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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-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | #ifndef DUMUX_MATERIAL_THERMALCONDUCTIVITY_AVERAGE_HH | ||
| 8 | #define DUMUX_MATERIAL_THERMALCONDUCTIVITY_AVERAGE_HH | ||
| 9 | |||
| 10 | #include <algorithm> | ||
| 11 | |||
| 12 | namespace Dumux { | ||
| 13 | |||
| 14 | /*! | ||
| 15 | * \addtogroup EffectiveHeatConductivity | ||
| 16 | * \copydetails Dumux::ThermalConductivityAverage | ||
| 17 | */ | ||
| 18 | |||
| 19 | /*! | ||
| 20 | * \ingroup EffectiveHeatConductivity | ||
| 21 | * \brief Effective thermal conductivity based on weighted arithmetic average | ||
| 22 | * | ||
| 23 | * ### Average (multiple fluid phases, one solid phase) | ||
| 24 | * | ||
| 25 | * The effective thermal conductivity of `ThermalConductivityAverage` | ||
| 26 | * is calculated as a weighted arithmetic average of the thermal | ||
| 27 | * conductivities of the solid and the fluid phases. The weights are determined by the volume | ||
| 28 | * fraction the phase occupies. Denoting the volume fractions by \f$ n_\alpha \f$, we have | ||
| 29 | * \f[ | ||
| 30 | * \lambda_\text{eff} = \sum_\alpha \lambda_\alpha n_\alpha / \sum_\alpha n_\alpha, | ||
| 31 | * \f] | ||
| 32 | * summing over both fluid and solid phases. With the porosity \f$ \phi \f$ as | ||
| 33 | * the sum of all fluid volume fractions, we can equivalently write | ||
| 34 | * \f[ | ||
| 35 | * \lambda_\text{eff} = \lambda_\text{s} (1-\phi) + \lambda_\text{f} \phi, | ||
| 36 | * \f] | ||
| 37 | * where \f$ \lambda_\text{s} \f$ is the thermal conductivity of the solid phase, | ||
| 38 | * and the effective thermal conductivity of the liquid phases is computed as | ||
| 39 | * an arithmetic average weighted with the fluid saturations. | ||
| 40 | */ | ||
| 41 | template<class Scalar> | ||
| 42 | class ThermalConductivityAverage | ||
| 43 | { | ||
| 44 | public: | ||
| 45 | /*! | ||
| 46 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ | ||
| 47 | * \param volVars volume variables | ||
| 48 | * \return Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ | ||
| 49 | */ | ||
| 50 | template<class VolumeVariables> | ||
| 51 | 16188546 | static Scalar effectiveThermalConductivity(const VolumeVariables& volVars) | |
| 52 | { | ||
| 53 | 16188546 | constexpr int numFluidPhases = VolumeVariables::numFluidPhases(); | |
| 54 | |||
| 55 | // Get the thermal conductivities and the porosity from the volume variables | ||
| 56 | 16188546 | Scalar lambdaFluid = 0.0; | |
| 57 |
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32377092 | for (int phaseIdx = 0; phaseIdx < numFluidPhases; ++phaseIdx) |
| 58 | 16188546 | lambdaFluid += volVars.fluidThermalConductivity(phaseIdx)*volVars.saturation(phaseIdx); | |
| 59 | |||
| 60 | 32352260 | const Scalar lambdaSolid = volVars.solidThermalConductivity(); | |
| 61 | 32352260 | const Scalar porosity = volVars.porosity(); | |
| 62 | |||
| 63 | 16188546 | return lambdaSolid*(1-porosity) + lambdaFluid*porosity; | |
| 64 | } | ||
| 65 | }; | ||
| 66 | |||
| 67 | } // end namespace Dumux | ||
| 68 | |||
| 69 | #endif | ||
| 70 |