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Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation

SSiddarth .20 Jan 2023
CFD

Aim: Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation

objective: simulate the same problem as in week 1 but by applying Symmetry Boundary Condition. You will do the simulation for the below mentioned angles using both symmetry and wedge boundary conditions and validate them with HP equations like you did in week 11 challenge.

theory;

wedge bounday condtion in open foam

For 2 dimensional axi-symmetric cases, e.g. a cylinder, the geometry is specified as a wedge of small angle (e.g. ) and 1 cell thick running along the plane of symmetry, straddling one of the coordinate planes, as shown in Figure 4.3. The axi-symmetric wedge planes must be specified as separate patches of wedge type.

Symmetry Boundary Condition:

The symmetry boundary condition defines a mirror face/surface. It should only be used if the physical object or geometry and the expected flow field pattern of the developed solution are mirrored along that surface.

case set up

matlab code to generate blockMeshDict file

#for 10 degree angle
close all;
clear all;
clc;
% Define the angle of the wedge (in degrees)
theta = 10;
% Define the radius of the wedge
r = 5;
L=100;

% Generate the data for the wedge

y = r*cosd(theta/2);
z = r*sind(theta/2);

f1=fopen('blockmeshdict.txt','wt');%txt file ceated in name blockMeshdict.txt

fprintf(f1,'/--------------------------------- C++ -----------------------------------\n');
fprintf (f1,'=========                |\n')
fprintf (f1,'\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf (f1,' \\    /   O peration     | Website:  https://openfoam.org\n');
fprintf  (f1,'    \\  /    A nd           | Version:  10\n');
fprintf  (f1,'     \\/     M anipulation  |\n');
fprintf(f1, '')
fprintf(f1,'\*---------------------------------------------------------------------------*/\n');
fprintf(f1,'FoamFile\n{\n')
fprintf(f1,'format      ascii;\n');
fprintf(f1,'    class       dictionary;\n');
fprintf(f1,'    object      blockMeshDict;\n}\n');

fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n');
fprintf(f1,'convertToMeters 1;\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'    (0 0 0)\n')
fprintf(f1,'    (0 %g -%g)\n',y,z)
fprintf(f1,'    (0 %g %g)\n',y,z)
fprintf(f1,'    (%g 0 0)\n',L)
fprintf(f1,'    (%g %g -%g)\n',L,y,z)
fprintf(f1,'    (%g %g %g)\n',L,y,z)
fprintf(f1,');\n');
fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'    hex (0 1 2 0 3 4 5 3) (100 1 40) simpleGrading (1 1 1)\n')
fprintf(f1,');\n');
fprintf(f1,'edges\n');
fprintf(f1,'(\n');
fprintf(f1,'    arc 1 2 (0 %g 0)\n',r)

fprintf(f1,'    arc 4 5 (%g %g 0)\n',L,r)
fprintf(f1,');\n');
fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'inlet\n   {\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n(\n');
fprintf(f1,'      (0 2 1 0)\n);\n   }\n');    
fprintf(f1,'outlet\n{\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n   (\n');
fprintf(f1,'     (3 4 5 3)\n);\n}\n');
fprintf(f1,'upperWall\n{\n');
fprintf(f1,'       type wall;\n');
fprintf(f1,'      faces\n   (\n');
fprintf(f1,'      (1 2 5 4)\n);\n}\n');
fprintf(f1,'axis\n{\n');
fprintf(f1,'       type empty;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 3 0)\n);\n}\n');
fprintf(f1,'front\n{\n');
fprintf(f1,'       type wedge;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 5 2)\n);\n}\n');
fprintf(f1,'   Back\n{\n');
fprintf(f1,'       type wedge;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'       (0 1 4 3)\n);\n}\n);\n');
fprintf(f1,'mergePatchPairs\n(\n);\n');




#for 25 degree angle
close all;
clear all;
clc;
% Define the angle of the wedge (in degrees)
theta = 25;
% Define the radius of the wedge
r = 5;
L=100;

