| Line | Branch | Exec | Source |
|---|---|---|---|
| 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 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::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 | using ShomateMethod = Dumux::ShomateMethod<Scalar, 3>; // three regions | ||
| 38 | |||
| 39 | public: | ||
| 40 | static const ShomateMethod shomateMethod; | ||
| 41 | |||
| 42 | /*! | ||
| 43 | * \brief A human readable name for the \f$O_2\f$. | ||
| 44 | */ | ||
| 45 |
5/10✓ Branch 1 taken 1 times.
✗ Branch 2 not taken.
✓ Branch 4 taken 1 times.
✗ Branch 5 not taken.
✓ Branch 7 taken 1 times.
✗ Branch 8 not taken.
✓ Branch 10 taken 1 times.
✗ Branch 11 not taken.
✓ Branch 13 taken 1 times.
✗ Branch 14 not taken.
|
17 | static std::string name() |
| 46 |
11/21✓ Branch 1 taken 1 times.
✓ Branch 2 taken 1 times.
✓ Branch 4 taken 1 times.
✗ Branch 5 not taken.
✓ Branch 7 taken 1 times.
✗ Branch 8 not taken.
✓ Branch 10 taken 1 times.
✗ Branch 11 not taken.
✓ Branch 13 taken 1 times.
✗ Branch 14 not taken.
✓ Branch 16 taken 1 times.
✗ Branch 17 not taken.
✓ Branch 19 taken 1 times.
✗ Branch 20 not taken.
✓ Branch 22 taken 1 times.
✗ Branch 23 not taken.
✓ Branch 25 taken 1 times.
✗ Branch 26 not taken.
✓ Branch 28 taken 1 times.
✗ Branch 29 not taken.
✗ Branch 3 not taken.
|
17 | { return "O2"; } |
| 47 | |||
| 48 | /*! | ||
| 49 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular oxygen. | ||
| 50 | */ | ||
| 51 | static constexpr Scalar molarMass() | ||
| 52 | { return 32e-3; } | ||
| 53 | |||
| 54 | /*! | ||
| 55 | * \brief Returns the critical temperature in \f$\mathrm{[K]}\f$ of molecular oxygen. | ||
| 56 | */ | ||
| 57 | static constexpr Scalar criticalTemperature() | ||
| 58 | { return 154.581; /* [K] */ } | ||
| 59 | |||
| 60 | /*! | ||
| 61 | * \brief Returns the critical pressure in \f$\mathrm{[Pa]}\f$ of molecular oxygen. | ||
| 62 | */ | ||
| 63 | static constexpr Scalar criticalPressure() | ||
| 64 | { return 5.0804e6; /* [N/m^2] */ } | ||
| 65 | |||
| 66 | /*! | ||
| 67 | * \brief Returns the temperature in \f$\mathrm{[K]}\f$ at molecular oxygen's triple point. | ||
| 68 | */ | ||
| 69 | static constexpr Scalar tripleTemperature() | ||
| 70 | { return 54.359; /* [K] */ } | ||
| 71 | |||
| 72 | /*! | ||
| 73 | * \brief Returns the pressure in \f$\mathrm{[Pa]}\f$ at molecular oxygen's triple point. | ||
| 74 | */ | ||
| 75 | static constexpr Scalar triplePressure() | ||
| 76 | { return 148.0; /* [N/m^2] */ } | ||
| 77 | |||
| 78 | /*! | ||
| 79 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular oxygen | ||
| 80 | * at a given temperature. | ||
| 81 | * | ||
| 82 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 83 | * | ||
| 84 | * Taken from: | ||
| 85 | * | ||
| 86 | * R. Prydz (1972, pp. 1-4) \cite prydz1972 | ||
| 87 | */ | ||
| 88 | 3 | static Scalar vaporPressure(Scalar T) | |
| 89 | { | ||
| 90 |
1/2✗ Branch 0 not taken.
