Nitrogen (N2) fluid properties as a function of pressure (Pa) and temperature (K). More...

#include <NitrogenFluidProperties.h>

Inheritance diagram for NitrogenFluidProperties:

Public Member Functions
	NitrogenFluidProperties (const InputParameters &parameters)

virtual std::string	fluidName () const override
	Fluid name. More...

virtual Real	molarMass () const override
	Molar mass [kg/mol]. More...

virtual Real	mu_from_rho_T (Real density, Real temperature) const override

virtual void	mu_from_rho_T (Real density, Real temperature, Real ddensity_dT, Real &mu, Real &dmu_drho, Real &dmu_dT) const override
	Dynamic viscosity and its derivatives wrt density and temperature TODO: this shouldn't need 3 input args - AD will assume/call the 2-input version. More...

virtual Real	mu_from_p_T (Real pressure, Real temperature) const override

virtual void	mu_from_p_T (Real pressure, Real temperature, Real &mu, Real &dmu_dp, Real &dmu_dT) const override

virtual void	rho_mu_from_p_T (Real pressure, Real temperature, Real &rho, Real &mu) const override

virtual void	rho_mu_from_p_T (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT, Real &mu, Real &dmu_dp, Real &dmu_dT) const override
	Density and viscosity and their derivatives wrt pressure and temperature. More...

virtual Real	k_from_rho_T (Real density, Real temperature) const override

virtual Real	k_from_p_T (Real pressure, Real temperature) const override

virtual void	k_from_p_T (Real pressure, Real temperature, Real &k, Real &dk_dp, Real &dk_dT) const override

virtual Real	henryConstant (Real temperature) const override
	Henry's law constant for dissolution in water. More...

virtual void	henryConstant (Real temperature, Real &Kh, Real &dKh_dT) const override
	Henry's law constant for dissolution in water and derivative wrt temperature. More...

virtual Real	criticalPressure () const override
	Critical pressure. More...

virtual Real	criticalTemperature () const override
	Critical temperature. More...

virtual Real	criticalDensity () const override
	Critical density. More...

virtual Real	triplePointPressure () const override
	Triple point pressure. More...

virtual Real	triplePointTemperature () const override
	Triple point temperature. More...

virtual Real	vaporPressure (Real temperature) const override
	Vapor pressure. More...

virtual void	vaporPressure (Real temperature, Real &psat, Real &dpsat_dT) const override
	Vapor pressure. More...

Real	saturatedLiquidDensity (Real temperature) const
	Saturated liquid density of N2 Valid for temperatures between the triple point temperature and critical temperature. More...

Real	saturatedVaporDensity (Real temperature) const
	Saturated vapor density of N2 Valid for temperatures between the triple point temperature and critical temperature. More...

virtual Real	rho_from_p_T (Real pressure, Real temperature) const override

virtual void	rho_from_p_T (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT) const override

virtual Real	e_from_p_T (Real pressure, Real temperature) const override
	Internal energy from pressure and temperature. More...

virtual void	e_from_p_T (Real p, Real T, Real &e, Real &de_dp, Real &de_dT) const override
	Internal energy and its derivatives from pressure and temperature. More...

virtual Real	c_from_p_T (Real pressure, Real temperature) const override

virtual Real	cp_from_p_T (Real pressure, Real temperature) const override

virtual Real	cv_from_p_T (Real pressure, Real temperature) const override

virtual Real	s_from_p_T (Real pressure, Real temperature) const override

virtual void	s_from_p_T (Real p, Real T, Real &s, Real &ds_dp, Real &ds_dT) const override

virtual Real	h_from_p_T (Real pressure, Real temperature) const override

virtual void	h_from_p_T (Real p, Real T, Real &h, Real &dh_dp, Real &dh_dT) const override

virtual Real	p_from_rho_T (Real rho, Real T) const
	Pressure as a function of density and temperature. More...

virtual Real	rho (Real p, Real T) const
	Density from pressure and temperature. More...

e e e e s T T T T T rho v v T virtual e Real	s (Real pressure, Real temperature) const

virtual Real	beta_from_p_T (Real, Real) const

virtual void	beta_from_p_T (Real, Real, Real &, Real &, Real &) const

virtual void	rho_dpT (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT) const
	Density and its derivatives from pressure and temperature. More...

virtual Real	v_from_p_T (Real p, Real T) const
	Specific volume from pressure and temperature. More...

virtual void	v_from_p_T (Real p, Real T, Real &v, Real &dv_dp, Real &dv_dT) const
	Specific volume and its derivatives from pressure and temperature. More...

virtual Real	e_spndl_from_v (Real v) const
	Specific internal energy from temperature and specific volume. More...

virtual void	v_e_spndl_from_T (Real T, Real &v, Real &e) const
	Specific internal energy from temperature and specific volume. More...

virtual Real	h (Real p, Real T) const
	Specific enthalpy from pressure and temperature. More...

virtual void	h_dpT (Real pressure, Real temperature, Real &h, Real &dh_dp, Real &dh_dT) const
	Specific enthalpy and its derivatives from pressure and temperature. More...

virtual Real	e (Real pressure, Real temperature) const

virtual void	e_dpT (Real pressure, Real temperature, Real &e, Real &de_dp, Real &de_dT) const

virtual Real	beta (Real pressure, Real temperature) const

virtual Real	T_from_p_h (Real pressure, Real enthalpy) const
	Temperature from pressure and specific enthalpy. More...

virtual Real	criticalInternalEnergy () const
	Critical specific internal energy. More...

virtual void	rho_e_from_p_T (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT, Real &e, Real &de_dp, Real &de_dT) const
	Density and internal energy and their derivatives wrt pressure and temperature. More...

virtual void	rho_e_dpT (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT, Real &e, Real &de_dp, Real &de_dT) const

virtual Real	c (Real pressure, Real temperature) const

virtual Real	gamma_from_v_e (Real v, Real e) const
	Adiabatic index - ratio of specific heats. More...

virtual Real	gamma_from_p_T (Real pressure, Real temperature) const
	Adiabatic index - ratio of specific heats. More...

virtual Real	mu (Real pressure, Real temperature) const
	Dynamic viscosity. More...

virtual void	mu_dpT (Real pressure, Real temperature, Real &mu, Real &dmu_dp, Real &dmu_dT) const
	Dynamic viscosity and its derivatives wrt pressure and temperature. More...

virtual void	mu_drhoT_from_rho_T (Real density, Real temperature, Real ddensity_dT, Real &mu, Real &dmu_drho, Real &dmu_dT) const

virtual void	rho_mu (Real pressure, Real temperature, Real &rho, Real &mu) const
	Density and viscosity. More...

virtual void	rho_mu_dpT (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT, Real &mu, Real &dmu_dp, Real &dmu_dT) const

virtual Real	k (Real pressure, Real temperature) const
	Thermal conductivity. More...

virtual void	k_dpT (Real pressure, Real temperature, Real &k, Real &dk_dp, Real &dk_dT) const
	Thermal conductivity and its derivatives wrt pressure and temperature. More...

virtual void	henryConstant_dT (Real temperature, Real &Kh, Real &dKh_dT) const

virtual void	vaporPressure_dT (Real temperature, Real &psat, Real &dpsat_dT) const

virtual void	execute () final

virtual void	initialize () final

virtual void	finalize () final

virtual void	threadJoin (const UserObject &) final

virtual void	subdomainSetup () final

Protected Member Functions
virtual Real	alpha (Real delta, Real tau) const override
	Helmholtz free energy. More...

virtual Real	dalpha_ddelta (Real delta, Real tau) const override
	Derivative of Helmholtz free energy wrt delta. More...

virtual Real	dalpha_dtau (Real delta, Real tau) const override
	Derivative of Helmholtz free energy wrt tau. More...

virtual Real	d2alpha_ddelta2 (Real delta, Real tau) const override
	Second derivative of Helmholtz free energy wrt delta. More...

virtual Real	d2alpha_dtau2 (Real delta, Real tau) const override
	Second derivative of Helmholtz free energy wrt tau. More...

virtual Real	d2alpha_ddeltatau (Real delta, Real tau) const override
	Second derivative of Helmholtz free energy wrt delta and tau. More...

virtual Real	henryConstantIAPWS (Real temperature, Real A, Real B, Real C) const
	IAPWS formulation of Henry's law constant for dissolution in water From Guidelines on the Henry's constant and vapour liquid distribution constant for gases in H20 and D20 at high temperatures, IAPWS (2004) More...

virtual void	henryConstantIAPWS (Real temperature, Real &Kh, Real &dKh_dT, Real A, Real B, Real C) const

virtual void	henryConstantIAPWS_dT (Real temperature, Real &Kh, Real &dKh_dT, Real A, Real B, Real C) const

Protected Attributes
const Real	_Mn2
	Nitrogen molar mass (kg/mol) More...

const Real	_p_critical
	Critical pressure (Pa) More...

const Real	_T_critical
	Critical temperature (K) More...

const Real	_rho_molar_critical
	Critical molar density (mol/l) More...

const Real	_rho_critical
	Critical density (kg/m^3) More...

const Real	_p_triple
	Triple point pressure (Pa) More...

const Real	_T_triple
	Triple point temperature (K) More...

const std::array< Real, 8 >	_a
	Coefficients for ideal gas component of the Helmholtz free energy. More...

const std::array< Real, 6 >	_N1
	Coefficients for residual component of the Helmholtz free energy. More...

const std::array< unsigned int, 6 >	_i1 {{1, 1, 2, 2, 3, 3}}

const std::array< Real, 6 >	_j1 {{0.25, 0.875, 0.5, 0.875, 0.375, 0.75}}

const std::array< Real, 26 >	_N2

const std::array< unsigned int, 26 >	_i2

const std::array< Real, 26 >	_j2

const std::array< unsigned int, 26 >	_l2

const std::array< Real, 4 >	_N3

const std::array< unsigned int, 4 >	_i3 {{1, 1, 3, 2}}

const std::array< unsigned int, 4 >	_j3 {{0, 1, 2, 3}}

const std::array< unsigned int, 4 >	_l3 {{2, 2, 2, 2}}

const std::array< Real, 4 >	_phi3 {{20.0, 20.0, 15.0, 25.0}}

const std::array< Real, 4 >	_beta3 {{325.0, 325.0, 300.0, 275.0}}

const std::array< Real, 4 >	_gamma3 {{1.16, 1.16, 1.13, 1.25}}

const std::array< Real, 5 >	_bmu {{0.431, -0.4623, 0.08406, 0.005341, -0.00331}}
	Coefficients for viscosity. More...

const std::array< Real, 5 >	_Nmu {{10.72, 0.03989, 0.001208, -7.402, 4.62}}

const std::array< Real, 5 >	_tmu {{0.1, 0.25, 3.2, 0.9, 0.3}}

const std::array< Real, 5 >	_dmu {{2, 10, 12, 2, 1}}

const std::array< Real, 5 >	_lmu {{0, 1, 1, 2, 3}}

const std::array< Real, 5 >	_gammamu {{0.0, 1.0, 1.0, 1.0, 1.0}}

const std::array< Real, 6 >	_Nk {{8.862, 31.11, -73.13, 20.03, -0.7096, 0.2672}}
	Coefficients for thermal conductivity. More...

const std::array< Real, 6 >	_tk {{0.0, 0.03, 0.2, 0.8, 0.6, 1.9}}

const std::array< unsigned int, 6 >	_dk {{1, 2, 3, 4, 8, 10}}

const std::array< unsigned int, 6 >	_lk {{0, 0, 1, 2, 2, 2}}

const std::array< Real, 6 >	_gammak {{0.0, 0.0, 1.0, 1.0, 1.0}}

const Real	_R
	Universal gas constant (J/mol/K) More...

const Real	_T_c2k
	Conversion of temperature from Celsius to Kelvin. More...

const bool	_allow_imperfect_jacobians
	Flag to set unimplemented Jacobian entries to zero. More...

	propfunc (p, v, e) propfunc(T
	Compute a fluid property given for the state defined by two given properties. More...

e	propfunc (c, v, e) propfunc(cp

e e	propfunc (cv, v, e) propfunc(mu

e e e	propfunc (k, v, e) propfunc(s

e e e e	propfunc (s, h, p) propfunc(rho

e e e e s	propfunc (e, v, h) propfunc(s

e e e e s T	propfunc (pp_sat, p, T) propfunc(mu

e e e e s T T	propfunc (k, rho, T) propfunc(c

e e e e s T T T	propfunc (cp, p, T) propfunc(cv

e e e e s T T T T	propfunc (mu, p, T) propfunc(k

e e e e s T T T T T	propfunc (rho, p, T) propfunc(e

e e e e s T T T T T rho	propfunc (e, T, v) propfunc(p

e e e e s T T T T T rho v	propfunc (h, T, v) propfunc(s

e e e e s T T T T T rho v v	propfunc (cv, T, v) propfunc(h

e e e e s T T T T T rho v v T	propfunc (p, h, s) propfunc(g

	v

e	v

e e	v

e e e	v

e e e e s T T T T T rho v v T	v

e e e e	p

e e e e s	p

e e e e s T T	p

e e e e s T T T	p

e e e e s T T T T	p

e e e e s T T T T T	p

e e e e s T T T T T rho v v	p

e e e e s T	rho

e e e e s T T T T T rho	T

e e e e s T T T T T rho v	T

Detailed Description

Nitrogen (N2) fluid properties as a function of pressure (Pa) and temperature (K).

Thermodynamic properties calculated from: Span,. Lemmon, Jacobsen, Wagner and Yokozeki, A reference equation of state for the thermodynamic properties of nitrogen for temeperatures from 63.151 to 1000 K and pressures to 2200 MPa, Journal of Physical and Chemical Reference Data, 29, 1361–1433 (2000)

Viscosity and thermal conductivity calculated from: Lemmon and Jacobsen, Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air, International Journal of Thermophysics, 25, 21–69 (2004)

Definition at line 39 of file NitrogenFluidProperties.h.

Constructor & Destructor Documentation

◆ NitrogenFluidProperties()

NitrogenFluidProperties::NitrogenFluidProperties ( const InputParameters & parameters )

Definition at line 26 of file NitrogenFluidProperties.C.

   : HelmholtzFluidProperties(parameters),
     _Mn2(28.01348e-3),
     _p_critical(3.3958e6),
     _T_critical(126.192),
     _rho_molar_critical(11.1839),
     _rho_critical(313.3),
     _p_triple(12.523e3),
     _T_triple(63.151)
 {
 }

Member Function Documentation

◆ alpha()

Real NitrogenFluidProperties::alpha	(	Real	delta,
		Real	tau
	)		const

overrideprotectedvirtual

Helmholtz free energy.

Parameters

delta	scaled density (-)
tau	scaled temperature (-)

Returns: alpha Helmholtz free energy

Implements HelmholtzFluidProperties.

Definition at line 311 of file NitrogenFluidProperties.C.

 {
   // Ideal gas component of the Helmholtz free energy
   const Real alpha0 = std::log(delta) + _a[0] * std::log(tau) + _a[1] + _a[2] * tau + _a[3] / tau +
                       _a[4] / Utility::pow<2>(tau) + _a[5] / Utility::pow<3>(tau) +
                       _a[6] * std::log(1.0 - std::exp(-_a[7] * tau));
 
   // Residual component of the Helmholtz free energy
   Real alphar = 0.0;
 
   for (std::size_t i = 0; i < _N1.size(); ++i)
     alphar += _N1[i] * MathUtils::pow(delta, _i1[i]) * std::pow(tau, _j1[i]);
 
   for (std::size_t i = 0; i < _N2.size(); ++i)
     alphar += _N2[i] * MathUtils::pow(delta, _i2[i]) * std::pow(tau, _j2[i]) *
               std::exp(-MathUtils::pow(delta, _l2[i]));
 
   for (std::size_t i = 0; i < _N3.size(); ++i)
     alphar += _N3[i] * MathUtils::pow(delta, _i3[i]) * std::pow(tau, _j3[i]) *
               std::exp(-_phi3[i] * Utility::pow<2>(delta - 1.0) -
                        _beta3[i] * Utility::pow<2>(tau - _gamma3[i]));
 
   // The Helmholtz free energy is the sum of these two
   return alpha0 + alphar;
 }

◆ beta()

Real SinglePhaseFluidProperties::beta	(	Real	pressure,
		Real	temperature
	)		const

virtualinherited

Definition at line 154 of file SinglePhaseFluidProperties.C.

Referenced by SimpleFluidProperties::beta_from_p_T(), and Water97FluidProperties::vaporTemperature().

 {
   return beta_from_p_T(p, T);
 }

◆ beta_from_p_T() [1/2]

Real SinglePhaseFluidProperties::beta_from_p_T	(	Real	p,
		Real	T
	)		const

virtualinherited

Reimplemented in SimpleFluidProperties.

Definition at line 79 of file SinglePhaseFluidProperties.C.

Referenced by SinglePhaseFluidProperties::beta().

 {
   // The volumetric thermal expansion coefficient is defined as
   //   1/v dv/dT)_p
   // It is the fractional change rate of volume with respect to temperature change
   // at constant pressure. Here it is coded as
   //   - 1/rho drho/dT)_p
   // using chain rule with v = v(rho)
 
   Real rho, drho_dp, drho_dT;
   rho_from_p_T(p, T, rho, drho_dp, drho_dT);
   return -drho_dT / rho;
 }

◆ beta_from_p_T() [2/2]

void SinglePhaseFluidProperties::beta_from_p_T	(	Real	,
		Real	,
		Real &	,
		Real &	,
		Real &
	)		const

virtualinherited

Reimplemented in SimpleFluidProperties.

Definition at line 73 of file SinglePhaseFluidProperties.C.

 {
   mooseError(name(), ": ", __PRETTY_FUNCTION__, " is not implemented.");
 }

◆ c()

Real SinglePhaseFluidProperties::c	(	Real	pressure,
		Real	temperature
	)		const

virtualinherited

Definition at line 336 of file SinglePhaseFluidProperties.C.

Referenced by StiffenedGasFluidProperties::c_from_v_e(), IdealGasFluidProperties::c_from_v_e(), Water97FluidProperties::densityRegion3(), Water97FluidProperties::subregionVolume(), and Water97FluidProperties::vaporPressure().

 {
   mooseDeprecated(name(), ": c() is deprecated. Use c_from_p_T() instead");
 
   return c_from_p_T(p, T);
 }

◆ c_from_p_T()

Real HelmholtzFluidProperties::c_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtualinherited

Definition at line 100 of file HelmholtzFluidProperties.C.

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   const Real da_dd = dalpha_ddelta(delta, tau);
 
   Real w = 2.0 * delta * da_dd + delta * delta * d2alpha_ddelta2(delta, tau);
   w -= Utility::pow<2>(delta * da_dd - delta * tau * d2alpha_ddeltatau(delta, tau)) /
        (tau * tau * d2alpha_dtau2(delta, tau));
 
   return std::sqrt(_R * temperature * w / molarMass());
 }

◆ cp_from_p_T()

Real HelmholtzFluidProperties::cp_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtualinherited

Definition at line 118 of file HelmholtzFluidProperties.C.

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   const Real da_dd = dalpha_ddelta(delta, tau);
 
   const Real cp = _R *
                   (-tau * tau * d2alpha_dtau2(delta, tau) +
                    Utility::pow<2>(delta * da_dd - delta * tau * d2alpha_ddeltatau(delta, tau)) /
                        (2.0 * delta * da_dd + delta * delta * d2alpha_ddelta2(delta, tau))) /
                   molarMass();
 
   return cp;
 }

◆ criticalDensity()

Real NitrogenFluidProperties::criticalDensity ( ) const

overridevirtual

Critical density.

Returns: critical density (kg/m^3)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 63 of file NitrogenFluidProperties.C.

 {
   return _rho_critical;
 }

◆ criticalInternalEnergy()

Real SinglePhaseFluidProperties::criticalInternalEnergy ( ) const

virtualinherited

Critical specific internal energy.

Returns: specific internal energy (J/kg)

Reimplemented in StiffenedGasFluidProperties.

Definition at line 124 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::p_T_from_v_e().

 {
   mooseError(name(), ": criticalInternalEnergy() is not implemented");
 }

◆ criticalPressure()

Real NitrogenFluidProperties::criticalPressure ( ) const

overridevirtual

Critical pressure.

Returns: critical pressure (Pa)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 51 of file NitrogenFluidProperties.C.

 {
   return _p_critical;
 }

◆ criticalTemperature()

Real NitrogenFluidProperties::criticalTemperature ( ) const

overridevirtual

Critical temperature.

Returns: critical temperature (K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 57 of file NitrogenFluidProperties.C.

 {
   return _T_critical;
 }

◆ cv_from_p_T()

Real HelmholtzFluidProperties::cv_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtualinherited

Definition at line 138 of file HelmholtzFluidProperties.C.

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   return -_R * tau * tau * d2alpha_dtau2(delta, tau) / molarMass();
 }

◆ d2alpha_ddelta2()

Real NitrogenFluidProperties::d2alpha_ddelta2	(	Real	delta,
		Real	tau
	)		const

overrideprotectedvirtual

Second derivative of Helmholtz free energy wrt delta.

Parameters

delta	scaled density (-)
tau	scaled temperature (-)

Returns: second derivative of Helmholtz free energy wrt delta

Implements HelmholtzFluidProperties.

Definition at line 393 of file NitrogenFluidProperties.C.

 {
   // Ideal gas component of the Helmholtz free energy
   const Real dalpha0 = -1.0 / delta / delta;
 
   // Residual component of the Helmholtz free energy
   Real dalphar = 0.0;
 
   for (std::size_t i = 0; i < _N1.size(); ++i)
     dalphar +=
         _N1[i] * _i1[i] * (_i1[i] - 1.0) * MathUtils::pow(delta, _i1[i]) * std::pow(tau, _j1[i]);
 
   for (std::size_t i = 0; i < _N2.size(); ++i)
     dalphar += _N2[i] * MathUtils::pow(delta, _i2[i]) * std::pow(tau, _j2[i]) *
                std::exp(-MathUtils::pow(delta, _l2[i])) *
                ((_i2[i] - _l2[i] * MathUtils::pow(delta, _l2[i])) *
                     (_i2[i] - 1.0 - _l2[i] * MathUtils::pow(delta, _l2[i])) -
                 _l2[i] * _l2[i] * MathUtils::pow(delta, _l2[i]));
 
   for (std::size_t i = 0; i < _N3.size(); ++i)
     dalphar += _N3[i] * MathUtils::pow(delta, _i3[i]) * std::pow(tau, _j3[i]) *
                std::exp(-_phi3[i] * Utility::pow<2>(delta - 1.0) -
                         _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                (Utility::pow<2>(_i3[i] - 2.0 * delta * _phi3[i] * (delta - 1.0)) - _i3[i] -
                 2.0 * delta * delta * _phi3[i]);
 
   // The Helmholtz free energy
   return dalpha0 + dalphar / delta / delta;
 }

◆ d2alpha_ddeltatau()

Real NitrogenFluidProperties::d2alpha_ddeltatau	(	Real	delta,
		Real	tau
	)		const

overrideprotectedvirtual

Second derivative of Helmholtz free energy wrt delta and tau.

Parameters

delta	scaled density (-)
tau	scaled temperature (-)

Returns: second derivative of Helmholtz free energy wrt delta and tau

Implements HelmholtzFluidProperties.

Definition at line 455 of file NitrogenFluidProperties.C.

 {
   // Residual component of the Helmholtz free energy (second derivative of ideal
   // component wrt delta and tau is 0)
   Real dalphar = 0.0;
 
   for (std::size_t i = 0; i < _N1.size(); ++i)
     dalphar += _N1[i] * _i1[i] * _j1[i] * MathUtils::pow(delta, _i1[i]) * std::pow(tau, _j1[i]);
 
   for (std::size_t i = 0; i < _N2.size(); ++i)
     dalphar += _N2[i] * _j2[i] * MathUtils::pow(delta, _i2[i]) * std::pow(tau, _j2[i]) *
                std::exp(-MathUtils::pow(delta, _l2[i])) *
                (_i2[i] - _l2[i] * MathUtils::pow(delta, _l2[i]));
 
   for (std::size_t i = 0; i < _N3.size(); ++i)
     dalphar += _N3[i] * MathUtils::pow(delta, _i3[i]) * std::pow(tau, _j3[i]) *
                std::exp(-_phi3[i] * Utility::pow<2>(delta - 1.0) -
                         _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                (_i3[i] - 2.0 * delta * _phi3[i] * (delta - 1.0)) *
                (_j3[i] - 2.0 * tau * _beta3[i] * (tau - _gamma3[i]));
 
   // The Helmholtz free energy
   return dalphar / delta / tau;
 }

◆ d2alpha_dtau2()

Real NitrogenFluidProperties::d2alpha_dtau2	(	Real	delta,
		Real	tau
	)		const

overrideprotectedvirtual

Second derivative of Helmholtz free energy wrt tau.

Parameters

delta	scaled density (-)
tau	scaled temperature (-)

Returns: second derivative of Helmholtz free energy wrt tau

Implements HelmholtzFluidProperties.

Definition at line 424 of file NitrogenFluidProperties.C.

 {
   // Ideal gas component of the Helmholtz free energy
   const Real dalpha0 = -_a[0] + 2.0 * _a[3] / tau + 6.0 * _a[4] / Utility::pow<2>(tau) +
                        12.0 * _a[5] / Utility::pow<3>(tau) -
                        _a[6] * _a[7] * _a[7] * tau * tau * std::exp(_a[7] * tau) /
                            Utility::pow<2>(std::exp(_a[7] * tau) - 1.0);
 
   // Residual component of the Helmholtz free energy
   Real dalphar = 0.0;
 
   for (std::size_t i = 0; i < _N1.size(); ++i)
     dalphar +=
         _N1[i] * _j1[i] * (_j1[i] - 1.0) * MathUtils::pow(delta, _i1[i]) * std::pow(tau, _j1[i]);
 
   for (std::size_t i = 0; i < _N2.size(); ++i)
     dalphar += _N2[i] * _j2[i] * (_j2[i] - 1.0) * MathUtils::pow(delta, _i2[i]) *
                std::pow(tau, _j2[i]) * std::exp(-MathUtils::pow(delta, _l2[i]));
 
   for (std::size_t i = 0; i < _N3.size(); ++i)
     dalphar += _N3[i] * MathUtils::pow(delta, _i3[i]) * std::pow(tau, _j3[i]) *
                std::exp(-_phi3[i] * Utility::pow<2>(delta - 1.0) -
                         _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                (Utility::pow<2>(_j3[i] - 2.0 * tau * _beta3[i] * (tau - _gamma3[i])) - _j3[i] -
                 2.0 * tau * tau * _beta3[i]);
 
   // The Helmholtz free energy is the sum of these two
   return (dalpha0 + dalphar) / tau / tau;
 }

◆ dalpha_ddelta()

Real NitrogenFluidProperties::dalpha_ddelta	(	Real	delta,
		Real	tau
	)		const

overrideprotectedvirtual

Derivative of Helmholtz free energy wrt delta.

Parameters

delta	scaled density (-)
tau	scaled temperature (-)

Returns: derivative of Helmholtz free energy wrt delta

Implements HelmholtzFluidProperties.

Definition at line 338 of file NitrogenFluidProperties.C.

 {
   // Ideal gas component of the Helmholtz free energy
   const Real dalpha0 = 1.0 / delta;
 
   // Residual component of the Helmholtz free energy
   Real dalphar = 0.0;
 
   for (std::size_t i = 0; i < _N1.size(); ++i)
     dalphar += _N1[i] * _i1[i] * MathUtils::pow(delta, _i1[i]) * std::pow(tau, _j1[i]);
 
   for (std::size_t i = 0; i < _N2.size(); ++i)
     dalphar += _N2[i] * MathUtils::pow(delta, _i2[i]) * std::pow(tau, _j2[i]) *
                std::exp(-MathUtils::pow(delta, _l2[i])) *
                (_i2[i] - _l2[i] * MathUtils::pow(delta, _l2[i]));
 
   for (std::size_t i = 0; i < _N3.size(); ++i)
     dalphar += _N3[i] * MathUtils::pow(delta, _i3[i]) * std::pow(tau, _j3[i]) *
                std::exp(-_phi3[i] * Utility::pow<2>(delta - 1.0) -
                         _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                (_i3[i] - 2.0 * delta * _phi3[i] * (delta - 1.0));
 
   // The Helmholtz free energy is the sum of these two
   return dalpha0 + dalphar / delta;
 }

◆ dalpha_dtau()

Real NitrogenFluidProperties::dalpha_dtau	(	Real	delta,
		Real	tau
	)		const

overrideprotectedvirtual

Derivative of Helmholtz free energy wrt tau.

Parameters

delta	scaled density (-)
tau	scaled temperature (-)

Returns: derivative of Helmholtz free energy wrt tau

Implements HelmholtzFluidProperties.

Definition at line 365 of file NitrogenFluidProperties.C.

 {
   // Ideal gas component of the Helmholtz free energy
   const Real dalpha0 = _a[0] + _a[2] * tau - _a[3] / tau - 2.0 * _a[4] / Utility::pow<2>(tau) -
                        3.0 * _a[5] / Utility::pow<3>(tau) +
                        _a[6] * _a[7] * tau / (std::exp(_a[7] * tau) - 1.0);
 
   // Residual component of the Helmholtz free energy
   Real dalphar = 0.0;
 
   for (std::size_t i = 0; i < _N1.size(); ++i)
     dalphar += _N1[i] * _j1[i] * MathUtils::pow(delta, _i1[i]) * std::pow(tau, _j1[i]);
 
   for (std::size_t i = 0; i < _N2.size(); ++i)
     dalphar += _N2[i] * _j2[i] * MathUtils::pow(delta, _i2[i]) * std::pow(tau, _j2[i]) *
                std::exp(-MathUtils::pow(delta, _l2[i]));
 
   for (std::size_t i = 0; i < _N3.size(); ++i)
     dalphar += _N3[i] * MathUtils::pow(delta, _i3[i]) * std::pow(tau, _j3[i]) *
                std::exp(-_phi3[i] * Utility::pow<2>(delta - 1.0) -
                         _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                (_j3[i] - 2.0 * tau * _beta3[i] * (tau - _gamma3[i]));
 
   // The Helmholtz free energy is the sum of these two
   return (dalpha0 + dalphar) / tau;
 }

◆ e()

Real SinglePhaseFluidProperties::e	(	Real	pressure,
		Real	temperature
	)		const

virtualinherited

Definition at line 291 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": e() is deprecated. Use e_from_p_T() instead");
 
   return e_from_p_T(p, T);
 }

◆ e_dpT()

void SinglePhaseFluidProperties::e_dpT	(	Real	pressure,
		Real	temperature,
		Real &	e,
		Real &	de_dp,
		Real &	de_dT
	)		const

virtualinherited

Definition at line 299 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": e_dpT() is deprecated. Use e_from_p_T() instead");
 
   e_from_p_T(p, T, e, de_dp, de_dT);
 }

◆ e_from_p_T() [1/2]

Real HelmholtzFluidProperties::e_from_p_T	(	Real	p,
		Real	T
	)		const

overridevirtualinherited

Internal energy from pressure and temperature.

Parameters

[in]	p	pressure (Pa)
[in]	T	temperature (K)

Returns: internal energy (J/kg)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 65 of file HelmholtzFluidProperties.C.

Referenced by HelmholtzFluidProperties::e_from_p_T().

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   return _R * temperature * tau * dalpha_dtau(delta, tau) / molarMass();
 }

◆ e_from_p_T() [2/2]

void HelmholtzFluidProperties::e_from_p_T	(	Real	p,
		Real	T,
		Real &	e,
		Real &	de_dp,
		Real &	de_dT
	)		const

overridevirtualinherited

Internal energy and its derivatives from pressure and temperature.

Parameters

[in]	p	pressure (Pa)
[in]	T	temperature (K)
[out]	e	internal energy (J/kg)
[out]	de_dp	derivative of internal energy w.r.t. pressure
[out]	de_dT	derivative of internal energy w.r.t. temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 77 of file HelmholtzFluidProperties.C.

 {
   e = this->e_from_p_T(pressure, temperature);
 
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   const Real da_dd = dalpha_ddelta(delta, tau);
   const Real d2a_dd2 = d2alpha_ddelta2(delta, tau);
   const Real d2a_ddt = d2alpha_ddeltatau(delta, tau);
 
   de_dp = tau * d2a_ddt / (density * (2.0 * da_dd + delta * d2a_dd2));
   de_dT = -_R *
           (delta * tau * d2a_ddt * (da_dd - tau * d2a_ddt) / (2.0 * da_dd + delta * d2a_dd2) +
            tau * tau * d2alpha_dtau2(delta, tau)) /
           molarMass();
 }

◆ e_spndl_from_v()

Real SinglePhaseFluidProperties::e_spndl_from_v ( Real v ) const

virtualinherited

Specific internal energy from temperature and specific volume.

Parameters

[in]	T	temperature
[in]	v	specific volume

Reimplemented in StiffenedGasFluidProperties.

Definition at line 451 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::p_T_from_v_e().

 {
   mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
 }

◆ execute()

virtual void FluidProperties::execute ( )

inlinefinalvirtualinherited

Definition at line 35 of file FluidProperties.h.

35 {}

◆ finalize()

virtual void FluidProperties::finalize ( )

inlinefinalvirtualinherited

Definition at line 37 of file FluidProperties.h.

37 {}

◆ fluidName()

std::string NitrogenFluidProperties::fluidName ( ) const

overridevirtual

Fluid name.

Returns: string representing fluid name

Reimplemented from SinglePhaseFluidProperties.

Definition at line 39 of file NitrogenFluidProperties.C.

 {
   return "nitrogen";
 }

◆ gamma_from_p_T()

Real SinglePhaseFluidProperties::gamma_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

virtualinherited

Adiabatic index - ratio of specific heats.

