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CO2FluidProperties Class Reference

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
 Density from pressure and temperature. More...
 
virtual void rho_from_p_T (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT) const override
 Density and its derivatives from pressure and temperature. 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 Real mu_from_rho_T (Real density, Real temperature) const override
 Dynamic viscosity as a function of density 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 override
 Dynamic viscosity and its derivatives wrt density and temperature. More...
 
virtual std::string fluidName () const override
 Fluid name. More...
 
virtual Real molarMass () const override
 Molar mass [kg/mol]. 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...
 
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 Real henryConstant (Real temperature) const override
 Henry's law constant for dissolution in water. More...
 
virtual void henryConstant_dT (Real temperature, Real &Kh, Real &dKh_dT) const override
 Henry's law constant for dissolution in water and derivative wrt temperature. 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
 Thermal conductivity. More...
 
virtual void k_from_p_T (Real pressure, Real temperature, Real &k, Real &dk_dp, Real &dk_dT) const override
 Thermal conductivity and its derivatives wrt pressure and temperature. More...
 
virtual Real k_from_rho_T (Real density, Real temperature) const override
 Thermal conductivity as a function of density and temperature. More...
 
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 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 override
 Density and internal energy and their derivatives wrt pressure and temperature. More...
 
virtual Real c_from_p_T (Real pressure, Real temperature) const override
 Speed of sound. More...
 
virtual Real cp_from_p_T (Real pressure, Real temperature) const override
 Isobaric specific heat capacity. More...
 
virtual Real cv_from_p_T (Real pressure, Real temperature) const override
 Isochoric specific heat. More...
 
virtual void rho_mu (Real pressure, Real temperature, Real &rho, Real &mu) const override
 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 override
 Density and viscosity and their derivatives wrt pressure and temperature. More...
 
virtual Real s_from_p_T (Real pressure, Real temperature) const override
 Specific entropy from pressure and temperature. More...
 
virtual void s_from_p_T (Real p, Real T, Real &s, Real &ds_dp, Real &ds_dT) const override
 Specific entropy and its derivatives from pressure and temperature. More...
 
virtual Real h_from_p_T (Real pressure, Real temperature) const override
 Specific enthalpy from pressure and temperature. More...
 
virtual void h_from_p_T (Real p, Real T, Real &h, Real &dh_dp, Real &dh_dT) const override
 Specific enthalpy and its derivatives from pressure and temperature. More...
 
virtual Real p_from_v_e (Real v, Real e) const
 Pressure from specific volume and specific internal energy. More...
 
virtual void p_from_v_e (Real v, Real e, Real &p, Real &dp_dv, Real &dp_de) const
 Pressure and its derivatives from specific volume and specific internal energy. More...
 
virtual Real T_from_v_e (Real v, Real e) const
 Temperature from specific volume and specific internal energy. More...
 
virtual void T_from_v_e (Real v, Real e, Real &T, Real &dT_dv, Real &dT_de) const
 Temperature and its derivatives from specific volume and specific internal energy. More...
 
virtual Real c_from_v_e (Real v, Real e) const
 Sound speed from specific volume and specific internal energy. More...
 
virtual void c_from_v_e (Real v, Real e, Real &c, Real &dc_dv, Real &dc_de) const
 Sound speed and its derivatives from specific volume and specific internal energy. More...
 
virtual Real cp_from_v_e (Real v, Real e) const
 Isobaric (constant-pressure) specific heat from specific volume and specific internal energy. More...
 
virtual Real cv_from_v_e (Real v, Real e) const
 Isochoric (constant-volume) specific heat from specific volume and specific internal energy. More...
 
virtual Real mu_from_v_e (Real v, Real e) const
 Dynamic viscosity from specific volume and specific internal energy. More...
 
virtual Real k_from_v_e (Real v, Real e) const
 Thermal conductivity from specific volume and specific internal energy. More...
 
virtual Real s_from_v_e (Real v, Real e) const
 Specific entropy from specific volume and specific internal energy. More...
 
virtual void s_from_v_e (Real v, Real e, Real &s, Real &ds_dv, Real &ds_de) const
 Specific entropy and its derivatives from specific volume and specific internal energy. More...
 
virtual Real s (Real pressure, Real temperature) const
 
virtual Real s_from_h_p (Real h, Real p) const
 Specific entropy from specific enthalpy and pressure. More...
 
virtual void s_from_h_p (Real h, Real p, Real &s, Real &ds_dh, Real &ds_dp) const
 Specific entropy and its derivatives from specific enthalpy and pressure. More...
 
virtual Real rho_from_p_s (Real p, Real s) const
 Density from pressure and specific entropy. More...
 
virtual void rho_from_p_s (Real p, Real s, Real &rho, Real &drho_dp, Real &drho_ds) const
 Density and its derivatives from pressure and specific entropy. More...
 
virtual Real e_from_v_h (Real v, Real h) const
 Specific internal energy as a function of specific volume and specific enthalpy. More...
 
virtual void e_from_v_h (Real v, Real h, Real &e, Real &de_dv, Real &de_dh) const
 Specific internal energy and derivatives as a function of specific volume and specific enthalpy. More...
 
virtual Real rho (Real p, Real T) const
 
virtual void rho_dpT (Real pressure, Real temperature, Real &rho, Real &drho_dp, Real &drho_dT) const
 
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_from_p_rho (Real p, Real rho) const
 Specific internal energy from pressure and density. More...
 
virtual void e_from_p_rho (Real p, Real rho, Real &e, Real &de_dp, Real &de_drho) const
 Specific internal energy and its derivatives from pressure and density. 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 e_from_T_v (Real T, Real v) const
 Specific volume and specific internal energy from temerature at the vapor spinodal. More...
 
virtual void e_from_T_v (Real T, Real v, Real &e, Real &de_dT, Real &de_dv) const
 Specific internal energy and its derivatives from temperature and specific volume. More...
 
virtual Real p_from_T_v (Real T, Real v) const
 Pressure from temperature and specific volume. More...
 
virtual void p_from_T_v (Real T, Real v, Real &p, Real &dp_dT, Real &dp_dv) const
 Pressure and its derivatives from temperature and specific volume. More...
 
virtual Real h_from_T_v (Real T, Real v) const
 Specific enthalpy from temperature and specific volume. More...
 
virtual void h_from_T_v (Real T, Real v, Real &h, Real &dh_dT, Real &dh_dv) const
 Specific enthalpy and its derivatives from temperature and specific volume. More...
 
virtual Real s_from_T_v (Real T, Real v) const
 Specific entropy from temperature and specific volume. More...
 
virtual void s_from_T_v (Real T, Real v, Real &s, Real &ds_dT, Real &ds_dv) const
 Specific entropy and its derivatives from temperature and specific volume. More...
 
virtual Real cv_from_T_v (Real T, Real v) const
 Specific isochoric heat capacity from temperature and specific volume. More...
 
virtual Real h (Real p, Real T) const
 
virtual void h_dpT (Real pressure, Real temperature, Real &h, Real &dh_dp, Real &dh_dT) const
 
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 p_from_h_s (Real h, Real s) const
 Pressure from specific enthalpy and specific entropy. More...
 
virtual void p_from_h_s (Real h, Real s, Real &p, Real &dp_dh, Real &dp_ds) const
 Pressure and its derivatives from specific enthalpy and specific entropy. More...
 
virtual Real g_from_v_e (Real v, Real e) const
 Gibbs free energy from specific volume and specific internal energy. More...
 
virtual Real beta_from_p_T (Real p, Real T) const
 Thermal expansion coefficient from pressure and temperature. More...
 
virtual Real beta (Real pressure, Real temperature) const
 
virtual Real pp_sat_from_p_T (Real p, Real T) const
 Partial pressure at saturation in a gas mixture. More...
 
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 Real c (Real pressure, Real temperature) const
 
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 Real k (Real pressure, Real temperature) const
 
virtual void k_dpT (Real pressure, Real temperature, Real &k, Real &dk_dp, Real &dk_dT) const
 
virtual void vaporPressure_dT (Real temperature, Real &psat, Real &dpsat_dT) const
 Vapor pressure. More...
 
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_dT (Real temperature, Real &Kh, Real &dKh_dT, Real A, Real B, Real C) const
 IAPWS formulation of Henry's law constant for dissolution in water and derivative wrt temperature. 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 _R
 Universal gas constant (J/mol/K) More...
 
const Real _T_c2k
 Conversion of temperature from Celsius to Kelvin. More...
 

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 43 of file CO2FluidProperties.h.

Constructor & Destructor Documentation

◆ CO2FluidProperties()

CO2FluidProperties::CO2FluidProperties ( const InputParameters &  parameters)

Definition at line 28 of file CO2FluidProperties.C.

29  : HelmholtzFluidProperties(parameters)
30 {
31 }
HelmholtzFluidProperties(const InputParameters &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
deltascaled density (-)
tauscaled temperature (-)
Returns
alpha Helmholtz free energy

Implements HelmholtzFluidProperties.

Definition at line 156 of file CO2FluidProperties.C.

Referenced by k_from_rho_T().

