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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 hydrogen \f$H_2\f$. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_H2_HH | ||
| 13 | #define DUMUX_H2_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 hydrogen \f$H_2\f$. | ||
| 29 | * | ||
| 30 | * \tparam Scalar The type used for scalar values | ||
| 31 | */ | ||
| 32 | template <class Scalar> | ||
| 33 | class H2 | ||
| 34 | : public Components::Base<Scalar, H2<Scalar> > | ||
| 35 | , public Components::Gas<Scalar, H2<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$H_2\f$. | ||
| 45 | */ | ||
| 46 | static std::string name() | ||
| 47 |
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|
8 | { return "H2"; } |
| 48 | |||
| 49 | /*! | ||
| 50 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular hydrogen. | ||
| 51 | */ | ||
| 52 | static constexpr Scalar molarMass() | ||
| 53 | { return 2.01588e-3; } | ||
| 54 | |||
| 55 | /*! | ||
| 56 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of molecular hydrogen. | ||
| 57 | */ | ||
| 58 | static Scalar criticalTemperature() | ||
| 59 | { return 33.2; /* [K] */ } | ||
| 60 | |||
| 61 | /*! | ||
| 62 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of molecular hydrogen. | ||
| 63 | */ | ||
| 64 | static Scalar criticalPressure() | ||
| 65 | { return 13.0e5; /* [N/m^2] */ } | ||
| 66 | |||
| 67 | /*! | ||
| 68 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at molecular hydrogen's triple point. | ||
| 69 | */ | ||
| 70 | static Scalar tripleTemperature() | ||
| 71 | { return 14.0; /* [K] */ } | ||
| 72 | |||
| 73 | /*! | ||
| 74 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular hydrogen | ||
| 75 | * at a given temperature. | ||
| 76 | * | ||
| 77 | *\param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 78 | * | ||
| 79 | * Taken from: | ||
| 80 | * | ||
| 81 | * See: R. Reid, et al. (1987, pp 208-209, 669) \cite reid1987 | ||
| 82 | * | ||
| 83 | * \todo implement the Gomez-Thodos approach... | ||
| 84 | */ | ||
| 85 | static Scalar vaporPressure(Scalar temperature) | ||
| 86 | { | ||
| 87 | if (temperature > criticalTemperature()) | ||
| 88 | return criticalPressure(); | ||
| 89 | if (temperature < tripleTemperature()) | ||
| 90 | return 0; // H2 is solid: We don't take sublimation into | ||
| 91 | // account | ||
| 92 | |||
| 93 | // antoine equatuion | ||
| 94 | const Scalar A = -7.76451; | ||
| 95 | const Scalar B = 1.45838; | ||
| 96 | const Scalar C = -2.77580; | ||
| 97 | |||
| 98 | using std::exp; | ||
| 99 | return 1e5 * exp(A - B/(temperature + C)); | ||
| 100 | } | ||
| 101 | |||
| 102 | /*! | ||
| 103 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of \f$H_2\f$ at a given pressure and temperature. | ||
| 104 | * | ||
| 105 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 106 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 107 | */ | ||
| 108 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 109 | { | ||
| 110 | // Assume an ideal gas | ||
| 111 | 202 | return IdealGas::density(molarMass(), temperature, pressure); | |
| 112 | } | ||
| 113 | |||
| 114 | /*! | ||
| 115 | * \brief The molar density of \f$H_2\f$ in \f$\mathrm{[mol/m^3]}\f$, | ||
| 116 | * depending on pressure and temperature. | ||
| 117 | * \param temperature The temperature of the gas | ||
| 118 | * \param pressure The pressure of the gas | ||
| 119 | */ | ||
| 120 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 121 | { return IdealGas::molarDensity(temperature, pressure); } | ||
| 122 | |||
| 123 | /*! | ||
| 124 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 125 | */ | ||
| 126 | static constexpr bool gasIsCompressible() | ||
| 127 | { return true; } | ||
| 128 | |||
| 129 | /*! | ||
| 130 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 131 | */ | ||
| 132 | static constexpr bool gasIsIdeal() | ||
| 133 | { return true; } | ||
| 134 | |||
| 135 | /*! | ||
| 136 | * \brief The pressure of gaseous \f$H_2\f$ in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 137 | * | ||
| 138 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 139 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 140 | */ | ||
| 141 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 142 | { | ||
| 143 | // Assume an ideal gas | ||
