LehrMilliesMewesCoalescence.H

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Class
    Foam::populationBalance::coalescenceModels::LehrMilliesMewesCoalescence
 
Description
    Model of Lehr et al. (2002). The coalescence rate is calculated by
 
    \f[
        \frac{\pi}{4} (d_i + d_j)^2 \mathrm{min}(u^{\prime}, u_{\mathrm{crit}})
        \mathrm{exp}
        \left[
          - \left(\frac{\alpha_{\mathrm{max}}^{1/3}}{\alpha^{1/3}} - 1\right)^2
        \right]\,,
    \f]
 
    where
 
    \f[
        u^{\prime}
      =
        \mathrm{max}
        \left(
            \sqrt{2} \epsilon_c^{1/3} \sqrt{d_i^{2/3} + d_j^{2/3}},
            |\vec{u}_i - \vec{u}_j|
        \right)
    \f]
 
    is the characteristic velocity for coalescence. Note that a velocity
    difference between bubble i and j is only present if the corresponding
    groups are assigned to different phases.
 
    \vartable
        d_i          |  Diameter of bubble i [m]
        d_j          |  Diameter of bubble j [m]
        \epsilon_c   |  Turbulent dissipation rate of continuous phase [m^2/s^3]
        \alpha       |  Total void fraction of the bubbles [-]
        \alpha_{max} |  Maximum packing density of the bubbles [-]
        u_{crit}     |  Critical velocity for coalescence [m/s]
        \vec{u}_i    |  Velocity vector of bubble i [m/s]
        \vec{u}_j    |  Velocity vector of bubble j [m/s]
    \endvartable
 
    Reference:
    \verbatim
        Lehr, F., Millies, M., & Mewes, D. (2002).
        Bubble‐size distributions and flow fields in bubble columns.
        AIChE Journal, 48(11), 2426-2443.
    \endverbatim
 
Usage
    \table
        Property     | Description                | Required    | Default value
        uCrit        | Crit. coalescence velocity | no          | 0.08
        alphaMax     | Maximum packing density    | no          | 0.6
    \endtable
 
SourceFiles
    LehrMilliesMewesCoalescence.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef LehrMilliesMewesCoalescence_H
#define LehrMilliesMewesCoalescence_H
 
#include "coalescenceModel.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
namespace populationBalance
{
namespace coalescenceModels
{
 
/*---------------------------------------------------------------------------*\
                 Class LehrMilliesMewesCoalescence Declaration
\*---------------------------------------------------------------------------*/
 
class LehrMilliesMewesCoalescence
:
    public coalescenceModel
{
    // Private Data
 
        //- Critical velocity for coalescence, defaults to 0.08 m/s
        dimensionedScalar uCrit_;
 
        //- Maximum packing density of the bubbles, defaults to 0.6
        dimensionedScalar alphaMax_;
 
 
public:
 
    //- Runtime type information
    TypeName("LehrMilliesMewes");
 
    // Constructor
 
        LehrMilliesMewesCoalescence
        (
            const populationBalanceModel& popBal,
            const dictionary& dict
        );
 
 
    //- Destructor
    virtual ~LehrMilliesMewesCoalescence()
    {}
 
 
    // Member Functions
 
        //- Return the coalescence rate between two groups
        virtual tmp<volScalarField::Internal> rate
        (
            const label i,
            const label j
        ) const;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace coalescenceModels
} // End namespace populationBalance
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //