Week 2 Air standard Cycle

ANSWER

DEFINITIONS AND THEORY :-

otto cycle processes :-

The four-stroke Otto cycle is made up of the following four internally reversible processes: 1–2, isentropic compression; 2–3, constant-volume heat addition; 3–4, isentropic expansion; and 4–1, constant-volume heat rejection.

thermal efficiency :-

1.The thermal efficiency rate is the amount of energy that goes into powering the crankshaft of a combustion engine — at least those with pistons.

2.the efficiency of a heat engine measured by the ratio of the work done by it to the heat supplied to it.

FORMULA :-

efficiency = 1-(T4-T1)/(T3-T2)

EFFICIENCY = 62.98%

following are the program for the otto cycle

"""	
	oto cycle simulator
"""

import math
import matplotlib.pyplot as plt


def engine_kinematics(bore, stroke, con_rod, cr, start_crank, end_crank):
	"""
		engine kinematics
	"""

	# 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) 


	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


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

# geometric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 12


# volume computation
v_s = (math.pi/4)*pow(bore,2)*stroke
v_c = v_s/(cr-1)
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 | 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
v4 = v1

#p4v4^gamma = p3v3^gamma

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


# p4v4/t4 = rhs

t4 = p4*v4/rhs

# thermal efficiency

efficiency = (1 - (t4-t1)/(t3-t2))
print(' = {} %'. format(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.xlabel('Volume (m^3)')
plt.ylabel('Pressure (pa)')
plt.title('PV AND TS DIAGRAM OF OTTO CYCLE')
plt.show()