/*---------------------------------------------------------------------------*\
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\\ / O peration |
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\\/ M anipulation |
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License
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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 ;
epsilonr ;
// Option-2: multiphase
phases
{
alpha.air
{
sigma ;
epsilonr ;
}
alpha.water
{
sigma ;
epsilonr ;
}
alpha.mercury
{
sigma ;
epsilonr ;
}
...
}
// Optional entries
nCorr ;
writeDerivedFields ;
V ;
electricField ;
E ;
fvOptions ;
// 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 | int | no | 1
writeDerivedFields | Flag to write extra fields | bool | no | false
V | Name of electric potential field | word | no | electricPotential:V
electricField | Flag to calculate electric field | bool | no | false
E | Name of electric field | word | no | electricPotential:E
fvOptions | List of finite-volume options | dict | no | -
\endtable
The inherited entries are elaborated in:
- \link functionObject.H \endlink
- \link fvOption.H \endlink
Fields written out when the \c writeDerivedFields entry is \c true:
\table
Operand | Type | Location
Current density | volVectorField | \/electricPotential:J
Charge density | volScalarField | \/electricPotential:rho
\endtable
Note
- Only constraint-type finite-volume options can be used.
SourceFiles
electricPotential.C
\*---------------------------------------------------------------------------*/
#ifndef functionObjects_electricPotential_H
#define functionObjects_electricPotential_H
#include "fvMeshFunctionObject.H"
#include "volFields.H"
#include "fvOptionList.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 phases_;
//- List of isotropic electrical conductivity of phases
PtrList sigmas_;
//- Isotropic electrical conductivity of a single phase
dimensionedScalar sigma_;
//- List of isotropic relative permittivity of phases
PtrList epsilonrs_;
//- Isotropic relative permittivity of a single phase
dimensionedScalar epsilonr_;
//- Name of electric potential field
word Vname_;
//- Name of electric field
word Ename_;
//- Run-time selectable finite volume options
fv::optionList fvOptions_;
//- Number of corrector iterations
int nCorr_;
//- Flag to write derived fields of
//- electric field, current density and free-charge density
bool writeDerivedFields_;
//- Flag to calculate electric field
bool electricField_;
// Private Member Functions
//- Return requested field from the object registry
//- or read+register the field to the object registry
volScalarField& getOrReadField(const word& fieldName) const;
//- Return the isotropic electrical conductivity field of the mixture
tmp sigma() const;
//- Return the isotropic permittivity field of the mixture
tmp 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
// ************************************************************************* //