Thermodynamics for Energy Engineering (ESE 1205)
Thermodynamic Cycles Analysis
Rankine Cycle
Presented By:
Md. Sohag Hossain
Lecturer
Department of Energy Science and Engineering
Khulna University of Engineering & Technology
Khulna-9203, Bangladesh.
Rankine Cycle
• Many of the practical difficulties associated with
the Carnot vapor power cycle are eliminated in
Rankine cycle.
• The steam coming out of the boiler is usually in
the superheated state, and expands in the
turbine.
• After expanding in the turbine, the steam
is condensed completely in the condenser.
Fig: p-v and T-s diagram for Carnot Vapor Cycle.
Principal Components of Turbine The vapour leaving the boiler
Vapour Power Plant enters the turbine, where it expands
isentropically to the condenser pressure
at the state 2. The work produced by the
turbine is rotary (shaft) work and is
used to drive an electric generator or
machine.
Boiler The heat is supplied to the Condenser The condenser is attached at
working fluid (feed water) in the boiler the exit of the turbine. The vapour
and thus vapour is generated. The leaving the turbine is wet vapour and it
vapour leaving the boiler is either is condensed completely in the
saturated at the state 1 or superheated at condenser to the state 3, by giving its
the state 1, depending upon the amount latent heat to some other cooling fluid
of heat supplied in the boiler. like water.
Pump The liquid condensate leaving
the condenser at the state 3 is pumped
to the operating pressure of the boiler.
The pump operation is considered
isentropic.
Operation of Rankine cycle
Cont’d an ideal Rankine cycle
Cycle 1-2-3-4- 1 using saturated steam
an ideal Rankine cycle with
Cycle 1'-2'-3-4 -1' superheated steam at the turbine
entry
• Process 1-2 Isentropic expansion of the working fluid in the turbine from boiler pressure to
condenser pressure.
• Process 2-3 Heat rejection from the working fluid at constant pressure in the condenser till the
fluid reaches the saturated liquid state 3.
• Process 3-4 Isentropic compression of the working fluid in the pump to the boiler pressure at state
4 in the compressed liquid region.
• Process 4-1 Heat addition to working fluid at constant pressure in the boiler from state 4 to 1.
Analysis of Rankine Cycle
Cont’d
Mathematical Problem
Problem 01:The Simple Ideal Rankine Cycle
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 condenser at a pressure of 75 kPa.
Determine the thermal efficiency of this cycle.
Mathematical Problem
Problem -02:
• A steam power plant has boiler and condenser pressures of 60 bar and 0.1 bar,
respectively. Steam coming out of the boiler is dry and saturated. The plant operates on
the Rankine cycle. Calculate thermal efficiency.
Deviation of Actual Rankine Cycle from the Ideal Cycle
The actual vapor power cycle differs from the ideal Rankine cycle because of
irreversibilities in various components. Fluid friction and heat losses are two common
sources of irreversibilities.
❑ Fluid friction causes pressure drops in the boiler, the condenser, and the piping between
various components. As a result, steam leaves the boiler at a somewhat lower pressure.
Also, the pressure at the turbine inlet is somewhat lower than that at the boiler exit due
to the pressure drop in the connecting pipes. This requires a larger pump and larger
work input to the pump.
❑ heat loss from the steam to the surroundings as the steam flows through various
components. To maintain the same level of net work output, more heat needs to be
transferred to the steam in the boiler to compensate for these undesired heat losses.
Deviation of Actual Rankine Cycle from the Ideal Cycle
(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.
ℎ −ℎ
Pump efficiency, 𝜂𝑝 = 2𝑠 1
ℎ2𝑎 −ℎ1
ℎ3 −ℎ4𝑎
Turbine efficiency, 𝜂 𝑇 =
ℎ3 −ℎ4𝑠
HOW CAN WE INCREASE THE EFFICIENCY OF THE RANKINE CYCLE?
(1)Lowering the Condenser Pressure (Lowers Tlow,avg)
• Steam exists as a saturated mixture in the condenser at the
saturation temperature corresponding to the pressure inside the
condenser. Therefore, lowering the operating pressure of the
condenser automatically lowers the temperature of the steam,
and thus the temperature at which heat is rejected.
