Week 2 Air standard Cycle

Aim : To write a program for Engine kinematics of a Otto Cycle in PYTHon

Objective : Calculate the efficiency of the otto cycle and plot the P-V diagram

Theory : An otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston cyclinder.

• Process 0–1 a mass of air is drawn into piston/cylinder arrangement at constant pressure.
• Process 1–2 is an adiabatic (isentropic) compression of the charge as the piston moves from bottom dead centre (BDC) to top dead center (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 center. 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 center.
• Process 1–0 the mass of air is released to the atmosphere in a constant pressure process.

Procedure :

PYTHON Code

"""
	otto cycle simulator
"""

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore, stroke, con_rod, cr, srart_crank, end_crank):
	# Engine Kinematics

	# Geometric parameters
	bore = 0.1
	stroke = 0.1
	con_rod = 0.15
	cr = 8
	a = stroke/2
	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(srart_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(pow(R,2) - pow(math.sin(theta),2),0.5)
		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 | 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))


#state point 3
v3 = v2

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

t4 = p4*v4/rhs

# Efficiency of OTTO Cycle

Efficiency = 1-((t4-t1)/(t3-t2))
print(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.xlabel('Volume')
plt.ylabel('Pressure')
plt.title('P-V Diagram of OTTO cycle')
plt.show()

Output :

P-V diagram of Otto Cycle

Efficiency of Otto Cycle :

EFficiency = `1-(t4-t1)/(t3-t2)` = 56.47%