johansen.hh

Go to the documentation of this file.

 // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*****************************************************************************
 *   See the file COPYING for full copying permissions.                      *
 *                                                                           *
 *   This program is free software: you can redistribute it and/or modify    *
 *   it under the terms of the GNU General Public License as published by    *
 *   the Free Software Foundation, either version 3 of the License, or       *
 *   (at your option) any later version.                                     *
 *                                                                           *
 *   This program is distributed in the hope that it will be useful,         *
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
 *   GNU General Public License for more details.                            *
 *                                                                           *
 *   You should have received a copy of the GNU General Public License       *
 *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
 *****************************************************************************/
#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 lambdaSaturated = lambdaSolid * pow(lambdaW / lambdaSolid, porosity);
        const Scalar lambdaDry = (0.135*rhoBulk + 64.7)/(rhoSolid - 0.947*rhoBulk);
        const Scalar Ke = (kappa*satW)/(1+(kappa-1)*satW);// Kersten number, equation 13
 
        return lambdaDry + Ke * (lambdaSaturated - lambdaDry); // equation 14
    }
};
} // end namespace Dumux
#endif