Founder’s Scholarship – Your Gateway to a Dream Engineering Career! Only 1̶0̶0̶ +10 Seats Available.

00D 00H 00M 00S

Menu

Executive Programs

Workshops

Projects

Blogs

Careers

Placements

Student Reviews

For Business

More

Academic Training

Informative Articles

Find Jobs

We are Hiring!

All Courses

Choose a category

Mechanical

Electrical

Civil

Computer Science

Electronics

Offline Program

All Courses

All Courses

logo

CHOOSE A CATEGORY

Mechanical

Electrical

Civil

Computer Science

Electronics

Offline Program

Top Job Leading Courses

Automotive

CFD

FEA

Design

MBD

Med Tech

Courses by Software

Design

Solver

Automation

Vehicle Dynamics

CFD Solver

Preprocessor

Courses by Semester

First Year

Second Year

Third Year

Fourth Year

Courses by Domain

Automotive

CFD

Design

FEA

Tool-focused Courses

Design

Solver

Automation

Preprocessor

CFD Solver

Vehicle Dynamics

Machine learning

Machine Learning and AI

POPULAR COURSES

coursePost Graduate Program in Hybrid Electric Vehicle Design and Analysis
coursePost Graduate Program in Computational Fluid Dynamics
coursePost Graduate Program in CAD
coursePost Graduate Program in CAE
coursePost Graduate Program in Manufacturing Design
coursePost Graduate Program in Computational Design and Pre-processing
coursePost Graduate Program in Complete Passenger Car Design & Product Development
Executive Programs
Workshops
For Business

Success Stories

Placements

Student Reviews

More

Projects

Blogs

Academic Training

Find Jobs

Informative Articles

We're Hiring!

phone+91 9342691281Log in
  1. Home/
  2. Ravi Shankar Yadav/
  3. Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation

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

Objective: To study the effect of the wedge angle and the Boundary Conditions on the simulation of an axisymmetric laminar flow in a cylindrical pipe. The given wedge angles in degrees are- 10 25 45   Axi-symmetric flow: A flow pattern is axisymmetric when it is identical in every plane that passes through…

  • CFD
  • MATLAB
  • OPENFOAM

  • Ravi Shankar Yadav

    updated on 11 Jan 2022

Objective:

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

The given wedge angles in degrees are-

  • 10
  • 25
  • 45

 

Axi-symmetric flow:

A flow pattern is axisymmetric when it is identical in every plane that passes through a certain straight line. The straight line is the symmetry axis. Every longitudinal plane through the axis would exhibit the same streamline pattern.

Hagen Poiseuille's Equation:

In nonideal fluid dynamics, the Hagen–Poiseuille equation 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 a constant cross-section. 

Laminar Flow:

In fluid dynamics, laminar flow is a type of fluid flow in which the fluid travels smoothly or in regular paths.

 

The diagrammatic representation of flow through the pipe. This is what the fluid profile looks like.

ex13.f1

 

Assumption:

  • Flow is steady, incompressible, and laminar.
  • Flow is two-dimensional.
  • Fluid properties are constant (viscosity, density, etc)

 

Given:

  • Reynolds number: 2100
  • Working fluid: Water
  • Fluid temperature: 250C
  • Diameter of the pipe, D = 0.02 m
  • Dynamic viscosity, (μ) = 0.89×10−3Pa-s
  • Kinematic Viscosity,ν= 0.89×10−6 m2s−1
  • ΔP=32⋅μ⋅L⋅VavgD2
  • θ = wedge angle
  • L = 2.52 m

 

Analytical Solution:

  • Average Velocity, Vavg=Re⋅μρ⋅D = 0.09373 ms−1
  • Maximum velocity, Vmax=2⋅Vavg = 0.18746 ms−1
  • Pressure Drop = 32×0.00089×2.52×0.093730.022 = 16.817 Pa
  • Kinematic Pressure Drop, ΔPP = 0.016817 m

 

MATLAB:

The code for Wedge Boundary Condition (Wedge angle will be taken from user input)

% Matlab code for generating the blockMeshDict file
% Wedge Boundary Condition
% Wedge angles = 10, 25, 45 degrees 

clear all
close all
clc

% Inputs
% Wedge angle
% Take angle as input from 10, 25, 45 degrees
theta = input('Enter the value of wedge angle = ');
% Reynolds number
Re =2100;
% Diameter
D=0.02;
% Length
L=0.06*Re*D;
% Radius
R=D/2;
% Dynamic viscosity
mu=0.89e-3;
% Density
rho=997.0;
% Kinematic viscosity
nu=mu/rho; 

% Pressure and  velocity
v_avg=Re*mu/(D*rho);
v_max=2*v_avg;
del_P =(32*mu*v_avg*L)/(D^2);
kin_P=del_P/rho; 
n1=50;
n2=1;
n3=300;
gfactor=0.5; 

% Vertices of the wedge
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)]; 

% Printing the contents of blockMesh file 

string1='/*-------------------------------------*- C++ -*---------------------*\';
string2=' =========                    |                                        ';
string3=' \       / F ield             |                                        ';
string4='  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    ';
string5='   \   /   A nd               |Version: 9                              ';
string6='    \ /    M anipulation      |Website: https://openfoam.org           ';
string7='\*-------------------------------------------------------------------*/';
string8='FoamFile';
string9='{';
string10='     version    2.0;';
string11='     format     ascii;';
string12='     class      dictionary;';
string13='     object     blockMeshDict;';
string14='}';
string15='//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //';
string16='//*******************************************************************//';

fpointer=fopen('blockMeshDict.txt','wt');

fprintf(fpointer,'%s\n',string1);
fprintf(fpointer,'%s\n',string2);
fprintf(fpointer,'%s\n',string3);
fprintf(fpointer,'%s\n',string4);
fprintf(fpointer,'%s\n',string5);
fprintf(fpointer,'%s\n',string6); 
fprintf(fpointer,'%s\n \n',string7);

fprintf(fpointer,'%s\n',string8);
fprintf(fpointer,'%s\n',string9);
fprintf(fpointer,'%s\n',string10);
fprintf(fpointer,'%s\n',string11);
fprintf(fpointer,'%s\n',string12);
fprintf(fpointer,'%s\n',string13);
fprintf(fpointer,'%s\n',string14);
fprintf(fpointer,'%s\n \n',string15);

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

fprintf(fpointer,'%s\n','vertices');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V0(1),V0(2),V0(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V1(1),V1(2),V1(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V2(1),V2(2),V2(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V3(1),V3(2),V3(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V4(1),V4(2),V4(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V5(1),V5(2),V5(3));
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n');

fprintf(fpointer,'%s\n','blocks');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s %s \n',blanks(5),'hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1)');
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n'); 
fprintf(fpointer,'%s\n','edges');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s arc 1 2 (%f %f %f)\n',blanks(5),0,R,0);
fprintf(fpointer,'%s arc 4 5 (%f %f %f)\n',blanks(5),0,R,0);
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n');

fprintf(fpointer,'%s\n','boundary');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s %s\n',blanks(5),'inlet');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type patch;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 1 2 0 )');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'outlet');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type patch;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(3 4 5 3)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'front');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type wedge;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 3 5 2)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'back');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type wedge;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 1 4 3)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'pipe');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type wall;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(1 4 5 2)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'axis');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type empty;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 3 3 0)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n'); 
fprintf(fpointer,'%s\n','mergePatchPairs'); 
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s\n',');'); 
fprintf(fpointer,'\n');
fprintf(fpointer,'%s\n',string16);
fclose(fpointer);

 

The blockMeshDict File for wedge boundary condition at 45 degrees

/*-------------------------------------*- C++ -*---------------------*\
 =========                    |                                        
 \       / F ield             |                                        
  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    
   \   /   A nd               |Version: 9                              
    \ /    M anipulation      |Website: https://openfoam.org           
\*-------------------------------------------------------------------*/
 
FoamFile
{
     version    2.0;
     format     ascii;
     class      dictionary;
     object     blockMeshDict;
}
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //
 
convertToMeters 1;
vertices
(
      (0.000000 0.000000 0.000000)
      (0.000000 0.009239 -0.003827)
      (0.000000 0.009239 0.003827)
      (2.520000 0.000000 0.000000)
      (2.520000 0.009239 -0.003827)
      (2.520000 0.009239 0.003827)
);

blocks
(
      hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1) 
);

edges
(
      arc 1 2 (0.000000 0.010000 0.000000)
      arc 4 5 (0.000000 0.010000 0.000000)
);

boundary
(
      inlet
      {
           type patch;
           faces
           (
                (0 1 2 0 )
           );
      }
      outlet
      {
           type patch;
           faces
           (
                (3 4 5 3)
           );
      }
      front
      {
           type wedge;
           faces
           (
                (0 3 5 2)
           );
      }
      back
      {
           type wedge;
           faces
           (
                (0 1 4 3)
           );
      }
      pipe
      {
           type wall;
           faces
           (
                (1 4 5 2)
           );
      }
      axis
      {
           type empty;
           faces
           (
                (0 3 3 0)
           );
      }
);

mergePatchPairs
(
);

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

 

The blockMeshDict File for wedge boundary condition at 25 degrees

/*-------------------------------------*- C++ -*---------------------*\
 =========                    |                                        
 \       / F ield             |                                        
  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    
   \   /   A nd               |Version: 9                              
    \ /    M anipulation      |Website: https://openfoam.org           
\*-------------------------------------------------------------------*/
 
FoamFile
{
     version    2.0;
     format     ascii;
     class      dictionary;
     object     blockMeshDict;
}
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //
 
convertToMeters 1;
vertices
(
      (0.000000 0.000000 0.000000)
      (0.000000 0.009763 -0.002164)
      (0.000000 0.009763 0.002164)
      (2.520000 0.000000 0.000000)
      (2.520000 0.009763 -0.002164)
      (2.520000 0.009763 0.002164)
);

blocks
(
      hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1) 
);

edges
(
      arc 1 2 (0.000000 0.010000 0.000000)
      arc 4 5 (0.000000 0.010000 0.000000)
);

boundary
(
      inlet
      {
           type patch;
           faces
           (
                (0 1 2 0 )
           );
      }
      outlet
      {
           type patch;
           faces
           (
                (3 4 5 3)
           );
      }
      front
      {
           type wedge;
           faces
           (
                (0 3 5 2)
           );
      }
      back
      {
           type wedge;
           faces
           (
                (0 1 4 3)
           );
      }
      pipe
      {
           type wall;
           faces
           (
                (1 4 5 2)
           );
      }
      axis
      {
           type empty;
           faces
           (
                (0 3 3 0)
           );
      }
);

mergePatchPairs
(
);

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

 

The blockMeshDict File for wedge boundary condition at 10 degrees

/*-------------------------------------*- C++ -*---------------------*\
 =========                    |                                        
 \       / F ield             |                                        
  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    
   \   /   A nd               |Version: 9                              
    \ /    M anipulation      |Website: https://openfoam.org           
\*-------------------------------------------------------------------*/
 
FoamFile
{
     version    2.0;
     format     ascii;
     class      dictionary;
     object     blockMeshDict;
}
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //
 
convertToMeters 1;
vertices
(
      (0.000000 0.000000 0.000000)
      (0.000000 0.009962 -0.000872)
      (0.000000 0.009962 0.000872)
      (2.520000 0.000000 0.000000)
      (2.520000 0.009962 -0.000872)
      (2.520000 0.009962 0.000872)
);

blocks
(
      hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1) 
);

edges
(
      arc 1 2 (0.000000 0.010000 0.000000)
      arc 4 5 (0.000000 0.010000 0.000000)
);

boundary
(
      inlet
      {
           type patch;
           faces
           (
                (0 1 2 0 )
           );
      }
      outlet
      {
           type patch;
           faces
           (
                (3 4 5 3)
           );
      }
      front
      {
           type wedge;
           faces
           (
                (0 3 5 2)
           );
      }
      back
      {
           type wedge;
           faces
           (
                (0 1 4 3)
           );
      }
      pipe
      {
           type wall;
           faces
           (
                (1 4 5 2)
           );
      }
      axis
      {
           type empty;
           faces
           (
                (0 3 3 0)
           );
      }
);

mergePatchPairs
(
);

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

 

ControlDict File for wedge Boundary Condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         10;

deltaT          0.001;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

 

Pressure File for Wedge Boundary Condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     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 0.0168682;
    }

    axis
    {
        type            empty;
    }
    
    pipe
    {
    	type		 zeroGradient;
    }
    
    front
    {
    	type		 wedge;
    }
    
    back
    {
    	type		 wedge;
    }
}

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

 

Velocity File for Wedge Boundary Condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform (0 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value		 uniform (0.0937312 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
    
    pipe
    {
    	type		 noSlip;
    }
    
    front
    {
    	type		 wedge;
    }
    
    back
    {
    	type		 wedge;
    }
}
// ************************************************************************* //

 

TransportProperties File for Wedge Boundary Condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "constant";
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu              [0 2 -1 0 0 0 0] 8.927e-07;


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

 

 

The code for Symmetry Boundary Condition (Wedge angle will be taken from user input)

% Matlab code for generating the blockMeshDict file
% Symmetry Boundary Condition
% Wedge angles = 10, 25, 45 degrees 

clear all
close all
clc

% Inputs
% Wedge angle
% Take angle as input from 10, 25, 45 degrees
theta = input('Enter the value of wedge angle = ');
% Reynolds number
Re =2100;
% Diameter
D=0.02;
% Length
L=0.06*Re*D;
% Radius
R=D/2;
% Dynamic viscosity
mu=0.89e-3;
% Density
rho=997.0;
% Kinematic viscosity
nu=mu/rho; 

% Pressure and  velocity
v_avg=Re*mu/(D*rho);
v_max=2*v_avg;
del_P =(32*mu*v_avg*L)/(D^2);
kin_P=del_P/rho; 
n1=50;
n2=1;
n3=300;
gfactor=0.5; 

% Vertices of the wedge
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)]; 

% Printing the contents of blockMesh file 

string1='/*-------------------------------------*- C++ -*---------------------*\';
string2=' =========                    |                                        ';
string3=' \       / F ield             |                                        ';
string4='  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    ';
string5='   \   /   A nd               |Version: 9                              ';
string6='    \ /    M anipulation      |Website: https://openfoam.org           ';
string7='\*-------------------------------------------------------------------*/';
string8='FoamFile';
string9='{';
string10='     version    2.0;';
string11='     format     ascii;';
string12='     class      dictionary;';
string13='     object     blockMeshDict;';
string14='}';
string15='//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //';
string16='//*******************************************************************//';

fpointer=fopen('blockMeshDict.txt','wt');

fprintf(fpointer,'%s\n',string1);
fprintf(fpointer,'%s\n',string2);
fprintf(fpointer,'%s\n',string3);
fprintf(fpointer,'%s\n',string4);
fprintf(fpointer,'%s\n',string5);
fprintf(fpointer,'%s\n',string6); 
fprintf(fpointer,'%s\n \n',string7);

fprintf(fpointer,'%s\n',string8);
fprintf(fpointer,'%s\n',string9);
fprintf(fpointer,'%s\n',string10);
fprintf(fpointer,'%s\n',string11);
fprintf(fpointer,'%s\n',string12);
fprintf(fpointer,'%s\n',string13);
fprintf(fpointer,'%s\n',string14);
fprintf(fpointer,'%s\n \n',string15);

