Rankine cycle

The Rankine cycle is the fundamental operating cycle of all power plants where an operating fluid is continuously
evaporated and condensed. The selection of operating fluid depends mainly on the available temperature
range. Figure 1 shows the idealized Rankine cycle.
The pressure-enthalpy (p-h) and temperature-entropy (T-s) diagrams of this cycle are given in Figure 2. The
Rankine cycle operates in the following steps:
1-2-3 Isobaric Heat Transfer. High pressure liquid enters the boiler from the feed pump (1) and is heated to the
saturation temperature (2). Further addition of energy causes evaporation of the liquid until it is fully
converted to saturated steam (3).
3-4 Isentropic Expansion. The vapor is expanded in the turbine, thus producing work which may be converted
to electricity. In practice, the expansion is limited by the temperature of the cooling medium and by the
erosion of the turbine blades by liquid entrainment in the vapor stream as the process moves further into the
two-phase region. Exit vapor qualities should be greater than 90%.
4-5 Isobaric Heat Rejection. The vapor-liquid mixture leaving the turbine (4) is condensed at low pressure,
usually in a surface condenser using cooling water. In well designed and maintained condensers, the pressure
of the vapor is well below atmospheric pressure, approaching the saturation pressure of the operating fluid at
the cooling water temperature.
5-1 Isentropic Compression. The pressure of the condensate is raised in the feed pump. Because of the low
specific volume of liquids, the pump work is relatively small and often neglected in thermodynamic
calculations.

Figure 1. Rankine cycle.

Figure 2. T-s and p-h diagrams.

The efficiency of power cycles is defined as
(1)

Values of heat and work can be determined by applying the First Law of Thermodynamics to each step. The steam
quality x at the turbine outlet is determined from the assumption of isentropic expansion, i.e.,
(2)

where is the entropy of vapor and Si* the entropy of liquid.

Inefficiencies of Real Rankine Cycles
The efficiency of the ideal Rankine cycle as described in the previous section is close to the Carnot efficiency
(see Carnot Cycle). In real plants, each stage of the Rankine cycle is associated with irreversible processes, reducing
the overall efficiency. Turbine and pump irreversibilitys can be included in the calculation of the overall cycle
efficiency by defining a turbine efficiency according to Figure 3
(3)

where subscript act indicates actual values and subscript is indicates isentropic values and a pump efficiency
(4)

Figure 3. Turbine efficiency.

If t and p are known, the actual enthalpy after the compression and expansion steps can be determined from the
values for the isentropic processes. The turbine efficiency directly reduces the work produced in the turbine and,
therefore the overall efficiency. The inefficiency of the pump increases the enthalpy of the liquid leaving the pump
and, therefore, reduces the amount of energy required to evaporate the liquid. However, the energy to drive the
pump is usually more expensive than the energy to feed the boiler.

Figure 4. Rankine cycle with vapor superheating.

Even the most sophisticated boilers transform only 40% of the fuel energy into useable steam energy. There are
two main reasons for this wastage:
The combustion gas temperatures are between 1000C and 2000C, which is considerably higher than the
highest vapor temperatures. The transfer of heat across a large temperature difference increases the entropy.
 Combustion (oxidation) at technically feasible temperatures is highly irreversible.
Since the heat transfer surface in the condenser has a finite value, the condensation will occur at a temperature
higher than the temperature of the cooling medium. Again, heat transfer occurs across a temperature difference,
causing the generation of entropy. The deposition of dirt in condensers during operation with cooling water
reduces the efficiency.
Increasing the Efficiency of Rankine Cycles
Pressure difference
The net work produced in the Rankine cycle is represented by the area of the cycle process in Figure 2. Obviously,
this area can be increased by increasing the pressure in the boiler and reducing the pressure in the condenser.

Figure 5. Regenerative feed liquid heating.

