Week 2 Air standard Cycle

OBJECTIVE :- To write a python program for air standerd cycle and create a PV diagram & calculate otto cycle thermal efficiency.

PROBLEM STATEMENT :-

In this challenge I need to do-

• Write a code for air standerd cycle I.e. Otto cycle and create a PV diagram
• Also calculate thermal efficiency of the engine which is a output.
• Attach all relevant snapshots.

SOLUTION PROCEDURES :-

For creating PV diagram I adopted following procedures-

1. First off all I import math and plot function at the top.
2. Define all terminology which we have to required while creating PV diagram and finding thermal efficiency.
3. Define stroke volume and clearance volume- Vs = pi/4*(bore)^2*stroke
4. Crank start and crank end angle are defined in degree
5. Define total number of values and dtheta
6. Create empty matrix for volume
7. Define total volume by compression volume equation and appended it in total volume by using for loop and return it each time after running the for loop.
8. These all the function for engine kinematics.
9. Then define pressure, temperature and gamma also bore, stroke, connecting rod length, compression ratio, initial and final temperatre.
10. Engine kinematics function put in volume compression by using for loop.
11. Do the same process for volume expansion.
12. Plot some PV diagram by changing compression ratio (I.e. cr).

PYTHON CODE :-

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore, stroke, con_rod, cr, start_crank, end_crank):
	# geometric parameters
	a = stroke/2     #crank pin radius
	R = con_rod/a    # piston radius

	# V_s = pi/4*B^2*L
	V_s = math.pi*(1/4)*pow(bore,2)*stroke
	V_c = V_s/(cr-1)

	sc = math.radians(start_crank)       #crank start in degree
	ec = math.radians(end_crank)         # crank end in degree

	num_values = 50      # number of values in curve

	dtheta = (ec-sc)/(num_values-1)
	V = []              # volume


		# V/Vc = 1 + 0.5(cr-1)[R + 1 - cos(theta) - (R^2 - sin^2(theta))^0.5]
	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                #pressure
t1 = 500                   #temperature
gamma = 1.4
t3 = 2300

# geometric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15                   #connecting rod
cr = 8                           #compression ratio

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

#state point-2
v2 = v_c
p2 = p1*pow(v1,gamma)/pow(v2,gamma)
rhs = p1*v1/t1
t2 = p2*v2/rhs
V_compression = engine_kinematics(bore, stroke, con_rod, cr, 180, 0)                   #compression volume
constant = p1*pow(v1, gamma)
p_compression = []                                                                     #compression pressure


for v in V_compression:                                   #compression volume
	p_compression.append(constant/pow(v, gamma))

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:                                    #expansion volume
	p_expansion.append(constant/pow(v, gamma))

v4 = v1
p4 = p3*pow(v3,gamma)/pow(v4,gamma)
t4 = p4*v4/rhs


# Otto cycle thermal efficiency
a = 1/pow(cr,(gamma-1))
thermal_efficiency = (1 - a)*100
print(thermal_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.savefig("PV diagram")
plt.show()

RESULTS :-

PV diagram for different compression ratio are as follows-

1. PV diagram of straight line :-

This is the simple otto cycle without using the formula, P*V^gamma = constant.

2. PV diagram for CR = 6 :-

3. PV diagram for CR = 8 :-

4. PV diagram for CR = 12 :-

5. PV diagram for CR = 15 :-

DISCUSSION :-

From above PV diagram we can say that, otto cycle intercepted area is depends on compression ratio. As compression ratio increases intercepted area also decreases and vice-versa.

Straight line PV diagram at compression and expansion shows that P*V^gamma = constant not applied.

Curve line PV diagram is a theorotical cycle at constant pressure.

THERMAL EFFICIENCY :-

Formula for thermal efficiency-

Thermal efficiency = (1 - ((1/((compression ratio)^(gamma-1))))*100.

It is depends on compression ratio. For different compression ratio different efficiency are as follows-

1. For compression ratio =6 :-

Thermal efficiency = 51.16%

2. For compression ratio =8 :-

Thermal efficiency = 56.47%

3. For compression ratio =12 :-

Thermal efficiency = 63%

4. For compression ratio =15 :-

Thermal efficiency = 66.15%

CONCLUSIONS :-

From above python code and PV diagram we can conclude that-

1. Compression stroke start at BDC and end at TDC at 180 degree and similerly expansion start at TDC and end at BDC at 180 degree.
2. As much more number of values on compression and expansion curve, we get the soft curve.
3. Inscribed area of PV diagram is totally depends on compression ratio (cr). as compression ratio increases inscribed area of PV diagram decreases and vice-versa.
4. Thermal efficiency also depends on compression ratio. As compression ratio changes thermal efficiency also changes.
5. For normal compression ratio=12, thermal efficiency is nearly equal to 63%.

In this way, I write a python code for otto cycle efficiency and calculate thermal efficiency for different compression ratio. I analyse everything and write final conclusions, also write all python code procedures.