| 144 | return IdealGas::pressure(temperature, density/molarMass()); | ||
| 145 | } | ||
| 146 | |||
| 147 | /*! | ||
| 148 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure hydrogen gas. | ||
| 149 | * Shomate Equation is used for a temperature range of 298K to 6000K. | ||
| 150 | * | ||
| 151 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 152 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 153 | */ | ||
| 154 | ✗ | static const Scalar gasEnthalpy(Scalar temperature, | |
| 155 | Scalar pressure) | ||
| 156 | { | ||
| 157 |
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101 | const auto h = shomateMethod.enthalpy(temperature); // KJ/mol |
| 158 | 101 | return h * 1e3 / molarMass(); // J/kg | |
| 159 | } | ||
| 160 | |||
| 161 | /*! | ||
| 162 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure | ||
| 163 | * hydrogen gas. | ||
| 164 | * Shomate Equation is used for a temperature range of 298K to 6000K. | ||
| 165 | * | ||
| 166 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 167 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 168 | * | ||
| 169 | * See: R. Reid, et al. (1987, pp 154, 657, 665) \cite reid1987 | ||
| 170 | */ | ||
| 171 | ✗ | static const Scalar gasHeatCapacity(Scalar T, | |
| 172 | Scalar pressure) | ||
| 173 | { | ||
| 174 |
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101 | const auto cp = shomateMethod.heatCapacity(T); // J/(mol K) |
| 175 | 101 | return cp / molarMass(); // J/(kg K) | |
| 176 | } | ||
| 177 | |||
| 178 | /*! | ||
| 179 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$H_2\f$ at a given pressure and temperature. | ||
| 180 | * | ||
| 181 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 182 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 183 | * | ||
| 184 | * See: | ||
| 185 | * | ||
| 186 | * See: R. Reid, et al.: The Properties of Gases and Liquids, | ||
| 187 | * 4th edition (1987, pp 396-397, 667) \cite reid1987 <BR> | ||
| 188 | * 5th edition (2001, pp 9.7-9.8 (omega and V_c taken from p. A.19)) \cite poling2001 | ||
| 189 | */ | ||
| 190 | 101 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 191 | { | ||
| 192 | 101 | const Scalar Tc = criticalTemperature(); | |
| 193 | 101 | const Scalar Vc = 65.0; // critical specific volume [cm^3/mol] | |
| 194 | 101 | const Scalar omega = -0.216; // accentric factor | |
| 195 | 101 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
| 196 | 101 | const Scalar dipole = 0.0; // dipole moment [debye] | |
| 197 | |||
| 198 | using std::sqrt; | ||
| 199 | 101 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | |
| 200 | 101 | mu_r4 *= mu_r4; | |
| 201 | 101 | mu_r4 *= mu_r4; | |
| 202 | |||
| 203 | using std::pow; | ||
| 204 | using std::exp; | ||
| 205 | 101 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
| 206 | 101 | Scalar Tstar = 1.2593 * temperature/Tc; | |
| 207 | 101 | Scalar Omega_v = | |
| 208 | 202 | 1.16145*pow(Tstar, -0.14874) + | |
| 209 | 101 | 0.52487*exp(- 0.77320*Tstar) + | |
| 210 | 101 | 2.16178*exp(- 2.43787*Tstar); | |
| 211 | 101 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
| 212 | |||
| 213 | // conversion from micro poise to Pa s | ||
| 214 | 101 | return mu/1e6 / 10; | |
| 215 | } | ||
| 216 | }; | ||
| 217 | |||
| 218 | /*! | ||
| 219 | * \brief Shomate parameters for hydrogen published by NIST \cite NIST | ||
| 220 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Units=SI&Mask=1&Type=JANAFG&Table=on#JANAFG | ||
| 221 | * First row defines the temperature ranges, further rows give the parameters (A,B,C,D,E,F,G,H) for the respective temperature ranges. | ||
| 222 | */ | ||
| 223 | template <class Scalar> | ||
| 224 | const typename H2<Scalar>::ShomateMethod H2<Scalar>::shomateMethod{ | ||
| 225 | /*temperature*/{298.0, 1000.0, 2500.0, 6000.0}, | ||
| 226 | typename H2<Scalar>::ShomateMethod::Coefficients{{ | ||
| 227 | {33.066178, -11.363417, 11.432816, -2.772874, -0.158558, -9.980797, 172.707974, 0.0}, | ||
| 228 | {18.563083, 12.257357, -2.859786, 0.268238, 1.97799, -1.147438, 156.288133, 0.0}, | ||
| 229 | {43.41356, -4.293079, 1.272428, -0.096876, -20.533862, -38.515158, 162.081354, 0.0} | ||
| 230 | }} | ||
| 231 | }; | ||
| 232 | |||
| 233 | } // end namespace Components | ||
| 234 | } // end namespace Dumux | ||
| 235 | |||
| 236 | #endif | ||
| 237 |