Week 2 Air standard Cycle

AIM : To write a code for the PV diagram of an Air Standard Cycle (Otto Cycle), also to calculate the thermal efficiency of the engine.

THEORY :

The air-standard-Otto cycle is the idealized cycle for the spark-ignition internal combustion engines.

This cycle is shown above on p-v and T-s diagrams.

The Otto cycle 1-2-3-4 consists of following four process:

Process 1-2: Reversible adiabatic compression of air.
Process 2-3: Heat addition at constant volume.
Process 3-4: Reversible adiabatic expansion of air.
Process 4-1: Heat rejection at constant volume.

Air standard efficiency = Net work done / net heat added

Geometric Inputs : Bore, Stroke, crank pin radius, connecting rod length, starting angle of the crank and ending angle of the crank.

Volume trace :

Here,

a=stroke/2;
R=cond_rod/a;

PYTHON code :

import math
import matplotlib.pyplot as plt
def engine_kinematics(bor,stroke,con_rod,cr,start_crank,end_crank):

#Inputs
a = stroke/2
R =con_rod/a

# Volume computation

sc = math.radians(start_crank)
ec = math.radians(end_crank)

num_values = 100

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(term3,0.5)
V.append((1 + term1*(term2 - term3))*v_c)
return V
#Inputs

p1 = 101325
t1 = 500
gamma = 1.4
t3 = 2300

#geomatric parameters
bore = 0.10
stroke = 0.1
con_rod = 0.15
cr = 12

# 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
rhs= p2*v2/t2
#p3v3/t3 = p2v2/t2 ! rhs = p2v2/t2 ! p3 +rhs*t3/v3
p3 = (rhs*t3)/v3

v_expansion = engine_kinematics(bore, stroke, con_rod, cr,0,180)
constant = p3*pow(v3,gamma)
P_expention = []
for v in v_expansion:
P_expention.append(constant/pow(v,gamma))

#state point 4
v4 = v1

#p4v4^gamma = p3v3^gamma
p4 = p3*pow(v3,gamma)/pow(v4,gamma)

#t4 = p4*v4/rhs
t4 = p4*v4/rhs

plt.plot([v2,v3],[p2,p3])
plt.plot(v_compression,P_compression)
plt.plot([v4,v1],[p4,p1])
plt.plot(v_expansion,P_expention)
plt.show()
#v = engine_kinematics(bore,stroke,con_rod,cr,180,0)

end

Figure :-