vapour power cycles

8/3/2019 Vapour Power Cycles

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Vapour Power Cycles

Introduction

Carnot Cycle

Rankine Cycle

Reheat Cycle

Regenerative Cycle

Steam Cycles for Nuclear Power

Plants

Plant Efficiency


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Introduction

Transfer of heat from a reservoir to a

working fluid taken through athermodynamic cycle

Working fluid is a condensable vapour

Cycle consists of a succession ofsteady flow processes

Each process carried out in a separatecomponent designed for the purpose

Each component is an open system

All components are connected inseries and the working fluid passes


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through a cycle of mechanical andthermodynamic states

To simplify analysis change in kineticand potential energy of the fluid areassumed to be negligible

Operating cost related to overall

efficiency of plant

SourceFuel and Air Products ofCombustion

Sink

(atmosphere)

Q1

Q2

W


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Overall Efficiency = Cycle Efficiency xCombustion Efficiency

Cycle efficiency expresses theproportion of the heat available that isconverted into useful mechanical work

Efficiency of a vapour power cycle isknown as the Ideal Cycle Efficiency ()

when all the processes are assumedto be reversible.

Ratio of actual cycle efficiency to ideal

cycle efficiency is called the efficiency

ratio.

Ratio of the network output (|W|) to the

gross work output is defined as the

Work Ratio (rw)

A direct indication of the size of vapour

power plant is provided by the Specific

Steam Consumption (SSC) usually

expressed in kg/kWh

SSC is the mass flow of steam

required per unit power output


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It can be shown that

||

3600

WSSC =

Carnot Vapour Power Cycle


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An ideal cycle in which the heat is

taken in at a constant upper

temperature and rejected at a constantlower temperature suggested by Sadi

Carnot.

Consists of two reversible isothermal

processes connected by two isentropicprocesses.

Saturated water in state 1 is

evapourated in the boiler at constant

pressure to form saturated steam in

state 2.

Heat added to the boiler

1212 hhQ =

Steam is expanded isentropically to

state 3, while doing work in a turbine.

Turbine work

3223 hhW =


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After the expansion, steam is partially

condensed at constant pressure until

state 4 is reached.

Heat rejected in the condenser

4334 hhQ =

Finally, steam is subjected to

compression isentropically, in thecompressor to state 1.

Compressor work

4141 hhW =

Ideal Cycle Efficiency

( ) ( ) ( )[ ]( )12

4132

12

4123

12

||||||

hh

hhhh

Q

WW

Q

W

=

==

or

1

31

T

TT =

Work Ratio


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( ) ( ) ( )[ ]( )32

4132

23

4123

23

||||||

hh

hhhh

W

WW

W

Wrw

=

==

Specific Steam Consumption

( ) ( ) ( )[ ]41324123

3600

||||

3600

||

3600

hhhhWWWSSC

=

==

Drawbacks ofCarnot VapourPower Cycle

Possesses a low Work Ratio

Having to run a bulky compressor

with higher power consumption

Practical difficulties associated with

the compression

Difficult to control the condensation

process so that it stops at state 4.


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Compression of a very wet vapour

in the compressor. i.e. Liquid tends

to separate out from the vapourbecause of the non-homogeneous

nature of the mixture.

Hence Carnot cycle is not used inpractice.

Simple Rankine Cycle

Vapour is completely condensed in the

condenser and a small feed pump


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compresses the liquid to the boiler

pressure.

Efficiency of the cycle is less than that

of the Carnot cycle operating between

the same temperatures, since all the

heat supplied is not transferred at the

upper temperature High Work Ratio

Less Specific Steam Consumption

Smaller plant size

The processes of Rankine cycle are as

follows

Saturated water in state 5 is

evapourated in the boiler at constant

pressure to form saturated steam in

state 2.

Heat added to the boiler

5212 hhQ =


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Steam is expanded isentropically to

state 3, while doing work in a turbine.

Turbine work

3223 hhW =

After the expansion in the turbine,

steam is completely condensed at

constant pressure.

Heat rejected in the condenser

4334 hhQ =

Finally, liquid is compressed to boiler

pressure isentropically, in the feedpump.

Feed pump work

( )4545 ppvW f =

or

From steady flow energy equation

4545 hhW =



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( ) ( ) ( )[ ]( )52

4532

52

4523

52

||||||

hh

hhhh

Q

WW

Q

W

=

==

Work Ratio

( ) ( ) ( )[ ]( )32

4532

23

4523

23

||||||

hh

hhhh

W

WW

W

Wrw

=

==


( ) ( ) ( )[ ]45324523

3600

||||

3600

||

3600

hhhhWWWSSC

=

==

Rankine Cycle with superheat

It is possible to raise the steam

temperature without raising the boiler

pressure by sending the saturated

steam away from the boiler to a


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separate bank of tubes placed in the

combustion gases which is known as

the super-heater.

Average temperature at which heat is

supplied is increased by superheating

and hence the ideal cycle efficiency is

increased. Considerable reduction in SSC


( ) ( ) ( )[ ]( )25

1265

25

1256

25

||||||

hh

hhhh

Q

WW

Q

W

=

==

Work Ratio

( ) ( ) ( )[ ]( )65

1265

56

1256

56

||||||

hh

hhhh

W

WW

W

Wrw

=

==


( ) ( ) ( )[ ]12651256

3600

||||

3600

||

3600

hhhhWWWSSC

=

==


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Although superheating increases the

dryness fraction of steam at the turbine

outlet, with the present metallurgicallimit it is not always sufficient to

maintain the dryness fraction above

the specified value (88%)

Reheat Cycle

Expansion takes place in two turbines

Steam expands in the high pressure

turbine to some intermediate pressure

Sent through another bank of tubes in

the boiler where it is reheated at

constant pressure, generally to the

original superheat temperature


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Expands in the low pressure turbine to

the condenser pressure

Ideal Cycle Efficiency( )

6725

127856

6725

||||||||

QQ

WWW

QQ

W

+

+=

+

=

( ) ( ) ( )[ ]( ) ( )[ ]6725

128765

hhhh

hhhhhh

+

+=

Work Ratio

( )

7856

127856

7856

||||||||

WW

WWW

WW

Wrw

+

+=

+

=

( ) ( ) ( )[ ]

( ) ( )[ ]8765

128765

hhhh

hhhhhhrw

+

+=


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( )|||||| 3600||3600 127856 WWWWSSC

+

==

( ) ( ) ( )[ ]128765

3600

hhhhhhSSC

+

=

Regenerative Cycle

Raises the ideal cycle efficiency by

increasing the average temperature at

which heat is added from an external

source to the working fluid.


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Steam is expanded to an intermediate

state 3, at which a certain quantity is

bled off and taken to a feed waterheater.

Remaining quantity is expanded to

condenser pressure and leaves the

turbine in state 4. After condensationwater is compressed in the first feed

pump to the bleeding pressure.

It is mixed in the feed water heater

with the bled steam in state 3 and total

mixture leaves the heater in state 7.

A second feed pump compresses the

water to boiler pressure at state 1.

It can be shown that the cycle

efficiency is a maximum when the

temperature

2

423

TTT

+=


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Consider the feed water heater as an

adiabatic open system (Q=0) for

calculating the appropriate mass y kg to

be bled off. No work is done and the

energy equation reduces to( ) 637 110 hyyhh = Also h6=h5

53

57

hh

hhy

=

Ideal Cycle Efficiency( )

12

71563423

12

||||||||||

Q

WWWW

Q

W +==

( ) ( ) ( ) ( ) ( ) ( )[ ]( )12

71564332 11

hh

hhhhyhhyhhy

+=

Work Ratio( )

3423

71563423

3423

||||||||||

WW

WWWW

WW

Wrw

+

+=

+

=

( ) ( ) ( ) ( ) ( ) ( )[ ]( ) ( ) ( )4332

71564332

1

11

hhyhhy

hhhhyhhyhhyrw

+

+=



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( )||||||||3600

||

3600

71563423 WWWWWSSC

+

==

( ) ( ) ( ) ( ) ( ) ( )[ ]71564332 113600

hhhhyhhyhhySSC

+

=

Economiser and Air preheater

vapour power cycles

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