6. Thermodynamic Cycles
Objective
•Classification of Thermodynamics Cycles
•Analysis & Calculation of Power Cycles
Carnot Vapor Cycle, Rankie Cycle, Regeneration
Rankie Cycle,Reheat Rankie Cycle
• Cogeneration
• Gas Refrigeration Cycle
• Vapor-Compression Refrigeration Cycle
• Refrigerant
• Other Refrigeration Cycles
6.1 Classification of Thermodynamics Cycles
Power Cycle (+)
Heat Energy
Mechanical Energy
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 Fluid
Gas 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.
6.2 Carnot Vapor Cycle
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.
6.2 Carnot Vapor Cycle
6.3 Rankine Vapor Cycle
Principle
6
4
4-6 Constant pressure heat
addition in a boiler
S
1
6-1 to Superheat Vapor
1-2 Isentropic expansion in
a turbine
2
2-3 Constant pressure heat
rejection in a condenser
3
3-4 Isentropic compression in
a pump
6.3 Rankine Vapor Cycle
6.3 Rankine Vapor Cycle
p
6
4
p1
4
S
5
6
p2
3
1
1
2
v
T
2
1
3
5
6
4
3
2
s
6.3 Rankine Vapor Cycle
Efficiency
4-5-6-1 Constant pressure heat addition in a boiler
q1  h1  h4
1-2 Isentropic expansion in a turbine
wtT  h1  h2
2-3 Constant pressure heat rejection in a condenser
q2  h2  h3
3-4 Isentropic compression in a pump
wtP  h4  h3
6.3 Rankine Vapor Cycle
Because of uncompressibility of water
wtP  v( p4  p3 )
wtT
h4  h3
Ek  0, Ep  0
wo  wtT  wtP  q1  q2  h1  h2  ws
wo h1  h2
t 

q1 h1  h3
6.3 Rankine Vapor Cycle
Q1
Q2
T1 
T2 
S1
S2
T2
t  1 
T1
Definition:
3600 3600
d

wo
h1  h2
d — the steam required to generate work of 1kW h
d t , equipment size  , investment 
6.3 Rankine Vapor Cycle
Influencing factors
wo h1  h2
t 

q1 h1  h3
p1 , t 1
h1  Entralpy of steam, turbine inlet
h2  Entralpy of exhaust air , turbine outlet
h3  Entralpy of condensed water
p2
6.3 Rankine Vapor Cycle
1.
p1 － Pressure of Steam, Turbine Inlet
1’
t1 , p2 －Unchange
1
p1
5’
Two Cycles:
① 3-4-5-1-2-3
② 3-4-5’-1’-2’-3
5
4
3
p1'
2’
2
6.3 Rankine Vapor Cycle
T1 '  T1
1’ 1
 p1  t 
5’
Disadvantages:
5
1. p1 
4
x
decrease the turbine efficiency and
erodes the turbine blades.
3
2’
2. p1 
2
Increase of requirements on pressure
vessels and equipment investment.
6.3 Rankine Vapor Cycle
2. t1 － Temperature of Steam, Turbine Inlet
1’
1
5
6
4
3
2 2’
p1 , p2－Unchange
t1
t1 '
Two Cycles:
① 3-4-5-6-1-2-3
② 3-4-5-6-1’-2’-3
6.3 Rankine Vapor Cycle
Advantages:
1’
1
5
i
T1'  T1  t 
ii it decreases the moisture content
6
of the steam at the turbine exit.
4
3
2 2’
Disadvantages:
Superheating temperature is limited
by metallurgical considerations.
t1  600℃
6.3 Rankine Vapor Cycle
3.
p2 － Condenser Pressure, Turbine Exit
t1 , p1 －Unchange
1
5
4’
6
4
2
3
3’
2’
p2
p2 '
Two Cycles:
① 1-2-3-4-5-6-1
② 1-2’-3’-4’-5-6-1
6.3 Rankine Vapor Cycle
i
T2 '  T2 t 
1
5
4’
6
ii
4
2
3
3’
2’
Disadvantages:
i Condense pressure is limited
by the sink temperature.
ii It increases the moisture
content which is highly
undesirable.
6.3 Rankine Vapor Cycle
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 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 ℃
State 1:
p1  2.5MPa, t1  350℃
h1  3128.2 kJ/kg
s1  6.8442 kJ/kg  K
State 2:
p2  70kPa, s2  s1
s2 '  1.1921kJ/(kg  K), s2 ''  7.4804kJ/(kg  K)
h2 '  376.77kJ/kg, h2 "  2660.1kJ/kg
sx  s '
x
s '' s '
6.8442  1.1921

 0.8988
7.4804  1.1921
 h2  h ' xh ''
Ideal Rankine Cycle
 376.77  0.8988  2660.1  2767.7kJ/kg
State 3:
p3  70kPa, Saturate Liquid
h3  376.77kJ/kg
v3  0.00104m3 /kg
State 4:
p4  2.5MPa, s4  s3
wtp  v3 ( p4  p3 )  2.53kJ/kg
h4  h3  wtp  376.77  2.53
=381.83kJ/kg
q1  h1  h4  3128.2  381.83  2746.37
q2  h2  h3  2767.7  376.77  2390.93
q2
t  1   12.9%
q1
6.3 Rankine Vapor Cycle
Actual cycle
Irreversibility
• Flow friction
• Heat transfer under temperature
difference
• Heat loss to the surroundings
6.3 Rankine Vapor Cycle
Actual Rankine Vapor Cycle
wtT '  h1  h2 '
Turbine Efficiency
1
wtT ' h1  h2 '
i 

 0.92
wtT
h1  h2
5
6
Ideal Cycle
2
2’
Consumed Steam kg/h
D h1  h2
N0  
d
3600
Actual Cycle
D h1  h2 '
Ni  
 i N 0
d
3600
6.3 Rankine Vapor Cycle
Mechanical Efficiency
Ne
m 
Ni
Relative Effective Efficiency
Effective
Power
Boiler Efficiency
Heat Absorbed in Boiler
B 
Heat Rejected by Feul
Equipment Efficiency
Output Net work

Heat Rejected by Feul
Ne
e 
N0
6.4 Improvement to Rankine Cycle
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.
T
6
5
3(4)
e
d
1
Disadvantages:
7
It is difficult to control the temperature
2
The dryness is small
s
6.4 Improvement to Rankine Cycle
Ideal Regenerative Cycle
T
1
6
5
7
2
3(4)
e
d
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
1
Extracting
Regeneration
Turbine
Boiler

Mixing Chamber
7
2
1
Regenerator
Condenser
6
5
Pump II
4
Pump I
3
Ideal Regenerative Cycle
T
a (h7  h5 )  (1  a )(h5  h4 )
1
5
6 1kg
akg
h5  h4
a
h7  h5
7
w0  (h1  h7 )  (1  a )(h7  h2 )  wtp
(1-a)kg
3(4)
2
q1  h1  h5
s
w0
t 
q1
>0
h2  h3
t  1 
 Rankine
a
(h1  h3 ) 
(h1  h7 )
1 a
Ideal Regenerative Cycle
1
T
Turbine

Boiler
9
8
Regenerator
Mixing
Chamber
8
7
1
2
6
4
5
4
7
1
3
3

5
Condenser
9
6
1
2
s
Pump II
Pump I
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。
Ideal Reheat Cycle
pb  intermediate pressure
1
a
5
6
b
(h1  hb )  (ha  h2 )
t 
(h1  h3 )  (ha  hb )
4
3
c
2
6.4 Improvement to Rankine Cycle
1
Extracting
Regeneration
Turbine
Boiler
7
2
Mixing Chamber
Regenerator
Condenser
6
5
Pump II
4
Pump I
3
6.4 Improvement to Rankine Cycle
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
q2
q2
T2
c 


w0 q1  q2 T1  T2
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 T1 is constant
T2   c  w0 
6.5 Gas Refrigeration Cycle
Condenser
3
2
Compressor
Turbine
4
Cold
Source
1-2
2-3
3-4
4-1
1
Isotropic Compress
Isotonic Heat Rejection to Surrounding
Isotropic Expansion
Isotonic Heat Absorption
6.5 Gas Refrigeration Cycle
p
3
Cp— Constant, Ideal Gas
2
• Heat Absorbed from Cold Source
q2  h1  h4  cp (T1  T4 )
4
1
• Heat Rejected to the condenser
v
T
T3
T1
2
q1  h2  h3  cp (T2  T3 )
• Work of Compressor
wc  h2  h1  cp (T2  T1 )
3
1
• Work of Turbine
4
s
we  h3  h4  cp (T3  T4 )
6.5 Gas Refrigeration Cycle
 w0  wc  we  q1  q2  c p (T2  T3 )  c p (T1  T4 )
T1  T4
q2
= 
w0 (T2  T3 )  (T1  T4 )
T
1  2, 3  4 Isotropic Process
2  3, 4  1 Isotonic Process
p3 k k1 T3
T2
p2 k k1
 ( ) ( ) 
T1
p1
p4
T4
T3
T1
T4
T1
1
 


k 1
T3  T4 T2  T1
p2 k
( ) 1
p1
T1
   c 
T3  T1
2
3
3’
2’
1
4
4’
s
6.5 Gas Refrigeration Cycle
4
Condenser
3
2
Compressor
Turbine
5
6
T
3’
3
4
5’
2
5
1
6
Cold
Source
1
g
k
m
n
s
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
q2
q2
c 

w0 q1  q2
T2

T1  T2
Impracticalities:
1.Large moisture content is highly
undesirable for compressor and turbine.
2.Work output is limited by liquid expansion
in the turbine.
Vapor-Compression Refrigeration Cycle
• So…practical vapor-compression refrigeration cycle is:
2
3
2
4
3
4
1
1
6
5
Vapor-Compression Refrigeration Cycle
1-2
2
2-3-4 Isotonic condensed to
saturated liquid
4
3
1
6
Isotropic compress to
superheated vapor
4-5
Isentropic expansion in a
turbine
4-6
Isotropic expansion through
throttle to humidity vapor
5-1
Constant pressure heat
absorption in a cool source
to dry saturate vapor
5
Vapor-Compression Refrigeration Cycle
q2  h1  h 5
q1  h2  h4
2
wc  h2  h1
4
Throttle:
3
1
6
5
Work difference between
Turbine and throttle
h4  h 5
q2 h1  h4
c 

