GasTransportUtils.h

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html
 
#pragma once
 
#include "MooseTypes.h"
#include "PhysicalConstants.h"
#include "libmesh/libmesh_common.h"
 
#include <cmath>
#include <string>
 
namespace GasTransportUtils
{
struct LennardJonesParameters
{
  Real sigma;
  Real epsilon_over_k;
};
 
const LennardJonesParameters & lennardJonesParameters(const std::string & name);
 
template <typename CppType>
CppType
collisionIntegral11(const CppType & T_reduced)
{
  using std::exp, std::pow;
  return 1.06036 / pow(T_reduced, 0.15610) + 0.19300 * exp(-0.47635 * T_reduced) +
         1.03587 * exp(-1.52996 * T_reduced) + 1.76474 * exp(-3.89411 * T_reduced);
}
 
template <typename CppType>
CppType
collisionIntegral22(const CppType & T_reduced)
{
  using std::exp, std::pow;
  return 1.16145 / pow(T_reduced, 0.14874) + 0.52487 * exp(-0.77320 * T_reduced) +
         2.16178 * exp(-2.43787 * T_reduced);
}
 
template <typename CppType>
CppType
viscosity(const CppType & T, const Real molar_mass, const LennardJonesParameters & lj)
{
  using std::sqrt;
  const Real molecular_mass = molar_mass / PhysicalConstants::avogadro_number;
  return 5.0 / 16.0 *
         sqrt(molecular_mass * PhysicalConstants::boltzmann_constant * T / libMesh::pi) /
         (lj.sigma * lj.sigma * collisionIntegral22(T / lj.epsilon_over_k));
}
 
template <typename CppType>
CppType
binaryDiffusionCoefficient(const CppType & p,
                           const CppType & T,
                           const Real molar_mass_i,
                           const Real molar_mass_j,
                           const LennardJonesParameters & lj_i,
                           const LennardJonesParameters & lj_j)
{
  using std::sqrt;
  const Real sigma = 0.5 * (lj_i.sigma + lj_j.sigma);
  const Real epsilon_over_k = std::sqrt(lj_i.epsilon_over_k * lj_j.epsilon_over_k);
  const Real reduced_mass = molar_mass_i * molar_mass_j / (molar_mass_i + molar_mass_j) /
                            PhysicalConstants::avogadro_number;
  const Real k_B = PhysicalConstants::boltzmann_constant;
  return 3.0 / 16.0 * sqrt(2 * libMesh::pi * k_B * T / reduced_mass) * k_B * T /
         (p * libMesh::pi * sigma * sigma * collisionIntegral11(T / epsilon_over_k));
}
 
template <typename CppType>
CppType
modifiedEuckenConductivity(const CppType & mu, const CppType & cp_over_R, const Real R_specific)
{
  return mu * R_specific * (1.32 * cp_over_R + 0.45);
}
 
template <typename CppType>
CppType
steamViscosityZeroDensity(const CppType & T)
{
  using std::sqrt;
  // Critical temperature of water [K]
  const CppType Tbar = T / 647.096;
  const CppType sum =
      1.67752 + 2.20462 / Tbar + 0.6366564 / (Tbar * Tbar) - 0.241605 / (Tbar * Tbar * Tbar);
  // The formulation gives the viscosity in micropascal seconds
  return 1e-6 * 100 * sqrt(Tbar) / sum;
}
 
template <typename CppType>
CppType
steamConductivityZeroDensity(const CppType & T)
{
  using std::sqrt;
  // Critical temperature of water [K]
  const CppType Tbar = T / 647.096;
  const CppType sum =
      2.443221e-3 +
      (1.323095e-2 + (6.770357e-3 + (-3.454586e-3 + 4.096266e-4 / Tbar) / Tbar) / Tbar) / Tbar;
  // The formulation gives the conductivity in milliwatts per meter and kelvin
  return 1e-3 * sqrt(Tbar) / sum;
}
}