seprodthermochapter5refrigeration
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seprodthermochapter5refrigerationTRANSCRIPT
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.
Introduction toRefrigeration Air Conditioning
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Applied Thermodynamics & Heat Engines
S.Y. B. Tech.
ME0223 SEM - IV
Production Engineering
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Outline
Applications of Refrigeration.
BellColeman Cycle.
COP and Power Calculations
VapourCompression Refrigeration System.
Presentation on T-S and P-h diagram.
VapourAbsorption System.
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Refrigeration
REFRIGERATION Science of producing and maintaining temperature below that of
sur rounding / atmosphere.
REFRIGERATION Cooling of or removal of heat from a system.
Refrigerating System Equipment employed to maintain the system at a low temperature.
Refrigerated System System which i s kept at lower temperatur e.
Refrigeration 1) By melting of a solid,
2) By subl imation of a solid,
3) By evaporation of a liquid.
Most of the commercial refrigeration production : Evaporation of liquid.
This liquid is known as Refrigerant.
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.
Refrigeration Circuit
Refrigeration Circuit
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Evaporator
Compressor
CondenserExpansion
Valve
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Refrigeration - Elements
Compressor
Condenser
Evaporator
Expansion
Valve
Wnet, in
Surrounding Air
Refrigerated Space
QH
QL
High Temp
Source
Low Temp
Sink
QH
QL
Wnet, in
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Refrigeration - Applications
1. Ice making.
2. Transportation of food itemsabove and below freezing.
2. Industrial AirConditioning.
4. Comfort AirConditioning.
5. Chemical and related industries.
6. Medical and Surgical instruments.7. Processing food products andbeverages.
8. Oil Refining.
9. Synthetic Rubber Manufacturing.
10. Manufacture and treatment of metals.
11.Freezing food products.
12. Manufacturing Solid Carbon Dioxide.
13. Production of extremely low temperatures (Cryogenics)
14. Plumbing.
15. Building Construction.
Applications :
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Refrigeration Systems
1. Ice Refrigeration System.
2. Air Refrigeration System.
2. Vapour Compression Refrigeration System.
4. Vapour Absorption Refrigeration System.
5. Adsorption Refrigeration System.
6. Cascade Refrigeration System.
7. Mixed Refrigeration System.
8. Thermoelectric Refrigeration System.
9. Steam Jet Refrigeration System.
10. Vortex Tube Refrigeration System.
Refrigeration Systems :
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Performance - COP
COP Ratio of H eat absorbed by the Refrigerant while passing through the Evaporator
to the Work I nput requi red to compress the Refr igerant in the Compressor.
Performance of Refrigeration System :- Measured in terms of COP (Coefficient of Performance).
If; Rn= Net Refrigerating Effect. W = Work required by the machine.
Then;W
RCOP n
COPlTheoretica
COPActual
COPlative Re
Actual COP = Ratio of Rnand Wactually measured.
Theoretical COP = Ratio of Theoretical values of Rnand Wobtained by applying
Laws of Thermodynamicsto the Refrigerating Cycle.
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Performance - Rating
Rating of Refrigeration System :- Refrigeration Effect / Amount of Heat extracted from a body in a given time.
Unit :
- Standard commercial Tonne of Refrigeration / TR Capacity
Definition :
- Refrigeration Effect produced by melting 1 tonne of ice from and at 0 C in 24 hours.
Latent Heat of ice = 336 kJ/kg.
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Air Refrigeration System
One of the earliest method.
Obsolete due to low COPandhigh operating cost.
Preferred in Aircraft Refrigeration due to its low weight.
Characteristic :
- Throughout the cycle, Refrigerant remains in gaseousstate.
Air Refrigeration
Closed System Open System
Air refrigerant contained within
piping or components of system.
Pressures above atm. Pr.
Refrigerator space is actual room to be cooled.
Air expansion to atm. Pr. And then
compressed to cooler pressure.
Pressures limited to near atm. Pr. levels..
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Air Refrigeration System
1. Suction to compressor in Closed System may be at high pressures. Hence,
the size of Expander and Compressor can be kept small.
Closed System Vs. Open System :
2. In Open Systems, air picks up the moisturefrom refrigeration chamber. This
moisture freezes and chokes the valves.
3. Expansionin Open System is limited to atm. Pr. Level only. No such restriction
to Closed System.
