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Week 12 - Symmetry vs Wedge vs HP equation

SSaurabh Kumar Sharma8 Jun 2020

Symmetry vs Wedge vs HP equation

In the following project a script was written in matlab to generate the blockMeshDict file according to the wedge angle, diameter and length of a pipe using symmetry boundary condition.

Simulation results obtained for 10,25 and 45 degree angle (symmetry boundary condition) are compared with wedge boundary condition simulation and analytical results.

Symmetry boundary condition:- This boundary condition is used to enforce symmetry constraint. It is applied on the side of the pipe. And the pipe geometry is specified as a symmetry of angle(10,25,45Degrees) and 1 cell thick, running around the centreLine.

The script to generate blockMeshDict file is as follows:

clear all
close all
clc

% Script to generate blocmesh.dict for any wedge angle for a pipe with
% diameter D and lenght L

%% input parameters
theta = 45; % required wedge angle
Re = 2100; % reynolds number
D = 0.025;% Diameter of pipe in meters
L = 0.06*Re*D; % length of pipe in meters
R = D/2; % radius

%% co-ordinates for the vertices will be as follows using trignometric
% relatiuons

c0 = [0 0 0]; % point of origin;
c1 = [0 R*(cosd(theta/2)) R*(sind(theta/2))];
c2 = [0 R*(cosd(theta/2)) -R*(sind(theta/2))];
c3 = [L 0 0];
c4 = [L R*(cosd(theta/2)) R*(sind(theta/2))];
c5 = [L R*(cosd(theta/2)) -R*(sind(theta/2))];

%%strings for blockMeshDict file

h1 = ('/*--------------------------------*- C++ -*----------------------------------*\');
h2 = ('| =========                                                                   |');
h3 = ('| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |');
h4 = ('|  \\    /   O peration     | Version:  4.1                                   |');
h5 = ('|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |');
h6 = ('|    \\/     M anipulation  |                                                 |');
h7 = ('\*---------------------------------------------------------------------------*/');
h8 = ('// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');

%% Generating a blockMeshDict file

%Header
name = sprintf('blockMeshDict_%d',theta);
fileID = fopen(name,'w');
fprintf(fileID,'%s\n',h1);
fprintf(fileID,'%s\n',h2);
fprintf(fileID,'%s\n',h3);
fprintf(fileID,'%s\n',h4);
fprintf(fileID,'%s\n',h5);
fprintf(fileID,'%s\n',h6);
fprintf(fileID,'%s\n',h7);
fprintf(fileID,'FoamFile\n{\n');
fprintf(fileID,'%16s \t 2.0;\n','version');
fprintf(fileID,'%16s \t ascii;\n','format');
fprintf(fileID,'%16s \t dictionary;\n','class');
fprintf(fileID,'%16s \t blockMeshDict;\n}\n','object');
fprintf(fileID,'%s\n\n',h8);