w0 h2  h1
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
Vapor-Compression Refrigeration Cycle
Regeneration — more realistic cycle
Advantages:
1.
T
2.
q2  h1 ' h5 ' 
c 
2
Supercooled
Liquid
3.Superheated vapor is desirable
3
4
4’
Superheated
Vapor
1’
5’
5
1
s
Vapor-Compression Refrigeration Cycle
Condenser
2
4
1’
Compressor
Regenerator
Throttle Valve
h1 ' h1  h4  h4 '
4’
1
5’
Conditions:
Cold
Source
t4  t1 '
Vapor-Compression Refrigeration Cycle
ln p
4
2 2’
3
Q2
qm 
h1  h5
qV  qm v1 ''
5
N  qm w
Irreversibility 1-2’
Isotropic Compress Efficiency
1
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。
ad
h2  h1

h2 ' h1
w '  h2 ' h1 
 '  ad
w
ad
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  , c p , k
• being nontoxic ,non-corrosive, nonflammable, chemically steady;
• low cost
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.
Geothermal Energy
Solar Energy
Absorption refrigeration system involves the absorption of
a refrigerant by a transport medium .
Ammonia — Water
NH3－ H2O
Water — lithium bromide
H2O － LiBr
6.8 Absorption Refrigeration System
Principle
Q－Solar Energy
Q1
Generator
rectifier
NH3
Q4
NH3-H2O
Condenser
Weak
Rich
Adjust
Valve
Expansion Valve
Absorber
Evaporation
NH3
pump
NH3-H2O
Q2
Cooling
Water
Q3
6.8 Absorption Refrigeration System
Thermodynamic Analysis
Q2  Q4  Wp  Q1  Q3
Thermal Efficiency
Q2
Q2


Q4  W p Q4
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
Q1
Condenser
P V  T
Diffuser
pump
Expansion
Valve
Evaporation
Q2
Boiler
Mixture
Nozzle
P V  T
6.9 Vapor-Jet Refrigeration System
Q1
T
4
Condenser
3
pump
Expansion
Valve
1’
5
5’
1
2
Evaporation
3
4
5’
Q2
Boiler
Q3
1
2’
5
2’
2
s
1’
6.9 Vapor-Jet Refrigeration System
Thermodynamic Analysis
Q1  Q2  Q3  Wp
Thermal Efficiency
Q2
Q2


Q3  W p Q3
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
2
8
1
Gas-Liquid Coefficient
y  1 x
6
5
Quality at
State 4
4
s
Wmin  T0 ( S1  S6 )  ( H1  H6 )
6.10.2 Linde Cycle
Principle
Condenser
Compressor
P2
T
P1
2
Heat
Exchanger
2
1
3
1
7
3
Expansion
Valve
6
5
5
4
4
s
Separator
6
Liquid Removed
6.10.2 Linde Cycle
Thermodynamic Analysis
P2
T
P1
2
1
3
q  h  wt
7
6
Take the Heat Exchanger,
Expansion Valve,
Separator
as system.
Liquid: y kg ; gas: (1-y) kg
h2  y h6  (1  y )h1
5
h1  h2
y
h1  h6
4
s
Heat of liquefaction y kg:
q2  y(h1  h6 )  h1  h2
6.10.2 Linde Cycle
Thermodynamic Analysis
Irreversibility in liquefaction
of gas:
P2
T
P1
2
1
3
q ''  y h6  (1  y )h7  h2
h2  q ''  y h6  (1  y )h1  q '
7
6
① heat loss in heat exchanger q’
② non-adiabatic, heat addition from
surrounding q’’
h1  h2  q ' q ''
y
h1  h6
5
4
s
q2  h1  h2  q ' q ''
6.10.2 Linde Cycle
Thermodynamic Analysis
Irreversibility in compression
P2
of gas:
T
P1
① isothermal compression 1-2
② isothermal efficiency (0.59)
2
1
3
7
6
Actual work consumption
RT1
p2
ws 
ln
T
p1
5
4
s
ws
wys 
y
cannot be treated
as Ideal Gas
6.10.3 Claude Cycle
Thermodynamic Analysis
Condenser
Compressor
2
1
HE1
1 y
Turbine
1
3

HE2
4
HE3
4’
6
Expansion
Valve
Separator
8
7
a-y
9
y
Liquid Removed
h2  (1   )h4  q ' q ''  y h9  (1  y )h1  (1   )h3
(h1  h2 )  (1   )(h3  h4 )  q ' q ''
y
h1  h9
q2  (h1  h2 )  (1   )(h3  h4 )  q ' q ''
h3  h4
s 
h3  h4 '
Piston expander：s
Turbine：
 0.65  0.75
s  0.80  0.85
Considering mechanical efficiency m
p2
ws 
ln  m (1   )(h3  h4 )
T
p1
RT