College of Engineering and Technology

School of Mechanical and Automotive Engineering (SMAE)

POWER PLANT ENGINEERING COURSE MATERIAL (MEng5211)

Chapter 2 Analysis Of Steam Cycles

By: Girma Sh.
1
 Review of Thermodynamic Cycles

 Thermodynamics is the science of many processes involved in one

form of energy being changed into another.
 Energy is transformed from one form or state to the other.
 The zeroth law of thermodynamics states that if two bodies are
each in thermal equilibrium with a third, they must also be in
thermal equilibrium with each other.
 The first law of thermodynamics says that energy can’t be
destroyed or created.
2
 Cont’d

 When one energy form is converted into another, the total

amount of energy remains constant.

 The second law of thermodynamics is the entropy law, which says

that all physical processes proceed in such a way that the
availability of the energy involved decreases.
 This means that no transformation of energy resource can
ever be 100% efficient.
 Entropy is a measure of disorder.
3
 Cont’d

 The third law of thermodynamics is the law of unattainability of

absolute zero temperature.
 Entropy of an ideal crystal at zero degrees Kelvin is zero.
 Thermodynamic cycles can be primarily classified based on their
utility such as for power generation, refrigeration etc.
 Based on this thermodynamic cycles can be categorized as;
(i) Power cycles,
(ii) Refrigeration and heat pump cycles.
4
 Cont’d
i. Power cycles: Thermodynamic cycles which are used in
devices producing power are called power cycles.

 Power production can be had by using working fluid either in

vapour form or in gaseous form.

ii. Refrigeration and heat pump cycles: Thermodynamic cycles

used for refrigeration and heat pump are under this category.

 Similar to power cycles, here also these cycles can be

5
 Cont’d
Power cycle

Vapor Power Cycle Gas Power Cycle

Carnot cycle Carnot gas
Otto cycle
cycle
Rankine cycle
Diesel cycle
Regenerative Ericsson
cycle cycle Dual cycle
Reheat cycle
Binary vapor Brayton Sterling
cycle cycle
cycle
6
 Vapour power cycle
 A steam power plant continuously converts the energy stored in
fossil fuels into shaft work and ultimately into electricity.

Fig 2.1: steam power plant- bulk energy converter from fuel to electricity

7
 Cont’d
 The energy released by the burning of fuel is transferred to
water in the boiler (B) to generate steam at a high-pressure
and temperature.

 which then expands in the turbine (T) to a low pressure to

produce shaft work.

 The steam leaving the turbine is condensed into water in

the condenser (C) where cooling water from a river or sea
circulates carrying away the heat released during8
 Cont’d
 The net energy transferred to the unit mass of the fluid as heat during life cycle
must equal the net energy transfer as work from the fluid,
𝑸𝒏𝒆𝒕 = 𝑾𝒏𝒆𝒕
𝒄𝒚𝒍𝒆 𝒄𝒚𝒄𝒍𝒆
OR 𝑸𝒊𝒏 − 𝑸𝒐𝒖𝒕 = 𝑾𝒐𝒖𝒕 − 𝑾𝒊𝒏
Where:
𝑸𝟏 - heat transferred to the working fluid, kJ/kg
𝑸𝟐 = heat rejected from the working fluid, KJ/kg
𝑾𝑻 = work transferred from the working fluid, kJ/kg
𝑾 = work transferred into the working fluid, KJ/kg
The efficiency 𝒑of the vapor power cycle would thus be
𝑾𝒏𝒆𝒕
𝜼𝒄𝒚𝒄𝒍𝒆 =
𝑸𝟏
9
 Carnot cycle
 It has not been possible to construct a practical plant on this cycle.
• Is an ideal cycle having highest thermodynamic efficiency.
• The Carnot cycle is the most efficient cycle operating between two
specified temperature limits.

Fig. 2.2: T-s diagram of Carnot cycle Fig. 2.3: Schematic diagram of Carnot cycle
10
 Cont’d
It is not a suitable model for power cycles.
 Process 1-2: limiting the heat transfer processes to two-phase systems

 limits the maximum temperature that can be used in the cycle.

 Process 2-3: the turbine cannot handle steam with high moisture content.

 Process 4-1: it is not practical to design a pump that handles two phases.

