Moran M.J., Shapiro H.N. Fundamentals of Engineering Thermodynamics

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356 Chapter 8 Vapor Power Systems

In this section we consider aspects of vapor cycles related to working fluid characteristics,

binary vapor cycles, and cogeneration systems.

WORKING FLUID CHARACTERISTICS. Water is used as the working fluid in the vast majority

of vapor power systems because it is plentiful and low in cost, nontoxic, chemically stable, and

relatively noncorrosive. In addition, water has a relatively large change in specific enthalpy

when it vaporizes at ordinary steam generator pressures, which tends to limit the mass flow

rate for a desired power plant output. The properties of liquid water and water vapor are also

such that the back work ratios achieved are characteristically quite low, and the techniques of

superheat, reheat, and regeneration can be effective for increasing power plant efficiencies.

Water is less satisfactory insofar as some other desirable working fluid characteristics

are concerned. For example, the critical temperature of water is only 374.14C, which

is about 225C below the maximum allowable turbine inlet temperatures. Accordingly,

to achieve a high average temperature of heat addition and realize the attendant higher

thermal efficiency, it may be necessary for the steam generator to operate at supercritical

pressures. This requires costly piping and heat exchanger tubes capable of withstanding great

stresses. Another undesirable characteristic of water is that its saturation pressure at ordinary

condenser temperatures is well below atmospheric pressure. As a result, air can leak into the

system, necessitating the use of special ejector pumps attached to the condenser or deaera-

ting feedwater heaters to remove the air.

Although water has some shortcomings as a working fluid, no other single working fluid

has been found that is more satisfactory overall for large electrical generating plants. Still,

vapor power cycles intended for special uses may employ working fluids that are better

matched to the application at hand than water. Cycles that operate at relatively low temper-

atures may perform best with a refrigerant such as ammonia as the working fluid. Power sys-

tems for high-temperature applications may employ substances having desirable performance

characteristics at these temperatures. Moreover, water may be used together with some other

substance in a binary vapor cycle to achieve better overall performance than could be real-

ized with water alone.

BINARY VAPOR CYCLE. In a binary vapor power cycle two working fluids are used, one

with good high-temperature characteristics and another with good characteristics at the lower-

temperature end of the operating range.  for example. . . Fig. 8.13 shows a schematic

diagram and an accompanying T–s diagram of a binary vapor cycle using water and a suitable

liquid metal, with each substance in both the liquid and vapor phases. In this arrangement,

two ideal Rankine cycles are combined, with the heat rejection from the high-temperature cy-

cle (the topping cycle) being used as the energy input for the low-temperature cycle. This

energy transfer is accomplished in an interconnecting heat exchanger, which serves as the

condenser for the metal cycle and the boiler for the water cycle. Since the increase in the spe-

cific enthalpy of the water as it passes through the heat exchanger is typically several times

the magnitude of the specific enthalpy decrease of the metal, several units of mass of metal

must circulate in the topping cycle for each unit of mass of water in the other cycle. 

Binary vapor power cycles can operate with higher average temperatures of heat addition

than conventional cycles using water only and thus can attain higher thermal efficiencies.

However, the higher efficiencies achieved in this manner must justify the increased costs

related to the construction and operation of the more complex cycle arrangement.

COGENERATION. The binary cycle considered above is just one example of how systems

can be linked to obtain overall systems that utilize fuel more effectively. Other examples are



8.5 Other Vapor Cycle Aspects

binary cycle

8.5 Other Vapor Cycle Aspects 357

discussed in Secs. 7.6 and 7.7, including the multiple-use strategy known as cogeneration.

In each of the following two paragraphs we consider applications of cogeneration.

Direct combustion heating and the generation of process steam together account for a sub-

stantial portion of industrial energy resource use. But because the heat and steam are often

required at a relatively low temperature, good use is not made of the relatively high-

temperature products of combustion obtained by burning fuel. This source of inefficiency

can be reduced with a cogeneration arrangement in which fuel is consumed to produce both

electricity and steam (or heat), but with a total cost less than would be required to produce

them individually. A schematic of such a cogeneration system is shown in Fig. 8.14. The

figure is labeled with the fractions of the total flow entering the steam turbine that remain at

various locations. On the basis of a unit of mass entering the turbine at state 1, a fraction y

is extracted at an intermediate point 2 and diverted to some process that requires steam at

Metal condenser

and steam boiler

Steam superheater

and metal boiler

Liquid metal

Steam

condenser

Water vapor

Water cycle:

a–b–c–d–e

Metal

topping cycle:

1–2–3–4–1

Pump Pump

Turbine

 Figure 8.13 Water–metal binary vapor cycle.

Steam

generator

Condenser

System

requiring

process

steam

Pump 2

(1) (1 – y)

(1 – y)

(1)

Turbine

Pump 1

 Figure 8.14 Schematic

of a cogeneration system in

which process steam is bled

from the turbine.

cogeneration

358 Chapter 8 Vapor Power Systems

this condition. The remaining fraction, 1  y, expands to the turbine exit at state 3, producing

power in addition to that developed by the first turbine stage. Eventually this fraction rejoins

the amount extracted and the combined stream is returned to the steam generator. When no

process steam is required, all of the steam generated by the steam generator is allowed to

expand through the turbine.

Industries such as pulp and paper production and food processing, which require steam

for various processes in addition to electricity for operating machines, lighting, etc., are

particularly well suited for the use of cogeneration. Another cogeneration arrangement

being used increasingly involves district heating. In this application a power plant is in-

tegrated into a community so that it provides electricity for industrial, commercial, and do-

mestic use together with steam for process needs, space heating, and domestic water heat-

ing. District heating is commonly used in northern Europe and is being increasingly used

in the United States.



8.6 Case Study: Exergy Accounting of a

Vapor Power Plant

The discussions to this point show that a useful picture of power plant performance can be

obtained with the conservation of mass and conservation of energy principles. However,

these principles provide only the quantities of energy transferred to and from the plant and

do not consider the utility of the different types of energy transfer. For example, with the

conservation principles alone, a unit of energy exiting as generated electricity is regarded

as equivalent to a unit of energy exiting in relatively low-temperature cooling water, even

though the electricity has greater utility and economic value. Also, nothing can be learned

with the conservation principles alone about the relative significance of the irreversibilities

present in the various plant components and the losses associated with those components.

The method of exergy analysis introduced in Chap. 7 allows issues such as these to be dealt

with quantitatively.

EXERGY ACCOUNTING. In this section we account for the exergy entering a power plant

with the fuel. (Means for evaluating the fuel exergy are introduced in Sec. 13.6.) A portion

of the fuel exergy is ultimately returned to the plant surroundings as the net work developed.

However, the largest part is either destroyed by irreversibilities within the various plant com-

ponents or carried from the plant by the cooling water, stack gases, and unavoidable heat

transfers with the surroundings. These considerations are illustrated in the present section by

three solved examples, treating respectively the boiler, turbine and pump, and condenser of

a simple vapor power plant.

The irreversibilities present in each power plant component exact a tariff on the ex-

ergy supplied to the plant, as measured by the exergy destroyed in that component. The

component levying the greatest tariff is the boiler, for a significant portion of the exergy

entering the plant with the fuel is destroyed by irreversibilities within it. There are two

main sources of irreversibility in the boiler: (1) the irreversible heat transfer occurring be-

tween the hot combustion gases and the working fluid of the vapor power cycle flowing

through the boiler tubes, and (2) the combustion process itself. To simplify the present

discussion, the boiler is considered to consist of a combustor unit in which fuel and air

are burned to produce hot combustion gases, followed by a heat exchanger unit where the

cycle working fluid is vaporized as the hot gases cool. This idealization is illustrated in

Fig. 8.15.

Chapter 7 is a prerequisite for the study of this section.

district heating

8.6 Case Study: Exergy Accounting of a Vapor Power Plant 359

For the purposes of illustration, let us assume that 30% of the exergy entering the com-

bustion unit with the fuel is destroyed by the combustion irreversibility and 1% of the fuel

exergy exits the heat exchanger unit with the stack gases. The corresponding values for an

actual power plant might differ from these nominal values. However, they provide charac-

teristic values for discussion. (Means for evaluating the combustion exergy destruction and

the exergy accompanying the exiting stack gases are introduced in Chap. 13.) Using the fore-

going values for the combustion exergy destruction and stack gas loss, it follows that a maxi-

mum of 69% of the fuel exergy remains for transfer from the hot combustion gases to the

cycle working fluid. It is from this portion of the fuel exergy that the net work developed by

the plant is obtained. In Examples 8.7 through 8.9, we account for the exergy supplied by

the hot combustion gases passing through the heat exchanger unit. The principal results of

this series of examples are reported in Table 8.1. Carefully note that the values of Table 8.1

are keyed to the vapor power plant of Example 8.2 and thus have only qualitative signifi-

cance for vapor power plants in general.

