alphatWallBoilingWallFunctionFvPatchScalarField.C

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#include "alphatWallBoilingWallFunctionFvPatchScalarField.H"
#include "alphatJayatillekeWallFunctionFvPatchScalarField.H"
#include "fluidThermophysicalTransportModel.H"
#include "phaseSystem.H"
#include "heatTransferPhaseSystem.H"
#include "compressibleMomentumTransportModel.H"
#include "phaseCompressibleMomentumTransportModel.H"
#include "interfaceSaturationTemperatureModel.H"
#include "rhoFluidMulticomponentThermo.H"
 
#include "fixedValueFvPatchFields.H"
#include "zeroGradientFvPatchFields.H"
#include "fixedGradientFvPatchFields.H"
#include "mixedFvPatchFields.H"
 
#include "addToRunTimeSelectionTable.H"
 
using namespace Foam::constant::mathematical;
 
// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
template<>
const char* Foam::NamedEnum
<
    Foam::compressible::alphatWallBoilingWallFunctionFvPatchScalarField::
        phaseType,
    3
>::names[] = {"vapour", "vapor", "liquid"};
 
const Foam::NamedEnum
<
    Foam::compressible::alphatWallBoilingWallFunctionFvPatchScalarField::
        phaseType,
    3
>
Foam::compressible::alphatWallBoilingWallFunctionFvPatchScalarField::
    phaseTypeNames_;
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
namespace compressible
{
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
struct alphatWallBoilingWallFunctionFvPatchScalarField::properties
{
    // Data
 
        //- Wall function field
        const alphatWallBoilingWallFunctionFvPatchScalarField& field;
 
        //- Phase
        const phaseModel& phase;
 
        //- Other phase
        const phaseModel& otherPhase;
 
        //- Volume fraction
        const scalarField& alphaw;
 
        //- Other volume fraction
        const scalarField& otherAlphaw;
 
        //- Interface
        const phaseInterface interface;
 
        //- Phase thermophysical transport model
        const fluidThermophysicalTransportModel& ttm;
 
        //- Phase convective turbulent thermal diffusivity
        const scalarField alphatConv;
 
 
    //- Constructor
    properties
    (
        const alphatWallBoilingWallFunctionFvPatchScalarField& field,
        const phaseModel& phase,
        const phaseModel& otherPhase
    )
    :
        field(field),
        phase(phase),
        otherPhase(otherPhase),
        alphaw(phase.boundaryField()[patchi()]),
        otherAlphaw(otherPhase.boundaryField()[patchi()]),
        interface(phase, otherPhase),
        ttm
        (
            field.db().lookupType<fluidThermophysicalTransportModel>
            (
                phase.name()
            )
        ),
        alphatConv
        (
            alphatJayatillekeWallFunctionFvPatchScalarField::alphat
            (
                ttm,
                field.Prt_,
                patchi()
            )
        )
    {}
 
 
    // Member Functions
 
        //- Patch
        inline const fvPatch& patch() const
        {
            return field.patch();
        }
 
        //- Patch index
        inline label patchi() const
        {
            return patch().index();
        }
};
 
 
struct alphatWallBoilingWallFunctionFvPatchScalarField::boilingLiquidProperties
:
    public alphatWallBoilingWallFunctionFvPatchScalarField::properties
{
    // Data
 
        //- Name of the volatile specie
        const word volatileSpecie;
 
        //- Patch area by neighbouring cell volume ratio
        const scalarField AbyV;
 
        //- Liquid density
        const tmp<scalarField> trhoLiquidw;
        const scalarField& rhoLiquidw;
 
        //- Vapour density
        const tmp<scalarField> trhoVapourw;
        const scalarField& rhoVapourw;
 
        //- Liquid heat capacity
        const scalarField& Cpw;
 
        //- Liquid laminar kinematic viscosity
        const tmp<scalarField> tnuw;
        const scalarField& nuw;
 
        //- Liquid laminar thermal diffusivity
        const scalarField kappaByCp;
 
        //- Liquid viscosity wall function
        const nutWallFunctionFvPatchScalarField& nutw;
 
        //- Dimensionless wall distance
        const scalarField yPlus;
 
        //- Smoothing function
        const scalarField P;
 
        //- Cell temperature
        const scalarField Tc;
 
        //- Saturation temperature
        const scalarField Tsat;
 
        //- Latent heat
        const scalarField L;
 
 
    //- Constructor
    boilingLiquidProperties
    (
        const alphatWallBoilingWallFunctionFvPatchScalarField& field,
        const phaseModel& liquid,
        const phaseModel& vapour
    )
    :
        properties(field, liquid, vapour),
        volatileSpecie
        (
            liquid.fluid().lookupOrDefault<word>("volatile", "none")
        ),
        AbyV
        (
            patch().magSf()
           /scalarField
            (
                patch().boundaryMesh().mesh().V(),
                patch().faceCells()
            )
        ),
        trhoLiquidw(liquid.thermo().rho(patchi())),
        rhoLiquidw(trhoLiquidw()),
        trhoVapourw(vapour.thermo().rho(patchi())),
        rhoVapourw(trhoVapourw()),
        Cpw(liquid.thermo().Cp().boundaryField()[patchi()]),
        tnuw(liquid.fluidThermo().nu(patchi())),
        nuw(tnuw()),
        kappaByCp(liquid.thermo().kappa().boundaryField()[patchi()]/Cpw),
        nutw
        (
            nutWallFunctionFvPatchScalarField::nutw
            (
                ttm.momentumTransport(),
                patchi()
            )
        ),
        yPlus
        (
            pow025(nutw.Cmu())
           *sqrt(ttm.momentumTransport().k()().boundaryField()[patchi()])
           *ttm.momentumTransport().yb()[patchi()]
           /nuw
        ),
        P
        (
            alphatJayatillekeWallFunctionFvPatchScalarField::P
            (
                rhoLiquidw*nuw/kappaByCp/field.Prt_
            )
        ),
        Tc
        (
            liquid.thermo().T().boundaryField()[patchi()].patchInternalField()
        ),
        Tsat
        (
            liquid.fluid().lookupInterfacialModel
            <
                interfaceSaturationTemperatureModel
            >
            (interface)
           .Tsat(liquid.fluidThermo().p())()
           .boundaryField()[patchi()]
        ),
        L
        (
            volatileSpecie != "none"
         ? -refCast<const heatTransferPhaseSystem>(liquid.fluid())
           .Li
            (
                interface,
                volatileSpecie,
                scalarField(patch().size(), +1),
                Tsat,
                patch().faceCells(),
                heatTransferPhaseSystem::latentHeatScheme::upwind
            )
         : -refCast<const heatTransferPhaseSystem>(liquid.fluid())
           .L
            (
                interface,
                scalarField(patch().size(), +1),
                Tsat,
                patch().faceCells(),
                heatTransferPhaseSystem::latentHeatScheme::upwind
            )
        )
    {}
};
 
 
// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
tmp<scalarField>
alphatWallBoilingWallFunctionFvPatchScalarField::calcBoiling
(
    const boilingLiquidProperties& props,
    const scalarField& Tw,
    scalarField& dDeparture,
    scalarField& fDeparture,
    scalarField& nucleationSiteDensity,
    scalarField& qQuenching,
    scalarField& qEvaporative,
    scalarField& dmdtf
) const
{
    scalarField Tl;
    if (!useLiquidTemperatureWallFunction_)
    {
        Tl = props.Tc;
    }
    else
    {
        // Liquid temperature at y+=250 is estimated from the
        // logarithmic thermal wall function of Koncar, Krepper
        // & Egorov (2005)
        const scalarField TyPlus250
        (
            Prt_
           *(
                log(props.nutw.E()*250)
               /props.nutw.kappa()
              + props.P
           )
        );
 
        const scalarField TyPlus
        (
            Prt_
           *(
                log(props.nutw.E()*max(props.yPlus, scalar(11)))
               /props.nutw.kappa()
              + props.P
            )
        );
 
        Tl = Tw - (TyPlus250/TyPlus)*(Tw - props.Tc);
    }
 
    // Bubble departure diameter
    dDeparture =
        departureDiameterModel_->dDeparture
        (
            props.phase,
            props.otherPhase,
            patch().index(),
            Tl,
            props.Tsat,
            props.L
        );
 
    // Bubble departure frequency
    fDeparture =
        departureFrequencyModel_->fDeparture
        (
            props.phase,
            props.otherPhase,
            patch().index(),
            Tl,
            props.Tsat,
            props.L,
            dDeparture
        );
 
    // Nucleation site density
    nucleationSiteDensity =
        nucleationSiteModel_->nucleationSiteDensity
        (
            props.phase,
            props.otherPhase,
            patch().index(),
            Tl,
            props.Tsat,
            props.L,
            dDeparture,
            fDeparture
        );
 
    // Del Valle & Kenning (1985)
    const scalarField Ja
    (
        props.rhoLiquidw
       *props.Cpw
       *max(props.Tsat - Tl, scalar(0))
       /(props.rhoVapourw*props.L)
    );
 
    const scalarField Al
    (
        wetFraction_*4.8*exp(min(-Ja/80, log(vGreat)))
    );
 
    scalarField A2
    (
        min(pi*sqr(dDeparture)*nucleationSiteDensity*Al/4, scalar(1))
    );
    const scalarField A1(max(1 - A2, scalar(1e-4)));
    scalarField A2E
    (
        min(pi*sqr(dDeparture)*nucleationSiteDensity*Al/4, scalar(5))
    );
 
    if (props.volatileSpecie != "none" && !props.phase.pure())
    {
        const scalarField& Yvolatile =
            props.phase
           .Y(props.volatileSpecie)
           .boundaryField()[patch().index()];
        A2E *= Yvolatile;
        A2 *= Yvolatile;
    }
 
    // Volumetric mass source in the near wall cell due to the
    // wall boiling
    dmdtf = (1.0/6.0)*A2E*dDeparture*props.rhoVapourw*fDeparture*props.AbyV;
 
    // Quenching heat transfer coefficient
    const scalarField hQ
    (
        2*props.kappaByCp*props.Cpw*fDeparture
       *sqrt
        (
            tau_
           /max(fDeparture, small)
           /(pi*props.kappaByCp/props.rhoLiquidw)
        )
    );
 
    // Quenching heat flux
    qQuenching = A2*hQ*max(Tw - Tl, scalar(0));
 
    // Evaporation heat flux
    qEvaporative = dmdtf*props.L/props.AbyV;
 
    // Return total sum of convective, quenching and evaporative heat fluxes
    const scalarField gradTw
    (
        patch().deltaCoeffs()*max(Tw - props.Tc, small*props.Tc)
    );
    return A1*props.alphatConv*props.Cpw*gradTw + qQuenching_ + qEvaporative_;
}
 
 
tmp<scalarField>
alphatWallBoilingWallFunctionFvPatchScalarField::calcBoiling
(
    const boilingLiquidProperties& props,
    const scalarField& Tw
) const
{
    scalarField dDeparture(dDeparture_);
    scalarField fDeparture(fDeparture_);
    scalarField nucleationSiteDensity(nucleationSiteDensity_);
    scalarField qQuenching(qQuenching_);
    scalarField qEvaporative(qEvaporative_);
    scalarField dmdtf(dmdtf_);
 
    return
        calcBoiling
        (
            props,
            Tw,
            dDeparture,
            fDeparture,
            nucleationSiteDensity,
            qQuenching,
            qEvaporative,
            dmdtf
        );
}
 
 
tmp<scalarField>
alphatWallBoilingWallFunctionFvPatchScalarField::evaluateBoiling
(
    const boilingLiquidProperties& props,
    const scalarField& Tw
)
{
    return
        calcBoiling
        (
            props,
            Tw,
            dDeparture_,
            fDeparture_,
            nucleationSiteDensity_,
            qQuenching_,
            qEvaporative_,
            dmdtf_
        );
}
 
 
const fvPatchScalarField&
alphatWallBoilingWallFunctionFvPatchScalarField::getTemperaturePatchField
(
    const boilingLiquidProperties& props,
    scalarField& isFixed,
    scalarField& h,
    scalarField& hTaPlusQa
) const
{
    isFixed.setSize(patch().size());
    h.setSize(patch().size());
    hTaPlusQa.setSize(patch().size());
 
    const fvPatchScalarField& Tw =
        props.phase.thermo().T().boundaryField()[patch().index()];
 
