gas Turbine Combustion Chambers,” College of Aeronautics Note 169,
Craneld, UK, 1966.
19. Holdeman, J. D., Walker, R. E., and Kors, D. L., “Mixing of Multiple Dilution
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Crossow,” AIAA Paper 83-1200, 1983.
22. Holdeman, J. D., Srinivasan, R., and Berenfeld, Α., “Experiments in Dilution Jet
Mixing,” AIAA Journal, Vol. 22, No. 10, pp. 1436–43, 1984.
23. Holdeman, J. D., Srinivasan, R., Coleman, E. B., Meyers, G. D., and White, C. D.,
“Experiments in Dilution Jet Mixing—Effects of Multiple Rows and Noncircular
Orices,” AIAA Paper 85-1104, 1985.
24. Kamotani, Y., and Greber, I., “Experiments on Conned Turbulent Jets in Cross
Flow,” NASA CR-2392, 1974.
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121217, 1973.
26. Srinivasan, R., Berenfeld, Α., and Mongia, H. C., “Dilution Jet Mixing Program
Phase I Report,” NASA CR-168031, 1982.
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AIAA Paper 86-1611, 1986.
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Opposed Rows of Jets Injected into Conned Crossow,” Journal of Propulsion
and Power, Vol. 11, No. 5, pp. 885–93, 1995.
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of Cross-Stream Mixing in a Cylindrical Duct,” AIAA Paper 91-2459, 1991.
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of Jet Mixing in Low NO
x
Flametube Combustors,” Journal of Engineering for Gas
Turbines and Power, Vol. 114, No. 2, pp. 416–24, 1992.
31. Hatch, M. S., Sowa, W. Α., Samuelsen, G. Α., and Holdeman, J. D., “Geometry
and Flow Inuences on Jet Mixing in a Cylindrical Duct,” Journal of Propulsion
and Power, Vol. 11, No. 3, pp. 393–402, 1995.
32. Zhu, G., Lai, M. C., and Lee, T., “Penetration and Mixing of Radial Jets in Neck-
Down Cylindrical Crossow,” Journal of Propulsion and Power, Vol. 11, No. 2,
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Aerodynamics 151
34. Holdeman, J. D., Srinivasan, R., Coleman, E. B., Meyers, G. D., and White, C. D.,
“Effects of Multiple Rows and Non-Circular Orices on Dilution Jet Mixing,”
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35. Holdeman, J. D., and Srinivasan, R., “Modeling of Dilution Jet Flowelds,”
Combustion Fund Research, NASA CP-2309, pp. 175–87, 1984.
36. Holdeman, J. D., and Srinivasan, R., “Modeling Dilution Jet Flowelds,” Journal
of Propulsion and Power, Vol. 2, No. 1, pp. 4–10, 1986.
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Effects of Curvature and Convergence on Dilution Jet Mixing,” AIAA Paper
88-3180, 1988.
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Jets,” Journal of Propulsion and Power, Vol. 12, No. 2, pp. 225–30, 1996.
39. Wittig, S. L. K., Elbahar, O. M. F., Nott, B. E., and Kutz, R., “Temperature
Prole Development in Turbulent Mixing of Coolant Jets with a Conned Hot
Crossow,” Journal of Engineering for Gas Turbines and Power, Vol. 106, No. 1,
pp. 193–7, 1984.
40. Dodds, W. J., and Bahr, D. W., “Combustion System Design,” in A. M. Mellor,
ed., Design of Modern Gas Turbine Combustors, pp. 343–476, Academic Press,
San Diego, CA, 1990.
41. Chin, J. S., and Lefebvre, A. H., “Effective Values of Evaporation Constant for
Hydrocarbon Fuel Drops,” Proceedings of the Twentieth Automotive Technology
Development Contractor Coordination Meeting, SAEP-120, pp. 325–32, Society of
Automotive Engineers, Warrendale, PA, 1982.
42. Gupta, A. K., Lilley, D. G., and Syred, N., Swirl Flows, Abacus Press, Tunbridge
Wells, UK, 1984.