Parameters

pressure	fluid pressure (Pa)
temperature	fluid temperature (K)

Returns: gamma (-)

Reimplemented in IdealGasFluidProperties.

Definition at line 148 of file SinglePhaseFluidProperties.C.

 {
   return cp_from_p_T(p, T) / cv_from_p_T(p, T);
 }

◆ gamma_from_v_e()

Real SinglePhaseFluidProperties::gamma_from_v_e	(	Real	v,
		Real	e
	)		const

virtualinherited

Adiabatic index - ratio of specific heats.

Parameters

v	specific volume
e	specific internal energy

Returns: gamma (-)

Reimplemented in IdealGasFluidProperties.

Definition at line 142 of file SinglePhaseFluidProperties.C.

 {
   return cp_from_v_e(v, e) / cv_from_v_e(v, e);
 }

◆ h()

Real SinglePhaseFluidProperties::h	(	Real	p,
		Real	T
	)		const

virtualinherited

Specific enthalpy from pressure and temperature.

Parameters

[in]	p	pressure (Pa)
[in]	T	temperature (K)

Returns: h (J/kg)

Definition at line 428 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": h() is deprecated. Use h_from_p_T() instead");
 
   return h_from_p_T(p, T);
 }

◆ h_dpT()

void SinglePhaseFluidProperties::h_dpT	(	Real	pressure,
		Real	temperature,
		Real &	h,
		Real &	dh_dp,
		Real &	dh_dT
	)		const

virtualinherited

Specific enthalpy and its derivatives from pressure and temperature.

Parameters

[in]	p	pressure (Pa)
[in]	T	temperature (K)
[out]	h	specific enthalpy (J/kg)
[out]	dh_dp	derivative of specific enthalpy w.r.t. pressure
[out]	dh_dT	derivative of specific enthalpy w.r.t. temperature

Definition at line 436 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": h_dpT() is deprecated. Use h_from_p_T() instead");
 
   h_from_p_T(p, T, h, dh_dp, dh_dT);
 }

◆ h_from_p_T() [1/2]

Real HelmholtzFluidProperties::h_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtualinherited

Definition at line 185 of file HelmholtzFluidProperties.C.

Referenced by HelmholtzFluidProperties::h_from_p_T().

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   return _R * temperature * (tau * dalpha_dtau(delta, tau) + delta * dalpha_ddelta(delta, tau)) /
          molarMass();
 }

◆ h_from_p_T() [2/2]

void HelmholtzFluidProperties::h_from_p_T	(	Real	p,
		Real	T,
		Real &	h,
		Real &	dh_dp,
		Real &	dh_dT
	)		const

overridevirtualinherited

Definition at line 198 of file HelmholtzFluidProperties.C.

 {
   h = this->h_from_p_T(pressure, temperature);
 
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   const Real da_dd = dalpha_ddelta(delta, tau);
   const Real d2a_dd2 = d2alpha_ddelta2(delta, tau);
   const Real d2a_ddt = d2alpha_ddeltatau(delta, tau);
 
   dh_dp = (da_dd + delta * d2a_dd2 + tau * d2a_ddt) / (density * (2.0 * da_dd + delta * d2a_dd2));
   dh_dT = _R *
           (delta * da_dd * (1.0 - tau * d2a_ddt / da_dd) * (1.0 - tau * d2a_ddt / da_dd) /
                (2.0 + delta * d2a_dd2 / da_dd) -
            tau * tau * d2alpha_dtau2(delta, tau)) /
           molarMass();
 }

◆ henryConstant() [1/2]

Real NitrogenFluidProperties::henryConstant ( Real temperature ) const

overridevirtual

Henry's law constant for dissolution in water.

Parameters

temperature fluid temperature (K)

Returns: Henry's constant

Reimplemented from SinglePhaseFluidProperties.

Definition at line 242 of file NitrogenFluidProperties.C.

 {
   return henryConstantIAPWS(temperature, -9.67578, 4.72162, 11.70585);
 }

◆ henryConstant() [2/2]

void NitrogenFluidProperties::henryConstant	(	Real	temperature,
		Real &	Kh,
		Real &	dKh_dT
	)		const

overridevirtual

Henry's law constant for dissolution in water and derivative wrt temperature.

Parameters

	temperature	fluid temperature (K)
[out]	Kh	Henry's constant
[out]	dKh_dT	derivative of Kh wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 248 of file NitrogenFluidProperties.C.

 {
   henryConstantIAPWS(temperature, Kh, dKh_dT, -9.67578, 4.72162, 11.70585);
 }

◆ henryConstant_dT()

void SinglePhaseFluidProperties::henryConstant_dT	(	Real	temperature,
		Real &	Kh,
		Real &	dKh_dT
	)		const

virtualinherited

Definition at line 255 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": henryConstant_dT() is deprecated. Use henryConstant() instead");
 
   henryConstant(T, Kh, dKh_dT);
 }

◆ henryConstantIAPWS() [1/2]

Real SinglePhaseFluidProperties::henryConstantIAPWS	(	Real	temperature,
		Real	A,
		Real	B,
		Real	C
	)		const

protectedvirtualinherited

IAPWS formulation of Henry's law constant for dissolution in water From Guidelines on the Henry's constant and vapour liquid distribution constant for gases in H20 and D20 at high temperatures, IAPWS (2004)

Definition at line 160 of file SinglePhaseFluidProperties.C.

Referenced by MethaneFluidProperties::henryConstant(), henryConstant(), HydrogenFluidProperties::henryConstant(), CO2FluidProperties::henryConstant(), and SinglePhaseFluidProperties::henryConstantIAPWS_dT().

 {
   const Real Tr = T / 647.096;
   const Real tau = 1.0 - Tr;
 
   const Real lnkh =
       A / Tr + B * std::pow(tau, 0.355) / Tr + C * std::pow(Tr, -0.41) * std::exp(tau);
 
   // The vapor pressure used in this formulation
   const std::vector<Real> a{
       -7.85951783, 1.84408259, -11.7866497, 22.6807411, -15.9618719, 1.80122502};
   const std::vector<Real> b{1.0, 1.5, 3.0, 3.5, 4.0, 7.5};
   Real sum = 0.0;
 
   for (std::size_t i = 0; i < a.size(); ++i)
     sum += a[i] * std::pow(tau, b[i]);
 
   return 22.064e6 * std::exp(sum / Tr) * std::exp(lnkh);
 }

◆ henryConstantIAPWS() [2/2]

void SinglePhaseFluidProperties::henryConstantIAPWS	(	Real	temperature,
		Real &	Kh,
		Real &	dKh_dT,
		Real	A,
		Real	B,
		Real	C
	)		const

protectedvirtualinherited

Definition at line 181 of file SinglePhaseFluidProperties.C.

 {
   const Real pc = 22.064e6;
   const Real Tc = 647.096;
 
   const Real Tr = T / Tc;
   const Real tau = 1.0 - Tr;
 
   const Real lnkh =
       A / Tr + B * std::pow(tau, 0.355) / Tr + C * std::pow(Tr, -0.41) * std::exp(tau);
   const Real dlnkh_dT =
       (-A / Tr / Tr - B * std::pow(tau, 0.355) / Tr / Tr - 0.355 * B * std::pow(tau, -0.645) / Tr -
        0.41 * C * std::pow(Tr, -1.41) * std::exp(tau) - C * std::pow(Tr, -0.41) * std::exp(tau)) /
       Tc;
 
   // The vapor pressure used in this formulation
   const std::vector<Real> a{
       -7.85951783, 1.84408259, -11.7866497, 22.6807411, -15.9618719, 1.80122502};
   const std::vector<Real> b{1.0, 1.5, 3.0, 3.5, 4.0, 7.5};
   Real sum = 0.0;
   Real dsum = 0.0;
 
   for (std::size_t i = 0; i < a.size(); ++i)
   {
     sum += a[i] * std::pow(tau, b[i]);
     dsum += a[i] * b[i] * std::pow(tau, b[i] - 1.0);
   }
 
   const Real p = pc * std::exp(sum / Tr);
   const Real dp_dT = -p / Tc / Tr * (sum / Tr + dsum);
 
   // Henry's constant and its derivative wrt temperature
   Kh = p * std::exp(lnkh);
   dKh_dT = (p * dlnkh_dT + dp_dT) * std::exp(lnkh);
 }

◆ henryConstantIAPWS_dT()

void SinglePhaseFluidProperties::henryConstantIAPWS_dT	(	Real	temperature,
		Real &	Kh,
		Real &	dKh_dT,
		Real	A,
		Real	B,
		Real	C
	)		const

protectedvirtualinherited

Definition at line 219 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(),
                   ":henryConstantIAPWS_dT() is deprecated. Use henryConstantIAPWS() instead");
 
   henryConstantIAPWS(T, Kh, dKh_dT, A, B, C);
 }

◆ initialize()

virtual void FluidProperties::initialize ( )

inlinefinalvirtualinherited

Definition at line 36 of file FluidProperties.h.

36 {}

◆ k()

Real SinglePhaseFluidProperties::k	(	Real	pressure,
		Real	temperature
	)		const

virtualinherited

Thermal conductivity.

Parameters

pressure	fluid pressure (Pa)
temperature	fluid temperature (K)

Returns: thermal conductivity (W/m/K)

Definition at line 404 of file SinglePhaseFluidProperties.C.

Referenced by SinglePhaseFluidProperties::k_dpT(), MethaneFluidProperties::k_from_p_T(), SimpleFluidProperties::k_from_p_T(), k_from_p_T(), HydrogenFluidProperties::k_from_p_T(), NaClFluidProperties::k_from_p_T(), IdealGasFluidProperties::k_from_p_T(), StiffenedGasFluidProperties::k_from_p_T(), TabulatedFluidProperties::k_from_p_T(), and CO2FluidProperties::k_from_p_T().

 {
   mooseDeprecated(name(), ": k() is deprecated. Use k_from_p_T() instead");
 
   return k_from_p_T(p, T);
 }

◆ k_dpT()

void SinglePhaseFluidProperties::k_dpT	(	Real	pressure,
		Real	temperature,
		Real &	k,
		Real &	dk_dp,
		Real &	dk_dT
	)		const

virtualinherited

Thermal conductivity and its derivatives wrt pressure and temperature.

Parameters

	pressure	fluid pressure (Pa)
	temperature	fluid temperature (K)
[out]	thermal	conductivity (W/m/K)
[out]	derivative	of thermal conductivity wrt pressure
[out]	derivative	of thermal conductivity wrt temperature

Definition at line 412 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": k_dpT() is deprecated. Use k_from_p_T() instead");
 
   k_from_p_T(p, T, k, dk_dp, dk_dT);
 }

◆ k_from_p_T() [1/2]

Real NitrogenFluidProperties::k_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtual

Definition at line 220 of file NitrogenFluidProperties.C.

Referenced by k_from_p_T().

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   return k_from_rho_T(density, temperature);
 }

◆ k_from_p_T() [2/2]

void NitrogenFluidProperties::k_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	k,
		Real &	dk_dp,
		Real &	dk_dT
	)		const

overridevirtual

Definition at line 228 of file NitrogenFluidProperties.C.

 {
   k = this->k_from_p_T(pressure, temperature);
   // Calculate derivatives using finite differences
   const Real eps = 1.0e-6;
   const Real peps = pressure * eps;
   const Real Teps = temperature * eps;
 
   dk_dp = (this->k_from_p_T(pressure + peps, temperature) - k) / peps;
   dk_dT = (this->k_from_p_T(pressure, temperature + Teps) - k) / Teps;
 }

◆ k_from_rho_T()

Real NitrogenFluidProperties::k_from_rho_T	(	Real	density,
		Real	temperature
	)		const

overridevirtual

Definition at line 199 of file NitrogenFluidProperties.C.

Referenced by k_from_p_T().

 {
   // Scale the input density and temperature
   const Real delta = density / _rho_critical;
   const Real tau = _T_critical / temperature;
 
   // The dilute gas component
   const Real lambda0 =
       1.511 * mu_from_rho_T(0.0, temperature) * 1.0e6 + 2.117 / tau - 3.332 * std::pow(tau, -0.7);
 
   // The residual component
   Real lambdar = 0.0;
   for (std::size_t i = 0; i < _Nk.size(); ++i)
     lambdar += _Nk[i] * std::pow(tau, _tk[i]) * MathUtils::pow(delta, _dk[i]) *
                std::exp(-_gammak[i] * MathUtils::pow(delta, _lk[i]));
 
   // The thermal conductivity (note: critical enhancement not implemented)
   return (lambda0 + lambdar) * 1.0e-3;
 }

◆ molarMass()

Real NitrogenFluidProperties::molarMass ( ) const

overridevirtual

Molar mass [kg/mol].

Returns: molar mass

Reimplemented from SinglePhaseFluidProperties.

Definition at line 45 of file NitrogenFluidProperties.C.

 {
   return _Mn2;
 }

◆ mu()

Real SinglePhaseFluidProperties::mu	(	Real	pressure,
		Real	temperature
	)		const

virtualinherited

Dynamic viscosity.

Parameters

pressure	fluid pressure (Pa)
temperature	fluid temperature (K)

Returns: viscosity (Pa.s)

Definition at line 344 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": mu() is deprecated. Use mu_from_p_T() instead");
 
   return mu_from_p_T(p, T);
 }

◆ mu_dpT()

void SinglePhaseFluidProperties::mu_dpT	(	Real	pressure,
		Real	temperature,
		Real &	mu,
		Real &	dmu_dp,
		Real &	dmu_dT
	)		const

virtualinherited

Dynamic viscosity and its derivatives wrt pressure and temperature.

Parameters

	pressure	fluid pressure (Pa)
	temperature	fluid temperature (K)
[out]	mu	viscosity (Pa.s)
[out]	dmu_dp	derivative of viscosity wrt pressure
[out]	dmu_dT	derivative of viscosity wrt temperature

Definition at line 352 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": mu_dpT() is deprecated. Use mu_from_p_T() instead");
 
   mu_from_p_T(p, T, mu, dmu_dp, dmu_dT);
 }

◆ mu_drhoT_from_rho_T()

void SinglePhaseFluidProperties::mu_drhoT_from_rho_T	(	Real	density,
		Real	temperature,
		Real	ddensity_dT,
		Real &	mu,
		Real &	dmu_drho,
		Real &	dmu_dT
	)		const

virtualinherited

Definition at line 235 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ":mu_drhoT_from_rho_T() is deprecated. Use mu_from_rho_T() instead");
 
   mu_from_rho_T(rho, T, drho_dT, mu, dmu_drho, dmu_dT);
 }

◆ mu_from_p_T() [1/2]

Real NitrogenFluidProperties::mu_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtual

Definition at line 153 of file NitrogenFluidProperties.C.

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   return mu_from_rho_T(density, temperature);
 }

◆ mu_from_p_T() [2/2]

void NitrogenFluidProperties::mu_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	mu,
		Real &	dmu_dp,
		Real &	dmu_dT
	)		const

overridevirtual

Definition at line 161 of file NitrogenFluidProperties.C.

 {
   Real rho, drho_dp, drho_dT;
   rho_from_p_T(pressure, temperature, rho, drho_dp, drho_dT);
 
   Real dmu_drho;
   mu_from_rho_T(rho, temperature, drho_dT, mu, dmu_drho, dmu_dT);
   dmu_dp = dmu_drho * drho_dp;
 }

◆ mu_from_rho_T() [1/2]

Real NitrogenFluidProperties::mu_from_rho_T	(	Real	density,
		Real	temperature
	)		const

overridevirtual

Definition at line 81 of file NitrogenFluidProperties.C.

Referenced by k_from_rho_T(), mu_from_p_T(), and rho_mu_from_p_T().

 {
   // Scale the input density and temperature
   const Real delta = density / _rho_critical;
   const Real tau = _T_critical / temperature;
   const Real logTstar = std::log(temperature / 98.94);
 
   // The dilute gas component
   Real logOmega = 0.0;
   for (std::size_t i = 0; i < _bmu.size(); ++i)
     logOmega += _bmu[i] * MathUtils::pow(logTstar, i);
 
   const Real mu0 =
       0.0266958 * std::sqrt(1000.0 * _Mn2 * temperature) / (0.3656 * 0.3656 * std::exp(logOmega));
 
   // The residual component
   Real mur = 0.0;
   for (std::size_t i = 0; i < _Nmu.size(); ++i)
     mur += _Nmu[i] * std::pow(tau, _tmu[i]) * MathUtils::pow(delta, _dmu[i]) *
            std::exp(-_gammamu[i] * MathUtils::pow(delta, _lmu[i]));
 
   // The viscosity in Pa.s
   return (mu0 + mur) * 1.0e-6;
 }

◆ mu_from_rho_T() [2/2]

void NitrogenFluidProperties::mu_from_rho_T	(	Real	density,
		Real	temperature,
		Real	ddensity_dT,
		Real &	mu,
		Real &	dmu_drho,
		Real &	dmu_dT
	)		const

overridevirtual

Dynamic viscosity and its derivatives wrt density and temperature TODO: this shouldn't need 3 input args - AD will assume/call the 2-input version.

Parameters

	density	fluid density (kg/m^3)
	temperature	fluid temperature (K)
	ddensity_dT	derivative of density wrt temperature
[out]	mu	viscosity (Pa.s)
[out]	dmu_drho	derivative of viscosity wrt density
[out]	dmu_dT	derivative of viscosity wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 107 of file NitrogenFluidProperties.C.

 {
   // Scale the input density and temperature
   const Real delta = density / _rho_critical;
   const Real tau = _T_critical / temperature;
   const Real logTstar = std::log(temperature / 98.94);
 
   // The dilute gas component
   Real logOmega = 0.0, dlogOmega_dT = 0.0;
   for (std::size_t i = 0; i < _bmu.size(); ++i)
   {
     logOmega += _bmu[i] * MathUtils::pow(logTstar, i);
     dlogOmega_dT += i * _bmu[i] * MathUtils::pow(logTstar, i) / (temperature * logTstar);
   }
 
   const Real mu0 =
       0.0266958 * std::sqrt(1000.0 * _Mn2 * temperature) / (0.3656 * 0.3656 * std::exp(logOmega));
   const Real dmu0_dT = 26.6958 * _Mn2 * (1.0 - 2.0 * temperature * dlogOmega_dT) *
                        std::exp(-logOmega) /
                        (2.0 * std::sqrt(1000.0 * _Mn2 * temperature) * 0.3656 * 0.3656);
 
   // The residual component
   Real mur = 0.0, dmur_drho = 0.0, dmur_dT = 0.0;
   Real term;
   for (std::size_t i = 0; i < _Nmu.size(); ++i)
   {
     term = _Nmu[i] * std::pow(tau, _tmu[i]) * MathUtils::pow(delta, _dmu[i]) *
            std::exp(-_gammamu[i] * MathUtils::pow(delta, _lmu[i]));
     mur += term;
     dmur_drho += (_dmu[i] - _lmu[i] * _gammamu[i] * MathUtils::pow(delta, _lmu[i])) * term / delta /
                  _rho_molar_critical / (1000.0 * _Mn2);
     dmur_dT += -_tmu[i] * term / temperature;
   }
 
   // The viscosity in Pa.s
   mu = (mu0 + mur) * 1.0e-6;
   dmu_drho = dmur_drho * 1.0e-6;
   dmu_dT = (dmu0_dT + dmur_dT) * 1.0e-6 + dmu_drho * ddensity_dT;
 }

◆ p_from_rho_T()

Real HelmholtzFluidProperties::p_from_rho_T	(	Real	rho,
		Real	T
	)		const

virtualinherited

Pressure as a function of density and temperature.

Parameters

rho	density (kg/m^3)
T	temperature (K)

Returns: pressure (Pa)

Reimplemented in CO2FluidProperties.

Definition at line 222 of file HelmholtzFluidProperties.C.

Referenced by CO2FluidProperties::p_from_rho_T(), and HelmholtzFluidProperties::rho_from_p_T().

 {
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   return _R * density * temperature * delta * dalpha_ddelta(delta, tau) / molarMass();
 }

◆ propfunc() [1/15]

SinglePhaseFluidProperties::propfunc	(	p	,
		v	,
		e
	)

inherited

Compute a fluid property given for the state defined by two given properties.

For all functions, the first two arguments are the given properties that define the fluid state. For the two-argument variants, the desired property is the return value. The five-argument variants also provide partial derivatives dx/da and dx/db where x is the desired property being computed, a is the first given property, and b is the second given property. The desired property, dx/da, and dx/db are stored into the 3rd, 4th, and 5th arguments respectively.

Properties/parameters used in these function are listed below with their units:

p pressure [Pa] T temperature [K] e specific internal energy [J/kg] v specific volume [m^3/kg] rho density [kg/m^3] h specific enthalpy [J/kg] s specific entropy [J/(kg*K)] mu viscosity [Pa*s] k thermal conductivity [W/(m*K)] c speed of sound [m/s] cp constant-pressure specific heat [J/K] cv constant-volume specific heat [J/K] beta volumetric thermal expansion coefficient [1/K] g Gibbs free energy [J] pp_sat partial pressure at saturation [Pa]

As an example:

// calculate pressure given specific vol and energy: auto pressure = your_fluid_properties_object.p_from_v_e(specific_vol, specific_energy);

// or use the derivative variant: Real dp_dv = 0; // derivative will be stored into here Real dp_de = 0; // derivative will be stored into here your_fluid_properties_object.p_from_v_e(specific_vol, specific_energy, pressure, dp_dv, dp_de);

Automatic differentiation (AD) support is provided through x_from_a_b(DualReal a, DualReal b) versions of the functions where a and b must be ADReal/DualNumber's calculated using all AD-supporting values:

auto v = 1/rho; // rho must be an AD non-linear variable. auto e = rhoE/rho - vel_energy; // rhoE and vel_energy must be AD variables/numbers also. auto pressure = your_fluid_properties_object.p_from_v_e(v, e); // pressure now contains partial derivatives w.r.t. all degrees of freedom

◆ propfunc() [2/15]

e SinglePhaseFluidProperties::propfunc	(	c	,
		v	,
		e
	)

inherited

◆ propfunc() [3/15]

e e SinglePhaseFluidProperties::propfunc	(	cv	,
		v	,
		e
	)

inherited

◆ propfunc() [4/15]

e e e SinglePhaseFluidProperties::propfunc	(	k	,
		v	,
		e
	)

inherited

◆ propfunc() [5/15]

e e e e SinglePhaseFluidProperties::propfunc	(	s	,
		h	,
		p
	)

inherited

◆ propfunc() [6/15]

e e e e s SinglePhaseFluidProperties::propfunc	(	e	,
		v	,
		h
	)

inherited

◆ propfunc() [7/15]

e e e e s T SinglePhaseFluidProperties::propfunc	(	pp_sat	,
		p	,
		T
	)

inherited

◆ propfunc() [8/15]

e e e e s T T SinglePhaseFluidProperties::propfunc	(	k	,
		rho	,
		T
	)

inherited

◆ propfunc() [9/15]

e e e e s T T T SinglePhaseFluidProperties::propfunc	(	cp	,
		p	,
		T
	)

inherited

◆ propfunc() [10/15]

e e e e s T T T T SinglePhaseFluidProperties::propfunc	(	mu	,
		p	,
		T
	)

inherited

◆ propfunc() [11/15]

e e e e s T T T T T SinglePhaseFluidProperties::propfunc	(	rho	,
		p	,
		T
	)

inherited

◆ propfunc() [12/15]

e e e e s T T T T T rho SinglePhaseFluidProperties::propfunc	(	e	,
		T	,
		v
	)

inherited

◆ propfunc() [13/15]

e e e e s T T T T T rho v SinglePhaseFluidProperties::propfunc	(	h	,
		T	,
		v
	)

inherited

◆ propfunc() [14/15]

e e e e s T T T T T rho v v SinglePhaseFluidProperties::propfunc	(	cv	,
		T	,
		v
	)

inherited

◆ propfunc() [15/15]

e e e e s T T T T T rho v v T SinglePhaseFluidProperties::propfunc	(	p	,
		h	,
		s
	)

inherited

◆ rho()

virtual Real SinglePhaseFluidProperties::rho	(	Real	p,
		Real	T
	)		const

virtualinherited

Density from pressure and temperature.