    if (isA<fixedValueFvPatchScalarField>(Tw))
    {
        isFixed = 1;
        h = rootVGreat;
        hTaPlusQa = rootVGreat*Tw;
    }
    else if (isA<zeroGradientFvPatchScalarField>(Tw))
    {
        isFixed = 0;
        h = 0;
        hTaPlusQa = 0;
    }
    else if (isA<fixedGradientFvPatchScalarField>(Tw))
    {
        const fixedGradientFvPatchScalarField& Twm =
            refCast<const fixedGradientFvPatchScalarField>(Tw);
 
        isFixed = 0;
        h = 0;
        hTaPlusQa = (*this)*props.Cpw*Twm.gradient();
    }
    else if (isA<mixedFvPatchScalarField>(Tw))
    {
        const mixedFvPatchScalarField& Twm =
            refCast<const mixedFvPatchScalarField>(Tw);
 
        isFixed = pos(Twm.valueFraction() - 1 + rootSmall);
        h =
            Twm.valueFraction()
           /max(1 - Twm.valueFraction(), rootVSmall)
           *(*this)*props.Cpw*patch().deltaCoeffs();
        hTaPlusQa =
            h*Twm.refValue()
          + (*this)*props.Cpw*Twm.refGrad();
    }
    else
    {
        FatalErrorInFunction
            << "Temperature boundary condition type not recognised"
            << exit(FatalError);
    }
 
    return Tw;
}
 
 
// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
alphatWallBoilingWallFunctionFvPatchScalarField::
alphatWallBoilingWallFunctionFvPatchScalarField
(
    const fvPatch& p,
    const DimensionedField<scalar, volMesh>& iF,
    const dictionary& dict
)
:
    fixedValueFvPatchScalarField(p, iF, dict),
    alphatPhaseChangeWallFunctionBase(p, iF, dict),
 
    phaseType_(phaseTypeNames_.read(dict.lookup("phaseType"))),
    useLiquidTemperatureWallFunction_
    (
        dict.lookupOrDefault<Switch>("useLiquidTemperatureWallFunction", true)
    ),
    tolerance_(dict.lookupOrDefault<scalar>("tolerance", rootSmall)),
 
    Prt_(dict.lookupOrDefault<scalar>("Prt", dimless, 0.85)),
    tau_(dict.lookupOrDefault<scalar>("bubbleWaitingTimeRatio", dimless, 0.8)),
 
    partitioningModel_(nullptr),
    nucleationSiteModel_(nullptr),
    departureDiameterModel_(nullptr),
    departureFrequencyModel_(nullptr),
 
    wetFraction_(p.size(), 0),
    dDeparture_(p.size(), 1e-5),
    fDeparture_(p.size(), 0),
    nucleationSiteDensity_(p.size(), 0),
    qQuenching_(p.size(), 0),
    qEvaporative_(p.size(), 0),
    dmdtf_(p.size(), 0)
{
    // Sub-Models
    partitioningModel_ =
        wallBoilingModels::partitioningModel::New
        (
            dict.subDict("partitioningModel")
        );
 
    if (phaseType_ == liquidPhase)
    {
        nucleationSiteModel_ =
            wallBoilingModels::nucleationSiteModel::New
            (
                dict.subDict("nucleationSiteModel")
            );
        departureDiameterModel_ =
            wallBoilingModels::departureDiameterModel::New
            (
                dict.subDictBackwardsCompatible
                (
                    {"departureDiameterModel", "departureDiamModel"}
                )
            );
        departureFrequencyModel_ =
            wallBoilingModels::departureFrequencyModel::New
            (
                dict.subDictBackwardsCompatible
                (
                    {"departureFrequencyModel", "departureFreqModel"}
                )
            );
    }
 
    // Backwards compatible reading for old field keywords
    auto readFieldBackwardsCompatible = [&p]
    (
        const dictionary& dict,
        const unitConversion& units,
        const wordList& keywords,
        scalarField& field
    )
    {
        forAll(keywords, i)
        {
            if (dict.found(keywords[i]))
            {
                field = scalarField(keywords[i], units, dict, p.size());
                return;
            }
        }
    };
 
