Moran M.J., Shapiro H.N. Fundamentals of Engineering Thermodynamics
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366 Chapter 8 Vapor Power Systems
Key Engineering Concepts
Rankine cycle p. 327
thermal efficiency p. 328
back work ratio p. 329
superheat p. 340
reheat p. 340
regeneration p. 346
cogeneration p. 357
Exercises: Things Engineers Think About
1. Do you know what kinds of power plants (coal-fired, hydro-
electric, nuclear, etc.) generate the electricity provided by your
local utility company?
2. Referring to your monthly electric bill, determine how much
you pay per kW h of electricity.
3. Might the thermal efficiency of a vapor power plant be
different in the winter than in the summer?
4. Power plants located in arid areas may accomplish condensa-
tion by air cooling instead of cooling with water flowing through
the condenser. How might air cooling affect the thermal
efficiency?
5. Is the Carnot vapor power cycle a suitable model for the sim-
ple vapor power plant?
6. Keeping states 1 and 2 fixed, how would Fig. 8.6 be modified
if the frictional pressure drops through the boiler and condenser
were considered?
7. Based on thermal efficiency, approximately two-thirds of the
energy input by heat transfer in the steam generator of a power
#
plant is ultimately rejected to cooling water flowing through the
condenser. Is the heat rejected an indicator of the inefficiency of
the power plant?
8. Brainstorm some ways to use the cooling water exiting the
condenser of a large power plant.
9. What effects on a river’s ecology might result from a power
plant’s use of river water for condenser cooling?
10. Referring to Fig. 8.1, what environmental impacts might
result from the two plumes shown on the figure?
11. Referring to Example 8.5, what are the principal sources of
internal irreversibility?
12. Why is water the most commonly used working fluid in vapor
power plants?
13. What do you think about using solar energy to generate
electric power?
Problems: Developing Engineering Skills
Analyzing Rankine Cycles
8.1 Water is the working fluid in an ideal Rankine cycle. The
condenser pressure is 8 kPa, and saturated vapor enters the tur-
bine at
(a) 18 MPa and (b) 4 MPa. The net power output of
the cycle is 100 MW. Determine for each case the mass flow
rate of steam, in kg/h, the heat transfer rates for the working
fluid passing through the boiler and condenser, each in kW,
and the thermal efficiency.
8.2 Water is the working fluid in an ideal Rankine cycle. Su-
perheated vapor enters the turbine at 8 MPa, 480C. The con-
denser pressure is 8 kPa. The net power output of the cycle is
100 MW. Determine for the cycle
(a) the rate of heat transfer to the working fluid passing
through the steam generator, in kW.
(b) the thermal efficiency.
(c) the mass flow rate of condenser cooling water, in kg/h, if
the cooling water enters the condenser at 15C and exits
at 35C with negligible pressure change.
8.3 Water is the working fluid in a Carnot vapor power cycle.
Saturated liquid enters the boiler at a pressure of 8 MPa, and
saturated vapor enters the turbine. The condenser pressure is
8 kPa. Determine
(a) the thermal efficiency.
(b) the back work ratio.
(c) the heat transfer to the working fluid per unit mass pass-
ing through the boiler, in kJ/kg.
(d) the heat transfer from the working fluid per unit mass pass-
ing through the condenser, in kJ/kg.
(e) Compare the results of parts (a)–(d), with the correspon-
ding values of Example 8.1, and comment.
8.4 Plot each of the quantities calculated in Problem 8.2 versus
condenser pressure ranging from 6 kPa to 0.1 MPa. Discuss.
8.5 Plot each of the quantities calculated in Problem 8.2 versus
steam generator pressure ranging from 4 MPa to 24 MPa.
Maintain the turbine inlet temperature at 480C. Discuss.
8.6 Water is the working fluid in an ideal Rankine cycle. Sat-
urated vapor enters the turbine at 18 MPa. The condenser pres-
sure is 6 kPa. Determine
(a) the net work per unit mass of steam flowing, in kJ/kg.
(b) the heat transfer to the steam passing through the boiler,
in kJ per kg of steam flowing.
(c) the thermal efficiency.
(d) the heat transfer to cooling water passing through the con-
denser, in kJ per kg of steam condensed.
Problems: Developing Engineering Skills 367
8.7 Water is the working fluid in a Carnot vapor power cycle.
Saturated liquid enters the boiler at a pressure of 18 MPa, and
saturated vapor enters the turbine. The condenser pressure is
6 kPa. Determine
(a) the thermal efficiency.
(b) the back work ratio.
(c) the net work of the cycle per unit mass of water flowing,
in kJ/kg.
(d) the heat transfer from the working fluid passing through
the condenser, in kJ per kg of steam flowing.
(e) Compare the results of parts (a)–(d) with those of Problem
8.6, respectively, and comment.
8.8 Plot each of the quantities calculated in Problem 8.6 versus
turbine inlet temperature ranging from the saturation temper-
ature at 18 MPa to 560C. Discuss.