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Reverse Carnot Cycle
3
2
14
Isotherms
Adiabatic
T2
Expansion
Compression
T1
Pressure
Volume
PV Diagram
3 2
14T1
Expansion Compression
T2
Tempera
tu
re
Entropy
14
TsDiagram
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
3 2
14T1
Expansion Compression
T2
Tempera
tu
re
Entropy
14
Operation :
3 4 : Adiabatic Expansion.
Temp. falls from T2to T1.
Cylinder in contact with Cold Body at T1.
4 1 :Isothermal Expansion.
Heat Extraction from Cold Body.
1 2 : Adiabatic Compression.
Requires external power.
Temp. rises from T1to T2.
Cylinder in contact with Hot Body at T2
2 3 :Isothermal Compression.
Heat Rejection to Hot Body.
Reverse Carnot Cycle
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
3 2
14T1
Expansion Compression
T2
Tempera
tur
e
Entropy
14
Heat extracted from cold Body : Area 1-1-4-4
= T1X 1-4
Work done per cycle : Area 1-2-3-4
= (T2T1) X 1-4
12
1
12
1
)41()(
)41(
4321
4'4'11
TT
T
XTT
XT
Area
Area
DoneWork
ExtractedHeatCOP
Reverse Carnot Cycle
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 1
A Carnot Refrigerator requires 1.3 kW per tonne of refrigeration to maintain a region at
low temperature of -38 C. Determine:i) COP of Carnot Refrigerator.
ii) Higher temperature of the cycle.
iii) Heat delivered and COP, if the same device is used Heat Pump.
99.2
)sec/3600()3.1(
/000,14
3.1
1
hrkW
hrkJ
kW
tonne
doneWork
absorbedHeatCOPrefrig .ANS
KTKT
K
TT
TCOPrefrig 6.313
235
23599.2 1
212
1
.ANS
Heat Delivered as Heat Pump ;
sec/189.53.13600
/000,143.11 kJ
hrkJkWtonne
doneWorkabsorbedHeat
.ANS
99.3
3.1
sec/189.5
kW
kJ
doneWork
deliveredHeatCOPHP .ANS
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 2
A refrigerating system works on reverse Carnot cycle. The higher temperature in the
system is 35 C and the lower temperature is -15 C. The capacity is to be 12 tonnes.Determine :
i) COP of Carnot Refrigerator.
ii) Heat rejected from the system per hour.
iii) Power required.
18.5258308
258
12
1 KK
K
TT
TCOPrefrig .ANS
hrkJInputWork
InputWork
hrkJX
InputWork
tonne
InputWork
Ef fectfrigCOPrefrig
/32558
/000,14121216.5
.Re
.ANSkWhrkJhrInputWork
Power 04.9
3600
/32558
3600
/
Heat Rejected / hr = Refrig. Effect / hr + Work Input / hr
= 12 x 14,000 (kJ/hr) + 32,558 (kJ/hr) = 2,00,558 kJ/hr. .ANS
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 3
Ice is formed at 0 C from water at 20 C. The temperature of the brine is -8 C. Find out
the kg of ice per kWh. Assume that the system operates on reversed Carnot cycle. Takelatent heat of ice as 335 kJ/kg.
46.9265293
265
12
1
KK
K
TT
TCOPrefrig
Heat to be extracted per kg of water ( to from ice at 0 C)Rn = 1 (kg)x Cpw(kJ/kg.K)x (293273) (K)+ Latent Heat (kJ/kg) of ice
= 1 (kg)x 4.18 (kJ/kg.K)x 20 (K)+ 335 (kJ/kg)
= 418.6 kJ/kg.
Also, 1 kWh = 1 (kJ)x 3600(sec/hr)= 3600 kJ.
kgmkJ
kgkJXkgm
kJdoneWork
kJEf fectfrig
W
RCOP
iceice
nrefrig
35.813600
)/(6.418)(46.9
)(
)(.Re
.ANS
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
BellColeman / Reverse Bryaton Cycle
Elements of this system :
1. Compressor.
2. Heat Exchanger.
3. Expander.
4. Refrigerator.
Work gained from Expanderis used
to drive Compressor.
Hence, less external work is required.
