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Class
    Foam::populationBalance::coalescenceModels::Luo

Description
    Model of Luo (1993). The coalescence rate is calculated by

    \f[
        \frac{\pi}{4} (d_i + d_j)^2 u_{ij}
        \mathrm{exp}
        \left[
          - C_1
            \frac
            {[0.75(1 + \xi_{ij}^2)(1 + \xi_{ij}^3)]^{1/2}}
            {(\rho_d/\rho_c + C_{vm})^{1/2} (1 + \xi_{ij})^3}
            \left(\frac{\rho_c d_i u_{ij}^2}{\sigma}\right)^{1/2}
        \right]\,,
    \f]

    where

    \f[
        u_{ij} = \sqrt{\beta} (\epsilon_c d_i)^{1/3} \sqrt{1 + \xi_{ij}^{-2/3}}
    \f]

    is the mean approach velocity of the bubbles and

    \f[
        \xi_{ij} = d_i/d_j
    \f]

    their size ratio.

    \vartable
        d_i         |  Diameter of bubble i [m]
        d_j         |  Diameter of bubble j [m]
        u_{ij}      |  Mean approach velocity [m/s]
        \xi_{ij}    |  Bubble size ratio [-]
        \rho_d      |  Density of dispersed phase [kg/m^3]
        \rho_c      |  Density of continuous phase [kg/m^3]
        \sigma      |  Surface tension [N/m]
        C_{vm}      |  Virtual mass coefficient [-]
        C_1         |  Coefficient [-]
        \beta       |  Coefficient [-]
        \epsilon_c  |  Continuous phase turbulent dissipation rate [m^2/s^3]
    \endvartable

    Reference:
    \verbatim
        Luo, H. (1993).
        Coalescence, breakup and liquid circulation in bubble column reactors.
        Dr. Ing (Doctoral dissertation, Thesis, Department of Chemical
        Engineering, The Norwegian Institute of Technology, Trondheim, Norway).
    \endverbatim

Usage
    \table
        Property     | Description             | Required    | Default value
        beta         | Coefficient beta        | no          | 2.0
        C1           | Coefficient C1          | no          | 1.0
    \endtable

SourceFiles
    Luo.C

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

#ifndef Luo_H
#define Luo_H

#include "coalescenceModel.H"

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

namespace Foam
{
namespace populationBalance
{
namespace coalescenceModels
{

/*---------------------------------------------------------------------------*\
                             Class Luo Declaration
\*---------------------------------------------------------------------------*/

class Luo
:
    public coalescenceModel
{
    // Private Data

        //- Coefficient beta, defaults to 2.0
        dimensionedScalar beta_;

        //- Optional coefficient C1, defaults to 1.0
        dimensionedScalar C1_;


public:

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

    // Constructor

        Luo
        (
            const populationBalanceModel& popBal,
            const dictionary& dict
        );


    //- Destructor
    virtual ~Luo()
    {}


    // Member Functions

        //- Add to coalescenceRate
        virtual void addToCoalescenceRate
        (
            volScalarField::Internal& coalescenceRate,
            const label i,
            const label j
        );
};


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

} // End namespace coalescenceModels
} // End namespace populationBalance
} // End namespace Foam

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

#endif

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