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Class
Foam::fv::solidificationMelting
Description
This source is designed to model the effect of solidification and melting
processes, e.g. windshield defrosting.
The isotherm phase change occurs at the melting temperature, \c Tsol (= \c
Tliq). The not isotherm phase change occurs between solidus and liquidus
temperature, \c Tsol < \c Tliq respectively, as long as the melt fraction is
greater than the max eutectic melt fraction, \c alpha1e (0 = pure_substance,
1 = eutectic_mixture is not permitted), where a linear eutectic melt
fraction to temperature relation is considered; e.g. given a specific
quantity of a binary system, \c alpha1 is its melt fraction and \c alpha0 is
its solid fraction, such that \c alpha0 = 1 - \c alpha1 therefore, assuming
infinite solute diffusion, the quantity of a component in solid phase is
(1 - \c alpha1) * \c CS where \c CS is the solid concentration of the
considered component and the quantity of a component in liquid phase is \c
alpha1 * \c CL where \c CL is the melt concentration of the considered
component; considering that the total quantity of a component must be equal
to the sum of the quantities of the considered component in the liquid and
solid phases, if \c C0 is the initial concentration of the considered
component before the phase change, then:
\c C0 = (1 - \c alpha1) * \c CS + \c alpha1 * \c CL (lever rule)
from which: \c alpha1 = (\c C0 - \c CS) / (\c CL - \c CS)
and thus:
- for a miscible binary system \c alpha1e = 0;
- for a binary system not miscible at solid state
\c alpha1e = \c C0 / \c CLE where \c CLE is eutectic melt concentration;
- for a binary system partially-miscible at solid state
\c alpha1e = (\c C0 - \c CSE) / (\c CLE - \c CSE) where \c CSE is eutectic
solid concentration of the relative solid solution.
The presence of the solid phase in the flow field is incorporated into the
model as a momentum porosity contribution; the energy associated with the
phase change is added as an enthalpy contribution.
References:
\verbatim
Voller, V. R., & Prakash, C. (1987).
A fixed grid numerical modelling methodology for convection-diffusion
mushy region phase-change problems.
International Journal of Heat and Mass Transfer, 30(8), 1709-1719.
Swaminathan, C. R., & Voller, V. R. (1992).
A general enthalpy method for modeling solidification processes.
Metallurgical transactions B, 23(5), 651-664.
\endverbatim
The model generates the field \c \:alpha1 which can be visualised to
to show the melt distribution as a fraction [0-1].
Usage
Example usage:
\verbatim
solidificationMelting1
{
type solidificationMelting;
cellZone iceZone;
Tsol 273;
L 334000;
thermoMode thermo;
beta 50e-6;
rhoRef 800;
}
\endverbatim
Where:
\table
Property | Description | Required | Default value
Tsol | Solidus temperature [K] | yes |
Tliq | Liquidus temperature [K] | no | Tsol
alpha1e | Max eutectic melt fraction [0-1[ | no | 0
L | Latent heat of fusion [J/kg] | yes |
relax | Relaxation coefficient [0-1] | no | 0.9
thermoMode | Thermo mode [thermo or lookup] | yes |
rhoRef | Reference (solid) density [kg/m^3] | yes |
rho | Name of density field | no | rho
T | Name of temperature field | no | T
Cp | Name of specific heat field | no | Cp
U | Name of velocity field | no | U
phi | Name of flux field | no | phi
Cu | Model coefficient [1/s] | no | 100000
q | Model coefficient | no | 0.001
beta | Thermal expansion coefficient [1/K] | yes |
g | Acceleration due to gravity | no |
\endtable
SourceFiles
solidificationMelting.C
\*---------------------------------------------------------------------------*/
#ifndef solidificationMelting_H
#define solidificationMelting_H
#include "fvModel.H"
#include "fvCellZone.H"
#include "fvMesh.H"
#include "volFields.H"
#include "NamedEnum.H"
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
namespace Foam
{
namespace fv
{
/*---------------------------------------------------------------------------*\
Class solidificationMelting Declaration
