Python Code to obtain PV diagram of Otto cycle Air standard cycle and to calculate the thermal efficiency of the cycle

Objective:

To write a code to obtain PV diagram of Otto cycle (Air standard cycle) and to calculate the thermal efficiecy of the cycle using Python.

Background:

Introduction:

Process:

1) Intake stroke; a mixture of both air and gasoline are drawn into the engine (5-1)

2) Compression stroke; pressure and temperature increases through an adiabatic process (1-2)

3) Combustion; via the spark plug igniting the fuel; volume remains constant in this stage (2-3)

4) Power stroke; adiabatic expansion process (3-4)

5) Valve opens to exhaust waste gas (4-5)

6) Exhaust stroke; piston moves back to push any remaining waste gas out of the engine (1-5)

Output:

Thermal efficiency of the engine = 56.47 %

Snap1:

Snap2:

Code for program as below:

# Otto Cycle Simulator

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,cr,start_angle,end_angle):
	\"\"\"
	Engine Kinematics
	\"\"\"
	# Engine Parameters
	a = stroke/2
	R = con_rod/a

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

	sc = math.radians(start_angle)
	ec = math.radians(end_angle)

	num_values = 50
	dtheta = (sc-ec)/(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 = 600
gamma = 1.4
t3 = 2300

# engine parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 8

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

# Stage2
v2 = v_c

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

# Stage3
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))

# Stage4
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(\'Volume\')
plt.ylabel(\'Pressure\')
plt.show()

# Thermal efficiency
n = 1 - (pow(cr,(1-gamma)))
print(n)