Simulation of Otto cycle

The project is to write a python code which solves an Otto cycle problem, calculates the efficiency and makes a p-v diagram plot for it.

I have chosen a problem which has the pressure p1 = 0.1 Mpa, temperature t1 = 300K, t3 = 2800K, volume v1 = 0.5 m^3, compression ratio r = 8 and isentropic expansion factor gamma γ = 1.4 as the inputs for the problem. With the given inputs i had solved the problem to find p2,v2,t2,p3,v3,p4,v4 and the overall efficiency η.

The problem is solved by considering the equations for the particular processes,

1-2 isentropic expansion PV^γ = constant

2-3 constant volume heat addition V2=V3

3-4 isentropic compression PV^γ = constant

4-1 constant volume heat rejection V4=V1

Thus the efficiency calculated using the formula η = 1 - 1/(r^(γ-1)).

The P-V diagram is plotted using the appropriate pressure and volume values.

#simulation of otto cycle

import math

import matplotlib.pyplot as plt


#pressure p1 in Megapascal
p1 = 0.1

#compression ratio
r  = 8

#temperature t1 in kelvin
t1 = 300

#temperature t3 in kelvin
t3 = 2800

#volume v1 in m^3
v1 = 0.5

#gas constant
g = 1.4

#v2 
v2 = v1/r

n=10

volume = []
pressure = []

for i in range(0,n):
	tmp = v1 -i*((v1 -v2)/(n-1))
	volume.append(tmp)
	pressure.append(p1*(v1/tmp)**g)


#p2
p2 = p1*r**g

#t2
t2 = r**(g-1)*t1

#p3
p3 = (t3/t2)*p2

#v3
v3 = v2

#v4
v4 = v1

volume1 = []
pressure1 = []

for i in range(0,n):
	tmp1 = v3 + i*(v4-v3)/(n-1)
	volume1.append(tmp1)
	pressure1.append(p3*(v3/tmp1)**g)

#p4 
p4 = r**-g*p3


efficiency = 1-(1/r**(g-1))
efficiency = efficiency * 100

print ('p2 =',p2,'v2 =', v2, 'p3 =', p3, 'v3 =',v3,'p4 =',p4,'v4 =', v4)
print('thermal efficiency =', efficiency)

plt.figure()
plt.plot(volume,pressure)
plt.plot([v2,v3],[p2,p3])
plt.plot(volume1, pressure1)
plt.plot([v4,v1],[p4,p1])
plt.xlabel('volume')
plt.ylabel('pressure')
plt.show()

The pressure, volume and the efficiency are printed as output of the program.

p2 = 1.8379173679952558 v2 = 0.0625 p3 = 7.466666666666668 v3 = 0.0625 p4 = 0.4062569295381914 v4 = 0.5
thermal efficiency = 56.472471835193794
[Finished in 8.2s]

The plot of the P-V diagram is shown below in the Image below.