Simulation of Flow through a pipe in OpenFoam
- Density of water = 998 kg/m3
- Dynamic viscosity of water = 8.90 *10-4 Pa. s
- Reynolds no = 2100
- Let the Diameter = 0.01 m
- Inlet velocity = 0.1874 m/s
Entry length for a laminar pipe is = L = 0.05*Re*D = 1.05 m
Therefore for the simulation, a length of 1.5 m has been taken which is greater than the entry length.
According to Hagen-Poiseuille theory,
According to Hagen-Poiseuille theory,
Uavg = (Re*μ)/(ρ*D) = 0.1874 m/s
Umax = 2* Uavg = 0.3748 m/s
Pressure drop = (32* μ* Uavg*L) / D2 = 80.06 Pa
Kinetic pressure drop = 80.06/998 = 0.0802 m2s-2
Matlab Code to generate blockMesh file:
clear all
close all
clc
%% Inputs
L = 1.5;
theta = 3;
r = 0.005;
a = 1;
b = 0.2;
c = 1;
nx = 200;
ny = 20;
nz =1;
%%
line1=\'/*--------------------------------*- C++ -*----------------------------------*\\\';
line2=\' ========= | \';
line3=\' \\\\ / F ield | OpenFOAM: The Open Source CFD Toolbox \';
line4=\' \\\\ / O peration | Version: 4.1 \';
line5=\' \\\\ / A nd | Web: www.OpenFOAM.org \';
line6=\' \\\\/ M anipulation | \';
line7=\'\\*---------------------------------------------------------------------------*/\';
line8=\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *//\';
line9=\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *//\';
bmd = fopen(\'blockMeshDict\',\'wt\')
fprintf(bmd,\'%s\\n\',line1);
fprintf(bmd,\'%s\\n\',line2);
fprintf(bmd,\'%s\\n\',line3);
fprintf(bmd,\'%s\\n\',line4);
fprintf(bmd,\'%s\\n\',line5);
fprintf(bmd,\'%s\\n\',line6);
fprintf(bmd,\'%s\\n\',line7);
fprintf(bmd,\'FoamFile\\n{\\n\');
fprintf(bmd,\'%18s \\t 2.0;\\n\',\'version\');
fprintf(bmd,\'%18s \\t ascii;\\n\',\'format\');
fprintf(bmd,\'%18s \\t dictionary;\\n\',\'class\');
fprintf(bmd,\'%18s \\t blockMeshDict;\\n\',\'object\');
fprintf(bmd,\'}\\n\');
fprintf(bmd, \'%s\\n\\n\',line8);
%% Vertices and blocks
fprintf(bmd, \'convertToMeters 1; \\n\\n\');
fprintf(bmd, \'vertices\\n(\\n\');
fprintf(bmd, \'\\t (%d %d %d)\\n\', 0,0,0);
fprintf(bmd, \'\\t (%d %d %d)\\n\', L,0,0);
fprintf(bmd, \'\\t (%d %d %d)\\n\', L, r*cosd(theta/2), r*sind(theta/2));
fprintf(bmd, \'\\t (%d %d %d)\\n\', 0, r*cosd(theta/2), r*sind(theta/2));
fprintf(bmd, \'\\t (%d %d %d)\\n\', 0, r*cosd(theta/2), -r*sind(theta/2));
fprintf(bmd, \'\\t (%d %d %d)\\n\', L, r*cosd(theta/2), -r*sind(theta/2));
fprintf(bmd, \');\\n\\n\');
fprintf(bmd, \'blocks\\n(\\n\');
fprintf(bmd,\'\\t hex (0 1 5 4 0 1 2 3)(%d %d %d)\', nx,ny,nz);
fprintf(bmd, \'simplegrading (%d %d %d)\\n\',a,b,c);
fprintf(bmd, \');\\n\\n\');
fprintf(bmd, \'edges\\n(\\n\\t arc %d %d (%d %d %d)\\n\',4,3,0,r,0);
fprintf(bmd, \'\\t arc %d %d (%d %d %d)\\n\',5,2,L,r,0);
fprintf(bmd, \');\\n\\n\');
fprintf(bmd, \'boundary\\n(\\n\');
%% Inlet patch
fprintf(bmd, \'\\t inlet\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type patch;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,0,3,4);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Outlet : patch
fprintf(bmd, \'\\t outlet\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type patch;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 1,5,2,1);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Front surface: wedge 1
fprintf(bmd, \'\\t front\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type wedge;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,1,2,3);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Back Surface : wedge 2
fprintf(bmd, \'\\t back\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type wedge;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,4,5,1);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Axis : empty
fprintf(bmd, \'\\t axis\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type empty;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,1,1,0);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Pipe Wall : wall
fprintf(bmd, \'\\t pipewall\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type wall;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 3,2,5,4);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
fprintf(bmd, \');\\n\');
%%
fprintf(bmd, \'mergePatchPairs\\n(\\n\');
fprintf(bmd, \');\\n\');
fprintf(bmd, \'%s \\n\', line9);
fclose (bmd)Generated BlockMeshDict file:
/*--------------------------------*- 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)
(1.500000e+00 0 0)
(1.500000e+00 4.998287e-03 1.308847e-04)
(0 4.998287e-03 1.308847e-04)
(0 4.998287e-03 -1.308847e-04)
(1.500000e+00 4.998287e-03 -1.308847e-04)
);
blocks
(
hex (0 1 5 4 0 1 2 3)(200 20 1)simplegrading (1 2.000000e-01 1)
);
edges
(
arc 4 3 (0 5.000000e-03 0)
arc 5 2 (1.500000e+00 5.000000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 0 3 4)
);
}
outlet
{
type patch;
faces
(
(1 5 2 1)
);
}
front
{
type wedge;
faces
(
(0 1 2 3)
);
}
back
{
type wedge;
faces
(
(0 4 5 1)
);
}
axis
{
type empty;
faces
(
(0 1 1 0)
);
}
pipewall
{
type wall;
faces
(
(3 2 5 4)
);
}
);
mergePatchPairs
(
);
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *// Pressure Boundary Condition:
/*--------------------------------*- 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 0.0802;
}
axis
{
type empty;
}
front
{
type wedge;
}
back
{
type wedge;
}
pipewall
{
type zeroGradient;
}
}
// ************************************************************************* //Velocity Boundary Condition:
/*--------------------------------*- 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 (0.1874 0 0);
}
outlet
{
type zeroGradient;
}
axis
{
type empty;
}
front
{
type wedge;
}
back
{
type wedge;
}
pipewall
{
type fixedValue;
value uniform (0 0 0);
}
}
// ************************************************************************* //ControlDict:
/*--------------------------------*- 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 1;
deltaT 0.000005;
writeControl timeStep;
writeInterval 300;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Meshing:
Velocity Field from inlet to outlet:
Initially, velocity will not be fully developed. Later it will go on developing. So initially at 0.005 m the velocity profile has been shown here. As the developing length is 1.05m, another profile has also been shown at 1.2 meter from the entrance and this shows that flow has become fully developed. The axes have not been shown in the snipped curves. Y axis is velocity magnitude. x- axis is the transverse length at specific positions of the pipe.
At 0.005 m:
At 1.2 m:
Change of pressure has also been shown throughout the pipe length.