404
11 Power Gas Turbines
the heat capacity of the combustion gas with respect to that of air, if constant values
of heat capacities are used. The adapted relations are listed hereafter. The subscripts
a and g refer to the air and the combustion gas. The subscripts c and t refer to the
compressor and the turbine.
Compressor (1 → 2):
Turbine (3 → 4):
Combustion chamber (2 → 3):
(11.35)
We adopt the simplification that there is no change in mass flow rate. The inlet
temperature of the compressor is taken as the reference temperature for the lower
heating value of the fuel, which comes from the point of view that heating is meant
for increasing the work capacity of the fluid, already realised by the compression.
The efficiency is
(11.36)
In principle, the values of the differential heat capacities of the combustion gas
in the combustion chamber equation and the turbine equation have to be different, as these are averages over a different temperature range. For the combustion
chamber γ ≈ 1.32 and for the turbine γ ≈ 1.30. We take here an average, which then
means c
R
c
R
pg
pa
/
.
/
.
≈
=
4 25
3 50
. For the compressor, we take γ = 1.40, so that c
R
pa /
.
= 3 50.
Table 11.5 illustrates the influence of the different parameters. The temperature ratio T T
03
01
/
is set at 5 and 6, corresponding to T 03 equal to 1440 K (= 1167 °C) and
1728 K (= 1455 °C) with T 01 equal to 288 K. The first part of Table 11.5 reproduces
the results obtained by the analysis of the previous section. The second part illustrates the efficiency drop caused by the increase of the heat capacity due to the
combustion. The reduction factor of the efficiency is about 85 %. The results also
show that efficiency becomes somewhat dependent on the temperature ratio. The
efficiency benefits from a higher temperature at the turbine inlet. The third part
02
02
01
01
01
01
(
)
(
1)
(
1).
c pa
R
c
c
pa
pa
p a
T
W c T
T
c T
c T r
T
h ∞
=
−
=
− =
−
03
04
03
(
)
(1
).
t
pg
R
c
t
p g
pg
W c T
T
c T
r
h ∞
−
=
−
=
−
∆Q c T
T
c T
T
pg
pa
=
−
−
−
(
)
(
) .
03
01
02
01
03
01
03
01
(1
) (
1)
.
(
1) (
1)
t
c pa
pg
c pa
R
R
c
c
pg
pa
R
c
pg
pa
c T
r
r
c T
c
T
r
c
T
h
h
h
h
∞
∞
∞
−
−
−
−
=
− −
−
11 Power Gas Turbines
the heat capacity of the combustion gas with respect to that of air, if constant values
of heat capacities are used. The adapted relations are listed hereafter. The subscripts
a and g refer to the air and the combustion gas. The subscripts c and t refer to the
compressor and the turbine.
Compressor (1 → 2):
Turbine (3 → 4):
Combustion chamber (2 → 3):
(11.35)
We adopt the simplification that there is no change in mass flow rate. The inlet
temperature of the compressor is taken as the reference temperature for the lower
heating value of the fuel, which comes from the point of view that heating is meant
for increasing the work capacity of the fluid, already realised by the compression.
The efficiency is
(11.36)
In principle, the values of the differential heat capacities of the combustion gas
in the combustion chamber equation and the turbine equation have to be different, as these are averages over a different temperature range. For the combustion
chamber γ ≈ 1.32 and for the turbine γ ≈ 1.30. We take here an average, which then
means c
R
c
R
pg
pa
/
.
/
.
≈
=
4 25
3 50
. For the compressor, we take γ = 1.40, so that c
R
pa /
.
= 3 50.
Table 11.5 illustrates the influence of the different parameters. The temperature ratio T T
03
01
/
is set at 5 and 6, corresponding to T 03 equal to 1440 K (= 1167 °C) and
1728 K (= 1455 °C) with T 01 equal to 288 K. The first part of Table 11.5 reproduces
the results obtained by the analysis of the previous section. The second part illustrates the efficiency drop caused by the increase of the heat capacity due to the
combustion. The reduction factor of the efficiency is about 85 %. The results also
show that efficiency becomes somewhat dependent on the temperature ratio. The
efficiency benefits from a higher temperature at the turbine inlet. The third part
02
02
01
01
01
01
(
)
(
1)
(
1).
c pa
R
c
c
pa
pa
p a
T
W c T
T
c T
c T r
T
h ∞
=
−
=
− =
−
03
04
03
(
)
(1
).
t
pg
R
c
t
p g
pg
W c T
T
c T
r
h ∞
−
=
−
=
−
∆Q c T
T
c T
T
pg
pa
=
−
−
−
(
)
(
) .
03
01
02
01
03
01
03
01
(1
) (
1)
.
(
1) (
1)
t
c pa
pg
c pa
R
R
c
c
pg
pa
R
c
pg
pa
c T
r
r
c T
c
T
r
c
T
h
h
h
h
∞
∞
∞
−
−
−
−
=
− −
−