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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 | /*! | ||
| 9 | * \file | ||
| 10 | * \ingroup FluidSystems | ||
| 11 | * \copybrief Dumux::FluidSystems::H2ON2O2 | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_H2O_N2_O2_FLUID_SYSTEM_HH | ||
| 14 | #define DUMUX_H2O_N2_O2_FLUID_SYSTEM_HH | ||
| 15 | |||
| 16 | #include <cassert> | ||
| 17 | #include <iomanip> | ||
| 18 | |||
| 19 | #include <dumux/common/exceptions.hh> | ||
| 20 | |||
| 21 | #include <dumux/material/fluidsystems/base.hh> | ||
| 22 | #include <dumux/material/idealgas.hh> | ||
| 23 | #include <dumux/material/constants.hh> | ||
| 24 | |||
| 25 | #include <dumux/material/components/n2.hh> | ||
| 26 | #include <dumux/material/components/h2o.hh> | ||
| 27 | #include <dumux/material/components/o2.hh> | ||
| 28 | |||
| 29 | #include <dumux/material/components/tabulatedcomponent.hh> | ||
| 30 | #include <dumux/material/binarycoefficients/h2o_n2.hh> | ||
| 31 | #include <dumux/material/binarycoefficients/h2o_o2.hh> | ||
| 32 | #include <dumux/material/binarycoefficients/n2_o2.hh> | ||
| 33 | |||
| 34 | #include <dumux/io/name.hh> | ||
| 35 | |||
| 36 | namespace Dumux { | ||
| 37 | namespace FluidSystems { | ||
| 38 | /*! | ||
| 39 | * \ingroup FluidSystems | ||
| 40 | * \brief Policy for the H2O-N2-O2 fluid system | ||
| 41 | */ | ||
| 42 | template<bool fastButSimplifiedRelations = false> | ||
| 43 | struct H2ON2O2DefaultPolicy | ||
| 44 | { | ||
| 45 | static constexpr bool useH2ODensityAsLiquidMixtureDensity() { return fastButSimplifiedRelations; } | ||
| 46 | static constexpr bool useIdealGasDensity() { return fastButSimplifiedRelations; } | ||
| 47 | static constexpr bool useN2ViscosityAsGasMixtureViscosity() { return fastButSimplifiedRelations; } | ||
| 48 | static constexpr bool useN2HeatConductivityAsGasMixtureHeatConductivity() { return fastButSimplifiedRelations; } | ||
| 49 | static constexpr bool useIdealGasHeatCapacities() { return fastButSimplifiedRelations; } | ||
| 50 | }; | ||
| 51 | |||
| 52 | /*! | ||
| 53 | * \ingroup FluidSystems | ||
| 54 | * \brief A two-phase (water and air) fluid system | ||
| 55 | * with water, nitrogen and oxygen as components. | ||
| 56 | * | ||
| 57 | * This fluidsystem uses tabulated version of water of the IAPWS-formulation. | ||
| 58 | * | ||
| 59 | * Also remember to initialize tabulated components (FluidSystem::init()), while this | ||
| 60 | * is not necessary for non-tabularized ones. | ||
| 61 | */ | ||
| 62 | template <class Scalar, class Policy = H2ON2O2DefaultPolicy<>> | ||
| 63 | class H2ON2O2 | ||
| 64 | : public Base<Scalar, H2ON2O2<Scalar, Policy> > | ||
| 65 | { | ||
| 66 | using ThisType = H2ON2O2<Scalar, Policy>; | ||
| 67 | |||
| 68 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 69 | using Constants = Dumux::Constants<Scalar>; | ||
| 70 | using TabulatedH2O = Components::TabulatedComponent<Dumux::Components::H2O<Scalar> >; | ||
| 71 | using SimpleN2 = Dumux::Components::N2<Scalar>; | ||
| 72 | using O2 = Dumux::Components::O2<Scalar>; | ||
| 73 | |||
| 74 | //! The components for pure water | ||
| 75 | using H2O = TabulatedH2O; | ||
| 76 | |||
| 77 | //! The components for pure nitrogen | ||
| 78 | using N2 = SimpleN2; | ||
| 79 | |||
| 80 | public: | ||
| 81 | static constexpr int numPhases = 2; //!< Number of phases in the fluid system | ||
| 82 | static constexpr int numComponents = 3; //!< Number of components in the fluid system | ||
| 83 | static constexpr int numSPhases = 0; // TODO: Remove | ||
| 84 | |||
| 85 | static constexpr int liquidPhaseIdx = 0; //!< index of the liquid phase | ||
| 86 | static constexpr int gasPhaseIdx = 1; //!< index of the gas phase | ||
| 87 | static constexpr int phase0Idx = liquidPhaseIdx; //!< index of the first phase | ||
| 88 | static constexpr int phase1Idx = gasPhaseIdx; //!< index of the second phase | ||
| 89 | |||
| 90 | static constexpr int H2OIdx = 0; | ||
| 91 | static constexpr int N2Idx = 1; | ||
| 92 | static constexpr int O2Idx = 2; | ||
| 93 | |||
| 94 | static constexpr int comp0Idx = H2OIdx; // first major component | ||
| 95 | static constexpr int comp1Idx = N2Idx; // second major component | ||
| 96 | static constexpr int comp2Idx = O2Idx; // secondary component | ||
| 97 | |||
| 98 | // main component at 20°C and 1 bar | ||
| 99 | static constexpr int liquidPhaseMainCompIdx = H2OIdx; | ||
| 100 | static constexpr int gasPhaseMainCompIdx = N2Idx; | ||
| 101 | |||
| 102 | /**************************************** | ||
| 103 | * Fluid phase related static parameters | ||
| 104 | ****************************************/ | ||
| 105 | /*! | ||
| 106 | * \brief Return the human readable name of a fluid phase | ||
| 107 | * | ||
| 108 | * \param phaseIdx The index of the fluid phase to consider | ||
| 109 | */ | ||
| 110 | 58 | static std::string phaseName(int phaseIdx) | |
| 111 | { | ||
| 112 |
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58 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 113 |
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58 | switch (phaseIdx) |
| 114 | { | ||
| 115 | 28 | case liquidPhaseIdx: return IOName::liquidPhase(); | |
| 116 | 30 | case gasPhaseIdx: return IOName::gaseousPhase(); | |
| 117 | } | ||
| 118 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 119 | } | ||
| 120 | |||
| 121 | /*! | ||
| 122 | * \brief Return whether a phase is gaseous | ||
| 123 | * | ||
| 124 | * \param phaseIdx The index of the fluid phase to consider | ||
| 125 | */ | ||
| 126 | static constexpr bool isGas(int phaseIdx) | ||
| 127 | { | ||
| 128 |
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12 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 129 | return phaseIdx == gasPhaseIdx; | ||
| 130 | } | ||
| 131 | |||
| 132 | /*! | ||
| 133 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 134 | * be an ideal mixture. | ||
| 135 | * | ||
| 136 | * We define an ideal mixture as a fluid phase where the fugacity | ||
| 137 | * coefficients of all components times the pressure of the phase | ||
| 138 | * are independent on the fluid composition. This assumption is true | ||
| 139 | * if Henry's law and Raoult's law apply. If you are unsure what | ||
| 140 | * this function should return, it is safe to return false. The | ||
| 141 | * only damage done will be (slightly) increased computation times | ||
| 142 | * in some cases. | ||
| 143 | * | ||
| 144 | * \param phaseIdx The index of the fluid phase to consider | ||
| 145 | */ | ||
| 146 | static bool isIdealMixture(int phaseIdx) | ||
| 147 | { | ||
| 148 | ✗ | assert(0 <= phaseIdx && phaseIdx < numPhases); | |
| 149 | // we assume Henry's and Raoult's laws for the water phase and | ||
| 150 | // and no interaction between gas molecules of different | ||
| 151 | // components, so all phases are ideal mixtures! | ||
| 152 | return true; | ||
| 153 | } | ||
| 154 | |||
| 155 | /*! | ||
| 156 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 157 | * be compressible. | ||
| 158 | * | ||
| 159 | * Compressible means that the partial derivative of the density | ||
| 160 | * to the fluid pressure is always larger than zero. | ||
| 161 | * | ||
| 162 | * \param phaseIdx The index of the fluid phase to consider | ||
| 163 | */ | ||
| 164 | static constexpr bool isCompressible(int phaseIdx) | ||
| 165 | { | ||
| 166 | assert(0 <= phaseIdx && phaseIdx < numPhases); | ||
| 167 | // gases are always compressible | ||
| 168 | if (phaseIdx == gasPhaseIdx) | ||
| 169 | return true; | ||
| 170 | // the water component decides for the liquid phase... | ||
| 171 | return H2O::liquidIsCompressible(); | ||
| 172 | } | ||
| 173 | |||
| 174 | /*! | ||
| 175 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 176 | * be an ideal gas. | ||
| 177 | * | ||
| 178 | * \param phaseIdx The index of the fluid phase to consider | ||
| 179 | */ | ||
| 180 | static bool isIdealGas(int phaseIdx) | ||
| 181 | { | ||
| 182 | assert(0 <= phaseIdx && phaseIdx < numPhases); | ||
| 183 | if (phaseIdx == gasPhaseIdx) | ||
| 184 | // let the components decide | ||
| 185 | return H2O::gasIsIdeal() && N2::gasIsIdeal() && O2::gasIsIdeal(); | ||
| 186 | return false; // not a gas | ||
| 187 | } | ||
| 188 | |||
| 189 | /*! | ||
| 190 | * \brief Returns whether the fluids are miscible | ||
| 191 | */ | ||
| 192 | static constexpr bool isMiscible() | ||
| 193 | { return true; } | ||
| 194 | |||
| 195 | /**************************************** | ||
| 196 | * Component related static parameters | ||
| 197 | ****************************************/ | ||
| 198 | /*! | ||
| 199 | * \brief Return the human readable name of a component | ||
| 200 | * | ||
| 201 | * \param compIdx The index of the component to consider | ||
| 202 | */ | ||
| 203 | 36 | static std::string componentName(int compIdx) | |
| 204 | { | ||
| 205 |
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36 | switch (compIdx) |
| 206 | { | ||
| 207 | 12 | case H2OIdx: return H2O::name(); | |
| 208 | 12 | case N2Idx: return N2::name(); | |
| 209 | 12 | case O2Idx: return O2::name(); | |
| 210 | } | ||
| 211 | |||
| 212 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx); | |
| 213 | } | ||
| 214 | |||
| 215 | /*! | ||
| 216 | * \brief Return the molar mass of a component in \f$\mathrm{[kg/mol]}\f$. | ||
| 217 | * | ||
| 218 | * \param compIdx The index of the component to consider | ||
| 219 | */ | ||
| 220 | static Scalar molarMass(int compIdx) | ||
| 221 | { | ||
| 222 | static const Scalar M[] = { | ||
| 223 | H2O::molarMass(), | ||
| 224 | N2::molarMass(), | ||
| 225 | O2::molarMass() | ||
| 226 | }; | ||
| 227 | |||
| 228 |
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8687376 | assert(0 <= compIdx && compIdx < numComponents); |
| 229 |
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9936375 | return M[compIdx]; |
| 230 | } | ||
| 231 | |||
| 232 | /*! | ||
| 233 | * \brief Critical temperature of a component \f$\mathrm{[K]}\f$. | ||
| 234 | * | ||
| 235 | * \param compIdx The index of the component to consider | ||
| 236 | */ | ||
| 237 | static Scalar criticalTemperature(int compIdx) | ||
| 238 | { | ||
| 239 | static const Scalar Tcrit[] = { | ||
| 240 | H2O::criticalTemperature(), | ||
| 241 | N2::criticalTemperature(), | ||
| 242 | O2::criticalTemperature() | ||
| 243 | }; | ||
| 244 | |||
| 245 | assert(0 <= compIdx && compIdx < numComponents); | ||
| 246 | return Tcrit[compIdx]; | ||
| 247 | } | ||
| 248 | |||
| 249 | /*! | ||
| 250 | * \brief Critical pressure of a component \f$\mathrm{[Pa]}\f$. | ||
| 251 | * | ||
| 252 | * \param compIdx The index of the component to consider | ||
| 253 | */ | ||
| 254 | static Scalar criticalPressure(int compIdx) | ||
| 255 | { | ||
| 256 | static const Scalar pcrit[] = { | ||
| 257 | H2O::criticalPressure(), | ||
| 258 | N2::criticalPressure(), | ||
| 259 | O2::criticalPressure() | ||
| 260 | }; | ||
| 261 | |||
| 262 | assert(0 <= compIdx && compIdx < numComponents); | ||
| 263 | return pcrit[compIdx]; | ||
| 264 | } | ||
| 265 | |||
| 266 | /*! | ||
| 267 | * \brief Molar volume of a component at the critical point \f$\mathrm{[m^3/mol]}\f$. | ||
| 268 | * | ||
| 269 | * \param compIdx The index of the component to consider | ||
| 270 | */ | ||
| 271 | static Scalar criticalMolarVolume(int compIdx) | ||
| 272 | { | ||
| 273 | DUNE_THROW(Dune::NotImplemented, | ||
| 274 | "H2ON2O2FluidSystem::criticalMolarVolume()"); | ||
| 275 | } | ||
| 276 | |||
| 277 | /*! | ||
| 278 | * \brief The acentric factor of a component \f$\mathrm{[-]}\f$. | ||
| 279 | * | ||
| 280 | * \param compIdx The index of the component to consider | ||
| 281 | */ | ||
| 282 | static Scalar acentricFactor(int compIdx) | ||
| 283 | { | ||
| 284 | static const Scalar accFac[] = { | ||
| 285 | H2O::acentricFactor(), | ||
| 286 | N2::acentricFactor(), | ||
| 287 | O2::acentricFactor() | ||
| 288 | }; | ||
| 289 | |||
| 290 | assert(0 <= compIdx && compIdx < numComponents); | ||
| 291 | return accFac[compIdx]; | ||
| 292 | } | ||
| 293 | |||
| 294 | /*! | ||
| 295 | * \brief Kelvin equation in \f$\mathrm{[Pa]}\f$ | ||
| 296 | * | ||
| 297 | * Calculate the increase vapor pressure over the | ||
| 298 | * curved surface of a drop with radius r | ||
| 299 | * | ||
| 300 | * \param fluidState An arbitrary fluid state | ||
| 301 | * \param phaseIdx The index of the fluid phase to consider | ||
| 302 | * \param compIdx The index of the component to consider | ||
| 303 | * \param radius The radius of the drop | ||
| 304 | */ | ||
| 305 | template <class FluidState> | ||
| 306 | static Scalar kelvinVaporPressure(const FluidState &fluidState, | ||
| 307 | const int phaseIdx, | ||
| 308 | const int compIdx, | ||
| 309 | const Scalar radius) | ||
| 310 | { | ||
| 311 | assert(0 <= phaseIdx && phaseIdx == liquidPhaseIdx); | ||
| 312 | assert(0 <= compIdx && compIdx == liquidPhaseMainCompIdx); | ||
| 313 | |||
| 314 | Scalar T = fluidState.temperature(phaseIdx); | ||
| 315 | |||
| 316 | Scalar vaporPressure = H2O::vaporPressure(T); | ||
| 317 | Scalar exponent = molarMass(compIdx)/(density(fluidState, phaseIdx) * Constants::R * T); | ||
| 318 | exponent *= (2 * surfaceTension(fluidState) / radius); | ||
| 319 | using std::exp; | ||
| 320 | Scalar kelvinVaporPressure = vaporPressure * exp(exponent); | ||
| 321 | |||
| 322 | return kelvinVaporPressure; | ||
| 323 | } | ||
| 324 | |||
| 325 | /*! | ||
| 326 | * \brief Vapor pressure including the Kelvin equation in \f$\mathrm{[Pa]}\f$ | ||
| 327 | * | ||
| 328 | * Calculate the decreased vapor pressure due to capillarity | ||
| 329 | * | ||
| 330 | * \param fluidState An arbitrary fluid state | ||
| 331 | * \param phaseIdx The index of the fluid phase to consider | ||
| 332 | * \param compIdx The index of the component to consider | ||
| 333 | */ | ||
| 334 | template <class FluidState> | ||
| 335 | static Scalar kelvinVaporPressure(const FluidState &fluidState, | ||
| 336 | const int phaseIdx, | ||
| 337 | const int compIdx) | ||
| 338 | { | ||
| 339 | assert(compIdx == liquidPhaseMainCompIdx && phaseIdx == liquidPhaseIdx); | ||
| 340 | |||
| 341 | using std::exp; | ||
| 342 | return fugacityCoefficient(fluidState, phaseIdx, compIdx) | ||
| 343 | * fluidState.pressure(phaseIdx) | ||
| 344 | * exp(-(fluidState.pressure(gasPhaseIdx)-fluidState.pressure(liquidPhaseIdx)) | ||
| 345 | / density(fluidState, phaseIdx) | ||
| 346 | / (Dumux::Constants<Scalar>::R / molarMass(compIdx)) | ||
| 347 | / fluidState.temperature()); | ||
| 348 | } | ||
| 349 | |||
| 350 | /*! | ||
| 351 | * \brief Calculate the surface tension between water and air in \f$\mathrm{[\frac{N}{m}]}\f$, | ||
| 352 | * according to IAPWS Release on Surface Tension from September 1994. | ||
| 353 | * The equation is valid between the triple Point (0.01C) and the critical temperature. | ||
| 354 | * | ||
| 355 | * \param fluidState An arbitrary fluid state | ||
| 356 | */ | ||
| 357 | template <class FluidState> | ||
| 358 | static Scalar surfaceTension(const FluidState &fluidState) | ||
| 359 | { | ||
| 360 | const Scalar T = fluidState.temperature(); //K | ||
| 361 | const Scalar B = 0.2358 ; // [N/m] | ||
| 362 | const Scalar T_c = H2O::criticalTemperature(); //K | ||
| 363 | const Scalar mu = 1.256; | ||
| 364 | const Scalar b = -0.625; | ||
| 365 | //Equation to calculate surface Tension of Water According to IAPWS Release on Surface Tension from September 1994 | ||
| 366 | using std::pow; | ||
| 367 | const Scalar surfaceTension = B*pow((1.-(T/T_c)),mu)*(1.+b*(1.-(T/T_c))); | ||
| 368 | return surfaceTension; //surface Tension [N/m] | ||
| 369 | } | ||
| 370 | /**************************************** | ||
| 371 | * thermodynamic relations | ||
| 372 | ****************************************/ | ||
| 373 | |||
| 374 | /*! | ||
| 375 | * \brief Initialize the fluid system's static parameters generically | ||
| 376 | * | ||
| 377 | * If a tabulated H2O component is used, we do our best to create | ||
| 378 | * tables that always work. | ||
| 379 | */ | ||
| 380 | static void init() | ||
| 381 | { | ||
| 382 | 3 | init(/*tempMin=*/273.15, | |
| 383 | /*tempMax=*/623.15, | ||
| 384 | /*numTemp=*/100, | ||
| 385 | /*pMin=*/0.0, | ||
| 386 | /*pMax=*/20e6, | ||
| 387 | /*numP=*/200); | ||
| 388 | } | ||
| 389 | |||
| 390 | /*! | ||
| 391 | * \brief Initialize the fluid system's static parameters using | ||
| 392 | * problem specific temperature and pressure ranges | ||
| 393 | * | ||
| 394 | * \param tempMin The minimum temperature used for tabulation of water \f$\mathrm{[K]}\f$ | ||
| 395 | * \param tempMax The maximum temperature used for tabulation of water \f$\mathrm{[K]}\f$ | ||
| 396 | * \param nTemp The number of ticks on the temperature axis of the table of water | ||
| 397 | * \param pressMin The minimum pressure used for tabulation of water \f$\mathrm{[Pa]}\f$ | ||
| 398 | * \param pressMax The maximum pressure used for tabulation of water \f$\mathrm{[Pa]}\f$ | ||
| 399 | * \param nPress The number of ticks on the pressure axis of the table of water | ||
| 400 | */ | ||
| 401 | 9 | static void init(Scalar tempMin, Scalar tempMax, unsigned nTemp, | |
| 402 | Scalar pressMin, Scalar pressMax, unsigned nPress) | ||
| 403 | { | ||
| 404 | 9 | std::cout << "The H2O-N2-O2 fluid system was configured with the following policy:\n"; | |
| 405 | 18 | std::cout << " - use H2O density as liquid mixture density: " << std::boolalpha << Policy::useH2ODensityAsLiquidMixtureDensity() << "\n"; | |
| 406 | 18 | std::cout << " - use ideal gas density: " << std::boolalpha << Policy::useIdealGasDensity() << "\n"; | |
| 407 | 18 | std::cout << " - use N2 viscosity as gas mixture viscosity: " << std::boolalpha << Policy::useN2ViscosityAsGasMixtureViscosity() << "\n"; | |
| 408 | 18 | std::cout << " - use N2 heat conductivity as gas mixture heat conductivity: " << std::boolalpha << Policy::useN2HeatConductivityAsGasMixtureHeatConductivity() << "\n"; | |
| 409 | 18 | std::cout << " - use ideal gas heat capacities: " << std::boolalpha << Policy::useIdealGasHeatCapacities() << std::endl; | |
| 410 | |||
| 411 | if (H2O::isTabulated) | ||
| 412 | { | ||
| 413 | 9 | TabulatedH2O::init(tempMin, tempMax, nTemp, | |
| 414 | pressMin, pressMax, nPress); | ||
| 415 | } | ||
| 416 | 9 | } | |
| 417 | |||
| 418 | using Base<Scalar, ThisType>::density; | ||
| 419 | /*! | ||
| 420 | * \brief Given a phase's composition, temperature, pressure, and | ||
| 421 | * the partial pressures of all components, return its | ||
| 422 | * density \f$\mathrm{[kg/m^3]}\f$. | ||
| 423 | * | ||
| 424 | * If Policy::useH2ODensityAsLiquidMixtureDensity() == false, we apply Eq. (7) | ||
| 425 | * in Class et al. (2002a) \cite A3:class:2002b <BR> | ||
| 426 | * for the liquid density. | ||
| 427 | * | ||
| 428 | * \param fluidState An arbitrary fluid state | ||
| 429 | * \param phaseIdx The index of the fluid phase to consider | ||
| 430 | */ | ||
| 431 | template <class FluidState> | ||
| 432 | 603436 | static Scalar density(const FluidState &fluidState, | |
| 433 | int phaseIdx) | ||
| 434 | { | ||
| 435 |
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603436 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 436 | |||
| 437 |
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603436 | Scalar T = fluidState.temperature(phaseIdx); |
| 438 |
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603436 | Scalar p = fluidState.pressure(phaseIdx); |
| 439 | |||
| 440 | // liquid phase | ||
| 441 |
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603436 | if (phaseIdx == liquidPhaseIdx) |
| 442 | { | ||
| 443 | // assume pure water | ||
| 444 | if (Policy::useH2ODensityAsLiquidMixtureDensity()) | ||
| 445 | 2 | return H2O::liquidDensity(T, p); | |
| 446 | |||
| 447 | // See: Eq. (7) in Class et al. (2002a) | ||
| 448 | // This assumes each gas molecule displaces exactly one | ||
| 449 | // molecule in the liquid. | ||
| 450 | else | ||
| 451 | 301715 | return H2O::liquidMolarDensity(T, p) | |
| 452 | 301715 | * (fluidState.moleFraction(liquidPhaseIdx, H2OIdx)*H2O::molarMass() | |
| 453 | 301715 | + fluidState.moleFraction(liquidPhaseIdx, N2Idx)*N2::molarMass() | |
| 454 | 603428 | + fluidState.moleFraction(liquidPhaseIdx, O2Idx)*O2::molarMass()); | |
| 455 | } | ||
| 456 | |||
| 457 | // gas phase | ||
| 458 | else if (phaseIdx == gasPhaseIdx) | ||
| 459 | { | ||
| 460 | |||
| 461 | // for the gas phase assume an ideal gas | ||
| 462 | using std::max; | ||
