GasTransportUtils Namespace Reference

Transport properties of dilute gases: Lennard-Jones parameters of the NASA 7-coefficient species, collision integrals, Chapman-Enskog viscosity and binary diffusion coefficients, the modified Eucken thermal conductivity, and the low-density viscosity and thermal conductivity of steam. More...

Classes
struct	LennardJonesParameters
	Parameters of the Lennard-Jones (12-6) potential of a species. More...

Functions
const LennardJonesParameters &	lennardJonesParameters (const std::string &name)
	Lennard-Jones parameters of a built-in species.
template<typename CppType >
CppType	collisionIntegral11 (const CppType &T_reduced)
	Reduced collision integral Omega(1,1)* of the Lennard-Jones potential, which enters the binary diffusion coefficient, from the fit of Neufeld et al.
template<typename CppType >
CppType	collisionIntegral22 (const CppType &T_reduced)
	Reduced collision integral Omega(2,2)* of the Lennard-Jones potential, which enters the viscosity, from the fit of Neufeld et al.
template<typename CppType >
CppType	viscosity (const CppType &T, const Real molar_mass, const LennardJonesParameters &lj)
	Chapman-Enskog viscosity of a dilute gas [Pa s].
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)
	Chapman-Enskog binary diffusion coefficient of a dilute gas pair [m^2/s], with the Lorentz-Berthelot combining rules for the Lennard-Jones parameters of the pair.
template<typename CppType >
CppType	modifiedEuckenConductivity (const CppType &mu, const CppType &cp_over_R, const Real R_specific)
	Thermal conductivity of a dilute gas from the modified Eucken correlation [W/(m K)], k = mu R_s (1.32 cp/R + 0.45), with the specific gas constant R_s.
template<typename CppType >
CppType	steamViscosityZeroDensity (const CppType &T)
	Viscosity of steam in the limit of zero density [Pa s], from the IAPWS 2008 formulation, as in Water97FluidProperties.
template<typename CppType >
CppType	steamConductivityZeroDensity (const CppType &T)
	Thermal conductivity of steam in the limit of zero density [W/(m K)], from the IAPWS 2011 formulation.

Detailed Description

Transport properties of dilute gases: Lennard-Jones parameters of the NASA 7-coefficient species, collision integrals, Chapman-Enskog viscosity and binary diffusion coefficients, the modified Eucken thermal conductivity, and the low-density viscosity and thermal conductivity of steam.

The functions are templated so that they accept automatic differentiation types.

Function Documentation

binaryDiffusionCoefficient()

template<typename CppType >

CppType GasTransportUtils::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
	)

Chapman-Enskog binary diffusion coefficient of a dilute gas pair [m^2/s], with the Lorentz-Berthelot combining rules for the Lennard-Jones parameters of the pair.

Parameters

[in]	p	pressure [Pa]
[in]	T	temperature [K]
[in]	molar_mass_i	molar mass of the first species [kg/mol]
[in]	molar_mass_j	molar mass of the second species [kg/mol]
[in]	lj_i	Lennard-Jones parameters of the first species
[in]	lj_j	Lennard-Jones parameters of the second species

Definition at line 101 of file GasTransportUtils.h.

{
  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));
}

Referenced by IdealGasMixtureFluidProperties::binaryDiffusionCoefficient_templ(), TEST_F(), TEST_F(), and TEST_F().

collisionIntegral11()

template<typename CppType >

CppType GasTransportUtils::collisionIntegral11

(

const CppType &

T_reduced

)

Reduced collision integral Omega(1,1)* of the Lennard-Jones potential, which enters the binary diffusion coefficient, from the fit of Neufeld et al.

(1972), valid for reduced temperatures from 0.3 to 100

Definition at line 50 of file GasTransportUtils.h.

{
  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);
}

Referenced by binaryDiffusionCoefficient().

collisionIntegral22()

template<typename CppType >

CppType GasTransportUtils::collisionIntegral22

(

const CppType &

T_reduced

)

Reduced collision integral Omega(2,2)* of the Lennard-Jones potential, which enters the viscosity, from the fit of Neufeld et al.

(1972), valid for reduced temperatures from 0.3 to 100

Definition at line 63 of file GasTransportUtils.h.

{
  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);
}

Referenced by viscosity().

lennardJonesParameters()

const LennardJonesParameters & GasTransportUtils::lennardJonesParameters

(

const std::string &

name

)

Lennard-Jones parameters of a built-in species.

Parameters

[in]

name

species name: H2, O2, H2O, CH4, CO, CO2, or N2

Definition at line 34 of file GasTransportUtils.C.

{
  for (const auto & [species, parameters] : lennard_jones_data)
    if (species == name)
      return parameters;
 
  mooseError("No Lennard-Jones parameters for species '", name, "'.");
}

Referenced by TEST_F(), TEST_F(), and TEST_F().

modifiedEuckenConductivity()

template<typename CppType >

CppType GasTransportUtils::modifiedEuckenConductivity	(	const CppType &	mu,
		const CppType &	cp_over_R,
		const Real	R_specific
	)

Thermal conductivity of a dilute gas from the modified Eucken correlation [W/(m K)], k = mu R_s (1.32 cp/R + 0.45), with the specific gas constant R_s.

Parameters

[in]	mu	viscosity [Pa s]
[in]	cp_over_R	molar isobaric heat capacity divided by the gas constant
[in]	R_specific	specific gas constant [J/(kg K)]

Definition at line 128 of file GasTransportUtils.h.

{
  return mu * R_specific * (1.32 * cp_over_R + 0.45);
}

Referenced by NASA7IdealGasFluidProperties::k_from_T().

steamConductivityZeroDensity()

template<typename CppType >

CppType GasTransportUtils::steamConductivityZeroDensity

(

const CppType &

T

)

Thermal conductivity of steam in the limit of zero density [W/(m K)], from the IAPWS 2011 formulation.

Water97FluidProperties uses the IAPS 1985 formulation, whose zero-density term agrees within 2% below 1500 K but decreases above about 2200 K and becomes negative near 3300 K.

Definition at line 157 of file GasTransportUtils.h.

{
  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;
}

Referenced by NASA7IdealGasFluidProperties::k_from_T(), TEST_F(), and TEST_F().

steamViscosityZeroDensity()

template<typename CppType >

CppType GasTransportUtils::steamViscosityZeroDensity

(

const CppType &

T

)

Viscosity of steam in the limit of zero density [Pa s], from the IAPWS 2008 formulation, as in Water97FluidProperties.

Definition at line 139 of file GasTransportUtils.h.

{
  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;
}

Referenced by NASA7IdealGasFluidProperties::mu_from_T(), TEST_F(), and TEST_F().

viscosity()

template<typename CppType >

CppType GasTransportUtils::viscosity	(	const CppType &	T,
		const Real	molar_mass,
		const LennardJonesParameters &	lj
	)

Chapman-Enskog viscosity of a dilute gas [Pa s].

Parameters

[in]	T	temperature [K]
[in]	molar_mass	molar mass [kg/mol]
[in]	lj	Lennard-Jones parameters

Definition at line 79 of file GasTransportUtils.h.

{
  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));
}

Referenced by NASA7IdealGasFluidProperties::k_from_T(), NASA7IdealGasFluidProperties::mu_from_T(), TEST_F(), and TEST_F().