• The colored area on this diagram represents the increase in net
work output as a result of lowering the condenser pressure
from P4 to P4’. The heat input requirements also increase
(represented by the area under curve 2’-2), but this increase is
very small. Thus the overall effect of lowering the condenser
pressure is an increase in the thermal efficiency of the cycle.
(2)Superheating the Steam to High Temperatures
(Increases Thigh,avg)
• The average temperature at which heat is transferred to
steam can be increased without increasing the boiler
pressure by superheating the steam to high temperatures.
• The colored area on this diagram represents the increase
in the net work. The total area under the process curve 3-
3’ represents the increase in the heat input. Thus both the
net work and heat input increase as a result of
superheating the steam to a higher temperature.
• It decreases the moisture content of the steam at the
turbine exit, as can be seen from the T-s diagram.
• The temperature to which steam can be superheated is
limited, however, by metallurgical considerations.
(620℃)
(3)Increasing the Boiler Pressure (Increases T high,avg)
• Another way of increasing the average temperature during
the heat-addition process is to increase the boiler’s operating
pressure, which automatically raises the temperature at
which boiling takes place. This, in turn, raises the average
temperature at which heat is transferred to the steam, thus
raising the cycle's thermal efficiency.
• Notice that for a fixed turbine inlet temperature, the cycle
shifts to the left, and the moisture content of steam at the
turbine exit increases. However, this undesirable side effect
can be corrected by reheating the steam, as discussed in the
next section.
• Operating pressures of boilers have gradually increased over
the years from about 2.7 MPa (400 psia) in 1922 to over 30
MPa (4500 psia) today.
THE IDEAL REHEAT RANKINE CYCLE
Note that increasing the boiler pressure increases the thermal efficiency of the
Rankine cycle, but it also increases the moisture content of the steam to
unacceptable levels. Now, we can increase the cycle efficiency by:
• Superheat the steam to very high temperatures before it enters the turbine. This
would be the desirable solution since the average temperature at which heat is
added would also increase, thus increasing the cycle efficiency. This is not a
viable solution, however, since it requires raising the steam temperature to
metallurgically unsafe levels.
• Expand the steam in the turbine in two stages, and reheat it in between. In other
words, modify the simple ideal Rankine cycle with a reheat process. Reheating
is a practical solution to the excessive moisture problem in turbines, and it is
commonly used in modern steam power plants.
Reheat Rankine Cycle
• The ideal reheat Rankine cycle differs from the simple ideal
Rankine cycle in that the expansion process takes place in two
stages.
• In the first stage (the high-pressure turbine), steam is expanded
isentropically to an intermediate pressure and sent back to the
boiler where it is reheated at constant pressure, usually to the
inlet temperature of the first turbine stage.
• Steam then expands isentropically in the second stage (low-
pressure turbine) to the condenser pressure.
• The incorporation of the single reheat in a modern power plant
improves the cycle efficiency by 4 to 5 percent by increasing the
average temperature at which heat is transferred to the steam.
• the sole purpose of the reheat cycle is to reduce the moisture
content of the steam at the final stages of the expansion process.
Reheat Rankine Cycle
Reheat Rankine Cycle
Mathematical Problem
• The Ideal Reheat Rankine Cycle
Consider a steam power plant operating on the ideal reheat Rankine cycle. Steam enters the high-pressure turbine at
15 MPa and 600℃ and is condensed in the condenser at a pressure of 10 kPa. If the moisture content of the steam at
the exit of the low-pressure turbine is not to exceed 10.4 percent, determine (a) the pressure at which the steam should
be reheated and (b) the thermal efficiency of the cycle. Assume the steam is reheated to the inlet temperature of the
high-pressure turbine.
The Ideal Regenerative Rankine Cycle
• Heat is transferred to the working fluid during process 4-4’ at a
relatively low temperature. This lowers the average heat addition
temperature and thus the cycle efficiency.
• To raise the temperature of the liquid leaving the pump (called the
feedwater) before it enters the boiler. One such possibility is to
transfer heat to the feedwater from the expanding steam in a
counter flow heat exchanger built into the turbine, that is, to use
regeneration.
• 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 Fig 10.14 The first part of the heat-
further in the turbine, is used to heat the feedwater instead. The addition process in the boiler takes
device where the feedwater is heated by regeneration is called a place at relatively low temperatures.
regenerator, or a feedwater heater (FWH).
