Week 2 Air standard Cycle

Aim : To plot a pv diagram and calculate the thermal efficiency of an otto cycle using python for given data

Introduction :

An otto cycle is an standard thermal cycle used in petrol engines.

The Otto cycle 1 → 2 → 3 → 4 consists of following four processes:

Process 1 → 2: Reversible adiabatic compression of air;

Process 2 → 3: Heat addition at constant volume;

Process 3 → 4: Reversible adiabatic expansion of air;

Process 4 → 1: Heat rejection at constant volume.

# otto cycle simulator

import math
import matplotlib.pyplot as plt


#inputs
#### state point 1 
p1 = 101325
t1 = 500
t3 = 2300 
gamma = 1.4

#geometric parameters

bore = 0.1 
stroke = 0.1
con_rod = 0.15
cr = 8

# Defining a function to calculate the volume of the piston in cylinder at any given crank angle

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/4)*stroke*pow(bore,2)
	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

#volume computation

# swept volume in cylinder
v_s = (math.pi/4)*stroke*pow(bore,2)
# clearnce volume in cylinder
v_c = v_s/(cr-1)
#total volume of cylinder
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

# p3v3/t3 = p2v2/t2 | rhs = p2v2/t2 | p3v3/t3 = rhs | p3 = rhs*t3/v3

rhs = p2*v3/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 = p3v3/t3 | rhs = p3v3/t3 | p4v4/t4 = rhs | t4 = p3v3/rhs

t4 = p4*v4/rhs
v = engine_kinematics(bore,stroke,con_rod,cr,0,180)

# Thermal efficiency of the engine
thermal_efficiency = (1-1/pow(cr,(gamma-1)))*100
print(thermal_efficiency)


# plotting the pv diagram
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.ylabel('pressure')
plt.xlabel('volume')
plt.show()

Result: Thermal efficiency of the engine is 56.472%

We have successfully created a pv plot for an otto cycle and calculated its thermal efficiency