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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 | |||
| 22 | namespace Dumux { | ||
| 23 | namespace Components { | ||
| 24 | |||
| 25 | /*! | ||
| 26 | * \ingroup Components | ||
| 27 | * \brief Properties of pure molecular nitrogen \f$N_2\f$. | ||
| 28 | * | ||
| 29 | * \tparam Scalar The type used for scalar values | ||
| 30 | */ | ||
| 31 | template <class Scalar> | ||
| 32 | class N2 | ||
| 33 | : public Components::Base<Scalar, N2<Scalar> > | ||
| 34 | , public Components::Gas<Scalar, N2<Scalar> > | ||
| 35 | { | ||
| 36 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 37 | |||
| 38 | public: | ||
| 39 | /*! | ||
| 40 | * \brief A human readable name for nitrogen. | ||
| 41 | */ | ||
| 42 | static std::string name() | ||
| 43 |
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|
404 | { return "N2"; } |
| 44 | |||
| 45 | /*! | ||
| 46 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular nitrogen. | ||
| 47 | */ | ||
| 48 | static constexpr Scalar molarMass() | ||
| 49 | { return 28.0134e-3;} | ||
| 50 | |||
| 51 | /*! | ||
| 52 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of molecular nitrogen | ||
| 53 | */ | ||
| 54 | static Scalar criticalTemperature() | ||
| 55 | { return 126.192; /* [K] */ } | ||
| 56 | |||
| 57 | /*! | ||
| 58 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of molecular nitrogen. | ||
| 59 | */ | ||
| 60 | static Scalar criticalPressure() | ||
| 61 | { return 3.39858e6; /* [N/m^2] */ } | ||
| 62 | |||
| 63 | /*! | ||
| 64 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at molecular nitrogen's triple point. | ||
| 65 | */ | ||
| 66 | static Scalar tripleTemperature() | ||
| 67 | { return 63.151; /* [K] */ } | ||
| 68 | |||
| 69 | /*! | ||
| 70 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at molecular nitrogen's triple point. | ||
| 71 | */ | ||
| 72 | static Scalar triplePressure() | ||
| 73 | { return 12.523e3; /* [N/m^2] */ } | ||
| 74 | |||
| 75 | /*! | ||
| 76 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular nitrogen | ||
| 77 | * at a given temperature. | ||
| 78 | * | ||
| 79 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 80 | * | ||
| 81 | * Taken from: | ||
| 82 | * | ||
| 83 | * R. Span, E.W. Lemmon, et al. (2000 ,pp. 1361-1433) \cite span2000 | ||
| 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; // N2 is solid: We don't take sublimation into | ||
| 91 | // account | ||
| 92 | |||
| 93 | // note: this is the ancillary equation given on page 1368 | ||
| 94 | using std::sqrt; | ||
| 95 | ✗ | Scalar sigma = Scalar(1.0) - T/criticalTemperature(); | |
| 96 | ✗ | Scalar sqrtSigma = sqrt(sigma); | |
| 97 | ✗ | const Scalar N1 = -6.12445284; | |
| 98 | ✗ | const Scalar N2 = 1.26327220; | |
| 99 | ✗ | const Scalar N3 = -0.765910082; | |
| 100 | ✗ | const Scalar N4 = -1.77570564; | |
| 101 | |||
| 102 | using std::exp; | ||
| 103 | return | ||
| 104 | ✗ | criticalPressure() * | |
| 105 | ✗ | exp(criticalTemperature()/T* | |
| 106 | ✗ | (sigma*(N1 + | |
| 107 | ✗ | sqrtSigma*N2 + | |
| 108 | ✗ | sigma*(sqrtSigma*N3 + | |
| 109 | ✗ | sigma*sigma*sigma*N4)))); | |
| 110 | } | ||
| 111 | |||
| 112 | /*! | ||
| 113 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of \f$N_2\f$ gas at a given pressure and temperature. | ||
| 114 | * | ||
| 115 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 116 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 117 | */ | ||
| 118 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 119 | { | ||
| 120 | // Assume an ideal gas | ||
| 121 |
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23697846 | return IdealGas::density(molarMass(), temperature, pressure); |
| 122 | } | ||
| 123 | |||
| 124 | /*! | ||
| 125 | * \brief The molar density of \f$N_2\f$ gas in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 126 | * | ||
| 127 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 128 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 129 | * | ||
| 130 | */ | ||
| 131 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 132 | 23697620 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 133 | |||
| 134 | /*! | ||
| 135 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 136 | */ | ||
| 137 | static constexpr bool gasIsCompressible() | ||
| 138 | { return true; } | ||
| 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$N_2\f$ 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 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 153 | { | ||
| 154 | // Assume an ideal gas | ||
| 155 | 18 | return IdealGas::pressure(temperature, density/molarMass()); | |
| 156 | } | ||
| 157 | |||
| 158 | /*! | ||
| 159 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure nitrogen gas. | ||
| 160 | * | ||
| 161 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 162 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 163 | */ | ||
