Air standard Cycle: otto cycle

Objective:

1. To write a code that can solve an otto cycle and to make plots for it.

2. To create a PV diagram

3. To output the thermal efficiency of the engine.

Otto cycle :

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

Top and bottom of the loop: a pair of quasi-parallel and isentropic processes (frictionless, adiabatic reversible).

Left and right sides of the loop: a pair of parallel isochoric processes (constant volume).

Thermal efficiency is the quotient of the net work from the system, to the heat added to system.

The equation of thermal efficiency:

Code:

'''
otto cycle simulator
'''

import math
import matplotlib.pyplot as plt

#inputs

p1 = 101325
t1 = 500
gamma = 1.4
t3 = 2300

#geometric parameters

cr = 12
bore = 0.1
stroke = 0.1
con_rad = 0.15
a= stroke/2
R = con_rad/a

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

def engine_kinematics(bore,stroke,con_rad,cr,start_crank,end_crank):

	a= stroke/2
	R = con_rad/a

	# volumetric calculations
	v_s = (math.pi)*pow(bore,2)*stroke/4
	v_c = v_s/(cr-1)

	sc = math.radians(start_crank)
	ed = math.radians(end_crank)

	n_values = 50
	d_theta = (ed-sc)/(n_values-1)

	v =[]

	for i in range(0,50):
	
		theta = sc + i*d_theta

		term1 = 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+(0.5*term1*(term2-term3))))

	return v




#state point 2
v2= v_c
p2 = p1*pow(v1,gamma)/pow(v2,gamma)
v_compression = engine_kinematics(bore,stroke,con_rad,cr,180,0)

 
#p*v^gamma = constant

constant = p1*pow(v1,gamma)
p_compression = []

for v in v_compression:
	p_compression.append(constant/pow(v,gamma))

# pv/t = constant2
constant2 = p1*v1/t1
#t2 = p2*v2/constant2


# state point 3
v3 = v2

# pv/t = constant

p3 = constant2*t3/v3

# state point 4

v4 = v1
   
# pv^r =constant

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

# pv/t = constant

t4 = p4*v4/constant2

v_expansion = engine_kinematics(bore,stroke,con_rad,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))


Thermal_efficiency = (1-(1/pow(cr,gamma-1)))*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.show()

Function:

import math
import matplotlib.pyplot as plt

def v = engine kinematics(bore,stroke,con_rad,cr,start_crank,end_crank):

	#inputs

	p1 = 101325
	t1 = 500
	gamma = 1.4
	t3 = 2300

	#geometric parameters

	cr = 12
	bore = 0.1
	stroke = 0.1
	con_rad = 0.15
	a= stroke/2
	R = con_rad/a

	# volumetric calculations
	v_s = (math.pi)*pow(bore,2)*stroke/4
	v_c = v_s/(cr-1)

	theta = math.radians(0)

	term1 = cr-1
	term2 = R+1-math.cos(theta)
	term3 = pow(pow(R,2)-pow(math.sin(theta),2),0.5)

	v = v_c*(1+(0.5*term1*(term2-term3)))

Output: