Thermodynamic Cycles

Thermodynamic Cycles

Objective•Classification of Thermodynamics Cycles•Analysis & Calculation of Thermodynamic Cycles Carnot Vapor Cycle, Rankie Cycle, Regeneration Ran

kie Cycle,Reheat Rankie Cycle

• Cogeneration• Gas Refrigeration Cycle• Vapor-Compression Refrigeration Cycle• Refrigerant• Other Refrigeration Cycles

Classification of Thermodynamics Cycles

Heat Energy Mechanical EnergyPower Cycle (+)

Heat Pump Cycle (－ )

Refrigeration Cycle: keep low temperature of heat source with low temperature

Heat Pump Cycle: keep high temperature of heat source with high temperature

Working FluidGas Cycle: no phase-change of working fluid during cycle

Vapor Cycle: phase-change of working fluid during cycle

Combustion form Inner Combustion Outer Combustion

Combustion occurs in system Combustion occurs out of system

Gas is also the working fluid.The heat is transferred to working fluid through heat exchanger.

Carnot Vapor Cycle

Several impracticalities are associated with this cycle:

1. It is impractical to design a compressor that will handle two phases for

isentropic compression process(4-1).

2. The quality of steam decrease during isentropic expansion process(2-3)

which do harm to turbine blades.

3. The critical point limits the maximum temperature used in the cycle

which also limits the thermal efficiency.

4. The specific volume of steam is much higher than that of water which

means large amount of work and equipments input.

Carnot Vapor Cycle

Rankine Vapor Cycle

4-6 Constant pressure heat addition in a boiler

6-1 to Superheated Vapor

1-2 Isentropic expansion in a turbine

2-3 Constant pressure heat rejection in a condenser

3-4 Isentropic compression in a pump

S

4

6

1

2

3

Rankine Vapor Cycle

S

4

6

1

2

3

T

s

1

6

5

4

3 2

p

v

1654

32

p1

p2

Thermal Efficiency of Rankine Vapor Cycle

4-5-6-1 Constant pressure heat addition in a boiler

1 1 4q h h


tT 1 2w h h

2-3 Constant pressure heat rejection in a condenser

2 2 3q h h

3-4 Isentropic compression in a pump

tP 4 3w h h


1.Hard compressibility of water

2. tP tTw w

( )tP 4 3

4 3

w v p p

h h

o tT tP 1 2 1 2 s

o 1 2t

1 1 3

w w w q q h h w

w h h

q h h

Ek,Ep=0


1 21 2

1 2

2t

1

Q QT T

S S

T1

T

Definition:

o 1 2

3600 3600d

w h h

d( 汽耗率 ) — the heat rate required to generate work of

kW h1 td

Increase Efficiency of Rankine Vapor Cycle

o 1 2t

1 1 3

w h h

q h h

Entralpy of steam, turbine inlet

Entralpy of exhaust air , turbine outlet

Entralpy of condensed water

1

2

3

h

h

h

,1 1p t

2p

1. － Pressure of Steam, Turbine Inlet


1p

3

4

5

5’

1’ 1

22’

,1 2t p － Unchange

1p '1p

Two Cycles:

① 3-4-5-1-2-3

② 3-4-5’-1’-2’-3

3

4

5

5’

1’ 1

22’

'1 1

1 t

T T

p

Disadvantages:

1p 1. x


The presence of large quantities of moisture is highly desirable because itdecrease the turbine efficiency anderodes the turbine blades.

2. 1p Increase of requirements on pressurevessels and equipment investment.


2. － Temperature of Steam, Turbine Inlet1t

3

4

5

11’

2’2

6


1p '1p

Two Cycles:

① 3-4-5-6-1-2-3

② 3-4-5-6-1’-2’-3


3

4

51

1’

2’2

6

Advantages:

' ,1 1 1 2

1 t

T T p p

t

i

ii Superheating the steam to higher temperature is desirable becauseit decreases the moisture contentof the steam at the turbine exit.

Disadvantages:

Superheating temperature is limitedby metallurgical considerations.

1t 600 ℃


3. － Condenser Pressure, Turbine Exit2p


2p '2p

Two Cycles:

① 1-2-3-4-5-6-1

② 1-2’-3’-4’-5-6-13

4

5

1

3’ 2’

2

6

4’


3

4

5

1

3’ 2’

2

6

4’

,'2 2 1 2

2 t

p p t t

p

i

iiDisadvantages:

i Condense pressure is limited

by saturation pressure

corresponding to the

temperature.

ii It increases the moisture

content which is highly

undesirable.


