StandardChemistryModel.C

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    Copyright (C) 2020-2021,2023 OpenCFD Ltd.
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#include "StandardChemistryModel.H"
#include "reactingMixture.H"
#include "UniformField.H"
#include "extrapolatedCalculatedFvPatchFields.H"

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

template<class ReactionThermo, class ThermoType>
Foam::StandardChemistryModel<ReactionThermo, ThermoType>::StandardChemistryModel
(
    ReactionThermo& thermo
)
:
    BasicChemistryModel<ReactionThermo>(thermo),
    ODESystem(),
    Y_(this->thermo().composition().Y()),
    reactions_
    (
        dynamic_cast<const reactingMixture<ThermoType>&>(this->thermo())
    ),
    specieThermo_
    (
        dynamic_cast<const reactingMixture<ThermoType>&>
            (this->thermo()).speciesData()
    ),

    nSpecie_(Y_.size()),
    nReaction_(reactions_.size()),
    Treact_
    (
        BasicChemistryModel<ReactionThermo>::template getOrDefault<scalar>
        (
            "Treact",
            0.0
        )
    ),
    RR_(nSpecie_),
    c_(nSpecie_),
    dcdt_(nSpecie_)
{
    // Create the fields for the chemistry sources
    forAll(RR_, fieldi)
    {
        RR_.set
        (
            fieldi,
            new volScalarField::Internal
            (
                IOobject
                (
                    "RR." + Y_[fieldi].name(),
                    this->mesh().time().timeName(),
                    this->mesh(),
                    IOobject::NO_READ,
                    IOobject::NO_WRITE
                ),
                this->mesh(),
                dimensionedScalar(dimMass/dimVolume/dimTime, Zero)
            )
        );
    }

    Info<< "StandardChemistryModel: Number of species = " << nSpecie_
        << " and reactions = " << nReaction_ << endl;
}


// * * * * * * * * * * * * * * * * Destructor  * * * * * * * * * * * * * * * //

template<class ReactionThermo, class ThermoType>
Foam::StandardChemistryModel<ReactionThermo, ThermoType>::
~StandardChemistryModel()
{}


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

template<class ReactionThermo, class ThermoType>
void Foam::StandardChemistryModel<ReactionThermo, ThermoType>::omega
(
    const scalarField& c,
    const scalar T,
    const scalar p,
    scalarField& dcdt
) const
{
    scalar pf, cf, pr, cr;
    label lRef, rRef;

    dcdt = Zero;

    forAll(reactions_, i)
    {
        const Reaction<ThermoType>& R = reactions_[i];

        scalar omegai = omega
        (
            R, c, T, p, pf, cf, lRef, pr, cr, rRef
        );

        forAll(R.lhs(), s)
        {
            const label si = R.lhs()[s].index;
            const scalar sl = R.lhs()[s].stoichCoeff;
            dcdt[si] -= sl*omegai;
        }

        forAll(R.rhs(), s)
        {
            const label si = R.rhs()[s].index;
            const scalar sr = R.rhs()[s].stoichCoeff;
            dcdt[si] += sr*omegai;
        }
    }
}


template<class ReactionThermo, class ThermoType>
Foam::scalar Foam::StandardChemistryModel<ReactionThermo, ThermoType>::omegaI
(
    const label index,
    const scalarField& c,
    const scalar T,
    const scalar p,
    scalar& pf,
    scalar& cf,
    label& lRef,
    scalar& pr,
    scalar& cr,
    label& rRef
) const
{
    const Reaction<ThermoType>& R = reactions_[index];
    scalar w = omega(R, c, T, p, pf, cf, lRef, pr, cr, rRef);
    return(w);
}


template<class ReactionThermo, class ThermoType>
Foam::scalar Foam::StandardChemistryModel<ReactionThermo, ThermoType>::omega
(
    const Reaction<ThermoType>& R,
    const scalarField& c,
    const scalar T,
    const scalar p,
    scalar& pf,
    scalar& cf,
    label& lRef,
    scalar& pr,
    scalar& cr,
    label& rRef
) const
{
    const scalar kf = R.kf(p, T, c);
    const scalar kr = R.kr(kf, p, T, c);

    pf = 1.0;
    pr = 1.0;

    const label Nl = R.lhs().size();
    const label Nr = R.rhs().size();

    label slRef = 0;
    lRef = R.lhs()[slRef].index;

    pf = kf;
    for (label s = 1; s < Nl; s++)
    {
        const label si = R.lhs()[s].index;

        if (c[si] < c[lRef])
        {
            const scalar exp = R.lhs()[slRef].exponent;
            pf *= pow(max(c[lRef], 0.0), exp);
            lRef = si;
            slRef = s;
        }
        else
        {
            const scalar exp = R.lhs()[s].exponent;
            pf *= pow(max(c[si], 0.0), exp);
        }
    }
    cf = max(c[lRef], 0.0);

    {
        const scalar exp = R.lhs()[slRef].exponent;
        if (exp < 1.0)
        {
            if (cf > SMALL)
            {
                pf *= pow(cf, exp - 1.0);
            }
            else
            {
                pf = 0.0;
            }
        }
        else
        {
            pf *= pow(cf, exp - 1.0);
        }
    }

    label srRef = 0;
    rRef = R.rhs()[srRef].index;

    // Find the matrix element and element position for the rhs
    pr = kr;
    for (label s = 1; s < Nr; s++)
    {
        const label si = R.rhs()[s].index;
        if (c[si] < c[rRef])
        {
            const scalar exp = R.rhs()[srRef].exponent;
            pr *= pow(max(c[rRef], 0.0), exp);
            rRef = si;
            srRef = s;
        }
        else
        {
            const scalar exp = R.rhs()[s].exponent;
            pr *= pow(max(c[si], 0.0), exp);
        }
    }
    cr = max(c[rRef], 0.0);

    {
        const scalar exp = R.rhs()[srRef].exponent;
        if (exp < 1.0)
        {
            if (cr>SMALL)
            {
                pr *= pow(cr, exp - 1.0);
            }
            else
            {
                pr = 0.0;
            }
        }
        else
        {
            pr *= pow(cr, exp - 1.0);
        }
    }

    return pf*cf - pr*cr;
}


template<class ReactionThermo, class ThermoType>
void Foam::StandardChemistryModel<ReactionThermo, ThermoType>::derivatives
(
    const scalar time,
    const scalarField& c,
    scalarField& dcdt
) const
{
    const scalar T = c[nSpecie_];
    const scalar p = c[nSpecie_ + 1];

    forAll(c_, i)
    {
        c_[i] = max(c[i], 0.0);
    }

    omega(c_, T, p, dcdt);

    // Constant pressure
    // dT/dt = ...
    scalar rho = 0.0;
    for (label i = 0; i < nSpecie_; i++)
    {
        const scalar W = specieThermo_[i].W();
        rho += W*c_[i];
    }
    scalar cp = 0.0;
    for (label i=0; i<nSpecie_; i++)
    {
        cp += c_[i]*specieThermo_[i].cp(p, T);
    }
    cp /= rho;

    scalar dT = 0.0;
    for (label i = 0; i < nSpecie_; i++)
    {
        const scalar hi = specieThermo_[i].ha(p, T);
        dT += hi*dcdt[i];
    }
    dT /= rho*cp;

    dcdt[nSpecie_] = -dT;

    // dp/dt = ...
    dcdt[nSpecie_ + 1] = 0.0;
}


template<class ReactionThermo, class ThermoType>
void Foam::StandardChemistryModel<ReactionThermo, ThermoType>::jacobian
(
    const scalar t,
    const scalarField& c,
    scalarField& dcdt,
    scalarSquareMatrix& dfdc
) const
{
    const scalar T = c[nSpecie_];
    const scalar p = c[nSpecie_ + 1];

    forAll(c_, i)
    {
        c_[i] = max(c[i], 0.0);
    }

    dfdc = Zero;

    // Length of the first argument must be nSpecie_
    omega(c_, T, p, dcdt);

    forAll(reactions_, ri)
    {
        const Reaction<ThermoType>& R = reactions_[ri];

        const scalar kf0 = R.kf(p, T, c_);
        const scalar kr0 = R.kr(kf0, p, T, c_);

        forAll(R.lhs(), j)
        {
            const label sj = R.lhs()[j].index;
            scalar kf = kf0;
            forAll(R.lhs(), i)
            {
                const label si = R.lhs()[i].index;
                const scalar el = R.lhs()[i].exponent;
                if (i == j)
                {
                    if (el < 1.0)
                    {
                        if (c_[si] > SMALL)
                        {
                            kf *= el*pow(c_[si], el - 1.0);
                        }
                        else
                        {
                            kf = 0.0;
                        }
                    }
                    else
                    {
                        kf *= el*pow(c_[si], el - 1.0);
                    }
                }
                else
                {
                    kf *= pow(c_[si], el);
                }
            }

            forAll(R.lhs(), i)
            {
                const label si = R.lhs()[i].index;
                const scalar sl = R.lhs()[i].stoichCoeff;
                dfdc(si, sj) -= sl*kf;
            }
            forAll(R.rhs(), i)
            {
                const label si = R.rhs()[i].index;
                const scalar sr = R.rhs()[i].stoichCoeff;
                dfdc(si, sj) += sr*kf;
            }
        }

        forAll(R.rhs(), j)
        {
            const label sj = R.rhs()[j].index;
            scalar kr = kr0;
            forAll(R.rhs(), i)
            {
                const label si = R.rhs()[i].index;
                const scalar er = R.rhs()[i].exponent;
                if (i == j)
                {
                    if (er < 1.0)
                    {
                        if (c_[si] > SMALL)
                        {
                            kr *= er*pow(c_[si], er - 1.0);
                        }
                        else
                        {
                            kr = 0.0;
                        }
                    }
                    else
                    {
                        kr *= er*pow(c_[si], er - 1.0);
                    }
                }
                else
                {
                    kr *= pow(c_[si], er);
                }
            }

            forAll(R.lhs(), i)
            {
                const label si = R.lhs()[i].index;
                const scalar sl = R.lhs()[i].stoichCoeff;
                dfdc(si, sj) += sl*kr;
            }
            forAll(R.rhs(), i)
            {
                const label si = R.rhs()[i].index;
                const scalar sr = R.rhs()[i].stoichCoeff;
                dfdc(si, sj) -= sr*kr;
            }
        }
    }

    // Calculate the dcdT elements numerically
    const scalar delta = 1.0e-3;

    omega(c_, T + delta, p, dcdt_);
    for (label i=0; i<nSpecie_; i++)
    {
        dfdc(i, nSpecie_) = dcdt_[i];
    }

    omega(c_, T - delta, p, dcdt_);
    for (label i=0; i<nSpecie_; i++)
    {
        dfdc(i, nSpecie_) = 0.5*(dfdc(i, nSpecie_) - dcdt_[i])/delta;
    }

    dfdc(nSpecie_, nSpecie_) = 0;
    dfdc(nSpecie_ + 1, nSpecie_) = 0;
}


template<class ReactionThermo, class ThermoType>
Foam::tmp<Foam::volScalarField>
Foam::StandardChemistryModel<ReactionThermo, ThermoType>::tc() const
{
    tmp<volScalarField> ttc
    (
        new volScalarField
        (
            IOobject
            (
                "tc",
                this->time().timeName(),
                this->mesh(),
                IOobject::NO_READ,
                IOobject::NO_WRITE,
                IOobject::NO_REGISTER
            ),
            this->mesh(),
            dimensionedScalar(word::null, dimTime, SMALL),
            fvPatchFieldBase::extrapolatedCalculatedType()
        )
    );

    scalarField& tc = ttc.ref();

    tmp<volScalarField> trho(this->thermo().rho());
    const scalarField& rho = trho();

    const scalarField& T = this->thermo().T();
    const scalarField& p = this->thermo().p();

    const label nReaction = reactions_.size();

    scalar pf, cf, pr, cr;
    label lRef, rRef;

    if (this->chemistry_)
    {
        forAll(rho, celli)
        {
            const scalar rhoi = rho[celli];
            const scalar Ti = T[celli];
            const scalar pi = p[celli];

            scalar cSum = 0.0;

            for (label i=0; i<nSpecie_; i++)
            {
                c_[i] = rhoi*Y_[i][celli]/specieThermo_[i].W();
                cSum += c_[i];
            }

            forAll(reactions_, i)
            {
                const Reaction<ThermoType>& R = reactions_[i];

                omega(R, c_, Ti, pi, pf, cf, lRef, pr, cr, rRef);

                forAll(R.rhs(), s)
                {
                    tc[celli] += R.rhs()[s].stoichCoeff*pf*cf;
                }
            }

            tc[celli] = nReaction*cSum/tc[celli];
        }
    }

    ttc.ref().correctBoundaryConditions();

    return ttc;
}


template<class ReactionThermo, class ThermoType>
Foam::tmp<Foam::volScalarField>
Foam::StandardChemistryModel<ReactionThermo, ThermoType>::Qdot() const
{
    tmp<volScalarField> tQdot
    (
        new volScalarField
        (
            IOobject
            (
                "Qdot",
                this->mesh_.time().timeName(),
                this->mesh_,
                IOobject::NO_READ,
                IOobject::NO_WRITE,
                IOobject::NO_REGISTER
            ),
            this->mesh_,
            dimensionedScalar(dimEnergy/dimVolume/dimTime, Zero)
        )
    );

    if (this->chemistry_)
    {
        scalarField& Qdot = tQdot.ref();

        forAll(Y_, i)
        {
            forAll(Qdot, celli)
            {
                const scalar hi = specieThermo_[i].Hc();
                Qdot[celli] -= hi*RR_[i][celli];
            }
        }
        tQdot.ref().correctBoundaryConditions();
    }

    return tQdot;
}


template<class ReactionThermo, class ThermoType>
Foam::tmp<Foam::DimensionedField<Foam::scalar, Foam::volMesh>>
Foam::StandardChemistryModel<ReactionThermo, ThermoType>::calculateRR
(
    const label ri,
    const label si
) const
{
    scalar pf, cf, pr, cr;
    label lRef, rRef;

    tmp<volScalarField::Internal> tRR
    (
        new volScalarField::Internal
        (
            IOobject
            (
                "RR",
                this->mesh().time().timeName(),
                this->mesh(),
                IOobject::NO_READ,
                IOobject::NO_WRITE
            ),
            this->mesh(),
            dimensionedScalar(dimMass/dimVolume/dimTime, Zero)
        )
    );

    volScalarField::Internal& RR = tRR.ref();

    tmp<volScalarField> trho(this->thermo().rho());
    const scalarField& rho = trho();

    const scalarField& T = this->thermo().T();
    const scalarField& p = this->thermo().p();

    forAll(rho, celli)
    {
        const scalar rhoi = rho[celli];
        const scalar Ti = T[celli];
        const scalar pi = p[celli];

        for (label i=0; i<nSpecie_; i++)
        {
            const scalar Yi = Y_[i][celli];
            c_[i] = rhoi*Yi/specieThermo_[i].W();
        }

        const scalar w = omegaI
        (
            ri,
            c_,
            Ti,
            pi,
            pf,
            cf,
            lRef,
            pr,
            cr,
            rRef
        );

        RR[celli] = w*specieThermo_[si].W();
    }

    return tRR;
}


template<class ReactionThermo, class ThermoType>
void Foam::StandardChemistryModel<ReactionThermo, ThermoType>::calculate()
{
    if (!this->chemistry_)
    {
        return;
    }

    tmp<volScalarField> trho(this->thermo().rho());
    const scalarField& rho = trho();

    const scalarField& T = this->thermo().T();
    const scalarField& p = this->thermo().p();

    forAll(rho, celli)
    {
        const scalar rhoi = rho[celli];
        const scalar Ti = T[celli];
        const scalar pi = p[celli];

        for (label i=0; i<nSpecie_; i++)
        {
            const scalar Yi = Y_[i][celli];
            c_[i] = rhoi*Yi/specieThermo_[i].W();
        }

        omega(c_, Ti, pi, dcdt_);

        for (label i=0; i<nSpecie_; i++)
        {
            RR_[i][celli] = dcdt_[i]*specieThermo_[i].W();
        }
    }
}


template<class ReactionThermo, class ThermoType>
template<class DeltaTType>
Foam::scalar Foam::StandardChemistryModel<ReactionThermo, ThermoType>::solve
(
    const DeltaTType& deltaT
)
{
    BasicChemistryModel<ReactionThermo>::correct();

    scalar deltaTMin = GREAT;

    if (!this->chemistry_)
    {
        return deltaTMin;
    }

    tmp<volScalarField> trho(this->thermo().rho());
    const scalarField& rho = trho();

    const scalarField& T = this->thermo().T();
    const scalarField& p = this->thermo().p();

    scalarField c0(nSpecie_);

    forAll(rho, celli)
    {
        scalar Ti = T[celli];

        if (Ti > Treact_)
        {
            const scalar rhoi = rho[celli];
            scalar pi = p[celli];

            for (label i=0; i<nSpecie_; i++)
            {
                c_[i] = rhoi*Y_[i][celli]/specieThermo_[i].W();
                c0[i] = c_[i];
            }

            // Initialise time progress
            scalar timeLeft = deltaT[celli];

            // Calculate the chemical source terms
            while (timeLeft > SMALL)
            {
                scalar dt = timeLeft;
                this->solve(c_, Ti, pi, dt, this->deltaTChem_[celli]);
                timeLeft -= dt;
            }

            deltaTMin = min(this->deltaTChem_[celli], deltaTMin);

            this->deltaTChem_[celli] =
                min(this->deltaTChem_[celli], this->deltaTChemMax_);

            for (label i=0; i<nSpecie_; i++)
            {
                RR_[i][celli] =
                    (c_[i] - c0[i])*specieThermo_[i].W()/deltaT[celli];
            }
        }
        else
        {
            for (label i=0; i<nSpecie_; i++)
            {
                RR_[i][celli] = 0;
            }
        }
    }

    return deltaTMin;
}


template<class ReactionThermo, class ThermoType>
Foam::scalar Foam::StandardChemistryModel<ReactionThermo, ThermoType>::solve
(
    const scalar deltaT
)
{
    // Don't allow the time-step to change more than a factor of 2
    return min
    (
        this->solve<UniformField<scalar>>(UniformField<scalar>(deltaT)),
        2*deltaT
    );
}


template<class ReactionThermo, class ThermoType>
Foam::scalar Foam::StandardChemistryModel<ReactionThermo, ThermoType>::solve
(
    const scalarField& deltaT
)
{
    return this->solve<scalarField>(deltaT);
}


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