Week 2 Air standard Cycle

Objectives :- To plot the PV Diagram for an Otto cycle and make a plot using the forward kinematics.

Procedure :- There are various Process in Otto Cycle.

If p1 and t1 are the inputs and t3 output parameters then we can calculate v1, v2 , p2, p3, p4, t2, t4 even it has two constant volume processes so v2 = v3 and v1 = v4.

We have to Calculate the thermal efficiency of the otto cycle.

Otto Cycle There are Various process in the Otto Cycle they are as follows:-

1) Process 1-2 is an adiabatic (isentropic) compression.

2) Process 2-3 is constant volume heat transfer

3) Process 3-4 is an adiabatic (isentropic) expansion.

4) Process 4-1 completes the cycle with constant volume process in heat is rejected.

Thermal Efficiency of engine is given by

Where η = Thermal efficiency.

r = compression ratio that is ‘cr’.

K = value of gamma is 1.4 adiabatic process.

import math
import matplotlib.pyplot as plt

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


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

    sc = math.radians(start_angle)
    ec = math.radians(end_angle)


    num_values = 50
    dtheta = (sc-ec)/(num_values)
    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


        # engine parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 8


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


        # Stage2
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)


constant = p1*pow(v1,gamma)


p_compression = []


for v in v_compression:
    p_compression.append(constant/pow(v,gamma))


# Stage 3 
v3 = v2 
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))

# Stage 4
v4 = v1


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

t4 = p4*v4/rhs




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.show()

# Thermal efficiency
n = 1-(pow(cr,(1-gamma)))
print(n)  

The PV Plot

Result :- The thermal efficiency