CO2 fluid properties Most thermophysical properties taken from: Span and Wagner, "A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100K at Pressures up to 800 MPa", J. More...

#include <CO2FluidProperties.h>

Inheritance diagram for CO2FluidProperties:

[legend]

Public Member Functions
	CO2FluidProperties (const InputParameters &parameters)

virtual	~CO2FluidProperties ()

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	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 Real	mu_from_rho_T (Real density, Real temperature) const override

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

virtual void	rho_mu_from_p_T (Real pressure, Real temperature, Real &rho, Real &mu) const override
	Combined methods. More...

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

virtual std::string	fluidName () const override

virtual Real	molarMass () const override
	Fluid name. 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...

Real	meltingPressure (Real temperature) const
	Melting pressure. More...

Real	sublimationPressure (Real temperature) const
	Sublimation pressure. More...

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

virtual void	vaporPressure (Real temperature, Real &psat, Real &dpsat_dT) const override

Real	saturatedLiquidDensity (Real temperature) const
	Saturated liquid density of CO2 Valid for temperatures between the triple point temperature and critical temperature. More...

Real	saturatedVaporDensity (Real temperature) const
	Saturated vapor density of CO2 Valid for temperatures between the triple point temperature and critical temperature. More...

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

virtual std::vector< Real >	henryCoefficients () const override
	Henry's law coefficients for dissolution in water. More...

Real	partialDensity (Real temperature) const
	Partial density of dissolved CO2 From Garcia, Density of aqueous solutions of CO2, LBNL-49023 (2001) More...

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	k_from_rho_T (Real density, Real temperature) const override

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

virtual void	e_from_p_T (Real p, Real T, Real &e, Real &de_dp, Real &de_dT) const override

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	criticalInternalEnergy () const
	Critical specific internal energy. 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...

DualReal	vaporPressure (const DualReal &T) const

virtual Real	vaporTemperature (Real p) const
	Vapor temperature. More...

virtual void	vaporTemperature (Real p, Real &Tsat, Real &dTsat_dp) const

DualReal	vaporTemperature (const DualReal &p) const

virtual void	rho_mu_from_p_T (const DualReal &p, const DualReal &T, DualReal &rho, DualReal &mu) const

virtual void	rho_e_from_p_T (Real p, Real T, Real &rho, Real &drho_dp, Real &drho_dT, Real &e, Real &de_dp, Real &de_dT) const

virtual void	execute () final

virtual void	initialize () final

virtual void	finalize () final

virtual void	threadJoin (const UserObject &) final

virtual void	subdomainSetup () final

Static Public Attributes
static const Real	_R = 8.3144598
	Universal gas constant (J/mol/K) More...

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...

Protected Attributes
const Real	_Mco2 = 44.0098e-3
	Molar mass of CO2 (kg/mol) More...

const Real	_critical_pressure = 7.3773e6
	Critical pressure (Pa) More...

const Real	_critical_temperature = 304.1282
	Critical temperature (K) More...

const Real	_critical_density = 467.6
	Critical density (kg/m^3) More...

const Real	_triple_point_pressure = 0.51795e6
	Triple point pressure (Pa) More...

const Real	_triple_point_temperature = 216.592
	Triple point temperature (K) More...

const Real	_Rco2 = 188.9241
	Specific gas constant (J/mol/K) More...

const std::array< Real, 5 >	_a0 {{1.99427042, 0.62105248, 0.41195293, 1.04028922, 0.08327678}}
	Coefficients for the ideal gas component of the Helmholtz free energy. More...

const std::array< Real, 5 >	_theta0 {{3.15163, 6.11190, 6.77708, 11.32384, 27.08792}}

const std::array< Real, 7 >	_n1
	Coefficients for the residual component of the Helmholtz free energy. More...

const std::array< unsigned int, 7 >	_d1 {{1, 1, 1, 1, 2, 2, 3}}

const std::array< Real, 7 >	_t1 {{0.0, 0.75, 1.0, 2.0, 0.75, 2.0, 0.75}}

const std::array< Real, 27 >	_n2

const std::array< unsigned int, 27 >	_d2

const std::array< Real, 27 >	_t2

const std::array< unsigned int, 27 >	_c2

const std::array< Real, 5 >	_n3

const std::array< unsigned int, 5 >	_d3 {{2, 2, 2, 3, 3}}

const std::array< unsigned int, 5 >	_t3 {{1, 0, 1, 3, 3}}

const std::array< Real, 5 >	_alpha3 {{25.0, 25.0, 25.0, 15.0, 20.0}}

const std::array< Real, 5 >	_beta3 {{325.0, 300.0, 300.0, 275.0, 275.0}}

const std::array< Real, 5 >	_gamma3 {{1.16, 1.19, 1.19, 1.25, 1.25}}

const std::array< Real, 5 >	_eps3 {{1.0, 1.0, 1.0, 1.0, 1.0}}

const std::array< Real, 3 >	_n4 {{-0.66642276540751, 0.72608632349897, 0.055068668612842}}

const std::array< Real, 3 >	_a4 {{3.5, 3.5, 3.5}}

const std::array< Real, 3 >	_b4 {{0.875, 0.925, 0.875}}

const std::array< Real, 3 >	_beta4 {{0.3, 0.3, 0.3}}

const std::array< Real, 3 >	_A4 {{0.7, 0.7, 0.7}}

const std::array< Real, 3 >	_B4 {{0.3, 0.3, 1.0}}

const std::array< Real, 3 >	_C4 {{10.0, 10.0, 12.5}}

const std::array< Real, 3 >	_D4 {{275.0, 275.0, 275.0}}

const std::array< Real, 5 >	_mu_a {{0.235156, -0.491266, 5.211155e-2, 5.347906e-2, -1.537102e-2}}
	Coefficients for viscosity. More...

const std::array< Real, 5 >	_mu_d

const std::array< Real, 3 >	_k_g1 {{0.0, 0.0, 1.5}}
	Coefficients for the thermal conductivity. More...

const std::array< Real, 7 >	_k_g2 {{0.0, 1.0, 1.5, 1.5, 1.5, 3.5, 5.5}}

const std::array< unsigned int, 3 >	_k_h1 {{1, 5, 1}}

const std::array< unsigned int, 7 >	_k_h2 {{1, 2, 0, 5, 9, 0, 0}}

const std::array< Real, 3 >	_k_n1 {{7.69857587, 0.159885811, 1.56918621}}

const std::array< Real, 7 >	_k_n2

const std::array< Real, 12 >	_k_a

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...

Private Member Functions
template<typename... Args>
void	fluidPropError (Args... args) const

e e e e p h T T T T T v v v s h	propfuncWithDefault (beta, p, T) propfuncWithDefault(v

e e e e p h T T T T T v v v s h T	propfuncWithDefault (e, p, T) propfuncWithDefault(gamma

	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(T

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

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

e e e e p h T	propfunc (mu, rho, T) propfunc(k

e e e e p h T T	propfunc (c, p, T) propfunc(cp

e e e e p h T T T	propfunc (cv, p, T) propfunc(mu

e e e e p h T T T T	propfunc (k, p, T) propfunc(rho

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

e e e e p h T T T T T v	propfunc (p, T, v) propfunc(h

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

e e e e p h T T T T T v v v	propfunc (h, p, T) propfunc(p

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

	v

e	v

e e	v

e e e	v

e e e e p	v

e e e e p h T T T T T v v v s h T	v

e e e e	h

e e e e p h T T T T T v v v	h

e e e e p h	p

e e e e p h T T	p

e e e e p h T T T	p

e e e e p h T T T T	p

e e e e p h T T T T T v v v s	p

e e e e p h T T T T T v v v s h	p

e e e e p h T	rho

e e e e p h T T T T T	T

e e e e p h T T T T T v	T

e e e e p h T T T T T v v	T

e e e e p h T T T T T v v v s h T e	propfuncWithDefault (gamma, p, T)

Detailed Description

CO2 fluid properties Most thermophysical properties taken from: Span and Wagner, "A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100K at Pressures up to 800 MPa", J.

Phys. Chem. Ref. Data, 25 (1996)

Note: the Span and Wagner EOS uses density and temperature as the primary variables. As a result, density must first be found using iteration, after which the other properties can be calculated directly.

Viscosity from: Fenghour et al., The viscosity of carbon dioxide, J. Phys. Chem. Ref.Data, 27, 31-44 (1998) Note: critical enhancement not included Valid for 217 K < T < 1000K and rho < 1400 kg/m^3

Thermal conductivity from: Scalabrin et al., A Reference Multiparameter Thermal Conductivity Equation for Carbon Dioxide with an Optimized Functional Form, J. Phys. Chem. Ref. Data 35 (2006)

Definition at line 45 of file CO2FluidProperties.h.

Constructor & Destructor Documentation

◆ CO2FluidProperties()

CO2FluidProperties::CO2FluidProperties ( const InputParameters & parameters )

Definition at line 28 of file CO2FluidProperties.C.

   : HelmholtzFluidProperties(parameters)
 {
 }

◆ ~CO2FluidProperties()

CO2FluidProperties::~CO2FluidProperties ( )

virtual

Definition at line 33 of file CO2FluidProperties.C.

33 {}

Member Function Documentation

◆ alpha()

Real CO2FluidProperties::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 162 of file CO2FluidProperties.C.

 {
   // Ideal gas component of the Helmholtz free energy
   Real sum0 = 0.0;
   for (std::size_t i = 0; i < _a0.size(); ++i)
     sum0 += _a0[i] * std::log(1.0 - std::exp(-_theta0[i] * tau));
  
   Real phi0 = std::log(delta) + 8.37304456 - 3.70454304 * tau + 2.5 * std::log(tau) + sum0;
  
   // Residual component of the Helmholtz free energy
   Real theta, Delta, Psi;
   Real phir = 0.0;
   for (std::size_t i = 0; i < _n1.size(); ++i)
     phir += _n1[i] * MathUtils::pow(delta, _d1[i]) * std::pow(tau, _t1[i]);
  
   for (std::size_t i = 0; i < _n2.size(); ++i)
     phir += _n2[i] * MathUtils::pow(delta, _d2[i]) * std::pow(tau, _t2[i]) *
             std::exp(-MathUtils::pow(delta, _c2[i]));
  
   for (std::size_t i = 0; i < _n3.size(); ++i)
     phir += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
             std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
                      _beta3[i] * Utility::pow<2>(tau - _gamma3[i]));
  
   for (std::size_t i = 0; i < _n4.size(); ++i)
   {
     theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
     Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
     Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
     phir += _n4[i] * std::pow(Delta, _b4[i]) * delta * Psi;
   }
  
   // The Helmholtz free energy is the sum of these components
   return phi0 + phir;
 }

Referenced by k_from_rho_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 CO2FluidProperties::criticalDensity ( ) const

overridevirtual

Critical density.

Returns: critical density (kg/m^3)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 60 of file CO2FluidProperties.C.

 {
   return _critical_density;
 }

◆ criticalInternalEnergy()

Real SinglePhaseFluidProperties::criticalInternalEnergy ( ) const

virtualinherited

Critical specific internal energy.

Returns: specific internal energy (J/kg)

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 126 of file SinglePhaseFluidProperties.C.

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

Referenced by IdealRealGasMixtureFluidProperties::p_T_from_v_e(), and IdealRealGasMixtureFluidProperties::T_from_p_v().

◆ criticalPressure()

Real CO2FluidProperties::criticalPressure ( ) const

overridevirtual

Critical pressure.

Returns: critical pressure (Pa)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 48 of file CO2FluidProperties.C.

 {
   return _critical_pressure;
 }

◆ criticalTemperature()

Real CO2FluidProperties::criticalTemperature ( ) const

overridevirtual

Critical temperature.

Returns: critical temperature (K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 54 of file CO2FluidProperties.C.

 {
   return _critical_temperature;
 }

◆ 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 CO2FluidProperties::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 283 of file CO2FluidProperties.C.

 {
   // Second derivative of the ideal gas component wrt gamma
   Real d2phi0dd2 = -1.0 / delta / delta;
  
   // Second derivative of the residual component wrt gamma
   Real d2phirdd2 = 0.0;
   Real theta, Delta, Psi, dDelta_dd, dPsi_dd, d2Delta_dd2, d2Psi_dd2;
  
   for (std::size_t i = 0; i < _n1.size(); ++i)
     d2phirdd2 += _n1[i] * _d1[i] * (_d1[i] - 1.0) * MathUtils::pow(delta, _d1[i] - 2) *
                  std::pow(tau, _t1[i]);
  
   for (std::size_t i = 0; i < _n2.size(); ++i)
     d2phirdd2 += _n2[i] * std::exp(-MathUtils::pow(delta, _c2[i])) *
                  MathUtils::pow(delta, _d2[i] - 2) * std::pow(tau, _t2[i]) *
                  ((_d2[i] - _c2[i] * MathUtils::pow(delta, _c2[i])) *
                       (_d2[i] - 1.0 - _c2[i] * MathUtils::pow(delta, _c2[i])) -
                   _c2[i] * _c2[i] * MathUtils::pow(delta, _c2[i]));
  
   for (std::size_t i = 0; i < _n3.size(); ++i)
     d2phirdd2 +=
         _n3[i] * MathUtils::pow(tau, _t3[i]) *
         std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
                  _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
         (-2.0 * _alpha3[i] * MathUtils::pow(delta, _d3[i]) +
          4.0 * _alpha3[i] * _alpha3[i] * MathUtils::pow(delta, _d3[i]) *
              Utility::pow<2>(delta - _eps3[i]) -
          4.0 * _d3[i] * _alpha3[i] * MathUtils::pow(delta, _d3[i] - 1.0) * (delta - _eps3[i]) +
          _d3[i] * (_d3[i] - 1.0) * MathUtils::pow(delta, _d3[i] - 2.0));
  
   for (std::size_t i = 0; i < _n4.size(); ++i)
   {
     theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
     Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
     Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
     dPsi_dd = -2.0 * _C4[i] * (delta - 1.0) * Psi;
     dDelta_dd = (delta - 1.0) *
                 (_A4[i] * theta * 2.0 / _beta4[i] *
                      std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) +
                  2.0 * _B4[i] * _a4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 1.0));
     d2Psi_dd2 = 3.0 * _D4[i] * Psi * (2.0 * _C4[i] * Utility::pow<2>(delta - 1.0) - 1.0);
     d2Delta_dd2 = 1.0 / (delta - 1.0) * dDelta_dd +
                   (delta - 1.0) * (delta - 1.0) *
                       (4.0 * _B4[i] * _a4[i] * (_a4[i] - 1.0) *
                            std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 2.0) +
                        2.0 * _A4[i] * _A4[i] *
                            Utility::pow<2>(std::pow(Utility::pow<2>(delta - 1.0),
                                                     1.0 / (2.0 * _beta4[i]) - 1.0)) /
                            _beta4[i] / _beta4[i] +
                        (4.0 / _beta4[i]) * _A4[i] * theta * (1.0 / (2.0 * _beta4[i]) - 1.0) *
                            std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 2.0));
     d2phirdd2 +=
         _n4[i] *
         (std::pow(Delta, _b4[i]) * (2.0 * dPsi_dd + delta * d2Psi_dd2) +
          2.0 * _b4[i] * std::pow(Delta, _b4[i] - 1.0) * dDelta_dd * (Psi + delta * dPsi_dd) +
          _b4[i] *
              (std::pow(Delta, _b4[i] - 1.0) * d2Delta_dd2 +
               (_b4[i] - 1.0) * std::pow(Delta, _b4[i] - 2.0) * Utility::pow<2>(dDelta_dd)) *
              delta * Psi);
   }
   // The second derivative of the free energy wrt delta is the sum of these components
   return d2phi0dd2 + d2phirdd2;
 }

◆ d2alpha_ddeltatau()

Real CO2FluidProperties::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 398 of file CO2FluidProperties.C.