8.9 A power plant based on the Rankine cycle is under
development to provide a net power output of 10 MW. Solar
collectors are to be used to generate Refrigerant 22 vapor at
1.6 MPa, 50C, for expansion through the turbine. Cooling
water is available at 20C. Specify the preliminary design of
the cycle and estimate the thermal efficiency and the refriger-
ant and cooling water flow rates, in kg/h.
8.10 Refrigerant 134a is the working fluid in a solar power plant
operating on a Rankine cycle. Saturated vapor at 60C enters
the turbine, and the condenser operates at a pressure of 6 bar.
The rate of energy input to the collectors from solar radiation
is 0.4 kW per m
2
of collector surface area. Determine the min-
imum possible solar collector surface area, in m
2
, per kW of
power developed by the plant.
8.11 The cycle of Problem 8.3 is modified to include the ef-
fects of irreversibilities in the adiabatic expansion and com-
pression processes. If the states at the turbine and pump inlets
remain unchanged, repeat parts (a)–(d) of Problem 8.3 for the
modified Carnot cycle with
t
0.80 and
p
0.70.
8.12 Steam enters the turbine of a simple vapor power plant
with a pressure of 10 MPa and temperature T, and expands
adiabatically to 6 kPa. The isentropic turbine efficiency is 85%.
Saturated liquid exits the condenser at 6 kPa and the isentropic
pump efficiency is 82%.
(a) For T 580C, determine the turbine exit quality and the
cycle thermal efficiency.
(b) Plot the quantities of part (a) versus T ranging from 580
to 700C.
8.13 Reconsider the analysis of Problem 8.2, but include in the
analysis that the turbine and pump have isentropic efficiencies
of 85 and 70%, respectively. Determine for the modified cycle
(a) the thermal efficiency.
(b) the mass flow rate of steam, in kg/h, for a net power out-
put of 100 MW.
(c) the mass flow rate of condenser cooling water, in kg/h, if
the cooling water enters the condenser at 15C and exits
at 35C with negligible pressure change.
8.14 Reconsider Problem 8.8, but include in the analysis that
the turbine and pump each have isentropic efficiencies of
(a) 90%, (b) 80%, (c) 70%. Answer the same questions for the
modified cycle as in Problem 8.8.
8.15 Superheated steam at 8 MPa and 480C leaves the steam
generator of a vapor power plant. Heat transfer and frictional
effects in the line connecting the steam generator and the tur-
bine reduce the pressure and temperature at the turbine inlet
to 7.6 MPa and 440C, respectively. The pressure at the exit
of the turbine is 10 kPa, and the turbine operates adiabatically.
Liquid leaves the condenser at 8 kPa, 36C. The pressure is in-
creased to 8.6 MPa across the pump. The turbine and pump
isentropic efficiencies are 88%. The mass flow rate of steam
is 79.53 kg/s. Determine
(a) the net power output, in kW.
(b) the thermal efficiency.
(c) the rate of heat transfer from the line connecting the steam
generator and the turbine, in kW.
(d) the mass flow rate of condenser cooling water, in kg/s, if
the cooling water enters at 15C and exits at 35C with
negligible pressure change.
8.16 Superheated steam at 18 MPa, 560C, enters the turbine
of a vapor power plant. The pressure at the exit of the turbine
is 0.06 bar, and liquid leaves the condenser at 0.045 bar, 26C.
The pressure is increased to 18.2 MPa across the pump. The
turbine and pump have isentropic efficiencies of 82 and 77%,
respectively. For the cycle, determine
(a) the net work per unit mass of steam flow, in kJ/kg.
(b) the heat transfer to steam passing through the boiler, in kJ
per kg of steam flowing.
(c) the thermal efficiency.
(d) the heat transfer to cooling water passing through the con-
denser, in kJ per kg of steam condensed.
8.17 In the preliminary design of a power plant, water is chosen
as the working fluid and it is determined that the turbine inlet
temperature may not exceed 520C. Based on expected cool-
ing water temperatures, the condenser is to operate at a pres-
sure of 0.06 bar. Determine the steam generator pressure
required if the isentropic turbine efficiency is 80% and the
quality of steam at the turbine exit must be at least 90%.
Considering Reheat and Supercritical Cycles
8.18 Steam at 10 MPa, 600C enters the first-stage turbine of
an ideal Rankine cycle with reheat. The steam leaving the
reheat section of the steam generator is at 500C, and the con-
denser pressure is 6 kPa. If the quality at the exit of the second-
stage turbine is 90%, determine the cycle thermal efficiency.
8.19 The ideal Rankine cycle of Problem 8.2 is modified to in-
clude reheat. In the modified cycle, steam expands though the
first-stage turbine to 0.7 MPa and then is reheated to 480C.
If the net power output of the modified cycle is 100 MW,
determine for the modified cycle
(a) the rate of heat transfer to the working fluid passing
through the steam generator, in MW.
(b) the thermal efficiency.
(c) the rate of heat transfer to cooling water passing through
the condenser, in MW.
368 Chapter 8 Vapor Power Systems
8.20 For the cycle of Problem 8.19, investigate the effects on
cycle performance as the reheat pressure and final reheat tem-
perature take on other values. Construct suitable plots and dis-
cuss. Reconsider the analysis assuming that the pump and each
turbine stage has an isentropic efficiency of 80%.
8.21 Steam at 32 MPa, 520C enters the first stage of a super-
critical reheat cycle including three turbine stages. Steam ex-
iting the first-stage turbine at pressure p is reheated at constant
pressure to 440C, and steam exiting the second-stage turbine
at 0.5 MPa is reheated at constant pressure to 360C. Each tur-
bine stage and the pump has an isentropic efficiency of 85%.
The condenser pressure is 8 kPa.
(a) For p 4 MPa, determine the net work per unit mass of
steam flowing, in kJ/kg, and the thermal efficiency.
(b) Plot the quantities of part (a) versus p ranging from 0.5 to
10 MPa.
8.22 An ideal Rankine cycle with reheat uses water as the work-
ing fluid. The conditions at the inlet to the first-stage turbine
are 14 MPa, 600C and the steam is reheated between the
turbine stages to 600C. For a condenser pressure of 6 kPa,
plot the cycle thermal efficiency versus reheat pressure for
pressures ranging from 2 to 12 MPa.
Analyzing Regenerative Cycles
8.23 Modify the ideal Rankine cycle of Problem 8.2 to include
one open feedwater heater operating at 0.7 MPa. Saturated liq-
uid exits the feedwater heater at 0.7 MPa. Answer the same
questions about the modified cycle as in Problem 8.2 and
discuss the results.
8.24 For the cycle of Problem 8.23, investigate the effects on
cycle performance as the feedwater heater pressure takes on
other values. Construct suitable plots and discuss. Reconsider
the analysis assuming that each turbine stage and each pump
has an isentropic efficiency of 80%.
8.25 A power plant operates on a regenerative vapor power cy-
cle with one open feedwater heater. Steam enters the first tur-
bine stage at 12 MPa, 520C and expands to 1 MPa, where
some of the steam is extracted and diverted to the open feed-
water heater operating at 1 MPa. The remaining steam expands
through the second turbine stage to the condenser pressure of
6 kPa. Saturated liquid exits the open feedwater heater at
1 MPa. For isentropic processes in the turbines and pumps, de-
termine for the cycle
(a) the thermal efficiency and (b) the
mass flow rate into the first turbine stage, in kg/h, for a net
power output of 330 MW.
8.26 Reconsider the cycle of Problem 8.25 as the feedwater
heater pressure takes on other values. Plot the thermal effi-
ciency and the rate of exergy destruction within the feedwater
heater, in kW, versus the feedwater heater pressure ranging
from 0.5 to 10 MPa. Let T
0
293 K.
8.27 Compare the results of Problem 8.25 with those for an
ideal Rankine cycle having the same turbine inlet conditions
and condenser pressure, but no regenerator.
8.28 For the cycle of Problem 8.25, investigate the effects on cy-
cle performance as the feedwater heater pressure takes on other
values. Construct suitable plots and discuss. Assume that each
turbine stage and each pump has an isentropic efficiency of 80%.
8.29 Modify the ideal Rankine cycle of Problem 8.6 to include
superheated vapor entering the first turbine stage at 18 MPa,
560C, and one open feedwater heater operating at 1 MPa. Sat-
urated liquid exits the open feedwater heater at 1 MPa. Deter-
mine for the modified cycle
(a) the net work, in kJ per kg of steam entering the first tur-
bine stage.
(b) the thermal efficiency.
(c) the heat transfer to cooling water passing through the con-
denser, in kJ per kg of steam entering the first turbine stage.
8.30 Reconsider the cycle of Problem 8.29, but include in the
analysis that each turbine stage and pump has an isentropic
efficiency of 85%.
8.31 Modify the ideal Rankine cycle of Problem 8.2 to include
one closed feedwater heater using extracted steam at 0.7 MPa.
Condensate drains from the feedwater heater as saturated liquid
at 0.7 MPa and is trapped into the condenser. The feedwater
leaves the heater at 8 MPa and a temperature equal to the satu-
ration temperature at 0.7 MPa. Answer the same questions about
the modified cycle as in Problem 8.2 and discuss the results.
8.32 For the cycle of Problem 8.31, investigate the effects on cy-
cle performance as the extraction pressure takes on other values.
Assume that condensate drains from the closed feedwater heater
as saturated liquid at the extraction pressure. Also, feedwater
leaves the heater at 8 MPa and a temperature equal to the satu-
ration temperature at the extraction pressure. Construct suitable
plots and discuss. Reconsider the analysis assuming that each
turbine stage and the pump has an isentropic efficiency of 80%.
8.33 A power plant operates on a regenerative vapor power cycle
with one closed feedwater heater. Steam enters the first turbine
stage at 120 bar, 520C and expands to 10 bar, where some of
the steam is extracted and diverted to a closed feedwater heater.
