Air standard cycles carnot, stirling, ericsson

1. Unit-1
AIR STANDARD CYCLES
S K Singh
Centre for Energy Studies
IIT Delhi
CARNOT CYCLE
STIRLING CYCLE
ERICSSON CYCLE
…..OTTO CYCLE
……DIESEL CYCLE
20-May-21

2. Air standard cycles
• Cycles using perfect gas as working medium
• Generally air- which behaves nearly as perfect gas
• Assumptions:
• working medium – perfect gas-throughout the cycle
• Fixed mass of air in closed system
• Cp and Cv remains constant
• No chemical change
• Reversible heat add and reject
• Compression & expansion- reversible adiabatic
• Negligible K.E and P.E
• Frictionless engine operation
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3. The Carnot Cycle
• Idealized thermodynamic cycle consisting of four reversible processes
(working fluid can be any substance):
• The four steps for a Carnot Heat Engine are:
 Reversible isothermal expansion (1-2, TH= constant)
 Reversible adiabatic expansion (2-3, Q = 0, THTL)
 Reversible isothermal compression (3-4, TL=constant)
 Reversible adiabatic compression (4-1, Q=0, TLTH)
1-2 2-3 3-4 4-1
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4. The Carnot Cycle (cont’d)
Work done by the gas =  PdV, i.e. area
under the process curve 1-2-3.
1
2
3
3
4
1
Work done on gas = PdV, area under the
process curve 3-4-1
subtract
Net work
1
2
3
4
dV>0 from 1-2-3
PdV>0
Since dV<0
PdV<0
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5. The Carnot Principles/Corollaries
1. The efficiency of an irreversible, i.e. a real, heat engine is always less than the
efficiency of a reversible one operating between the same two reservoirs. hth, irrev
< hth, rev
2. The efficiencies of all reversible heat engines operating between the same two
thermal reservoirs are the same. (hth, rev)A= (hth, rev)B
• Both of the above statements can be demonstrated using the second law (K-P
statement and C-statement). Therefore, the Carnot heat engine defines the
maximum efficiency any practical heat engine can (hope to) achieve.
• Thermal efficiency hth=Wnet/QH=1-(QL/QH) = f(TL,TH)
• Can you show that hth=1-(QL/QH)=1-(TL/TH).
• This relationship is often called the Carnot efficiency since it is usually
defined in terms of a Carnot Heat Engine .
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6. Carnot Efficiency
Consider an ideal gas undergoing a Carnot cycle between two temperatures TH
and TL.
 1 to 2, isothermal expansion, DU12 = 0
QH = Q12 = W12 = PdV = mRTHln(V2/V1) (1)
 2 to 3, adiabatic expansion, Q23 = 0
(TL/TH) = (V2/V3)k-1 (2)
 3 to 4, isothermal compression, DU34 = 0
QL = Q34 = W34 = - mRTLln(V4/V3) (3)
 4 to 1, adiabatic compression, Q41 = 0
(TL/TH) = (V1/V4)k-1 (4)
From (2) & (4): (V2/V3) = (V1/V4)  (V2/V1) = (V3/V4)
Since ln(V2/V1) = - ln(V4/V3); substituting for ln(V4/V3) in (1)
 (QL/QH )= (TL/TH)
Hence: hth = 1-(QL/QH )= 1-(TL/TH)
It has been proven that hth = 1-(QL/QH )= 1-(TL/TH) for all Carnot engines since
the Carnot efficiency is independent of the working substance.
Example: A typical steam power plant operates between TH=800 K (boiler) and
TL=300 K(cooling tower). For this plant, the maximum achievable efficiency is
62.5%.

