Otto Cycle using Python

OBJECTIVE - To write a code for P_V diagram of an Otto cycle and calculate thermal efficiency

 

PROCEDURE –

ASSUMPTIONS

  • Initially state variables p1,t1,t3 and gamma are assumed.
  • Necessary Engine geometric parameters are also assumed.

 

PROGRAM AND EXPLANATION-

  • First the required inputs are given and with the help of the inputs sept volume(vs) and clearance volume(vc) are calculated.
  • Then volume at state point 1 and 2 are calculated using the formula given below.

V1=vs+vs   v2=vc

  • Then state variables at state point 2,3 and 4 are caluclated and stored respectively .
  • To capture the processes on the final P-V plot,a function named piston_kinematics is used,in which the relation between the volume covered by the piston in the combustion chamber during the compression and expansion processes and the clearance volume is expressed as a function of crank angle(theta).The relation is given by:

 

  =1+1/2(rc-1){R+1-cosө -(R2-sin2ө)1/2}

 

Where ,

             V= volume covered by the piston

             Vc=clearance volume

              rc=compression ratio

            

             R= length of connecting rod*2/stroke length

  • After obtaining the respective values of V and P for both compression and expansion processes.Values of P-compression are stored in empty array.
  • All the state points are plotted on P-V diagram, with (Pcompression,Vcompression) and (Pexpansion ,Vexpansiom) plotted instead of (p3 v3) and (p4 v4).
  • Thermal Efficiency also calculated.
# Otto Cycle Simulator
import math
import matplotlib.pyplot as plt
#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 calculation
v_s = (math.pi/4)*pow(bore,2)*stroke
v_c = v_s/(cr-1)
v1 = v_s + v_c


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

#Parameters
 a = stroke/2
 R = con_rod/a
 
 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)

 numvalues = 100
 dtheta = (ec-sc)/(numvalues-1)
 V = []
 for i in range (0,numvalues):
			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
		


#state point 2
v2 = v_c
p2 = p1*pow(v1,gamma)/pow(v2,gamma)
rhs = p1*v1/t1
t2 = p2*v2/rhs
V_compression = engine_kinematics(bore, stroke, con_rod, cr, 180, 0)
constant1 = p1*pow(v1,gamma)
P_compression = []
for v in V_compression:
		P_compression.append(constant1/pow(v,gamma))

#state point 3
v3 = v2
rhs = p2*v2/t2
p3 = rhs*t3/v3
V_expansion = engine_kinematics(bore, stroke, con_rod, cr, 0, 180)
constant2 = p3*pow(v3,gamma)
P_expansion = []
for v in V_expansion:
		P_expansion.append(constant2/pow(v,gamma))
v4 =v1
p4 = p3*pow(v3,gamma)/pow(v4,gamma)
t4 = p4*v4/rhs  

#Thermal Efficiency
Thermal_eff = (1-((t4-t1)/(t3-t2)))*100
print('Thermal efficiency =')
print(Thermal_eff)

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.show()

OUTPUT OF THE PROGRAM -

 

CONCLUSION –

Thus the code was written and P-V diagram was plotted and thermal efficiency was calculated using PYTHON.

 

 


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The End