Week 2 Air standard Cycle

Aim: Write a Python program to solve an Otto cycle and make necessary plots.

Objectives :

Write a program to plot PV diagram.
Write a program to calculate the thermal efficiency.

Procedure:

1. Import the math and plot functions from the python library.
2. Define the function for the inputs in the separate section.
3. Provide values for the theta and open the for loop.
4. Give inputs.
5. Provide the compression and expansion values.
6. Plot the results.
7. Find the thermal efficiency.

Description:

Program :

import math
import matplotlib.pyplot as plt


def engine_kinematics(bore,stroke,con_rod,cr,c_s,c_e):

    a=stroke/2
    R=con_rod/a

    sc=math.radians(c_s)
    ec=math.radians(c_e)

    num_values=100
    dtheta=(ec-sc)/(num_values-1)
    v=[]

    for i in range(0,num_values):
        theta=sc+i*dtheta
        print(theta)

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

v1=v_s+v_c
v2=v_c

#State point 2
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
t3=p3*v3*t2/(p2*v2)


#state point 4
v4=v1
p4=p3*pow(v3,gamma)/pow(v4,gamma)

v_expansion=engine_kinematics(bore,stroke,con_rod,12,0,180)
constant=p3*pow(v3,gamma)

p_expansion=[]

for v in v_expansion:
    p_expansion.append(constant/pow(v,gamma))

plt.plot([v2,v3],[p2,p3])
plt.plot(v_compression,p_compression)
plt.plot([v4,v1],[p4,p1])
plt.plot(v_expansion,p_expansion)

plt.show()

#to calculate thermal efficiency
E=1-(t1/t2)
print(E)

Results:

The thermal efficiency of the provided air standard cycle= 62.98%

Conclusion:

For plotting the graph using python, we have to include functions. Since the curve is not linear during isentropic process, we have to find the expansion and compression values of pressure and volume, which is included in the function.