Introduction to Thermodynamics, Lecture 24
Prof. G. Ciccarelli (2012)
Vapor Power Systems
Power plants work on a cycle that produces net work
from a fossil fuel (natural gas, oil, coal) nuclear, or solar
input.
For Vapor power plants the working fluid, typically
water, is alternately vaporized and condensed.
Consider the following Simple Vapor Power Plant
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Consider subsystem A, each unit of mass periodically
undergoes a thermodynamic cycle as the working fluid
circulates through the four interconnected components
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For the purpose of analyzing the performance of the
system, the following cycle describes the basic system
Consider each process separately applying conservation
of energy
For steady-state, neglecting KE and PE effects,
conservation of energy applied to a CV yields
1 dE Q CV WCV
2


 (hin  hout )  1 / 2(Vin2  Vout
)  g ( zin  z out )
m dt
m
m
Q CV WCV
0

 (hin  hout )
m
m
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12 Turbine (adiabatic expansion)
Q W out
0 
 (h1  h2 )
m
m
wout
1
W out ()
W out

 (h1  h2 )
m
23 Condenser (no work)
2
2
 Q out W
0
  (h2  h3 )
m
m
qout
Q out

 (h2  h3 )
m
Q out ()
3
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34 Pump (Adiabatic)
Q  Win
0 
 (h3  h4 )
m
m
4
3
Win ()
W in
win 
 (h4  h3 )
m
41 Steam Generator (no work)
Q in W
0
  (h4  h1 )
m m
1
Q in ()
Q in
qin 
 (h1  h4 )
m
4
Rankine Cycle Thermal Efficiency
net work out W out / m   Win / m  wout  win
 



heat input
Qin / m
qin
 Rankine 
(h1  h2 )  (h4  h3 )
h1  h4
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Back Work Ratio (bwr)
W in / m
w
work input (pump)
bwr 

 in
work output (turbine) W out / m wout
bwr 
h4  h3
h1  h2
Ideal Rankine Cycle - no irreversibilities present in any
of the processes: no fluid friction so no pressure drop, and
no heat loss to surroundings
1.
2.
3.
4.
Steam generation occurs at constant pressure 41
Isentropic expansion in the turbine 12
Condensation occurs at constant pressure 23
Isentropic compression in the pump 34
Pboiler
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With superheating
Pcondense
r
Note: For an ideal cycle no irreversibilities present so the
pump work can be evaluated by
4
 W p 

    vdP
 m  int
3

 rev
if the working fluid entering the pump at state 3 is pure
liquid, then
4
 W p 
   vdP  v3 P4  P3 
win  

 m  int 3
rev
The negative sign has been dropped to be consistent with
previous use of win
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Factors Affecting Cycle Efficiency
 
wout  win qin  qout
q

 1  out
qin
qin
qin
Recall: for a reversible heat addition process q   Tds
Consider qin at the boiler and qout at the condenser
T
qin
1
1
qin  q41   Tds
4
4
 shaded area
s
Define mean temperature for process 4  1
1
Tin 
 Tds
4
s1  s4
 qin   Tds  Tin  ds  Tin s1  s4 
1
1
4
4
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3
qout  q23   Tds
T
2
Tout
3
qout
 Tout s2  s3 
2
 shaded area
s
Noting s2  s3  s1  s4 , the Ideal Rankine cycle thermal
efficiency is
 Ideal
Rankine
qout
Tout ( s2  s3 )
Tout
 1
 1
 1
qin
Tin ( s1  s4 )
Tin
Note: this is identical to the Carnot Engine efficiency
which is also a reversible cycle
The back work ratio is
bwrIdeal

Rankine
win v3 P4  P3 

h1  h2 s 
wout
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Increase Rankine Cycle Efficiency
T
 Ideal  1  out
Tin
Rankine
Cycle efficiency can be improved by either:
- increasing the average temperature during heat
addition (Tin )
- decreasing the condenser temperature (Tout)
Increase the amount of superheat (41’)
’
1
2
’
Amount of superheating is limited by metallurgical
considerations of the turbine (T1 < 670C)
Added benefit is that the quality of the steam at the
turbine exit is higher
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Increase boiler pressure (4  1’)
’
’
’
Disadvantages:
- Requires more robust equipment
- Vapor quality at 2’ lower than at 2
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Decrease Condenser Pressure (2’  3’)
’
’
’
Tout is limited to the temperature of the cooling medium
(e.g., lake at 15C need 10C temperature difference for
heat transfer so Tout >25C)
Disadvantages:
- Note: for water Psat(25C)= 3.2 kPa lower than
atmospheric, possible air leakage into lines
- Vapor quality lower at lower pressure not good for
turbine
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The most common method to increase the cycle thermal
efficiency is to use a two-stage turbine and reheat the
steam in the boiler after the first stage
 
net work out wout  win w12  w34   w56


q61  q23 
heat input
qin
 Rankine 
w / reheat
(h1  h2 )  (h3  h4 )  (h6  h5 )
h1  h6   h3  h2 
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