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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 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup PoreNetworkFlux | ||
| 10 | * \brief This file contains the data which is required to calculate | ||
| 11 | * diffusive heat fluxes with Fourier's law. | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_FLUX_PNM_GRAIN_FOURIERS_LAW_HH | ||
| 14 | #define DUMUX_FLUX_PNM_GRAIN_FOURIERS_LAW_HH | ||
| 15 | |||
| 16 | #include <cmath> | ||
| 17 | #include <dumux/common/math.hh> | ||
| 18 | #include <dumux/common/parameters.hh> | ||
| 19 | |||
| 20 | namespace Dumux::PoreNetwork { | ||
| 21 | |||
| 22 | /*! | ||
| 23 | * \ingroup PoreNetworkFlux | ||
| 24 | * \brief Specialization of Fourier's Law for the pore-network SOLID model. | ||
| 25 | * \note See Koch et al (2021) https://doi.org/10.1007/s11242-021-01602-5 | ||
| 26 | * and Khan et al (2019) https://doi.org/10.1016/j.compchemeng.2018.12.025 | ||
| 27 | */ | ||
| 28 | template <class Scalar> | ||
| 29 | struct TruncatedPyramidGrainFouriersLaw | ||
| 30 | { | ||
| 31 | template<class Problem, class Element, class FVElementGeometry, class ElementVolumeVariables, class ElementFluxVariablesCache> | ||
| 32 | 112320 | static Scalar flux(const Problem& problem, | |
| 33 | const Element& element, | ||
| 34 | const FVElementGeometry& fvGeometry, | ||
| 35 | const ElementVolumeVariables& elemVolVars, | ||
| 36 | const typename FVElementGeometry::SubControlVolumeFace& scvf, | ||
| 37 | const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 38 | { | ||
| 39 | 224640 | const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx()); | |
| 40 | 224640 | const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx()); | |
| 41 | 112320 | const auto& insideVolVars = elemVolVars[insideScv]; | |
| 42 | 112320 | const auto& outsideVolVars = elemVolVars[outsideScv]; | |
| 43 | 112320 | const auto& fluxVarsCache = elemFluxVarsCache[scvf]; | |
| 44 | |||
| 45 | 112320 | const Scalar topSideLength = 2.0*fluxVarsCache.throatInscribedRadius(); | |
| 46 | |||
| 47 | // We assume that the distance between pore centroid and throat | ||
| 48 | // centroid (i.e., the height of the pyramid) equals the inscribed pore radius. | ||
| 49 | 112320 | const Scalar insideHeight = insideVolVars.poreInscribedRadius(); | |
| 50 | 112320 | const Scalar outsideHeight = outsideVolVars.poreInscribedRadius(); | |
| 51 | |||
| 52 | 112320 | auto getPyramidBaseLengthFromVolume = [&](const Scalar v, const Scalar h) | |
| 53 | { | ||
| 54 | // Using the formula for the volume of a pyramid frustum to calculate its base length: | ||
| 55 | // v = 1/3 h * (a^2 + a*b + b^2), where a is the base side length, b the top side length, | ||
| 56 | // h the height and v the volume of the frustum. | ||
| 57 | ✗ | const Scalar b = topSideLength; | |
| 58 | using std::sqrt; | ||
| 59 | ✗ | return 0.5*sqrt(3.0) * sqrt(-(b*b*h-4.0*v)/h) -0.5*b; | |
| 60 | }; | ||
| 61 | |||
| 62 | // the pyramid base length of the inside pore | ||
| 63 | 112320 | const Scalar insideBaseSideLength = [&]() | |
| 64 | { | ||
| 65 |
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112320 | static const bool useAdaptedVolume = getParamFromGroup<bool>(problem.paramGroup(), "FouriersLaw.UseVolumeEqualPyramid", false); |
| 66 | |||
| 67 |
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112320 | if (useAdaptedVolume) |
| 68 | ✗ | return getPyramidBaseLengthFromVolume(0.5*insideVolVars.poreVolume(), insideHeight); | |
| 69 | else | ||
| 70 | 112320 | return 2.0 * insideVolVars.poreInscribedRadius(); | |
| 71 | 112320 | }(); | |
| 72 | |||
| 73 | // the pyramid base length of the outside pore | ||
| 74 | 112320 | const Scalar outsideBaseSideLength = [&]() | |
| 75 | { | ||
| 76 |
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112320 | static const bool useAdaptedVolume = getParamFromGroup<bool>(problem.paramGroup(), "FouriersLaw.UseVolumeEqualPyramid", false); |
| 77 | |||
| 78 |
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112320 | if (useAdaptedVolume) |
