Python - AIR STANDARD CYCLE

Air Standard Cycle

Objective

To write a program using python to check the engine kinematics of an engine operating on the otto cycle and to make the PV diagram plot and display/print the total thermal efficiency of the engine.

Procedure

An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.

The processes are described by

• 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 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.
• Process 1–0 the mass of air is released to the atmosphere in a constant pressure process.

Fig : PV relation in an otto cycle

The geometric parameters for the engine chosen are as given:

bore = 0.1
stroke = 0.1
con_rod = 0.15
cr =12
a = stroke/2 #crankpinradius
R = con_rod/a
gamma = 1.4

State point 1 :

p1 = 101325
t1 = 500
v1 = v_swept + v_clearance

State point 3 :
t3 = 2300

Formulae for Thermal efficiency for engine running on otto cycle

``n = 1 - (t4 - t1)/(t3 - t2)`

Program:

"""
otto cycle 
"""

import math 
import matplotlib.pyplot as plt

def engine(bore,stroke,con_rod,cr,scr,ecr):

		
		sc = math.radians(scr)
		ec = math.radians(ecr)

		num_values = 1000

		V = []

		dtheta = (ec-sc)/(num_values-1)

		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_clearance)
		return V



#geometric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr =12
a = stroke/2 #crankpinradius
R = con_rod/a
gamma = 1.4

# volume computation
v_swept = (math.pi/4)*pow(bore,2)*stroke
v_clearance = v_swept/(cr-1)


# state point 1 
p1 = 101325
t1 = 500
v1 = v_swept + v_clearance

rhs = p1*v1/t1
# state point 2 
v2 = v_clearance
p2 = p1*pow(v1,gamma)/pow(v2,gamma)
t2 =p2*v2/rhs

v_compression = engine(bore,stroke,con_rod,cr,180,0)

constant = p1*pow(v1,gamma)

p_compression = []

for vol in v_compression :
 	p_compression.append(constant/pow(vol,gamma))



#state point 3 
t3 = 2300
v3 = v2 
p3 = t3*rhs/v3

v_expansion = engine(bore,stroke,con_rod,cr,0,180)

constant = p3*pow(v3,gamma)

p_expansion = []

for vol in v_expansion :
 	p_expansion.append(constant/pow(vol,gamma))



#state point 4 
v4 = v1
p4 = p3*pow(v3,gamma)/pow(v4,gamma)
t4 = p4*v4/rhs


#thermal efficiency 
k = 0.4
eff = 1 - (t4-t1)/(t3-t2)
print(eff)

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()

Resulting PV diagram plot:

Thermal Efficiency = 0.6298928275128466

Conclusion

The following code was written in python to give the PV diagram of the air standard cycle and the thermal efficiency is foud to be 0.62989.