Transcript Chapter 10: Vapor and Combined Power Cycles

Chapter 10
Vapor and Combined Power Cycles
Introduction
Vapour power cycles in which the working fluid is alternatively
vaporized and condensed.
Steam is the most common working fluid used in vapor power
cycles because of its many desirable characteristics, such as low
cost, availability, and high enthalpy of vaporization.
Steam power plants are commonly referred to as coal plants,
nuclear plants, or natural gas plants, depending on the type of fuel
used to supply heat to the steam.
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Introduction
The steam power plant is composed of several distinct components:
1.
2.
3.
4.
Steam generator or boiler.
Turbine and electric generator.
Condenser and cooling water system.
Pumps.
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Introduction
Photo courtesy of Progress Energy Carolinas, Inc.
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10–1 THE CARNOT VAPOR CYCLE
Carnot cycle is the most efficient cycle operating between two specified
temperature limits.
We consider power cycles where the working fluid undergoes a phase change.
The best example of this cycle is the steam power cycle where water (steam) is
the working fluid.
 th , Carnot
Wnet
Qout

 1
Qin
Qin
 1
TL
TH
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10–1 THE CARNOT VAPOR CYCLE
Several impracticalities are associated with the Carnot cycle:
The compression of
a liquid–vapor
mixture.
The quality
of the steam
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10–1 THE CARNOT VAPOR CYCLE
Several impracticalities are associated with the Carnot cycle:
Isentropic
compression to
extremely high
pressures.
Isothermal heat
transfer at variable
pressures
10–1 THE CARNOT VAPOR CYCLE
Reasons why the Carnot cycle is not used:
• Pumping process 1-2 requires the pumping of a mixture of saturated
liquid and saturated vapor at state 1 and the delivery of a saturated liquid
at state 2.
• To superheat the steam to take advantage of a higher temperature,
elaborate controls are required to keep TH constant while the steam
expands and does work.
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10–2 Rankine Cycle
To resolve the difficulties associated with the Carnot cycle, the Rankine cycle
was devised.
Rankine cycle is the ideal cycle for vapor power plants.
Ideal Rankine Cycle Processes
Process
1-2
2-3
3-4
4-1
Description
Isentropic compression in pump
Constant pressure heat addition in boiler
Isentropic expansion in turbine
Constant pressure heat rejection in condenser
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10–2 Rankine Cycle
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10–2 Rankine Cycle
10–2 Rankine Cycle
Example 10-1
Compute the thermal efficiency of an ideal Rankine cycle for which steam
leaves the boiler as superheated vapor at 6 MPa, 350oC, and is condensed
at 10 kPa.
We use the power system and T-s diagram
shown above.
P2 = P3 = 6 MPa = 6000 kPa
T3 = 350oC
P1 = P4 = 10 kPa
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10–2 Rankine Cycle
Pump
Since the ideal pumping
process 1-2 is isentropic,
ds = 0.
Using the steam tables
kJ

h1  h f  191.81

kg
P1  10 kPa  

Sat. liquid  
m3
v  v f  0.00101
 1
kg
The pump work is calculated from
 1 ( P2  P1 )
W pump  m (h2  h1 )  mv
The incompressible liquid
assumption allows
v  v1  const .
h2  h1  v1 ( P2  P1 )
w pump 
W pump
m
 v1 ( P2  P1 )
w pump  v1 ( P2  P1 )
m3
kJ
 0.00101 (6000  10) kPa 3
kg
m kPa
kJ
 6.05
kg
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10–2 Rankine Cycle
Boiler
To find the heat supplied in the boiler, we apply the steady-flow conservation of
mass and energy to the boiler. If we neglect the potential and kinetic energies, and
note that no work is done on the steam in the boiler, then:
kJ

We find the
h

3043.9
3
properties at
P3  6000 kPa  
kg

state 3 from the

o
T

350
C
3
  s  6.3357 kJ
superheated
3

tables as
kg  K

h2  wpump  h1
kJ
kJ
 191.81
kg
kg
kJ
 197.86
kg
 6.05
10–2 Rankine Cycle
Turbine
The turbine work is obtained from the application of the conservation of mass
and energy for steady flow. We assume the process is adiabatic and reversible
and neglect changes in kinetic and potential energies.
m 3  m 4  m
m h  W  m h
3 3
turb
4 4
Wturb  m (h3  h4 )
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10–2 Rankine Cycle
Turbine
We find the properties at state 4 from the steam tables by noting s4 = s3 = 6.3357 kJ/kg-K.
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10–2 Rankine Cycle
Turbine
The turbine work per unit mass is
wturb  h3  h4
kJ
 (3043.9  2005.0)
kg
kJ
 1038.9
kg
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10–2 Rankine Cycle
Cycle
The net work done by the cycle is
wnet  wturb  wpump
kJ
 (1038.9  6.05)
kg
kJ
 1032.8
kg
The thermal efficiency is
kJ
1032.8
wnet
kg
th 

kJ
qin
2845.1
kg
 0.363 or 36.3%
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10–3 Deviation of actual vapour power cycles
Piping losses--frictional effects reduce the available energy content of the steam.
Turbine losses--turbine isentropic (or adiabatic) efficiency.
P3
T
3
turb
4a
wactual
h3  h4 a


wisentropic h3  h4 s
P4
h4a  h3  turb (h3  h4 s )
4s
s
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10–3 Deviation of actual vapour power cycles
Pump losses--pump isentropic (or adiabatic) efficiency.
2a
T
P2
2s
 pump 
P1
1
wisentropic
wactual
h2 a  h1 

1
 pump
h2 s  h1
h2 a  h1
(h2 s  h1 )
s
Condenser losses--relatively small losses that result from cooling the condensate
below the saturation temperature in the condenser.
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10–3 Deviation of actual vapour power cycles
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10–3 Deviation of actual vapour power cycles
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10–3 Deviation of actual vapour power cycles
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10–4 Increasing the efficiency of the Rankine cycle
Ways to improve the simple Rankine cycle efficiency:
1. Superheat the vapor:
Average temperature is higher during heat addition.
Moisture is reduced at turbine exit (we want x4 in the above example > 85
percent).
The temperature to which steam can be
superheated
is
limited,
however,
by
metallurgical considerations. Any increase in
this value depends on improving the present
materials: Ceramics are very promising in
this regard.
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10–4 Increasing the efficiency of the Rankine cycle
Ways to improve the simple Rankine cycle efficiency:
2. Increase boiler pressure (for fixed
maximum temperature):
Availability of steam is higher at higher
pressures,
however,
the
moisture
is
increased at turbine exit.
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10–4 Increasing the efficiency of the Rankine cycle
Ways to improve the simple Rankine cycle efficiency:
3. Lower condenser pressure:
Less energy is lost to surroundings.
Drawbacks: it increases the moisture
content of the steam at the final stages of
the turbine, also it creates the possibility of
air leakage into the condenser.
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10–4 Increasing the efficiency of the Rankine cycle
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10–5 The ideal reheat Rankine cycle:
To increase the efficiency at higher boiler pressures:
Superheat the steam to very high temperatures before it enters the turbine.
Expand the steam in the turbine in two stages, and reheat it in between.
The reheat cycle allows the use of higher boiler pressures and provides a means
to keep the turbine exit moisture (x > 0.85 to 0.90) at an acceptable level.
10–5 The ideal reheat Rankine cycle:
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10–5 The ideal reheat Rankine cycle:
The average temperature at which heat is transferred during
reheating increases as the number of reheat stages is increased.
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10–5 The ideal reheat Rankine cycle:
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10–6 The ideal Regenerative Rankine cycle:
The first part of the heat-addition process in the
boiler takes place at relatively low temperatures.
10–6 The ideal Regenerative Rankine cycle:
A practical regeneration process in steam power plants is accomplished by
extracting, or “bleeding,” steam from the turbine at various points.
This steam, which could have produced more work by expanding further in the
turbine, is used to heat the feedwater instead.
To improve the cycle thermal efficiency, the average temperature at which heat is
added must be increased.
The device where the feedwater is heated by regeneration is called a regenerator,
or a feedwater heater (FWH).
10–6 The ideal Regenerative Rankine cycle:
By allowing the steam to leave the boiler to expand the steam in the turbine to an
intermediate pressure. A portion of the steam is extracted from the turbine and sent
to a regenerative heater to preheat the condensate before entering the boiler. This
approach increases the average temperature at which heat is added in the boiler.
However, this reduces the mass of steam expanding in the lower- pressure stages of
the turbine, and, thus, the total work done by the turbine. The work that is done is
done more efficiently.
The preheating of the condensate is done in a combination of open and closed
heaters:
1. Open Feedwater Heaters:
The extracted steam and the condensate are physically mixed.
2. Closed Feedwater Heaters:
The extracted steam and the condensate are not mixed.
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10–6 The ideal Regenerative Rankine cycle:
1. Open Feedwater Heaters:
The ideal regenerative Rankine cycle with an open feedwater heater.
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10–6 The ideal Regenerative Rankine cycle:
1. Open Feedwater Heaters:
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10–6 The ideal Regenerative Rankine cycle:
1. Open Feedwater Heaters:
10–6 The ideal Regenerative Rankine cycle:
1. Open Feedwater Heaters:
Because of the regeneration process raises the average temperature at which