Heat ExchangerCooling
Water
Refrigerator
CompressorExpander
Cold Air
Very Cold AirWarm Air
Hot Air
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
BellColeman / Reverse Bryaton Cycle
32
1
4
Isobars
Adiabatic
Expansion
Compression
Pressure
Volume
PV Diagram
3
2
1
4
Expansion
Compression
Tempera
tu
re
Entropy
Isobars
Adiabatic
TsDiagram
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
BellColeman / Reverse Bryaton Cycle
3
2
1
4
Expansion
Compression
Tempera
ture
Entropy
Isobars
Adiabatic
Heat Absorbed in Refrigerator :
)( 41 TTCmQ Padded
Heat Rejected in Heat Exchanger :
)( 32 TTCmQ Prejected
If process changes from Adiabaticto Polytropic;
11221
VPVPn
nQcomp
4433exp1
VPVPn
nQ n
We know,
1PCR
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
BellColeman / Reverse Bryaton Cycle
Net Work Done :
1234
4312
44331122
exp
1
1
1
1
TTTTCmn
n
TTTTRmn
n
VPVPVPVPn
n
WWW
P
ncomp
For Isentropic Process :
1234
exp
TTTTCm
WWW
P
ncomp
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
BellColeman / Reverse Bryaton Cycle
COP :
1234
41
1
1
)(
TTTTCmn
n
TTCm
W
Q
QQ
AddedWorkCOP
P
P
net
added
addedrejected
1234
41
1
1
)(
TTTTn
n
TTCOP
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Air Refrigeration Cycle - Merits / Demerits
Merits :
1. No risk of fire (as in case of NH3); as air is nonflammable.
2. Cheaper (than other systems); as air is easily available.
3. Weight per tonne of refrigeration is quite low (compared to other systems).
Demerits :
1. Low COP (compared with other systems).
2. Weight of air (as Refrigerant) is more (compared to other systems).
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 4
A BellColeman refrigerator operates between pressure limits of 1 bar and 8 bar. Air is
drawn from the cold chamber at 9 C, compressed and then cooled to 29 C beforeentering the expansion cylinder. Expansion and compression follow the law PV1.35= Const.
Calculate the theoretical COP.
For air, take = 1.4 and Cp= 1.003 kJ/kg.
Polytropic Compression 1-2 :
Kbar
barK
P
PTT
n
n
2.4821
8)282(
35.1
135.11
1
212
Polytropic Expansion 3-4 :
KT
bar
barTK
P
PTT
n
n
6.176
1
8)302(
4
35.1
135.1
4
1
4
343
3 2
14
PV1.35=C
Pr
essure
Volume
P2= 8 bar
P1= 1 bar
282 K
302 K
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Heat Extracted from Cold Chamber:kgkJKKXkgkJTTCP /7.105)6.176282()/(003.1)( 41
Example 4.contd
Heat Rejected to Heat Exchanger:
kgkJKKXkgkJTTCP /7.180)3022.482()/(003.1)( 32
Net Work Done :
kgkJW
KKKKkgkJW
TTTTCmn
nW
net
net
Pnet
/8.82
2822.4823026.176)/003.1(4.1
14.1
135.1
35.1
1
1 1234
27.1/8.82
/7.105
kgkJ
kgkJ
doneWork
absorbedHeatCOPrefrig .ANS
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 5
An air refrigeration open system operating between 1 MPa and 100 kPa is required to
produce a cooling effect of 2000 kJ/min. temperature of the air leaving the cold chamber is-5 C, and at leaving the cooler is 30 C. Neglect losses and clearance in the compressor
and expander. Determine :
i) Mass of air circulated per min. ii) Compressor Work, Expander Work, Cycle Work.
ii) COP and Power in kW required.
3 2
14
PV=C
Pre
ssure
Volume
P2= 1 MPa
P1= 100 kPa
268 K
303 K
Polytropic Expansion 3-4 :
KT
MPa
MPaTK
P
PTT
9.156
1.0
1)302(
4
4.1
14.1
4
1
4
343
Refrig. Effect per kg:
kgkJ
KKXkgkJ
TTCP
/66.111
)9.156268()/(003.1
)( 41
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 5.contd
min/91.17/66.111
min/2000
.Re
.Rekg
kgkJ
kJ
kgperEffectfrig
Effectfrig
Mass of air circulated per min :
.ANS
Polytropic Compression 1-2 :KkPa
kPa
KP
P
TT 4.517100
1000
)268(
4.1
14.11
1
2
12
.ANS
Compressor Work :
min/85.4486
2684.517)/287.0(min)/91.17(14.1
4.11
12
kJW
KKkgkJkgW
TTRmW
comp
comp
comp
.ANS
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Expander Work :
min/42.2628
9.156303)/287.0(min)/91.17(14.1
4.1
1 43exp
kJW
KKkgkJkgW
TTRmW
comp
comp
.ANS
Example 5.contd
Cycle Work = Wcycle= WcompWexp
= 4486.85 kJ/min2628.42 kJ/min = 1858.43 kJ/minANS
076.1min/43.1858
min/2000.Re kJkJ
requiredWorkEffectfrigCOPrefrig .ANS
Power required : kWkJ
time
WP
cycle97.30
minsec/60
min/43.1858 .ANS
i f i i Ai C i i i
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression System
Elements of this system :
1. Compressor.
2. Condenser.
3. Expansion Valve.
4. Evaporator.
Vapour @ Pr. and Temp. (State 1)
Isentropic Compression:
Pr. and Temp. (State 2)
Condenser : Pr. Liquid (State 3)
Throttling : Pr. Temp. (State 4)
Evaporator : Heat Extraction from surrounding;
Pr. vapour (State 1).
1
2
3
4
1
23
4
I d i R f i i d Ai C di i i
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression System
Merits :
1. High COP; as very close to Reverse Carnot Cycle.
2. Running Cost is 1/5th of that of Air Refrigeration Cycle.
3. Size of Evaporator is small; for same Refrigeration Effect.
Demerits :
1. Initial cost is high.
2. Inflammability.
4. Evaporator temperature adjustment is simple; by adjusting Throttle Valve.
3. Leakage.
4. Toxicity.
I t d ti t R f i ti d Ai C diti i
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression System : T-sDiagram
Case A. Dry and Saturated Vapour after Compression :
Work done by Compressor
= W = Area 1-2-3-4-1
Heat Absorbed
= W = Area 1-4-g-f-1
Entropy, s
Temperature,
T Condensation
Compression
Evaporation
Expansion
T2
T1
3
4
2
1
Compressor Work,
(W)
Net Refrig. Effect,(Rn)
Sat. Vapour L ine
Sat. Liq. Line
fg
12
41
14321
141
hh
hh
Area
fgArea
DoneWork
AbsorbedHeatCOP
I t d ti t R f i ti d Ai C diti i
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression System : T-sDiagram
Case B. Superheated Vapour after Compression :
Work done by Compressor
= W = Area 1-2-2-3-4-1
Heat Absorbed
= W = Area 1-4-g-f-1
12
41
143'221
141
hh
hh
Area
fgArea
DoneWork
AbsorbedHeatCOP
Entropy, s
Temperature,
T Condensation
Compression
Evaporation
Expansion
T2
T1
3
4
2
1
Compressor Work,
(W)
Net Refrig. Effect,(Rn)
Sat. Vapour L ine
Sat. Liq. Line
fg
2
NOTE : h2= h2 + Cp(TsupTsat)
I t d ti t R f i ti d Ai C diti i
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression System : T-sDiagram
Case C. Wet Vapour after Compression :
Work done by Compressor
= W = Area 1-2-3-4-1
Heat Absorbed
= W = Area 1-4-g-f-1
Entropy, s
Temperature,
T Condensation
Compression
Evaporation
Expansion
T2
T1
3
4
2
1
Compressor Work,
(W)
Net Refrig. Effect,(Rn)
Sat. Vapour L ine
Sat. Liq. Line
fg
12
41
14321
141
hh
hh
Area
fgArea
DoneWork
AbsorbedHeatCOP
NOTE : h2= (hf + x.hfg)2
Introd ction to Refrigeration and Air Conditioning
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression System : P-hDiagram
Enthalpy, h
Pressure,
P
r
Isothermal,
T=Const
Isenthalpic,
h=
Const.
Isobaric,
P = Const
Sub-cooled
L iq. region 2 phase
region
Superheated
region
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Introduction to Refrigeration and Air Conditioning
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Factors Affecting Vapour Compression System
A. Effect of Suction Pressure :
Enthalpy, h
Pressure,
Pr
1
23
4
14
2
P1
P212
41
hh
hh
W
RCOP n
COP of Original Cycle :
COP when Suction Pr. decreased :
2'2'1112
'1141
'1'2
'4'1
hhhhhh
hhhh
hh
hh
W
RCOP n
Thus,
Refrig. Effect Work Input COP
Introduction to Refrigeration and Air Conditioning
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Introduction to Refrigeration and Air - Conditioning
S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Factors Affecting Vapour Compression System
B. Effect of Delivery Pressure :
12
41
hh
hh
W
RCOP n
COP of Original Cycle :
COP when Delivery Pr. increased :
2'212
4'441
1'2
'41
hhhh
hhhh
hh
hh
W
RCOP n
Thus,
Refrig. Effect Work Input COP
Enthalpy, h
Pressure,
Pr
1
2
3
4
3
4
2
P1
P2
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Factors Affecting Vapour Compression System
C. Effect of Superheating :
12
41
hh
hh
W
RCOP n
COP of Original Cycle :
Thus,
Refrig. Effect Work Input or COP or
Enthalpy, h
Pressure,
Pr
1
23
4
1
2
P1
P2
1'12'212
1'141
'1'2
4'1
hhhhhh
hhhh
hh
hh
W
RCOP n
COP when Delivery Pr. increased :
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
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Factors Affecting Vapour Compression System
D. Effect of Sub-cooling :
12
41
hh
hh
W
RCOP n
COP of Original Cycle :
Thus,
Refrig. Effect Work Input : SAME
COP
12
'4441
12
'41
hh
hhhh
hh
hh
W
RCOP n
COP when Delivery Pr. increased :
Enthalpy, h
Pressure,
Pr
1
23
4
1
3
P1
P2
4
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
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Factors Affecting Vapour Compression System
E. Effect of Suction & Condenser Temperatures :
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Now, Condenser Temp. Evaporator Temp.
12
41
'1'4'3'2'1
1'44'11
hh
hh
Area
fgArea
DoneWorkAbsorbedHeatCOP
COP of Modified Cycle :
COP of Original Cycle :
12
41
14321
141
hh
hh
Area
fgArea
DoneWork
AbsorbedHeatCOP
COP Entropy, s
Temperature,
T Condensation
Compression
Evaporation
Expansion
T2
T1
3
4
2
1
fg
1
4
23
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Vapour Compression SystemMathematical Analysis
A. Refrigerating Effect :
)/(41 kgkJHeatdSuperheateHeatLatenthhQevap
= Amount of Heat absorbed in Evaporator.
B. Mass of Refrigerant :
= Amount of Heat absorbed / Refrigerating Effect.
)sec/(
3600
000,14
41
tonnekghh
m
1 TR = 14,000 kJ/hr
C. Theoretical Piston Displacement := Mass of Refrigerant X Sp. Vol. of Refrigerant Gas (vg)1.
)sec/(
3600
000,14.. 3
141
tonnemvhh
DisplPistonTh g
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S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression SystemMathematical Analysis
)(
)/(
12
12
kWhhmP
kgkJhhW
theor
comp
a) Isentropic Compression :D. Theoretical Power Required :
)(1
)/(1
1122
1122
kWVPVPn
nmP
kgkJVPVPn
nW
theor
comp
a) Polytropic Compression :
E. Heat removed through Condenser :
)/(32 kgkJhhmQcond
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S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 7Example 6A refrigeration machine is required to produce ice at 0 C from water at 20 C. The
machine has a condenser temperature of 298 K while the evaporator temperature is 268K. The relative efficiency of the machine is 50 % and 6 kg of Freon-12 refrigerant is
circulated through the system per minute. The refrigerant enters the compressor with a
dryness fraction of 0.6. Specific heat of water is 4.187 kJ/kg.K and the latent heat of ice is
335 kJ/kg. Calculate the amount of ice produced on 24 hours. The table of properties if
Freon-12 is given below:
Temperature
(K)
Liquid Heat
(kJ/kg)
Latent Heat
(kJ/kg)
Entropy of Liquid
(kJ/kg)
298 59.7 138.0 0.2232
268 31.4 154.0 0.1251
hf1 = 31.4 kJ/kghfg1= 154.0 kJ/kg
hf2 = 59.7 kJ/kg
hfg2= 138.0 kJ/kg
hf3 = h4= 59.7 kJ/kg
m =6 kg/minrel=50 %
x2 = 0.6
Cpw= 4.187 kJ/kg.K
Latent Heat of ice = 335.7 kJ/kgGiven :
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Example 6.contd
Entropy, s
Tem
perature,
T298 K
268 K
3
4
2
1
Sat. Vapour L ine
Sat. Liq. Line
fg
kgkJhxhh fgf /8.1230.154)6.0(4.31111
kgkJhxhh fgf /2.1330.138)5325.0(7.5922 22
5325.0
268
0.1546.01251.0
298
0.1382232.0
2
2
1
1
112
2
22
111222
12
x
x
T
h
xsT
h
xs
sxssxs
ss
fg
f
fg
f
fgffgf
Isentropic Compression :1-2
kgkJhh f /7.5934
COP of Original Cycle :
