johansen.hh

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#ifndef DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_JOHANSEN_HH
#define DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_JOHANSEN_HH
 
#include <cmath>
#include <algorithm>
 
namespace Dumux {
 
template<class Scalar>
class ThermalConductivityJohansen
{
public:
    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(volVars.wettingPhase());
        const Scalar lambdaW = volVars.fluidThermalConductivity(volVars.wettingPhase());
        const Scalar lambdaN = volVars.fluidThermalConductivity(1-volVars.wettingPhase());
        const Scalar lambdaSolid = volVars.solidThermalConductivity();
        const Scalar porosity = volVars.porosity();
        const Scalar rhoSolid = volVars.solidDensity();
 
        return effectiveThermalConductivity_(sw, lambdaW, lambdaN, lambdaSolid, porosity, rhoSolid);
    }
 
private:
    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;
 
        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