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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup Components | ||
| 10 | * \brief A simple class for the air fluid properties | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_AIR_HH | ||
| 13 | #define DUMUX_AIR_HH | ||
| 14 | |||
| 15 | #include <dune/common/math.hh> | ||
| 16 | |||
| 17 | #include <dumux/common/exceptions.hh> | ||
| 18 | #include <dumux/material/components/base.hh> | ||
| 19 | #include <dumux/material/components/gas.hh> | ||
| 20 | #include <dumux/material/idealgas.hh> | ||
| 21 | |||
| 22 | namespace Dumux { | ||
| 23 | namespace Components { | ||
| 24 | |||
| 25 | /*! | ||
| 26 | * \ingroup Components | ||
| 27 | * \brief A class for the air fluid properties | ||
| 28 | * | ||
| 29 | * \tparam Scalar The type used for scalar values | ||
| 30 | */ | ||
| 31 | template <class Scalar> | ||
| 32 | class Air | ||
| 33 | : public Components::Base<Scalar, Air<Scalar> > | ||
| 34 | , public Components::Gas<Scalar, Air<Scalar> > | ||
| 35 | { | ||
| 36 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 37 | |||
| 38 | public: | ||
| 39 | /*! | ||
| 40 | * \brief A human readable name for Air. | ||
| 41 | */ | ||
| 42 | static std::string name() | ||
| 43 |
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|
548354 | { return "Air"; } |
| 44 | |||
| 45 | /*! | ||
| 46 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of Air. | ||
| 47 | * | ||
| 48 | * Taken from constrelair.hh. | ||
| 49 | */ | ||
| 50 | static constexpr Scalar molarMass() | ||
| 51 | { return 0.02896; /* [kg/mol] */ } | ||
| 52 | |||
| 53 | /*! | ||
| 54 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of Air. | ||
| 55 | */ | ||
| 56 | static Scalar criticalTemperature() | ||
| 57 | { return 132.6312; /* [K] */ } | ||
| 58 | |||
| 59 | /*! | ||
| 60 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of Air. | ||
| 61 | */ | ||
| 62 | static Scalar criticalPressure() | ||
| 63 | { return 37.86e5; /* [Pa] */ } | ||
| 64 | |||
| 65 | /*! | ||
| 66 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of Air at a given pressure and temperature. | ||
| 67 | * | ||
| 68 | * Ideal gas is assumed. | ||
| 69 | * | ||
| 70 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 71 | * \param pressure pressure of phase in \f$\mathrm{[Pa]}\f$ | ||
| 72 | */ | ||
| 73 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 74 | { | ||
| 75 | // Assume an ideal gas | ||
| 76 | 119985604 | return IdealGas::density(molarMass(), temperature, pressure); | |
| 77 | } | ||
| 78 | |||
| 79 | /*! | ||
| 80 | * \brief The molar density of air in \f$\mathrm{[mol/m^3]}\f$, | ||
| 81 | * depending on pressure and temperature. | ||
| 82 | * \param temperature The temperature of the gas | ||
| 83 | * \param pressure The pressure of the gas | ||
| 84 | */ | ||
| 85 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 86 | 94946988 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 87 | |||
| 88 | /*! | ||
| 89 | * \brief Returns true, the gas phase is assumed to be compressible | ||
| 90 | */ | ||
| 91 | static constexpr bool gasIsCompressible() | ||
| 92 | { return true; } | ||
| 93 | |||
| 94 | /*! | ||
| 95 | * \brief Returns true, the gas phase is assumed to be ideal | ||
| 96 | */ | ||
| 97 | static constexpr bool gasIsIdeal() | ||
| 98 | { return true; } | ||
| 99 | |||
| 100 | /*! | ||
| 101 | * \brief Returns true if the gas phase viscosity is constant | ||
| 102 | */ | ||
| 103 | static constexpr bool gasViscosityIsConstant() | ||
| 104 | { return false; } | ||
| 105 | |||
| 106 | /*! | ||
| 107 | * \brief The pressure \f$\mathrm{[Pa]}\f$ of gaseous Air at a given density and temperature. | ||
