electricPotential.H

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/*---------------------------------------------------------------------------*\
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    Copyright (C) 2021 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.
 
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    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
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    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.
 
    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
Class
    Foam::functionObjects::electricPotential
 
Group
    grpSolversFunctionObjects
 
Description
    Computes the steady-state equation of charge conservation to obtain
    the electric potential by strictly assuming a quasi-static electrostatic
    field for single-phase and multiphase applications.
 
    The steady-state equation of the charge conservation:
 
    \f[
        \nabla \cdot \left( \sigma \nabla V \right) = 0
    \f]
 
    where
    \vartable
      V       | Electric potential                [volt = kg m^2/(A s^3)]
      \sigma  | Isotropic conductivity of mixture [S/m = A^2 s^3/(kg m^3)]
    \endvartable
 
    Optionally, electric field, current density and free-charge
    density fields can be written out by using the following equations:
 
    \f[
        \vec{E} = - \nabla V
    \f]
 
    \f[
        \vec{J} = \sigma \vec{E} = - \sigma \nabla V
    \f]
 
    \f[
        \rho_E = \nabla \cdot \left(\epsilon_m \vec{E} \right)
               = \nabla \cdot \left(\epsilon_0 \epsilon_r \vec{E} \right)
    \f]
 
    where
    \vartable
      \vec{E}    | Electric field                       [m kg/(s^3 A)]
      \vec{J}    | Current density                      [A/m^2]
      \rho_E     | Volume charge density                [C/m^3 = A s/m^3]
      \epsilon_m | Isotropic permittivity of mixture    [F/m = A^2 s^4/(kg m^3)]
      \epsilon_0 | Isotropic vacuum permittivity        [F/m = A^2 s^4/(kg m^3)]
      \epsilon_r | Isotropic relative permittivity of mixture [-]
    \endvartable
 
    For multiphase applications, \c sigma and \c epsilonr are blended
    (to consider their interface values) by using the simple weighted
    arithmetic mean interpolation, for example:
 
    \f[
        \sigma = \alpha_1 \sigma_1 + \alpha_2 \sigma_2
               = \alpha_1 \sigma_1 + (1 - \alpha_1) \sigma_2
    \f]
 
Usage
    Minimal example by using \c system/controlDict.functions:
    \verbatim
    electricPotential1
    {
        // Mandatory entries
        type            electricPotential;
        libs            (solverFunctionObjects);
 
        // Conditional entries
 
            // Option-1: single-phase
            sigma       <scalar>;
            epsilonr    <scalar>;
 
            // Option-2: multiphase
            phases
            {
                alpha.air
                {
                    sigma       <scalar>;
                    epsilonr    <scalar>;
                }
                alpha.water
                {
                    sigma       <scalar>;
                    epsilonr    <scalar>;
                }
                alpha.mercury
                {
                    sigma       <scalar>;
                    epsilonr    <scalar>;
                }
                ...
            }
 
        // Optional entries
        nCorr                 <label>;
        writeDerivedFields    <bool>;
        fieldName             <word>;
 
        // Inherited entries
        ...
    }
    \endverbatim
 
    where the entries mean:
    \table
      Property  | Description                         | Type | Reqd | Deflt
      type      | Type name: electricPotential        | word | yes  | -
      libs      | Library name: solverFunctionObjects | word | yes  | -
      sigma     | Isotropic electrical conductivity of phase | scalar | yes | -
      epsilonr  | Isotropic relative permittivity of phase   | scalar | no  | -
      nCorr     | Number of corrector iterations     | label | no   | 1
      writeDerivedFields | Flag to write extra fields | bool | no   | false
      fieldName | Name of operand field   | word | no | electricPotential:V
    \endtable
 
    The inherited entries are elaborated in:
      - \link functionObject.H \endlink
 
    Fields written out when the \c writeDerivedFields entry is \c true:
    \table
      Operand         | Type             | Location
      Electric field  | volVectorField   | <time>/electricPotential:E
      Current density | volVectorField   | <time>/electricPotential:J
      Charge density  | volScalarField   | <time>/electricPotential:rho
    \endtable
 
SourceFiles
    electricPotential.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef functionObjects_electricPotential_H
#define functionObjects_electricPotential_H
 
#include "fvMeshFunctionObject.H"
#include "volFields.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
namespace functionObjects
{
 
/*---------------------------------------------------------------------------*\
                       Class electricPotential Declaration
\*---------------------------------------------------------------------------*/
 
class electricPotential
:
    public fvMeshFunctionObject
{
    // Private Data
 
        //- Dictionary of phase data
        dictionary phasesDict_;
 
        //- List of phase names
        wordList phaseNames_;
 
        //- Unallocated list of phase fields
        UPtrList<volScalarField> phases_;
 
        //- List of isotropic electrical conductivity of phases
        PtrList<dimensionedScalar> sigmas_;
 
        //- Isotropic electrical conductivity of a single phase
        dimensionedScalar sigma_;
 
        //- List of isotropic relative permittivity of phases
        PtrList<dimensionedScalar> epsilonrs_;
 
        //- Isotropic relative permittivity of a single phase
        dimensionedScalar epsilonr_;
 
        //- Name of the operand field
        word fieldName_;
 
        //- Number of corrector iterations
        label nCorr_;
 
        //- Flag to write derived fields of
        //- electric field, current density and free-charge density
        bool writeDerivedFields_;
 
 
    // Private Member Functions
 
        //- Return reference to the registered operand field
        volScalarField& operandField();
 
        //- Return the isotropic electrical conductivity field of the mixture
        tmp<volScalarField> sigma() const;
 
        //- Return the isotropic permittivity field of the mixture
        tmp<volScalarField> epsilonm() const;
 
 
        //- No copy construct
        electricPotential(const electricPotential&) = delete;
 
        //- No copy assignment
        void operator=(const electricPotential&) = delete;
 
 
public:
 
    //- Runtime type information
    TypeName("electricPotential");
 
 
    // Constructors
 
        //- Construct from Time and dictionary
        electricPotential
        (
            const word& name,
            const Time& runTime,
            const dictionary& dict
        );
 
 
    //- Destructor
    virtual ~electricPotential() = default;
 
 
    // Member Functions
 
        //- Read the function object data
        virtual bool read(const dictionary& dict);
 
        //- Calculate the function object
        virtual bool execute();
 
        //- Write the function object output
        virtual bool write();
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace functionObjects
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //