Thermodynamic Analysis

of Air-Cooled Gas Turbine Plants

At present high temperature, internally cooled gas turbines form the basis for the devel-
opment of highly efficient plants for utility and industrial markets. Minimizing irrevers-
ibility of processes in all components of a gas turbine plant leads to greater plant effi-
ciency. Turbine cooling, like all real processes, is an irreversible process and results in
E. A. Khodak lost opportunity for producing work. Traditional tools based on the first and second laws
of thermodynamics enable performance parameters of a plant to be evaluated, but they
G. A. Romakhova give no way of separating the losses due to cooling from the overall losses. This limitation
arises from the fact that the two processes, expansion and cooling, go on simultaneously
St.-Petersburg State Technical University,
in the turbine. Part of the cooling losses are conventionally attributed to the turbine
St.-Petersburg, Russia
losses. This study was intended for the direct determination of lost work due to cooling.
To this end, a cooled gas turbine plant has been treated as a work-producing thermody-
namic system consisting of two systems that exchange heat with one another. The con-
cepts of availability and exergy have been used in the analysis of such a system. The
proposed approach is applicable to gas turbines with various types of cooling: open-air,
closed-steam, and open-steam cooling. The open-air cooling technology has found the
most wide application in current gas turbines. Using this type of cooling as an example,
the potential of the developed method is shown. Losses and destructions of exergy in the
conversion of the fuel exergy into work are illustrated by the exergy flow diagram.
关DOI: 10.1115/1.1341204兴

1 Introduction cycle cannot be said to be the basis of this plant. The fuel energy
is supplied to the part of the compressed air mass flow rate only.
Today, efficiency levels for new large natural-gas-fired gas tur-
The remainder of the air mass flow is extracted from the compres-
bine plants are in the range of 34–36 percent. Gas turbine based
sor, ducted to the turbine blades, and used as a coolant. Absorbing
combined plants achieved efficiencies of 54–56 percent. The use
the heat extracted through wall and the heat extracted from the
of advanced cooling techniques and improvements in materials
fluid stream as the result of mixing cooling flows produce work
provide the opportunity for increasing the turbine inlet tempera-
during the expansion in the turbine. Cooling losses derive from
ture and for improving plants efficiencies. This trend will the introduction of supplementary irreversibilities associated with
continue. the modification of the open circuit to the turbine cool. The deter-
There are two opposing effects, if the turbine inlet temperature mination of such losses is a matter for thermodynamic analysis.
is raised without improving a cooling technology. Raising the
turbine inlet temperature tends to the higher mean temperature of
heat supply and to increase the plant efficiency. But with an in-
crease in turbine inlet temperature there is an increase in heat 2 Methodology
flows from the hot gases to the coolant, if the mean blade tem- An air-cooled gas turbine power plant is an open-circuit steady-
perature is kept on. This means increasing the required coolant flow device which converts energy of fuel into mechanical work.
flow. The transfer of heat over a finite temperature difference A distinguishing feature of recent turbines is that large cooling air
between the gas and coolant flows represents a lost opportunity usage is required for good cooling.
for producing work. The irreversibility occurs in each process An established open-air cooling system for a turbine incorpo-
through which the coolant goes, and represents, also, a lost oppor- rates a rotor cooling circuit and several stationary cooling circuits
tunity for producing work. Thus raising the turbine inlet tempera- provided by the air extracted from the compressor discharge and
ture tends to increase irreversibility associated with cooling. A from interstate compressor bleeds. If the temperature of the bled
gain in efficiency due to an increase in the mean temperature of air is too high to be used directly to cool turbine hot components,
heat supply may sometimes be partly or more than offset by the the air flows may be precooled in external coolers. Currently
effect of resulting greater irreversibility. highly complex cooling schemes are used to cool vanes and
The amount of lost work due to cooling is greatly dependent on blades. When passing through cooling channels the cooling air
cooling effectiveness falling drastically with an improvement in absorbs the heat extracted from the hot gases. The heated coolant
cooling technology. This would result in a higher plant efficiency is ejected into blade path through exit holes in aerofoils, trailing
additional to that resulting from the increase in the turbine inlet edges, and leading edges and is mixed with the main flow. The
temperature. compressor bleed air is also supplied to interstage disk cavities to
In defining ‘‘cooling losses,’’ it is first necessary to establish cool disk and to interstage seals to preclude the injection of hot
the type and the location of these losses. Conventional air cooling gases.
is now widely used in gas turbines, and this is the type of cooling Thus the expansion in the air-cooled turbine is accompanied by
considered in this paper. Cooled and uncooled gas turbine plants nearly-continuous mixing with cooling air. As the working fluid
differ in open circuits on which they operate. The Joule–Brayton temperature drops, the intensity of the cooling air supply de-
creases. The flow through the turbine is no longer treated as being
Contributed by the Advanced Energy Systems of THE AMERICAN SOCIETY OF adiabatic. An air-cooled turbine is an open thermodynamic system
MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF ENGINEER-
ING FOR GAS TURBINES AND POWER. Manuscript received by the AES Division,
that exchanges both energy and mass with the exterior. Figure 1
July 14, 2000; final revision received by the ASME Headquarters Aug. 1, 2000. shows the simplest arrangement of a plant with cooling air sup-
Editor: H. D. Nelson. plied ‘‘continuously’’ to the turbine.

Journal of Engineering for Gas Turbines and Power APRIL 2001, Vol. 123 Õ 265
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 Figure 2 shows an interpretation of how an air-cooled gas tur-
bine plant can perform as a hypothetical ‘‘combined’’ plant. The
plant contained within control surface X comprises the topping
plant and that within control surface Y comprises the bottoming
plant.
The air entering the plant is split before compression into two
streams (M a ) and (M c0 ). After compression the first stream en-
ters the combustion chamber, the flue gases from which supply
the working fluid 共the gas兲 for the gas turbine in the topping plant.
The second stream (M c0 ) is split into infinite number of flows
after compression. They enter an infinite number of coils, being
placed between an infinite number of turbine stages, as shown in
Fig. 2. The pressure drop across each stage is infinitely small. The
velocities of all streams are so small that kinetic energies may be
ignored. An elementary quantity of air (dM c ) enters the coil at
some temperature below the temperature of the incoming gas
stream. When passing through a coil it absorbs the heat (dQ c ),
and its temperature increases only an infinitesimal amount less
Fig. 1 Gas turbine plant with continuous air supply for cooling
than the leaving gas stream. The two fluid streams, gas and cool-
ant, leaving a coil are at the same pressure, but they do not mix, as
in the case of a real plant. The heat transfer from the gas to the
The two open circuits together form an air-cooled gas turbine coolant takes place across a variable finite temperature difference
plant. The air entering the combustion chamber after leaving the
and so is irreversible. Heated coolant expands through its own
compressor (M a ) and the products of combustion 共M g ⫽M a
work-producing turbine. Part of the turbine work developed is
⫹M f , where M f is the mass rate of the fuel supplied兲 pass
used to drive compressors.
through one of them 共see Fig. 1兲. The other circuit is the coolant
circuit through which the cooling air flows (M c0 ) pass. The es- The expansion of the gas in its own turbine is accompanied by
sential difference of the first circuit from the conventional circuit heat transfer and the expansion of the coolant in its own turbine
on which an uncooled gas turbine plant operates is that the expan- takes place in the presence of energy transfer, so both processes
sion of the products of combustion in the turbine is accompanied are not adiabatic. The pressure and temperature drops are the
by heat removing. This heat is supplied to the coolant circuit. same across each turbine.
An air-cooled gas turbine plant can be treated as a binary plant, The extraction of heat (Q c ) causes a reduction in the work done
in which a combination of working substances is used. The upper by the gas, but this reduction is partially offset by the work output
plant is supplied with reactants 共fuel and air兲, produces power, from the bottoming plant. When Q c ⫽0, ‘‘the combined plant’’
rejects heat during the expansion in the turbine, and discharges the becomes a conventional uncooled gas turbine plant.
products of combustion. This plant acts as a topping plant to a The quantity of heat extracted (Q c ) meets the sum of the heat
bottoming plant using the heat rejected as a heat source. The air removed from the gas through walls of blades, and that removed
bled from the compressor to cool gas turbine components 共the by mixing the gas and the cooling air flows. The former is much
coolant兲 is a working substance for the bottoming plant. In an less than the latter 共Table 1兲. It represents the heat that must be
air-cooled gas turbine plant a topping open circuit is superposed extracted through wall to achieve required metal temperature and
directly on a bottoming circuit. is determined by the external heat transfer process in turbine
blades. The latter depends on the required cooling air flow rate,
and so varies with cooling effectiveness.
Thus an air-cooled gas turbine plant may be treated as a hypo-
thetical combined plant, the upper part operating on an open cir-
cuit, producing work (W g ), rejecting the products of combustion
(M g ) and heat (Q c ). This heat is supplied to the lower part of the
plant producing work (W c ) and rejecting the air mass flow (M c0 ).
In terms of thermodynamic systems, an air-cooled gas turbine
plant represents a compound system comprising two systems that
exchange heat with one another. Let us call the former system the
gas system and the letter system the coolant system.
Compared to an uncooled gas turbine plant, there are three
features that result in additional lost opportunities for producing
work:
1 the irreversibility involved in transfer of heat between the gas
and the coolant flows 共between the topping and the bottoming
plants, or in other words, between the gas and the coolant
systems兲;
2 irreversibilities involved in all processes that make up the
coolant circuit 共irreversibilities within the bottoming plant兲;
3 the irreversibility of the mixing process of two streams dif-
ferent in chemical composition.
Since the lost work due to irreversibility is equal to the increase
in the anergy 共energy being unavailable for work producing兲, so
only the concepts of thermodynamic availability and exery pro-
Fig. 2 Topping and bottoming circuits. 1—power to drive com- vide a possibility of determining ‘‘the cooling losses.’’ Exergy
pressors, 2—work input to compressors principles and their applications are described by Szargut et al.

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 关2兴, Kotas 关3兴, and Moran and Sciubba 关4兴. The application of the
concept of exergy to an air-cooled gas turbine plant is illustrated
in Sections 3 and 4.
Having determined the temperatures and pressures at all points
of both circuits, as well as determined the quantity of heat re-
moved from the gas, conventional criteria of thermodynamic per-
formance may be used to illustrate how much work is done by the
gas and coolant.
The overall efficiency of the plant 共␩兲 may be written in terms
of the overall efficiencies ( ␩ g ) and ( ␩ c ) of the hypothetical top-
ping and bottoming plants:
W W g ⫹W c W g Q c W c
␩⫽ ⫽ ⫽ ⫹ ⫽ ␩ g⫹ ␹ c␩ c , (1)
F F F F Qc
where F is the fuel energy supplied and ␹ c ⫽Q c /F is the ratio of
the heat extracted from the topping plant to the fuel energy
supplied. Fig. 3 Exergy balance
This elementary equation may be illustrated for a sample gas
turbine plant. Details of the plant are given in Section 4. The plant
develops 167.4 MW. The efficiency of the plant, with the heat
supplied at 470.6 MW 共based on the lower calorific value of the where E Qg denotes the rate of exergy transfer accompanying the
fuel兲, is 0.356. The rate of work output from the topping plant is rate of heat transfer (Q c ) and represents the exergy waste due to
154.2 MW with a heat removed during expansion of 72.7 MW. heat rejection for the topping plant 共for the gas system兲. In terms
The bottoming plant is supplied with this heat and develops 13.2 of available energy E Qg represents the work potential of the heat
MW. rejected. The term E Dg accounts for the destruction of exergy due
The efficiencies of the topping and bottoming plants are ␩ g to irreversibilities within control volume X 共the combustion irre-
⫽154.2/470.6⫽0.328 and ␩ c ⫽13.2/72.7⫽0.182, respectively. versibility; frictional pressure drops in the combustion chamber
About 15.5 percent ( ␹ c ⫽72.4/470.6⫽0.155) of the fuel energy is and ducting; and frictional effects in flow through the turbine and
not converted into work by the topping plant, but is removed the compressor兲.
during the expansion and is supplied to the bottoming plant of the For control volume Y, the exergy balance may be written as
efficiency ␩ c ⫽0.182. Power output in the topping plant ( ␩ g
⫽0.328) plus bottoming plant power output (0.15* 0.182 M c0 e c in⫹E Qc ⫺E H ⫺W c ⫺M c0 e c out⫺E Dc ⫽0, (4)
⫽0.028) gives a total power output per unit energy of fuel sup- where E Qc represents the rate of exergy transfer with heat sup-
plied ␩⫽0.328⫹0.028⫽0.356. plied (Q c ) for the bottoming plant 共for the coolant system兲; the
On the other hand, should the gas turbine plant be able to op- term E Dc accounts for the destruction of exergy due to irrevers-
erate without cooling, the work output (W 0 ) would be greater by ibilities within control volume Y, the term E H represents the rate
⌬W g then that from the topping plant (W g ) and the efficiency of exergy transferred with heat extracted in an external cooler, if it
would be ␩ 0 ⫽W 0 /F⫽(W g ⫹⌬W g )/F⫽ ␩ g ⫹⌬ ␩ g . This is the takes place.
basic case which may be used as a comparison, in particular, to There are the following main sources of irreversibility within