CASE STUDY CONCLUSIONS. The entries of Table 8.1 suggest some general observa-

tions about vapor power plant performance. First, the table shows that the exergy destruc-

tions are more significant than the plant losses. The largest portion of the exergy entering

the plant with the fuel is destroyed, with exergy destruction in the boiler overshadowing

all others. By contrast, the loss associated with heat transfer to the cooling water is rela-

tively unimportant. The cycle thermal efficiency (calculated in the solution to Ex. 8.2) is

31.4%, so over two-thirds (68.6%) of the energy supplied to the cycle working fluid is

subsequently carried out by the condenser cooling water. By comparison, the amount of

exergy carried out is virtually negligible because the temperature of the cooling water is

raised only a few degrees over that of the surroundings and thus has limited utility. The

loss amounts to only 1% of the exergy entering the plant with the fuel. Similarly, losses

accompanying unavoidable heat transfer with the surroundings and the exiting stack gases

typically amount only to a few percent of the exergy entering the plant with the fuel and

are generally overstated when considered from the perspective of conservation of energy

alone.

Hot combustion

products

Combustor

unit

Fuel

Air

Cycle working

fluid

Condenser

Cooling

water in

Cooling

water out

Pump

Net power out

Turbine

Heat exchanger unit

Exiting stack gases

 Figure 8.15 Power

plant schematic for the

exergy analysis case study.

360 Chapter 8 Vapor Power Systems

An exergy analysis allows the sites where destructions or losses occur to be identified and

rank ordered for significance. This knowledge is useful in directing attention to aspects of

plant performance that offer the greatest opportunities for improvement through the applica-

tion of practical engineering measures. However, the decision to adopt any particular modi-

fication is governed by economic considerations that take into account both economies in

fuel use and the costs incurred to achieve those economies.

The calculations presented in the following examples illustrate the application of exergy

principles through the analysis of a simple vapor power plant. There are no fundamental dif-

ficulties, however, in applying the methodology to actual power plants, including consider-

ation of the combustion process. The same procedures also can be used for exergy accounting

of the gas turbine power plants considered in Chap. 9 and other types of thermal systems.

The following example illustrates the exergy analysis of the heat exchanger unit of the

boiler of the case study vapor power plant.

EXAMPLE 8.7 Cycle Exergy Analysis—Heat Exchanger Unit

The heat exchanger unit of the boiler of Example 8.2 has a stream of water entering as a liquid at 8.0 MPa and exiting as a satu-

rated vapor at 8.0 MPa. In a separate stream, gaseous products of combustion cool at a constant pressure of 1 atm from 1107 to

547C. The gaseous stream can be modeled as air as an ideal gas. Let T

 22C, p

 1 atm. Determine (a) the net rate at which

exergy is carried into the heat exchanger unit by the gas stream, in MW, (b) the net rate at which exergy is carried from the heat

exchanger by the water stream, in MW, (c) the rate of exergy destruction, in MW, (d) the exergetic efficiency given by Eq. 7.45.

SOLUTION

Known: A heat exchanger at steady state has a water stream entering and exiting at known states and a separate gas stream

entering and exiting at known states.

Find: Determine the net rate at which exergy is carried into the heat exchanger by the gas stream, in MW, the net rate at

which exergy is carried from the heat exchanger by the water stream, in MW, the rate of exergy destruction, in MW, and the

exergetic efficiency.

TABLE 8.1 Vapor Power Plant Exergy Accounting

Outputs

Net power out

30%

Losses

Condenser cooling water

Stack gases (assumed) 1%

Exergy Destruction

Boiler

Combustion unit (assumed) 30%

Heat exchanger unit

30%

Turbine

Pump

—

Condenser

Total 100%

All values are expressed as a percentage of

Example 8.9.

the exergy carried into the plant with the fuel.

