Environmental Engineering Reference
In-Depth Information
Combustion products
T
Steam
w
Turbine
5
5
Steam
6
3
q
Steam
4
Water
Steam + Water
Fuel
2
1
q
6
2
Water
Air
1
s
Pump
Boiler
Condenser
Figure 3.3
The Rankine cycle is a steady flow cycle where water is turned to steam at high pressure in a
boiler
(
2
→
5
)
and then passes through a turbine to generate mechanical power
(
5
→
6
)
, after which the
steam is condensed to water
(
6
→
1
)
and pumped back into the boiler
(
1
→
2
)
. (In the
T
-
s
diagram on the
left, the area underneath the dashed line delineates the conditions where both steam and liquid water coexist,
in contrast to steam only to the right and liquid water to the left.)
may be expressed, through equation (3.18), as
5
5
6
v
w
t
=
h
5
−
h
6
=
dh
=
dp
6
There is a similar expression for the work required to operate the pump. The net work
w
produced
in the cycle may then be expressed as
p
b
p
c
(v
s
−
v
w
)
w
=
dp
(3.36)
where
v
w
are the specific volumes of the steam in the turbine and water in the pump and
p
b
and
p
c
are the boiler and condenser pressures. Because the specific volume of liquid water is
so much smaller than that of steam, the power to run the pump is only a tiny fraction of the power
produced by the turbine, a mechanically robust attribute of the Rankine cycle.
Because the heating and cooling processes of the ideal Rankine cycle (2
v
s
and
1) occur
at constant pressure while the work processes are isentropic, the thermodynamic efficiency may be
expressed as
→
5, 6
→
Tds
5
2
η
th
=
(
h
5
−
h
6
)
−
(
h
2
−
h
1
)
h
6
−
h
1
=
1
−
h
2
=
(3.37)
h
5
−
h
2
h
5
−
Tds
There are several aspects of the Rankine cycle that deserve notice. First of all, unlike the Carnot
cycle, its thermodynamic efficiency depends explicitly upon the properties of the working fluid,
water, as may be seen in Figure 3.3 and equation (3.37). Secondly, the cycle efficiency is increased
if the boiler pressure (and steam temperature) is increased. At the same time, high boiler pressures
increase the amount of work produced per unit mass of water flowing through the system, reducing
the cost of the turbine per unit of power output. The basic cycle is capable of improvements in
efficiency by use of internal heat exchange at intermediate pressure levels.
