Thermal PowerOrigins of Steam Power

Papin (1690) First Steam-operated pistoni) water boiled in cylindrical chamber containing tight fitting pistonii) steam exerted force on piston, causing it to riseiii) piston retracted into chamber after walls cooled down(cycle time – many minutes)

Savery (1699)Rate of steam condensation increased by spraying cold water over outside of pistonchamber (cycle time ~ a minute)Newcomen (1712)Rate of steam condensation improved still further by injecting cold water directly intosteam chamber (cycle time 5-10 seconds) Watt (1775)Incorporated separate condenser, thereby removing need to reheat walls of piston chamber. Commercial steam engines of 20 kW power in use by 1800

Thermal Power Stations

Note: thermal includes fossil-fuel and nuclear powerHeat source is part of Steam CycleThermodynamics of cycle independent of nature of heat source

Steam Cycle: Main Components

WaterPump

Boiler

Heat in

Turbine (expander)

Electrical powerCondenser

Cooling waterHeat out

Properties of SteamTemperature K

Specific entropy kJ/kg/K

Critical pressure 221 bar

p=0.006 bar

Sub-criticaldry steam

Super-criticalfluid

Sub-criticalwater-steam

mixture(wet steam)

100% water0% steam

0% water100% steam

Ice-water vapour mixture

Entropy/temperature diagram is best for power station cycles

Any TWO thermodynamic parameters are sufficient to define state of fluideg S,T or P,H (Steam Tables)

Dryness fraction (quality) x = mvapour/(mvapour +mwater)

s = (1 x) swater + x svapour

T

s

Carnot Cycle (Ideal Cycle)1) Heat absorption at constant temperature, Ta (boiler) 122) Isentropic expansion work output (turbine) 233) Heat rejection at constant temperature, Tb (condenser) 344) Isentropic compression (pump) 41

1 2

4 3

T

Tb

Ta

Q12

Q34

W23W41

S

Energy Conservation (1st Law of Thermodynamics) Q12 + W23+ Q34+ W41= 0

(Note: Q12 > 0, W23 < 0, Q34 < 0, W41 > 0)

Cycle efficiency, c (Useful work out)/(Heat input at Ta)ie c (| W23| W41)/ Q12| (Ta Tb)/ Ta 1 Tb/ Ta

(Note: T measured in K (absolute temperature) – formaldefinition of absolute temperature scale)

Practical difficulties in using a Carnot Cycle

1) Boiler operates only in wet-steam regime otherwise temperature would rise when all the water has turned to steam, violating condition for Carnot Cycle turbine expands wet steam water droplets hit turbine blades (damage)

2) Maximum temperature (Ta) is limited to ~650 K efficiency of cycle is severely constrained

3) Compression of water/steam mixture is thermodynamically unstable (water droplets) very large volume compressor (expensive)

Rankine Cycle overcomes all these problems

Rankine Cycle

Step 1:a) Condense all the steam to waterin the condenserb) Pumping water to high pressure requiressmall volume machine and little energy

T

Tb

S

2a

1b1a

2b2c

Step 2: Use 3-stage boiler (~ constant pressure)a) Economiser – water heated at constant pressureb) Evaporator – water/steam mixture heated at constant pressurec) Superheater – dry steam heated at constant pressure

[Note that there is a small drop in pressure through the boiler tube in order to overcome frictional losses]

Ta

Tb

T

S

Step 3:Expand dry steam through a turbineto generate shaft power

In practice, water droplets still form in the low pressure end of the turbine, so the steam is reheated at various stages

Ta

Tb

T

S

reheaters

from boiler

to condenser

HP: high pressure turbineIP: intermediate pressure turbineLP: low pressure turbine

HP IP LP

Frictional losses across turbine blades vary like u2 (FD=½CDAu2)ie very large for large u (near speed of sound)

Losses reduced significantly by using many stages in series (~50 stages)

The loss of kinetic energy at each stage is small and turbulence is reduced

Other practical effects limiting efficiency

a) Boiler tubes have finite thickness, so outer wall temperature is higher than water/steam temperatureb) Metallurgical limit to temperature/pressure difference boiler tubes can withstand (creep/crack formation)c) Many pipes/tubes in flow circuit frictional losses

d) Condenser is a vacuum chamber air leaks in but can not condense, so ‘air blanket’ forms, preventing water vapour from condensing on cold surface of condenser tubes

3

4

T

S

1

2

Q23

W34

Q41

W12

Efficiency of Rankine Cycle

Condenser at 30 C at a pressure of 0.04 barCompressor increases pressure to 170 barThree-stage boiler at 170 bar a) economiser raises temperature to 352 C b) evaporator at 352 C c) superheater raises temperature to 600 CAdiabatic turbine

T p hf hg sf sg

Water/Steam 30 0.04 126 2566 0.436 8.452Water/Steam 352 170 1690 2548 3.808 5.181Dry Steam 600 170 3564 6.603

where hf and hg are the specific enthalpies and sf and sg are thespecific entropies of the fluid and gas, respectively, in kJ/kg.

Specific enthalpy h u +pvisobaric, constant pressure, dh du + pdv dQdh Tds + vdp so isentropic dh vdp or h W

i) W12 V(p2 p1) = 10(170 0.04) 1017 kJ/kg 3

4

T

S1

2

Q23

W34

Q41

W12

ii) 12 isentropic so h2h1 + W12 126 + 17 143 kJ/kg

iii) 23 isobaric so Q23 h3 – h2 3564 143 = 3421 kJ/kg

iv) 34 isentropic so W34 h3 – h4 and s3 s4

s4 (1x)sf4 + xsg4

6.603 (1x)0.436 + 8.452 x x 0.769

3

4

T

S1

2

Q23

W34

Q41

W12

v) h4 (1x)hf4 + xhg4

h4 (1x)126 + 2566 x x 0.769 h4 2002 kJ/kg

34 isentropic so W34 h3 – h4

3564 – 2002 1562 kJ/kg

vi) useful work/heat in (W14 – W12)/Q23 (1562 – 17)/3421 0.452 45.2%

vii) cf Carnot Cycle c(T3 T4)/T3 (873 303)/873 0.653 65.3%

Combined Cycle Gas Turbine (CCGT) Stations

In recent years gas turbines and steam turbines have been combined toincrease the efficiency to around 50-60% (upper temperature ~1200 C)

Gas Turbine

CombustionChamber

Gaseousfuel

air

compressedair

Compressor Turbine

Exhaust gas

a) Heat generated by internal combustion rather than via a high temperature heat exchanger (boiler)

b) No cooler required since exhaust gases vented to atmospherePlant much smaller. Work done by compressor issignificant, though this is compensated by very hightemperature ~ 1200 C (Turbine blades ceramic coatedand water cooled)

Tp

patmosTmax

S

Brayton CycleCompressor

Combustion

Turbine

CCGT Station

Heat out

CombustionChamberGaseous

fuel

air

compressedair

Compressor Turbine

Exhaust gasWaterPump

Boiler

Heat in

Turbine

Condenser

Cooling water

Exhaust gas

T

S

Rankine Cycle

BraytonCycle

Heat of exhaust gases used to helpraise steam for steam turbine

Many CCGTs have been built in the UK in the 90s due to availability ofcheap gas and relaxation of governmental controls

CCGT Station

660 MW Power Plant

Stator for a 660 MWgenerator being assembled

Low pressure turbine, part of a 660 MW assembly