Week 2 Air standard Cycle

Aim:Air Standard Cycle (i.e.OTTO Cycle) analysis using PYTHON Programming.

Theory: The otto cycle is a air standard cycle which consists of 4 process.It has two isentropic process and two constant volume process.

For isentropic process 1-2 & 3-4,

p1*v1^n=p2*v2^n

where n=gamma=specific heat ratio

Formulas used:1.PV^gamma=constant

2.PV/T=constant

3.Swept Volume=pi/4*bore^2*stroke

4.Clearance Volume=Swept Volume/(cr-1)

5.Thermal Efficiency=1-1/(cr^gamma-1)

Problem Statement: 1.To write theprogram for PV diagram.

2.To give output as thermal efficiency.

Python Program:

"""OTTO CYCLE SIMULATOR"""

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):
	import math
	bore=.1
	stroke=.1
	con_rod=.15
	cr=8
	a=stroke/2
	R=con_rod/a

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

	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=.5*(cr-1)
		term2=R + 1 - math.cos(theta)
		term3=pow(R,2) - pow(math.sin(theta),2)
		term3=pow(term3,.5)

		V.append((1+ term1*(term2 - term3))*V_c)

	return V



#Inputs
p1=101325
t1=500
t3=2300
gamma=1.4

#Geometric Parameters
con_rod=.15
bore=.1
stroke=.1
cr=8

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

#State variables at point 2
v2=v_c

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

#p1v1/t1=p2v2/t2 | p1v1/t1=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 variables at point 3
v3=v2

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 variables at point 4
v4=v1

p4=p3*pow(v3,gamma)/pow(v4,gamma)

t4=p4*v4/rhs

#Calculation of thermal efficiency
k=pow(cr,gamma-1)
thermal_eff=1-(1/k)
efficiency=thermal_eff*100
print('Thermal Efficiency is:',efficiency,'%')

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()

Procedure:

1.First of all the input variables are assumed and then assigning of variables.

2.With the help of formulas different variables is find out at different state points.

3.A function is defined for simplicity of program.

4.Then thermal efficiency is calculated.

5.Finally the plot is obtained.

Result: PV Diagram:

Thermal Efficiency: