Week 2 Air standard Cycle

Aim : To plot PV diagram for air standard otto cycle and calculate its thermal efficiency using python

Theory : The air-standard-Otto cycle is the idealized cycle for the spark-ignition internal
combustion engines.

The code is given below :

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):

	#geometric parameters

	a = stroke/2
	R = con_rod/a

	#volume computation
	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 = 50

	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)
	


#geometric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 7



#input
p1 = 101325
t1 = 500
gamma = 1.4
t3= 2300

v_s = (math.pi/4)*pow(bore,2)*stroke
v_c = v_s/(cr-1)


v1 = v_c + v_s

#state point 2
v2 = v_c

#+p2v2^gamma = p1v1^gamma
p2 = p1*pow(v1,gamma)/pow(v2,gamma)

#p2v2/t2 = p1v1/t1 | rhs = p1v1/t1 | rhs = p2v2/t2 | t2 = p2v2/rhs
rhs = p1*v1/t1
t2 = p2*v2/rhs
constant = p1*pow(v1,gamma)
V_compression = engine_kinematics(bore,stroke,con_rod,cr,180,0)
P_compression = []

for v in V_compression :
	P_compression.append(constant/pow(v,gamma))
#state point 3
v3 = v2

# p3v3/t3 = p2v2/t2 | rhs = p2v2/t2 | p3 = rhs*t3/v3

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))

#state point 4
v4 = v1

#p4v4/gamma = p3v3/gamma
p4 = p3*pow(v3,gamma)/pow(v4,gamma)

#p4v4/t4 = p3v3/t3

t4 = p4*v4/rhs


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()


#thermal efficiency
therm_eff = 1 - (1/pow((cr),(gamma-1)))
print ("Thermal efficiency of the given otto cycle is :", therm_eff)

PV diagram :

Thermal Efficiency calculation :

Conclusion :

PV diagram and thermal efficiency have been demonstrated.