%vertices

fprintf(fileID,'convertToMeters 1;\n\n');
fprintf(fileID,'vertices\n(\n');
fprintf(fileID,'\t(%d %d %d)\n',c0(1),c0(2),c0(3));
fprintf(fileID,'\t(%d %d %d)\n',c1(1),c1(2),c1(3));
fprintf(fileID,'\t(%d %d %d)\n',c2(1),c2(2),c2(3));
fprintf(fileID,'\t(%d %d %d)\n',c3(1),c3(2),c3(3));
fprintf(fileID,'\t(%d %d %d)\n',c4(1),c4(2),c4(3));
fprintf(fileID,'\t(%d %d %d)\n);\n\n',c5(1),c5(2),c5(3));
fprintf(fileID,'blocks\n(\n');
fprintf(fileID,'\t hex (0 3 5 2 0 3 4 1) (400 40 1) simplegrading (1 0.1 1)\n');
fprintf(fileID,');\n');
fprintf(fileID,'edges\n(\n');
fprintf(fileID,'\t arc 1 2 (%d %d %d)\n',0, R, 0);
fprintf(fileID,'\t arc 4 5 (%d %d %d)\n',L, R, 0);
fprintf(fileID,');\n');
fprintf(fileID,'boundary\n(\n');
fprintf(fileID,'\t Inlet\n');
fprintf(fileID,'\t {\n');
fprintf(fileID,'\t type patch;\n');
fprintf(fileID,'\t faces\n');
fprintf(fileID,'\t (\n');
fprintf(fileID,'\t\t (0 1 2 0)\n');
fprintf(fileID,'\t );\n');
fprintf(fileID,'\t }\n\n');
fprintf(fileID,'\t Outlet\n');
fprintf(fileID,'\t {\n');
fprintf(fileID,'\t type patch;\n');
fprintf(fileID,'\t faces\n');
fprintf(fileID,'\t (\n');
fprintf(fileID,'\t\t (3 4 5 3)\n');
fprintf(fileID,'\t );\n');
fprintf(fileID,'\t }\n');
fprintf(fileID,'\t Top\n');
fprintf(fileID,'\t {\n');
fprintf(fileID,'\t type patch;\n');
fprintf(fileID,'\t faces\n');
fprintf(fileID,'\t (\n');
fprintf(fileID,'\t\t (1 2 5 4)\n');
fprintf(fileID,'\t );\n');
fprintf(fileID,'\t }\n');
fprintf(fileID,'\t wedgeback\n');
fprintf(fileID,'\t {\n');
fprintf(fileID,'\t type symmetry;\n');
fprintf(fileID,'\t faces\n');
fprintf(fileID,'\t (\n');
fprintf(fileID,'\t\t (0 1 4 3)\n');
fprintf(fileID,'\t );\n');
fprintf(fileID,'\t }\n');
fprintf(fileID,'\t wedgefront\n');
fprintf(fileID,'\t {\n');
fprintf(fileID,'\t type symmetry;\n');
fprintf(fileID,'\t faces\n');
fprintf(fileID,'\t (\n');
fprintf(fileID,'\t\t (0 2 5 3)\n');
fprintf(fileID,'\t );\n');
fprintf(fileID,'\t }\n');
fprintf(fileID,'\t axis\n');
fprintf(fileID,'\t {\n');
fprintf(fileID,'\t type empty;\n');
fprintf(fileID,'\t faces\n');
fprintf(fileID,'\t (\n');
fprintf(fileID,'\t\t (0 3 3 0)\n');
fprintf(fileID,'\t );\n');
fprintf(fileID,'\t }\n');
fprintf(fileID,');\n');
fprintf(fileID,'mergePatchPairs\n');
fprintf(fileID,'(\n');
fprintf(fileID,');\n');

fprintf(fileID,h8);

blockMeshDict files for 10,25, and 45 deg are as follows:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                                                                   |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
         version 	 2.0;
          format 	 ascii;
           class 	 dictionary;
          object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	(0 0 0)
	(0 1.245243e-02 1.089447e-03)
	(0 1.245243e-02 -1.089447e-03)
	(3.150000e+00 0 0)
	(3.150000e+00 1.245243e-02 1.089447e-03)
	(3.150000e+00 1.245243e-02 -1.089447e-03)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (400 40 1) simplegrading (1 0.1 1)
);
edges
(
	 arc 1 2 (0 1.250000e-02 0)
	 arc 4 5 (3.150000e+00 1.250000e-02 0)
);
boundary
(
	 Inlet
	 {
	 type patch;
	 faces
	 (
		 (0 1 2 0)
	 );
	 }

	 Outlet
	 {
	 type patch;
	 faces
	 (
		 (3 4 5 3)
	 );
	 }
	 Top
	 {
	 type patch;
	 faces
	 (
		 (1 2 5 4)
	 );
	 }
	 wedgeback
	 {
	 type symmetry;
	 faces
	 (
		 (0 1 4 3)
	 );
	 }
	 wedgefront
	 {
	 type symmetry;
	 faces
	 (
		 (0 2 5 3)
	 );
	 }
	 axis
	 {
	 type empty;
	 faces
	 (
		 (0 3 3 0)
	 );
	 }
);
mergePatchPairs
(
);
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
/*--------------------------------*- C++ -*----------------------------------*\
| =========                                                                   |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
         version 	 2.0;
          format 	 ascii;
           class 	 dictionary;
          object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	(0 0 0)
	(0 1.220370e-02 2.705495e-03)
	(0 1.220370e-02 -2.705495e-03)
	(3.150000e+00 0 0)
	(3.150000e+00 1.220370e-02 2.705495e-03)
	(3.150000e+00 1.220370e-02 -2.705495e-03)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (400 40 1) simplegrading (1 0.1 1)
);
edges
(
	 arc 1 2 (0 1.250000e-02 0)
	 arc 4 5 (3.150000e+00 1.250000e-02 0)
);
boundary
(
	 Inlet
	 {
	 type patch;
	 faces
	 (
		 (0 1 2 0)
	 );
	 }

	 Outlet
	 {
	 type patch;
	 faces
	 (
		 (3 4 5 3)
	 );
	 }
	 Top
	 {
	 type patch;
	 faces
	 (
		 (1 2 5 4)
	 );
	 }
	 wedgeback
	 {
	 type symmetry;
	 faces
	 (
		 (0 1 4 3)
	 );
	 }
	 wedgefront
	 {
	 type symmetry;
	 faces
	 (
		 (0 2 5 3)
	 );
	 }
	 axis
	 {
	 type empty;
	 faces
	 (
		 (0 3 3 0)
	 );
	 }
);
mergePatchPairs
(
);
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 /*--------------------------------*- C++ -*----------------------------------*\
    | =========                                                                   |
    | \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
    |  \\    /   O peration     | Version:  4.1                                   |
    |   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
    |    \\/     M anipulation  |                                                 |
    \*---------------------------------------------------------------------------*/
    FoamFile
    {
             version 	 2.0;
              format 	 ascii;
               class 	 dictionary;
              object 	 blockMeshDict;
    }
    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

    convertToMeters 1;

    vertices
    (
        (0 0 0)
        (0 1.154849e-02 4.783543e-03)
        (0 1.154849e-02 -4.783543e-03)
        (3.150000e+00 0 0)
        (3.150000e+00 1.154849e-02 4.783543e-03)
        (3.150000e+00 1.154849e-02 -4.783543e-03)
    );

    blocks
    (
         hex (0 3 5 2 0 3 4 1) (400 40 1) simplegrading (1 0.1 1)
    );
    edges
    (
         arc 1 2 (0 1.250000e-02 0)
         arc 4 5 (3.150000e+00 1.250000e-02 0)
    );
    boundary
    (
         Inlet
         {
         type patch;
         faces
         (
             (0 1 2 0)
         );
         }

         Outlet
         {
         type patch;
         faces
         (
             (3 4 5 3)
         );
         }
         Top
         {
         type patch;
         faces
         (
             (1 2 5 4)
         );
         }
         wedgeback
         {
         type symmetry;
         faces
         (
             (0 1 4 3)
         );
         }
         wedgefront
         {
         type symmetry;
         faces
         (
             (0 2 5 3)
         );
         }
         axis
         {
         type empty;
         faces
         (
             (0 3 3 0)
         );
         }
    );
    mergePatchPairs
    (
    );
    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

The velocity profiles obtained for the above angles are as follows:

At 3.15m from inlet.

The observations from above simulations is as follows:

Angle

Max CFL number

Clock Time

(seconds)

Max Velocity (Simulation) (m/s)

Max Velocity (Analytically)(m/s)

4

0.383

6535

0.1485

0.15

10

0.383

5826

0.1485

0.15

25

0.387

5936

0.1487

0.15

45

0.396

5498

0.1490

0.15

Observations:

1. As wedge angle increases CFL number also increases.

2. Symmetry boundary condition requires less time as compared to wedge boundary condtion for solving.

3. Higher the wedge angle more accurate are the results of simulation.

Conclusion:

As we can observe that there is slight difference in the values obtained through simulation for different angles with symmetry and wedge boundary condition, among which symmetry boundary condition with higher angle value gives more accurate results.

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