| 108 | * | ||
| 109 | * Ideal gas is assumed. | ||
| 110 | * | ||
| 111 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 112 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 113 | */ | ||
| 114 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 115 | { | ||
| 116 | // Assume an ideal gas | ||
| 117 | 40818 | return IdealGas::pressure(temperature, density/molarMass()); | |
| 118 | } | ||
| 119 | |||
| 120 | /*! | ||
| 121 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of Air at a given pressure and temperature. | ||
| 122 | * | ||
| 123 | * Critical specific volume calculated by \f$V_c = (R*T_c)/p_c\f$. | ||
| 124 | * | ||
| 125 | * Reid et al. (1987, pp 396-397, 667) \cite reid1987 <BR> | ||
| 126 | * Poling et al. (2001, pp 9.7-9.8) \cite poling2001 <BR> | ||
| 127 | * | ||
| 128 | * Accentric factor taken from: <BR> | ||
| 129 | * Adebiyi (2003) \cite adebiyi2003 | ||
| 130 | * | ||
| 131 | * air is a non-polar substance, | ||
| 132 | * thus dipole moment mu is zero, as well the dimensionless dipole moment mu_r | ||
| 133 | * therefore not considered below | ||
| 134 | * the same holds for the correction value kappa for highly polar substances | ||
| 135 | * | ||
| 136 | * This calculation was introduced into Dumux in 2012 although the method here | ||
| 137 | * is designed for general polar substances. Air, however, is (a) non-polar, | ||
| 138 | * and (b) there are more precise methods available | ||
| 139 | * | ||
| 140 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 141 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 142 | */ | ||
| 143 | static Scalar oldGasViscosity(Scalar temperature, Scalar pressure) | ||
| 144 | { | ||
| 145 | const Scalar Tc = criticalTemperature(); | ||
| 146 | const Scalar Vc = 84.525138; // critical specific volume [cm^3/mol] | ||
| 147 | const Scalar omega = 0.078; // accentric factor | ||
| 148 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | ||
| 149 | |||
| 150 | const Scalar Fc = 1.0 - 0.2756*omega; | ||
| 151 | const Scalar Tstar = 1.2593*temperature/Tc; | ||
| 152 | |||
| 153 | using std::exp; | ||
| 154 | using std::pow; | ||
| 155 | const Scalar Omega_v = 1.16145*pow(Tstar, -0.14874) | ||
| 156 | + 0.52487*exp(-0.77320*Tstar) | ||
| 157 | + 2.16178*exp(-2.43787*Tstar); | ||
| 158 | |||
| 159 | using std::cbrt; | ||
| 160 | using std::sqrt; | ||
| 161 | const Scalar mu = 40.785 * Fc * sqrt(M * temperature)/(cbrt(Vc * Vc) * Omega_v); | ||
| 162 | |||
| 163 | // conversion from micro poise to Pa s | ||
| 164 | return mu/1.0e6/10.0; | ||
| 165 | } | ||
| 166 | |||
| 167 | /*! | ||
| 168 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of Air at a given pressure and temperature. | ||
| 169 | * | ||
| 170 | * Simple method, already implemented in MUFTE-UG, but pretty accurate. | ||
| 171 | * | ||
| 172 | * The pressure correction is even simpler and developed and tested by | ||
| 173 | * Holger Class in 2016 against the results of the Lemmon and Jacobsen (2004) | ||
| 174 | * approach \cite Lemmon2004a | ||
| 175 | * It shows very reasonable results throughout realistic pressure and | ||
| 176 | * temperature ranges up to several hundred Kelvin and up to 500 bar | ||
| 177 | * | ||
| 178 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 179 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 180 | */ | ||
| 181 | 110271552 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 182 | { | ||
| 183 | // above 1200 K, the function becomes inaccurate | ||
| 184 | // since this should realistically never happen, we can live with it | ||
| 185 | 110271552 | const Scalar tempCelsius = temperature - 273.15; | |
