Short Notes: Air-Standard Otto, Diesel and Dual Cycles | Short Notes for Mechanical Engineering PDF Download

 Page 1


Air-Standard Otto, Diesel and Dual Cycles
Cycle: A cycle is defined as a repeated series of operations occurring in a certain 
order. In other words, any process or series of processes whose end states are 
identical termed as cycle.
Assumptions of Air Standard Cycle:
• Assume working medium as perfect gas (ideal gas).
• No change in mass of working period.
• Reversible processes.
• Supply of heat from a constant high temperature source (not from chemical 
reactions) and rejection of heal to a constant low temperature source.
• Not heat losses from the system to surroundings.
• Constant specific heats through the cycle.
Types of Cycles
Carnot Cycle: Carnot cycle is an ideal cycle in which all the processes constituting 
a reversible cycle. This cycle consists of two isothermal and two reversible 
adiabatic processes. •
• Process 1 - 2 is isothermal compression process
• Process 2 - 3 is adiabatic process (isentropic process)
• Process 3 - 4 is isothermal expansive process
Page 2


Air-Standard Otto, Diesel and Dual Cycles
Cycle: A cycle is defined as a repeated series of operations occurring in a certain 
order. In other words, any process or series of processes whose end states are 
identical termed as cycle.
Assumptions of Air Standard Cycle:
• Assume working medium as perfect gas (ideal gas).
• No change in mass of working period.
• Reversible processes.
• Supply of heat from a constant high temperature source (not from chemical 
reactions) and rejection of heal to a constant low temperature source.
• Not heat losses from the system to surroundings.
• Constant specific heats through the cycle.
Types of Cycles
Carnot Cycle: Carnot cycle is an ideal cycle in which all the processes constituting 
a reversible cycle. This cycle consists of two isothermal and two reversible 
adiabatic processes. •
• Process 1 - 2 is isothermal compression process
• Process 2 - 3 is adiabatic process (isentropic process)
• Process 3 - 4 is isothermal expansive process
Process 4 - 1 is adiabatic process (isentropic process)
All the processes are reversible.
where, 7 "i = Temperature at process 1, and 73 = Temperature at process 3.
Carnot cycle has a low mean effective pressure because of very low work output. 
The Stirling Cycle: It is modified form of Carnot cycle with high mean effective 
pressure. It consists of two isothermal and two constant volume processes.
p
1 isotherm al
* V ------ s
p - V diagram fe y Stirling cycte r.s d ia < )ra m (of S tir1 in g cycit
• Isothermal process:
1 — 2
3 ^ 4
• Constant volume process
2 ^ 3 
4 — 1
(same as Carnot cycle)
• In practical Stirling cycle, efficiency will be less than Carnot efficiency.
• For heat exchange efficiency:
J R(T3- T I)iog r
• ' • * r ; log( r - ( l - . E ) C v(T - T ;)
where, £ = Heat exchanger effectiveness.
The Ericsson Cycle: It consists of two isothermal and two constant pressure 
processes. The processes are
• Process 1-2 is reversible isothermal compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible isothermal expansion
• Process 4-1 is constant pressure heat rejection
The advantage of the Ericsson cycle is its small pressure ratio for given ratio of 
maximum to minimum specific volume with higher mean effective pressure. 
Ericsson cycle is applied by a gas turbine employing a large number of stages with 
heat exchangers, insulators and repeater
Page 3


Air-Standard Otto, Diesel and Dual Cycles
Cycle: A cycle is defined as a repeated series of operations occurring in a certain 
order. In other words, any process or series of processes whose end states are 
identical termed as cycle.
Assumptions of Air Standard Cycle:
• Assume working medium as perfect gas (ideal gas).
• No change in mass of working period.
• Reversible processes.
• Supply of heat from a constant high temperature source (not from chemical 
reactions) and rejection of heal to a constant low temperature source.
• Not heat losses from the system to surroundings.
• Constant specific heats through the cycle.
Types of Cycles
Carnot Cycle: Carnot cycle is an ideal cycle in which all the processes constituting 
a reversible cycle. This cycle consists of two isothermal and two reversible 
adiabatic processes. •
• Process 1 - 2 is isothermal compression process
• Process 2 - 3 is adiabatic process (isentropic process)
• Process 3 - 4 is isothermal expansive process
Process 4 - 1 is adiabatic process (isentropic process)
All the processes are reversible.
where, 7 "i = Temperature at process 1, and 73 = Temperature at process 3.
Carnot cycle has a low mean effective pressure because of very low work output. 
The Stirling Cycle: It is modified form of Carnot cycle with high mean effective 
pressure. It consists of two isothermal and two constant volume processes.
p
1 isotherm al
* V ------ s
p - V diagram fe y Stirling cycte r.s d ia < )ra m (of S tir1 in g cycit
• Isothermal process:
1 — 2
3 ^ 4
• Constant volume process
2 ^ 3 
4 — 1
(same as Carnot cycle)
• In practical Stirling cycle, efficiency will be less than Carnot efficiency.
• For heat exchange efficiency:
J R(T3- T I)iog r
• ' • * r ; log( r - ( l - . E ) C v(T - T ;)
where, £ = Heat exchanger effectiveness.
The Ericsson Cycle: It consists of two isothermal and two constant pressure 
processes. The processes are
• Process 1-2 is reversible isothermal compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible isothermal expansion
• Process 4-1 is constant pressure heat rejection
The advantage of the Ericsson cycle is its small pressure ratio for given ratio of 
maximum to minimum specific volume with higher mean effective pressure. 
Ericsson cycle is applied by a gas turbine employing a large number of stages with 
heat exchangers, insulators and repeater
The thermal efficiency of Ericsson, cycle is given by,
The Otto Cycle: The Otto cycle is a set of processes used by spark ignition internal 
combustion engines (2-stroke or 4-stroke cycles). Petrol engine works on the Otto 
cycle. In petrol engine, fuel burnt by spark ignition. It consists, two isentropic 
processes (reversible adiabatic) and two constant volume processes.
T - a d i a g r a m t o r O O c c y c t o
• Process 1-2 is reversible adiabatic compression of air
• Process 2-3 is heat addition constant volume.
• Process 3-4 is reversible isothermal expansion of air
• Process 4-1 is heat rejection at constant volume.
^ 7 afro
_ a - &
Q :
1
i r f -1
Compression ratio
where, Qs = Heat supplied during the isothermal process.
Q r = Heat rejected during the isothermal expression process 
Work Output (W): It can be measures as
( & - & ) = nm Qs
where, Qs = Heat supplied, and Q r = Heat rejected 
Heat supplied:
Qs = m Cy (Ts - T2)
Heat rejected:
Qr = mCv (T4 -Tf)
rr = {r - 1 ) (r1 ¦ E- 1 )
y -1 p
where, y = Specific heat ratio, and rp = Pressure ratio 
Pressure ratio:
Page 4


Air-Standard Otto, Diesel and Dual Cycles
Cycle: A cycle is defined as a repeated series of operations occurring in a certain 
order. In other words, any process or series of processes whose end states are 
identical termed as cycle.
Assumptions of Air Standard Cycle:
• Assume working medium as perfect gas (ideal gas).
• No change in mass of working period.
• Reversible processes.
• Supply of heat from a constant high temperature source (not from chemical 
reactions) and rejection of heal to a constant low temperature source.
• Not heat losses from the system to surroundings.
• Constant specific heats through the cycle.
Types of Cycles
Carnot Cycle: Carnot cycle is an ideal cycle in which all the processes constituting 
a reversible cycle. This cycle consists of two isothermal and two reversible 
adiabatic processes. •
• Process 1 - 2 is isothermal compression process
• Process 2 - 3 is adiabatic process (isentropic process)
• Process 3 - 4 is isothermal expansive process
Process 4 - 1 is adiabatic process (isentropic process)
All the processes are reversible.
where, 7 "i = Temperature at process 1, and 73 = Temperature at process 3.
Carnot cycle has a low mean effective pressure because of very low work output. 
The Stirling Cycle: It is modified form of Carnot cycle with high mean effective 
pressure. It consists of two isothermal and two constant volume processes.
p
1 isotherm al
* V ------ s
p - V diagram fe y Stirling cycte r.s d ia < )ra m (of S tir1 in g cycit
• Isothermal process:
1 — 2
3 ^ 4
• Constant volume process
2 ^ 3 
4 — 1
(same as Carnot cycle)
• In practical Stirling cycle, efficiency will be less than Carnot efficiency.
• For heat exchange efficiency:
J R(T3- T I)iog r
• ' • * r ; log( r - ( l - . E ) C v(T - T ;)
where, £ = Heat exchanger effectiveness.
The Ericsson Cycle: It consists of two isothermal and two constant pressure 
processes. The processes are
• Process 1-2 is reversible isothermal compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible isothermal expansion
• Process 4-1 is constant pressure heat rejection
The advantage of the Ericsson cycle is its small pressure ratio for given ratio of 
maximum to minimum specific volume with higher mean effective pressure. 