 {
   // Note: second derivative of the ideal gas component wrt delta and tau is 0
   // Derivative of the residual component wrt gamma
   Real theta, Delta, Psi, dDelta_dd, dPsi_dd, dDelta_dt, dPsi_dt, d2Delta_ddt, d2Psi_ddt;
   Real d2phirddt = 0.0;
   for (std::size_t i = 0; i < _n1.size(); ++i)
     d2phirddt += _n1[i] * _d1[i] * _t1[i] * MathUtils::pow(delta, _d1[i] - 1.0) *
                  std::pow(tau, _t1[i] - 1.0);
  
   for (std::size_t i = 0; i < _n2.size(); ++i)
     d2phirddt += _n2[i] * std::exp(-MathUtils::pow(delta, _c2[i])) *
                  (MathUtils::pow(delta, _d2[i] - 1.0) * _t2[i] * std::pow(tau, _t2[i] - 1.0) *
                   (_d2[i] - _c2[i] * MathUtils::pow(delta, _c2[i])));
  
   for (std::size_t i = 0; i < _n3.size(); ++i)
     d2phirddt += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
                  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
                           _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                  (_d3[i] / delta - 2.0 * _alpha3[i] * (delta - _eps3[i])) *
                  (_t3[i] / tau - 2.0 * _beta3[i] * (tau - _gamma3[i]));
  
   for (std::size_t i = 0; i < _n4.size(); ++i)
   {
     theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
     Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
     Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
     dPsi_dd = -2.0 * _C4[i] * (delta - 1.0) * Psi;
     dPsi_dt = -2.0 * _D4[i] * (tau - 1.0) * Psi;
     d2Psi_ddt = 4.0 * _C4[i] * _D4[i] * (delta - 1.0) * (tau - 1.0) * Psi;
     dDelta_dd = (delta - 1.0) *
                 (_A4[i] * theta * 2.0 / _beta4[i] *
                      std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) +
                  2.0 * _B4[i] * _a4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 1.0));
     dDelta_dt = -2.0 * theta * _b4[i] * std::pow(Delta, _b4[i] - 1.0);
     d2Delta_ddt = -2.0 * _A4[i] * _b4[i] / _beta4[i] * std::pow(Delta, _b4[i] - 1.0) *
                       (delta - 1.0) *
                       std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) -
                   2.0 * theta * _b4[i] * (_b4[i] - 1.0) * std::pow(Delta, _b4[i] - 2.0) * dDelta_dd;
  
     d2phirddt += _n4[i] * (std::pow(Delta, _b4[i]) * (dPsi_dt + delta * d2Psi_ddt) +
                            delta * _b4[i] * std::pow(Delta, _b4[i] - 1.0) * dDelta_dd * dPsi_dt +
                            dDelta_dt * (Psi + delta * dPsi_dd) + d2Delta_ddt * delta * Psi);
   }
  
   return d2phirddt;
 }

◆ d2alpha_dtau2()

Real CO2FluidProperties::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 349 of file CO2FluidProperties.C.

 {
   // Second derivative of the ideal gas component wrt tau
   Real sum0 = 0.0;
   for (std::size_t i = 0; i < _a0.size(); ++i)
     sum0 += _a0[i] * _theta0[i] * _theta0[i] * std::exp(-_theta0[i] * tau) /
             Utility::pow<2>(1.0 - std::exp(-_theta0[i] * tau));
  
   Real d2phi0dt2 = -2.5 / tau / tau - sum0;
  
   // Second derivative of the residual component wrt tau
   Real d2phirdt2 = 0.0;
   Real theta, Delta, Psi, dPsi_dt, dDelta_dt, d2Delta_dt2, d2Psi_dt2;
  
   for (std::size_t i = 0; i < _n1.size(); ++i)
     d2phirdt2 += _n1[i] * _t1[i] * (_t1[i] - 1.0) * MathUtils::pow(delta, _d1[i]) *
                  std::pow(tau, _t1[i] - 2.0);
  
   for (std::size_t i = 0; i < _n2.size(); ++i)
     d2phirdt2 += _n2[i] * _t2[i] * (_t2[i] - 1.0) * MathUtils::pow(delta, _d2[i]) *
                  std::exp(-MathUtils::pow(delta, _c2[i])) * std::pow(tau, _t2[i] - 2.0);
  
   for (std::size_t i = 0; i < _n3.size(); ++i)
     d2phirdt2 += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
                  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
                           _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                  (Utility::pow<2>(_t3[i] / tau - 2.0 * _beta3[i] * (tau - _gamma3[i])) -
                   _t3[i] / tau / tau - 2.0 * _beta3[i]);
  
   for (std::size_t i = 0; i < _n4.size(); ++i)
   {
     theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
     Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
     Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
     dDelta_dt = -2.0 * theta * _b4[i] * std::pow(Delta, _b4[i] - 1.0);
     d2Delta_dt2 = 2.0 * _b4[i] * std::pow(Delta, _b4[i] - 1.0) +
                   4.0 * theta * theta * _b4[i] * (_b4[i] - 1.0) * std::pow(Delta, _b4[i] - 2.0);
     dPsi_dt = -2.0 * _D4[i] * (tau - 1.0) * Psi;
     d2Psi_dt2 = 2.0 * _D4[i] * (2.0 * _D4[i] * (tau - 1.0) * (tau - 1.0) - 1.0) * Psi;
     d2phirdt2 +=
         _n4[i] * delta *
         (Psi * d2Delta_dt2 + 2.0 * dDelta_dt * dPsi_dt + std::pow(Delta, _b4[i]) * d2Psi_dt2);
   }
  
   // The second derivative of the free energy wrt tau is the sum of these components
   return d2phi0dt2 + d2phirdt2;
 }

◆ dalpha_ddelta()

Real CO2FluidProperties::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 199 of file CO2FluidProperties.C.

 {
   // Derivative of the ideal gas component wrt gamma
   Real dphi0dd = 1.0 / delta;
  
   // Derivative of the residual component wrt gamma
   Real theta, Delta, Psi, dDelta_dd, dPsi_dd;
   Real dphirdd = 0.0;
  
   for (std::size_t i = 0; i < _n1.size(); ++i)
     dphirdd += _n1[i] * _d1[i] * MathUtils::pow(delta, _d1[i] - 1.0) * std::pow(tau, _t1[i]);
  
   for (std::size_t i = 0; i < _n2.size(); ++i)
     dphirdd += _n2[i] * std::exp(-MathUtils::pow(delta, _c2[i])) *
                (MathUtils::pow(delta, _d2[i] - 1.0) * std::pow(tau, _t2[i]) *
                 (_d2[i] - _c2[i] * MathUtils::pow(delta, _c2[i])));
  
   for (std::size_t i = 0; i < _n3.size(); ++i)
     dphirdd += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
                std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
                         _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                (_d3[i] / delta - 2.0 * _alpha3[i] * (delta - _eps3[i]));
  
   for (std::size_t i = 0; i < _n4.size(); ++i)
   {
     theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
     Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
     Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
     dPsi_dd = -2.0 * _C4[i] * (delta - 1.0) * Psi;
     dDelta_dd = (delta - 1.0) *
                 (_A4[i] * theta * 2.0 / _beta4[i] *
                      std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) +
                  2.0 * _B4[i] * _a4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 1.0));
  
     dphirdd += _n4[i] * (std::pow(Delta, _b4[i]) * (Psi + delta * dPsi_dd) +
                          _b4[i] * std::pow(Delta, _b4[i] - 1.0) * dDelta_dd * delta * Psi);
   }
  
   // The derivative of the free energy wrt delta is the sum of these components
   return dphi0dd + dphirdd;
 }

◆ dalpha_dtau()

Real CO2FluidProperties::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 242 of file CO2FluidProperties.C.

 {
   // Derivative of the ideal gas component wrt tau
   Real sum0 = 0.0;
   for (std::size_t i = 0; i < _a0.size(); ++i)
     sum0 += _a0[i] * _theta0[i] * (1.0 / (1.0 - std::exp(-_theta0[i] * tau)) - 1.0);
  
   Real dphi0dt = -3.70454304 + 2.5 / tau + sum0;
  
   // Derivative of the residual component wrt tau
   Real theta, Delta, Psi, dDelta_dt, dPsi_dt;
   Real dphirdt = 0.0;
   for (std::size_t i = 0; i < _n1.size(); ++i)
     dphirdt += _n1[i] * _t1[i] * MathUtils::pow(delta, _d1[i]) * std::pow(tau, _t1[i] - 1.0);
  
   for (std::size_t i = 0; i < _n2.size(); ++i)
     dphirdt += _n2[i] * _t2[i] * MathUtils::pow(delta, _d2[i]) * std::pow(tau, _t2[i] - 1.0) *
                std::exp(-MathUtils::pow(delta, _c2[i]));
  
   for (std::size_t i = 0; i < _n3.size(); ++i)
     dphirdt += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
                std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
                         _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
                (_t3[i] / tau - 2.0 * _beta3[i] * (tau - _gamma3[i]));
  
   for (std::size_t i = 0; i < _n4.size(); ++i)
   {
     theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
     Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
     Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
     dDelta_dt = -2.0 * theta * _b4[i] * std::pow(Delta, _b4[i] - 1.0);
     dPsi_dt = -2.0 * _D4[i] * (tau - 1.0) * Psi;
  
     dphirdt += _n4[i] * delta * (Psi * dDelta_dt + std::pow(Delta, _b4[i]) * dPsi_dt);
   }
  
   // The derivative of the free energy wrt tau is the sum of these components
   return dphi0dt + dphirdt;
 }

◆ e_from_p_T() [1/2]

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

overridevirtualinherited

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_from_p_T() [2/2]

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

overridevirtualinherited

Definition at line 65 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 * temperature * tau * dalpha_dtau(delta, tau) / molarMass();
 }

Referenced by HelmholtzFluidProperties::e_from_p_T().

◆ 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 IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 286 of file SinglePhaseFluidProperties.C.

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

Referenced by IdealRealGasMixtureFluidProperties::p_T_from_v_e(), and IdealRealGasMixtureFluidProperties::T_from_p_v().

◆ execute()

virtual void FluidProperties::execute ( )

inlinefinalvirtualinherited

Definition at line 34 of file FluidProperties.h.

34 {}

◆ finalize()

virtual void FluidProperties::finalize ( )

inlinefinalvirtualinherited

Definition at line 36 of file FluidProperties.h.

36 {}

◆ fluidName()

std::string CO2FluidProperties::fluidName ( ) const

overridevirtual

Definition at line 36 of file CO2FluidProperties.C.

 {
   return "co2";
 }

◆ fluidPropError()

template<typename... Args>

void SinglePhaseFluidProperties::fluidPropError ( Args... args ) const

inlineprivateinherited

Definition at line 326 of file SinglePhaseFluidProperties.h.

   {
     if (_allow_imperfect_jacobians)
       mooseDoOnce(mooseWarning(std::forward<Args>(args)...));
     else
       mooseError(std::forward<Args>(args)...);
   }

Referenced by SinglePhaseFluidProperties::vaporPressure(), and SinglePhaseFluidProperties::vaporTemperature().

◆ h_from_p_T() [1/2]

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();
 }

◆ h_from_p_T() [2/2]

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

overridevirtualinherited

Definition at line 185 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 * temperature * (tau * dalpha_dtau(delta, tau) + delta * dalpha_ddelta(delta, tau)) /
          molarMass();
 }

Referenced by HelmholtzFluidProperties::h_from_p_T().

◆ henryCoefficients()

std::vector< Real > CO2FluidProperties::henryCoefficients ( ) const

overridevirtual

Henry's law coefficients for dissolution in water.

Returns: Henry's constant coefficients

Reimplemented from SinglePhaseFluidProperties.

Definition at line 637 of file CO2FluidProperties.C.

 {
   return {-8.55445, 4.01195, 9.52345};
 }

◆ initialize()

virtual void FluidProperties::initialize ( )

inlinefinalvirtualinherited

Definition at line 35 of file FluidProperties.h.

35 {}

◆ k_from_p_T() [1/2]

Real CO2FluidProperties::k_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtual

Definition at line 643 of file CO2FluidProperties.C.

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

Referenced by k_from_p_T().

◆ k_from_p_T() [2/2]

void CO2FluidProperties::k_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	k,
		Real &	dk_dp,
		Real &	dk_dT
	)		const

overridevirtual

Definition at line 651 of file CO2FluidProperties.C.

 {
   k = this->k_from_p_T(pressure, temperature);
   // Calculate derivatives using finite differences. Note: this will be slow as
   // multiple calculations of density are required
   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 CO2FluidProperties::k_from_rho_T	(	Real	density,
		Real	temperature
	)		const

overridevirtual

Definition at line 666 of file CO2FluidProperties.C.

 {
   // Check the temperature is in the range of validity (216.592 K <= T <= 1000 K)
   if (temperature <= _triple_point_temperature || temperature >= 1000.0)
     throw MooseException("Temperature " + Moose::stringify(temperature) +
                          "K out of range (200K, 1000K) in " + name() + ": k()");
  
   // Scaled variables
   Real Tr = temperature / _critical_temperature;
   Real rhor = density / _critical_density;
  
   Real sum1 = 0.0;
   for (std::size_t i = 0; i < _k_n1.size(); ++i)
     sum1 += _k_n1[i] * std::pow(Tr, _k_g1[i]) * MathUtils::pow(rhor, _k_h1[i]);
  
   Real sum2 = 0.0;
   for (std::size_t i = 0; i < _k_n2.size(); ++i)
     sum2 += _k_n2[i] * std::pow(Tr, _k_g2[i]) * MathUtils::pow(rhor, _k_h2[i]);
  
   // Near-critical enhancement
   Real alpha =
       1.0 - _k_a[9] * std::acosh(1.0 + _k_a[10] * std::pow(Utility::pow<2>(1.0 - Tr), _k_a[11]));
   Real lambdac =
       rhor *
       std::exp(-std::pow(rhor, _k_a[0]) / _k_a[0] - Utility::pow<2>(_k_a[1] * (Tr - 1.0)) -
                Utility::pow<2>(_k_a[2] * (rhor - 1.0))) /
       std::pow(std::pow(Utility::pow<2>(
                             1.0 - 1.0 / Tr +
                             _k_a[3] * std::pow(Utility::pow<2>(rhor - 1.0), 1.0 / (2.0 * _k_a[4]))),
                         _k_a[5]) +
                    std::pow(Utility::pow<2>(_k_a[6] * (rhor - alpha)), _k_a[7]),
                _k_a[8]);
  
   return 4.81384 * (sum1 + std::exp(-5.0 * rhor * rhor) * sum2 + 0.775547504 * lambdac) / 1000.0;
 }

Referenced by k_from_p_T().

◆ meltingPressure()

Real CO2FluidProperties::meltingPressure ( Real temperature ) const

Melting pressure.

Used to delineate solid and liquid phases Valid for temperatures greater than the triple point temperature

Eq. 3.10, from Span and Wagner (reference above)

Parameters

temperature CO2 temperature (K)

Returns: melting pressure (Pa)

Definition at line 78 of file CO2FluidProperties.C.

 {
   if (temperature < _triple_point_temperature)
     throw MooseException("Temperature is below the triple point temperature in " + name() +
                          ": meltingPressure()");
  
   Real Tstar = temperature / _triple_point_temperature;
  
   return _triple_point_pressure *
          (1.0 + 1955.539 * (Tstar - 1.0) + 2055.4593 * Utility::pow<2>(Tstar - 1.0));
 }

Referenced by rho_from_p_T().

◆ molarMass()

Real CO2FluidProperties::molarMass ( ) const

overridevirtual

Fluid name.

Returns: string representing fluid name Molar mass [kg/mol]; molar mass

Reimplemented from SinglePhaseFluidProperties.

Definition at line 42 of file CO2FluidProperties.C.

 {
   return _Mco2;
 }

◆ mu_from_p_T() [1/2]

Real CO2FluidProperties::mu_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtual

Definition at line 509 of file CO2FluidProperties.C.

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

◆ mu_from_p_T() [2/2]

void CO2FluidProperties::mu_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	mu,
		Real &	dmu_dp,
		Real &	dmu_dT
	)		const

overridevirtual

Definition at line 516 of file CO2FluidProperties.C.

 {
   Real rho, drho_dp, drho_dT;
   HelmholtzFluidProperties::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 CO2FluidProperties::mu_from_rho_T	(	Real	density,
		Real	temperature
	)		const

overridevirtual

Definition at line 528 of file CO2FluidProperties.C.

 {
   // Check that the input parameters are within the region of validity
   if (temperature < 216.0 || temperature > 1000.0 || density > 1400.0)
     throw MooseException("Parameters out of range in " + name() + ": mu_from_rho_T()");
  
   Real Tstar = temperature / 251.196;
  
   // Viscosity in the zero-density limit
   Real sum = 0.0;
  
   for (std::size_t i = 0; i < _mu_a.size(); ++i)
     sum += _mu_a[i] * MathUtils::pow(std::log(Tstar), i);
  
   Real mu0 = 1.00697 * std::sqrt(temperature) / std::exp(sum);
  
   // Excess viscosity due to finite density
   Real mue = _mu_d[0] * density + _mu_d[1] * Utility::pow<2>(density) +
              _mu_d[2] * Utility::pow<6>(density) / Utility::pow<3>(Tstar) +
              _mu_d[3] * Utility::pow<8>(density) + _mu_d[4] * Utility::pow<8>(density) / Tstar;
  
   return (mu0 + mue) * 1.0e-6; // convert to Pa.s
 }

Referenced by mu_from_p_T(), and rho_mu_from_p_T().

◆ mu_from_rho_T() [2/2]

void CO2FluidProperties::mu_from_rho_T	(	Real	density,
		Real	temperature,
		Real	ddensity_dT,
		Real &	mu,
		Real &	dmu_drho,
		Real &	dmu_dT
	)		const

Definition at line 553 of file CO2FluidProperties.C.

