Mut Wall Function for Spalart Allmaras model

on
I implemented a new wall function for mut which was derived from the analytic solution of SA model in near wall region proposed by Allmaras et al. (Eq.(33) in [1]).

Wall Function profiles compared to u+ = y+ and u+ = 2.5*log(y+) + 5.45

2 source codes were created.


References
1. S.R. Allmaras, F.T. Johnson, P.R. Spalart, Modifications and Clarifications for the Implementation of the Spalart-Allmaras Turbulence Model, ICCFD7-1902, 7th International Conference on Computational Fluid Dynamics, 2012.

mutSAWallFunctionFvPatchScalarField.H
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#ifndef compressibleMutSAWallFunctionFvPatchScalarField_H
#define compressibleMutSAWallFunctionFvPatchScalarField_H

#include "mutWallFunctionFvPatchScalarField.H"

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

namespace Foam
{
namespace compressible
{
namespace RASModels
{

/*---------------------------------------------------------------------------*\
      Class mutSAWallFunctionFvPatchScalarField Declaration
\*---------------------------------------------------------------------------*/

class mutSAWallFunctionFvPatchScalarField
:
    public mutWallFunctionFvPatchScalarField
{
protected:

    // Protected data

        //- model constants
        scalar Bbar_;

        scalar a1_;

        scalar a2_;
       
        scalar b1_;
       
        scalar b2_;
       
        scalar c1_;
       
        scalar c2_;
       
        scalar c3_;
       
        scalar c4_;

    // Protected member functions

        //- Calculate yPLus
        virtual tmp<scalarField> calcYPlus(const scalarField& magUp) const;

        //- Calculate the turbulence viscosity
        virtual tmp<scalarField> calcMut() const;


public:

    //- Runtime type information
    TypeName("mutSAWallFunction");


    // Constructors

        //- Construct from patch and internal field
        mutSAWallFunctionFvPatchScalarField
        (
            const fvPatch&,
            const DimensionedField<scalar, volMesh>&
        );

        //- Construct from patch, internal field and dictionary
        mutSAWallFunctionFvPatchScalarField
        (
            const fvPatch&,
            const DimensionedField<scalar, volMesh>&,
            const dictionary&
        );

        //- Construct by mapping given
        //  mutSAWallFunctionFvPatchScalarField
        //  onto a new patch
        mutSAWallFunctionFvPatchScalarField
        (
            const mutSAWallFunctionFvPatchScalarField&,
            const fvPatch&,
            const DimensionedField<scalar, volMesh>&,
            const fvPatchFieldMapper&
        );

        //- Construct as copy
        mutSAWallFunctionFvPatchScalarField
        (
            const mutSAWallFunctionFvPatchScalarField&
        );

        //- Construct and return a clone
        virtual tmp<fvPatchScalarField> clone() const
        {
            return tmp<fvPatchScalarField>
            (
                new mutSAWallFunctionFvPatchScalarField(*this)
            );
        }

        //- Construct as copy setting internal field reference
        mutSAWallFunctionFvPatchScalarField
        (
            const mutSAWallFunctionFvPatchScalarField&,
            const DimensionedField<scalar, volMesh>&
        );

        //- Construct and return a clone setting internal field reference
        virtual tmp<fvPatchScalarField> clone
        (
            const DimensionedField<scalar, volMesh>& iF
        ) const
        {
            return tmp<fvPatchScalarField>
            (
                new mutSAWallFunctionFvPatchScalarField(*this, iF)
            );
        }


    // Member functions

        // Evaluation functions

            //- Calculate and return the yPlus at the boundary
            virtual tmp<scalarField> yPlus() const;


        // I-O

            //- Write
            virtual void write(Ostream& os) const;
};


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

} // End namespace RASModels
} // End namespace compressible
} // End namespace Foam

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

#endif

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

mutSAWallFunctionFvPatchScalarField.C
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#include "mutSAWallFunctionFvPatchScalarField.H"
#include "fvPatchFieldMapper.H"
#include "volFields.H"
#include "RASModel.H"
#include "addToRunTimeSelectionTable.H"

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

namespace Foam
{
namespace compressible
{
namespace RASModels
{

// * * * * * * * * * * * * Protected Member Functions  * * * * * * * * * * * //

tmp<scalarField> mutSAWallFunctionFvPatchScalarField::calcYPlus
(
    const scalarField& magUp
) const
{
    const label patchi = patch().index();

    const RASModel& rasModel = db().lookupObject<RASModel>("RASProperties");

    const scalarField& y = rasModel.y()[patchi];
    const fvPatchScalarField& rhow = rasModel.rho().boundaryField()[patchi];
    const fvPatchScalarField& muw = rasModel.mu().boundaryField()[patchi];

    tmp<scalarField> tyPlus(new scalarField(patch().size(), 0.0));
    scalarField& yPlus = tyPlus();

    forAll(yPlus, faceI)
    {
        scalar Re = magUp[faceI]*y[faceI]/(muw[faceI]/rhow[faceI]);

        scalar yp = yPlusLam_;

        int iter = 0;
        scalar yPlusLast = 0.0;

        do
        {
            yPlusLast = yp;
            scalar f = Bbar_
                     + c1_*log(sqr(yp + a1_) + sqr(b1_))
                     - c2_*log(sqr(yp + a2_) + sqr(b2_))
                     - c3_*atan2(b1_, yp+a1_)
                     - c4_*atan2(b2_, yp+a2_);
           
            yp = (Re + kappa_*yp)/(kappa_ + f);

        } while (mag(yp - yPlusLast) > 0.01 && ++iter < 10);

        yPlus[faceI] = max(0.0, yp);
    }

    return tyPlus;
}


tmp<scalarField>
mutSAWallFunctionFvPatchScalarField::calcMut() const
{
    const label patchi = patch().index();

    const RASModel& rasModel = db().lookupObject<RASModel>("RASProperties");

    const fvPatchVectorField& Uw = rasModel.U().boundaryField()[patchi];
    const scalarField magUp = mag(Uw.patchInternalField() - Uw);
    const scalarField& muw = rasModel.mu().boundaryField()[patchi];

    tmp<scalarField> tyPlus = calcYPlus(magUp);
    scalarField& yPlus = tyPlus();

    tmp<scalarField> tmutw(new scalarField(patch().size(), 0.0));
    scalarField& mutw = tmutw();

    forAll(yPlus, faceI)
    {
        {
            scalar f = Bbar_
                     + c1_*log(sqr(yPlus[faceI] + a1_) + sqr(b1_))
                     - c2_*log(sqr(yPlus[faceI] + a2_) + sqr(b2_))
                     - c3_*atan2(b1_, yPlus[faceI]+a1_)
                     - c4_*atan2(b2_, yPlus[faceI]+a2_);

            mutw[faceI] = max(muw[faceI]*(yPlus[faceI]/f - 1.0), scalar(0.0));
        }
    }

    return tmutw;
}


// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //

mutSAWallFunctionFvPatchScalarField::mutSAWallFunctionFvPatchScalarField
(
    const fvPatch& p,
    const DimensionedField<scalar, volMesh>& iF
)
:
    mutWallFunctionFvPatchScalarField(p, iF),
    Bbar_(5.0333908790505579),
    a1_(8.148221580024245),
    a2_(-6.9287093849022945),
    b1_(7.4600876082527945),
    b2_(7.468145790401841),
    c1_(2.5496773539754747),
    c2_(1.3301651588535228),
    c3_(3.599459109332379),
    c4_(3.6397531868684494)
{}


mutSAWallFunctionFvPatchScalarField::mutSAWallFunctionFvPatchScalarField
(
    const mutSAWallFunctionFvPatchScalarField& ptf,
    const fvPatch& p,
    const DimensionedField<scalar, volMesh>& iF,
    const fvPatchFieldMapper& mapper
)
:
    mutWallFunctionFvPatchScalarField(ptf, p, iF, mapper),
    Bbar_(ptf.Bbar_),
    a1_(ptf.a1_),
    a2_(ptf.a2_),
    b1_(ptf.b1_),
    b2_(ptf.b2_),
    c1_(ptf.c1_),
    c2_(ptf.c2_),
    c3_(ptf.c3_),
    c4_(ptf.c4_)
{}