Parameters

[in]	p	pressure (Pa)
[in]	T	temperature (K)

Returns: density (kg/m^3)

◆ rho_dpT()

void SinglePhaseFluidProperties::rho_dpT	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	drho_dp,
		Real &	drho_dT
	)		const

virtualinherited

Density and its derivatives from pressure and temperature.

Parameters

[in]	p	pressure (Pa)
[in]	T	temperature (K)
[out]	rho	density (kg/m^3)
[out]	drho_dp	derivative of density w.r.t. pressure
[out]	drho_dT	derivative of density w.r.t. temperature

Definition at line 282 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": rho_dpT() is deprecated. Use rho_from_p_T() instead");
 
   rho_from_p_T(p, T, rho, drho_dp, drho_dT);
 }

◆ rho_e_dpT()

void SinglePhaseFluidProperties::rho_e_dpT	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	drho_dp,
		Real &	drho_dT,
		Real &	e,
		Real &	de_dp,
		Real &	de_dT
	)		const

virtualinherited

Definition at line 321 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": rho_e_dpT() is deprecated. Use rho_e_from_p_T() instead");
 
   rho_e_from_p_T(p, T, rho, drho_dp, drho_dT, e, de_dp, de_dT);
 }

◆ rho_e_from_p_T()

void SinglePhaseFluidProperties::rho_e_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	drho_dp,
		Real &	drho_dT,
		Real &	e,
		Real &	de_dp,
		Real &	de_dT
	)		const

virtualinherited

Density and internal energy and their derivatives wrt pressure and temperature.

Parameters

	pressure	fluid pressure (Pa)
	temperature	fluid temperature (K)
[out]	rho	density (kg/m^3)
[out]	drho_dp	derivative of density wrt pressure
[out]	drho_dT	derivative of density wrt temperature
[out]	e	internal energy (J/kg)
[out]	de_dp	derivative of internal energy wrt pressure
[out]	de_dT	derivative of internal energy wrt temperature

Definition at line 307 of file SinglePhaseFluidProperties.C.

Referenced by SinglePhaseFluidProperties::rho_e_dpT().

 {
   rho_from_p_T(p, T, rho, drho_dp, drho_dT);
   e_from_p_T(p, T, e, de_dp, de_dT);
 }

◆ rho_from_p_T() [1/2]

Real HelmholtzFluidProperties::rho_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtualinherited

Reimplemented in CO2FluidProperties.

Definition at line 29 of file HelmholtzFluidProperties.C.

Referenced by HelmholtzFluidProperties::c_from_p_T(), HelmholtzFluidProperties::cp_from_p_T(), HelmholtzFluidProperties::cv_from_p_T(), HelmholtzFluidProperties::e_from_p_T(), HelmholtzFluidProperties::h_from_p_T(), k_from_p_T(), HydrogenFluidProperties::k_from_p_T(), mu_from_p_T(), CO2FluidProperties::mu_from_p_T(), HydrogenFluidProperties::mu_from_p_T(), HelmholtzFluidProperties::rho_from_p_T(), CO2FluidProperties::rho_from_p_T(), rho_mu_from_p_T(), HydrogenFluidProperties::rho_mu_from_p_T(), and HelmholtzFluidProperties::s_from_p_T().

 {
   Real density;
   // Initial estimate of a bracketing interval for the density
   Real lower_density = 1.0e-2;
   Real upper_density = 100.0;
 
   // The density is found by finding the zero of the pressure
   auto pressure_diff = [&pressure, &temperature, this](Real x) {
     return this->p_from_rho_T(x, temperature) - pressure;
   };
 
   BrentsMethod::bracket(pressure_diff, lower_density, upper_density);
   density = BrentsMethod::root(pressure_diff, lower_density, upper_density);
 
   return density;
 }

◆ rho_from_p_T() [2/2]

void HelmholtzFluidProperties::rho_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	drho_dp,
		Real &	drho_dT
	)		const

overridevirtualinherited

Reimplemented in CO2FluidProperties.

Definition at line 48 of file HelmholtzFluidProperties.C.

 {
   rho = this->rho_from_p_T(pressure, temperature);
 
   // Scale the density and temperature
   const Real delta = rho / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
   const Real da_dd = dalpha_ddelta(delta, tau);
   const Real d2a_dd2 = d2alpha_ddelta2(delta, tau);
 
   drho_dp = molarMass() / (_R * temperature * delta * (2.0 * da_dd + delta * d2a_dd2));
   drho_dT = rho * (tau * d2alpha_ddeltatau(delta, tau) - da_dd) / temperature /
             (2.0 * da_dd + delta * d2a_dd2);
 }

◆ rho_mu()

void SinglePhaseFluidProperties::rho_mu	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	mu
	)		const

virtualinherited

Density and viscosity.

Parameters

	pressure	fluid pressure (Pa)
	temperature	fluid temperature (K)
[out]	rho	density (kg/m^3)
[out]	mu	viscosity (Pa.s)

Definition at line 360 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": rho_mu() is deprecated. Use rho_mu_from_p_T() instead");
 
   rho_mu_from_p_T(p, T, rho, mu);
 }

◆ rho_mu_dpT()

void SinglePhaseFluidProperties::rho_mu_dpT	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	drho_dp,
		Real &	drho_dT,
		Real &	mu,
		Real &	dmu_dp,
		Real &	dmu_dT
	)		const

virtualinherited

Definition at line 375 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": rho_mu_dpT() is deprecated. Use rho_mu_from_p_T() instead");
 
   rho_mu_from_p_T(p, T, rho, drho_dp, drho_dT, mu, dmu_dp, dmu_dT);
 }

◆ rho_mu_from_p_T() [1/2]

void NitrogenFluidProperties::rho_mu_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	mu
	)		const

overridevirtual

Reimplemented from SinglePhaseFluidProperties.

Definition at line 173 of file NitrogenFluidProperties.C.

 {
   rho = rho_from_p_T(pressure, temperature);
   mu = mu_from_rho_T(rho, temperature);
 }

◆ rho_mu_from_p_T() [2/2]

void NitrogenFluidProperties::rho_mu_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	drho_dp,
		Real &	drho_dT,
		Real &	mu,
		Real &	dmu_dp,
		Real &	dmu_dT
	)		const

overridevirtual

Density and viscosity and their derivatives wrt pressure and temperature.

Parameters

	pressure	fluid pressure (Pa)
	temperature	fluid temperature (K)
[out]	rho	density (kg/m^3)
[out]	drho_dp	derivative of density wrt pressure
[out]	drho_dT	derivative of density wrt temperature
[out]	mu	viscosity (Pa.s)
[out]	dmu_dp	derivative of viscosity wrt pressure
[out]	dmu_dT	derivative of viscosity wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 183 of file NitrogenFluidProperties.C.

 {
   rho_from_p_T(pressure, temperature, rho, drho_dp, drho_dT);
   Real dmu_drho;
   mu_from_rho_T(rho, temperature, drho_dT, mu, dmu_drho, dmu_dT);
   dmu_dp = dmu_drho * drho_dp;
 }

◆ s()

Real SinglePhaseFluidProperties::s	(	Real	pressure,
		Real	temperature
	)		const

virtualinherited

Definition at line 420 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": s() is deprecated. Use s_from_p_T() instead");
 
   return s_from_p_T(p, T);
 }

◆ s_from_p_T() [1/2]

Real HelmholtzFluidProperties::s_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtualinherited

Definition at line 150 of file HelmholtzFluidProperties.C.

Referenced by HelmholtzFluidProperties::s_from_p_T().

 {
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   return _R * (tau * dalpha_dtau(delta, tau) - alpha(delta, tau)) / molarMass();
 }

◆ s_from_p_T() [2/2]

void HelmholtzFluidProperties::s_from_p_T	(	Real	p,
		Real	T,
		Real &	s,
		Real &	ds_dp,
		Real &	ds_dT
	)		const

overridevirtualinherited

Definition at line 162 of file HelmholtzFluidProperties.C.

 {
   s = this->s_from_p_T(pressure, temperature);
 
   // Require density first
   const Real density = rho_from_p_T(pressure, temperature);
   // Scale the input density and temperature
   const Real delta = density / criticalDensity();
   const Real tau = criticalTemperature() / temperature;
 
   const Real da_dd = dalpha_ddelta(delta, tau);
   const Real da_dt = dalpha_dtau(delta, tau);
   const Real d2a_dd2 = d2alpha_ddelta2(delta, tau);
   const Real d2a_dt2 = d2alpha_dtau2(delta, tau);
   const Real d2a_ddt = d2alpha_ddeltatau(delta, tau);
 
   ds_dp = tau * (d2a_ddt - da_dd) / (density * temperature * (2.0 * da_dd + delta * d2a_dd2));
   ds_dT = -_R * tau * (da_dt - alpha(delta, tau) + tau * (d2a_dt2 - da_dt)) /
           (molarMass() * temperature);
 }

◆ saturatedLiquidDensity()

Real NitrogenFluidProperties::saturatedLiquidDensity ( Real temperature ) const

Saturated liquid density of N2 Valid for temperatures between the triple point temperature and critical temperature.

Eq. (5), from Span et al (reference above)

Parameters

temperature N2 temperature (K)

Returns: saturated liquid density (kg/m^3)

Definition at line 277 of file NitrogenFluidProperties.C.

 {
   if (temperature < _T_triple || temperature > _T_critical)
     throw MooseException("Temperature is out of range in " + name() + ": vaporPressure()");
 
   const Real Tr = temperature / _T_critical;
   const Real theta = 1.0 - Tr;
 
   const Real logpressure =
       1.48654237 * std::pow(theta, 0.3294) - 0.280476066 * std::pow(theta, 2.0 / 3.0) +
       0.0894143085 * std::pow(theta, 8.0 / 3.0) - 0.119879866 * std::pow(theta, 35.0 / 6.0);
 
   return _rho_critical * std::exp(logpressure);
 }

◆ saturatedVaporDensity()

Real NitrogenFluidProperties::saturatedVaporDensity ( Real temperature ) const

Saturated vapor density of N2 Valid for temperatures between the triple point temperature and critical temperature.