7. Factors which affect Carnot Efficiency
Example: Consider a Carnot heat engine operating between a high-
temperature source at 900 K and rejecting heat to a low-temperature reservoir
at 300 K. (a) Determine the thermal efficiency of the engine; (b) Show how the
thermal efficiency changes as the temperature of the high-temperature source
is decreased; (b) Determine the change in thermal efficiency as the
temperature of the low-temperature sink is decreased
h
h
h
th
L
H
th H
H
th H
L
T
T
K
T
T
K
T
T
     

 

 
1 1
300
900
0 667 66 7%
300
1
300
900
1
900
. .
( )
( )
( )
( )
Fixed T and lowering T
The higher the temperature, the higher the "quality"
of the energy: More work can be done
Fixed T and increasing T
L H
H L
200 400 600 800 1000
0
0.2
0.4
0.6
0.8
1
Temperature (TH)
Efficiency
Th( )
T
T
200 400 600 800 1000
0
0.2
0.4
0.6
0.8
1
Temperature (TL)
Efficiency
TH( )
TL
TL
Lower TH
Increase TL
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8. Carnot Efficiency & Quality of Energy
• The previous example illustrates that higher the
temperature of the low-temperature sink, more difficult it
becomes for a heat engine to reject/transfer heat into it.
• This results in a lower thermal efficiency
• One reason why low-temperature reservoirs such as rivers, lakes and
atmosphere are popular for heat rejection from power plants.
• Similarly, the thermal efficiency of an engine, e.g a gas
turbine engine, can be increased by increasing the
temperature of the combustion chamber.
•This may sometimes conflict with other design requirements. Example:
turbine blades can not withstand high temperature (and pressure) gases,
which can leads to early fatigue. A Solution: better materials and/or
innovative cooling design.
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9. Quality of Energy.. Contd..
•This illustrates that the quality of energy is an important
factor in determining the efficiencies of systems. E.g. for the
same amount (quantity) of total energy, it is easier – more
efficient – to produce work from a high temperature reservoir
than a low temperature reservoir. Consequently, extracting
energy from low-temperature reservoirs such as rivers and
lakes is not very efficient. E.g. solar pond/lake have typical
efficiencies of around 5%
•Also, work is in general more valuable – of a higher quality -
relative to heat, since work can convert to heat almost with
almost 100% efficiency but not the other way around.
Energy becomes less useful when it is transferred to and
stored in a low-temperature reservoir.
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10. CYCLES HAVING SAME EFFICIENCY AS CARNOT CYCLE
• Carnot cycle,s mean effective pressure is low
• Modified carnot cycle: Stirling & Ericsson
(produces higher m.e.p)
• Like carnot cycle, operate between two
constant temperature reservoirs having
isothermal heat exchange with them
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11. The Stirling Cycle
• Process 1-2: Isothermal
expansion
• 2-3: Constant-volume
cooling
• 3-4: Isothermal
compression
• 4-1: Constant-volume
heating
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12. Efficiency of Stirling cycle
• Efficiency = RT1 loge (V2/V1 ) – RT3 loge (V3/V4 )
RT1 loge (V2/V1 )
Since V1 = V4 and V2= V3
Striling Efficiency = T1 – T2
T1
same as carnot efficiency ? ? Then difference ?
20-May-21

13. The Stirling Cycle
• Consists of 2 isothermal and two constant volume
process
• Heat rejection- heat add- at constant volume process,
which are irreversible. So the basic Stirling cycle is
externally irreversible.
• The Stirling cycle is made reversible and efficiency
equal to carnot efficiency is achieved by incorporating
a perfect heat exchanger into the system which
absorbs the heat rejected during the constant volume
process and supplies it back to the cycle during
constant volume process. Then two processes taken
together are adiabatic.
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14. The Stirling Engine
• First developed in 1816 by Reverend Dr. Robert
Stirling
• After development, had little use until the mid
1900’s, when it became more common but later
abandoned in favor of Otto and diesel cycle
• Stirling engine involved difficulties in design and
construction of heat exchanger to operate
continuously at very high temp (around 2500oC)
• However, due to latest research in metallurgy –
this engine has attained a comeback and
acquired practical importance
20-May-21

15. The Stirling Engine: some applications
• Main application of the Stirling cycle
• Uses pistons and cylinders to rotate a
crankshaft
• Two types/configurations – Alpha and Beta
• Alpha Stirling engines use two cylinders and
two pistons
• Beta Stirling engines use one cylinder, one
piston and a “displacer”
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16. Stirling engine : Contd…
• Mechanically very simple in comparison to
internal combustion engines
• Lightweight, compact
• Not limited by fuel or heat source
• Aside from a longer warm-up time, reliable in
cold weather (unlike some engines)
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17. Stirling engine: Conclusions
• Low torque
• In order to be more efficient, it requires
metals with very high thermal conductivity,
which can be expensive
• Rotation is not always smooth – the fluid
sometimes heats up faster than it cools off
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18. Alpha Stirling Engine
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19. Beta Stirling Engine
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20. Applications contd..
• This one runs
off of body heat
• Probably no real
application, just
cool
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21. Applications contd..
• Solar Stirling
engine
• Uses reflected
sun rays as heat
source
• Green energy
• Could power a
house
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22. Applications contd..
• Very large
solar Stirling
engine
• Could
probably
power a small
city
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23. Applications contd..
• Theoretical solar
Stirling engine
• Uses residual heat
produced from a
solar panel sitting
in the sun as heat
source
• Converts the
unused heat into
electrical energy
that can be used
20-May-21

24. ERICSSON CYCLE:
John Ericsson (1803-89)
• The Ericsson cycle consists of
two isothermal and two
constant pressure processes.
• The processes are:
• Process A-B: Constant
pressure heat rejection
• Process B-C: Reversible
isothermal compression.
• Process C-D: Constant
pressure heat addition
• Process D-A: Reversible
isothermal expansion.
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25. ERICSSON CYCLE contd..
• Ericsson cycle is externally irreversible but by employing a
perfect heat exchanger, would produce a theoretically
reversible cycle.
• The Ericsson cycle does not find practical application in piston
engines but is approached by a gas turbine employing a large
number of heat exchangers, intercoolers and reheaters.
• The advantage of the Ericsson cycle over the Carnot and
Stirling cycles is its
• smaller pressure ratio for a given ratio of maximum to
minimum specific volume with higher mean effective
pressure.
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26. ERICSSON CYCLE DETAILS
• The Ericsson cycle comprises of two isothermal and two
constant pressure (isobaric) processes. The addition of heat
takes place during constant pressure as well as isothermal
processes.
1) Isothermal expansion and heat addition process D-A
During this process the air, which acts as a working fluid, is
heated from the externally added heat. The heat of the air
increases at constant temperature T1 and it expands. It is
during this process that the work is obtained from the engine.
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27. ERICSSON CYCLE
• 2) Constant pressure or isobaric heat rejection process A-B:
The air is then passed through the regenerator, where its
temperature reduces to T3 at constant pressure. The heat
absorbed by the regenerator is used for heating in the next
part of the cycle. The air after passing through the
regenerator is released as the exhaust gas.
• 3) Isothermal compression process B-C: During this process
the air drawn into the engine is compressed at constant
temperature, by applying an intercooler. The pressurized air is
then drawn into the air storage tank.
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28. ERICSSON CYCLE
• 4) Constant pressure or isobaric heat absorption process C-D:
The compressed air at high pressure passes through the
regenerator and absorbs the previously stored heat. It then
flows to the piston and cylinder where it gets expanded and
produces work during process 1-2. Thus the cycle keeps on
repeating.
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29. ERICSSON CYCLE
• The efficiency of Ericsson cycle is (T1-T3)/T1 or 1-T1/T3
• Where, T1 & T3 are the absolute temperatures measure in
Kelvin.
• Important Aspects of Ericsson Cycle
• The Ericsson engine based on Ericsson cycle is an external
combustion engine since the burning of the working fluid
occurs outside the engine. This is opposite to the internal
combustion (IC) engines in which the burning of fuel occurs
inside the engine.
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30. ERICSSON CYCLE
• Due to practical problems the principle of
Ericsson cycle is not used in the piston and
cylinder types of engines; rather it is used in
the gas turbines that have large number of
stages with a number of heat exchangers,
insulators and reheaters. The Ericsson cycle
can be most closely compared with the Stirling
cycle. Ericsson cycle is now more popularly
know as Brayton cycle.
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31. COMPARE: CARNOT, STIRLING,
ERICSSON CYCLE
• If the source and sink temperature is same
and equal specific volumes for all the above
cycles
• Work output is largest for stirling and smallest
for Carnot and work of Ericsson cycle is in
between striling and carnot
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