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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 nitrogen \f$N_2\f$. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_N2_HH | ||
| 13 | #define DUMUX_N2_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 nitrogen \f$N_2\f$. | ||
| 29 | * | ||
| 30 | * \tparam Scalar The type used for scalar values | ||
| 31 | */ | ||
| 32 | template <class Scalar> | ||
| 33 | class N2 | ||
| 34 | : public Components::Base<Scalar, N2<Scalar> > | ||
| 35 | , public Components::Gas<Scalar, N2<Scalar> > | ||
| 36 | { | ||
| 37 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 38 | using ShomateMethod = Dumux::ShomateMethod<Scalar, 3>; // 3 regions | ||
| 39 | |||
| 40 | public: | ||
| 41 | static const ShomateMethod shomateMethod; | ||
| 42 | /*! | ||
| 43 | * \brief A human readable name for nitrogen. | ||
| 44 | */ | ||
| 45 | static std::string name() | ||
| 46 |
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|
396 | { return "N2"; } |
| 47 | |||
| 48 | /*! | ||
| 49 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular nitrogen. | ||
| 50 | */ | ||
| 51 | static constexpr Scalar molarMass() | ||
| 52 | { return 28.0134e-3;} | ||
| 53 | |||
| 54 | /*! | ||
| 55 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of molecular nitrogen | ||
| 56 | */ | ||
| 57 | static Scalar criticalTemperature() | ||
| 58 | { return 126.192; /* [K] */ } | ||
| 59 | |||
| 60 | /*! | ||
| 61 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of molecular nitrogen. | ||
| 62 | */ | ||
| 63 | static Scalar criticalPressure() | ||
| 64 | { return 3.39858e6; /* [N/m^2] */ } | ||
| 65 | |||
| 66 | /*! | ||
| 67 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at molecular nitrogen's triple point. | ||
| 68 | */ | ||
| 69 | static Scalar tripleTemperature() | ||
| 70 | { return 63.151; /* [K] */ } | ||
| 71 | |||
| 72 | /*! | ||
| 73 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at molecular nitrogen's triple point. | ||
| 74 | */ | ||
| 75 | static Scalar triplePressure() | ||
| 76 | { return 12.523e3; /* [N/m^2] */ } | ||
| 77 | |||
| 78 | /*! | ||
| 79 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular nitrogen | ||
| 80 | * at a given temperature. | ||
| 81 | * | ||
| 82 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 83 | * | ||
| 84 | * Taken from: | ||
| 85 | * | ||
| 86 | * R. Span, E.W. Lemmon, et al. (2000 ,pp. 1361-1433) \cite span2000 | ||
| 87 | */ | ||
| 88 | 3 | static Scalar vaporPressure(Scalar T) | |
| 89 | { | ||
| 90 |
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3 | if (T > criticalTemperature()) |
| 91 | return criticalPressure(); | ||
| 92 | ✗ | if (T < tripleTemperature()) | |
| 93 | return 0; // N2 is solid: We don't take sublimation into | ||
| 94 | // account | ||
| 95 | |||
| 96 | // note: this is the ancillary equation given on page 1368 | ||
| 97 | using std::sqrt; | ||
| 98 | ✗ | Scalar sigma = Scalar(1.0) - T/criticalTemperature(); | |
| 99 | ✗ | Scalar sqrtSigma = sqrt(sigma); | |
| 100 | ✗ | const Scalar N1 = -6.12445284; | |
| 101 | ✗ | const Scalar N2 = 1.26327220; | |
| 102 | ✗ | const Scalar N3 = -0.765910082; | |
| 103 | ✗ | const Scalar N4 = -1.77570564; | |
| 104 | |||
| 105 | using std::exp; | ||
| 106 | return | ||
| 107 | ✗ | criticalPressure() * | |
| 108 | ✗ | exp(criticalTemperature()/T* | |
| 109 | ✗ | (sigma*(N1 + | |
| 110 | ✗ | sqrtSigma*N2 + | |
| 111 | ✗ | sigma*(sqrtSigma*N3 + | |
| 112 | ✗ | sigma*sigma*sigma*N4)))); | |
| 113 | } | ||
| 114 | |||
| 115 | /*! | ||
| 116 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of \f$N_2\f$ gas at a given pressure and temperature. | ||
| 117 | * | ||