The thermal efficiency (η) of Carnot cycle is as follows:

(𝑇1 − 𝑇2 )
𝜂 =
1. critically evaluate the processes
𝑡ℎ in Carnot 𝑇cycle and see why it is not
1
practically possible?
Where, 𝑇1 = Temperature of heat source, 𝑇2 = Temperature of receiver
11
 Exercise 1.1
1. A steady-flow Carnot cycle uses water as the working fluid.
Water changes from saturated liquid to saturated vapor as heat
is transferred to it from a source at 250°C. Heat rejection takes
place at a pressure of 20 kPa. Show the cycle on a T-s diagram
relative to the saturation lines, and determine (a) the thermal
efficiency, (b) the amount of heat rejected, in kJ/kg, and (c) the
net work output.
12
 Rankine Cycle
 Many impossibility with the Carnot cycle can be eliminated by superheating
the steam in the boiler and condensing it completely in the condenser.

Fig 2.3: The ideal Rankine cycle (layout diagram and T-s diagram)

13
 Cont’d
 Water enters the boiler as a compressed liquid at state 1 and leaves as a
superheated vapor at state 2.

 The superheated vapor at state 2 enters the turbine, where it expands

isentropically and produces work by rotating the shaft connected to an
electric generator.

 The pressure and the temperature of steam drop during this process to
the values at state 3.

 Where steam enters condenser at state 3, steam is usually a saturated

liquid–vapor mixture with a high quality.
14
 Cont’d
 Steam is condensed at constant pressure in the condenser, by
rejecting heat to a cooling medium.
 Steam leaves the condenser as saturated liquid and enters the
pump, completing the cycle.
• The area under process curve 1-2 represents the heat transferred to
the water in the boiler and
• The area under the process curve 3-4 represents the heat rejected in
the condenser.

15
 Cont’d
Energy Analysis

Using energy balance for a steady flow system

𝑉2 𝑉2
𝑄−𝑊 = 𝑚 𝑕+ + 𝑔𝑧 − 𝑚 𝑕+ + 𝑔𝑧
2 2
𝑜𝑢𝑡 𝑖𝑛
• For single stream (one-inlet-one-exit) systems, mass flow rate remains constant.

𝑉22 − 𝑉12
𝑄 − 𝑊 = 𝑚 𝑕2 − 𝑕1 + + 𝑔(𝑧1 − 𝑧2 )
2
• If KE and PE are negligible, the energy equation becomes
𝑄 − 𝑊 = 𝑚(𝑕2 − 𝑕1 )

16
 Cont’d
a) Boiler

• Since there is no work interaction between the working fluid and surrounding,

W=0. Thus, heat added to the working fluid.

𝑘𝑗
𝑊 = 0 → 𝑞𝑖𝑛 = 𝑕2 − 𝑕1 𝑘𝑔b) Turbine

• Since the expansion process is assumed to be isentropic (reversible

adiabatic), then Q=0. Thus, the amount of work produced by the turbine is

𝑘𝑗
𝑞 = 0 → 𝑊𝑡 = 𝑕2 − 𝑕3 𝑘𝑔
17
 Cont’d
c) Condenser
• No work interaction between the working fluid and surrounding,
W=0. Heat rejected from working fluid to the cooling water.

𝑘𝑗
𝑊 = 0 → 𝑞𝑜𝑢𝑡 = 𝑕4 − 𝑕3 𝑘𝑔

d) Feed water pump

• Since the pumping process is assumed to be isentropic, then Q=0.
Thus, the amount of work required by feedwater pump is
𝑞 = 0 → 𝑊𝑝 = 𝑕1 − 𝑕4 = 𝑣(P1 − P4 )
18
 Cont’d
Performance of steam plant
a) Specific steam consumption (SSC)
• The steam flow rate in kg/hr required to develop 1 kW of power output.

1 1 𝑘𝑔
𝑆𝑆𝐶 = = .𝑠
𝑊𝑛𝑒𝑡 𝑊𝑡 − 𝑊𝑝 𝑘𝑊

3600
= 𝑘𝑔/𝑘𝑊. 𝑕𝑟
𝑊𝑡 − 𝑊𝑝

b) Work ratio (WR)

• The ratio of the net work produced by the plant to the work produced by the turbine.

