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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 IAPWS | ||
| 11 | * \brief Implements the equations for region 2 of the IAPWS '97 formulation. | ||
| 12 | * See: | ||
| 13 | * | ||
| 14 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 15 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 16 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 17 | */ | ||
| 18 | #ifndef DUMUX_IAPWS_REGION2_HH | ||
| 19 | #define DUMUX_IAPWS_REGION2_HH | ||
| 20 | |||
| 21 | #include <cmath> | ||
| 22 | #include <iostream> | ||
| 23 | #include <dumux/common/exceptions.hh> | ||
| 24 | |||
| 25 | namespace Dumux { | ||
| 26 | namespace IAPWS { | ||
| 27 | |||
| 28 | /*! | ||
| 29 | * \ingroup IAPWS | ||
| 30 | * \brief Implements the equations for region 2 of the IAPWS '97 formulation. | ||
| 31 | * \tparam Scalar The type used for scalar values | ||
| 32 | * See: | ||
| 33 | * | ||
| 34 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 35 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 36 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 37 | */ | ||
| 38 | template <class Scalar> | ||
| 39 | class Region2 | ||
| 40 | { | ||
| 41 | public: | ||
| 42 | /*! | ||
| 43 | * \brief Returns true if IAPWS region 2 applies for a | ||
| 44 | * (temperature, pressure) pair. | ||
| 45 | * | ||
| 46 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 47 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 48 | * \param propertyName the name for which property the check is performed | ||
| 49 | */ | ||
| 50 | 51730968 | static void checkValidityRange(Scalar temperature, Scalar pressure, | |
| 51 | const std::string& propertyName = "This property") | ||
| 52 | { | ||
| 53 | // actually this is: | ||
| 54 | /* (273.15 <= temperature && temperature <= 623.15 && pressure <= vaporPressure(temperature)) || | ||
| 55 | (623.15 < temperature && temperature <= 863.15 && pressure <= auxPressure(temperature)) || | ||
| 56 | (863.15 < temperature && temperature <= 1073.15 && pressure < 100e6); */ | ||
| 57 |
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51730968 | if ((temperature <= 623.15 && pressure <= 100e6) || |
| 58 | ✗ | (temperature > 623.15 && temperature <= 1073.15 && pressure <= 16.532e6 )) | |
| 59 | 51730968 | return; | |
| 60 | |||
| 61 | ✗ | DUNE_THROW(NumericalProblem, | |
| 62 | propertyName << " of steam is only implemented for temperatures below 623.15K and " | ||
| 63 | "pressures below 100MPa. (T=" << temperature << ", p=" << pressure << ")"); | ||
| 64 | } | ||
| 65 | |||
| 66 | /*! | ||
| 67 | * \brief Returns the reduced temperature (dimensionless) for IAPWS region 2. | ||
| 68 | * | ||
| 69 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 70 | */ | ||
| 71 | static constexpr Scalar tau(Scalar temperature) | ||
| 72 | 11226290 | { return 540.0 / temperature; } | |
| 73 | |||
| 74 | /*! | ||
| 75 | * \brief Returns the derivative of the reduced temperature to the | ||
| 76 | * temperature for IAPWS region 2. | ||
| 77 | * | ||
| 78 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 79 | */ | ||
| 80 | static constexpr Scalar dTau_dt(Scalar temperature) | ||
| 81 | { return - 540.0 / (temperature*temperature); } | ||
| 82 | |||
| 83 | /*! | ||
| 84 | * \brief Returns the reduced pressure (dimensionless) for IAPWS region 2. | ||
| 85 | * | ||
| 86 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 87 | */ | ||
| 88 | static constexpr Scalar pi(Scalar pressure) | ||
| 89 | 41842888 | { return pressure / 1e6; } | |
| 90 | |||
| 91 | /*! | ||
| 92 | * \brief Returns the derivative of the reduced pressure to the | ||
| 93 | * pressure for IAPWS region 2 in \f$\mathrm{[1/Pa]}\f$. | ||
| 94 | * | ||
| 95 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 96 | */ | ||
| 97 | ✗ | static constexpr Scalar dPi_dp(Scalar pressure) | |
| 98 | ✗ | { return 1.0 / 1e6; } | |
| 99 | |||
| 100 | /*! | ||
