Week 2 Air standard Cycle

ASSIGNMENT-2 : PLOT A GRAPH FOR AIR STANDARD CYCLE

OBJECTIVE : WRITE A CODE TO PLOT A GRAPH FOR AIR STANDARFD CYCLE AND CALCULATE EFFICIENCY

PROCEDURE:-

• Step 1 : Import the libraries required for ploting and mathematical module provides access to the mathematical functions

• import matplotlib.pyplot as plt
  import math
  import numpy as np

• Step 2 : Define input variables

• #Pressure
  • p1 = 101325
    #TemperaturE at starting
    t1 = 500
  • #Heat Capacity ratio
    gamma = 1.4
  • bore = 0.1
    stroke = 0.1
  • CONNECTION ROD
    con_rod =0.15
  • COMPRESSION RATIO
    cr = 8
  • a = stroke/2
    R = con_rod/a

• Step 3: Define funtion to calculate the Engine kinematics ie .Volume in Isentropic compression and Expansion process

  • # Engine kinematics
    def engine_kinematice(bore,stroke,con_rod,cr,start_crank, end_crank):

    a = stroke/2
    R = con_rod/a
    theta = math.radians(0)
    #Volume parameters
    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

    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

• Step 4 : Calculate the 4 points required at all for process mainly for ploting pressure and volume graph.

  • 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

    # p1v1^gamma = p2v2^gamma
    p2 = p1*pow(v1,gamma)/pow(v2,gamma)

    
    #p2v2/t2 = p1v1/t1 , rhs = p2v2/t2 ,rhs = p1v1/t1
    rhs = p1*v1/t1
    t2 = p2*v2/rhs

    
    V_compression = engine_kinematice(bore,stroke,con_rod,cr,180, 0)
    constant = p1*pow(v1,gamma)
    #P_compression*V_compression= constant
    P_compression = []
    for v in V_compression:
    P_compression.append(constant/pow(v,gamma))

    #state point 3
    t3 = 2300
    v3 =v2

    
    # p3v3/t3=p2v2/t2

    rhs = p2*v2/t2
    p3 = rhs*t3/v3

    #state point 4
    v4 = v1

    #p4v4^gama =p3v3^gamma
    p4 = p3*pow(v3,gamma)/pow(v4,gamma)

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

    V_expansion = engine_kinematice(bore,stroke,con_rod,cr,0, 180)

    constant = p3*pow(v3,gamma)

    #P_expansion*V_expansion= constant
    P_expansion = []
    for v in V_expansion:
    P_expansion.append(constant/pow(v,gamma))

• Step 5: Efficiency calculation

• # Efficiency Calculation

  E = 1-(1/(pow(cr,(gamma-1))))
  print(E)

• Step 6: Plotting the Pressure and Volume Graph

• plt.plot([v2,v3],[p2,p3])
  plt.plot(V_expansion,P_expansion)
  plt.plot([v1,v4],[p1,p4])
  plt.xlabel('Volume')
  plt.ylabel('Pressure')
  plt.title('P VS V GRAPH FOR AIR STANDARD CYCLE')
  plt.legend(['ISENTROPIC COMPRESSION','ISOCHORIC COMPRESSION','ISENTROPIC EXPANSION','ISOCHORIC EXPANSION'])
  plt.show()

• Full code for program given below:-

"""
OTTO CYCLE
"""
import matplotlib.pyplot as plt
import math
import numpy as np
# Defining Input Variables

#pressure

p1 = 101325
t1 = 500
gamma = 1.4
bore = 0.1
stroke = 0.1
con_rod =0.15
cr = 8
a = stroke/2
R = con_rod/a
# Engine kinematics
def engine_kinematice(bore,stroke,con_rod,cr,start_crank, end_crank):

	a = stroke/2
	R = con_rod/a
	theta = math.radians(0)
	#Volume parameters
	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

	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


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

# p1v1^gamma = p2v2^gamma
p2 = p1*pow(v1,gamma)/pow(v2,gamma) 


#p2v2/t2 = p1v1/t1 , rhs = p2v2/t2 ,rhs = p1v1/t1
rhs = p1*v1/t1
t2 = p2*v2/rhs


V_compression = engine_kinematice(bore,stroke,con_rod,cr,180, 0)
constant = p1*pow(v1,gamma)
#P_compression*V_compression= constant
P_compression = []
for v in V_compression:
	P_compression.append(constant/pow(v,gamma))



#state point 3
t3 = 2300
v3 =v2


# p3v3/t3=p2v2/t2

rhs = p2*v2/t2
p3 = rhs*t3/v3

#state point 4
v4 = v1

#p4v4^gama =p3v3^gamma
p4 = p3*pow(v3,gamma)/pow(v4,gamma) 

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

V_expansion = engine_kinematice(bore,stroke,con_rod,cr,0, 180)

constant =  p3*pow(v3,gamma)   

#P_expansion*V_expansion= constant
P_expansion = []
for v in V_expansion:
	P_expansion.append(constant/pow(v,gamma))




# Efficiency Calculation

E = 1-(1/(pow(cr,(gamma-1))))
print(E)


plt.plot([v2,v3],[p2,p3])
plt.plot(V_expansion,P_expansion)
plt.plot([v1,v4],[p1,p4])
plt.xlabel('Volume')
plt.ylabel('Pressure')
plt.title('P VS V GRAPH FOR AIR STANDARD CYCLE')
plt.legend(['ISENTROPIC COMPRESSION','ISOCHORIC COMPRESSION','ISENTROPIC EXPANSION','ISOCHORIC EXPANSION'])
plt.show()

Result

1. Graph for AIR STANDARD CYCLE FOR PRESSURE VS VOLUME

• 
• EFFICIENCY CALCULATION
•