BlogFor BusinessTalk to a counsellor
CoursesIIT ProgramsPlacementsLog in
BlogFor Business
Talk to a counsellor
Challenge

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

SSuruguri Vinay22 Oct 2022
CFD

AIM : 

  • To simulate an axis-symmetric laminar flow through the constant cross-sectional of the pipe by applying the symmetry boundary condition.
  • To simulating for the mentioned angles i.e for 10, 25, 45 degrees using both symmetry and wedge boundary conditions and validate them with HP equations.

Angles to test :

`10^o`

`25^o`

`45^o`

WEDGE BOUNDARY CONDITION USAGE AND APPLICATION:

  • The wedge boundary condition (BC) is used in computational fluid dynamics to define an axisymmetry situation, for eg. Cylinder. The model and flow must be axisymmetry along a central line such that all physical variables of the flow have the same value and distribution at a given radius for all angles.
  • This boundary condition is specified by two planes that must be selected on separate sides of the domain (referred to as front and back) on the surface running along the axis. 

SYMMETRY BOUNDARY CONDITION USAGE AND APPLICATION:

  • This boundary condition is used to apply mirror-symmetry conditions to a structure.
  • It can be applied to the faces of a structure and no other user input is needed. If a symmetry plane condition is applied to a face, the displacement of this face is locked in a normal direction but free to slide in tangential directions.

Hagen-Poiseuille's law:

In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross-section. The pressure drop is given by:

`DeltaP = 32muLVD2`

where,

`DeltaP` is the pressure drop.

 `mu` is the dynamic viscosity.

  L is the length of the pipe.

 V is the velocity.

At the entrance, the flow is said to be in the hydrodynamic entrance region where the velocity profile gradually takes the shape of a parabola from a straight line. As soon as the parabolic velocity profile becomes steady the flow is said to be in its fully developed state. Normally Hagen Poiseuille's Equation is applicable for a fully developed flow which helps us to calculate the pressure loss.

EQUATIONS USED :

Average velocity

`V_(avg)=RemurhoD m/s`

Maximum velocity

`V_(max)=2.V_(avg) m/s`

Pressure drop

`DeltaP=32muLVD2pa`

kinematic pressure drop = `DeltaPrho`

PROCEDURE :

  • Will start with copying the cavity file from the tutorial to the FOAM_RUN folder.
  • In the run folder only we are going to simulate and whatever we want to do the changes in the blockMeshDict file and pressure and velocity files and controlDict files we will be doing here.
  • creating the block in the OpenFoam here we are creating the wedge after making the required changes in the blockMeshDict file to check the geometry run the blockMesh command.
  • After creating the wedge assign the boundary conditions, and also sitting the simulation end time and time-step in such a way that the courant number should be less than 0.5 and also in the transportProperties enter the kinematic viscosity.
  • Run the simulation using the icoFoam solver after calculating the time needed for the fluid to travel from inlet to outlet
  • After the simulation, use paraFoam to view the flow inside the wedge and use plot over line command to plot the velocity and shear stress changes at a point after the hydrodynamical entry region so that we analyse the fully developed region of the fluid. 
  • Use Matlab to parse the blockMeshDict so that the same file can be used for any wedge values.

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 :

 Conclusion :

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.

Your portfolio, next

Ship work like this
in your own course.

Talk to a career counsellor

Free 20-minute call. We'll map the right course to where you want to work.

By submitting you agree to our Terms and Privacy Policy.