| 186 | 110271552 | const Scalar pressureCorrectionFactor = 9.7115e-9*tempCelsius*tempCelsius - 5.5e-6*tempCelsius + 0.0010809; | |
| 187 | |||
| 188 | using std::sqrt; | ||
| 189 | 220543104 | const Scalar mu = 1.496e-6 * sqrt(temperature * temperature * temperature) / (temperature + 120.0) | |
| 190 | 110271552 | * (1.0 + (pressure/1.0e5 - 1.0)*pressureCorrectionFactor); | |
| 191 | 110271552 | return mu; | |
| 192 | } | ||
| 193 | |||
| 194 | /*! | ||
| 195 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of Air at a given pressure and temperature. | ||
| 196 | * | ||
| 197 | * Simple method, already implemented in MUFTE-UG, but pretty accurate | ||
| 198 | * at atmospheric pressures. | ||
| 199 | * Gas viscosity is not very dependent on pressure. Thus, for | ||
| 200 | * low pressures one might switch the pressure correction off | ||
| 201 | * | ||
| 202 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 203 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 204 | */ | ||
| 205 | static Scalar simpleGasViscosity(Scalar temperature, Scalar pressure) | ||
| 206 | { | ||
| 207 | // above 1200 K, the function becomes inaccurate | ||
| 208 | // since this should realistically never happen, we can live with it | ||
| 209 | using std::sqrt; | ||
| 210 | return 1.496e-6 * sqrt(temperature * temperature * temperature) / (temperature + 120.0); | ||
| 211 | } | ||
| 212 | |||
| 213 | /*! | ||
| 214 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of Air at a given pressure and temperature. | ||
| 215 | * | ||
| 216 | * This is a very exact approach by Lemmon and Jacobsen (2004) \cite Lemmon2004a | ||
| 217 | * All the values and parameters used below are explained in their paper | ||
| 218 | * Since they use ''eta'' for dyn. viscosity, we do it as well for easier | ||
| 219 | * comparison with the paper | ||
| 220 | * | ||
| 221 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 222 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 223 | */ | ||
| 224 | static Scalar exactGasViscosity(Scalar temperature, Scalar pressure) | ||
| 225 | { | ||
| 226 | const Scalar epsk = 103.3; // [K] | ||
| 227 | |||
| 228 | using std::log; | ||
| 229 | using std::exp; | ||
| 230 | using std::sqrt; | ||
| 231 | const Scalar logTstar = log(temperature/epsk); | ||
| 232 | const Scalar Omega = exp(0.431 | ||
| 233 | - 0.4623*logTstar | ||
| 234 | + 0.08406*logTstar*logTstar | ||
| 235 | + 0.005341*logTstar*logTstar*logTstar | ||
| 236 | - 0.00331*logTstar*logTstar*logTstar*logTstar); | ||
| 237 | |||
| 238 | const Scalar sigma = 0.36; // [nm] | ||
| 239 | const Scalar eta0 = 0.0266958*sqrt(1000.0*molarMass()*temperature)/(sigma*sigma*Omega); | ||
| 240 | |||
| 241 | using std::pow; | ||
| 242 | using Dune::power; | ||
| 243 | const Scalar tau = criticalTemperature()/temperature; | ||
| 244 | const Scalar rhoc = 10.4477; // [mol/m^3] | ||
| 245 | const Scalar delta = 0.001*pressure/(temperature*8.3144598)/rhoc; | ||
| 246 | const Scalar etaR = 10.72 * pow(tau, 0.2) * delta | ||
| 247 | + 1.122 * pow(tau, 0.05) * power(delta, 4) | ||
| 248 | + 0.002019 * pow(tau, 2.4) * power(delta, 9) | ||
| 249 | - 8.876 * pow(tau, 0.6) * delta * exp(-delta) | ||
| 250 | - 0.02916 * pow(tau, 3.6) * power(delta, 8) * exp(-delta); | ||
| 251 | |||
| 252 | return (eta0 + etaR)*1e-6; | ||
| 253 | } | ||
| 254 | |||
| 255 | /*! | ||
| 256 | * \brief Specific enthalpy of Air \f$\mathrm{[J/kg]}\f$ | ||
| 257 | * with 273.15 \f$ K \f$ as basis. | ||
| 258 | * | ||
| 259 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 260 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 261 | * | ||
| 262 | * Kays et al. (2005, 431ff) \cite kays2005 <BR> | ||
| 263 | */ | ||