mutSAWallFunctionFvPatchScalarField::mutSAWallFunctionFvPatchScalarField
(
    const fvPatch& p,
    const DimensionedField<scalar, volMesh>& iF,
    const dictionary& dict
)
:
    mutWallFunctionFvPatchScalarField(p, iF, dict),
    Bbar_(dict.lookupOrDefault<scalar>("Bbar", 5.0333908790505579)),
    a1_(dict.lookupOrDefault<scalar>("a1", 8.148221580024245)),
    a2_(dict.lookupOrDefault<scalar>("a2", -6.9287093849022945)),
    b1_(dict.lookupOrDefault<scalar>("b1", 7.4600876082527945)),
    b2_(dict.lookupOrDefault<scalar>("b2", 7.468145790401841)),
    c1_(dict.lookupOrDefault<scalar>("c1", 2.5496773539754747)),
    c2_(dict.lookupOrDefault<scalar>("c2", 1.3301651588535228)),
    c3_(dict.lookupOrDefault<scalar>("c3", 3.599459109332379)),
    c4_(dict.lookupOrDefault<scalar>("c4", 3.6397531868684494))
{}


mutSAWallFunctionFvPatchScalarField::mutSAWallFunctionFvPatchScalarField
(
    const mutSAWallFunctionFvPatchScalarField& wfpsf
)
:
    mutWallFunctionFvPatchScalarField(wfpsf),
    Bbar_(wfpsf.Bbar_),
    a1_(wfpsf.a1_),
    a2_(wfpsf.a2_),
    b1_(wfpsf.b1_),
    b2_(wfpsf.b2_),
    c1_(wfpsf.c1_),
    c2_(wfpsf.c2_),
    c3_(wfpsf.c3_),
    c4_(wfpsf.c4_)
{}


mutSAWallFunctionFvPatchScalarField::mutSAWallFunctionFvPatchScalarField
(
    const mutSAWallFunctionFvPatchScalarField& wfpsf,
    const DimensionedField<scalar, volMesh>& iF
)
:
    mutWallFunctionFvPatchScalarField(wfpsf, iF),
    Bbar_(wfpsf.Bbar_),
    a1_(wfpsf.a1_),
    a2_(wfpsf.a2_),
    b1_(wfpsf.b1_),
    b2_(wfpsf.b2_),
    c1_(wfpsf.c1_),
    c2_(wfpsf.c2_),
    c3_(wfpsf.c3_),
    c4_(wfpsf.c4_)
{}


// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

tmp<scalarField>
mutSAWallFunctionFvPatchScalarField::yPlus() const
{
    const label patchi = patch().index();

    const RASModel& rasModel = db().lookupObject<RASModel>("RASProperties");
    const fvPatchVectorField& Uw = rasModel.U().boundaryField()[patchi];
    const scalarField magUp = mag(Uw.patchInternalField() - Uw);

    return calcYPlus(magUp);
}


void mutSAWallFunctionFvPatchScalarField::write(Ostream& os) const
{
    fvPatchField<scalar>::write(os);
    writeLocalEntries(os);
    os.writeKeyword("Bbar") << Bbar_ << token::END_STATEMENT << nl;
    os.writeKeyword("a1") << a1_ << token::END_STATEMENT << nl;
    os.writeKeyword("a2") << a2_ << token::END_STATEMENT << nl;
    os.writeKeyword("b1") << b1_ << token::END_STATEMENT << nl;
    os.writeKeyword("b2") << b2_ << token::END_STATEMENT << nl;
    os.writeKeyword("c1") << c1_ << token::END_STATEMENT << nl;
    os.writeKeyword("c2") << c2_ << token::END_STATEMENT << nl;
    os.writeKeyword("c3") << c3_ << token::END_STATEMENT << nl;
    os.writeKeyword("c4") << c4_ << token::END_STATEMENT << nl;
    writeEntry("value", os);
}


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

makePatchTypeField(fvPatchScalarField, mutSAWallFunctionFvPatchScalarField);

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

} // End namespace RASModels
} // End namespace compressible
} // End namespace Foam

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

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