Eq. (6), from Span et al (reference above)

Parameters

temperature N2 temperature (K)

Returns: saturated vapor density (kg/m^3)

Definition at line 293 of file NitrogenFluidProperties.C.

 {
   if (temperature < _T_triple || temperature > _T_critical)
     throw MooseException("Temperature is out of range in " + name() + ": vaporPressure()");
 
   const Real Tr = temperature / _T_critical;
   const Real theta = 1.0 - Tr;
 
   const Real logpressure =
       (-1.70127164 * std::pow(theta, 0.34) - 3.70402649 * std::pow(theta, 5.0 / 6.0) +
        1.29859383 * std::pow(theta, 7.0 / 6.0) - 0.561424977 * std::pow(theta, 13.0 / 6.0) -
        2.68505381 * std::pow(theta, 14.0 / 3.0)) /
       Tr;
 
   return _rho_critical * std::exp(logpressure);
 }

◆ subdomainSetup()

virtual void FluidProperties::subdomainSetup ( )

inlinefinalvirtualinherited

Definition at line 40 of file FluidProperties.h.

40 {}

◆ T_from_p_h()

Real SinglePhaseFluidProperties::T_from_p_h	(	Real	pressure,
		Real	enthalpy
	)		const

virtualinherited

Temperature from pressure and specific enthalpy.

Parameters

[in]	pressure	pressure (Pa)
[in]	enthalpy	enthalpy (J/kg)

Returns: Temperature (K)

Reimplemented in IdealGasFluidProperties.

Definition at line 463 of file SinglePhaseFluidProperties.C.

 {
   const Real s = s_from_h_p(h, p);
   const Real rho = rho_from_p_s(p, s);
   const Real v = 1. / rho;
   const Real e = e_from_v_h(v, h);
   return T_from_v_e(v, e);
 }

◆ threadJoin()

virtual void FluidProperties::threadJoin ( const UserObject & )

inlinefinalvirtualinherited

Definition at line 39 of file FluidProperties.h.

39 {}

◆ triplePointPressure()

Real NitrogenFluidProperties::triplePointPressure ( ) const

overridevirtual

Triple point pressure.

Returns: triple point pressure (Pa)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 69 of file NitrogenFluidProperties.C.

 {
   return _p_triple;
 }

◆ triplePointTemperature()

Real NitrogenFluidProperties::triplePointTemperature ( ) const

overridevirtual

Triple point temperature.

Returns: triple point temperature (K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 75 of file NitrogenFluidProperties.C.

 {
   return _T_triple;
 }

◆ v_e_spndl_from_T()

void SinglePhaseFluidProperties::v_e_spndl_from_T	(	Real	T,
		Real &	v,
		Real &	e
	)		const

virtualinherited

Specific internal energy from temperature and specific volume.

Parameters

[in]	T	temperature
[in]	v	specific volume

Reimplemented in StiffenedGasFluidProperties.

Definition at line 457 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::v_from_p_T().

 {
   mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
 }

◆ v_from_p_T() [1/2]

Real SinglePhaseFluidProperties::v_from_p_T	(	Real	p,
		Real	T
	)		const

virtualinherited

Specific volume from pressure and temperature.

Parameters

[in]	p	pressure
[in]	T	temperature

Definition at line 53 of file SinglePhaseFluidProperties.C.

Referenced by GeneralVaporMixtureFluidProperties::c_from_p_T(), GeneralVaporMixtureFluidProperties::cp_from_p_T(), GeneralVaporMixtureFluidProperties::cv_from_p_T(), GeneralVaporMixtureFluidProperties::k_from_p_T(), GeneralVaporMixtureFluidProperties::mu_from_p_T(), GeneralVaporMixtureFluidProperties::v_from_p_T(), and IdealRealGasMixtureFluidProperties::xs_prim_from_p_T().

 {
   const Real rho = rho_from_p_T(p, T);
   return 1.0 / rho;
 }

◆ v_from_p_T() [2/2]

void SinglePhaseFluidProperties::v_from_p_T	(	Real	p,
		Real	T,
		Real &	v,
		Real &	dv_dp,
		Real &	dv_dT
	)		const

virtualinherited

Specific volume and its derivatives from pressure and temperature.

Parameters

[in]	p	pressure
[in]	T	temperature
[out]	v	specific volume
[out]	dv_dp	derivative of specific volume w.r.t. pressure
[out]	dv_dT	derivative of specific volume w.r.t. temperature

Definition at line 60 of file SinglePhaseFluidProperties.C.

 {
   Real rho, drho_dp, drho_dT;
   rho_from_p_T(p, T, rho, drho_dp, drho_dT);
 
   v = 1.0 / rho;
   const Real dv_drho = -1.0 / (rho * rho);
 
   dv_dp = dv_drho * drho_dp;
   dv_dT = dv_drho * drho_dT;
 }

◆ vaporPressure() [1/2]

Real NitrogenFluidProperties::vaporPressure ( Real temperature ) const

overridevirtual

Vapor pressure.

Used to delineate liquid and gas phases. Valid for temperatures between the triple point temperature and the critical temperature

Parameters

temperature water temperature (K)

Returns: saturation pressure (Pa)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 254 of file NitrogenFluidProperties.C.

 {
   if (temperature < _T_triple || temperature > _T_critical)
     throw MooseException("Temperature is out of range in " + name() + ": vaporPressure()");
 
   const Real Tr = temperature / _T_critical;
   const Real theta = 1.0 - Tr;
 
   const Real logpressure =
       (-6.12445284 * theta + 1.2632722 * std::pow(theta, 1.5) - 0.765910082 * std::pow(theta, 2.5) -
        1.77570564 * Utility::pow<5>(theta)) /
       Tr;
 
   return _p_critical * std::exp(logpressure);
 }

◆ vaporPressure() [2/2]

void NitrogenFluidProperties::vaporPressure	(	Real	temperature,
		Real &	psat,
		Real &	dpsat_dT
	)		const

overridevirtual

Vapor pressure.

Used to delineate liquid and gas phases. Valid for temperatures between the triple point temperature and the critical temperature

Parameters

	temperature	water temperature (K)
[out]	saturation	pressure (Pa)
[out]	derivative	of saturation pressure wrt temperature (Pa/K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 271 of file NitrogenFluidProperties.C.

 {
   mooseError(name(), ": vaporPressure() is not implemented");
 }

◆ vaporPressure_dT()

void SinglePhaseFluidProperties::vaporPressure_dT	(	Real	temperature,
		Real &	psat,
		Real &	dpsat_dT
	)		const

virtualinherited

Definition at line 274 of file SinglePhaseFluidProperties.C.

 {
   mooseDeprecated(name(), ": vaporPressure_dT() is deprecated. Use vaporPressure() instead");
 
   vaporPressure(T, psat, dpsat_dT);
 }

Member Data Documentation

◆ _a

const std::array<Real, 8> NitrogenFluidProperties::_a

protected

Initial value:

{{2.5,
                                -12.76952708,
                                -0.00784163,
                                -1.934819e-4,
                                -1.247742e-5,
                                6.678326e-8,
                                1.012941,
                                26.65788}}

Coefficients for ideal gas component of the Helmholtz free energy.

Definition at line 152 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_dtau2(), and dalpha_dtau().

◆ _allow_imperfect_jacobians

const bool FluidProperties::_allow_imperfect_jacobians

protectedinherited

Flag to set unimplemented Jacobian entries to zero.

Definition at line 46 of file FluidProperties.h.

Referenced by SinglePhaseFluidProperties::fluidPropError().

◆ _beta3

const std::array<Real, 4> NitrogenFluidProperties::_beta3 {{325.0, 325.0, 300.0, 275.0}}

protected

Definition at line 192 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _bmu

const std::array<Real, 5> NitrogenFluidProperties::_bmu {{0.431, -0.4623, 0.08406, 0.005341, -0.00331}}

protected

Coefficients for viscosity.

Definition at line 196 of file NitrogenFluidProperties.h.

Referenced by mu_from_rho_T().

◆ _dk

const std::array<unsigned int, 6> NitrogenFluidProperties::_dk {{1, 2, 3, 4, 8, 10}}

protected

Definition at line 206 of file NitrogenFluidProperties.h.

Referenced by k_from_rho_T().

◆ _dmu

const std::array<Real, 5> NitrogenFluidProperties::_dmu {{2, 10, 12, 2, 1}}

protected

Definition at line 199 of file NitrogenFluidProperties.h.

Referenced by mu_from_rho_T().

◆ _gamma3

const std::array<Real, 4> NitrogenFluidProperties::_gamma3 {{1.16, 1.16, 1.13, 1.25}}

protected

Definition at line 193 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _gammak

const std::array<Real, 6> NitrogenFluidProperties::_gammak {{0.0, 0.0, 1.0, 1.0, 1.0}}

protected

Definition at line 208 of file NitrogenFluidProperties.h.

Referenced by k_from_rho_T().

◆ _gammamu

const std::array<Real, 5> NitrogenFluidProperties::_gammamu {{0.0, 1.0, 1.0, 1.0, 1.0}}

protected

Definition at line 201 of file NitrogenFluidProperties.h.

Referenced by mu_from_rho_T().

◆ _i1

const std::array<unsigned int, 6> NitrogenFluidProperties::_i1 {{1, 1, 2, 2, 3, 3}}

protected

Definition at line 167 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _i2

const std::array<unsigned int, 26> NitrogenFluidProperties::_i2

protected

Initial value:

{

{1, 1, 1, 3, 3, 4, 6, 6, 7, 7, 8, 8, 1, 2, 3, 4, 5, 8, 4, 5, 5, 8, 3, 5, 6, 9}}

Definition at line 178 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _i3

const std::array<unsigned int, 4> NitrogenFluidProperties::_i3 {{1, 1, 3, 2}}

protected

Definition at line 188 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _j1

const std::array<Real, 6> NitrogenFluidProperties::_j1 {{0.25, 0.875, 0.5, 0.875, 0.375, 0.75}}

protected

Definition at line 168 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _j2

const std::array<Real, 26> NitrogenFluidProperties::_j2

protected

Initial value:

{{0.5,  0.75, 2.0,  1.25, 3.5,  1.0, 0.5, 3.0, 0.0,
                                  2.75, 0.75, 2.5,  4.0,  6.0,  6.0, 3.0, 3.0, 6.0,
                                  16.0, 11.0, 15.0, 12.0, 12.0, 7.0, 4.0, 16.0}}

Definition at line 180 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _j3

const std::array<unsigned int, 4> NitrogenFluidProperties::_j3 {{0, 1, 2, 3}}

protected

Definition at line 189 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _l2

const std::array<unsigned int, 26> NitrogenFluidProperties::_l2

protected

Initial value:

{

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4}}

Definition at line 183 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _l3

const std::array<unsigned int, 4> NitrogenFluidProperties::_l3 {{2, 2, 2, 2}}

protected

Definition at line 190 of file NitrogenFluidProperties.h.

◆ _lk

const std::array<unsigned int, 6> NitrogenFluidProperties::_lk {{0, 0, 1, 2, 2, 2}}

protected

Definition at line 207 of file NitrogenFluidProperties.h.

Referenced by k_from_rho_T().

◆ _lmu

const std::array<Real, 5> NitrogenFluidProperties::_lmu {{0, 1, 1, 2, 3}}

protected

Definition at line 200 of file NitrogenFluidProperties.h.

Referenced by mu_from_rho_T().

◆ _Mn2

const Real NitrogenFluidProperties::_Mn2

protected

Nitrogen molar mass (kg/mol)

Definition at line 137 of file NitrogenFluidProperties.h.

Referenced by molarMass(), and mu_from_rho_T().

◆ _N1

const std::array<Real, 6> NitrogenFluidProperties::_N1

protected

Initial value:

{{0.924803575275,
                                 -0.492448489428,
                                 0.661883336938,
                                 -0.192902649201e1,
                                 -0.622469309629e-1,
                                 0.349943957581}}

Coefficients for residual component of the Helmholtz free energy.

Definition at line 161 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _N2

const std::array<Real, 26> NitrogenFluidProperties::_N2

protected

Initial value:

{
      {0.564857472498,     -0.161720005987e1,  -0.481395031883,    0.421150636384,
       -0.161962230825e-1, 0.172100994165,     0.735448924933e-2,  0.168077305479e-1,
       -0.107626664179e-2, -0.137318088513e-1, 0.635466899859e-3,  0.304432279419e-2,
       -0.435762336045e-1, -0.723174889316e-1, 0.389644315272e-1,  -0.21220136391e-1,
       0.4808822981509e-2, -0.551990017984e-4, -0.462016716479e-1, -0.300311716011e-2,
       0.368825891208e-1,  -0.25585684622e-2,  0.896915264558e-2,  -0.44151337035e-2,
       0.133722924858e-2,  0.264832491957e-3}}

Definition at line 170 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _N3

const std::array<Real, 4> NitrogenFluidProperties::_N3

protected

Initial value:

{

{0.196688194015e2, -0.20911560073e2, 0.167788306989e-1, 0.262767566274e4}}

Definition at line 186 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _Nk

const std::array<Real, 6> NitrogenFluidProperties::_Nk {{8.862, 31.11, -73.13, 20.03, -0.7096, 0.2672}}

protected

Coefficients for thermal conductivity.

Definition at line 204 of file NitrogenFluidProperties.h.

Referenced by k_from_rho_T().

◆ _Nmu

const std::array<Real, 5> NitrogenFluidProperties::_Nmu {{10.72, 0.03989, 0.001208, -7.402, 4.62}}

protected

Definition at line 197 of file NitrogenFluidProperties.h.

Referenced by mu_from_rho_T().

◆ _p_critical

const Real NitrogenFluidProperties::_p_critical

protected

Critical pressure (Pa)

Definition at line 139 of file NitrogenFluidProperties.h.

Referenced by criticalPressure(), and vaporPressure().

◆ _p_triple

const Real NitrogenFluidProperties::_p_triple

protected

Triple point pressure (Pa)

Definition at line 147 of file NitrogenFluidProperties.h.

Referenced by triplePointPressure().

◆ _phi3

const std::array<Real, 4> NitrogenFluidProperties::_phi3 {{20.0, 20.0, 15.0, 25.0}}

protected

Definition at line 191 of file NitrogenFluidProperties.h.

Referenced by alpha(), d2alpha_ddelta2(), d2alpha_ddeltatau(), d2alpha_dtau2(), dalpha_ddelta(), and dalpha_dtau().

◆ _R

const Real SinglePhaseFluidProperties::_R

protectedinherited

Universal gas constant (J/mol/K)

Definition at line 530 of file SinglePhaseFluidProperties.h.

Referenced by HelmholtzFluidProperties::c_from_p_T(), IdealGasFluidProperties::c_from_p_T(), HelmholtzFluidProperties::cp_from_p_T(), HelmholtzFluidProperties::cv_from_p_T(), HelmholtzFluidProperties::e_from_p_T(), HelmholtzFluidProperties::h_from_p_T(), IdealGasFluidProperties::IdealGasFluidProperties(), HelmholtzFluidProperties::p_from_rho_T(), HelmholtzFluidProperties::rho_from_p_T(), IdealGasFluidProperties::rho_from_p_T(), and HelmholtzFluidProperties::s_from_p_T().

◆ _rho_critical

const Real NitrogenFluidProperties::_rho_critical

protected

Critical density (kg/m^3)

Definition at line 145 of file NitrogenFluidProperties.h.

Referenced by criticalDensity(), k_from_rho_T(), mu_from_rho_T(), saturatedLiquidDensity(), and saturatedVaporDensity().

◆ _rho_molar_critical

const Real NitrogenFluidProperties::_rho_molar_critical

protected

Critical molar density (mol/l)

Definition at line 143 of file NitrogenFluidProperties.h.

Referenced by mu_from_rho_T().

◆ _T_c2k

const Real FluidProperties::_T_c2k

protectedinherited

Conversion of temperature from Celsius to Kelvin.

Definition at line 44 of file FluidProperties.h.

Referenced by NaClFluidProperties::cp_from_p_T(), BrineFluidProperties::cp_from_p_T_X(), NaClFluidProperties::h_from_p_T(), BrineFluidProperties::h_from_p_T_X(), BrineFluidProperties::haliteSolubility(), NaClFluidProperties::k_from_p_T(), BrineFluidProperties::k_from_p_T_X(), BrineFluidProperties::mu_from_p_T_X(), CO2FluidProperties::partialDensity(), NaClFluidProperties::rho_from_p_T(), and BrineFluidProperties::rho_from_p_T_X().

◆ _T_critical

const Real NitrogenFluidProperties::_T_critical

protected

Critical temperature (K)

Definition at line 141 of file NitrogenFluidProperties.h.

Referenced by criticalTemperature(), k_from_rho_T(), mu_from_rho_T(), saturatedLiquidDensity(), saturatedVaporDensity(), and vaporPressure().

◆ _T_triple

const Real NitrogenFluidProperties::_T_triple

protected

Triple point temperature (K)

Definition at line 149 of file NitrogenFluidProperties.h.

Referenced by triplePointTemperature().

◆ _tk

const std::array<Real, 6> NitrogenFluidProperties::_tk {{0.0, 0.03, 0.2, 0.8, 0.6, 1.9}}

protected

Definition at line 205 of file NitrogenFluidProperties.h.

Referenced by k_from_rho_T().

◆ _tmu

const std::array<Real, 5> NitrogenFluidProperties::_tmu {{0.1, 0.25, 3.2, 0.9, 0.3}}

protected

Definition at line 198 of file NitrogenFluidProperties.h.

Referenced by mu_from_rho_T().

◆ p [1/7]

e e e e SinglePhaseFluidProperties::p

inherited

Definition at line 146 of file SinglePhaseFluidProperties.h.

◆ p [2/7]

e e e e s SinglePhaseFluidProperties::p

inherited

Definition at line 148 of file SinglePhaseFluidProperties.h.

◆ p [3/7]

e e e e s T T SinglePhaseFluidProperties::p

inherited

Definition at line 152 of file SinglePhaseFluidProperties.h.

◆ p [4/7]

e e e e s T T T SinglePhaseFluidProperties::p

inherited

Definition at line 154 of file SinglePhaseFluidProperties.h.

◆ p [5/7]

e e e e s T T T T SinglePhaseFluidProperties::p

inherited

Definition at line 156 of file SinglePhaseFluidProperties.h.

◆ p [6/7]

e e e e s T T T T T SinglePhaseFluidProperties::p

inherited

Definition at line 158 of file SinglePhaseFluidProperties.h.

◆ p [7/7]

e e e e s T T T T T rho v v SinglePhaseFluidProperties::p

inherited

Definition at line 164 of file SinglePhaseFluidProperties.h.

◆ rho

Real SinglePhaseFluidProperties::rho

inherited

Definition at line 150 of file SinglePhaseFluidProperties.h.

◆ T [1/2]

e e e e s T T T T T rho SinglePhaseFluidProperties::T

inherited

Definition at line 160 of file SinglePhaseFluidProperties.h.

◆ T [2/2]

e e e e s T T T T T rho v SinglePhaseFluidProperties::T

inherited

Definition at line 162 of file SinglePhaseFluidProperties.h.

◆ v [1/5]

SinglePhaseFluidProperties::v

inherited

Definition at line 138 of file SinglePhaseFluidProperties.h.

◆ v [2/5]

e SinglePhaseFluidProperties::v

inherited

Definition at line 140 of file SinglePhaseFluidProperties.h.

◆ v [3/5]

e e SinglePhaseFluidProperties::v

inherited

Definition at line 142 of file SinglePhaseFluidProperties.h.

◆ v [4/5]

e e e SinglePhaseFluidProperties::v

inherited

Definition at line 144 of file SinglePhaseFluidProperties.h.

◆ v [5/5]

e e e e s T T T T T rho v v T SinglePhaseFluidProperties::v

inherited

Definition at line 166 of file SinglePhaseFluidProperties.h.

The documentation for this class was generated from the following files:

fluid_properties/include/userobjects/NitrogenFluidProperties.h
fluid_properties/src/userobjects/NitrogenFluidProperties.C

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ NitrogenFluidProperties()

Member Function Documentation

◆ alpha()

◆ beta()

◆ beta_from_p_T() [1/2]

◆ beta_from_p_T() [2/2]

◆ c()

◆ c_from_p_T()

◆ cp_from_p_T()

◆ criticalDensity()

◆ criticalInternalEnergy()

◆ criticalPressure()

◆ criticalTemperature()

◆ cv_from_p_T()

◆ d2alpha_ddelta2()

◆ d2alpha_ddeltatau()

◆ d2alpha_dtau2()

◆ dalpha_ddelta()

◆ dalpha_dtau()

◆ e()

◆ e_dpT()

◆ e_from_p_T() [1/2]

◆ e_from_p_T() [2/2]

◆ e_spndl_from_v()

◆ execute()

◆ finalize()

◆ fluidName()

◆ gamma_from_p_T()

◆ gamma_from_v_e()

◆ h()

◆ h_dpT()

◆ h_from_p_T() [1/2]

◆ h_from_p_T() [2/2]

◆ henryConstant() [1/2]

◆ henryConstant() [2/2]

◆ henryConstant_dT()

◆ henryConstantIAPWS() [1/2]

◆ henryConstantIAPWS() [2/2]

◆ henryConstantIAPWS_dT()

◆ initialize()

◆ k()

◆ k_dpT()

◆ k_from_p_T() [1/2]

◆ k_from_p_T() [2/2]

◆ k_from_rho_T()

◆ molarMass()

◆ mu()

◆ mu_dpT()

◆ mu_drhoT_from_rho_T()

◆ mu_from_p_T() [1/2]

◆ mu_from_p_T() [2/2]

◆ mu_from_rho_T() [1/2]

◆ mu_from_rho_T() [2/2]

◆ p_from_rho_T()

◆ propfunc() [1/15]

◆ propfunc() [2/15]

◆ propfunc() [3/15]

◆ propfunc() [4/15]

◆ propfunc() [5/15]

◆ propfunc() [6/15]

◆ propfunc() [7/15]

◆ propfunc() [8/15]

◆ propfunc() [9/15]

◆ propfunc() [10/15]

◆ propfunc() [11/15]

◆ propfunc() [12/15]

◆ propfunc() [13/15]

◆ propfunc() [14/15]

◆ propfunc() [15/15]

◆ rho()

◆ rho_dpT()

◆ rho_e_dpT()

◆ rho_e_from_p_T()

◆ rho_from_p_T() [1/2]

◆ rho_from_p_T() [2/2]