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|---|---|---|---|
| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup EffectiveHeatConductivity | ||
| 10 | * \brief Relation for the saturation-dependent effective thermal conductivity | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_JOHANSEN_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_JOHANSEN_HH | ||
| 15 | |||
| 16 | #include <cmath> | ||
| 17 | #include <algorithm> | ||
| 18 | |||
| 19 | namespace Dumux { | ||
| 20 | |||
| 21 | /*! | ||
| 22 | * \addtogroup EffectiveHeatConductivity | ||
| 23 | * \copydetails Dumux::ThermalConductivityJohansen | ||
| 24 | */ | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup EffectiveHeatConductivity | ||
| 28 | * \brief Relation for the saturation-dependent effective thermal conductivity | ||
| 29 | * | ||
| 30 | * ### Johansen (two fluid phases) | ||
| 31 | * | ||
| 32 | * `ThermalConductivityJohansen` \cite johansen1977 computes the thermal conductivity of dry and the | ||
| 33 | * wet soil material and interpolates using the Kersten number. The effective wet conductivity | ||
| 34 | * is based on a geometric average and the effective dry conductivity is based on a semi-emprical | ||
| 35 | * relation and fitted to medium quartz sand. | ||
| 36 | * | ||
| 37 | * The effective thermal conductivity is given by | ||
| 38 | * \f[ | ||
| 39 | * \lambda_\text{eff} = \lambda_{\text{dry}} + \text{Ke} \left(\lambda_\text{wet} - \lambda_\text{dry}\right), \quad | ||
| 40 | * \lambda_\text{wet} = \lambda_\text{s}^{\left(1-\phi\right)} \lambda_\text{w}^\phi, \quad | ||
| 41 | * \lambda_\text{dry} = \frac{0.135 \rho_\text{s} \phi + 64.7}{\rho_\text{s} - 0.947 \rho_\text{s} \phi}, | ||
| 42 | * \f] | ||
| 43 | * where \f$ \phi \f$ is the porosity, \f$ \lambda_\alpha \f$ is the thermal conductivity | ||
| 44 | * of phase \f$ \alpha \f$, \f$ \rho_\text{s} \f$ denotes the density of the solid phase, and the | ||
| 45 | * Kersten number is given by \f$ \text{Ke} = (\kappa S_\text{w})/(1 + (1-\kappa) S_\text{w}) \f$, | ||
| 46 | * with the wetting phase saturation \f$ S_w \f$ and a fitting parameter \f$ \kappa = 15.6 \f$ | ||
| 47 | * for medium quartz sand. | ||
| 48 | */ | ||
| 49 | template<class Scalar> | ||
| 50 | class ThermalConductivityJohansen | ||
| 51 | { | ||
| 52 | public: | ||
| 53 | /*! | ||
| 54 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 55 | * \param volVars volume variables | ||
| 56 | * \return Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 57 | */ | ||
| 58 | template<class VolumeVariables> | ||
| 59 | 1001 | static Scalar effectiveThermalConductivity(const VolumeVariables& volVars) | |
| 60 | { | ||
| 61 | using FluidSystem = typename VolumeVariables::FluidSystem; | ||
| 62 | static_assert(FluidSystem::numPhases == 2, "ThermalConductivitySomerton only works for two-phase fluid systems!"); | ||
| 63 | // TODO: there should be an assertion that the indices are correct and 0 is actually the wetting phase! | ||
| 64 | |||
| 65 | 1001 | const Scalar sw = volVars.saturation(volVars.wettingPhase()); | |
| 66 | 1001 | const Scalar lambdaW = volVars.fluidThermalConductivity(volVars.wettingPhase()); | |
| 67 | 1001 | const Scalar lambdaN = volVars.fluidThermalConductivity(1-volVars.wettingPhase()); | |
| 68 | 1001 | const Scalar lambdaSolid = volVars.solidThermalConductivity(); | |
| 69 | 1001 | const Scalar porosity = volVars.porosity(); | |
| 70 | 1001 | const Scalar rhoSolid = volVars.solidDensity(); | |
| 71 | |||
| 72 | 1001 | return effectiveThermalConductivity_(sw, lambdaW, lambdaN, lambdaSolid, porosity, rhoSolid); | |
| 73 | } | ||
| 74 | |||
| 75 | private: | ||
| 76 | /*! | ||
| 77 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 78 | * | ||
| 79 | * \param Sw The saturation of the wetting phase | ||
| 80 | * \param lambdaW The thermal conductivity of the wetting phase in \f$\mathrm{W/(m K)}\f$ | ||
| 81 | * \param lambdaN The thermal conductivity of the nonwetting phase in \f$\mathrm{W/(m K)}\f$ | ||
| 82 | * \param lambdaSolid The thermal conductivity of the solid phase in \f$\mathrm{W/(m K)}\f$ | ||
| 83 | * \param porosity The porosity | ||
| 84 | * \param rhoSolid The density of solid phase in \f$\mathrm{kg/m^3}\f$ | ||
| 85 | * | ||
| 86 | * \return Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 87 | */ | ||
| 88 | 1001 | static Scalar effectiveThermalConductivity_(const Scalar Sw, | |
| 89 | const Scalar lambdaW, | ||
| 90 | const Scalar lambdaN, | ||
| 91 | const Scalar lambdaSolid, | ||
| 92 | const Scalar porosity, | ||
| 93 | const Scalar rhoSolid) | ||
| 94 | { | ||
| 95 | using std::max; | ||
| 96 |
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1001 | const Scalar satW = max<Scalar>(0.0, Sw); |
| 97 | |||
| 98 | 1001 | const Scalar kappa = 15.6; // fitted to medium quartz sand | |
| 99 | 1001 | const Scalar rhoBulk = rhoSolid*porosity; | |
| 100 | |||
| 101 | using std::pow; | ||
| 102 | |||
| 103 | 1001 | const Scalar lambdaSaturated = lambdaSolid * pow(lambdaW / lambdaSolid, porosity); | |
| 104 | 1001 | const Scalar lambdaDry = (0.135*rhoBulk + 64.7)/(rhoSolid - 0.947*rhoBulk); | |
| 105 | 1001 | const Scalar Ke = (kappa*satW)/(1+(kappa-1)*satW);// Kersten number, equation 13 | |
| 106 | |||
| 107 | 1001 | return lambdaDry + Ke * (lambdaSaturated - lambdaDry); // equation 14 | |
| 108 | } | ||
| 109 | }; | ||
| 110 | |||
| 111 | } // end namespace Dumux | ||
| 112 | |||
| 113 | #endif | ||
| 114 |