Ericsson cycle is applied by a gas turbine employing a large number of stages with 
heat exchangers, insulators and repeater
The thermal efficiency of Ericsson, cycle is given by,
The Otto Cycle: The Otto cycle is a set of processes used by spark ignition internal 
combustion engines (2-stroke or 4-stroke cycles). Petrol engine works on the Otto 
cycle. In petrol engine, fuel burnt by spark ignition. It consists, two isentropic 
processes (reversible adiabatic) and two constant volume processes.
T - a d i a g r a m t o r O O c c y c t o
• Process 1-2 is reversible adiabatic compression of air
• Process 2-3 is heat addition constant volume.
• Process 3-4 is reversible isothermal expansion of air
• Process 4-1 is heat rejection at constant volume.
^ 7 afro
_ a - &
Q :
1
i r f -1
Compression ratio
where, Qs = Heat supplied during the isothermal process.
Q r = Heat rejected during the isothermal expression process 
Work Output (W): It can be measures as
( & - & ) = nm Qs
where, Qs = Heat supplied, and Q r = Heat rejected 
Heat supplied:
Qs = m Cy (Ts - T2)
Heat rejected:
Qr = mCv (T4 -Tf)
rr = {r - 1 ) (r1 ¦ E- 1 )
y -1 p
where, y = Specific heat ratio, and rp = Pressure ratio 
Pressure ratio:
¦
m E i = E±
Pi Pi
Value of y (Ratio of Specific Heat):
• For monoatomic gas y = 1-67
• For air y = 1.40
• For exhaust gas y = 1 -30
Mean Effective Pressure: It is defined as the ratio of the net work done to the 
displacement volume of the piston.
Work output 
* ) < r ' Swept volume
Swept volume = V1 - V2 = V2 (r - 1)
P P ir .- l) (r1 -7 ‘ ll -1 
P" (7 -1 ) (r- 1)
where, pm = Mean effective pressure, rp = Pressure ratio, and y = Specific heat ratio. 
The Diesel Cycle: This cycle is used in diesel engine. In diesel engine, fuel is burnt 
by compressing the air up to high pressure. It consists of two isentropic processes, 
one constant volume process and one constant pressure process.
fh V diagram for chesef cydc T-s diagram for cyde
• Process 1-2 is reversible adiabatic compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible adiabatic compression
• Process 4-1 is constant volume heat rejection
tfd ie *; 1 , s |
A
701-1) J
Volume ratio or cut-off ratio:
V
v:
T3
f :
Compression ratio:
K
Work Output: Work output can be calculated by the following relation.
H'= pz (V,-Va )+
7-1
P g tjrP ^ O
7-1
rr =
, . t
Pix .r
i 7 - 1 i
IT ( r , - l ) - r *- (r. -D ]
7 - 1
Page 5


Air-Standard Otto, Diesel and Dual Cycles
Cycle: A cycle is defined as a repeated series of operations occurring in a certain 
order. In other words, any process or series of processes whose end states are 
identical termed as cycle.
Assumptions of Air Standard Cycle:
• Assume working medium as perfect gas (ideal gas).
• No change in mass of working period.
• Reversible processes.
• Supply of heat from a constant high temperature source (not from chemical 
reactions) and rejection of heal to a constant low temperature source.
• Not heat losses from the system to surroundings.
• Constant specific heats through the cycle.
Types of Cycles
Carnot Cycle: Carnot cycle is an ideal cycle in which all the processes constituting 
a reversible cycle. This cycle consists of two isothermal and two reversible 
adiabatic processes. •
• Process 1 - 2 is isothermal compression process
• Process 2 - 3 is adiabatic process (isentropic process)
• Process 3 - 4 is isothermal expansive process
Process 4 - 1 is adiabatic process (isentropic process)
All the processes are reversible.
where, 7 "i = Temperature at process 1, and 73 = Temperature at process 3.
Carnot cycle has a low mean effective pressure because of very low work output. 
The Stirling Cycle: It is modified form of Carnot cycle with high mean effective 
pressure. It consists of two isothermal and two constant volume processes.
p
1 isotherm al
* V ------ s
p - V diagram fe y Stirling cycte r.s d ia < )ra m (of S tir1 in g cycit
• Isothermal process:
1 — 2
3 ^ 4
• Constant volume process
2 ^ 3 
4 — 1
(same as Carnot cycle)
• In practical Stirling cycle, efficiency will be less than Carnot efficiency.
