Week 2 Air standard Cycle

Objective:

Write a code that can solve an otto cycle and make plots for it.

Problem statement:

Code should create a PV diagram

Code should give output; the thermal efficiency of the engine.

Program:

# Otto cycle simulator

import math
import matplotlib.pyplot as plt

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

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

	# Volume Parameters
	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_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)	

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


	return V


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

# Geomteric 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_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.plot(V_compression,P_compression)
plt.plot([v2,v3],[p2,p3])
plt.plot(V_expansion,P_expansion)
plt.plot([v4,v1],[p4,p1])
plt.show()

#thermal efficiency

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

Result: