Week 2 Air standard Cycle

Aim :- write code that can solve an otto cycle and make plots for it.

Requirements :

1) Your code should create a PV diagram

2) You should output the thermal efficiency of the engine.

Program :

defining fumction code .

# engine kinematics
import math
import matplotlib.pyplot as plt

def engine_kinematics( bore, stroke, con_rod,start_crank,end_crank):
#geometric parameters

bore = 0.10
stroke = 0.1
con_rod = 0.15
cr = 12
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)
theta = math.radians(0)

term1 = 0.5*(cr-1)
term2 = R+1 - math.cos(theta)
term3 = pow(R,2)-pow(math.sin(theta),20)
term3 = pow(term3,0.5)

V = (1+ term1*(term2-term3))*V_c

print((V_c))
print(V)

Program :

program provide PV diagram

# otto cycle simulator

import math
import matplotlib.pyplot as plt

def engine_kinematics( bore, stroke, con_rod,start_crank,end_crank):
    # engine kinematics
    import math
    import matplotlib.pyplot as plt

    # geometric parameters
    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(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), 20)
        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

# 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 | t2 = p2v2/rhs
rhs = p1*v1/t1
t2 = p2*v2/rhs
V_compression = engine_kinematics( bore, stroke, con_rod,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,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

# Thermal efficiency
thermal_efficiency = 1 - (1/pow((cr),(gamma-1)))
print('thermal efficiency of given otto cycle is :',thermal_efficiency*100,"%")

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.show()

Output :

1) PV diagram -

2) Thermal Efficiency