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Simulation of flow through a pipe of circular cross section by wedge symmetry

RRavish Bhatnagar23 Feb 2020
CFD

AIM:- To simulate a laminar flow through a pipe of circular cross section

Hagen poiseulli flow is defined as a fully developed laminar flow through a pipe. It is an exact solution of navier stokes equation.

considering water as the test fluid, the thermo-physical properties are:

  • reynolds number : 2100
  • dynamic viscocity: 0.89e-3
  • density : 997 kg/m^3
  • diameter of pipe : 0.020m
  • entry length L_e: 0.06*Re*D
  • length for fully developed flow :L_e+o.3

the average velocity is given by :`(Re*mu)/(rho*d)`

pressure `trianglep`:`(32*mu*v*l)/d^2`

kinematic pressure :`(triangle p)/rho`

calculated values for above conditions:

  • pressure = 0.018876
  • velocity = 0.1874

CODE STRUCTURE:-

the simulation of flow through entire cross section of a pipe is very resource intensive calculation so to compensate for this we can simulate the flow through a wedge shaped element of the pipe and since the pipe is of a circular cross section the results obtained will be of symmetric nature .

matlab can be used to automate the process of setting up an openFoam case.

  1. progam to ask for input of the thermo-physical quantities of the fluid. 
    #a program to simulate laminar flow through a pipe of circular cross section
#input variables and conditions

clear all
close all
clc

#flow variables
disp(\'input flow variables\')
Re = input(\'specify the reynolds number of the flow:\');
mu = input(\'dynamic viscocity of fluid:\');
D = input(\'diameter of pipe:\');
R = D/2;
Rho = input(\'the density of liquid:\');
L_e = 0.06*Re*D;
L = L_e+0.3;

#simulation variables
disp(\'input simulation parameters\')
endTime = input(\'specify the end time for simulation:\');
deltaT = input(\'specify the time step for simulation:\');

#initial calculations
#velocity 
v = (Re*mu)/(Rho*D)
#pressure
p = (32*mu*L*v)/(D^2);
#kinematic pressure
P = p/Rho

#pipe geometry
theta = input(\'input wedge angle\');
x = L;
y = R*cosd(theta/2);
z = R*sind(theta/2);

#setting up an openFoam case for the simulation
openFoam_case_gen

velocity_gen(v);
cd ..
cd ..
pressure_gen(P);
cd ..
cd ..
controldict_gen(endTime ,deltaT);
cd ..
cd ..
blockmesh_gen(x,y,z,R);
cd ..
cd ..
transportproperties_gen(mu);
cd ..

​
    the program asks user to specify the properties of the fluid, calculates the initial condition of pressure and velocity and asks for the wedge geometry , simulation time and time step. after taking the inputs it calls on different functions to set openfoam case.
  2. openFoam case generator 
    #function for setting up an openFoam case
function out = openFoam_case_gen

mkdir pipe_flow_solution; 
mkdir pipe_flow_solution constant;
mkdir pipe_flow_solution system;
mkdir pipe_flow_solution 0;

end
​
    this is a function to create the folders which are typically found in a openFoam case such as constant , system and 0
  3. initial value generators 
    #function to generate velocity file_in_loadpath
function out = velocity_gen(v);
  
     cd pipe_flow_solution
     cd  0
   
h1 = (\'/*--------------------------------*- C++ -*----------------------------------*\\\');
h2 = \'\\*---------------------------------------------------------------------------*/\';
fid = fopen(\'u.txt\',\'w\');
fprintf(fid,h1)
fprintf(fid,\'\\n\')
fprintf(fid,\'  =========                |\\n\')
fprintf(fid,\'  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\\n\')
fprintf(fid,\'   \\\\    /   O peration     | Website:  https://openfoam.org\\n\')
fprintf(fid,\'    \\\\  /    A nd           | Version:  7\\n\')
fprintf(fid,\'     \\\\/     M anipulation  |\\n\')
fprintf(fid,\'%s\\n\',h2);
fprintf(fid,\'\\n\')
fprintf(fid,\'FoamFile\\n\')
fprintf(fid,\'{\\n\')
fprintf(fid,\'    version     2.0;\\n\')
fprintf(fid,\'    format      ascii;\\n\')
fprintf(fid,\'    class       dictionary;\\n\')
fprintf(fid,\'    location    \"constant\";\\n\')
fprintf(fid,\'    object      transportProperties;\\n\')
fprintf(fid,\'}\\n\')
fprintf(fid,\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'dimensions      [0 1 -1 0 0 0 0];\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'internalField   uniform (0 0 0);\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'boundaryField\\n\')
fprintf(fid,\'{\\n\')
fprintf(fid,\'    inlet\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type            fixedValue;\\n\')
fprintf(fid,\'	value		uniform (%f 0 0);\\n\',v)
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    outlet\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type            zeroGradient;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    axis\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type            empty;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    top\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'  	type		noSlip;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    front\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'	type		wedge;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    back\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'	type		wedge;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'}\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'// ************************************************************************* //\\n\')
fclose (fid)

