Week 2 Air standard Cycle

Aim:

To create a python program to solve an otto cycle, make plots for it and to output the thermal efficiency.

Main code:

"""
Engine kinematics Otto cycle

-Raaghul V
"""

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

    #volumetric parameters
    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

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

#Engine geometric parameters
bore=0.1
stroke=0.1
con_rod=0.15
cr=10

#volume calculation
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*v2^gamma=p1*v1^gamma
p2=p1*pow(v1,gamma)/pow(v2,gamma)

#p2v2/t2=p1v1/t1 | rhs=p1v1/t1 | t2= p2v2/rhs
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

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

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

#rhs=p4*v4/t4
t4=p4*v4/rhs

#thermal efficiency
n_otto=(1-(1/pow(cr,gamma-1)))*100
print(n_otto)

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()

Output:

For the compression ratio 10, the thermal efficiency is as 60.189282944650266.