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Challenge

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

RRagam Vinay Kumar29 Jun 2022
CFDHTML

1.In this challenge you will 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.

Angles to test:

  • 10^0
  • 25^0
  • 45^0

Expected Results

  1. Validate Hydro-dynamic length with the numerical result
  2. Validate the fully developed flow velocity profile with its analytical profile
  3. Validate maximum velocity and pressured drop for fully developed flow
  4. Post-process Shear stress and validate wall shear stress for fully developed flow
  5. Highligh the differences in both boundary conditions in terms of their usage and aplication

EXPLANATION :

EQUATION :

`trianglep = 8muLQ/A^2`

where,

trianglep = is the pressure difference between the two ends

L = is the length of pipe

mu = is the dynamic viscosity

Q = is the volumetric flow rate

R = is the pipe radius

A = is the cross section of pipe.

Procedure :

1. First the geometry is created in the blockmesh dict file,this is done by creating the file through the matlab code.

2.The mesh is generated according to requirement.

3.The velocity and pressure are applied.

4.The controlDict file is edited for simulation run ttime and timestep.

5.After the geometry is input the simulation can be started by calling 'icoFoam' command in terminal.

6.'paraviewWindows' command helps to open paraview.

7.The shear stress diagram is obtained by post-processing the velocity results obtained from openfoam.

Matlab Code For Writing blockMeshDict File of theta- 10 degrees :

clear
close all
clc

Re = 2100;
Ld = 2;
nu = 8.917e-7;
rho = 997;
D = 0.01;
mu = nu*rho;
le = 0.06*Re*D;
l = le +Ld;
V_avg =  mu*Re/(rho*D);
V_max = 2*V_avg;


r = D/2 ;


% Hagen Poisulle equation
delta_p = 8*mu*V_avg*(l/r^2);
kinematic_p = delta_p/rho;
% calculating shear stress
R = linspace(0,D/2,1000);

% Wedge angle
theta = 10;

for i =  1:length(R)
     tau(i) = 2*mu*V_max*(abs(R(i)))/r^2;
end

% plot
plot(R,tau)
xlabel('Radius in m')
ylabel('shear stress')
title('variation of shear stress along radius cylinder')
grid on
hold on


%  Defining the vertices of block

v0 = [0 0 0];
v1 = [0 r*cosd(theta/2) -r*sind(theta/2)];
v2 = [0 r*cosd(theta/2)  r*sind(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)];

% header file

h1 ='/*--------------------------------*- C++ -*----------------------------------*\'
h2 ='| =========                 |                                                 |'
h3 ='| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |'
h4 ='|  \\    /   O peration     | Version:  v2112                                 |'
h5 ='|   \\  /    A nd           | Website:  www.openfoam.com                      |'
h6 ='|    \\/     M anipulation  |                                                 |'
h7 ='\*---------------------------------------------------------------------------*/'
h8 ='FoamFile'
h9 ='{'
h10 =' version     2.0;'
h11 =' format      ascii;'
h12 =' class       dictionary;'
h13 =' object      blockMeshDict;'
h14 ='}'
h15 =' // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'






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

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',h7);
fprintf(f1,'\n');
fprintf(f1,'%s \n',h8);
fprintf(f1,'%s \n',h9);
fprintf(f1,'%s \n',h10);
fprintf(f1,'%s \n',h11);
fprintf(f1,'%s \n',h12);
fprintf(f1,'%s \n',h13);
fprintf(f1,'%s \n',h14);
fprintf(f1,'%s \n',h15);
fprintf(f1 ,'\n');

fprintf(f1,'%2s \n','convertToMeters 1;');
fprintf(f1,'\n');

% Defining vertices

fprintf(f1,'%s \n','vertices');
fprintf(f1,'%s \n','(');
fprintf(f1,'\t(%d %d %d)\n',v0(1),v0(2),v0(3));
fprintf(f1,'\t(%d %d %d)\n',v1(1),v1(2),v1(3));
fprintf(f1,'\t(%d %d %d)\n',v2(1),v2(2),v2(3));
fprintf(f1,'\t(%d %d %d)\n',v3(1),v3(2),v3(3));
fprintf(f1,'\t(%d %d %d)\n',v4(1),v4(2),v4(3));
fprintf(f1,'\t(%d %d %d)\n',v5(1),v5(2),v5(3));
fprintf(f1,'%s \n',');');
 
 
 
% Defining blocks
fprintf(f1,'\n');
fprintf(f1,'%s \n','blocks');
fprintf(f1,'%s \n','(');
fprintf(f1,'\t hex (0 3 4 1 0 3 5 2) (%d %d %d) simpleGrading (1 1 1)\n',200,50,1);
fprintf(f1,'%s \n',');');
 
 
 
 %  Defining edges
fprintf(f1,'\n');
fprintf(f1,'%s \n','edges');
fprintf(f1,'%s \n','(');
fprintf(f1,' \t arc 1 2 (%d %d %d)\n',0,r,0);
fprintf(f1,' \t arc 4 5 (%d %d %d)\n',l,r,0);
fprintf(f1,'%s \n',');');
 

fprintf(f1, 'boundary\n')
fprintf(f1, '(\n')
fprintf(f1, '\t inlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 1 2 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t outlet\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (3 5 4 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t top\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wall;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (1 4 5 2)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t front\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 4 1)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t back\n')
 
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 2 5 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t axis\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type empty;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 3 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '); \n\n')
fprintf(f1, 'mergePatchPairs\n')
fprintf(f1, '(\n')
fprintf(f1, ');\n')
header9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'
fprintf(f1, '%s\n',header9)
fclose(f1)

blockMeshDict File Generated By Matlab :

/*--------------------------------*- C++ -*----------------------------------*\ 
| =========                 |                                                 | 
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           | 
|  \\    /   O peration     | Version:  v2112                                 | 
|   \\  /    A nd           | Website:  www.openfoam.com                      | 
|    \\/     M anipulation  |                                                 | 
\*---------------------------------------------------------------------------*/ 

FoamFile 
{ 
 version     2.0; 
 format      ascii; 
 class       dictionary; 
 object      blockMeshDict; 
} 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // 

convertToMeters 1; 

vertices 
( 
	(0 0 0)
	(0 4.980973e-03 -4.357787e-04)
	(0 4.980973e-03 4.357787e-04)
	(3.260000e+00 0 0)
	(3.260000e+00 4.980973e-03 -4.357787e-04)
	(3.260000e+00 4.980973e-03 4.357787e-04)
); 

blocks 
( 
	 hex (0 3 4 1 0 3 5 2) (200 50 1) simpleGrading (1 1 1)
); 

edges 
( 
 	 arc 1 2 (0 5.000000e-03 0)
 	 arc 4 5 (3.260000e+00 5.000000e-03 0)
); 
boundary
(
	 inlet 
	 {
		 type patch;
		 faces
		 (
			 (0 1 2 0)
		 );
	 }
	 outlet
	 {
		 type patch;
		 faces
		 (
			 (3 5 4 3)
		 );
	 }
	 top
	 {
		 type wall;
		 faces
		 (
			 (1 4 5 2)
		 );
	 }
	 front
	 {
		 type wedge;
		 faces
		 (
			 (0 3 4 1)
		 );
	 }
	 back
	 {
		 type wedge;
		 faces
		 (
			 (0 2 5 3)
		 );
	 }
	 axis
	 {
		 type empty;
		 faces
		 (
			 (0 3 3 0)
		 );
	 }
); 

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

Matlab Code For Writing blockMeshDict File of theta- 25 degrees :

clear
close all
clc

Re = 2100;
Ld = 2;
nu = 8.917e-7;
rho = 997;
D = 0.01;
mu = nu*rho;
le = 0.06*Re*D;
l = le +Ld;
V_avg =  mu*Re/(rho*D);
V_max = 2*V_avg;


r = D/2 ;


% Hagen Poisulle equation
delta_p = 8*mu*V_avg*(l/r^2);
kinematic_p = delta_p/rho;
% calculating shear stress
R = linspace(0,D/2,1000);

% Wedge angle
theta = 25;

for i =  1:length(R)
     tau(i) = 2*mu*V_max*(abs(R(i)))/r^2;
end

% plot
plot(R,tau)
xlabel('Radius in m')
ylabel('shear stress')
title('variation of shear stress along radius cylinder')
grid on
hold on


%  Defining the vertices of block

v0 = [0 0 0];
v1 = [0 r*cosd(theta/2) -r*sind(theta/2)];
v2 = [0 r*cosd(theta/2)  r*sind(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)];

% header file

h1 ='/*--------------------------------*- C++ -*----------------------------------*\'
h2 ='| =========                 |                                                 |'
h3 ='| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |'
h4 ='|  \\    /   O peration     | Version:  v2112                                 |'
h5 ='|   \\  /    A nd           | Website:  www.openfoam.com                      |'
h6 ='|    \\/     M anipulation  |                                                 |'
h7 ='\*---------------------------------------------------------------------------*/'
h8 ='FoamFile'
h9 ='{'
h10 =' version     2.0;'
h11 =' format      ascii;'
h12 =' class       dictionary;'
h13 =' object      blockMeshDict;'
h14 ='}'
h15 =' // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'






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

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',h7);
fprintf(f1,'\n');
fprintf(f1,'%s \n',h8);
fprintf(f1,'%s \n',h9);
fprintf(f1,'%s \n',h10);
fprintf(f1,'%s \n',h11);
fprintf(f1,'%s \n',h12);
fprintf(f1,'%s \n',h13);
fprintf(f1,'%s \n',h14);
fprintf(f1,'%s \n',h15);
fprintf(f1 ,'\n');

fprintf(f1,'%2s \n','convertToMeters 1;');
fprintf(f1,'\n');

% Defining vertices

fprintf(f1,'%s \n','vertices');
fprintf(f1,'%s \n','(');
fprintf(f1,'\t(%d %d %d)\n',v0(1),v0(2),v0(3));
fprintf(f1,'\t(%d %d %d)\n',v1(1),v1(2),v1(3));
fprintf(f1,'\t(%d %d %d)\n',v2(1),v2(2),v2(3));
fprintf(f1,'\t(%d %d %d)\n',v3(1),v3(2),v3(3));
fprintf(f1,'\t(%d %d %d)\n',v4(1),v4(2),v4(3));
fprintf(f1,'\t(%d %d %d)\n',v5(1),v5(2),v5(3));
fprintf(f1,'%s \n',');');
 
 
 
% Defining blocks
fprintf(f1,'\n');
fprintf(f1,'%s \n','blocks');
fprintf(f1,'%s \n','(');
fprintf(f1,'\t hex (0 3 4 1 0 3 5 2) (%d %d %d) simpleGrading (1 1 1)\n',200,50,1);
fprintf(f1,'%s \n',');');
 
 
 
 %  Defining edges
fprintf(f1,'\n');
fprintf(f1,'%s \n','edges');
fprintf(f1,'%s \n','(');
fprintf(f1,' \t arc 1 2 (%d %d %d)\n',0,r,0);
fprintf(f1,' \t arc 4 5 (%d %d %d)\n',l,r,0);
fprintf(f1,'%s \n',');');
 

fprintf(f1, 'boundary\n')
fprintf(f1, '(\n')
fprintf(f1, '\t inlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 1 2 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t outlet\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (3 5 4 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t top\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wall;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (1 4 5 2)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t front\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 4 1)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t back\n')
 
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 2 5 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t axis\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type empty;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 3 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '); \n\n')
fprintf(f1, 'mergePatchPairs\n')
fprintf(f1, '(\n')
fprintf(f1, ');\n')
header9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'
fprintf(f1, '%s\n',header9)
fclose(f1)

blockMeshDict File Generated By Matlab :

/*--------------------------------*- C++ -*----------------------------------*\ 
| =========                 |                                                 | 
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           | 
|  \\    /   O peration     | Version:  v2112                                 | 
|   \\  /    A nd           | Website:  www.openfoam.com                      | 
|    \\/     M anipulation  |                                                 | 
\*---------------------------------------------------------------------------*/ 

FoamFile 
{ 
 version     2.0; 
 format      ascii; 
 class       dictionary; 
 object      blockMeshDict; 
} 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // 

convertToMeters 1; 

vertices 
( 
	(0 0 0)
	(0 4.881480e-03 -1.082198e-03)
	(0 4.881480e-03 1.082198e-03)
	(3.260000e+00 0 0)
	(3.260000e+00 4.881480e-03 -1.082198e-03)
	(3.260000e+00 4.881480e-03 1.082198e-03)
); 

blocks 
( 
	 hex (0 3 4 1 0 3 5 2) (200 50 1) simpleGrading (1 1 1)
); 

edges 
( 
 	 arc 1 2 (0 5.000000e-03 0)
 	 arc 4 5 (3.260000e+00 5.000000e-03 0)
); 
boundary
(
	 inlet 
	 {
		 type patch;
		 faces
		 (
			 (0 1 2 0)
		 );
	 }
	 outlet
	 {
		 type patch;
		 faces
		 (
			 (3 5 4 3)
		 );
	 }
	 top
	 {
		 type wall;
		 faces
		 (
			 (1 4 5 2)
		 );
	 }
	 front
	 {
		 type wedge;
		 faces
		 (
			 (0 3 4 1)
		 );
	 }
	 back
	 {
		 type wedge;
		 faces
		 (
			 (0 2 5 3)
		 );
	 }
	 axis
	 {
		 type empty;
		 faces
		 (
			 (0 3 3 0)
		 );
	 }
); 

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

Matlab Code For Writing blockMeshDict File of theta- 45 degrees :

clear
close all
clc

Re = 2100;
Ld = 2;
nu = 8.917e-7;
rho = 997;
D = 0.01;
mu = nu*rho;
le = 0.06*Re*D;
l = le +Ld;
V_avg =  mu*Re/(rho*D);
V_max = 2*V_avg;


r = D/2 ;


% Hagen Poisulle equation
delta_p = 8*mu*V_avg*(l/r^2);
kinematic_p = delta_p/rho;
% calculating shear stress
R = linspace(0,D/2,1000);

% Wedge angle
theta = 45;

for i =  1:length(R)
     tau(i) = 2*mu*V_max*(abs(R(i)))/r^2;
end

% plot
plot(R,tau)
xlabel('Radius in m')
ylabel('shear stress')
title('variation of shear stress along radius cylinder')
grid on
hold on


%  Defining the vertices of block

v0 = [0 0 0];
v1 = [0 r*cosd(theta/2) -r*sind(theta/2)];
v2 = [0 r*cosd(theta/2)  r*sind(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)];

% header file

h1 ='/*--------------------------------*- C++ -*----------------------------------*\'
h2 ='| =========                 |                                                 |'
h3 ='| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |'
h4 ='|  \\    /   O peration     | Version:  v2112                                 |'
h5 ='|   \\  /    A nd           | Website:  www.openfoam.com                      |'
h6 ='|    \\/     M anipulation  |                                                 |'
h7 ='\*---------------------------------------------------------------------------*/'
h8 ='FoamFile'
h9 ='{'
h10 =' version     2.0;'
h11 =' format      ascii;'
h12 =' class       dictionary;'
h13 =' object      blockMeshDict;'
h14 ='}'
h15 =' // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'






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

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',h7);
fprintf(f1,'\n');
fprintf(f1,'%s \n',h8);
fprintf(f1,'%s \n',h9);
fprintf(f1,'%s \n',h10);
fprintf(f1,'%s \n',h11);
fprintf(f1,'%s \n',h12);
fprintf(f1,'%s \n',h13);
fprintf(f1,'%s \n',h14);
fprintf(f1,'%s \n',h15);
fprintf(f1 ,'\n');

fprintf(f1,'%2s \n','convertToMeters 1;');
fprintf(f1,'\n');

% Defining vertices

fprintf(f1,'%s \n','vertices');
fprintf(f1,'%s \n','(');
fprintf(f1,'\t(%d %d %d)\n',v0(1),v0(2),v0(3));
fprintf(f1,'\t(%d %d %d)\n',v1(1),v1(2),v1(3));
fprintf(f1,'\t(%d %d %d)\n',v2(1),v2(2),v2(3));
fprintf(f1,'\t(%d %d %d)\n',v3(1),v3(2),v3(3));
fprintf(f1,'\t(%d %d %d)\n',v4(1),v4(2),v4(3));
fprintf(f1,'\t(%d %d %d)\n',v5(1),v5(2),v5(3));
fprintf(f1,'%s \n',');');
 
 
 
% Defining blocks
fprintf(f1,'\n');
fprintf(f1,'%s \n','blocks');
fprintf(f1,'%s \n','(');
fprintf(f1,'\t hex (0 3 4 1 0 3 5 2) (%d %d %d) simpleGrading (1 1 1)\n',200,50,1);
fprintf(f1,'%s \n',');');
 
 
 
 %  Defining edges
fprintf(f1,'\n');
fprintf(f1,'%s \n','edges');
fprintf(f1,'%s \n','(');
fprintf(f1,' \t arc 1 2 (%d %d %d)\n',0,r,0);
fprintf(f1,' \t arc 4 5 (%d %d %d)\n',l,r,0);
fprintf(f1,'%s \n',');');
 

fprintf(f1, 'boundary\n')
fprintf(f1, '(\n')
fprintf(f1, '\t inlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 1 2 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t outlet\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (3 5 4 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t top\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wall;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (1 4 5 2)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t front\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 4 1)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t back\n')
 
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 2 5 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t axis\n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type empty;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 3 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '); \n\n')
fprintf(f1, 'mergePatchPairs\n')
fprintf(f1, '(\n')
fprintf(f1, ');\n')
header9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'
fprintf(f1, '%s\n',header9)
fclose(f1)

blockMeshDict File Generated By Matlab :

/*--------------------------------*- C++ -*----------------------------------*\ 
| =========                 |                                                 | 
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           | 
|  \\    /   O peration     | Version:  v2112                                 | 
|   \\  /    A nd           | Website:  www.openfoam.com                      | 
|    \\/     M anipulation  |                                                 | 
\*---------------------------------------------------------------------------*/ 

FoamFile 
{ 
 version     2.0; 
 format      ascii; 
 class       dictionary; 
 object      blockMeshDict; 
} 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // 

convertToMeters 1; 

vertices 
( 
	(0 0 0)
	(0 4.619398e-03 -1.913417e-03)
	(0 4.619398e-03 1.913417e-03)
	(3.260000e+00 0 0)
	(3.260000e+00 4.619398e-03 -1.913417e-03)
	(3.260000e+00 4.619398e-03 1.913417e-03)
); 

blocks 
( 
	 hex (0 3 4 1 0 3 5 2) (200 50 1) simpleGrading (1 1 1)
); 

edges 
( 
 	 arc 1 2 (0 5.000000e-03 0)
 	 arc 4 5 (3.260000e+00 5.000000e-03 0)
); 
boundary
(
	 inlet 
	 {
		 type patch;
		 faces
		 (
			 (0 1 2 0)
		 );
	 }
	 outlet
	 {
		 type patch;
		 faces
		 (
			 (3 5 4 3)
		 );
	 }
	 top
	 {
		 type wall;
		 faces
		 (
			 (1 4 5 2)
		 );
	 }
	 front
	 {
		 type wedge;
		 faces
		 (
			 (0 3 4 1)
		 );
	 }
	 back
	 {
		 type wedge;
		 faces
		 (
			 (0 2 5 3)
		 );
	 }
	 axis
	 {
		 type empty;
		 faces
		 (
			 (0 3 3 0)
		 );
	 }
); 

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

controlDict File For theta- 10,25 and 45 degrees :

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2112                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         8;

deltaT          0.005;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

transportProperties File For theta -10,25 and 45 degrees :

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2112                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu              [0 2 -1 0 0 0 0] 8.9e-7;


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

pressure File For theta -10,25 and 45 degrees :

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2112                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform 0;

boundaryField
{
    axis
    {
        type            empty;

    }
    top
    {
        type            zeroGradient;
    }
    inlet
    {
        type            zeroGradient;
    }

    outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    
     }
}


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

velocity File For theta- 10,25 and 45 degrees :

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2112                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform (0 0 0);

boundaryField
{
    axis
    {
       type             empty;
     }
    top
    {

       type             noSlip;
     }
    inlet
    {
        type            fixedValue;
        value           uniform (0.187 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
}


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

Plot Generated in Matlab :

The above plot is generated in matlab by running the Matlab Code of 10,25 and 45 degress theta value.

BlockMesh Geometry Of theta - 10 degrees :

Velocity Profile for fully developed flow of theta - 10 degrees :

The above plot is generated in the openfoam by using plotoverline .

The velocity profile changes until the flow is fully developed.Distance from inlet ,the velocity attains its characteristics parabola shape

The plot of velocity profile is parabolic in nature with max velocity attained at the center of the pipe.

Shear-stress profile by post processing process :

Shear stress increases the friction on the walls of the pipe because of which the velocity is maximum at the center of the pipe.

The shear stress plot is obtained after post-processing and it is found that the shear stress is maximum at the walls and zero at the center of the pipe.

BlockMesh Geometry for theta -25 degrees :

Velocity profile for fully developed flow of theta -25 degrees :

Shear-stress Profile generated by Post processing process :

BlockMesh Geometry for theta -45 degrees :

Velocity profile for theta -45 degrees :

Shear - Stress generated by Post Processing Process :

The above plots are generated for theta -10,25 and 45 degress by using the ubuntu and openfoam.

1.We can see from the plots that, the fully developed flow at the Hydrodynamic Entrannce length is validated.

2.The Velocity profile and Shear stress profile is successfully validated.

3.With the above results,we can see that the values with the Wedge Boundary condition is slightly accurate than the Symmetry boundary Condition.

4.We can see that there is gradual decrease in accuracy when increasing angle,due to the decrease in the quality of the Mesh especially at the Near -Wall region.

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