| 463 | if (Policy::useIdealGasDensity()) | ||
| 464 | 4 | return IdealGas::molarDensity(T, p) * fluidState.averageMolarMass(gasPhaseIdx); | |
| 465 | |||
| 466 | // assume ideal mixture: steam, nitrogen and oxygen don't "see" each other | ||
| 467 | else | ||
| 468 | 603430 | return H2O::gasDensity(T, fluidState.partialPressure(gasPhaseIdx, H2OIdx)) | |
| 469 | 603430 | + N2::gasDensity(T, fluidState.partialPressure(gasPhaseIdx, N2Idx)) | |
| 470 | 905143 | + O2::gasDensity(T, fluidState.partialPressure(gasPhaseIdx, O2Idx)); | |
| 471 | } | ||
| 472 | |||
| 473 | DUNE_THROW(Dune::InvalidStateException, "Unknown phase index " << phaseIdx); | ||
| 474 | } | ||
| 475 | |||
| 476 | using Base<Scalar, ThisType>::molarDensity; | ||
| 477 | //! \copydoc Base<Scalar,ThisType>::molarDensity(const FluidState&,int) | ||
| 478 | template <class FluidState> | ||
| 479 | 603436 | static Scalar molarDensity(const FluidState &fluidState, int phaseIdx) | |
| 480 | { | ||
| 481 |
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603436 | const Scalar T = fluidState.temperature(phaseIdx); |
| 482 |
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603436 | const Scalar p = fluidState.pressure(phaseIdx); |
| 483 | |||
| 484 |
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603436 | if (phaseIdx == liquidPhaseIdx) |
| 485 | { | ||
| 486 | // assume pure water or that each gas molecule displaces exactly one | ||
| 487 | // molecule in the liquid. | ||
| 488 | 301717 | return H2O::liquidMolarDensity(T, p); | |
| 489 | } | ||
| 490 | else | ||
| 491 | { | ||
| 492 | if (Policy::useIdealGasDensity()) | ||
| 493 | { //assume ideal gas | ||
| 494 | 4 | return IdealGas::molarDensity(T,p); | |
| 495 | } | ||
| 496 | |||
| 497 | 603430 | return H2O::gasMolarDensity(T, fluidState.partialPressure(gasPhaseIdx, H2OIdx)) | |
| 498 | 603430 | + N2::gasMolarDensity(T, fluidState.partialPressure(gasPhaseIdx, N2Idx)) | |
| 499 | 905143 | + O2::gasMolarDensity(T, fluidState.partialPressure(gasPhaseIdx, O2Idx)); | |
| 500 | } | ||
| 501 | } | ||
| 502 | |||
| 503 | using Base<Scalar, ThisType>::viscosity; | ||
| 504 | /*! | ||
| 505 | * \brief Calculate the dynamic viscosity of a fluid phase \f$\mathrm{[Pa*s]}\f$ | ||
| 506 | * | ||
| 507 | * Compositional effects in the gas phase are accounted by the Wilke method. | ||
| 508 | * See Reid et al. (1987) \cite reid1987 <BR> | ||
| 509 | * 4th edition, McGraw-Hill, 1987, 407-410 | ||
| 510 | * 5th edition, McGraw-Hill, 20001, p. 9.21/22 | ||
| 511 | * \note Compositional effects for a liquid mixture have to be implemented. | ||
| 512 | * | ||
| 513 | * \param fluidState An arbitrary fluid state | ||
| 514 | * \param phaseIdx The index of the fluid phase to consider | ||
| 515 | */ | ||
| 516 | template <class FluidState> | ||
| 517 | 603436 | static Scalar viscosity(const FluidState &fluidState, | |
| 518 | int phaseIdx) | ||
| 519 | { | ||
| 520 |
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603436 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 521 | |||
| 522 |
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603436 | Scalar T = fluidState.temperature(phaseIdx); |
| 523 |
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603436 | Scalar p = fluidState.pressure(phaseIdx); |
| 524 | |||
| 525 | // liquid phase | ||
| 526 |
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603436 | if (phaseIdx == liquidPhaseIdx) { |
| 527 | // assume pure water for the liquid phase | ||
| 528 | 301717 | return H2O::liquidViscosity(T, p); | |
| 529 | } | ||
| 530 | |||
| 531 | // gas phase | ||
| 532 | if (Policy::useN2ViscosityAsGasMixtureViscosity()) | ||
| 533 | { | ||
| 534 | // assume pure nitrogen for the gas phase | ||
| 535 | 2 | return N2::gasViscosity(T, p); | |
| 536 | } | ||
| 537 | else | ||
| 538 | { | ||
| 539 | // Wilke method (Reid et al.): | ||
| 540 | 301717 | Scalar muResult = 0; | |
| 541 | 905151 | const Scalar mu[numComponents] = { | |
| 542 | 301717 | h2oGasViscosityInMixture(T, p), | |
| 543 | 301717 | N2::gasViscosity(T, p), | |
| 544 | 301717 | O2::gasViscosity(T, p) | |
| 545 | }; | ||
| 546 | |||
| 547 | 301717 | Scalar sumx = 0.0; | |
| 548 | using std::max; | ||
| 549 |
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1206868 | for (int compIdx = 0; compIdx < numComponents; ++compIdx) |
| 550 | 1810290 | sumx += fluidState.moleFraction(phaseIdx, compIdx); | |
| 551 |
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301717 | sumx = max(1e-10, sumx); |
| 552 | |||
| 553 |
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1206868 | for (int i = 0; i < numComponents; ++i) { |
| 554 | Scalar divisor = 0; | ||
| 555 | using std::pow; | ||
| 556 | using std::sqrt; | ||
| 557 |
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3620604 | for (int j = 0; j < numComponents; ++j) { |
| 558 | 8146359 | Scalar phiIJ = 1 + sqrt(mu[i]/mu[j]) * pow(molarMass(j)/molarMass(i), 1/4.0); | |
| 559 | 2715453 | phiIJ *= phiIJ; | |
| 560 | 2715453 | phiIJ /= sqrt(8*(1 + molarMass(i)/molarMass(j))); | |
| 561 | 5430870 | divisor += fluidState.moleFraction(phaseIdx, j)/sumx * phiIJ; | |
