populationBalanceModel.H

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Class
    Foam::diameterModels::populationBalanceModel

Description
    Class that solves the univariate population balance equation by means of
    a class method (also called sectional or discrete method). The internal
    coordinate is set to the particle volume, so the equation is based on
    a transport equation of the volume-based number density function. The
    discretization is done using the fixed pivot technique of Kumar and
    Ramkrishna (1996). The source terms are written in a way that particle
    number and mass are preserved. Coalescence (aggregation), breakup, drift
    (growth and surface loss) as well as nucleation are supported.
    For the discrete breakup term two recipes are available, depending on the
    model choice. For models which state a total breakup rate and a separate
    daughter size distribution function, the formulation of Kumar and Ramkrishna
    (1996) is applied which is applicable for binary and multiple breakup
    events. The second formulation is given by Liao et al. (2018). It is useful
    for binary breakup models which give the breakup rate between a sizeGroup
    pair directly, without an explicit expression for the daughter size
    distribution. The drift term is implemented using a finite difference upwind
    scheme. Although it is diffusive, it ensures a stable and
    number-conservative solution.

    The implementation allows to split the population balance over multiple
    velocity fields using the capability of reactingMultiphaseEulerFoam to solve
    for n momentum equations. It is also possible to define multiple population
    balances, e.g. bubbles and droplets simultaneously.

    References:
    \verbatim
        Coalescence and breakup term formulation:
        Kumar, S., & Ramkrishna, D. (1996).
        On the solution of population balance equations by discretization-I. A
        fixed pivot technique.
        Chemical Engineering Science, 51(8), 1311-1332.
    \endverbatim

    \verbatim
        Binary breakup term formulation:
        Liao, Y., Oertel, R., Kriebitzsch, S., Schlegel, F., & Lucas, D. (2018).
        A discrete population balance equation for binary breakage.
        International Journal for Numerical Methods in Fluids, 87(4), 202-215.
    \endverbatim

Usage
    Example excerpt from a phaseProperties dictionary.
    \verbatim
    type populationBalanceTwoPhaseSystem;

    phases (air water);

    populationBalances (bubbles);

    air
    {
        type            purePhaseModel;
        diameterModel   velocityGroup;
        velocityGroupCoeffs
        {
            populationBalance    bubbles;

            formFactor      0.5235987756;

            sizeGroups
            (
                f0{d  1.00e-3; value 0;}
                f1{d  1.08e-3; value 0;}
                f2{d  1.16e-3; value 0.25;}
                f3{d  1.25e-3; value 0.5;}
                f4{d  1.36e-3; value 0.25;}
                f5{d  1.46e-3; value 0;}
                ...
            );
        }

        residualAlpha   1e-6;
    }

    populationBalanceCoeffs
    {
        bubbles
        {
            continuousPhase water;

            coalescenceModels
            (
                hydrodynamic
                {
                    C 0.25;
                }
            );

            binaryBreakupModels
            ();

            breakupModels
            (
                exponential
                {
                    C 0.5;
                    exponent 0.01;
                    daughterSizeDistributionModel uniformBinary;
                }
            );

            driftModels
            (
                densityChange{}
            );

            nucleationModels
            ();
        }
    }
    \endverbatim

See also
    Foam::diameterModels::sizeGroup
    Foam::diameterModels::velocityGroup

SourceFiles
    populationBalanceModel.C

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

#ifndef populationBalanceModel_H
#define populationBalanceModel_H

#include "sizeGroup.H"
#include "phasePair.H"
#include "pimpleControl.H"
#include "phaseCompressibleTurbulenceModelFwd.H"

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

namespace Foam
{

class phaseSystem;

namespace diameterModels
{

class coalescenceModel;
class breakupModel;
class binaryBreakupModel;
class driftModel;
class nucleationModel;

/*---------------------------------------------------------------------------*\
                   Class populationBalanceModel Declaration
\*---------------------------------------------------------------------------*/

class populationBalanceModel
:
    public regIOobject
{
    // Private Typedefs

        typedef
            HashTable<autoPtr<phasePair>, phasePairKey, phasePairKey::hash>
            phasePairTable;


    // Private Data

        //- Reference to the phaseSystem
        const phaseSystem& fluid_;

        //- Interfacial Mass transfer rate between velocityGroups
        HashPtrTable<volScalarField, phasePairKey, phasePairKey::hash>& pDmdt_;

        //- Reference to the mesh
        const fvMesh& mesh_;

        //- Name of the populationBalance
        word name_;

        //- Dictionary
        dictionary dict_;

        //- Reference to pimpleControl
        const pimpleControl& pimple_;

        //- Continuous phase
        const phaseModel& continuousPhase_;

        //- velocityGroups belonging to this populationBalance
        UPtrList<velocityGroup> velocityGroups_;

        //- sizeGroups belonging to this populationBalance
        UPtrList<sizeGroup> sizeGroups_;

        //- List of unordered phasePairs in this populationBalance
        phasePairTable phasePairs_;

        //- sizeGroup boundaries
        PtrList<dimensionedScalar> v_;

        //- Section width required for binary breakup formulation
        PtrList<PtrList<dimensionedScalar>> delta_;

        //- Explicitly treated sources
        PtrList<volScalarField> Su_;

