[MontelukastNa]

Hello, CFDers & OpenFOAMers

Recently, i am trying to validate the drag coefficient of sphere & spherical bubble at Re=1 with OpenFoam

In my opinion, i think the difference between flow around sphere(fixed position) and spherical bubble(fixed position) is only depends on the boundary condition of the interface. In a word, if the boundary is no-slip, it's a sphere, otherwise, a spherical bubble has slip interface. this topic is derived from professor Duineveld's publication:
Bel Fdhila, R., Duineveld, P.C., 1996. The effect of surfactant on the rise of a spherical bubble at high Reynolds and Peclet numbers. Phys. Fluids 8, 310–321.


The result of pimpleFoam simulated the sphere show me an perfect result, when Re is 1, the drag coefficient is 27.6, it is consistent with Schiller-Newman equation(Cd=24/Re*(1+0.15*Re^0.687)).

But, when I change the boundary condition from no-slip to slip, the result is not consistent with H-R equation(Cd=16/Re), my Cd result of spherical bubble is approximately equal to 13. that shoud be 16!

Here are my case code:
constant/transportProperties

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "constant";
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
transportModel  Newtonian;
nu              [0 2 -1 0 0 0 0] 2;

0.orig/p

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v1812                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
|    \\/     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;
    }

    bubbleInterface
    {
        type            slip;
        //type            fixedFluxPressure;
        //value           $internalField;
    }

    symmetry
    {
        type            symmetry;
    }
    
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
}

0.orig/U

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v1812                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    location    "0";
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform (1 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (1 0 0);
    }
    outlet
    {
        type            zeroGradient;
    }

    bubbleInterface
    {
        type            slip;
    }

    symmetry
    {
        type            symmetry;
    }
    
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
}

system/fvSchemes

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
    default         backward;
}

gradSchemes
{
    default 	     cellLimited leastSquares 1;
}

divSchemes
{
    default         none;
    div(phi,U)      Gauss upwind;
    div((nuEff*dev2(T(grad(U)))))	Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear limited 1;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         limited 1;
}

system/fvSolution

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    p
    {
        solver           GAMG;
        tolerance        1e-6;
        relTol           0;
        smoother         GaussSeidel;
        nPreSweeps       0;
        nPostSweeps      2;
        cacheAgglomeration on;
        agglomerator     faceAreaPair;
        nCellsInCoarsestLevel 100;
        mergeLevels      1;
	minIter 	2;
    }

    pFinal
    {
        $p;
        relTol          0;
	minIter 	2;
    }

    "(U|UFinal)"
    {
        solver          PBiCGStab;
        preconditioner  DILU;
        tolerance       1e-08;
        relTol          0;
    }
}

PIMPLE
{
    momentumPredictor yes;
    consistent 		yes;   
    nOuterCorrectors 2;
    nCorrectors 2;
    nNonOrthogonalCorrectors 1;

    //pRefCell        0;
    //pRefValue       0;
}

relaxationFactors
{
    fields
    {
        ".*"   0.9;
    }
    equations
    {
        ".*"   0.9;
    }
}

system/controlDict

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v1812                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     pimpleFoam;
startFrom       latestTime;
startTime       0;
stopAt          endTime;
endTime         50;
deltaT          1;
writeControl    adjustableRunTime;
writeInterval   1;
purgeWrite      0;
writeFormat     ascii;
writePrecision  8;
writeCompression off;
timeFormat      general;
timePrecision   6;
runTimeModifiable yes;
adjustTimeStep  yes;
maxCo           1;
maxDeltaT       0.01;

functions

{
     Forces
     {
         type forces;
         libs ("libforces.so");
         patches (bubbleNoSlipWall bubbleSlipWall);
         log false;
         rho rhoInf;
         rhoInf 1;
         CofR (0 0 0);
         liftDir (0 1 0); 
         dragDir (1 0 0); 
         writeControl    adjustableRunTime;
         writeInterval   1;
     }

     forceCoeffs
     {
         type forceCoeffs;
         libs ("libforces.so");
         patches (bubbleNoSlipWall bubbleSlipWall); 
         log true; 
         rho rhoInf; 
         rhoInf 1; 
         CofR (0 0 0);
         liftDir (0 1 0); 
         dragDir (1 0 0); 
         pitchAxis (0 0 1);
         magUInf 1; // the velocity of flow at far field is 1/ms, then, Re=U*D/nu=1*2/2=1;
         lRef 2; //Diameter is 2, radiu is 1
         Aref 0.04363323129985824;  //5°Wedge Mesh, the project area is PI*1*1*5/360;
         writeControl    adjustableRunTime; 
         writeInterval   1; 
     }
};

Could you give me some suggestions or help me to debug the drag coefficient of spherical Bubble, thanks!

Thanks!

All Best,
Na