Week 11 - Simulation of Flow through a pipe in OpenFoam
Project Title Simulation of flow through pipe using OpenFoam.
Description: In engineering is facinated with fluid flows having lamimar and turbulent flows. Fundamentally we can corrrelate the the pipe flow with laminar and turbulent nature. We defined non dimensional number called Reynolds Number.
`Re=(rho*v*d)/(mu)`
where `rho=density`
`d=diameter`
`mu=(dynamic-vis cosity)`
when Re>2300 flow becomes turbulent.
`Re <= 2100` Flow is Laminar
Velocity Variation along Pipe
`V_(r)=1/(4(mu))*((dp)/dx)*(R^2-r^2)`
So from above relation the velocity is varying in parabolic Nature.
and It will be maximum at center of pipe.
According Hagen poiseuille's equation the pressure drop is given by
`Deltap=(32 mu*Vavg*L)/(D^2)`
Pipe flow velocity and boundary layer formation according to mathematical model
So for this problem `Re=2100`
diamter=0.01
`mu=0.00089 Pa S`
`rho=1000 (Kg)/(m^3)`
So our average velocity is
`2100=(1000*Vavg*0.01)/(0.00089)`
`Vavg=0.1869 m/sec`
To determine length of Pipe for laminar flow for Fully Developed condition
`L=0.05*(Re*D)`
`L=0.05*2100*0.01`
`L=1.05 m` now assuming `L=1.2 m`
Now
`DeltaP=(32 *0.00089 *0.1869*1.2)/(0.01^2)`
`DeltaP=63.87 Pa`
For OpenFoam Simulation we can take following inputs
`L=1.2 m`
`D=0.01 m`
`mu=0.00000089 m^2/sec`
`Velocity at entry =0.1869 m/sec`
`(Pressure)/(rho)=(63.87/1000) m^2/sec^2``=0.06387 m^2/sec^2`
Generation of BlockMeshDict File
By inputing various wedge angle the blockmesh file can be generated.
Commonly %s and %f symbols are used.
File can be written as f2=fopen(f2,'blockMeshDict.c','w')
clc
clear all
close all
%Input the following Data
theta=input('enter the value of the wedge angle thea=');
diameter=0.01;
radius=(diameter)/2;
length=1.2;
conv='convertToMeters';
b='blocks';
e='edges';
b1='boundary'
v='vertices';
m='mergePatchPairs'
x1=blanks(5);
x2=blanks(8);
%........................OpenFOAM................blockMeshDict.................
h1='/*––––––––––––––––––––––––––––––--*- C++ -*–––––––––––––––––––––––––––––––––-*\ ';
h2='| ========= | ';
h3='| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox ';
h4='| \\ / O peration | Version: 4.0 ';
h5='| \\ / A nd | Web: www.OpenFOAM.org ';
h6='| \\/ M anipulation | ';
h7=' \*–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*/ ';
h8='FoamFile'
h9='{';
h10=' version 2.0;'
h11=' format ascii;'
h12=' class dictionary;'
h13=' object blockMeshDict;'
h14='}';
h15='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
%...............................................................................................
h18='// ************************************************************************* //'
%......................Assigning Vertices.........................
v0=[0 0 0];
v1=[radius*sind(theta/2) radius*cosd(theta/2) 0];
v2=[-radius*sind(theta/2) radius*cosd(theta/2) 0];
v3=[0 0 length];
v4=[radius*sind(theta/2) radius*cosd(theta/2) length];
v5=[-radius*sind(theta/2) radius*cosd(theta/2) length];
block=' hex (0 0 1 2 3 3 4 5) (1 50 250) simpleGrading (1 0.2 1)';
edge1='arc 1 2';
edge2='arc 4 5';
e1=[0 radius 0];
e2=[0 radius length];
inflow='(0 1 2 0)';
outflow='(3 5 4 3)';
wedge1='(0 3 4 1)';
wedge2='(0 2 5 3)';
wall='(1 4 5 2)';
axis='(0 3 3 0)';
f2=fopen('blockMeshDict.C','w')
fprintf(f2,'%s \n',h1);
fprintf(f2,'%s \n',h2);
fprintf(f2,'%s \n',h3);
fprintf(f2,'%s \n',h4);
fprintf(f2,'%s \n',h5);
fprintf(f2,'%s \n',h6);
fprintf(f2,'%s \n',h7);
fprintf(f2,'%s \n',h8);
fprintf(f2,'%s \n',h9);
fprintf(f2,'%s \n',h10);
fprintf(f2,'%s \n',h11);
fprintf(f2,'%s \n',h12);
fprintf(f2,'%s \n',h13);
fprintf(f2,'%s \n',h14);
fprintf(f2,'%s \n',h15);
fprintf(f2,'%s %d %s \n',conv,1,';');
fprintf(f2,'%s \n',v);
fprintf(f2,'%s \n','(');
fprintf(f2,'%s (%6.7f %6.7f %6.7f)\n', x1,v0(1),v0(2),v0(3));
fprintf(f2,'%s (%6.7f %6.7f %6.7f)\n', x1,v1(1),v1(2),v1(3));
fprintf(f2,'%s (%6.7f %6.7f %6.7f)\n', x1,v2(1),v2(2),v2(3));
fprintf(f2,'%s (%6.7f %6.7f %6.7f)\n', x1,v3(1),v3(2),v3(3));
fprintf(f2,'%s (%6.7f %6.7f %6.7f)\n', x1,v4(1),v4(2),v4(3));
fprintf(f2,'%s (%6.7f %6.7f %6.7f)\n', x1,v5(1),v5(2),v5(3));
fprintf(f2,'%s \n',');');
fprintf(f2,'%s \n',b);
fprintf(f2,'%s \n','(');
fprintf(f2,'%s %s \n',x1,block);
fprintf(f2,'%s \n',');');
fprintf(f2,'%s \n',e);
fprintf(f2,'%s \n','(');
fprintf(f2,'%s %s (%6.7f %6.7f %6.7f)\n', x1,edge1,e1(1),e1(2),e1(3));
fprintf(f2,'%s %s (%6.7f %6.7f %6.7f)\n', x1,edge2,e2(1),e2(2),e2(3));
fprintf(f2,'%s \n',');');
fprintf(f2,'%s \n',b1);
fprintf(f2,'%s \n','(');
fprintf(f2,'%s %s \n',x1,'inlet');
fprintf(f2,'%s %s \n',x1,'{');
fprintf(f2,'%s %s \n',x2,'type patch;');
fprintf(f2,'%s %s \n',x2,'faces');
fprintf(f2,'%s %s \n',x2,'(');
fprintf(f2,'%s %s \n',x2,inflow);
fprintf(f2,'%s %s \n',x2,');');
fprintf(f2,'%s %s \n',x1,'}');
fprintf(f2,'%s %s \n',x1,'outlet');
fprintf(f2,'%s %s \n',x1,'{');
fprintf(f2,'%s %s \n',x2,'type patch;');
fprintf(f2,'%s %s \n',x2,'faces');
fprintf(f2,'%s %s \n',x2,'(');
fprintf(f2,'%s %s \n',x2,outflow);
fprintf(f2,'%s %s \n',x2,');');
fprintf(f2,'%s %s \n',x1,'}');
fprintf(f2,'%s %s \n',x1,'front');
fprintf(f2,'%s %s \n',x1,'{');
fprintf(f2,'%s %s \n',x2,'type wedge;');
fprintf(f2,'%s %s \n',x2,'faces');
fprintf(f2,'%s %s \n',x2,'(');
fprintf(f2,'%s %s \n',x2,wedge1);
fprintf(f2,'%s %s \n',x2,');');
fprintf(f2,'%s %s \n',x1,'}');
fprintf(f2,'%s %s \n',x1,'back');
fprintf(f2,'%s %s \n',x1,'{');
fprintf(f2,'%s %s \n',x2,'type wedge;');
fprintf(f2,'%s %s \n',x2,'faces');
fprintf(f2,'%s %s \n',x2,'(');
fprintf(f2,'%s %s \n',x2,wedge2);
fprintf(f2,'%s %s \n',x2,');');
fprintf(f2,'%s %s \n',x1,'}');
fprintf(f2,'%s %s \n',x1,'wall');
fprintf(f2,'%s %s \n',x1,'{');
fprintf(f2,'%s %s \n',x2,'type wall;');
fprintf(f2,'%s %s \n',x2,'faces');
fprintf(f2,'%s %s \n',x2,'(');
fprintf(f2,'%s %s \n',x2,wall);
fprintf(f2,'%s %s \n',x2,');');
fprintf(f2,'%s %s \n',x1,'}');
fprintf(f2,'%s %s \n',x1,'axis');
fprintf(f2,'%s %s \n',x1,'{');
fprintf(f2,'%s %s \n',x2,'type empty;');
fprintf(f2,'%s %s \n',x2,'faces');
fprintf(f2,'%s %s \n',x2,'(');
fprintf(f2,'%s %s \n',x2,axis);
fprintf(f2,'%s %s \n',x2,');');
fprintf(f2,'%s %s \n',x1,'}');
fprintf(f2,'%s \n',');');
fprintf(f2,'%s \n',m);
fprintf(f2,'%s \n','(');
fprintf(f2,'%s \n',');');
fprintf(f2,'%s \n',h18);
fclose(f2);
After running above Code with wedge angle `2 ^(0)`
The blockMesh file is generated as below.
Mainly axisymmetric pipe is modelled for this case
/*––––––––––––––––––––––––––––––--*- C++ -*–––––––––––––––––––––––––––––––––-*\
| ========= |
| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox
| \\ / O peration | Version: 4.0
| \\ / A nd | Web: www.OpenFOAM.org
| \\/ M anipulation |
\*–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1 ;
vertices
(
(0.0000000 0.0000000 0.0000000)
(0.0000873 0.0049992 0.0000000)
(-0.0000873 0.0049992 0.0000000)
(0.0000000 0.0000000 1.2000000)
(0.0000873 0.0049992 1.2000000)
(-0.0000873 0.0049992 1.2000000)
);
blocks
(
hex (0 0 1 2 3 3 4 5) (1 50 250) simpleGrading (1 0.2 1)
);
edges
(
arc 1 2 (0.0000000 0.0050000 0.0000000)
arc 4 5 (0.0000000 0.0050000 1.2000000)
);
boundary
(
inlet
{
type patch;
faces
(
(0 1 2 0)
);
}
outlet
{
type patch;
faces
(
(3 5 4 3)
);
}
front
{
type wedge;
faces
(
(0 3 4 1)
);
}
back
{
type wedge;
faces
(
(0 2 5 3)
);
}
wall
{
type wall;
faces
(
(1 4 5 2)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
Now generate blockMesh is OpenFoam.
Set 0 folder with initial comditions such as
Pressure
/*--------------------------------*- 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 0.063874;
}
wall
{
type zeroGradient;
}
front
{
type wedge;
}
back
{
type wedge;
}
axis
{
type empty;
}
}
// ************************************************************************* //Insert Velocity Conditions
/*--------------------------------*- 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 0 0.1869);
}
wall
{
type noSlip;
value uniform (0 0 0);
}
front
{
type wedge;
}
back
{
type wedge;
}
axis
{
type empty;
}
outlet
{
type zeroGradient;
}
}
// ************************************************************************* //Now Set ControlDict As below
/*--------------------------------*- 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 0.005;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Now Run icoFoam
Results and Discussions
- Its observed that maximum velocity is around 0.37 m/sec around centreline of pipe
- From analytical calculation its 2*Vavg so its around 0.3738 m/sec
- So simulation results are matching perfectly with analytical calculations. So we can validate our results
Velocity Comparison
- Maximum velocity is obseved in wedge 4 degree case.
- The results are validated with analytical results.
- By simulation Vmax=0.37 m/sec and by analytical calaculation Vmax=0.3738 m/sec.
- Deviation of 1% which is in acceptable limits.