82.6
/8.1232.133
/7.598.123
12
41
kgkJ
kgkJ
hh
hh
W
RCOP n
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
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oduc o o e ge o d Co d o g
S. Y. B. Tech. Prod Engg.
Example 6.contd
Actual COP = relX COPtheor= 0.5 X 6.82 = 3.41
Heat extracted from 1 kg of water at 20 C to form 1 kg of ice at 0 C :
kgkJ
kgkJ
CXKkgkJXkg
/74.418
)/(335
)()020()./(187.4)(1
Entropy, s
Temperatur
e,
T298 K
268 K
3
4
2
1
Sat. Vapour L ine
Sat. Liq. Line
fg
Now;
.ANS
hrsintonneXX
kg
kgkJ
kgkJXkgm
hhm
Xm
W
RCOP
ice
iceactualn
actual
24661.01000
2460459.0
min/459.0
41.3/74.418
)/(8.1232.133)(6
74.41841.3
12
)(
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
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g g
S. Y. B. Tech. Prod Engg.
Example 7
28 tonnes of ice from and at 0 C is produced per day in an ammonia refrigerator. The
temperature range in the compressor is from 25 C to -15oC. The vapour is dry andsaturated at the end of compression and an expansion valve is used. Assuming a
co-efficient of performance of 62% of the theoretical, calculate the power required to
drive the compressor. Take latent heat of ice = 335 kJ/kg.
Temp
(C)
Enthalpy (kJ/kg) Entropy of
Liquid(kJ/kg.K)
Entropy of Vapour
(kJ/kg.K)Liquid Vapour
25 100.04 1319.22 0.3473 4.4852
-15 -54.56 1304.99 -2.1338 5.0585
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
hf1 = -54.56 kJ/kghg1= 1304.99kJ/kg
hf2 = 100.04 kJ/kg
hg2= 1319.22 kJ/kg
hf3 = h4= 100.04 kJ/kg
Tcond =25 CTevap=-15 C
x2 = 1.dry saturated vapour
COPactual= 0.62 (COPtheor)
Latent Heat of ice = 335.7 kJ/kgGiven :
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g g
S. Y. B. Tech. Prod Engg.
91.823.119622.1319
04.10023.1196
12
41
hh
hhCOP ltheoreticaCOP of the Cycle :
Entropy, s
Temperatur
e,
T298 K
258 K
3
4
2
1
Sat. Vapour L ine
Sat. Liq. Line
fg
Example 7.contd
processcIsenthalpikgkJhh ...../04.10043
kgkJ
hxhh fgf
/23.1196
)56.54(99.1304)92.0()56.54(
)( 1111
92.0
1338.20585.5)1338.2(4852.4
2
1
1112
12
x
x
sxss
ss
fgfg
Isentropic Compression :1-2
kgkJhh g /22.131922
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g g
S. Y. B. Tech. Prod Engg.
Example 7.contd
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Actual COP = relX COPtheor
= 0.62 X 8.91
= 5.52
Entropy, s
Temperatur
e,
T298 K
258 K
3
4
2
1
Sat. Vapour L ine
Sat. Liq. Line
fg
Actual Rn= COPactualX Work done
= 5.52 X (h2h1)
= 5.52 X (1319.221196.23)
= 678.9 kJ/kg
Heat extracted from 28 tonnes of water at 0 C to form ice at 0 C :
)(sec/56.108
)(sec/3600)(24
)/(335)/(1000)(28
kWkJ
hrXhr
kgkJXtonnekgXkg
Mass of refrigerant : kg
kgkJ
kJ1599.0
)/(9.678
sec)/(56.108
Total Work done by Compressor :
)(sec/67.19
/)23.119622.1319()(1599.012
kWkJ
kgkJXkghhXmrefrig
.ANS
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g g
S. Y. B. Tech. Prod Engg.
Example 8
In a standard vapour compression refrigeration cycle, operating between an evaporator
temperature of -10 C and a condenser temperature of 40 C, the enthalpy of therefrigerant, Freon-12, at the end of compression is 220 kJ/kg. Show the cycle diagram on
T-s plane. Calculate:
1. The C.O.P. of the cycle.
2. The refrigerating capacity and the compressor power assuming a refrigerant flow
rate of 1 kg/min.
