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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 Properties of pure molecular oxygen \f$O_2\f$. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_O2_HH | ||
| 13 | #define DUMUX_O2_HH | ||
| 14 | |||
| 15 | #include <dumux/material/idealgas.hh> | ||
| 16 | |||
| 17 | #include <cmath> | ||
| 18 | |||
| 19 | #include <dumux/material/components/base.hh> | ||
| 20 | #include <dumux/material/components/gas.hh> | ||
| 21 | #include <dumux/material/components/shomate.hh> | ||
| 22 | |||
| 23 | namespace Dumux { | ||
| 24 | namespace Components { | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup Components | ||
| 28 | * \brief Properties of pure molecular oxygen \f$O_2\f$. | ||
| 29 | * | ||
| 30 | * \tparam Scalar The type used for scalar values | ||
| 31 | */ | ||
| 32 | template <class Scalar> | ||
| 33 | class O2 | ||
| 34 | : public Components::Base<Scalar, O2<Scalar> > | ||
| 35 | , public Components::Gas<Scalar, O2<Scalar> > | ||
| 36 | { | ||
| 37 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 38 | using ShomateMethod = Dumux::ShomateMethod<Scalar, 3>; // three regions | ||
| 39 | |||
| 40 | public: | ||
| 41 | static const ShomateMethod shomateMethod; | ||
| 42 | |||
| 43 | /*! | ||
| 44 | * \brief A human readable name for the \f$O_2\f$. | ||
| 45 | */ | ||
| 46 | static std::string name() | ||
| 47 |
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34 | { return "O2"; } |
| 48 | |||
| 49 | /*! | ||
| 50 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular oxygen. | ||
| 51 | */ | ||
| 52 | static constexpr Scalar molarMass() | ||
| 53 | { return 32e-3; } | ||
| 54 | |||
| 55 | /*! | ||
| 56 | * \brief Returns the critical temperature in \f$\mathrm{[K]}\f$ of molecular oxygen. | ||
| 57 | */ | ||
| 58 | static constexpr Scalar criticalTemperature() | ||
| 59 | { return 154.581; /* [K] */ } | ||
| 60 | |||
| 61 | /*! | ||
| 62 | * \brief Returns the critical pressure in \f$\mathrm{[Pa]}\f$ of molecular oxygen. | ||
| 63 | */ | ||
| 64 | static constexpr Scalar criticalPressure() | ||
| 65 | { return 5.0804e6; /* [N/m^2] */ } | ||
| 66 | |||
| 67 | /*! | ||
| 68 | * \brief Returns the temperature in \f$\mathrm{[K]}\f$ at molecular oxygen's triple point. | ||
| 69 | */ | ||
| 70 | static constexpr Scalar tripleTemperature() | ||
| 71 | { return 54.359; /* [K] */ } | ||
| 72 | |||
| 73 | /*! | ||
| 74 | * \brief Returns the pressure in \f$\mathrm{[Pa]}\f$ at molecular oxygen's triple point. | ||
| 75 | */ | ||
| 76 | static constexpr Scalar triplePressure() | ||
| 77 | { return 148.0; /* [N/m^2] */ } | ||
| 78 | |||
| 79 | /*! | ||
| 80 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular oxygen | ||
| 81 | * at a given temperature. | ||
| 82 | * | ||
| 83 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 84 | * | ||
| 85 | * Taken from: | ||
| 86 | * | ||
| 87 | * R. Prydz (1972, pp. 1-4) \cite prydz1972 | ||
| 88 | */ | ||
| 89 | 3 | static Scalar vaporPressure(Scalar T) | |
| 90 | { | ||
| 91 |
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3 | if (T > criticalTemperature()) |
| 92 | return criticalPressure(); | ||
| 93 | ✗ | if (T < tripleTemperature()) | |
| 94 | return 0; // O2 is solid: We don't take sublimation into account | ||
| 95 | |||
| 96 | // vapor pressure between tripe and critical points. See the | ||
| 97 | // paper of Prydz for a discussion | ||
| 98 | ✗ | Scalar X = | |
| 99 | ✗ | (1 - tripleTemperature()/T) / | |
