Challenge

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

SSaquib Hazari16 Jul 2022

Aim: To perform the effect of the wedge angle and the Boundary Conditions on the simulation of an axisymmetric laminar flow in a cylindrical pipe.

objective: 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.

Procedure:

1. The procedure for this challenge involves editing the previously made MATLAB code and changing the input and the Boundary Conditions in OpenFoam.

2. In the Automated BlockMeshDict file, we need to edit the wedge angle for one particular boundary condition. The angles at which we are performing the simulation and then later studying the simulation results are:
a. 10o10o
b. 25o25o
c. 45o45o

The code for Wedge Boundary Condition at a wedge angle of 45 deg is as follows:

clear all
close all
clc

%Inputs:
l= 1.5;         %Length of the pipe.
theta = 45.0;    %Wedge angle.
d = 0.01;       %Diameter of the pipe.
c = 1.0;        %Conversion Factor. 
r = d/2;        %Radius of the Cylinder.
nx = 500;       %number of Mesh points in x-direction on the block.
ny= 25;         %Number of Mesh points in the y-direction on the block.
nz= 1;          %number of Mesh Points in the z-direction on the block.
gx = 1;         %Grading along the x-direction.
gy = 1;         %Grading along the y-direction.
gz = 1;         %Grading along the z-direction.


f1 = fopen('BlockMeshDict.txt','w');
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:  8 n');
fprintf(f1,'     /     M anipulation  | n');
fprintf(f1,'/*------------------------------------------------------------------*/ n');
fprintf(f1, 'FoamFile n');
fprintf(f1,'{ n');
fprintf(f1,'    version     2.0; n');
fprintf(f1,'    format      ascii; n' );
fprintf(f1,'    class       dictionary; n');
fprintf(f1,'    object      blockMeshDict; n');
fprintf(f1,'} n');
fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // n');

fprintf(f1,'convertToMeters %0.1f; n',c);
fprintf(f1,'n');
fprintf(f1,'vertices n');
fprintf(f1,'( n');
fprintf(f1,'(0 0 0) n');
fprintf(f1,'(%0.6f %0.6f %0.3f)n',r*sind(theta/2),r*cosd(theta/2),0);
fprintf(f1, '(%0.6f %0.6f %0.3f)n',-r*sind(theta/2),r*cosd(theta/2),0);
fprintf(f1,'(0 0 %0.3f) n',-l);
fprintf(f1,'(%0.6f %0.6f %0.3f)n',r*sind(theta/2),r*cosd(theta/2),-l);
fprintf(f1, '(%0.6f %0.6f %0.3f)n',-r*sind(theta/2),r*cosd(theta/2),-l);
fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'blocks n');
fprintf(f1,'( n');
fprintf(f1,'hex (0 3 5 2 0 3 4 1) (%0.0f %0.0f %0.0f) simpleGrading (%0.0f %0.0f %0.0f) n',nx,ny,nz,gx,gy,gz);
fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'edges n');
fprintf(f1,'( n');
fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'boundary n');
fprintf(f1,'( n');
fprintf(f1,'in n');
fprintf(f1,'{ n');
fprintf(f1,'type patch; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(0 1 2 0) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'out n');
fprintf(f1,'{ n');
fprintf(f1,'type patch; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(3 5 4 3) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'ft n');
fprintf(f1,'{ n');
fprintf(f1,'type wedge; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(0 3 4 1) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'bk n');
fprintf(f1,'{ n');
fprintf(f1,'type wedge; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(3 0 2 5) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'top n');
fprintf(f1,'{ n');
fprintf(f1,'type wall; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(5 2 1 4) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'axis n');
fprintf(f1,'{ n');
fprintf(f1,'type empty; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(0 3 3 0) n');
fprintf(f1,'); n');
fprintf(f1, '} n');

fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'mergePatchPairs n');
fprintf(f1,'( n');
fprintf(f1,'); n');
fprintf(f1,'n');
fprintf(f1,'// ************************************************************************* // n');


%END

The code for Symmetry Boundary Condition at a wedge angle of 45 deg is as follows:

clear all
close all
clc

%Inputs:
l= 1.5;         %Length of the pipe.
theta = 45.0;    %Wedge angle.
d = 0.01;       %Diameter of the pipe.
c = 1.0;        %Conversion Factor. 
r = d/2;        %Radius of the Cylinder.
nx = 500;       %number of Mesh points in x-direction on the block.
ny= 25;         %Number of Mesh points in the y-direction on the block.
nz= 3;          %number of Mesh Points in the z-direction on the block.
gx = 1;         %Grading along the x-direction.
gy = 1;         %Grading along the y-direction.
gz = 1;         %Grading along the z-direction.


f1 = fopen('BlockMeshDict.txt','w');
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:  8 n');
fprintf(f1,'     /     M anipulation  | n');
fprintf(f1,'/*------------------------------------------------------------------*/ n');
fprintf(f1, 'FoamFile n');
fprintf(f1,'{ n');
fprintf(f1,'    version     2.0; n');
fprintf(f1,'    format      ascii; n' );
fprintf(f1,'    class       dictionary; n');
fprintf(f1,'    object      blockMeshDict; n');
fprintf(f1,'} n');
fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // n');

fprintf(f1,'convertToMeters %0.1f; n',c);
fprintf(f1,'n');
fprintf(f1,'vertices n');
fprintf(f1,'( n');
fprintf(f1,'(0 0 0) n');
fprintf(f1,'(%0.6f %0.6f %0.3f)n',r*sind(theta/2),r*cosd(theta/2),0);
fprintf(f1, '(%0.6f %0.6f %0.3f)n',-r*sind(theta/2),r*cosd(theta/2),0);
fprintf(f1,'(0 0 %0.3f) n',-l);
fprintf(f1,'(%0.6f %0.6f %0.3f)n',r*sind(theta/2),r*cosd(theta/2),-l);
fprintf(f1, '(%0.6f %0.6f %0.3f)n',-r*sind(theta/2),r*cosd(theta/2),-l);
fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'blocks n');
fprintf(f1,'( n');
fprintf(f1,'hex (0 3 5 2 0 3 4 1) (%0.0f %0.0f %0.0f) simpleGrading (%0.0f %0.0f %0.0f) n',nx,ny,nz,gx,gy,gz);
fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'edges n');
fprintf(f1,'( n');
fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'boundary n');
fprintf(f1,'( n');
fprintf(f1,'in n');
fprintf(f1,'{ n');
fprintf(f1,'type patch; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(0 1 2 0) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'out n');
fprintf(f1,'{ n');
fprintf(f1,'type patch; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(3 5 4 3) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'ft n');
fprintf(f1,'{ n');
fprintf(f1,'type symmetry; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(0 3 4 1) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'bk n');
fprintf(f1,'{ n');
fprintf(f1,'type symmetry; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(3 0 2 5) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'top n');
fprintf(f1,'{ n');
fprintf(f1,'type wall; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(5 2 1 4) n');
fprintf(f1,'); n');
fprintf(f1,'} n');

fprintf(f1,'axis n');
fprintf(f1,'{ n');
fprintf(f1,'type empty; n');
fprintf(f1,'faces n');
fprintf(f1,'( n');
fprintf(f1,'(0 3 3 0) n');
fprintf(f1,'); n');
fprintf(f1, '} n');

fprintf(f1,'); n');
fprintf(f1,'n');

fprintf(f1,'mergePatchPairs n');
fprintf(f1,'( n');
fprintf(f1,'); n');
fprintf(f1,'n');
fprintf(f1,'// ************************************************************************* // n');


%END

3. So, we must run the simulation and plot the necessary graphs at all the Boundary Conditions' angles, i.e. Wedge Boundary conditions and the Symmetry Boundary Condition. We must make use of the plot over line command to study how the shear force is varying with a change in the distance along the radial direction. In contrast, the Pressure drop is to be studied in the fully developed region along the Axial Direction.

To plot the line, we must use the plot over line command. This will help us study the data variation along that line.

Then, we must plot the co-ordinates along which we want to study the data. Here, we need to properly give the coordinates as they will determine the plot and the data we study.
The coordinates are given as follows:

The line is drawn, as shown below:

4. We must change the Boundary condition for this and then run the simulation for the same angles. Another location where we need to change is the Initial Conditions. For the wedge's front and Back faces, we must specify the condition as Symmetry instead of Wedge.

5. After all the simulations were run, the results are to be compared and then findings are to be studied.

Result:

1. The first simulation comparison is with the Wedge Boundary condition. Within this Boundary Condition, the simulation comparison for all the above-mentioned angles is as follows.
We will compare the Shear Stress developed for both the boundary conditions at all three angles.

a.Shear Stress Variation with respect to the Radial Distance.

The Shear Stress plot for both the Boundary Conditions, the wedge Boundary Condition and the Symmetry Boundary Condition are shown at 10degrees. We can see that when we apply the Symmetry Boundary Condition, the slope of the curve is much higher than when we apply the Wedge Boundary Condition. So, when we apply the Symmetry Boundary Condition, the Mesh becomes 3D, and the computation is done for all three global axes. This affects the calculation as well. The peak value in the Wedge Boundary Condition is approximately 0.145 units, but whereas when we apply the Symmetry Boundary Condition, the peak value touches around 0.140units.

The graph shown above is comparing the Shear Stress for both the boundary conditions for when the wedge angle is 25degrees.

Similarly, we plot and study all the graphs, as shown below:

This graph compares the Shear Stress at 45 Deg for both the Boundary conditions.

b. Velocity Variation with respect to Radial Distance.

Velocity variation at 10degrees for the two Boundary Conditions.

Velocity variation at 25 degrees for the two Boundary Conditions.

Velocity variation at 45 degrees for the two Boundary Conditions.

c. Pressure Drop across the axial Distance

Pressure drop at 10 degrees across the Axial Distance.

Pressure drop at 25 degrees across the Axial Distance.

Pressure drop at 45 degrees across the Axial Distance.
Result:

Velocity profile before the Hydrodynamic Length

Here is the velocity profile before the Hydrodynamic Length. We can see that this plot is not properly parabolic.

The location where the velocity was measured for the above plot:

Whereas, if we compare the velocity profile at a location after the hydrodynamic length and in the fully developed region, the velocity profile will be much more defined and proper.
Result:

Velocity after the Hydrodynamic length

The location where the velocity was measured for the above plot:

d. Shear Stress Plot:

Shear Stress Plot
Conclusion: Hence we have we have obtain the effect of the wedge angle and the Boundary Conditions on the simulation of an axisymmetric laminar flow in a cylindrical pipe.

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

Ship work like this
in your own course.

Talk to a career counsellor

Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.