enable the decrease in efficiency due to cooling to be determined: control volume Y: frictional effects in flows through compressors
␩ 0 ⫺ ␩ ⫽ ␩ 0 ⫺ ␩ g ⫺ ␹ c ␩ c ⫽⌬ ␩ g ⫺ ␹ c ␩ c . (2) and the turbine; frictional pressure drops in air pipes between
compressors and the turbine; and frictional pressure drop in cool-
At the same fuel heat input of 470.6 MW the following values ing passages 共coils in the hypothetical plant are the counterpart of
would be obtained: W 0 ⫽178.8 MW and ␩ 0 ⫽0.38. The decrease cooling passages in blades and vanes of a real turbine兲.
in the work output from the topping plant as a fraction of the fuel As pointed out above, for the topping plant the heat extracted
heat supplied would be ⌬ ␩ g ⫽(178.8⫺154.2)/470.6⫽0.052. Part (Q c ) is the waste heat and the exergy (E Qg ) transferred with this
of this lost work would be restored by the bottoming plant heat represents a waste of exergy. The bottoming plant is supplied
(W c /F⫽ ␹ c ␩ c ⫽0.028), thus the total decrease in efficiency of the with exergy input (E Qc ) derived from the topping plant. The
whole plant would be given by ⌬ ␩ g ⫺ ␹ c ␩ ⫽0.052⫺0.028 work output from the bottoming plant (W c ) is exergy in transit
⫽0.024. while the remainder of the supplied exergy is partly destroyed by
An important effect that must not be neglected is the reduction irreversibilities (E Dc ) and is partly discharged to the surroundings
in the work potential of the discharge exhaust gases. This would 共M c0 e c out and E H 兲.
be reflected directly in the loss of work output from the bottoming Since the transfer of heat between systems is not reversible, the
plant in which heat is supplied from the gas turbine exhaust. The term E DQ ⫽E Qg ⫺E Qc is the exergy destruction due to irrevers-
drop in the turbine exhaust temperature due to cooling is indirect ibility in transfer of heat. The rate of destruction of exergy
evidence that the work potential is decreased. For the considered (E DQ ⫹E Dc ), may be interpreted as the loss of work potential due
example, the reduction in this temperature is about 90°C. to cooling—‘‘the cooling losses.’’ To this value must be added
the amount of the destruction of exergy due to mixing (E D mix),
which inevitably occurs if two different gaseous components are
3 Applying Exergy Principles mixing. Finally, the rate of the destruction of exergy due to cool-
ing is
A simplified diagram of the plant shown in Fig. 2 is given in
Fig. 3. Symbols are defined in the figure. After expansion of each ED cool⫽E DQ ⫹E Dc ⫹E D mix . (5)
working fluid in its own turbine, they are mixed within control
volume Z. The creation of entropy of mixing is the same as in the The ratio of the destruction of exergy due to cooling (E D cool) to
real turbine. the supplied exergy of fuel is a measure of inefficiency of cooling
For each control volume the exergy balance may be written. technology.
For control volume X the exergy balance is The presented equations based on the use of straightforward
thermodynamics are intended for performance evaluation of the
M a e a in⫹M f e f in⫺W g ⫺M g e g out⫺E Qg ⫺E Dg ⫽0, (3) hypothetical gas turbine plant which may be regarded as a model

