6. Thermodynamic Cycles Objective Classification of Thermodynamics Cycles Analysis & Calculation of...

6. Thermodynamic Cycles

Objective•Classification of Thermodynamics Cycles•Analysis & Calculation of Power 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

6.1 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.

6.2 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

needs big equipments and large amount of work input.


6.3 Rankine Vapor Cycle

4-6 Constant pressure heat addition in a boiler

6-1 to Superheat 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

Principle

S

4

6

1

2

3

T

s

1

6

5

4

3 2

p

v

1654

32

p1

p2


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

6.3 Rankine Vapor CycleEfficiency

Because of uncompressibility of water

( )tP 4 3 tTw v p p w

4 3h 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

0, 0k pE E


1 21 2

1 2

2t

1

Q QT T

S S

T1T

Definition:

o 1 2

3600 3600d

w h h

d — the steam required to generate work of 1kW h

, equipment size , investmenttd


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


Influencing factors

1. － Pressure of Steam, Turbine Inlet1p

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 decrease 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

,1 2p p－ Unchange

1t '1t

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 tT T i

ii it decreases the moisture contentof the steam at the turbine exit.

Disadvantages:

Superheating temperature is limitedby metallurgical considerations.

6001t ℃


3. － Condenser Pressure, Turbine Exit2p

,1 1t p － Unchange

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 tT T i

iiDisadvantages:

i Condense pressure is limited

by the sink 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. Determin

e

(a)The thermal efficiency of this power plant

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

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

MPa while the turbine inlet temperature is maintain at 600

℃


State 1:

State 2:

1 1

1

1

2.5MPa, 350

3128.2 kJ/kg

6.8442 kJ/kg K

℃p t

h

s

Ideal Rankine Cycle

State 4:

1 1 4

2 2 3

3128.2 381.83 2746.37

2767.7 376.77 2390.93

q h h

q h h

2

1

1 12.9% t

q

q

4 4 3

3 4 3

4 3

2.5MPa,

( ) 2.53kJ/kg

376.77 2.53

=381.83kJ/kg

tp

tp

p s s

w v p p

h h w

3

3

33

70kPa, Saturate Liquid

376.77kJ/kg

0.00104m /kg

p

h

v

State 3:

Irreversibility

• Flow friction• Heat transfer under temperature

difference• Heat loss to the surroundings


Actual cycle

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

Consumed Steam kg/h

Actual Rankine Vapor Cycle


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


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 exch

anger built into the turbine ,called Regeneration.

3(4)e

2

7

1

d

5 6

T

s

Disadvantages:

It is difficult to control the temperature

The dryness is small

6.4 Improvement to Rankine Cycle

3(4)e

2

7

1

d

5 6

T

s

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-5

Same Efficiency

Regenerative Rankine

Ideal Regenerative Cycle



Boiler Turbine

Regenerator

Condenser

Mixing Chamber

Pump II Pump I

1

27

34

56

ExtractingRegeneration

1


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

1

1

6.3.2 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

Boiler Turbine

Regenerator

Condenser

Mixing Chamber

Pump II Pump I

1

27

34

56

ExtractingRegeneration


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


6.5 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

6.5 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

6.5 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

1

T

s

2

3

4

T1

T32’

3’

4’


Turbine

Condenser

ColdSource

Compre-ssor

1

2

34

5

6

1

2

33’

5’

6

5

4

T

sg m nk

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 changed 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。

6.7 Refrigerant

Definition

The work fluid cycling flowing in refrigeration

system while transferring energy with surrounding

in order to refrigerate.

Thermodynamic Request

• Critical temperature should be much higher than temperature of surroundings. ① steam easier be condensed; ② larger range of latent heat; ③ heat absorption and heat rejection closer to isothermal process

6.7 Refrigerant

Thermodynamic Request

• Solidification temperature should be lower than evaporation

temperature to prevent blocking the pipes.

• Larger latent heat is more desirable.

• appropriate saturate pressure

• small

• being nontoxic ,non-corrosive, nonflammable, chemically steady;

• low cost

, ,pc k

Environment & Safety Request

Ammonia 氨， Feron 氟利昂

6.8 Absorption Refrigeration System

Definition

The form of refrigeration that inexpensive thermal energy

instead of mechanical energy or electric power is consumed to

transfer heat form low temperature to high temperature is

absorption refrigeration.

