Week 2 Air standard Cycle

OBJECTIVE:

• To create the PV diagram of Otto Cycle for the given inputs such as engine dimensions, pressure, and temperature, using Python programming.
• To obtain the thermal efficiency of the engine.

CODE:

#otto cycle simulator

import math
import matplotlib.pyplot as plt

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

	#Engine kinematics function


	#Geometric parameters

	a=stroke/2  #crank pin radius
	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_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=0.5*(cr-1)
		term2=R+1-math.cos(theta)
		term3=pow(R,2)-pow(math.sin(theta),2)
		term3=pow(term3,0.5)

		#volume trace

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


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

#geometric parameters
bore=0.1
stroke=0.1
con_rod=0.15
cr=12

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

#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,gamma)

P_compression=[]

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

#P_compression*V_compression^gamma=comstant

#state point3
v3=v2

#p3v3/t3=p2v2/t2 | rhs=p2v2/t2 |p3=rhs*t3/v3
rhs=p2*v2/t2
p3=rhs*t3/v3

#print(p3>p2)

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 point4

v4=v1

#p4v4^gamma=p3v3^gamma

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

#p4v4/t4=p3v3/t3
#p4v4/t4=rhs

t4=p4*v4/rhs

plt.plot([v2,v3],[p2,p3],label='const vol heat addition')
plt.plot(V_compression,P_compression,label='isentropic compression')
plt.plot(V_expansion,P_expansion,label='isentropic expansion ')
plt.plot([v4,v1],[p4,p1],label='const vol heat rejection')
plt.xlabel('Volume (m^3)')
plt.ylabel('Pressure (Pa)')
plt.title("PV diagram for Otto cycle")
plt.legend(loc='best')
plt.savefig('Otto cycle')
plt.show()

thermal_efficiency=1-(1/(pow(cr,gamma-1)))
print('Thermal Efficiency of the engine is :',thermal_efficiency*100,'%')

OUTPUT:

REFERENCE:

https://www.mechanicalbooster.com/2017/10/otto-cycle.html