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