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    Website: https://hzdr.de

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Class
    Foam::dragModels::PorombkaHoehne

Description

    Reference:
    \verbatim
        Porombka, P., & Höhne, T. (2015).
        Drag and turbulence modelling for free surface flows within the
        two-fluid Euler–Euler framework.
        Chemical Engineering Science, 134, 348-359.
    \endverbatim

    Interfacial momentum transfer due to drag
    \f[
        \vec{M}_\alpha = K\,\left(\vec{U}_1-\vec{U}_2\right)
    \f]

    Dragfunction K
    \f[
        K = max\left(0.01\rho_{mix}A_{i}\left|\vec{U}_\alpha-\vec{U}_2\right|,
            \frac{\left(\alpha_1\left|\vec{t}_{fs,1}\right|+
            \alpha_2\left|\vec{t}_{fs,2}\right|\right)a_{12}}
            {\left|\vec{U}_1-\vec{U}_2\right|}\right)
    \f]
    with
    \f[
        \vec{t}_{fs,\varphi} = \vec{t}_\varphi-\left(\hat{\vec{n}}\cdot
            \vec{t}_\varphi\right)\hat{\vec{n}}
    \f]
    \f[
        \vec{t}_\varphi = \tau_\varphi\cdot\hat{\vec{n}}
    \f]
    \f[
        \tau_\varphi = \nu_\varphi \rho_\varphi \left(\nabla\vec{U}_\varphi+
            \left(\nabla\vec{U}_\varphi\right)^T\right)-
            \frac{1}{3}\delta_{ij}\nabla\vec{U}_\varphi
    \f]
    \f[
        \hat{\vec{n}} = -\frac{\alpha_2\nabla\alpha_1-\alpha_1\nabla\alpha_2}
            {\left|\alpha_2\nabla\alpha_1-\alpha_1\nabla\alpha_2\right|}
    \f]
    \f[
        A_{i} = \frac{2\left|\nabla\alpha_1\right|
            \left|\nabla\alpha_2\right|}
            {\left|\nabla\alpha_1\right|+\left|\nabla\alpha_2\right|}
    \f]
    \f[
        \rho_{mix} = \alpha_1\rho_1+\alpha_2\rho_2
    \f]
    The interfacial area density is clipped to be not smaller than
    \f$1/L_{max}\f$.

Usage
    \table
        Parameter       | Name  | Description       | Default value
        \f$U_{r,min}\f$ | residualSlip | minimum slip velocity  | -
        \f$L_{max}\f$   | LMax  | maximum length scale for area density  | 1 m
    \endtable

SourceFiles
    PorombkaHoehne.C

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

#ifndef PorombkaHoehne_H
#define PorombkaHoehne_H

#include "dragModel.H"
#include "segregatedPhaseInterface.H"

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

namespace Foam
{
namespace dragModels
{

/*---------------------------------------------------------------------------*\
                       Class PorombkaHoehne Declaration
\*---------------------------------------------------------------------------*/

class PorombkaHoehne
:
    public dragModel
{
    // Private Data

        //- Interface
        const segregatedPhaseInterface interface_;

        //- Length scale to calculate minimum interfacial area density
        const dimensionedScalar LMax_;

        //- Residual slip velocity to avoid division by zero
        const dimensionedScalar residualSlip_;


    // Private Member Functions

        //- Return viscous stress tensor
        inline tmp<volSymmTensorField> tauVisc
        (
            const phaseModel& phase
        ) const;


public:

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


    // Constructors

        //- Construct from a dictionary and an interface
        PorombkaHoehne
        (
            const dictionary& dict,
            const phaseInterface& interface,
            const bool registerObject
        );


    //- Destructor
    virtual ~PorombkaHoehne();


    // Member Functions

        //- Return the drag coefficient K
        //  used in the momentum equations
        //    ddt(alpha1*rho1*U1) + ... = ... K*(U1-U2)
        //    ddt(alpha2*rho2*U2) + ... = ... K*(U2-U1)
        virtual tmp<volScalarField> K() const;

        //- Return the drag coefficient Kf
        //  used in the face-momentum equations
        virtual tmp<surfaceScalarField> Kf() const;
};


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

} // End namespace dragModels
} // End namespace Foam

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

#endif

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