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London, 1972.
44. Mathur, M. L., and Maccallum, N. R. L., “Swirling Air Jets Issuing from Vane
Swirlers, part I, Free Jets,” Journal of the Institute of Fuel, Vol. 40, pp. 214–25,
1967.
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Chambers,” Aeronautical Research Council R and Μ 2987, UK, 1957.
153
5
Combustion Performance
5.1 Introduction
Combustion chambers are required to burn stably over a wide range of
operating conditions with levels of combustion efciency close to 100%.
Another important requirement is easy and reliable lightup during ground
starting while the engine is being cranked up to its self-sustaining speed.
The aircraft gas turbine has the additional requirement of rapid relighting of
the combustor after a ameout in ight. Thus, the combustion performance
parameters of prime importance to the gas turbine are combustion efciency,
stability, and ignition. The essential features of these three major topics are
reviewed in this chapter.
5.2 Combustion Efficiency
Failure to achieve high levels of combustion efciency is generally regarded
as unacceptable, partly because combustion inefciency represents a waste of
fuel, but mainly because it is manifested in the form of pollutant emissions,
such as unburned hydrocarbons and carbon monoxide. That is why current
emissions regulations call for combustion efciencies in excess of 99%. For
the modern aircraft engine, combustion efciency is effectively 100% at take-
off conditions. To avoid the production of “white” smoke, efciency must
exceed 96% and at no point in the operating cycle is it less than 90%. High
combustion efciency is necessary at this “off design” point because, with
the engine windmilling, the pressure and temperature of the air owing
through the combustor are close to ambient values. At high altitudes, these
are so low that the stability limits are very narrow. This means that when the
engine control system attempts to compensate for combustion inefciency
by supplying more fuel to the combustor, this extra fuel may cause a “rich
extinction” of the ame. Thus, an important design requirement for an air-
craft combustor is that it be sized large enough to ensure an adequate level of
154 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition
combustion efciency during engine restart at the highest altitude at which
relight capability is required.
5.2.1 The Combustion Process
The primary purpose of combustion is to raise the temperature of the
airow by efcient burning of fuel. From a design viewpoint, an impor-
tant requirement is a means of relating combustion efciency to the operat-
ing variables of air pressure, temperature, and mass ow rate, and to the
combustor dimensions. Unfortunately, the various processes taking place
within the combustion zone are highly complex and a detailed theoretical
treatment is precluded at this time. Until more information is available,
suitable parameters for relating combustion performance to combustor
dimensions and operating conditions can be derived only through the
use of very simplied models to represent the combustion process. One
such model starts from the well-established and widely accepted notion
that the total time required to burn a liquid fuel is the sum of the times
required for fuel evaporation, mixing of fuel vapor with air and combus-
tion products, and chemical reaction. As the time available for combustion
is inversely proportional to the airow rate, the combustion efciency may
be expressed [1] as
η
c
airflowrate
evaporationratemixing
=
(
)
+
−
f
1
11
rrate reaction rate
+
−
1
1
.
(5.1)
In practical combustion systems, the maximum rate of heat release
under any given operating conditions may be governed by either evapora-
tion, mixing, or chemical reaction, but rarely by all three at the same time.
However, when the combustion process is in transition from one regime to
another, two of the three key rates will participate in determining the over-
all combustion efciency. Before exploring that situation, let us examine
the separate effects on combustion efciency of chemical reaction, mixing,
and evaporation.
5.3 Reaction-Controlled Systems
The two most widely used approaches for describing combustion efciency
under conditions where the overall rate of heat release is limited by chemical
kinetics are the burning velocity and stirred reactor models.
Combustion Performance 155
5.3.1 Burning Velocity Model
Here, the combustion zone is envisaged as being similar in structure to
the ame brush produced on a Bunsen burner under turbulent ow condi-
tions. Combustion performance is then described as a function of the ratio
of turbulent burning velocity to the velocity of the fresh mixture entering
the combustion zone. It is assumed that evaporation rates and mixing rates
are both innitely fast, and that all of the fuel that burns does so completely.
