Week 2 Air standard Cycle

"""
otto cycle simulator
By Himalaya Singh

"""
import math
import matplotlib.pyplot as plt
import numpy as np

def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):

"""
engine_kinematics
"""

#geometric parameters
#crank pin radius
a=stroke/2
R=con_rod/a

#volume comutation
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_value=50

dtheta=(ec-sc)/(num_value-1)

V=[]

for i in range(0,num_value):
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

bore=0.1
stroke=0.1
con_rod=0.15
cr=13

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

#state point 2
v2=v_c

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

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

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

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=p3v3/t3 | rhs=p3v3/t3 | p4v4/t4=rhs |

rhs=p3*v3/t3

t4=p4*v4/rhs
plt.figure(1)
plt.plot(V_compression,P_compression,label='Adiabatic compression')
plt.plot([v2,v3],[p2,p3],label='Constant volume heat addition')
plt.plot(V_expansion,P_expansion,label='Adiabatic expansion')
plt.plot([v4,v1],[p4,p1],label='Constant volume heat rejection')
plt.xlabel('volume')
plt.ylabel('pressure')
plt.legend()
plt.savefig('otto cycle pv diagram')
plt.show()

#thermal efficiency

eff=1-(1/pow(cr,(gamma-1)))
eff=str(eff*100)
print('thermal efficiency =' + eff + '%')