thermalconductivityjohansen.hh

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#ifndef DUMUX_MATERIAL_THERMALCONDUCTIVITY_JOHANSEN_HH
#define DUMUX_MATERIAL_THERMALCONDUCTIVITY_JOHANSEN_HH
 
#include <cmath>
#include <algorithm>
 
namespace Dumux {
 
struct JohansenIndices
{
    static const int wPhaseIdx = 0;
    static const int nPhaseIdx = 1;
};
 
template<class Scalar, class Indices = JohansenIndices>
class ThermalConductivityJohansen
{
public:
    template<class VolumeVariables, class SpatialParams, class Element, class FVGeometry>
    [[deprecated("Signature deprecated. Use signature with volume variables only!")]]
    static Scalar effectiveThermalConductivity(const VolumeVariables& volVars,
                                               const SpatialParams& spatialParams,
                                               const Element& element,
                                               const FVGeometry& fvGeometry,
                                               const typename FVGeometry::SubControlVolume& scv)
    {
        return effectiveThermalConductivity(volVars);
    }
 
    template<class VolumeVariables>
    static Scalar effectiveThermalConductivity(const VolumeVariables& volVars)
    {
        using FluidSystem = typename VolumeVariables::FluidSystem;
        static_assert(FluidSystem::numPhases == 2, "ThermalConductivitySomerton only works for two-phase fluid systems!");
        // TODO: there should be an assertion that the indices are correct and 0 is actually the wetting phase!
 
        const Scalar sw = volVars.saturation(Indices::wPhaseIdx);
        const Scalar lambdaW = volVars.fluidThermalConductivity(Indices::wPhaseIdx);
        const Scalar lambdaN = volVars.fluidThermalConductivity(Indices::nPhaseIdx);
        const Scalar lambdaSolid = volVars.solidThermalConductivity();
        const Scalar porosity = volVars.porosity();
        const Scalar rhoSolid = volVars.solidDensity();
 
        return effectiveThermalConductivity(sw, lambdaW, lambdaN, lambdaSolid, porosity, rhoSolid);
    }
 
    static Scalar effectiveThermalConductivity(const Scalar Sw,
                                               const Scalar lambdaW,
                                               const Scalar lambdaN,
                                               const Scalar lambdaSolid,
                                               const Scalar porosity,
                                               const Scalar rhoSolid)
    {
        using std::max;
        const Scalar satW = max<Scalar>(0.0, Sw);
 
        const Scalar kappa = 15.6; // fitted to medium quartz sand
        const Scalar rhoBulk = rhoSolid*porosity;
        // lambdaSolid^(1-porosity) * lambdaW^porosity =
 
        using std::pow;
        const Scalar lSat = lambdaSolid * pow(lambdaW / lambdaSolid, porosity);
        const Scalar lDry = (0.135*rhoBulk + 64.7)/(rhoSolid - 0.947*rhoBulk);
        const Scalar Ke = (kappa*satW)/(1+(kappa-1)*satW);// Kersten number, equation 13
 
        return lDry + Ke * (lSat - lDry); // equation 14
    }
};
} // end namespace Dumux
#endif