More Thermodynamic Cycles
P M V Subbarao
Professor
Mechanical Engineering Department
The Engineering Systems for High end Extrasomatic Needs…
Brayton Cycle for Power Generation
1-2 Adiabatic compression (in a compressor)
2-3 Constant pressure heat addition
3-4 IAdiabaticexpansion (in a turbine)
4-1 Constant pressure heat rejection
Thermodynamic Analysis of Adiabatic Compression
m 1  h1  m 2  h2  WComp
  2

m 1  h1  m 2  h2    m  vdp 
1


For an infinitesimal compression:
 h  m
  h  dh   m
 vdp
m
m  dh  m vdp
c p dT  vdp
Model for infinitesimal Adiabatic Process by a
perfect Gas
 dT    1  dp 
 
 
  p
 T 
 1
ln T 
ln p  ln C



 T 
ln   1   ln C
p  


T
p
 1

  1 
ln T  ln  p   ln C




1
C
Tp

C
Finite Compression of Perfect gas
1
Tp

pv  C
C
  2

m  h1  m  h2    m  vdp 
1


  2 dp 
m  h1  m  h2    m  C 1 

 
1
p 


 
 p
m  h1  m  h2    m C
 1 


1 1 p2


 

 p
Wcomp  m h1  h2     m C
 1 


p1
1 1 p2

p1
Constant Pressure Heat Addition (combustion)
Adiabatic Expansion

 

 p
Wturb  m h3  h4     m C
 1 


1 1 p4

p3
Cycle Analysis
1 –2 : Specific work input :
wcomp  h2  h1  c p (T2  T1 )
2 – 3 : Specific heat input :
qin  h3  h2  c p (T3  T2 )
3 – 4 : Specific work output :
wtur  h3  h4  c p (T3  T4 )
4 – 1 : Specific heat rejection :
qout  h4  h1  c p (T4  T1 )
Adiabatic Processes:
T2  p2 
  
T1  p1 
 1

T3  p3 
  
T4  p4 
 1

wnet  wtur  wcomp  h3  h4   h2  h1 
wnet  c p (T3  T4 )  (T2  T1 )
wnet


T3
 c p (T3  )  ( T1  T1 )



   1 

  T1 (   1)
 c p T3 
   


 T3

wnet  c p (T3  T1 )    T1 



qin  h3  h2  c p (T3  T1 )
wnet
th 
qin
wnet
th 
qin

 T3

c p (T3  T1 )    T1 




c p T3  T1
T3

c p   T1 



 1
c p T3  T1
 1
1
 1

rp
 1
1

Pressure Ratio Vs Efficiency
th
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
rp
20
30
Reciprocating IC Engine : A Heat Engine
Qout
Qin
Wout
Greatness of Heat Engines


in
i
i
Qi 1   iWi 1
Qi 1   i Qi 1   iWi 1   iWi 1
out
in
out
• Balance Sheet for A Heat Engine:
– All heat inputs consume resources : Total Input Heat :
Qin (Cost incurred).
– All heat outputs are just mere a loss.
– Net work Out put is positive and this is the final
benefit : Wnet (Benefit Achieved)
– Performance : Benefit to cost ratio (in energy units).
Otto’s Engine for Propulsion
Modification of Brayton Cycle for Air Craft
Propulsion : Invented by Frank Whittle
Large Aircrafts : Boeing 747
Physical Properties of Standard
Atmosphere
Altitude Temperature
Pressure
(meters)
(K)
(kPa)
0
288.15
101.3
1,000
281.65
89.87
2,000
275.15
79.49
3,000
268.65
70.10
4,000
262.15
61.64
5,000
255.65
54.02
6,000
249.15
47.18
7,000
242.65
41.06
8,000
236.15
35.59
9,000
229.65
30.74
10,000
223.15
26.43
12,000
216.65
19.33
15,000
216.65
12.04
Air Craft Engine Bleed for Refrigeration System
Air Standard Refrigeration Cycle for Aircraft
Cooling
Air Craft Engine Refrigeration System
Air to Cabin
Gas Refrigeration Systems
•The gas power cycle can be used as refrigeration cycles by
simply reversing them.
•Of these, the reversed Brayton cycle, which is also known as
the gas refrigeration cycle, is used to cool aircraft.
• Further Modification this cycle is used to obtain very low
(cryogenic) temperatures.
•The work output of the turbine can be used to reduce the
work input requirements to the compressor.
•Thus, the performance index of a gas refrigeration cycle is
defined as
qL
qL
COPR 

wnet , in wcomp , in  wturb , out
More Cycles for Exotic Needs of Urban World …….
An Urban world that was present till the end of first
decade of the 20th century.
• Only fresh foods that could be grown locally were available,
and they had to be purchased and used on a daily basis.
• Meat was bought during the daily trip to the butcher's; the
milkman made his rounds every morning.
• If you could afford weekly deliveries of ice blocks—harvested
in the winter from frozen northern lakes—you could keep
some perishable foods around for 2 or 3 days in an icebox.
• New York was a virtual ghost town in the summer months.
• Homes were built with natural cooling in mind.
• Ceilings were high, porches were deep and shaded, and
windows were placed to take every possible advantage of
cross-ventilation
Urban Life after the end of first decade of the 21st
century.
• Frozen foods of all kinds were available just about
anywhere in the world all year round.
• The milkman was all but gone and forgotten, and the
butcher now did his work behind a counter at the
supermarket.
• Indeed, many families concentrated the entire week's food
shopping into one trip to the market, stocking the
refrigerator with perishables that would last a week or
more.
• New York is a busy town even in the summer months.
• Buildings are totally isolated from fresh air.
Creation of Artificial Temperature/Quality
Why not use the reversed Rankine cycle for Refrigeration ?
• Very costly to expand the liquid using a turbine with very low
or negligible power output!?!
• May become negative under friction.
• Cheaper to have irreversible expansion through an expansion
valve.
Thermodynamics of Ideal VCR Cycle
• Ideal Vapor-Compression Refrigeration Cycle
• Process
Description
• 1-2
Adiabatic compression
• 2-3
Constant pressure heat rejection in the condenser
• 3-4
Throttling in an expansion valve
• 4-1
Constant pressure heat addition in the evaporator
Performance Index
The performance of refrigerators and heat pumps is expressed in
terms of coefficient of performance (COP), defined as
Desired output Cooling effect
QL
COPR 


Required input
Work input
Wnet ,in
Desired output Heating effect
QH
COPHP 


Required input
Work input
Wnet ,in
Under the same operating conditions, the COPs are related by
COPHP  COPR  1
Samsung Split A/c Model No : AQ24UUA
Cooling Capacity : 7.03kW
Power Consumption (Cooling) : 2,600Watts
Refrigerant Type R22
The refrigerant leaves the evaporator at 7.2oC
Condenser pressure : 2.71 MPa.
Heat Pump Systems