of 12
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Vapor Power Systems
Power plants work on a cycle that produces net work
from a fossil fuel (natural gas, oil, coal) nuclear, or solarinput.
For Vapor power plants the working fluid, typically
water, is alternately vaporized and condensed.
Consider the following Simple Vapor Power Plant
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
)()(2/1)(1 22
outinoutinoutinCVCV zzgVVhhm
W
m
Q
dt
dE
m+++=
&
&
&
&
&
)(0 outinCVCV hhm
W
m
Q+=
&
&
&
&
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12 Turbine (adiabatic expansion)
)(0 21 hhm
W
m
Q out +=&
&
&
&
)( 21 hhm
Ww outout ==
&
&
23 Condenser (no work)
)(0 32 hhm
W
m
Qout +
=&
&
&
&
)( 32 hhm
Q
qout
out== &
&
1
2
)(+outW&
2
3
)(outQ&
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34 Pump (Adiabatic)
)(0 43 hhmW
mQ in +=
&&
&&
)( 34 hhm
Ww inin ==
&
&
41 Steam Generator (no work)
)(0 14 hhm
W
m
Qin +=&
&
&
&
)( 41 hhm
Q
qin
in== &
&
Rankine Cycle Thermal Efficiency
( ) ( )
in
inout
in
inout
q
ww
mQ
mWmW =
==
&&
&&&&
/
//
inputheat
outnet work
41
3421 )()(
hh
hhhhRankine
=
3
4
)(inW&
1
4
)(+inQ&
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Back Work Ratio (bwr)
21
34
/
/
(turbine)outputwork
(pump)inputwork
hh
hhbwr
w
w
mW
mW
bwr out
in
out
in
=
===&&
&&
Ideal Rankine Cycle - no irreversibilities present in anyof the processes: no fluid friction so no pressure drop, and
no heat loss to surroundings
1.Steam generation occurs at constant pressure 41
2. Isentropic expansion in the turbine 12
3.Condensation occurs at constant pressure 23
4. Isentropic compression in the pump 34
Pboiler
Pcondenser
With superheating
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Note: For an ideal cycle no irreversibilities present so the
pump work can be evaluated by
=
4
3int
vdPm
W
rev
p
&
&
if the working fluid entering the pump at state 3 is pure
liquid, then
( ) ==
=
4
3343
intPPvvdP
m
Ww
rev
pin
&
&
The negative sign has been dropped to be consistent with
previous use ofwin
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Factors Affecting Cycle Efficiency
in
out
in
outin
in
inout
q
q
q
q
ww=
=
=
1
Recall: for a reversible heat addition process = Tdsq
Consider qin at the boiler and qoutat the condenser
areashaded
1
414
=
== Tdsqqin
Define mean temperature for process 4 1
41
1
4
ss
Tds
Tin
=
( )411
4
1
4
ssTdsTTdsq ininin ===
T
s
4
1qin
inT
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( )
areashaded
32
3
232
=
=
==
ssT
Tdsqq
out
out
Noting 4132 ssss = , the Ideal Rankine cycle thermal
efficiency is
in
out
in
out
in
out
RankineIdeal
T
T
ssT
ssT
q
q=
== 1
)(
)(11
41
32
Note: this is identical to the Carnot Engine efficiency
which is also a reversible cycle
The back work ratio is
( )( )sout
in
RankineIdeal
hh
PPv
w
wbwr
21
343
==
T
s
3 2qout
Tout
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Increase Rankine Cycle Efficiency
in
out
RankineIdeal T
T=
1
Cycle efficiency can be improved by either:
- increasing the average temperature during heat
addition ( inT )
- decreasing the condenser temperature (Tout)
Increase the amount of superheat(41)
Amount of superheating is limited by metallurgicalconsiderations of the turbine (T1 < 670C)
Added benefit is that the quality of the steam at the
turbine exit is higher
1
2
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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)
Toutis 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
( )( )3216
654321
inputheat
outnet work
+
+=
==
www
q
ww
in
inout
( ) ( )2361564321
/
)()()(
hhhh
hhhhhh
reheatwRankine
+
+=