Example 8.7.

Values are rounded to the nearest full percent.

Example 8.8.

Exergy losses associated with stray heat trans-

Example 8.8.

fer from plant components are ignored.

Example 8.9.

Example 8.8

8.6 Case Study: Exergy Accounting of a Vapor Power Plant 361

Schematic and Given Data:

1107°C,

1 atm

Air

547°C,

1 atm

Steam

saturated vapor,

8.0 MPa

Liquid,

8.0 MPa

 Figure E8.7

Assumptions:

1. The control volume shown in the accompanying figure operates at steady state with .

2. Kinetic and potential energy effects can be ignored.

3. The gaseous combustion products are modeled as air as an ideal gas.

4. The air and the water each pass through the steam generator at constant pressure.

5. Only 69% of the exergy entering the plant with the fuel remains after accounting for the stack loss and combustion exergy

destruction.

6. T

 22C, p

 1 atm.

Analysis: The analysis begins by evaluating the mass flow rate of the air in terms of the mass flow rate of the water. The

air and water pass through the boiler in separate streams. Hence, at steady state the conservation of mass principle requires

Using these relations, an energy rate balance for the overall control volume reduces a steady state to

where by assumption 1, and the kinetic and potential energy terms are dropped by assumption 2. In this equa-

tion and denote, respectively, the mass flow rates of the air and water. On solving

The solution to Example 8.2 gives h

 2758 kJ/kg and h

 183.36 kJ/kg. From Table A-22, h

 1491.44 kJ/kg and h



843.98 kJ/kg. Hence

From Example 8.2, . Thus, .

(a) The net rate at which exergy is carried into the heat exchanger unit by the gaseous stream can be evaluated using Eq. 7.36

Since the gas pressure remains constant, Eq. 6.21a giving the change in specific entropy of an ideal gas reduces to s

 s



s

. Thus, with h and s values from Table A-22



8.326  10

kJ/h

3600 s/ h

1 MW

kJ/s

` 231.28 MW

 e

2 117.694  10

kg/h2 11491.44  843.982 kJ/kg  1295 K213.34474  2.745042 kJ/kg

K

 m

h

 h

 T

 s

2

net rate at which exergy

is carried in by the

gaseous stream

§ m

 e

 17.694  10

kg/hm

 4.449  10

kg/h



2758  183.36

1491.44  843.98

 3.977

kg 1air2

kg 1steam2



 h

 W

 0

0  Q

 W

 m

 h

2 m

 h

 m

1water2

 m

1air2

 W

 0

362 Chapter 8 Vapor Power Systems

(b) The net rate at which exergy is carried out of the boiler by the water stream is determined similarly

From Table A-3, s

 5.7432 kJ/kg K. Double interpolation in Table A-5 at 8.0 MPa and h

 183.36 kJ/kg gives s



0.5957 kJ/kg K. Substituting known values

With the results of parts (a) and (b)

(d) The exergetic efficiency given by Eq. 7.45 is

This calculation indicates that 43.6% of the exergy supplied to the heat exchanger unit by the cooling combustion prod-

ucts is destroyed. However, since only 69% of the exergy entering the plant with the fuel is assumed to remain after the stack

loss and combustion exergy destruction are accounted for (assumption 5), it can be concluded that 0.69  43.6%  30% of

the exergy entering the plant with the fuel is destroyed within the heat exchanger. This is the value listed in Table 8.1.

Since energy is conserved, the rate at which energy is transferred to the water as it flows through the heat exchanger equals

the rate at which energy is transferred from the cooling gas passing through the heat exchanger. By contrast, the decrease

in exergy of the gas as it passes through the heat exchanger exceeds the increase in the exergy of the water by the amount

of exergy destroyed.

The rate of exergy destruction can be determined alternatively by evaluating the rate of entropy production, from an

entropy rate balance and multiplying by T

to obtain

Underlying the assumption that each stream passes through the heat exchanger at constant pressure is the neglect of fric-

tion as an irreversibility. Thus, the only contributor to exergy destruction in this case is heat transfer from the higher-

temperature combustion products to the vaporizing water.