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

fprintf(fpointer,'%s\n','vertices');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V0(1),V0(2),V0(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V1(1),V1(2),V1(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V2(1),V2(2),V2(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V3(1),V3(2),V3(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V4(1),V4(2),V4(3));
fprintf(fpointer,'%s (%f %f %f)\n',blanks(5),V5(1),V5(2),V5(3));
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n');

fprintf(fpointer,'%s\n','blocks');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s %s \n',blanks(5),'hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1)');
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n'); 
fprintf(fpointer,'%s\n','edges');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s arc 1 2 (%f %f %f)\n',blanks(5),0,R,0);
fprintf(fpointer,'%s arc 4 5 (%f %f %f)\n',blanks(5),0,R,0);
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n');

fprintf(fpointer,'%s\n','boundary');
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s %s\n',blanks(5),'inlet');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type patch;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 1 2 0 )');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'outlet');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type patch;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(3 4 5 3)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'front');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type symmetry;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 3 5 2)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'back');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type symmetry;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 1 4 3)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'pipe');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type wall;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(1 4 5 2)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');

fprintf(fpointer,'%s %s\n',blanks(5),'axis');
fprintf(fpointer,'%s %s\n',blanks(5),'{');
fprintf(fpointer,'%s %s\n',blanks(10),'type empty;');
fprintf(fpointer,'%s %s\n',blanks(10),'faces');
fprintf(fpointer,'%s %s\n',blanks(10),'(');
fprintf(fpointer,'%s %s\n',blanks(15),'(0 3 3 0)');
fprintf(fpointer,'%s %s\n',blanks(10),');');
fprintf(fpointer,'%s %s\n',blanks(5),'}');
fprintf(fpointer,'%s\n',');');
fprintf(fpointer,'\n'); 
fprintf(fpointer,'%s\n','mergePatchPairs'); 
fprintf(fpointer,'%s\n','(');
fprintf(fpointer,'%s\n',');'); 
fprintf(fpointer,'\n');
fprintf(fpointer,'%s\n',string16);
fclose(fpointer);

 

The blockMeshDict File for symmetry boundary condition at 45 degrees

/*-------------------------------------*- C++ -*---------------------*\
 =========                    |                                        
 \       / F ield             |                                        
  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    
   \   /   A nd               |Version: 9                              
    \ /    M anipulation      |Website: https://openfoam.org           
\*-------------------------------------------------------------------*/
 
FoamFile
{
     version    2.0;
     format     ascii;
     class      dictionary;
     object     blockMeshDict;
}
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //
 
convertToMeters 1;
vertices
(
      (0.000000 0.000000 0.000000)
      (0.000000 0.009239 -0.003827)
      (0.000000 0.009239 0.003827)
      (2.520000 0.000000 0.000000)
      (2.520000 0.009239 -0.003827)
      (2.520000 0.009239 0.003827)
);

blocks
(
      hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1) 
);

edges
(
      arc 1 2 (0.000000 0.010000 0.000000)
      arc 4 5 (0.000000 0.010000 0.000000)
);

boundary
(
      inlet
      {
           type patch;
           faces
           (
                (0 1 2 0 )
           );
      }
      outlet
      {
           type patch;
           faces
           (
                (3 4 5 3)
           );
      }
      front
      {
           type symmetry;
           faces
           (
                (0 3 5 2)
           );
      }
      back
      {
           type symmetry;
           faces
           (
                (0 1 4 3)
           );
      }
      pipe
      {
           type wall;
           faces
           (
                (1 4 5 2)
           );
      }
      axis
      {
           type empty;
           faces
           (
                (0 3 3 0)
           );
      }
);

mergePatchPairs
(
);

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

 

The blockMeshDict File for symmetry boundary condition at 25 degrees

/*-------------------------------------*- C++ -*---------------------*\
 =========                    |                                        
 \       / F ield             |                                        
  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    
   \   /   A nd               |Version: 9                              
    \ /    M anipulation      |Website: https://openfoam.org           
\*-------------------------------------------------------------------*/
 
FoamFile
{
     version    2.0;
     format     ascii;
     class      dictionary;
     object     blockMeshDict;
}
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //
 
convertToMeters 1;
vertices
(
      (0.000000 0.000000 0.000000)
      (0.000000 0.009763 -0.002164)
      (0.000000 0.009763 0.002164)
      (2.520000 0.000000 0.000000)
      (2.520000 0.009763 -0.002164)
      (2.520000 0.009763 0.002164)
);

blocks
(
      hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1) 
);

edges
(
      arc 1 2 (0.000000 0.010000 0.000000)
      arc 4 5 (0.000000 0.010000 0.000000)
);

boundary
(
      inlet
      {
           type patch;
           faces
           (
                (0 1 2 0 )
           );
      }
      outlet
      {
           type patch;
           faces
           (
                (3 4 5 3)
           );
      }
      front
      {
           type symmetry;
           faces
           (
                (0 3 5 2)
           );
      }
      back
      {
           type symmetry;
           faces
           (
                (0 1 4 3)
           );
      }
      pipe
      {
           type wall;
           faces
           (
                (1 4 5 2)
           );
      }
      axis
      {
           type empty;
           faces
           (
                (0 3 3 0)
           );
      }
);

mergePatchPairs
(
);

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

 

The blockMeshDict File for symmetry boundary condition at 10 degrees

/*-------------------------------------*- C++ -*---------------------*\
 =========                    |                                        
 \       / F ield             |                                        
  \     /  O peration         |OPENFOAM:The Open Source CFD Toolbox    
   \   /   A nd               |Version: 9                              
    \ /    M anipulation      |Website: https://openfoam.org           
\*-------------------------------------------------------------------*/
 
FoamFile
{
     version    2.0;
     format     ascii;
     class      dictionary;
     object     blockMeshDict;
}
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  //
 
convertToMeters 1;
vertices
(
      (0.000000 0.000000 0.000000)
      (0.000000 0.009962 -0.000872)
      (0.000000 0.009962 0.000872)
      (2.520000 0.000000 0.000000)
      (2.520000 0.009962 -0.000872)
      (2.520000 0.009962 0.000872)
);

blocks
(
      hex (0 1 2 0 3 4 5 3 ) (50 1 200) simpleGrading (0.5 1 1) 
);

edges
(
      arc 1 2 (0.000000 0.010000 0.000000)
      arc 4 5 (0.000000 0.010000 0.000000)
);

boundary
(
      inlet
      {
           type patch;
           faces
           (
                (0 1 2 0 )
           );
      }
      outlet
      {
           type patch;
           faces
           (
                (3 4 5 3)
           );
      }
      front
      {
           type symmetry;
           faces
           (
                (0 3 5 2)
           );
      }
      back
      {
           type symmetry;
           faces
           (
                (0 1 4 3)
           );
      }
      pipe
      {
           type wall;
           faces
           (
                (1 4 5 2)
           );
      }
      axis
      {
           type empty;
           faces
           (
                (0 3 3 0)
           );
      }
);

mergePatchPairs
(
);

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

 

Pressure File for symmetry boundary condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     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 0.0168682;
    }

    axis
    {
        type            empty;
    }
    
    pipe
    {
    	type		 zeroGradient;
    }
    
    front
    {
    	type		 symmetry;
    }
    
    back
    {
    	type		 symmetry;
    }
}

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

 

Velocity File for symmetry boundary condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform (0 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value		 uniform (0.0937312 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
    
    pipe
    {
    	type		 noSlip;
    }
    
    front
    {
    	type		 symmetry;
    }
    
    back
    {
    	type		 symmetry;
    }
}
// ************************************************************************* //

 

Output:

Velocity Profile

Wedge BC at 10-degree                                               Symmetry BC at 10 degree

ex ex

 

Wedge BC at 25-degree                                               Symmetry BC at 25 degree

ex ex

 

Wedge BC at 45-degree                                               Symmetry BC at 45 degree

ex ex

 

Pressure Profile

Wedge BC at 10-degree                                               Symmetry BC at 10 degree

ex ex

 

Wedge BC at 25-degree                                               Symmetry BC at 25 degree

ex ex

 

Wedge BC at 45-degree                                               Symmetry BC at 45 degree

ex ex

 

Velocity Graph

Wedge BC at 10-degree                                               Symmetry BC at 10 degree

ex ex

 

Wedge BC at 25-degree                                               Symmetry BC at 25 degree

ex ex

 

Wedge BC at 45-degree                                               Symmetry BC at 45 degree

ex ex

 

Pressure Graph

Wedge BC at 10-degree                                               Symmetry BC at 10 degree

ex ex

 

Wedge BC at 25-degree                                               Symmetry BC at 25 degree

ex ex

 

Wedge BC at 45-degree                                               Symmetry BC at 45 degree

ex ex

 

Shear Stress Graph

Wedge BC at 10-degree                                               Symmetry BC at 10 degree

ex ex

 

Wedge BC at 25-degree                                               Symmetry BC at 25 degree

ex ex

 

Wedge BC at 45-degree                                               Symmetry BC at 45 degree

ex ex

 

Results:

  1. From Velocity graphs, we can observe that the slope for symmetry BC is more than that of wedge BC. Also, for both wedge BC and symmetry BC slope is increasing as the wedge angle is increasing.
  2. From Pressure graphs, we can observe that for wedge BC the line is straight, but not for symmetry BC.
  3. From shear stress graphs, we can observe that the slope for wedge BC is more than that of symmetry BC. Also, for both wedge BC and symmetry BC slope is increasing as the wedge angle is increasing.

 

To validate the Hydrodynamic length with the Numerical Result:

In fluid dynamics, the entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed.
Numerically, we know that the velocity profile will be different before and after the Hydrodynamic entry length. After the Hydrodynamic entry length, the Velocity profile will be the final parabolic profile that it must have in a fully developed region.

To calculate the Hydrodynamic length analytically,

Lh=0.005⋅Re⋅D

where, Re = Reynolds number; D = Diameter. 
Lh = 0.005*2100*0.02 = 0.21 m

 

To validate Maximum Pressure drop in the Fully developed Region:

Pressure Drop, ΔP = 32×0.00089×2.52×0.093730.022 = 16.817 Pa

From the graph, max P = 0.039 * 1000 Pa; min P = 0.022 * 1000 Pa

so, Pressure drop = 0.017*1000 = 17 Pa

Error in drop = Numerical - Practical = 17 - 16.817 = 0.183 Pa

 

To validate Maximum Velocity:

Average Velocity, Vavg=Re⋅μρ⋅D = 0.09373 ms−1

Maximum velocity, Vmax=2⋅Vavg = 0.18746 ms−1

From the graph, we can that observe max velocity is 0.15 ms−1

Error = |Numerical Velocity - Graphical Velocity| = |0.15 - 0.18746| = 0.03746

 

Comparison between the two Boundary Conditions:

  1. We have performed Simulations for two Boundary Conditions, which are Symmetry Boundary Condition and the Wedge Boundary Condition.
  2. During the Wedge Boundary condition simulation, the simulation across the arc of the wedge is not done, but whereas in the case of Symmetry Boundary Condition, the calculation across the arc of the wedge is done. Hence, the simulation time is higher in that case.
  3. The Courant number is increasing slightly in the case of wedge Boundary Condition and hence the Symmetry Boundary Condition will be slightly more accurate.
  4. The Symmetry Boundary condition considers the Mesh as 3D and the calculation is done along all the three global axes.

 

Leave a comment

Thanks for choosing to leave a comment. Please keep in mind that all the comments are moderated as per our comment policy, and your email will not be published for privacy reasons. Please leave a personal & meaningful conversation.

Please  login to add a comment

Other comments...

No comments yet!
Be the first to add a comment

Read more Projects by Ravi Shankar Yadav (25)

Week-11 : Discretization of 3D intake manifold using GEM-3D

Objective:

Aim: Discretization of 3D intake manifold using GEM-3D   Objective: 1. Tutorial- single cyl DI add case 2 with discretization length 0.1 mm for intake runner and compare with default case 1 Parameters-Torque, BSFC, max cylinder pressure simulation time 2. Explore tutorial no 2 (GEM3D) - “Building intake…

calendar

31 Aug 2022 05:57 AM IST

    Read more

    Week-7 : Converting a detailed engine model to a FRM model

    Objective:

    Aim: Converting a detailed engine model to an FRM model.   Objective:  Explore tutorial number 9 and write a detailed report. Build FRM Model for the following configuration using the FRM builder approach. Bore 102 mm stroke 115 mm CR 17 No of cylinder 6 CI engine Twin Scroll Turbine GT Controller Run all cases…

    calendar

    30 Aug 2022 02:54 AM IST

      Read more

      Week-6 : Turbocharger Modelling

      Objective:

      Aim: Turbocharger Modelling using GT POWER   Objective: List down different TC and locate examples from GT Power Explore tutorial number 6 and 7 Plot operating points on compressor and turbine maps In which application Variable Geometry Turbine is beneficial? Explore example- Diesel VGT EGR and understand the modeling…

      calendar

      22 Aug 2022 10:30 AM IST

        Read more

        Week-4 : Basic Calibration of Single cylinder CI-Engine

        Objective:

        Aim: Basic Calibration of Single cylinder CI-Engine   Objective: 1. Compare SI vs CI and list down differences (assignment no 2-SI) 2. Comments on the following parameters BSFC Exhaust Temperature A/F ratios 3. Change MFB 50 and observe the impact on performance   Comparison: SI vs CI S.No./Engine type  …

        calendar

        15 Aug 2022 03:48 PM IST

          Read more

          Schedule a counselling session

          Please enter your name
          Please enter a valid email
          Please enter a valid number

          Related Courses

          coursecardcoursetype

          Post Graduate Program in CFD Solver Development

          4.8

          119 Hours of Content

          coursecard

          Introduction to OpenFOAM Development

          4.9

          18 Hours of Content

          coursecardcoursetype

          Post Graduate Program in Battery Technology for Mechanical Engineers

          4.8

          81 Hours of Content

          coursecard

          Simulation and Design of Power Converters for EV using MATLAB and Simulink

          4.9

          22 Hours of Content

          coursecard

          Introduction to Hybrid Electric Vehicle using MATLAB and Simulink

          4.8

          23 Hours of Content

          Schedule a counselling session

          Please enter your name
          Please enter a valid email
          Please enter a valid number

          logo

          Skill-Lync offers industry relevant advanced engineering courses for engineering students by partnering with industry experts.

          https://d27yxarlh48w6q.cloudfront.net/web/v1/images/facebook.svghttps://d27yxarlh48w6q.cloudfront.net/web/v1/images/insta.svghttps://d27yxarlh48w6q.cloudfront.net/web/v1/images/twitter.svghttps://d27yxarlh48w6q.cloudfront.net/web/v1/images/youtube.svghttps://d27yxarlh48w6q.cloudfront.net/web/v1/images/linkedin.svg

          Our Company

          News & EventsBlogCareersGrievance RedressalSkill-Lync ReviewsTermsPrivacy PolicyBecome an Affiliate
          map
          EpowerX Learning Technologies Pvt Ltd.
          4th Floor, BLOCK-B, Velachery - Tambaram Main Rd, Ram Nagar South, Madipakkam, Chennai, Tamil Nadu 600042.
          mail
          info@skill-lync.com
          mail
          ITgrievance@skill-lync.com

          Top Individual Courses

          Computational Combustion Using Python and CanteraIntroduction to Physical Modeling using SimscapeIntroduction to Structural Analysis using ANSYS WorkbenchIntroduction to Structural Analysis using ANSYS Workbench

          Top PG Programs

          Post Graduate Program in Hybrid Electric Vehicle Design and AnalysisPost Graduate Program in Computational Fluid DynamicsPost Graduate Program in CADPost Graduate Program in Electric Vehicle Design & Development

          Skill-Lync Plus

          Executive Program in Electric Vehicle Embedded SoftwareExecutive Program in Electric Vehicle DesignExecutive Program in Cybersecurity

          Trending Blogs

          Heat Transfer Principles in Energy-Efficient Refrigerators and Air Conditioners Advanced Modeling and Result Visualization in Simscape Exploring Simulink and Library Browser in Simscape Advanced Simulink Tools and Libraries in SimscapeExploring Simulink Basics in Simscape

          © 2025 Skill-Lync Inc. All Rights Reserved.

                      Do You Want To Showcase Your Technical Skills?
                      Sign-Up for our projects.