| 118 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 119 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 120 | */ | ||
| 121 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 122 | { | ||
| 123 | // Assume an ideal gas | ||
| 124 |
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23878580 | return IdealGas::density(molarMass(), temperature, pressure); |
| 125 | } | ||
| 126 | |||
| 127 | /*! | ||
| 128 | * \brief The molar density of \f$N_2\f$ gas in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 129 | * | ||
| 130 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 131 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 132 | * | ||
| 133 | */ | ||
| 134 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 135 | 23878354 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 136 | |||
| 137 | /*! | ||
| 138 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 139 | */ | ||
| 140 | static constexpr bool gasIsCompressible() | ||
| 141 | { return true; } | ||
| 142 | |||
| 143 | /*! | ||
| 144 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 145 | */ | ||
| 146 | static constexpr bool gasIsIdeal() | ||
| 147 | { return true; } | ||
| 148 | |||
| 149 | /*! | ||
| 150 | * \brief The pressure of gaseous \f$N_2\f$ in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 151 | * | ||
| 152 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 153 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 154 | */ | ||
| 155 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 156 | { | ||
| 157 | // Assume an ideal gas | ||
| 158 | 18 | return IdealGas::pressure(temperature, density/molarMass()); | |
| 159 | } | ||
| 160 | |||
| 161 | /*! | ||
| 162 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure nitrogen gas. | ||
| 163 | * Shomate Equation is used for a temperature range of 100K to 6000K. | ||
| 164 | * | ||
| 165 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 166 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 167 | */ | ||
| 168 | ✗ | static const Scalar gasEnthalpy(Scalar temperature, | |
| 169 | Scalar pressure) | ||
| 170 | { | ||
| 171 |
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21046182 | const auto h = shomateMethod.enthalpy(temperature); // KJ/mol |
| 172 | 21081474 | return h * 1e3 / molarMass(); // J/kg | |
| 173 | } | ||
| 174 | |||
| 175 | /*! | ||
| 176 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure nitrogen gas. | ||
| 177 | * | ||
| 178 | * Definition of enthalpy: \f$h= u + pv = u + p / \rho\f$. | ||
| 179 | * | ||
| 180 | * Rearranging for internal energy yields: \f$u = h - pv\f$. | ||
| 181 | * | ||
| 182 | * Exploiting the Ideal Gas assumption (\f$pv = R_{\textnormal{specific}} T\f$)gives: \f$u = h - R / M T \f$. | ||
| 183 | * | ||
| 184 | * The universal gas constant can only be used in the case of molar formulations. | ||
| 185 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 186 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 187 | */ | ||
| 188 | static const Scalar gasInternalEnergy(Scalar temperature, | ||
| 189 | Scalar pressure) | ||
| 190 | { | ||
| 191 | return | ||
| 192 | gasEnthalpy(temperature, pressure) - | ||
| 193 | 1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)] | ||
| 194 | IdealGas::R*temperature; // = pressure * spec. volume for an ideal gas | ||
| 195 | } | ||
| 196 | |||
| 197 | /*! | ||
| 198 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure nitrogen gas. | ||
| 199 | * Shomate Equation is used for a temperature range of 100K to 6000K. | ||
| 200 | */ | ||
| 201 | ✗ | static const Scalar gasHeatCapacity(Scalar T, | |
| 202 | Scalar pressure) | ||
| 203 | { | ||
| 204 |
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118 | const auto cp = shomateMethod.heatCapacity(T); // J/(mol K) |