 {
   // Check that the input parameters are within the region of validity
   if (temperature < 216.0 || temperature > 1000.0 || density > 1400.0)
     throw MooseException("Parameters out of range in " + name() + ": mu_drhoT()");
  
   Real Tstar = temperature / 251.196;
   Real dTstar_dT = 1.0 / 251.196;
  
   // Viscosity in the zero-density limit. Note this is only a function of T.
   // Start the sum at i = 1 so the derivative is defined
   Real sum0 = _mu_a[0], dsum0_dTstar = 0.0;
  
   for (std::size_t i = 1; i < _mu_a.size(); ++i)
   {
     sum0 += _mu_a[i] * MathUtils::pow(std::log(Tstar), i);
     dsum0_dTstar += i * _mu_a[i] * MathUtils::pow(std::log(Tstar), i - 1) / Tstar;
   }
  
   Real mu0 = 1.00697 * std::sqrt(temperature) / std::exp(sum0);
   Real dmu0_dT = (0.5 * 1.00697 / std::sqrt(temperature) -
                   1.00697 * std::sqrt(temperature) * dsum0_dTstar * dTstar_dT) /
                  std::exp(sum0);
  
   // Excess viscosity due to finite density
   Real mue = _mu_d[0] * density + _mu_d[1] * Utility::pow<2>(density) +
              _mu_d[2] * Utility::pow<6>(density) / Utility::pow<3>(Tstar) +
              _mu_d[3] * Utility::pow<8>(density) + _mu_d[4] * Utility::pow<8>(density) / Tstar;
  
   Real dmue_drho = _mu_d[0] + 2.0 * _mu_d[1] * density +
                    6.0 * _mu_d[2] * Utility::pow<5>(density) / Utility::pow<3>(Tstar) +
                    8.0 * _mu_d[3] * Utility::pow<7>(density) +
                    8.0 * _mu_d[4] * Utility::pow<7>(density) / Tstar;
  
   Real dmue_dT = (-3.0 * _mu_d[2] * Utility::pow<6>(density) / Utility::pow<4>(Tstar) -
                   _mu_d[4] * Utility::pow<8>(density) / Tstar / Tstar) *
                  dTstar_dT;
  
   // Viscosity in Pa.s is
   mu = (mu0 + mue) * 1.0e-6;
   dmu_drho = dmue_drho * 1.0e-6;
   dmu_dT = (dmu0_dT + dmue_dT) * 1.0e-6 + dmu_drho * ddensity_dT;
 }

◆ p_from_rho_T()

Real CO2FluidProperties::p_from_rho_T	(	Real	rho,
		Real	T
	)		const

overridevirtual

Pressure as a function of density and temperature.

Parameters

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

Returns: pressure (Pa)

Reimplemented from HelmholtzFluidProperties.

Definition at line 447 of file CO2FluidProperties.C.

 {
   // Check that the input parameters are within the region of validity
   if (temperature < 216.0 || temperature > 1100.0 || density <= 0.0)
     throw MooseException("Parameters out of range in " + name() + ": pressure()");
  
   Real pressure = 0.0;
  
   if (temperature > _triple_point_temperature && temperature < _critical_temperature)
   {
     Real gas_density = saturatedVaporDensity(temperature);
     Real liquid_density = saturatedLiquidDensity(temperature);
  
     if (density < gas_density || density > liquid_density)
       pressure = HelmholtzFluidProperties::p_from_rho_T(density, temperature);
     else
       pressure = vaporPressure(temperature);
   }
   else
     pressure = HelmholtzFluidProperties::p_from_rho_T(density, temperature);
  
   return pressure;
 }

Referenced by rho_from_p_T().

◆ partialDensity()

Real CO2FluidProperties::partialDensity ( Real temperature ) const

Partial density of dissolved CO2 From Garcia, Density of aqueous solutions of CO2, LBNL-49023 (2001)

Parameters

temperature fluid temperature (K)

Returns: partial molar density (kg/m^3)

Definition at line 626 of file CO2FluidProperties.C.

 {
   // This correlation uses temperature in C
   Real Tc = temperature - _T_c2k;
   // The parial volume
   Real V = 37.51 - 9.585e-2 * Tc + 8.74e-4 * Tc * Tc - 5.044e-7 * Tc * Tc * Tc;
  
   return 1.0e6 * _Mco2 / V;
 }

◆ propfunc() [1/16]

e e e e p h T T SinglePhaseFluidProperties::propfunc	(	c	,
		p	,
		T
	)

inherited

◆ propfunc() [2/16]

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

inherited

◆ propfunc() [3/16]

e e e e p h T T T SinglePhaseFluidProperties::propfunc	(	cv	,
		p	,
		T
	)

inherited

◆ propfunc() [4/16]

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

inherited

◆ propfunc() [5/16]

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

inherited

◆ propfunc() [6/16]

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

inherited

◆ propfunc() [7/16]

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

inherited

◆ propfunc() [8/16]

e e e e p h T T T T SinglePhaseFluidProperties::propfunc	(	k	,
		p	,
		T
	)

inherited

◆ propfunc() [9/16]

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

inherited

◆ propfunc() [10/16]

e e e e p h T SinglePhaseFluidProperties::propfunc	(	mu	,
		rho	,
		T
	)

inherited

◆ propfunc() [11/16]

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

inherited

◆ propfunc() [12/16]

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:

@begincode 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] gamma Adiabatic ratio (cp/cv) [-]

As an example:

@begincode // 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) and x_from_a_b(DualReal a, DualReal b, DualReal x, DualReal dx_da, DualReal dx_db) versions of the functions where a and b must be ADReal/DualNumber's calculated using all AD-supporting values:

@begincode 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() [13/16]

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

inherited

◆ propfunc() [14/16]

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

inherited

◆ propfunc() [15/16]

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

inherited

◆ propfunc() [16/16]

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

inherited

◆ propfuncWithDefault() [1/2]

e e e e p h T T T T T v v v s h SinglePhaseFluidProperties::propfuncWithDefault	(	beta	,
		p	,
		T
	)

inherited

◆ propfuncWithDefault() [2/2]

e e e e p h T T T T T v v v s h T SinglePhaseFluidProperties::propfuncWithDefault	(	e	,
		p	,
		T
	)

inherited

◆ rho_e_from_p_T()

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

virtualinherited

Definition at line 242 of file SinglePhaseFluidProperties.C.

 {
   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 CO2FluidProperties::rho_from_p_T	(	Real	pressure,
		Real	temperature
	)		const

overridevirtual

Reimplemented from HelmholtzFluidProperties.

Definition at line 472 of file CO2FluidProperties.C.

 {
   // Check that the input parameters are within the region of validity
   if (temperature < 216.0 || temperature > 1100.0 || pressure <= 0.0)
     throw MooseException("Parameters out of range in " + name() + ": rho_from_p_T()");
  
   // Also check that the pressure and temperature are not in the solid phase region
   if (((temperature > _triple_point_temperature) && (pressure > meltingPressure(temperature))) ||
       ((temperature < _triple_point_temperature) && (pressure > sublimationPressure(temperature))))
     throw MooseException("Input pressure and temperature in " + name() +
                          ": rho_from_p_T() correspond to solid CO2 phase");
  
   Real density;
   // Initial estimate of a bracketing interval for the density
   Real lower_density = 100.0;
   Real upper_density = 1000.0;
  
   // The density is found by finding the zero of the pressure calculated using the
   // Span and Wagner EOS minus the input pressure
   auto pressure_diff = [&pressure, &temperature, this](Real x) {
     return 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;
 }

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

◆ rho_from_p_T() [2/2]

void CO2FluidProperties::rho_from_p_T	(	Real	pressure,
		Real	temperature,
		Real &	rho,
		Real &	drho_dp,
		Real &	drho_dT
	)		const

overridevirtual

Reimplemented from HelmholtzFluidProperties.

Definition at line 502 of file CO2FluidProperties.C.

 {
   HelmholtzFluidProperties::rho_from_p_T(pressure, temperature, rho, drho_dp, drho_dT);
 }

◆ rho_mu_from_p_T() [1/3]

void SinglePhaseFluidProperties::rho_mu_from_p_T	(	const DualReal &	p,
		const DualReal &	T,
		DualReal &	rho,
		DualReal &	mu
	)		const

virtualinherited

Definition at line 277 of file SinglePhaseFluidProperties.C.

 {
   rho = rho_from_p_T(p, T);
   mu = mu_from_p_T(p, T);
 }

◆ rho_mu_from_p_T() [2/3]

void CO2FluidProperties::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

Reimplemented from SinglePhaseFluidProperties.

Definition at line 610 of file CO2FluidProperties.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;
 }

◆ rho_mu_from_p_T() [3/3]

void CO2FluidProperties::rho_mu_from_p_T	(	Real	p,
		Real	T,
		Real &	rho,
		Real &	mu
	)		const

overridevirtual

Combined methods.

These methods are particularly useful for the PorousFlow module, where density and viscosity are typically both computed everywhere. The combined methods allow the most efficient means of calculating both properties, especially where rho(p, T) and mu(rho, T). In this case, an extra density calculation would be required to calculate mu(p, T). All propery names are described above.

Reimplemented from SinglePhaseFluidProperties.

Definition at line 603 of file CO2FluidProperties.C.

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

◆ s_from_p_T() [1/2]

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);
 }

◆ s_from_p_T() [2/2]

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

overridevirtualinherited

Definition at line 150 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 * dalpha_dtau(delta, tau) - alpha(delta, tau)) / molarMass();
 }

Referenced by HelmholtzFluidProperties::s_from_p_T().

◆ saturatedLiquidDensity()

Real CO2FluidProperties::saturatedLiquidDensity ( Real temperature ) const

Saturated liquid density of CO2 Valid for temperatures between the triple point temperature and critical temperature.

Eq. 3.14, from Span and Wagner (reference above)

Parameters

temperature CO2 temperature (K)

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

Definition at line 130 of file CO2FluidProperties.C.

 {
   if (temperature < _triple_point_temperature || temperature > _critical_temperature)
     throw MooseException("Temperature is out of range in " + name() + ": saturatedLiquiDensity()");
  
   Real Tstar = temperature / _critical_temperature;
  
   Real logdensity = 1.9245108 * std::pow(1.0 - Tstar, 0.34) -
                     0.62385555 * std::pow(1.0 - Tstar, 0.5) -
                     0.32731127 * std::pow(1.0 - Tstar, 10.0 / 6.0) +
                     0.39245142 * std::pow(1.0 - Tstar, 11.0 / 6.0);
  
   return _critical_density * std::exp(logdensity);
 }

Referenced by p_from_rho_T().

◆ saturatedVaporDensity()

Real CO2FluidProperties::saturatedVaporDensity ( Real temperature ) const

Saturated vapor density of CO2 Valid for temperatures between the triple point temperature and critical temperature.

Eq. 3.15, from Span and Wagner (reference above)

Parameters

temperature CO2 temperature (K)

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

Definition at line 146 of file CO2FluidProperties.C.

 {
   if (temperature < _triple_point_temperature || temperature > _critical_temperature)
     throw MooseException("Temperature is out of range in " + name() + ": saturatedVaporDensity()");
  
   Real Tstar = temperature / _critical_temperature;
  
   Real logdensity =
       (-1.7074879 * std::pow(1.0 - Tstar, 0.34) - 0.82274670 * std::pow(1.0 - Tstar, 0.5) -
        4.6008549 * (1.0 - Tstar) - 10.111178 * std::pow(1.0 - Tstar, 7.0 / 3.0) -
        29.742252 * std::pow(1.0 - Tstar, 14.0 / 3.0));
  
   return _critical_density * std::exp(logdensity);
 }

Referenced by p_from_rho_T().

◆ subdomainSetup()

virtual void FluidProperties::subdomainSetup ( )

inlinefinalvirtualinherited

Definition at line 39 of file FluidProperties.h.

39 {}

◆ sublimationPressure()

Real CO2FluidProperties::sublimationPressure ( Real temperature ) const

Sublimation pressure.

Used to delineate solid and gas phases Valid for temperatures less than the triple point temperature

Eq. 3.12, from Span and Wagner (reference above)

Parameters

temperature CO2 temperature (K)

Returns: sublimation pressure (Pa)

Definition at line 91 of file CO2FluidProperties.C.

 {
   if (temperature > _triple_point_temperature)
     throw MooseException("Temperature is above the triple point temperature in " + name() +
                          ": sublimationPressure()");
  
   Real Tstar = temperature / _triple_point_temperature;
  
   Real pressure = _triple_point_pressure *
                   std::exp((-14.740846 * (1.0 - Tstar) + 2.4327015 * std::pow(1.0 - Tstar, 1.9) -
                             5.3061778 * std::pow(1.0 - Tstar, 2.9)) /
                            Tstar);
  
   return pressure;
 }

Referenced by rho_from_p_T().

◆ threadJoin()

virtual void FluidProperties::threadJoin ( const UserObject & )

inlinefinalvirtualinherited

Definition at line 38 of file FluidProperties.h.

38 {}

◆ triplePointPressure()

Real CO2FluidProperties::triplePointPressure ( ) const

overridevirtual

Triple point pressure.

Returns: triple point pressure (Pa)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 66 of file CO2FluidProperties.C.

 {
   return _triple_point_pressure;
 }

◆ triplePointTemperature()

Real CO2FluidProperties::triplePointTemperature ( ) const

overridevirtual

Triple point temperature.

Returns: triple point temperature (K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 72 of file CO2FluidProperties.C.

 {
   return _triple_point_temperature;
 }

◆ 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 IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 292 of file SinglePhaseFluidProperties.C.

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

Referenced by IdealRealGasMixtureFluidProperties::v_from_p_T().

◆ vaporPressure() [1/3]

DualReal SinglePhaseFluidProperties::vaporPressure ( const DualReal & T ) const

inherited

Definition at line 198 of file SinglePhaseFluidProperties.C.

 {
   Real p = 0.0;
   Real temperature = T.value();
   Real dpdT = 0.0;
  
   vaporPressure(temperature, p, dpdT);
  
   DualReal result = p;
   result.derivatives() = T.derivatives() * dpdT;
  
   return result;
 }

◆ vaporPressure() [2/3]

Real CO2FluidProperties::vaporPressure ( Real T ) const

overridevirtual

Vapor pressure.

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

Parameters

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

Reimplemented from SinglePhaseFluidProperties.

Definition at line 108 of file CO2FluidProperties.C.

 {
   if (temperature < _triple_point_temperature || temperature > _critical_temperature)
     throw MooseException("Temperature is out of range in " + name() + ": vaporPressure()");
  
   Real Tstar = temperature / _critical_temperature;
  
   Real logpressure =
       (-7.0602087 * (1.0 - Tstar) + 1.9391218 * std::pow(1.0 - Tstar, 1.5) -
        1.6463597 * Utility::pow<2>(1.0 - Tstar) - 3.2995634 * Utility::pow<4>(1.0 - Tstar)) /
       Tstar;
  
   return _critical_pressure * std::exp(logpressure);
 }

Referenced by p_from_rho_T().

◆ vaporPressure() [3/3]

void CO2FluidProperties::vaporPressure	(	Real	temperature,
		Real &	psat,
		Real &	dpsat_dT
	)		const

overridevirtual

Reimplemented from SinglePhaseFluidProperties.

Definition at line 124 of file CO2FluidProperties.C.

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

◆ vaporTemperature() [1/3]

DualReal SinglePhaseFluidProperties::vaporTemperature ( const DualReal & p ) const

inherited

Definition at line 227 of file SinglePhaseFluidProperties.C.

 {
   Real T = 0.0;
   Real pressure = p.value();
   Real dTdp = 0.0;
  
   vaporTemperature(pressure, T, dTdp);
  
   DualReal result = T;
   result.derivatives() = p.derivatives() * dTdp;
  
   return result;
 }

◆ vaporTemperature() [2/3]

Real SinglePhaseFluidProperties::vaporTemperature ( Real p ) const

virtualinherited

Vapor temperature.

Used to delineate liquid and gas phases. Valid for pressures between the triple point pressure and the critical pressure

Parameters

	p	fluid pressure (Pa)
[out]	saturation	temperature (K)
[out]	derivative	of saturation temperature wrt pressure

Reimplemented in Water97FluidProperties.

Definition at line 212 of file SinglePhaseFluidProperties.C.

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

Referenced by PorousFlowWaterVapor::thermophysicalProperties(), and SinglePhaseFluidProperties::vaporTemperature().

◆ vaporTemperature() [3/3]

void SinglePhaseFluidProperties::vaporTemperature	(	Real	p,
		Real &	Tsat,
		Real &	dTsat_dp
	)		const

virtualinherited

Reimplemented in Water97FluidProperties.

Definition at line 218 of file SinglePhaseFluidProperties.C.

 {
   fluidPropError(name(), ": ", __PRETTY_FUNCTION__, " derivatives not implemented.");
  
   dT_dp = 0.0;
   T = vaporTemperature(p);
 }

Member Data Documentation

◆ _a0

const std::array<Real, 5> CO2FluidProperties::_a0 {{1.99427042, 0.62105248, 0.41195293, 1.04028922, 0.08327678}}

protected

Coefficients for the ideal gas component of the Helmholtz free energy.

Definition at line 195 of file CO2FluidProperties.h.

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

◆ _a4

const std::array<Real, 3> CO2FluidProperties::_a4 {{3.5, 3.5, 3.5}}

protected

Definition at line 232 of file CO2FluidProperties.h.

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

◆ _A4

const std::array<Real, 3> CO2FluidProperties::_A4 {{0.7, 0.7, 0.7}}

protected

Definition at line 235 of file CO2FluidProperties.h.

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

◆ _allow_imperfect_jacobians

const bool FluidProperties::_allow_imperfect_jacobians

protectedinherited

Flag to set unimplemented Jacobian entries to zero.

Definition at line 48 of file FluidProperties.h.

Referenced by SinglePhaseFluidProperties::fluidPropError().

◆ _alpha3

const std::array<Real, 5> CO2FluidProperties::_alpha3 {{25.0, 25.0, 25.0, 15.0, 20.0}}

protected

Definition at line 227 of file CO2FluidProperties.h.

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

◆ _b4

const std::array<Real, 3> CO2FluidProperties::_b4 {{0.875, 0.925, 0.875}}

protected

Definition at line 233 of file CO2FluidProperties.h.

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

◆ _B4

const std::array<Real, 3> CO2FluidProperties::_B4 {{0.3, 0.3, 1.0}}

protected

Definition at line 236 of file CO2FluidProperties.h.

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

◆ _beta3

const std::array<Real, 5> CO2FluidProperties::_beta3 {{325.0, 300.0, 300.0, 275.0, 275.0}}

protected

Definition at line 228 of file CO2FluidProperties.h.

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

◆ _beta4

const std::array<Real, 3> CO2FluidProperties::_beta4 {{0.3, 0.3, 0.3}}

protected

Definition at line 234 of file CO2FluidProperties.h.

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

◆ _c2

const std::array<unsigned int, 27> CO2FluidProperties::_c2

protected

Initial value:

{

{1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6}}

Definition at line 221 of file CO2FluidProperties.h.

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

◆ _C4

const std::array<Real, 3> CO2FluidProperties::_C4 {{10.0, 10.0, 12.5}}

protected

Definition at line 237 of file CO2FluidProperties.h.

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

◆ _critical_density

const Real CO2FluidProperties::_critical_density = 467.6

protected

Critical density (kg/m^3)

Definition at line 186 of file CO2FluidProperties.h.

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

◆ _critical_pressure

const Real CO2FluidProperties::_critical_pressure = 7.3773e6

protected

Critical pressure (Pa)

Definition at line 182 of file CO2FluidProperties.h.

Referenced by criticalPressure(), and vaporPressure().

◆ _critical_temperature

const Real CO2FluidProperties::_critical_temperature = 304.1282

protected

Critical temperature (K)

Definition at line 184 of file CO2FluidProperties.h.

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

◆ _d1

const std::array<unsigned int, 7> CO2FluidProperties::_d1 {{1, 1, 1, 1, 2, 2, 3}}

protected

Definition at line 206 of file CO2FluidProperties.h.

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

◆ _d2

const std::array<unsigned int, 27> CO2FluidProperties::_d2

protected

Initial value:

{

{1, 2, 4, 5, 5, 5, 6, 6, 6, 1, 1, 4, 4, 4, 7, 8, 2, 3, 3, 5, 5, 6, 7, 8, 10, 4, 8}}

Definition at line 216 of file CO2FluidProperties.h.

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

◆ _d3

const std::array<unsigned int, 5> CO2FluidProperties::_d3 {{2, 2, 2, 3, 3}}

protected

Definition at line 225 of file CO2FluidProperties.h.

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

◆ _D4

const std::array<Real, 3> CO2FluidProperties::_D4 {{275.0, 275.0, 275.0}}

protected

Definition at line 238 of file CO2FluidProperties.h.

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

◆ _eps3

const std::array<Real, 5> CO2FluidProperties::_eps3 {{1.0, 1.0, 1.0, 1.0, 1.0}}

protected

Definition at line 230 of file CO2FluidProperties.h.

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

◆ _gamma3

const std::array<Real, 5> CO2FluidProperties::_gamma3 {{1.16, 1.19, 1.19, 1.25, 1.25}}

protected

Definition at line 229 of file CO2FluidProperties.h.

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

◆ _k_a

const std::array<Real, 12> CO2FluidProperties::_k_a

protected

Initial value:

{

{3.0, 6.70697, 0.94604, 0.3, 0.3, 0.39751, 0.33791, 0.77963, 0.79857, 0.9, 0.02, 0.2}}

Definition at line 253 of file CO2FluidProperties.h.

Referenced by k_from_rho_T().

◆ _k_g1

const std::array<Real, 3> CO2FluidProperties::_k_g1 {{0.0, 0.0, 1.5}}

protected

Coefficients for the thermal conductivity.

Definition at line 246 of file CO2FluidProperties.h.

Referenced by k_from_rho_T().

◆ _k_g2

const std::array<Real, 7> CO2FluidProperties::_k_g2 {{0.0, 1.0, 1.5, 1.5, 1.5, 3.5, 5.5}}

protected

Definition at line 247 of file CO2FluidProperties.h.

Referenced by k_from_rho_T().

◆ _k_h1

const std::array<unsigned int, 3> CO2FluidProperties::_k_h1 {{1, 5, 1}}

protected

Definition at line 248 of file CO2FluidProperties.h.

Referenced by k_from_rho_T().

◆ _k_h2

const std::array<unsigned int, 7> CO2FluidProperties::_k_h2 {{1, 2, 0, 5, 9, 0, 0}}

protected

Definition at line 249 of file CO2FluidProperties.h.

Referenced by k_from_rho_T().

◆ _k_n1

const std::array<Real, 3> CO2FluidProperties::_k_n1 {{7.69857587, 0.159885811, 1.56918621}}

protected

Definition at line 250 of file CO2FluidProperties.h.

Referenced by k_from_rho_T().

◆ _k_n2

const std::array<Real, 7> CO2FluidProperties::_k_n2

protected

Initial value:

{

{-6.73400790, 16.3890156, 3.69415242, 22.3205514, 66.1420950, -0.171779133, 0.00433043347}}

Definition at line 251 of file CO2FluidProperties.h.

Referenced by k_from_rho_T().

◆ _Mco2

const Real CO2FluidProperties::_Mco2 = 44.0098e-3

protected

Molar mass of CO2 (kg/mol)

Definition at line 180 of file CO2FluidProperties.h.

Referenced by molarMass(), and partialDensity().

◆ _mu_a

const std::array<Real, 5> CO2FluidProperties::_mu_a {{0.235156, -0.491266, 5.211155e-2, 5.347906e-2, -1.537102e-2}}

protected

Coefficients for viscosity.

Definition at line 241 of file CO2FluidProperties.h.

Referenced by mu_from_rho_T().

◆ _mu_d

const std::array<Real, 5> CO2FluidProperties::_mu_d

protected

Initial value:

{

{0.4071119e-2, 0.7198037e-4, 0.2411697e-16, 0.2971072e-22, -0.1627888e-22}}

Definition at line 242 of file CO2FluidProperties.h.

Referenced by mu_from_rho_T().

◆ _n1

const std::array<Real, 7> CO2FluidProperties::_n1

protected

Initial value:

{{0.38856823203161,
                                 2.9385475942740,
                                 -5.5867188534934,
                                 -0.76753199592477,
                                 0.31729005580416,
                                 0.54803315897767,
                                 0.12279411220335}}

Coefficients for the residual component of the Helmholtz free energy.

Definition at line 199 of file CO2FluidProperties.h.

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

◆ _n2

const std::array<Real, 27> CO2FluidProperties::_n2

protected

Initial value:

{
      {2.1658961543220,      1.5841735109724,    -0.23132705405503,   0.058116916431436,
       -0.55369137205382,    0.48946615909422,   -0.024275739843501,  0.062494790501678,
       -0.12175860225246,    -0.37055685270086,  -0.016775879700426,  -0.11960736637987,
       -0.045619362508778,   0.035612789270346,  -0.0074427727132052, -0.0017395704902432,
       -0.021810121289527,   0.024332166559236,  -0.037440133423463,  0.14338715756878,
       -0.13491969083286,    -0.023151225053480, 0.012363125492901,   0.0021058321972940,
       -0.00033958519026368, 0.0055993651771592, -0.00030335118055646}}

Definition at line 208 of file CO2FluidProperties.h.

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

◆ _n3

const std::array<Real, 5> CO2FluidProperties::_n3

protected

Initial value:

{

{-213.65488688320, 26641.569149272, -24027.212204557, -283.41603423999, 212.47284400179}}

Definition at line 223 of file CO2FluidProperties.h.

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

◆ _n4

const std::array<Real, 3> CO2FluidProperties::_n4 {{-0.66642276540751, 0.72608632349897, 0.055068668612842}}

protected

Definition at line 231 of file CO2FluidProperties.h.

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

◆ _R

const Real FluidProperties::_R = 8.3144598

staticinherited

Universal gas constant (J/mol/K)

Definition at line 42 of file FluidProperties.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(), HelmholtzFluidProperties::p_from_rho_T(), HelmholtzFluidProperties::rho_from_p_T(), IdealGasFluidProperties::rho_from_p_T(), and HelmholtzFluidProperties::s_from_p_T().

◆ _Rco2

const Real CO2FluidProperties::_Rco2 = 188.9241

protected

Specific gas constant (J/mol/K)

Definition at line 192 of file CO2FluidProperties.h.

◆ _t1

const std::array<Real, 7> CO2FluidProperties::_t1 {{0.0, 0.75, 1.0, 2.0, 0.75, 2.0, 0.75}}

protected

Definition at line 207 of file CO2FluidProperties.h.

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

◆ _t2

const std::array<Real, 27> CO2FluidProperties::_t2

protected

Initial value:

{{1.5,  1.5,  2.5,  0.0,  1.5,  2.0, 0.0, 1.0,  2.0,
                                  3.0,  6.0,  3.0,  6.0,  8.0,  6.0, 0.0, 7.0,  12.0,
                                  16.0, 22.0, 24.0, 16.0, 24.0, 8.0, 2.0, 28.0, 14.0}}

Definition at line 218 of file CO2FluidProperties.h.

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

◆ _t3

const std::array<unsigned int, 5> CO2FluidProperties::_t3 {{1, 0, 1, 3, 3}}

protected

Definition at line 226 of file CO2FluidProperties.h.

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

◆ _T_c2k

const Real FluidProperties::_T_c2k

protectedinherited

Conversion of temperature from Celsius to Kelvin.

Definition at line 46 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(), partialDensity(), NaClFluidProperties::rho_from_p_T(), and BrineFluidProperties::rho_from_p_T_X().

◆ _theta0

const std::array<Real, 5> CO2FluidProperties::_theta0 {{3.15163, 6.11190, 6.77708, 11.32384, 27.08792}}

protected

Definition at line 196 of file CO2FluidProperties.h.

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

◆ _triple_point_pressure

const Real CO2FluidProperties::_triple_point_pressure = 0.51795e6

protected

Triple point pressure (Pa)

Definition at line 188 of file CO2FluidProperties.h.

Referenced by meltingPressure(), sublimationPressure(), and triplePointPressure().

◆ _triple_point_temperature

const Real CO2FluidProperties::_triple_point_temperature = 216.592

protected

Triple point temperature (K)

Definition at line 190 of file CO2FluidProperties.h.

Referenced by meltingPressure(), p_from_rho_T(), rho_from_p_T(), sublimationPressure(), and triplePointTemperature().

◆ h [1/2]

e e e e SinglePhaseFluidProperties::h

inherited

Definition at line 163 of file SinglePhaseFluidProperties.h.

◆ h [2/2]

e e e e p h T T T T T v v v SinglePhaseFluidProperties::h

inherited

Definition at line 183 of file SinglePhaseFluidProperties.h.

◆ p [1/6]

e e e e p h SinglePhaseFluidProperties::p

inherited

Definition at line 167 of file SinglePhaseFluidProperties.h.

◆ p [2/6]

e e e e p h T T SinglePhaseFluidProperties::p

inherited

Definition at line 171 of file SinglePhaseFluidProperties.h.

◆ p [3/6]

e e e e p h T T T SinglePhaseFluidProperties::p

inherited

Definition at line 173 of file SinglePhaseFluidProperties.h.

◆ p [4/6]

e e e e p h T T T T SinglePhaseFluidProperties::p

inherited

Definition at line 175 of file SinglePhaseFluidProperties.h.

◆ p [5/6]

e e e e p h T T T T T v v v s SinglePhaseFluidProperties::p

inherited

Definition at line 185 of file SinglePhaseFluidProperties.h.

◆ p [6/6]

e e e e p h T T T T T v v v s h SinglePhaseFluidProperties::p

inherited

Definition at line 187 of file SinglePhaseFluidProperties.h.

◆ propfuncWithDefault

e e e e p h T T T T T v v v s h T e SinglePhaseFluidProperties::propfuncWithDefault(gamma, p, T)

inherited

Definition at line 190 of file SinglePhaseFluidProperties.h.

◆ rho

e e e e p h T SinglePhaseFluidProperties::rho

inherited

Definition at line 169 of file SinglePhaseFluidProperties.h.

◆ T [1/3]

e e e e p h T T T T T SinglePhaseFluidProperties::T

inherited

Definition at line 177 of file SinglePhaseFluidProperties.h.

◆ T [2/3]

e e e e p h T T T T T v SinglePhaseFluidProperties::T

inherited

Definition at line 179 of file SinglePhaseFluidProperties.h.

◆ T [3/3]

e e e e p h T T T T T v v SinglePhaseFluidProperties::T

inherited

Definition at line 181 of file SinglePhaseFluidProperties.h.

◆ v [1/6]

SinglePhaseFluidProperties::v

inherited

Definition at line 155 of file SinglePhaseFluidProperties.h.

◆ v [2/6]

e SinglePhaseFluidProperties::v

inherited

Definition at line 157 of file SinglePhaseFluidProperties.h.

◆ v [3/6]

e e SinglePhaseFluidProperties::v

inherited

Definition at line 159 of file SinglePhaseFluidProperties.h.

◆ v [4/6]

e e e SinglePhaseFluidProperties::v

inherited

Definition at line 161 of file SinglePhaseFluidProperties.h.

◆ v [5/6]

e e e e p SinglePhaseFluidProperties::v

inherited

Definition at line 165 of file SinglePhaseFluidProperties.h.

◆ v [6/6]

e e e e p h T T T T T v v v s h T SinglePhaseFluidProperties::v

inherited

Definition at line 189 of file SinglePhaseFluidProperties.h.

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

fluid_properties/include/userobjects/CO2FluidProperties.h
fluid_properties/src/userobjects/CO2FluidProperties.C

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ CO2FluidProperties()

◆ ~CO2FluidProperties()

Member Function Documentation

◆ alpha()

◆ 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_from_p_T() [1/2]

◆ e_from_p_T() [2/2]

◆ e_spndl_from_v()

◆ execute()

◆ finalize()

◆ fluidName()

◆ fluidPropError()

◆ h_from_p_T() [1/2]

◆ h_from_p_T() [2/2]

◆ henryCoefficients()

◆ initialize()

◆ k_from_p_T() [1/2]

◆ k_from_p_T() [2/2]

◆ k_from_rho_T()

◆ meltingPressure()

◆ molarMass()

◆ 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()

◆ partialDensity()

◆ propfunc() [1/16]

◆ propfunc() [2/16]

◆ propfunc() [3/16]

◆ propfunc() [4/16]

◆ propfunc() [5/16]

◆ propfunc() [6/16]

◆ propfunc() [7/16]

◆ propfunc() [8/16]

◆ propfunc() [9/16]

◆ propfunc() [10/16]

◆ propfunc() [11/16]

◆ propfunc() [12/16]

◆ propfunc() [13/16]

◆ propfunc() [14/16]

◆ propfunc() [15/16]

◆ propfunc() [16/16]

◆ propfuncWithDefault() [1/2]

◆ propfuncWithDefault() [2/2]

◆ rho_e_from_p_T()

◆ rho_from_p_T() [1/2]

◆ rho_from_p_T() [2/2]

◆ rho_mu_from_p_T() [1/3]

◆ rho_mu_from_p_T() [2/3]

◆ rho_mu_from_p_T() [3/3]

◆ s_from_p_T() [1/2]

◆ s_from_p_T() [2/2]

◆ saturatedLiquidDensity()

◆ saturatedVaporDensity()

◆ subdomainSetup()

◆ sublimationPressure()

◆ threadJoin()

◆ triplePointPressure()

◆ triplePointTemperature()

◆ v_e_spndl_from_T()

◆ vaporPressure() [1/3]