You may use the extract of Freon-12 property table given below:
Temp (C) Pr (MPa) hf(kJ/kg) hg(kJ/kg)
-10 0.2191 26.85 183.1
40 0.9607 74.53 203.1
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
hf1 = 26.85 kJ/kghg1= h1=183.1 kJ/kg
hf2 = 74.53 kJ/kg
hg2= 203.1 kJ/kg
hf3 = h4= 74.53 kJ/kg
Tcond =40 C
Tevap=-10 C
x1 = 1.dry saturated vapour
h2=220 kJ/kgGiven :
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S. Y. B. Tech. Prod Engg.
Example 8.contd
COP of Original Cycle :
94.2/1.1830.220
/53.741.183
12
41
kgkJ
kgkJ
hh
hh
W
R
COP
n
.ANS
Refrigerating Capacity :
min/57.108
/53.741.183)(141
kJ
kgkJXkghhm
.ANS
Compressor Power :
kW
kJ
kgkJXkghhm
615.0
min/9.36
/1.1830.220)(112
.ANS
Entropy, s
Temperatu
re,
T40 C
-10 C
3
4
2
1
Sat. Vapour L ine
Sat. Liq. Line
fg
2
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S. Y. B. Tech. Prod Engg.
Example 9
A Freon-12 refrigerator producing a cooling effect of 20 kJ/sec operates on a simple
cycle with pressure limits of 1.509 bar and 9.607 bar. The vapour leaves the evaporatordry saturated and there is no undercooling. Determine the power required by the
machine. If the compressor operates at 300 rpm and has a clearance volume of 3% of
stroke volume, determine the piston displacement of the compressor. For compressor
assume that the expansion following the law PV1.3= Constant.
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Temp
(oC)
Ps(bar)
vg
(m3/kg)
Enthalpy
hf
(kJ/kg)
Enthalpy
hg
(kJ/kg)
Entropy
sf
(kJ/kg)
Entropy
sg
(kJ/kg)
Specific
heat
(kJ/kg.K)
-20 1.509 0.1088 17.8 178.61 0.073 0.7082 ---
40 9.607 --- 74.53 203.05 0.2716 0.682 0.747
hf1 = 17.8 kJ/kghg1= h1=178.61 kJ/kg
hf2 = 74.53 kJ/kg
hg2= 203.05 kJ/kg
hf3 = h4= 74.53 kJ/kg
Tcond =40 C
Tevap=-20 C
x1 = 1.dry saturated vapour
h2=220 kJ/kgGiven :
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Example 9.contd
Refrigerating Capacity :
sec/192.0
/53.7461.1782041
kgm
kgkJXmkWhhm
KT
T
TTCss
ss
P
2.324
313ln747.0682.07082.0
ln
2
2
'2
2'21
21
Isentropic Compression :1-2
kgkJ
KKkgkJkgkJ
TTChh P
/4.211
0.3132.324./747.0)/(05.203
'22'22
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Entropy, s
Tempera
ture,
T313 K
253 K
3
4
2
1
Sat. Vapour L ine
Sat. Liq. Line
fg
2
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Example 9
.ANS
Power Required :
kW
kgkJXkghhm
29.6
/61.1784.211sec)/(192.012
Vol. Efficiency :
%6.87
509.1
607.903.003.01
1
13.1/1
/1
bar
bar
P
Pkk
n
S
dvol
Vol of Refrigerant
at Intake :
sec/02089.0)/(1088.0sec)/(192.0
3
3
mkgmXkg
vm g
Piston Displ. Vol. : 3
3
00477.0)(300876.0
min)(sec/60sec)/(02089.0
)(
.m
rpm
m
rpm
VolActual
vol
.ANS
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Entropy, s
Temperature,
T313 K
253 K
3
4
2
1
Sat. Vapour L ine
Sat. Liq. Line
fg
2
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S. Y. B. Tech. Prod Engg.