| 205 | 118 | return cp / molarMass(); // J/(kg K) | |
| 206 | } | ||
| 207 | |||
| 208 | /*! | ||
| 209 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$N_2\f$ at a given pressure and temperature. | ||
| 210 | * | ||
| 211 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 212 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 213 | * | ||
| 214 | * See: | ||
| 215 | * | ||
| 216 | * See: R. Reid, et al.: The Properties of Gases and Liquids, | ||
| 217 | * 4th edition (1987, pp 396-397) \cite reid1987 <BR> | ||
| 218 | * 5th edition (2001, pp 9.7-9.8 (omega and V_c taken from p. A.19)) \cite poling2001 | ||
| 219 | * | ||
| 220 | */ | ||
| 221 | 16801757 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 222 | { | ||
| 223 | 16801757 | const Scalar Tc = criticalTemperature(); | |
| 224 | 16801757 | const Scalar Vc = 90.1; // critical specific volume [cm^3/mol] | |
| 225 | 16801757 | const Scalar omega = 0.037; // accentric factor | |
| 226 | 16801757 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
| 227 | 16801757 | const Scalar dipole = 0.0; // dipole moment [debye] | |
| 228 | |||
| 229 | using std::sqrt; | ||
| 230 | 16801757 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | |
| 231 | 16801757 | mu_r4 *= mu_r4; | |
| 232 | 16801757 | mu_r4 *= mu_r4; | |
| 233 | |||
| 234 | using std::pow; | ||
| 235 | using std::exp; | ||
| 236 | 16801757 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
| 237 | 16801757 | Scalar Tstar = 1.2593 * temperature/Tc; | |
| 238 | 16801757 | Scalar Omega_v = | |
| 239 | 33603514 | 1.16145*pow(Tstar, -0.14874) + | |
| 240 | 16801757 | 0.52487*exp(- 0.77320*Tstar) + | |
| 241 | 16801757 | 2.16178*exp(- 2.43787*Tstar); | |
| 242 | 16801757 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
| 243 | |||
| 244 | // conversion from micro poise to Pa s | ||
| 245 | 16801757 | return mu/1e6 / 10; | |
| 246 | } | ||
| 247 | |||
| 248 | /*! | ||
| 249 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of nitrogen. | ||
| 250 | * | ||
| 251 | * Isobaric Properties for Nitrogen and Oxygen in: NIST Standard | ||
| 252 | * Reference Database Number 69, Eds. P.J. Linstrom and | ||
| 253 | * W.G. Mallard evaluated at p=.1 MPa, does not | ||
| 254 | * change dramatically with p and can be interpolated linearly with temperature | ||
| 255 | * | ||
| 256 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 257 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 258 | */ | ||
| 259 | ✗ | static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 260 | { | ||
| 261 | 18031377 | return 6.525e-5 * (temperature - 273.15) + 0.024031; | |
| 262 | } | ||
| 263 | }; | ||
| 264 | |||
| 265 | /*! | ||
| 266 | * \brief Shomate parameters for nitrogen published by NIST \cite NIST | ||
| 267 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C7727379&Units=SI&Mask=1&Type=JANAFG&Table=on#JANAFG | ||
| 268 | * First row defines the temperature ranges, further rows give the parameters (A,B,C,D,E,F,G,H) for the respective temperature ranges. | ||
| 269 | */ | ||
| 270 | template <class Scalar> | ||
| 271 | const typename N2<Scalar>::ShomateMethod N2<Scalar>::shomateMethod{ | ||
| 272 | /*temperature*/{100.0,500.0,2000.0,6000.0}, | ||
| 273 | typename N2<Scalar>::ShomateMethod::Coefficients{{ | ||
| 274 | {28.98641, 1.853978, -9.647459, 16.63537, 0.000117, -8.671914, 226.4168, 0.0}, | ||
| 275 | {19.50583, 19.88705, -8.598535, 1.369784, 0.527601, -4.935202, 212.39, 0.0}, | ||
| 276 | {35.51872, 1.128728, -0.196103, 0.014662, -4.55376, -18.97091, 224.981, 0.0} | ||
| 277 | }} | ||
| 278 | }; | ||
| 279 | |||
| 280 | } // end namespace Components | ||
| 281 | } // end namespace Dumux | ||
| 282 | |||
| 283 | #endif | ||
| 284 |