Condensate exiting the feedwater heater as saturated liquid at
10 bar passes through a trap into the condenser. The feedwater
exits the heater at 120 bar with a temperature of 170C. The
condenser pressure is 0.06 bar. For isentropic processes in each
turbine stage and the pump, determine for the cycle
(a) the
thermal efficiency and (b) the mass flow rate into the first-stage
turbine, in kg/h, if the net power developed is 320 MW.
8.34 Reconsider the cycle of Problem 8.33, but include in the
analysis that each turbine stage has an isentropic efficiency of
82%. The pump efficiency remains 100%.
8.35 Modify the cycle of Problem 8.31 such that the saturated
liquid condensate from the feedwater heater at 0.7 MPa is
pumped into the feedwater line rather than being trapped into
the condenser. Answer the same questions about the modified
cycle as in Problem 8.31. List advantages and disadvantages
of each scheme for removing condensate from the closed feed-
water heater.
8.36 Modify the ideal Rankine cycle of Problem 8.6 to include
superheated vapor entering the first turbine stage at 18 MPa,
Problems: Developing Engineering Skills 369
560C, and one closed feedwater heater using extracted steam
at 1 MPa. Condensate drains from the feedwater heater as sat-
urated liquid at 1 MPa and is trapped into the condenser. The
feedwater leaves the heater at 18 MPa and a temperature equal
to the saturation temperature at 1 MPa. Determine for the
modified cycle.
(a) the net work, in kJ per kg of steam entering the first tur-
bine stage.
(b) the thermal efficiency.
(c) the heat transfer to cooling water passing through the con-
denser, in kJ per kg of steam entering the first turbine stage.
8.37 Reconsider the cycle of Problem 8.36, but include in the
analysis that the isentropic efficiencies of the turbine stages
and the pump are 85%.
8.38 Referring to Fig. 8.12, if the fractions of the total flow en-
tering the first turbine stage (state 1) extracted at states 2, 3,
6, and 7 are y
2
, y
3
, y
6
, and y
7
, respectively, what are the frac-
tions of the total flow at states 8, 11, and 17?
8.39 Consider a regenerative vapor power cycle with two feed-
water heaters, a closed one and an open one. Steam enters the
first turbine stage at 8 MPa, 480C, and expands to 2 MPa.
Some steam is extracted at 2 MPa and fed to the closed feed-
water heater. The remainder expands through the second-stage
turbine to 0.3 MPa, where an additional amount is extracted
and fed into the open feedwater heater, which operates at
0.3 MPa. The steam expanding through the third-stage turbine
exits at the condenser pressure of 8 kPa. Feedwater leaves the
closed heater at 205C, 8 MPa, and condensate exiting as
saturated liquid at 2 MPa is trapped into the open heater.
Saturated liquid at 0.3 MPa leaves the open feedwater heater.
The net power output of the cycle is 100 MW. If the turbine
stages and pumps are isentropic, determine
(a) the thermal efficiency.
(b) the mass flow rate of steam entering the first turbine, in
kg/h.
8.40 For the cycle of Problem 8.39, investigate the effects on
cycle performance as the higher extraction pressure takes on
other values. The operating conditions for the open feedwater
heater are unchanged from those in Problem 8.39. Assume that
condensate drains from the closed feedwater heater as satu-
rated liquid at the higher extraction pressure. Also, feedwater
leaves the heater at 8 MPa and a temperature equal to the sat-
uration temperature at the extraction pressure. Construct suit-
able plots and discuss. Reconsider the analysis assuming that
each turbine stage and the pump has an isentropic efficiency
of 80%.
8.41 A power plant operates on a regenerative vapor power
cycle with two feedwater heaters. Steam enters the first tur-
bine stage as 12 MPa, 520C and expands in three stages to
the condenser pressure of 6 kPa. Between the first and sec-
ond stages, some steam is diverted to a closed feedwater
heater at 1 MPa, with saturated liquid condenstate being
pumped ahead into the boiler feedwater line. The feedwater
leaves the closed heater at 12 MPa, 170C. Steam is extracted
between the second and third turbine stages at 0.15 MPa and
fed into an open feedwater heater operating at that pressure.
Saturated liquid at 0.15 MPa leaves the open feedwater heater.
For isentropic processes in the pumps and turbines, determine
for the cycle
(a) the thermal efficiency and (b) the mass flow
rate into the first-stage turbine, in kg/h, if the net power
developed is 320 MW.
8.42 Reconsider the cycle of Problem 8.41, but include in the
analysis that each turbine stage has an isentropic efficiency of
82% and each pump an efficiency of 100%.
8.43 Modify the ideal Rankine cycle of Problem 8.6 to include
superheated vapor entering the first turbine stage at 18 MPa,
560C, and two feedwater heaters. One closed feedwater heater
uses extracted steam at 4 MPa, and one open feedwater heater
operates with extracted steam at 0.3 MPa. Saturated liquid con-
densate drains from the closed heater at 4 MPa and is trapped
into the open heater. The feedwater leaves the closed heater at
18 MPa and a temperature equal to the saturation temperature
at 4 MPa. Saturated liquid leaves the open heater at 0.3 MPa.