end​
    #function to generate pressure file
function out = pressure_gen(P) 
   cd pipe_flow_solution
   cd  0
h1 = (\'/*--------------------------------*- C++ -*----------------------------------*\\\');
h2 = \'\\*---------------------------------------------------------------------------*/\';
fid = fopen(\'p.txt\',\'w\');
fprintf(fid,h1)
fprintf(fid,\'\\n\')
fprintf(fid,\'  =========                |\\n\')
fprintf(fid,\'  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\\n\')
fprintf(fid,\'   \\\\    /   O peration     | Website:  https://openfoam.org\\n\')
fprintf(fid,\'    \\\\  /    A nd           | Version:  7\\n\')
fprintf(fid,\'     \\\\/     M anipulation  |\\n\')
fprintf(fid,\'%s\\n\',h2);
fprintf(fid,\'\\n\')
fprintf(fid,\'FoamFile\\n\')
fprintf(fid,\'{\\n\')
fprintf(fid,\'    version     2.0;\\n\')
fprintf(fid,\'    format      ascii;\\n\')
fprintf(fid,\'    class       dictionary;\\n\')
fprintf(fid,\'    location    \"constant\";\\n\')
fprintf(fid,\'    object      transportProperties;\\n\')
fprintf(fid,\'}\\n\')
fprintf(fid,\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\\n\')

fprintf(fid,\'dimensions      [0 2 -2 0 0 0 0];\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'internalField   uniform 0;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'boundaryField\\n\')
fprintf(fid,\'{\\n\')
fprintf(fid,\'    inlet\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type            zeroGradient;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    outlet\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type            fixedValue;\\n\')
fprintf(fid,\'	value		uniform (%f);\\n\',P)
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    axis\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type            empty;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\' \\n\')   
fprintf(fid,\'    top\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'  	type		zeroGradient;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    front\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'	type		wedge;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    back\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'	type		wedge;\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'}\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'// ************************************************************************* //\\n\')
fclose(fid)

end​

    the functions take their inputs form the main program and create initial condition files of pressure and velocity in the 0 folder.

  4. system generator functions: 
    #function to generate controldict file for simulation
function out = controldict_gen(endTime ,deltaT)

 cd pipe_flow_solution
 cd  system
 
h1 = (\'/*--------------------------------*- C++ -*----------------------------------*\\\');
h2 = \'\\*---------------------------------------------------------------------------*/\';
fid = fopen(\'controlDict.txt\',\'w\');
fprintf(fid,h1)
fprintf(fid,\'\\n\')
fprintf(fid,\'  =========                |\\n\')
fprintf(fid,\'  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\\n\')
fprintf(fid,\'   \\\\    /   O peration     | Website:  https://openfoam.org\\n\')
fprintf(fid,\'    \\\\  /    A nd           | Version:  7\\n\')
fprintf(fid,\'     \\\\/     M anipulation  |\\n\')
fprintf(fid,\'%s\\n\',h2);
fprintf(fid,\'\\n\')
fprintf(fid,\'FoamFile\\n\')
fprintf(fid,\'{\\n\')
fprintf(fid,\'    version     2.0;\\n\')
fprintf(fid,\'    format      ascii;\\n\')
fprintf(fid,\'    class       dictionary;\\n\')
fprintf(fid,\'    location    \"constant\";\\n\')
fprintf(fid,\'    object      transportProperties;\\n\')
fprintf(fid,\'}\\n\')
fprintf(fid,\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'application     icoFoam;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'startFrom       startTime;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'startTime       0;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'stopAt          endTime;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'endTime         %f;\\n\',endTime)
fprintf(fid,\'\\n\')
fprintf(fid,\'deltaT          %f;\\n\',deltaT)
fprintf(fid,\'\\n\')
fprintf(fid,\'writeControl    timeStep;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'writeInterval   20;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'purgeWrite      0;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'writeFormat     ascii;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'writePrecision  6;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'writeCompression off;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'timeFormat      general;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'timePrecision   6;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'runTimeModifiable true;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'// ************************************************************************* //\\n\')

