402
11 Power Gas Turbines
on the compressor path feature a somewhat higher pressure than on the turbine path.
We consider this pressure difference as necessary to bring the cooling air from the
compressor to the turbine. It is e.g. assumed in a first iteration that 90 % of the air
aspirated by the compressor is supplied to the combustion chamber, i.e. 10 % of the
air is used as cooling air. For a given air flow rate into the combustion chamber, the
fuel flow rate required to attain a specified turbine inlet temperature (TIT) can thus
be determined. The specific heat and the gas constant for the first expansion stage
can be determined that way. Cooling air is mixed with the gas at the end of each
stage. The gas composition changes and adapted values of specific heat and gas
constant are determined. The procedure is repeated for the further fictitious turbine
stages until the gas temperature reaches the allowable blade temperature. From that
point, calculations are performed without cooling, i.e. with κ= 0. When the expansion has been fully calculated, the air flow rate to be extracted from the compressor
at the various pressure levels is known. The air flow rate supplied to the combustion
chamber is recalculated and the foregoing procedure repeated until convergence is
attained. Thereafter, the power input to the compressor and the power output by the
turbine are calculated, taking the mass flow rates in the various stages into account.
11.3 Performance of Simple-Cycle Power Gas Turbines
11.3.1 Idealised Simple Cycle
In a simple-cycle gas turbine, the flow passes in sequence through a compressor, a
combustion chamber and a turbine. The main loss with this cycle is thermal in the
sense of unused heat in the exhaust gas of the turbine. Thermodynamic losses range
in second order. They encompass work dissipated into heat within the compressor
and the turbine and the work loss by cooling of the turbine. Mechanical losses in the
work transfer from the turbine to the compressor and to the external load range in
third order. To estimate the influence of the various losses, we first analyse a cycle
with only thermal loss, i.e. η ∞c = η ∞t = η m = 1 and κ= 0 and with unchanged fluid in
the cycle.
Atmospheric conditions: p 0 0
,T .
Compressor (1→2):
Combustion chamber (2→3):
We adopt the simplification that there is no change in mass flow rate and in heat
capacity of the gas.
r p
p
p
p
02
01
02
0
= = /
/ ,
1
01
02
01
02
02
02
(
)
(1
)
(1
).
c
p
p
p
T
W c T
T
c T
c T
r
T
g
g
−
−
=
−
=
−
=
−
∆Q c T
T
p
=
−
(
) .
03
02
11 Power Gas Turbines
on the compressor path feature a somewhat higher pressure than on the turbine path.
We consider this pressure difference as necessary to bring the cooling air from the
compressor to the turbine. It is e.g. assumed in a first iteration that 90 % of the air
aspirated by the compressor is supplied to the combustion chamber, i.e. 10 % of the
air is used as cooling air. For a given air flow rate into the combustion chamber, the
fuel flow rate required to attain a specified turbine inlet temperature (TIT) can thus
be determined. The specific heat and the gas constant for the first expansion stage
can be determined that way. Cooling air is mixed with the gas at the end of each
stage. The gas composition changes and adapted values of specific heat and gas
constant are determined. The procedure is repeated for the further fictitious turbine
stages until the gas temperature reaches the allowable blade temperature. From that
point, calculations are performed without cooling, i.e. with κ= 0. When the expansion has been fully calculated, the air flow rate to be extracted from the compressor
at the various pressure levels is known. The air flow rate supplied to the combustion
chamber is recalculated and the foregoing procedure repeated until convergence is
attained. Thereafter, the power input to the compressor and the power output by the
turbine are calculated, taking the mass flow rates in the various stages into account.
11.3 Performance of Simple-Cycle Power Gas Turbines
11.3.1 Idealised Simple Cycle
In a simple-cycle gas turbine, the flow passes in sequence through a compressor, a
combustion chamber and a turbine. The main loss with this cycle is thermal in the
sense of unused heat in the exhaust gas of the turbine. Thermodynamic losses range
in second order. They encompass work dissipated into heat within the compressor
and the turbine and the work loss by cooling of the turbine. Mechanical losses in the
work transfer from the turbine to the compressor and to the external load range in
third order. To estimate the influence of the various losses, we first analyse a cycle
with only thermal loss, i.e. η ∞c = η ∞t = η m = 1 and κ= 0 and with unchanged fluid in
the cycle.
Atmospheric conditions: p 0 0
,T .
Compressor (1→2):
Combustion chamber (2→3):
We adopt the simplification that there is no change in mass flow rate and in heat
capacity of the gas.
r p
p
p
p
02
01
02
0
= = /
/ ,
1
01
02
01
02
02
02
(
)
(1
)
(1
).
c
p
p
p
T
W c T
T
c T
c T
r
T
g
g
−
−
=
−
=
−
=
−
∆Q c T
T
p
=
−
(
) .
03
02