| 101 | * \brief Returns the derivative of the pressure to the | ||
| 102 | * reduced pressure for IAPWS region 2 (dimensionless). | ||
| 103 | * | ||
| 104 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 105 | */ | ||
| 106 | static constexpr Scalar dp_dPi(Scalar pressure) | ||
| 107 | { return 1e6; } | ||
| 108 | |||
| 109 | /*! | ||
| 110 | * \brief The Gibbs free energy for IAPWS region 2 (i.e. sub-critical | ||
| 111 | * steam) (dimensionless). | ||
| 112 | * | ||
| 113 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 114 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 115 | * | ||
| 116 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 117 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 118 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 119 | */ | ||
| 120 | static Scalar gamma(Scalar temperature, Scalar pressure) | ||
| 121 | { | ||
| 122 | Scalar tau = tau(temperature); /* reduced temperature */ | ||
| 123 | Scalar pi = pi(pressure); /* reduced pressure */ | ||
| 124 | |||
| 125 | Scalar result; | ||
| 126 | |||
| 127 | // ideal gas part | ||
| 128 | using std::pow; | ||
| 129 | result = ln(pi); | ||
| 130 | for (int i = 0; i < 9; ++i) | ||
| 131 | result += n_g(i)*pow(tau, J_g(i)); | ||
| 132 | |||
| 133 | // residual part | ||
| 134 | for (int i = 0; i < 43; ++i) | ||
| 135 | result += n_r(i)* | ||
| 136 | pow(pi, I_r(i))* | ||
| 137 | pow(tau - 0.5, J_r(i)); | ||
| 138 | return result; | ||
| 139 | } | ||
| 140 | |||
| 141 | /*! | ||
| 142 | * \brief The partial derivative of the Gibbs free energy to the | ||
| 143 | * normalized temperature for IAPWS region 2 (i.e. sub-critical | ||
| 144 | * steam) dimensionless). | ||
| 145 | * | ||
| 146 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 147 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 148 | * | ||
| 149 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 150 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 151 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 152 | */ | ||
| 153 | 3524827 | static Scalar dGamma_dTau(Scalar temperature, Scalar pressure) | |
| 154 | { | ||
| 155 | 7049654 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 156 | 7049654 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 157 | |||
| 158 | // ideal gas part | ||
| 159 | using std::pow; | ||
| 160 | 3524827 | Scalar result = 0; | |
| 161 |
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35248270 | for (int i = 0; i < 9; i++) { |
| 162 | 126893772 | result += n_g(i) * | |
| 163 | 95170329 | J_g(i) * | |
| 164 | 63446886 | pow(tau_, J_g(i) - 1); | |
| 165 | } | ||
| 166 | |||
| 167 | // residual part | ||
| 168 |
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155092388 | for (int i = 0; i < 43; i++) { |
| 169 | 454702683 | result += n_r(i) * | |
| 170 | 303135122 | pow(pi_, I_r(i)) * | |
| 171 | 303135122 | J_r(i) * | |
| 172 | 151567561 | pow(tau_ - 0.5, J_r(i) - 1); | |
| 173 | } | ||
| 174 | |||
| 175 | 3524827 | return result; | |
| 176 | } | ||
| 177 | |||
| 178 | /*! | ||
| 179 | * \brief The partial derivative of the Gibbs free energy to the | ||
| 180 | * normalized pressure for IAPWS region 2 (i.e. sub-critical | ||
| 181 | * steam) (dimensionless). | ||
| 182 | * | ||
| 183 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 184 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 185 | * | ||
| 186 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 187 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 188 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 189 | */ | ||
| 190 | 48769579 | static Scalar dGamma_dPi(Scalar temperature, Scalar pressure) | |
| 191 | { | ||
| 192 | 97539158 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 193 | 97539158 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 194 | |||
| 195 | // ideal gas part | ||
| 196 | 48769579 | Scalar result = 1/pi_; | |
| 197 | |||
| 198 | // residual part | ||
| 199 | using std::pow; | ||