Absorption refrigeration system involves the absorption of a refrigerant by a transport medium .

Ammonia — Water

NH3 － H2O

Water — lithium bromide

H2O － LiBr

Geothermal EnergySolar Energy


Condenser

Evaporation

Q － Solar Energy

Expansion Valve AdjustValve

NH3-H2O

NH3-H2O

Absorber

Generator

pump

rectifier

CoolingWater

Q1

Q2 Q3

Q4NH3

NH3

RichWeak

Principle


Thermodynamic Analysis

2 4 1 3pQ Q W Q Q Thermal Efficiency

2 2

4 4p

Q Q

Q W Q

Advantage:

A liquid is compressed instead of a vapor , and

thus the work input for absorption refrigeration system

is very small.

6.9 Vapor-Jet Refrigeration System

Principle

Mixture

Condenser

Evaporation

ExpansionValve

pump

Q1

Q2

Boiler

Nozzle

P V T

Diffuser

P V T


1

1’

3

22’5

4

5’

T

s

Condenser

Evaporation

ExpansionValve

pump

Q1

Q2

Boiler1’

12

3

4

5’

5

2’

Q3



1 2 3 pQ Q Q W Thermal Efficiency

2 2

3 3p

Q Q

Q W Q

Disadvantage:

Irreversibility such as mixture process and

heat transfer with temperature difference;

Large exergy loss

6.10 Liquefaction of Gases

The liquefaction of gases has always been an important area of

refrigeration since many important scientific and engineering process

at cryogenic temperature depend on liquefied gas.

Example:• separation of oxygen and nitrogen from air• preparation of liquid propellants for rockets• the study of material properties at low temperature• the study of exciting phenomenon such as superconductivity

气体液化循环中的工质，在循环中即作为冷却剂使用，同时本身又被液化并输出液态产品。

6.10.1 Min. Work in Liquefaction of Gases

T

s

12 8

64

5

min 0 1 6 1 6( ) ( )W T S S H H

Gas-Liquid Coefficient

1y x

Quality at State 4

6.10.2 Linde Cycle

Condenser

ExpansionValve

HeatExchanger

Separator

Liquid Removed

Compressor

1

2

3

4

5

6

PrincipleT

s

12

64

5

3

7

P1

P2

6.10.2 Linde Cycle


T

s

12

64

5

3

7

P1

P2Take the Heat Exchanger,

Expansion Valve,

Separator

as system.

Liquid: y kg ; gas: (1-y) kg

( )t

2 6 1

1 2

1 6

q h w

h y h 1 y h

h hy

h h

Heat of liquefaction y kg:

( )2 1 6 1 2q y h h h h


T

s

12

64

5

3

7

P1

P2

6.10.2 Linde Cycle

Irreversibility in liquefaction

of gas: ① heat loss in heat exchanger q’

② non-adiabatic, heat addition from

surrounding q’’'' ( )

'' ( ) '

' ''

' ''

6 7 2

2 6 1

1 2

1 6

2 1 2

q y h 1 y h h

h q y h 1 y h q

h h q qy

h h

q h h q q

Thermodynamic Analysis Irreversibility in compression

of gas:

① isothermal compression 1-2

② isothermal efficiency (0.59)

ln1 2s

T 1

sys

RT pw

p

ww

y

T

s

12

64

5

3

7

P1

P2

6.10.2 Linde Cycle

Actual work consumption

cannot be treated as Ideal Gas

6.10.3 Claude Cycle

Thermodynamic AnalysisCondenser

Liquid Removed

2Compressor

HE1

HE2

HE3

Turbine

ExpansionValve

Separator

1

3

4

4’

6

7

8

9

1

y

a-y

1 y

23 4

1

ln (1 )( )

s mT

pRTw h h

p

2 4 9 1 3

1 2 3 4

1 9

2 1 2 3 4

3 4

3 4

(1 ) ' '' (1 ) (1 )

( ) (1 )( ) ' ''

( ) (1 )( ) ' ''

'

s

h h q q y h y h h

h h h h q qy

h h

q h h h h q q

h h

h h

Piston expander ：

Turbine ：

0.65 0.75

0.80 0.85s

s

Considering mechanical efficiency m

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