| 562 | } | ||
| 563 | 1810290 | muResult += fluidState.moleFraction(phaseIdx, i)/sumx * mu[i] / divisor; | |
| 564 | } | ||
| 565 | return muResult; | ||
| 566 | } | ||
| 567 | } | ||
| 568 | |||
| 569 | using Base<Scalar, ThisType>::fugacityCoefficient; | ||
| 570 | /*! | ||
| 571 | * \brief Returns the fugacity coefficient \f$\mathrm{[-]}\f$ of a component in a | ||
| 572 | * phase. | ||
| 573 | * | ||
| 574 | * The fugacity coefficient \f$\phi^\kappa_\alpha\f$ of | ||
| 575 | * component \f$\kappa\f$ in phase \f$\alpha\f$ is connected to | ||
| 576 | * the fugacity \f$f^\kappa_\alpha\f$ and the component's mole | ||
| 577 | * fraction \f$x^\kappa_\alpha\f$ by means of the relation | ||
| 578 | * | ||
| 579 | * \f[ | ||
| 580 | f^\kappa_\alpha = \phi^\kappa_\alpha\;x^\kappa_\alpha\;p_\alpha | ||
| 581 | \f] | ||
| 582 | * where \f$p_\alpha\f$ is the pressure of the fluid phase. | ||
| 583 | * | ||
| 584 | * For liquids with very low miscibility this boils down to the | ||
| 585 | * Henry constant for the solutes and the saturated vapor pressure | ||
| 586 | * both divided by phase pressure. | ||
| 587 | * \param fluidState An arbitrary fluid state | ||
| 588 | * \param phaseIdx The index of the fluid phase to consider | ||
| 589 | * \param compIdx The index of the component to consider | ||
| 590 | */ | ||
| 591 | template <class FluidState> | ||
| 592 | 1810308 | static Scalar fugacityCoefficient(const FluidState &fluidState, | |
| 593 | int phaseIdx, | ||
| 594 | int compIdx) | ||
| 595 | { | ||
| 596 |
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1810308 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 597 |
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1810308 | assert(0 <= compIdx && compIdx < numComponents); |
| 598 | |||
| 599 |
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1810308 | Scalar T = fluidState.temperature(phaseIdx); |
| 600 |
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1810308 | Scalar p = fluidState.pressure(phaseIdx); |
| 601 | |||
| 602 | // liquid phase | ||
| 603 |
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1810308 | if (phaseIdx == liquidPhaseIdx) |
| 604 | { | ||
| 605 |
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905151 | switch(compIdx){ |
| 606 | 301717 | case H2OIdx: return H2O::vaporPressure(T)/p; | |
| 607 | 301717 | case N2Idx: return BinaryCoeff::H2O_N2::henry(T)/p; | |
| 608 | 301717 | case O2Idx: return BinaryCoeff::H2O_O2::henry(T)/p; | |
| 609 | }; | ||
| 610 | } | ||
| 611 | |||
| 612 | // for the gas phase, assume an ideal gas when it comes to | ||
| 613 | // fugacity (-> fugacity == partial pressure) | ||
| 614 | return 1.0; | ||
| 615 | } | ||
| 616 | |||
| 617 | using Base<Scalar, ThisType>::diffusionCoefficient; | ||
| 618 | //! \copydoc Base<Scalar,ThisType>::diffusionCoefficient(const FluidState&,int,int) | ||
| 619 | template <class FluidState> | ||
| 620 | 30 | static Scalar diffusionCoefficient(const FluidState &fluidState, | |
| 621 | int phaseIdx, | ||
| 622 | int compIdx) | ||
| 623 | { | ||
| 624 |
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330 | DUNE_THROW(Dune::NotImplemented, "Diffusion coefficients"); |
| 625 | } | ||
| 626 | |||
| 627 | using Base<Scalar, ThisType>::binaryDiffusionCoefficient; | ||
| 628 | //! \copydoc Base<Scalar,ThisType>::binaryDiffusionCoefficient(const FluidState&,int,int,int) | ||
| 629 | template <class FluidState> | ||
| 630 | 1206942 | static Scalar binaryDiffusionCoefficient(const FluidState &fluidState, | |
| 631 | int phaseIdx, | ||
| 632 | int compIIdx, | ||
| 633 | int compJIdx) | ||
| 634 | |||
| 635 | { | ||
| 636 |
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1206942 | if (compIIdx > compJIdx) |
| 637 | { | ||
| 638 | using std::swap; | ||
| 639 | 301743 | swap(compIIdx, compJIdx); | |
| 640 | } | ||
| 641 | |||
| 642 | #ifndef NDEBUG | ||
| 643 |
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1206942 | if (compIIdx == compJIdx || |
| 644 |
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1206912 | phaseIdx > numPhases - 1 || |
| 645 | compJIdx > numComponents - 1) | ||
| 646 | { | ||
| 647 |
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420 | DUNE_THROW(Dune::InvalidStateException, |
| 648 | "Binary diffusion coefficient of components " | ||
| 649 | << compIIdx << " and " << compJIdx | ||
| 650 | << " in phase " << phaseIdx << " is undefined!\n"); | ||
| 651 | } | ||
| 652 | #endif | ||
| 653 | |||
| 654 |
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1206912 | Scalar T = fluidState.temperature(phaseIdx); |
| 655 |
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1206912 | Scalar p = fluidState.pressure(phaseIdx); |
| 656 | |||
| 657 | // liquid phase | ||
| 658 |
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1206912 | if (phaseIdx == liquidPhaseIdx) { |
| 659 |
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603450 | if (compIIdx == H2OIdx && compJIdx == N2Idx) |
| 660 | 603442 | return BinaryCoeff::H2O_N2::liquidDiffCoeff(T, p); | |
| 661 |
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301729 | if (compIIdx == H2OIdx && compJIdx == O2Idx) |