Example

Consider a steam power plant operating on the ideal Rankine cycle.

The steam enters the turbine at 2.5MPa and 350 and is condensed℃in the condenser at pressure of 70kPa. Determine

(a)The thermal efficiency of this power plant

(b)The thermal efficiency if steam is condensed at pressure of 10kPa

(c) The thermal efficiency if steam is superheated to 600 ℃(d)The thermal efficiency if the boiler pressure is raised to 15MPa

while the turbine inlet temperature is maintain at 600 ℃

70kPa

2.5MPa

1

2

3

4

1

1

31

70 , Saturate Liquid

376.77kJ/kg

0.00104m /kg

p kPa

h

v

State 1:

2 2 1

, 1 2 1

2 1 ,

2.5 ,

( ) 2.53kJ/kg

376.77 2.53

=381.83kJ/kg

pump in

pump in

p MPa s s

w v p p

h h w

State 2:

1 2h h

State 3:

3 2

3

3

2.5MPa, 350

3128.2 kJ/kg

6.8442 kJ/kg K

p t

h

s

℃

Ideal Rankine Cycle

70kPa

2.5MPa

1

2

3

4

State 4:

3 4 3

4

70 Pa,

' ( '' ')

'

'' '6.8442 1.1921

0.89887.4804 1.1921

' ''

376.77 0.8988 2660.1 2767.7kJ/kg

x

x

p k s s

s s x s s

s sx

s s

h h xh

3 2

4 1

3128.2 381.83 2746.37

2767.7 376.77 2390.93

in

out

q h h

q h h

1 12.9% outt

in

q

q

1

1

31

10 , Saturate Liquid

191.83kJ/kg

0.00101m /kg

p kPa

h

v

State 1:

2 2 1

, 1 2 1

2 1 ,

2.5 ,

( ) 3.02kJ/kg

191.83 3.02

=194.85kJ/kg

pump in

pump in

p MPa s s

w v p p

h h w

State 2:

1 2h h

State 3:

3 2

3

3

2.5MPa, 350

3128.2 kJ/kg

6.8442 kJ/kg K

p t

h

s

℃

(b)

Lowing thepressure ofCondenser

State 4:

3 4 3

4

10 Pa,

' ( '' ')

'

'' '6.8442 0.6493

0.82588.1511 0.6493

' ''

191.83 0.8258 2584.8 2326.4kJ/kg

x

x

p k s s

s s x s s

s sx

s s

h h xh

2.5MPa

3 2

4 1

3128.2 194.35 2933.85

2326.4 191.83 2134.57in

out

q h h

q h h

1 27.2%outt

in

q

q

Actual Rankine Vapor Cycle

Irreversibility

• Fluid friction• Heat transfer under temperature

difference• Heat loss to the surroundings


2’

3(4

)

2

1

56

1 2' 'tTw h h Turbine Efficiency

1 2

1 2

' '0.92tT

itT

w h h

w h h

Ideal Cycle

1 20 3600

h hDN

d

Actual Cycle

1 20

'

3600i i

h hDN N

d


Mechanical Efficiency

em

i

N

N Effective

Power 0

ee

N

N

Relative Effective Efficiency

Boiler Efficiency

Heat Absorbed in Boiler

Heat Rejected by FeulB

Equipment Efficiency

Output Net work

Heat Rejected by Feul

Ideal Regenerative Cycle

3(4)e

2

7

1

d

56

T

s

预热锅炉给水，使其温度升高后再进入锅炉，可提高水在锅炉内的平均吸热温度，减小水与高温热源的温差，对提高循环效率有利。利用汽轮机中的蒸汽预热锅炉给水，称为回热。Transfer heat to the feedwater from the

expanding steam in a heat exchanger built

into the turbine ,called Regeneration.

Regenerative Cycle: 1-7-d-3-4-5-6-1

General Carnot Cycle:3-4-5-7-d-3

Ideal Carnot Cycle: 5-7-2-e-5Same

Efficiency

Regenerative Rankine


Boiler Turbine

Regenerator

Condenser

Mixing Chamber

Pump II Pump I

1

27

34

56

ExtractingRegeneration


3(4) 2

7

1

6

5

1kg

akg

(1-a)kg

T

s

( ) ( )( )

( ) ( )( )

7 5 5 4

5 4

7 5

0 1 7 7 2 tp

1 1 5

0t

1

a h h 1 a h h

h ha

h h

w h h 1 a h h w

q h h

w

q

( ) ( )

2 3t Rankine

1 3 1 7

h h1

ah h h h

1 a

>0


Boiler Turbine

Regenerator

Cond-enser

Mixing Chamber

Pump II Pump I

1

27

34

56

8

93 2

7

1

6

5

T

s

4

89

Ideal Reheat Cycle

蒸汽经汽轮机绝热膨胀至某一中间压力时全部引出，进入锅炉中特设的再加热器中再加热。温度升高后再全部引入汽轮机绝热膨胀做功。称为再热循环。

3 c 2

a1

5

4

6 b

Ideal Reheat Cycle

bp intermediate pressure

( ) ( )

( ) ( )1 b a 2

t1 3 a b

h h h h

h h h h

Cogeneration

Definition

Cogeneration is the production of more than one

useful form of energy from the same energy source.• electric power• heat in low quality

背压式热电联供抽气式热电联供

Gas Refrigeration Cycle

Ideal Reversed Carnot Cycle

2 2 2c

0 1 2 1 2

q q T

w q q T T

T1 — Temperature of heat source with high temperature,

surrounding temperature

T2 — Temperature of heat source with low temperature,

cold source

q1 — Heat rejected to the surroundings

q2 — Heat absorbed from cold source

w0 — Work input

if is constant1

2 c 0

T

T w


Turbine

Compressor

Condenser

ColdSource

1

23

4

1-2 Isotropic Compress

2-3 Isotonic Heat Rejection to Surrounding

3-4 Isotropic Expansion

4-1 Isotonic Heat Absorption

Gas Refrigeration Cyclep

v

1

23

4

1

T

s

2

3

4

T1

T3

Cp— Constant, Ideal Gas

• Heat Absorbed from Cold Source

( )2 1 4 p 1 4q h h c T T

• Heat Rejected to the condenser

( )1 2 3 p 2 3q h h c T T

• Work of Turbine

• Work of Compressor

( )c 2 1 p 2 1w h h c T T

( )e 3 4 p 3 4w h h c T T

Gas Refrigeration Cycle( ) ( )

=( ) ( )

, Isotropic Process

, Isotonic Process

( ) ( )

( )

0 c e 1 2 p 2 3 p 1 4

1 42

0 2 3 1 4

k 1 k 13 32 2 k k

1 1 4 4

4 1k 1

3 4 2 1 2 k

1

1c

3 1

w w w q q c T T c T T

T Tq

w T T T T

1 2 3 4

2 3 4 1

p TT p

T p p T

T T 1

T T T T p1

p

T

T T


Vapor-Compression Refrigeration Cycle

• Shortcomings of Gas-Compression Refrigeration Cycle

1.small Refrigeration-Coefficient because heat absorption

and rejection are not isothermal process;

2.Lower refrigeration capability of refrigerant (gas)

• So…refrigerant is change to Vapor

The highest efficiency is that of Vapor Carnot Reverse Cycle

Impracticalities:

1.Large moisture content is highly

undesirable for compressor and turbine.

2.Work output is limited by liquid expansion

in the turbine.

2 2c

0 1 2

2

1 2

q q

w q q

T

T T


• So…practical vapor-compression refrigeration cycle is:

1

23

4

1

2

34

56


1

2

34

56

1-2 Isotropic compress to superheated vapor

2-3-4 Isotonic condensed to saturated liquid


4-6 Isotropic expansion through throttle to humidity vapor

5-1 Constant pressure heat absorption in a cool source to dry saturate vapor


1

2

34

56

2 1 5

1 2 4

c 2 1

q h h

q h h

w h h

Throttle:

4 5h h1 42

c0 2 1

h hq

w h h

Work difference between Turbine and throttle

① fluid with low quality is difficult to be compressed.

② work loss is relatively small ③ easily adjust pressure of fluid

and temperature of cold source


Regeneration — more realistic cycle

T

s

11’

2

34

4’

5’ 5

Superheated Vapor

Super-cooled Liquid

Advantages:

1.

2.

3.Superheated vapor is desirable

c ' '2 1 5q h h


Compressor

Condenser

ColdSource

1’

24

4’

Regenerator

Throttle Valve

5’

1

Conditions:

' '

'1 1 4 4

4 1

h h h h

t t


1

2 2’4

5

3

ln p

h

''

2m

1 5

V m 1

m

Qq

h h

q q v

N q w

Irreversibility 1-2’Isotropic Compress Efficiency

'

' '

'

2 1ad

2 1

2 1ad

ad

h h

h h

ww h h

制冷机的制冷能力是随工作条件不同而变化的，因此，给出制冷能力时，必须指明相应的工作条件。

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Thermodynamic Cycles

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