The Ideal Regenerative Rankine Cycle
❖ A feedwater heater is basically a heat exchanger where heat is transferred
from the steam to the feedwater either by mixing the two fluid streams
(open feedwater heaters) or without mixing them (closed feedwater heaters).
❑Advantages of Regeneration
1. It raises the temperature of feed water to saturation temperature, and
thus the amount of heat addition in the boiler reduces.
2. The heat is added in the boiler at a higher average temperaure.
3. Open feed water heater serves as a deaerator to remove the air and
other non-condensable gases from the feed water, otherwise they
would cause corrosion.
Regeneration with Open Feedwater Heater
• A part of superheated steam which enters the turbine at the state 1, is
extracted from the turbine at the intermediate state 2 of turbine-
expansion process.
• The extracted steam is supplied to a heat exchanger known as feed water
heater. The remaining amount of steam in the turbine expands completely
to condenser pressure (state 3).
• The condensate, a saturate liquid at state 4 is pumped isentropically by
low pressure (LP) pump to the pressure of extracted steam.
• The compressed liquid at the state 5 enters the feed water heater and it
mixes with steam extracted from the turbine. Due to direct mixing
process, the feed water heater is called open or direct-contact type
feedwater heater.
• The portion of steam extracted is so adjusted to make the mixture leaving
the feed water to be saturated at the state 6.
• Now this saturated water is pumped by high pressure (HP) pump to the
boiler pressure state 7.
Analysis
❑Since the masses of steam flowing through the various components of
the cycle vary ,thus the analysis of this cycle differs from previous
one.
❑Let 1 kg of steam be leaving the boiler and entering the turbine. m1 kg
of steam per kg, is extracted at the state 2 from the turbine at
intermediate pressure p2.
❑(1 – m1) kg of steam per kg flow through the remaining part of the
turbine during expansion from 2–3, condensation from 3–4 and
pumping from 4–5.
❑(1 – m1) kg of steam enters in open feed water heater and mixed with
m1 kg of steam blown from the turbine at the state 2. After mixing, the
mass of saturated liquid becomes 1 kg at the state 6 and it is pumped
to boiler pressure at the state 7.
Analysis
Regeneration with Closed Feedwater
Heater
❑ A closed feed-water heater is an indirect contact type feed
water heater, usually a shell and tube type heat exchanger,
in which heat is transferred from extracted steam to feed-
water without mixing of two fluid streams.
❑ Figure 12.42 shows two arrangement for removing the
condensate from the closed feedwater heater.
❑ In Fig. 12.42(a), the condensate is pumped forward to a
feed-water line.
❑ In Fig. 12.42(b), the condensate is allowed to pass
another feed-water heater or condenser through a device
called a steam trap. A trap is a type of valve that allows
only liquid to be throttled to a lower pressure, but it traps
the vapour.
Regeneration with Closed Feedwater Heater
➢ the total steam expands through first stage turbine from state 1 to state 2.
➢ At state 2, a part of steam (m1, kg) is extracted and is supplied to closed
feed-water heater, where it condenses, on outside of tubes, carrying the
feedwater.
➢ The saturated liquid at extraction pressure exits the feed-water heater at
state 5 and is routed to the condenser through a trap, where it is mixed
with the condensate of steam passing the second stage turbine.
➢ In the trap, the steam is throttled from state 5 to state 6. It is an
irreversible process, and thus shown by dotted line.
➢ Then total condensate as saturate liquid at state 7 is pumped to boiler
pressure and enters the feedwater at state 8.
➢ The temperature of feedwater in the heater is raised to state 4.
➢ The cycle completes as working fluid enters the boiler and heated at
constant pressure from state 4 to state 1.
Comparison
The open and closed feedwater heaters can be compared as follows.
❖Open feedwater heaters are simple and inexpensive and have good heat transfer
characteristics. They also bring the feedwater to the saturation state. For each
heater, however, a pump is required to handle the feedwater.
❖ The closed feedwater heaters are more complex because of the internal tubing
network, and thus they are more expensive.
❖Heat transfer in closed feedwater heaters is also less effective since the two streams
are not allowed to be in direct contact.
❖ However, closed feedwater heaters do not require a separate pump for each heater
since the extracted steam and the feedwater can be at different pressures.
