multiphaseSystem.C

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  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
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    Copyright (C) 2011-2018 OpenFOAM Foundation
    Copyright (C) 2020-2022 OpenCFD Ltd.
-------------------------------------------------------------------------------
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.
 
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    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
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#include "multiphaseSystem.H"
#include "alphaContactAngleFvPatchScalarField.H"
#include "fixedValueFvsPatchFields.H"
#include "Time.H"
#include "subCycle.H"
#include "MULES.H"
#include "surfaceInterpolate.H"
#include "fvcGrad.H"
#include "fvcSnGrad.H"
#include "fvcDiv.H"
#include "fvcFlux.H"
#include "fvcAverage.H"
 
#include "unitConversion.H"
 
// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
void Foam::multiphaseSystem::calcAlphas()
{
    scalar level = 0.0;
    alphas_ == 0.0;
 
    for (const phaseModel& phase : phases_)
    {
        alphas_ += level * phase;
        level += 1.0;
    }
}
 
 
void Foam::multiphaseSystem::solveAlphas()
{
    PtrList<surfaceScalarField> alphaPhiCorrs(phases_.size());
    int phasei = 0;
 
    for (phaseModel& phase : phases_)
    {
        volScalarField& alpha1 = phase;
 
        alphaPhiCorrs.set
        (
            phasei,
            new surfaceScalarField
            (
                "phi" + alpha1.name() + "Corr",
                fvc::flux
                (
                    phi_,
                    phase,
                    "div(phi," + alpha1.name() + ')'
                )
            )
        );
 
        surfaceScalarField& alphaPhiCorr = alphaPhiCorrs[phasei];
 
        for (phaseModel& phase2 : phases_)
        {
            volScalarField& alpha2 = phase2;
 
            if (&phase2 == &phase) continue;
 
            surfaceScalarField phir(phase.phi() - phase2.phi());
 
            const auto cAlpha = cAlphas_.cfind(interfacePair(phase, phase2));
 
            if (cAlpha.good())
            {
                surfaceScalarField phic
                (
                    (mag(phi_) + mag(phir))/mesh_.magSf()
                );
 
                phir += min(cAlpha()*phic, max(phic))*nHatf(phase, phase2);
            }
 
            const word phirScheme
            (
                "div(phir," + alpha2.name() + ',' + alpha1.name() + ')'
            );
 
            alphaPhiCorr += fvc::flux
            (
                -fvc::flux(-phir, phase2, phirScheme),
                phase,
                phirScheme
            );
        }
 
        phase.correctInflowOutflow(alphaPhiCorr);
 
        MULES::limit
        (
            1.0/mesh_.time().deltaTValue(),
            geometricOneField(),
            phase,
            phi_,
            alphaPhiCorr,
            zeroField(),
            zeroField(),
            oneField(),
            zeroField(),
            true
        );
 
        ++phasei;
    }
 
    MULES::limitSum(alphaPhiCorrs);
 
    volScalarField sumAlpha
    (
        IOobject
        (
            "sumAlpha",
            mesh_.time().timeName(),
            mesh_
        ),
        mesh_,
        dimensionedScalar("sumAlpha", dimless, 0)
    );
 
    phasei = 0;
 
    for (phaseModel& phase : phases_)
    {
        surfaceScalarField& alphaPhi = alphaPhiCorrs[phasei];
        alphaPhi += upwind<scalar>(mesh_, phi_).flux(phase);
        phase.correctInflowOutflow(alphaPhi);
 
        MULES::explicitSolve
        (
            geometricOneField(),
            phase,
            alphaPhi
        );
 
        phase.alphaPhi() = alphaPhi;
 
        Info<< phase.name() << " volume fraction, min, max = "
            << phase.weightedAverage(mesh_.V()).value()
            << ' ' << min(phase).value()
            << ' ' << max(phase).value()
            << endl;
 
        sumAlpha += phase;
 
        ++phasei;
    }
 
    Info<< "Phase-sum volume fraction, min, max = "
        << sumAlpha.weightedAverage(mesh_.V()).value()
        << ' ' << min(sumAlpha).value()
        << ' ' << max(sumAlpha).value()
        << endl;
 
    // Correct the sum of the phase-fractions to avoid 'drift'
    volScalarField sumCorr(1.0 - sumAlpha);
    for (phaseModel& phase : phases_)
    {
        volScalarField& alpha = phase;
        alpha += alpha*sumCorr;
    }
 
    calcAlphas();
}
 
 
Foam::tmp<Foam::surfaceVectorField> Foam::multiphaseSystem::nHatfv
(
    const volScalarField& alpha1,
    const volScalarField& alpha2
) const
{
    /*
    // Cell gradient of alpha
    volVectorField gradAlpha =
        alpha2*fvc::grad(alpha1) - alpha1*fvc::grad(alpha2);
 
    // Interpolated face-gradient of alpha
    surfaceVectorField gradAlphaf = fvc::interpolate(gradAlpha);
    */
 
    surfaceVectorField gradAlphaf
    (
        fvc::interpolate(alpha2)*fvc::interpolate(fvc::grad(alpha1))
      - fvc::interpolate(alpha1)*fvc::interpolate(fvc::grad(alpha2))
    );
 
    // Face unit interface normal
    return gradAlphaf/(mag(gradAlphaf) + deltaN_);
}
 
 
Foam::tmp<Foam::surfaceScalarField> Foam::multiphaseSystem::nHatf
(
    const volScalarField& alpha1,
    const volScalarField& alpha2
) const
{
    // Face unit interface normal flux
    return nHatfv(alpha1, alpha2) & mesh_.Sf();
}
 
 
// Correction for the boundary condition on the unit normal nHat on
// walls to produce the correct contact angle.
 
// The dynamic contact angle is calculated from the component of the
// velocity on the direction of the interface, parallel to the wall.
 
void Foam::multiphaseSystem::correctContactAngle
(
    const phaseModel& phase1,
    const phaseModel& phase2,
    surfaceVectorField::Boundary& nHatb
) const
{
    const volScalarField::Boundary& gbf
        = phase1.boundaryField();
 
    const fvBoundaryMesh& boundary = mesh_.boundary();
 
    forAll(boundary, patchi)
    {
        if
        (
            isA<multiphaseEuler::alphaContactAngleFvPatchScalarField>
            (
                gbf[patchi]
            )
        )
        {
            const auto& acap =
                refCast
                <
                    const multiphaseEuler::alphaContactAngleFvPatchScalarField
                >
                (
                    gbf[patchi]
                );
 
            vectorField& nHatPatch = nHatb[patchi];
 
            vectorField AfHatPatch
            (
                mesh_.Sf().boundaryField()[patchi]
               /mesh_.magSf().boundaryField()[patchi]
            );
 
            const auto tp =
                acap.thetaProps().cfind(interfacePair(phase1, phase2));
 
            if (!tp.good())
            {
                FatalErrorInFunction
                    << "Cannot find interface " << interfacePair(phase1, phase2)
                    << "\n    in table of theta properties for patch "
                    << acap.patch().name()
                    << exit(FatalError);
            }
 
            bool matched = (tp.key().first() == phase1.name());
 
            const scalar theta0 = degToRad(tp().theta0(matched));
            scalarField theta(boundary[patchi].size(), theta0);
 
            scalar uTheta = tp().uTheta();
 
            // Calculate the dynamic contact angle if required
            if (uTheta > SMALL)
            {
                const scalar thetaA = degToRad(tp().thetaA(matched));
                const scalar thetaR = degToRad(tp().thetaR(matched));
 
                // Calculated the component of the velocity parallel to the wall
                vectorField Uwall
                (
                    phase1.U().boundaryField()[patchi].patchInternalField()
                  - phase1.U().boundaryField()[patchi]
                );
                Uwall -= (AfHatPatch & Uwall)*AfHatPatch;
 
                // Find the direction of the interface parallel to the wall
                vectorField nWall
                (
                    nHatPatch - (AfHatPatch & nHatPatch)*AfHatPatch
                );
 
                // Normalise nWall
                nWall /= (mag(nWall) + SMALL);
 
                // Calculate Uwall resolved normal to the interface parallel to
                // the interface
                scalarField uwall(nWall & Uwall);
 
                theta += (thetaA - thetaR)*tanh(uwall/uTheta);
            }
 
 
            // Reset nHatPatch to correspond to the contact angle
 
            scalarField a12(nHatPatch & AfHatPatch);
 
            scalarField b1(cos(theta));
 
            scalarField b2(nHatPatch.size());
 
            forAll(b2, facei)
            {
                b2[facei] = cos(acos(a12[facei]) - theta[facei]);
            }
 
            scalarField det(1.0 - a12*a12);
 
            scalarField a((b1 - a12*b2)/det);
            scalarField b((b2 - a12*b1)/det);
 
            nHatPatch = a*AfHatPatch + b*nHatPatch;
 
            nHatPatch /= (mag(nHatPatch) + deltaN_.value());
        }
    }
}
 
 
Foam::tmp<Foam::volScalarField> Foam::multiphaseSystem::K
(
    const phaseModel& phase1,
    const phaseModel& phase2
) const
{
    tmp<surfaceVectorField> tnHatfv = nHatfv(phase1, phase2);
 
    correctContactAngle(phase1, phase2, tnHatfv.ref().boundaryFieldRef());
 
    // Simple expression for curvature
    return -fvc::div(tnHatfv & mesh_.Sf());
}
 
 
// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
Foam::multiphaseSystem::multiphaseSystem
(
    const volVectorField& U,
    const surfaceScalarField& phi
)
:
    IOdictionary
    (
        IOobject
        (
            "transportProperties",
            U.time().constant(),
            U.db(),
            IOobject::MUST_READ_IF_MODIFIED,
            IOobject::NO_WRITE
        )
    ),
 
    phases_(lookup("phases"), phaseModel::iNew(U.mesh())),
 
    mesh_(U.mesh()),
    phi_(phi),
 
    alphas_
    (
        IOobject
        (
            "alphas",
            mesh_.time().timeName(),
            mesh_,
            IOobject::NO_READ,
            IOobject::AUTO_WRITE
        ),
        mesh_,
        dimensionedScalar("alphas", dimless, 0.0)
    ),
 
    sigmas_(lookup("sigmas")),
    dimSigma_(1, 0, -2, 0, 0),
    cAlphas_(lookup("interfaceCompression")),
    Cvms_(lookup("virtualMass")),
    deltaN_
    (
        "deltaN",
        1e-8/cbrt(average(mesh_.V()))
    )
{
    calcAlphas();
    alphas_.write();
 
    interfaceDictTable dragModelsDict(lookup("drag"));
 
    forAllConstIters(dragModelsDict, iter)
    {
        dragModels_.set
        (
            iter.key(),
            multiphaseEuler::dragModel::New
            (
                iter(),
                *phases_.lookup(iter.key().first()),
                *phases_.lookup(iter.key().second())
            ).ptr()
        );
    }
 
    for (const phaseModel& phase1 : phases_)
    {
        for (const phaseModel& phase2 : phases_)
        {
            if (&phase2 == &phase1)
            {
                continue;
            }
 
            const interfacePair key(phase1, phase2);
 
            if (sigmas_.found(key) && !cAlphas_.found(key))
            {
                WarningInFunction
                    << "Compression coefficient not specified for phase pair ("
                    << phase1.name() << ' ' << phase2.name()
                    << ") for which a surface tension coefficient is specified"
                    << endl;
            }
        }
    }
}
 
 
// * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * * //
 
Foam::tmp<Foam::volScalarField> Foam::multiphaseSystem::rho() const
{
    auto iter = phases_.cbegin();
 
    tmp<volScalarField> trho = iter()*iter().rho();
    volScalarField& rho = trho.ref();
 
    for (++iter; iter != phases_.cend(); ++iter)
    {
        rho += iter()*iter().rho();
    }
 
    return trho;
}
 
 
Foam::tmp<Foam::scalarField>
Foam::multiphaseSystem::rho(const label patchi) const
{
    auto iter = phases_.cbegin();
 
    tmp<scalarField> trho = iter().boundaryField()[patchi]*iter().rho().value();
    scalarField& rho = trho.ref();
 
    for (++iter; iter != phases_.cend(); ++iter)
    {
        rho += iter().boundaryField()[patchi]*iter().rho().value();
    }
 
    return trho;
}
 
 
Foam::tmp<Foam::volScalarField> Foam::multiphaseSystem::nu() const
{
    auto iter = phases_.cbegin();
 
    tmp<volScalarField> tmu = iter()*(iter().rho()*iter().nu());
    volScalarField& mu = tmu.ref();
 
    for (++iter; iter != phases_.cend(); ++iter)
    {
        mu += iter()*(iter().rho()*iter().nu());
    }
 
    return tmu/rho();
}
 
 
Foam::tmp<Foam::scalarField>
Foam::multiphaseSystem::nu(const label patchi) const
{
    auto iter = phases_.cbegin();
 
    tmp<scalarField> tmu =
        iter().boundaryField()[patchi]
       *(iter().rho().value()*iter().nu().value());
    scalarField& mu = tmu.ref();
 
    for (++iter; iter != phases_.cend(); ++iter)
    {
        mu +=
            iter().boundaryField()[patchi]
           *(iter().rho().value()*iter().nu().value());
    }
 
    return tmu/rho(patchi);
}
 
 
Foam::tmp<Foam::volScalarField> Foam::multiphaseSystem::Cvm
(
    const phaseModel& phase
) const
{
    auto tCvm = volScalarField::New
    (
        "Cvm",
        IOobject::NO_REGISTER,
        mesh_,
        dimensionedScalar(dimDensity, Zero)
    );
 
    for (const phaseModel& phase2 : phases_)
    {
        if (&phase2 == &phase)
        {
            continue;
        }
 
        auto iterCvm = Cvms_.cfind(interfacePair(phase, phase2));
 
        if (iterCvm.good())
        {
            tCvm.ref() += iterCvm()*phase2.rho()*phase2;
        }
        else
        {
            iterCvm = Cvms_.cfind(interfacePair(phase2, phase));
 
            if (iterCvm.good())
            {
                tCvm.ref() += iterCvm()*phase.rho()*phase2;
            }
        }
    }
 
    return tCvm;
}
 
 
Foam::tmp<Foam::volVectorField> Foam::multiphaseSystem::Svm
(
    const phaseModel& phase
) const
{
    auto tSvm = volVectorField::New
    (
        "Svm",
        IOobject::NO_REGISTER,
        mesh_,
        dimensionedVector
        (
            dimensionSet(1, -2, -2, 0, 0),
            Zero
        )
    );
 
    for (const phaseModel& phase2 : phases_)
    {
        if (&phase2 == &phase)
        {
            continue;
        }
 
        auto Cvm = Cvms_.cfind(interfacePair(phase, phase2));
 
        if (Cvm.good())
        {
            tSvm.ref() += Cvm()*phase2.rho()*phase2*phase2.DDtU();
        }
        else
        {
            Cvm = Cvms_.cfind(interfacePair(phase2, phase));
 
            if (Cvm.good())
            {
                tSvm.ref() += Cvm()*phase.rho()*phase2*phase2.DDtU();
            }
        }
    }
 
    volVectorField::Boundary& SvmBf =
        tSvm.ref().boundaryFieldRef();
 
    // Remove virtual mass at fixed-flux boundaries
    forAll(phase.phi().boundaryField(), patchi)
    {
        if
        (
            isA<fixedValueFvsPatchScalarField>
            (
                phase.phi().boundaryField()[patchi]
            )
        )
        {
            SvmBf[patchi] = Zero;
        }
    }
 
    return tSvm;
}
 
 
Foam::autoPtr<Foam::multiphaseSystem::dragCoeffFields>
Foam::multiphaseSystem::dragCoeffs() const
{
    auto dragCoeffsPtr = autoPtr<dragCoeffFields>::New();
 
    forAllConstIters(dragModels_, iter)
    {
        const multiphaseEuler::dragModel& dm = *iter();
 
        volScalarField* Kptr =
            (
                max
                (
                    // fvc::average(dm.phase1()*dm.phase2()),
                    // fvc::average(dm.phase1())*fvc::average(dm.phase2()),
                    dm.phase1()*dm.phase2(),
                    dm.residualPhaseFraction()
                )
               *dm.K
                (
                    max
                    (
                        mag(dm.phase1().U() - dm.phase2().U()),
                        dm.residualSlip()
                    )
                )
            ).ptr();
 
        volScalarField::Boundary& Kbf = Kptr->boundaryFieldRef();
 
        // Remove drag at fixed-flux boundaries
        forAll(dm.phase1().phi().boundaryField(), patchi)
        {
            if
            (
                isA<fixedValueFvsPatchScalarField>
                (
                    dm.phase1().phi().boundaryField()[patchi]
                )
            )
            {
                Kbf[patchi] = 0.0;
            }
        }
 
        dragCoeffsPtr().set(iter.key(), Kptr);
    }
 
    return dragCoeffsPtr;
}
 
 
Foam::tmp<Foam::volScalarField> Foam::multiphaseSystem::dragCoeff
(
    const phaseModel& phase,
    const dragCoeffFields& dragCoeffs
) const
{
    auto tdragCoeff = volScalarField::New
    (
        "dragCoeff",
        IOobject::NO_REGISTER,
        mesh_,
        dimensionedScalar(dimensionSet(1, -3, -1, 0, 0), Zero)
    );
 
    dragModelTable::const_iterator dmIter = dragModels_.begin();
    dragCoeffFields::const_iterator dcIter = dragCoeffs.begin();
    for
    (
        ;
        dmIter.good() && dcIter.good();
        ++dmIter, ++dcIter
    )
    {
        if
        (
            &phase == &dmIter()->phase1()
         || &phase == &dmIter()->phase2()
        )
        {
            tdragCoeff.ref() += *dcIter();
        }
    }
 
    return tdragCoeff;
}
 
 
Foam::tmp<Foam::surfaceScalarField> Foam::multiphaseSystem::surfaceTension
(
    const phaseModel& phase1
) const
{
    auto tSurfaceTension = surfaceScalarField::New
    (
        "surfaceTension",
        IOobject::NO_REGISTER,
        mesh_,
        dimensionedScalar(dimensionSet(1, -2, -2, 0, 0), Zero)
    );
    tSurfaceTension.ref().setOriented();
 
    for (const phaseModel& phase2 : phases_)
    {
        if (&phase2 == &phase1)
        {
            continue;
        }
 
        const auto sigma = sigmas_.cfind(interfacePair(phase1, phase2));
 
        if (sigma.good())
        {
            tSurfaceTension.ref() +=
                dimensionedScalar("sigma", dimSigma_, *sigma)
               *fvc::interpolate(K(phase1, phase2))*
                (
                    fvc::interpolate(phase2)*fvc::snGrad(phase1)
                  - fvc::interpolate(phase1)*fvc::snGrad(phase2)
                );
        }
    }
 
    return tSurfaceTension;
}
 
 
Foam::tmp<Foam::volScalarField>
Foam::multiphaseSystem::nearInterface() const
{
    auto tnearInt = volScalarField::New
    (
        "nearInterface",
        IOobject::NO_REGISTER,
        mesh_,
        dimensionedScalar(dimless, Zero)
    );
 
    for (const phaseModel& phase : phases_)
    {
        tnearInt.ref() =
            max(tnearInt(), pos0(phase - 0.01)*pos0(0.99 - phase));
    }
 
    return tnearInt;
}
 
 
void Foam::multiphaseSystem::solve()
{
    for (phaseModel& phase : phases_)
    {
        phase.correct();
    }
 
    const Time& runTime = mesh_.time();
 
    const dictionary& alphaControls = mesh_.solverDict("alpha");
    label nAlphaSubCycles(alphaControls.get<label>("nAlphaSubCycles"));
 
    if (nAlphaSubCycles > 1)
    {
        dimensionedScalar totalDeltaT = runTime.deltaT();
 
        PtrList<volScalarField> alpha0s(phases_.size());
        PtrList<surfaceScalarField> alphaPhiSums(phases_.size());
 
        label phasei = 0;
        for (phaseModel& phase : phases_)
        {
            volScalarField& alpha = phase;
 
            alpha0s.set
            (
                phasei,
                new volScalarField(alpha.oldTime())
            );
 
            alphaPhiSums.set
            (
                phasei,
                new surfaceScalarField
                (
                    IOobject
                    (
                        "phiSum" + alpha.name(),
                        runTime.timeName(),
                        mesh_
                    ),
                    mesh_,
                    dimensionedScalar(dimensionSet(0, 3, -1, 0, 0), Zero)
                )
            );
 
            ++phasei;
        }
 
        for
        (
            subCycleTime alphaSubCycle
            (
                const_cast<Time&>(runTime),
                nAlphaSubCycles
            );
            !(++alphaSubCycle).end();
        )
        {
            solveAlphas();
 
            label phasei = 0;
            for (const phaseModel& phase : phases_)
            {
                alphaPhiSums[phasei] += phase.alphaPhi()/nAlphaSubCycles;
 
                ++phasei;
            }
        }
 
        phasei = 0;
        for (phaseModel& phase : phases_)
        {
            volScalarField& alpha = phase;
 
            phase.alphaPhi() = alphaPhiSums[phasei];
 
            // Correct the time index of the field
            // to correspond to the global time
            alpha.timeIndex() = runTime.timeIndex();
 
            // Reset the old-time field value
            alpha.oldTime() = alpha0s[phasei];
            alpha.oldTime().timeIndex() = runTime.timeIndex();
 
            ++phasei;
        }
    }
    else
    {
        solveAlphas();
    }
}
 
 
bool Foam::multiphaseSystem::read()
{
    if (regIOobject::read())
    {
        bool readOK = true;
 
        PtrList<entry> phaseData(lookup("phases"));
        label phasei = 0;
 
        for (phaseModel& phase : phases_)
        {
            readOK &= phase.read(phaseData[phasei++].dict());
        }
 
        lookup("sigmas") >> sigmas_;
        lookup("interfaceCompression") >> cAlphas_;
        lookup("virtualMass") >> Cvms_;
 
        return readOK;
    }
    else
    {
        return false;
    }
}
 
 
// ************************************************************************* //