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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 Effective thermal conductivity after Somerton | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_SOMERTON_TWO_P_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_SOMERTON_TWO_P_HH | ||
| 15 | |||
| 16 | #include <algorithm> | ||
| 17 | #include <cmath> | ||
| 18 | |||
| 19 | namespace Dumux { | ||
| 20 | |||
| 21 | /*! | ||
| 22 | * \addtogroup EffectiveHeatConductivity | ||
| 23 | * \copydetails Dumux::ThermalConductivitySomertonTwoP | ||
| 24 | */ | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup EffectiveHeatConductivity | ||
| 28 | * \brief Effective thermal conductivity after Somerton | ||
| 29 | * | ||
| 30 | * ### Somerton (two fluid phases) | ||
| 31 | * | ||
| 32 | * The Somerton method \cite somerton1974 computes the thermal conductivity of dry and the wet soil material. | ||
| 33 | * It uses a root function of the water saturation to compute the | ||
| 34 | * effective thermal conductivity for a two-phase fluidsystem. The individual thermal | ||
| 35 | * conductivities are calculated as geometric mean of the thermal conductivity of the porous | ||
| 36 | * material and of the respective fluid phase. | ||
| 37 | * | ||
| 38 | * The effective thermal conductivity of `ThermalConductivitySomertonTwoP` is given by | ||
| 39 | * \f[ | ||
| 40 | * \lambda_\text{eff} = \lambda_\text{g,eff} + \sqrt{S_\text{w}} \left(\lambda_\text{w,eff} - \lambda_\text{g,eff}\right) | ||
| 41 | * \f] | ||
| 42 | * | ||
| 43 | * with \f$ S_\text{w} \f$ the water saturation, | ||
| 44 | * \f$ S_\text{n} \f$ the NAPL saturation, the effective phase saturations given by | ||
| 45 | * \f$ \lambda_{\alpha,\text{eff}} = (\lambda_\text{s})^{\left(1-\phi\right)} (\lambda_\alpha)^\phi, \alpha \in \lbrace\text{w,n,g}\rbrace \f$ | ||
| 46 | * (geometric mean) and \f$ \lambda_\text{s} \f$ is the thermal conductivity of the solid phase. | ||
| 47 | * The effective conductivity \f$ \lambda_\text{g,eff} \f$ corresponds to dry conditions, whereas the | ||
| 48 | * effective conductivity \f$ \lambda_\text{g,eff} \f$ corresponds to wet conditions. | ||
| 49 | */ | ||
| 50 | template<class Scalar> | ||
| 51 | class ThermalConductivitySomertonTwoP | ||
| 52 | { | ||
| 53 | public: | ||
| 54 | /*! | ||
| 55 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 56 | * \param volVars volume variables | ||
| 57 | * \return Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 58 | */ | ||
| 59 | template<class VolumeVariables> | ||
| 60 | 63583206 | static Scalar effectiveThermalConductivity(const VolumeVariables& volVars) | |
| 61 | { | ||
| 62 | using FluidSystem = typename VolumeVariables::FluidSystem; | ||
| 63 | static_assert(FluidSystem::numPhases == 2, "ThermalConductivitySomertonTwoP only works for two-phase fluid systems!"); | ||
| 64 | static_assert((FluidSystem::isGas(0) && !FluidSystem::isGas(1)) || (!FluidSystem::isGas(0) && FluidSystem::isGas(1)), | ||
| 65 | "ThermalConductivitySomertonTwoP only works if one phase is gaseous and one is liquid!"); | ||
| 66 | |||
| 67 | 63583206 | constexpr int liquidPhaseIdx = FluidSystem::isGas(0) ? 1 : 0; | |
| 68 | 63583206 | constexpr int gasPhaseIdx = FluidSystem::isGas(0) ? 0 : 1; | |
| 69 | |||
| 70 | 63583206 | const Scalar satLiquid = volVars.saturation(liquidPhaseIdx); | |
| 71 | 63583206 | const Scalar lambdaLiquid = volVars.fluidThermalConductivity(liquidPhaseIdx); | |
| 72 | 63583189 | const Scalar lambdaGas = volVars.fluidThermalConductivity(gasPhaseIdx); | |
| 73 | 63583189 | const Scalar lambdaSolid = volVars.solidThermalConductivity(); | |
| 74 | 63583189 | const Scalar porosity = volVars.porosity(); | |
| 75 | |||
| 76 | 63583189 | return effectiveThermalConductivity_(satLiquid, lambdaLiquid, lambdaGas, lambdaSolid, porosity); | |
| 77 | } | ||
| 78 | |||
| 79 | private: | ||
| 80 | /*! | ||
| 81 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 82 | * | ||
| 83 | * \param satLiquid The saturation of the liquid phase | ||
| 84 | * \param lambdaLiquid The thermal conductivity of the liquid phase in \f$\mathrm{W/(m K)}\f$ | ||
| 85 | * \param lambdaGas The thermal conductivity of the gas phase in \f$\mathrm{W/(m K)}\f$ | ||
| 86 | * \param lambdaSolid The thermal conductivity of the solid phase in \f$\mathrm{W/(m K)}\f$ | ||
| 87 | * \param porosity The porosity | ||
| 88 | * | ||
| 89 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for two phases | ||
| 90 | */ | ||
| 91 | 63559279 | static Scalar effectiveThermalConductivity_(const Scalar satLiquid, | |
| 92 | const Scalar lambdaLiquid, | ||
| 93 | const Scalar lambdaGas, | ||
| 94 | const Scalar lambdaSolid, | ||
| 95 | const Scalar porosity) | ||
| 96 | { | ||
| 97 | using std::max; | ||
| 98 | using std::pow; | ||
| 99 | using std::sqrt; | ||
| 100 |
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63559279 | const Scalar satLiquidPhysical = max<Scalar>(0.0, satLiquid); |
| 101 | // geometric mean, using ls^(1-p)*l^p = ls*(l/ls)^p | ||
| 102 | 63559279 | const Scalar lambdaSaturated = lambdaSolid * pow(lambdaLiquid / lambdaSolid, porosity); | |
| 103 | 63559279 | const Scalar lambdaDry = lambdaSolid * pow(lambdaGas / lambdaSolid, porosity); | |
| 104 | |||
| 105 | 63559279 | return lambdaDry + sqrt(satLiquidPhysical) * (lambdaSaturated - lambdaDry); | |
| 106 | } | ||
| 107 | }; | ||
| 108 | |||
| 109 | |||
| 110 | } // end namespace Dumux | ||
| 111 | |||
| 112 | #endif | ||
| 113 |