Air Standard Cycle

# ENGINE KINEMATICS

import math
import matplotlib.pyplot as plt

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

# Geaometric parameters

a = stroke / 2
R = con_rod / a

# Volume parameters
V_s = math.pi*(1/4)*pow(bore, 2)*stroke
V_c = V_s/(cr-1)

#Crank Angle gives us the idea about position of piston(either at TDC OR BDC)
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

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

# geometric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 12

# Value computation
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)

rhs = p1*v1/t1
t2 = p2*v2/rhs
V_compression = engine_kinematics(bore, stroke, con_rod, cr, 180, 0) # (180 -0) is compresison

constant = p1*pow(v1,gamma)

P_compression = []

for v in V_compression:
P_compression.append(constant/pow(v, gamma))
print("Pressure values during compression:")
print(P_compression)

# state point 3
v3 = v2

rhs = p2*v2/t2
p3 = rhs*t3/v3

V_expansion = engine_kinematics(bore, stroke, con_rod, cr, 0, 180) # (0-180) is expansion

constant = p3*pow(v3,gamma)

P_expansion = []

for v in V_expansion:
P_expansion.append(constant/pow(v, gamma))
print("Pressure values durig expansion:")
print(P_expansion)

# state point 4
v4 = v1

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

# p4v4/t4 = rhs
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.xlabel("Volume")
plt.ylabel("Pressure")
plt.show()

P-V Diagram