2.
Course Outcomes
• Ability to acquire and explain the basic
concepts in thermodynamics.
• Ability to apply and correlate the concept with
the appropriate equations and principles to
analyze and solve engineering problems.
3.
Course Learning Outcomes
The student should be able to:
• Describe the principles of carnot vapor cycles and its
impracticalities
• Explain the principles of an ideal rankine power cycle
• Explain how pressure and temperature affect thermal
efficiency of an ideal rankine power cycle
• Explain the principle of the reheat Rankine power cycles.
• Sketch the T-s diagram for carnot,ideal rankine and ideal
reheat rankine cycles.
• Solve problems related to ideal rankine and reheat rankine
cycles.
5.
8.1 Carnot Vapor Cycle
It is most efficient cycle operating between two specified temperature limits BUT it IS
NOT a suitable model for power cycles, BECAUSE:
Process 1-2 Limiting the heat transfer processes to two-phase systems severely limits
the maximum temperature that can be used in the cycle (374°C for water)
Process 2-3 The turbine cannot handle steam with a high moisture content because of
the impingement of liquid droplets on the turbine blades causing erosion and wear.
Process 4-1 It is not easy to control the condensation process so precisely to achieve
quality at point 1. And it is not practical to design a compressor that handles two
phases.
1-2 isothermal heat addition
in a boiler
2-3 isentropic expansion in a
turbine
3-4 isothermal heat rejection
in a condenser
4-1 isentropic compression in
a compressor
T-s diagram of two Carnot vapor cycles.
6.
Those problems can be eliminated by executing Carnot cycle in
figure (b), HOWEVER this cycle presents other problem.
isentropic compression to extremely high pressures
isothermal heat transfer at variable pressures.
Conclusion
Carnot cycle cannot be approximated in actual devices
It is not realistic model for vapor power cycles
IDEAL CYCLE for vapor power cycle is
RANKINE CYCLE
7.
8.2 Rankine Vapor Cycle
Impracticalities associated with the Carnot cycle can be eliminated by
superheating the steam in the boiler and
condensing it completely in the condenser.
The ideal Rankine cycle does not involve any internal irreversibilities.
The simple ideal Rankine cycle.
8.
Energy Analysis of the Ideal Rankine Cycle
Steady-flow energy equation
( q in -q o u t ) - ( w o u t -w in ) = h e
- hi
(k J /k g )
The thermal efficiency can be interpreted as the ratio of the area enclosed
by the cycle on a T-s diagram to the area under the heat-addition process.
9.
Example 10.1
Consider a steam power plant operating on the simple ideal Rankine cycle.
Steam enters the turbine at 3 MPa and 350° and is condensed in the
C
condenser at a pressure of 75 kPa. Determine the thermal efficiency of this
cycle.
10.
Problem 10.22
Consider a steam power plant that operates on a simple ideal A
simple Rankine cycle and has a net power output of 45 MW.
Steam enters the turbine at 7 MPa and 500° and is cooled in the
C
condenser at pressure of 10 kPa by running cooling water from
the lake through the tubes of condenser at rate of 2000 kg/s.
i.
ii.
iii.
iv.
Show the T-s diagram with respect to saturation line
Determine the thermal efficiency of the cycle
Determine the mass flowrate of the steam
Determine the temperature rise of the cooling water.
11.
HOW CAN WE INCREASE THE EFFICIENCY OF THE RANKINE
CYCLE?
To increase the thermal efficiency…
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.
Lowering the Condenser Pressure
(Lowers Tlow,avg)
Superheating the
Steam to High Temperatures
(Increases Thigh,avg)
Increasing the Boiler Pressure
(Increases Thigh,avg)
12.
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 cannot be lower than Psat
corresponding to 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.
13.
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.
Side effect: Superheating to higher
temperatures decreases the moisture
content of the steam at the turbine exit,
which is desirable.
The effect of superheating the
steam to higher temperatures on
the ideal Rankine cycle.
The temperature is limited by
metallurgical considerations. Presently the
highest steam temperature allowed at the
turbine inlet is about 620°C.
14.
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.
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.
15.
Example 10.3
Consider a steam power plant operating on the ideal Rankine cycle. Steam
enters the turbine at 3 MPa and 350° and is condensed in the condenser at a
C
pressure of 10 kPa.
Determine:
(a) The thermal efficiency of this power plant
(b) The thermal efficiency if steam is superheated of 600° instead of 350°C
C
(c) The thermal efficiency if the boiler pressure is raised to 15 MPa while the
turbine inlet temperature is maintained at 600°
C.
16.
8.3 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?
Answer:
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)
18.
Additional info.:
• 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
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 onefourth of the maximum cycle pressure.
The average temperature at which heat is
transferred during reheating increases as the
number of reheat stages is increased.
What is the purpose of reheat cycle?
19.
Example 10.4
Consider a steam power plant operates on the ideal reheat Rankine cycle.
Steam enters the high-pressure turbine at 15 MPa and 600° and is
C
condensed in the condenser at a pressure of 10 kPa. If the moisture content of
the steam at the exit of the low-pressure is not to exceed 10.4 percent,
determine:
(a) The pressure at which the steam should be reheated
(b) The thermal efficiency of the cycle
Assume the steam is reheated to the inlet temperature of the high-pressure
turbine.
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