Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
AIM:- To Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation.
OBJECTIVE:-
- Validate Hydro-dynamic length with the numerical result
- Validate the fully developed flow velocity profile with its analytical profile
- Validate maximum velocity and pressured drop for fully developed flow
- Post-process Shear stress and validate wall shear stress for fully developed flow
- Highligh the differences in both boundary conditions in terms of their usage and aplication
Angles to test:
- `10^0`
- `25^0`
- `45^0`
THEORY:-
Hagen- Poiseuille's equation:-
- 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 constant cross section.
- The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter. Also Poiseuille's equation describes the pressure drop due to the viscosity of the fluid.
- Observations based on Hagen Poiseuille equation:-
- Diameter of the pipe `D=0.02 m`
- hydrodynamic entrance length`L=0.06⋅Re⋅D =2.52m`
- Wedge angle `theta=` `10^0`, `25^0` and`45^0`
- Dynamic Viscosity of water `μ=0.89e-3 Pascal-sec`
- Density of water `ρ=997 (Kg)/(m3)`
- Kinematic Viscosity `ν=μρ=(8.9268e−07)m^2-sec`
- Average Velocity `V_(avg)=μ⋅Re⋅ρ⋅D=0.0937m/sec`
- Maximum Velocity=`u_max=2⋅vavg= 0.1875 m/sec`
- Pressure Drop for Laminar Flow `=ΔP=(32⋅μ⋅v_(avg)⋅L_c)/(D^2)=0.0188Kpa`
- `L_c=L+0.3=2.82m`
- Shear Stress `τ=(2⋅μ⋅u_(max)⋅r)/(R^2)`
where, r= Radiual distance
R= Radius of Pipe
A) wedge Boundary Method:-
1. Wedge `theta=10^0`
- blockMeshDict File:-
/*--------------------------------*- 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;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0.000000 0.000000 0.000000) //0 origin
(0.000000 0.009962 -0.000872) //1
(0.000000 0.009962 0.000872) //2
(2.820000 0.000000 0.000000) //3
(2.820000 0.009962 -0.000872) //4
(2.820000 0.009962 0.000872) //5
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.4 1 1)
);
edges
(
arc 1 2 (0.000000 0.010000 0.000000)
arc 4 5 (2.820000 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)
);
}
Top
{
type wall;
faces
(
(2 1 4 5)
);
}
Axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
- ControlDict File:-
/*--------------------------------*- 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 31;
deltaT 0.01;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //
TransportProperties File:-
/*--------------------------------*- 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] 8.9268e-7;
// ************************************************************************* //
- Velocity File:-
/*--------------------------------*- 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 (0.0937 0 0);
}
outlet
{
type zeroGradient;
}
Front
{
type wedge;
}
Back
{
type wedge;
}
Top
{
type noSlip;
}
Axis
{
type empty;
}
}
// ************************************************************************* //
- Pressure File:-
/*--------------------------------*- 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 0.0188;
}
Front
{
type wedge;
}
Back
{
type wedge;
}
Top
{
type zeroGradient;
}
Axis
{
type empty;
}
}
// ************************************************************************* //
- Geometry and Mesh:-
- Velocity Distribution Profile
- Velocity Profile at 2.52 m distance
- Pressure Plot at entire Domain:-
- Shear Stress Plot from OpenFoam:-
Simulattion of Wedge of `10^0`
2. Wedge `theta=25^0`
blockMeshDict File:-
/*--------------------------------*- 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;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0.000000 0.000000 0.000000) //0 origin
(0.000000 0.009763 -0.002164) //1
(0.000000 0.009763 0.002164) //2
(2.820000 0.000000 0.000000) //3
(2.820000 0.009763 -0.002164) //4
(2.820000 0.009763 0.002164) //5
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.4 1 1)
);
edges
(
arc 1 2 (0.000000 0.010000 0.000000)
arc 4 5 (2.820000 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)
);
}
Top
{
type wall;
faces
(
(2 1 4 5)
);
}
Axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
Here controlDict File, transportProperties File, Velocity File and Pressure File are same for `theta=25^0`and `theta=45^0` Wedge.
Geometry for `theta=25^0`
- Velocity Profile:-
- Pressure Profile:-
- Velocity Distribution Plot
- Pressure Distribution Plot
- Shear Stress Plot:-
Simulation of Wedge of `25^0`
- Wedge `theta=45^0`
- blockMeshDict File:-
/*--------------------------------*- 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;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0.000000 0.000000 0.000000) //0 origin
(0.000000 0.009239 -0.003827) //1
(0.000000 0.009239 0.003827) //2
(2.820000 0.000000 0.000000) //3
(2.820000 0.009239 -0.003827) //4
(2.820000 0.009239 0.003827) //5
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.4 1 1)
);
edges
(
arc 1 2 (0.000000 0.010000 0.000000)
arc 4 5 (2.820000 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)
);
}
Top
{
type wall;
faces
(
(2 1 4 5)
);
}
Axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
Here controlDict File, transportProperties File, Velocity File and Pressure File are same for `theta=25^0`and `theta=45^0` Wedge.