157 {
158  // Ideal gas component of the Helmholtz free energy
159  Real sum0 = 0.0;
160  for (std::size_t i = 0; i < _a0.size(); ++i)
161  sum0 += _a0[i] * std::log(1.0 - std::exp(-_theta0[i] * tau));
162 
163  Real phi0 = std::log(delta) + 8.37304456 - 3.70454304 * tau + 2.5 * std::log(tau) + sum0;
164 
165  // Residual component of the Helmholtz free energy
166  Real theta, Delta, Psi;
167  Real phir = 0.0;
168  for (std::size_t i = 0; i < _n1.size(); ++i)
169  phir += _n1[i] * MathUtils::pow(delta, _d1[i]) * std::pow(tau, _t1[i]);
170 
171  for (std::size_t i = 0; i < _n2.size(); ++i)
172  phir += _n2[i] * MathUtils::pow(delta, _d2[i]) * std::pow(tau, _t2[i]) *
173  std::exp(-MathUtils::pow(delta, _c2[i]));
174 
175  for (std::size_t i = 0; i < _n3.size(); ++i)
176  phir += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
177  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
178  _beta3[i] * Utility::pow<2>(tau - _gamma3[i]));
179 
180  for (std::size_t i = 0; i < _n4.size(); ++i)
181  {
182  theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
183  Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
184  Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
185  phir += _n4[i] * std::pow(Delta, _b4[i]) * delta * Psi;
186  }
187 
188  // The Helmholtz free energy is the sum of these components
189  return phi0 + phir;
190 }
const std::array< Real, 3 > _D4
const std::array< Real, 7 > _t1
const std::array< unsigned int, 5 > _d3
const std::array< Real, 27 > _n2
const std::array< Real, 7 > _n1
Coefficients for the residual component of the Helmholtz free energy.
const std::array< Real, 3 > _C4
const std::array< Real, 5 > _theta0
const std::array< Real, 3 > _b4
const std::array< Real, 3 > _a4
const std::array< Real, 5 > _n3
const std::array< unsigned int, 27 > _c2
const std::array< Real, 5 > _eps3
const std::array< Real, 3 > _A4
const std::array< Real, 3 > _B4
const std::array< Real, 5 > _gamma3
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const std::array< Real, 3 > _n4
const std::array< Real, 5 > _alpha3
const std::array< unsigned int, 5 > _t3
const std::array< Real, 3 > _beta4
const std::array< Real, 5 > _a0
Coefficients for the ideal gas component of the Helmholtz free energy.
const std::array< Real, 27 > _t2
const std::array< Real, 5 > _beta3
const std::array< unsigned int, 7 > _d1
const std::array< unsigned int, 27 > _d2

◆ beta()

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

Definition at line 256 of file SinglePhaseFluidProperties.C.

Referenced by Water97FluidProperties::vaporTemperature().

257 {
259 }
virtual Real beta_from_p_T(Real p, Real T) const
Thermal expansion coefficient from pressure and temperature.
const std::string temperature
Definition: NS.h:27
const std::string pressure
Definition: NS.h:26

◆ beta_from_p_T()

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

Thermal expansion coefficient from pressure and temperature.

Parameters
[in]ppressure (Pa)
[in]Ttemperature (K)
Returns
beta (1/K)

Reimplemented in SimpleFluidProperties.

Definition at line 171 of file SinglePhaseFluidProperties.C.

Referenced by SinglePhaseFluidProperties::beta().

172 {
173  // The volumetric thermal expansion coefficient is defined as
174  // 1/v dv/dT)_p
175  // It is the fractional change rate of volume with respect to temperature change
176  // at constant pressure. Here it is coded as
177  // - 1/rho drho/dT)_p
178  // using chain rule with v = v(rho)
179 
180  Real rho, drho_dp, drho_dT;
181  rho_from_p_T(p, T, rho, drho_dp, drho_dT);
182  return -drho_dT / rho;
183 }
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real p, Real T) const
Density from pressure and temperature.

◆ c()

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

◆ c_from_p_T()

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

Speed of sound.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
Returns
speed of sound (m/s)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 123 of file HelmholtzFluidProperties.C.

124 {
125  // Require density first
126  const Real density = rho_from_p_T(pressure, temperature);
127  // Scale the input density and temperature
128  const Real delta = density / criticalDensity();
129  const Real tau = criticalTemperature() / temperature;
130 
131  const Real da_dd = dalpha_ddelta(delta, tau);
132 
133  Real w = 2.0 * delta * da_dd + delta * delta * d2alpha_ddelta2(delta, tau);
134  w -= Utility::pow<2>(delta * da_dd - delta * tau * d2alpha_ddeltatau(delta, tau)) /
135  (tau * tau * d2alpha_dtau2(delta, tau));
136 
137  return std::sqrt(_R * temperature * w / molarMass());
138 }
virtual Real d2alpha_ddeltatau(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta and tau.
virtual Real d2alpha_dtau2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt tau.
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
virtual Real d2alpha_ddelta2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta.
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real dalpha_ddelta(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt delta.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26

◆ c_from_v_e() [1/2]

Real SinglePhaseFluidProperties::c_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Sound speed from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 50 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties(), and NSMachAux::computeValue().

51 {
52  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
53 }
const std::string name
Definition: Setup.h:22

◆ c_from_v_e() [2/2]

void SinglePhaseFluidProperties::c_from_v_e ( Real  v,
Real  e,
Real &  c,
Real &  dc_dv,
Real &  dc_de 
) const
virtualinherited

Sound speed and its derivatives from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy
[out]dc_dvderivative of sound speed w.r.t. specific volume
[out]dc_dederivative of sound speed w.r.t. specific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 56 of file SinglePhaseFluidProperties.C.

57 {
58  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
59 }
const std::string name
Definition: Setup.h:22

◆ cp_from_p_T()

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

Isobaric specific heat capacity.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
Returns
cp (J/kg/K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 141 of file HelmholtzFluidProperties.C.

142 {
143  // Require density first
144  const Real density = rho_from_p_T(pressure, temperature);
145  // Scale the input density and temperature
146  const Real delta = density / criticalDensity();
147  const Real tau = criticalTemperature() / temperature;
148 
149  const Real da_dd = dalpha_ddelta(delta, tau);
150 
151  const Real cp = _R *
152  (-tau * tau * d2alpha_dtau2(delta, tau) +
153  Utility::pow<2>(delta * da_dd - delta * tau * d2alpha_ddeltatau(delta, tau)) /
154  (2.0 * delta * da_dd + delta * delta * d2alpha_ddelta2(delta, tau))) /
155  molarMass();
156 
157  return cp;
158 }
virtual Real d2alpha_ddeltatau(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta and tau.
virtual Real d2alpha_dtau2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt tau.
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
virtual Real d2alpha_ddelta2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta.
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real dalpha_ddelta(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt delta.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26

◆ cp_from_v_e()

Real SinglePhaseFluidProperties::cp_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Isobaric (constant-pressure) specific heat from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 61 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties(), and GeneralVaporMixtureFluidProperties::cp_from_p_T().

62 {
63  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
64 }
const std::string name
Definition: Setup.h:22

◆ 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.

61 {
62  return _critical_density;
63 }
const Real _critical_density
Critical density (kg/m^3)

◆ criticalInternalEnergy()

Real SinglePhaseFluidProperties::criticalInternalEnergy ( ) const
virtualinherited

Critical specific internal energy.

Returns
specific internal energy (J/kg)

Reimplemented in StiffenedGasFluidProperties.

Definition at line 232 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::p_T_from_v_e().

233 {
234  mooseError(name(), ": criticalInternalEnergy() is not implemented");
235 }
const std::string name
Definition: Setup.h:22

◆ criticalPressure()

Real CO2FluidProperties::criticalPressure ( ) const
overridevirtual

Critical pressure.

Returns
critical pressure (Pa)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 48 of file CO2FluidProperties.C.

49 {
50  return _critical_pressure;
51 }
const Real _critical_pressure
Critical pressure (Pa)

◆ criticalTemperature()

Real CO2FluidProperties::criticalTemperature ( ) const
overridevirtual

Critical temperature.

Returns
critical temperature (K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 54 of file CO2FluidProperties.C.

55 {
56  return _critical_temperature;
57 }
const Real _critical_temperature
Critical temperature (K)

◆ cv_from_p_T()

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

Isochoric specific heat.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
Returns
cv (J/kg/K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 161 of file HelmholtzFluidProperties.C.

162 {
163  // Require density first
164  const Real density = rho_from_p_T(pressure, temperature);
165  // Scale the input density and temperature
166  const Real delta = density / criticalDensity();
167  const Real tau = criticalTemperature() / temperature;
168 
169  return -_R * tau * tau * d2alpha_dtau2(delta, tau) / molarMass();
170 }
virtual Real d2alpha_dtau2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt tau.
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26

◆ cv_from_T_v()

Real SinglePhaseFluidProperties::cv_from_T_v ( Real  T,
Real  v 
) const
virtualinherited

Specific isochoric heat capacity from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 568 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::cv_from_p_T(), and IdealRealGasMixtureFluidProperties::cv_from_T_v().

569 {
570  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
571 }
const std::string name
Definition: Setup.h:22

◆ cv_from_v_e()

Real SinglePhaseFluidProperties::cv_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Isochoric (constant-volume) specific heat from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 66 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties(), and GeneralVaporMixtureFluidProperties::cv_from_p_T().

67 {
68  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
69 }
const std::string name
Definition: Setup.h:22

◆ d2alpha_ddelta2()

Real CO2FluidProperties::d2alpha_ddelta2 ( Real  delta,
Real  tau 
) const
overrideprotectedvirtual

Second derivative of Helmholtz free energy wrt delta.

Parameters
deltascaled density (-)
tauscaled temperature (-)
Returns
second derivative of Helmholtz free energy wrt delta

Implements HelmholtzFluidProperties.

Definition at line 277 of file CO2FluidProperties.C.