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 for an actual plant. But the science of thermodynamics is not bled air is cooled to 200°C by being passed through external cool-
sufficient to predict performance of a turbine with a finite number ers before being supplied to cooling channels. Maximum material
of stages at large velocities. temperature of vanes and blades is 800°C.
Heat transfer process between the gas and the coolant flows is Table 1 gives details of data obtained from step by step calcu-
more complicated in such turbines. Two processes, heat transfer lation of the gas turbine. The mean section performance of the
and mixing, go on simultaneously at large velocities. As the result stages was determined using experimental turbine loss data, the
of mixing the gas and the coolant flows exchange momentum, the gas-dynamic, thermodynamic, and heat transfer equations. To de-
coolant accelerating to the main flow velocity. The flux of the gas termine the heat flow into the each blade row, and the required
momentum drops and the flux of the coolant momentum in- cooling mass flow rate, the empirical Nusselt–Reynolds–Prandtl
creases. The dissipation of the kinetic energy therewith occurs. number relations given by Bodunov and Lokay 关1兴 were
The terms accounting for the change in momentum and for the employed.
destruction of exergy due to kinetic energy dissipation may be The results presented were obtained for convective vane and
added to Eqs. 共3兲 and 共4兲. blade cooling technology. It is assumed that the heat transferred
by convection is removed both from the nozzle rows at constant
stagnation pressure before expansion, and from the rotor rows at
4 Exergy Flow Diagram constant relative pressure before expansion. To simplify the
The exergy flow diagram may be used to illustrate the thermo- analysis, it is also assumed that specific ‘‘heat transferred from the
dynamic features of an air-cooled gas turbine plant and the dis- gas to the coolant by mixing’’ is equal to the stagnation enthalpy
cussed method. As an example, consider the gas turbine plant drop in the gas flow during the mixing process. It is worth em-
operating in the presence of an environment at the pressure of phasizing that this stagnation enthalpy drop does not correspond
0.1013 MPa and the temperature of 15°C. The relative humidity directly to the transferred heat, since there is, in addition, the
of ambient air is 60 percent. The condition for the inflow air at the change in the flux of momentum, that is, ‘‘work in transit’’ from
compressor is taken as ambient air condition. The turbine outlet the gas to the coolant flow.
stagnation pressure is assumed to be 0.1056 MPa 共the diffuser is Table 1 illustrates working fluid conditions, work and destruc-
outside control surface兲. The mass flow rate of the air entering the tion of exergy in the air-cooled gas turbine. The total amount of
compressor is 500 kg/s and the compressor pressure ratio is 15. exergy destroyed is 10.9⫹8.4⫹3.1⫹1.2⫽23.6 MW. The domi-
Air is extracted from the compressor at three points and from the nant factor is the irreversibility due to profile and secondary losses
compressor discharge to cool turbine balding. in flow through turbine cascades 共10.9⫹1.2⫽12.1 MW or 51 per-
Methane of chemical exergy 52172 kJ/kg is supplied to the cent of the total amount兲. The irreversibility involved in transfer
combustion chamber of 99.5 percent efficiency at a pressure of of heat between the gas and coolant flows is the second largest
2.28 MPa. The temperature at turbine inlet is 1260°C. The first factor: 8.4*100/23.6⫽36 percent of the total destruction of ex-
two of four stages in the turbine are cooled. Cooling air for the ergy. Destruction of exergy due to friction in cooling passages is
first stage vanes is supplied from the compressor discharge and for about 13 percent of the total one. 共The cooling air flows are as-
the other rows from intermediate compressor bleed points. The sumed to enter cooling passages at the local pressures 0.1 MPa
higher than those of the working fluid at inlet to the respective
cascades.兲
The rate of work of about 321.0 MW is obtained from the gas
Table 1 Working fluid conditions, work, destruction of exergy flow with the rate of heat removed of 72.7 MW. The coolant flow
in cooled gas turbine is supplied with this heat and produces 42.3 MW in the turbine
共about 11.6 percent of the total work developed兲.
The locations and magnitudes of destructions of exergy for the
gas turbine plant are given in Table 2. The values in the second
column are given as percentages of the exergy of the fuel sup-
plied. In the gas system, the largest irreversibility occurs in com-
bustion. The corresponding amount of exergy destroyed is about
29 percent of the fuel exergy supplied or about 86 percent of the
total value within the gas system. The most exergy destructions in
a combustion chamber can be reduced by raising the turbine inlet
temperature.
The 1.7 percent of fuel exergy supplied is destroyed between
the gas and coolant systems, and about the same value 共1.7 per-
cent兲 is destroyed within the coolant system. The former is due to
heat transfer over finite temperature difference, which takes place
between the gas and coolant streams, and may be reduced by

