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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 IAPWS | ||
| 10 | * \brief Implements the equations for region 1 of the IAPWS '97 formulation. | ||
| 11 | * See: | ||
| 12 | * | ||
| 13 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 14 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 15 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 16 | */ | ||
| 17 | #ifndef DUMUX_IAPWS_REGION1_HH | ||
| 18 | #define DUMUX_IAPWS_REGION1_HH | ||
| 19 | |||
| 20 | #include <cmath> | ||
| 21 | #include <iostream> | ||
| 22 | #include <dumux/common/exceptions.hh> | ||
| 23 | |||
| 24 | namespace Dumux { | ||
| 25 | namespace IAPWS { | ||
| 26 | /*! | ||
| 27 | * \ingroup IAPWS | ||
| 28 | * \brief Implements the equations for region 1 of the IAPWS '97 formulation. | ||
| 29 | * \tparam Scalar The type used for scalar values | ||
| 30 | * See: | ||
| 31 | * | ||
| 32 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 33 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 34 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 35 | */ | ||
| 36 | template <class Scalar> | ||
| 37 | class Region1 | ||
| 38 | { | ||
| 39 | public: | ||
| 40 | /*! | ||
| 41 | * \brief Returns true if IAPWS region 1 applies for a | ||
| 42 | * (temperature in \f$\mathrm{[K]}\f$, pressure in \f$\mathrm{[Pa]}\f$) pair. | ||
| 43 | * | ||
| 44 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 45 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 46 | * \param propertyName the name for which property the check is performed | ||
| 47 | */ | ||
| 48 | 161417718 | static void checkValidityRange(Scalar temperature, Scalar pressure, | |
| 49 | const std::string& propertyName = "This property") | ||
| 50 | { | ||
| 51 | // actually this is: | ||
| 52 | /* 273.15 <= temperature && | ||
| 53 | temperature <= 623.15 && | ||
| 54 | pressure >= vaporPressure(temperature) && | ||
| 55 | pressure <= 100e6 */ | ||
| 56 |
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161417718 | if (temperature <= 623.15 && pressure <= 100e6) |
| 57 | 161417712 | return; | |
| 58 | |||
| 59 |
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161417736 | DUNE_THROW(NumericalProblem, |
| 60 | propertyName << " of water is only implemented for temperatures below 623.15K and " | ||
| 61 | "pressures below 100MPa. (T=" << temperature << ", p=" << pressure << ")"); | ||
| 62 | } | ||
| 63 | |||
| 64 | /*! | ||
| 65 | * \brief Returns the reduced temperature for IAPWS region 1. | ||
| 66 | * | ||
| 67 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 68 | */ | ||
| 69 | 174645782 | static constexpr Scalar tau(Scalar temperature) | |
| 70 | 13957193 | { return 1386.0 / temperature; } | |
| 71 | |||
| 72 | /*! | ||
| 73 | * \brief Returns the derivative of the reduced temperature to the | ||
| 74 | * temperature for IAPWS region 1 in \f$\mathrm{[1/K]}\f$. | ||
| 75 | * | ||
| 76 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 77 | */ | ||
| 78 | static constexpr Scalar dTau_dt(Scalar temperature) | ||
| 79 | { return - 1386.0 / (temperature*temperature); } | ||
| 80 | |||
| 81 | /*! | ||
| 82 | * \brief Returns the reduced pressure for IAPWS region 1. | ||
| 83 | * | ||
| 84 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 85 | */ | ||
| 86 | 322090812 | static constexpr Scalar pi(Scalar pressure) | |
| 87 | 148605625 | { return pressure / 16.53e6; } | |
| 88 | |||
| 89 | /*! | ||
| 90 | * \brief Returns the derivative of the reduced pressure to the | ||
| 91 | * pressure for IAPWS region 1 in \f$\mathrm{[1/Pa]}\f$. | ||
| 92 | * | ||
| 93 | * \param pressure temperature of component in \f$\mathrm{[Pa]}\f$ | ||
| 94 | */ | ||
| 95 | static constexpr Scalar dPi_dp(Scalar pressure) | ||
| 96 | { return 1.0 / 16.53e6; } | ||
| 97 | |||
| 98 | /*! | ||
| 99 | * \brief Returns the derivative of the pressure to the | ||
| 100 | * reduced pressure for IAPWS region 1 in \f$\mathrm{[Pa]}\f$. | ||
| 101 | * | ||
| 102 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 103 | */ | ||
| 104 | static constexpr Scalar dp_dPi(Scalar pressure) | ||
| 105 | { return 16.53e6; } | ||
| 106 | |||
| 107 | /*! | ||
| 108 | * \brief The Gibbs free energy (dimensionless) for IAPWS region 1 (i.e. liquid) | ||
| 109 | * | ||
| 110 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 111 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 112 | * | ||