Combustion inefciency arises when some of the mixture succeeds in pass-
ing through the combustion zone without being entrained by a turbulent
ame front (see Figure 5.1).
This model was used by Greenhough and Lefebvre [2] in deriving a param-
eter that was shown to correlate experimental data on combustion efciency
obtained over wide ranges of pressure, temperature, and airow rate for
various designs of combustion chamber. The model is described only briey
below; for further details, reference should be made to the original paper and
to the subsequent development of the model [3].
Combustion efciency is dened as:
η
c
(heatreleasedincombustion)/(heat availabl= eeinfuel),
(5.2)
=∆
(
)
(
)
ρ
gfTp A
AS cT qm H/.
(5.3)
Now c
p
ΔT = qH, by denition; also the ame area, A
f
, may be assumed
to be proportional to the combustor reference area, A
ref
. Thus, Equation 5.3
simplies to:
η
cTref
∝SU/.
(5.4)
Air
Diffuser
Liner
Fuel
Turbulent
flame zone
Figure 5.1
Burning velocity model for combustion efciency.
156 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition
If one expresses U
ref
in terms of
m
A
, P
3
, and A
ref
and describes S
T
in terms of
laminar burning velocity and turbulence intensity (which, in turn, is related
to the liner pressure loss factor), Equation 5.4 becomes
η
cref refALref
=
(
)
(
)
∆PA PD TbmPq
m
33 3
exp///
[[]
05.
.
m
(5.5)
Lefebvre and Halls [3] demonstrated that combustion efciency data
obtained during low pressure tests on several types of combustion cham-
bers could be satisfactorily correlated by assigning values to m and b of 0.75
and 300, respectively. Substitution of these values into Equation 5.5, and
neglecting the pressure loss term that varies little between one combustor
and another, leads to the well-known θ parameter
ηθ
θ
=
(
)
=
(
)
[
ffPADT m
3
175
075
3
300
.
.
exp/ /
refref A
]]
.
(5.6)
Equation 5.6 has been applied with considerable success to the correlation
of experimental data on combustion efciency, and has proved very useful
in reducing the amount of rig testing required to evaluate new combustor
designs. As shown in Figure 5.2, only a few test points are needed to establish
the complete performance curve for a chamber. Furthermore, it is possible to
predict, with reasonable accuracy, combustion efciencies at ow conditions
that lie outside the capacity of the test facility—provided, of course, that at
these extrapolated conditions the combustion performance is not limited by
fuel evaporation or by any factor other than chemical reaction rates.
The main advantage of Equation 5.6 is that it provides a method of scal-
ing combustor dimensions and operating conditions to common values so
that any differences in performance that remain can be attributed directly
to differences in design. This is a tremendous asset when one is attempting to
select a design for a new combustion chamber from several existing designs,
none of which is of the required size or has been tested at the relevant operat-
ing conditions.
The manner in which the θ parameter is used can be demonstrated by
reference to Figure 5.3, which shows performance curves for two different
combustor designs. Clearly, design A is superior to design B, because for any
given value of combustion efciency the θ parameter has a lower value. This
means that under any given operating conditions of
m
A
, P
3
, and T
3
, design
A can equal the combustion efciency of design B, and yet be made smaller
in size.
Any new chamber design must be based to a large extent on previous
experience. A most useful way in which past experience can be summarized
is by the use of charts where combustion efciency data from all known sys-
tems are correlated against all the relevant variables. Such a chart is shown
in Figure 5.4, in which the hatched areas include experimental data obtained
Combustion Performance 157
from a large number of multi-can, can-annular, and annular chambers.
Figure 5.4 may be used to determine the size of chamber needed to meet
any stipulated performance requirement. For all types of engines, the most
arduous operating conditions are those at which the inlet pressure P
3
, is a
minimum. For aircraft engines, this usually corresponds to the engine wind-
milling after a ameout at high altitude.
