Four processes:
Energy Analysis of the Ideal Rankine Cycle
Steady-flow energy equation
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DEVIATION OF ACTUAL VAPOR POWER
CYCLES FROM IDEALIZED ONES
The actual vapor power cycle differs from the ideal
Rankine cycle as a result of irreversibilities in various
components.
Fluid friction and heat loss to the surroundings are the
two common sources of irreversibilities.
Isentropic efficiencies
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(a) Deviation of actual vapor power cycle from the
ideal Rankine cycle.
(b) The effect of pump and turbine irreversibilities on
the ideal Rankine cycle.
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HOW CAN WE INCREASE THE EFFICIENCY OF THE
RANKINE CYCLE?
The basic idea behind all the modifications to increase
the thermal efficiency of a power cycle is the same:
Increase the average temperature at which heat is
transferred to the working fluid in the boiler, or
decrease the average temperature at which heat is
rejected from the working fluid in the condenser.
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Lowering the Condenser Pressure (Lowers Tlow,avg)
To take advantage of the increased
efficiencies at low pressures, the
condensers of steam power plants
usually operate well below the
atmospheric pressure. There is a
lower limit to this pressure depending
on the temperature of the cooling
medium
Side effect: Lowering the condenser
pressure increases the moisture
content of the steam at the final
stages of the turbine.
The effect of lowering the condenser pressure on the ideal
Rankine cycle.
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1. An increase in net work output as a result of
lowering the condenser pressure since ( h3-h4 >
h3-h4’)
2. The increase in the heat added is negligible
3. The thermal efficiency increases
Superheating the Steam to High Temperatures
(Increases Thigh,avg)
Both the net work and heat input increase as a result
of superheating the steam to a higher temperature.
The overall effect is an increase in thermal efficiency
since the average temperature at which heat is added
increases.
Superheating to higher temperatures decreases the
moisture content of the steam at the turbine exit,
which is desirable.
The temperature is limited by metallurgical
considerations. Presently the highest steam
temperature allowed at the turbine inlet is about
620°C.
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The effect of superheating the steam to higher
temperatures on the ideal Rankine cycle.
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1. Both the net work and heat input increase as
a result of superheating the steam to a higher
temperature.
2. Generally, increases the thermal efficiency
3. It decreases the moisture content of the
steam at the turbine exit
4. Superheating is limited by metal
stress
Increasing the Boiler Pressure (Increases Thigh,avg)
For a fixed turbine inlet temperature, the cycle shifts
to the left and the moisture content of steam at the
turbine exit increases. This side effect can be
corrected by reheating the steam.
The effect of increasing the boiler pressure on the
ideal Rankine cycle. 20
1. the moisture content of steam at the turbine exit
increases.
2. Both the net work and heat input increase as a
result of superheating the steam to a higher
temperature.
3. Generally, increases the thermal efficiency
4. Increasing boiler pressure is
limited by metal stress
Today many modern steam
power plants operate at
supercritical pressures (P >
22.06 MPa) and have
thermal efficiencies of about
40% for fossil-fuel plants
and 34% for nuclear plants.
A supercritical Rankine cycle.
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Expand the steam in the turbine in two stages, and
reheat it in between.
Reheating is a practical solution to the excessive
moisture problem in turbines, and it is commonly
used in modern steam power plants.
THE IDEAL REHEAT RANKINE CYCLE
How can we take advantage of the increased efficiencies
at higher boiler pressures without facing the problem of
excessive moisture at the final stages of the turbine?
1. Superheat the steam to very high temperatures. It is
limited metallurgically.
2. Expand the steam in the turbine in two stages, and
reheat it in between (reheat)
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The ideal reheat Rankine cycle.
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The single reheat in a modern power plant improves the
cycle efficiency by 4 to 5% by increasing the average
temperature at which heat is transferred to the steam.
The average temperature during the reheat process can be
increased by increasing the number of expansion and
reheat stages. As the number of stages is increased, the
expansion and reheat processes approach an isothermal
process at the maximum temperature. The use of more than
two reheat stages is not practical. The theoretical
improvement in efficiency from the second reheat is about
half of that which results from a single reheat.
The reheat temperatures are very close or equal to the
turbine inlet temperature.
The optimum reheat pressure is about one-fourth of the
maximum cycle pressure.
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The average temperature at which heat is transferred
during reheating increases as the number of reheat
stages is increased.
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solution
