Environmental Engineering Reference
In-Depth Information
available to convert to work by use of an array of Carnot engines. It is the maximum possible
work that can be generated if the fuel is burned at constant ambient pressure when the ambient
environment temperature is
T
c
.
If we assume that the constant-pressure specific heat of product gas is constant, then equation
(3.34) may be integrated to find the thermodynamic efficiency
η
,
ln
(
T
ad
/
T
c
)
η
=
1
−
(3.35)
(
T
ad
/
T
c
)
−
1
For the values of
T
ad
=
2173 K and
T
c
=
η
=
298 K used above,
68%. While this is an improve-
ment on the previous case [equation (3.33),
η
=
46%], it is still lower than the Carnot efficiency
of 86.3% for
T
h
2173 K. Evidently, considerable complication is required to boost ideal ther-
modynamic efficiencies for fossil-fueled cycles above 50%, and there is little hope of approaching
the Carnot efficiency at the adiabatic flame temperature. The Carnot cycle is an important guide to
understanding how a simple heat engine might work, but it is not a very practical cycle.
=
3.10.2
The Rankine Cycle
From the beginning of the industrial revolution until the eve of the twentieth century, most me-
chanical power generated by the burning of fossil fuel utilized the steam cycle, called the Rankine
cycle. In a steam power plant, fuel mixed with air is burned to heat water in a boiler to convert it
to steam, which then powers a turbine. This is an external combustion system where the working
fluid, water/steam, is heated in pipes that are contacted by hot flue gas formed in the combustion
chamber of the furnace. In an efficient steam plant, nearly all the fuel's heating value is transferred
to the boiler fluid, but of course only part of that amount is converted to turbine work. The steam
cycle is mechanically robust, providing mechanical power even when the boiler and turbine are
not perfectly efficient, accounting for its nearly universal use through the end of the nineteenth
century.
15
The thermodynamic processes of the Rankine cycle are illustrated in Figure 3.3, showing (on
the left) the changes in temperature and entropy that the working fluid undergoes. In a steam power
plant, ambient temperature water is pumped to a high pressure and injected into a boiler (1
2
in Figure 3.3), whereupon it is heated to its boiling point (3), completely turned into steam (4),
and then usually heated further to a higher temperature (5). This heating within the boiler occurs
at a constant high pressure
p
b
. The stream of steam flows through a turbine (5
→
6) undergoing a
pressure reduction to a much lower value,
p
c
, while the turbine produces mechanical power. The
low-pressure steam leaving the turbine is cooled to an ambient temperature liquid in the condenser
(6
→
1) and then pumped into the boiler to complete the cycle.
In the idealized Rankine cycle of Figure 3.3, the adiabatic steady flow work per unit mass of
steam
→
h
6
across the turbine, by
virtue of the first law equation (3.20). As this is ideally an isentropic process, the enthalpy change
w
t
produced by the turbine is equal to the enthalpy change
h
5
−
15
Among the earlier American automobiles was the Stanley steamer, powered by a Rankine cycle engine.
Although it established a speed record in its day, it was soon surpassed by the more practical gasoline engine.
