Week 2 Air standard Cycle

Thermal efficiency of the engine is given by

where

1, η = thermal efficiency

2, r = compression ratio that is 'cr'

3, K = the value of gamma that is 1.4 adiabatic process.

Formulas used :

Swept Volume= pi/4*bore^2*stroke

Clearance volume= Swept volume/cr-1

Pressure*volume^gamma=constant

pressure*volume/temperature= constant

efficiency=(1-(1/cr)^(gamma-1))*10

#Otto Cycle Simulator

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore, storke, con_rod , cr , start_crank , end_crank):

	#Geometric Parameters
	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)

	#Defining the Angles
	sc = math.radians(start_crank)
	ec = math.radians(end_crank)

	num_values = 50
	dtheta = (ec-sc)/(num_values-1)

	V = []

	#For Tracing the Volume Curve
	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 Parametres
bore= 0.1
stroke= 0.1
#length of connetcing rod
con_rod= 0.15
#compression Ratio
cr= 12

"""
Volume Computation
v_c= Clerance volume, v_s= Swept Volume
State Point 1 (Isentropic Compression Process)
"""
v_s= (math.pi/4)*pow(bore,2)*stroke
v_c= v_s/(cr-1)
v1= v_c + v_s


#State Point 2 (Constant Volume Heat Addition process)
v2= v_c

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

#Ideal Gas Law
# p1v1/t1 = p2v2/t2 | rhs=p1v1/t1 | rhs=p2v2/t2 | 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 (Isentropic Expansion Process)
v3=v2

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

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


#State point 4 (Constant Volume Heat Rejcetion Process)

v4=v1
#p4v4^gamma = p3v3^gamma

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

#p4v4/t4= rhs
t4=p4*v4/rhs

#ploting 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.show()

#Thermal Efficiency of Engine
n = 1-(pow(cr,(1-gamma)))
print(n)

Thermal Efficiency of Engine is 62.98%