Week 2 Air standard Cycle

AIM: To write a program that can solve an otto cycle and make plots for it.

THEORY: An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine.The Otto cycle is a description of what happens to a mass of gas as it is subjected to changes of pressure, temperature, volume, addition of heat, and removal of heat.

This is the Ideal otto cycle diagram

OBJECTIVE: To write the program to solve the otto cycle and make plots for it

1) Program to create PV diagram

2) Calculate thermal efficiency of the engine

PROCEDURE:

The program to solve the otto cycle is

# otto cycle

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,cr,start_cranck,end_crank):
"""
Engine kinematics
"""

#Geometric parameters
a=stroke/2
R=con_rod/a

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

sc=math.radians(start_cranck)
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=1/2*(cr-1)
term2=R+1-math.cos(theta)
term3=pow(R,2)-pow(math.sin(theta),2)
term4=pow(term3,1/2)

V.append((1+term1*(term2-term4))*V_c)

return(V)

#Inputs
p1=101525
t1=475
gama=1
t3=2100

#Geometric prametres
bore=2/5
stroke=1/5
con_rod=4/25
cr=8

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

#State point 2
v2=v_c

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

#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,gama)
P_compression=[]

for v in V_compression:
P_compression.append(constant/pow(v,gama))

#State point 3
v3=v2

#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,gama)
P_expansion=[]

for v in V_expansion:
P_expansion.append(constant/pow(v,gama))

#State point 4
v4=v1

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

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

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()

RESULT: The PV diagram of the otto cycle from the python program is given below.

CONCLUSION: By using the program the otto cycle has been solved and the PV diagram of the cycle is shown.