| 662 | 603442 | return BinaryCoeff::H2O_O2::liquidDiffCoeff(T, p); | |
| 663 |
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112 | DUNE_THROW(Dune::InvalidStateException, |
| 664 | "Binary diffusion coefficient of components " | ||
| 665 | << compIIdx << " and " << compJIdx | ||
| 666 | << " in phase " << phaseIdx << " is undefined!\n"); | ||
| 667 | } | ||
| 668 | // gas phase | ||
| 669 |
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603462 | if (phaseIdx == gasPhaseIdx) { |
| 670 |
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603462 | if (compIIdx == H2OIdx && compJIdx == N2Idx) |
| 671 | 301725 | return BinaryCoeff::H2O_N2::gasDiffCoeff(T, p); | |
| 672 |
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301737 | if (compIIdx == H2OIdx && compJIdx == O2Idx) |
| 673 | 12 | return BinaryCoeff::H2O_O2::gasDiffCoeff(T, p); | |
| 674 |
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301725 | if(compIIdx == N2Idx && compJIdx == O2Idx) |
| 675 | 301725 | return BinaryCoeff::N2_O2::gasDiffCoeff(T, p); | |
| 676 | ✗ | DUNE_THROW(Dune::InvalidStateException, | |
| 677 | "Binary diffusion coefficient of components " | ||
| 678 | << compIIdx << " and " << compJIdx | ||
| 679 | << " in phase " << phaseIdx << " is undefined!\n"); | ||
| 680 | } | ||
| 681 | |||
| 682 | ✗ | DUNE_THROW(Dune::InvalidStateException, | |
| 683 | "Binary diffusion coefficient of components " | ||
| 684 | << compIIdx << " and " << compJIdx | ||
| 685 | << " in phase " << phaseIdx << " is undefined!\n"); | ||
| 686 | } | ||
| 687 | |||
| 688 | using Base<Scalar, ThisType>::enthalpy; | ||
| 689 | /*! | ||
| 690 | * \brief Given a phase's composition, temperature, pressure and | ||
| 691 | * density, calculate its specific enthalpy \f$\mathrm{[J/kg]}\f$. | ||
| 692 | * | ||
| 693 | * \note This fluid system neglects the contribution of | ||
| 694 | * gas-molecules in the liquid phase. This contribution is | ||
| 695 | * probably not big. Somebody would have to find out the | ||
| 696 | * enthalpy of solution for this system. ... | ||
| 697 | * | ||
| 698 | * \param fluidState An arbitrary fluid state | ||
| 699 | * \param phaseIdx The index of the fluid phase to consider | ||
| 700 | */ | ||
| 701 | template <class FluidState> | ||
| 702 | 278818 | static Scalar enthalpy(const FluidState &fluidState, | |
| 703 | int phaseIdx) | ||
| 704 | { | ||
| 705 |
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278818 | Scalar T = fluidState.temperature(phaseIdx); |
| 706 |
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278818 | Scalar p = fluidState.pressure(phaseIdx); |
| 707 | |||
| 708 | // liquid phase | ||
| 709 |
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278818 | if (phaseIdx == liquidPhaseIdx) { |
| 710 | 139408 | return H2O::liquidEnthalpy(T, p); | |
| 711 | } | ||
| 712 | // gas phase | ||
| 713 |
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139410 | else if (phaseIdx == gasPhaseIdx) |
| 714 | { | ||
| 715 | // assume ideal mixture: which means | ||
| 716 | // that the total specific enthalpy is the sum of the | ||
| 717 | // "partial specific enthalpies" of the components. | ||
| 718 | 139410 | Scalar hH2O = | |
| 719 | fluidState.massFraction(gasPhaseIdx, H2OIdx) | ||
| 720 | 278814 | * H2O::gasEnthalpy(T, p); | |
| 721 | 139410 | Scalar hN2 = | |
| 722 | fluidState.massFraction(gasPhaseIdx, N2Idx) | ||
| 723 | 278814 | * N2::gasEnthalpy(T,p); | |
| 724 | 139410 | Scalar hO2 = | |
| 725 | fluidState.massFraction(gasPhaseIdx, O2Idx) | ||
| 726 | 278814 | * O2::gasEnthalpy(T,p); | |
| 727 | 139410 | return hH2O + hN2 + hO2; | |
| 728 | } | ||
| 729 | else | ||
| 730 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 731 | } | ||
| 732 | |||
| 733 | /*! | ||
| 734 | * \brief Returns the specific enthalpy \f$\mathrm{[J/kg]}\f$ of a component in a specific phase | ||
| 735 | * \param fluidState An arbitrary fluid state | ||
| 736 | * \param phaseIdx The index of the fluid phase to consider | ||
| 737 | * \param componentIdx The index of the component to consider | ||
| 738 | */ | ||
| 739 | template <class FluidState> | ||
| 740 | static Scalar componentEnthalpy(const FluidState &fluidState, | ||
| 741 | int phaseIdx, | ||
| 742 | int componentIdx) | ||
| 743 | { | ||
| 744 | const Scalar T = fluidState.temperature(phaseIdx); | ||
| 745 | const Scalar p = fluidState.pressure(phaseIdx); | ||
| 746 | |||
| 747 | if (phaseIdx == phase0Idx) | ||
| 748 | { | ||
| 749 | if (componentIdx == H2OIdx) | ||
| 750 | return H2O::liquidEnthalpy(T, p); | ||
| 751 | else if (componentIdx == N2Idx) | ||
| 752 | DUNE_THROW(Dune::NotImplemented, "Component enthalpy of nitrogen in liquid phase"); | ||
| 753 | else if (componentIdx == O2Idx) | ||
| 754 | DUNE_THROW(Dune::NotImplemented, "Component enthalpy of oxygen in liquid phase"); | ||
| 755 | else | ||
| 756 | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx); | ||
| 757 | } | ||
| 758 | else if (phaseIdx == phase1Idx) | ||
| 759 | { | ||
| 760 | if (componentIdx == H2OIdx) | ||
| 761 | return H2O::gasEnthalpy(T, p); | ||
