Chpt09SG.vapour Power Cycle

8/10/2019 Chpt09SG.vapour Power Cycle

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Chapter 9-1

Chapter 9: Vapor and Combined Power Cycles

We consider power cycles where the working fluid undergoes a phase

change. The best example of this cycle is the steam power cycle where

water (steam) is the working fluid.

Carnot Vapor Cycle

The heat engine may be composed of the following components.

Steam Power Cycle

Turbine

2

Pump

Condenser

Wturb

1

3

QI n

Qout

4

Boiler

Wp

Heat source

TH> TL

QH

QL

Heat Sink

TL

Heat

engineWnet


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Chapter 9-2

The working fluid, steam (water), undergoes a thermodynamic cycle from

1-2-3-4-1. The cycle is shown on the following T-sdiagram.

The thermal efficiency of this cycle is given as

th Carnotnet

in

out

in

L

H

W

Q

Q

Q

T

T

, = =

=

1

1

Note the effect of THand TLon th, Carnot.

The larger the THthe larger the th, Carnot The smaller the TLthe larger the th, Carnot

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

0

100

200

300

400

500

600

700700

s [kJ/kg-K]

T

[C]

6000 kPa

100 kPa

Carnot Vapor Cycle Using Steam

1

2 3

4


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Chapter 9-3

To increase the thermal efficiency in any power cycle, we try to increase the

maximum temperature at which heat is added.

Reasons why the Carnot cycle is not used:

Pumping process 1-2 requires the pumping of a mixture of saturatedliquid and saturated vapor at state 1 and the delivery of a saturated liquid

at state 2.

To superheat the steam to take advantage of a higher temperature,

elaborate controls are required to keep THconstant while the steam

expands and does work.

To resolve the difficulties associated with the Carnot cycle, the Rankine

cycle was devised.

Rankine Cycle

The simple Rankine cycle has the same component layout as the Carnot

cycle shown above. The simple Rankine cycle continues the condensation

process 4-1 until the saturated liquid line is reached.

Ideal Rankine Cycle Processes

Process Description1-2 Isentropic compression in pump

2-3 Constant pressure heat addition in boiler

3-4 Isentropic expansion in turbine

4-1 Constant pressure heat rejection in condenser

The T-sdiagram for the Rankine cycle is given below. Locate the processes

for heat transfer and work on the diagram.


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Chapter 9-4

Example 9-1

Compute the thermal efficiency of an ideal Rankine cycle for which steam

leaves the boiler as superheated vapor at 6 MPa, 350oC, and is condensed at

10 kPa.

We use the power system and T-sdiagram shown above.

P2=P3= 6 MPa = 6000 kPa

T3= 350oC

P1=P4= 10 kPa

Pump

The pump work is obtained from the conservation of mass and energy for

steady-flow but neglecting potential and kinetic energy changes and

assuming the pump is adiabatic and reversible.

( )

m m m

m h W m h

W m h h

pump

pump

1 2

1 1 2 2

2 1

= =

+ =

=

0 2 4 6 8 10 1212

0

100

200

300

400

500

s [kJ/kg-K]

T[C]

6000 kPa

10 kPa

Rankine Vapor Power Cycle

1

2

3

4


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Chapter 9-6

w v P P

m

kg kPa

kJ

m kPa

kJ

kg

pump =

=

=

1 2 1

3

30 00101 6000 10

6 05

( )

. ( )

.

Now, h2is found from

h w h

kJ

kg

kJ

kg

kJ

kg

pump2 1

6 05 19183

197 88

= +

= +

=

. .

.

Boiler

To find the heat supplied in the boiler, we apply the steady-flow

conservation of mass and energy to the boiler. If we neglect the potentialand kinetic energies, and note that no work is done on the steam in the boiler,

then

( )

m m m

m h Q m h

Q m h h

in

in

2 3

2 2 3 3

3 2

= =

+ =

=

We find the properties at state 3 from the superheated tables as

P kPa

T C

h kJ

kg

s kJ

kg K

o

3

3

3

3

6000

350

30430

6335

=

=

UVW

=

=

R

S||

T||

.

.


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Chapter 9-7

The heat transfer per unit mass is

q

Q

m h h

kJ

kg

kJ

kg

in

in

= =

=

=

( . . )

.

3 2

30403 19788

28452

Turbine

The turbine work is obtained from the application of the conservation of

mass and energy for steady flow. We assume the process is adiabatic and

reversible and neglect changes in kinetic and potential energies.

( )

m m m

m h W m h

W m h h

turb

turb

3 4

3 3 4 4

3 4

= =

= +

=

We find the properties at state 4 from the steam tables by notings4=s3and

asking three questions.

at P kPa s kJ

kg Ks

kJ

kg K

is s s

is s s s

is s s

f g

f

f g

g

4

4

4

4

10 0 6483 81502= =

=

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Chpt09SG.vapour Power Cycle