Otto cycle program using python

Objective: To write program for engine kinematics of ottto cycle and plot PV diagram and calculate thermal efficiency.

Introduction: The Otto cycle consists of isentropic compression, heat addition at constant volume, isentropic expansion, and rejection of heat at constant volume.

The processes are described by

• Process 1–2 is an adiabatic (isentropic) compression of the charge as the piston moves from bottom dead centre (BDC) to top dead centre (TDC).
• Process 2–3 is a constant-volume heat transfer to the working gas from an external source while the piston is at top dead centre. This process is intended to represent the ignition of the fuel-air mixture and the subsequent rapid burning.
• Process 3–4 is an adiabatic (isentropic) expansion (power stroke).
• Process 4–1 completes the cycle by a constant-volume process in which heat is rejected from the air while the piston is at bottom dead centre.

Solution:

Python program for otto cycle;

import math
import matplotlib.pyplot as plt

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

	# geometric 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_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,.5)
		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 = 8


# 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
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 = 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

t4 = p4*v4/rhs

# thermal efficiency
thermal_efficiency = (1-(1/pow(cr,gamma-1)))*100
print (thermal_efficiency)

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.show()

Result:

Thermal efficiency of otto cycle = 56.472471835193794 %

PV diagram of Otto cycle is drawn using python program. Thermal efficiency is calculated by using the given formula

For compression ratio = 8 ; Thermal_efficiency of ottto cycle is 56.472471835193794 %