| 100 | (1 - tripleTemperature()/criticalTemperature()); | ||
| 101 | ✗ | const Scalar A = 7.568956; | |
| 102 | ✗ | const Scalar B = 5.004836; | |
| 103 | ✗ | const Scalar C = -2.137460; | |
| 104 | ✗ | const Scalar D = 3.454481; | |
| 105 | ✗ | const Scalar epsilon = 1.514; | |
| 106 | |||
| 107 | using std::exp; | ||
| 108 | using std::pow; | ||
| 109 | ✗ | return triplePressure()*exp(X*(A + X*(B + C*X) + D*pow(1 - X, epsilon))); | |
| 110 | } | ||
| 111 | |||
| 112 | /*! | ||
| 113 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 114 | */ | ||
| 115 | static constexpr bool gasIsCompressible() | ||
| 116 | { return true; } | ||
| 117 | |||
| 118 | /*! | ||
| 119 | * \brief The density in \f$\mathrm{[kg/m^3]}\f$ of pure \f$O_2\f$ at a given pressure and temperature. | ||
| 120 | * | ||
| 121 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 122 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 123 | * | ||
| 124 | * \todo: density liquid oxygen | ||
| 125 | */ | ||
| 126 | static constexpr Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 127 | { | ||
| 128 | // Assume an ideal gas | ||
| 129 |
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603656 | return IdealGas::density(molarMass(), temperature, pressure); |
| 130 | } | ||
| 131 | |||
| 132 | /*! | ||
| 133 | * \brief The molar density of pure \f$O_2\f$ in \f$\mathrm{[mol/m^3]}\f$, | ||
| 134 | * depending on pressure and temperature. | ||
| 135 | * \param temperature The temperature of the gas | ||
| 136 | * \param pressure The pressure of the gas | ||
| 137 | */ | ||
| 138 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 139 | 603430 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 140 | |||
| 141 | /*! | ||
| 142 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 143 | */ | ||
| 144 | static constexpr bool gasIsIdeal() | ||
| 145 | { return true; } | ||
| 146 | |||
| 147 | /*! | ||
| 148 | * \brief The pressure of gaseous \f$O_2\f$ in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 149 | * | ||
| 150 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 151 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 152 | */ | ||
| 153 | static constexpr Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 154 | { | ||
| 155 | // Assume an ideal gas | ||
| 156 | 18 | return IdealGas::pressure(temperature, density/molarMass()); | |
| 157 | } | ||
| 158 | |||
| 159 | /*! | ||
| 160 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure oxygen gas. | ||
| 161 | * Shomate Equation is used for a temperature range of 100K to 6000K. | ||
| 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 | ✗ | static Scalar gasEnthalpy(Scalar temperature, | |
| 167 | Scalar pressure) | ||
| 168 | { | ||
| 169 |
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139517 | const auto h = shomateMethod.enthalpy(temperature); // KJ/mol |
| 170 | 139517 | return h * 1e3 / molarMass(); // J/kg | |
| 171 | } | ||
| 172 | |||
| 173 | /*! | ||
| 174 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure oxygen gas. | ||
| 175 | * Shomate Equation is used for a temperature range of 100K to 6000K. | ||
| 176 | * | ||
| 177 | * \param T absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 178 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 179 | * | ||
| 180 | * See: R. Reid, et al. (1987, pp 154, 657, 665) \cite reid1987 | ||
| 181 | */ | ||
| 182 | ✗ | static Scalar gasHeatCapacity(Scalar T, | |
| 183 | Scalar pressure) | ||
| 184 | { | ||
| 185 |
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112 | const auto cp = shomateMethod.heatCapacity(T); // J/(mol K) |
| 186 | 112 | return cp / molarMass(); // J/(kg K) | |
| 187 | } | ||
| 188 | |||
| 189 | /*! | ||
| 190 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$O_2\f$ at a given pressure and temperature. | ||
| 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 | * See: | ||
| 196 | * | ||
| 197 | * See: R. Reid, et al. (1987, pp 396-397, 664) \cite reid1987 | ||
| 198 | */ | ||
| 199 | 301825 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 200 | { | ||
| 201 | 301825 | const Scalar Tc = criticalTemperature(); | |
| 202 | 301825 | const Scalar Vc = 73.4; // critical specific volume [cm^3/mol] | |
| 203 | 301825 | const Scalar omega = 0.025; // accentric factor | |
| 204 | 301825 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
| 205 | 301825 | const Scalar dipole = 0.0; // dipole moment [debye] | |
| 206 | |||
| 207 | using std::sqrt; | ||
| 208 | 301825 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | |
| 209 | 301825 | mu_r4 *= mu_r4; | |
| 210 | 301825 | mu_r4 *= mu_r4; | |
| 211 | |||
| 212 | 301825 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
| 213 | 301825 | Scalar Tstar = 1.2593 * temperature/Tc; | |
| 214 | |||
| 215 | using std::pow; | ||
| 216 | using std::exp; | ||
| 217 | 301825 | Scalar Omega_v = | |
| 218 | 603650 | 1.16145*pow(Tstar, -0.14874) + | |
| 219 | 301825 | 0.52487*exp(- 0.77320*Tstar) + | |
| 220 | 301825 | 2.16178*exp(- 2.43787*Tstar); | |
| 221 | 301825 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
| 222 | |||
| 223 | // conversion from micro poise to Pa s | ||
| 224 | 301825 | return mu/1e6 / 10; | |
| 225 | } | ||
| 226 | |||
| 227 | /*! | ||
| 228 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of nitrogen. | ||
| 229 | * | ||
| 230 | * Isobaric Properties for Nitrogen and Oxygen in: NIST Standard | ||
| 231 | * Reference Database Number 69, Eds. P.J. Linstrom and | ||
| 232 | * W.G. Mallard evaluated at p=.1 MPa, does not | ||
| 233 | * change dramatically with p and can be interpolated linearly with temperature | ||
| 234 | * | ||
| 235 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 236 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 237 | */ | ||
| 238 | ✗ | static constexpr Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 239 | { | ||
| 240 | 139517 | return 8.044e-5 * (temperature - 273.15) + 0.024486; | |
| 241 | } | ||
| 242 | }; | ||
| 243 | |||
| 244 | /*! | ||
| 245 | * \brief Shomate parameters for oxygen published by NIST \cite NIST | ||
| 246 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782447&Units=SI&Mask=1&Type=JANAFG&Table=on#JANAFG | ||
| 247 | * First row defines the temperature ranges, further rows give the parameters (A,B,C,D,E,F,G,H) for the respective temperature ranges. | ||
| 248 | */ | ||
| 249 | template <class Scalar> | ||
| 250 | const typename O2<Scalar>::ShomateMethod O2<Scalar>::shomateMethod{ | ||
| 251 | /*temperature*/{100.0, 700.0, 2000.0, 6000.0}, | ||
| 252 | typename O2<Scalar>::ShomateMethod::Coefficients{{ | ||
| 253 | {31.32234, -20.23531, 57.86644, -36.50624, -0.007374, -8.903471, 246.7945, 0.0}, | ||
| 254 | {30.03235, 8.772972, -3.988133, 0.788313, -0.741599, -11.32468, 236.1663, 0.0}, | ||
| 255 | {20.91111, 10.72071, -2.020498, 0.146449, 9.245722, 5.337651, 237.6185, 0.0} | ||
| 256 | }} | ||
| 257 | }; | ||
| 258 | |||
| 259 | } // end namespace Components | ||
| 260 | } // end namespace Dumux | ||
| 261 | |||
| 262 | #endif | ||
| 263 |