ENH: Added new solidification and melting fvOption

src/fvOptions/Make/files

@@ -12,6 +12,7 @@ $(generalSources)/semiImplicitSource/semiImplicitSource.C
 
 derivedSources=sources/derived
 $(derivedSources)/actuationDiskSource/actuationDiskSource.C
+$(derivedSources)/effectivenessHeatExchangerSource/effectivenessHeatExchangerSource.C
 $(derivedSources)/explicitPorositySource/explicitPorositySource.C
 $(derivedSources)/MRFSource/MRFSource.C
 $(derivedSources)/pressureGradientExplicitSource/pressureGradientExplicitSource.C
@@ -27,7 +28,8 @@ $(derivedSources)/rotorDiskSource/trimModel/trimModel/trimModel.C
 $(derivedSources)/rotorDiskSource/trimModel/trimModel/trimModelNew.C
 $(derivedSources)/rotorDiskSource/trimModel/fixed/fixedTrim.C
 $(derivedSources)/rotorDiskSource/trimModel/targetCoeff/targetCoeffTrim.C
-$(derivedSources)/effectivenessHeatExchangerSource/effectivenessHeatExchangerSource.C
+$(derivedSources)/solidificationMeltingSource/solidificationMeltingSource.C
+$(derivedSources)/solidificationMeltingSource/solidificationMeltingSourceIO.C
 
 interRegion = sources/interRegion
 $(interRegion)/interRegionHeatTransferModel/constantHeatTransfer/constantHeatTransfer.C