| 762 | else if (componentIdx == N2Idx) | ||
| 763 | return N2::gasEnthalpy(T, p); | ||
| 764 | else if (componentIdx == O2Idx) | ||
| 765 | return O2::gasEnthalpy(T, p); | ||
| 766 | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx); | ||
| 767 | } | ||
| 768 | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | ||
| 769 | } | ||
| 770 | |||
| 771 | using Base<Scalar, ThisType>::thermalConductivity; | ||
| 772 | /*! | ||
| 773 | * \brief Thermal conductivity of a fluid phase \f$\mathrm{[W/(m K)]}\f$. | ||
| 774 | * | ||
| 775 | * Use the conductivity of air and water as a first approximation. | ||
| 776 | * | ||
| 777 | * http://en.wikipedia.org/wiki/List_of_thermal_conductivities | ||
| 778 | * \param fluidState An arbitrary fluid state | ||
| 779 | * \param phaseIdx The index of the fluid phase to consider | ||
| 780 | */ | ||
| 781 | template <class FluidState> | ||
| 782 | 278818 | static Scalar thermalConductivity(const FluidState &fluidState, | |
| 783 | const int phaseIdx) | ||
| 784 | { | ||
| 785 |
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278818 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 786 |
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278818 | Scalar temperature = fluidState.temperature(phaseIdx) ; |
| 787 |
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278818 | Scalar pressure = fluidState.pressure(phaseIdx); |
| 788 | |||
| 789 |
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278818 | if (phaseIdx == liquidPhaseIdx) |
| 790 | { | ||
| 791 | 139408 | return H2O::liquidThermalConductivity(temperature, pressure); | |
| 792 | } | ||
| 793 | else | ||
| 794 | { | ||
| 795 | 139410 | Scalar lambdaPureN2 = N2::gasThermalConductivity(temperature, pressure); | |
| 796 | 139410 | Scalar lambdaPureO2 = O2::gasThermalConductivity(temperature, pressure); | |
| 797 | if (!Policy::useN2HeatConductivityAsGasMixtureHeatConductivity()) | ||
| 798 | { | ||
| 799 | 139408 | Scalar xN2 = fluidState.moleFraction(phaseIdx, N2Idx); | |
| 800 | 139408 | Scalar xO2 = fluidState.moleFraction(phaseIdx, O2Idx); | |
| 801 | 139408 | Scalar xH2O = fluidState.moleFraction(phaseIdx, H2OIdx); | |
| 802 | 139408 | Scalar lambdaN2 = xN2 * lambdaPureN2; | |
| 803 | 139408 | Scalar lambdaO2 = xO2 * lambdaPureO2; | |
| 804 | 139408 | Scalar partialPressure = pressure * xH2O; | |
| 805 | 139408 | Scalar lambdaH2O = xH2O * H2O::gasThermalConductivity(temperature, partialPressure); | |
| 806 | 139408 | return lambdaN2 + lambdaH2O + lambdaO2; | |
| 807 | } | ||
| 808 | else | ||
| 809 | 2 | return lambdaPureN2; | |
| 810 | } | ||
| 811 | } | ||
| 812 | |||
| 813 | using Base<Scalar, ThisType>::heatCapacity; | ||
| 814 | //! \copydoc Base<Scalar,ThisType>::heatCapacity(const FluidState&,int) | ||
| 815 | template <class FluidState> | ||
| 816 | 5 | static Scalar heatCapacity(const FluidState &fluidState, | |
| 817 | int phaseIdx) | ||
| 818 | { | ||
| 819 | 5 | if (phaseIdx == liquidPhaseIdx) { | |
| 820 | 2 | return H2O::liquidHeatCapacity(fluidState.temperature(phaseIdx), | |
| 821 | 2 | fluidState.pressure(phaseIdx)); | |
| 822 | } | ||
| 823 | |||
| 824 | Scalar c_pN2; | ||
| 825 | Scalar c_pO2; | ||
| 826 | Scalar c_pH2O; | ||
| 827 | // let the water and nitrogen components do things their own way | ||
| 828 | if (!Policy::useIdealGasHeatCapacities()) { | ||
| 829 | 2 | c_pN2 = N2::gasHeatCapacity(fluidState.temperature(phaseIdx), | |
| 830 | fluidState.pressure(phaseIdx) | ||
| 831 | 2 | * fluidState.moleFraction(phaseIdx, N2Idx)); | |
| 832 | |||
| 833 | 2 | c_pH2O = H2O::gasHeatCapacity(fluidState.temperature(phaseIdx), | |
| 834 | fluidState.pressure(phaseIdx) | ||
| 835 | 2 | * fluidState.moleFraction(phaseIdx, H2OIdx)); | |
| 836 | 2 | c_pO2 = O2::gasHeatCapacity(fluidState.temperature(phaseIdx), | |
| 837 | fluidState.pressure(phaseIdx) | ||
| 838 | 2 | * fluidState.moleFraction(phaseIdx, O2Idx)); | |
| 839 | } | ||
| 840 | else { | ||
| 841 | // assume an ideal gas for both components. See: | ||
| 842 | // | ||
| 843 | //http://en.wikipedia.org/wiki/Heat_capacity | ||
| 844 | 1 | Scalar c_vN2molar = Constants::R*2.39; | |
| 845 | 1 | Scalar c_pN2molar = Constants::R + c_vN2molar; | |
| 846 | |||
| 847 | 1 | Scalar c_vO2molar = Constants::R*2.43; | |
| 848 | 1 | Scalar c_pO2molar = Constants::R + c_vO2molar; | |
| 849 | |||
| 850 | 1 | Scalar c_vH2Omolar = Constants::R*3.37; // <- correct?? | |
| 851 | 1 | Scalar c_pH2Omolar = Constants::R + c_vH2Omolar; | |
| 852 | |||
| 853 | 1 | c_pN2 = c_pN2molar/molarMass(N2Idx); | |
| 854 | 1 | c_pO2 = c_pO2molar/molarMass(O2Idx); | |
| 855 | 1 | c_pH2O = c_pH2Omolar/molarMass(H2OIdx); | |
| 856 | } | ||
| 857 | |||
| 858 | // mangle all components together | ||
| 859 | return | ||
| 860 | 3 | c_pH2O*fluidState.massFraction(gasPhaseIdx, H2OIdx) | |
| 861 | 3 | + c_pN2*fluidState.massFraction(gasPhaseIdx, N2Idx) | |
| 862 | 3 | + c_pO2*fluidState.massFraction(gasPhaseIdx, O2Idx); | |
| 863 | } | ||
| 864 | |||
| 865 | }; | ||
| 866 | |||
| 867 | } // end namespace FluidSystems | ||
| 868 | } // end namespace Dumux | ||
| 869 | |||
| 870 | #endif | ||
| 871 |