| 164 | ✗ | static const Scalar gasEnthalpy(Scalar temperature, | |
| 165 | Scalar pressure) | ||
| 166 | { | ||
| 167 | 42257582 | return gasHeatCapacity(temperature, pressure) * temperature; | |
| 168 | } | ||
| 169 | |||
| 170 | /*! | ||
| 171 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure nitrogen gas. | ||
| 172 | * | ||
| 173 | * Definition of enthalpy: \f$h= u + pv = u + p / \rho\f$. | ||
| 174 | * | ||
| 175 | * Rearranging for internal energy yields: \f$u = h - pv\f$. | ||
| 176 | * | ||
| 177 | * Exploiting the Ideal Gas assumption (\f$pv = R_{\textnormal{specific}} T\f$)gives: \f$u = h - R / M T \f$. | ||
| 178 | * | ||
| 179 | * The universal gas constant can only be used in the case of molar formulations. | ||
| 180 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 181 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 182 | */ | ||
| 183 | static const Scalar gasInternalEnergy(Scalar temperature, | ||
| 184 | Scalar pressure) | ||
| 185 | { | ||
| 186 | return | ||
| 187 | gasEnthalpy(temperature, pressure) - | ||
| 188 | 1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)] | ||
| 189 | IdealGas::R*temperature; // = pressure * spec. volume for an ideal gas | ||
| 190 | } | ||
| 191 | |||
| 192 | /*! | ||
| 193 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure | ||
| 194 | * nitrogen gas. | ||
| 195 | * | ||
| 196 | * This is equivalent to the partial derivative of the specific | ||
| 197 | * enthalpy to the temperature. | ||
| 198 | * | ||
| 199 | * See: R. Reid, et al. (1987, pp 154, 657, 665) \cite reid1987 | ||
| 200 | */ | ||
| 201 | ✗ | static const Scalar gasHeatCapacity(Scalar T, | |
| 202 | Scalar pressure) | ||
| 203 | { | ||
| 204 | // method of Joback | ||
| 205 | 21128909 | const Scalar cpVapA = 31.15; | |
| 206 | 21128909 | const Scalar cpVapB = -0.01357; | |
| 207 | 21128909 | const Scalar cpVapC = 2.680e-5; | |
| 208 | 21128909 | const Scalar cpVapD = -1.168e-8; | |
| 209 | |||
| 210 | return | ||
| 211 | 1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)] | ||
| 212 | 21128909 | (cpVapA + T* | |
| 213 | 21128909 | (cpVapB/2 + T* | |
| 214 | 21128909 | (cpVapC/3 + T* | |
| 215 | 21128909 | (cpVapD/4)))); | |
| 216 | } | ||
| 217 | |||
| 218 | /*! | ||
| 219 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$N_2\f$ at a given pressure and temperature. | ||
| 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 | * See: | ||
| 225 | * | ||
| 226 | * See: R. Reid, et al.: The Properties of Gases and Liquids, | ||
| 227 | * 4th edition (1987, pp 396-397) \cite reid1987 <BR> | ||
| 228 | * 5th edition (2001, pp 9.7-9.8 (omega and V_c taken from p. A.19)) \cite poling2001 | ||
| 229 | * | ||
| 230 | */ | ||
| 231 | 16838318 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 232 | { | ||
| 233 | 16838318 | const Scalar Tc = criticalTemperature(); | |
| 234 | 16838318 | const Scalar Vc = 90.1; // critical specific volume [cm^3/mol] | |
| 235 | 16838318 | const Scalar omega = 0.037; // accentric factor | |
| 236 | 16838318 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
| 237 | 16838318 | const Scalar dipole = 0.0; // dipole moment [debye] | |
| 238 | |||
| 239 | using std::sqrt; | ||
| 240 | 16838318 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | |
| 241 | 16838318 | mu_r4 *= mu_r4; | |
| 242 | 16838318 | mu_r4 *= mu_r4; | |
| 243 | |||
| 244 | using std::pow; | ||
| 245 | using std::exp; | ||
| 246 | 16838318 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
| 247 | 16838318 | Scalar Tstar = 1.2593 * temperature/Tc; | |
| 248 | 16838318 | Scalar Omega_v = | |
| 249 | 33676636 | 1.16145*pow(Tstar, -0.14874) + | |
| 250 | 16838318 | 0.52487*exp(- 0.77320*Tstar) + | |
| 251 | 16838318 | 2.16178*exp(- 2.43787*Tstar); | |
| 252 | 16838318 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
| 253 | |||
| 254 | // conversion from micro poise to Pa s | ||
| 255 | 16838318 | return mu/1e6 / 10; | |
| 256 | } | ||
| 257 | |||
| 258 | /*! | ||
| 259 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of nitrogen. | ||
| 260 | * | ||
| 261 | * Isobaric Properties for Nitrogen and Oxygen in: NIST Standard | ||
| 262 | * Reference Database Number 69, Eds. P.J. Linstrom and | ||
| 263 | * W.G. Mallard evaluated at p=.1 MPa, does not | ||
| 264 | * change dramatically with p and can be interpolated linearly with temperature | ||
| 265 | * | ||
| 266 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 267 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 268 | */ | ||
| 269 | ✗ | static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 270 | { | ||
| 271 | 18067090 | return 6.525e-5 * (temperature - 273.15) + 0.024031; | |
| 272 | } | ||
| 273 | }; | ||
| 274 | |||
| 275 | } // end namespace Components | ||
| 276 | |||
| 277 | } // end namespace Dumux | ||
| 278 | |||
| 279 | #endif | ||
| 280 |