Week 2 Air standard Cycle

Otto cycle

Procedure

• funtion is defined and volume for a range of angle is taken.
• input parameters and geometric parameters are provided.
• volume and pressure during compression and expansion is calculated .also pressure ,volume and temp at end points are computed
• the obtained points are ploted .
• To find the thermal efficiency equation is used.
• the result is printed out.

program

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore, stroke, con_rod, cr, start_angle, end_angle):
	#engine parameters
	a = stroke/2
	R = con_rod/a

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

	#angle range
	sc = math.radians(start_angle)
	ec = math.radians(end_angle)
	num_values = 100
	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_s+v_c

#statr point 2
v2 =v_c
#p2v2^gamma = p1v1^gamma
p2 = p1*pow(v1,gamma)/pow(v2,gamma)
#p2v2/t2 = p1v1/t1 | rhs = p1v1/t1
rhs = p1*v1/t1
t2 = p2*v2/rhs

v_comp = engine_kinematics(bore,stroke,con_rod,cr,180,0)
constant = p1*pow(v1,gamma)
p_comp =[]
for v in v_comp:
	p_comp.append(constant/pow(v,gamma))

#state point 3
v3 = v2
rhs = p2*v2/t2
p3 = rhs*t3/v3

v_exp = engine_kinematics(bore,stroke,con_rod,cr,0,180)
constant = p3*pow(v3,gamma)
p_exp = []
for v in v_exp:
	p_exp.append(constant/pow(v,gamma))

#state point 4
v4 = v1
#p4v4^gamma = p3v3^gamma
p4 = p3*pow(v3,gamma)/pow(v4,gamma)

t4 = p4*v4/rhs

#ploting
plt.plot([v2,v3],[p2,p3])
plt.plot(v_comp,p_comp)
plt.plot(v_exp,p_exp)
plt.plot([v4,v1],[p4,p1])
plt.show()

#thermal efficiency
therm_eff = 1-(1/pow(cr,(gamma-1)))
print('thermal efficiency = ',therm_eff)

Result

Conclusion

P-V diagram ploted for otto cycle and thermal efficiency calculated for the provided condition.