Rankine Steam Cycles

8/11/2019 Rankine Steam Cycles

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IIA Paper 3A5 Energy & Power Generation/HPH/CAH

3-1

3

Steam Cycles

3.1Introduction

Cyclic steam-based power plants are the World's biggest man-made power source1.

The steam turbine was introduced by Sir Charles Parsons in the 1880s.

All steam cycles are based on the Rankine cycle which is a true thermodynamic cycle.

Steam power plants use heat to generate 50 to 2000 MW of electricity from

combustion of fossil fuels (oil, coal, gas)

the exhaust of combined cycles

nuclear reactions

1The Gas Turbine is the World's second biggest power source.


3-2

3.2

Basic Steam Plant and the Rankine Cycle

The simplest form of steam plant comprises the following four components

A feed pump to compress liquid water.

A constant pressure boiler and superheater.

An adiabatic turbine.

A constant pressure condenser.

3

s

T

4s 4

2

1

3

s

h

4s 4

2

1


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3-3

4

3

2

1

Qinfrom combustion gas

WP

WT

feed

pump

steam

turbine

steam generator

condenser

Qoutto cooling water

.

. .

.

Working per unit mass of steam circulating, the feed pump work input is given by combining

the SFEE with Tds= dhdp/ and assuming that the water is incompressible:

P

s

PP

sP

ppdphh

hhw12

2

1

1212

1)(

=

==

where Pis the isentropic efficiency of the feed pump and is the density of water

The final expression above is more accurate and much more convenient to use than interpolating

for liquid enthalpies in the steam tables.


3-4

The heat input is given by

23 hhqin =

In large UK power stations built after about 1960,

the boiler pressure became standardised at 150-165 bar (cf. critical pressure of ~220 bar)

the maximum steam temperature at 540-560 C

and both

are limited by metallurgical considerations (in particular, high-temperature creep).

The turbine work output is given by

)( 4343 sTT hhhhw ==

where Tis the isentropic (not polytropic) efficiency of the whole turbine.


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3-5

The heat rejected in the condenser is given by

14 hhqout =

The pressure in the condenser is set by the cooling water temperature and is usually in the range

40-80 mbar corresponding to saturation temperatures of 29-42 C.

The cycle efficiency is therefore given by

)(

)(

)(

)(

)(

)()(

23

43

23

43

23

1243

hh

hh

hh

hh

hh

hhhh

q

ww sT

in

PTc

=

=

=

The feed pump work ( )12 hhwp = can be neglected in the final expression because

wT>> wP


3-6

3.2.1 Additional Notes on the cycle

1.The work input needed to compress the liquid is very much less than that needed to compress

a gas. The effects of irreversibilities (due to design, wear & tear) in the feed pump are far less

than in the compressors of gas turbines. The fact that wT>> wPis one of the great advantages

of steam plant.

2.Very high pressure is needed to achieve a high temperature of heat input. This high pressure

is applied to literally 'miles' of tubing in the boiler and as a result the tubes are highly stressed.

The tubes are also in a very corrosive environment (flue gases) and so they cannot stand too

high a temperature before suffering from creep, corrosion and eventual failure.

3.

The low temperature of heat rejection (almost ambient) increases the efficiency. The cooling

water (which passes through tubes in the condenser) is either drawn from the sea or a river, or

circulates in a separate loop via a cooling tower. There is strict legislation controlling the

temperature at which the cooling water is returned in order to prevent environmental damage.

4.The maximum temperature achieved in steam cycles is about 600C, well below the

temperature in gas turbines. Even so, efficiencies are over 40% - better than most gas turbine

or IC engines. This is mainly due to the low condenser temperature.


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3-7

The HP and LP cylinders of a small steam

turbine

5.

The pressure ratio across the turbine is so

huge (150/0.04 = 3750) that many turbine

stages are required.

6.The HP (high pressure), IP (intermediate

pressure) and LP (low pressure) turbines aremounted on just one shaft with the electrical

generator at the end. The isentropic

efficiency of the HP and IP turbines are

nowadays very high (90-92%) but the LP

turbine efficiency is lower (85%). This is

mainly because the LP turbine operates with

wet steam typically every 1% of wetness

gives a 1% loss in isentropic efficiency. In

addition, the LP turbine blades are very long

giving greater aerodynamic losses.


3-8

Low Pressure Rotor from a large steam turbine

(approx 150 MW per cylinder)

7.The density falls so much through

the turbines that the volume flow

rate cannot be accommodated in one

cylinder. Therefore, the turbine

might be divided into one single-flow HP cylinder with 15-20 stages,

one double-flow IP cylinder with

about 12 stages and two, three or

four double-flow LP cylinders each

with 5 or 6 stages.

8.

The exit of the LP turbine has to be

very large to accommodate the flow.

Typically the last blades of a large

turbine are about 4m diameter.


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3-9

9.The steam leaving the LP turbine is usually in

the two-phase region with a dryness fraction of

about 90 %. The water is mostly in the form of a

fog of minute droplets with diameter of order 1

micron. However, larger droplets, like raindrops,

are formed when the small drops deposit on the

blades and coalesce. The large droplets causeerosion on the rotating blades of the last stage.

Blade erosion after 2.5 years


3-10

3.3

General principles for increasing cycle efficiency

Qout

Qin

2

1

S

T

Consider the reversible cycle shown above. Heat transfer to the cycle is considered positive so

Qoutis a negative quantity. From 1 2, the cycle is receiving heat so,

=2

1

dQQin , =2

1

12T

dQSS .


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3-11

Themean temperature of heat receptionis defined by,

=

=

2

1

2

1

12 )(

T

dQ

dQ

SS

QT inin .

From 2 1, the cycle is rejecting heat so,

=1

2

dQQout , =1

2

21T

dQSS .

Themean temperature of heat rejectionis defined by,

=

=

1

2

1

2

21 )(

T

dQ

dQ

SS

QT out

out .


3-12

The cycle efficiency is given by,

in

out

in

outc

T

T

Q

Q=+= 11 (5)

which is the same as a Carnot cycle operating between inT and outT .

Equation (5) only holds for reversible cycles. However, for real cycles, it is still desirable to

make inT as high as possible and outT as low as possible.

There are, therefore, three principal ways in which the thermodynamic performance of power

plant can be improved :

By reducing lost work (and therefore irreversibilities).

By increasing inT .

By reducing outT .


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3-13

Note that in the basic Rankine cycle

the mean temperature of heat reception is well below T3. The efficiency is therefore much

less than a Carnot cycle operating with a uniform top temperature of T3.

the mean temperature of heat rejection (T1= T4) is constant and is very close to the ambient

temperature, so it is hard to reduce outT .

In order to improve the cycle efficiency, we must increase the mean temperature of heat

reception for a given T3. This can be achieved by

1.increasing the boiler pressure,

2.reheating the steam, or

3.using feed water heating.


3-14

3.4

Effect of Boiler Pressure

Increasing p

3 2 1

3 2 1Tmax

s

T

T-sdiagram showing the effect of increasing the boiler pressure while maintaining the

maximum steam temperature constant.


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3-15

Cycle 2 has

a higher boiler pressure than Cycle 1

has a higher mean temperature of heat reception

has unchanged temperature of heat rejection

increased cycle efficiency.

Cycle 3,

has a boiler pressure greater than the critical pressure of 220 bar

is said to be supercritical

requires a once-through steam generator of different design as boiling no longer occurs

not worth the effort without also increasing the maximum temperature.

Over the last ten years improved materials have allowed the development of supercritical cycles

(particularly by Japanese companies) and several are now operational. Typical pressures and top

temperatures are 275-350 bar and 580-600 C.


3-16

3.5

Steam Reheat

Increasing the boiler pressure

increases the mean temperature of heat reception and therefore efficiency but

tends to result in an increased turbine exhaust wetness fraction resulting in lower turbineefficiency and more erosion problems.

Reheatin a steam cycle

involves returning the steam, after it has passed through the HP turbine, to the superheatingsection of the steam generator. The steam is then routed to the IP and LP turbines.

reduces the wetness fraction at turbine exhaust improving the LP turbine efficiency

increases the specific work output (recall that cyclewTds= )

can increase the mean temperature of heat reception and therefore efficiency


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3-17

3

2

1

Qinfrom combustion gas

WP

WT,HP

feed

pump

HP steam

turbine

steam generator

condenser

Qoutto cooling water

.

. .

.

4

WT,LP.

6

5

from combustion gas

reheater

QR.

LP steam

turbine

Single reheat steam cycle


3-18

4

2

1 6

3 5

s

T

T-sdiagram for a cycle with single reheat.

In a supercritical plant, a second reheat after the IP cylinder is usually necessary to limit the LP

turbine exhaust wetness2

2Double reheat has occasionally been used on conventional plant but this is not usual.


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3-19

Reheating increases the specific work output as is evident by the increased area enclosed by

cycle on the T-sdiagram.

The effect on the cycle efficiency depends on the reheat pressure p45

High reheat pressure gives a high inT for the reheater but only a small extra heat input, Qin

= h5 h4, leading to a small increase in cycle efficiency. Low reheat pressure means that inT for the reheater is much the same as for the main cycle

so there is no significant improvement in cycle efficiency.

Between these extremes, the optimum reheat pressure for maximum cycle efficiency is usually

about 1/4 of the main boiler pressure. This optimum can only be found by numerical calculation.

The reheat pressure on most UK stations is about 40 bar.

The improvement in cycle efficiency from a single reheat is only 2-3 percentage points.

Although this is not dramatic, it is a useful gain which can be obtained without major

modification to the plant. More importantly, it ensures a longer life for the LP turbine blades.


3-20

h-sdiagram showing HP, IP and LP

exapansion lines with reheat at 40 bar

between HP and IP cylinders


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3-21

3.6

Feedheating

Thefeed wateris the water feeding the evaporator tubes in the boiler.

In a conventional cycle, the economiser(actually just a water heater)

raises the temperature of the high pressure water delivered by the feed pump to the boiler

saturation temperature.

For a boiler pressure of 150 bar,

the saturation temperature is 342 C,

so

the mean temperature of heat addition in the economiser is very low (around 200 C)

the cycle efficiency would increase if this mean temperature could be increased using

feedheating.


3-22

3.6.1 Direct Contact Feed Heating

DC FeedHeater

Turbine

WP1

feed

pump 1

WT

Qout.

.

.

feed

pump 2

Boiler

Conden

serb

2a

f

2b

34

1

Qin.

water (state )wet saturated

f

steam(state b

m)

water (state 2 )

1-m

a

Steam plant with a single stage of direct-contact feedheating


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3-23

b

(m)

(1m)

(1)

2b

f

2a

3

s

T

41

T-sdiagram for a steam plant with a single stage of direct contact feedheating


3-24

In the above plant

A small steam flow rate is extracted from the turbine at state band is mixed directly withthe feed water at state 2aat approximately constant pressure.

The extracted steam flow rate fraction mis such that the final state of the mixed flows issaturated liquid water with temperature Tfat the steam extraction pressure.

The feed water temperature is therefore raised from T2ato Tfwithout external heat input.

The mixing process is inherently irreversible (ab

TT2

> ), but the net effect is an

improvement in cycle efficiency.

Note that, for single or multiple feedheaters

An extra pump is needed for each feedheater to raise the water pressure to the steam

extraction pressurepf(so that the pressures are matched for mixing). The last pump brings

the mixture up to boiler pressure.

After the last pump, a reduced heat input in the economiser (at a higher mean temperature)

brings the feed water temperature from T2bto the saturation temperature for evaporation.


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3-25

For unit mass flow rate through the boiler, if the mass flow rate of steam extracted from the

turbine is mthe mass flow rate through the condenser is (1m). Writing the SFEE for the mixingprocess in the feedheater

baf mhhmh += 2)1(.1

Hence, the mass fraction of steam extracted is

1

1

2

2hhhh

hhhhm

b

f

ab

af

=

The heat input is now

fbin hhhhq = 323 )(

and the net work output is

)()()1())(1()( 21243 fbabbnet hhhhmhhmhhw +=

Tw Pw


3-26

Neglecting the feed pump work, the cycle efficiency is therefore given by

)()(

)()(

)(

))(1()(

113

443

3

43

hhhh

hhmhh

hh

hhmhh

f

b

f

bbc

=

+

Note that

although the work output has been reduced by m(hbh4),

the heat input has been reduced by the larger quantity (hfh1).

the cycle efficiency has therefore been increased.

Also

the temperature of the bled steam (Tb ) is much greater than the temperature of the waterentering the feedheater (T2a).

the mixing process in the feedheater is therefore irreversible and results in an unwanted

exergy loss.


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3-27

3.6.2 Indirect contact feedheating

Indirect contact feedheaters are simple heat exchangers.

The condensate from one heater is usually throttled down to the pressure of the adjacent one and

the condensate from the last is fed into the condenser.

The throttling results in a small loss but the advantage is that only one feed pump is required.

They are rarely used

water water

bled steam

water

Pump

Boiler

Turbine

Condenser


3-28

3.6.3 Maximum benefit of feedheating

Conceptually, the feed water temperature could be raised to Tf

by a fully reversible process

using an infinite number of feedheaters as indicated in the T-sdiagram below

f

3

s

T

41


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3-29

Note that the pointfhas been conveniently chosen so that the horizontal constant pressure line

passing through it intersects the turbine expansion line in the wet region.3We also postulate that

the turbine expansion 3-4 is isentropic.

The conceptual practicalities of how reversibility can be maintained in the feedheating system

can be ignored if we lump the turbine, condenser and feedheating train into a single control

volume.

The problem then simplifies to one of finding the maximum work obtainable from the control

volume when steam enters at a given state 3 and water leaves at a given statef.

3The theory also applies if steam is bled from the turbine in the superheated region. However, the analysis

becomes a little tedious as it involves (in principle) an infinite train of compressors and coolers to bring thestate of the bled steam to the saturated state isothermally and reversibly.


3-30

Wmax

f 3

Qout

Qin

Steam Generator

Reversible

Turbine

Condenser

Feed Heaters

Feed Pumps

This maximum work is given by the decrease in steady-flow exergy (or availability function)

from state 3 to statef. Hence, for unit mass circulating through the steam generator

)()()( 13133max fff sThsTheew ==

where it has been assumed that the environment is at condenser temperature T1(so that there isno exergy loss associated with the external heat transfer Qout). Noting the direction of the arrow

for qout, the SFEE is

)( 3max fout hhqw =+


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3-31

Hence

)( 31 fout ssTq =

Another expression for qoutcan be obtained by noting that, if the total mass flow rate of steam

extracted for feedheating is m, then the mass flow rate through the condenser is (1m). Hence

)()1()()1())(1( 13114114 ssTmssTmhhmqout ===

Equating the two expressions for qoutgives

13

31

ss

ssm

f

=

Finally, the efficiency of a fully reversible cycle with feedheating is given by

)(

)(1

)(

)()(

3

31

3

313

f

f

f

ffchh

ssT

hh

ssThh

=

=


3-32

Example

boiler pressure = 100 bar

condenser pressure = 0.05 bar (T1= 32.9 C)

turbine inlet temperature = 550 C

feedwater is heated to 240 C.

The maximum possible cycle efficiency is then

496.0)8.10410.3500(

)710.2756.6(0.3061

)(

)(1

3

31=

=

=

f

fc

hh

ssT

This should be contrasted with the maximum cycle efficiency without feedheating

428.0)8.1370.3500(

)476.0756.6(0.3061

)(

)(1

13

131 =

=

=

hh

ssTc

which is almost 7 percentage points lower.


17/26


3-33

In practice

6-9 feedheaters are usually installed on a large steam power plant

The cycle efficiency increases by about 4 percentage points.

The optimum distribution is when the overall temperature rise is shared equally between

the feedheaters.

However, it is only practical to extract steam from the turbine in the inter-stage gapfollowing a rotating blade row. This constrains the possible bleed pressures, which in turn

fixes the feedheater outlet saturation temperatures.


3-34

3.7

Worked Example

A conventional steam cycle has a boiler pressure of 60 bar and a condenser pressure of 0.04 bar.

There is no reheater and the turbine entry temperature is 450 C. The turbine isentropicefficiency is 0.85 and the feed pump work may be neglected. Calculate the specific work output

and the cycle efficiency

(i) Without feedheating

(ii) If there is a single stage of feedheating using steam bled from the turbine at a pressure

of 5 bar to heat the feedwater to the saturation temperature.

Assume that the expansion line of the turbine is straight on the Mollier (h-s) diagram.

Without Feedheating

From the tables h3 = 3303.0 kJ/kg, s3 = 6.723 kJ/kgK

From the chart h5s = 2025.0 kJ/kg

Turbine work 3.1086)0.20250.3303(85.0)( 53 === stt hhw kJ/kg

Hence h5 = 3303.0 1086.3 = 2216.7 kJ/kg

From the tables h1 = 121.4 kJ/kg

Heat input ( ) ( )1323 hhhhqin = = 3303.0 121.4 = 3181.6 kJ/kg


18/26


19/26


3-37

From the steam chart, h4 = 2825.0 kJ/kg

SFEE for the feedheater, 214 )1( hhmhm =+

4.1210.2825

4.1211.640

14

12

=

=

hh

hhm = 0.192

Turbine work tw = (h3h4) + (1m) (h4h5)

tw = (3303.0 2825.0) + 0.808 (2825.0 2216.7) = 969.5 kJ/kg

Heat input ( )23 hhqin = 3303.0 640.1 = 2662.9 kJ/kg

Cycle efficiency9.2662

5.969=

=

in

t

in

ptc

q

w

q

ww = 0.364


3-38

3.8

The Combustion Process, the Boiler and Overall Efficiency

The efficiency of the steam cycle is not the same as the overall efficiency of the steam plant.

3.8.1 The Combustion Process

To find the overall efficiency of the steam plant, we consider the efficiency with which the heat

released by the combustion process is transferred to the steam.

The best possible situation is shown in the diagram below where the

fuel and stoichiometric air enter at the standard state temperature of T0= 25 C

products of combustion leave the stack having been cooled down within the plant to 25 C.

Heat input to steam cycle = ][ 0Hmf

Products

(ma + mf at 25 C)Fuel (mfat 25 C)

Air (maat 25 C)

Combustion


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3-39

Under these conditions, the heat transferred from the combustion to the steam per unit mass of

fuel is the lower calorific value (LCV = H0). The SFEE therefore takes the form

0000 )(][ pfaaafffin hmmhmhmHmQ ++==&

where subscript 0 implies evaluation at 25 C.

In practice, some 10% excess air is always used to ensure complete combustion. This does not

affect the SFEE at all because the extra air both enters and leaves the plant at 25 C.

In reality, the situation is as shown below, the products and excess air leaving the chimney stack

at a temperature TX(for exhaust) rather higher than 25 C.

Heat input to steam cycle = Qin

Products

(ma + mf at TX)Fuel (mfat 25 C)

Air (maat 25 C)

Combustion

.


3-40

For the same fuel and air mass flow rates, a smaller quantity of inQ& is transferred to the steam.

This is given by the SFEE which is now written

pXfaaaffin hmmhmhmQ )(00 ++=&

which can also be written as

( ){ }000000

)(][

)(

pfaaafff

pXfaaaffin

hmmhmhmHm

hmmhmhmQ

+++

++=&

00 )(][ ppXfafin hhmmHmQ +=&

3.8.2

The Boiler Efficiency

The boiler efficiency is defined by

][

)(][

][ 0

00

0 Hm

hhmmHm

Hm

Q

f

ppXfaf

f

inboiler

+=

=

&

][

)()1(1

][

])[1(1

0

0

0

0

H

TTcA

H

hhA XppppXboiler

+

+=

whereAis the air/fuel ratio and cppis the specific heat capacity of the products.


21/26


3-41

3.8.3 The Overall Efficiency

We can now consider the complete plant (combustion circuit and steam cycle) as an open circuit

power plant as shown below

WnetHeat from

condenser

Products

(ma + mf at TX)

Fuel (mfat 25 C)

Air (maat 25 C)

Combustion

circuit

andsteam cycle

The plant overall efficiency is therefore given by

boilercycle

f

in

in

net

f

netov

Hm

Q

Q

W

Hm

W =

=

=

][][ 00

The important quantity is therefore the product of the steam cycle and boiler efficiencies.


3-42

To maximise ov

maximise boiler

keep the stack temperature as low as possible

but

problems arise at low temperatures

water vapour in the flue gas condenses in the stack causing corrosion

condensation particularly serious for fuels containing sulphur (sulphuric acid forms)

therefore

stack temperature > dew point temperature

80C for sulphur-free fuels

135C fuels with sulphur (the dew-point of H2SO4is around 130 C)

typical boiler efficiencies are around 95%.


22/26


3-43

Another problem

with feedheating, the flue gas leaving the boiler must be hotter than the feed water at inlet

to the boiler

boiler feed temperature is typically 200-250 C, which requires a high stack temperature

leading to poor boiler efficiency.

The solution

use heat exchanger to cool the exhaust gas by preheating the inlet air and gives anacceptably low stack temperature.

Fuel

ProductsAir

Qin to steam

To stackAir in

Combustion

Air

Preheater


3-44

Conventional coal fired steam boiler


23/26


3-45

3.9

Effect of Cycle Parameters on Efficiency

To increase the cycle efficiency, we can

raise the average temperature at which we at heat

lower the temperature at which we reject heat

Year Boiler

Pressure

(atm)

Condenser

Pressure

(atm)

Max cycle

temperature

(deg. C)

Efficiency1

T

Tmin

max

Power

(MW)

1884 6.4 1 161 4% 14% 0.0075

1895 6.5 0.07 162 8% 28% 0.075

1905 14.6 0.07 197 20 % 33% 5

1938 41 0.05 454 28 % 58% 30

1958 100 0.05 538 36 % 62% 120

1973 157 0.04 565 40 % 64% 660

1995 157 0.04 565 41 % 64% 1200

2000 275 0.04 580 45% 65% 2000


3-46

The most important technical innovations have involved

Increasing the steam pressure and temperature.

The use of feed water heating.

The use of steam reheating.

Improving steam turbine isentropic efficiency (particularly of LP turbines).

Special cycles for use with nuclear power plant.

Special bottoming cycles for use in combined power plant.

The recent introduction of supercritical steam cycles.


24/26


3-47

30

35

40

45

50

55

60

1960 1970 1980 1990 2000 2010 2020

PowerStatio

nEfficiency(%)

Subcritical

Supercritical

Target

Thermie

Avedore 2

Nordjyllandsvaerket

Fynsvaerket

Ratcliffe

Ferry Bridge

Castle Peak

Drax

Meri Pori

Hemweg

Efficiencies of large coal-fired subcritical and supercritical steam plant.

Japanese companies and Europe (Thermie) are developing supercritical steam plant

boiler exit conditions of 350 bar, 700C and a target plant efficiency of 55%.

they will still be unable to compete in terms of efficiency with the latest combined-cycles

are only likely to find favour when coal is the fuel of choice.


3-48

3.10

Exergy Analysis of a typical coal-fired steam power plant

HP, IP and LP Steam Turbines

(single shaft)

Feedheating Train

Air Preheater

Condenser

Economiser

Reheater

Evaporator

Superheater

Electrical

generator

A typical large coal-fired steam plant - single reheat and 7 feedheaters.


25/26


3-49

Steam-based, multiple feed heated, single stage reheat cycles are

coal-fired or oil-fired

used to generate almost all of Worlds electricity until the mid-1980s

still being built in significant numbers where coal reserves are large & natural gas not

available (needed for combined cycles)

often grouped as four 500 MW, or three 660 MW sets to give ~2000 MW electrical output.

Cycle conditions typically

165 bar and 565C at turbine inlet

steam reheated after the HP turbine at about 40 bar to 565C

7 or 8 feedheaters used to increase the cycle efficiency by 4-5 percentage points.

%6.44=

cycle

%4.42== cycleboileroverall


3-50

T-s diagram for the steam cycle and combustion circuit.


26/26


3-51

Exergy analysis for the steam plant. All values are lost work except for Net Work

Output. Net work plus lost work sum to 100%.


Exergy analysis shows major losses result from

irreversible combustion reaction (as always when fuel is burned)

heat transfer to the steam across large temperature differences (see T-s diagram)

- with only 10% excess air, the combustion temperature approaches 2000 C

Note also

Small loss associated with the steam turbine

Very low exhaust loss (due to use of air preheater)

Heat transferred from the condenser to the cooling water is enormous (high energy flowrate) but the associated exergy loss is almost negligible (low temperature difference).

Rankine Steam Cycles

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