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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 Components | ||
| 10 | * \brief Material properties of pure water \f$H_2O\f$. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_H2O_HH | ||
| 13 | #define DUMUX_H2O_HH | ||
| 14 | |||
| 15 | #include <cmath> | ||
| 16 | #include <cassert> | ||
| 17 | |||
| 18 | #include <dumux/nonlinear/findscalarroot.hh> | ||
| 19 | #include <dumux/material/idealgas.hh> | ||
| 20 | #include <dumux/common/exceptions.hh> | ||
| 21 | |||
| 22 | #include "iapws/common.hh" | ||
| 23 | #include "iapws/region1.hh" | ||
| 24 | #include "iapws/region2.hh" | ||
| 25 | #include "iapws/region4.hh" | ||
| 26 | |||
| 27 | #include <dumux/material/components/base.hh> | ||
| 28 | #include <dumux/material/components/liquid.hh> | ||
| 29 | #include <dumux/material/components/gas.hh> | ||
| 30 | |||
| 31 | namespace Dumux::Components { | ||
| 32 | |||
| 33 | /*! | ||
| 34 | * \ingroup Components | ||
| 35 | * \brief Material properties of pure water \f$H_2O\f$. | ||
| 36 | * \tparam Scalar The type used for scalar values | ||
| 37 | * | ||
| 38 | * See: | ||
| 39 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 40 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 41 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 42 | */ | ||
| 43 | template <class Scalar> | ||
| 44 | class H2O | ||
| 45 | : public Components::Base<Scalar, H2O<Scalar> > | ||
| 46 | , public Components::Liquid<Scalar, H2O<Scalar> > | ||
| 47 | , public Components::Gas<Scalar, H2O<Scalar> > | ||
| 48 | { | ||
| 49 | |||
| 50 | using Common = IAPWS::Common<Scalar>; | ||
| 51 | using Region1 = IAPWS::Region1<Scalar>; | ||
| 52 | using Region2 = IAPWS::Region2<Scalar>; | ||
| 53 | using Region4 = IAPWS::Region4<Scalar>; | ||
| 54 | |||
| 55 | // specific gas constant of water | ||
| 56 | static constexpr Scalar Rs = Common::Rs; | ||
| 57 | |||
| 58 | public: | ||
| 59 | /*! | ||
| 60 | * \brief A human readable name for the water. | ||
| 61 | */ | ||
| 62 |
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458420 | static std::string name() |
| 63 |
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458420 | { return "H2O"; } |
| 64 | |||
| 65 | /*! | ||
| 66 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of water. | ||
| 67 | */ | ||
| 68 | static constexpr Scalar molarMass() | ||
| 69 | { return Common::molarMass; } | ||
| 70 | |||
| 71 | /*! | ||
| 72 | * \brief The acentric factor \f$\mathrm{[-]}\f$ of water. | ||
| 73 | */ | ||
| 74 | static constexpr Scalar acentricFactor() | ||
| 75 | { return Common::acentricFactor; } | ||
| 76 | |||
| 77 | /*! | ||
| 78 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of water | ||
| 79 | */ | ||
| 80 | static constexpr Scalar criticalTemperature() | ||
| 81 | { return Common::criticalTemperature; } | ||
| 82 | |||
| 83 | /*! | ||
| 84 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of water. | ||
| 85 | */ | ||
| 86 | static constexpr Scalar criticalPressure() | ||
| 87 | { return Common::criticalPressure; } | ||
| 88 | |||
| 89 | /*! | ||
| 90 | * \brief Returns the molar volume \f$\mathrm{[m^3/mol]}\f$ of water at the critical point | ||
| 91 | */ | ||
| 92 | static constexpr Scalar criticalMolarVolume() | ||
| 93 | { return Common::criticalMolarVolume; } | ||
| 94 | |||
| 95 | /*! | ||
| 96 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at water's triple point. | ||
| 97 | */ | ||
| 98 | static constexpr Scalar tripleTemperature() | ||
| 99 | { return Common::tripleTemperature; } | ||
| 100 | |||
| 101 | /*! | ||
| 102 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at water's triple point. | ||
| 103 | */ | ||
| 104 | static constexpr Scalar triplePressure() | ||
| 105 | { return Common::triplePressure; } | ||
| 106 | |||
| 107 | /*! | ||
| 108 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure water | ||
| 109 | * at a given temperature. | ||
| 110 | * | ||
| 111 | *\param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 112 | * | ||
| 113 | * See: | ||
| 114 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 115 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 116 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 117 | */ | ||
| 118 | 237988795 | static Scalar vaporPressure(Scalar T) | |
| 119 | { | ||
| 120 | using std::min; | ||
| 121 | using std::max; | ||
| 122 |
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237988794 | T = min(T, criticalTemperature()); |
| 123 |
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237988794 | T = max(T,tripleTemperature()); |
| 124 | |||
| 125 | 237988795 | return Region4::saturationPressure(T); | |
| 126 | } | ||
| 127 | |||
| 128 | /*! | ||
| 129 | * \brief The vapor temperature in \f$\mathrm{[K]}\f$ of pure water | ||
| 130 | * at a given pressure. | ||
| 131 | * | ||
| 132 | *\param pressure pressure in \f$\mathrm{[Pa]}\f$ | ||
| 133 | * | ||
| 134 | * See: | ||
| 135 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 136 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 137 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 138 | */ | ||
| 139 | 101966 | static Scalar vaporTemperature(Scalar pressure) | |
| 140 | { | ||
| 141 | using std::min; | ||
| 142 | using std::max; | ||
| 143 |
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101966 | pressure = min(pressure, criticalPressure()); |
| 144 |
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101966 | pressure = max(pressure, triplePressure()); |
| 145 | |||
| 146 | 101966 | return Region4::vaporTemperature(pressure); | |
| 147 | } | ||
| 148 | |||
| 149 | /*! | ||
| 150 | * \brief Specific enthalpy of water steam \f$\mathrm{[J/kg]}\f$. | ||
| 151 | * | ||
| 152 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 153 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 154 | * | ||
| 155 | * See: | ||
| 156 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 157 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 158 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 159 | */ | ||
| 160 | 6281315 | static const Scalar gasEnthalpy(Scalar temperature, | |
| 161 | Scalar pressure) | ||
| 162 | { | ||
| 163 |
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6281315 | Region2::checkValidityRange(temperature, pressure, "Enthalpy"); |
| 164 | |||
| 165 | // regularization | ||
| 166 |
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6281315 | if (pressure < triplePressure() - 100) { |
| 167 | // We assume an ideal gas for low pressures to avoid the | ||
| 168 | // 0/0 for the gas enthalpy at very low pressures. The | ||
| 169 | // enthalpy of an ideal gas does not exhibit any | ||
| 170 | // dependence on pressure, so we can just return the | ||
| 171 | // specific enthalpy at the point of regularization, i.e. | ||
| 172 | // the triple pressure - 100Pa | ||
| 173 | 100453 | return enthalpyRegion2_(temperature, triplePressure() - 100); | |
| 174 | } | ||
| 175 | 6180862 | Scalar pv = vaporPressure(temperature); | |
| 176 |
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6180862 | if (pressure > pv) { |
| 177 | // the pressure is too high, in this case we use the slope | ||
| 178 | // of the enthalpy at the vapor pressure to regularize | ||
| 179 | 3621212 | Scalar dh_dp = | |
| 180 | 3621212 | Rs*temperature* | |
| 181 | 3621212 | Region2::tau(temperature)* | |
| 182 | Region2::dPi_dp(pv)* | ||
| 183 | 3621212 | Region2::ddGamma_dTaudPi(temperature, pv); | |
| 184 | |||
| 185 | return | ||
| 186 | 3621212 | enthalpyRegion2_(temperature, pv) + | |
| 187 | 3621212 | (pressure - pv)*dh_dp; | |
| 188 | } | ||
| 189 | |||
| 190 | 2559650 | return enthalpyRegion2_(temperature, pressure); | |
| 191 | } | ||
| 192 | |||
| 193 | /*! | ||
| 194 | * \brief Specific enthalpy of liquid water \f$\mathrm{[J/kg]}\f$. | ||
| 195 | * | ||
| 196 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 197 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 198 | * | ||
| 199 | * See: | ||
| 200 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 201 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 202 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 203 | */ | ||
| 204 | 4977516 | static const Scalar liquidEnthalpy(Scalar temperature, | |
| 205 | Scalar pressure) | ||
| 206 | { | ||
| 207 |
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4977516 | Region1::checkValidityRange(temperature, pressure, "Enthalpy"); |
| 208 | |||
| 209 | // regularization | ||
| 210 | 4977516 | Scalar pv = vaporPressure(temperature); | |
| 211 |
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4977516 | if (pressure < pv) { |
| 212 | // the pressure is too low, in this case we use the slope | ||
| 213 | // of the enthalpy at the vapor pressure to regularize | ||
| 214 | 83455 | Scalar dh_dp = | |
| 215 | 83455 | Rs * temperature* | |
| 216 | 83455 | Region1::tau(temperature)* | |
| 217 | Region1::dPi_dp(pv)* | ||
| 218 | 83455 | Region1::ddGamma_dTaudPi(temperature, pv); | |
| 219 | |||
| 220 | return | ||
| 221 | 83455 | enthalpyRegion1_(temperature, pv) + | |
| 222 | 83455 | (pressure - pv)*dh_dp; | |
| 223 | } | ||
| 224 | |||
| 225 | 4894061 | return enthalpyRegion1_(temperature, pressure); | |
| 226 | } | ||
| 227 | |||
| 228 | /*! | ||
| 229 | * \brief Specific isobaric heat capacity of water steam \f$\mathrm{[J/(kg*K)}\f$. | ||
| 230 | * | ||
| 231 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 232 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 233 | * | ||
| 234 | * See: | ||
| 235 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 236 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 237 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 238 | */ | ||
| 239 | 2825615 | static const Scalar gasHeatCapacity(Scalar temperature, | |
| 240 | Scalar pressure) | ||
| 241 | { | ||
| 242 |
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2825615 | Region2::checkValidityRange(temperature, pressure, "Heat capacity"); |
| 243 | |||
| 244 | // regularization | ||
| 245 |
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2825615 | if (pressure < triplePressure() - 100) { |
| 246 | 100396 | return heatCap_p_Region2_(temperature, triplePressure() - 100); | |
| 247 | } | ||
| 248 | 2725219 | Scalar pv = vaporPressure(temperature); | |
| 249 |
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2725219 | if (pressure > pv) { |
| 250 | // the pressure is too high, in this case we use the heat | ||
| 251 | // cap at the vapor pressure to regularize | ||
| 252 | 370410 | return heatCap_p_Region2_(temperature, pv); | |
| 253 | } | ||
| 254 | 2354809 | return heatCap_p_Region2_(temperature, pressure); | |
| 255 | } | ||
| 256 | |||
| 257 | /*! | ||
| 258 | * \brief Specific isobaric heat capacity of liquid water \f$\mathrm{[J/(kg*K)]}\f$. | ||
| 259 | * | ||
| 260 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 261 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 262 | * | ||
| 263 | * See: | ||
| 264 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 265 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 266 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 267 | */ | ||
| 268 | 2825983 | static const Scalar liquidHeatCapacity(Scalar temperature, | |
| 269 | Scalar pressure) | ||
| 270 | { | ||
| 271 |
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2825983 | Region1::checkValidityRange(temperature, pressure, "Heat capacity"); |
| 272 | |||
| 273 | // regularization | ||
| 274 | 2825983 | Scalar pv = vaporPressure(temperature); | |
| 275 |
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2825983 | if (pressure < pv) { |
| 276 | // the pressure is too low, in this case we use the heat cap at the vapor pressure to regularize | ||
| 277 | 83211 | return heatCap_p_Region1_(temperature, pv); | |
| 278 | } | ||
| 279 | |||
| 280 | 2742772 | return heatCap_p_Region1_(temperature, pressure); | |
| 281 | } | ||
| 282 | |||
| 283 | /*! | ||
| 284 | * \brief Specific internal energy of liquid water \f$\mathrm{[J/kg]}\f$. | ||
| 285 | * | ||
| 286 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 287 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 288 | * | ||
| 289 | * See: | ||
| 290 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 291 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 292 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 293 | */ | ||
| 294 | 1235383 | static const Scalar liquidInternalEnergy(Scalar temperature, | |
| 295 | Scalar pressure) | ||
| 296 | { | ||
| 297 |
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1235383 | Region1::checkValidityRange(temperature, pressure, "Internal energy"); |
| 298 | |||
| 299 | // regularization | ||
| 300 | 1235383 | Scalar pv = vaporPressure(temperature); | |
| 301 |
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1235383 | if (pressure < pv) { |
| 302 | // the pressure is too low, in this case we use the slope | ||
| 303 | // of the internal energy at the vapor pressure to | ||
| 304 | // regularize | ||
| 305 | |||
| 306 | /* | ||
| 307 | // calculate the partial derivative of the internal energy | ||
| 308 | // to the pressure at the vapor pressure. | ||
| 309 | Scalar tau = Region1::tau(temperature); | ||
| 310 | Scalar dGamma_dPi = Region1::dGamma_dPi(temperature, pv); | ||
| 311 | Scalar ddGamma_dTaudPi = Region1::ddGamma_dTaudPi(temperature, pv); | ||
| 312 | Scalar ddGamma_ddPi = Region1::ddGamma_ddPi(temperature, pv); | ||
| 313 | Scalar pi = Region1::pi(pv); | ||
| 314 | Scalar dPi_dp = Region1::dPi_dp(pv); | ||
| 315 | Scalar du_dp = | ||
| 316 | Rs*temperature* | ||
| 317 | (tau*dPi_dp*ddGamma_dTaudPi + dPi_dp*dPi_dp*dGamma_dPi + pi*dPi_dp*ddGamma_ddPi); | ||
| 318 | */ | ||
| 319 | |||
| 320 | // use a straight line for extrapolation. use forward | ||
| 321 | // differences to calculate the partial derivative to the | ||
| 322 | // pressure at the vapor pressure | ||
| 323 | static const Scalar eps = 1e-7; | ||
| 324 | 217 | Scalar uv = internalEnergyRegion1_(temperature, pv); | |
| 325 | 217 | Scalar uvPEps = internalEnergyRegion1_(temperature, pv + eps); | |
| 326 | 217 | Scalar du_dp = (uvPEps - uv)/eps; | |
| 327 | 217 | return uv + du_dp*(pressure - pv); | |
| 328 | } | ||
| 329 | |||
| 330 | 1235166 | return internalEnergyRegion1_(temperature, pressure); | |
| 331 | } | ||
| 332 | |||
| 333 | /*! | ||
| 334 | * \brief Specific internal energy of steam and water vapor \f$\mathrm{[J/kg]}\f$. | ||
| 335 | * | ||
| 336 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 337 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 338 | * | ||
| 339 | * See: | ||
| 340 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 341 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 342 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 343 | */ | ||
| 344 | 205023 | static Scalar gasInternalEnergy(Scalar temperature, Scalar pressure) | |
| 345 | { | ||
| 346 |
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205023 | Region2::checkValidityRange(temperature, pressure, "Internal energy"); |
| 347 | |||
| 348 | // regularization | ||
| 349 |
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205023 | if (pressure < triplePressure() - 100) { |
| 350 | // We assume an ideal gas for low pressures to avoid the | ||
| 351 | // 0/0 for the internal energy of gas at very low | ||
| 352 | // pressures. The enthalpy of an ideal gas does not | ||
| 353 | // exhibit any dependence on pressure, so we can just | ||
| 354 | // return the specific enthalpy at the point of | ||
| 355 | // regularization, i.e. the triple pressure - 100Pa, and | ||
| 356 | // subtract the work required to change the volume for an | ||
| 357 | // ideal gas. | ||
| 358 | return | ||
| 359 | ✗ | enthalpyRegion2_(temperature, triplePressure() - 100) | |
| 360 | - | ||
| 361 | ✗ | Rs*temperature; // = p*v for an ideal gas! | |
| 362 | } | ||
| 363 | 205023 | Scalar pv = vaporPressure(temperature); | |
| 364 |
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205023 | if (pressure > pv) { |
| 365 | // the pressure is too high, in this case we use the slope | ||
| 366 | // of the internal energy at the vapor pressure to | ||
| 367 | // regularize | ||
| 368 | |||
| 369 | /* | ||
| 370 | // calculate the partial derivative of the internal energy | ||
| 371 | // to the pressure at the vapor pressure. | ||
| 372 | Scalar tau = Region2::tau(temperature); | ||
| 373 | Scalar dGamma_dPi = Region2::dGamma_dPi(temperature, pv); | ||
| 374 | Scalar ddGamma_dTaudPi = Region2::ddGamma_dTaudPi(temperature, pv); | ||
| 375 | Scalar ddGamma_ddPi = Region2::ddGamma_ddPi(temperature, pv); | ||
| 376 | Scalar pi = Region2::pi(pv); | ||
| 377 | Scalar dPi_dp = Region2::dPi_dp(pv); | ||
| 378 | Scalar du_dp = | ||
| 379 | Rs*temperature* | ||
| 380 | (tau*dPi_dp*ddGamma_dTaudPi + dPi_dp*dPi_dp*dGamma_dPi + pi*dPi_dp*ddGamma_ddPi); | ||
| 381 | |||
| 382 | // use a straight line for extrapolation | ||
| 383 | Scalar uv = internalEnergyRegion2_(temperature, pv); | ||
| 384 | return uv + du_dp*(pressure - pv); | ||
| 385 | */ | ||
| 386 | |||
| 387 | // use a straight line for extrapolation. use backward | ||
| 388 | // differences to calculate the partial derivative to the | ||
| 389 | // pressure at the vapor pressure | ||
| 390 | static const Scalar eps = 1e-7; | ||
| 391 | 189 | Scalar uv = internalEnergyRegion2_(temperature, pv); | |
| 392 | 189 | Scalar uvMEps = internalEnergyRegion2_(temperature, pv - eps); | |
| 393 | 189 | Scalar du_dp = (uv - uvMEps)/eps; | |
| 394 | 189 | return uv + du_dp*(pressure - pv); | |
| 395 | } | ||
| 396 | |||
| 397 | 204834 | return internalEnergyRegion2_(temperature, pressure); | |
| 398 | } | ||
| 399 | |||
| 400 | /*! | ||
| 401 | * \brief Specific isochoric heat capacity of liquid water \f$\mathrm{[J/(m^3*K)]}\f$. | ||
| 402 | * | ||
| 403 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 404 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 405 | * | ||
| 406 | * See: | ||
| 407 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 408 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 409 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 410 | */ | ||
| 411 | static const Scalar liquidHeatCapacityConstVolume(Scalar temperature, | ||
| 412 | Scalar pressure) | ||
| 413 | { | ||
| 414 | Region1::checkValidityRange(temperature, pressure, "Heat capacity for a constant volume"); | ||
| 415 | |||
| 416 | // regularization | ||
| 417 | Scalar pv = vaporPressure(temperature); | ||
| 418 | if (pressure < pv) { | ||
| 419 | // the pressure is too low, in this case we use the heat cap at the vapor pressure to regularize | ||
| 420 | |||
| 421 | return heatCap_v_Region1_(temperature, pv); | ||
| 422 | } | ||
| 423 | |||
| 424 | return heatCap_v_Region1_(temperature, pressure); | ||
| 425 | } | ||
| 426 | |||
| 427 | /*! | ||
| 428 | * \brief Specific isochoric heat capacity of steam and water vapor \f$\mathrm{[J/(kg*K)}\f$. | ||
| 429 | * | ||
| 430 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 431 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 432 | * | ||
| 433 | * See: | ||
| 434 | * | ||
| 435 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 436 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 437 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 438 | */ | ||
| 439 | static Scalar gasHeatCapacityConstVolume(Scalar temperature, Scalar pressure) | ||
| 440 | { | ||
| 441 | Region2::checkValidityRange(temperature, pressure, "Heat capacity for a constant volume"); | ||
| 442 | |||
| 443 | // regularization | ||
| 444 | if (pressure < triplePressure() - 100) { | ||
| 445 | return | ||
| 446 | heatCap_v_Region2_(temperature, triplePressure() - 100); | ||
| 447 | } | ||
| 448 | Scalar pv = vaporPressure(temperature); | ||
| 449 | if (pressure > pv) { | ||
| 450 | return heatCap_v_Region2_(temperature, pv); | ||
| 451 | } | ||
| 452 | |||
| 453 | return heatCap_v_Region2_(temperature, pressure); | ||
| 454 | } | ||
| 455 | |||
| 456 | /*! | ||
| 457 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 458 | */ | ||
| 459 | static constexpr bool gasIsCompressible() | ||
| 460 | { return true; } | ||
| 461 | |||
| 462 | /*! | ||
| 463 | * \brief Returns true if the liquid phase is assumed to be compressible | ||
| 464 | */ | ||
| 465 | static constexpr bool liquidIsCompressible() | ||
| 466 | { return true; } | ||
| 467 | |||
| 468 | /*! | ||
| 469 | * \brief The density of steam in \f$\mathrm{[kg/m^3]}\f$ at a given pressure and temperature. | ||
| 470 | * | ||
| 471 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 472 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 473 | * | ||
| 474 | * See: | ||
| 475 | * | ||
| 476 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 477 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 478 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 479 | */ | ||
| 480 | 49808950 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | |
| 481 | { | ||
| 482 |
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49808950 | Region2::checkValidityRange(temperature, pressure, "Density"); |
| 483 | |||
| 484 | // regularization | ||
| 485 |
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49808950 | if (pressure < triplePressure() - 100) { |
| 486 | // We assume an ideal gas for low pressures to avoid the | ||
| 487 | // 0/0 for the internal energy and enthalpy. | ||
| 488 | 7934053 | Scalar rho0IAPWS = 1.0/volumeRegion2_(temperature, | |
| 489 | triplePressure() - 100); | ||
| 490 | 7934053 | Scalar rho0Id = IdealGas<Scalar>::density(molarMass(), | |
| 491 | temperature, | ||
| 492 | triplePressure() - 100); | ||
| 493 | return | ||
| 494 | 7934053 | rho0IAPWS/rho0Id * | |
| 495 | 7934053 | IdealGas<Scalar>::density(molarMass(), | |
| 496 | temperature, | ||
| 497 | 7934053 | pressure); | |
| 498 | } | ||
| 499 | 41874897 | Scalar pv = vaporPressure(temperature); | |
| 500 |
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41874897 | if (pressure > pv) { |
| 501 | // the pressure is too high, in this case we use the slope | ||
| 502 | // of the density energy at the vapor pressure to | ||
| 503 | // regularize | ||
| 504 | |||
| 505 | // calculate the partial derivative of the specific volume | ||
| 506 | // to the pressure at the vapor pressure. | ||