Determine for the modified cycle
(a) the net work, in kJ per kg of steam entering the first turbine
stage.
(b) the thermal efficiency.
(c) the heat transfer to cooling water passing through the con-
denser, in kJ per kg of steam entering the first turbine stage.
8.44 Reconsider the cycle of Problem 8.43, but include in the
analysis that the isentropic efficiencies of the turbine stages
and pumps are 85%.
8.45 Modify the regenerative vapor power cycle in Problem
8.39 to include reheat at 2 MPa. The portion of the flow that
passes through the second turbine stage is reheated to 440C
before it enters the second turbine stage. Determine the ther-
mal efficiency of the modified cycle.
8.46 Reconsider the cycle of Problem 8.45, but include in the
analysis that each turbine stage has an isentropic efficiency of
85% and each pump an efficiency of 82%.
8.47 Steam enters the first turbine stage of a vapor power cy-
cle with reheat and regeneration at 32 MPa, 600C, and ex-
pands to 8 MPa. A portion of the flow is diverted to a closed
feedwater heater at 8 MPa, and the remainder is reheated to
560C before entering the second turbine stage. Expansion
through the second turbine stage occurs to 1 MPa, where an-
other portion of the flow is diverted to a second closed feed-
water heater at 1 MPa. The remainder of the flow expands
through the third turbine stage to 0.15 MPa, where a portion
of the flow is diverted to an open feedwater heater operating
at 0.15 MPa, and the rest expands through the fourth turbine
stage to the condenser pressure of 6 kPa. Condensate leaves
each closed feedwater heater as saturated liquid at the respec-
tive extraction pressure. The feedwater streams leave each
closed feedwater heater at a temperature equal to the satura-
tion temperature at the respective extraction pressure. The con-
densate streams from the closed heaters each pass through traps
into the next lower-pressure feedwater heater. Saturated liquid
exiting the open heater is pumped to the steam generator
370 Chapter 8 Vapor Power Systems
pressure. If each turbine stage has an isentropic efficiency of
85% and the pumps operate isentropically
(a) sketch the layout of the cycle and number the principal
state points.
(b) determine the thermal efficiency of the cycle.
(c) calculate the mass flow rate into the first turbine stage, in
kg/h, for a net power output of 500 MW.
Considering Other Vapor Cycle Aspects
8.48 A binary vapor power cycle consists of two ideal Rankine
cycles with steam and ammonia as the working fluids. In the
steam cycle, superheated vapor enters the turbine at 6 MPa,
640C, and saturated liquid exits the condenser at 60C. The
heat rejected from the steam cycle is provided to the ammo-
nia cycle, producing saturated vapor at 50C, which enters the
ammonia turbine. Saturated liquid leaves the ammonia con-
denser at 1 MPa. For a net power output of 20 MW from the
binary cycle, determine
(a) the power output of the steam and ammonia turbines,
respectively, in MW.
(b) the rate of heat addition to the binary cycle, in MW.
(c) the thermal efficiency.
8.49 Water is the working fluid in a cogeneration cycle that gen-
erates electricity and provides heat for campus buildings.
Steam at 2 MPa, 320C, enters a two-stage turbine with a mass
flow rate of 0.82 kg/s. A fraction of the total flow, 0.141, is
extracted between the two stages at 0.15 MPa to provide for
building heating, and the remainder expands through the sec-
ond stage to the condenser pressure of 0.06 bar. Condensate
returns from the campus buildings at 0.1 MPa, 60C and passes
through a trap into the condenser, where it is reunited with the
main feedwater flow. Saturated liquid leaves the condenser at
0.06 bar. Each turbine stage has an isentropic efficiency of
80%, and the pumping process can be considered isentropic.
Determine
(a) the rate of heat transfer to the working fluid passing
through the steam generator, in kJ/h.
(b) the net power developed, in kJ/h.
(c) the rate of heat transfer for building heating, in kJ/h.
(d) the rate of heat transfer to the cooling water passing
through the condenser, in kJ/h.
8.50 Consider a cogeneration system operating as illustrated in
Fig. 8.14. The steam generator provides a 10
6
kg/h of steam
at 8 MPa, 480C, of which 4 10
5
kg/h is extracted between
the first and second turbine stages at 1 MPa and diverted to a
process heating load. Condensate returns from the process
heating load at 0.95 MPa, 120C and is mixed with liquid ex-
iting the lower-pressure pump at 0.95 MPa. The entire flow is
then pumped to the steam generator pressure. Saturated liquid
at 8 kPa leaves the condenser. The turbine stages and the pumps
operate with isentropic efficiencies of 86 and 80%, respec-
tively. Determine
(a) the heating load, in kJ/h.
(b) the power developed by the turbine, in kW.
(c) the rate of heat transfer to the working fluid passing
through the steam generator, in kJ/h.
8.51 Figure P8.51 shows the schematic diagram of a cogen-
eration cycle. In the steam cycle, superheated vapor enters
the turbine with a mass flow rate of 5 kg/s at 40 bar, 440C
and expands isentropically to 1.5 bar. Half of the flow is ex-
tracted at 1.5 bar and used for industrial process heating. The
rest of the steam passes through a heat exchanger, which
serves as the boiler of the Refrigerant 134a cycle and the
condenser of the steam cycle. The condensate leaves the heat
exchanger as saturated liquid at 1 bar, where it is combined
with the return flow from the process, at 60C and 1 bar, be-
fore being pumped isentropically to the steam generator
pressure. The Refrigerant 134a cycle is an ideal Rankine cy-
cle with refrigerant entering the turbine at 16 bar, 100C and
saturated liquid leaving the condenser at 9 bar. Determine,
in kW,
(a) the rate of heat transfer to the working fluid passing
through the steam generator of the steam cycle.
(b) the net power output of the binary cycle.
(c) the rate of heat transfer to the industrial process.
Steam
generator
1
2
a
4
b
c
3 d
5
6
R-134a
cycle
Pump
Pump
Condenser
1.5 bar
To industrial
process
Refrigerant
cycle
Return flow from
industrial process
1 bar, 60°C
H
2
O cycle
H
2
O/R-134a
heat
exchanger
Q
·
in
W
·
t
1
Turbine
W
·
t
2
Turbine
Q
·
out
W
·
p
2
W
·
p
1
Figure P8.51
Vapor Cycle Exergy Analysis
8.52 The steam generator of a vapor power plant can be con-
sidered for simplicity to consist of a combustor unit in which
Design & Open Ended Problems: Exploring Engineering Practice 371
fuel and air are burned to produce hot combustion gases, fol-
lowed by a heat exchanger unit where the cycle working fluid
is vaporized and superheated as the hot gases cool. Consider
water as the working fluid undergoing the cycle of Problem
8.13. Hot combustion gases, which are assumed to have the
properties of air, enter the heat exchanger portion of the steam
generator at 1200 K and exit at 500 K with a negligible change
in pressure. Determine for the heat exchanger unit
(a) the net rate at which exergy is carried in by the gas stream,
in kW.
(b) the net rate at which exergy is carried out by the water
stream, in kW.
(c) the rate of exergy destruction, in kW.
(d) the exergetic efficiency given by Eq. 7.45.
Let T
0
15C, p
0
0.1 MPa.
8.53 Determine the rate of exergy input, in MW, to the work-
ing fluid passing through the steam generator in Problem 8.13.
Perform calculations to account for all outputs, losses, and de-
structions of this exergy. Let T
0
15C, p
0
0.1 MPa.
8.54 Determine the rate of exergy input, in MW, to the work-
ing fluid passing through the steam generator in Problem 8.47.
Perform calculations to account for all outputs, losses, and de-
structions of this exergy. Let T
0
15C, p
0
1 bar.
8.55 Determine the rate of exergy transfer, in MW, to the work-
ing fluid passing through the steam generator in Problem 8.31.
Perform calculations to account for all outputs, losses, and de-
structions of this exergy. Let T
0
15C, p
0
0.1 MPa.
8.56 Steam enters the turbine of a vapor power plant at 100 bar,
520C and expands adiabatically, exiting at 0.08 bar with a
quality of 90%. Condensate leaves the condenser as saturated
liquid at 0.08 bar. Liquid exits the pump at 100 bar, 43C. The
specific exergy of the fuel entering the combustor unit of the
steam generator is estimated to be 14,700 kJ/kg. No exergy is
carried in by the combustion air. The exergy of the stack gases
leaving the steam generator is estimated to be 150 kJ per kg
of fuel. The mass flow rate of the steam is 3.92 kg per kg of
fuel. Cooling water enters the condenser at T
0
20C, p
0
1 atm and exits at 35C, 1 atm. Develop a full accounting of
the exergy entering the plant with the fuel.
Design & Open Ended Problems: Exploring Engineering Practice
8.1D Vast quantities of water circulate through the condensers
of large power plants, exiting at temperatures 10 to 15C above
the ambient temperature. What possible uses could be made of
the condenser cooling water? Does this warm water represent
a significant resource? What environmental concerns are as-
sociated with cooling water? Discuss.
8.2D Early commercial vapor power plants operated with tur-
bine inlet conditions of about 12 bar and 200C. Plants are
under development today that can operate at over 34 MPa, with
turbine inlet temperatures of 650C or higher. How have steam
generator and turbine designs changed over the years to allow
for such increases in pressure and temperature? Discuss.
8.3D Among the options for meeting future power needs are
the use of biomass as a fuel and nuclear power. As assigned
by your instructor, complete one of the following:
(a) Consider the feasibility of using biomass to fuel a 500-MW
electric power plant. Write a report discussing the advan-
tages and disadvantages of biomass in comparison to
conventional fossil fuels for power plants. Include in your
analysis plant operations, environmental issues, and costs.
(b) Many nuclear power plants are nearing the end of their
useful lives, and the construction of new nuclear
power plants is unlikely for the foreseeable future. What
challenges are presented by the existing nuclear power
plants as they age? What are the options for repowering
existing plants? What concepts are under investigation for
future nuclear power plant technology? Will nuclear power
play a significant role in the United States in the future?
Write a paper discussing these issues.
8.4D Sunlight can be converted directly into electrical output
by photovoltaic cells. These cells have been used for auxiliary
power generation in spaceflight applications as well as for ter-
restrial applications in remote areas. Investigate the principle
of operation of photovoltaic cells for electric power genera-
tion. What efficiencies are achieved by present designs, and
how are the efficiencies defined? What is the potential for more
widespread use of this technology? Summarize your findings
in a memorandum.
8.5D One way for power plants to meet peak demands is to use
excess generation capacity during off-peak hours to produce
ice, which can then be used as a low-temperature reservoir for
condenser heat rejection during peak demand periods. Criti-
cally evaluate this concept for improved power plant utiliza-
tion and write a report of your findings.
8.6D Many hospitals, industrial facilities, college campuses,
and towns employ cogeneration plants that provide district
heating/cooling and generate electricity. Sketch the main com-
ponents and layout of such an existing cogeneration system in
your locale. Determine the heating and cooling loads served
by the system and its electrical generating capacity. Estimate
the cost savings observed through the use of cogeneration com-
pared to meeting these loads individually. Discuss.
8.7D A significant supply of geothermal hot water at 12 bar,
180C exists at a particular location. Develop the preliminary
design of a 10-MW electric power plant using flash evaporation
to provide steam to the turbine-generator. Propose a way to dis-
pose of the excess water and spent brine from the flashing
process.
372 Chapter 8 Vapor Power Systems
8.8D Figure P8.8D shows a thermosyphon Rankine power plant
having one end immersed in a solar pond and the other ex-
posed to the ambient air. At the lower end, a working fluid is
vaporized by heat transfer from the hot water of the solar pond.
The vapor flows upward through an axial-flow turbine to the
upper end, where condensation occurs by heat transfer to the
ambient air. The condensate drains to the lower end by grav-
ity. Evaluate the feasibility of producing power in the 0.1–0.25
kW range using such a device. What working fluids would be
suitable? Write a report of your findings.
8.9D Cleaner is Better (see box Sec. 8.2). Write a report
discussing the state-of-the-art of (a) fluidized bed combustion,
(b) IGCC plants. Include at least three references.
Insulation
Ambient air
Solar pond
Vapor
W
·
Q
·
out
Q
·
in
Working fluid
Vapor formation
Condensate
downpipe
Condensate
formation
Figure P8.8D
373
9
C
H
A
P
T
E
R
Gas Power
Systems
Figure 9.1 is a sketch of a reciprocating internal combustion engine consisting of a piston that
moves within a cylinder fitted with two valves. The sketch is labeled with some special terms.
The bore of the cylinder is its diameter. The stroke is the distance the piston moves in one
chapter objective
spark-ignition
compression-ignition
ENGINEERING CONTEXT The vapor power systems studied in
Chap. 8 use working fluids that are alternately vaporized and condensed. The objective of
the present chapter is to study power systems utilizing working fluids that are always a gas.
Included in this group are gas turbines and internal combustion engines of the spark-ignition
and compression-ignition types. In the first part of the chapter, internal combustion engines
are considered. Gas turbine power plants are discussed in the second part of the chapter. The
chapter concludes with a brief study of compressible flow in nozzles and diffusers, which are
components in gas turbines for aircraft propulsion and other devices of practical importance.
INTERNAL COMBUSTION ENGINES
This part of the chapter deals with internal combustion engines. Although most gas turbines
are also internal combustion engines, the name is usually applied to reciprocating internal com-
bustion engines of the type commonly used in automobiles, trucks, and buses. These engines
differ from the power plants considered in Chap. 8 because the processes occur within recip-
rocating piston–cylinder arrangements and not in interconnected series of different components.
Two principal types of reciprocating internal combustion engines are the spark-ignition
engine and the compression-ignition engine. In a spark-ignition engine, a mixture of fuel
and air is ignited by a spark plug. In a compression-ignition engine, air is compressed to a
high enough pressure and temperature that combustion occurs spontaneously when fuel is
injected. Spark-ignition engines have advantages for applications requiring power up to about
225 kW. Because they are relatively light and lower in cost, spark-ignition engines are par-
ticularly suited for use in automobiles. Compression-ignition engines are normally preferred
for applications when fuel economy and relatively large amounts of power are required (heavy
trucks and buses, locomotives and ships, auxiliary power units). In the middle range, spark-
ignition and compression-ignition engines are used.
9.1 Introducing Engine Terminology
374 Chapter 9 Gas Power Systems
direction. The piston is said to be at top dead center when it has moved to a position where
the cylinder volume is a minimum. This minimum volume is known as the clearance volume.