heat is transferred to the steam in the boiler by raising the temperature of the
water before it enters the boiler, the thermal efficiency of the Rankine cycle
increases.
The cycle efficiency increases further as the number of feedwater heaters is
increased. Many large plants in operation today use as many as eight
feedwater heaters.
The optimum number of feedwater heaters is determined from economical
considerations. The use of an additional feedwater heater cannot be justified
unless it saves more from the fuel costs than its own cost.
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10–6 The ideal Regenerative Rankine cycle:
1. Open Feedwater Heaters:
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10–6 The ideal Regenerative Rankine cycle:
2. Closed Feedwater Heaters:
The ideal regenerative Rankine cycle with a closed feedwater heater.
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10–6 The ideal Regenerative Rankine cycle:
2. Closed Feedwater Heaters:
In the closed feedwater heater the heat is transferred from the extracted
steam to the feedwater without any mixing taking place.
The two streams now can be at different pressures, since they do not mix.
The condensed steam is then either pumped to the feedwater line or routed to
another heater or to the condenser through a device called a trap.
A trap allows the liquid to be throttled to a lower pressure region but traps the
vapor. The enthalpy of steam remains constant during this throttling process.
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10–6 The ideal Regenerative Rankine cycle:
Open feedwater heaters
closed feedwater heaters
Simple in construction.
Complex because of the internal tubing network.
Inexpensive.
More expensive.
Good heat transfer characteristics.
Less effective since the two streams are not allowed to be in
direct contact.
For each heater, however, a pump is required to handle the
feedwater.
Do not require a separate pump for each heater .
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10–6 The ideal Regenerative Rankine cycle:
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10–6 The ideal Regenerative Rankine cycle:
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10–7 Second-Law analysis of vapour power cycles:
The ideal Carnot cycle is a totally reversible cycle, while the ideal Rankine
cycles (simple, reheat, or regenerative), however, are only internally reversible.
The exergy destruction for a steady-flow system can be expressed, in the
rate form, as:
Or on a unit mass basis for a one-inlet, one-exit, steady-flow device as:
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10–7 Second-Law analysis of vapour power cycles:
The exergy destruction associated with a cycle depends on the magnitude of the
heat transfer with the high- and low-temperature reservoirs involved, and their
temperatures.
It can be expressed on a unit mass basis as
For a cycle that involves heat transfer only with a source at TH and a sink at TL ,
the exergy destruction becomes
The exergy of a fluid stream c at any state can be determined from
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10–7 Second-Law analysis of vapour power cycles:
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10–8 Cogeneration:
The cogeneration is the production of more than one useful form of
energy (such as process heat and electric power) from the same energy
source.
The shown process heating seems like
a perfect operation with practically no
waste of energy, but from the secondlaw point of view, however, things do not
look so perfect.
Notice the absence of a condenser.
A simple process-heating plant.
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10–8 Cogeneration:
There is no heat rejected from this plant as
waste heat. In other words, all the energy
transferred to the steam in the boiler is
utilized as either process heat or electric
power.
Thus it is appropriate to define a
utilization factor u for a cogeneration
plant as:
An ideal cogeneration plant.
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10–8 Cogeneration:
The utilization factor also can be expressed as:
where Qout represents the heat rejected in the condenser. And therefore, the
utilization factor of the ideal steam-turbine cogeneration plant is obviously 100
percent.
Qout includes all the undesirable heat losses from the piping and other
components, but they are usually small and thus neglected. It also includes
combustion inefficiencies.
Actual cogeneration plants have utilization factors as high as 80 percent.
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10–8 Cogeneration:
The ideal steam-turbine cogeneration
plant described above is not practical
because it cannot adjust to the variations
in power and process-heat loads.
At times of high demand for process heat,
all the steam is routed to the processheating units and none to the condenser.
The waste heat is zero in this mode.
When there is no demand for process
heat, all the steam passes through the
turbine and the condenser, and the
cogeneration plant operates as an
ordinary steam power plant.
A cogeneration plant
with adjustable loads.
10–8 Cogeneration:
An expansion or
pressure-reducing
valve (PRV).
10–8 Cogeneration:
10–9 Combined Gas-Vapor power cycles: