1

Vapor Power Cycles

Reading: Cengel & Boles, Chapter 9

2

Vapor Power Cycles

• Produce over 90% of the world’s electricity

• Four primary components– boiler: heat addition– turbine: power output– condenser: heat rejection– pump: increasing fluid pressure

• Heat sources– combustion of hydrocarbon fuel

• e.g., coal, natural gas, oil, biomass

– nuclear fission or fusion– solar energy– geothermal energy– ocean thermal energy

3

Carnot Vapor Power Cycle

• Consists of four reversible processes inside the vapor dome (see Figure 9-1 in text) and yields maximum

• Carnot vapor power cycle is not a practical model since – isothermal heat addition can only occur

at temperatures less than Tcr

– pumps or compressors cannot handle two-phase mixtures efficiently

– turbines suffer severe blade erosion from liquid droplets in two-phase mixtures

th

4

The Rankine Cycle

• The Rankine cycle serves as a more practical ideal model for vapor power plants:– pumping process is moved to the

compressed liquid phase

– boiler superheats the vapor to prevent excessive moisture in the turbine expansion process

• Steam (H2O) is, by far, the most common working fluid; however, low boiling point fluids such as ammonia and R-134a can be used with low temperature heat sources.

5

Analysis of Rankine Power Cycles

• Typical assumptions:– steady-state conditions

– negligible KE and PE effects

– negligible P across boiler & condenser

– turbine, pump, and piping are adiabatic

– if cycle is considered ideal, then turbine and pump are isentropic

• Energy balance for each device has the following general form:

ie

ie

hhwq

hhmWQ

or

)(

6

Analysis of Rankine Power Cycles, cont.• Pump (q = 0)

• Boiler (w = 0)

• Turbine (q = 0)

)( where

or )(

4343

43,43,

sT

outturboutturb

hhhh

hhwhhmW

P

Ps

inpumpinpump

PPv

hhhh

hhwhhmW

/)(

/)( where

or )(

121

1212

12,12,

2323 or )( hhqhhmQ inin

7

Analysis of Rankine Power Cycles, cont.

• Condenser (w = 0)

• Thermal Efficiency

• Back Work Ratio (rbw)

inpumpoutturbnet

in

out

in

netth

www

q

q

q

w

,, where

1

43

12

,

,

hh

hh

w

wr

outturb

inpumpbw

1414 or )( hhqhhmQ outout

8

Increasing Rankine Cycle Efficiency• It can be shown that

• To increase cycle efficiency, want:– high average boiler temperature, which

implies high pressure

– low condenser temperature, which implies low pressure

• This holds true for actual vapor power cycles as well

in

out

boiler

condenseridealth T

T

T

T 1 1 ,

9

Increasing Rankine Cycle Efficiency, cont.• Methods used in all vapor power

plants to increase efficiency:

1) Use low condenser pressure– decreases Tout

– limitation: Tout > Tambient

– Pcond < Patm requires leak-proof system

– increases moisture content in turbine

2) Use high boiler pressure– increases Tin

– limitation: approx. 30 MPa

– increases moisture content in turbine

10

Increasing Rankine Cycle Efficiency, cont.

3) Superheat vapor in boiler to high temperature– increases Tin

– limitation: approx. 620°C

– decreases moisture content in turbine

4) Use multistage turbine with reheat– allows use of high boiler pressures

without excessive moisture in turbine

– limitation: adds cost, but 2-3 stages are usually cost-effective

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Increasing Rankine Cycle Efficiency, cont.

5) Preheat liquid entering boiler using feedwater heaters (FWHs)– bleed 10-20% of steam from turbine

and use to preheat boiler feedwater

– limitation: adds cost, but as many as 6-8 units are often cost-effective

– open feedwater heaters: steam directly heats feedwater in a mixing chamber; can also be used to deaerate the water

– closed feedwater heaters: steam indirectly heats feedwater in a heat exchanger; condensed steam is routed to condenser or a lower pressure FWH