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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 | |||
| 22 | namespace Dumux { | ||
| 23 | namespace Components { | ||
| 24 | |||
| 25 | /*! | ||
| 26 | * \ingroup Components | ||
| 27 | * \brief Properties of pure molecular oxygen \f$O_2\f$. | ||
| 28 | * | ||
| 29 | * \tparam Scalar The type used for scalar values | ||
| 30 | */ | ||
| 31 | template <class Scalar> | ||
| 32 | class O2 | ||
| 33 | : public Components::Base<Scalar, O2<Scalar> > | ||
| 34 | , public Components::Gas<Scalar, O2<Scalar> > | ||
| 35 | { | ||
| 36 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 37 | |||
| 38 | public: | ||
| 39 | /*! | ||
| 40 | * \brief A human readable name for the \f$O_2\f$. | ||
| 41 | */ | ||
| 42 | static std::string name() | ||
| 43 |
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|
34 | { return "O2"; } |
| 44 | |||
| 45 | /*! | ||
| 46 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular oxygen. | ||
| 47 | */ | ||
| 48 | static constexpr Scalar molarMass() | ||
| 49 | { return 32e-3; } | ||
| 50 | |||
| 51 | /*! | ||
| 52 | * \brief Returns the critical temperature in \f$\mathrm{[K]}\f$ of molecular oxygen. | ||
| 53 | */ | ||
| 54 | static constexpr Scalar criticalTemperature() | ||
| 55 | { return 154.581; /* [K] */ } | ||
| 56 | |||
| 57 | /*! | ||
| 58 | * \brief Returns the critical pressure in \f$\mathrm{[Pa]}\f$ of molecular oxygen. | ||
| 59 | */ | ||
| 60 | static constexpr Scalar criticalPressure() | ||
| 61 | { return 5.0804e6; /* [N/m^2] */ } | ||
| 62 | |||
| 63 | /*! | ||
| 64 | * \brief Returns the temperature in \f$\mathrm{[K]}\f$ at molecular oxygen's triple point. | ||
| 65 | */ | ||
| 66 | static constexpr Scalar tripleTemperature() | ||
| 67 | { return 54.359; /* [K] */ } | ||
| 68 | |||
| 69 | /*! | ||
| 70 | * \brief Returns the pressure in \f$\mathrm{[Pa]}\f$ at molecular oxygen's triple point. | ||
| 71 | */ | ||
| 72 | static constexpr Scalar triplePressure() | ||
| 73 | { return 148.0; /* [N/m^2] */ } | ||
| 74 | |||
| 75 | /*! | ||
| 76 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular oxygen | ||
| 77 | * at a given temperature. | ||
| 78 | * | ||
| 79 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 80 | * | ||
| 81 | * Taken from: | ||
| 82 | * | ||
| 83 | * R. Prydz (1972, pp. 1-4) \cite prydz1972 | ||
| 84 | */ | ||
| 85 | 3 | static Scalar vaporPressure(Scalar T) | |
| 86 | { | ||
| 87 |
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3 | if (T > criticalTemperature()) |
| 88 | return criticalPressure(); | ||
| 89 | ✗ | if (T < tripleTemperature()) | |
| 90 | return 0; // O2 is solid: We don't take sublimation into account | ||
| 91 | |||
| 92 | // vapor pressure between tripe and critical points. See the | ||
| 93 | // paper of Prydz for a discussion | ||
| 94 | ✗ | Scalar X = | |
| 95 | ✗ | (1 - tripleTemperature()/T) / | |
| 96 | (1 - tripleTemperature()/criticalTemperature()); | ||
| 97 | ✗ | const Scalar A = 7.568956; | |
| 98 | ✗ | const Scalar B = 5.004836; | |
| 99 | ✗ | const Scalar C = -2.137460; | |
| 100 | ✗ | const Scalar D = 3.454481; | |
| 101 | ✗ | const Scalar epsilon = 1.514; | |
| 102 | |||
| 103 | using std::exp; | ||
| 104 | using std::pow; | ||
| 105 | ✗ | return triplePressure()*exp(X*(A + X*(B + C*X) + D*pow(1 - X, epsilon))); | |
| 106 | } | ||
| 107 | |||
| 108 | /*! | ||
| 109 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 110 | */ | ||
| 111 | static constexpr bool gasIsCompressible() | ||
| 112 | { return true; } | ||
| 113 | |||
| 114 | /*! | ||
| 115 | * \brief The density in \f$\mathrm{[kg/m^3]}\f$ of pure \f$O_2\f$ at a given pressure and temperature. | ||
| 116 | * | ||
| 117 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 118 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 119 | * | ||
| 120 | * \todo: density liquid oxygen | ||
| 121 | */ | ||
| 122 | static constexpr Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 123 | { | ||
| 124 | // Assume an ideal gas | ||
| 125 |
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603656 | return IdealGas::density(molarMass(), temperature, pressure); |
| 126 | } | ||
| 127 | |||
| 128 | /*! | ||
| 129 | * \brief The molar density of pure \f$O_2\f$ in \f$\mathrm{[mol/m^3]}\f$, | ||
| 130 | * depending on pressure and temperature. | ||
| 131 | * \param temperature The temperature of the gas | ||
| 132 | * \param pressure The pressure of the gas | ||
| 133 | */ | ||
| 134 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 135 | 603430 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 136 | |||
| 137 | /*! | ||
| 138 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 139 | */ | ||
| 140 | static constexpr bool gasIsIdeal() | ||
| 141 | { return true; } | ||
| 142 | |||
| 143 | /*! | ||
| 144 | * \brief The pressure of gaseous \f$O_2\f$ in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 145 | * | ||
| 146 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 147 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 148 | */ | ||
| 149 | static constexpr Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 150 | { | ||
| 151 | // Assume an ideal gas | ||
| 152 | 18 | return IdealGas::pressure(temperature, density/molarMass()); | |
| 153 | } | ||
| 154 | |||
| 155 | /*! | ||
| 156 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure oxygen gas. | ||
| 157 | * | ||
| 158 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 159 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 160 | */ | ||
| 161 | ✗ | static Scalar gasEnthalpy(Scalar temperature, | |
| 162 | Scalar pressure) | ||
| 163 | { | ||
| 164 | 279034 | return gasHeatCapacity(temperature, pressure) * temperature; | |
| 165 | } | ||
| 166 | |||
| 167 | /*! | ||
| 168 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure | ||
| 169 | * oxygen gas. | ||
| 170 | * | ||
| 171 | * This is equivalent to the partial derivative of the specific | ||
| 172 | * enthalpy to the temperature. | ||
| 173 | * \param T absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 174 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 175 | * | ||
| 176 | * See: R. Reid, et al. (1987, pp 154, 657, 665) \cite reid1987 | ||
| 177 | */ | ||
| 178 | ✗ | static Scalar gasHeatCapacity(Scalar T, | |
| 179 | Scalar pressure) | ||
| 180 | { | ||
| 181 | // method of Joback | ||
| 182 | 139629 | const Scalar cpVapA = 28.11; | |
| 183 | 139629 | const Scalar cpVapB = -3.680e-6; | |
| 184 | 139629 | const Scalar cpVapC = 1.746e-5; | |
| 185 | 139629 | const Scalar cpVapD = -1.065e-8; | |
| 186 | |||
| 187 | return | ||
| 188 | 1/molarMass()* // conversion from [J/(mol*K)] to [J/(kg*K)] | ||
| 189 | 139629 | (cpVapA + T* | |
| 190 | 139629 | (cpVapB/2 + T* | |
| 191 | 139629 | (cpVapC/3 + T* | |
| 192 | 139629 | (cpVapD/4)))); | |
| 193 | } | ||
| 194 | |||
| 195 | /*! | ||
| 196 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$O_2\f$ at a given pressure and temperature. | ||
| 197 | * | ||
| 198 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 199 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 200 | * | ||
| 201 | * See: | ||
| 202 | * | ||
| 203 | * See: R. Reid, et al. (1987, pp 396-397, 664) \cite reid1987 | ||
| 204 | */ | ||
| 205 | 301825 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 206 | { | ||
| 207 | 301825 | const Scalar Tc = criticalTemperature(); | |
| 208 | 301825 | const Scalar Vc = 73.4; // critical specific volume [cm^3/mol] | |
| 209 | 301825 | const Scalar omega = 0.025; // accentric factor | |
| 210 | 301825 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
| 211 | 301825 | const Scalar dipole = 0.0; // dipole moment [debye] | |
| 212 | |||
| 213 | using std::sqrt; | ||
| 214 | 301825 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | |
| 215 | 301825 | mu_r4 *= mu_r4; | |
| 216 | 301825 | mu_r4 *= mu_r4; | |
| 217 | |||
| 218 | 301825 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
| 219 | 301825 | Scalar Tstar = 1.2593 * temperature/Tc; | |
| 220 | |||
| 221 | using std::pow; | ||
| 222 | using std::exp; | ||
| 223 | 301825 | Scalar Omega_v = | |
| 224 | 603650 | 1.16145*pow(Tstar, -0.14874) + | |
| 225 | 301825 | 0.52487*exp(- 0.77320*Tstar) + | |
| 226 | 301825 | 2.16178*exp(- 2.43787*Tstar); | |
| 227 | 301825 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
| 228 | |||
| 229 | // conversion from micro poise to Pa s | ||
| 230 | 301825 | return mu/1e6 / 10; | |
| 231 | } | ||
| 232 | |||
| 233 | /*! | ||
| 234 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of nitrogen. | ||
| 235 | * | ||
| 236 | * Isobaric Properties for Nitrogen and Oxygen in: NIST Standard | ||
| 237 | * Reference Database Number 69, Eds. P.J. Linstrom and | ||
| 238 | * W.G. Mallard evaluated at p=.1 MPa, does not | ||
| 239 | * change dramatically with p and can be interpolated linearly with temperature | ||
| 240 | * | ||
| 241 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 242 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 243 | */ | ||
| 244 | ✗ | static constexpr Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 245 | { | ||
| 246 | 139517 | return 8.044e-5 * (temperature - 273.15) + 0.024486; | |
| 247 | } | ||
| 248 | }; | ||
| 249 | |||
| 250 | } // end namespace Components | ||
| 251 | |||
| 252 | } // end namespace Dumux | ||
| 253 | |||
| 254 | #endif | ||
| 255 |