chapter 5 thermodynamic analysis of supercritical rankine...

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


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


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


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


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


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


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


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


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


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(%

)


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(%

)


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.

chapter 5 thermodynamic analysis of supercritical rankine...

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