    // State
    readFieldBackwardsCompatible
    (
        dict,
        unitFraction,
        {"wetFraction", "wallLiquidFraction"},
        wetFraction_
    );
 
    if (phaseType_ == liquidPhase)
    {
        readFieldBackwardsCompatible
        (
            dict,
            dimLength,
            {"dDeparture"},
            dDeparture_
        );
 
        readFieldBackwardsCompatible
        (
            dict,
            dimless/dimTime,
            {"fDeparture", "depFrequency"},
            fDeparture_
        );
 
        readFieldBackwardsCompatible
        (
            dict,
            dimless/dimArea,
            {"nucleationSiteDensity", "nucSiteDensity"},
            nucleationSiteDensity_
        );
 
        readFieldBackwardsCompatible
        (
            dict,
            dimPower/dimArea,
            {"qQuenching"},
            qQuenching_
        );
 
        readFieldBackwardsCompatible
        (
            dict,
            dimPower/dimArea,
            {"qEvaporative"},
            qEvaporative_
        );
 
        readFieldBackwardsCompatible
        (
            dict,
            dimDensity/dimTime,
            {"dmdtf"},
            dmdtf_
        );
    }
}
 
 
alphatWallBoilingWallFunctionFvPatchScalarField::
alphatWallBoilingWallFunctionFvPatchScalarField
(
    const alphatWallBoilingWallFunctionFvPatchScalarField& psf,
    const fvPatch& p,
    const DimensionedField<scalar, volMesh>& iF,
    const fieldMapper& mapper
)
:
    fixedValueFvPatchScalarField(psf, p, iF, mapper),
    alphatPhaseChangeWallFunctionBase(psf),
 
    phaseType_(psf.phaseType_),
    useLiquidTemperatureWallFunction_(psf.useLiquidTemperatureWallFunction_),
    tolerance_(psf.tolerance_),
 
    Prt_(psf.Prt_),
    tau_(psf.tau_),
 
    partitioningModel_(psf.partitioningModel_, false),
    nucleationSiteModel_(psf.nucleationSiteModel_, false),
    departureDiameterModel_(psf.departureDiameterModel_, false),
    departureFrequencyModel_(psf.departureFrequencyModel_, false),
 
    wetFraction_(mapper(psf.wetFraction_)),
    dDeparture_(mapper(psf.dDeparture_)),
    fDeparture_(mapper(psf.fDeparture_)),
    nucleationSiteDensity_(mapper(psf.nucleationSiteDensity_)),
    qQuenching_(mapper(psf.qQuenching_)),
    qEvaporative_(mapper(psf.qEvaporative_)),
    dmdtf_(mapper(psf.dmdtf_))
{}
 
 
alphatWallBoilingWallFunctionFvPatchScalarField::
alphatWallBoilingWallFunctionFvPatchScalarField
(
    const alphatWallBoilingWallFunctionFvPatchScalarField& psf,
    const DimensionedField<scalar, volMesh>& iF
)
:
    fixedValueFvPatchScalarField(psf, iF),
    alphatPhaseChangeWallFunctionBase(psf),
 
    phaseType_(psf.phaseType_),
    useLiquidTemperatureWallFunction_(psf.useLiquidTemperatureWallFunction_),
    tolerance_(psf.tolerance_),
 
    Prt_(psf.Prt_),
    tau_(psf.tau_),
 
    partitioningModel_(psf.partitioningModel_, false),
    nucleationSiteModel_(psf.nucleationSiteModel_, false),
    departureDiameterModel_(psf.departureDiameterModel_, false),
    departureFrequencyModel_(psf.departureFrequencyModel_, false),
 
    wetFraction_(psf.wetFraction_),
    dDeparture_(psf.dDeparture_),
    fDeparture_(psf.fDeparture_),
    nucleationSiteDensity_(psf.nucleationSiteDensity_),
    qQuenching_(psf.qQuenching_),
    qEvaporative_(psf.qEvaporative_),
    dmdtf_(psf.dmdtf_)
{}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
void alphatWallBoilingWallFunctionFvPatchScalarField::map
(
    const fvPatchScalarField& ptf,
    const fieldMapper& mapper
)
{
    fixedValueFvPatchScalarField::map(ptf, mapper);
 
    const alphatWallBoilingWallFunctionFvPatchScalarField& tiptf =
        refCast<const alphatWallBoilingWallFunctionFvPatchScalarField>(ptf);
 
    mapper(wetFraction_, tiptf.wetFraction_);
    mapper(dDeparture_, tiptf.dDeparture_);
    mapper(fDeparture_, tiptf.fDeparture_);
    mapper(nucleationSiteDensity_, tiptf.nucleationSiteDensity_);
    mapper(qQuenching_, tiptf.qQuenching_);
    mapper(qEvaporative_, tiptf.qEvaporative_);
    mapper(dmdtf_, tiptf.dmdtf_);
}
 
 
void alphatWallBoilingWallFunctionFvPatchScalarField::reset
(
    const fvPatchScalarField& ptf
)
{
    fixedValueFvPatchScalarField::reset(ptf);
 
    const alphatWallBoilingWallFunctionFvPatchScalarField& tiptf =
        refCast<const alphatWallBoilingWallFunctionFvPatchScalarField>(ptf);
 
    wetFraction_.reset(tiptf.wetFraction_);
    dDeparture_.reset(tiptf.dDeparture_);
    fDeparture_.reset(tiptf.fDeparture_);
    nucleationSiteDensity_.reset(tiptf.nucleationSiteDensity_);
    qQuenching_.reset(tiptf.qQuenching_);
    qEvaporative_.reset(tiptf.qEvaporative_);
    dmdtf_.reset(tiptf.dmdtf_);
}
 
 
void alphatWallBoilingWallFunctionFvPatchScalarField::updateCoeffs()
{
    if (updated())
    {
        return;
    }
 
    // Lookup the fluid model and the phases
    const phaseSystem& fluid =
        db().lookupObject<phaseSystem>(phaseSystem::propertiesName);
 
    switch (phaseType_)
    {
        case vapourPhase:
        case vaporPhase:
        {
            const phaseModel& vapour = fluid.phases()[internalField().group()];
            const phaseModel& liquid = fluid.phases()[otherPhaseName_];
 
            // Construct boiling properties
            const properties props(*this, vapour, liquid);
 
            // Partitioning. Note: Assumes that there is only only one liquid
            // phase and all other phases are vapour.
            wetFraction_ = partitioningModel_->wetFraction(props.otherAlphaw);
 
            operator==
            (
                (1 - wetFraction_)
               /max(1 - props.otherAlphaw, rootSmall)
               *props.alphatConv
            );
 
            break;
        }
 
        case liquidPhase:
        {
            const phaseModel& liquid = fluid.phases()[internalField().group()];
            const phaseModel& vapour = fluid.phases()[otherPhaseName_];
 
            // Boiling is enabled by the presence of saturation temperature
            // modelling. This is consistent with interfacial thermal phase
            // changes.
            if
            (
               !fluid.foundInterfacialModel
                <
                    interfaceSaturationTemperatureModel
                >(phaseInterface(liquid, vapour))
            )
            {
                // Construct non-boiling properties
                const properties props(*this, liquid, vapour);
 
                Info<< "Saturation model for interface "
                    << props.interface.name()
                    << " not found. Wall boiling disabled." << endl;
 
                operator==(props.alphatConv);
            }
            else
            {
                // Construct boiling properties
                const boilingLiquidProperties props(*this, liquid, vapour);
 
                // Partitioning. Note: Assumes that there is only only one
                // liquid phase and all other phases are vapour.
                wetFraction_ = partitioningModel_->wetFraction(props.alphaw);
 
                // Get the temperature boundary condition and extract its
                // physical parameters
                scalarField TwpfIsFixed, TwpfH, TwpfHTaPlusQa;
                const fvPatchScalarField& Twpf =
                    getTemperaturePatchField
                    (
                        props,
                        TwpfIsFixed,
                        TwpfH,
                        TwpfHTaPlusQa
                    );
 
                // Define the residual. This should be monotonic in Tw.
                auto R = [&](const scalarField& Tw)
                {
                    return calcBoiling(props, Tw) - TwpfHTaPlusQa + TwpfH*Tw;
                };
 
                // Solve using interval bisection. Boiling cannot occur below
                // the saturation temperature, so that is taken to be the lower
                // bound. The upper bound is harder to define. For now, take
                // twice the current superheat as the maximum. The solution is
                // likely to be below this value. If it is not, then the
                // iteration will converge to this upper limit, creating a new
                // superheat of twice the current value. Subsequent time-steps
                // will then double this superheat again and again until it
                // does eventually bound the solution.
                const scalarField isBoiling(neg(R(props.Tsat)));
                scalarField Tw0(props.Tsat);
                scalarField Tw1
                (
                    max
                    (
                        Twpf + (Twpf - props.Tsat),
                        props.Tsat*(1 + sqrt(tolerance_))
                    )
                );
                scalar e =
                    gMax((1 - TwpfIsFixed)*isBoiling*(Tw1 - Tw0)/(Tw0 + Tw1));
                for (; e > tolerance_; e /= 2)
                {
                    const scalarField TwM((Tw0 + Tw1)/2);
                    const scalarField rM(R(TwM));
                    Tw0 = pos(rM)*Tw0 + neg0(rM)*TwM;
                    Tw1 = pos(rM)*TwM + neg0(rM)*Tw1;
                }
                const scalarField Tw
                (
                    TwpfIsFixed*Twpf + (1 - TwpfIsFixed)*(Tw0 + Tw1)/2
                );
 
                // Use solution to re-evaluate the boiling and set the thermal
                // diffusivity to recover the calculated heat flux
                const scalarField gradTw
                (
                    patch().deltaCoeffs()*max(Tw - props.Tc, small*props.Tc)
                );
 
                const scalarField q(evaluateBoiling(props, Tw));
 
                operator==
                (
                    isBoiling*q/props.Cpw/gradTw/max(props.alphaw, rootSmall)
                  + (1 - isBoiling)*props.alphatConv
                );
            }
 
            break;
        }
    }
 
    fixedValueFvPatchScalarField::updateCoeffs();
}
 
 
void alphatWallBoilingWallFunctionFvPatchScalarField::write(Ostream& os) const
{
    fixedValueFvPatchScalarField::write(os);
    alphatPhaseChangeWallFunctionBase::write(os);
 
    // Controls
    writeEntry(os, "phaseType", phaseTypeNames_[phaseType_]);
    writeEntry
    (
        os,
        "useLiquidTemperatureWallFunction",
        useLiquidTemperatureWallFunction_
    );
    writeEntry(os, "tolerance", tolerance_);
 
    // Parameters
    writeEntry(os, "Prt", Prt_);
    writeEntry(os, "bubbleWaitingTimeRatio", tau_);
 
    // Sub-models
    writeKeyword(os, "partitioningModel") << nl;
    os  << indent << token::BEGIN_BLOCK << incrIndent << nl;
    partitioningModel_->write(os);
    os  << decrIndent << indent << token::END_BLOCK << nl;
 
    if (phaseType_ == liquidPhase)
    {
        writeKeyword(os, "nucleationSiteModel") << nl;
        os  << indent << token::BEGIN_BLOCK << incrIndent << nl;
        nucleationSiteModel_->write(os);
        os  << decrIndent << indent << token::END_BLOCK << nl;
 
        writeKeyword(os, "departureDiameterModel") << nl;
        os  << indent << token::BEGIN_BLOCK << incrIndent << nl;
        departureDiameterModel_->write(os);
        os  << decrIndent << indent << token::END_BLOCK << nl;
 
        writeKeyword(os, "departureFrequencyModel") << nl;
        os  << indent << token::BEGIN_BLOCK << incrIndent << nl;
        departureFrequencyModel_->write(os);
        os  << decrIndent << indent << token::END_BLOCK << nl;
    }
 
    // State
    writeEntry(os, "wetFraction", wetFraction_);
 
    if (phaseType_ == liquidPhase)
    {
        writeEntry(os, "dDeparture", dDeparture_);
        writeEntry(os, "fDeparture", fDeparture_);
        writeEntry(os, "nucleationSiteDensity", nucleationSiteDensity_);
        writeEntry(os, "qQuenching", qQuenching_);
        writeEntry(os, "qEvaporative", qEvaporative_);
        writeEntry(os, "dmdtf", dmdtf_);
    }
}
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
makePatchTypeField
(
    fvPatchScalarField,
    alphatWallBoilingWallFunctionFvPatchScalarField
);
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace compressible
} // End namespace Foam
 
// ************************************************************************* //