Week 2 Air standard Cycle

Variation of volume in cylinder:

Thermal efficiency of otto cycle:

where γ=1.4

"""
otto cycle simulator by Abhishek M B
"""
import math
import matplotlib.pyplot as plt
#Geometric Parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 8
def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):
    """
    Engine Kinematics
    """
    #Geometric Parameters
    a = stroke/2
    R = con_rod/a
    #Volume Parameters
    v_s = (math.pi/4)*pow(bore,2)*stroke
    v_c = v_s/(cr-1)
    sc = math.radians(start_crank)
    ec = math.radians(end_crank)
    num_values = 100
    dtheta = (ec - sc)/num_values
    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 #unit-pascal
t1 = 500
gamma = 1.4
t3 = 2300
#Volume 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
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))
#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))
#State Point 4
v4 = v1
p4 = p3*pow(v3,gamma)/pow(v4,gamma)
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(m^3)')
plt.ylabel('Pressure (10^5 Pa)')
plt.show()
#Thermal efficiency
Thermal_efficiency = 1 - (pow(cr,(1-gamma)))
print(Thermal_efficiency)