vapour power cycle
TRANSCRIPT
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
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 22outinoutinoutin
CVCV zzgVVhhm
Wm
QdtdE
m−+−+−+−=
&
&
&
&
&
)(0 outinCVCV hhm
Wm
Q−+−=
&
&
&
&
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1 2 Turbine (adiabatic expansion)
)(0 21 hhm
WmQ out −+−=
&
&
&
&
)( 21 hhm
Ww outout −==
&
&
2 3 Condenser (no work)
)(0 32 hhmW
mQout −+−
−=
&
&
&
&
1 )(+&
2
2
)( 32 hhm
Qq outout −==
&
& 3
W
out&
)(−outQ157
3 4 Pump (Adiabatic)
)(0 43 hhmW
mQ in −+
−−=
&
&
&
&
3
4
&
)( 34 hhm
Ww inin −==
&
&
4 1 Steam Generator (no work)
)(+inQ& )(0 14 hhmW
mQin −+−=
&
&
&
&
)( 41 hhm
Qq inin −==
&
& 4
Rankine Cycle Thermal Efficiency
( ) ( )i
out
in
inout
qw
mQmWmW −
=−
==&&
&&&&
///
inputheat outnet work
η
41
3421 )()(hh
hhhhRankine −
−−−=η
)(−inW
1
n
inw
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Back Work Ratio (bwr)
21
34
//
(turbine)output work (pump)input work
hhhhbwr
ww
mWmWbwr
out
in
out
in
−−
=
===&&&&
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. Steam generation occurs at constant pressure 4 1 2. Isentropic expansion in the turbine 1 2 3. Condensation occurs at constant pressure 2 3 4. Isentropic compression in the pump 3 4
Pboiler
With superheating
Pcondenser
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Note: For an ideal cycle no irreversibilities present so the pump work can be evaluated by
∫−=
4
3intvdP
mW
rev
p
&
&
if the working fluid entering the pump at state 3 is pure liquid, then
( )∫ −==
=
4
3343
intPPvvdP
mW
wrev
pin
&
&
The negative sign has been dropped to be consistent with previous use of win
160
Factors Affecting Cycle Efficiency
in
out
in
outin
in
inout
qqq
qww
−=−
=−
= 1η
Recall: for a reversible heat addition process ∫= Tdsq Consider qin at the boiler and qout at the condenser
area shaded
1
414
=
== ∫→ TdsqqinT
in qin
1
4
T
s Define mean temperature for process 4 1
41
1
4
ss
TdsTin −
=∫
( )41
1
4
1
4ssTdsTTdsq ininin −===∴ ∫∫
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( )area shaded
32
3
232
=−=
== ∫→
ss T
Tdsqq
out
out
3 2 qout
T
Tout
s Noting , the Ideal Rankine cycle thermal efficiency is
4132 ssss −=−
in
out
in
out
in
out
RankineIdeal T
TssTssT
−=−−
−=−= 1)()(11
41
32η
Note: this is identical to the Carnot Engine efficiency which is also a reversible cycle The back work ratio is
( )( )sout
in
RankineIdeal hh
PPvwwbwr
21
343
−−
==
162
Increase Rankine Cycle Efficiency
in
out
RankineIdeal T
T−=1η
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 (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
164
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
( )( )3216
654321
inputheat outnet work
→→
→→→
+−+
=−
wwwq
ww
in
inoutη
( ) ( )2361
564321
/
)()()(hhhh
hhhhhhreheatw
Rankine −+−−−−+−
=η
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