combustionlocalresidual.hh

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#ifndef DUMUX_ENERGY_COMBUSTION_LOCAL_RESIDUAL_HH
#define DUMUX_ENERGY_COMBUSTION_LOCAL_RESIDUAL_HH
 
#include <cmath>
#include <dumux/common/spline.hh>
#include <dumux/common/exceptions.hh>
#include <dumux/common/properties.hh>
 
#include <dumux/porousmediumflow/nonequilibrium/thermal/localresidual.hh>
 
namespace Dumux {

template<class TypeTag>
class CombustionEnergyLocalResidual
: public  EnergyLocalResidualNonEquilibrium<TypeTag, 1/*numEnergyEqFluid*/>
{
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Element = typename GridView::template Codim<0>::Entity;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
 
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using Indices = typename ModelTraits::Indices;
 
    static constexpr auto numEnergyEqFluid = ModelTraits::numEnergyEqFluid();
    static constexpr auto numEnergyEqSolid = ModelTraits::numEnergyEqSolid();
    static constexpr auto energyEq0Idx = Indices::energyEq0Idx;
 
public:
    static void computeSourceEnergy(NumEqVector& source,
                                    const Element& element,
                                    const FVElementGeometry& fvGeometry,
                                    const ElementVolumeVariables& elemVolVars,
                                    const SubControlVolume &scv)
    {
        //specialization for 2 fluid phases
        const auto& volVars = elemVolVars[scv];
        const auto& fs = volVars.fluidState() ;
        const Scalar characteristicLength = volVars.characteristicLength()  ;
 
        //interfacial area
        // Shi & Wang, Transport in porous media (2011)
        const Scalar as = volVars.fluidSolidInterfacialArea();
 
        //temperature fluid is the same for both fluids
        const Scalar TFluid = volVars.temperatureFluid(0);
        const Scalar TSolid = volVars.temperatureSolid();
 
        const Scalar satW = fs.saturation(0) ;
        const Scalar satN = fs.saturation(1) ;
 
        const Scalar eps = 1e-6 ;
        Scalar solidToFluidEnergyExchange ;
 
        Scalar fluidConductivity ;
        if (satW < 1.0 - eps)
            fluidConductivity = volVars.fluidThermalConductivity(1) ;
        else if (satW >= 1.0 - eps)
            fluidConductivity = volVars.fluidThermalConductivity(0) ;
        else
            DUNE_THROW(Dune::NotImplemented, "wrong range");
 
        const Scalar factorEnergyTransfer   = volVars.factorEnergyTransfer()  ;
 
        solidToFluidEnergyExchange = factorEnergyTransfer * (TSolid - TFluid) / characteristicLength * as * fluidConductivity ;
        const Scalar epsRegul = 1e-3 ;
 
        if (satW < (0 + eps) )
        {
            solidToFluidEnergyExchange *=  volVars.nusseltNumber(1) ;
        }
        else if ( (satW >= 0 + eps) and (satW < 1.0-eps) )
        {
            solidToFluidEnergyExchange *=  (volVars.nusseltNumber(1) * satN );
            Scalar qBoil ;
            if (satW<=epsRegul)
            {// regularize
                typedef Dumux::Spline<Scalar> Spline;
                    Spline sp(0.0, epsRegul,                           // x1, x2
                        QBoilFunc(volVars, 0.0), QBoilFunc(volVars, epsRegul),       // y1, y2
                        0.0,dQBoil_dSw(volVars, epsRegul));    // m1, m2
 
                qBoil = sp.eval(satW);
            }
 
            else if (satW>= (1.0-epsRegul) )
            {   // regularize
                typedef Dumux::Spline<Scalar> Spline;
                Spline sp(1.0-epsRegul, 1.0,    // x1, x2
                        QBoilFunc(volVars, 1.0-epsRegul), 0.0,    // y1, y2
                        dQBoil_dSw(volVars, 1.0-epsRegul), 0.0 );      // m1, m2
 
                qBoil = sp.eval(satW) ;
            }
            else
            {
                qBoil = QBoilFunc(volVars, satW)  ;
            }
 
            solidToFluidEnergyExchange += qBoil;
        }
        else if (satW >= 1.0-eps)
        {
            solidToFluidEnergyExchange *=  volVars.nusseltNumber(0) ;
        }
        else
            DUNE_THROW(Dune::NotImplemented, "wrong range");
 
        using std::isfinite;
        if (!isfinite(solidToFluidEnergyExchange))
            DUNE_THROW(NumericalProblem, "Calculated non-finite source, " << "TFluid="<< TFluid << " TSolid="<< TSolid);
 
        for(int energyEqIdx =0; energyEqIdx<numEnergyEqFluid+numEnergyEqSolid; ++energyEqIdx)
        {
            switch (energyEqIdx)
            {
            case 0 :
                source[energyEq0Idx + energyEqIdx] += solidToFluidEnergyExchange;
                break;
            case 1 :
                source[energyEq0Idx + energyEqIdx] -=   solidToFluidEnergyExchange;
                break;
            default:
                DUNE_THROW(Dune::NotImplemented,
                        "wrong index");
            } // end switch
        }// end energyEqIdx
    }// end source
 

    static Scalar QBoilFunc(const VolumeVariables & volVars,
                            const  Scalar satW)
    {
        // using saturation as input (instead of from volVars)
        // in order to make regularization (evaluation at different points) easyer
        const auto& fs = volVars.fluidState();
        const Scalar g( 9.81 );
        const Scalar gamma(0.0589);
        const Scalar TSolid = volVars.temperatureSolid();
        using std::pow;
        const Scalar as = volVars.fluidSolidInterfacialArea();
        const Scalar mul = fs.viscosity(0);
        const Scalar deltahv = fs.enthalpy(1) - fs.enthalpy(0);
        const Scalar deltaRho = fs.density(0) - fs.density(1);
        const Scalar firstBracket = pow(g * deltaRho / gamma, 0.5);
        const Scalar cp = FluidSystem::heatCapacity(fs, 0);
        // This use of Tsat is only justified if the fluid is always boiling (tsat equals boiling conditions)
        // If a different state is to be simulated, please use the actual fluid temperature instead.
        const Scalar Tsat = FluidSystem::vaporTemperature(fs, 1 ) ;
        const Scalar deltaT = TSolid - Tsat;
        const Scalar secondBracket = pow( (cp *deltaT / (0.006 * deltahv)  ) , 3.0 );
        const Scalar Prl = volVars.prandtlNumber(0);
        const Scalar thirdBracket = pow( 1/Prl , (1.7/0.33));
        const Scalar QBoil = satW * as * mul * deltahv * firstBracket * secondBracket * thirdBracket;
        return QBoil;
    }

    static Scalar dQBoil_dSw(const VolumeVariables & volVars,
                                const Scalar satW)
    {
        // on the fly derive w.r.t. Sw.
        // Only linearly depending on it (directly)
        return (QBoilFunc(volVars, satW) / satW ) ;
    }
};
} // end namespace Dumux
 
#endif //