Week 2 Air standard Cycle

Week 2 Air standard Cycle

Air standard Cycle

AIM- To Plot the PV Diagram of Otto cycle and derive the thermal efficiency of the otto cycle

OBJECTIVE

• Write a program to plot the curves of PV- diagram of the Otto Cycle.
  • Find the Thermal Efficiency of the Otto Cycle.

GOVERNING EQUATIONS

Otto cycle - An ideal thermodynamic combustion cycle consists of 4 processes as follows: a compression at constant entropy; a constant-volume heat transfer to the system; an expansion at constant entropy; and a constant-volume heat transfer from the system.

Calculation of different parameters of otto cycle

Engine Geometric Parameters:-

Bore – 0.1

Stroke – 0.1

Connecting Rod Length – 0.15

Compression Ratio (CR) – 12

Swept Volume = ( /4)*Bore^2*Stroke

Clearance Volume = SweptVolume/(CR-1)

Given Parameters

P1 = 101325 Pa

T1 = 500 K

T3 = 2300 K

Gamma = 1.4

Parameters for State Point-1

V1 = Swept Volume + Clearance Volume

V2= Clearance Volume

Parameters for State Point-2

P2V2^ = P1V1^gamma

P2 = P1(V1/V2)^gamma

T2 = P2V2T1/P1V1

Parameters for State Point-3

V3 = V2

P3 = P2V2T3/T2V3

Parameters for State Point-4

V4 = V1

P4 = P3(V3/V4)^gamma

Calculation of Thermal Efficiency Of Otto Cycle

Thermal Efficiency = 1-(1/CR^(gamma-1))

% Thermal Efficiency = Thermal Efficiency* 100

Volume Trace – V/Vc = 1 + ½(CR-1)[R +1 – costheta – (R^2 – sintheta^2)^(1/2)

Where,

a = Stroke/2

R = connecting Rod length/a

PYTHON CODE

import math

import matplotlib.pyplot as plt

 

def Engine_Kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):

 

 

                                                         #Inputs

         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_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

t3 = 2300

gamma = 1.4

 

                                               #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_s + v_c

 

                                                  #State Point-2

 

v2 = v_c
                                   
                                                  #p1v1^gamma = p2v2^gamma

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

 

                                     # 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))

 

 

                                                    # state point-3

v3 = v2

 

#p2v2/t2 = p3v3/t3 = rhs | 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

 

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

rhs = p3*v3/t3

t4 = p4*v4/rhs

 

                                                  # plotting the graph

 

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

 

Therm_eff = 1 - (pow(cr,(1 - gamma)))

print(Therm_eff)

EXPLAINATION OF MAIN CODE

• First we set the given value of the offer i.e.; Gamma, T3, P1, T1, Engine Geometry Parameters such as Bore, Stroke, connecting rod length, competitive rating.

• After that we calculate the Swept Volume and Clearance Volume calculation using the engine geometry. V1 = hot volume + and specified volume

• Where the changing conditions of State 2 are found i.e.; V2 = acquisition volume.

• P2 and T2 are also calculated with state-2.

• V_compression and P_compression values ​​are calculated using engine kinematics function.

• Thereafter the State variance rates in the state area - 3 were counted.
• V3 and P3 are listed.

• V_expension adjustment is calculated using engine kinematics function.

• Condition variability in point-4 is calculated. P4 and V4 are listed.

• P_compression and V_compression writing sites are listed after P1, V1 architecture.

• P_expension and V_expension placement sites are provided after the P3, V3 building order.

Output Plots

Conclusion

Therefore, the otto cycle plot is submitted and thermal efficiency is calculated.