[albet]

Hello,

I have a problem with simulation of a flow around a cylinder in high Re number.
I tried to read all related posts and threads, but it doesn't solve my problem. so I need your help to get rid of it.
It is a 2D case with a cylinder (D=54 cm) in the middle. I am modelling it with the komegaSST model. the Strouhal number from my simulation is always 0.17, however, it should be around 0.13.
the Re number is 2e5, and I am not sure that the komegaSST is able to solve it properly!

I am going to provide as much detail as I can here to be sure that my solution is correct. I will appreciate if somebody gives me feedback.
U

/

internalField   uniform (0.3 0 0);

boundaryField
{
    INLET
    {
        type            fixedValue;
        value           uniform (0.3 0 0);
    }
    SIDES
    {
        type            symmetry;
    }
    CYLINDER
    {
        type            fixedValue;
        value           uniform (0 0 0);
    }
    OUTLET
    {
        type            zeroGradient;
    }
    UPODOWN
    {
        type            empty;
    }
}

p

internalField   uniform 0;

boundaryField
{
    INLET
    {
        type            zeroGradient;
    }
    SIDES
    {
        type            symmetry;
    }
    CYLINDER
    {
        type            zeroGradient;
    }
    OUTLET
    {
        type            fixedValue;
        value           uniform 0;
    }
    UPODOWN
    {
        type            empty;
    }
}

omega

internalField   uniform 0.07;

boundaryField
{
    INLET
    {
        type            turbulentMixingLengthFrequencyInlet;
        mixingLength    0.54;
        phi             phi;
        k               k;
        value           uniform 1;
    }
    SIDES
    {
        type            symmetry;
    }
    CYLINDER
    {
        type            omegaWallFunction;
        value           uniform 0.07;
    }
    OUTLET
    {
        type            inletOutlet;
        inletValue      uniform 0.07;
        value           uniform 0.07;
    }
    UPODOWN
    {
        type            empty;
    }
}

nut

internalField   uniform 0.1;

boundaryField
{
    INLET
    {
        type            calculated;
        value           uniform 0;
    }
    SIDES
    {
        type            symmetry;
    }
    CYLINDER
    {
        type            nutUWallFunction;
        value           uniform 0.1;
    }
    OUTLET
    {
        type            calculated;
        value           uniform 0;
    }
    UPODOWN
    {
        type            empty;
    }
}

k

internalField   uniform 0.000398;

boundaryField
{
    INLET
    {
        type            turbulentIntensityKineticEnergyInlet;
        intensity       0.05;
        value           uniform 0.000398;
    }
    SIDES
    {
        type            symmetry;
    }
    CYLINDER
    {
        type            kqRWallFunction;
        value           uniform 0.000398;
    }
    OUTLET
    {
        type            inletOutlet;
        inletValue      uniform 0.000398;
        value           uniform 0.000398;
    }
    UPODOWN
    {
        type            empty;
    }
}

controlDict

application     pimpleFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         500;

deltaT          0.001;

writeControl    adjustableRunTime;

writeInterval   50;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression uncompressed;

timeFormat      general;

timePrecision   6;

runTimeModifiable yes;

adjustTimeStep  yes;

maxCo           0.5;

fvScheme

ddtSchemes
{
    default          backward; 
}

gradSchemes
{                            
    default              leastSquares; 
//    grad(U)           cellLimited Gauss linear 1;
}  

divSchemes
{
    div(phi,U)        Gauss linearUpwindV Gauss linear; 
    div(phi,k)        Gauss linearUpwind Gauss linear; 
    div(phi,omega)    Gauss linearUpwind Gauss linear;
    div((nuEff*dev(T(grad(U))))) Gauss linear;
}

laplacianSchemes
{
    default           Gauss linear  corrected; 
}

interpolationSchemes
{
    default          linear;
}

snGradSchemes
{
    default          corrected;
}
fluxRequired
{
    default         no;
    p               ;
}

fvSolution

solvers
{

    p
    {
        solver           GAMG;
        tolerance        1e-6;
        relTol           0.001;
        smoother         GaussSeidel;
        nPreSweeps       0;
        nPostSweeps      2;
        cacheAgglomeration on;
        agglomerator     faceAreaPair;
        nCellsInCoarsestLevel 10;
        mergeLevels      1;
 
    }

    pFinal
    {
        $p;
        relTol          0;
    }

   "U|k|omega"
    {
   
        solver          PBiCG;  
        preconditioner  DILU;
        tolerance       1e-06;
        relTol          0.001;
    }

    "(U|k|omega)Final"
    {
        $U;
        tolerance       1e-05;
        relTol          0;
    }

}

PIMPLE
{
    nOuterCorrectors 1;
    nCorrectors     2;
    nNonOrthogonalCorrectors 2;
}

and also I generated the mesh with ICEM and O-grid method.
Regards,
Amir

[Tobi]

Question. How do you estimate the frequency?

[albet]

Dear Tobi,
Many thanks for your reply.
I calculate the Strouhal number by measuring the Cl on the cylinder and by following the time period of each full sinusoidal move in the graph or using the fast Fourier transform method.
I attached here the results of my Cl here.
Regards,
Amir

[Tobi]

I agree that the estimation of the function is correct. However, Re = 200.000, is high turbulent and your statement does not fit to the physical behavior of the Strouhal Number and my reference [1]. Here, the following is stated:

• 80 < Re < 300 --> 0.14 < Sr < 0.21
• 300 < Re < 1e5 --> Sr = 0.21
• 1e5 < Re < 3.5e6 --> No preferred frequency - No Sr calculation
• 3.5e6 < Re --> 0.25 < Sr < 0.30

As your Reynolds number is 2e5 and my literature stats that there no preferred frequency, I am not sure that things are fine here. The other way around. That would mean that your Sr number is inbetween 0.21 - 0.25 which is in contradiction to your beautiful frequency.

Summing up. You are saying that you should get a Sr number of around 0.13. However, that would imply that you should have a Re number of around 80. This would agrees well to my studies that I made a few years ago. And if that is the case, you are laminar and no turbulence model is needed. I attached a figure of my previous work. You can see that c_d is arount 0.9x and the Reynolds number was 300.


KaramanCd.jpg

[1] H.Schlichting, K.Gersten: Grenzschichttheorie, Springer–Verlag Berlin Heidelberg (2007)

[albet]

Dear Tobi,

I made a mistake in my statement, the values I mentioned was for the frequency of the vortex shedding for my case from the Sr number.

the frequency of vortex shedding for Sr=0.21 for my case should be around 0.13, but from simulation, the frequency is around 0.17 which is equivalent to Sr =0.28.
I am sorry for the mistake.
Regards,
Amir

[pete20r2]

How close are your boundaries to the sphere?
Have you done a mesh dependancy study?

[albet]

Dear Peter,

Many thanks for your reply,
to be sure that everything is fine, I tried it with different size of the domain.
I have attached one of them. the quality of mesh is very good in case of max angle, and also I checked it with checkMesh and everything is ok. this mesh includes 33000 cells.
The only thing that I think can cause a problem is the min yplus around the cylinder.
min y+ =1.33
max y+=78.5
average y+=42
since I used the nutUwallFunction!
I checked it with nutUSpaldingWallFunction, and got the same results.

Kind regards,
Amir