% Generate the data for the wedge

y = r*cosd(theta/2);
z = r*sind(theta/2);

f1=fopen('blockmeshdict.txt','wt');%txt file ceated in name blockMeshdict.txt

fprintf(f1,'/--------------------------------- C++ -----------------------------------\n');
fprintf (f1,'=========                |\n')
fprintf (f1,'\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf (f1,' \\    /   O peration     | Website:  https://openfoam.org\n');
fprintf  (f1,'    \\  /    A nd           | Version:  10\n');
fprintf  (f1,'     \\/     M anipulation  |\n');
fprintf(f1, '')
fprintf(f1,'\*---------------------------------------------------------------------------*/\n');
fprintf(f1,'FoamFile\n{\n')
fprintf(f1,'format      ascii;\n');
fprintf(f1,'    class       dictionary;\n');
fprintf(f1,'    object      blockMeshDict;\n}\n');

fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n');
fprintf(f1,'convertToMeters 1;\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'    (0 0 0)\n')
fprintf(f1,'    (0 %g -%g)\n',y,z)
fprintf(f1,'    (0 %g %g)\n',y,z)
fprintf(f1,'    (%g 0 0)\n',L)
fprintf(f1,'    (%g %g -%g)\n',L,y,z)
fprintf(f1,'    (%g %g %g)\n',L,y,z)
fprintf(f1,');\n');
fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'    hex (0 1 2 0 3 4 5 3) (100 1 40) simpleGrading (1 1 1)\n')
fprintf(f1,');\n');
fprintf(f1,'edges\n');
fprintf(f1,'(\n');
fprintf(f1,'    arc 1 2 (0 %g 0)\n',r)

fprintf(f1,'    arc 4 5 (%g %g 0)\n',L,r)
fprintf(f1,');\n');
fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'inlet\n   {\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n(\n');
fprintf(f1,'      (0 2 1 0)\n);\n   }\n');    
fprintf(f1,'outlet\n{\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n   (\n');
fprintf(f1,'     (3 4 5 3)\n);\n}\n');
fprintf(f1,'upperWall\n{\n');
fprintf(f1,'       type wall;\n');
fprintf(f1,'      faces\n   (\n');
fprintf(f1,'      (1 2 5 4)\n);\n}\n');
fprintf(f1,'axis\n{\n');
fprintf(f1,'       type empty;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 3 0)\n);\n}\n');
fprintf(f1,'front\n{\n');
fprintf(f1,'       type wedge;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 5 2)\n);\n}\n');
fprintf(f1,'   Back\n{\n');
fprintf(f1,'       type wedge;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'       (0 1 4 3)\n);\n}\n);\n');
fprintf(f1,'mergePatchPairs\n(\n);\n');


#for 45 degree angle
close all;
clear all;
clc;
% Define the angle of the wedge (in degrees)
theta = 45;
% Define the radius of the wedge
r = 5;
L=100;

% Generate the data for the wedge

y = r*cosd(theta/2);
z = r*sind(theta/2);

f1=fopen('blockmeshdict.txt','wt');%txt file ceated in name blockMeshdict.txt

fprintf(f1,'/--------------------------------- C++ -----------------------------------\n');
fprintf (f1,'=========                |\n')
fprintf (f1,'\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf (f1,' \\    /   O peration     | Website:  https://openfoam.org\n');
fprintf  (f1,'    \\  /    A nd           | Version:  10\n');
fprintf  (f1,'     \\/     M anipulation  |\n');
fprintf(f1, '')
fprintf(f1,'\*---------------------------------------------------------------------------*/\n');
fprintf(f1,'FoamFile\n{\n')
fprintf(f1,'format      ascii;\n');
fprintf(f1,'    class       dictionary;\n');
fprintf(f1,'    object      blockMeshDict;\n}\n');

fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n');
fprintf(f1,'convertToMeters 1;\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'    (0 0 0)\n')
fprintf(f1,'    (0 %g -%g)\n',y,z)
fprintf(f1,'    (0 %g %g)\n',y,z)
fprintf(f1,'    (%g 0 0)\n',L)
fprintf(f1,'    (%g %g -%g)\n',L,y,z)
fprintf(f1,'    (%g %g %g)\n',L,y,z)
fprintf(f1,');\n');
fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'    hex (0 1 2 0 3 4 5 3) (100 1 40) simpleGrading (1 1 1)\n')
fprintf(f1,');\n');
fprintf(f1,'edges\n');
fprintf(f1,'(\n');
fprintf(f1,'    arc 1 2 (0 %g 0)\n',r)

fprintf(f1,'    arc 4 5 (%g %g 0)\n',L,r)
fprintf(f1,');\n');
fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'inlet\n   {\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n(\n');
fprintf(f1,'      (0 2 1 0)\n);\n   }\n');    
fprintf(f1,'outlet\n{\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n   (\n');
fprintf(f1,'     (3 4 5 3)\n);\n}\n');
fprintf(f1,'upperWall\n{\n');
fprintf(f1,'       type wall;\n');
fprintf(f1,'      faces\n   (\n');
fprintf(f1,'      (1 2 5 4)\n);\n}\n');
fprintf(f1,'axis\n{\n');
fprintf(f1,'       type empty;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 3 0)\n);\n}\n');
fprintf(f1,'front\n{\n');
fprintf(f1,'       type wedge;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 5 2)\n);\n}\n');
fprintf(f1,'   Back\n{\n');
fprintf(f1,'       type wedge;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'       (0 1 4 3)\n);\n}\n);\n');
fprintf(f1,'mergePatchPairs\n(\n);\n');

these file for wedge bc for symmetry instead of wedge add symmetry bc 

#symmetry bc for 10 degree angle
close all;
clear all;
clc;
% Define the angle of the wedge (in degrees)
theta = 10;
% Define the radius of the wedge
r = 5;
L=100;

% Generate the data for the wedge

y = r*cosd(theta/2);
z = r*sind(theta/2);

f1=fopen('blockmeshdict.txt','wt');%txt file ceated in name blockMeshdict.txt

fprintf(f1,'/--------------------------------- C++ -----------------------------------\n');
fprintf (f1,'=========                |\n')
fprintf (f1,'\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf (f1,' \\    /   O peration     | Website:  https://openfoam.org\n');
fprintf  (f1,'    \\  /    A nd           | Version:  10\n');
fprintf  (f1,'     \\/     M anipulation  |\n');
fprintf(f1, '')
fprintf(f1,'\*---------------------------------------------------------------------------*/\n');
fprintf(f1,'FoamFile\n{\n')
fprintf(f1,'format      ascii;\n');
fprintf(f1,'    class       dictionary;\n');
fprintf(f1,'    object      blockMeshDict;\n}\n');

fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n');
fprintf(f1,'convertToMeters 1;\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'    (0 0 0)\n')
fprintf(f1,'    (0 %g -%g)\n',y,z)
fprintf(f1,'    (0 %g %g)\n',y,z)
fprintf(f1,'    (%g 0 0)\n',L)
fprintf(f1,'    (%g %g -%g)\n',L,y,z)
fprintf(f1,'    (%g %g %g)\n',L,y,z)
fprintf(f1,');\n');
fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'    hex (0 1 2 0 3 4 5 3) (100 1 40) simpleGrading (1 1 1)\n')
fprintf(f1,');\n');
fprintf(f1,'edges\n');
fprintf(f1,'(\n');
fprintf(f1,'    arc 1 2 (0 %g 0)\n',r)

fprintf(f1,'    arc 4 5 (%g %g 0)\n',L,r)
fprintf(f1,');\n');
fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'inlet\n   {\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n(\n');
fprintf(f1,'      (0 2 1 0)\n);\n   }\n');    
fprintf(f1,'outlet\n{\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n   (\n');
fprintf(f1,'     (3 4 5 3)\n);\n}\n');
fprintf(f1,'upperWall\n{\n');
fprintf(f1,'       type wall;\n');
fprintf(f1,'      faces\n   (\n');
fprintf(f1,'      (1 2 5 4)\n);\n}\n');
fprintf(f1,'axis\n{\n');
fprintf(f1,'       type empty;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 3 0)\n);\n}\n');
fprintf(f1,'front\n{\n');
fprintf(f1,'       type symmetry;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 5 2)\n);\n}\n');
fprintf(f1,'   Back\n{\n');
fprintf(f1,'       type symmetry;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'       (0 1 4 3)\n);\n}\n);\n');
fprintf(f1,'mergePatchPairs\n(\n);\n');


close all;
clear all;
clc;
% Define the angle of the wedge (in degrees)
theta = 25;
% Define the radius of the wedge
r = 5;
L=100;

% Generate the data for the wedge

y = r*cosd(theta/2);
z = r*sind(theta/2);

f1=fopen('blockmeshdict.txt','wt');%txt file ceated in name blockMeshdict.txt

fprintf(f1,'/--------------------------------- C++ -----------------------------------\n');
fprintf (f1,'=========                |\n')
fprintf (f1,'\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf (f1,' \\    /   O peration     | Website:  https://openfoam.org\n');
fprintf  (f1,'    \\  /    A nd           | Version:  10\n');
fprintf  (f1,'     \\/     M anipulation  |\n');
fprintf(f1, '')
fprintf(f1,'\*---------------------------------------------------------------------------*/\n');
fprintf(f1,'FoamFile\n{\n')
fprintf(f1,'format      ascii;\n');
fprintf(f1,'    class       dictionary;\n');
fprintf(f1,'    object      blockMeshDict;\n}\n');

fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n');
fprintf(f1,'convertToMeters 1;\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'    (0 0 0)\n')
fprintf(f1,'    (0 %g -%g)\n',y,z)
fprintf(f1,'    (0 %g %g)\n',y,z)
fprintf(f1,'    (%g 0 0)\n',L)
fprintf(f1,'    (%g %g -%g)\n',L,y,z)
fprintf(f1,'    (%g %g %g)\n',L,y,z)
fprintf(f1,');\n');
fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'    hex (0 1 2 0 3 4 5 3) (100 1 40) simpleGrading (1 1 1)\n')
fprintf(f1,');\n');
fprintf(f1,'edges\n');
fprintf(f1,'(\n');
fprintf(f1,'    arc 1 2 (0 %g 0)\n',r)

fprintf(f1,'    arc 4 5 (%g %g 0)\n',L,r)
fprintf(f1,');\n');
fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'inlet\n   {\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n(\n');
fprintf(f1,'      (0 2 1 0)\n);\n   }\n');    
fprintf(f1,'outlet\n{\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n   (\n');
fprintf(f1,'     (3 4 5 3)\n);\n}\n');
fprintf(f1,'upperWall\n{\n');
fprintf(f1,'       type wall;\n');
fprintf(f1,'      faces\n   (\n');
fprintf(f1,'      (1 2 5 4)\n);\n}\n');
fprintf(f1,'axis\n{\n');
fprintf(f1,'       type empty;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 3 0)\n);\n}\n');
fprintf(f1,'front\n{\n');
fprintf(f1,'       type symmetry;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 5 2)\n);\n}\n');
fprintf(f1,'   Back\n{\n');
fprintf(f1,'       type symmetry;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'       (0 1 4 3)\n);\n}\n);\n');
fprintf(f1,'mergePatchPairs\n(\n);\n');




close all;
clear all;
clc;
% Define the angle of the wedge (in degrees)
theta = 45;
% Define the radius of the wedge
r = 5;
L=100;

% Generate the data for the wedge

y = r*cosd(theta/2);
z = r*sind(theta/2);

f1=fopen('blockmeshdict.txt','wt');%txt file ceated in name blockMeshdict.txt

fprintf(f1,'/--------------------------------- C++ -----------------------------------\n');
fprintf (f1,'=========                |\n')
fprintf (f1,'\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf (f1,' \\    /   O peration     | Website:  https://openfoam.org\n');
fprintf  (f1,'    \\  /    A nd           | Version:  10\n');
fprintf  (f1,'     \\/     M anipulation  |\n');
fprintf(f1, '')
fprintf(f1,'\*---------------------------------------------------------------------------*/\n');
fprintf(f1,'FoamFile\n{\n')
fprintf(f1,'format      ascii;\n');
fprintf(f1,'    class       dictionary;\n');
fprintf(f1,'    object      blockMeshDict;\n}\n');

fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n');
fprintf(f1,'convertToMeters 1;\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'    (0 0 0)\n')
fprintf(f1,'    (0 %g -%g)\n',y,z)
fprintf(f1,'    (0 %g %g)\n',y,z)
fprintf(f1,'    (%g 0 0)\n',L)
fprintf(f1,'    (%g %g -%g)\n',L,y,z)
fprintf(f1,'    (%g %g %g)\n',L,y,z)
fprintf(f1,');\n');
fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'    hex (0 1 2 0 3 4 5 3) (100 1 40) simpleGrading (1 1 1)\n')
fprintf(f1,');\n');
fprintf(f1,'edges\n');
fprintf(f1,'(\n');
fprintf(f1,'    arc 1 2 (0 %g 0)\n',r)

fprintf(f1,'    arc 4 5 (%g %g 0)\n',L,r)
fprintf(f1,');\n');
fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'inlet\n   {\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n(\n');
fprintf(f1,'      (0 2 1 0)\n);\n   }\n');    
fprintf(f1,'outlet\n{\n');
fprintf(f1,'     type patch;\n');
fprintf(f1,'     faces\n   (\n');
fprintf(f1,'     (3 4 5 3)\n);\n}\n');
fprintf(f1,'upperWall\n{\n');
fprintf(f1,'       type wall;\n');
fprintf(f1,'      faces\n   (\n');
fprintf(f1,'      (1 2 5 4)\n);\n}\n');
fprintf(f1,'axis\n{\n');
fprintf(f1,'       type empty;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 3 0)\n);\n}\n');
fprintf(f1,'front\n{\n');
fprintf(f1,'       type symmetry;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'      (0 3 5 2)\n);\n}\n');
fprintf(f1,'   Back\n{\n');
fprintf(f1,'       type symmetry;\n');
fprintf(f1,'      faces\n(\n');
fprintf(f1,'       (0 1 4 3)\n);\n}\n);\n');
fprintf(f1,'mergePatchPairs\n(\n);\n');

afetr blockmeshDict file velocity and pressure boundary condtions were set same as previous challenge

gedit 0/U file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform (0.021 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.021 0 0);
    }
    outlet
    {
        type            zeroGradient;
    }
    upperWall
    {
        type            noSlip;
    }
    axis
    {
        type            empty;
    }

    front
    {
        type            wedge;
    }
    Back
    {
        type            wedge;
    }
}

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

gedit 0/p flle 

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //


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

internalField   uniform 0;

boundaryField
{
   inlet
    {
        type            zeroGradient;
    }
    outlet
    {
         type            fixedValue;
         value           uniform 0;
    }
    upperWall
    {
        type            zeroGradient;
    }
    axis
    {
        type            empty;
    }

    front
    {
        type            wedge;
    }
    Back
    {
        type            wedge;
    }
}

after voundary condion set up then block mesh and run the solver icoFoam and wait till simultion runs

Result:

the simulation is ran for 6 cases and the results were dicused here

wedge `10^o`

boundary layer formation

pressure drop

shear stress

velocity profile

wedge `25^o`

boundary layer formation

pressure drop

shear stress

velocity profile

wedge `45^o`

boundary layer formation

pressure drop

shear stress

velocity profile

symmetry `10^o`

boundary layer

pressure drop

shear stress

velocity profile

boundary layer

pressure drop

shear stress

velocity profile

symmetry `45^o`

boundary layer

pressure drop

shear stress

velocity profile

conclusion

`u=Re*nu/D`

`u=2100*10^-6/0.01`

u=0.21 m/s

pressure drop across pipe

`nabla p=-8*mu*L*u/r^2`

where

mu is dydnamic viscosity

L is length of pipe

U is avrge velocity of fluid flow in pipe

r is radius of pipe

`nabla p=-8*0.001*0.3/0.05^2`

`nabla p=0.02016 pa`

`tau_w=mu*(du)/dy`

`tau_w=0.001*(du)/(dy)`

the results matchs with velocity profile and wall shear stress profile

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