PRESSURE-VOLUME DIAGRAM THERMAL EFFICIENCY OF OTTO CYCLE AIR STANDARD CYCLE USING PYTHON

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AIR STANDARD CYCLE - OTTO CYCLE - PV DIAGRAM & THERMAL EFFICIENCY
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import math
import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):
			# file name - engine_kinematics.py


	\"\"\"
	Engine Kinematics
	\"\"\"
	import math
	# Geometric parameters

	bore = 0.10
	stroke = 0.1
	con_rod = 0.15
	cr = 12
	a = stroke/2
	R = con_rod/a

	# Volume parameters

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

	# theta = math.radians(180)
	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):
		#print(i)
		theta = sc + i*dtheta
		#print(theta)
		#print(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)
		#V = (1+ term1*(term2-term3))*V_c
		#print(V_c+V_s)
		#print(V)
	return V  

		# at theta = 0 : V=V_c & at theta = 180 : V=V_c+V_s


# 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

#print(v_s)

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)
#print(p2)
#print(p1)

# p2v2/t2 = p1v1/t1 | rhs = p1v1/t1 | p2v2/t2 = rhs | t2 = p2v2/rhs

rhs = p1 * v1 / t1

t2 = p2*v2/rhs
#print(t2)

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))
# print(P_compression)

# state point  3

v3 = v2

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

rhs = p2*v2/t2
p3 = rhs*t3/v3
#print(p3)
#print(p3>p2)
#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))
#print(P_expansion)


# state point 4
v4 = v1

# p4v4^gamma =p3v3^gamma

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

# p4v4/t4 = rhs

t4 = p4*v4/rhs
#print(t4)

#thermal efficiency of otto cycle
efficiency=(1-(1/pow(cr,gamma-1)))*100
print(\'THe thermal efficiency of otto cycle is\',efficiency)

# plt.plot([v1,v2,v3,v4,v1],[p1,p2,p3,p4,p1])
# plt.show()

#V = engine_kinematics(bore,stroke,con_rod,cr,180,0)
#print(V)

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(\'volume\')
plt.ylabel(\'pressure\')
plt.title(\'Otto Cycle P-V Diagram\')
plt.show()

Python coding, PV diagram & Screenshot of program and various outputs. However above program - print commands were converted to comments.

Thermal efficiency = 62.989%