multiphaseMixture.C

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    Copyright (C) 2011-2017 OpenFOAM Foundation
    Copyright (C) 2021 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.

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    under the terms of the GNU General Public License as published by
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    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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#include "multiphaseMixture.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 "unitConversion.H"
#include "alphaContactAngleFvPatchScalarField.H"

// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //

void Foam::multiphaseMixture::calcAlphas()
{
    scalar level = 0.0;
    alphas_ == 0.0;

    for (const phase& ph : phases_)
    {
        alphas_ += level * ph;
        level += 1.0;
    }
}


// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //

Foam::multiphaseMixture::multiphaseMixture
(
    const volVectorField& U,
    const surfaceScalarField& phi
)
:
    IOdictionary
    (
        IOobject
        (
            "transportProperties",
            U.time().constant(),
            U.db(),
            IOobject::READ_MODIFIED,
            IOobject::NO_WRITE,
            IOobject::REGISTER
        )
    ),

    phases_(lookup("phases"), phase::iNew(U, phi)),

    mesh_(U.mesh()),
    U_(U),
    phi_(phi),

    rhoPhi_
    (
        IOobject
        (
            "rhoPhi",
            mesh_.time().timeName(),
            mesh_
        ),
        mesh_,
        dimensionedScalar(dimMass/dimTime, Zero)
    ),

    alphas_
    (
        IOobject
        (
            "alphas",
            mesh_.time().timeName(),
            mesh_,
            IOobject::NO_READ,
            IOobject::AUTO_WRITE,
            IOobject::REGISTER
        ),
        mesh_,
        dimensionedScalar(dimless, Zero)
    ),

    nu_
    (
        IOobject
        (
            "nu",
            mesh_.time().timeName(),
            mesh_
        ),
        mu()/rho()
    ),

    sigmas_(lookup("sigmas")),
    dimSigma_(1, 0, -2, 0, 0),
    deltaN_
    (
        "deltaN",
        1e-8/cbrt(average(mesh_.V()))
    )
{
    rhoPhi_.setOriented();

    calcAlphas();
    alphas_.write();
}


// * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * * //

Foam::tmp<Foam::volScalarField>
Foam::multiphaseMixture::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::multiphaseMixture::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::multiphaseMixture::mu() 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;
}


Foam::tmp<Foam::scalarField>
Foam::multiphaseMixture::mu(const label patchi) const
{
    auto iter = phases_.cbegin();

    tmp<scalarField> tmu =
    (
        iter().boundaryField()[patchi]
       *iter().rho().value()
       *iter().nu(patchi)
    );

    scalarField& mu = tmu.ref();

    for (++iter; iter != phases_.cend(); ++iter)
    {
        mu +=
        (
            iter().boundaryField()[patchi]
           *iter().rho().value()
           *iter().nu(patchi)
        );
    }

    return tmu;
}


Foam::tmp<Foam::surfaceScalarField>
Foam::multiphaseMixture::muf() const
{
    auto iter = phases_.cbegin();

    tmp<surfaceScalarField> tmuf =
        fvc::interpolate(iter())*iter().rho()*fvc::interpolate(iter().nu());
    surfaceScalarField& muf = tmuf.ref();

    for (++iter; iter != phases_.cend(); ++iter)
    {
        muf +=
            fvc::interpolate(iter())*iter().rho()*fvc::interpolate(iter().nu());
    }

    return tmuf;
}


Foam::tmp<Foam::volScalarField>
Foam::multiphaseMixture::nu() const
{
    return nu_;
}


Foam::tmp<Foam::scalarField>
Foam::multiphaseMixture::nu(const label patchi) const
{
    return nu_.boundaryField()[patchi];
}


Foam::tmp<Foam::surfaceScalarField>
Foam::multiphaseMixture::nuf() const
{
    return muf()/fvc::interpolate(rho());
}


Foam::tmp<Foam::surfaceScalarField>
Foam::multiphaseMixture::surfaceTensionForce() const
{
    auto tstf = surfaceScalarField::New
    (
        "surfaceTensionForce",
        IOobject::NO_REGISTER,
        mesh_,
        dimensionedScalar(dimensionSet(1, -2, -2, 0, 0), Zero)
    );

    surfaceScalarField& stf = tstf.ref();
    stf.setOriented();

    forAllConstIters(phases_, iter1)
    {
        const phase& alpha1 = iter1();

        auto iter2 = iter1;

        for (++iter2; iter2 != phases_.cend(); ++iter2)
        {
            const phase& alpha2 = iter2();

            auto sigma = sigmas_.cfind(interfacePair(alpha1, alpha2));

            if (!sigma.good())
            {
                FatalErrorInFunction
                    << "Cannot find interface " << interfacePair(alpha1, alpha2)
                    << " in list of sigma values"
                    << exit(FatalError);
            }

            stf += dimensionedScalar("sigma", dimSigma_, *sigma)
               *fvc::interpolate(K(alpha1, alpha2))*
                (
                    fvc::interpolate(alpha2)*fvc::snGrad(alpha1)
                  - fvc::interpolate(alpha1)*fvc::snGrad(alpha2)
                );
        }
    }

    return tstf;
}


void Foam::multiphaseMixture::solve()
{
    correct();

    const Time& runTime = mesh_.time();

    volScalarField& alpha = phases_.first();

    const dictionary& alphaControls = mesh_.solverDict("alpha");
    label nAlphaSubCycles(alphaControls.get<label>("nAlphaSubCycles"));
    scalar cAlpha(alphaControls.get<scalar>("cAlpha"));

    if (nAlphaSubCycles > 1)
    {
        surfaceScalarField rhoPhiSum
        (
            mesh_.newIOobject("rhoPhiSum"),
            mesh_,
            dimensionedScalar(rhoPhi_.dimensions(), Zero)
        );

        dimensionedScalar totalDeltaT = runTime.deltaT();

        for
        (
            subCycle<volScalarField> alphaSubCycle(alpha, nAlphaSubCycles);
            !(++alphaSubCycle).end();
        )
        {
            solveAlphas(cAlpha);
            rhoPhiSum += (runTime.deltaT()/totalDeltaT)*rhoPhi_;
        }

        rhoPhi_ = rhoPhiSum;
    }
    else
    {
        solveAlphas(cAlpha);
    }

    // Update the mixture kinematic viscosity
    nu_ = mu()/rho();
}


void Foam::multiphaseMixture::correct()
{
    for (phase& ph : phases_)
    {
        ph.correct();
    }
}


Foam::tmp<Foam::surfaceVectorField> Foam::multiphaseMixture::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::multiphaseMixture::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::multiphaseMixture::correctContactAngle
(
    const phase& alpha1,
    const phase& alpha2,
    surfaceVectorField::Boundary& nHatb
) const
{
    const volScalarField::Boundary& gb1f = alpha1.boundaryField();
    const volScalarField::Boundary& gb2f = alpha2.boundaryField();

    const fvBoundaryMesh& boundary = mesh_.boundary();

    forAll(boundary, patchi)
    {
        if (isA<alphaContactAngleFvPatchScalarField>(gb1f[patchi]))
        {
            const alphaContactAngleFvPatchScalarField& acap =
                refCast<const alphaContactAngleFvPatchScalarField>(gb1f[patchi]);

            correctBoundaryContactAngle(acap, patchi, alpha1, alpha2, nHatb);
        }
        else if (isA<alphaContactAngleFvPatchScalarField>(gb2f[patchi]))
        {
            const alphaContactAngleFvPatchScalarField& acap =
                refCast<const alphaContactAngleFvPatchScalarField>(gb2f[patchi]);

            correctBoundaryContactAngle(acap, patchi, alpha2, alpha1, nHatb);
        }
    }
}


void Foam::multiphaseMixture::correctBoundaryContactAngle
(
    const alphaContactAngleFvPatchScalarField& acap,
    label patchi,
    const phase& alpha1,
    const phase& alpha2,
    surfaceVectorField::Boundary& nHatb
) const
{
    const fvBoundaryMesh& boundary = mesh_.boundary();

    vectorField& nHatPatch = nHatb[patchi];

    vectorField AfHatPatch
    (
        mesh_.Sf().boundaryField()[patchi]
       /mesh_.magSf().boundaryField()[patchi]
    );

    const auto tp = acap.thetaProps().cfind(interfacePair(alpha1, alpha2));

    if (!tp.good())
    {
        FatalErrorInFunction
            << "Cannot find interface " << interfacePair(alpha1, alpha2)
            << "\n    in table of theta properties for patch "
            << acap.patch().name()
            << exit(FatalError);
    }

    const bool matched = (tp.key().first() == alpha1.name());

    const scalar theta0 = degToRad(tp().theta0(matched));
    scalarField theta(boundary[patchi].size(), theta0);

    const 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
        (
            U_.boundaryField()[patchi].patchInternalField()
          - 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::multiphaseMixture::K
(
    const phase& alpha1,
    const phase& alpha2
) const
{
    tmp<surfaceVectorField> tnHatfv = nHatfv(alpha1, alpha2);

    correctContactAngle(alpha1, alpha2, tnHatfv.ref().boundaryFieldRef());

    // Simple expression for curvature
    return -fvc::div(tnHatfv & mesh_.Sf());
}


Foam::tmp<Foam::volScalarField>
Foam::multiphaseMixture::nearInterface() const
{
    auto tnearInt = volScalarField::New
    (
        "nearInterface",
        IOobject::NO_REGISTER,
        mesh_,
        dimensionedScalar(dimless, Zero)
    );

    for (const phase& ph : phases_)
    {
        tnearInt.ref() = max(tnearInt(), pos0(ph - 0.01)*pos0(0.99 - ph));
    }

    return tnearInt;
}


void Foam::multiphaseMixture::solveAlphas
(
    const scalar cAlpha
)
{
    static label nSolves(-1);
    ++nSolves;

    const word alphaScheme("div(phi,alpha)");
    const word alpharScheme("div(phirb,alpha)");

    surfaceScalarField phic(mag(phi_/mesh_.magSf()));
    phic = min(cAlpha*phic, max(phic));

    PtrList<surfaceScalarField> alphaPhiCorrs(phases_.size());
    int phasei = 0;

    for (phase& alpha : phases_)
    {
        alphaPhiCorrs.set
        (
            phasei,
            new surfaceScalarField
            (
                "phi" + alpha.name() + "Corr",
                fvc::flux
                (
                    phi_,
                    alpha,
                    alphaScheme
                )
            )
        );

        surfaceScalarField& alphaPhiCorr = alphaPhiCorrs[phasei];

        for (phase& alpha2 : phases_)
        {
            if (&alpha2 == &alpha) continue;

            surfaceScalarField phir(phic*nHatf(alpha, alpha2));

            alphaPhiCorr += fvc::flux
            (
                -fvc::flux(-phir, alpha2, alpharScheme),
                alpha,
                alpharScheme
            );
        }

        MULES::limit
        (
            1.0/mesh_.time().deltaTValue(),
            geometricOneField(),
            alpha,
            phi_,
            alphaPhiCorr,
            zeroField(),
            zeroField(),
            oneField(),
            zeroField(),
            true
        );

        ++phasei;
    }

    MULES::limitSum(alphaPhiCorrs);

    rhoPhi_ = dimensionedScalar(dimMass/dimTime, Zero);

    volScalarField sumAlpha
    (
        mesh_.newIOobject("sumAlpha"),
        mesh_,
        dimensionedScalar(dimless, Zero)
    );

    phasei = 0;

    for (phase& alpha : phases_)
    {
        surfaceScalarField& alphaPhi = alphaPhiCorrs[phasei];
        alphaPhi += upwind<scalar>(mesh_, phi_).flux(alpha);

        MULES::explicitSolve
        (
            geometricOneField(),
            alpha,
            alphaPhi
        );

        rhoPhi_ += alphaPhi*alpha.rho();

        Info<< alpha.name() << " volume fraction, min, max = "
            << alpha.weightedAverage(mesh_.V()).value()
            << ' ' << min(alpha).value()
            << ' ' << max(alpha).value()
            << endl;

        sumAlpha += alpha;

        ++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 (phase& alpha : phases_)
    {
        alpha += alpha*sumCorr;
    }

    calcAlphas();
}


bool Foam::multiphaseMixture::read()
{
    if (transportModel::read())
    {
        bool readOK = true;

        PtrList<entry> phaseData(lookup("phases"));
        label phasei = 0;

        for (phase& ph : phases_)
        {
            readOK &= ph.read(phaseData[phasei++].dict());
        }

        readEntry("sigmas", sigmas_);

        return readOK;
    }

    return false;
}


// ************************************************************************* //