Week 2 Air standard Cycle

AIM: -

Write a program in python to find out the PV Diagram of the Otto cycle and also find the thermal efficiency of the engine.

OTTO CYCLE: -

An Otto cycle consists of four processes:

1. Two isentropic (reversible adiabatic) processes

2. Two isochoric (constant volume) processes

These processes can be easily understood if we understand p-V (Pressure-Volume) and T-s (Temperature-Entropy) diagrams of the Otto cycle.

In the above diagrams,

p → pressure V → Volume T → temperature s → Entropy Vc → Clearance Volume Vs → Stroke Volume

DATA GIVEN: -

Bore=0.1m

Stroke length=0.1m

Connecting Rod length= 0.15m

Compression ratio= 8

P1= 101325 pa

T1= 500 k

T3= 2300 k

gamma=1.4

SOURCE CODE: -

# Otto cycle simulator

import math

import numpy as np

import matplotlib.pyplot as plt

#Engine geometrical parameters

bore=0.8

stroke=0.2

con_rod=0.15

cr=10

def engine_kinematics(bore,stroke,con_rod,cr,theta1,theta2):

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

v_clear=v_stroke/(cr-1)

a=stroke/2;

R=con_rod/a

theta=np.linspace(theta1,theta2,180)

V=[]

for t in theta:

A=(0.5)*(cr-1)

B=R+1-math.cos(math.radians(t))

C=pow((R**2)-(math.sin(math.radians(t))**2),0.5)

V.append((1+(A*(B-C)))*v_clear)

return V

#known state variables

p1=101325

#gamma

y=1.4

t1=450

t3=3050

#calculation of volumes

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

v_clear=v_stroke/(cr-1)

#state 1

v1=v_stroke+v_clear

#state 2

v2=v_clear

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

t2=pow(v1/v2,y-1)*t1

#state 3

v3=v2

p3=p2*(t3/t2)

#state 4

v4=v1

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

t4=pow(v3/v4,y-1)*t3

#During Compression stroke

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

c1=p1*pow(v1,y)

p_comp=[]

for v in v_comp:

p_comp.append(c1/(pow(v,y)))

#During Expansion stroke

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

c2=p3*pow(v3,y)

p_exp=[]

for ve in v_exp:

p_exp.append(c2/(pow(ve,y)))

#Calculation efficiency

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

print('Efficiency of engine = ', n);

#plotting state point

plt.plot(v1,p1,'*')

plt.plot(v2,p2,'*')

plt.plot(v3,p3,'*')

plt.plot(v4,p4,'*')

plt.plot(v_comp,p_comp, "-b",linewidth=3,label="Compression Stroke")

plt.plot([v2,v3],[p2,p3], "-r",linewidth=3,label="Heat Addition")

plt.plot(v_exp,p_exp, "-g",linewidth=3,label="Expansion Stroke")

plt.plot([v1,v4],[p1,p4], "-y",linewidth=3,label="Heat Rejection")

plt.xlabel('Volume (m^3)')

plt.ylabel('Pressure (pa)')

plt.legend()

plt.title('OTTO CYCLE')

plt.grid()

plt.show()

GRAPHS: -

The thermal Efficiency output is

The thermal efficiency of the otto cycle is 60.189%.