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OTTO CYCLE AND ITS PROCESS

The Otto cycle is the air standard cycle of the S.I Engine. It is named after Nikolaus A. Otto, a German   engineer, who first built a successful four - stroke SI Engine in 1876 using the cycle proposed by Frenchman Alphouse Beau de Rochas in 1862. In most spark Ignition Engines, the piston executes four   complete strokes within the cylinder, and the crankshaft completes two revolutions for each   thermodynamic cycle. These engines are called Four-stroke Internal combustion Engines.  




 Process 1-2 : Intake 

 The inlet valve is open, the piston moves to the right, admitting fuel-air mixture into the cylinder at   constant pressure.

 Process  2-3 : Compression

 Both the valves are closed, the piston compresses the combustible mixture to the minimum volume. 

 Process  3-4 : Combustion 

 The mixture is then ignited by means of a spark, combustion takes place, and there is an increase in   temperature and pressure. 

 Process  4-5 : Expansion 

 The products of the combustion do work on the piston which moves to the right, and the pressure and   temperature of the gases decrease.

 Process 5-6 : Blow - Down 

 The exhaust valve opens and the pressure drops to the initial pressure. 

 Process 6-1 : Exhaust 

 With the exhaust valve open, the piston moves inwards to expel the combustion products from the   cylinder at constant pressure. 




The series of processes are described above constitute a mechanical cycle, and not a thermodynamic cycle. The cycle is completed in four strokes of the piston. 

Air is compressed in process 1-2 reversibly and adiabatically. Heat is then added to air reversibly at constant volume in process 2-3. Work is done by air in expanding reversibly and adiabatically in process 3-4. Heat is then rejected by air reversibly at constant volume in process 4-1, and the system (air ) comes back to its initial state. Heat transfer processes have been substituted for the combustion and blow - down processes of the engine. The intake and exhaust processes of the engine cancel each other. 

Let m be the fixed mass of air undergoing the cycle of operations described above. 

Heat Supplied Q1 = Q2-3 = m Cv (T3-T2).

Heat Rejected Q2 = Q4-1 = m Cv (T4 - T1).

Efficiency N = 1- (Q2 / Q1)

                  N = 1- ((T4-T1) / (T3-T2))                                (1)

Process 1-2, 

                  T2 / T1 = (V1 / V2) ^ (Y-1)                                 (2)

Process  3-4, 

                  T3 / T4 = (V4 / V3) ^ (Y-1) = (V1 / V2) ^ (Y-1)      (3)

                   T2 / T1 = T3 / T4 

    or               T2 / T3 = T1 / T4 

                   (T2/T3)-1 = (T1 / T4) -1 

                     (T2 -T3) / (T1-T4) = T3 / T4 

From (3)

              ie,  (T2 -T3) / (T1-T4)  =  (V1 / V2) ^ (Y-1)  

                    (T4 -T1) / (T3 -T2 ) = (V2 / V1) ^ (Y-1) 

From (1) 

                                 N = 1 - (V2 / V1)^(Y-1)

or                          N otto = 1- (1 / rk^(y-1))

where rk is called the compression ratio and given by 

rk = Volume at the beginning of compression / Volume at the end of  the compression

rk  = V1 / V2 = v1 /v2

Work Output:

The net work output for an Otto cycle can be expressed,

Wnet = ( (p3V3 - p4V4) / (Y-1) ) - ( ( p2V2 - p1V1) / (Y-1) )

Now, 

v1 / v2 = V1 / V2 = rk , or V1 = V2rk =V4 

p2 / p1 = p3 / p4 = (V1 / V2)^Y = rk^y 

p3 / p2 = p4 / p1  = rp (say) 

W net = (p1V1 / (Y-1)) (rp-1)((rk^(y-1)) -1 ) 


Mean Effective Pressure, 

The mean effective pressure (m.e.p) of the cycle is given by ,

Pm = (Network output / Swept Volume) 

where swept volume = V1 - V2 = V2 (rk-1)

  

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