6. thermodynamic cycles objective classification of thermodynamics cycles analysis & calculation...
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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.
6.2 Carnot Vapor Cycle
6.2 Carnot Vapor Cycle
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
6.3 Rankine Vapor Cycle
S
4
6
1
2
3
T
s
1
6
5
4
3 2
p
v
1654
32
p1
p2
6.3 Rankine Vapor Cycle
4-5-6-1 Constant pressure heat addition in a boiler
1 1 4q h h
1-2 Isentropic expansion in a turbine
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
6.3 Rankine Vapor Cycle
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
6.3 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
6.3 Rankine Vapor Cycle
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
6.3 Rankine Vapor Cycle
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.
6.3 Rankine Vapor Cycle
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
6.3 Rankine Vapor Cycle
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 ℃
6.3 Rankine Vapor Cycle
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’
6.3 Rankine Vapor Cycle
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.
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. 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
℃
6.3 Rankine Vapor Cycle
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
6.3 Rankine Vapor Cycle
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
6.3 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
6.3 Rankine Vapor 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 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
6.4 Improvement to Rankine Cycle
Ideal Regenerative Cycle
Boiler Turbine
Regenerator
Condenser
Mixing Chamber
Pump II Pump I
1
27
34
56
ExtractingRegeneration
1
Ideal Regenerative Cycle
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
Ideal Regenerative Cycle
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
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
6.4 Improvement to Rankine Cycle
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
6.5 Gas Refrigeration Cycle
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’
6.5 Gas Refrigeration Cycle
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
Vapor-Compression Refrigeration Cycle
• So…practical vapor-compression refrigeration cycle is:
1
23
4
1
2
34
56
Vapor-Compression Refrigeration Cycle
1
2
34
56
1-2 Isotropic compress to superheated vapor
2-3-4 Isotonic condensed to saturated liquid
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
Vapor-Compression Refrigeration Cycle
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
Vapor-Compression Refrigeration Cycle
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
Vapor-Compression Refrigeration Cycle
Compressor
Condenser
ColdSource
1’
24
4’
Regenerator
Throttle Valve
5’
1
Conditions:
' '
'1 1 4 4
4 1
h h h h
t t
Vapor-Compression Refrigeration Cycle
1
2 2’4
5
3
ln p
h
''
2m
1 5
V m 1
m
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
6.8 Absorption Refrigeration System
Condenser
Evaporation
Q - Solar Energy
Expansion Valve AdjustValve
NH3-H2O
NH3-H2O
Absorber
Generator
pump
rectifier
CoolingWater
Q1
Q2 Q3
Q4NH3
NH3
RichWeak
Principle
6.8 Absorption Refrigeration System
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
6.9 Vapor-Jet Refrigeration System
1
1’
3
22’5
4
5’
T
s
Condenser
Evaporation
ExpansionValve
pump
Q1
Q2
Boiler1’
12
3
4
5’
5
2’
Q3
6.9 Vapor-Jet Refrigeration System
Thermodynamic Analysis
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
Thermodynamic Analysis
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
Thermodynamic Analysis
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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