n2.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
//
// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
// SPDX-License-Identifier: GPL-3.0-or-later
//
#ifndef DUMUX_N2_HH
#define DUMUX_N2_HH
 
#include <dumux/material/idealgas.hh>
 
#include <cmath>
 
#include <dumux/material/components/base.hh>
#include <dumux/material/components/gas.hh>
#include <dumux/material/components/shomate.hh>
 
namespace Dumux {
namespace Components {
 
template <class Scalar>
class N2
: public Components::Base<Scalar, N2<Scalar> >
, public Components::Gas<Scalar, N2<Scalar> >
{
    using IdealGas = Dumux::IdealGas<Scalar>;
    using ShomateMethod = Dumux::ShomateMethod<Scalar, 3>; // 3 regions
 
public:
    static const ShomateMethod shomateMethod;
    static std::string name()
    { return "N2"; }
 
    static constexpr Scalar molarMass()
    { return 28.0134e-3;}
 
    static Scalar criticalTemperature()
    { return 126.192; /* [K] */ }
 
    static Scalar criticalPressure()
    { return 3.39858e6; /* [N/m^2] */ }
 
    static Scalar tripleTemperature()
    { return 63.151; /* [K] */ }
 
    static Scalar triplePressure()
    { return 12.523e3; /* [N/m^2] */ }
 
    static Scalar vaporPressure(Scalar T)
    {
        if (T > criticalTemperature())
            return criticalPressure();
        if (T < tripleTemperature())
            return 0; // N2 is solid: We don't take sublimation into
                      // account
 
        // note: this is the ancillary equation given on page 1368
        using std::sqrt;
        Scalar sigma = Scalar(1.0) - T/criticalTemperature();
        Scalar sqrtSigma = sqrt(sigma);
        const Scalar N1 = -6.12445284;
        const Scalar N2 = 1.26327220;
        const Scalar N3 = -0.765910082;
        const Scalar N4 = -1.77570564;
 
        using std::exp;
        return
            criticalPressure() *
            exp(criticalTemperature()/T*
                     (sigma*(N1 +
                             sqrtSigma*N2 +
                             sigma*(sqrtSigma*N3 +
                                    sigma*sigma*sigma*N4))));
    }
 
    static Scalar gasDensity(Scalar temperature, Scalar pressure)
    {
        // Assume an ideal gas
        return IdealGas::density(molarMass(), temperature, pressure);
    }
 
    static Scalar gasMolarDensity(Scalar temperature, Scalar pressure)
    { return IdealGas::molarDensity(temperature, pressure); }
 
    static constexpr bool gasIsCompressible()
    { return true; }
 
    static constexpr bool gasIsIdeal()
    { return true; }
 
    static Scalar gasPressure(Scalar temperature, Scalar density)
    {
        // Assume an ideal gas
        return IdealGas::pressure(temperature, density/molarMass());
    }
 
    static const Scalar gasEnthalpy(Scalar temperature,
                                    Scalar pressure)
    {
        const auto h = shomateMethod.enthalpy(temperature); // KJ/mol
        return h * 1e3 / molarMass(); // J/kg
    }
 
    static const Scalar gasInternalEnergy(Scalar temperature,
                                          Scalar pressure)
    {
        return
            gasEnthalpy(temperature, pressure) -
            1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
            IdealGas::R*temperature; // = pressure * spec. volume for an ideal gas
    }
 
    static const Scalar gasHeatCapacity(Scalar T,
                                        Scalar pressure)
    {
        const auto cp = shomateMethod.heatCapacity(T); // J/(mol K)
        return cp / molarMass(); // J/(kg K)
    }
 
    static Scalar gasViscosity(Scalar temperature, Scalar pressure)
    {
        const Scalar Tc = criticalTemperature();
        const Scalar Vc = 90.1; // critical specific volume [cm^3/mol]
        const Scalar omega = 0.037; // accentric factor
        const Scalar M = molarMass() * 1e3; // molar mas [g/mol]
        const Scalar dipole = 0.0; // dipole moment [debye]
 
        using std::sqrt;
        Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc);
        mu_r4 *= mu_r4;
        mu_r4 *= mu_r4;
 
        using std::pow;
        using std::exp;
        Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4;
        Scalar Tstar = 1.2593 * temperature/Tc;
        Scalar Omega_v =
            1.16145*pow(Tstar, -0.14874) +
            0.52487*exp(- 0.77320*Tstar) +
            2.16178*exp(- 2.43787*Tstar);
        Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v);
 
        // conversion from micro poise to Pa s
        return mu/1e6 / 10;
    }
 
    static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure)
    {
        return 6.525e-5 * (temperature - 273.15) + 0.024031;
    }
};
 
template <class Scalar>
const typename N2<Scalar>::ShomateMethod N2<Scalar>::shomateMethod{
    /*temperature*/{100.0,500.0,2000.0,6000.0},
    typename N2<Scalar>::ShomateMethod::Coefficients{{
        {28.98641, 1.853978, -9.647459, 16.63537, 0.000117, -8.671914, 226.4168, 0.0},
        {19.50583, 19.88705, -8.598535, 1.369784, 0.527601, -4.935202, 212.39, 0.0},
        {35.51872, 1.128728, -0.196103, 0.014662, -4.55376, -18.97091, 224.981, 0.0}
    }}
};
 
} // end namespace Components
} // end namespace Dumux
 
#endif