somerton.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
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#ifndef DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_SOMERTON_HH
#define DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_SOMERTON_HH
 
#include <algorithm>
#include <cmath>
 
namespace Dumux {
 
template<class Scalar>
class ThermalConductivitySomerton
{
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!");
        static_assert((FluidSystem::isGas(0) && !FluidSystem::isGas(1)) || (!FluidSystem::isGas(0) && FluidSystem::isGas(1)),
                     "ThermalConductivitySomerton only works if one phase is gaseous and one is liquid!");
 
        constexpr int liquidPhaseIdx = FluidSystem::isGas(0) ? 1 : 0;
        constexpr int gasPhaseIdx = FluidSystem::isGas(0) ? 0 : 1;
 
        const Scalar satLiquid = volVars.saturation(liquidPhaseIdx);
        const Scalar lambdaLiquid = volVars.fluidThermalConductivity(liquidPhaseIdx);
        const Scalar lambdaGas = volVars.fluidThermalConductivity(gasPhaseIdx);
        const Scalar lambdaSolid = volVars.solidThermalConductivity();
        const Scalar porosity = volVars.porosity();
 
        return effectiveThermalConductivity_(satLiquid, lambdaLiquid, lambdaGas, lambdaSolid, porosity);
    }
 
private:
    static Scalar effectiveThermalConductivity_(const Scalar satLiquid,
                                                const Scalar lambdaLiquid,
                                                const Scalar lambdaGas,
                                                const Scalar lambdaSolid,
                                                const Scalar porosity,
                                                const Scalar rhoSolid = 0.0 /*unused*/)
    {
        using std::max;
        using std::pow;
        using std::sqrt;
        const Scalar satLiquidPhysical = max<Scalar>(0.0, satLiquid);
        // geometric mean, using ls^(1-p)*l^p = ls*(l/ls)^p
        const Scalar lambdaSaturated = lambdaSolid * pow(lambdaLiquid / lambdaSolid, porosity);
        const Scalar lambdaDry = lambdaSolid * pow(lambdaGas / lambdaSolid, porosity);
 
        return lambdaDry + sqrt(satLiquidPhysical) * (lambdaSaturated - lambdaDry);
    }
};
 
} // end namespace Dumux
 
#endif