𝑊𝑛𝑒𝑡 𝑊𝑡 − 𝑊𝑝
𝑊𝑅 = =
𝑊𝑡 𝑊𝑡
19
 Cont’d
c)Thermal efficiency (𝜼𝒕𝒉 )
 Ratio of net work produced by the plant to the amount of heat added to the
working fluid

𝑊𝑛𝑒𝑡 𝑊𝑛𝑒𝑡 𝑄𝑜𝑢𝑡

𝜂𝑡ℎ = = = 1−
𝑄𝑖𝑛 𝑄𝑖𝑛 𝑄𝑖𝑛
𝑊𝑛𝑒𝑡 = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡 = 𝑊𝑡𝑢𝑟𝑏,𝑜𝑢𝑡 − 𝑊𝑝𝑢𝑚𝑝,𝑖𝑛

d) Isentropic efficiency (his)

 The actual expansion and pumping processes are neither adiabatic nor reversible.
Thus, they are not isentropic
20
 Cont’d
e) Back work ratio
 work supplied to the feedwater pump to the work produced by turbine

𝑊𝑝
𝑏𝑤𝑟 =
𝑊𝑡
f) Efficiency ratio

𝑡𝑕𝑒𝑟𝑚𝑎𝑙 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝑜𝑓 𝑎𝑐𝑡𝑢𝑎𝑙 𝑐𝑦𝑐𝑙𝑒

𝜂𝑟𝑎𝑡𝑖𝑜 =
𝑖𝑑𝑒𝑎𝑙 𝑟𝑎𝑛𝑘𝑖𝑛𝑒 𝑐𝑦𝑐𝑙𝑒 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

g) Effect of operating conditions on Rankine cycle efficiency:

How Can We Increase the Efficiency of the Rankine Cycle?

o Increase the average temperature at which heat is transferred to the working fluid in the boiler, or
o decrease the average temperature at which heat is rejected from the working fluid in the condenser.

21
 Cont’d
This can be achieved by:
I. Increasing boiler pressure. It has been observed that by increasing the boiler pressure (other factors
remaining the same) the cycle tends to rise and reaches a maximum value.
II. Superheating the Steam to High Temperatures (Increases Thigh, avg). All other factors remaining
the same, if the steam is superheated before allowing it to expand the Rankine cycle efficiency may
be increased. The use of superheated steam also ensures longer turbine blade life because of the
absence of erosion from high velocity water particles that are suspended in wet vapor.
III. Reducing condenser pressure. The thermal efficiency of the cycle can be simply improved by
reducing the condenser pressure (hence by reducing the temperature at which heat is rejected).

22
 Ideal Reheat Rankine Cycle
 Steam is extracted from a suitable point in the turbine and reheated
generally to the original temperature by flue gases.

Fig. 2.6: shows a schematic and T-s diagram of reheat cycle.

23
 Cont’d
 The optimal way of increasing the boiler pressure but not increase the
moisture content is;

 to reheat the vapor after it exits from a first-stage turbine and redirects
this reheated vapor into a second-stage turbine.

 In ideal reheat Rankine cycle 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.

24
 Cont’d
 In the second stage (low-pressure turbine),

 steam expands isentropically to the condenser pressure.

 Thus, the total heat input and the total turbine work output
for a reheat cycle become:

𝒒𝒊𝒏 = 𝒒𝒑𝒓𝒎𝒊𝒂𝒓𝒚 + 𝒒𝒓𝒆𝒉𝒆𝒂𝒕 = (𝒉𝟑 − 𝒉𝟐 ) + (𝒉𝟓 − 𝒉𝟒 )

𝑾𝒐𝒖𝒕 = 𝑾 𝒕𝒖𝒓𝒃𝒊𝒏𝒆𝟏 + 𝑾 𝒕𝒖𝒓𝒃𝒊𝒏𝒆𝟐 = (𝒉𝟑 − 𝒉𝟒 ) + (𝒉𝟓 − 𝒉𝟔 )

25
 Cont’d
• Efficiency of reheat cycle:
𝛈𝐭𝐡 = 𝐧𝐞𝐭 𝐖𝐨𝐫𝐤 𝐃𝐨𝐧𝐞/𝐇𝐞𝐚𝐭 𝐒𝐮𝐩𝐩𝐥𝐢𝐞𝐝
𝑊𝑛𝑒𝑡 𝑊𝑡 −𝑊𝑝
𝜂𝑡ℎ = =
𝑄𝑖𝑛 𝑄𝑖𝑛

 The incorporation of the single reheat in a modern power plant

improves the cycle efficiency by 4 to 5 percent.
• The average temperature during the reheat process can be increased by
increasing the number of expansion and reheat stages.

26
 Cont’d
 The use of more than two reheat stages, however, is not
practical.
 If the turbine inlet pressure is not high enough, double
reheat would result in superheated exhaust.
 The sole purpose of the reheat cycle is to reduce the moisture
content of the steam at the final stages of the expansion
process.

27
Ideal Regenerative Rankine Cycle
 A practical regeneration process is accomplished by
extracting, or “bleeding,” steam from the turbine at various
points.

 The device where the feed water is heated by regeneration

is called a regenerator, or a feed water heater (FWH).

28
 Cont’d
 A feed water heater is basically a heat exchanger where
heat is transferred from the steam to the feed water.
 By mixing the two fluid streams (open feed water
heaters)

 Without mixing they (closed feed water heaters).

 Heat-addition process in the boiler takes place at

relatively low temperatures. 29
 Cont’d
 This lowers the average heat addition temperature and
thus the cycle efficiency.

 To raise the temperature of the liquid leaving the pump

(called the feed water) before it enters the boiler.

 Regeneration not only improves cycle efficiency, but

also removing the air that leaks in at the condenser.
 Prevent corrosion in the boiler. 30
 Cont’d
Open Feed water Heater
 An open (or direct-contact) feed water heater is basically a
mixing chamber.
 Steam extracted from the turbine mixes with the feed water
exiting from the pump.

31
 Cont’d
 Steam enters the turbine at the boiler pressure (state 5) and
expands isentropically to an intermediate pressure (state 6).

 Some steam is extracted at this state and routed to the feed

water heater, while the remaining steam continues to expand
isentropically to the condenser pressure (state 7).

 This steam leaves the condenser as a saturated liquid at the

condenser pressure (state 1).
32
 Cont’d
 The condensed water, then enters an isentropic pump, where it
is compressed to the feed water heater pressure (state 2).

 The fraction of the steam extracted and condensate water is

mixed in OFWH and leaves the heater as a saturated liquid at
the heater pressure (state 3).

 A second pump raises the pressure of a saturated liquid to the

boiler pressure (state 4).

 The cycle is completed by heating the water in the boiler to the

33
 Cont’d
 For each 1 kg of steam leaving the boiler, y kg expands
partially in the turbine and is extracted at (state 6).

 The remaining (1 - y) kg expands completely to the condenser

pressure.

 Therefore, the mass flow rates are different in different

components.

 If the mass flow rate through the boiler is m, it is (1-y) m,

34
 Cont’d
 The heat and work interactions of a regenerative Rankine cycle with one feedwater
heater can be expressed per unit mass of steam flowing through the boiler as follows:
𝑞𝑖𝑛 = 𝑕5 − 𝑕4
𝑞𝑜𝑢𝑡 = (1 − 𝑦)(𝑕7 −𝑕1 )
𝑤𝑡𝑢𝑟𝑏,𝑜𝑢𝑡 = 𝑕5 − 𝑕6 + (1 − 𝑦) 𝑕6 − 𝑕7
𝑤𝑝𝑢𝑚𝑝,𝑖𝑛 = 1 − 𝑦 𝑤𝑝𝑢𝑚𝑝 𝐼,𝑖𝑛 + 𝑤𝑝𝑢𝑚𝑝 𝐼𝐼,𝑖𝑛

Where;
ℎ −ℎ
𝑦 = ℎ3 −ℎ2 (Fraction of steam extracted)
6 2
𝑤𝑝𝑢𝑚𝑝 𝐼,𝑖𝑛 = 𝑣1 𝑃2 − 𝑃1
𝑤𝑝𝑢𝑚𝑝 𝐼𝐼,𝑖𝑛 = 𝑣3 𝑃4 − 𝑃3
𝒘𝒏𝒆𝒕
𝜼𝒓𝒆𝒈𝒆𝒏. =
𝒒𝒊𝒏
35
 Cont’d
Closed Feedwater Heaters
 Another type of feedwater heater frequently used in steam power plants is
the closed feedwater heater.

 Heat is transferred from the extracted steam to the feedwater without

any mixing taking place.

36
 Cont’d
• In an ideal closed feedwater heater, the feedwater is heated to
the exit temperature of the extracted steam, which ideally leaves
the heater as a saturated liquid at the extraction pressure.

