Analysis of Rankine Cycle: Techno-economically Feasible Thermodynamic Model

n appropriate selection of operational parameters & Processes

P M V Subbarao

Professor

Mechanical Engineering Department

Optimal Design of Vapour Power Plant

Effect of Maximum Temperature

0.370.380.390.40.410.420.430.440.45

300 400 500 600 700 800

Maximum Temperature C

Effic

ienc

y

pmax=10MPa

Effect of Maximum Temperature

100

110

120

130140

150

160

170

300 400 500 600 700 800

Tmax, C

MEP

, kPa

pmax=10MPa

050010001500200025003000350040004500

7 7.5 8 8.5 9 9.5 10 10.5

Enth

alpy

Max. Entropy

Max. Entroy Vs Enthalpy

hturb,in

hturb,out

smin smax

If Carnot Studies The Rankine Cycle !

Carnotization of Rankine Cycle

• Equivalent Carnot cycle of Rankine Cycle

23

3

2

3

2

3

2

hhdhdss

hTdsq

pin

23

233

2

3

2, ss

hh

ds

Tds

T inm

• Heat Addition in Steam Generator, qin

• Mean Effective Temperature of heat addition for equivalent isothermal process or entropy averaged temperature

Equivalent Carnot Model of Rankine Model

• Heat rejection in Steam Condenser, qin

41

1

4

1

4

1

4

hhdhdss

hTdsq

pout

cond

condoutm T

ss

ssT

ss

hh

ds

Tds

T

41

41

41

411

4

1

4,

• Mean Effective Temperature of heat rejection for equivalent isothermal process.

Equivalent Carnot Model of Rankine Model

smin smax

Tm,out

Tm,in

Analysis of Equivalent Carnot Model

• Net work out put =

• Heat Input =

TdSWnet

max

min

S

S

in TdSQ

outminmnet TTSSw ,,minmax

inmin TSSQ ,minmax

Efficiency, inm

outm

inm

outminm

in

netRankine T

T

T

TT

Q

W

,

,

,

,, 1

Parametric Study of Rankine Cycle

Tmax

D.S.S.

1MPa

3MPa

6MPa10MPa18MPa

22MPa

23.5MPa

Ideal Rankine Cycle : P-h Diagram

1

23

4

1

23

4

Tmax=5500C

pmax=5Mpaequi=246.30C

pmax=17Mpaequi=284.40C

0.35

0.36

0.37

0.38

0.39

0.40

0.41

0 5 10 15 20 25

Selection of Optimum Boiler Pressure

Pressure, MPa

h

Tmax = 450 oC

Selection of Optimum Boiler Pressure

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0 5 10 15 20 25

Pressure, MPa

x

Tmax = 450 oC

0.2820.2840.2860.2880.2900.2920.2940.2960.2980.3000.3020.304

0 2 4 6 8 10 12 14 16 18 20 22 24

Selection of Optimum Boiler Pressure

Pressure, MPa

xh

Tmax = 450 oC

Progress in Rankine Cycle

Year 1907 1919 1938 1950 1958 1959 1966 1973 1975

MW 5 20 30 60 120 200 500 660 1300

p,MPa 1.3 1.4 4.1 6.2 10.3 16.2 15.9 15.9 24.1

Th oC 260 316 454 482 538 566 566 565 538

Tr oC -- -- -- -- 538 538 566 565 538

FHW -- 2 3 4 6 6 7 8 8

Pc,kPa 13.5 5.1 4.5 3.4 3.7 3.7 4.4 5.4 5.1

,% -- ~17 27.6 30.5 35.6 37.5 39.8 39.5 40

Pressure Vs Entroy

5

5.5

6

6.5

7

7.5

8

0 5 10 15 20 25

Pressure, MPa

Entro

py, k

J/kg

K

Pressure Vs Q & W

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25

Pressure, MPa

wnet

qin

0

500

1000

1500

2000

2500

3000

3500

5 5.5 6 6.5 7 7.5 8

Q o

r W

Max. Entropy

Max. Entropy Vs Q & W

qin

wnet

051015202530354045

5 5.5 6 6.5 7 7.5 8

Max. Entropy

Max. Entropy Vs Efficiency

Pressure Vs Enthalpy

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25

Pressure (MPa)

htur.,in

htur.,out

15001700190021002300250027002900310033003500

5 5.5 6 6.5 7 7.5 8

h, KJ/k

g

Max. Entropy, kJ/kg K

Max. Entropy Vs Enthalpy

htur.,in

htur.,out

Optimaization of Boiler Pressure

1500

2000

2500

3000

3500

5 5.5 6 6.5 7 7.5 8

Entropy, kJ/kg K

h3 &

h4

0.2820.2840.2860.2880.2900.2920.2940.2960.2980.3000.3020.304

0 2 4 6 8 10 12 14 16 18 20 22 24

Selection of Optimum Boiler Pressure

Pressure, MPa

xh

Tmax = 450 oC

Parametric Study of Rankine Cycle

Tmax, 0C

wkJ/kg

D.S.S. 1MPa3MPa

6MPa

10MPa

18MPa

22MPa

23.5MPa