• For heat exchange efficiency:
J R(T3- T I)iog r
• ' • * r ; log( r - ( l - . E ) C v(T - T ;)
where, £ = Heat exchanger effectiveness.
The Ericsson Cycle: It consists of two isothermal and two constant pressure 
processes. The processes are
• Process 1-2 is reversible isothermal compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible isothermal expansion
• Process 4-1 is constant pressure heat rejection
The advantage of the Ericsson cycle is its small pressure ratio for given ratio of 
maximum to minimum specific volume with higher mean effective pressure. 
Ericsson cycle is applied by a gas turbine employing a large number of stages with 
heat exchangers, insulators and repeater
The thermal efficiency of Ericsson, cycle is given by,
The Otto Cycle: The Otto cycle is a set of processes used by spark ignition internal 
combustion engines (2-stroke or 4-stroke cycles). Petrol engine works on the Otto 
cycle. In petrol engine, fuel burnt by spark ignition. It consists, two isentropic 
processes (reversible adiabatic) and two constant volume processes.
T - a d i a g r a m t o r O O c c y c t o
• Process 1-2 is reversible adiabatic compression of air
• Process 2-3 is heat addition constant volume.
• Process 3-4 is reversible isothermal expansion of air
• Process 4-1 is heat rejection at constant volume.
^ 7 afro
_ a - &
Q :
1
i r f -1
Compression ratio
where, Qs = Heat supplied during the isothermal process.
Q r = Heat rejected during the isothermal expression process 
Work Output (W): It can be measures as
( & - & ) = nm Qs
where, Qs = Heat supplied, and Q r = Heat rejected 
Heat supplied:
Qs = m Cy (Ts - T2)
Heat rejected:
Qr = mCv (T4 -Tf)
rr = {r - 1 ) (r1 ¦ E- 1 )
y -1 p
where, y = Specific heat ratio, and rp = Pressure ratio 
Pressure ratio:
¦
m E i = E±
Pi Pi
Value of y (Ratio of Specific Heat):
• For monoatomic gas y = 1-67
• For air y = 1.40
• For exhaust gas y = 1 -30
Mean Effective Pressure: It is defined as the ratio of the net work done to the 
displacement volume of the piston.
Work output 
* ) < r ' Swept volume
Swept volume = V1 - V2 = V2 (r - 1)
P P ir .- l) (r1 -7 ‘ ll -1 
P" (7 -1 ) (r- 1)
where, pm = Mean effective pressure, rp = Pressure ratio, and y = Specific heat ratio. 
The Diesel Cycle: This cycle is used in diesel engine. In diesel engine, fuel is burnt 
by compressing the air up to high pressure. It consists of two isentropic processes, 
one constant volume process and one constant pressure process.
fh V diagram for chesef cydc T-s diagram for cyde
• Process 1-2 is reversible adiabatic compression
• Process 2-3 is constant pressure heat addition
• Process 3-4 is reversible adiabatic compression
• Process 4-1 is constant volume heat rejection
tfd ie *; 1 , s |
A
701-1) J
Volume ratio or cut-off ratio:
V
v:
T3
f :
Compression ratio:
K
Work Output: Work output can be calculated by the following relation.
H'= pz (V,-Va )+
7-1
P g tjrP ^ O
7-1
rr =
, . t
Pix .r
i 7 - 1 i
IT ( r , - l ) - r *- (r. -D ]
7 - 1
• Process 1-2 is reversible adiabatic compression
• Process 2-3 is constant volume heat addition
• Process 3-4 is constant pressure heat addition
• Process 4-5 is reversible adiabatic expansion
• Process 5-1 is constant volume heat rejection
T-s diagram (or Dual cyde
• Efficiency
Y Y* — 1
_______ p c A ________
(T _ ; - 1 ) + r _ ; /C ri - 1 )
• Work output
I7=l = -
• Mean effective pressure
7 r r (rc - 1)+ r' f ) ¦ - 1) - r(r r ( - 1)
Pm~ A (y - 1) (r - 1)
Comparison of Efficiencies in Cycles:
For same compression ratio and heat addition
’ 'a fr o ^ ^ V tju z t.
For same compression ratio and heat rejection
Same peak pressure, peak temperature and heat rejection
^ j.ffl ty r t u n l tfonc
Same maximum pressure and heat input
^ ' ni: '' ^ lo a o
Same maximum pressure and work output
W > V & * > % no