Week 2 Air standard Cycle
Aim :
Your code should create a PV diagram
Your should output the thermal efficiency of the engine.
Solution :
The code for the PV diagram is as follows :
import math
import matplotlib.pyplot as plt
#inputs
p1=101325
t1=500
gamma=1.4
t3=2300
#Geometric dimensions :
bore=0.1
stroke=0.1
con_rod=0.15
cr=12
#volume computation
v_s=(math.pi/4)*pow(bore,4)
v_c= v_s/(cr-1)
v1=v_c+v_s
print(v_s)
#state point 2
v2=v_c
# p2v2^gamma =p1v1^gamma
p2=p1*pow(v1,gamma)/pow(v2,gamma)
rhs=p1*v1/t1
t2= p2*v2/rhs
print(t2)
#state point 3
v3=v2
rhs=p2*v2/t2
p3=rhs*t3/v3
#State 4
v4=v1
p4 =p3*pow(v3,gamma)/pow(v4,gamma)
plt.plot([v1,v2,v3,v4,v1],[p1,p2,p3,p4,p1])
plt.show()We get the following graph :
The thermal efficiency is given by the following :
def enginekinematics(bore,stroke,con_rod,cr,start_crank,end_crank):
#inputs
p1=101325
t1=500
gamma=1.4
t3=2300
a=stroke/2
R=con_rod/a
sc=math.radians(start_crank)
ec=math.radians(end_crank)
n=10
dth=end_crank-start_crank/(n-1)
v_s=(math.pi/4)*pow(bore,4)
v_c= v_s/(cr-1)
v1=v_c+v_s
V=[]
for i in range(0,n):
theta=sc + i*dth
th1=0.5*(cr-1)
th2=R + 1 - math.cos(theta)
th3=pow(R,2) - pow(pow(math.sin(theta),2),0.5)
th3=pow(th3,0.5)
V.append((1+th1*(th2-th3))*v_c)
print(V)
return(V)
#inputs
p1=101325
t1=500
gamma=1.4
t3=2300
#Geometric dimensions :
bore=0.1
stroke=0.1
con_rod=0.15
cr=12
#volume computation
v_s=(math.pi/4)*pow(bore,4)
v_c= v_s/(cr-1)
v1=v_c+v_s
print(v_s)
#state point 2
v2=v_c
# p2v2^gamma =p1v1^gamma
p2=p1*pow(v1,gamma)/pow(v2,gamma)
rhs=p1*v1/t1
t2= p2*v2/rhs
vcompression=enginekinematics(bore,stroke,con_rod,cr,180,0)
constant=p1*pow(v1,gamma)
P_compression=[]
for v in vcompression:
P_compression.append(constant/pow(v,gamma))
print(t2)
#state point 3
v3=v2
rhs=p2*v2/t2
p3=rhs*t3/v3
#State 4
v4=v1
p4 =p3*pow(v3,gamma)/pow(v4,gamma)
plt.plot([v1,v2,v3,v4,v1],[p1,p2,p3,p4,p1])
plt.show()
We get the following :
