OpenFoam Simulation of Flow through a Pipe using Axi-symmetric Boundary Condition

 

Formulae involved:

a) Entry Length of a Pipe for Laminar Flow, L = 0.07*Re*D

b) Velocity = (Re*mu)/(rho*Diameter)

c) Hagen-Poiseuille's Pressure Drop, dP = -(32*mu*u_avg*L)/(D*D)
   Here, u_avg = u_max/2

d) Hagen-Poiseuille's Velocity Distribution, u(r) = -[1/(4*mu)]*(dP/dX)*[(R*R)-(r*r)]
   Here, r = Radius at which Velocity to be calculated

e) Shear Stress Distribution, Tau(r) = -(r/2)*(dP/dX)
   Here, r = Radius at which Shear Stress to be calculated

In the above Equations,
   dX = X_out-X_in, D = Diameter, R = Outer Radius, L = Length,
   Re = Reynold's Number, mu = Dynamic Viscosity

INPUTS:
        Re = 1900;
        rho = 997;                                 % kg/m3
        Diameter = 0.01;                           % meter
        Radius = Diameter/2;                       % meter
        Wedge Angle = 4;                           % Degree
        mu = 8.9e-4;                               % Pa.sec
        Kinematic Outlet Pressure = 90             % m2/sec2
        Inlet Velocity = 0.1696                    % m/sec  
        (from Reynold's No. Formula)
        Graded Mesh = 0.2

        Solver used = icoFoam

 

 

SCREENSHOTS  of  the  ParaView:

Velocity  Contour  in  Wedged  Pipe:

w

 

 

Pressure  Contour:

a

 

 

Velocity  Profile  obtained from  Hagen-Poiseuille's  Equation:

b

 

 

POST  PROCESS  of  the  Simulation:

Velocity  Profile  obtained  at  the  Starting  of  the  Pipe:

c

 

 

Velocity  Profile  obtained  at  the  Middle  of  the  Pipe:

d

 

 

Velocity  Profile  obtained  at  the  End  of  the  Pipe:

e

 

 

Comparison  of  Velocity  Profile  at  the  End  of  the  Pipe:

c

 

 

Shear  Stress  Profile  obtained:

g

 

NBSince the flow was simulated for axi-symmetric BC, the above profiles are half of the Actual Profiles.

 

 

Kinematic  Pressure  Distribution  obtained  along  the  Length  of  the  Pipe:

h

 

 

Results:

(1)  Entry Length = 1.33 m

 

(2)as

 

(3) mx

 

(4)  Pressure Drop (dP) acccording to Hagen-Poiseuille = 64.2417664 Pa

 

(5)  Kinematic Inlet Pressure obtained after the Simulation = 92.326 m2/sec2

 

(6)  Kinematic Pressure drop obtained after the Simulation = 2.326 m2/sec2

 

(7)  Maximum Shear Stress obtained after the Simulation = 0.00437 Pa

 

 

Result  Discussion:

If we look at the above Plots and Results, we will find that at the initial stage,flow was not fully developed.But at the Exit of the Pipe(Total Length = Entry Length = 1.33 m),velocity and its profile closely matched with that of the Hagen Poiseuillei's Equation.So we can say that the Entry Length is sufficient to produce a fully developed flow in a circular pipe. Again, Shear Stress profile also   looks fine.

 


Projects by Jishnu Handique

  Assembled  Machine  Vice:       Drafting: (1)  Clamping  Plate:     (2)  Handle  Cap:     (3)  Handle:     (4)  Jaw:     (5)  Lock Read more

  (1)  Pipe  Vice:   (2)  Knuckle  Joint:   (3)  Screw  Jack:   (4)  Toy  Train  Model:   (5)  Socket  Spigot  Joint:   (6)  AirCraft  Model: &nbs Read more

  Sheet Metal Designs:       Surface Models:           Read more

                                              Read more

  (a) Symmetrically Simulated for Wedge Angle = 10 Degree, 25 Degree and 45 Degree (b) Axi-Symmetrically Simulated for Wedge Angle = 4 Degree   SCREENSHOT  of  the  25  Degree  Wedged  Pipe'  Inlet  in  ParaVi Read more

  import matplotlib.pyplot as plt import numpy as np # Functions def f(p): return pow(p,3)*(1-pow(beta,2))+(0.4*h*pow(beta,2)-sigma*pow(h,2)/pow(r,2))*pow(p,2)+(pow(sigma,2)*pow(h,4)/(3*pow(r,4)))*p-pow((sigma/3)*(pow(h,2)/pow(r,2)),3) def fprime(p) Read more

TAKEN INPUTS: Diameter = 0.04 m Length = 0.1 m Density of Air = 1.225 kg/m3 Dynamic Viscosity = 18.6e-6 Pa.sec at 20 Degree Celsius Reynold No. = 20, 40, 100 We know that, Reynold No. = (Density x Velocity x Diameter)/Dynamic Viscosity By applying above inp Read more

TAKEN INPUTS: Diameter = 0.04 m Length = 0.1 m Density of Air = 1.225 kg/m3 Dynamic Viscosity = 18.6e-6 Pa.sec at 20 Degree Celsius Reynold No. = 20, 40, 100 We know that, Reynold No. = (Density x Velocity x Diameter)/Dynamic Viscosity By applying above inp Read more

  Total  Number of Iterations  taken  for  Simulation  =  500   CUT  PLOTs  Obtained  for  Velocity: (A)  Outlet  Velocity =  10 m/sec:     (B)  Outlet  Read more


Loading...

The End