interfaceOxideRate.H

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Class
    Foam::meltingEvaporationModels::interfaceOxideRate
 
Description
    The \c interfaceOxideRate is a simple model to calculate the formation
    rate of oxide inclusions (\c mDotOxide), which is a local function of
    the volume fraction of reducing agent (\c alpha), temperature (\c T)
    and oxide-inclusion density (\c chi).
 
    The oxide-inclusion formation rate is modelled as follows:
 
    \f[
        S_\chi = C_\chi S_\alpha S_T S_\rho
    \f]
 
    with
 
    \f[
        S_\alpha = \alpha (1 - \alpha)
    \f]
 
    \f[
        S_T =
        \exp{
            1 - \frac{1}{max(T - T_{solidus}/(T_liquidus - T_solidus), 1e-6)}
        }
    \f]
 
    \f[
        S_\rho =
            max \left(\frac{\chi_{crit} - \chi_{curr}}{\chi_{curr}}, 0\right)
    \f]
 
    where
    \vartable
      S_\chi   | Oxide-inclusion formation rate          [kg/(m^3 s)]
      C_\chi   | Oxide-inclusion formation rate constant [kg/(m^3 s)]
      S_\alpha | Formation factor due to volume fraction of reducing agent [-]
      S_T      | Formation factor due to temperature     [-]
      S_\rho   | Formation factor due to oxide-inclusion density [-]
      \alpha   | Volume fraction of reducing agent       [-]
      T        | Local temperature                       [K]
      T_{solidus}  | Solidus temperature of reducing agent  [K]
      T_{liquidus} | Liquidus temperature of reducing agent [K]
      \chi_{crit}  | Critical oxide-inclusion density    [kg/m^3]
      \chi_{curr}  | Current oxide-inclusion density     [kg/m^3]
    \endvartable
 
    References:
    \verbatim
        Oxide-inclusion model (tag:CSC):
            Cao, L., Sun, F., Chen, T., Tang, Y., & Liao, D. (2018).
            Quantitative prediction of oxide inclusion defects inside
            the casting and on the walls during cast-filling processes.
            International Journal of Heat and Mass Transfer, 119, 614-623.
            DOI:10.1016/j.ijheatmasstransfer.2017.11.127
    \endverbatim
 
Usage
    Minimal example by using \c constant/phaseProperties.massTransferModel:
    \verbatim
    massTransferModel
    (
        (liquid to oxide)
        {
            type                interfaceOxideRate;
            C                   <scalar>;
            Tliquidus           <scalar>;
            Tsolidus            <scalar>;
            oxideCrit           <scalar>;
            isoAlpha            <scalar>;
        }
    );
    \endverbatim
 
    where the entries mean:
    \table
      Property  | Description                             | Type | Reqd | Deflt
      type      | Type name: interfaceOxideRate           | word   | yes | -
      C         | Oxide-inclusion formation rate constant | scalar | yes | -
      Tliquidus | Liquidus temperature of reducing agent  | scalar | yes | -
      Tsolidus  | Solidus temperature of reducing agent   | scalar | yes | -
      oxideCrit | Critical oxide-inclusion density        | scalar | yes | -
      isoAlpha  | Location of the source                  | scalar | no  | 0.5
    \endtable
 
Note
  - \c oxideCrit should be determined experimentally (CSC:p. 616).
  - \c C should be determined by practical production (CSC:p. 616).
 
SourceFiles
    interfaceOxideRate.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef meltingEvaporationModels_interfaceOxideRate_H
#define meltingEvaporationModels_interfaceOxideRate_H
 
#include "InterfaceCompositionModel.H"
 
// * * * * * * * * * * * * * * * * *  * * * * * * * * * * * * * * * * * * * *//
 
namespace Foam
{
 
// Forward Declarations
class phasePair;
 
namespace meltingEvaporationModels
{
 
/*---------------------------------------------------------------------------*\
                    Class interfaceOxideRate Declaration
\*---------------------------------------------------------------------------*/
 
template<class Thermo, class OtherThermo>
class interfaceOxideRate
:
    public InterfaceCompositionModel<Thermo, OtherThermo>
{
    // Private Data
 
        //- Oxide-inclusion formation rate constant
        const dimensionedScalar C_;
 
        //- Liquidus temperature of reducing agent (e.g. a casting metal)
        const dimensionedScalar Tliquidus_;
 
        //- Solidus temperature of reducing agent (e.g. a casting metal)
        const dimensionedScalar Tsolidus_;
 
        //- Critical oxide-inclusion density
        const dimensionedScalar oxideCrit_;
 
        //- Oxide-inclusion formation rate
        volScalarField mDotOxide_;
 
        //- Interface Iso-value
        scalar isoAlpha_;
 
 
public:
 
    //- Runtime type information
    TypeName("interfaceOxideRate");
 
 
    // Constructors
 
        //- Construct from components
        interfaceOxideRate
        (
            const dictionary& dict,
            const phasePair& pair
        );
 
 
    //- Destructor
    virtual ~interfaceOxideRate() = default;
 
 
    // Member Functions
 
        //- Explicit total mass transfer coefficient
        virtual tmp<volScalarField> Kexp
        (
            const volScalarField& field
        );
 
        //- Implicit mass transfer coefficient
        virtual tmp<volScalarField> KSp
        (
            label modelVariable,
            const volScalarField& field
        );
 
        //- Explicit mass transfer coefficient
        virtual tmp<volScalarField> KSu
        (
            label modelVariable,
            const volScalarField& field
        );
 
        //- Return solidus temperature of reducing agent
        virtual const dimensionedScalar& Tactivate() const noexcept
        {
            return Tsolidus_;
        }
 
        //- Add/subtract alpha*div(U) as a source term
        //- for alpha, substituting div(U) = mDot(1/rho1 - 1/rho2)
        virtual bool includeDivU() const noexcept
        {
            return true;
        }
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace meltingEvaporationModels
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#ifdef NoRepository
#   include "interfaceOxideRate.C"
#endif
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
#endif
 
// ************************************************************************* //