[Goli]

Hi everyone,

I am simulating a 2D incompressible flow with a Reynolds number of 6e6 around a NACA 0012 airfoil with 0-degree angle of attack using simpleFoam with Spalart-Allmaras model. The average y+ is 0.12 (min=0.007, max=0.15) over the airfoil, and I am not using any wall function. The anisotropic grids around the airfoil are structured, and around this layer, the grids are unstructured.

I calculate the vorticity in Paraview (v5.9.0) using these two ways:
1- Defining curl(U) in PythonCalculator.
2- Setting U for “Scalar Array” in GradientOfUnstructuredDataSet, then defining “Gradients_3-Gradients_1” in Calculator.

Both of these two approaches give the same vorticity profile, and there are some unwanted artifacts, which appear strictly at meshes around the airfoil. I also tried different gradSchemes, but the vorticity profile didn’t improve.

Figures 1, 2 and 3 are pictures of these artifacts after I rescale the vorticity to the range -7 and 7 (the range of vorticity at the outlet).

Also, as seen in figure 4, the vorticity has very high values on the airfoil, which I am not sure if it is something usual or not.

Here are the boundary conditions:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v1906                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      nut;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 2 -1 0 0 0 0];

internalField   uniform 8.58e-06;

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform 8.58e-06;
    }

    outlet
    {
        type            zeroGradient;
    }

    top
    {
        type            fixedValue;
        value           uniform 8.58e-06;
    }

    bottom
    {
        type            fixedValue;
        value           uniform 8.58e-06;
    }

    walls
    {
        type            fixedValue;
        value           uniform 0;
    }

    frontAndBack
    {
        type            empty;
    }
}

// ************************************************************************* //

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v1906                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      nuTilda;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 2 -1 0 0 0 0];

internalField   uniform 3.432e-5;

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform 3.432e-5;
    }

    outlet
    {
        type            zeroGradient;
    }

    top
    {
        type            fixedValue;
        value           uniform 3.432e-5;
    }

    bottom
    {
        type            fixedValue;
        value           uniform 3.432e-5;
    }

    walls
    {
        type            fixedValue;
        value           uniform 0;
    }

    frontAndBack
    {
        type            empty;
    }
}

// ************************************************************************* //

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v1906                                 |
|   \\  /    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;
    }
    
    top
    {
        type            zeroGradient;
    }

    bottom
    {
        type            zeroGradient;
    }

    walls
    {
        type            zeroGradient;
    }

    frontAndBack
    {
        type            empty;
    }
}

// ************************************************************************* //

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v1906                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform (51.4815 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (51.4815 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    top
    {
        type            fixedValue;
        value           uniform (51.4815 0 0);
    }

    bottom
    {
        type            fixedValue;
        value           uniform (51.4815 0 0);
    }

    walls
    {
        type            fixedValue;
        value           uniform (0 0 0);
    }

    frontAndBack
    {
        type            empty;
    }
}

// ************************************************************************* //

I am struggling with this problem for several weeks, but I couldn’t figure it out. I would be very grateful if anyone has any idea regarding how to solve this problem.