| 200 |
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2145861476 | for (int i = 0; i < 43; i++) { |
| 201 | 6291275691 | result += n_r(i) * | |
| 202 | 4194183794 | I_r(i) * | |
| 203 | 4194183794 | pow(pi_, I_r(i) - 1) * | |
| 204 | 2097091897 | pow(tau_ - 0.5, J_r(i)); | |
| 205 | } | ||
| 206 | |||
| 207 | 48769579 | return result; | |
| 208 | } | ||
| 209 | |||
| 210 | /*! | ||
| 211 | * \brief The partial derivative of the Gibbs free energy to the | ||
| 212 | * normalized pressure and to the normalized temperature | ||
| 213 | * for IAPWS region 2 (i.e. sub-critical steam) (dimensionless). | ||
| 214 | * | ||
| 215 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 216 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 217 | * | ||
| 218 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 219 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 220 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 221 | */ | ||
| 222 | 677612 | static Scalar ddGamma_dTaudPi(Scalar temperature, Scalar pressure) | |
| 223 | { | ||
| 224 | 1355224 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 225 | 1355224 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 226 | |||
| 227 | // ideal gas part | ||
| 228 | 677612 | Scalar result = 0; | |
| 229 | |||
| 230 | // residual part | ||
| 231 | using std::pow; | ||
| 232 |
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29814928 | for (int i = 0; i < 43; i++) { |
| 233 | 87411948 | result += n_r(i) * | |
| 234 | 58274632 | I_r(i) * | |
| 235 | 58274632 | J_r(i) * | |
| 236 | 58274632 | pow(pi_, I_r(i) - 1) * | |
| 237 | 29137316 | pow(tau_ - 0.5, J_r(i) - 1); | |
| 238 | } | ||
| 239 | |||
| 240 | 677612 | return result; | |
| 241 | } | ||
| 242 | |||
| 243 | /*! | ||
| 244 | * \brief The second partial derivative of the Gibbs free energy | ||
| 245 | * to the normalized pressure for IAPWS region 2 | ||
| 246 | * (i.e. sub-critical steam) (dimensionless). | ||
| 247 | * | ||
| 248 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 249 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 250 | * | ||
| 251 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 252 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 253 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 254 | */ | ||
| 255 | static Scalar ddGamma_ddPi(Scalar temperature, Scalar pressure) | ||
| 256 | { | ||
| 257 | Scalar tau_ = tau(temperature); /* reduced temperature */ | ||
| 258 | Scalar pi_ = pi(pressure); /* reduced pressure */ | ||
| 259 | |||
| 260 | // ideal gas part | ||
| 261 | Scalar result = -1/(pi_*pi_); | ||
| 262 | |||
| 263 | // residual part | ||
| 264 | using std::pow; | ||
| 265 | for (int i = 0; i < 43; i++) { | ||
| 266 | result += n_r(i) * | ||
| 267 | I_r(i) * | ||
| 268 | (I_r(i) - 1) * | ||
| 269 | pow(pi_, I_r(i) - 2) * | ||
| 270 | pow(tau_ - 0.5, J_r(i)); | ||
| 271 | } | ||
| 272 | |||
| 273 | return result; | ||
| 274 | } | ||
| 275 | |||
| 276 | /*! | ||
| 277 | * \brief The second partial derivative of the Gibbs free energy to the | ||
| 278 | * normalized temperature for IAPWS region 2 (i.e. sub-critical | ||
| 279 | * steam) (dimensionless). | ||
| 280 | * | ||
| 281 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 282 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 283 | * | ||
| 284 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 285 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 286 | * http://www.iapws.org/relguide/IF97-Rev.pdf | ||
| 287 | */ | ||
| 288 | 2805615 | static Scalar ddGamma_ddTau(Scalar temperature, Scalar pressure) | |
| 289 | { | ||
| 290 | 5611230 | Scalar tau_ = tau(temperature); /* reduced temperature */ | |
| 291 | 5611230 | Scalar pi_ = pi(pressure); /* reduced pressure */ | |
| 292 | |||
| 293 | // ideal gas part | ||
| 294 | using std::pow; | ||
| 295 | 2805615 | Scalar result = 0; | |
| 296 |
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28056150 | for (int i = 0; i < 9; i++) { |