• In actual power plants, the feedwater leaves the heater below

the exit temperature of the extracted steam because a
temperature difference of at least a few degrees is required for
any effective heat transfer to take place.
37
Binary vapor cycle
 If we use steam as the working medium the temperature
rise is accompanied by rise in pressure and at critical
temperature of 374.15°C the pressure is as high as 225
bars which will create many difficulties in design,
operation and control.
 It would be desirable to use some fluid other than steam
which has more desirable thermodynamic properties than38
 Cont’d
 An ideal fluid for this purpose should have a very high critical
temperature combined with low pressure.

 Mercury is the only working fluid which has been

successfully used in practice.

 It has high critical temperature (588.4°C) and

correspondingly low critical pressure (21 bar abs.).
The mercury alone cannot be used as its saturation
39
 Cont’d
 Hence, binary Vapour cycle is generally used to increase the
overall efficiency of the plant
 Two fluids (mercury and water) are used in cascade in the binary
cycle for production of power.

40
Working principle of binary vapor cycle

41
Fig. 2.10b: Schematic of binary vapour cycle and T-s diagram
42
 Cont’d
 There are two distinct circuits, one for mercury and the other
for steam.

 Saturated mercury vapor from the mercury boiler at state 1

enters the mercury turbine, expands to state 2, and is
condensed at state 3.

 The condensate is pumped back to the boiler by the

mercury pump at state 4.
43
 Cont’d
 The heat rejected in the mercury condenser is used to vaporize
water into steam at state e.

 Thus, the mercury condenser also acts as the steam boiler.

 Note that there is a considerable temperature differential

between condensing mercury and boiling water.

 Saturated steam is then superheated to state a as shown,

expanded in the steam turbine to state b and then
44
 Cont’d
 The heat losses to the surroundings, in the following analysis, are neglected.
Net work from cycle shall be, 𝑊𝑛𝑒𝑡 = 𝑊𝑀𝑇 + 𝑊𝑆𝑇 − 𝑊𝑝𝑢𝑚𝑝
Work from mercury turbine, 𝑊𝑀𝑇 = 𝑚𝑀𝑇 × (𝑕1 − 𝑕2 )
Work from steam turbine, 𝑊𝑆𝑇 = 𝑚𝑆𝑇 × (𝑕𝑎 − 𝑕𝑏 )
Pump work= 𝑚𝑀𝑇 × 𝑕4 − 𝑕3 + 𝑚𝑆𝑇 × (𝑕𝑑 − 𝑕𝑐 )
Heat added to the cycle, 𝑄𝑎𝑑𝑑 = 𝑚𝑀𝑇 × 𝑕1 − 𝑕4 + 𝑚𝑆𝑇 × (𝑕𝑎 − 𝑕𝑒 )
𝑊𝑛𝑒𝑡
Binary cycle efficiency, 𝑏𝑖𝑛𝑎𝑟𝑦 =
𝑄𝑎𝑑𝑑

𝑚𝑀𝑇 × 𝑕1 − 𝑕2 + 𝑚𝑆𝑇 × 𝑕𝑎 − 𝑕𝑏 − 𝑚𝑀𝑇 × 𝑕4 − 𝑕3 − 𝑚𝑆𝑇 × (𝑕𝑑 − 𝑕𝑐 )

=
𝑚𝑀𝑇 × 𝑕1 − 𝑕4 + 𝑚𝑆𝑇 × (𝑕𝑎 − 𝑕𝑒 )

 Heat lost by mercury Vapour = Heat gained by steam

45
 Cont’d
The few more properties required for an ideal binary fluid used in high
temperature limit are listed below:
1. It should have high critical temperature at reasonably low pressure.
2. It should have high heat of vaporization to keep the weight of fluid in
the cycle to minimum.
3. Freezing temperature should be below room temperature.
4. It should have chemical stability through the working cycle.
5. It must be non-corrosive to the metals normally used in power plants.
6. It must have an ability to wet the metal surfaces to promote the heat
46
 Cont’d

7. The Vapour pressure at a desirable condensation temperature

should be nearly atmospheric which will eliminate requirement of
power for maintenance of vacuum in the condenser.
8. After expansion through the prime mover the vapour should be
nearly saturated so that desirable heats transfer co-efficient can be
obtained which will reduce the size of the condenser required.
9. It must be available in large quantities at reasonable cost.
47
 End of Chapter 2

Next Lecture

Chapter 3: Fuels and Combustion

48