| 113 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 114 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 115 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 116 | */ | ||
| 117 | static Scalar gamma(Scalar temperature, Scalar pressure) | ||
| 118 | { | ||
| 119 | Scalar tau_ = tau(temperature); /* reduced temperature */ | ||
| 120 | Scalar pi_ = pi(pressure); /* reduced pressure */ | ||
| 121 | |||
| 122 | Scalar result = 0; | ||
| 123 | for (int i = 0; i < 34; ++i) { | ||
| 124 | result += n(i)*pow(7.1 - pi_, I(i))*pow(tau_ - 1.222, J(i)); | ||
| 125 | } | ||
| 126 | |||
| 127 | return result; | ||
| 128 | } | ||
| 129 | |||
| 130 | |||
| 131 | /*! | ||
| 132 | * \brief The partial derivative of the Gibbs free energy to the | ||
| 133 | * normalized temperature for IAPWS region 1 (i.e. liquid) (dimensionless). | ||
| 134 | * | ||
| 135 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 136 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 137 | * | ||
| 138 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 139 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 140 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 141 | */ | ||
| 142 | 6213116 | static Scalar dGamma_dTau(Scalar temperature, Scalar pressure) | |
| 143 | { | ||
| 144 | 6213116 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 145 | 6213116 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 146 | |||
| 147 | using std::pow; | ||
| 148 | 6213116 | Scalar result = 0.0; | |
| 149 |
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217459060 | for (int i = 0; i < 34; i++) { |
| 150 | 211245944 | result += n(i) * | |
| 151 | 211245944 | pow(7.1 - pi_, I(i)) * | |
| 152 | 211245944 | pow(tau_ - 1.222, J(i)-1) * | |
| 153 | J(i); | ||
| 154 | } | ||
| 155 | |||
| 156 | 6213116 | return result; | |
| 157 | } | ||
| 158 | |||
| 159 | /*! | ||
| 160 | * \brief The partial derivative of the Gibbs free energy to the | ||
| 161 | * normalized pressure for IAPWS region 1 (i.e. liquid) dimensionless). | ||
| 162 | * | ||
| 163 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 164 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 165 | * | ||
| 166 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 167 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 168 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 169 | */ | ||
| 170 | 156484129 | static Scalar dGamma_dPi(Scalar temperature, Scalar pressure) | |
| 171 | { | ||
| 172 | 156484129 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 173 | 156484129 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 174 | |||
| 175 | using std::pow; | ||
| 176 | 156484129 | Scalar result = 0.0; | |
| 177 |
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5476944515 | for (int i = 0; i < 34; i++) { |
| 178 | 5320460386 | result += -n(i) * | |
| 179 | 5320460386 | I(i) * | |
| 180 | 5320460386 | pow(7.1 - pi_, I(i) - 1) * | |
| 181 | 5320460386 | pow(tau_ - 1.222, J(i)); | |
| 182 | } | ||
| 183 | |||
| 184 | 156484129 | return result; | |
| 185 | } | ||
| 186 | |||
| 187 | /*! | ||
| 188 | * \brief The partial derivative of the Gibbs free energy to the | ||
| 189 | * normalized pressure and to the normalized temperature | ||
| 190 | * for IAPWS region 1 (i.e. liquid water) (dimensionless). | ||
| 191 | * | ||
| 192 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 193 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 194 | * | ||
| 195 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 196 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 197 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 198 | */ | ||
| 199 | 83455 | static Scalar ddGamma_dTaudPi(Scalar temperature, Scalar pressure) | |
| 200 | { | ||
| 201 | 83455 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 202 | 83455 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 203 | |||
| 204 | using std::pow; | ||
| 205 | 83455 | Scalar result = 0.0; | |
| 206 |
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2920925 | for (int i = 0; i < 34; i++) { |
| 207 | 2837470 | result += -n(i) * | |
| 208 | 2837470 | I(i) * | |
| 209 | 2837470 | J(i) * | |
| 210 | 2837470 | pow(7.1 - pi_, I(i) - 1) * | |
| 211 | 2837470 | pow(tau_ - 1.222, J(i) - 1); | |
| 212 | } | ||
| 213 | |||
| 214 | 83455 | return result; | |
| 215 | } | ||
| 216 | |||
| 217 | /*! | ||
| 218 | * \brief The second partial derivative of the Gibbs free energy | ||
