Week 2 Air standard Cycle

Objective:

Write code that can solve an otto cycle and make plots for it.

1. Your code should create a PV diagram

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

Syntax:

import math

import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):

#a=stroke/2

#R=con_rod/a

#v_s = (math.pi/4)*pow(bore,2)*stroke

#v_c = v_s/(cr-1)

sc = math.radians(start_crank)

ec = math.radians(end_crank)

num_value = 50

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

v = []

for i in range(0,num_value):

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

bore = 0.1

stroke = 0.1

cr = 10

con_rod = 0.15

R = 3

gamma = 1.4

v_s = (math.pi)/4*pow(bore,2)*stroke

v_c = v_s/(cr-1)

p1 = 101235

t1 = 300

t3 = 3000

v1 = v_c + v_s

v2 = v_c

p2 = p1*pow((v1/v2),gamma)

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 = [constant/pow(v,gamma) for v in v_compression]

v3 = v2

p3 = (rhs*t3)/v3

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

constant = p3*pow(v3,gamma)

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

v4 = v1

p4 = p3*pow((v3/v4),gamma)

t4 = (p4*v4)/rhs

eeta = 1 - 1/pow(cr,gamma-1)

print('Thermal efficiency:',eeta)

plt.figure()

plt.plot(v_compression,p_compression)

plt.plot([v2,v3],[p2,p3])

plt.plot(v_expansion,p_expansion)

plt.plot([v4,v1],[p4,p1])

plt.xlabel('volume')

plt.ylabel('pressure')

plt.savefig('otto_cycle_PV_diagram.png')

plt.show()

Results:

Thermal efficiency: 0.6018928294465027

Design optimization of the engine can made by observing the thermal efficiency, for the different input values.