1. Vapor and Combined Power Cycles
CHAPTER 10
Vapor and Combined Power Cycles

2. 10-1 The Carnot Vapor Cycle

3. FIGURE10-1 T-s diagram of two Carnot vapor cycles.
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FIGURE10-1 T-s diagram of two Carnot vapor cycles.

4. Operating principles TH TC
WNET QH QC
(1)
(2)

5. 10-2 Rankine Cycle: The Ideal Cycle for Vapor Power Cycles
Operating principles
Vapor power plants
The ideal Rankine vapor power cycle
Efficiency
Improved efficiency - superheat

6. The conventional vapor power plant
QIN
QOUT
WTURBINE
WPUMP

7. The conventional vapor power plant
QIN
QOUT
WTURBINE
WPUMP
High temperature heat addition.
Low temperature heat rejection
Work input to compress working fluid
Turbine to obtain work by expansion of working fluid.

8. FIGURE 10-2 The simple ideal Rankine cycle.
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FIGURE 10-2 The simple ideal Rankine cycle.

9. A hypothetical vapor power cycle
Assume a Carnot cycle operating between
two fixed temperatures as shown. T s 1 2 3 4

10. The ideal Rankine cycles T 1 2 3 4 3* 4*
All processes are internally reversible.

11. The ideal Rankine cycles T 1 2 3 4 3* 4*
Reversible constant pressure heat rejection (4  1)
Reversible constant pressure heat addition (2  3)
Isentropic compression (1  2)
Isentropic expansion to produce work (3  4) or (3*  4*)
All processes are internally reversible.

12. The ideal Rankine cycle (h-s diagram)4 3 2
WOUT QH QC 1
WIN

13. Rankine cycle efficiencyh s 4 3 2
WOUT QH QC 1
WIN s
(3)

14. Ideal Turbine Work s h (4) Isentropic process, s = constant s1 = s2 p1
All accessible states lie
to the right of the process (1 2).
(4)

15. Ideal turbine work Steady state. Constant mass flow
Isentropic Expansion (s = Constant)
Adiabatic and reversible
No entropy production
No changes in KE and PE
Usual assumption is to neglect KE and PE effects at inlet and outlet of turbine.

16. Ideal turbine work
(4)
(5)

17. Work of Compression
(6)
(7)

18. Improved Rankine cycle efficiencyh s 4 3* 2
WOUT QH QC 1
WIN
Increased average temperature of heat addition

19. Improved Rankine cycle efficiency
(8)
(9)

20. 10-3 Deviation of Actual Vapor Power Cycles from Idealized Ones

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FIGURE 10-4 (a) Deviation of actual vapor power cycle from the ideal Rankine cycle. (b) The effect of pump and turbine irreversibilities on the ideal Rankine cycle.

22. Raising the average temperature of heat addition
The Improved Rankine Cycle How Can We Increase the Efficiency of the Rankine Cycle
Raising the average temperature of heat addition

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FIGURE 10-6 The effect of lowering the condenser pressure on the ideal Rankine cycle.

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FIGURE 10-7 The effect of superheating the steam to higher temperatures on the ideal Rankine cycle.

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FIGURE 10-8 The effect of increasing the boiler pressure on the ideal Rankine cycle.

26. FIGURE 10-9 A supercritical Rankine cycle.
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FIGURE 10-9 A supercritical Rankine cycle.

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FIGURE T-s diagrams of the three cycles discussed in Example 9–3.

28. 10-5 The Ideal Reheat Rankine Cycle

29. A hypothetical vapor power cycle
Assume a Carnot cycle operating between
two fixed temperatures as shown. T s 1 2 3 4

30. A hypothetical vapor power cycle with superheat
Superheating the working fluid raises the
average temperature of heat addition. T s 1 2 3 4
TH,2
TH,1

31. A hypothetical vapor power cycle: A Rankine cycle with superheatb T a c d s
Superheating the working fluid raises the average
temperature with a reservoir at a higher temperature.

32. The Rankine cycle with reheat
The extra expansion via reheating to state “d” allows a greater enthalpy to be released between states “c” to “e”. s T f a b c p1 p2 d e

33. The reheat cycle QOUT WIN a b e f QH WOUT QC c d
Single stage reheat. Work
produced in both turbines.

34. Reheat Cycle Efficiency
(1)

35. FIGURE 10-11 The ideal reheat Rankine cycle.
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FIGURE The ideal reheat Rankine cycle.

36. Example 1

37. Example - 1: A Carnot cycle
To begin our analysis of Rankine cycle operations, consider a
steady Carnot cycle (a-b-c-d-a) with water as the working fluid
operating between to given temperature limits as shown. The
given data are that the boiler pressure is 500 psi (pa = 500 psi) and
the condenser temperature is 70o F (Tc = 70o F). Determine the
work output, thermal efficiency, irreversibility, and work ratio. T s a b c d T1 T2 p1 p2 b c d a T1 T2

38. Example 1 - Given data

39. Example 1 - Computed data

40. Example 1 - Process quantitiesD H
BTU/lbm d W Q S
BTU/
lbm-R
Q/T
BTU/lbm- R s
a-b
755
0.8147
b-c
-430
430
c-d
-432
d-a
107
-107
Net
323
To get the above process quantities, the First Law for open systems
has been used assuming KE and PE effects are negligible. The
entropy production was obtained from an entropy balance for an
open system. Note that the cyclic heat equals the cyclic work as
required by the First Law and that entropy production is zero as
required by the Clausius Equality.

41. Example 1 - Thermal efficiency and back work ratio

42. Example 2

43. Example 2 - A Rankine cycle without superheat
A Rankine cycle with water as the working fluid operates between
the same limits as in Example l, pa = 500 psi and a condensing
temperature of 70o F. Assuming all processes to be internally
reversible, determine the work output, efficiency, entropy
production, work ratio. T s a b c d T1 T2 pa pd

44. Example 2 - Computed data

45. Example 2 - Process quantities
Work output = BTU/lbm
Thermal efficiency = 36.8%
Work ratio =
Entropy production = 0

46. Example 3

47. Example 3 - Effect of irreversibility in the turbine and pump
A Rankine cycle operates between the same limits as above and has pump and turbine efficiencies of 80%. Determine the work
output, efficiency, work ratio, and entropy production. Assume the condensing and ambient temperatures to be the same. T1 T2 s a b c d pa pd c’ a’ T

48. Example 3 - Computed data
The states at a’ and c’ are determined via the First Law for an
open system and the definition of isentropic efficiency for turbines
and pumps as appropriate.

49. Example 3 - Process quantities
Isentropic processes are determined prior to actual processes where
irreversibility is involved.
Work output = 342 BTU/lbm Thermal efficiency = 29.4%
Work ratio = Entropy production =
BTU/lbm-R

50. Example 3 - Comparison

51. Example 4

52. Example 4 - Superheat
An internally reversible Rankine cycle is determined by specifying
a maximum temperature of 800o F, a quality at the turbine
discharge of 0.9, and a minimum condensing temperature of 70oF.
Compare the thermal efficiency with that of a Carnot cycle
operating between the same temperature limits. b a c d pd pa T s

53. Example 4 - Given and computed data

54. Example 4 - Thermal efficiency
The Carnot efficiency

55. Example 5

56. Example 5 - The reheat cyclef a b c pa pc s d e T

57. Example 5 - Given and computed data
The state at “c” has the same as the pressure specified in Example 4.
This determines state “b”. State “a” is determined via the usual
approximation for an incompressible liquid under going process
f-a.

58. Example 5 - Process quantities
Work output = 701 BTU/lbm
Thermal efficiency = 701/( ) = 0.424
Carnot efficiency = 1-(530/1260) = 0.579

59. Example 6

60. Variation of the (First Law) cycle efficiency with a variation
of the pressure of heat addition in a basic Rankine cycle with no
super heat. The condenser pressure was assumed to be 14 psia.

61. T s 1 2 3 5 6 4 p2
pmiddle

62. The variation of cycle efficiency of a Rankine cycle with one
stage of reheat as a function of the pressure at which reheat is
done. Pup is the pressure of high temperature heat addition.

63. Rankine cycle with reheat Rankine cycle with regeneration
Key terms and concepts
Cycle efficiency
Rankine cycle with reheat
Rankine cycle with regeneration
Work ratio

64. 10-6 The Ideal Regenerative Rankine cycle
Another technique to raise the average temperature of the heat addition process.

65. Review - The reheat cylce The Rankine Cycle with regeneration Example
Overview
Review - The reheat cylce
The Rankine Cycle with regeneration
Open and closed feedwater heaters
Example

66. The Reheat Cycle
Reheating the expanding fluid with primary heat source is made at inter-mediate points in the expansion process.
Net effect is to raise the average expansion temperature of the turbine without raising the temperature of the heat source.

67. The Reheat Cycle s p1 The extra expansion allows a greater enthapy
to be released between
states 3 to 4.
Here one additional
reheat process has
been added. T s 1 2 3 5 6 4 p2 p1
The Objective of Reheating: Increase work output
The reheat process takes place form State 5 to 6. The expansion from States 6 to 4 takes place with no moisture in the turbine as shown here. The second stage of expansion is entirely in the superheat region. Without the reheat process, a single exzpansion would have produced a two-pahse (x < 1) mixture when the temperture dropped blow the saturation temperature at State 5.
With reheat, the total work output of the cycle is larger than it would have been with a single expansion process.
If State 4 yet lies in the vapor-liquid region (x < 1), at least additional work was extracted and the existense of the two-phase mixture at presumably a high quality (x near unity) would not be too detrimental to the low pressure turbine.
As discussedin your text (Moran and Shapiro, pp ), the condsensing process is designed to operate at the lowest possible temeperature, usually the ambinetn. A lower condenser pressure allows the cycle to produce work with the largest possible pressure range and, hence, extract more work. In such systems, the condenser is sealed, and the entire system operates (ideally) in a closed loop.

68. T s 1 2 3 5 6 4 p2 p1

69. The Rankine cycle with regeneration

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FIGURE The first part of the heat-addition process in the boiler takes place at relatively low temperatures.

71. Principle of the regenerative cycleb f
WOUT
WIN QH QC
A higher feed water inlet
temperature as a result of
heating from States a - b. e d

72. Impacted processes
Heating of some of the compressed liquid is done to raise the average temperature of heat addition.
Heat is supplied after the liquid is compressed to a high pressure at State a.

73. The T-s diagram for the regenerative cycleb c s
Internal heat transfer to feed water heater. e d a

74. Practical considerations...
Turbines cannot be designed economically with internal heat exchangers.
Condensation could occur in the turbine.
Not practical!

75. The practical regenerative cycle5
Q2-3 = 0 1 2 3
W2,out
WIN,1 QH 6
WIN,2 7 QC 4
W1,out
Feedwater heater
The Practical Regnerative Cycle Configuration
A feedwazter heater is inserted between the stages of expansion. The expansion in each turbine is carried out isentropically. Note that after a fraction of mass flow is drawn off at State 6 for the feewater heater, the reminaing fraction passes through states 7 to 2. A unit mass of the working fluid is returned to the high tempeaure source at State 4 for heat addition.
The net work of the cycle is obtained in the two stages of expansion less the work input to the two feewater pumps.
The feedwater heater (Stated 2 - 3) as depicted here is “closed” feedwater heater. No additional liquid is provided, i.e., makup water is not used. Thus mass conservation is easily determined when a mass balance is made for the device. Idally, the feedwater heater accomplished its purpose adiabatically, i.e., Q2-3 = 0.

76. The h-s diagram for the regenerative cycle1 3 4 2
WOUT,1 QH QC
WIN,1 5 6 7
WOUT,2
WIN,2
(1 kg)
(y kg)
(1-y kg)

77. Energy balances and thermal efficiency1 3 4 2
WOUT,1 QH QC
WIN,1 5 6 7
WOUT,2
WIN,2
(1 kg)
(y kg)
(1-y kg)

78. Open and Closed Feedwater Heaters

79. Regeneration with an open feedwater heaterQH y
1-y
WIN,1
WIN,2
WOUT
Regeneration with an open feedwater heater at the mass
fraction rate of “y” per unit mass of primary the flow rate. QC

80. The open feedwater heatery
From the outlet
of the condenser
and first feedwater
pump. (1-y kg.)
From the
turbine.
(y kg.)
To the second
feedwater pump.
(1 kg.)
1-y

81. Regenerative cycle with a closed feedwater heater5 1 2 3 4 6 7 8 y
1-y QH QC WT
Closed
feedwater
heater
Trap
Condenser

82. T-s diagram for a regenerative cycle with a closed feedwater heater1 2 3 4 5 6 7 8 s T

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FIGURE The ideal regenerative Rankine cycle with an open feedwater heater.

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FIGURE The ideal regenerative Rankine cycle with a closed feedwater heater.

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FIGURE A steam power plant with one open and three closed feedwater heaters.

86. Example - Regeneration with a single extraction and an open feedwater heater

87. Example A regenerative Rankine cycle with a single extraction
provides saturated steam at 500 psi a the turbine inlet.
Condensation takes place at 70o F. One open regenerative
feedwater heater is included, using extracted steam at a
temperature midway between the limits of the cycle.
All processes are assumed to be internally reversible
except that in the regenerative heater. Neglect KE and
PE effects, and determine the thermal efficiency,
the internal irreversibility, and the extraction pressure.
Assume steady operation.

88. Example - Plant diagram
WOUT QC a d e c b QH y
1-y
WIN,1
WIN,2 g f

89. Example - T-s diagram a b c d e f g y
1-y 1 T s

90. Example - Mass fraction at State “c”
The mass fraction of fluid extracted at State c is obtained
from the energy balance for an open system applied to
the feedwater heater. Assume adiabatic mixing. a b c d e f g y
1-y 1 T s

91. Example - Entropy balance for the feedwater heater
Apply the entropy balance for an open system to the
feedwater heater.

92. Example - Given data

93. Example - Computed data

94. Example - Process quantities

95. Example - Process quantities
Note the positive entropy production in the feedwater heater.

96. Example - Thermal efficiency
Note that regeneration has increased thermal
efficiency above that of the previous example at
the expense of some work output per lbm of steam.

97. Commercial steam-power plants
Reheat (multiple stages)
Regeneration (multiple extractions)
Nearly ideal heat addition
Constant temperature boiling for water

98. Commercial steam-power plants
Heat transfer characteristics of steam and water permit external combustion systems
Compression of condensed liquid produces a favorable work ratio.

99. Commercial steam-power plants
The Rankine cycle with reheat and regeneration is advantageous for large plants.
Small plants do not have economies of scale
Internal combustion for heat addition.
A different thermodynamic cycle

100. 10-7 Second-Law Analysis of Vapor Power Cycles

101. 10-8 Cogeneration

102. FIGURE 10-20 A simple process-heating plant.
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FIGURE A simple process-heating plant.

103. FIGURE 10-21 An ideal cogeneration plant.
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FIGURE An ideal cogeneration plant.

104. FIGURE 10-22 A cogeneration plant with adjustable loads.
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FIGURE A cogeneration plant with adjustable loads.

105. 10-9 Combined /gas-Vapor Power Cycles

106. FIGURE 10-24 Combined gas–steam power plant.
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FIGURE Combined gas–steam power plant.

107. FIGURE 10-26 Mercury–water binary vapor cycle.
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FIGURE Mercury–water binary vapor cycle.