PV Diagram Of Otto Cycle With Its Efficiency

In an Ideal otto cycle four process occurs:

1 Isentropic Compression (PV^gamma=constant)

2 Isochoric or Constant Volume Heat Addition

3 Isentropic Expansion

4 Constant Volume Heat Rejection

We are given

P1=101325 pa

t1= 330k

gamma=1.4

Maximum temperature t3 =3500k

Bore and Stroke are both 0.5

Connecting rod length =0.25

Compression ratio=8

v_s is swept volume from BDC to TDC

v_c is clearence volume which is above TDC

Heat In - qin =t3-t2

Heat Out - qout =t4-t1

Thermal Efficiency is n_thermal=1-(q_out/q_in)

For compression crank angle goes from 180 to 0 and for expansion it goes 0 to 180

Conclusion : The PV Diagram of otto cycle and its thermal efficiency has been obtained.

import math
import matplotlib.pyplot as plt
def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):

	
			
	a=stroke/2
	R=con_rod/a
	v_s=math.pi*1/4*pow(bore,2)*stroke
	v_c=v_s/(cr-1)
	sc=math.radians(start_crank)
	ec=math.radians(end_crank)
	num_values=70
	dtheta=(ec-sc)/(num_values-1)
		
	V=[]
	for i in range(0,num_values):
		theta=sc+i*dtheta
				
		term1=0.5*(cr-1)
		term2=R+1-math.cos(theta)
		term3=pow(R,2)-pow(math.sin(theta),2)
		term3=pow(term3,0.5)
		V.append((1+term1*(term2-term3))*v_c)		
	return V
   
p1=101325
t1=330
gamma = 1.4
t3=3500
bore=0.5
stroke=0.5
con_rod=0.25
cr=8
v_s = (math.pi/4)*pow(bore,2)*stroke
v_c = v_s/(cr-1)
# For state point 2
v1=v_c+v_s
v2=v_c
p2=p1*pow(v1,gamma)/pow(v2,gamma)
rhs=p1*v1/t1
t2=p2*v2/rhs
V_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0)
constant=p1*pow(v1,gamma)
P_compression=[]
for V in V_compression:
	P_compression.append(constant/pow(V,gamma))
	# for state point 3
v3=v2
rhs=p2*v2/t2
p3=rhs*t3/v3
V_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,180)
constant=p3*pow(v3,gamma)
P_expansion=[]
for V in V_expansion:
	P_expansion.append(constant/pow(V,gamma))
	#for state point 4
v4=v1
p4=p3*pow(v3,gamma)/pow(v4,gamma)
t4=p4*v4/rhs
q_out=t4-t1
q_in=t3-t2
n_thermal=1-(q_out/q_in)
print(n_thermal)
plt.plot([v2,v3],[p2,p3])
plt.plot(V_compression,P_compression)
plt.plot(V_expansion,P_expansion)
plt.plot([v4,v1],[p4,p1])
plt.show()