| 264 | static Scalar gasEnthalpy(Scalar temperature, Scalar pressure) | ||
| 265 | { | ||
| 266 | 55187108 | return gasHeatCapacity(temperature, pressure) * (temperature-273.15); | |
| 267 | } | ||
| 268 | |||
| 269 | /*! | ||
| 270 | * \brief Specific internal energy of Air \f$\mathrm{[J/kg]}\f$. | ||
| 271 | * | ||
| 272 | * Definition of enthalpy: \f$h= u + pv = u + p / \rho\f$. | ||
| 273 | * Rearranging for internal energy yields: \f$u = h - pv\f$. | ||
| 274 | * Exploiting the Ideal Gas assumption | ||
| 275 | * (\f$pv = R_{\textnormal{specific}} T\f$) gives: \f$u = h - R / M T \f$. | ||
| 276 | * | ||
| 277 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 278 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 279 | */ | ||
| 280 | static const Scalar gasInternalEnergy(Scalar temperature, | ||
| 281 | Scalar pressure) | ||
| 282 | { | ||
| 283 | return gasEnthalpy(temperature, pressure) | ||
| 284 | - IdealGas::R * temperature // = pressure * molar volume for an ideal gas | ||
| 285 | / molarMass(); // conversion from [J/(mol K)] to [J/(kg K)] | ||
| 286 | } | ||
| 287 | |||
| 288 | /*! | ||
| 289 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure | ||
| 290 | * air. | ||
| 291 | * | ||
| 292 | * This methods uses the formula for "zero-pressure" heat capacity that | ||
| 293 | * is only dependent on temperature, because the pressure dependence is rather small. | ||
| 294 | * This one should be accurate for a pressure of 1 atm. | ||
| 295 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 296 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 297 | * | ||
| 298 | * Values taken from Hollis (1996) \cite hollis1996 <BR> | ||
| 299 | * "Tables of Thermal Properties of Gases" | ||
| 300 | */ | ||
| 301 | 123124980 | static const Scalar gasHeatCapacity(Scalar temperature, | |
| 302 | Scalar pressure) | ||
| 303 | { | ||
| 304 | // scale temperature with reference temp of 100K | ||
| 305 | 123124980 | Scalar phi = temperature/100; | |
| 306 | |||
| 307 | using std::pow; | ||
| 308 | using Dune::power; | ||
| 309 | 123124980 | Scalar c_p = 0.661738E+01 | |
| 310 | 123124980 | -0.105885E+01 * phi | |
| 311 | 123124980 | +0.201650E+00 * power(phi,2) | |
| 312 | 123124980 | -0.196930E-01 * power(phi,3) | |
| 313 | 123124980 | +0.106460E-02 * power(phi,4) | |
| 314 | 123124980 | -0.303284E-04 * power(phi,5) | |
| 315 | 123124980 | +0.355861E-06 * power(phi,6); | |
| 316 | 123124980 | c_p += -0.549169E+01 * power(phi,-1) | |
| 317 | 123124980 | +0.585171E+01 * power(phi,-2) | |
| 318 | 123124980 | -0.372865E+01 * power(phi,-3) | |
| 319 | 123124980 | +0.133981E+01 * power(phi,-4) | |
| 320 | 123124980 | -0.233758E+00 * power(phi,-5) | |
| 321 | 123124980 | +0.125718E-01 * power(phi,-6); | |
| 322 | 123124980 | c_p *= IdealGas::R / molarMass(); // in J/(mol*K) / (kg/mol) | |
| 323 | |||
| 324 | 123124980 | return c_p; | |
| 325 | } | ||
| 326 | |||
| 327 | /*! | ||
| 328 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of air. | ||
| 329 | * | ||
| 330 | * Isobaric Properties for Nitrogen in: NIST Standard \cite NIST <BR> | ||
| 331 | * evaluated at p=.1 MPa, T=20°C <BR> | ||
| 332 | * Nitrogen: 0.025398 <BR> | ||
| 333 | * Oxygen: 0.026105 <BR> | ||
| 334 | * lambda_air is approximately 0.78*lambda_N2+0.22*lambda_O2 | ||
| 335 | * | ||
| 336 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 337 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 338 | */ | ||
| 339 | ✗ | static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 340 | { | ||
| 341 | ✗ | return 0.0255535; | |
| 342 | } | ||
| 343 | }; | ||
| 344 | |||
| 345 | } // end namespace Components | ||
| 346 | } // end namespace Dumux | ||
| 347 | |||
| 348 | #endif | ||
| 349 |