Center for Advanced Energy Systems
Michael R. Muller, Director
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•
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Gas Turbine Problem Set
Problem 1:
The backwork ratio for a gas turbine is defined as the ratio of the work used to power the compressor to
the work produced by the turbine.
Consider a simple Brayton cycle using air as the working fluid, has a
pressure ratio of 12, has a maximum cycle temperature of 600
°
C, and operates the compressor inlet at 90
kPa, 15
°
C.
Which will have the greatest impact on the backwork ratio, a compressor efficiency of 90%
or a turbine efficiency of 90%?
Solution:
Using the isentropic process relations for an ideal gas gives
(
)
K
P
P
T
T
k
k
s
586
90
1080
288
4
.
1
/
4
.
0
/
1
1
2
1
2
=
⎟
⎠
⎞
⎜
⎝
⎛
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
−
Correcting this for the efficiency of the compressor gives
K
T
T
T
T
s
619
1
2
1
2
=
−
+
=
η
Similarly,
K
T
s
429
1080
90
873
4
.
1
/
4
.
0
4
=
⎟
⎠
⎞
⎜
⎝
⎛
=
Correcting this for the turbine efficiency
( )
K
T
T
T
T
s
t
473
4
3
3
4
=
−
−
=
Applying the first law to the two work interaction processes gives
()
( )
()
kg
kJ
w
kg
kJ
T
T
c
w
s
p
s
/
0
.
299
586
288
0035
.
1
/
6
.
445
429
873
0035
.
1
2
1
4
3
4
3
−
=
−
=
=
−
=
−
=
With a reversible compressor and turbine, the backwork ratio is
answer
r
bw
⇐
=
=
6710
.
0
6
.
445
0
.
299
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View Full DocumentCenter for Advanced Energy Systems
Michael R. Muller, Director
When the compressor is not reversible,
()
( )
kg
kJ
T
T
c
w
p
/
2
.
332
619
288
0035
.
1
2
1
2
1
−
=
−
=
−
=
and the backwork ratio becomes
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 Fall '10
 Muller
 Thermodynamics, Michael R. Muller, Advanced Energy Systems

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