Week 2 Air standard Cycle

#otto cycle
import math
import matplotlib.pyplot as plt
import numpy as np

def getVFromTheta(theta,R,v_c,cr):
    """
    Relation between V and theta
    v/v_c = 1+0.5*(cr-1)*(R+1-cos(theta)-(R^2 - (sin(theta))^2)^(0.5))
    """
    return v_c * (1+0.5*(cr-1)*(R+1-np.cos(theta)-(R**2 - np.sin(theta)**2)**0.5))

# Inputs
# Pressure
p1 = 101325
# Temperature
T1 = 500
T3 = 2300
gamma = 1.4

# Geometry
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 12
# Crank pin radius
a = stroke/2
R = con_rod/a

# Volume calculation
# Stroke volume
v_s = np.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))

# Temperature
# p1v1/T1 = p2v2/T2
tmp = p1*v1/T1
T2 = p2*v2/tmp

theta = np.linspace(0,np.pi,100)
v_compression = getVFromTheta(theta,R,v_c,cr)

constant = p1*pow(v1,gamma)
p_compression = [constant/pow(v,gamma) for v in v_compression]


# State point 3
v3 =  v2
# p3v3/T3 = p2v2/T2
tmp = p2*v2/T2
p3 = tmp*T3/v3

# State point 4
v4 = v1

# p4v4^gamma = p3v4^gamma
p4 = p3*pow(v3,gamma)/pow(v4,gamma)

theta = np.linspace(np.pi,2*np.pi,100)
v_expansion = getVFromTheta(theta,R,v_c,cr)

constant = p3*pow(v3,gamma)
p_expansion = [constant/pow(v,gamma) for v in v_expansion]

# p4v4/T4 = p3v3/T3
tmp = p3*v3/T3
T4 = p4*v4/tmp

# Calculate thermal efficiency
# eta_th = 1 - 1/(pow(cr,gamma-1))
eta_th = 1 - (T4-T1)/(T3-T2)
print("Thermal efficiency of the otto cycle = {:.3f}%".format(eta_th*100))

# Plot the otto cycle

plt.figure("Otto cyce")
# Plot state points
plt.plot([v1,v2,v3,v4,v1],[p1,p2,p3,p4,p1],'*',c='b',label='State points')
# Plot from state 1 to 2
plt.plot(v_compression,p_compression,'-',c='black',label='Compression')
# Plot from state 2 to 3
plt.plot([v2,v3],[p2,p3],'-',c='y',label='Heat injection')
# Plot from state 3 to 4
plt.plot(v_compression2,p_compression2,'-',c='r',label='Expansion')
# Plot from state 4 to 1
plt.plot([v4,v1],[p4,p1],'-',c='k',label='Heat rejection')
plt.xlabel("Volume [m3]")
plt.ylabel("Pressure [Pa]")
plt.title("Otto cycle")
plt.legend(loc=1)
# Save figure
plt.savefig("Otto_cycle.png")

OUTPUT:-

The Otto cycle is a cycle of engine operation which requires four strokes of the piston: for induction, compression, ignition, and exhaust. The fuel and air mixture is compressed before combustion is started by an electrical spark or other means.

An Otto cycle consists of four processes:

* Process 1-2: Isentropic compression

* Process 2-3: Constant Volume Heat Addition

* Process 3-4: Isentropic expansion

* Process 4-1: Constant Volume Heat Rejection

EXPLANATION OF CODE:-

1)For getting the pv dia of otto cycles we need pressure and volume values at 4 processess

2)By using the relation p1v1^gamma=p2v2^gamma we calculate pressure and volume values

3)we calculated swept and clearance volume by using parameters like bore,stroke,connecting rod,compression ratio by using these swept volume and clearance volume we got to know pressure and volume values

4)we then calculated volume expansion and volume compression by using function

5)we got to know the thermal efficiency by using the formula [1 - (T4-T1)/(T3-T2)]

6) By using plot command we plotted the above pv diagram of otto cycle

7)In this way we plotted pv graph and calcuted thermal efficiency of otto cycle