\*---------------------------------------------------------------------------*/
class solidificationMelting
:
public fvModel
{
public:
enum class thermoMode
{
thermo,
lookup
};
static const NamedEnum thermoModeTypeNames_;
private:
// Private Data
//- The cellZone the fvModel applies to
mutable fvCellZone zone_;
//- Temperature at which isotherm melting occurs
// and not isotherm melting starts e.g. eutectic [K]
scalar Tsol_;
//- Temperature at which not isotherm melting stops (Tliq > Tsol) [K]
scalar Tliq_;
//- Max eutectic melt fraction [0-1[
// where 0 = pure substance is default value,
// 1 = eutectic mixture is not permitted
scalar alpha1e_;
//- Latent heat of fusion [J/kg]
scalar L_;
//- Phase fraction under-relaxation coefficient
scalar relax_;
//- Thermodynamics mode
thermoMode mode_;
//- Reference density - typically the solid density
scalar rhoRef_;
//- Name of temperature field - default = "T" (optional)
word TName_;
//- Name of specific heat capacity field - default = "Cp" (optional)
word CpName_;
//- Name of velocity field - default = "U" (optional)
word UName_;
//- Name of flux field - default = "phi" (optional)
word phiName_;
//- Mushy region momentum sink coefficient [1/s]; default = 10^5
scalar Cu_;
//- Coefficient used in porosity calc - default = 0.001
scalar q_;
//- Thermal expansion coefficient [1/K]
scalar beta_;
//- Reference heat capacity for thermoMode::lookup
scalar CpRef_;
//- Gravitational acceleration
vector g_;
//- Phase fraction indicator field
mutable volScalarField alpha1_;
//- Current time index (used for updating)
mutable label curTimeIndex_;
//- Temperature change cached for source calculation when alpha1 updated
mutable scalarField deltaT_;
// Private Member Functions
//- Non-virtual read
void readCoeffs(const dictionary& dict);
//- Return the specific heat capacity field
tmp Cp() const;
//- Return the gravity vector
vector g() const;
//- Update the model
void update(const volScalarField& Cp) const;
//- Helper function to apply to the energy equation
template
inline void apply(const RhoFieldType& rho, fvMatrix& eqn) const;
public:
//- Runtime type information
TypeName("solidificationMelting");
// Constructors
//- Construct from explicit source name and mesh
solidificationMelting
(
const word& name,
const word& modelType,
const fvMesh& mesh,
const dictionary& dict
);
//- Disallow default bitwise copy construction
solidificationMelting
(
const solidificationMelting&
) = delete;
// Member Functions
// Checks
//- Return the list of fields for which the fvModel adds source term
// to the transport equation
virtual wordList addSupFields() const;
// Evaluation
//- Add explicit contribution to enthalpy equation
virtual void addSup
(
const volScalarField& he,
fvMatrix& eqn
) const;
//- Add implicit contribution to momentum equation
virtual void addSup
(
const volVectorField& U,
fvMatrix& eqn
) const;
//- Add explicit contribution to compressible enthalpy equation
virtual void addSup
(
const volScalarField& rho,
const volScalarField& he,
fvMatrix& eqn
) const;
//- Add implicit contribution to compressible momentum equation
virtual void addSup
(
const volScalarField& rho,
const volVectorField& U,
fvMatrix& eqn
) const;
// Mesh changes
//- Update for mesh motion
virtual bool movePoints();
//- Update topology using the given map
virtual void topoChange(const polyTopoChangeMap&);
//- Update from another mesh using the given map
virtual void mapMesh(const polyMeshMap&);
//- Redistribute or update using the given distribution map
virtual void distribute(const polyDistributionMap&);
// IO
//- Read source dictionary
virtual bool read(const dictionary& dict);
// Member Operators
//- Disallow default bitwise assignment
void operator=(const solidificationMelting&) = delete;
};
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
} // End namespace fv
} // End namespace Foam
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
#endif
// ************************************************************************* //