8/13/2019 ch08 - Copy

1/12

Introducing Vapor Power Plants

In fossil-fueled plants, the energy required for

vaporization originates in combustion of the fuel.

8/13/2019 ch08 - Copy

2/12

Power Cycle Review

in

cycle

Q

W

The first law of thermodynamicsrequires the net work developedby a

system undergoing a power cycle to

equalthe net energy added by heat

transferto the system:

The thermal efficiencyof a power

cycle is

Wcycle= QinQout

8/13/2019 ch08 - Copy

3/12

Power Cycle Review

The second law of thermodynamics requires the thermal

efficiency to be less than 100%. Most of todays vapor power

plants have thermal efficiencies ranging up to about 40%.

Thermal efficiencytends to increase as the average

temperature at which energy is added by heat transfer

increasesand/or the average temperature at which energy is

rejected by heat transfer decreases.

Improved thermodynamic performanceof power cycles, as

measured by increased thermal efficiency, for example, also

accompanies the reduction of irreversibilities and losses.

The extent of improved power cycle performance is limited,

however, by constraints imposed by thermodynamicsand

economics.

8/13/2019 ch08 - Copy

4/12

The Rankine CycleEach unit of mass of water circulating through the

interconnected components of Subsystem B ofFig. 8.1(a)undergoes a thermodynamic cycle known as the Rankine cycle.

All energy transfersby work and heat are taken as positive in

the directions of the arrowson the schematic and energy

balances are written accordingly.

There are four principal

control volumes involving

these components:

Turbine

Condenser

Pump

Boiler

http://www.wiley.com/college/moran/0470495901/ig/Ch8/pages/fig_08_03.htm

8/13/2019 ch08 - Copy

5/12

Turbine

Condenser

Pump

Boiler

The Rankine Cycle

34

p

hhm

W

21t hhm

W

41in hhm

Q

(Eq. 8.3)

(Eq. 8.4)

(Eq. 8.2)

(Eq. 8.1)

32out hhm

Q

Applying mass and energy rate balances

8/13/2019 ch08 - Copy

6/12

Thermal Efficiency

The Rankine Cycle

)(

)(

/

/bwr

21

34

t

p

hh

hh

mW

mW

(Eq. 8.6)

(Eq. 8.5a)

Performance parameters

)(

)()(

/

//

41

3421

in

pt

in

cycle

hh

hhhh

mQ

mWmW

Q

W

Back Work Ratio

Back work ratio is characteristically low for vapor

power plants. For instance, in Example 8.1, the

power required by the pump is less than 1% of the

power developed by the turbine.

8/13/2019 ch08 - Copy

7/12

Ideal Rankine Cycle

Since the ideal Rankine cycle involvesinternally reversible processes, results from

Sec. 6.13apply.

Applying Eq. 6.51c, the pump work input perunit of mass flowing is evaluated as follows

)( 343

s

ppp

m

W

v

(Eq. 8.7b)

wherev3is the specific volume at the pump

inletand the subscript ssignals the isentropic

processof the liquid flowing through the pump.

8/13/2019 ch08 - Copy

8/12

8/13/2019 ch08 - Copy

9/12

)()(

/

)/(

s21

21

st

t

t hh

hh

mW

mW

Principal Irreversibilities

Isentropic turbine efficiency, introduced in Sec. 6.12.1,

accounts for the effects of irreversibilities within the turbinein

terms of actual and isentropic turbine work, each per unit of

mass flowing through the turbine.

(Eq. 8.9)

work developed in the actual

expansion from turbine inlet state

to the turbine exit pressure

work developed in an isentropic

expansion from turbine inlet

state to exit pressure

8/13/2019 ch08 - Copy

10/12

)()(

/

)/(

34

3s4

p

sp

phh

hh

mW

mW

Principal Irreversibilities

While pumpwork input is much less than turbine work

output, irreversibilities in the pump affect net power outputofthe vapor plant.

Isentropic pump efficiency, introduced in Sec. 6.12.3,

accounts for the effects of irreversibilities within the pumpin

terms of actual and isentropic pump work input, each per unit

of mass flowing through the pump.

(Eq. 8.10a)

work input for the actual process from pump

inlet state to the pump exit pressure

work input for an isentropic process

from pump inlet state to exit pressure

8/13/2019 ch08 - Copy

11/12

With fraction yknown, mass and energy rate

balancesapplied to control volumes around theother componentsyield the following expressions,

each on the basis of a unit of mass entering the

first turbine stage.

Regenerative Vapor Power Cycle Using

an Open Feedwater Heater

Applying steady-state mass and energy ratebalancesto a control volume enclosing the

feedwater heater, the fraction of the total flow yis

(Eq. 8.12)

8/13/2019 ch08 - Copy

12/12

Regenerative Vapor Power Cycle Using

an Open Feedwater Heater

For the pumps

(Eq. 8.14)

For the steam generator

(Eq. 8.15) (Eq. 8.16)

For the condenser

For the turbine stages

(Eq. 8.13)