src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSource.C

@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2013-2014 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    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/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "solidificationMeltingSource.H"
+#include "fvMatrices.H"
+#include "basicThermo.H"
+#include "uniformDimensionedFields.H"
+#include "zeroGradientFvPatchFields.H"
+#include "addToRunTimeSelectionTable.H"
+#include "geometricOneField.H"
+
+// * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
+
+namespace Foam
+{
+    template<>
+    const char* NamedEnum
+    <
+        fv::solidificationMeltingSource::thermoMode,
+        2
+    >::names[] =
+    {
+        "thermo",
+        "lookup"
+    };
+
+    namespace fv
+    {
+        defineTypeNameAndDebug(solidificationMeltingSource, 0);
+
+        addToRunTimeSelectionTable
+        (
+            option,
+            solidificationMeltingSource,
+            dictionary
+        );
+    }
+}
+
+const Foam::NamedEnum<Foam::fv::solidificationMeltingSource::thermoMode, 2>
+    Foam::fv::solidificationMeltingSource::thermoModeTypeNames_;
+
+
+// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
+
+bool Foam::fv::solidificationMeltingSource::solveField
+(
+    const word& fieldName
+) const
+{
+    bool result = true;
+
+    switch (mode_)
+    {
+        case mdThermo:
+        {
+            const basicThermo& thermo =
+                mesh_.lookupObject<basicThermo>("thermophysicalProperties");
+
+            if (fieldName != thermo.he().name())
+            {
+                result = false;
+            }
+            break;
+        }
+        case mdLookup:
+        {
+            if (fieldName != TName_)
+            {
+                result = false;
+            }
+            break;
+        }
+        default:
+        {
+            FatalErrorIn
+            (
+                "bool Foam::fv::solidificationMeltingSource::solveField"
+                "("
+                    "const word&"
+                ") const"
+            )
+                << "Unhandled thermo mode: " << thermoModeTypeNames_[mode_]
+                << abort(FatalError);
+        }
+    }
+    return result;
+}
+
+
+Foam::tmp<Foam::volScalarField>
+Foam::fv::solidificationMeltingSource::Cp() const
+{
+    switch (mode_)
+    {
+        case mdThermo:
+        {
+            const basicThermo& thermo =
+                mesh_.lookupObject<basicThermo>("thermophysicalProperties");
+
+            return thermo.Cp();
+            break;
+        }
+        case mdLookup:
+        {
+            if (CpName_ == "CpRef")
+            {
+                scalar CpRef = readScalar(coeffs_.lookup("CpRef"));
+
+                return tmp<volScalarField>
+                (
+                    new volScalarField
+                    (
+                        IOobject
+                        (
+                            name_ + ":Cp",
+                            mesh_.time().timeName(),
+                            mesh_,
+                            IOobject::NO_READ,
+                            IOobject::NO_WRITE
+                        ),
+                        mesh_,
+                        dimensionedScalar
+                        (
+                            "Cp",
+                            dimEnergy/dimMass/dimTemperature,
+                            CpRef
+                        ),
+                        zeroGradientFvPatchScalarField::typeName
+                    )
+                );
+            }
+            else
+            {
+                return mesh_.lookupObject<volScalarField>(CpName_);
+            }
+
+            break;
+        }
+        default:
+        {
+            FatalErrorIn
+            (
+                "Foam::tmp<Foam::volScalarField> "
+                "Foam::fv::solidificationMeltingSource::Cp() const"
+            )
+                << "Unhandled thermo mode: " << thermoModeTypeNames_[mode_]
+                << abort(FatalError);
+        }
+    }
+
+    return tmp<volScalarField>(NULL);
+}
+
+
+Foam::vector Foam::fv::solidificationMeltingSource::g() const
+{
+    if (mesh_.foundObject<uniformDimensionedVectorField>("g"))
+    {
+        const uniformDimensionedVectorField& value =
+            mesh_.lookupObject<uniformDimensionedVectorField>("g");
+        return value.value();
+    }
+    else
+    {
+        return coeffs_.lookup("g");
+    }
+}
+
+
+void Foam::fv::solidificationMeltingSource::update(const volScalarField& Cp)
+{
+    if (curTimeIndex_ == mesh_.time().timeIndex())
+    {
+        return;
+    }
+
+    if (debug)
+    {
+        Info<< type() << ": " << name_ << " - updating phase indicator" << endl;
+    }
+
+    // update old time alpha1 field
+    alpha1_.oldTime();
+
+    const volScalarField& T = mesh_.lookupObject<volScalarField>(TName_);
+
+    forAll(cells_, i)
+    {
+        label cellI = cells_[i];
+
+        scalar Tc = T[cellI];
+        scalar Cpc = Cp[cellI];
+        scalar alpha1New = alpha1_[cellI] + relax_*Cpc*(Tc - Tmelt_)/L_;
+
+        alpha1_[cellI] = max(0, min(alpha1New, 1));
+        deltaT_[i] = Tc - Tmelt_;
+    }
+
+    alpha1_.correctBoundaryConditions();
+
+    curTimeIndex_ = mesh_.time().timeIndex();
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::fv::solidificationMeltingSource::solidificationMeltingSource
+(
+    const word& sourceName,
+    const word& modelType,
+    const dictionary& dict,
+    const fvMesh& mesh
+)
+:
+    option(sourceName, modelType, dict, mesh),
+    Tmelt_(readScalar(coeffs_.lookup("Tmelt"))),
+    L_(readScalar(coeffs_.lookup("L"))),
+    relax_(coeffs_.lookupOrDefault("relax", 0.9)),
+    mode_(thermoModeTypeNames_.read(coeffs_.lookup("thermoMode"))),
+    rhoRef_(readScalar(coeffs_.lookup("rhoRef"))),
+    TName_(coeffs_.lookupOrDefault<word>("TName", "T")),
+    CpName_(coeffs_.lookupOrDefault<word>("CpName", "Cp")),
+    UName_(coeffs_.lookupOrDefault<word>("UName", "U")),
+    phiName_(coeffs_.lookupOrDefault<word>("phiName", "phi")),
+    Cu_(coeffs_.lookupOrDefault<scalar>("Cu", 100000)),
+    q_(coeffs_.lookupOrDefault("q", 0.001)),
+    beta_(readScalar(coeffs_.lookup("beta"))),
+    alpha1_
+    (
+        IOobject
+        (
+            name_ + ":alpha1",
+            mesh.time().timeName(),
+            mesh,
+            IOobject::READ_IF_PRESENT,
+            IOobject::AUTO_WRITE
+        ),
+        mesh,
+        dimensionedScalar("alpha1", dimless, 0.0),
+        zeroGradientFvPatchScalarField::typeName
+    ),
+    curTimeIndex_(-1),
+    deltaT_(cells_.size(), 0)
+{
+    fieldNames_.setSize(1, "source");
+    applied_.setSize(1, false);
+}
+
+
+// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+
+bool Foam::fv::solidificationMeltingSource::alwaysApply() const
+{
+    return true;
+}
+
+
+void Foam::fv::solidificationMeltingSource::addSup
+(
+    fvMatrix<scalar>& eqn,
+    const label fieldI
+)
+{
+    apply(geometricOneField(), eqn);
+}
+
+
+void Foam::fv::solidificationMeltingSource::addSup
+(
+    const volScalarField& rho,
+    fvMatrix<scalar>& eqn,
+    const label fieldI
+)
+{
+    apply(rho, eqn);
+}
+
+
+void Foam::fv::solidificationMeltingSource::addSup
+(
+    fvMatrix<vector>& eqn,
+    const label fieldI
+)
+{
+    const volVectorField& U = eqn.psi();
+
+    if (U.name() != UName_)
+    {
+        return;
+    }
+
+    if (debug)
+    {
+        Info<< type() << ": applying source to " << UName_ << endl;
+    }
+
+    const volScalarField Cp(this->Cp());
+
+    update(Cp);
+
+    vector g = this->g();
+
+    scalarField& Sp = eqn.diag();
+    vectorField& Su = eqn.source();
+    const scalarField& V = mesh_.V();
+
+    forAll(cells_, i)
+    {
+        label cellI = cells_[i];
+
+        scalar Vc = V[cellI];
+        scalar alpha1c = alpha1_[cellI];
+
+        scalar S = -Cu_*sqr(1.0 - alpha1c)/(pow3(alpha1c) + q_);
+        vector Sb = rhoRef_*g*beta_*deltaT_[i];
+
+        Sp[cellI] += Vc*S;
+        Su[cellI] += Vc*Sb;
+    }
+}
+
+
+void Foam::fv::solidificationMeltingSource::addSup
+(
+    const volScalarField& rho,
+    fvMatrix<vector>& eqn,
+    const label fieldI
+)
+{
+    // momentum source uses a Boussinesq approximation - redirect
+    addSup(eqn, fieldI);
+}
+
+
+// ************************************************************************* //

src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSource.H

@@ -0,0 +1,280 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2013-2014 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    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::fv::solidificationMeltingSource
+
+Description
+    This source is designed to model the effect of solidification and melting
+    processes, e.g. windhield defrosting.  The phase change occurs at the
+    melting temperature, \c Tmelt.
+
+    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.
+
+    Based on the references:
+
+      1. V.R. Voller and C. Prakash, A fixed grid numerical modelling
+         methodology for convection-diffusion mushy phase-change problems,
+         Int. J. Heat Mass Transfer 30(8):17091719, 1987.
+      2. C.R. Swaminathan. and V.R. Voller, A general enthalpy model for
+         modeling solidification processes, Metallurgical Transactions
+         23B:651664, 1992.
+
+    The model generates a field \c \<name\>:alpha1 which can be visualised to
+    to show the melt distribution as a fraction [0-1]
+
+    \heading Source usage
+    Example usage:
+    \verbatim
+    solidificationMeltingSource1
+    {
+        type            solidificationMeltingSource;
+        active          on;
+        selectionMode   cellZone;
+        cellZone        iceZone;
+
+        solidificationMeltingSourceCoeffs
+        {
+            Tmelt           273;
+            L               334000;
+            thermoMode      thermo;
+            beta            50e-6;
+            rhoRef          800;
+        }
+    }
+    \endverbatim
+
+    Where:
+    \table
+        Property     | Description             | Required    | Default value
+        Tmelt        | Melting temperature [K] | yes         |
+        L            | Latent heat of fusion [J/kg] | yes    |
+        relax        | Relaxation coefficient [0-1] | no     | 0.9
+        thermoMode   | Thermo mode [thermo|lookup] | yes     |
+        rhoRef       | Reference (solid) density | yes       |
+        rhoName      | Name of density field   | no          | rho
+        TName        | Name of temperature field | no        | T
+        CpName       | Name of specific heat capacity field | no | Cp
+        UName        | Name of velocity field  | no          | U
+        phiName      | Name of flux field      | no          | phi
+        Cu           | Model coefficient       | no          | 100000
+        q            | Model coefficient       | no          | 0.001
+        beta         | Thermal expansion coefficient [1/K] | yes |
+        g            | Accelerartion due to gravity | no     |
+    \endtable
+
+SourceFiles
+    solidificationMeltingSource.C
+    solidificationMeltingSourceIO.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef solidificationMeltingSource_H
+#define solidificationMeltingSource_H
+
+#include "fvMesh.H"
+#include "volFields.H"
+#include "fvOption.H"
+#include "NamedEnum.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace fv
+{
+
+/*---------------------------------------------------------------------------*\
+                 Class solidificationMeltingSource Declaration
+\*---------------------------------------------------------------------------*/
+
+class solidificationMeltingSource
+:
+    public option
+{
+public:
+
+    enum thermoMode
+    {
+        mdThermo,
+        mdLookup
+    };
+
+    static const NamedEnum<thermoMode, 2> thermoModeTypeNames_;
+
+
+private:
+
+    // Private data
+
+        //- Temperature at which melting occurs [K]
+        scalar Tmelt_;
+
+        //- 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_;
+
+        //- Phase fraction indicator field
+        volScalarField alpha1_;
+
+        //- Current time index (used for updating)
+        label curTimeIndex_;
+
+        //- Temperature change cached for source calculation when alpha1 updated
+        scalarField deltaT_;
+
+
+    // Private Member Functions
+
+        //- Flag to indicate whether to solve for given field
+        bool solveField(const word& fieldName) const;
+
+        //- Return the specific heat capacity field
+        tmp<volScalarField> Cp() const;
+
+        //- Return the gravity vector
+        vector g() const;
+
+        //- Update the model
+        void update(const volScalarField& Cp);
+
+        //- Helper function to apply to the energy equation
+        template<class RhoFieldType>
+        void apply(const RhoFieldType& rho, fvMatrix<scalar>& eqn);
+
+        //- Disallow default bitwise copy construct
+        solidificationMeltingSource(const solidificationMeltingSource&);
+
+        //- Disallow default bitwise assignment
+        void operator=(const solidificationMeltingSource&);
+
+
+public:
+
+    //- Runtime type information
+    TypeName("solidificationMeltingSource");
+
+
+    // Constructors
+
+        //- Construct from explicit source name and mesh
+        solidificationMeltingSource
+        (
+            const word& sourceName,
+            const word& modelType,
+            const dictionary& dict,
+            const fvMesh& mesh
+        );
+
+
+    // Member Functions
+
+        //- Flag to bypass the apply flag list checking
+        virtual bool alwaysApply() const;
+
+
+        // Add explicit and implicit contributions
+
+            //- Add explicit contribution to enthalpy equation
+            virtual void addSup(fvMatrix<scalar>& eqn, const label fieldI);
+
+            //- Add implicit contribution to momentum equation
+            virtual void addSup(fvMatrix<vector>& eqn, const label fieldI);
+
+
+        // Add explicit and implicit contributions to compressible equation
+
+            //- Add explicit contribution to compressible enthalpy equation
+            virtual void addSup
+            (
+                const volScalarField& rho,
+                fvMatrix<scalar>& eqn,
+                const label fieldI
+            );
+
+            //- Add implicit contribution to compressible momentum equation
+            virtual void addSup
+            (
+                const volScalarField& rho,
+                fvMatrix<vector>& eqn,
+                const label fieldI
+            );
+
+
+        // I-O
+
+            //- Write the source properties
+            virtual void writeData(Ostream&) const;
+
+            //- Read source dictionary
+            virtual bool read(const dictionary& dict);
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace fv
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#ifdef NoRepository
+    #include "solidificationMeltingSourceTemplates.C"
+#endif
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSourceIO.C

@@ -0,0 +1,68 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2013-2014 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    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/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "solidificationMeltingSource.H"
+
+// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
+
+void Foam::fv::solidificationMeltingSource::writeData(Ostream& os) const
+{
+    os  << indent << name_ << endl;
+    dict_.write(os);
+}
+
+
+bool Foam::fv::solidificationMeltingSource::read(const dictionary& dict)
+{
+    if (option::read(dict))
+    {
+        coeffs_.lookup("Tmelt") >> Tmelt_;
+        coeffs_.lookup("L") >> L_;
+
+        coeffs_.readIfPresent("relax", relax_);
+
+        mode_ = thermoModeTypeNames_.read(coeffs_.lookup("thermoMode"));
+
+        coeffs_.lookup("rhoRef") >> rhoRef_;
+        coeffs_.readIfPresent("TName", TName_);
+        coeffs_.readIfPresent("UName", UName_);
+
+        coeffs_.readIfPresent("Cu", Cu_);
+        coeffs_.readIfPresent("q", q_);
+
+        coeffs_.readIfPresent("beta", beta_);
+
+        return true;
+    }
+    else
+    {
+        return false;
+    }
+
+    return false;
+}
+
+
+// ************************************************************************* //

src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSourceTemplates.C

@@ -0,0 +1,70 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2014 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    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/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "fvMatrices.H"
+#include "fvcDdt.H"
+
+// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
+
+template<class RhoFieldType>
+void Foam::fv::solidificationMeltingSource::apply
+(
+    const RhoFieldType& rho,
+    fvMatrix<scalar>& eqn
+)
+{
+    if (!solveField(eqn.psi().name()))
+    {
+        return;
+    }
+
+    if (debug)
+    {
+        Info<< type() << ": applying source to " << eqn.psi().name() << endl;
+    }
+
+    const volScalarField Cp(this->Cp());
+
+    update(Cp);
+
+    dimensionedScalar L("L", dimEnergy/dimMass, L_);
+
+    // contributions added to rhs of solver equation
+    if (eqn.psi().dimensions() == dimTemperature)
+    {
+        // isothermal phase change - only include time derivative
+//        eqn -= L/Cp*(fvc::ddt(rho, alpha1_) + fvc::div(phi, alpha1_));
+        eqn -= L/Cp*(fvc::ddt(rho, alpha1_));
+    }
+    else
+    {
+        // isothermal phase change - only include time derivative
+//        eqn -= L*(fvc::ddt(rho, alpha1_) + fvc::div(phi, alpha1_));
+        eqn -= L*(fvc::ddt(rho, alpha1_));
+    }
+}
+
+
+// ************************************************************************* //