Transcript No Slide Title

CHAPTER
10
Vapor and Combined
Power Cycles
10-1 The Carnot Vapor Cycle
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FIGURE10-1
T-s diagram of two
Carnot vapor
cycles.
Operating principles
TH
 TC 
Wmax  QH 1 

 TH 
TC
   max  1 
TH
QH
(1)
(2)
WNET
TC
QC
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
The conventional vapor power plant
QIN
WTURBINE
WPUMP
QOUT
The conventional vapor power plant
QIN
High temperature
heat addition.
Turbine to obtain
work by expansion
of working fluid.
Work input to
compress working
fluid
WTURBINE
WPUMP
QOUT
Low temperature
heat rejection
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FIGURE 10-2
The simple ideal
Rankine cycle.
A hypothetical vapor power cycle
Assume a Carnot cycle operating between
two fixed temperatures as shown.
T
2
3
1
4
s
The ideal Rankine cycle
T
3
3*
4
4*
2
1
s
All processes are internally reversible.
The ideal Rankine cycle
Reversible constant
pressure heat addition
(2  3)
T
3
3*
4
4*
Isentropic
expansion to
produce work
(3  4) or
(3*  4*)
2
Isentropic
compression
(1  2)
1
Reversible constant
pressure heat rejection
(4  1)
s
All processes are internally reversible.
The ideal Rankine cycle
(h-s diagram)
h
3
QH
WOUT
WIN
2
4
1
QC
s
Rankine cycle efficiency
h
3
QH
WOUT
WIN
2
4
1
WOUT  h3  h4
WIN  h2  h1
QH  h3  h4
QC
s
W NET

QH
s
(3)
p1
1
h
Ideal Turbine Work
Isentropic process, s = constant
2
p2
All accessible states lie
to the right of the process (1 2).
s
s1 = s 2
dE(t )
 CS  W CS 
Q
dt
dSCV

dt

j
Q j

Tj

N
 i h  ke  pei
m
i 1
(4)
 m s   m s  
i i
i
e e
e
CV
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.
Ideal turbine work
dE(t )
 Q CS  W CS 
dt

N
 i h  ke  pei
m
i 1

WOut
 h3  h4
m
(4)
(5)
Work of Compression
W IN
 h2  h1
m
W IN
 v1 P2  P1 

m
(6)
(7)
Improved Rankine cycle efficiency
Increased average
temperature of heat
addition
h
3*
QH
WOUT
WIN
2
4
1
QC
s
Improved Rankine cycle efficiency

h3*  h4   h2  h1 

h3*  h2

0
h3*
(8)
(9)
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.
The Improved Rankine Cycle
10-4 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.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-8
The effect of
increasing the boiler
pressure on the ideal
Rankine cycle.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-9
A supercritical
Rankine cycle.
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FIGURE 10-10
T-s diagrams of
the three cycles
discussed in
Example 9–3.
10-5 The Ideal Reheat Rankine Cycle
A hypothetical vapor power cycle
Assume a Carnot cycle operating between
two fixed temperatures as shown.
T
2
3
1
4
s
A hypothetical vapor power cycle with
superheat
T
3
TH,2
2
TH,1
1
4
s
Superheating the working fluid raises the
average temperature of heat addition.
A hypothetical vapor power cycle: A Rankine
cycle with superheat
b
T
a
TH
TH
T
d
c
s
Superheating the working fluid raises the average
temperature with a reservoir at a higher temperature.
The Rankine cycle with reheat
p1
T
p2
b
TH
d
a
TC
c
f
e
s
The extra expansion via reheating to state “d” allows a
greater enthalpy to be released between states “c” to “e”.
The reheat cycle
QH
b
a
d
f
WIN
c
QOUT
QC
WOUT
e
Single stage reheat. Work
produced in both turbines.
Reheat Cycle Efficiency


Wb c  Wd e  W f  a
Qa b  Qc  d
hb  hc   (hd  he )  (ha  h f )
hb  ha   hd
 hc 
(1)
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-11
The ideal reheat Rankine
cycle.
Example 1
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
T1
p1
a
a
T1
b
d
T2
c
b
p2
T2
d
c
s
Example 1 - Given data
State
T
P
h
s
R
psi
BTU/lbm
BTU/
lbm-R
a
500
b
500
c
530
d
530
x
Example 1 - Computed data
State
T
P
h
s
x
R
psi
BTU/lbm
BTU/
lbm-R
a
927
500
449
0.6487
0
b
927
500
1204
1.4634
1
c
530
0.361
774
1.4634
0.698
d
530
0.361
342
0.6487
0.288
Example 1 - Process quantities
Process
DH
BTU/lbm
dW
BTU/lbm
dQ
BTU/lbm
a-b
b-c
c-d
d-a
Net
755
-430
-432
107
0
0
430
0
-107
323
755
0
-432
0
323
DS
BTU/
lbm-R
0.8147
0
-0.8147
0
0
dQ/T
BTU/lbmR
0.8147
0
-0.8147
0
0
s
BTU/
lbm-R
0
0
0
0
0
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.
Example 1 - Thermal efficiency and back work ratio
Thermal efficiency
W
323


 0.428
QH 755
Work ratio
Win
107
r

 0.249
WTurbine 430
Example 2
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
T1
T2
pa
b
a
pd
d
c
s
Example 2 - Computed data
State
T
P
h
s
x
R
psi
BTU/lbm
BTU/
lbm-R
a
927
500
39.5
0.0745
0
b
927
500
1204
1.4634
1
c
530
0.361
774
1.4634
0.698
d
530
0.361
38.0
0.0745
0
Example 2 - Process quantities
Process
DH
BTU/lbm
dW
BTU/lbm
dQ
BTU/lbm
a-b
b-c
c-d
d-a
N et
1164.5
-430
-736
1.5
0
0
430
0
-1.5
428.5
1164.5
0
-736
0
428.5
Work output =
Thermal efficiency =
Work ratio =
Entropy production =
DS
BTU/
lbm-R
1.3889
0
-1.3889
0
0
dQ/T
BTU/lbmR
1.3889
0
-1.3889
0
0
s
BTU/
lbm-R
0
0
0
0
0
428.5 BTU/lbm
36.8%
0.0035
0
Example 3
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.
T
pa
T1
a’
a
b
pd
T2
d
c’ c
s
Example 3 - Computed data
State
a
a’
b
c
c’
d
T
R
530
530
927
530
530
530
P
psi
500
500
500
0.3631
0.3631
0.3631
h
BTU/lbm
39.5
39.9
1204
774
860
38.0
s
BTU/lbm-R
0.0745
0.0753
1.4364
1.4364
1.6262
0.0745
x
…
…
1
0.698
0.780
0
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.
Example 3 - Process quantities
Process
(a’-a)
a-b
(b-c’)
b-c
c-d
(d -a’)
d -a
N et
Dh
BTU/ lbm
(0.4)
1164
(-430)
-344
-822
(1.5)
1.9
0
dW
BTU/ lbm
(0)
0
(0)
344
0
(-1.5)
-1.9
342
dQ
BTU/ lbm
(0.4)
1164
(0)
0
-822
(0)
0
342
Ds
BTU/
lbm -R
(0.0008)
1.3881
(0)
0.1628
-1.5517
(0)
0.008
0
dQ/ T
BTU/
lbm -R
(0.0008)
1.3881
(0)
0
-1.5517
(0)
0
-0..1636
s
BTU/
lbm -R
(0)
0
(0)
0.1628
0
(0)
0.0008
+0.1636
Isentropic processes are determined prior to actual processes where
irreversibility is involved.
Work output = 342 BTU/lbm
Work ratio = 0.0054
Thermal efficiency = 29.4%
Entropy production = 0.1636
BTU/lbm-R
Example 3 - Comparison
Work
Work Ratio
Thermal Efficiency
Entropy Production
Example 1
Carnot
Example 2
Basic Rankine
323
0.249
42.8%
0
428.5
0.0035
36.8%
0
Example 3
Pump and Turbine
Irreversibility
342
0.0054
29.4%
0.1636
Example 4
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
pa
T
a
d
c
pd
s
Example 4 - Given and computed data
State
T
R
530
1260
530
530
a
b
c
d
P
psi
84
84
0.3631
0.3631
h
BTU/lbm
38.3
1429.5
988
38
s
BTU/lbm-R
0.0745
1.8645
1.8645
0.0745
x
…
…
0.9
0
Process
DH
BTU/lbm
dW
BTU/lbm
dQ
BTU/lbm
a-b
b-c
c-d
d-a
Net
1391
-441.5
-950
0.5
0
0
441.5
0
-0.5
1391
0
-950
0
441
Example 4 - Thermal efficiency
Thermal efficiency
441

 0.316
1391
The Carnot efficiency
TC
530
C  1 
 1
0.579
TH
1230
Example 5
Example 5 - The reheat cycle
T
o
800
F
b
pa p
c
d
TC
a
c
xc  0.90
70o F
f
xe  0.90 e
s
Example 5 - Given and computed data
State
a
b
c
d
e
f
T
R
530
1260
775
1260
530
530
P
psi
1600
1600
84
84
0.3631
0.3631
h
BTU/lbm
42.8
1358
1094
1430
988
38
s
BTU/lbm,-R
0.0745
1.499
1.499
1.864
1.864
0.0745
x
…
…
0.9
…
0.9
0
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.
Example 5 - Process quantities
Process
a-b
b-c
c-d
d-e
e-f
f-a
N et
DH
BTU/lbm
1315
-264
336
-442
-950
5
0
dW
BTU/lbm
0
264
0
442
0
-5
701
dQ
BTU/lbm
1315
0
336
0
-950
0
701
Work output = 701 BTU/lbm
Thermal efficiency = 701/(1315+336) = 0.424
Carnot efficiency = 1-(530/1260) = 0.579
Example 6
0.3
0.28

0.26
0.24
0.22
0.2
300
350
400
450
500
550
600
650
700
Pupper (psia)
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.
T
p2
2
3
6
pmiddle
5
1
4
s
W35  W6 4  W1 2

Q23  Q56

h3  h5   (h6  h4 )  (h2  h1 )

h3  h2   h6  h5 
0.3
0.28

0.26
0.24
Pup = 400 psia
0.22
Pup = 500 psia
Pup = 600 psia
0.2
0
100
200
300
400
500
600
Pm iddle (psia)
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.
Key terms and concepts
Cycle efficiency
Rankine cycle with reheat
Rankine cycle with regeneration
Work ratio
10-6 The Ideal Regenerative Rankine cycle
Another technique to raise the average temperature of the
heat addition process.
Overview
• Review - The reheat cylce
• The Rankine Cycle with regeneration
– Open and closed feedwater heaters
• Example
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.
The Reheat Cycle
The extra expansion
allows a greater enthapy
to be released between
states 3 to 4.
3
T
p1
6
2
5
1
p2
4
Here one additional
reheat process has
been added.
s
3
T
p1
6
2
5
1
p2
4
W35  W64  W12

Q23  Q56

h3  h5   (h6  h4 )  (h2  h1 )

h3  h2   h6  h5 
s
The Rankine cycle with regeneration
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-14
The first part of the
heat-addition process
in the boiler takes
place at relatively low
temperatures.
Principle of the regenerative cycle
c
WOUT
QH
b
d
e
a
A higher feed water inlet
temperature as a result of
heating from States a - b.
QC
WIN
f
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.
The T-s diagram for the regenerative cycle
c
T
b
a
d
f
e
s
Internal heat transfer to feed water heater.
Practical considerations...
• Turbines cannot be designed economically with internal heat
exchangers.
• Condensation could occur in the turbine.
Not practical!
The practical regenerative cycle
W1,out
5
QH
W2,out
6
7
4
WIN,1
3
2
1
QC
WIN,2
Q2-3 = 0
Feedwater heater
The h-s diagram for the regenerative cycle
h
5
QH
WOUT,1
6
WIN,2
2
WIN,1
(1 kg)
4
WOUT,2
3
(y kg)
(1-y kg)
1
WOUT ,1  h5  h6
WIN ,1  h4  h3
QH  h5  h4
7
QC
and WOUT , 2  (1  y)h6  h7 
and WIN , 2  1  y h2  h1 
s
Energy balances and thermal efficiency

h5  h6   (1  y )h6  h7   h4  h3   (1  y )h2  h1 

h5  h4
h
5
QH
WOUT,1
6
WIN,2
2
WIN,1
(1 kg)
4
WOUT,2
3
(y kg)
(1-y kg)
1
7
QC
s
Feedwater heaters
Open and Closed
Feedwater Heaters
Regeneration with an open feedwater heater
WOUT
QH
y
Regeneration with
an open feedwater
heater at the mass
fraction rate of “y”
per unit mass of
primary the flow
rate.
1-y
QC
WIN,1
WIN,2
The open feedwater heater
y
From the
turbine.
(y kg.)
To the second
feedwater pump.
(1 kg.)
1-y
From the outlet
of the condenser
and first feedwater
pump. (1-y kg.)
Regenerative cycle with a closed feedwater
heater
1-y
1
WT
QH
2
y
6
Closed
feedwater
heater
3
5
QC
Condenser
4
1-y
7
8
Trap
y
T-s diagram for a regenerative cycle with a
closed feedwater heater
T
1
6
2
7
5
4
8
3
s
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-15
The ideal
regenerative
Rankine cycle
with an open
feedwater heater.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-16
The ideal
regenerative
Rankine cycle
with a closed
feedwater heater.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-17
A steam power
plant with one
open and three
closed feedwater
heaters.
Example - Regeneration with a single extraction and an
open feedwater heater
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.
Example - Plant diagram
WOUT
b
QH
c
y
g
1-y
QC
f
a
WIN,1
d
e
WIN,2
Example - T-s diagram
T
1
a
y
f
g
e
1-y
b
c
1-y
d
s
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.
m c hc  m  m c h f  m hg
T
yhc  1  y h f  hg
1
y, hc
a
y
f
g
e
hg
1 y, h f
1-y
b
c
1-y
d
s
Example - Entropy balance for the feedwater heater
Apply the entropy balance for an open system to the
feedwater heater.
  sg  ysc  1  y s f
 ys g  sc   1  y s g  s f 
y, hc , sc
hg , s g
1 y, h f , s f
Example - Given data
Given Data
STATE
a
b
c
d
e
f
g
T
R
728.7
728.5
530
530
530
728.7
P
psi
500
500
h
BTU/ lbm
s
x
BTU/lbm-R
…
1
0
…
0
Example - Computed data
Com p u ted Data (From Tables)
STATE
T
P
R
p si
a
728.7
500
b
927
500
c
728.5
41
d
530
0.361
e
530
0.361
f
530
41
g
728.7
41
h
BTU/ lbm
239.1
1204.4
1016
774
38
38.1
237.6
s
x
BTU/lbm-R
0.3940
1.4364
1.4364
1.4364
0.0745
0.0745
0.3940
…
1
0.835
0.698
0
…
0
Example - Process quantities
Process Quantities
Process
DH
BTU/ lbm
a-b
965
b-c
-188
c-d
-242
d -e
-736
e-f
0.1
f-g
199.5
c-g
-778
g-a
1.5
N et
…
m
1
1
0.796
0.796
0.796
0.796
0.204
1
…
mDh
BTU/ lbm
965
-188
-193
-586
0.1
159
-159
1.5
0
dW
BTU/ lbm
0
188
193
0
-0.1
0
-1.5
379.4
Example - Process quantities
Process Quantities
Process
dQ
BTU/ lbm
a-b
b-c
c-d
d -e
e-f
f-g
c-g
g-a
N et
965.3
0
0
-586
0
0
0
379.3
ds
BTU/ lbm-R
yd s
BTU/ lbm-R
1.0694
0
0
-1.3889
0
0.3195
-1.0694
0
…
1.0694
0
0
-1.1056
0
0.2543
-0.2180
0
0
dQ/T

BTU/ BTU/
lbm-R lbm-R
1.0694
0
0
0
0
0
-1.1056
0
0
0
0 0.0363
0
0
-0.0362
0.0363
Note the positive entropy production in
the feedwater heater.
Example - Thermal efficiency
W 379.4


 0.393
QH
965
Note that regeneration has increased thermal
efficiency above that of the previous example at
the expense of some work output per lbm of steam.
Commercial steam-power plants
• Reheat (multiple stages)
• Regeneration (multiple extractions)
• Nearly ideal heat addition
– Constant temperature boiling for water
Commercial steam-power plants
• Heat transfer characteristics of steam and water
permit external combustion systems
• Compression of condensed liquid produces a
favorable work ratio.
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
10-7 Second-Law Analysis of
Vapor Power Cycles
10-8 Cogeneration
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-20
A simple processheating plant.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-21
An ideal
cogeneration
plant.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-22
A cogeneration plant with
adjustable loads.
10-9 Combined /gas-Vapor Power Cycles
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-24
Combined gas–
steam power plant.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 10-26
Mercury–water binary
vapor cycle.