| 297 | 101002140 | result += n_g(i) * | |
| 298 | 75751605 | J_g(i) * | |
| 299 | 75751605 | (J_g(i) - 1) * | |
| 300 | 50501070 | pow(tau_, J_g(i) - 2); | |
| 301 | } | ||
| 302 | |||
| 303 | // residual part | ||
| 304 | using std::pow; | ||
| 305 |
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123447060 | for (int i = 0; i < 43; i++) { |
| 306 | 361924335 | result += n_r(i) * | |
| 307 | 241282890 | pow(pi_, I_r(i)) * | |
| 308 | 241282890 | J_r(i) * | |
| 309 | 241282890 | (J_r(i) - 1.) * | |
| 310 | 120641445 | pow(tau_ - 0.5, J_r(i) - 2.); | |
| 311 | } | ||
| 312 | |||
| 313 | 2805615 | return result; | |
| 314 | } | ||
| 315 | |||
| 316 | private: | ||
| 317 | static Scalar n_g(int i) | ||
| 318 | { | ||
| 319 | 56973978 | constexpr const Scalar n[9] = { | |
| 320 | -0.96927686500217e1, 0.10086655968018e2, -0.56087911283020e-2, | ||
| 321 | 0.71452738081455e-1, -0.40710498223928, 0.14240819171444e1, | ||
| 322 | -0.43839511319450e1, -0.28408632460772, 0.21268463753307e-1 | ||
| 323 | }; | ||
| 324 | 56973978 | return n[i]; | |
| 325 | } | ||
| 326 | |||
| 327 | 2398438219 | static Scalar n_r(int i) | |
| 328 | { | ||
| 329 | 2398438219 | constexpr const Scalar n[43] = { | |
| 330 | -0.17731742473213e-2, -0.17834862292358e-1, -0.45996013696365e-1, | ||
| 331 | -0.57581259083432e-1, -0.50325278727930e-1, -0.33032641670203e-4, | ||
| 332 | -0.18948987516315e-3, -0.39392777243355e-2, -0.43797295650573e-1, | ||
| 333 | -0.26674547914087e-4, 0.20481737692309e-7, 0.43870667284435e-6, | ||
| 334 | -0.32277677238570e-4, -0.15033924542148e-2, -0.40668253562649e-1, | ||
| 335 | -0.78847309559367e-9, 0.12790717852285e-7, 0.48225372718507e-6, | ||
| 336 | 0.22922076337661e-5, -0.16714766451061e-10, -0.21171472321355e-2, | ||
| 337 | -0.23895741934104e2, -0.59059564324270e-17, -0.12621808899101e-5, | ||
| 338 | -0.38946842435739e-1, 0.11256211360459e-10, -0.82311340897998e1, | ||
| 339 | 0.19809712802088e-7, 0.10406965210174e-18, -0.10234747095929e-12, | ||
| 340 | -0.10018179379511e-8, -0.80882908646985e-10, 0.10693031879409, | ||
| 341 | -0.33662250574171, 0.89185845355421e-24, 0.30629316876232e-12, | ||
| 342 | -0.42002467698208e-5, -0.59056029685639e-25, 0.37826947613457e-5, | ||
| 343 | -0.12768608934681e-14, 0.73087610595061e-28, 0.55414715350778e-16, | ||
| 344 | -0.94369707241210e-6 | ||
| 345 | }; | ||
| 346 | 2398438219 | return n[i]; | |
| 347 | } | ||
| 348 | |||
| 349 | 2398438219 | static Scalar I_r(int i) | |
| 350 | { | ||
| 351 | 2398438219 | constexpr const short int I[43] = { | |
| 352 | 1, 1, 1, | ||
| 353 | 1, 1, 2, | ||
| 354 | 2, 2, 2, | ||
| 355 | 2, 3, 3, | ||
| 356 | 3, 3, 3, | ||
| 357 | 4, 4, 4, | ||
| 358 | 5, 6, 6, | ||
| 359 | 6, 7, 7, | ||
| 360 | 7, 8, 8, | ||
| 361 | 9, 10, 10, | ||
| 362 | 10, 16, 16, | ||
| 363 | 18, 20, 20, | ||
| 364 | 20, 21, 22, | ||
| 365 | 23, 24, 24, | ||
| 366 | 24 | ||
| 367 | }; | ||
| 368 | 2398438219 | return I[i]; | |
| 369 | } | ||
| 370 | |||
| 371 | static Scalar J_g(int i) | ||
| 372 | { | ||
| 373 | 139198491 | constexpr const short int J[9] = { | |
| 374 | 0, 1, -5, | ||
| 375 | -4, -3, -2, | ||
| 376 | -1, 2, 3 | ||
| 377 | }; | ||
| 378 | 56973978 | return J[i]; | |
| 379 | } | ||
| 380 | |||
| 381 | 2427575535 | static Scalar J_r(int i) | |
| 382 | { | ||
| 383 | 2427575535 | constexpr const short int J[43] = { | |
| 384 | 0, 1, 2, | ||
| 385 | 3, 6, 1, | ||
| 386 | 2, 4, 7, | ||
| 387 | 36, 0, 1, | ||
| 388 | 3, 6, 35, | ||
| 389 | 1, 2, 3, | ||
| 390 | 7, 3, 16, | ||
| 391 | 35, 0, 11, | ||
| 392 | 25, 8, 36, | ||
| 393 | 13, 4, 10, | ||
| 394 | 14, 29, 50, | ||
| 395 | 57, 20, 35, | ||
| 396 | 48, 21, 53, | ||
| 397 | 39, 26, 40, | ||
| 398 | 58 | ||
| 399 | }; | ||
| 400 | 2427575535 | return J[i]; | |
| 401 | } | ||
| 402 | |||
| 403 | }; | ||
| 404 | |||
| 405 | } // end namespace IAPWS | ||
| 406 | } // end namespace Dumux | ||
| 407 | |||
| 408 | #endif | ||
| 409 |