 T

e 

 e



130.53 MW

231.28 MW

 0.564 156.4%2

 231.28 MW  130.53 MW  100.75 MW

 m

 e

2 m

 e



4.699  10

kJ/h

3600 s/ h

kJ/s

` 130.53 MW

 e

2 14.449  10

212758  183.362 29515.7432  0.59572

 m

h

 h

 T

 s

2

net rate at which exergy

is carried out by the

water stream

§ m

 e

❸

❶

❷

❸

❷

❶

In the next example, we determine the exergy destruction rates in the turbine and pump

of the case study vapor power plant.

EXAMPLE 8.8 Cycle Exergy Analysis—Turbine and Pump

Reconsider the turbine and pump of Example 8.2. Determine for each of these components the rate at which exergy is de-

stroyed, in MW. Express each result as a percentage of the exergy entering the plant with the fuel. Let T

 22C, p

 1 atm.

SOLUTION

Known: A vapor power cycle operates with steam as the working fluid. The turbine and pump each has an isentropic effi-

ciency of 85%.

Find: For the turbine and the pump individually, determine the rate at which exergy is destroyed, in MW. Express each result

as a percentage of the exergy entering the plant with the fuel.

8.6 Case Study: Exergy Accounting of a Vapor Power Plant 363

Schematic and Given Data:

Condenser

0.008 MPa

8.0 MPa

Pump

Cooling

water

Saturated

vapor

8.0 MPa

Saturated

liquid at

0.008 MPa

Turbine

out

Boiler

2s 23

Assumptions:

1. The turbine and the pump can each be analyzed as a control volume at steady state.

2. The turbine and pump operate adiabatically and each has an efficiency of 85%.

3. Kinetic and potential energy effects are negligible.

4. Only 69% of the exergy entering the plant with the fuel remains after accounting for the stack loss and combustion exergy

destruction.

5. T

 22C, p

 1 atm.

Analysis: The rate of exergy destruction can be found by reducing the exergy rate balance or by use of the relationship

where is the rate of entropy production from an entropy rate balance. With either approach, the rate of ex-

ergy destruction for the turbine can be expressed as

From Table A-3, s

 5.7432 kJ/kg K. Using h

 1939.3 kJ/kg from the solution to Example 8.2, the value of s

can be

determined from Table A-3 as s

 6.2021 kJ/kg K. Substituting values

From the solution to Example 8.7, the net rate at which exergy is supplied by the cooling combustion gases is 231.28 MW.

The turbine rate of exergy destruction expressed as a percentage of this is (16.72231.28)(100%)  7.23%. However, since

only 69% of the entering fuel exergy remains after the stack loss and combustion exergy destruction are accounted for, it can

be concluded that 0.69  7.23%  5% of the exergy entering the plant with the fuel is destroyed within the turbine. This is

the value listed in Table 8.1.

Similarly, the exergy destruction rate for the pump is

With s

from Table A-3 and s

from the solution to Example 8.7

 a4.07  10

1 h

3600 s

1 MW

kJ/s

` 0.11 MW

 14.449  10

kg/h21295 K210.5957  0.592621kJ/kg

 m

 s

 a0.602  10

3600 s

` `

1 MW

kJ/s

` 16.72 MW

 14.449  10

kg/h21295 K216.2021  5.743221kJ/kg

 m

 s

 T

 Figure E8.8

364 Chapter 8 Vapor Power Systems

Expressing this as a percentage of the exergy entering the plant as calculated above, we have (0.11231.28)(69%)  0.03%.

This value is rounded to zero in Table 8.1.

The net power output of the vapor power plant of Example 8.2 is 100 MW. Expressing this as a percentage of the rate at

which exergy is carried into the plant with the fuel, (100231.28)(69%)  30%, as shown in Table 8.1.

The following example illustrates the exergy analysis of the condenser of the case study

vapor power plant.

EXAMPLE 8.9 Cycle Exergy Analysis—Condenser

The condenser of Example 8.2 involves two separate water streams. In one stream a two-phase liquid–vapor mixture enters

at 0.008 MPa and exits as a saturated liquid at 0.008 MPa. In the other stream, cooling water enters at 15C and exits at 35C.

(a) Determine the net rate at which exergy is carried from the condenser by the cooling water, in MW. Express this result as

a percentage of the exergy entering the plant with the fuel. (b) Determine for the condenser the rate of exergy destruction, in

MW. Express this result as a percentage of the exergy entering the plant with the fuel. Let T

 22C and p

 1 atm.