✓ Branch 1 taken 3 times.
|
3 | if (T > criticalTemperature()) |
| 91 | return criticalPressure(); | ||
| 92 | ✗ | if (T < tripleTemperature()) | |
| 93 | return 0; // O2 is solid: We don't take sublimation into account | ||
| 94 | |||
| 95 | // vapor pressure between tripe and critical points. See the | ||
| 96 | // paper of Prydz for a discussion | ||
| 97 | ✗ | Scalar X = | |
| 98 | ✗ | (1 - tripleTemperature()/T) / | |
| 99 | (1 - tripleTemperature()/criticalTemperature()); | ||
| 100 | ✗ | const Scalar A = 7.568956; | |
| 101 | ✗ | const Scalar B = 5.004836; | |
| 102 | ✗ | const Scalar C = -2.137460; | |
| 103 | ✗ | const Scalar D = 3.454481; | |
| 104 | ✗ | const Scalar epsilon = 1.514; | |
| 105 | |||
| 106 | using std::exp; | ||
| 107 | using std::pow; | ||
| 108 | ✗ | return triplePressure()*exp(X*(A + X*(B + C*X) + D*pow(1 - X, epsilon))); | |
| 109 | } | ||
| 110 | |||
| 111 | /*! | ||
| 112 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 113 | */ | ||
| 114 | static constexpr bool gasIsCompressible() | ||
| 115 | { return true; } | ||
| 116 | |||
| 117 | /*! | ||
| 118 | * \brief The density in \f$\mathrm{[kg/m^3]}\f$ of pure \f$O_2\f$ at a given pressure and temperature. | ||
| 119 | * | ||
| 120 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 121 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 122 | * | ||
| 123 | * \todo: density liquid oxygen | ||
| 124 | */ | ||
| 125 |
2/2✓ Branch 0 taken 1 times.
✓ Branch 1 taken 2 times.
|
301828 | static constexpr Scalar gasDensity(Scalar temperature, Scalar pressure) |
| 126 | { | ||
| 127 | // Assume an ideal gas | ||
| 128 |
2/2✓ Branch 0 taken 1 times.
✓ Branch 1 taken 2 times.
|
301828 | return IdealGas::density(molarMass(), temperature, pressure); |
| 129 | } | ||
| 130 | |||
| 131 | /*! | ||
| 132 | * \brief The molar density of pure \f$O_2\f$ in \f$\mathrm{[mol/m^3]}\f$, | ||
| 133 | * depending on pressure and temperature. | ||
| 134 | * \param temperature The temperature of the gas | ||
| 135 | * \param pressure The pressure of the gas | ||
| 136 | */ | ||
| 137 | 301715 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | |
| 138 | 301715 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 139 | |||
| 140 | /*! | ||
| 141 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 142 | */ | ||
| 143 | static constexpr bool gasIsIdeal() | ||
| 144 | { return true; } | ||
| 145 | |||
| 146 | /*! | ||
| 147 | * \brief The pressure of gaseous \f$O_2\f$ in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 148 | * | ||
| 149 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 150 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 151 | */ | ||
| 152 | 9 | static constexpr Scalar gasPressure(Scalar temperature, Scalar density) | |
| 153 | { | ||
| 154 | // Assume an ideal gas | ||
| 155 | 9 | return IdealGas::pressure(temperature, density/molarMass()); | |
| 156 | } | ||
| 157 | |||
| 158 | /*! | ||
| 159 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure oxygen gas. | ||
| 160 | * Shomate Equation is used for a temperature range of 100K to 6000K. | ||
| 161 | * | ||
| 162 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 163 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 164 | */ | ||
| 165 | 139517 | static Scalar gasEnthalpy(Scalar temperature, | |
| 166 | Scalar pressure) | ||
| 167 | { | ||
| 168 |
1/2✓ Branch 1 taken 101 times.
✗ Branch 2 not taken.
|
139517 | const auto h = shomateMethod.enthalpy(temperature); // KJ/mol |
| 169 | 139517 | return h * 1e3 / molarMass(); // J/kg | |
| 170 | } | ||
| 171 | |||
| 172 | /*! | ||
| 173 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure oxygen gas. | ||
| 174 | * Shomate Equation is used for a temperature range of 100K to 6000K. | ||
| 175 | * | ||
| 176 | * \param T absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 177 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 178 | * | ||
| 179 | * See: R. Reid, et al. (1987, pp 154, 657, 665) \cite reid1987 | ||
| 180 | */ | ||
| 181 | 112 | static Scalar gasHeatCapacity(Scalar T, | |
| 182 | Scalar pressure) | ||
| 183 | { | ||
| 184 |
1/2✓ Branch 1 taken 101 times.