fclose(fid)

end
​
    #function to create the blockmesh part file
function out = blockmesh_gen(x,y,z,R)
 cd pipe_flow_solution
 cd  system
fid = fopen(\'blockmeshDict.txt\' , \'w\')

h1 = (\'/*--------------------------------*- C++ -*----------------------------------*\\\');
h2 = \'\\*---------------------------------------------------------------------------*/\';

fprintf(fid,h1)
fprintf(fid,\'\\n\')
fprintf(fid,\'  =========                |\\n\')
fprintf(fid,\'  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\\n\')
fprintf(fid,\'   \\\\    /   O peration     | Website:  https://openfoam.org\\n\')
fprintf(fid,\'    \\\\  /    A nd           | Version:  7\\n\')
fprintf(fid,\'     \\\\/     M anipulation  |\\n\')
fprintf(fid,\'%s\\n\',h2);
fprintf(fid,\'\\n\')
fprintf(fid,\'FoamFile\\n\')
fprintf(fid,\'{\\n\')
fprintf(fid,\'    version     2.0;\\n\')
fprintf(fid,\'    format      ascii;\\n\')
fprintf(fid,\'    class       dictionary;\\n\')
fprintf(fid,\'    location    \"constant\";\\n\')
fprintf(fid,\'    object      transportProperties;\\n\')
fprintf(fid,\'}\\n\')
fprintf(fid,\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'convertToMeters 1;\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'vertices\\n\') 
fprintf(fid,\'\\n\')
fprintf(fid,\'(\\n\')
fprintf(fid,\'   (0 0 0)\\n\')
fprintf(fid,\'   (0 %f %f)\\n\',y,z)
fprintf(fid,\'   (0 %f %f)\\n\',y,-z)
fprintf(fid,\'   (%f 0 0)\\n\',x)
fprintf(fid,\'   (%f %f% f)\\n\',x,y,z)
fprintf(fid,\'   (%f %f %f)\\n\',x,y,-z)
fprintf(fid,\'\\n\')
fprintf(fid,\');\\n\')
fprintf(fid,\'blocks\\n\')
fprintf(fid,\'(    hex (0 3 5 2 0 3 4 1) (300 10 1) simpleGrading (1 1 1));\\n\')
fprintf(fid,\'edges\\n\')
fprintf(fid,\'(\\n\')
fprintf(fid,\'arc 1 2 (0 %f 0)\\n\',R)
fprintf(fid,\'arc 4 5 (%f %f 0)\\n\',x,R)
fprintf(fid,\');\\n\')
fprintf(fid,\'boundary\\n\')
fprintf(fid,\'(\\n\')
fprintf(fid,\'    inlet\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type patch;\\n\')
fprintf(fid,\'        faces\\n\')
fprintf(fid,\'        (\\n\')
fprintf(fid,\'            (1 2 0 0)\\n\')
fprintf(fid,\'         );\\n\')
fprintf(fid,\'     }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    outlet\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'    	type patch;\\n\')
fprintf(fid,\'	faces\\n\')
fprintf(fid,\'	(\\n\')
fprintf(fid,\'	    (3 5 4 3)\\n\')
fprintf(fid,\'	);\\n\')
fprintf(fid,\'     }\\n\')    
fprintf(fid,\'	\\n\')
fprintf(fid,\'    top\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type wall;\\n\')
fprintf(fid,\'        faces\\n\')
fprintf(fid,\'        (\\n\')
fprintf(fid,\'            (2 1 4 5)\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'        );\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'    front\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'	type wedge;\\n\')
fprintf(fid,\'	faces\\n\')
fprintf(fid,\'	(\\n\')
fprintf(fid,\'	(3 4 1 0)\\n\')
fprintf(fid,\'	);\\n\')
fprintf(fid,\'     }\\n\')
fprintf(fid,\'     \\n\')
fprintf(fid,\'     back\\n\')
fprintf(fid,\'     {\\n\')
fprintf(fid,\'	type wedge;\\n\')
fprintf(fid,\'	faces\\n\')
fprintf(fid,\'   	(\\n\')
fprintf(fid,\'	(3 5 2 0)\\n\')
fprintf(fid,\'	);\\n\')
fprintf(fid,\'     }\\n\')
fprintf(fid,\'	\\n\')
fprintf(fid,\'     axis\\n\')
fprintf(fid,\'    {\\n\')
fprintf(fid,\'        type empty;\\n\')
fprintf(fid,\'        faces\\n\')
fprintf(fid,\'        (\\n\')
fprintf(fid,\'            (0 3 3 0)\\n\')
fprintf(fid,\'        );\\n\')
fprintf(fid,\'    }\\n\')
fprintf(fid,\');\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'mergePatchPairs\\n\')
fprintf(fid,\'(\\n\')
fprintf(fid,\');\\n\')

fclose (fid)

end
​

    the functions controldict_gen and blockmesh_gen creates controlDict and blockmeshDict file in the system folder of the case

