Analysis of Rankine Cycle with FWH

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T DelhiEngineering solution to Pure Thoughts ..…..

Regeneration Cycle with Open FWH

Analysis of OFWH

h3

h6

y

h2

1-y

Conservation of energy:

326 1 hhyhy 2326 hhhhy

26

23

hh

hhy

Haywood MethodologyAnalysis of Engineering Cycles : R.W. Haywood

PB

26

23

hh

hhy

26

361hh

hhy

45

17111

hh

hhy

q

q

in

out

26

36

45

171hh

hh

hh

hh

• Assumptions :

1. The Difference between local steam enthalpy and enthalpy of saturated water at the same pressure is constant throughout the expansion.

2. Constant ‘β’ Assumption by Haywood.

By assuming that the turbine expansion line follows a path on the diagram such that the (h-hf)=constant= β

Where, h- local enthalpy on the turbine expansion line at a given

pressure. hf=Enthalpy of saturated water at that pressure .

173645 hhhhhh f

Let the enthalpy rise of feed water in the heater is .

23 hh

263623 hhhhhh

45

2

26

36

45

17 11hhhh

hh

hh

hh

4f

45

2

26

36

45

17 11hhhh

hh

hh

hh

f

ff

hh

hhhhhh

44

444545

4f

Maximum irreversibility to be eliminated = The total enthalpy rise of feed water = h4f – h1

Let 14 hh f

fhh 44

1444 hhhh ff

14 hh

4f

23 hh

Pump work input is negligible

There fore the efficiency can be written as

Here β and α are fixed and is variable. So, there is an optimum value of γ for which η is a maximum. On differentiation,

02

d

d

There fore = α / 2

The cycle efficiency is maximum when the total enthalpy rise of feed water (h4f – h1) from the condenser temperature to the boiler saturation temperature is divided equally between the feed water heater and the economizer ( i.e. h4f – h4 = h3 – h2) in a single bleed cycle.

2

26

36

45

17 11hh

hh

hh

hh

So the temperature rise in the feed water heater is

ΔT = ½ ( Tboiler saturation – T condenser)

And the corresponding cycle efficiency is

2

2

2

4

For a non-regenerative cycle,

0

The maximum gain in efficiency due to regeneration

2

2

02

This is positive. This shows that the cycle efficiency has improved due to regeneration.

Location of Haywood’s Optimum OFWH

h3

h6

y

h2

1-y

26

23

hh

hhy

2

2423

hhhh f

26

24

2 hh

hhy f

224

3

hhh f

Analysis of Regeneration through OFWH

26

23

hh

hhy

45 hhmQ in

171 hhymQOut

pumpscondbleednet WWWW

3412 & hhhh 0

pumpsW

7565 1 hhyhhymWWW condbleednet

45

7565 1

hhm

hhyhhym

in

net

Q

W

35

7565 1

hh

hhyhhy

35

75

35

65 1

hh

hhy

hh

hhy

condensing bleed

16

13

26

23

hh

hh

hh

hhy

16

1311hh

hhy

16

361hh

hhy

35

65

16

13

35

65

hh

hh

hh

hh

hh

hhybleed

16

75

35

36condensing hh

hh

hh

hh

t workoutpuspecific fractional steam bled offraction bleed

t workoutpuspecific fractional steam condensing offraction bleed

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10 15 20

16

13

hh

hhy

35

65

hh

hh

Analysis of Bleed Steam Performance

pbleed, MPa

Analysis of Condensing Steam Performance

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5 10 15 20

35

36

hh

hh

16

75

hh

hh

pbleed, MPa

Comparison of Performance of Bleed & Condensing steams

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10 15 20

Pregen, MPa

cond

bleed

Performance of FWH Cycle

0.45

0.455

0.46

0.465

0.47

0.475

0.48

0.485

0.49

0 5 10 15 20

pregen, MPa

total

~ 12MPa

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 5 10 15 20

35

65

hh

hhy

Performance of bleed Steam

pregen, MPa

bleed

~ 2 Mpa

wbl

eed

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20

65 hhy

Workoutput of bleed Steam

pregen, MPa

~ 12MPa

Fra

ctio

nal s

peci

fic

outp

utWorkoutput of bleed Steam

Fraction of Bleed Steam

0

200

400

600

800

1000

1200

1400

1600

0 0.1 0.2 0.3 0.4 0.5

wbl

eed

Workoutput of bleed Steam

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