Week 2 Air standard Cycle

1.AIM: Solvig an otto cycle and making plots for it.

2.GOVERNING EQUATIONS:

Adiabatic compression/expansion process: `P_1 V_1^γ= P_2 V_2^γ`

Ideal gas law: `(P_1 V_1)/T_1 = (P_2 V_2)/T_2`

Efficiency of the cycle: `η=1- 1/〖(rc)〗^(γ-1)`

`η=1- (T_4-T_1)/(T_3-T_2 )`

3.OBJECTIVE OF THE PROGRAME: This programe plots a PV diagram of Otto cycle. Also it calculates the thermal efficiency of the cycle.

4.EXPLANATION OF OTTO CYCLE: The Otto cycle is the ideal cycle for spark-ignition engines. Nikolaus Otto invented it in 1867. In ideal Otto cycles, air-standard assumption is used. The ideal Otto cycle consists of four internal reversible processes:

Process 1-2 Isentropic/Adiabatic compression

Process 2-3 Constant volume heat addition

Process 3-4 Isentropic/Adiabatic expansion

Process 4-1 Constant volume heat rejection

5.BODY OF THE CONTENT:

MAIN CODE:

#This programe is written in python
#Otto cycle simulator

import math
import matplotlib.pyplot as plt

#Engine kinematics
def engine(bore,stroke,con_rod,cr,start_crank,end_crank):
	import math
	import matplotlib.pyplot as plt

	#Geomtric parameters
	bore = 0.1
	stroke = 0.1
	con_rod = 0.15
	cr = 6
	a = stroke/2
	R = con_rod/a

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

	ec = math.radians(end_crank) 
	sc = math.radians(start_crank)
	#No of divisions in the range of angle
	n = 50

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

	V = []

	for i in range(0,n):
		theta = sc + (i*dtheta)
		term1 = 0.5*(cr-1)
		term2 = R+1-(math.cos(theta))
		term3 = pow((pow(R,2))-(pow(math.sin(theta),2)),0.5)

		V.append(v_c*(1+term1*(term2-term3)))
	return V	
	
#Inputs
gamma = 1.4

#Geomtric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 6

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

#State 1 | inputs
p1 = 101325
t1 = 500
t3 = 2300

#State 2
v2 = v_c

#P2*v2^gamma = p1*v1^gamma
p2 = (p1*pow(v1,gamma))/(pow(v2,gamma))

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

#Calling engine function
V_compresssion = engine(bore,stroke,con_rod,cr,180,0)

#P*v^gamma = constant
constant = p1*pow(v1,gamma)
P_compression = []

for v in V_compresssion:
	P_compression.append(constant/pow(v,gamma))

#State 3
v3 = v2

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

#Calling engine function
V_expansion = engine(bore,stroke,con_rod,cr,0,180)

#P*v^gamma = constant
constant = p3*pow(v3,gamma)
P_expansion = []

for v in V_expansion:
	P_expansion.append(constant/pow(v,gamma))

#State 4 
v4 = v1

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

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

#Plotting
plt.plot([v2,v3],[p2,p3])
plt.plot(V_compresssion,P_compression)
plt.plot(V_expansion,P_expansion)
plt.plot([v4,v1],[p4,p1])

#Title for the plot
plt.title('cycle')

#Labelling of X axis
plt.xlabel('Volume')

#Labelling of Y axis
plt.ylabel('Temperature')

#Marking the 4 points
plt.text(v1,p1,'1')
plt.text(v2,p2,'2')
plt.text(v3,p3,'3')
plt.text(v4,p4,'4')

#Plot is saved in the current folder
plt.savefig('Otto cycle')
plt.show()

#Efficiency of the cycle
eff = 1-((t4-t1)/(t3-t2))
print(eff)

EXPLANATION:

1. I have imported the math library and plot library for necessary plotting and calculations.
2. Then I have defined a function as engine in which the inputs will be bore, stroke, connecting rod, compression ratio, start crank angle, end crank angle.
3. Then i have given the geometric parameters of the piston.
4. Then according to the formula i have calculated the swept volume and clearance volume.
5. I have given two variables as sc and ec which are start crank angle and end crank angle in degree respectively.
6. Then I have defined the dtheta also created an empty array as V.
7. Then I have used a for loop according to the formula for the calculation of Volume.
8. This is the end of the function engine which returns the value of V.
9. Now for the main code by using gas laws and other equations i have calculated the pressure temperature and volume at state 1, state 2, state 3, state 4.
10. By using plot command i have joined the 4 state point and saved the PV plot.

6.OUTPUT:

PLOT:

Efficiency:

7.ERRORS AND DEBUGGING: I got a different plot when I made mistakes in formula.

8.CONCLUSION: From these program i got the PV diagram as output also the efficiency of the cycle. When I put different values of pressure, temperature, compression ratio , I get different PV diagram and different efficiency.