278 {
279  // Second derivative of the ideal gas component wrt gamma
280  Real d2phi0dd2 = -1.0 / delta / delta;
281 
282  // Second derivative of the residual component wrt gamma
283  Real d2phirdd2 = 0.0;
284  Real theta, Delta, Psi, dDelta_dd, dPsi_dd, d2Delta_dd2, d2Psi_dd2;
285 
286  for (std::size_t i = 0; i < _n1.size(); ++i)
287  d2phirdd2 += _n1[i] * _d1[i] * (_d1[i] - 1.0) * MathUtils::pow(delta, _d1[i] - 2) *
288  std::pow(tau, _t1[i]);
289 
290  for (std::size_t i = 0; i < _n2.size(); ++i)
291  d2phirdd2 += _n2[i] * std::exp(-MathUtils::pow(delta, _c2[i])) *
292  MathUtils::pow(delta, _d2[i] - 2) * std::pow(tau, _t2[i]) *
293  ((_d2[i] - _c2[i] * MathUtils::pow(delta, _c2[i])) *
294  (_d2[i] - 1.0 - _c2[i] * MathUtils::pow(delta, _c2[i])) -
295  _c2[i] * _c2[i] * MathUtils::pow(delta, _c2[i]));
296 
297  for (std::size_t i = 0; i < _n3.size(); ++i)
298  d2phirdd2 +=
299  _n3[i] * MathUtils::pow(tau, _t3[i]) *
300  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
301  _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
302  (-2.0 * _alpha3[i] * MathUtils::pow(delta, _d3[i]) +
303  4.0 * _alpha3[i] * _alpha3[i] * MathUtils::pow(delta, _d3[i]) *
304  Utility::pow<2>(delta - _eps3[i]) -
305  4.0 * _d3[i] * _alpha3[i] * MathUtils::pow(delta, _d3[i] - 1.0) * (delta - _eps3[i]) +
306  _d3[i] * (_d3[i] - 1.0) * MathUtils::pow(delta, _d3[i] - 2.0));
307 
308  for (std::size_t i = 0; i < _n4.size(); ++i)
309  {
310  theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
311  Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
312  Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
313  dPsi_dd = -2.0 * _C4[i] * (delta - 1.0) * Psi;
314  dDelta_dd = (delta - 1.0) *
315  (_A4[i] * theta * 2.0 / _beta4[i] *
316  std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) +
317  2.0 * _B4[i] * _a4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 1.0));
318  d2Psi_dd2 = 3.0 * _D4[i] * Psi * (2.0 * _C4[i] * Utility::pow<2>(delta - 1.0) - 1.0);
319  d2Delta_dd2 = 1.0 / (delta - 1.0) * dDelta_dd +
320  (delta - 1.0) * (delta - 1.0) *
321  (4.0 * _B4[i] * _a4[i] * (_a4[i] - 1.0) *
322  std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 2.0) +
323  2.0 * _A4[i] * _A4[i] *
324  Utility::pow<2>(std::pow(Utility::pow<2>(delta - 1.0),
325  1.0 / (2.0 * _beta4[i]) - 1.0)) /
326  _beta4[i] / _beta4[i] +
327  (4.0 / _beta4[i]) * _A4[i] * theta * (1.0 / (2.0 * _beta4[i]) - 1.0) *
328  std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 2.0));
329  d2phirdd2 +=
330  _n4[i] *
331  (std::pow(Delta, _b4[i]) * (2.0 * dPsi_dd + delta * d2Psi_dd2) +
332  2.0 * _b4[i] * std::pow(Delta, _b4[i] - 1.0) * dDelta_dd * (Psi + delta * dPsi_dd) +
333  _b4[i] *
334  (std::pow(Delta, _b4[i] - 1.0) * d2Delta_dd2 +
335  (_b4[i] - 1.0) * std::pow(Delta, _b4[i] - 2.0) * Utility::pow<2>(dDelta_dd)) *
336  delta * Psi);
337  }
338  // The second derivative of the free energy wrt delta is the sum of these components
339  return d2phi0dd2 + d2phirdd2;
340 }
const std::array< Real, 3 > _D4
const std::array< Real, 7 > _t1
const std::array< unsigned int, 5 > _d3
const std::array< Real, 27 > _n2
const std::array< Real, 7 > _n1
Coefficients for the residual component of the Helmholtz free energy.
const std::array< Real, 3 > _C4
const std::array< Real, 3 > _b4
const std::array< Real, 3 > _a4
const std::array< Real, 5 > _n3
const std::array< unsigned int, 27 > _c2
const std::array< Real, 5 > _eps3
const std::array< Real, 3 > _A4
const std::array< Real, 3 > _B4
const std::array< Real, 5 > _gamma3
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const std::array< Real, 3 > _n4
const std::array< Real, 5 > _alpha3
const std::array< unsigned int, 5 > _t3
const std::array< Real, 3 > _beta4
const std::array< Real, 27 > _t2
const std::array< Real, 5 > _beta3
const std::array< unsigned int, 7 > _d1
const std::array< unsigned int, 27 > _d2

◆ d2alpha_ddeltatau()

Real CO2FluidProperties::d2alpha_ddeltatau ( Real  delta,
Real  tau 
) const
overrideprotectedvirtual

Second derivative of Helmholtz free energy wrt delta and tau.

Parameters
deltascaled density (-)
tauscaled temperature (-)
Returns
second derivative of Helmholtz free energy wrt delta and tau

Implements HelmholtzFluidProperties.

Definition at line 392 of file CO2FluidProperties.C.

393 {
394  // Note: second derivative of the ideal gas component wrt delta and tau is 0
395  // Derivative of the residual component wrt gamma
396  Real theta, Delta, Psi, dDelta_dd, dPsi_dd, dDelta_dt, dPsi_dt, d2Delta_ddt, d2Psi_ddt;
397  Real d2phirddt = 0.0;
398  for (std::size_t i = 0; i < _n1.size(); ++i)
399  d2phirddt += _n1[i] * _d1[i] * _t1[i] * MathUtils::pow(delta, _d1[i] - 1.0) *
400  std::pow(tau, _t1[i] - 1.0);
401 
402  for (std::size_t i = 0; i < _n2.size(); ++i)
403  d2phirddt += _n2[i] * std::exp(-MathUtils::pow(delta, _c2[i])) *
404  (MathUtils::pow(delta, _d2[i] - 1.0) * _t2[i] * std::pow(tau, _t2[i] - 1.0) *
405  (_d2[i] - _c2[i] * MathUtils::pow(delta, _c2[i])));
406 
407  for (std::size_t i = 0; i < _n3.size(); ++i)
408  d2phirddt += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
409  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
410  _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
411  (_d3[i] / delta - 2.0 * _alpha3[i] * (delta - _eps3[i])) *
412  (_t3[i] / tau - 2.0 * _beta3[i] * (tau - _gamma3[i]));
413 
414  for (std::size_t i = 0; i < _n4.size(); ++i)
415  {
416  theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
417  Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
418  Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
419  dPsi_dd = -2.0 * _C4[i] * (delta - 1.0) * Psi;
420  dPsi_dt = -2.0 * _D4[i] * (tau - 1.0) * Psi;
421  d2Psi_ddt = 4.0 * _C4[i] * _D4[i] * (delta - 1.0) * (tau - 1.0) * Psi;
422  dDelta_dd = (delta - 1.0) *
423  (_A4[i] * theta * 2.0 / _beta4[i] *
424  std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) +
425  2.0 * _B4[i] * _a4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 1.0));
426  dDelta_dt = -2.0 * theta * _b4[i] * std::pow(Delta, _b4[i] - 1.0);
427  d2Delta_ddt = -2.0 * _A4[i] * _b4[i] / _beta4[i] * std::pow(Delta, _b4[i] - 1.0) *
428  (delta - 1.0) *
429  std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) -
430  2.0 * theta * _b4[i] * (_b4[i] - 1.0) * std::pow(Delta, _b4[i] - 2.0) * dDelta_dd;
431 
432  d2phirddt += _n4[i] * (std::pow(Delta, _b4[i]) * (dPsi_dt + delta * d2Psi_ddt) +
433  delta * _b4[i] * std::pow(Delta, _b4[i] - 1.0) * dDelta_dd * dPsi_dt +
434  dDelta_dt * (Psi + delta * dPsi_dd) + d2Delta_ddt * delta * Psi);
435  }
436 
437  return d2phirddt;
438 }
const std::array< Real, 3 > _D4
const std::array< Real, 7 > _t1
const std::array< unsigned int, 5 > _d3
const std::array< Real, 27 > _n2
const std::array< Real, 7 > _n1
Coefficients for the residual component of the Helmholtz free energy.
const std::array< Real, 3 > _C4
const std::array< Real, 3 > _b4
const std::array< Real, 3 > _a4
const std::array< Real, 5 > _n3
const std::array< unsigned int, 27 > _c2
const std::array< Real, 5 > _eps3
const std::array< Real, 3 > _A4
const std::array< Real, 3 > _B4
const std::array< Real, 5 > _gamma3
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const std::array< Real, 3 > _n4
const std::array< Real, 5 > _alpha3
const std::array< unsigned int, 5 > _t3
const std::array< Real, 3 > _beta4
const std::array< Real, 27 > _t2
const std::array< Real, 5 > _beta3
const std::array< unsigned int, 7 > _d1
const std::array< unsigned int, 27 > _d2

◆ d2alpha_dtau2()

Real CO2FluidProperties::d2alpha_dtau2 ( Real  delta,
Real  tau 
) const
overrideprotectedvirtual

Second derivative of Helmholtz free energy wrt tau.

Parameters
deltascaled density (-)
tauscaled temperature (-)
Returns
second derivative of Helmholtz free energy wrt tau

Implements HelmholtzFluidProperties.

Definition at line 343 of file CO2FluidProperties.C.

344 {
345  // Second derivative of the ideal gas component wrt tau
346  Real sum0 = 0.0;
347  for (std::size_t i = 0; i < _a0.size(); ++i)
348  sum0 += _a0[i] * _theta0[i] * _theta0[i] * std::exp(-_theta0[i] * tau) /
349  Utility::pow<2>(1.0 - std::exp(-_theta0[i] * tau));
350 
351  Real d2phi0dt2 = -2.5 / tau / tau - sum0;
352 
353  // Second derivative of the residual component wrt tau
354  Real d2phirdt2 = 0.0;
355  Real theta, Delta, Psi, dPsi_dt, dDelta_dt, d2Delta_dt2, d2Psi_dt2;
356 
357  for (std::size_t i = 0; i < _n1.size(); ++i)
358  d2phirdt2 += _n1[i] * _t1[i] * (_t1[i] - 1.0) * MathUtils::pow(delta, _d1[i]) *
359  std::pow(tau, _t1[i] - 2.0);
360 
361  for (std::size_t i = 0; i < _n2.size(); ++i)
362  d2phirdt2 += _n2[i] * _t2[i] * (_t2[i] - 1.0) * MathUtils::pow(delta, _d2[i]) *
363  std::exp(-MathUtils::pow(delta, _c2[i])) * std::pow(tau, _t2[i] - 2.0);
364 
365  for (std::size_t i = 0; i < _n3.size(); ++i)
366  d2phirdt2 += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
367  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
368  _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
369  (Utility::pow<2>(_t3[i] / tau - 2.0 * _beta3[i] * (tau - _gamma3[i])) -
370  _t3[i] / tau / tau - 2.0 * _beta3[i]);
371 
372  for (std::size_t i = 0; i < _n4.size(); ++i)
373  {
374  theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
375  Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
376  Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
377  dDelta_dt = -2.0 * theta * _b4[i] * std::pow(Delta, _b4[i] - 1.0);
378  d2Delta_dt2 = 2.0 * _b4[i] * std::pow(Delta, _b4[i] - 1.0) +
379  4.0 * theta * theta * _b4[i] * (_b4[i] - 1.0) * std::pow(Delta, _b4[i] - 2.0);
380  dPsi_dt = -2.0 * _D4[i] * (tau - 1.0) * Psi;
381  d2Psi_dt2 = 2.0 * _D4[i] * (2.0 * _D4[i] * (tau - 1.0) * (tau - 1.0) - 1.0) * Psi;
382  d2phirdt2 +=
383  _n4[i] * delta *
384  (Psi * d2Delta_dt2 + 2.0 * dDelta_dt * dPsi_dt + std::pow(Delta, _b4[i]) * d2Psi_dt2);
385  }
386 
387  // The second derivative of the free energy wrt tau is the sum of these components
388  return d2phi0dt2 + d2phirdt2;
389 }
const std::array< Real, 3 > _D4
const std::array< Real, 7 > _t1
const std::array< unsigned int, 5 > _d3
const std::array< Real, 27 > _n2
const std::array< Real, 7 > _n1
Coefficients for the residual component of the Helmholtz free energy.
const std::array< Real, 3 > _C4
const std::array< Real, 5 > _theta0
const std::array< Real, 3 > _b4
const std::array< Real, 3 > _a4
const std::array< Real, 5 > _n3
const std::array< unsigned int, 27 > _c2
const std::array< Real, 5 > _eps3
const std::array< Real, 3 > _A4
const std::array< Real, 3 > _B4
const std::array< Real, 5 > _gamma3
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const std::array< Real, 3 > _n4
const std::array< Real, 5 > _alpha3
const std::array< unsigned int, 5 > _t3
const std::array< Real, 3 > _beta4
const std::array< Real, 5 > _a0
Coefficients for the ideal gas component of the Helmholtz free energy.
const std::array< Real, 27 > _t2
const std::array< Real, 5 > _beta3
const std::array< unsigned int, 7 > _d1
const std::array< unsigned int, 27 > _d2