| 219 | * to the normalized pressure for IAPWS region 1 | ||
| 220 | * (i.e. liquid water) (dimensionless). | ||
| 221 | * | ||
| 222 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 223 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 224 | * | ||
| 225 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 226 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 227 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 228 | */ | ||
| 229 | static Scalar ddGamma_ddPi(Scalar temperature, Scalar pressure) | ||
| 230 | { | ||
| 231 | Scalar tau_ = tau(temperature); /* reduced temperature */ | ||
| 232 | Scalar pi_ = pi(pressure); /* reduced pressure */ | ||
| 233 | |||
| 234 | using std::pow; | ||
| 235 | Scalar result = 0.0; | ||
| 236 | for (int i = 0; i < 34; i++) { | ||
| 237 | result += n(i) * | ||
| 238 | I(i) * | ||
| 239 | (I(i) - 1) * | ||
| 240 | pow(7.1 - pi_, I(i) - 2) * | ||
| 241 | pow(tau_ - 1.222, J(i)); | ||
| 242 | } | ||
| 243 | |||
| 244 | return result; | ||
| 245 | } | ||
| 246 | |||
| 247 | /*! | ||
| 248 | * \brief The second partial derivative of the Gibbs free energy to the | ||
| 249 | * normalized temperature for IAPWS region 1 (i.e. liquid) (dimensionless). | ||
| 250 | * | ||
| 251 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 252 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 253 | * | ||
| 254 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 255 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 256 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 257 | */ | ||
| 258 | 2825983 | static Scalar ddGamma_ddTau(Scalar temperature, Scalar pressure) | |
| 259 | { | ||
| 260 | 2825983 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 261 | 2825983 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 262 | |||
| 263 | using std::pow; | ||
| 264 | 2825983 | Scalar result = 0.0; | |
| 265 |
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98909405 | for (int i = 0; i < 34; i++) { |
| 266 | 96083422 | result += n(i) * | |
| 267 | 96083422 | pow(7.1 - pi_, I(i)) * | |
| 268 | 96083422 | J(i) * | |
| 269 | 96083422 | (J(i) - 1) * | |
| 270 | 96083422 | pow(tau_ - 1.222, J(i) - 2); | |
| 271 | } | ||
| 272 | |||
| 273 | 2825983 | return result; | |
| 274 | } | ||
| 275 | |||
| 276 | private: | ||
| 277 | 5630627222 | static Scalar n(int i) | |
| 278 | { | ||
| 279 | 5630627222 | constexpr Scalar n[34] = { | |
| 280 | 0.14632971213167, -0.84548187169114, -0.37563603672040e1, | ||
| 281 | 0.33855169168385e1, -0.95791963387872, 0.15772038513228, | ||
| 282 | -0.16616417199501e-1, 0.81214629983568e-3, 0.28319080123804e-3, | ||
| 283 | -0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1, | ||
| 284 | -0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3, | ||
| 285 | -0.30001780793026e-3, 0.47661393906987e-4, -0.44141845330846e-5, | ||
| 286 | -0.72694996297594e-15,-0.31679644845054e-4, -0.28270797985312e-5, | ||
| 287 | -0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6, | ||
| 288 | -0.14341729937924e-12,-0.40516996860117e-6, -0.12734301741641e-8, | ||
| 289 | -0.17424871230634e-9, -0.68762131295531e-18, 0.14478307828521e-19, | ||
| 290 | 0.26335781662795e-22,-0.11947622640071e-22, 0.18228094581404e-23, | ||
| 291 | -0.93537087292458e-25 | ||
| 292 | }; | ||
| 293 | 5630627222 | return n[i]; | |
| 294 | } | ||
| 295 | |||
| 296 | 5630627222 | static short int I(int i) | |
| 297 | { | ||
| 298 | 5630627222 | constexpr short int I[34] = { | |
| 299 | 0, 0, 0, | ||
| 300 | 0, 0, 0, | ||
| 301 | 0, 0, 1, | ||
| 302 | 1, 1, 1, | ||
| 303 | 1, 1, 2, | ||
| 304 | 2, 2, 2, | ||
| 305 | 2, 3, 3, | ||
| 306 | 3, 4, 4, | ||
| 307 | 4, 5, 8, | ||
| 308 | 8, 21, 23, | ||
| 309 | 29, 30, 31, | ||
| 310 | 32 | ||
| 311 | }; | ||
| 312 | 5630627222 | return I[i]; | |
| 313 | } | ||
| 314 | |||
| 315 | 5630627222 | static short int J(int i) | |
| 316 | { | ||
| 317 | 5630627222 | constexpr short int J[34] = { | |
| 318 | -2, -1, 0, | ||
| 319 | 1, 2, 3, | ||
| 320 | 4, 5, -9, | ||
| 321 | -7, -1, 0, | ||
| 322 | 1, 3, -3, | ||
| 323 | 0, 1, 3, | ||
| 324 | 17, -4, 0, | ||
| 325 | 6, -5, -2, | ||
| 326 | 10, -8, -11, | ||
| 327 | -6, -29, -31, | ||
| 328 | -38, -39, -40, | ||
| 329 | -41 | ||
| 330 | }; | ||
| 331 | 5630627222 | return J[i]; | |
| 332 | } | ||
| 333 | |||
| 334 | }; | ||
| 335 | |||
| 336 | } // end namespace IAPWS | ||
| 337 | } // end namespace Dumux | ||
| 338 | |||
| 339 | #endif | ||
| 340 |