✗ Branch 2 not taken.
|
112 | const auto cp = shomateMethod.heatCapacity(T); // J/(mol K) |
| 185 | 112 | return cp / molarMass(); // J/(kg K) | |
| 186 | } | ||
| 187 | |||
| 188 | /*! | ||
| 189 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$O_2\f$ at a given pressure and temperature. | ||
| 190 | * | ||
| 191 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 192 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 193 | * | ||
| 194 | * See: | ||
| 195 | * | ||
| 196 | * See: R. Reid, et al. (1987, pp 396-397, 664) \cite reid1987 | ||
| 197 | */ | ||
| 198 | 301825 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 199 | { | ||
| 200 | 301825 | const Scalar Tc = criticalTemperature(); | |
| 201 | 301825 | const Scalar Vc = 73.4; // critical specific volume [cm^3/mol] | |
| 202 | 301825 | const Scalar omega = 0.025; // accentric factor | |
| 203 | 301825 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
| 204 | 301825 | const Scalar dipole = 0.0; // dipole moment [debye] | |
| 205 | |||
| 206 | using std::sqrt; | ||
| 207 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | ||
| 208 | mu_r4 *= mu_r4; | ||
| 209 | 301825 | mu_r4 *= mu_r4; | |
| 210 | |||
| 211 | 301825 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
| 212 | 301825 | Scalar Tstar = 1.2593 * temperature/Tc; | |
| 213 | |||
| 214 | using std::pow; | ||
| 215 | using std::exp; | ||
| 216 | 301825 | Scalar Omega_v = | |
| 217 | 301825 | 1.16145*pow(Tstar, -0.14874) + | |
| 218 | 301825 | 0.52487*exp(- 0.77320*Tstar) + | |
| 219 | 301825 | 2.16178*exp(- 2.43787*Tstar); | |
| 220 | 301825 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
| 221 | |||
| 222 | // conversion from micro poise to Pa s | ||
| 223 | 301825 | return mu/1e6 / 10; | |
| 224 | } | ||
| 225 | |||
| 226 | /*! | ||
| 227 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of nitrogen. | ||
| 228 | * | ||
| 229 | * Isobaric Properties for Nitrogen and Oxygen in: NIST Standard | ||
| 230 | * Reference Database Number 69, Eds. P.J. Linstrom and | ||
| 231 | * W.G. Mallard evaluated at p=.1 MPa, does not | ||
| 232 | * change dramatically with p and can be interpolated linearly with temperature | ||
| 233 | * | ||
| 234 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 235 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 236 | */ | ||
| 237 | 139516 | static constexpr Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 238 | { | ||
| 239 | 139517 | return 8.044e-5 * (temperature - 273.15) + 0.024486; | |
| 240 | } | ||
| 241 | }; | ||
| 242 | |||
| 243 | /*! | ||
| 244 | * \brief Shomate parameters for oxygen published by NIST \cite NIST | ||
| 245 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782447&Units=SI&Mask=1&Type=JANAFG&Table=on#JANAFG | ||
| 246 | * First row defines the temperature ranges, further rows give the parameters (A,B,C,D,E,F,G,H) for the respective temperature ranges. | ||
| 247 | */ | ||
| 248 | template <class Scalar> | ||
| 249 | const typename O2<Scalar>::ShomateMethod O2<Scalar>::shomateMethod{ | ||
| 250 | /*temperature*/{100.0, 700.0, 2000.0, 6000.0}, | ||
| 251 | typename O2<Scalar>::ShomateMethod::Coefficients{{ | ||
| 252 | {31.32234, -20.23531, 57.86644, -36.50624, -0.007374, -8.903471, 246.7945, 0.0}, | ||
| 253 | {30.03235, 8.772972, -3.988133, 0.788313, -0.741599, -11.32468, 236.1663, 0.0}, | ||
| 254 | {20.91111, 10.72071, -2.020498, 0.146449, 9.245722, 5.337651, 237.6185, 0.0} | ||
| 255 | }} | ||
| 256 | }; | ||
| 257 | |||
| 258 | } // end namespace Dumux::Components | ||
| 259 | |||
| 260 | #endif | ||
| 261 |