Week 2 Air standard Cycle

import math
import matplotlib.pyplot as plt
def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):
    r = stroke/2
    n = con_rod/r
    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-1)
    V = []
    for i in range (0,num_values):
        theta = sc+(i*dtheta)
        term1 = 0.5*(cr-1)
        term2 = n+1-math.cos(theta)
        term3 = (pow(n,2)-pow(math.sin(theta),2))
        term3 = pow(term3,0.5)
        V.append((1+term1*(term2-term3))*v_c)
    return V
P1 = int(input('Enter the pressure at 1st stage (in Pa):'))
T1 = int(input('Enter the temperature at 1st stage (in K):'))
gamma = float(input('Enter the specific heat ratio:'))
T3 = int(input('Enter the temperature at 3rd stage (in K):'))
bore = float(input('Enter the bore diameter (in m):'))
stroke = float(input('Enter the stroke length (in m):'))
con_rod = float(input('Enter the length of the connecting rod (in m):'))
cr = int(input('Enter the compression ratio:'))
v_swept = (math.pi/4)*pow(bore,2)*stroke
v_clearance = v_swept/(cr-1)
V1 = v_swept+v_clearance
V2 = v_clearance
P2 = P1*pow(cr,gamma)
T2 = P2*V2*T1/(P1*V1)
V_comp = engine_kinematics(bore,stroke,con_rod,cr,180,0)
C_const = P1*pow(V1,gamma)
P_comp = []
for v in V_comp:
    P_comp.append(C_const/pow(v,gamma))
V3 = V2
P3 = P2*T3/(T2)
V_exp = engine_kinematics(bore,stroke,con_rod,cr,0,180)
C_const = P3*pow(v,gamma)
P_exp = []
for v in V_exp:
    P_exp.append(C_const/pow(v,gamma))
V4 = V1
P4 = P3*pow(V3,gamma)/pow(V4,gamma)
T4 = P4*V4*T3/(P3*V3)
plt.figure()
plt.plot([V2,V3],[P2,P3])
plt.plot(V_exp,P_exp)
plt.plot([V4,V1],[P4,P1])
plt.plot(V_comp,P_comp)
plt.xlabel('Volume (m^3)')
plt.ylabel('Pressure (in Pa)')
plt.title('PV diagram of Otto cycle')
plt.grid()
plt.show()

CODING THE OTTO CYCLE SIMULATOR:

1. Import 'math' and matplotlib.pyplot' as plt respectively.
2. Define the 'engine_kinematics' function using 'def' command and declare all the required variables.
3. Enter the expressions used to calculate each variable respectively and the conditions for whicht the calculations have to be done.
4. Give the inputs required to obtain the PV graph and thermal efficiency of the cycle by using the 'input','int' and 'float' command.
5. Define the expressions required to calculate pressure, volume and temperature at all the stage points and thermal efficiency of the given cycle
6. By using the 'plt' command, plot the obtained volumes and pressures. and enter 'plt.show()' to display the graph

RESULTS:

Given inputs of the cycle and Thermal Efficiency

P-V Diagram of the given Otto Cycle