- Geometry and Mesh :-
- Velocity Profile:-
- Pressure Profile:-
- Velocity Plot at 2.52 m :-
- Pressure Plot at Entire Pipe:-
- Shear Stress Plot:-
Simulation For `theta=45^0`
B) By Symmetry method:-
In Symmetry Method we have to change 'wedge' Boundary Condition to 'symmetry' in blockMeshDict File, Pressure (p) File and Velocity (U) File as shown below.
1.`theta=10^0`
- blockMeshDict File:-
/*--------------------------------*- 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;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0.000000 0.000000 0.000000) //0 origin
(0.000000 0.009962 -0.000872) //1
(0.000000 0.009962 0.000872) //2
(2.820000 0.000000 0.000000) //3
(2.820000 0.009962 -0.000872) //4
(2.820000 0.009962 0.000872) //5
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.4 1 1)
);
edges
(
arc 1 2 (0.000000 0.010000 0.000000)
arc 4 5 (2.820000 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)
);
}
Top
{
type wall;
faces
(
(2 1 4 5)
);
}
Axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
here controlDict, Pressure(p) and Velocity(U) Files are same as `theta=45^0`
- Velocity Profile:-
- Pressure Profile:-
- Shear Stress Profile:-
Simulation for `theta=10^0`
2.`theta=25^0`
- blockMeshDict File:-
/*--------------------------------*- 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;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0.000000 0.000000 0.000000) //0 origin
(0.000000 0.009763 -0.002164) //1
(0.000000 0.009763 0.002164) //2
(2.820000 0.000000 0.000000) //3
(2.820000 0.009763 -0.002164) //4
(2.820000 0.009763 0.002164) //5
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.4 1 1)
);
edges
(
arc 1 2 (0.000000 0.010000 0.000000)
arc 4 5 (2.820000 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)
);
}
Top
{
type wall;
faces
(
(2 1 4 5)
);
}
Axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
here controlDict, Pressure(p) and Velocity(U) Files are same as `theta=45^0`
- Velocity Profile:-
- Pressure Profile:-
- Shear Stress Profile:-
- Simulation for `theta=25^0`
3. `theta=45^0`
- blockMeshDict File:-
/*--------------------------------*- 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;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0.000000 0.000000 0.000000) //0 origin
(0.000000 0.009239 -0.003827) //1
(0.000000 0.009239 0.003827) //2
(2.820000 0.000000 0.000000) //3
(2.820000 0.009239 -0.003827) //4
(2.820000 0.009239 0.003827) //5
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.4 1 1)
);
edges
(
arc 1 2 (0.000000 0.010000 0.000000)
arc 4 5 (2.820000 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)
);
}
Top
{
type wall;
faces
(
(2 1 4 5)
);
}
Axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
- controlDict File:-
/*--------------------------------*- 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 31;
deltaT 0.01;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //
- TransportProperties File:-
/*--------------------------------*- 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] 8.9268e-7;
// ************************************************************************* //
- Pressure(p) File:-
/*--------------------------------*- 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 0.0188;
}
Front
{
type symmetry;
}
Back
{
type symmetry;
}
Top
{
type zeroGradient;
}
Axis
{
type empty;
}
}
// ************************************************************************* //
- Velocity File:-
/*--------------------------------*- 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 (0.0937 0 0);
}
outlet
{
type zeroGradient;
}
Front
{
type symmetry;
}
Back
{
type symmetry;
}
Top
{
type noSlip;
}
Axis
{
type empty;
}
}
// ************************************************************************* //
- Velocity Profile
- Pressure Plot:-
- Shear Stress Plot:-
- Simulation In OpenFoam by icoFoam:-
Shear Stress Plot by MATLAB:-
CONCLUSION:-
- We can Conclude from above Observation that only diffrence in Wedge and symmetry boundary condition is more Execution Time taken by symmetry over wedge boundary condition for flow through pipe.
| a. Execution Time for wedge | b. Execution Time for symmetry |
| 1. for `10^0` = 423.31 sec | 1. for `10^0` = 472.31 sec |
| 2. for `25^0` = 439.74 sec | 2. for `25^0` = 428.37 sec |
| 3. for `45^0` = 412 sec | 3. for `45^0` = 424.93 sec |
- Analytical and graphical result are same no much difference in both .
- From above observation we can conclude no much change in Maximum Velocities in both wedge and symmetry boundary condition.
- The Courant number is slightly increasing in the case of wedge Boundary Condition over symmetry Condition.
- Maximum Pressure and Shear Stress is Similar in both wedge and symmetry boundary condition.