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Week 11 - Simulation of Flow through a pipe in OpenFoam

MMohan Babu H5 Apr 2022
CFD

Aim: Simulation of flow through a pipe in open Foam

Objectives:

  • Calculation of flow variables.
  • Generation of Block Mesh Dict using the Wedges of Boundary Conditions, to create the Block Mesh Dict file in octave such that the mesh is automatically created for any wedge angle.
  • Simulating the pipe flow in open foam using icoFoam solver.
  • Post process the velocity profile and shear stress and compare the simulation results.

Note: Consider the cylindrical pipe with the working fluid water entering the pipe with the laminar flow.

Assumption Made:

  • Steady flow , incompressible and laminar flow
  • Flow is two dimensional ( Flow WRT theta is ignored)
  • Constant fluid properties (Velocity, Density ...etc.)

Introduction to the laminar flow through pipe:

In this project we aim to simulate a section of pipe (Wedge shaped geometry) to understand various aspects of flow through a pipe. The fluid chosen is water and the flow is laminar and incompressible. Also we chosen to neglect any changes in cross section. The specified Reynolds number Re is specified as 2100.

Internal flow occurs when the fluid is filled entirely in a conduit and it is driven primarily by a pressure difference

Fluid Velocity in a pipe changes from zero at the surface because of the no-slip boundary condition to a maximum at the pipe center .The average velocity remains constant in a compressible flow when the cross section of the pipe is constant.

Reynolds number (Re):

The transition from the laminar flow to turbulent flow occurs from laminar to transition to turbulent for smooth pipe with no viscous dissipation .It depends on the geometry, face roughness, flow velocity, surface temperature etc.., Reynolds number is an important non-dimensional number which is the ratio of inertia force to viscous force and is expressed for internal flow in a circular pipe as

Hydrodynamic entry length:

The region from the pipe inlet to the point at which the velocity boundary layer merges at the center line is called the hydrodynamic entrance region. The region beyond the entrance region in which the velocity profile is fully developed is called the fully developed region

In laminar flow the entry length is given approximately as

Velocity Profile: The velocity profile for a fully developed laminar flow in a pipe is parabolic with a maximum at the centerline and minimum at R=0.

It is obtained for a fluid element at a radial distance from the center. The average velocity can be written as:

Hence the final expression for the velocity profile can be written as:

Hagen Poiseuilie’s equation:

In non-ideal fluid dynamics, the Hagen-poiseuilies equation is also known as Hagen-Poiseuilies law, is an incompressible and Newtonian fluid flowing through a long cylindrical cross section .The pressure drop is given as

For a pipe with a laminar flow there are basically two regions, Entrance length developing region where the flow is not fully developed and the laminar flow layers are at equal velocity to each other whereas is fully developed region the flow is fully developed and follow the Hagen-Poiseuille law.

Assumptions:

Analytical Solution:

Here for solving the problem numerically we will use icoFoam solver with the cavity tutorial make the geometry along with the mesh and make the blockMesh Dict with the help of Octave as shown below.

CODE FOR BLOCKMESH USING OCTAVE:

% To generate blockmesh Dict file for a wedge angle

clear all
close all
clc

% wedge angle and inputs
theta=input('Enter the value of wedge angle=');
Re=2100;
% Dia of the pipe
D=0.02;
% Length of the pipe
L=0.06*Re*D;
R=D/2;
% Dynamic viscosity @ 25 degree C
mu=0.89e-3;
% Density of water @ 25 degree C
rho=997.0;
% Kinematic viscosity @ 25 degree C
nu=mu/rho;


% pressure and Velocity
% Average Velocity
v_avg=Re*mu/(D*rho);
% maximum velocity
v_max=2*v_avg;
% pressure drop
del_p=(32*mu*v_avg*L)/(D^2);
% Kinematic pressure drop
kin_P=del_p/rho;

% Number of cells along the pipe
n1=50;
% Number of cells radially
n2=1;
% Number of cells on the curve
n3=300;
gfactor=0.5;


% Vertices of the wedge
v0=[0 0 0];
v1=[0 R*cosd(theta/2) -R*sin(theta/2)];
v2=[0 R*cosd(theta/2) R*sin(theta/2)];
v3=[L 0 0];
v4=[L R*cosd(theta/2) -R*sind(theta/2)];
v5=[L R*cosd(theta/2) R*sind(theta/2)];

grading=0.2;
b1=50;
b2=1;
b3=200;


% creating blockmesh dict file for openfoam

h1='/*--------------------------------*- C++ -*----------------------------------*\';
h2='|*  =========                 |                                               |';
h3='|*  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox         |';
h4='|*   \\    /   O peration     | Website:  https://openfoam.org                |';
h5='|*    \\  /    A nd           | Version:  9                                   |';
h6='|*     \\/     M anipulation  |                                               |';
h7='\*----------------------------------------------------------------------------*/';

h8='//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //';

f1=fopen('blockMeshDict','wt')

fprintf(f1,'%s\n',h1);
fprintf(f1,'%s\n',h2);
fprintf(f1,'$s\n',h3);
fprintf(f1,'%s\n',h4);
fprintf(f1,'%s\n',h5);
fprintf(f1,'%s\n',h6);
fprintf(f1,'%s\n \n',h7);

fprintf(f1,'FoamFile \n {\n');
fprintf(f1,'%16s %10s\n','Version',' 2.0;')
fprintf(f1,'%16s %12s\n','format',' ascii;')
fprintf(f1,'%16s %17s\n','class','dictionary;')
fprintf(f1,'%16s %20s\n','object','blockMeshDict;')
fprintf(f1,'%2s\n','}')

fprintf(f1,'%2s\n\n','//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //')
fprintf(f1,'%2s\n\n','convertToMeters 1;')
fprintf(f1,'vertices \n (\n')
fprintf(f1, '\t(%d %d %d)\n',v0)
fprintf(f1, '\t(%d %d %d)\n',v1)
fprintf(f1, '\t(%d %d %d)\n',v2)
fprintf(f1, '\t(%d %d %d)\n',v3)
fprintf(f1, '\t(%d %d %d)\n',v4)
fprintf(f1, '\t(%d %d %d)\n',v5)
fprintf(f1,'%2s\n|n', ');')

fprintf(f1,'blocks \n (\n')
fprintf(f1,' \t %s (%d %d %d) %s (%d 1 1) \n','hex (0 1 2 0 3 4 5 3)',b1,b2,b3,'simpleGrading',grading)
fprintf(f1,' %2s\n\n', ');')

fprintf(f1,'edges \n (\n')
fprintf(f1,'\t %s (0 %d 0)\n','arc 1 2',R)
fprintf(f1,'\t %s(%d %d 0)\n','arc 4 5',L,R)
fprintf(f1,' %2s\n\n', ');')

fprintf(f1,'boundary \n (\n')
fprintf(f1,' \t %5s \n','axis','{')
fprintf(f1,'\t %13s %s\n',' type','empty;')
fprintf(f1,'\t %14s\n %18s\n','faces','(')
fprintf(f1,'\t \t %15s\n %19s\n\n %14s\n\n','(0 3 3 0)',');','}')

fprintf(f1,' \t %5s \n','Wall','{')
fprintf(f1,'\t %13s %s\n',' type','Wall;')
fprintf(f1,'\t %14s\n %18s\n','faces','(')
fprintf(f1,'\t \t %15s\n %19s\n\n %14s\n\n','(2 5 4 1)',');','}')

fprintf(f1,' \t %5s \n','inlet','{')
fprintf(f1,'\t %13s %s\n',' type','patch;')
fprintf(f1,'\t %14s\n %18s\n','faces','(')
fprintf(f1,'\t \t %15s\n %19s\n\n %14s\n\n','(0 0 2 1)',');','}')

fprintf(f1,' \t %5s \n','outlet','{')
fprintf(f1,'\t %13s %s\n',' type','patch;')
fprintf(f1,'\t %14s\n %18s\n','faces','(')
fprintf(f1,'\t \t %15s\n %19s\n\n %14s\n\n','(3 4 5 3)',');','}')

