Gas Turbine Cycles - 5.pptx

Joule or Brayton Cycle contd..
 Air is the working fluid.
 Analysis done under steady flow conditions.
 Heat is transferred under constant pressure.
 Ideal efficiency is appreciably less than the Carnot
efficiency.
 Magnitude of compressor work is an appreciable
proportion of that of the expansion work.
 Hence work ratio is considerably less than unity.
 Has lower ideal efficiency than the Rankine cycle.
 Much more susceptible to irreversibilities.
 Applied in closed-cycle gas turbine cycles. 3

Open Cycle Gas Turbine Plant
 Source of energy is generally provided by the
combustion of fuel in air.
 Also known as the Internal-combustion Gas
Turbine.
4

Open Cycle Gas Turbine Plant
contd..
 Fuel is burned in the internal-combustion
chamber.
 Turbine exhaust gases are rejected to the
atmosphere.
 Plant is less bulky and less expensive than
an equivalent vapour power plant with its
large boiler and condenser.
 Small in size and low weight.
 Particularly used for aircraft propulsion. 5

Comparison of Open and Closed
Cycle Gas Turbine Plants
6
Closed Cycle Open Cycle
Working fluid is air. Working fluid is products of
combustion.
Fuel consumed externally while heat
is transferred to raise the
temperature of air.
Fuel consumed internally while air
changes to combustion products.
Turbine outlet is exhausted to a
cooler.
Turbine outlet is exhausted to the
atmosphere.
Compressor receives air from the
cooler.
Compressor receives air from the
atmosphere.

Analysis of simple Gas Turbine
cycles
 Assumptions
 Air standard cycles (Air is the working
fluid).
 Air has constant specific heat capacity.
 Kinetic energy of the working fluid is
same at both inlet and outlet of each
component of the cycle.
7

Simple Gas Turbine cycles contd..
8
)
(
)
(
|
| 1
2
1
2
12 T
T
c
h
h
W p 



Compressor Work
Turbine Work
)
(
)
(
|
| 4
3
4
3
34 T
T
c
h
h
W p 




9
)
(
)
(
|
| 2
3
2
3
23 T
T
c
h
h
Q p 



Heat supplied during the cycle
Cycle Efficiency
|
|
|
|
|
|
23
12
34
Q
W
W 


   
 
2
3
1
2
4
3
T
T
T
T
T
T







10
4
3
1
2
p
p
p
p
rp 

Cycle temperatures can be related to the pressure ratio
For isentropic compression and expansion
 



1
1
1











p
r
 

 1
1
2

 p
r
T
T and
 

 1
4
3

 p
r
T
T
Ideal air-standard efficiency

11
|
|
|
|
|
|
34
12
34
W
W
W
rw


Work ratio
   
 
4
3
1
2
4
3
T
T
T
T
T
T
rw





 

 1
3
1
1


 p
w r
T
T
r

12
   
1
2
4
3
|
| T
T
c
T
T
c
W p
p 



Net output per unit mass
 
 





 

















1
1
1
3 1
1
1
|
| p
p
p
p r
T
c
r
T
c
W
Taking T1 and T3 as constants and differentiating
with respect to rp and equating d|W|/drp to zero, it
can be shown that for maximum work output
 
1
2
1
3












T
T
rp

Effect of losses in Turbine and Compressor
13

Gas Turbine cycles with Heat Exchange
 With normal values of pressure ratio and
turbine inlet temperature, the turbine outlet
temperature is always above the
compressor outlet temperature.
 Improvement in cycle performance through
heat exchange.
 Transfers heat from the gas leaving the
turbine to the air, before it enters the
combustion chamber.
14

Gas Turbine cycles with Heat
Exchange contd..
Amount of heat required from an external source
15
   
4
3
3
3 T
T
c
T
T
c
Q p
x
p
x 




Gas Turbine cycles with Heat Exchange
 Ideal air standard efficiency
16
 



1
3
1
1


 p
r
T
T
 We obtain
 
1
2
1
3












T
T
rp
 When T2 = T4, heat exchanger becomes superfluous and
becomes a simple gas turbine plant.
 By equating this to simple ideal gas turbine plant efficiency,
 



1
1
1











p
r
 This is the optimum pressure ratio for maximum work
output.

