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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 | |||
22 | namespace Dumux { | ||
23 | namespace Components { | ||
24 | |||
25 | /*! | ||
26 | * \ingroup Components | ||
27 | * \brief Properties of pure molecular hydrogen \f$H_2\f$. | ||
28 | * | ||
29 | * \tparam Scalar The type used for scalar values | ||
30 | */ | ||
31 | template <class Scalar> | ||
32 | class H2 | ||
33 | : public Components::Base<Scalar, H2<Scalar> > | ||
34 | , public Components::Gas<Scalar, H2<Scalar> > | ||
35 | { | ||
36 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
37 | |||
38 | public: | ||
39 | /*! | ||
40 | * \brief A human readable name for the \f$H_2\f$. | ||
41 | */ | ||
42 | static std::string name() | ||
43 |
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|
8 | { return "H2"; } |
44 | |||
45 | /*! | ||
46 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular hydrogen. | ||
47 | */ | ||
48 | static constexpr Scalar molarMass() | ||
49 | { return 2.01588e-3; } | ||
50 | |||
51 | /*! | ||
52 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of molecular hydrogen. | ||
53 | */ | ||
54 | static Scalar criticalTemperature() | ||
55 | { return 33.2; /* [K] */ } | ||
56 | |||
57 | /*! | ||
58 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of molecular hydrogen. | ||
59 | */ | ||
60 | static Scalar criticalPressure() | ||
61 | { return 13.0e5; /* [N/m^2] */ } | ||
62 | |||
63 | /*! | ||
64 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at molecular hydrogen's triple point. | ||
65 | */ | ||
66 | static Scalar tripleTemperature() | ||
67 | { return 14.0; /* [K] */ } | ||
68 | |||
69 | /*! | ||
70 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular hydrogen | ||
71 | * at a given temperature. | ||
72 | * | ||
73 | *\param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
74 | * | ||
75 | * Taken from: | ||
76 | * | ||
77 | * See: R. Reid, et al. (1987, pp 208-209, 669) \cite reid1987 | ||
78 | * | ||
79 | * \todo implement the Gomez-Thodos approach... | ||
80 | */ | ||
81 | static Scalar vaporPressure(Scalar temperature) | ||
82 | { | ||
83 | if (temperature > criticalTemperature()) | ||
84 | return criticalPressure(); | ||
85 | if (temperature < tripleTemperature()) | ||
86 | return 0; // H2 is solid: We don't take sublimation into | ||
87 | // account | ||
88 | |||
89 | // antoine equatuion | ||
90 | const Scalar A = -7.76451; | ||
91 | const Scalar B = 1.45838; | ||
92 | const Scalar C = -2.77580; | ||
93 | |||
94 | using std::exp; | ||
95 | return 1e5 * exp(A - B/(temperature + C)); | ||
96 | } | ||
97 | |||
98 | /*! | ||
99 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of \f$H_2\f$ at a given pressure and temperature. | ||
100 | * | ||
101 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
102 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
103 | */ | ||
104 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
105 | { | ||
106 | // Assume an ideal gas | ||
107 | 202 | return IdealGas::density(molarMass(), temperature, pressure); | |
108 | } | ||
109 | |||
110 | /*! | ||
111 | * \brief The molar density of \f$H_2\f$ in \f$\mathrm{[mol/m^3]}\f$, | ||
112 | * depending on pressure and temperature. | ||
113 | * \param temperature The temperature of the gas | ||
114 | * \param pressure The pressure of the gas | ||
115 | */ | ||
116 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
117 | { return IdealGas::molarDensity(temperature, pressure); } | ||
118 | |||
119 | /*! | ||
120 | * \brief Returns true if the gas phase is assumed to be compressible | ||
121 | */ | ||
122 | static constexpr bool gasIsCompressible() | ||
123 | { return true; } | ||
124 | |||
125 | /*! | ||
126 | * \brief Returns true if the gas phase is assumed to be ideal | ||
127 | */ | ||
