MaxwellStefan.H

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Class
    Foam::turbulenceThermophysicalTransportModels::MaxwellStefan

Description
    Base class for multi-component Maxwell Stefan generalised Fick's law
    diffusion coefficients based temperature gradient heat flux model with
    optional Soret thermal diffusion of species.

    The binary mass diffusion coefficients are specified as Function2<scalar>s
    of pressure and temperature but independent of composition.

    The heat flux source is implemented as an implicit energy correction to the
    temperature gradient based flux source.  At convergence the energy
    correction is 0.

    References:
    \verbatim
        Taylor, R., & Krishna, R. (1993).
        Multicomponent mass transfer (Vol. 2).
        John Wiley & Sons.

        Merk, H. J. (1959).
        The macroscopic equations for simultaneous heat and mass transfer
        in isotropic, continuous and closed systems.
        Applied Scientific Research,
        Section A, 8(1), 73-99.
    \endverbatim

SourceFiles
    MaxwellStefan.C

\*---------------------------------------------------------------------------*/

#include "Function2.H"
#include "LUscalarMatrix.H"

#ifndef MaxwellStefan_H
#define MaxwellStefan_H

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

namespace Foam
{

/*---------------------------------------------------------------------------*\
                Class MaxwellStefan Declaration
\*---------------------------------------------------------------------------*/

template<class BasicThermophysicalTransportModel>
class MaxwellStefan
:
    public BasicThermophysicalTransportModel
{
    // Private data

        // Model coefficients

            //- Array of specie binary mass diffusion coefficient functions
            //  [m^2/s]
            List<PtrList<Function2<scalar>>> DFuncs_;

            //- List of specie Soret thermal diffusion coefficient
            //  functions [kg/m/s]
            PtrList<Function2<scalar>> DTFuncs_;

            //- Generalised Fick's law diffusion coefficients field list.
            //  This is the diagonal of the mass diffusion coefficient matrix
            PtrList<volScalarField> Dii_;

            //- List of fields of the explicit part of the mass diffusion flux
            // of the species
            PtrList<surfaceScalarField> jexp_;


        // Workspace for diffusion coefficient transformation

            //- Molecular weights of the species
            scalarField W;

            //- List of mass-fraction field pointers
            //  for the internal mesh or a patch
            List<const scalarField*> YPtrs;

            //- Matrix of mass diffusion coefficient field pointers
            //  for the internal mesh or a patch
            SquareMatrix<scalarField*> DijPtrs;

            //- Mass-fractions at a cell or face
            scalarField Y;

            //- Mole-fractions at a cell or face
            scalarField X;

            //- Binary mass diffusion coefficient matrix at a cell or face
            scalarSquareMatrix DD;

            //- Matrix form of the coefficients in the Maxwell-Stefan equation
            //  at a cell or face
            LUscalarMatrix A;

            //- Matrix of composition coefficients at a cell or face
            //  used to transform the binary mass diffusion coefficients into
            //  the generalised Fick's law diffusion coefficients
            scalarSquareMatrix B;

            //- Inverse of A
            scalarSquareMatrix invA;

            //- Matrix of the generalised Fick's law diffusion coefficients
            //  at a cell or face
            scalarSquareMatrix D;


    // Private member functions

        //- Transform the Binary mass diffusion coefficient matrix DD into the
        //  matrix of the generalised Fick's law diffusion coefficients D
        void transformDiffusionCoefficient();

        //- Calls transformDiffusionCoefficient() for each cell and patch face
        //  and maps the resulting D into DijPtrs
        void transformDiffusionCoefficientFields();

        //- Calls transformDiffusionCoefficientFields() for the internal mesh
        //  and each patch and maps the resulting DijPtrs into Dii_ and Dij
        void transform(List<PtrList<volScalarField>>& Dij);


public:

    typedef typename BasicThermophysicalTransportModel::alphaField
        alphaField;

    typedef typename
        BasicThermophysicalTransportModel::momentumTransportModel
        momentumTransportModel;

    typedef typename BasicThermophysicalTransportModel::thermoModel
        thermoModel;


    // Constructors

        //- Construct from a momentum transport model and a thermo model
        MaxwellStefan
        (
            const word& type,
            const momentumTransportModel& momentumTransport,
            const thermoModel& thermo
        );


    //- Destructor
    virtual ~MaxwellStefan()
    {}


    // Member Functions

        //- Read thermophysicalTransport dictionary
        virtual bool read();

        //- Effective mass diffusion coefficient
        //  for a given specie mass-fraction [kg/m/s]
        //  This is the self-diffusion coefficient
        virtual tmp<volScalarField> DEff(const volScalarField& Yi) const;

        //- Effective mass diffusion coefficient
        //  for a given specie mass-fraction for patch [kg/m/s]
        virtual tmp<scalarField> DEff
        (
            const volScalarField& Yi,
            const label patchi
        ) const;

        //- Return the heat flux [W/m^2]
        virtual tmp<surfaceScalarField> q() const;

        //- Return the source term for the energy equation
        virtual tmp<fvScalarMatrix> divq(volScalarField& he) const;

        //- Return the specie flux for the given specie mass-fraction [kg/m^2/s]
        virtual tmp<surfaceScalarField> j(const volScalarField& Yi) const;

        //- Return the source term for the given specie mass-fraction equation
        virtual tmp<fvScalarMatrix> divj(volScalarField& Yi) const;

        //- Update the diffusion coefficients and flux corrections
        virtual void correct();
};


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

} // End namespace Foam

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

#ifdef NoRepository
    #include "MaxwellStefan.C"
#endif

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

#endif

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