Example 10
A food storage locker requires a refrigeration capacity of 50 kW. It works between a
condenser temperature of 35 C and an evaporator temperature of -10 C. The refrigeratoris ammonia. It is sub-cooled by 5 C before entering the expansion valve. By the dry
saturated vapour leaving the evaporator. Assuming a single-cylinder, single-acting
compressor operating at 1000 rpm with stroke equal to 1.2 times the bore, determine :
1. The power required.
2. The cylinder dimensions.
Properties of ammonia are :
Sat.
Temp.
(oC)
Pr.(bar)
Enthalpy
(kJ/kg)
Entropy
(kJ/kg)
Sp. Vol.
(m3/kg)
Sp. Heat
(kJ/kg.K)
Liquid Vapour Liquid Vapour Liquid Vapour Liquid Vapour
-10 2.9157 154.056 1450.22 0.82965 5.7550 --- 0.417477 --- 2.49235 13.522 366.072 1488.57 1.56605 5.2086 1.7023 0.095629 4.556 2.903
ME0223 SEM-IV Applied Thermodynamics & Heat Engines
h1 = 1450.22 kJ/kg
h2 = 1488.57 kJ/kg
hf3 = 366.072 kJ/kg
Tcond =35 C
Tevap=-10 C
x1 = 1.dry saturated vapour
State 3 =Sub-cooled by 5 CGiven :
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Example 10.contd
kgkJ
kgkJkgkJ
TTChhh subcoolsatliqPf
/29.343
)/(30330856.405)/(07.366
34'3
KT
T
T
TCssss P
8.371
308ln903.22086.5755.5
ln
2
2
'2
2'2121
Isentropic Compression :1-2
kgkJ
KKkgkJkgkJ
TTChh P
/8.1673
0.3088.371./903.2)/(57.1488
'22'22
Entropy, s
Temper
ature,
T308 K
263 K
3
4
2
1Sat. Vapour L ine
Sat. Liq. Line
fg
2
3
303 K
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S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Example 10.contd
sec/04517.0
/29.34322.1450
)(50
/
)(50
41
kg
kgkJ
kW
kgkJhh
kWm
Mass of Refrigerant :
Compressor Power :
kW
kgkJXkg
hhm
1.10
/22.14508.1673)(04517.0
12
.ANS
Cylinder Dimensions :
mmL
mD
kgm
rpmDD
v
NLD
kgmg
228.0)19.0(2.1
19.0
/417477.0
60
)(1000)2.1(4604
sec)/(04517.03
22
.ANS
.ANS
Entropy, s
Tempe
rature,
T308 K
263 K
3
4
2
1Sat. Vapour L ine
Sat. Liq. Line
fg
2
3303 K
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S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Absorption System
1
2
4
3
Solubility of NH3in water @ Temp and Pr.is MOREthan that @ Temp. and Pr.
NH3vapour from Evaporator(State 1) is readily absorbed in Absorber. Heat Rejection
This solution is then pumped to Temp. and Pr. @Generator.
Reduction in stability of solution Vapour removed from Solution.
Vapour passes to Condenser.
Weak Solution returns to Absorber.
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S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Absorption System
Merits :
2. Work done on Compression is LESS.
1. Pumping work is much less than work for Compressing vapour.
Demerits :
2. Low COP.
1. Heat input to the Generator is required.
COP :
PumpLiquidondoneWorkGeneratorinpliedHeat
EvaporatorinextractedHeatCOP
sup
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S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines
Vapour Compression Vs. Vapour Absorption
Sr.No.
Particulars Vapour CompressionSystems
Vapour AbsorptionSystems
1. Type of Energy Supplied Mechanical High Grade Heat Low Grade2. Energy Supply Rate Low High3. Wear & Tear More Less4. Performance of Part
Load Poor Not affected at Part Load5. Suitability Used where High Grade Mechanical
Energy is available
Can be used at Remote
Places, as can be used with
simple Kerosene lamp
6. Charging of Refrigerant Simple Difficult7. Leakage More chances No chances, as no Compressor
or Reciprocating Part
8. Damage Liquid traces in Suction Linemay damage Compressor
No danger
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Thank You !