| 507 | 6212878 | const Scalar eps = pv*1e-8; | |
| 508 | 6212878 | Scalar v0 = volumeRegion2_(temperature, pv); | |
| 509 | 12425756 | Scalar v1 = volumeRegion2_(temperature, pv + eps); | |
| 510 | 6212878 | Scalar dv_dp = (v1 - v0)/eps; | |
| 511 | /* | ||
| 512 | Scalar pi = Region2::pi(pv); | ||
| 513 | Scalar dp_dPi = Region2::dp_dPi(pv); | ||
| 514 | Scalar dGamma_dPi = Region2::dGamma_dPi(temperature, pv); | ||
| 515 | Scalar ddGamma_ddPi = Region2::ddGamma_ddPi(temperature, pv); | ||
| 516 | |||
| 517 | Scalar RT = Rs*temperature; | ||
| 518 | Scalar dv_dp = | ||
| 519 | RT/(dp_dPi*pv) | ||
| 520 | * | ||
| 521 | (dGamma_dPi + pi*ddGamma_ddPi - v0*dp_dPi/RT); | ||
| 522 | */ | ||
| 523 | |||
| 524 | // calculate the partial derivative of the density to the | ||
| 525 | // pressure at vapor pressure | ||
| 526 | 6212878 | Scalar drho_dp = - 1/(v0*v0)*dv_dp; | |
| 527 | |||
| 528 | // use a straight line for extrapolation | ||
| 529 | 6212878 | return 1.0/v0 + (pressure - pv)*drho_dp; | |
| 530 | } | ||
| 531 | |||
| 532 | 35662019 | return 1.0/volumeRegion2_(temperature, pressure); | |
| 533 | } | ||
| 534 | |||
| 535 | /*! | ||
| 536 | * \brief The molar density of steam in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 537 | * | ||
| 538 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 539 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 540 | * | ||
| 541 | */ | ||
| 542 | 2511380 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | |
| 543 | 2511380 | { return gasDensity(temperature, pressure)/molarMass(); } | |
| 544 | |||
| 545 | /*! | ||
| 546 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 547 | */ | ||
| 548 | static constexpr bool gasIsIdeal() | ||
| 549 | { return false; } | ||
| 550 | |||
| 551 | /*! | ||
| 552 | * \brief The pressure of steam in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 553 | * | ||
| 554 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 555 | * \param density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 556 | * | ||
| 557 | * See: | ||
| 558 | * | ||
| 559 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 560 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 561 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 562 | */ | ||
| 563 | 3030232 | static Scalar gasPressure(Scalar temperature, Scalar density) | |
| 564 | { | ||
| 565 | // We use the newton method for this. For the initial value we | ||
| 566 | // assume steam to be an ideal gas | ||
| 567 | 3030232 | Scalar pressure = IdealGas<Scalar>::pressure(temperature, density/molarMass()); | |
| 568 | 3030232 | Scalar eps = pressure*1e-7; | |
| 569 | |||
| 570 | 3030232 | Scalar deltaP = pressure*2; | |
| 571 | using std::abs; | ||
| 572 |
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12284986 | for (int i = 0; i < 5 && abs(pressure*1e-9) < abs(deltaP); ++i) |
| 573 | { | ||
| 574 | 9254754 | const Scalar f = gasDensity(temperature, pressure) - density; | |
| 575 | |||
| 576 | Scalar df_dp; | ||
| 577 | 9254754 | df_dp = gasDensity(temperature, pressure + eps); | |
| 578 | 9254754 | df_dp -= gasDensity(temperature, pressure - eps); | |
| 579 | 9254754 | df_dp /= 2*eps; | |
| 580 | |||
| 581 | 9254754 | deltaP = - f/df_dp; | |
| 582 | |||
| 583 | 9254754 | pressure += deltaP; | |
| 584 | } | ||
| 585 | |||
| 586 | 3030232 | return pressure; | |
| 587 | } | ||
| 588 | |||
| 589 | /*! | ||
| 590 | * \brief The density of pure water in \f$\mathrm{[kg/m^3]}\f$ at a given pressure and temperature. | ||
| 591 | * | ||
| 592 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 593 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 594 | * | ||
| 595 | * See: | ||
| 596 | * | ||
| 597 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 598 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 599 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 600 | */ | ||
| 601 | 147370031 | static Scalar liquidDensity(Scalar temperature, Scalar pressure) | |
| 602 | { | ||
| 603 |
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147370031 | Region1::checkValidityRange(temperature, pressure, "Density"); |
| 604 | |||
| 605 | // regularization | ||
| 606 | 147370025 | Scalar pv = vaporPressure(temperature); | |
| 607 |
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147370025 | if (pressure < pv) { |
| 608 | // the pressure is too low, in this case we use the slope | ||
| 609 | // of the density at the vapor pressure to regularize | ||
| 610 | |||
| 611 | // calculate the partial derivative of the specific volume | ||
| 612 | // to the pressure at the vapor pressure. | ||
| 613 | 7878504 | const Scalar eps = pv*1e-8; | |
| 614 | 7878504 | Scalar v0 = volumeRegion1_(temperature, pv); | |
| 615 | 15757008 | Scalar v1 = volumeRegion1_(temperature, pv + eps); | |
| 616 | 7878504 | Scalar dv_dp = (v1 - v0)/eps; | |
| 617 | |||
| 618 | /* | ||
| 619 | Scalar v0 = volumeRegion1_(temperature, pv); | ||
| 620 | Scalar pi = Region1::pi(pv); | ||
| 621 | Scalar dp_dPi = Region1::dp_dPi(pv); | ||
| 622 | Scalar dGamma_dPi = Region1::dGamma_dPi(temperature, pv); | ||
| 623 | Scalar ddGamma_ddPi = Region1::ddGamma_ddPi(temperature, pv); | ||
| 624 | |||
| 625 | Scalar RT = Rs*temperature; | ||
| 626 | Scalar dv_dp = | ||
| 627 | RT/(dp_dPi*pv) | ||
| 628 | * | ||
| 629 | (dGamma_dPi + pi*ddGamma_ddPi - v0*dp_dPi/RT); | ||
| 630 | */ | ||
| 631 | |||
| 632 | // calculate the partial derivative of the density to the | ||
| 633 | // pressure at vapor pressure | ||
| 634 | 7878504 | Scalar drho_dp = - 1/(v0*v0)*dv_dp; | |
| 635 | |||
| 636 | // use a straight line for extrapolation | ||
| 637 | 7878504 | return 1.0/v0 + (pressure - pv)*drho_dp; | |
| 638 | } | ||
| 639 | |||
| 640 | 139491521 | return 1/volumeRegion1_(temperature, pressure); | |
| 641 | } | ||
| 642 | |||
| 643 | /*! | ||
| 644 | * \brief The molar density of water in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 645 | * | ||
| 646 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 647 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 648 | * | ||
| 649 | */ | ||
| 650 | 14 | static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure) | |
| 651 | 14 | { return liquidDensity(temperature, pressure)/molarMass(); } | |
| 652 | |||
| 653 | /*! | ||
| 654 | * \brief The pressure of liquid water in \f$\mathrm{[Pa]}\f$ at a given density and | ||
| 655 | * temperature. | ||
| 656 | * | ||
| 657 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 658 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 659 | * | ||
| 660 | * See: | ||
| 661 | * | ||
| 662 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 663 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 664 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 665 | */ | ||
| 666 | 4060592 | static Scalar liquidPressure(Scalar temperature, Scalar density) | |
| 667 | { | ||
| 668 | // We use Brent's method for this, with a pressure range including the surroundings of the | ||
| 669 | // vapor pressure line | ||
| 670 | 4060592 | Scalar minPressure = vaporPressure(temperature)/1.11; | |
| 671 | 4060592 | Scalar maxPressure = 100e6; | |
| 672 | 4060592 | const auto residualFunction = [&] (const Scalar pressure) { | |
| 673 |
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124006164 | return liquidDensity(temperature, pressure) - density; |
| 674 | }; | ||
| 675 | try | ||
| 676 | { | ||
| 677 |
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4060592 | return findScalarRootBrent(minPressure, maxPressure, residualFunction); |
| 678 | } | ||
| 679 | ✗ | catch (const NumericalProblem& e) | |
| 680 | { | ||
| 681 | ✗ | DUNE_THROW(NumericalProblem, | |
| 682 | "searched for pressure(T=" << temperature << ",rho=" << density | ||
| 683 | <<") in [" << minPressure << ", " << maxPressure << "]: " | ||
| 684 | << e.what()); | ||
| 685 | } | ||
| 686 | } | ||
| 687 | |||
| 688 | /*! | ||
| 689 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of steam. | ||
| 690 | * | ||
| 691 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 692 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 693 | * | ||
| 694 | * We assume pure water vapor here. For water in a mixture of other gaseous | ||
| 695 | * components, consider the free function h2oGasViscosityInMixture. | ||
| 696 | * | ||
| 697 | * We use the IAPWS Formulation, see: | ||
| 698 | * IAPWS: "Release on the IAPWS Formulation 2008 for the Viscosity | ||
| 699 | * of Ordinary Water Substance", http://www.iapws.org/relguide/visc.pdf \cite cooper2008 | ||
| 700 | * This method is only valid if pressure is below or at the vapor | ||
| 701 | * pressure of water. | ||
| 702 | */ | ||
| 703 | 3030440 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 704 | { | ||
| 705 |
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3030440 | Region2::checkValidityRange(temperature, pressure, "Viscosity"); |
| 706 | |||
| 707 | 3030440 | Scalar rho = gasDensity(temperature, pressure); | |
| 708 | 3030440 | return Common::viscosity(temperature, rho); | |
| 709 | } | ||
| 710 | |||
| 711 | |||
| 712 | /*! | ||
| 713 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of pure water. | ||
| 714 | * | ||
| 715 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 716 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 717 | * | ||
| 718 | * See: | ||
| 719 | * IAPWS: "Release on the IAPWS Formulation 2008 for the Viscosity | ||
| 720 | * of Ordinary Water Substance", http://www.iapws.org/relguide/visc.pdf \cite cooper2008 | ||
| 721 | */ | ||
| 722 | 5008805 | static Scalar liquidViscosity(Scalar temperature, Scalar pressure) | |
| 723 | { | ||
| 724 |
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5008805 | Region1::checkValidityRange(temperature, pressure, "Viscosity"); |
| 725 | |||
| 726 | 5008805 | Scalar rho = liquidDensity(temperature, pressure); | |
| 727 | 5008805 | return Common::viscosity(temperature, rho); | |
| 728 | } | ||
| 729 | |||
| 730 | /*! | ||
| 731 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of water (IAPWS) . | ||
| 732 | * | ||
| 733 | * Implementation taken from: | ||
| 734 | * freesteam - IAPWS-IF97 steam tables library | ||
| 735 | * copyright (C) 2004-2009 John Pye | ||
| 736 | * | ||
| 737 | * See: | ||
| 738 | * IAPWS: "Release on the IAPWS Formulation 2011 for the Thermal Conductivity | ||
| 739 | * of Ordinary Water Substance", http://www.iapws.org/relguide/ThCond.pdf | ||
| 740 | * \cite IAPWS_ThCond | ||
| 741 | * | ||
| 742 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 743 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 744 | */ | ||
| 745 | 3718777 | static Scalar liquidThermalConductivity( Scalar temperature, Scalar pressure) | |
| 746 | { | ||
| 747 | // Thermal conductivity of water is empirically fit. | ||
| 748 | // Evaluating that fitting-function outside the area of validity does not make sense. | ||
| 749 |
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3718777 | if ( !( (pressure <= 400e6 && (273.15 <= temperature) && (temperature <= 398.15)) |
| 750 |
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1658017 | || (pressure <= 200e6 && (398.15 < temperature) && (temperature <= 523.15)) |
