Week 2 Air standard Cycle

The main objective of the project is to calculate all unknowns of each state by help of governing equations and given values. After that plotting P-V diagram and calculating efficiency of the cycleds

Procedure

• Define all known engine parameters
• Use swept volume and Clearence volume formula
• Code to generate all the points in PV graph
• By this we got all the four points in PV graph but we need to generate code for all piston movement
• For this, we need to define a function
• After generating PV graph code to calculate the efficiency of otto cycle

# otto clycle simulator

import math
import matplotlib.pyplot as plt


def engine_kinamatics(bore, stroke, con_rod, cr, start_crank, end_crank):
	# engine_kinamatics

	# geometrical parameters
	bore = 0.1
	stroke = 0.1
	con_rod = 0.15
	cr = 12
	a = stroke/2
	R = con_rod/a

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

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

	num_values = 50
	v = []

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

	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

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

#volume computations
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_kinamatics(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*v2/t2
p3 = rhs*t3/v3

v_expansion = engine_kinamatics(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

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

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

#efficiency
A = 1/pow(cr,gamma-1)
ct = 'pv'
efficiency = 1-A
print(efficiency)


plt.figure()
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')
plt.ylabel('pressure')
plt.title('OTTOCYCLE')
plt.savefig('auto1' + '.png')
plt.show()

Result

The program outputs the efficiency of the otto cycle and PV graph.

The efficiency of the otto cycle is calculated as 62.98%