  5. transportproperties generator function 
    #function to create transportproperties file 

function out = transportproperties_gen(mu)
cd pipe_flow_solution
cd constant

h1 = (\'/*--------------------------------*- C++ -*----------------------------------*\\\');
h2 = \'\\*---------------------------------------------------------------------------*/\';
fid = fopen(\'transportProperties.txt\',\'w\');
fprintf(fid,h1)
fprintf(fid,\'\\n\')
fprintf(fid,\'  =========                |\\n\')
fprintf(fid,\'  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\\n\')
fprintf(fid,\'   \\\\    /   O peration     | Website:  https://openfoam.org\\n\')
fprintf(fid,\'    \\\\  /    A nd           | Version:  7\\n\')
fprintf(fid,\'     \\\\/     M anipulation  |\\n\')
fprintf(fid,\'%s\\n\',h2);
fprintf(fid,\'\\n\')
fprintf(fid,\'FoamFile\\n\')
fprintf(fid,\'{\\n\')
fprintf(fid,\'    version     2.0;\\n\')
fprintf(fid,\'    format      ascii;\\n\')
fprintf(fid,\'    class       dictionary;\\n\')
fprintf(fid,\'    location    \"constant\";\\n\')
fprintf(fid,\'    object      transportProperties;\\n\')
fprintf(fid,\'}\\n\')
fprintf(fid,\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'nu              [0 2 -1 0 0 0 0] %f;\\n\',mu)
fprintf(fid,\'\\n\')
fprintf(fid,\'\\n\')
fprintf(fid,\'// ************************************************************************* //\\n\')
fclose (fid)

end​
    creates transportproperties file in the constant folder

an example case for wedge angle of 4 degrees and simulation time of 10 and time step 0f 0.01s is shown

  1. blockmeshdict file: 
    /*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices 

(
   (0 0 0)
   (0 9.993908e-3 3.489950e-4)
   (0 9.993908e-3 -3.489950e-4)
   (2.82 0 0)
   (2.82 9.993908e-3 3.489950e-4)
   (2.82 9.993908e-3 -3.489950e-4)

);
blocks
(    hex (0 3 5 2 0 3 4 1) (300 10 1) simpleGrading (1 1 1));
edges
(
arc 1 2 (0 0.01 0)
arc 4 5 (2.82 0.01 0)
);
boundary
(
    inlet
    {
        type patch;
        faces
        (
            (1 2 0 0)
         );
     }

    outlet
    {
    	type patch;
	faces
	(
	    (3 5 4 3)
	);
     }    
	
    top
    {
        type wall;
        faces
        (
            (2 1 4 5)

        );
    }

    front
    {
	type wedge;
	faces
	(
	(3 4 1 0)
	);
     }
     
     back
     {
	type wedge;
	faces
   	(
	(3 5 2 0)
	);
     }
	
     axis
    {
        type empty;
        faces
        (
            (0 3 3 0)
        );
    }
);

mergePatchPairs
(
);

// ************************************************************************* //​
  2. controlDict file 
    /*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    \"system\";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         10;

deltaT          0.01;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


// ************************************************************************* //​
  3. u 
    /*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     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
{
    inlet
    {
        type            fixedValue;
	value		uniform (0.0937 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }

    top
    {
  	type		noSlip;
    }

    front
    {
	type		wedge;
    }

    back
    {
	type		wedge;
    }


}

// ************************************************************************* //​
  4. p 
    /*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    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 0.018;
    }

    axis
    {
        type            empty;
    }
    
    top
    {
  	type		zeroGradient;
    }

    front
    {
	type		wedge;
    }

    back
    {
	type		wedge;
    }


}

// ************************************************************************* //​

RESULTS:

  • initially the flow is not parabolic but as it crosses the entrance length the flow is fully developed and the velocity profile is parabolic
  • maximum velocity is at the center and minimum velocity is at the walls
  • wedge mesh:

  • pressure distribution:

velocity distribution:

development of flow :

0.2m

0.5m

0.9m

1.2m

2.4m

2.8m

it is evident from the above curves that as the length of the pipe increses the velocity profile achies parabolic shape

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