| 79 | ✗ | return getPyramidBaseLengthFromVolume(0.5*outsideVolVars.poreVolume(), outsideHeight); | |
| 80 | else | ||
| 81 | 112320 | return 2.0 * outsideVolVars.poreInscribedRadius(); | |
| 82 | 112320 | }(); | |
| 83 | |||
| 84 |
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112320 | auto insideThermalConducitivity = insideVolVars.solidThermalConductivity(); |
| 85 |
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112320 | auto outsideThermalConducitivity = outsideVolVars.solidThermalConductivity(); |
| 86 | |||
| 87 | 112320 | const Scalar gInside = 4.0*insideThermalConducitivity * 0.5*topSideLength * 0.5*insideBaseSideLength / insideHeight; | |
| 88 | 112320 | const Scalar gOutside = 4.0*outsideThermalConducitivity * 0.5*topSideLength * 0.5*outsideBaseSideLength / outsideHeight; | |
| 89 |
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112320 | const Scalar gThroat = Dumux::harmonicMean(insideThermalConducitivity, outsideThermalConducitivity) |
| 90 | 112320 | * fluxVarsCache.grainContactArea() / fluxVarsCache.throatLength(); | |
| 91 | |||
| 92 | 112320 | const Scalar g = 1.0 / (1.0/gInside + 1.0/gOutside + 1.0/gThroat); | |
| 93 | |||
| 94 | // calculate the temperature gradient | ||
| 95 | 336960 | const Scalar deltaT = insideVolVars.temperature() - outsideVolVars.temperature(); | |
| 96 | |||
| 97 | 112320 | return deltaT * g; | |
| 98 | } | ||
| 99 | }; | ||
| 100 | |||
| 101 | /*! | ||
| 102 | * \ingroup PoreNetworkFlux | ||
| 103 | * \brief Specialization of Fourier's Law for the pore-network SOLID model. | ||
| 104 | * \note See Koch et al (2021) https://doi.org/10.1007/s11242-021-01602-5 | ||
| 105 | */ | ||
| 106 | template <class Scalar> | ||
| 107 | struct SphereCapGrainFouriersLaw | ||
| 108 | { | ||
| 109 | template<class Problem, class Element, class FVElementGeometry, class ElementVolumeVariables, class ElementFluxVariablesCache> | ||
| 110 | static Scalar flux(const Problem& problem, | ||
| 111 | const Element& element, | ||
| 112 | const FVElementGeometry& fvGeometry, | ||
| 113 | const ElementVolumeVariables& elemVolVars, | ||
| 114 | const typename FVElementGeometry::SubControlVolumeFace& scvf, | ||
| 115 | const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 116 | { | ||
| 117 | const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx()); | ||
| 118 | const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx()); | ||
| 119 | const auto& insideVolVars = elemVolVars[insideScv]; | ||
| 120 | const auto& outsideVolVars = elemVolVars[outsideScv]; | ||
| 121 | const auto& fluxVarsCache = elemFluxVarsCache[scvf]; | ||
| 122 | |||
| 123 | auto gSphereCap = [&](const auto& scv, const auto& volVars) | ||
| 124 | { | ||
| 125 | const Scalar R = problem.spatialParams.extendedPoreRadius(scv.dofIndex()); | ||
| 126 | const Scalar lambda = volVars.solidThermalConductivity(); | ||
| 127 | const Scalar rC = volVars.poreRadius(); | ||
| 128 | using std::atanh; | ||
| 129 | return (lambda*M_PI*R) / atanh(rC/R); | ||
| 130 | }; | ||
| 131 | |||
| 132 | auto insideThermalConducitivity = insideVolVars.solidThermalConductivity(); | ||
| 133 | auto outsideThermalConducitivity = outsideVolVars.solidThermalConductivity(); | ||
| 134 | |||
| 135 | const Scalar gInside = gSphereCap(insideScv, insideVolVars); | ||
| 136 | const Scalar gOutside = gSphereCap(outsideScv, outsideVolVars); | ||
| 137 | const Scalar gThroat = Dumux::harmonicMean(insideThermalConducitivity, outsideThermalConducitivity) | ||
| 138 | * fluxVarsCache.grainContactArea() / fluxVarsCache.throatLength(); | ||
| 139 | |||
| 140 | const Scalar g = 1.0 / (1.0/gInside + 1.0/gOutside + 1.0/gThroat); | ||
| 141 | |||
| 142 | // calculate the temperature gradient | ||
| 143 | const Scalar deltaT = insideVolVars.temperature() - outsideVolVars.temperature(); | ||
| 144 | |||
| 145 | return deltaT * g; | ||
| 146 | } | ||
| 147 | |||
| 148 | }; | ||
| 149 | |||
| 150 | } // end namespace Dumux::PoreNetwork | ||
| 151 | |||
| 152 | #endif | ||
| 153 |