Table 2 Destruction of exergy in cooled gas turbine plant

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 Table 3 Exergy balances Table 3 shows exergy balances for each of system and for the
whole plant. Figure 4 shows the exergy flow diagram for such
plant. The exergy of the fuel supplied is taken as being 100 per-
cent. The specific exergy of ambient air is assigned to zero. The
destruction of exergy due to fuel throttling is added to that in the
combustion chamber.
The exergy balance indicates that 31.2 percent of the exergy of
fuel is converted into work by the gas system, about 33.9 percent
is destroyed within the system, and 11.3 percent is transferred to
the coolant system. The rest, 23.6 percent, is discharged with ex-
haust gas stream.
Since 1.7 percent of supplied fuel exergy is destroyed between
systems, 9.6 percent enters the coolant system, of which 2.7 per-
cent is obtained as work; 5.2 percent 共3.8 percent⫹1.4 percent
⫽5.2 percent兲 is discharged with exhaust stream and is transferred
with heat in coolers. The balance, 1.7 percent, is destroyed within
the system.
About 1.9 percent of supplied fuel exergy is destroyed due to
mixing of exhaust streams. This value was calculated from the
exergy balance for the mixing process, as shown in Fig. 3. The
chemical exergy of fuel and the thermal exergy of gases were
calculated in the way described by Shargut et al. 关2兴.
increasing blade heat exchange effectiveness. In the coolant sys- Thus the necessity to cool turbine blading in considered plant
tem, pressure losses can contribute significantly to the overall rate has led to the destruction of exergy in amount of 1.7 percent
of the destruction of exergy. This value is about of 24 percent ⫹1.7 percent⫹1.9 percent⫽5.3 percent of the fuel exergy supplied
共0.4*100 percent/1.7⫽24 percent兲 of the total one and may be and to the loss of exergy due to precooling in the amount of 1.4
minimized by selection, of optimum extraction points in the com- percent.
pressor. If coolant flows are cooled in external coolers, then there
is loss of exergy due to heat rejection. In the plant being consid-
ered, this loss is about 1.4 percent of the supplied fuel exergy. 5 Conclusions
In the thermodynamic sense, cooling losses are caused by irre-
versibilities which result from the modifications to the basic cycle
共circuit兲 to a turbine cool.
An air-cooled gas turbine plant may be treated as a plant in
which a combination of working fluids is used. A circuit on which
such a plant operates may be treated as a compound circuit com-
prising the open circuit with internal combustion and heat rejec-
tion during expansion, which is superposed directly on the other
circuit supplied with heat from the former. The latter uses a cool-
ant as working fluid.
Cooling losses derive both from the irreversible heat transfer
between circuits and from irreversible internal processes through
the coolant goes.
The type of analysis given in the paper for the simple air-cooled
gas turbine plant may be extend to any cooled gas turbine plant
that derives its energy from the combustion of organic fuel,
whether the system involves regeneration, reheat, or intercooling.
To this end, it is necessary to consider replacement of the existing
plant by the modified plant consisting of two plants. The first plant
produces work from the chemical energy of the fuel and uses air
and products of combustion as working fluids. The heat extracted
from products of combustion during the cooled expansion process
in one or more turbines is used as heat supply to the second plant
producing work and using the coolant as working fluid. The over-
all efficiency of the modified plant will be the same as that of a
considered plant.
The presented type of analysis may be interpreted by employ-
ing the concept of availability, allowing all irreversibilities to be
identified and quantified. No approach other than the exergy
method does appear to offer such possibilities for analyzing
cooled gas turbine plant.

Nomenclature
Q ⫽ heat
W ⫽ work
Fig. 4 Exergy flow diagram. 1, turbine. 2, compressors. 3, air M ⫽ mass flow rate
lines between compressors and turbine. 4, coolers ␩ ⫽ efficiency

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 E, e ⫽ flow exergy, specific flow exergy References
E D ⫽ destruction of exergy 关1兴 Bodunov, M. N., and Lokay, B. I., 1971, ‘‘The External Heat Transfer Coef-
Subscripts ficient,’’ High-Temperature Cooled Gas Turbines, Machinostroenye, Moscow,
pp. 23–44.
a ⫽ air 关2兴 Szargut, J., Morris D. R., and Steward, F. R., 1988, Exergy Analysis of
f ⫽ fuel Thermal, Chemical, and Metallurgical Processes, Hemisphere, New York.
关3兴 Kotas, T. J., 1985, The Exergy Method of Thermal Plant Analysis, Butter-
g ⫽ products of combustion 共gas兲; referring to the topping worths, London.
plant 关4兴 Moran, M. J., and Sciubba, E., 1994, ‘‘Exergy Analysis: Principles and Prac-
c ⫽ coolant; referring to the bottoming plant tice,’’ ASME J. Eng. Gas Turbines Power, 116, pp. 285–290.

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