When the piston has moved to the position of maximum cylinder volume, the piston is at
bottom dead center. The volume swept out by the piston as it moves from the top dead center
to the bottom dead center position is called the displacement volume. The compression ratio
r is defined as the volume at bottom dead center divided by the volume at top dead center.
The reciprocating motion of the piston is converted to rotary motion by a crank mechanism.
In a four-stroke internal combustion engine, the piston executes four distinct strokes within
the cylinder for every two revolutions of the crankshaft. Figure 9.2 gives a pressure–volume
diagram such as might be displayed electronically.
1. With the intake valve open, the piston makes an intake stroke to draw a fresh charge
into the cylinder. For spark-ignition engines, the charge is a combustible mixture of fuel
and air. Air alone is the charge in compression-ignition engines.
2. With both valves closed, the piston undergoes a compression stroke, raising the
temperature and pressure of the charge. This requires work input from the piston to the
cylinder contents. A combustion process is then initiated, resulting in a high-pressure,
high-temperature gas mixture. Combustion is induced near the end of the compression
stroke in spark-ignition engines by the spark plug. In compression-ignition engines,
combustion is initiated by injecting fuel into the hot compressed air, beginning near the
end of the compression stroke and continuing through the first part of the expansion.
3. A power stroke follows the compression stroke, during which the gas mixture expands
and work is done on the piston as it returns to bottom dead center.
4. The piston then executes an exhaust stroke in which the burned gases are purged from
the cylinder through the open exhaust valve.
Smaller engines operate on two-stroke cycles. In two-stroke engines, the intake, compression,
expansion, and exhaust operations are accomplished in one revolution of the crankshaft.
Although internal combustion engines undergo mechanical cycles, the cylinder contents
compression ratio
Spark plug or
fuel injector
Piston
Stroke
Bore
Crank mechanism
Reciprocating
motion
Top
dead center
Bottom
dead center
Rotary
motion
Valve
Clearance
volume
Cylinder
wall
Figure 9.2 Pressure–volume diagram for
a reciprocating internal combustion engine.
Top dead
center
Exhaust
valve
closes
Exhaust valve
opens
Exhaust
Compression
Power
Intake valve
closes
Intake
Volume
Bottom
dead center
p
X
X
X
Figure 9.1 Nomenclature for reciprocating
piston–cylinder engines.
9.2 Air-Standard Otto Cycle 375
do not execute a thermodynamic cycle, for matter is introduced with one composition and is
later discharged at a different composition.
A parameter used to describe the performance of reciprocating piston engines is the mean
effective pressure, or mep. The mean effective pressure is the theoretical constant pressure
that, if it acted on the piston during the power stroke, would produce the same net work as
actually developed in one cycle. That is
(9.1)
For two engines of equal displacement volume, the one with a higher mean effective pressure
would produce the greater net work and, if the engines run at the same speed, greater power.
AIR-STANDARD ANALYSIS. A detailed study of the performance of a reciprocating internal
combustion engine would take into account many features. These would include the combustion
process occurring within the cylinder and the effects of irreversibilities associated with friction
and with pressure and temperature gradients. Heat transfer between the gases in the cylinder and
the cylinder walls and the work required to charge the cylinder and exhaust the products of com-
bustion also would be considered. Owing to these complexities, accurate modeling of recipro-
cating internal combustion engines normally involves computer simulation. To conduct element-
ary thermodynamic analyses of internal combustion engines, considerable simplification is
required. One procedure is to employ an air-standard analysis having the following elements:
A fixed amount of air modeled as an ideal gas is the working fluid.
The combustion process is replaced by a heat transfer from an external source.
There are no exhaust and intake processes as in an actual engine. The cycle is com-
pleted by a constant-volume heat transfer process taking place while the piston is at the
bottom dead center position.
All processes are internally reversible.
In addition, in a cold air-standard analysis, the specific heats are assumed constant at their
ambient temperature values. With an air-standard analysis, we avoid dealing with the com-
plexities of the combustion process and the change of composition during combustion. A
comprehensive analysis requires that such complexities be considered, however. For a
discussion of combustion, see Chap. 13.
Although an air-standard analysis simplifies the study of internal combustion engines con-
siderably, values for the mean effective pressure and operating temperatures and pressures
calculated on this basis may depart significantly from those of actual engines. Accordingly,
air-standard analysis allows internal combustion engines to be examined only qualitatively.
Still, insights concerning actual performance can result with such an approach.
In the remainder of this part of the chapter, we consider three cycles that adhere to air-
standard cycle idealizations: the Otto, Diesel, and dual cycles. These cycles differ from each
other only in the way the heat addition process that replaces combustion in the actual cycle
is modeled.
mep
net work for one cycle
displacement volume
mean effective pressure
air-standard analysis:
internal combustion
engines
cold air-standard analysis
9.2 Air-Standard Otto Cycle
The air-standard Otto cycle is an ideal cycle that assumes the heat addition occurs instanta-
neously while the piston is at top dead center. The Otto cycle is shown on the p–v and T–s
Otto cycle