Week 2 Air standard Cycle

OBJECTIVE:

To write code that can solve an air standard cycle and make plots for the following condition.

1. To create a PV diagram

2. To obtain the thermal efficiency of the engine.

MAIN CODE:-(also the function code)

import math
import matplotlib.pyplot as plt

def eng_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 properties
bore=0.1
stroke=0.1
con_rod=0.15
cr=10

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

#state point two

v2=v_c

#p2v2^gamma=p1v1^gamma
p2=p1*pow(v1,gamma)/pow(v2,gamma)

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

V_compression= eng_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= eng_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

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

t4=p4*v4/rhs


#plottong
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

te=1-pow((v2/v1),(gamma-1))
print(te)

EXPLANATION:

An Otto cycle is a thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.

Here the objective is to obtain the PV diagram which can be done with the help of function code, that provides the relation between the volume and compression volume.

The bore, stroke, connecting rod, and cr values are assumed along with the initial pressure and temperature.

The volume is determined by using the v/vc relation which was partitioned into three terms.

The volume value is then returned for the rest of the main program

The for-loop is used to obtain the compression and expansion values concerning its state condition.

Then the plot is obtained which shows the isentropic expansion and compression with constant volume.

The thermal efficiency is then deduced by using the t1 and t2 values and it is found that the thermal efficiency of the cycle is 0.601 or 60%.

PLOT:

THERMAL EFFICIENCY:

0.6018 OR 60.18%

CONCLUSION:

Thus the PV diagram of an air standard cycle was obtained by using python and thermal efficiency of the cycle was obtained.