Week 2 Air standard Cycle

Aim –

To plot PV diagram for air standard Otto cycle and calculate thermal efficiency of Otto cycle

Introduction –

Petrol engine works on air standard Otto cycle. Cycle involves following phases

1. Process 1-2: Isentropic compression.
2. Process 2-3: Constant volume heat transfer.
3. Process 3-4: Isentropic expansion.
4. Process 4-1: Constant volume heat rejection.

Based on engine parameters clearance volume and swept volumes are calculated. Input parameters for efficiency calculations are p1,t1 and output parameters is t3.based on these parameters other parameters are calculated.

`V/(Vc)=1+(1/2)*(r-1)*[R+1-cos(θ)-(R^2-(sin⁡(θ) )^2 )^(1/2)]`

Where, R is obliquity ratio and Ѳ is crank angle

Thermal efficiency is given by,

`η=1-1/(r^(γ-1) )`

Where,

Ƞ is thermal efficiency, r is compression ratio and gamma is adiabatic index.

python code -

#otto cycle simulator
import math
import matplotlib.pyplot as plt

def engine_kinematics(bore,stroke,con_rod,r,start_angle,end_angle):
    #Engine parameters
    a =stroke/2
    R =con_rod/a

    #volume calculations
    v_s =(math.pi/4)*pow(bore,2)*stroke
    v_c =v_s/(r-1)

    start1 = math.radians(start_angle)
    end1 =  math.radians(end_angle)

    num_values =50
    dtheta =(start1-end1)/(num_values-1)
    v =[]
    for i in range(0,num_values):
        theta = start1+i*dtheta
        term1 =0.5*(r-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
r =8

#volume computatuon
v_s = (math.pi/4)*pow(bore,2)*stroke
v_c = v_s/(r-1)
v1 =v_s+v_c

#stage 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,r,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,r,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(r,(1-gamma)))
print(n)

Explaination of code -

importing libraries,defining the fuction to compute volume,calculating the state points ,ploting the result, calculating thermal efficiency.

output -

plot -

thermal efficiency -

hence thermal efficiency is 56.472%