air.hh

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#ifndef DUMUX_AIR_HH
#define DUMUX_AIR_HH
 
#include <dune/common/math.hh>
 
#include <dumux/common/exceptions.hh>
#include <dumux/material/components/base.hh>
#include <dumux/material/components/gas.hh>
#include <dumux/material/idealgas.hh>
 
namespace Dumux {
namespace Components {

template <class Scalar>
class Air
: public Components::Base<Scalar, Air<Scalar> >
, public Components::Gas<Scalar, Air<Scalar> >
{
    using IdealGas = Dumux::IdealGas<Scalar>;
 
public:
    static std::string name()
    { return "Air"; }

    static constexpr Scalar molarMass()
    { return 0.02896; /* [kg/mol] */ }

    static Scalar criticalTemperature()
    { return 132.6312; /* [K] */ }

    static Scalar criticalPressure()
    { return 37.86e5; /* [Pa] */ }

    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 constexpr bool gasViscosityIsConstant()
    { return false; }

    static Scalar gasPressure(Scalar temperature, Scalar density)
    {
        // Assume an ideal gas
        return IdealGas::pressure(temperature, density/molarMass());
    }

    static Scalar oldGasViscosity(Scalar temperature, Scalar pressure)
    {
        const Scalar Tc = criticalTemperature();
        const Scalar Vc = 84.525138; // critical specific volume [cm^3/mol]
        const Scalar omega = 0.078; // accentric factor
        const Scalar M = molarMass() * 1e3; // molar mas [g/mol]
 
        const Scalar Fc = 1.0 - 0.2756*omega;
        const Scalar Tstar = 1.2593*temperature/Tc;
 
        using std::exp;
        using std::pow;
        const Scalar Omega_v = 1.16145*pow(Tstar, -0.14874)
                               + 0.52487*exp(-0.77320*Tstar)
                               + 2.16178*exp(-2.43787*Tstar);
 
        using std::cbrt;
        using std::sqrt;
        const Scalar mu = 40.785 * Fc * sqrt(M * temperature)/(cbrt(Vc * Vc) * Omega_v);
 
        // convertion from micro poise to Pa s
        return mu/1.0e6/10.0;
    }

    static Scalar gasViscosity(Scalar temperature, Scalar pressure)
    {
        // above 1200 K, the function becomes inaccurate
        // since this should realistically never happen, we can live with it
        const Scalar tempCelsius = temperature - 273.15;
        const Scalar pressureCorrectionFactor = 9.7115e-9*tempCelsius*tempCelsius - 5.5e-6*tempCelsius + 0.0010809;
 
        using std::sqrt;
        const Scalar mu = 1.496e-6 * sqrt(temperature * temperature * temperature) / (temperature + 120.0)
                          * (1.0 + (pressure/1.0e5 - 1.0)*pressureCorrectionFactor);
        return mu;
    }

    static Scalar simpleGasViscosity(Scalar temperature, Scalar pressure)
    {
        // above 1200 K, the function becomes inaccurate
        // since this should realistically never happen, we can live with it
        using std::sqrt;
        return 1.496e-6 * sqrt(temperature * temperature * temperature) / (temperature + 120.0);
    }

    static Scalar exactGasViscosity(Scalar temperature, Scalar pressure)
    {
        const Scalar epsk = 103.3; // [K]
 
        using std::log;
        using std::exp;
        using std::sqrt;
        const Scalar logTstar = log(temperature/epsk);
        const Scalar Omega = exp(0.431
                                 - 0.4623*logTstar
                                 + 0.08406*logTstar*logTstar
                                 + 0.005341*logTstar*logTstar*logTstar
                                 - 0.00331*logTstar*logTstar*logTstar*logTstar);
 
        const Scalar sigma = 0.36; // [nm]
        const Scalar eta0 = 0.0266958*sqrt(1000.0*molarMass()*temperature)/(sigma*sigma*Omega);
 
        using std::pow;
        using Dune::power;
        const Scalar tau = criticalTemperature()/temperature;
        const Scalar rhoc = 10.4477; // [mol/m^3]
        const Scalar delta = 0.001*pressure/(temperature*8.3144598)/rhoc;
        const Scalar etaR = 10.72 * pow(tau, 0.2) * delta
                            + 1.122 * pow(tau, 0.05) * power(delta, 4)
                            + 0.002019 * pow(tau, 2.4) * power(delta, 9)
                            - 8.876 * pow(tau, 0.6) * delta * exp(-delta)
                            - 0.02916 * pow(tau, 3.6) * power(delta, 8) * exp(-delta);
 
        return (eta0 + etaR)*1e-6;
    }

    static Scalar gasEnthalpy(Scalar temperature, Scalar pressure)
    {
        return gasHeatCapacity(temperature, pressure) * (temperature-273.15);
    }

    static const Scalar gasInternalEnergy(Scalar temperature,
                                          Scalar pressure)
    {
        return gasEnthalpy(temperature, pressure)
               - IdealGas::R * temperature // = pressure * molar volume for an ideal gas
                 / molarMass(); // conversion from [J/(mol K)] to [J/(kg K)]
    }

    static const Scalar gasHeatCapacity(Scalar temperature,
                                        Scalar pressure)
    {
        // scale temperature with reference temp of 100K
        Scalar phi = temperature/100;
 
        using std::pow;
        using Dune::power;
        Scalar c_p = 0.661738E+01
                -0.105885E+01 * phi
                +0.201650E+00 * power(phi,2)
                -0.196930E-01 * power(phi,3)
                +0.106460E-02 * power(phi,4)
                -0.303284E-04 * power(phi,5)
                +0.355861E-06 * power(phi,6);
        c_p +=  -0.549169E+01 * power(phi,-1)
                +0.585171E+01 * power(phi,-2)
                -0.372865E+01 * power(phi,-3)
                +0.133981E+01 * power(phi,-4)
                -0.233758E+00 * power(phi,-5)
                +0.125718E-01 * power(phi,-6);
        c_p *= IdealGas::R / molarMass(); // in J/(mol*K) / (kg/mol)
 
        return  c_p;
    }

    static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure)
    {
        return 0.0255535;
    }
};
 
} // end namespace Components
} // end namespace Dumux
 
#endif