SOLUTION

Known: A condenser at steady state has two streams: (1) a two-phase liquid–vapor mixture entering and condensate exiting

at known states and (2) a separate cooling water stream entering and exiting at known temperatures.

Find: Determine the net rate at which exergy is carried from the condenser by the cooling water stream and the rate of ex-

ergy destruction for the condenser. Express both quantities in MW and as percentages of the exergy entering the plant with

the fuel.

Schematic and Given Data:

Saturated

liquid,

0.008 MPa

Liquid,

15°C

Two-phase

liquid-vapor mixture,

0.008 MPa

Liquid,

35°C

 Figure E8.9

Assumptions:

1. The control volume shown on the accompanying figure operates at steady state with .

2. Kinetic and potential energy effects can be ignored.

3. Only 69% of the fuel exergy remains after accounting for the stack loss and combustion exergy destruction.

4. T

 22C, p

 1 atm.

Analysis:

(a) The net rate at which exergy is carried out of the condenser can be evaluated by using Eq. 7.36:

 m

h

 h

 T

 s

2

net rate at which exergy

is carried out by the

cooling water

§ m

 e

 W

 0

Chapter Summary and Study Guide 365

where is the mass flow rate of the cooling water from the solution to Example 8.2. With saturated liquid values for spe-

cific enthalpy and entropy from Table A-2 at the specified inlet and exit temperatures of the cooling water

Expressing this as a percentage of the exergy entering the plant with the fuel, we get (2.23231.28)(69%)  1%. This is the

value listed in Table 8.1.

(b) The rate of exergy destruction for the condenser can be evaluated by reducing the exergy rate balance. Alternatively, the

relationship can be employed, where is the time rate of entropy production for the condenser determined from

an entropy rate balance. With either approach, the rate of exergy destruction can be expressed as

Substituting values

Expressing this as a percentage of the exergy entering the plant with the fuel, we get (11.56231.28)(69%)  3%. This is the

value listed in Table 8.1.

The cycle thermal efficiency evaluated in the solution to Example 8.2 is 31.4%. Thus, it can be concluded that over two-

thirds (68.6%) of the energy supplied by the cooling combustion gas to the cycle working fluid is subsequently carried out

by the condenser cooling water. However, the amount of exergy carried out with the cooling water is relatively minor be-

cause the temperature of the water is raised only a few degrees over that of the surroundings.



416.1  10

kJ/h

3600 s/h

1 MW

kJ/s

` 11.56 MW

 29514.449  10

210.5926  6.20212 19.39  10

210.5053  0.22452

 T

m

 s

2 m

 s

2

 T



8.019  10

kJ/h

3600 s/h

1 MW

kJ/s

` 2.23 MW

 e

2 19.39  10

kg/h2 1146.68  62.992 kJ/kg  1295 K210.5053  0.22452 kJ/kg

K

❶

Chapter Summary and Study Guide

In this chapter we have considered practical arrangements for

vapor power plants producing a net power output from a fos-

sil fuel, nuclear, or solar input. We have illustrated how vapor

power plants are modeled thermodynamically and considered

the principal irreversibilities and losses associated with such

plants. The main components of simple vapor power plants

are modeled by the Rankine cycle. In this chapter, we also

have introduced modifications to the simple vapor power cycle

aimed at improving overall performance. These include su-

perheat, reheat, regeneration, supercritical operation, cogen-

eration, and binary cycles. We have also included a case study

to illustrate the application of exergy analysis to vapor power

plants.

The following checklist provides a study guide for this

chapter. When your study of the text and end-of-chapter ex-

ercises has been completed you should be able to

 write out the meanings of the terms listed in the margin

throughout the chapter and understand each of the

related concepts. The subset of key concepts listed below

is particularly important.

 sketch schematic diagrams and accompanying T–s dia-

grams of Rankine, reheat, and regenerative vapor power

cycles.

 apply conservation of mass and energy, the second law,

and property data to determine power cycle performance,

including thermal efficiency, net power output, and mass

flow rates.

 discuss the effects on Rankine cycle performance of

varying steam generator pressure, condenser pressure,

and turbine inlet temperature.

 discuss the principal sources of exergy destruction and

loss in vapor power plants.