390
11 Power Gas Turbines
The similar result for an isentropic process is
So:
The obtained efficiency is termed polytropic efficiency. By convention it may also
be applied to entire stages and the entire compressor by
(11.12)
Assuming that the compression can be represented as polytropic, we calculate for
an ideal and perfect gas (Fig. 11.11, left) the following quantities.
Isentropic work (  isentropic head):
Reversible part of the work (  polytropic head):
Work available with isentropic re-expansion (  isentropic re-expansion head ):
With
Total work:
2
1
2s
1
1 ln( p / p ) ln( T / T ).
g
g
−
=
2s
1
2s
1
2
1
2
1
ln( T ) ln( T ) ln( h ) ln( h ) .
ln( T ) ln( T )
ln( h ) ln( h )
h ∞
−
−
=
=
−
−
02s
01
p
02
01
ln( h ) ln( h ) .
ln( h ) ln( h )
h
−
=
−
1
1
2s
2s
2
1
1
1
1
2
s
1
1
1
1
1
1
1
1
1
1
p
p
p
p
1
p
p
p
h
dp
d(
)
(
) d(
)
[(
)
1].
p
p
p
1
p
g
g
g
r
g
D
r
r
r
r
g
r
−
−
=
=
=
=
−
−
∫
∫
∫
1
n 1
2
2
1
1
2
n
n
r
1
1
1
1
1
1
1
p
p
p
1
p
p
n
h
dp
(
) d(
)
[(
)
1].
p
p
n 1
p
D
r
r
r
−
−
=
=
=
−
−
∫
∫
1
3s
2
1
sre
2
2
2
p
p
1
h
dp
[(
)
1].
1
p
g
g
g
D
r
g
r
−
= −
= −
−
−
∫
1
2
n
2
1
1
1
1
1
2
2
1
2
n
sre
1
1
2
1
1 1
1
n
1
2
2
1
1
1
p
(
) :
p
p p
p
p
h
(
) (
) [1 (
)
]
1
p
p
p
p p
p
(
)
[(
)
1].
1
p
p
g
g
g
g
g
g
g
r
r
g
D
g
r
g
g
r
−
−
−
−
−
=
= −
−
−
=
−
−
n 1
2
1
2
n
p 2
1
p 1
1
1
1
T
p
p
h C ( T T ) C T (
1 )
[(
)
1].
T
1
p
g
D
g
r
−
=
−
=
− =
−
−