Week 2 Air standard Cycle

1. The required libraries are imported
2. The function engine_kinematics was defined which calculates the volume
3. Outside the function block, the given parameters and the formulas to calculate the required values were coded
4. The function call was initiated for compression as well as expansion cycles with varying TDC and BDC
5. Then the thermal efficiency was calculated
6. At last, the PV diagram was plotted using matplotlib library

Results:

1. The PV diagram is plotted
2. The Thermal Efficiency is= 62.9892%

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):
    a=stroke/2
    R=con_rod/a

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

    #crank angle
    theta=math.radians(180)

    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)   #V/Vc eqn split into 3 terms
        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-state point-1
p1=101325 
t1=500
gamma=1.4

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

#Volume computation
v_s=(math.pi/4)*pow(bore,2)*stroke  #swept volume
v_c=v_s/(cr-1)  #clearance volume
v1=v_c+v_s

#state point-2
v2=v_c

#p2v2^gamma=p1v1^gamma
p2=p1*pow(v1,gamma)/pow(v2,gamma)   #Isentropic equation

#p2v2/t2=p1v1/t1 | rhs=p1v1/t1 | p2v2/t2=rhs | 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
t3=2300  #assumed temperature

#p3v3/t3=p2v2/t2 |rhs=p2v2/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

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

#p4v4/t4=p4v3/t3=rhs
t4=p4*v4/rhs

#Thermal Efficiency calculation
Efficiency= 1-((t4-t1)/(t3-t2))
print('Thermal Efficiency is=', Efficiency*100)

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()

PV Plot: