Week 2 Air standard Cycle

AIM:

learnt during the forward kinematics routine, go ahead and write code that can solve an otto cycle and make plots for it

PROCEDURE:

1.importing the math and matplot and numpy

2.input values are

specific heat ratio, gamma =1.4

pressure in state 1 ,p1 = 101325

temperature in state 1 ,t1 = 500

temperature in state 3 ,t1 = 2300

dia. of cranck shaft , bore = 0.1

stroke length , stroke = 0.1

connectiong rod length , con_rod = 0.15

compression ration , cr = 12

3. defining the function of volue is

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

in a engiines crank angle can vary in the crank strokes

paramerts in engine kinematic

crank pin radius, a = stroke/2

R = con_rod/a

swept volume, V_s = math.pi*(1/4)*pow(bore,2)*stroke

clearence volume, V_c = V_s / (cr-1)

4. taking the starting and ending crank angele

taking 50 values in bwtween the start crank and end crank

num_values =50

5.equation of caluclation the volume is a big formula , that can be spilt into several terms

term1 = 0.5*(cr-1)
term2 = R + 1 - math.cos(theta)
term3 = pow(R,2) - pow(math.sin(theta),2)

total volume is sume of term multiplied by clearance volume

V.append((1 + term1*(term2 - term3))*V_c)

6. state at point 1

swept volume , v_s = (math.pi/4)*pow(bore,2)*stroke

clearence volume , v_c = v_s/(cr-1)

volume at 1 , v1 = v_c + v_s

7.state at point 2

isentropic compression in 1-2

v2 = v_c

calculating the values of p2 and t2

p2 = p1*pow(v1,gamma)/pow(v2,gamma)

t2 = p2*v2/rhs

calculating the pressure compression for volume

P_compression.append(constant/pow(v,gamma))

8.state at point 3

constant volume heat addition in 2-3

v3 = v2

calculating the values of p3

p3 = rhs*t3/v3

calculating the pressure expansion for volume

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

8.state at point 4

isentropic expansion in 3-4

v4 = v1

calculating the values of p4 and t4

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

t4 = p4*v4/rhs

9. calculating the thermal efficiency of the engine ,by using this formula is ,

efficiency = 1 - pow((v2/v1),(gamma-1)

efficinecy is 63,

10. making the plot of volume and pressure ,

by adding 4 states in sepperaty to the plot

output plot is given below,

conclusion:

can be make coding for ploting the volume vs pressure plot

calculated the vlues of thermal efficiency

"""
  otto cycle simulator
"""

import math
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import odeint

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))


#nstate point 3
v3 = v2

# p3v3/t3 = p3v3/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

# calculating thermal efficiency
efficiency = (1 - pow((v2/v1),(gamma-1))) *100
print(efficiency)

#plotting rsults   
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()