fprintf(f1,' \t %5s \n','wedgeFront','{')
fprintf(f1,'\t %13s %s\n',' type','wedge;')
fprintf(f1,'\t %14s\n %18s\n','faces','(')
fprintf(f1,'\t \t %15s\n %19s\n\n %14s\n\n','(0 3 5 2)',');','}')

fprintf(f1,' \t %5s \n','wedgeBack','{')
fprintf(f1,'\t %13s %s\n',' type','wedge;')
fprintf(f1,'\t %14s\n %18s\n','faces','(')
fprintf(f1,'\t \t %15s\n %19s\n\n %14s\n\n','(0 1 4 3)',');','}')

fprintf(f1,'mergePatchPairs \n (\n);\n')
fprintf(f1,'%2s\n\n','//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //')

fclose(f1);

BLOCKMESH DICT FILE:

/*--------------------------------*- C++ -*----------------------------------*\
|*  =========                 |                                               |
$s
|*   \\    /   O peration     | Website:  https://openfoam.org                |
|*    \\  /    A nd           | Version:  9                                   |
|*     \\/     M anipulation  |                                               |
\*----------------------------------------------------------------------------*/
 
FoamFile 
 {
         Version       2.0;
          format       ascii;
           class       dictionary;
          object       blockMeshDict;
 }
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices 
 (
	(0 0 0)
	(0 0.00999657 -0.000261769)
	(0 0.00999657 0.000261769)
	(2.52 0 0)
	(2.52 0.00999657 -0.000261769)
	(2.52 0.00999657 0.000261769)
);
blocks 
 (
 	 hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (0.2 1 1) 
 );

edges 
 (
	 arc 1 2 (0 0.01 0)
	 arc 4 5 (2.52 0.01 0)
 );

boundary 
 (
 	  axis 
 	     { 
	          type empty;
	          faces
                  (
	 	       (0 3 3 0)
                  );

              }

 	  wall 
 	     { 
	          type wall;
	          faces
                  (
	 	       (2 5 4 1)
                  );

              }

 	 inlet 
 	     { 
	          type patch;
	          faces
                  (
	 	       (0 0 2 1)
                  );

              }

 	 outlet 
 	     { 
	          type patch;
	          faces
                  (
	 	       (3 4 5 3)
                  );

              }

 	 wedgeFront 
 	     { 
	          type wedge;
	          faces
                  (
	 	       (0 3 5 2)
                  );

              }

 	 wedgeBack 
 	     { 
	          type wedge;
	          faces
                  (
	 	       (0 1 4 3)
                  );

              }
);

mergePatchPairs 
 (
);
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

CONTROL DICT FILE:

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         50;

deltaT          0.01;

writeControl    timeStep;

writeInterval  200;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


// ************************************************************************* //

TRANSPORT PROPERTIES FILE:

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "constant";
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu              [0 2 -1 0 0 0 0] 1e-6;


// ************************************************************************* //

PRESSURE FILE:

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 2 -2 0 0 0 0];

internalField   uniform 0;

boundaryField
{
    axis
    {
        type            empty;
        
    }
    inlet
    {
       type            zeroGradient;
    
        
    }
    outlet
    {
    
       type             fixedValue;
       value            uniform 0.018;
    }

    wall
    {
        type            zeroGradient;
    }

    wedgeFront
    {
        type            wedge;
    }

    wedgeBack
    {
        type            wedge;
    }
}

// ************************************************************************* //

VELOCITY FILE:

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.0937312 0 0);

boundaryField
{
    axis
    {
        type            empty;
        
    }
    inlet
    {
        type            fixedValue;
        value           uniform (0.0937312 0 0);
    }
    outlet
    
    {
         type           zeroGradient;
    }
    wall
    {
        type            fixedvalue;
        value           uniform (0 0 0);
    }

   
    wedgeFront
    {
        type            wedge;
    }

    wedgeBack
    {
        type            wedge;
    }
}

// ************************************************************************* //

PRESSURE DISTRIBUTION ALONG THE LENGTH:

VELOCITY DISTRIBUTION ALONG ITS LENGTH:

Graph for velocity Distribution

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