Analysis of Rankine Cycle with Multiple OFWHs

P M V SubbaraoProfessor

Mechanical Engineering DepartmentI I T Delhi

Translation of an Engineering solution into Mathematical Model ..…..

Analysis of Regeneration through OFWH

26

23

hh

hhy

45 hhmQ in

171 hhymQOut

pumpscondbleednet WWWW

0

pumpsW

7565 1 hhyhhymWWW condbleednet

0

200

400

600

800

1000

1200

1400

1600

0 0.1 0.2 0.3 0.4 0.5

h5-h

6Workoutput of bleed Steam

26

23

hh

hhy

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

Open (Direct Contact) Feed Water Heater

                                   

Closed Feed Water Heater (Pumped Condensate)

Closed Feed Water Heater (Throttled Condensate)

Closed Feed Water Heater (Expanded Condensate)

Thermodynamic Analysis of A Power Plant

C

OFWH

OFWH

OFWH

Turbine

yj, hbjYj-11,hbj-1 Yj-2,hbj-2

1- yj – yj-1- yj-2

hf (j-3)

1- yj – yj-1

hf (j-2)

1- yj

hf (j-1)

1 ,hf (j)

A MATHEMATICAL MODEL

SG

A

B

C

n number of OFWHs require n+1 no of Pumps…..

ANALYSIS OF ‘ith’ FEED WATER HEATER

• Mass entering the turbine is STEAM TURBINE

n

iiSGcond ymm

1

1

y1,

hb1

yi,

hbi

y(i-1)

hb(i-1)

mie ,

hfi

mi,i,

hf(i-1)

STEAM IN

STEAM OUT

SGm

SGm

Mass of steam leaving the turbine is

OPTIMIZATION METHODOLOGY

The power developed by the bleed steam of ith heater before it is being extracted is given by

hs

yi

hbj

TURBINE

)( bisiSGbi hhymW

SGm

OPTIMIZATION METHODOLOGY (Contd..)

The work done by the all the feed water heaters is given by:

n

ibisiSG

n

ibi hhymW

11

)(

ANALYSIS OF ‘ith’ FEED WATER HEATER

)1(1

,

n

ijjSGei ymm

)1(,

n

ijjSGii ymm

yi , hbi

hfi h f i-1

ith heater

eim ,iim ,

Mass balance of the heater at inlet and exit is given by:

• Energy balance of the feed heater gives:

fi

n

ijjbiifi

n

ijj hyhyhy

11 11

yi , hbi

hfi h f i-1

ith heater

eim ,iim ,

fi

n

ijjbiifiifi

n

ijj hyhyhyhy

111

1

11

fieibiiSGfiii hmhymhm ,1,

fi

n

ijjSGbiiSGfi

n

ijjSG hymhymhym

11 11

1

11

1

ifif

n

ijjifbi hhyhhy

i

1

1

1

1

ifib

ififn

ijji hh

hhyy

Neglecting pump work

ifib

ififn

ijji hh

hhyy

1

1

21 1

1

11

2

1

ifib

ififi

n

ijji hh

hhyyy

1

1

1

1

22

11

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n

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hhyyy

1

1

1

1

2

11

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hhyy

1

1

1

1

2

11

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hhyy

1

1

1

12

3

11

ifib

ifif

ifib

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n

ijji hh

hh

hh

hhyyy

12

12

32 1

ifib

ififn

ijji hh

hhyy

1

1

1

1

12

12

33

111

ifib

ifif

ifib

ifif

ifib

ififn

ijj

n

ijji hh

hh

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hhyyy

1

1

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12

12

3

111

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ififn

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1

1

1

1

12

12

3

111

ifib

ifif

ifib

ifif

ifib

ififn

ijji hh

hh

hh

hh

hh

hhyy

1

1

1

1

12

12

21

21 11.....11

ifib

ifif

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ifib

ifif

nfnb

nfnf

ni hh

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1

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nfnfn hh

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1

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1

21

21

1

1 1.....11

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11

ifib

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ij jfjb

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01

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fb

ffn

j jfjb

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1

1

1 1

11

ifib

ififn

ij jfjb

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i hh

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1

1

1 1

1 111ifib

ififn

ij jfjb

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i hh

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1 1

1 111ifib

ififn

ij jfjb

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i hh

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