Otto Cycle Analysis

Otto Cycle 

Introduction

 
This section provides an Otto Cycle analysis when the working fluid is air. 

 

Analysis 
 

In the presented Otto Cycle analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value.  Ideal gas state equation is valid -- pv = RT. 
 

Air enters a cylinder at point 1 when compression starts and it ends at point 2.  Isentropic compression is considered with no entropy change.  Heat addition starts at point 2 and it ends at point 3.  At a constant volume, air gets heated and the working fluid temperature raises.  Expansion starts at point 3 and it ends at point 4.  Isentropic expansion is considered with no entropy change.  Air heat rejection starts at point 4 and it ends at point 1.   At a constant volume, air gets cooled and the working fluid temperature decreases.  It should be mentioned that air at point 1 enters the compression process again and the cycle is repeated. 
 

Figure 1 contains an Otto Cycle pressure vs volume diagram.   

Figure 1 - Otto Cycle Pressure vs Volume Diagram 


Figure 2 presents an Otto Cycle temperature vs entropy diagram.

Figure 2 - Otto Cycle Temperature vs Entropy Diagram 


Figure 3 presents the Otto Cycle efficiency as a function of the compression ratio.  It should be noted that the inlet conditions are standard ambient conditions:  temperature of 298 [K] and absolute pressure of 1 [atm]. 

Figure 3 - Otto Cycle Efficiency 


Figure 4 presents the Otto Cycle power output as a function of the combustion temperature and compression ratio.  It should be noted that the number of revolutions is 60 [1/s] for given geometry of the four cylinder and four stroke Otto engine. 

Figure 4 - Otto Cycle Power  Output 


One can notice that the Otto Cycle efficiency increases with an increase in the compression ratio values.  One can notice that the Otto Cycle power output increases with an increase in the combustion temperature.  The Otto Cycle power output is greater for the higher compression ratio values. 
 

Assumptions

 
Working fluid is air.  There is no friction.  Compression and expansion are isentropic -- there is no entropy change.  Ideal gas state equation is valid -- pv = RT.  Air behaves as a perfect gas -- specific heat has a constant value. 

 

Governing Equations 
 

T2/T1 = (V1/V2)^(ϰ-1)
V
1/V2 = (T2/T1)^1/(
ϰ-1)

T3/T4 = (V4/V3)^(ϰ-1)
V
4/V3 = (T3/T4)^1/(
ϰ-1)
ϰ = cp/cv
cp - cv = R
pv = RT
w = q
h - ql
qh = cv(T3 - T2)
q
l = cv(T4 - T1)
w = c
v(T3 - T2) - cv(T4 - T1)
W = (c
v(T3 - T2) - cv(T4 - T1))m
efficiency = 1 - 1/compression ratio^(
ϰ-1)
compression ratio = V
1/V2

 

Input Data 
 

T1 = 298 [K] 
p
1 = 1 [atm] 
T
3 =  1,200, 1,500 and 1,800 [K]

compression ratio = 2.5, 5, 7.5, 10 and 12.5 [/] 
R = 0.2867 [kJ/kg*K]
c
p = 1.004 [kJ/kg*K]  
 
ϰ = 1.4 [/] 
 

Results 
 

Otto Cycle Efficiency vs Compression Ratio 

Compression
Ratio
[/]

2.5

5

7.5

10

12.5

Otto Cycle
Efficiency
[%]

30.7

47.5

55.3

60.2

63.6

Otto Cycle Power Output

Power Output
[kW]

Compression Ratio
[/]

5

15

Combustion
Temperature
[K]

1,200

167.1

151.2

1,500

246.4

251.7

1,800

325.6

352.2

Conclusions 


The Otto Cycle efficiency increases with an increase in the compression ratio values.  Also, the Otto Cycle power output increases with an increase in the combustion temperature.  The Otto Cycle power output is greater for the higher compression ratio values. 
 

References 
 

JANAF Thermochemical Data - Tables, 1970 

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Last Update: November, 2019