◆ dalpha_ddelta()

Real CO2FluidProperties::dalpha_ddelta ( Real  delta,
Real  tau 
) const
overrideprotectedvirtual

Derivative of Helmholtz free energy wrt delta.

Parameters
deltascaled density (-)
tauscaled temperature (-)
Returns
derivative of Helmholtz free energy wrt delta

Implements HelmholtzFluidProperties.

Definition at line 193 of file CO2FluidProperties.C.

194 {
195  // Derivative of the ideal gas component wrt gamma
196  Real dphi0dd = 1.0 / delta;
197 
198  // Derivative of the residual component wrt gamma
199  Real theta, Delta, Psi, dDelta_dd, dPsi_dd;
200  Real dphirdd = 0.0;
201 
202  for (std::size_t i = 0; i < _n1.size(); ++i)
203  dphirdd += _n1[i] * _d1[i] * MathUtils::pow(delta, _d1[i] - 1.0) * std::pow(tau, _t1[i]);
204 
205  for (std::size_t i = 0; i < _n2.size(); ++i)
206  dphirdd += _n2[i] * std::exp(-MathUtils::pow(delta, _c2[i])) *
207  (MathUtils::pow(delta, _d2[i] - 1.0) * std::pow(tau, _t2[i]) *
208  (_d2[i] - _c2[i] * MathUtils::pow(delta, _c2[i])));
209 
210  for (std::size_t i = 0; i < _n3.size(); ++i)
211  dphirdd += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
212  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
213  _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
214  (_d3[i] / delta - 2.0 * _alpha3[i] * (delta - _eps3[i]));
215 
216  for (std::size_t i = 0; i < _n4.size(); ++i)
217  {
218  theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
219  Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
220  Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
221  dPsi_dd = -2.0 * _C4[i] * (delta - 1.0) * Psi;
222  dDelta_dd = (delta - 1.0) *
223  (_A4[i] * theta * 2.0 / _beta4[i] *
224  std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]) - 1.0) +
225  2.0 * _B4[i] * _a4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i] - 1.0));
226 
227  dphirdd += _n4[i] * (std::pow(Delta, _b4[i]) * (Psi + delta * dPsi_dd) +
228  _b4[i] * std::pow(Delta, _b4[i] - 1.0) * dDelta_dd * delta * Psi);
229  }
230 
231  // The derivative of the free energy wrt delta is the sum of these components
232  return dphi0dd + dphirdd;
233 }
const std::array< Real, 3 > _D4
const std::array< Real, 7 > _t1
const std::array< unsigned int, 5 > _d3
const std::array< Real, 27 > _n2
const std::array< Real, 7 > _n1
Coefficients for the residual component of the Helmholtz free energy.
const std::array< Real, 3 > _C4
const std::array< Real, 3 > _b4
const std::array< Real, 3 > _a4
const std::array< Real, 5 > _n3
const std::array< unsigned int, 27 > _c2
const std::array< Real, 5 > _eps3
const std::array< Real, 3 > _A4
const std::array< Real, 3 > _B4
const std::array< Real, 5 > _gamma3
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const std::array< Real, 3 > _n4
const std::array< Real, 5 > _alpha3
const std::array< unsigned int, 5 > _t3
const std::array< Real, 3 > _beta4
const std::array< Real, 27 > _t2
const std::array< Real, 5 > _beta3
const std::array< unsigned int, 7 > _d1
const std::array< unsigned int, 27 > _d2

◆ dalpha_dtau()

Real CO2FluidProperties::dalpha_dtau ( Real  delta,
Real  tau 
) const
overrideprotectedvirtual

Derivative of Helmholtz free energy wrt tau.

Parameters
deltascaled density (-)
tauscaled temperature (-)
Returns
derivative of Helmholtz free energy wrt tau

Implements HelmholtzFluidProperties.

Definition at line 236 of file CO2FluidProperties.C.

237 {
238  // Derivative of the ideal gas component wrt tau
239  Real sum0 = 0.0;
240  for (std::size_t i = 0; i < _a0.size(); ++i)
241  sum0 += _a0[i] * _theta0[i] * (1.0 / (1.0 - std::exp(-_theta0[i] * tau)) - 1.0);
242 
243  Real dphi0dt = -3.70454304 + 2.5 / tau + sum0;
244 
245  // Derivative of the residual component wrt tau
246  Real theta, Delta, Psi, dDelta_dt, dPsi_dt;
247  Real dphirdt = 0.0;
248  for (std::size_t i = 0; i < _n1.size(); ++i)
249  dphirdt += _n1[i] * _t1[i] * MathUtils::pow(delta, _d1[i]) * std::pow(tau, _t1[i] - 1.0);
250 
251  for (std::size_t i = 0; i < _n2.size(); ++i)
252  dphirdt += _n2[i] * _t2[i] * MathUtils::pow(delta, _d2[i]) * std::pow(tau, _t2[i] - 1.0) *
253  std::exp(-MathUtils::pow(delta, _c2[i]));
254 
255  for (std::size_t i = 0; i < _n3.size(); ++i)
256  dphirdt += _n3[i] * MathUtils::pow(delta, _d3[i]) * MathUtils::pow(tau, _t3[i]) *
257  std::exp(-_alpha3[i] * Utility::pow<2>(delta - _eps3[i]) -
258  _beta3[i] * Utility::pow<2>(tau - _gamma3[i])) *
259  (_t3[i] / tau - 2.0 * _beta3[i] * (tau - _gamma3[i]));
260 
261  for (std::size_t i = 0; i < _n4.size(); ++i)
262  {
263  theta = 1.0 - tau + _A4[i] * std::pow(Utility::pow<2>(delta - 1.0), 1.0 / (2.0 * _beta4[i]));
264  Delta = Utility::pow<2>(theta) + _B4[i] * std::pow(Utility::pow<2>(delta - 1.0), _a4[i]);
265  Psi = std::exp(-_C4[i] * Utility::pow<2>(delta - 1.0) - _D4[i] * Utility::pow<2>(tau - 1.0));
266  dDelta_dt = -2.0 * theta * _b4[i] * std::pow(Delta, _b4[i] - 1.0);
267  dPsi_dt = -2.0 * _D4[i] * (tau - 1.0) * Psi;
268 
269  dphirdt += _n4[i] * delta * (Psi * dDelta_dt + std::pow(Delta, _b4[i]) * dPsi_dt);
270  }
271 
272  // The derivative of the free energy wrt tau is the sum of these components
273  return dphi0dt + dphirdt;
274 }
const std::array< Real, 3 > _D4
const std::array< Real, 7 > _t1
const std::array< unsigned int, 5 > _d3
const std::array< Real, 27 > _n2
const std::array< Real, 7 > _n1
Coefficients for the residual component of the Helmholtz free energy.
const std::array< Real, 3 > _C4
const std::array< Real, 5 > _theta0
const std::array< Real, 3 > _b4
const std::array< Real, 3 > _a4
const std::array< Real, 5 > _n3
const std::array< unsigned int, 27 > _c2
const std::array< Real, 5 > _eps3
const std::array< Real, 3 > _A4
const std::array< Real, 3 > _B4
const std::array< Real, 5 > _gamma3
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const std::array< Real, 3 > _n4
const std::array< Real, 5 > _alpha3
const std::array< unsigned int, 5 > _t3
const std::array< Real, 3 > _beta4
const std::array< Real, 5 > _a0
Coefficients for the ideal gas component of the Helmholtz free energy.
const std::array< Real, 27 > _t2
const std::array< Real, 5 > _beta3
const std::array< unsigned int, 7 > _d1
const std::array< unsigned int, 27 > _d2

◆ e()

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

Definition at line 366 of file SinglePhaseFluidProperties.C.

Referenced by Water97FluidProperties::b2bc(), IdealGasFluidProperties::c_from_v_e(), StiffenedGasFluidProperties::c_from_v_e(), NaClFluidProperties::cp_from_p_T(), Water97FluidProperties::densityRegion3(), SinglePhaseFluidProperties::e_dpT(), StiffenedGasFluidProperties::e_from_p_rho(), IdealGasFluidProperties::e_from_p_rho(), HelmholtzFluidProperties::e_from_p_T(), IdealGasFluidPropertiesPT::e_from_p_T(), Water97FluidProperties::e_from_p_T(), IdealGasFluidProperties::e_from_p_T(), NaClFluidProperties::e_from_p_T(), StiffenedGasFluidProperties::e_from_p_T(), SimpleFluidProperties::e_from_p_T(), TabulatedFluidProperties::e_from_p_T(), SinglePhaseFluidProperties::e_from_p_T(), StiffenedGasFluidProperties::e_from_T_v(), IdealGasFluidProperties::e_from_T_v(), IdealGasFluidProperties::e_from_v_h(), StiffenedGasFluidProperties::e_from_v_h(), IdealGasFluidProperties::g_from_v_e(), StiffenedGasFluidProperties::g_from_v_e(), IdealGasFluidProperties::h_from_p_T(), NaClFluidProperties::h_from_p_T(), NitrogenFluidProperties::mu_drhoT_from_rho_T(), HydrogenFluidProperties::mu_drhoT_from_rho_T(), mu_drhoT_from_rho_T(), StiffenedGasFluidProperties::p_from_T_v(), IdealGasFluidProperties::p_from_v_e(), StiffenedGasFluidProperties::p_from_v_e(), HelmholtzFluidProperties::rho_e_dpT(), IdealGasFluidPropertiesPT::rho_e_dpT(), Water97FluidProperties::rho_e_dpT(), NaClFluidProperties::rho_e_dpT(), SimpleFluidProperties::rho_e_dpT(), TabulatedFluidProperties::rho_e_dpT(), StiffenedGasFluidProperties::s_from_T_v(), IdealGasFluidProperties::s_from_v_e(), StiffenedGasFluidProperties::s_from_v_e(), Water97FluidProperties::subregion3(), Water97FluidProperties::subregionVolume(), SinglePhaseFluidProperties::T_from_p_h(), StiffenedGasFluidProperties::T_from_v_e(), IdealGasFluidProperties::T_from_v_e(), StiffenedGasFluidProperties::v_e_spndl_from_T(), and Water97FluidProperties::vaporTemperature().

367 {
368  return e_from_p_T(p, T);
369 }
virtual Real e_from_p_T(Real p, Real T) const
Internal energy from pressure and temperature.

◆ e_dpT()

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

Definition at line 372 of file SinglePhaseFluidProperties.C.

374 {
375  e_from_p_T(pressure, temperature, e, de_dp, de_dT);
376 }
const std::string temperature
Definition: NS.h:27
virtual Real e_from_p_T(Real p, Real T) const
Internal energy from pressure and temperature.
const std::string pressure
Definition: NS.h:26
virtual Real e(Real pressure, Real temperature) const

◆ e_from_p_rho() [1/2]

Real SinglePhaseFluidProperties::e_from_p_rho ( Real  p,
Real  rho 
) const
virtualinherited

Specific internal energy from pressure and density.

Parameters
[in]ppressure
[in]rhodensity

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 502 of file SinglePhaseFluidProperties.C.

Referenced by StagnationTemperatureAux::computeValue(), InternalEnergyAux::computeValue(), and SinglePhaseFluidProperties::e_from_p_T().

503 {
504  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
505 }
const std::string name
Definition: Setup.h:22

◆ e_from_p_rho() [2/2]

void SinglePhaseFluidProperties::e_from_p_rho ( Real  p,
Real  rho,
Real &  e,
Real &  de_dp,
Real &  de_drho 
) const
virtualinherited

Specific internal energy and its derivatives from pressure and density.

Parameters
[in]ppressure
[in]rhodensity
[out]especific internal energy
[out]de_dpderivative of specific internal energy w.r.t. pressure
[out]de_drhoderivative of specific internal energy w.r.t. density

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 508 of file SinglePhaseFluidProperties.C.

509 {
510  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
511 }
const std::string name
Definition: Setup.h:22

◆ 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]ppressure (Pa)
[in]Ttemperature (K)
Returns
internal energy (J/kg)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 65 of file HelmholtzFluidProperties.C.

Referenced by HelmholtzFluidProperties::e_from_p_T(), and HelmholtzFluidProperties::rho_e_dpT().

66 {
67  // Require density first
69  // Scale the input density and temperature
70  const Real delta = density / criticalDensity();
71  const Real tau = criticalTemperature() / temperature;
72 
73  return _R * temperature * tau * dalpha_dtau(delta, tau) / molarMass();
74 }
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real dalpha_dtau(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt tau.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26

◆ 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]ppressure (Pa)
[in]Ttemperature (K)
[out]einternal energy (J/kg)
[out]de_dpderivative of internal energy w.r.t. pressure
[out]de_dTderivative of internal energy w.r.t. temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 77 of file HelmholtzFluidProperties.C.

79 {
80  e = this->e_from_p_T(pressure, temperature);
81 
82  // Require density first
84  // Scale the input density and temperature
85  const Real delta = density / criticalDensity();
86  const Real tau = criticalTemperature() / temperature;
87 
88  const Real da_dd = dalpha_ddelta(delta, tau);
89  const Real d2a_dd2 = d2alpha_ddelta2(delta, tau);
90  const Real d2a_ddt = d2alpha_ddeltatau(delta, tau);
91 
92  de_dp = tau * d2a_ddt / (density * (2.0 * da_dd + delta * d2a_dd2));
93  de_dT = -_R *
94  (delta * tau * d2a_ddt * (da_dd - tau * d2a_ddt) / (2.0 * da_dd + delta * d2a_dd2) +
95  tau * tau * d2alpha_dtau2(delta, tau)) /
96  molarMass();
97 }
virtual Real d2alpha_ddeltatau(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta and tau.
virtual Real d2alpha_dtau2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt tau.
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
virtual Real d2alpha_ddelta2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta.
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real dalpha_ddelta(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt delta.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26
virtual Real e(Real pressure, Real temperature) const
virtual Real e_from_p_T(Real pressure, Real temperature) const override
Internal energy from pressure and temperature.

◆ e_from_T_v() [1/2]

Real SinglePhaseFluidProperties::e_from_T_v ( Real  T,
Real  v 
) const
virtualinherited

Specific volume and specific internal energy from temerature at the vapor spinodal.

Parameters
[in]Ttemerature

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 513 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::e_from_T_v(), IdealRealGasMixtureFluidProperties::k_from_p_T(), IdealRealGasMixtureFluidProperties::k_from_T_v(), IdealRealGasMixtureFluidProperties::mu_from_p_T(), and IdealRealGasMixtureFluidProperties::mu_from_T_v().

514 {
515  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
516 }
const std::string name
Definition: Setup.h:22

◆ e_from_T_v() [2/2]

void SinglePhaseFluidProperties::e_from_T_v ( Real  T,
Real  v,
Real &  e,
Real &  de_dT,
Real &  de_dv 
) const
virtualinherited

Specific internal energy and its derivatives from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume
[out]especific internal energy (J/kg)
[out]de_dTderivative of specific internal energy w.r.t. temperature
[out]de_dvderivative of specific internal energy w.r.t. specific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 530 of file SinglePhaseFluidProperties.C.

531 {
532  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
533 }
const std::string name
Definition: Setup.h:22

◆ e_from_v_h() [1/2]

Real SinglePhaseFluidProperties::e_from_v_h ( Real  v,
Real  h 
) const
virtualinherited

Specific internal energy as a function of specific volume and specific enthalpy.

Parameters
[in]vspecific volume
[in]hspecific enthalpy

Reimplemented in StiffenedGasFluidProperties, and IdealGasFluidProperties.

Definition at line 114 of file SinglePhaseFluidProperties.C.

Referenced by SinglePhaseFluidProperties::T_from_p_h().

115 {
116  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
117 }
const std::string name
Definition: Setup.h:22

◆ e_from_v_h() [2/2]

void SinglePhaseFluidProperties::e_from_v_h ( Real  v,
Real  h,
Real &  e,
Real &  de_dv,
Real &  de_dh 
) const
virtualinherited

Specific internal energy and derivatives as a function of specific volume and specific enthalpy.

Parameters
[in]vspecific volume
[in]hspecific enthalpy
[out]de_dvderivative of specific internal energy w.r.t. specific volume
[out]de_dhderivative of specific internal energy w.r.t. specific enthalpy

Reimplemented in StiffenedGasFluidProperties, and IdealGasFluidProperties.

Definition at line 120 of file SinglePhaseFluidProperties.C.

121 {
122  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
123 }
const std::string name
Definition: Setup.h:22

◆ e_spndl_from_v()

Real SinglePhaseFluidProperties::e_spndl_from_v ( Real  v) const
virtualinherited

Specific internal energy from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume

Reimplemented in StiffenedGasFluidProperties.

Definition at line 518 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::p_T_from_v_e().

519 {
520  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
521 }
const std::string name
Definition: Setup.h:22

◆ execute()

virtual void FluidProperties::execute ( )
inlinefinalvirtualinherited

Definition at line 27 of file FluidProperties.h.

27 {}

◆ finalize()

virtual void FluidProperties::finalize ( )
inlinefinalvirtualinherited

Definition at line 29 of file FluidProperties.h.

29 {}

◆ fluidName()

std::string CO2FluidProperties::fluidName ( ) const
overridevirtual

Fluid name.

Returns
string representing fluid name

Reimplemented from SinglePhaseFluidProperties.

Definition at line 36 of file CO2FluidProperties.C.

37 {
38  return "co2";
39 }

◆ g_from_v_e()

Real SinglePhaseFluidProperties::g_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Gibbs free energy from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in StiffenedGasFluidProperties, and IdealGasFluidProperties.

Definition at line 595 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties().

596 {
597  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
598 }
const std::string name
Definition: Setup.h:22

◆ gamma_from_p_T()

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

Adiabatic index - ratio of specific heats.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
Returns
gamma (-)

Definition at line 250 of file SinglePhaseFluidProperties.C.

251 {
253 }
virtual Real cv_from_p_T(Real pressure, Real temperature) const
Isochoric specific heat.
const std::string temperature
Definition: NS.h:27
virtual Real cp_from_p_T(Real pressure, Real temperature) const
Isobaric specific heat capacity.
const std::string pressure
Definition: NS.h:26

◆ h()

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

◆ h_dpT()

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

Definition at line 480 of file SinglePhaseFluidProperties.C.

481 {
482  h_from_p_T(p, T, h, dh_dp, dh_dT);
483 }
virtual Real h(Real p, Real T) const
virtual Real h_from_p_T(Real p, Real T) const
Specific enthalpy from pressure and temperature.

