chapter 5 thermodynamic analysis of supercritical rankine...
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93
CHAPTER 5
THERMODYNAMIC ANALYSIS OF SUPERCRITICALRANKINE CYCLE WITH SINGLE REHEAT
A detailed thermodynamic analysis of supercritical Rankine cycle of
steam based 1000MW power plant was carried out in Chapter 4. In this
chapter, thermodynamic analysis of Rankine cycle with single reheat and
optimization of reheat pressure ratio of this cycle are presented.
5.1 SUPERCRITICAL CYCLE WITH SINGLE REHEAT
Figure 5.1 Schematic diagram of the supercritical Rankine cycle with singlereheat
Fig. 5.1 depicts the flow diagram of the supercritical Rankine cycle with
the incorporation of reheat. The high pressure and high temperature
steam from the boiler in the supercritical condition enters the turbine at
99
5.4.1 ESTIMATION OF IRREVERSIBILITY OR EXERGY LOSS INDIFFERENT COMPONENT OF SUPERCRITICAL RANKINE CYCLEWITH SINGLE REHEAT
5.4.1.1 Boiler:
The mass flow rate of steam required to be generated in the boiler to produce
an output of 1000 MW power can be found from the energy balance as given
below.
The mass flow rate of steam is calculated from the capacity of the power plant.
ms(Wnet) = 1000 MW
ms=1000x1000 kW/Wnet kg/s (5.6)
In this the mass flow rate of the flue gas (mg) required to obtain the
required steam can be found by the energy balance equation
Heat gained by the steam = Heat lost by the flue gas
ms((h1– h6 )+(h3-h2)) = mg(hA – hB)
mg = ms((h1– h6 )+(h3-h2)) /(hA – hB) kg/s (5.7)
Exergy or Availability at different state points are given below,
E1 = ms (h1-Tos1) kW (5.8)
E2 = ms (h2-Tos2) kW (5.9)
E3 = ms (h3-Tos3) kW (5.10)
E6 = ms (h6-Tos6) kW (5.11)
Irreversibility in the boiler is
Iboiler = (EA-EB) – (E1 – E6) –( E3 – E2)
Substituting the EA and EB from equations 4.8 and 4.9 is
100
Iboiler = mg(EA-EB) – ms((h1– h6 )-(h3-h2)) – (T0(s1-s6) – T0(s3 –s2)) kW (12)
5.4.1.2 Steam Turbine:
The irreversibility in the steam turbine given by Gouy-Stodola equation is
Iturbine=T0.ms((s2-s1)+(s4-s3)) kW (5.13)
5.4.1.3 Condenser:
Mass flow rate of cooling water required to be circulated to condense ms
kg/s, of steam can be obtained from the energy balance as shown below:
mcw Cpw (Twi-Two )= ms (h4-h5) (5.14)
mcw= ms(h4-h5)/ Cpw (Twi-Two )
Irreversibility in the condenser,
Icondenser=T0[ms(s4-s5)-mcwCpwln(Two/Twi)] kW (5.15)
5.4.1.4 Pump :
Irreversibility in the boiler feed pump,
I pump=ms T0(s6-s5) kW (5.16)
5.4.1.5 Exhaust:
Irreversibility of the exhaust, Iexhaust = EB (5.17)
5.4.1.6 Total Irreversibility:
Total Irreversibility is
I =(Iboiler + Iturbine + Ipump + Icondenser + Iexhaust ) kW (5.18)
5.4.1.7 Exergy Efficiency:
Exergy efficiency = 100*A
A
EIE (5. 19)
101
5.5 PARAMETRIC EFFECT ON THE PERFORMANCE OFSUPERCRITICAL POWER CYCLE WITH SINGLE REHEAT:
In the sections of 5.1 to 5.4 the fundamental aspects related to
supercritical power cycle with single reheat regarding its functioning;
energy and exergy analysis was discussed. Based on this, the effect of
different variables on the performance of the SCRC with single reheat
(SRH) is analyzed in detail and presented in the subsequent sections.
5.5.1 Optimization of Reheat Pressure Ratio
Figure 5.6 shows that the variations of energy efficiency of supercritical
Rankine cycle with single reheat with different reheat pressure ratio for
the given condenser pressure of 0.05 bar and turbine inlet pressure of
350 bar.
39
41
43
45
47
49
51
0.2 0.25 0.3 0.35 0.4Reheat Pressure Ratio
En
ergy
Effi
cien
cy(%
)
500550600650700750800
Fig 5.6 Variation of energy efficiency of SCRC with SRH with single reheatpressure ratio of different turbine inlet temperature
P1=350bar,Pc=0.05bar T1,(0C)
102
Energy efficiency increases with an increase of reheat pressure ratio from
0.2 to 0.25 and decreases from 0.25 to 0.4. Further, on careful
observation it may also be noted that optimum reheat pressure ratio is
0.25 at all turbine inlet temperatures in the range of 5000C-8000C.
Further, it may be noted that, the fall in the energy efficiency from 0.25
reheat pressure ratio to 0.3 is steep compared to the fall in the energy
efficiency for reheat pressure ratio from 0.3 to 0.4. In fact, the further fall
in energy efficiency for reheat pressure ratio beyond 0.4 is negligible. It
can be observed from the figure that, the fall in energy efficiency with
increase of reheat pressure ratio from 0.3 to 0.4 is only 0.44%, as the
slope of the line is very small. In view of this, it can be commented that,
further fall in energy efficiency for reheat pressure ratio beyond 0.4 is
negligible. It may also be noted that the maximum variation in the energy
efficiency at turbine inlet temperature of 5000C is 2.54%.
44
45
46
47
48
49
0.2 0.25 0.3 0.35 0.4Reheat Pressure Ratio
En
ergy
Eff
icie
ncy
(%)
225 250275 300325 350375 400425
T1=7000C,Pc=0.05bar
P1,(bar)
103
Fig 5.7 Variation of energy efficiency of SCRC with SRH with single reheatpressure ratio of different turbine inlet pressure
The variation in energy efficiency with reheat pressure ratio has been
presented at one turbine inlet pressure of 350 bar in Fig.5.6. However,
the variation in energy efficiency at different values of turbine inlet
pressure has been presented in the Fig.5.7. From this figure, it may be
noted that, the trend in the variation of energy efficiency with reheat
pressure ratio all the values of turbine inlet pressure is similar and the
optimum reheat pressure ratio is 0.25 for all the values of turbine inlet
pressure. It is significant to note that, the maximum variation in energy
efficiency with reheat pressure ratio is 2.54 at turbine inlet pressure of
425 bar.
Table 5.1 shows the values of energy efficiency at different reheat
pressure ratios of the SCRC along with SRH.
To offer the explanation for this trend in variation of energy efficiency
with reheat pressure ratio the values of turbine work, heat supplied and
energy efficiency at different reheat pressure ratios have been tabulated
in Table 5.1.
Table 5.1 Energy efficiency at different reheat pressure ratio
R Wt(kJ/kg)
Wp(kJ/kg)
Wnet(kJ/kg)
H.S.(kJ/kg)
EnergyEfficiency
(%)0.20 2040.404 41.376 1999.028 4223.60 47.330.25 2033.026 41.376 1991.650 4114.98 48.400.30 1968.747 41.376 1927.371 4072.20 47.330.35 1966.827 41.376 1925.451 4069.86 47.310.40 1866.475 41.376 1825.099 4037.83 45.20
104
From the table it may be noted that the work output of the turbine and
heat supplied to the boiler decreases with increase of reheat pressure
ratio but it is interesting to note that the fall in the turbine work output
when the reheat pressure ratio increases from 0.2 to 0.25 is marginal
(7.37 kJ/kg) and the fall in the heat supplied is significant (108.61
kJ/kg) which resulted in increase in the energy efficiency from 47.33% to
48.40%. Further fall, in the turbine work output from the turbine as the
reheat pressure ratio increases from 0.25 to 0.3 is quite significant
(64.27 kJ/kg) and the fall in the heat supplied is only is small (42.78
kJ/kg) which resulted in the fall of efficiency from 48.40% to 47.30%. For
further increases in the reheat pressure ratio to 0.35 to 0.40 it may also
be noted that the rate of fall in turbine work output is more than that of
rate of fall in the heat supplied to the boiler which ultimately resulted in
fall in the energy efficiency.
The turbine work output falls as the steam is reheated in between the
expansion process and at all values of reheat pressure the turbine work
output reduces. This is due to withdrawal of steam at one portion of
turbine for reheating which results in less amount of force exited on the
turbine blades by the steam.
Figure 5.8 shows the variation of exergy efficiency with reheat pressure
ratio of supercritical cycle with single reheat at a turbine inlet pressure of
350 bar and condenser pressure of 0.05 bar.
105
56
58
60
62
64
66
68
0.2 0.25 0.3 0.35 0.4Reheat Pressure Ratio
Exe
rgy
Effi
cien
cy(%
) 500550600650700750800
Fig 5.8 Variation of exergy efficiency of SCRC with SRH with reheat pressureratio of different turbine inlet pressure
It may be noted from this figure that the exergy efficiency reaches an
optimum value at a reheat pressure ratio of 0.25 values of exergy
efficiency at a reheat pressure ratio of 0.25 at 5000C, 6000C, 7000C and
8000C were found to be 61.19 %, 63.39 %, 65.67% and 67.76%
respectively. Further, a maximum variation in exergy efficiency with
reheat pressure ratio was found to be 0.25 at a turbine inlet temperature
of 4.14%. Also a similar trend in the variation of exergy efficiency was
observed in the Fig.5.9 at all values of turbine inlet pressures which is
presented in the range of 22bar to 425bar. It may be noted that exergy
efficiency at a reheat pressure of 0.25 at 225bar, 250bar, 300bar,
350bar, 400bar and 425bar were found to be 63.01%, 63.76%, 64.81%,
65.67%, 66.35% and 66.59%, respectively.
TFGi =10000C,TFGo =1000C,P1=350bar,Pc=0.05bar
T1,(0C)
106
59
60
61
62
63
64
65
66
67
0.2 0.25 0.3 0.35 0.4Reheat Pressure Ratio
Exe
rgy
Effi
cien
cy(%
)225250300350400425
Fig 5.9 Variation of exergy efficiency of SCRC with SRH with reheat pressureratio of different turbine inlet temperature
The values of irreversibilities in different components of the cycle, and
exergy efficiency at different values of reheat pressure ratio have been
found and presented in Table 5.2 for the sake of analysis.
The following may be the possible reason for increase in the exergy
efficiency in the reheat pressure ratio from 0.20 to 0.25 and the
subsequent fall in reheat pressure ratio range of 0.25 to 0.4.
Table 5.2 Exergy efficiency at different reheat pressure ratioR Iboiler
kWIturbine
kWIcondenser
kWIpump
kWIexhaust
kWIsum
kWExergyEfficiency
(%)0.20 216824.84 98207.81 20993.96 2396.13 13075.68 351498.41 64.980.25 210601.42 97536.34 21005.89 2363.79 13075.68 344583.12 65.670.30 221994.20 98835.27 21000.92 2425.88 13075.68 357331.94 64.400.35 226401.67 99432.95 21023.87 2454.20 13075.68 362388.38 63.900.40 230313.66 99998.03 21053.02 2480.89 13075.68 366921.28 63.45
Further, on careful observation one may note that the values in
irreversibility of boiler and irreversibility of turbine decreases with
increase in reheat pressure ratio from 0.2 to 0.25 and increases
TFGi =10000C,TFGo =1000CT1=7000C,Pc=0.05bar
P1,(bar)
107
subsequently with increase in reheat pressure ratio from 0.25 to 0.40.
This variation in total irreversibility results in increase in the exergy
efficiency from 0.2 to 0.25 of reheat pressure ratio and reduction in the
exergy efficiency form 0.25 to 0.40 of reheat pressure ratio, as the exergy
at boiler entrance remain unchanged(equation 4.08) for the different
values of reheat pressure ratio.
Hence, the trend in the variation of irreversibility of boiler and
irreversibility of turbine together dictates the trend in the variation of
total irreversibility (total exergy loss) which is presented in Fig.5.10.
Figure 5.10 shows the variation of total exergy loss on reheat pressure
ratio from 0.20 to 0.4 with different turbine inlet temperature at a
turbine inlet pressure of 350 bar.
300
325
350
375
400
425
450
0.2 0.25 0.3 0.35 0.4Reheat Pressure Ratio
Tota
l Exe
rgy
Loss
(MW
)
500550600650700750800
Fig 5.10 Variation of total exergy loss of SCRC with SRH with reheat pressureratio
TFGi =10000C,TFGo =1000C,P1=350bar,Pc=0.05bar
T1,(0C)
108
Figure 5.11 represents that the FEL of the SCRC with SRH. It may be
noted from the figure that the FEL of the boiler, turbine is slightly
increases with an increase of reheat pressure ratio. FEL of all the
components of cycle is not a strong function of reheat pressure ratio. It is
of academic interest to note that, FEL in boiler is about 62.77%, in
turbine is about 27.45% and remaining FEL takes place in condenser,
pump and exhaust together. About 1% change in FEL of the boiler in the
reheat pressure ratio range of 0.20 to 0.4.
0
10
20
30
40
50
60
70
0.2 0.25 0.3 0.35 0.4Reheat Pressure ratio
Frac
tion
al e
xerr
gy lo
ss(%
)
BoilerTurbineCondenserPumpExhaust
Fig 5.11 Variation of fractional exergy loss of SCRC with SRH with reheatpressure ratio
5.5.2 Effect of turbine inlet temperature and pressure on energyefficiency
Figure 5.12 shows the variation of energy efficiency of supercritical
Rankine cycle with single reheat with the turbine inlet steam
temperature at the various pressures. The energy efficiency increases of
the cycle with an increase of turbine inlet steam temperature at a given
TFGi =10000C,TFGo =1000C,P1=350bar,T1 =7000CPc=0.05bar
109
pressure. The energy efficiency at turbine inlet pressure of 425 bar and
at different turbine inlet temperature of 5000C, 6000C and 7000C is
41.86%, 44.83% and 47.32% respectively. However, the maximum
energy efficiency of 49.65% was found at a turbine inlet temperature of
8000C at a at a turbine inlet pressure of 425 bar.
42
44
46
48
50
52
500 550 600 650 700 750 800Turbine inlet temperature (
0C)
En
ergy
Effi
cien
cy(%
)
170200225250275300325350375400425
Fig. 5.12 Variation of energy efficiency of SCRC with SRH with turbine inlettemperature of steam
In order to identify the cause for the increase in energy efficiency with
increase in temperature the value of net work done, heat supplied at
different states have been found and tabulated in Table 5.3. Further, the
net work, heat supplied and energy efficiency at different turbine inlet
Pc=0.05bar,R=0.25
P1,(bar)
110
pressure and at a turbine inlet temperature of 7000C have been
tabulated in the Table 5.3.
Table 5.3 Energy efficiency at different turbine inlet pressures
P1bar
T1(0C)
Wt(kJ/kg)
Wp(kJ/kg)
Wnet(kJ/kg)
H.S(kJ/kg)
EnergyEfficiency
(%)225 700 2025.92 24.73 2001.19 4211.925 47.51250 700 2026.77 28.88 1997.89 4179.921 47.79300 700 2030.56 36.18 1994.38 4141.723 48.15350 700 2033.03 41.37 1991.65 4114.323 48.41400 700 2033.89 45.52 1988.37 4089.499 48.62425 700 2034.16 51.28 1982.98 4070.748 48.71
Table 5.3 reveals that turbine work marginally increases and network
output from the turbine marginally decreases with increase in turbine
inlet pressure at a given steam turbine inlet temperature, due to
significant increase in the pump work.
Further, it may be noticed from the Table 5.3 that, the energy input
(Heat Supplied) to the boiler also decreases as the turbine inlet pressure
increases at a given steam turbine inlet temperature.
So, as the steam turbine inlet pressure increases in both the Wnet and
heat supplied decreases marginally. But the rate of decrease of heat
supplied is more than the rate of decrease of Wnet. Hence, the energy
efficiency increases as the pressure increases at a given inlet turbine
temperature.
In order to appreciate, the effect of the turbine inlet pressure on the
performance of the plant, Figure 5.13 that represents the variation of
energy efficiency with turbine inlet pressure at different turbine inlet
111
temperatures of and at a condenser pressure, Pc=0.05bar and reheat
pressure ratio 0.25 has been drawn. It is observed from the figure that
the energy efficiency increases with increase of steam turbine pressure at
different temperatures. The energy efficiency at turbine inlet temperature
8000C and at different turbine inlet pressures of 250bar, 300bar, 350bar,
400bar and 425bar is 48.95%, 49.20%, 49.42% ,49.58% and 49.66%
respectively.
40
42
44
46
48
50
52
170 200 225 250 275 300 325 350 375 400 425
Turbine inlet pressure (bar)
En
ergy
Effi
cien
cy(%
)
500550600650700750800
Fig. 5.13 Variation of energy efficiency of SCRC with SRH with different turbineinlet pressure of steam
To identify the reason for this variation table 5.4 similar to the Table 5.3
have been presented below.
Table 5.4 Energy efficiency at different turbine inlet temperatures
P1bar
T1(0C)
Wt(kJ/kg)
Wp(kJ/kg)
Wnet(kJ/kg)
H.S.(kJ/kg)
EnergyEfficiency
(%)350 500 1541.65 41.37 1500.28 3432.35 43.71350 550 1642.31 41.37 1600.93 3603.26 44.43350 600 1797.05 41.37 1755.68 3773.23 46.53
Pc=0.05bar,R=0.25
T1(0C)
112
350 650 1918.71 41.37 1877.34 3943.14 47.61350 700 2033.02 41.37 1991.65 4114.98 48.41350 750 2058.26 41.37 2016.89 4284.92 49.17350 800 2262.12 41.37 2220.75 4454.86 49.85
On careful observation of table 5.4, it may be noted that the energy
efficiency of the supercritical cycle with single reheat increases
significantly with turbine inlet temperature due to faster rate of increase
of net work output compared to heat supplied.
5.5.3 Effect of turbine inlet temperature and pressure on exergyefficiency
In the section 4.7.2 the effect of turbine inlet temperature and turbine
inlet
pressure on the exergy efficiency of supercritical Rankine cycle without
reheat was discussed. Similarly, the effect of these parameters on the
exergy efficiency, total exergy loss of supercritical Rankine cycle with
reheat is presented on the Figures 5.14, 5.15, 5.16 and 5.17.
Figure 5.14 depicts the variations of exergy efficiency steam turbine
temperature at condenser pressure 0.05bar and at a reheat pressure
ratio of 0.25. The exergy efficiency increases with increase of steam
turbine inlet temperature at a given turbine inlet pressure. Further, a
similar trend in the variation was found at all the values of turbine inlet
pressure in the range of 170bar to 425bar. At a turbine inlet pressure of
425bar (maximum pressure), it is interesting to note the values of exergy
efficiency at 5000C, 6000C, 7000C and 8000C are 61.90%, 64.23%,
66.59% and 68.70% respectively.
113
52
56
60
64
68
500 550 600 650 700 750 800Turbine inlet temperature (0C)
Exe
rgy
Effi
cien
cy(%
)
170 200 225250 275 300325 350 375400 425
Fig. 5.14 Variation of Exergy efficiency of SCRC with SRH with turbine inlettemperature of steam
To analyze the possible reason for the increasing trend of exergy
efficiency of this cycle with turbine inlet temperature, Table 5.5 has been
presented below.
Table 5.5 Exergy efficiency at different turbine inlet pressures
Pbar
T(0C)
Iboiler
kW
Iturbine
kW
Icondenser
kW
Ipump
kW
Iexhaust
kW
Isum
kW
ExergyEfficiency
(%)225 700 237092.92 96754.61 23473.49 958.34 13075.68 371355.03 63.01250 700 229637.91 96890.01 22349.15 1849.81 13075.68 363802.56 63.76300 700 219284.12 97203.68 22127.88 1599.38 13075.68 353290.75 64.81350 700 210601.42 97536.34 21005.89 2363.79 13075.68 344583.12 65.67400 700 203708.98 97899.74 19946.22 3129.15 13075.68 337759.78 66.35425 700 201358.89 98085.62 19899.82 3006.86 13075.68 335426.88 66.59hA=1770892.62 kJ, hB=120400.21 kJ, EA =1003827.38 kJ, EB =13075.68 kJ
From the equation 4.8, it may be noted that EA is independent of turbine
inlet pressure and turbine inlet temperature, in fact EA is constant for all
values of turbine inlet pressure and turbine inlet temperature, as long as
Pc=0.05barR=0.25
P1,(bar)
114
flue gas inlet temperature of boiler is retained at same value. From the
Table 5.5, it can be observed that the exergy at the entry of the boiler
does not vary with turbine inlet temperature and pressure i.e., EA is
independent of variation of turbine inlet pressure and turbine inlet
temperature of supercritical cycle with single reheat. It may be noted that
the amount of irreversibility in the boiler and condenser reduces with
increase in turbine inlet pressure with a given turbine inlet temperature.
However, irreversibility in the turbine increases marginally but
irreversibility for the pump increases significantly with turbine inlet
pressure. It is also important to note that the amount of irreversibility at
exhaust does not vary with turbine inlet pressure. As a consequence of
these irreversibilities; the total irreversibility of all the components of the
supercritical cycle with single reheat put together is decreases with
increase in the turbine inlet pressure. This results in increase in the
exergy efficiency with turbine inlet pressure at a constant turbine inlet
temperature of the cycle.
The data of total irreversibility (total exergy loss) only at one value of
turbine inlet temperature and at different turbine inlet pressure is
presented in the table 5.5. However, the values of total exergy loss at
different values of turbine inlet temperature and turbine inlet pressure
are plotted in Fig.5.15
115
300
325
350
375
400
425
450
500 550 600 650 700 750 800
Turbine inlet temperature (0C)
Tota
l E
xerg
y Lo
ss(M
W)
170 200 225250 275 300325 350 375400 425
Fig. 5.15 Variation of total exergy loss of SCRC with SRH with different turbineinlet temperature
Figure 5.16 represents the variation of exergy efficiency with turbine inlet
steam pressure at condenser pressure 0.05 bar and at a reheat pressure
ratio of 0.25.
54
58
62
66
70
170 200 225 250 275 300 325 350 375 400 425
Turbine inlet pressure ( bar)
Exe
rgy
Effi
cien
cy(%
)
500 550 600650 700 750800
Fig. 5.16 Variation of exergy efficiency of SCRC with SRH with turbine inletpressure of steam
Pc=0.05bar,R=0.25
TFGi =10000C, TFGo =1000C,P1=350 bar, Pc=0.05bar,R=0.25
T1,(0C)
P1,(bar)
116
The exergy efficiency increases with increase of steam turbine pressure
at a given turbine inlet steam temperature. Further, a similar trend in
the variation was found at all the values of turbine inlet temperature in
the range of 5000C-8000C. At a turbine inlet temperature of 8000C, the
values of exergy efficiency at 225bar, 250bar, 300bar, 350bar, 400bar
and 425bar are 65.17%, 65.88%, 66.9%, 67.76% 68.45% and 68.7%
respectively.
The values of irreversibility in different components and exergy efficiency
at different turbine inlet temperature have been tabulated in Table 5.6,
which help in understanding the reason for this variation.
Table 5.6 Exergy efficiency at different turbine inlet pressuresPbar
T(0C)
Iboiler
kW
Iturbine
kW
Icondenser
kW
Ipump
kW
Iexhaust
kW
Isum
kW
ExergyEfficiency
(%)350 500 246125.48 101407.66 25771.24 3177.50 13075.68 389557.56 61.19350 550 238607.30 100125.36 24345.64 2926.77 13075.68 379080.75 62.24350 600 229413.94 99127.02 23122.01 2715.33 13075.68 367453.97 63.39350 650 219924.67 98282.55 22019.55 2529.75 13075.68 355832.22 64.55350 700 210601.42 97536.34 21005.89 2363.79 13075.68 344583.12 65.67350 750 201625.69 96861.27 20065.72 2213.97 13075.68 333842.34 66.74350 800 193081.09 96243.65 19190.81 2078.08 13075.68 323669.31 67.76
On careful observation it may be noted that the amount of irreversibility
in the boiler, turbine, condenser and pump reduces with increase in
turbine inlet temperature at a given turbine inlet pressure. It is also
important to note that the amount of irreversibility at exhaust does not
vary due to fixed boiler flue gas exit temperature. Hence, the total
irreversibility is decreases with increase in the turbine inlet temperature.
This results in increase in the exergy efficiency with turbine inlet
pressure at a turbine inlet temperature.
117
The data of (total exergy loss only at one value of turbine inlet pressure
and at different turbine inlet temperature is presented in the table 5.6.
However, the values of total exergy loss at different values of turbine inlet
temperature and turbine inlet pressure are plotted in Fig.5.17
300
325
350
375
400
425
450
170 200 225 250 275 300 325 350 375 400 425
Turbine inlet pressure ( bar)
Tota
l Exe
rgy
Loss
(MW
) 500 550600 650700 750800
Fig. 5.17 Effect of total exergy loss of SCRC with SRH with different turbineinlet pressure
TFGi =10000C,TFGo =1000C,T1=7000C,Pc=0.05bar,R=0.25
T1,(0C)
118
5.5.4 Effect of turbine inlet temperature and pressure on fractionalexergy loss
0
10
20
30
40
50
60
70
500 550 600 650 700 750 800Turbine inlet temperature (
0C)
Frac
tion
al E
xerg
y Lo
ss (%
)BoilerTurbineCondenserPumpExhaust
Fig. 5.18 Variation of turbine inlet temperature of SCRC with SRH withfractional exergy loss of different components
Figure 5.18 shows the fractional exergy loss of all components of a
supercritical Rankine cycle with single reheat. It should be noted that the
FEL of the boiler decrease from 63% to 59.65%, pump with increase of
temperature. FEL of the steam turbine increases from 26-30% with
increase of steam temperature. FEL of the condenser decreases 6.62% to
5.93%, FEL of the pump slightly decreases where as FEL of exhaust
increases with increase of steam turbine inlet temperature.
TFGi =10000C, TFGo =1000C,P1=350 bar, Pc=0.05bar,R=0.25
119
0
10
20
30
40
50
60
70
170 200 225 250 275 300 325 350 375 400 425
Turbine inlet pressure (bar)
Frac
tion
al E
xerg
y Lo
ss(%
)BoilerTurbineCondenserPumpExhaust
Fig. 5.19 Variation of turbine inlet pressure of SCRC with SRH with fractionalexergy loss of different components
Figure 5.19 shows that the effect of turbine inlet pressure on fractional
exergy loss of different components. FEL of the boiler decreases with an
increase of steam turbine pressure. FEL boiler at 250bar is 63.12%, at
300 bar is 62.07%, at 350bar is 61.12%, 400bar is 60.31%. FEL of the
turbine at 200bar is 25.49%, at 250bar is 26.63%, 300bar is 27.96%,
350bar is 28.31%, and 400bar is 28.99%. FEL of the condenser
decreases from 6.37% to 5.991%. FEL of the pump is less than 1% and
FEL of the exhaust increases from 3.36% to 3.91% with increase of
steam turbine inlet temperature at a given turbine inlet pressure.
TFGi =10000C, TFGo =1000C,T1=7000C, Pc=0.05bar,R=0.25
120
5.5.5 Effect of Condenser pressure on the performance
In the section 4.7.4, the effect of condenser pressure on the performance
of supercritical cycle has been analyzed for the cycle without reheat at
turbine inlet pressure of 350bar and reheat pressure ratio of 0.25.
42
44
46
48
50
52
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Condenser Pressure(bar)
En
ergy
effi
cien
cy(%
) 500550600650700750800
Fig. 5.20 Variation of energy efficiency of SCRC with SRH on condenserpressure of different turbine inlet temperature
In order to carry out a similar analysis for supercritical cycle with reheat
Fig. 5.20 has been drawn. From the figure, it may be observed that the
energy efficiency decreases with increase in the condenser at a given
turbine inlet temperature and the similar trend in the variation may also
be observed at all value turbine inlet temperatures considered in the
range of 5000C-8000C.
For examine the effect of the condenser pressure on the performance of
the cycle at different pressure on the performance of the cycle at different
TFGi =10000C, TFGo =1000C,P1=350bar, R=0.25
T1,(0C)
121
values of turbine inlet pressure Fig.5.21 has been plotted. It is easy to
conclude from the above figure that the variation in energy efficiency
with condenser pressure is similar at all values of turbine inlet pressure
in the range of 225 bar to 425 bar. The reason for this variation of energy
efficiency with variation of turbine inlet temperature and turbine inlet
pressure which is explained in the section 4.8.4 holds good in this case
of supercritical cycle with reheat.
46
47
48
49
50
51
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Condenser Pressure(bar)
En
ergy
effi
cien
cy(%
)
225 250300 350400 425
Fig. 5.21 Variation of energy efficiency of SCRC with SRH on condenserpressure of different turbine inlet pressure
To find the trend in the variation of exergy efficiency of the cycle with
condenser pressure, at turbine inlet pressure of 350 bar and a reheat
pressure ratio of 0.25 Fig.5.21 has been plotted for different turbine inlet
temperatures from 5000C-8000C.
TFGi =10000C,TFGo =1000C,T1=7000C,R=0.25
P1,(bar)
122
58
60
62
64
66
68
70
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Condenser Pressure(bar)
Exe
rgy
effic
ien
cy(%
)
500550600650700750800
Fig. 5.22 Variation of exergy efficiency of SCRC with SRH on condenserpressure of different turbine inlet temperature
It may be noted from Fig.5.22, the exergy efficiency decreases with
increase of condenser pressure at different turbine inlet temperatures as
the total exergy loss increases with condenser pressure as shown in
Fig.5.23.
It may also be noted that the maximum exergy efficiency occurred at a
condenser pressure of 0.03 bar at all turbine inlet temperatures. At a
turbine inlet pressure of 350 bar, the values of exergy efficiency at
5000C, 6000C, 7000C and 8000C are 61.98%, 64.22%, 66.55% and
68.95% respectively.
T1,(0C)
TFGi =10000C,TFGo =1000C,P1=350bar,R=0.25
123
300
320
340
360
380
400
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Condenser Pressure(bar)
Tota
l Exe
rgy
loss
, MW
500 550 600650 700 750800
Fig. 5.23 Variation of total exergy loss of SCRC with SRH on condenserpressure of different turbine inlet temperature
Fig.5.24 shows the variation of exergy efficiency with condenser pressure
at different turbine inlet pressures and at turbine inlet temperature of
7000C and reheat pressure ratio of 0.25.
62
63
64
65
66
67
68
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Condenser Pressure(bar)
Exe
rgy
effic
ienc
y(%
) 225 250300 350400 425
Fig. 5.24 Variation of exergy efficiency of SCRC with SRH on condenserpressure of different turbine inlet pressure
TFGi =10000C,TFGo =1000C,T1=7000C,R=0.25
P1,(bar)
TFGi =10000C, TFGo =1000C,P1=350bar, R=0.25
T1,(0C)
124
It may be noted that, the variation in exergy efficiency at all other values
of turbine inlet pressure is similar to that of variation in exergy efficiency
at 350 bar. It may be interesting to note that the maximum energy
efficiency occurred at a condenser pressure of 0.03 bar at all turbine
inlet pressures. At a turbine inlet temperature of 7000C, the values of
energy efficiency at 225bar, 250bar, 300bar, 350bar, 400bar and 425
bar are 65.15%, 65.50%, 66.14%, 66.55%, 66.79% and 67.04%
respectively.
The possible reason for the increasing trend in exergy efficiency of this
cycle explanation offered in section 4.7.4 for this variation supercritical
cycle without reheat holds good for this case also.
Figure 5.25 depicts the FEL of the individual components of a
supercritical cycle with single reheat. FEL of the boiler and turbine
decreases with increase of condenser pressure. FEL of the boiler at
condenser pressure of 0.03 bar is 64.05% and 0.1 bar is 56.92%. FEL of
the condenser increases drastically with increase of condenser pressure.
FEL of the turbine at condenser pressure of 0.03 bar is 28.86% and 0.1
bar is 26.28%. FEL of the condenser at condenser pressure of 0.03 bar
is 4.03% and 0.1 bar is 12.37%. FEL of the pump and exhaust increases
with decrease of condenser pressure.
125
0
10
20
30
40
50
60
70
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Condenser Pressure(bar)
Frac
tion
al E
xerg
y Lo
ss(%
)Boiler TurbineCondenser PumpExhaust
Fig 5.25 Variation of fractional exergy loss of SCRC with SRH withcondenser pressure
5.5.6 Effect of boiler inlet flue gas temperature on exergy efficiencyIn the section 4.7.5 the effect of boiler flue gas inlet temperature on
exergy efficiency of supercritical Rankine cycle without reheat has been
discussed. To carry out a similar analysis for supercritical Rankine cycle
with reheat, the data obtained has been plotted in Fig. 5.26 and Fig.5.27.
The trend in the variation of exergy efficiency and total exergy loss for a
SCRC without reheat and with single reheat does not alter and the
explanation provided in the chapter 4 in the section 4.7.5 for this
variation holds good for this also.
The effect of boiler inlet flue gas temperature varied 9000C to 14000C on
exergy efficiency for the given flue gas boiler exit temperature of 1000C,
turbine inlet temperature of 7000C, turbine inlet pressure of 350bar and
TFGi =10000C,TFGo =1000C,T1=7000C,P1=350 bar,R=0.25
126
reheat pressure ratio of 0.25 for the given capacity are shown in
Fig.5.27-5.30 respectively.
58
62
66
70
74
78
82
900 1000 1100 1200 1300 1400Boiler flue gas inlet temperature(
0C)
Exe
rgy
effic
ien
cy(%
)
500550600650700750800
Fig. 5.26 Variation of exergy efficiency of SCRC with SRH on boiler flue gasinlet temperature of different turbine inlet temperature
60
65
70
75
80
900 1000 1100 1200 1300 1400Boiler flue gas inlet temperature(
0C)
Exe
rgy
effic
ien
cy(%
)
225 250300 350400 425
P1,(bar)
Fig. 5.27 Variation of exergy efficiency of SCRC with SRH on boiler flue gasinlet temperature of different turbine inlet pressure
TFGo =1000C,T1=7000C,R=0.25
TFGo =1000C,P1=350bar,T1=7000C R=0.25
T1,(0C)
127
300
350
400
450
500
900 1000 1100 1200 1300 1400Boiler flue gas inlet temperature(0C)
Tota
l Exe
rgy
loss
, M
W
500 550 600650 700 750800
Fig. 5.28 Variation of total exergy loss of SCRC with SRH on boiler flue gas inlettemperature of different turbine inlet temperature
Figure 5.29 represents the variation of fractional exergy loss of different
components of a supercritical cycle with single reheat.
0
10
20
30
40
50
60
70
900 1000 1100 1200 1300 1400
Boiler flue gas inlet temperature(0C)
Frac
tion
al E
xerg
y Lo
ss(%
)
BoilerTurbineCondenserPumpExhaust
Fig. 5.29 Variation of fractional exergy loss of SCRC with SRH on boiler fluegas inlet temperature
TFGi =10000C,TFGo =1000CP1=350bar,R=0.25
T1,(0C)
TFGi =10000C,TFGo =1000CP1=350bar,T1 =7000CR=0.25
128
It may be noted from the figure that the FEL of the boiler increases with
an increase of flue gas inlet temperature. FEL of the boiler was found to
be 57.41% to 63.57% as the flue gas inlet temperature increases from
9000C-14000C. However, FEL of the turbine decreases from 31% to
12.34% with increase of boiler flue gas inlet temperature from 9000C-
14000C. FEL of the exhaust rapidly increases from 4.16% to 20.26% with
an increase of flue gas inlet temperature.
5.5.7 Effect of boiler flue gas outlet temperature on exergyefficiency
In the section 4.7.6 the effect of boiler flue gas outlet temperature on
exergy efficiency of SCRC without reheat has been discussed. To carry
out a similar analysis for supercritical Rankine cycle with reheat, the
data obtained has been plotted in Fig. 5.30 and Fig. 5.31.
The trend in the variation of exergy efficiency and total exergy loss for a
supercritical Rankine cycle without reheat and with single reheat does
not alter and the explanation provided in the chapter 4 in the section
4.7.6 for this variation holds good for this also.
The effect of boiler outlet flue gas temperature varied 800C to 3000C on
exergy efficiency for the given flue gas inlet temperature of boiler is
10000C, turbine inlet temperature of 7000C, turbine inlet pressure of 350
bar and reheat pressure ratio of 0.25 for the given capacity are shown in
Fig. 5.30-Fig. 5.33 respectively.
129
40
45
50
55
60
65
70
75
80 100 150 200 250 300Boiler flue gas outlet temperature(
0C)
Exe
rgy
effic
ien
cy(%
)
500550600650700750800
Fig. 5.30 Variation of exergy efficiency of SCRC with SRH on boiler flue gasoutlet temperature of different turbine inlet temperature
40
45
50
55
60
65
70
75
80 100 150 200 250 300Boiler flue gas outlet temperature(0C)
Exe
rgy
effic
ien
cy(%
)
225300400425
Fig. 5.31 Variation of exergy efficiency of SCRC with SRH on boiler flue gasoutlet temperature of different turbine inlet pressure
TFGi =10000C,P1=350bar,R=0.25
T1,(0C)
P1,(bar)
TFGi =10000CT1=7000C,R=0.25
130
300
350
400
450
500
550
600
650
80 100 150 200 250 300Boiler flue gas outlet temperature(0C)
Tota
l Exe
rgy
loss
, M
W
500 550 600650 700 750800
Fig. 5.32 Variation of exergy efficiency of SCRC with SRH on boiler flue gasoutlet temperature of different turbine inlet temperature
Figure 5.33 represents the variation of fractional exergy loss on boiler
flue gas outlet temperature.
0
10
20
30
40
50
60
70
80 100 150 200 250 300
Boiler flue gas outlet temperature(0C)
Frac
tion
al E
xerg
y Lo
ss(%
)
BoilerTurbineCondenserPumpExhaust
Fig. 5.33 Variation of fractional exergy loss of SCRC with SRH on boiler flue gasoutlet temperature of different turbine inlet temperature
TFGi =10000C,TFGo =1000C,P1=350bar,R=0.25
T1,(0C)
TFGi =10000C,TFGo =1000C,P1=350bar,T1=7000C,R=0.25
131
It may be noted that the FEL of boiler decreases with an increase of flue
gas outlet temperature. FEL of boiler at 800C is 61.8%, at 3000C is
53.87% respectively. FEL of the turbine decreases from 28.83% to
17.49%. FEL of the condenser decreases from 6.43 to 3.77%. FEL of the
exhaust at 800C is 2.21% and at 3000C is 24.44% respectively.
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