Environmental Engineering Reference
In-Depth Information
T
3
Fuel
p
c
Combustion
products
2
Air
4
Air
Combustion
chamber
1
2
3
4
p
i
1
w
Compressor
Turbine
s
Figure 3.6
The Brayton cycle models the gas turbine cycle, where air is compressed from the inlet pressure
p
i
in a compressor to the outlet pressure
p
c
(
1
→
2
)
, then burned with fuel to a higher temperature at the
constant pressure
p
c
(
2
→
3
)
, and subsequently expanded in the turbine
(
3
→
4
)
, producing net work
w
.
and the compressor work,
w
=
(
h
3
−
h
4
)
−
(
h
2
−
h
1
)
(3.40)
The heat
q
added to the fluid leaving the compressor, which replicates the temperature rise caused
by adiabatic combustion, is just the increase in enthalpy in the constant pressure process,
=
h
3
−
q
h
2
(3.41)
As a consequence, the thermodynamic efficiency
η
th
of the Brayton cycle is
Tds
2
η
th
=
q
=
(
h
3
−
h
4
)
−
(
h
2
−
h
1
)
h
4
−
h
1
=
1
−
h
2
=
(3.42)
h
3
−
h
2
h
3
−
Tds
where the final expression on the right of equation (3.42) follows from the equality of constant-
pressure heat addition and
Tds
.
The thermodynamic efficiency of the ideal Brayton cycle depends upon the pressure ratio
p
4
and the thermodynamic properties of air and combustion products. For simplifying
assumptions about these properties, this efficiency may be expressed as
p
2
/
p
1
=
p
3
/
1
η
th
=
1
−
(3.43)
(
p
2
/
p
1
)
(
1
−
c
v
/
c
p
)
showing that the efficiency increases with increasing pressure ratio. For example, if the pressure
ratio
p
2
/
p
1
=
10 and
c
p
/
c
v
=
.
η
th
=
.
2%.
There are several practical problems in building a successful gas turbine power plant. The
power produced by the turbine, and usually that absorbed by the compressor, is each greater than
the net power output, so that the total power of this machinery is considerably greater than the
net output power. The aerodynamic efficiencies of the compressor and turbine need both be high
so that as much net power is produced as possible. The thermodynamic efficiency of the cy-
cle can be improved by increasing the turbine inlet temperature, but the latter is limited by the
1
3, then
41