Superheating and reheating
The irreversibility of any process is reduced if it is performed as close as possible to the temperatures of the high
temperature and low temperature reservoirs. This is achieved by operating the condenser at sub atmospheric
pressure. The temperature in the boiler is limited by the saturation pressure. Further increase in temperature is
possible by superheating the saturated vapor, see Figure 4.
This has the additional advantage that the vapor quality after the turbine is increased and, therefore the erosion of
the turbine blades is reduced. It is quite common to reheat the vapor after expansion in the high pressure turbine
and expand the reheated vapor in a second, low pressure turbine.
Feed water preheating
The cold liquid leaving the feed pump is mixed with the saturated liquid in the boiler and/or re-heated to the
boiling temperature. The resulting irreversibility reduces the efficiency of the boiler. According to the Carnot
process, the highest efficiency is reached if heat transfer occurs isothermally. To preheat the feed liquid to its
saturation temperature, bleed vapor from various positions of the turbine is passed through external heat
exchangers (regenerators), as shown in Figure 5.
Ideally, the temperature of the bleed steam should be as close as possible to the temperature of the feed liquid.
Combined cycles
The high combustion temperature of the fuel is better utilized if a gas turbine or Brayton engine is used as "topping
cycle" in conjunction with a Rankine cycle. In this case, the hot gas leaving the turbine is used to provide the
energy input to the boiler. In co-generation systems, the energy rejected by the Rankine cycle is used for space
heating, process steam or other low temperature applications
Reheat Cycle
As has been already mentioned in Secs. 11.1 and 11.2, if very wet steam flows through a turbine, the
hydrodynamic conditions for the turbine blades and nozzles deteriorate sharply, causing a reduction of the internal
relative efficiency of the turbine, ; this in turn leads to a reduction of the effective (thermal) efficiency of the
power plant as a whole. For modern turbines the admissible dryness fraction of exhaust steam (at the turbine exit)
should be not less than x = 0.86 to 0.88.
As has already been mentioned, one of the ways to reduce the wetness of exhaust steam at the turbine exit is
to superheat the steam in the boiler. Superheating leads to an increase in the thermal efficiency of the cycle reali-
zed, and at the same time, on the T-s diagram it shifts the point corresponding to the conditions of exhaust steam
to the right, into the region of greater dryness fractions, as illustrated in Fig. 11.20a.
We have also found that with the same superheat temperature the use of high pressures increases the cycle
areas ratio and, consequently, the thermal efficiency of the cycle, but simultaneously a higher pressure diminishes
the dryness fraction of the exhaust steam and the internal relative efficiency of the turbine.

Fig. 11.20

One solution could be to further increase the superheat temperature (the dotted line in Fig. 11.206). However,
as was already mentioned, further temperature increases are restricted by the properties of construction mate-
rials. The economic advantage of this undertaking should also take into consideration increased investments
involved in building such a plant.
One way to reduce the final wetness of exhaust steam is to reheat the steam. After the flow of steam,
performing work in the turbine, expands to some pressure p*> p2, it is extracted from the turbine and directed to
flow into an additional superheated, or reheated, installed, for instance, in the boiler flue. In this reheated, steam
temperature rises to T*, and then the steam flows back into the turbine, in which it expands to the pressure p2. As
can be seen from the T-s diagram, shown in Fig. 11.20c, the final wetness of steam diminishes.
The diagram of a power plant with steam reheating is shown in Fig. 11.21, in which the reheat superheated,
or reheated, is designated by RS. When reheating the steam, the turbine is a two-cylinder unit, comprising a high-
pressure turbine and a low-pressure turbine[1] arranged on a common shaft along with a generator.
Figure 11.22 shows on a T-s diagram an internally reversible reheat cycle of the steam power
plant, practising superheating. It is clear that this cycle can be visualized as consisting of two individual cycles, the
conventional Rankine cycle (main) 5-4-6-1-2-3-5 and an additional cycle 2-7-8-9-2 (the line 7-8 is an
isobar p*= const). It can be assumed that the work done along the section 7-2 of the expansion adiabatic in the
main cycle is spent to ensure adiabatic compression of the working medium on the section 2-7 of the additional
cycle.

Fig. 11.21
 Fig. 11.22

The expression for the thermal efficiency of the reheat cycle can be presented in the following form:

(11.107)

If the thermal efficiency of the additional cycle,

(11.108)

is greater than the thermal efficiency of the main cycle,

(11.109)

then the thermal efficiency of the reheat cycle, , will be greater than the thermal efficiency of a Rankine cycle
without reheating (i.e. greater than that of the main cycle):

In fact, if , it means that the area ratio of the additional cycle is greater than that of the main
cycle and, consequently, the area ratio of the total reheat cycle is larger than the area ratio of the main cycle.
Steam reheating, practised at one time mainly to do away with the high wetness of steam in the last stages of
turbines, is now used to increase the thermal efficiency cycles.
Analyzing the T-s diagram, we see that if steam is returned for reheating at a temperature not very low and it is
being reheated to a temperature close to T1, the thermal efficiency of the additional cycle will be higher than the
thermal efficiency of the main cycle; in this case the area ratio of the additional cycle will be far greater than that
of the main cycle (Fig. 11.23).

Fig. 11.23

A cycle with steam reheating to a temperature T* = T1 is shown on the i-s diagram in Fig. 11.24.
 Fig. 11.24

Modern steam power plants are usually operated not only with single but with double steam reheating.
Steam reheating used in steam power plants as a means for raising the thermal efficiency of the plant, is similar to
the two-stage heat addition in gas-turbine plants, considered in Sec. 10.2.

Regenerative cycle
As in gas-turbine plants, the thermal efficiency of a steam power plant is raised by means of heat regeneration.
If a steam power plant is operated on a Rankine cycle without steam reheating and if complete regeneration of
heat is accomplished, then the thermal efficiency of this Rankine cycle will be equal to the thermal efficiency of a
Carnot cycle. Figure 11.25 shows the Rankine wet-steam cycle with full regeneration on a T-s diagram (it is
understood that we are speaking of internally reversible cycles).

Fig. 11.25

The efficiency of the Rankine cycle with steam reheating, even with maximum regeneration, will be inferior to
the thermal efficiency of the Carnot cycle in the same temperature interval: as it follows from the T-s diagram
shown in Fig. 11.26, with the thermal efficiency of the reheat Rankine cycle increasing appreciably, compared with
the cycle without regeneration.

Fig. 11.26
 The regenerative cycle shown in Fig. 11.26 is represented as an ideal cycle: as was shown in Sec. 10.2
equidistant heat addition and heat rejection lines (line 3-4and line 7-2r, respectively, in Fig. 11.26) can be ensured
provided an ideal regenerator is used.
It follows from the T-s diagram shown in Fig. 11.26 that the thermal efficiency of the Rankine cycle with
maximum regeneration is determined from the expression

(11.110)

In actual steam power cycles regeneration is effected with the aid of surface-type or direct-contact regenerative
feed-water heaters, either of which is supplied with steam from intermediate turbine stages (the regenerative
takeoff). The steam condenses in the regenerative feed-water heaters FWH 1 and FWH 2 heating the feed water
which is delivered to the boiler. Heating steam condensate is also delivered to the boiler or mixes with the main
flow of feed water (Fig. 11.27). Strictly speaking, the regenerative cycle of a steam power plant cannot be
represented on a two-dimensional T-s diagram, since this diagram is plotted for a constant amount of working
medium, whereas in a regenerative cycle, involving the use of regenerative feed-water heaters, the quantity of the
working m ed iu m varies along the turbine blading. Therefore, in investigating the cycle plotted on a flat T-
s diagram (Fig. 11.28), the hypothetical nature of this representation should be borne in mind; for emphasis, a
diagram representing the rate of steam flow through the turbine along its blading is shown adjacent to the T-
s diagram. This new diagram pertains to line 1-2 on the T-s diagram, the line of adiabatic expansion of steam in the
turbine. Thus, on the section 1-2 of the cycle, shown on the T-s diagram, the quantity of the working medium
diminishes with a drop in pressure, and along the section 5-4 the quantity of the working medium increases with
rising pressure (heating steam condensate is added to the feed water).

Fig. 11.27

Fig. 11.28
 Ideally, the regenerative cycle should be represented in a three-dimensional system of coordinates: T, s,
D. Figure 11.29 shows a regenerative cycle with two heating stages on a T-s-D diagram. The T-s diagrams of the
cycles realized by three fractions of the steam flow are shown in the same illustration: the fraction of steam bled
into the first heating stage ( ), the fraction of steam bled from the turbine into the second heating stage (
) and the fraction passing into the condenser [ ]. Since it is rather difficult to make use of the
three-dimensional system of coordinates, they find no practical application.

Fig. 11.29

When not surface-type but direct-contact regenerative heaters are used, in accordance with the layout of the
steam power plant shown in Fig. 11.27, several pumps must be installed, since water pressure should be increased
in steps: the pressure of the water flowing into a direct-contact heater should be equal to the pressure of the
steam bled for this heater. In the diagram the number of pumps exceeds the number of steam bleeding points by
one.
Let us consider in detail the cycle of the regenerative steam power plant with two direct-contact feed-water
heaters, depicted in Fig. 11.27 (an internally reversible cycle is considered). Denote the fraction of the working
medium bled from the turbine by . If the rate of steam flow at the turbine entry is denoted by D, then kg/h
of steam is bled from the turbine and directed into the first regenerative heater FWH1, and kg/h of steam is
bled into the second regenerative heater FWH2.
Hence, up to the first bleeding point D kg/h of steam performs work in the turbine, downstream from this
point kg/h of steam performs work, and downstream from the second bleeding
point kg/h of steam performs work.
Correspondingly, kg/h of exhaust steam passes into the condenser;
kg/h of water (condensate) from the condenser and kg/h of steam from the second
bleeding point are delivered into the second regenerative heater. As a result of the mixing of bled steam and
condensate kg/h of heated feed water leaves the second regenerative heater. Directed into the first
regenerative heater is kg/h of water from the second heater and kg/h of steam from the first
bleeding point; the water and steam mix and D kg/h of heated feed water leaves this heater. The feed water flows
to the feed pump which delivers it to the boiler. Let us find out on what basis the values of and are
selected.
 The conditions of the steam bled from the turbine are preset. Let us denote steam pressure at the first bleeding
point by and the pressure of steam at the second bleeding point by .
The pump delivers kg/h of feed water from the condenser into the second regenerative
heater at a pressure of . This water is not heated to the boiling point corresponding to the pressure ; the
temperature of this feed water is somewhat higher than T2. Let us denote its enthalpy by . From the bleeding
point kg/h of superheated steam is delivered into the heater at the same pressure . Denote the enthalpy
of this superheated steam by . The value of is selected so that the mixing of superheated steam and water at
a temperature below the boiling point will yield feedwater heated to the boiling point corresponding to the
pressure . The enthalpy of saturated water at the pressure will be denoted by . The heat balance
equation for the second regenerative heater takes the following form:

(11.111)

The first regenerative feed-water heater receives water in the amount of kg/h at a pressure
; denote its enthalpy by . Superheated steam flows from the first bleeding point into the heater in the amount
of kg/h; denote the enthalpy of this steam by . Just as for the second regenerative heater, the rate of flow
from the first bleeding point into the first heater is selected so that water leaves the heater at the boiling

point corresponding to the pressure ; the enthalpy of this feed water is denoted .
The heat balance equation for the first regenerative heater takes the following form:

(11.112)

Equations (11.111) and (11.112) yield:

(11.113)

(11.114)
As a result of regenerative heating, feed water is delivered into the boiler at a temperature of , i.e. at the
saturation temperature corresponding to the pressure . The enthalpy of water

(11.115)

In the condenser an amount of heat (i2 i 3 ) is removed from each kilogram of steam. However, since we have
shown that from each kilogram of steam entering the turbine only kilograms of exhaust steam
enters the condenser, it is clear that the heat rejected from one kilogram of exhaust steam amounts to

(11.116)

It follows that, in accordance with the general relationship (9.1), the equation for the thermal efficiency of the
regenerative feed-water cycle with two steam bleedings can be presented in the following form:
 (11.117)

The problem of determining the thermal efficiency of the regenerative feed-water cycle can also be approached
in another way.
One kilogram of steam passing into the condenser produces in the turbine the following amount of work:

(11.118)

One kilogram of steam bled from the turbine into the second regenerative heater, performs in the turbine the
following amount of work prior to bleeding:

(11.119)

Finally, one kilogram of steam bled into the first regenerative heater does the following amount of work in the
turbine:

(11.120)

Taking into account Eqs. (11.118) to (11.120), the work of the regenerative cycle[2] can be presented in the form

(11.121)

Taking Eq. (11.115) into account, we obtain from the above formula the following expression for the thermal
efficiency of the regenerative feed-water cycle:

(11.122)

Finally, the work done by the steam in the cycle will be equal to the work which would be done by 1 kg of steam
without bleeding minus the work which would be performed by the fractions of 1 kg of steam bled into the heaters
(if the fractions of steam were expanded in the turbine to the condenser pressure):

(11.123)

From Eq. (11.123) we obtain one more expression for the thermal efficiency of the regenerative cycle with two
steam bleedings:

(11.124)

It is understood that the three equations for the thermal efficiency of the regenerative cycle, (11.117), (11.122)
and (11.124), are identical.
Of a similar nature are the equations for the thermal efficiency of the regenerative cycle with any number of
heating stages. In particular, the expression similar to Eq. (11.124) for a cycle with n heating stages can be written
in the form
 (11.125)

An analysis shows that an increase of the number of regenerative heating stages leads to a higher cycle thermal
efficiency, for in this case the degree of regeneration in the cycle approaches the maximum (Fig. 11.26). However,
each subsequent stage of regenerative heating contributes less and less to the rise in thermal efficiency, as can be
seen from the graph in Fig. 11.30, where the rate of increase in the thermal efficiency of a regenerative cycle,
, is plotted as a function of the number of regenerative heating stages, n; the graph is plotted for the case of
uniform distribution of feed-water heating among individual stages.

Fig. 11.30

In modern high-power steam power plants operated at high steam conditions the number of regenerative
heating stages reaches nine.
The selection of bleeding points on a turbine for supplying steam to direct-contact regenerative feed-water
heaters (i.e. the selection of the temperature to which feed water is to be heated in each of the heating stages [3]) is
the subject for special analysis, a detailed consideration of which is beyond the scope of this book. It will only be
noted that the criterion in selecting a particular distribution of regenerative heating by stages is to ensure a maxi-
mum economy, usually attained by raising the thermal efficiency of the cycle. With an infinite number of feed-
heating stages the cycle thermal efficiency is determined unambiguously, but when a finite number of feed-
heating stages is operated, the cycle efficiency will differ depending on the mode of temperature distribution
between individual stages.

Rankine Reheat Cycle

Reheat Rankine Cycle is essentially a modification of simple rankine cycle. In reheat rankine cycle, the following
improvements are made to increase the efficiency of rankine cycle.
Lowering the condenser pressure
Increasing the temperature of steam while entering the turbine
Large variation in pressure between boiler and condenser
Implementation of reheat and regenerative system in the cycle
In simple rankine cycle, after the isentropic expansion in turbine , steam is directly fed into condenser for
condensation process. (Refer this article for better understanding). But in reheat system, two turbines
(high pressure turbine and low pressure turbine) are employed for improving efficiency. Steam, after expansion
from high pressure turbine, is sent again to boiler and heated till it reaches superheated condition. It is then left to
expand in low pressure turbine to attain condenser pressure.
h-s diagram of Reheat Rankine Cycle:
Reheat Rankine cycle can be understood well if you refer the following h-s diagram:
Processes in Reheat Rankine Cycle:
Six processes take place in reheat Rankine cycle. They are explained in detail below:

Process: 1-2 (high pressure turbine)

Here, dry saturated steam from the boiler is allowed to expand in a turbine isentropically i.e., Entropy remains
constant.

