Week 2 Air standard Cycle

AIM: Write a programme  for AIR STANDARD CYCLE

OBJECTION: The Otto cycle is an air-standard cycle which approximates the processes in petrol or diesel engines. It is based on constant volume heat addition (combustion) and heat rejection processes, and isentropic compression and expansion. 

BODY : 

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
	
	#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),2)
	    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 parameter

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


# 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 =  rhs | t2 = p2v2/rhs

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 = []
for v in V_compression:

	P_compression.append(constant/pow(v,gamma))

#state point 3

V3 = V2


rhs = p2*V2/t2
p3 = rhs*t3/V3

V_expansion = engine_kinematics(bore,stroke,con_rod,cr,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

efficency = abs( 1-(1/pow(cr,(gamma-1)))*100)

print(efficiency)

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()

STEPS TAKEN WRITE A PROGRAMME

1. First, we have to define the essential value in a initial state. so define p1,t1,gamma,bore stroke,con_rod,cr.
2. Calculate the swept volume and clearance volume
3.  Then use ideal gas law PV = constant according to this Temperature is constant.
4. According to this  p1v1^gamma = p2v2^gamma. By using this law we calculate the p2, v2,p3,p4,v3,v4.
5. Here we use a function called engine_kinematics. With the help of we call value.
6. In the function, we use a formula for calculating array volume.
7. Here we also use linspace command for different value of theta.
8. We take value different position for theta.
9. Then we have plot have to plot two graphs, one is for compression and expansion, and other one is for plot a simple graph b/w PV
10. Then we write a formula for calculating the thermal efficiency.

PLOT

RESULT

CONCLUSION:

The combustion process is idealized by a constant-volume process (SI cycle), a constant-pressure process (CI cycle), or a combination of both (CI Dual cycle).

Exhaust blow down is approximated by a constant-volume process.

All processes are considered reversible.