Week 2 Air standard Cycle

AIM: -

To solve an otto cycle and plots for it by using python program

An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines

The Otto cycle is the ideal cycle for spark-ignition engines, in honor of Nikolaus Otto, who invented it in 1867. In ideal Otto cycles, air-standard assumption is used. The ideal Otto cycle consists of four internal reversible processes:

1-2 Isentropic compression

2-3 Constant volume heat addition

3-4 Isentropic expansion

4-1 Constant volume heat rejection

Python code to find thermal efficiency and plotting graphs:-

'''
Otto Cycle simulation by rahematulla kaladagi

'''
#t- Temperature
#p - Pressure
#V & v - Volume

# import the required library and module 
import math
import matplotlib.pyplot as plt

# defining a function for kinematics of engine 
def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):

    """
    Engine kinematics
    """
    # Geomatric parameters
    a = stroke/2
    R = con_rod/a
    
    # Volume parameter
    v_s = math.pi*0.25*pow(bore,2)*stroke #swept volume
    v_c = v_s/(cr-1) # clearance volume
    
    # Conversion to radians
    sc = math.radians(start_crank)
    ec = math.radians(end_crank)
    
    num_values = 50 #Number of division 
    
    dtheta = (ec-sc)/(num_values-1) #Spacing between each division

    V = [] #array for volume

    for i in range(0,num_values): #updating V
    	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 = 510
gamma = 1.4
t3 = 2280

#Geometric parameter
bore = 0.1
con_rod = 0.15 
stroke = 0.1
cr = 8

# Volume computation 
v_s = (math.pi/4)*pow(bore,2)*stroke
v_c = v_s/(cr-1)
v1 = v_s+v_c


#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) #calling function for Compression Volume

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 | p3 = rhs*t3/v3

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

V_expansion = engine_kinematics(bore,stroke,con_rod,cr,180,0) #Calling function for expansion Volume

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

#Thermal efficiency 
eff = 1 - (1/pow(cr,(gamma-1)))
eff = str(eff*100)
print("Thermal Efficiency = " + eff + " %")

#Plotting PV diagram
plt.figure()
plt.plot(V_compression,P_compression,  label = 'isentropic compression')
plt.plot([v2,v3],[p2,p3], label = 'Heat addition')
plt.plot(V_expansion,P_expansion,  label = 'isentropic expansion')
plt.plot([v4,v1],[p4,p1], label = 'Heat rejection')
plt.xlabel('volume')
plt.ylabel('pressure')
plt.title('P-V diagram of Otto cycle')
plt.legend()
plt.show()

Explanation:-

The code begins with defining a function for Volume

variation that depends on factors like the bore,

stroke, compression ratio, and the start and end

positions of the crank. An array of Volume data is

returned wherever the function is called.

In the code p1,t1,t3 are three input values are known to find the output parameters v1,v2,p2,p3,p4,t2,t4.

In actually code starts from the importing libraries and modules. Then I have define the function which returns volume variation that depends on factors like the bore, stroke,comression ratio, and the start and end is returned wherever the fuction is called

Thereafter, all the inputs are defined and the

unknown temperatures, pressures, and volumes at

different points are found using the process

formulae. Also, the thermal efficiency of the process

is calculated and displayed.

At the end I have plotted the graphs as shown by using matplotlib.pyplot as plt as shown below

Results:-

Thermal efficiency = 56.472471835193794%