Let h1 be the enthalpy of steam entering the turbine

Let h2 be the enthalpy of steam leaving the turbine
Finally, the workdone by turbine is given by

WT = h 1 h 2
Calculation of h1 and h2 :
Using the pressure and temperature values at point 1, values for entropy (S 1) and enthalpy (h1) can be calculated
from superheated steam table or from Mollier diagram for steam.
After finding h1 and S1 ,dryness fraction (x2) can be calculated using the formula given below,
S1=S2=Sf2+x2Sfg2
Substitute the value of x2 in the following equation to find h2,
h2=hf2+x2hfg2
Process: 2-3 (boiler)
The expanded steam is made to attain the required temperature i.e., reheated in low pressure boiler at constant
pressure level. The enthalpy (h3) and entropy (S3) are calculated by the same method that we followed in process 1
to 2.
Process: 3-4 (Low pressure Turbine)
After attaining required temperature, steam is passed into low pressure turbine to carry out the remaining
expansion. The enthalpy (h4) and entropy (S4) values are calculated by the same method that we followed in
process 1 to 2 .
Process: 4-5 (condenser)
After expansion in turbine, steam is passed into condenser to preform condensation process. Here the remaining
heat in the steam is rejected into atmosphere.

Let h4 be the enthalpy of steam entering the condenser.

Let h5 be the enthalpy of water leaving the condenser.
Heat rejected from condenser is given by
QR = h4 h5 J or QR = h2 hf4 J
hf4 = h4 (Since, the output from condenser is a fluid and graphically, the enthalpy at point 4 and point 5 are same.)
Process: 5-6 (Pump)
Water from the condenser is pumped into the boiler using an external pump. During this process, pressure
increases P5 to P6 isentropically (The enthalpy and temperature of water also increase due to pump work).
Let P5 ,h5 be the pressure and enthalpy at stage 5 respectively.
Let P6 ,h6 be the pressure and enthalpy at stage 6 respectively.
The work done by pump is given by

Wp = h6 h5 = Vf5 (P6 P4) 100 J

Note :
All the values of pressure here are substituted in N/m and all values of enthalpy are substituted in Joules.

Process: 6-1 (boiler)

Here the saturated water from the pump is heated by using a constant heat source (such as furnace). The input
saturated water is heated till it reaches super-heated condition. Temperature and enthalpy of saturated water
raise to a great extent, but its pressure remains constant. The change of phase from liquid to vapour occurs in
boiler.

Let h6 be the enthalpy of saturated water entering the boiler.

Let h1 be the enthalpy of super-heated steam coming out of boiler.
Heat supplied is given by

QS = h h 6 J
h6 can be calculated by means of pump work done formula.
h6 = h 5 + Wp J
All processes can be understood well if you refer the h-s diagram above.
Efficiency of Reheat Rankine Cycle:
As we know, efficiency is the ratio between output and input. Here, the output is work done and input is heat
energy.

Net work done = work done in turbine (both H.P. turbine and L.P. turbine) + work done in pump .

Net heat transfer = heat supplied in boiler + heat rejected in condenser.

Efficiency of reheat Rankine cycle is given by:

reheat=(h1h2)+(h3h4)WPh1(h5+Wp)+(h3h2)
It is 30 to 40% greater than simple Rankine cycle.
References:

http://www.thermopedia.com/content/1072/

http://twt.mpei.ac.ru/TTHB/2/KiSyShe/eng/Chapter11/11-4-
Reheat-cycle.html

http://twt.mpei.ac.ru/TTHB/2/KiSyShe/eng/Chapter11/11-5-
Regenerative-cycle.html

http://mechteacher.com/reheat-rankine-cycle/
 Table of Contents

Power Cycles

I. Rankine Cycle

II. Reheat Cycle

III. Regenerative Cycle

IV. Rankine Reheat Cycle

 Research

Paper

in

Thermodynamics

II
(MWF 8:00-9:00AM)

Submitted by: JIKNI J. NOBLE

Submitted to: Engr. MARILOU SANON TOMENTOS

 PROJECT

in

Thermodynamics

II

(MWF 8:00-9:00AM)

Submitted by: JELOU CATIPAY

Submitted to: Engr. MARILOU S. TOMENTOS