128 | static constexpr bool gasIsIdeal() | ||
129 | { return true; } | ||
130 | |||
131 | /*! | ||
132 | * \brief The pressure of gaseous \f$H_2\f$ in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
133 | * | ||
134 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
135 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
136 | */ | ||
137 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
138 | { | ||
139 | // Assume an ideal gas | ||
140 | return IdealGas::pressure(temperature, density/molarMass()); | ||
141 | } | ||
142 | |||
143 | /*! | ||
144 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure hydrogen gas. | ||
145 | * | ||
146 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
147 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
148 | */ | ||
149 | ✗ | static const Scalar gasEnthalpy(Scalar temperature, | |
150 | Scalar pressure) | ||
151 | { | ||
152 | 202 | return gasHeatCapacity(temperature, pressure) * temperature; | |
153 | } | ||
154 | |||
155 | /*! | ||
156 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure | ||
157 | * hydrogen gas. | ||
158 | * | ||
159 | * This is equivalent to the partial derivative of the specific | ||
160 | * enthalpy to the temperature. | ||
161 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
162 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
163 | * | ||
164 | * See: R. Reid, et al. (1987, pp 154, 657, 665) \cite reid1987 | ||
165 | */ | ||
166 | ✗ | static const Scalar gasHeatCapacity(Scalar T, | |
167 | Scalar pressure) | ||
168 | { | ||
169 | // method of Joback | ||
170 | 202 | const Scalar cpVapA = 27.14; | |
171 | 202 | const Scalar cpVapB = 9.273e-3; | |
172 | 202 | const Scalar cpVapC = -1.381e-5; | |
173 | 202 | const Scalar cpVapD = 7.645e-9; | |
174 | |||
175 | return | ||
176 | 1/molarMass()* // conversion from [J/(mol*K)] to [J/(kg*K)] | ||
177 | 202 | (cpVapA + T* | |
178 | 202 | (cpVapB/2 + T* | |
179 | 202 | (cpVapC/3 + T* | |
180 | 202 | (cpVapD/4)))); | |
181 | } | ||
182 | |||
183 | /*! | ||
184 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$H_2\f$ at a given pressure and temperature. | ||
185 | * | ||
186 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
187 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
188 | * | ||
189 | * See: | ||
190 | * | ||
191 | * See: R. Reid, et al.: The Properties of Gases and Liquids, | ||
192 | * 4th edition (1987, pp 396-397, 667) \cite reid1987 <BR> | ||
193 | * 5th edition (2001, pp 9.7-9.8 (omega and V_c taken from p. A.19)) \cite poling2001 | ||
194 | */ | ||
195 | 101 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
196 | { | ||
197 | 101 | const Scalar Tc = criticalTemperature(); | |
198 | 101 | const Scalar Vc = 65.0; // critical specific volume [cm^3/mol] | |
199 | 101 | const Scalar omega = -0.216; // accentric factor | |
200 | 101 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
201 | 101 | const Scalar dipole = 0.0; // dipole moment [debye] | |
202 | |||
203 | using std::sqrt; | ||
204 | 101 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | |
205 | 101 | mu_r4 *= mu_r4; | |
206 | 101 | mu_r4 *= mu_r4; | |
207 | |||
208 | using std::pow; | ||
209 | using std::exp; | ||
210 | 101 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
211 | 101 | Scalar Tstar = 1.2593 * temperature/Tc; | |
212 | 101 | Scalar Omega_v = | |
213 | 202 | 1.16145*pow(Tstar, -0.14874) + | |
214 | 101 | 0.52487*exp(- 0.77320*Tstar) + | |
215 | 101 | 2.16178*exp(- 2.43787*Tstar); | |
216 | 101 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
217 | |||
218 | // conversion from micro poise to Pa s | ||
219 | 101 | return mu/1e6 / 10; | |
220 | } | ||
221 | }; | ||
222 | |||
223 | } // end namespace Components | ||
224 | |||
225 | } // end namespace Dumux | ||
226 | |||
227 | #endif | ||
228 |