        //- Sources treated implicitly or explicitly depending on sign
        PtrList<volScalarField> SuSp_;

        //- Field for caching sources
        volScalarField Sui_;

        //- Coalescence models
        PtrList<coalescenceModel> coalescence_;

        //- Coalescence rate
        autoPtr<volScalarField> coalescenceRate_;

        //- BreakupModels
        PtrList<breakupModel> breakup_;

        //- Breakup rate
        autoPtr<volScalarField> breakupRate_;

        //- Binary breakup models
        PtrList<binaryBreakupModel> binaryBreakup_;

        //- Binary breakup rate
        autoPtr<volScalarField> binaryBreakupRate_;

        //- Drift models
        PtrList<driftModel> drift_;

        //- Drift rate
        autoPtr<volScalarField> driftRate_;

        //- Ratio between successive representative volumes
        autoPtr<volScalarField> rx_;

        //- Ratio between successive class widths
        autoPtr<volScalarField> rdx_;

        //- Zeroeth order models
        PtrList<nucleationModel> nucleation_;

        //- Zeroeth order rate
        autoPtr<volScalarField> nucleationRate_;

        //- Total void fraction
        autoPtr<volScalarField> alphas_;

        //- Mean Sauter diameter
        autoPtr<volScalarField> dsm_;

        //- Average velocity
        autoPtr<volVectorField> U_;

        //- Counter for interval between source term updates
        label sourceUpdateCounter_;


    // Private Member Functions

        void registerVelocityGroups();

        void registerSizeGroups(sizeGroup& group);

        void createPhasePairs();

        void correct();

        void birthByCoalescence(const label j, const label k);

        void deathByCoalescence(const label i, const label j);

        void birthByBreakup(const label k, const label model);

        void deathByBreakup(const label i);

        void calcDeltas();

        void birthByBinaryBreakup(const label i, const label j);

        void deathByBinaryBreakup(const label j, const label i);

        void drift(const label i);

        void nucleation(const label i);

        void sources();

        void dmdt();

        void calcAlphas();

        tmp<volScalarField> calcDsm();

        void calcVelocity();

        //- Return whether the sources should be updated on this iteration
        bool updateSources();

        //- Return the number of corrections
        inline label nCorr() const;

        //- Return the interval at which the sources are updated
        inline label sourceUpdateInterval() const;

public:

    friend class sizeGroup;
    friend class velocityGroup;

    // Constructor

        populationBalanceModel
        (
            const phaseSystem& fluid,
            const word& name,
            HashPtrTable
            <
                volScalarField,
                phasePairKey,
                phasePairKey::hash
            >& pDmdt
        );

        //- Return clone
        autoPtr<populationBalanceModel> clone() const;

        //- Return a pointer to a new populationBalanceModel object created on
        //  freestore from Istream
        class iNew
        {
            const phaseSystem& fluid_;

            HashPtrTable<volScalarField, phasePairKey, phasePairKey::hash>&
                pDmdt_;

        public:

            iNew
            (
                const phaseSystem& fluid,
                HashPtrTable<volScalarField, phasePairKey, phasePairKey::hash>&
                    pDmdt
            )
            :
                fluid_(fluid),
                pDmdt_(pDmdt)
            {}

            autoPtr<populationBalanceModel> operator()(Istream& is) const
            {
                return autoPtr<populationBalanceModel>
                (
                    new populationBalanceModel(fluid_, word(is), pDmdt_)
                );
            }
        };


    //- Destructor
    virtual ~populationBalanceModel();

    // Member Functions

        //- Dummy write for regIOobject
        bool writeData(Ostream&) const;

        //- Return reference to the phaseSystem
        inline const phaseSystem& fluid() const;

        //- Return reference to the mesh
        inline const fvMesh& mesh() const;

        //- Return populationBalanceCoeffs dictionary
        inline const dictionary& dict() const;

        //- Return continuous phase
        inline const phaseModel& continuousPhase() const;

        //- Return the velocityGroups belonging to this populationBalance
        inline const UPtrList<velocityGroup>& velocityGroups() const;

        //- Return the sizeGroups belonging to this populationBalance
        inline const UPtrList<sizeGroup>& sizeGroups() const;

        //- Return list of unordered phasePairs in this populationBalance
        inline const phasePairTable& phasePairs() const;

        //- Return the sizeGroup boundaries
        inline const PtrList<dimensionedScalar>& v() const;

        //- Return total void of phases belonging to this populationBalance
        inline const volScalarField& alphas() const;

        //- Return average velocity
        inline const volVectorField& U() const;

        //- Return allocation coefficient
        const dimensionedScalar gamma
        (
            const label i,
            const dimensionedScalar& v
        ) const;

        //- Return the surface tension coefficient between a given dispersed
        //  and the continuous phase
        const tmp<volScalarField> sigmaWithContinuousPhase
        (
            const phaseModel& dispersedPhase
        ) const;

        //- Return reference to turbulence model of the continuous phase
        const phaseCompressibleTurbulenceModel& continuousTurbulence() const;

        //- Solve the population balance equation
        void solve();
};

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

} // End namespace diameterModels
} // End namespace Foam

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

#include "populationBalanceModelI.H"

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

#endif

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