| 751 |
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744817 | || (pressure <= 150e6 && (523.15 < temperature) && (temperature <= 673.15)) |
| 752 |
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17 | || (pressure <= 100e6 && (673.15 < temperature) && (temperature <= 1073.15)) )) |
| 753 | { | ||
| 754 |
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68 | DUNE_THROW(NumericalProblem, |
| 755 | "Evaluating the IAPWS fit function for thermal conductivity outside range of applicability." | ||
| 756 | "(T=" << temperature << ", p=" << pressure << ")"); | ||
| 757 | } | ||
| 758 | |||
| 759 | 3718760 | Scalar rho = liquidDensity(temperature, pressure); | |
| 760 | 3718760 | return Common::thermalConductivityIAPWS(temperature, rho); | |
| 761 | } | ||
| 762 | |||
| 763 | /*! | ||
| 764 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of steam (IAPWS) . | ||
| 765 | * | ||
| 766 | * Implementation taken from: | ||
| 767 | * freesteam - IAPWS-IF97 steam tables library | ||
| 768 | * copyright (C) 2004-2009 John Pye | ||
| 769 | * | ||
| 770 | * See: | ||
| 771 | * IAPWS: "Release on the IAPWS Formulation 2011 for the Thermal Conductivity | ||
| 772 | * of Ordinary Water Substance", http://www.iapws.org/relguide/ThCond.pdf | ||
| 773 | * \cite IAPWS_ThCond | ||
| 774 | * | ||
| 775 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 776 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 777 | */ | ||
| 778 | 3069808 | static Scalar gasThermalConductivity(const Scalar temperature, const Scalar pressure) | |
| 779 | { | ||
| 780 | // Thermal conductivity of water is empirically fit. | ||
| 781 | // Evaluating that fitting-function outside the area of validity does not make sense. | ||
| 782 |
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3069808 | if ( !( (pressure <= 400e6 && (273.15 <= temperature) && (temperature <= 398.15)) |
| 783 |
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1658000 | || (pressure <= 200e6 && (398.15 < temperature) && (temperature <= 523.15)) |
| 784 |
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744800 | || (pressure <= 150e6 && (523.15 < temperature) && (temperature <= 673.15)) |
| 785 | ✗ | || (pressure <= 100e6 && (673.15 < temperature) && (temperature <= 1073.15)) )) | |
| 786 | { | ||
| 787 | ✗ | DUNE_THROW(NumericalProblem, | |
| 788 | "Evaluating the IAPWS fit function for thermal conductivity outside range of applicability." | ||
| 789 | "(T=" << temperature << ", p=" << pressure << ")"); | ||
| 790 | } | ||
| 791 | |||
| 792 | 3069808 | Scalar rho = gasDensity(temperature, pressure); | |
| 793 | 3069808 | return Common::thermalConductivityIAPWS(temperature, rho); | |
| 794 | } | ||
| 795 | |||
| 796 | private: | ||
| 797 | // the unregularized specific enthalpy for liquid water | ||
| 798 | 4894061 | static constexpr Scalar enthalpyRegion1_(Scalar temperature, Scalar pressure) | |
| 799 | { | ||
| 800 | return | ||
| 801 | 9955032 | Region1::tau(temperature) * | |
| 802 | 4977516 | Region1::dGamma_dTau(temperature, pressure) * | |
| 803 | 4977516 | Rs*temperature; | |
| 804 | } | ||
| 805 | |||
| 806 | // the unregularized specific isobaric heat capacity | ||
| 807 | 2825983 | static constexpr Scalar heatCap_p_Region1_(Scalar temperature, Scalar pressure) | |
| 808 | { | ||
| 809 | return | ||
| 810 | 5651966 | - Region1::tau(temperature) * Region1::tau(temperature) * | |
| 811 | 2825983 | Region1::ddGamma_ddTau(temperature, pressure) * | |
| 812 | 2825983 | Rs; | |
| 813 | } | ||
| 814 | |||
| 815 | // the unregularized specific isochoric heat capacity | ||
| 816 | static Scalar heatCap_v_Region1_(Scalar temperature, Scalar pressure) | ||
| 817 | { | ||
| 818 | Scalar tau = Region1::tau(temperature); | ||
| 819 | Scalar num = Region1::dGamma_dPi(temperature, pressure) - tau * Region1::ddGamma_dTaudPi(temperature, pressure); | ||
| 820 | Scalar diff = num * num / Region1::ddGamma_ddPi(temperature, pressure); | ||
| 821 | |||
| 822 | return | ||
| 823 | - tau * tau * | ||
| 824 | Region1::ddGamma_ddTau(temperature, pressure) * Rs + | ||
| 825 | diff; | ||
| 826 | } | ||
| 827 | |||
| 828 | // the unregularized specific internal energy for liquid water | ||
| 829 | 1235600 | static constexpr Scalar internalEnergyRegion1_(Scalar temperature, Scalar pressure) | |
| 830 | { | ||
| 831 | return | ||
| 832 | 1235600 | Rs * temperature * | |
| 833 | 1235600 | ( Region1::tau(temperature)*Region1::dGamma_dTau(temperature, pressure) - | |
| 834 | 1235600 | Region1::pi(pressure)*Region1::dGamma_dPi(temperature, pressure)); | |
| 835 | } | ||
| 836 | |||
| 837 | // the unregularized specific volume for liquid water | ||
| 838 | 147370025 | static constexpr Scalar volumeRegion1_(Scalar temperature, Scalar pressure) | |
| 839 | { | ||
| 840 | return | ||
| 841 | 302618554 | Region1::pi(pressure)* | |
| 842 | 147370025 | Region1::dGamma_dPi(temperature, pressure) * | |
| 843 | 147370025 | Rs * temperature / pressure; | |
| 844 | } | ||
| 845 | |||
| 846 | // the unregularized specific enthalpy for steam | ||
| 847 | 2660103 | static constexpr Scalar enthalpyRegion2_(Scalar temperature, Scalar pressure) | |
| 848 | { | ||
| 849 | return | ||
| 850 | 12562630 | Region2::tau(temperature) * | |
| 851 | 6281315 | Region2::dGamma_dTau(temperature, pressure) * | |
| 852 | 6281315 | Rs*temperature; | |
| 853 | } | ||
| 854 | |||
| 855 | // the unregularized specific internal energy for steam | ||
| 856 | 205212 | static constexpr Scalar internalEnergyRegion2_(Scalar temperature, Scalar pressure) | |
| 857 | { | ||
| 858 | return | ||
| 859 | 205212 | Rs * temperature * | |
| 860 | 205212 | ( Region2::tau(temperature)*Region2::dGamma_dTau(temperature, pressure) - | |
| 861 | 205212 | Region2::pi(pressure)*Region2::dGamma_dPi(temperature, pressure)); | |
| 862 | } | ||
| 863 | |||
| 864 | // the unregularized specific isobaric heat capacity | ||
| 865 | 2825615 | static constexpr Scalar heatCap_p_Region2_(Scalar temperature, Scalar pressure) | |
| 866 | { | ||
| 867 | return | ||
| 868 | 5651230 | - Region2::tau(temperature) * Region2::tau(temperature) * | |
| 869 | 2825615 | Region2::ddGamma_ddTau(temperature, pressure) * | |
| 870 | 2825615 | Rs; | |
| 871 | } | ||
| 872 | |||
| 873 | // the unregularized specific isochoric heat capacity | ||
| 874 | static Scalar heatCap_v_Region2_(Scalar temperature, Scalar pressure) | ||
| 875 | { | ||
| 876 | Scalar tau = Region2::tau(temperature); | ||
| 877 | Scalar pi = Region2::pi(pressure); | ||
| 878 | Scalar num = 1 + pi * Region2::dGamma_dPi(temperature, pressure) + tau * pi * Region2::ddGamma_dTaudPi(temperature, pressure); | ||
| 879 | Scalar diff = num * num / (1 - pi * pi * Region2::ddGamma_ddPi(temperature, pressure)); | ||
| 880 | return | ||
| 881 | - tau * tau * | ||
| 882 | Region2::ddGamma_ddTau(temperature, pressure) * Rs | ||
| 883 | - diff; | ||
| 884 | } | ||
| 885 | |||
| 886 | // the unregularized specific volume for steam | ||
| 887 | 41874897 | static constexpr Scalar volumeRegion2_(Scalar temperature, Scalar pressure) | |
| 888 | { | ||
| 889 | return | ||
| 890 | 105830778 | Region2::pi(pressure)* | |
| 891 | 49808950 | Region2::dGamma_dPi(temperature, pressure) * | |
| 892 | 49808950 | Rs * temperature / pressure; | |
| 893 | } | ||
| 894 | }; | ||
| 895 | |||
| 896 | template <class Scalar> | ||
| 897 | struct IsAqueous<H2O<Scalar>> : public std::true_type {}; | ||
| 898 | |||
| 899 | } // end namespace Dumux::Components | ||
| 900 | |||
| 901 | namespace Dumux::FluidSystems::Detail { | ||
| 902 | |||
| 903 | // viscosity according to Reid, R.C. | ||
| 904 | template <class Scalar> | ||
| 905 | 63459392 | Scalar viscosityReid_(Scalar temperature) | |
| 906 | { | ||
| 907 | 63459392 | constexpr Scalar tc = 647.3; | |
| 908 | using std::max; | ||
| 909 |
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63459392 | const Scalar tr = max(temperature/tc, 1e-8); |
| 910 | |||
| 911 | 63459392 | const Scalar fp0 = 1.0 + 0.221*(0.96 + 0.1*(tr - 0.7)); | |
| 912 | 63459392 | constexpr Scalar xi = 3.334e-3; | |
| 913 | using std::pow; | ||
| 914 | using std::exp; | ||
| 915 | 63459392 | const Scalar eta_xi = (0.807*pow(tr, 0.618) - 0.357*exp((-0.449)*tr) | |
| 916 | 63459392 | + 0.34*exp((-4.058)*tr) + 0.018)*fp0; | |
| 917 | |||
| 918 | 63459392 | return 1.0e-7*eta_xi/xi; | |
| 919 | } | ||
| 920 | |||
| 921 | // viscosity according to Nagel, T. et al. | ||
| 922 | template <class Scalar> | ||
| 923 | 25428 | Scalar viscosityNagel_(Scalar temperature) | |
| 924 | { | ||
| 925 | 25428 | constexpr Scalar a1 = -4.4189440e-6; | |
| 926 | 25428 | constexpr Scalar a2 = 4.6876380e-8; | |
| 927 | 25428 | constexpr Scalar a3 = -5.3894310e-12; | |
| 928 | 25428 | constexpr Scalar a4 = 3.2028560e-16; | |
| 929 | 25428 | constexpr Scalar a5 = 4.9191790e-22; | |
| 930 | |||
| 931 | 25428 | return a1 + a2*temperature + a3*temperature*temperature | |
| 932 | 25428 | + a4*temperature*temperature*temperature | |
| 933 | 25428 | + a5*temperature*temperature*temperature*temperature; | |
| 934 | } | ||
| 935 | |||
| 936 | } // end Dumux::FluidSystems::Detail | ||
| 937 | |||
| 938 | namespace Dumux::FluidSystems { | ||
| 939 | |||
| 940 | /*! | ||
| 941 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of steam in a gas mixture. | ||
| 942 | * | ||
| 943 | * \param temperature temperature in \f$\mathrm{[K]}\f$ | ||
| 944 | * \param pressure pressure | ||
| 945 | * | ||
| 946 | * We assume here that water is in mixture with other gaseous components. | ||
| 947 | * For pure water, use the gasViscosity function of Components::H2O. | ||
| 948 | * | ||
| 949 | * We apply two different laws depending on the gas temperature. | ||
| 950 | * | ||
| 951 | * For temperatures below 480 K see: | ||
| 952 | * "Reid, R.C., Prausnitz, J.M., Poling, B.E.: The Properties of | ||
| 953 | * Gases and Liquids (1987)" | ||
| 954 | * Lucas corresponding states method | ||
| 955 | * https://www.osti.gov/scitech/biblio/6504847 \cite reid1987 | ||
| 956 | * | ||
| 957 | * For temperatures above 500 K see: | ||
| 958 | * Nagel, T. et al.: THC-Processes (2018) | ||
| 959 | * https://doi.org/10.1007/978-3-319-68225-9_12 | ||
| 960 | * | ||
| 961 | * In the range 480 - 500 K, we interpolate between the two laws. | ||
| 962 | */ | ||
| 963 | template <class Scalar> | ||
| 964 | 63484715 | Scalar h2oGasViscosityInMixture(Scalar temperature, Scalar pressure) | |
| 965 | { | ||
| 966 |
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63484715 | if (temperature < 480.0) |
| 967 | 63459287 | return Detail::viscosityReid_(temperature); | |
| 968 | |||
| 969 |
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25428 | else if (temperature > 500.0) |
| 970 | 25323 | return Detail::viscosityNagel_(temperature); | |
| 971 | |||
| 972 | else // interpolate | ||
| 973 | { | ||
| 974 | 105 | const Scalar op = (500.0 - temperature)/20.0; | |
| 975 | |||
| 976 | 105 | return op*Detail::viscosityReid_(temperature) | |
| 977 | 105 | + (1.0 - op)*Detail::viscosityNagel_(temperature); | |
| 978 | } | ||
| 979 | } | ||
| 980 | |||
| 981 | } // end namespace Dumux::FluidSystems | ||
| 982 | |||
| 983 | #endif | ||
| 984 |