Gas Turbine cycles with Heat
Exchange contd..
17
 If a heat exchanger is to be used, a
pressure ratio somewhat less than the
optimum must be adopted.
 In practice the heat exchanger is never
perfect and the actual temperature Tx
reached by compressed air is always less
than T4.

Inter-cooling & Re-heating
18
 Addition of a heat exchanger improves the
ideal cycle efficiency but does not improve
the work ratio.

Inter-cooling & Re-heating contd..
19
 If the compression is carried out in two
stages, 1 - 3 and 4 - 5, with the air cooled at
constant pressure pi between the stages,
some reduction in compression work can be
obtained.
 (T3 –T1) + (T5 –T4) < (T2 –T1)
 Ideally it is possible to cool the air to
atmospheric temperature (T4 =T1) and in
this case the inter-cooling is said to be
complete.

20
 With isentropic compression and complete
inter-cooling the compression work is
 Saving in work will depend on the choice of
the inter-cooling pressure pi.
   
4
5
1
3
|
| T
T
c
T
T
c
W p
p 



   










































1
1
|
|
1
2
1
1
1
1




i
p
i
p
p
p
T
c
p
p
T
c
W

21
 By equating d|W|/dpi to zero, the condition
for minimum work is found to be
 Hence or
 Therefore for minimum compressor work,
the compression ratios and work inputs for
the two stages are equal.
 
2
1 p
p
pi 
pi
i
i
r
p
p
p
p

 2
1
p
pi r
p
p
r 









1
2

22
 The compression work can be reduced
further by increasing the number of stages
and inter-coolers.
 However the additional complexity and cost
make more than two or three stages
uneconomical.
 It is possible to generalize the expression
for the minimum compression work to cover
n stages and to show that the pressure
ratios in all stages must be equal.

23

24
 Re-heating is employed in gas turbine
plants principally to increase the work ratio
and hence the specific work output and
decrease the effect of component losses.
 Expansion in the turbine in two stages with
re-heating to the metallurgical limit (T9 =T6)
is considered.
 Magnitude of the turbine work is increased
from |W67| to
   
10
9
8
6
10
,
9
8
,
6 |
|
|
| T
T
c
T
T
c
W
W p
p 





25
 It is possible to show that with isentropic
expansion the optimum intermediate pressure for
maximum work output is given by
or
 Re-heating can also be extended to more than two
stages, although this is seldom done in practice,
and with open-cycle plant a limit is set by the
oxygen available for combustion.
 
7
6 p
p
pi  p
pi r
r 

26
 Although inter-coolers and re-heaters improve the
work ratio, these devices by themselves can lead
to a decrease of ideal cycle efficiency.
 The full advantage is only realized if a heat
exchanger is also included in the plant as shown
in the figure below.
 Additional heat required for the colder air leaving
the compressor can then be obtained from the
hotter exhaust gases, and there is a gain in ideal
cycle efficiency as well as work ratio.

27

28
 The figure shows a cycle with large number of
stages (multi-stage compression and expansion,
with inter-cooling, re-heating, and heat exchange)

29
 It is evident that with an infinite number of stages
this cycle would have all its heat addition at the
upper temperature T3 and all its heat rejected at
the lower temperature T1.
 The compression and expansion processes
become isothermals, and the efficiency of the
cycle equals to the Carnot efficiency.
 This cycle is called the Ericsson cycle.

Closed Cycle Gas Turbine
30
 The system may be pressurized so that the size
of all components can be reduced for the same
mass flow rate.
 With a pressurized system it is possible to
accommodate changes in load by varying the
mass flow rate of fluid in the circuit instead of
reducing the turbine inlet temperature.
 Coal or oil of poor quality can be used as a fuel
since the combustion gases do not pass through
the turbine.

Gas Turbine Cycles - 5.pptx

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