# Gas Power Cycle - Internal Combustion Engine by pharmphresh28

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```									Gas Power Cycle - Internal Combustion Engine

Otto Cycle
Otto Cycle
P    3                                T                     3      • 1-2 isentropic compression
• 2-3 constant volume heat
transfer
4       2
2                                                              • 3-4 isentropic expansion
4
• 4-1 constant volume heat
1       1                        rejection
v                          s
Thermal efficiency of the system:
Wcycle       W34 + W12 m[( u3 − u4 ) + ( u1 − u2 )]    (u − u1 )
η=            =            =                             =1− 4
Qin            Q23           m( u3 − u2 )             ( u3 − u2 )
(u4 − u1 )      C (T − T1 )      T     T4 / T1 − 1 
For an ideal gas, u=C v T , η =1 −                     = 1− v 4          =1− 1                
( u3 − u2 )     Cv (T3 − T2 )    T2    T3 / T2 − 1 
Since T4 / T1 = T3 / T2 (why?)
T1
η = 1−      . From isentropic compression relation for an ideal gas
T2
γ −1
T1  V2                  1                V                                        cp
=                  =          , where r=  1  is the volume compression ratio, γ =
T2  V1 
                   r γ −1             V2                                      cv
Otto Cycle-2
100
Thermal efficiency of an Otto cycle,
80
thermal efficiency

1
60                                         η = 1 − γ −1
η( r )                                                      r
40
Typical value of r for a real engine:
20                                           between 7 and 10
0
0   3       6       9       12   15
r
compression ratio

• The higher the compression ratio, the higher the thermal
efficiency.
• Higher r will led to engine knock (spontaneous ignition)
problem.
Improvement of Performance
• Increase the compression ratio

• Increase the engine displacement: more power

• Compress more air into the cylinder during intake: using
supercharger and turbocharger.

• Cool the air before allowing it to enter the cylinder: cooler
air can expand more, thus, increase the work output.

• Reduce resistance during intake and exhaust stages: multiple
valve configuration: 4 cylinders/16 valves engine

• Fuel injection: do away with the carburetor and provide
precise metering of fuel into the cylinders.
Diesel Cycle
2-3: a constant pressure
P     2        3            T                            process (instead of a
3        constant volume process)
and is the only difference
2                        between an idealized
4
4        Diesel cycle and an
idealized Otto cycle.
1        1
v                        s
• Fuel injection for an extended period during the power stroke and therefore
maintaining a relatively constant pressure.
• Diesel cycle has a lower thermal efficiency as compared to an Otto cycle
under the same compression ratio.
• In general, Diesel engine has a higher thermal efficiency than spark-ignition
engine because the Diesel engine has a much higher compression ratio.
• Compression-ignition: very high compression ratio 10 to 20 or even higher.

Diesel Cycle                  Internal Combustion Engine
Thermal Efficiency of Diesel Cycle

• Introduce parameter β=V3/V2
• Show that the efficiency of an ideal Diesel cycle is:

1        βγ −1
η Diesel = 1 −
r γ −1   [γ ( β − 1)]

• It can also be shown that ηOtto > ηDiesel for the same
compression ratio. However, Diesel engines can usually
operate at higher compression ratio (Why?).
• If the maximum pressure is the same, the Diesel engine
has a higher efficiency than the Otto engine.
Dual Cycle
P 2.5   3
• Some heat is added at constant
volume (2 è 2.5)
2
4         • The remaining heat is added at
constant pressure (2.5 è 3)
1
v
• Define β=V3/V2.5, α=P3/P2

γ −1
1                  αβ γ − 1        
Show that: ηdual   =1−              (α − 1) + γα ( β − 1) 
r                                  

• It has an efficiency falling between the Otto and Diesel limits.

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