When ameout occurs in ight, the engine rotational speed falls rapidly to
its windmilling value. The relight sequence is rst to use the ignition system
to relight the combustor. When this has been accomplished, the next step
is to accelerate the engine up to its normal rotational speed. This normally
calls for a minimum combustion efciency of around 80%. As previously
discussed, a lower level of combustion efciency could result in a rich extinc-
tion of the ame, whereas a higher level would lead to an unnecessarily large
combustor.
Appropriate values of A
ref
and D
ref
may be obtained from Figure 5.4 by
reading off a value of θ at a point along a horizontal line within the hatched
100
90
80
70
60
50
Combustion efficiency, percent
AFR = 100
40
30
20
10
0
01
m
.
A
× 10
–4
P
3
1.75
exp (T
3
/300)
234
Figure 5.2
Correlation of combustion efciency data for an aircraft combustor.
158 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition
100
90
Design ‘B’
Design ‘A’
AFR = 60
80
70
60
Combustion efficiency, percent
50
40
30
20
10
0
0 0.2
m
.
A
0.4
0.75
P
3
1.75
A
ref
D
ref
exp (T
3
/300)
0.6 0.8 1.0
× 10
–4
Figure 5.3
Combustion efciency curves for two different combustion designs.
100
80
60
40
Combustion efficiency, percent
01
θ = P
3
1.75
A
ref
D
ref
1.75
exp (T
3
/300)/m
.
A
234
Tubular and
tuboannular
Annular
567 8 × 10
7
Figure 5.4
Design chart for conventional combustors.
Combustion Performance 159
area at 80% combustion efciency, and then substituting into it the values
of P
3
, T
3
, and
m
A
corresponding to the engine windmilling at the maximum
guaranteed relight altitude. The actual point chosen within the hatched area
will represent a balance between the conicting needs of high performance,
small combustor size, and low development cost.
A notable feature of the θ parameter is that it ignores the inuence of drop
size on combustion efciency. The fact that it has been shown to work success-
fully over wide ranges of combustor types and operating conditions tends to
conrm that drop sizes are indeed irrelevant to combustion efciency, as the
experimental study of Odgers et al. has demonstrated [4]. However, for fuels
heavier than Jet A (JP5), the effects of atomization and evaporation cannot
be ignored.
5.3.2 Stirred reactor Model
Another simplied approach to the problem of providing a quantitative
description of the combustion process in a gas turbine combustor is to regard
the combustion zone as a perfectly stirred reactor into which fuel and air are
fed at a constant rate and are instantaneously mixed with all the other mate-
rial within the zone. Burned material leaves the zone at a constant rate, with
temperature and composition identical to that within the zone.
The application of simple reaction rate theory to practical combustion
systems seems to have been considered rst by Childs [5], and then inde-
pendently by Avery and Hart [6] and Bragg [7]. The approach is based on
the notion that one limiting reaction governs the overall rate of combustion.
Examination of the chemistry of the process shows that this is unlikely, and
its justication lies entirely in the fact that it allows great simplication while
explaining experimental results to a satisfactory degree.
A drawback to the stirred reactor approach is that heat-release rates are
related to the reaction temperature. This is clearly a serious deciency in any
calculation aimed at determining combustion efciency because the com-
bustion efciency must be known, a priori, in order to calculate the reaction
temperature. However, Bragg [7] and Greenhough and Lefebvre [2] found
that overall heat-release rates could be expressed in terms of inlet air tem-
perature, as illustrated in Equation 5.6. We have
η
θ
=
(
)
[]
=fPVT mn
3
2
3
3002
cA
forexp/ /,
(5.7)
or
η
θ
=
(
)
[]
=fP VT mn
3
175
3
300175
.
exp/ /..
cA
for
(5.8)
(NOTE: The experiments of Longwell and Weiss [8] on stirred reactors indi-
cate a pressure exponent, n, of 1.8, which is in close agreement with the