Week 2 Air standard Cycle

AIM : To write a program that solves and plots an Otto cycle, to obtain its PV Diagram and Thermal efficiency.

THEORY :

By using the below formula, the plot is obtained

(V/V_c)=1+ 1/2 (cr-1)[R+1-cos(theta)-(R^2-sin^2(theta)^1/2)]

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

where,

cr = is compression ratio

And in above condition

((P1*V1)/T1) = ((P2*V2)/T3)

PV^gamma = constant

where,

P = pressure

V = volume

T = temperature

PROCEDURE :

"""
Otto cycle simulator
"""

import math
import matplotlib.pyplot as plt

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

	#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=0.5*(cr-1)
		term2=R+1-math.cos(theta)
		term3=pow(R,2)-pow(math.sin(theta),2)
		term4=pow(term3,0.5)
		V.append((1+term1*(term2-term4))*V_c)	
	return V


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


#Geometric prametres
bore=0.1
stroke=0.1
con_rod=0.15
cr=10


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


#State point 2
v2=v_c


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

#p2v2/t2=p1v1/t1 
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 (heat addition takes place)
v3=v2

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

p4=p3*pow(v3,gamma)/pow(v4,gamma)
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.xlabel('V')
plt.ylabel('P')
plt.show()

TE=1-1/pow(cr,(gamma-1))
print("Thermal efficiency is",TE)

Using the code above, with the help of the video, the plot for otto cycle was obtained and the thhermal efficiency was calculated.

RESULT :

Thermal efficiency is 0.6018928294465027
[Finished in 28.2s]

CONCLUSION : The plot for Otto cycle was created using this program, and the thermal efficiency was also calculated.