AIR STANDARD CYCLE USING PYTHON

AIM OF THE PROJECT:

Write a code on otto cycle and plot a PV diagram. and also calculate the thermal efficiency of the engine.

THEORY:

Air standard cycle:

The four strokes of a 4 stroke engine are –

1. Suction/Intake Stroke :-

In this stroke, the piston moves from TDC to BDC .The piston moves downward sucking the air-fuel mixture from the intake valve.

2. Compression Stroke :-

Here, the piston moves from BDC to TDC compressing the air-fuel mixture.

3. Power Stroke :-

Power stroke begins with the expansion of air-fuel mixture ignited with the help of spark plug. Here, the piston moves from TDC to BDC.

4. Exhaust Stroke :-

Again the momentum of flywheel moves the piston up from BDC to TDC thereby driving the exhaust gases outside through the exhaust valve.

0-1 INTAKE STROKE

p1=p0

1-2 ISOTROPIC COMPRESSION STROKE

P1*V1/T1=P2*V2/T2

2-3 CONSTANT VOLUME HEAT ADDITION

V3=V2

3-4 ISTROPIC EXPANSION STROKE

P3*V3/T3=P4*V4/T4

4-1 CONSTANT VOLUME HEAT REJECTION

V4=V1

1-0 EXHAUST AT CONSTANT TEMPERATURE

P0=P1

**Equation showing change in volume with different start_crank angle and end_crank angle.

** Thermal efficiency of the engine is:

import math
import matplotlib.pyplot as plt 

def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):
    #engine parameters
    a=stroke/2
    r=con_rod/a
   
    v_s=(math.pi/4)*pow(bore,2)*stroke
    v_c=v_s/(cr-1)
    
    # defining angles
    sc=math.radians(start_crank)
    ec=math.radians(end_crank)

    num_value=100

    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    



#inputs()

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

#geometric parameter

bore=0.11
stroke=0.1
con_rod=0.15
cr=12

#voiume computation

v_s=(math.pi/4)*pow(bore,2)*stroke
v_c=v_s/(cr-1)
v1=v_s+v_c

#state point 2

v2=v_c

#p2*pow(v2,gama)=p1*pow(v1,gama)
p2=p1*pow(v1,gama)/pow(v2,gama)

#p1*v1/t1=p2*v2/t2

t2=p2*v2*t1/(p1*v1)

v_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0)
constant=p1*pow(v1,gama)

p_compression=[]

for v in v_compression:
	p_compression.append(constant/pow(v,gama))

#state ppint 3

v3=v2

#p3*v3/t3=p2*v2/t2

p3=p2*v2*t3/(v3*t2)


v_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,180)
constant=p3*pow(v3,gama)

p_expansion=[]

for v in v_expansion:
	p_expansion.append(constant/pow(v,gama))

#state point 4

v4=v1

#p4*pow(v4,gama)=p3*pow(v3,gama)
p4=p3*pow(v3,gama)/pow(v4,gama)

#p4*v4/t4=p3*v3/t3
t4=p4*v4*t3/(p3*v3)

#plotting

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.show()


#thermal efficiency of engine
n1=pow(cr,gama-1)
n=1-(1/n1)
print(\"thermal efficiency of engine is\")
print(n)