◆ h_from_p_T() [1/2]

Real HelmholtzFluidProperties::h_from_p_T ( Real  p,
Real  T 
) const
overridevirtualinherited

Specific enthalpy from pressure and temperature.

Parameters
[in]ppressure (Pa)
[in]Ttemperature (K)
Returns
h (J/kg)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 229 of file HelmholtzFluidProperties.C.

Referenced by HelmholtzFluidProperties::h_from_p_T().

230 {
231  // Require density first
232  const Real density = rho_from_p_T(pressure, temperature);
233  // Scale the input density and temperature
234  const Real delta = density / criticalDensity();
235  const Real tau = criticalTemperature() / temperature;
236 
237  return _R * temperature * (tau * dalpha_dtau(delta, tau) + delta * dalpha_ddelta(delta, tau)) /
238  molarMass();
239 }
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real dalpha_ddelta(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt delta.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real dalpha_dtau(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt tau.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26

◆ 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

Specific enthalpy and its derivatives from pressure and temperature.

Parameters
[in]ppressure (Pa)
[in]Ttemperature (K)
[out]hspecific enthalpy (J/kg)
[out]dh_dpderivative of specific enthalpy w.r.t. pressure
[out]dh_dTderivative of specific enthalpy w.r.t. temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 242 of file HelmholtzFluidProperties.C.

244 {
245  h = this->h_from_p_T(pressure, temperature);
246 
247  // Require density first
248  const Real density = rho_from_p_T(pressure, temperature);
249  // Scale the input density and temperature
250  const Real delta = density / criticalDensity();
251  const Real tau = criticalTemperature() / temperature;
252 
253  const Real da_dd = dalpha_ddelta(delta, tau);
254  const Real d2a_dd2 = d2alpha_ddelta2(delta, tau);
255  const Real d2a_ddt = d2alpha_ddeltatau(delta, tau);
256 
257  dh_dp = (da_dd + delta * d2a_dd2 + tau * d2a_ddt) / (density * (2.0 * da_dd + delta * d2a_dd2));
258  dh_dT = _R *
259  (delta * da_dd * (1.0 - tau * d2a_ddt / da_dd) * (1.0 - tau * d2a_ddt / da_dd) /
260  (2.0 + delta * d2a_dd2 / da_dd) -
261  tau * tau * d2alpha_dtau2(delta, tau)) /
262  molarMass();
263 }
virtual Real d2alpha_ddeltatau(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta and tau.
virtual Real d2alpha_dtau2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt tau.
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
virtual Real h(Real p, Real T) const
const std::string temperature
Definition: NS.h:27
virtual Real d2alpha_ddelta2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta.
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real dalpha_ddelta(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt delta.
virtual Real h_from_p_T(Real pressure, Real temperature) const override
Specific enthalpy from pressure and temperature.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26

◆ h_from_T_v() [1/2]

Real SinglePhaseFluidProperties::h_from_T_v ( Real  T,
Real  v 
) const
virtualinherited

Specific enthalpy from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 546 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::cp_from_p_T(), and IdealRealGasMixtureFluidProperties::cp_from_T_v().

547 {
548  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
549 }
const std::string name
Definition: Setup.h:22

◆ h_from_T_v() [2/2]

void SinglePhaseFluidProperties::h_from_T_v ( Real  T,
Real  v,
Real &  h,
Real &  dh_dT,
Real &  dh_dv 
) const
virtualinherited

Specific enthalpy and its derivatives from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume
[out]hspecific enthalpy (J/kg)
[out]dh_dTderivative of specific enthalpy w.r.t. temperature
[out]dh_dvderivative of specific enthalpy w.r.t. specific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 552 of file SinglePhaseFluidProperties.C.

553 {
554  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
555 }
const std::string name
Definition: Setup.h:22

◆ henryConstant()

Real CO2FluidProperties::henryConstant ( Real  temperature) const
overridevirtual

Henry's law constant for dissolution in water.

Parameters
temperaturefluid temperature (K)
Returns
Henry's constant

Reimplemented from SinglePhaseFluidProperties.

Definition at line 608 of file CO2FluidProperties.C.

609 {
610  return henryConstantIAPWS(temperature, -8.55445, 4.01195, 9.52345);
611 }
const std::string temperature
Definition: NS.h:27
virtual Real henryConstantIAPWS(Real temperature, Real A, Real B, Real C) const
IAPWS formulation of Henry&#39;s law constant for dissolution in water From Guidelines on the Henry&#39;s con...

◆ henryConstant_dT()

void CO2FluidProperties::henryConstant_dT ( Real  temperature,
Real &  Kh,
Real &  dKh_dT 
) const
overridevirtual

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

Parameters
temperaturefluid temperature (K)
[out]KhHenry's constant
[out]dKh_dTderivative of Kh wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 614 of file CO2FluidProperties.C.

615 {
616  henryConstantIAPWS_dT(temperature, Kh, dKh_dT, -8.55445, 4.01195, 9.52345);
617 }
const std::string temperature
Definition: NS.h:27
virtual void henryConstantIAPWS_dT(Real temperature, Real &Kh, Real &dKh_dT, Real A, Real B, Real C) const
IAPWS formulation of Henry&#39;s law constant for dissolution in water and derivative wrt temperature...

◆ henryConstantIAPWS()

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 262 of file SinglePhaseFluidProperties.C.

Referenced by MethaneFluidProperties::henryConstant(), NitrogenFluidProperties::henryConstant(), HydrogenFluidProperties::henryConstant(), and henryConstant().

263 {
264  Real Tr = temperature / 647.096;
265  Real tau = 1.0 - Tr;
266 
267  Real lnkh = A / Tr + B * std::pow(tau, 0.355) / Tr + C * std::pow(Tr, -0.41) * std::exp(tau);
268 
269  // The vapor pressure used in this formulation
270  std::vector<Real> a{-7.85951783, 1.84408259, -11.7866497, 22.6807411, -15.9618719, 1.80122502};
271  std::vector<Real> b{1.0, 1.5, 3.0, 3.5, 4.0, 7.5};
272  Real sum = 0.0;
273 
274  for (std::size_t i = 0; i < a.size(); ++i)
275  sum += a[i] * std::pow(tau, b[i]);
276 
277  return 22.064e6 * std::exp(sum / Tr) * std::exp(lnkh);
278 }
const std::string temperature
Definition: NS.h:27
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)

◆ henryConstantIAPWS_dT()

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

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

Definition at line 281 of file SinglePhaseFluidProperties.C.

Referenced by MethaneFluidProperties::henryConstant_dT(), NitrogenFluidProperties::henryConstant_dT(), HydrogenFluidProperties::henryConstant_dT(), and henryConstant_dT().

283 {
284  Real pc = 22.064e6;
285  Real Tc = 647.096;
286 
287  Real Tr = temperature / Tc;
288  Real tau = 1.0 - Tr;
289 
290  Real lnkh = A / Tr + B * std::pow(tau, 0.355) / Tr + C * std::pow(Tr, -0.41) * std::exp(tau);
291  Real dlnkh_dT =
292  (-A / Tr / Tr - B * std::pow(tau, 0.355) / Tr / Tr - 0.355 * B * std::pow(tau, -0.645) / Tr -
293  0.41 * C * std::pow(Tr, -1.41) * std::exp(tau) - C * std::pow(Tr, -0.41) * std::exp(tau)) /
294  Tc;
295 
296  // The vapor pressure used in this formulation
297  std::vector<Real> a{-7.85951783, 1.84408259, -11.7866497, 22.6807411, -15.9618719, 1.80122502};
298  std::vector<Real> b{1.0, 1.5, 3.0, 3.5, 4.0, 7.5};
299  Real sum = 0.0;
300  Real dsum = 0.0;
301 
302  for (std::size_t i = 0; i < a.size(); ++i)
303  {
304  sum += a[i] * std::pow(tau, b[i]);
305  dsum += a[i] * b[i] * std::pow(tau, b[i] - 1.0);
306  }
307 
308  Real p = pc * std::exp(sum / Tr);
309  Real dp_dT = -p / Tc / Tr * (sum / Tr + dsum);
310 
311  // Henry's constant and its derivative wrt temperature
312  Kh = p * std::exp(lnkh);
313  dKh_dT = (p * dlnkh_dT + dp_dT) * std::exp(lnkh);
314 }
const std::string temperature
Definition: NS.h:27
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)

◆ initialize()

virtual void FluidProperties::initialize ( )
inlinefinalvirtualinherited

Definition at line 28 of file FluidProperties.h.

28 {}

◆ k()

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

◆ k_dpT()

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

Definition at line 461 of file SinglePhaseFluidProperties.C.

463 {
464  k_from_p_T(pressure, temperature, k, dk_dp, dk_dT);
465 }
const std::string temperature
Definition: NS.h:27
virtual Real k(Real pressure, Real temperature) const
virtual Real k_from_p_T(Real pressure, Real temperature) const
Thermal conductivity.
const std::string pressure
Definition: NS.h:26

◆ k_from_p_T() [1/2]

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

Thermal conductivity.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
Returns
thermal conductivity (W/m/K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 620 of file CO2FluidProperties.C.

Referenced by k_from_p_T().

621 {
622  // Require density first
625 }
virtual Real k_from_rho_T(Real density, Real temperature) const override
Thermal conductivity as a function of density and temperature.
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
const std::string pressure
Definition: NS.h:26

◆ 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

Thermal conductivity and its derivatives wrt pressure and temperature.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
[out]thermalconductivity (W/m/K)
[out]derivativeof thermal conductivity wrt pressure
[out]derivativeof thermal conductivity wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 628 of file CO2FluidProperties.C.

630 {
631  k = this->k_from_p_T(pressure, temperature);
632  // Calculate derivatives using finite differences. Note: this will be slow as
633  // multiple calculations of density are required
634  const Real eps = 1.0e-6;
635  const Real peps = pressure * eps;
636  const Real Teps = temperature * eps;
637 
638  dk_dp = (this->k_from_p_T(pressure + peps, temperature) - k) / peps;
639  dk_dT = (this->k_from_p_T(pressure, temperature + Teps) - k) / Teps;
640 }
const std::string temperature
Definition: NS.h:27
virtual Real k(Real pressure, Real temperature) const
virtual Real k_from_p_T(Real pressure, Real temperature) const override
Thermal conductivity.
const std::string pressure
Definition: NS.h:26

◆ k_from_rho_T()

Real CO2FluidProperties::k_from_rho_T ( Real  density,
Real  temperature 
) const
overridevirtual

Thermal conductivity as a function of density and temperature.

Parameters
densityfluid density (kg/m^3)
temperaturefluid temperature (K)
Returns
thermal conductivity (W/m/K)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 643 of file CO2FluidProperties.C.

Referenced by k_from_p_T().

644 {
645  // Check the temperature is in the range of validity (216.592 K <= T <= 1000 K)
646  if (temperature <= _triple_point_temperature || temperature >= 1000.0)
647  throw MooseException("Temperature " + Moose::stringify(temperature) +
648  "K out of range (200K, 1000K) in " + name() + ": k()");
649 
650  // Scaled variables
652  Real rhor = density / _critical_density;
653 
654  Real sum1 = 0.0;
655  for (std::size_t i = 0; i < _k_n1.size(); ++i)
656  sum1 += _k_n1[i] * std::pow(Tr, _k_g1[i]) * MathUtils::pow(rhor, _k_h1[i]);
657 
658  Real sum2 = 0.0;
659  for (std::size_t i = 0; i < _k_n2.size(); ++i)
660  sum2 += _k_n2[i] * std::pow(Tr, _k_g2[i]) * MathUtils::pow(rhor, _k_h2[i]);
661 
662  // Near-critical enhancement
663  Real alpha =
664  1.0 - _k_a[9] * std::acosh(1.0 + _k_a[10] * std::pow(Utility::pow<2>(1.0 - Tr), _k_a[11]));
665  Real lambdac =
666  rhor *
667  std::exp(-std::pow(rhor, _k_a[0]) / _k_a[0] - Utility::pow<2>(_k_a[1] * (Tr - 1.0)) -
668  Utility::pow<2>(_k_a[2] * (rhor - 1.0))) /
669  std::pow(std::pow(Utility::pow<2>(
670  1.0 - 1.0 / Tr +
671  _k_a[3] * std::pow(Utility::pow<2>(rhor - 1.0), 1.0 / (2.0 * _k_a[4]))),
672  _k_a[5]) +
673  std::pow(Utility::pow<2>(_k_a[6] * (rhor - alpha)), _k_a[7]),
674  _k_a[8]);
675 
676  return 4.81384 * (sum1 + std::exp(-5.0 * rhor * rhor) * sum2 + 0.775547504 * lambdac) / 1000.0;
677 }
const std::array< Real, 7 > _k_n2
const Real _critical_density
Critical density (kg/m^3)
const std::array< Real, 3 > _k_g1
Coefficients for the thermal conductivity.
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const std::array< unsigned int, 7 > _k_h2
const std::array< unsigned int, 3 > _k_h1
const std::string name
Definition: Setup.h:22
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const Real _critical_temperature
Critical temperature (K)
const std::array< Real, 12 > _k_a
const std::array< Real, 3 > _k_n1
const std::array< Real, 7 > _k_g2
virtual Real alpha(Real delta, Real tau) const override
Helmholtz free energy.

◆ k_from_v_e()

Real SinglePhaseFluidProperties::k_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Thermal conductivity from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 76 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties(), GeneralVaporMixtureFluidProperties::k_from_p_T(), IdealRealGasMixtureFluidProperties::k_from_p_T(), and IdealRealGasMixtureFluidProperties::k_from_T_v().

77 {
78  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
79 }
const std::string name
Definition: Setup.h:22

◆ 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
temperatureCO2 temperature (K)
Returns
melting pressure (Pa)

Definition at line 78 of file CO2FluidProperties.C.

Referenced by rho_from_p_T().

79 {
81  throw MooseException("Temperature is below the triple point temperature in " + name() +
82  ": meltingPressure()");
83 
85 
86  return _triple_point_pressure *
87  (1.0 + 1955.539 * (Tstar - 1.0) + 2055.4593 * Utility::pow<2>(Tstar - 1.0));
88 }
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
const Real _triple_point_temperature
Triple point temperature (K)
const Real _triple_point_pressure
Triple point pressure (Pa)

◆ molarMass()

Real CO2FluidProperties::molarMass ( ) const
overridevirtual

Molar mass [kg/mol].

Returns
molar mass

Reimplemented from SinglePhaseFluidProperties.

Definition at line 42 of file CO2FluidProperties.C.

43 {
44  return _Mco2;
45 }
const Real _Mco2
Molar mass of CO2 (kg/mol)

◆ mu()

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

◆ 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
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
[out]muviscosity (Pa.s)
[out]dmu_dpderivative of viscosity wrt pressure
[out]dmu_dTderivative of viscosity wrt temperature

Definition at line 418 of file SinglePhaseFluidProperties.C.

420 {
421  mu_from_p_T(pressure, temperature, mu, dmu_dp, dmu_dT);
422 }
virtual Real mu_from_p_T(Real pressure, Real temperature) const
virtual Real mu(Real pressure, Real temperature) const
Dynamic viscosity.
const std::string temperature
Definition: NS.h:27
const std::string pressure
Definition: NS.h:26

◆ mu_drhoT_from_rho_T()

void CO2FluidProperties::mu_drhoT_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.

Parameters
densityfluid density (kg/m^3)
temperaturefluid temperature (K)
ddensity_dTderivative of density wrt temperature
[out]muviscosity (Pa.s)
[out]dmu_drhoderivative of viscosity wrt density
[out]dmu_dTderivative of viscosity wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 547 of file CO2FluidProperties.C.

Referenced by mu_from_p_T().

553 {
554  // Check that the input parameters are within the region of validity
555  if (temperature < 216.0 || temperature > 1000.0 || density > 1400.0)
556  throw MooseException("Parameters out of range in " + name() + ": mu_drhoT()");
557 
558  Real Tstar = temperature / 251.196;
559  Real dTstar_dT = 1.0 / 251.196;
560 
561  // Viscosity in the zero-density limit. Note this is only a function of T.
562  // Start the sum at i = 1 so the derivative is defined
563  Real sum0 = _mu_a[0], dsum0_dTstar = 0.0;
564 
565  for (std::size_t i = 1; i < _mu_a.size(); ++i)
566  {
567  sum0 += _mu_a[i] * MathUtils::pow(std::log(Tstar), i);
568  dsum0_dTstar += i * _mu_a[i] * MathUtils::pow(std::log(Tstar), i - 1) / Tstar;
569  }
570 
571  Real mu0 = 1.00697 * std::sqrt(temperature) / std::exp(sum0);
572  Real dmu0_dT = (0.5 * 1.00697 / std::sqrt(temperature) -
573  1.00697 * std::sqrt(temperature) * dsum0_dTstar * dTstar_dT) /
574  std::exp(sum0);
575 
576  // Excess viscosity due to finite density
577  Real mue = _mu_d[0] * density + _mu_d[1] * Utility::pow<2>(density) +
578  _mu_d[2] * Utility::pow<6>(density) / Utility::pow<3>(Tstar) +
579  _mu_d[3] * Utility::pow<8>(density) + _mu_d[4] * Utility::pow<8>(density) / Tstar;
580 
581  Real dmue_drho = _mu_d[0] + 2.0 * _mu_d[1] * density +
582  6.0 * _mu_d[2] * Utility::pow<5>(density) / Utility::pow<3>(Tstar) +
583  8.0 * _mu_d[3] * Utility::pow<7>(density) +
584  8.0 * _mu_d[4] * Utility::pow<7>(density) / Tstar;
585 
586  Real dmue_dT = (-3.0 * _mu_d[2] * Utility::pow<6>(density) / Utility::pow<4>(Tstar) -
587  _mu_d[4] * Utility::pow<8>(density) / Tstar / Tstar) *
588  dTstar_dT;
589 
590  // Viscosity in Pa.s is
591  mu = (mu0 + mue) * 1.0e-6;
592  dmu_drho = dmue_drho * 1.0e-6;
593  dmu_dT = (dmu0_dT + dmue_dT) * 1.0e-6 + dmu_drho * ddensity_dT;
594 }
virtual Real mu(Real pressure, Real temperature) const
Dynamic viscosity.
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
const std::array< Real, 5 > _mu_a
Coefficients for viscosity.
const std::array< Real, 5 > _mu_d
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
virtual Real e(Real pressure, Real temperature) const

◆ mu_from_p_T() [1/2]

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

Reimplemented from SinglePhaseFluidProperties.

Definition at line 503 of file CO2FluidProperties.C.

504 {
506  return mu_from_rho_T(rho, temperature);
507 }
const std::string temperature
Definition: NS.h:27
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
const std::string pressure
Definition: NS.h:26
virtual Real mu_from_rho_T(Real density, Real temperature) const override
Dynamic viscosity as a function of density and 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

Reimplemented from SinglePhaseFluidProperties.

Definition at line 510 of file CO2FluidProperties.C.

512 {
513  Real rho, drho_dp, drho_dT;
515 
516  Real dmu_drho;
517  mu_drhoT_from_rho_T(rho, temperature, drho_dT, mu, dmu_drho, dmu_dT);
518  dmu_dp = dmu_drho * drho_dp;
519 }
virtual Real mu(Real pressure, Real temperature) const
Dynamic viscosity.
const std::string temperature
Definition: NS.h:27
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual void mu_drhoT_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.
const std::string pressure
Definition: NS.h:26

◆ mu_from_rho_T()

Real CO2FluidProperties::mu_from_rho_T ( Real  density,
Real  temperature 
) const
overridevirtual

Dynamic viscosity as a function of density and temperature.

Parameters
densityfluid density (kg/m^3)
temperaturefluid temperature (K)
Returns
viscosity (Pa.s)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 522 of file CO2FluidProperties.C.

Referenced by mu_from_p_T().

523 {
524  // Check that the input parameters are within the region of validity
525  if (temperature < 216.0 || temperature > 1000.0 || density > 1400.0)
526  throw MooseException("Parameters out of range in " + name() + ": mu_from_rho_T()");
527 
528  Real Tstar = temperature / 251.196;
529 
530  // Viscosity in the zero-density limit
531  Real sum = 0.0;
532 
533  for (std::size_t i = 0; i < _mu_a.size(); ++i)
534  sum += _mu_a[i] * MathUtils::pow(std::log(Tstar), i);
535 
536  Real mu0 = 1.00697 * std::sqrt(temperature) / std::exp(sum);
537 
538  // Excess viscosity due to finite density
539  Real mue = _mu_d[0] * density + _mu_d[1] * Utility::pow<2>(density) +
540  _mu_d[2] * Utility::pow<6>(density) / Utility::pow<3>(Tstar) +
541  _mu_d[3] * Utility::pow<8>(density) + _mu_d[4] * Utility::pow<8>(density) / Tstar;
542 
543  return (mu0 + mue) * 1.0e-6; // convert to Pa.s
544 }
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
const std::array< Real, 5 > _mu_a
Coefficients for viscosity.
const std::array< Real, 5 > _mu_d
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)

◆ mu_from_v_e()

Real SinglePhaseFluidProperties::mu_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Dynamic viscosity from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 71 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties(), GeneralVaporMixtureFluidProperties::mu_from_p_T(), IdealRealGasMixtureFluidProperties::mu_from_p_T(), and IdealRealGasMixtureFluidProperties::mu_from_T_v().

72 {
73  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
74 }
const std::string name
Definition: Setup.h:22

◆ p_from_h_s() [1/2]

Real SinglePhaseFluidProperties::p_from_h_s ( Real  h,
Real  s 
) const
virtualinherited

Pressure from specific enthalpy and specific entropy.

Parameters
[in]hspecific enthalpy
[in]sspecific entropy

Reimplemented in StiffenedGasFluidProperties, and IdealGasFluidProperties.

Definition at line 584 of file SinglePhaseFluidProperties.C.

Referenced by StagnationPressureAux::computeValue(), and StagnationTemperatureAux::computeValue().

585 {
586  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
587 }
const std::string name
Definition: Setup.h:22

◆ p_from_h_s() [2/2]

void SinglePhaseFluidProperties::p_from_h_s ( Real  h,
Real  s,
Real &  p,
Real &  dp_dh,
Real &  dp_ds 
) const
virtualinherited

Pressure and its derivatives from specific enthalpy and specific entropy.

Parameters
[in]hspecific enthalpy
[in]sspecific entropy

Reimplemented in StiffenedGasFluidProperties, and IdealGasFluidProperties.

Definition at line 590 of file SinglePhaseFluidProperties.C.

591 {
592  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
593 }
const std::string name
Definition: Setup.h:22

◆ 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
rhodensity (kg/m^3)
Ttemperature (K)
Returns
pressure (Pa)

Reimplemented from HelmholtzFluidProperties.

Definition at line 441 of file CO2FluidProperties.C.

Referenced by rho_from_p_T().

442 {
443  // Check that the input parameters are within the region of validity
444  if (temperature < 216.0 || temperature > 1100.0 || density <= 0.0)
445  throw MooseException("Parameters out of range in " + name() + ": pressure()");
446 
447  Real pressure = 0.0;
448 
450  {
451  Real gas_density = saturatedVaporDensity(temperature);
452  Real liquid_density = saturatedLiquidDensity(temperature);
453 
454  if (density < gas_density || density > liquid_density)
456  else
458  }
459  else
461 
462  return pressure;
463 }
Real saturatedLiquidDensity(Real temperature) const
Saturated liquid density of CO2 Valid for temperatures between the triple point temperature and criti...
virtual Real vaporPressure(Real temperature) const override
Vapor pressure.
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
Real saturatedVaporDensity(Real temperature) const
Saturated vapor density of CO2 Valid for temperatures between the triple point temperature and critic...
const std::string name
Definition: Setup.h:22
const Real _triple_point_temperature
Triple point temperature (K)
virtual Real p_from_rho_T(Real rho, Real T) const
Pressure as a function of density and temperature.
const Real _critical_temperature
Critical temperature (K)
const std::string pressure
Definition: NS.h:26

◆ p_from_T_v() [1/2]

Real SinglePhaseFluidProperties::p_from_T_v ( Real  T,
Real  v 
) const
virtualinherited

Pressure from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 535 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::p_from_T_v().

536 {
537  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
538 }
const std::string name
Definition: Setup.h:22

◆ p_from_T_v() [2/2]

void SinglePhaseFluidProperties::p_from_T_v ( Real  T,
Real  v,
Real &  p,
Real &  dp_dT,
Real &  dp_dv 
) const
virtualinherited

Pressure and its derivatives from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume
[out]ppressure (Pa)
[out]dp_dTderivative of pressure w.r.t. temperature
[out]dp_dvderivative of pressure w.r.t. specific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 541 of file SinglePhaseFluidProperties.C.

542 {
543  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
544 }
const std::string name
Definition: Setup.h:22

◆ p_from_v_e() [1/2]

Real SinglePhaseFluidProperties::p_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Pressure from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in IdealGasFluidProperties, StiffenedGasFluidProperties, and NaNInterfaceTestFluidProperties.

Definition at line 28 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties(), PressureAux::computeValue(), StagnationPressureAux::computeValue(), and StagnationTemperatureAux::computeValue().

29 {
30  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
31 }
const std::string name
Definition: Setup.h:22

◆ p_from_v_e() [2/2]

void SinglePhaseFluidProperties::p_from_v_e ( Real  v,
Real  e,
Real &  p,
Real &  dp_dv,
Real &  dp_de 
) const
virtualinherited

Pressure and its derivatives from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy
[out]ppressure
[out]dp_dvderivative of pressure w.r.t. specific volume
[out]dp_dederivative of pressure w.r.t. specific internal energy

Reimplemented in IdealGasFluidProperties, StiffenedGasFluidProperties, and NaNInterfaceTestFluidProperties.

Definition at line 34 of file SinglePhaseFluidProperties.C.

35 {
36  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
37 }
const std::string name
Definition: Setup.h:22

◆ partialDensity()

Real CO2FluidProperties::partialDensity ( Real  temperature) const

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

Parameters
temperaturefluid temperature (K)
Returns
partial molar density (kg/m^3)

Definition at line 597 of file CO2FluidProperties.C.

598 {
599  // This correlation uses temperature in C
600  Real Tc = temperature - _T_c2k;
601  // The parial volume
602  Real V = 37.51 - 9.585e-2 * Tc + 8.74e-4 * Tc * Tc - 5.044e-7 * Tc * Tc * Tc;
603 
604  return 1.0e6 * _Mco2 / V;
605 }
const Real _T_c2k
Conversion of temperature from Celsius to Kelvin.
const std::string temperature
Definition: NS.h:27
const Real _Mco2
Molar mass of CO2 (kg/mol)

◆ pp_sat_from_p_T()

Real SinglePhaseFluidProperties::pp_sat_from_p_T ( Real  p,
Real  T 
) const
virtualinherited

Partial pressure at saturation in a gas mixture.

Parameters
[in]ppressure (Pa)
[in]Ttemperature (K)
Returns
pp_sat (Pa)

Reimplemented in StiffenedGasFluidProperties.

Definition at line 196 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::xs_prim_from_p_T().

197 {
198  mooseError(name(), ": pp_sat_from_p_T is not implemented");
199 }
const std::string name
Definition: Setup.h:22

◆ rho()

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

Definition at line 491 of file SinglePhaseFluidProperties.C.

Referenced by SinglePhaseFluidProperties::beta_from_p_T(), StiffenedGasFluidProperties::c2_from_p_rho(), StiffenedGasFluidProperties::e_from_p_rho(), IdealGasFluidProperties::e_from_p_rho(), NaClFluidProperties::e_from_p_T(), SinglePhaseFluidProperties::e_from_p_T(), IdealGasFluidProperties::h_from_p_T(), Water97FluidProperties::k_from_p_T(), mu_from_p_T(), NitrogenFluidProperties::mu_from_p_T(), HydrogenFluidProperties::mu_from_p_T(), Water97FluidProperties::mu_from_p_T(), SinglePhaseFluidProperties::rho_dpT(), HelmholtzFluidProperties::rho_e_dpT(), IdealGasFluidPropertiesPT::rho_e_dpT(), Water97FluidProperties::rho_e_dpT(), NaClFluidProperties::rho_e_dpT(), SimpleFluidProperties::rho_e_dpT(), TabulatedFluidProperties::rho_e_dpT(), IdealGasFluidProperties::rho_from_p_s(), StiffenedGasFluidProperties::rho_from_p_s(), HelmholtzFluidProperties::rho_from_p_T(), IdealGasFluidPropertiesPT::rho_from_p_T(), StiffenedGasFluidProperties::rho_from_p_T(), rho_from_p_T(), IdealGasFluidProperties::rho_from_p_T(), Water97FluidProperties::rho_from_p_T(), NaClFluidProperties::rho_from_p_T(), SimpleFluidProperties::rho_from_p_T(), TabulatedFluidProperties::rho_from_p_T(), HelmholtzFluidProperties::rho_mu(), IdealGasFluidPropertiesPT::rho_mu(), SimpleFluidProperties::rho_mu(), Water97FluidProperties::rho_mu(), TabulatedFluidProperties::rho_mu(), HelmholtzFluidProperties::rho_mu_dpT(), IdealGasFluidPropertiesPT::rho_mu_dpT(), SimpleFluidProperties::rho_mu_dpT(), Water97FluidProperties::rho_mu_dpT(), TabulatedFluidProperties::rho_mu_dpT(), SinglePhaseFluidProperties::T_from_p_h(), and SinglePhaseFluidProperties::v_from_p_T().

492 {
493  return rho_from_p_T(p, T);
494 }
virtual Real rho_from_p_T(Real p, Real T) const
Density from pressure and temperature.

◆ rho_dpT()

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

Definition at line 359 of file SinglePhaseFluidProperties.C.

361 {
362  rho_from_p_T(pressure, temperature, rho, drho_dp, drho_dT);
363 }
const std::string temperature
Definition: NS.h:27
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real p, Real T) const
Density from pressure and temperature.
const std::string pressure
Definition: NS.h:26

◆ rho_e_dpT()

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

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

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
[out]rhodensity (kg/m^3)
[out]drho_dpderivative of density wrt pressure
[out]drho_dTderivative of density wrt temperature
[out]einternal energy (J/kg)
[out]de_dpderivative of internal energy wrt pressure
[out]de_dTderivative of internal energy wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 100 of file HelmholtzFluidProperties.C.

108 {
109  Real density, ddensity_dp, ddensity_dT;
110  rho_from_p_T(pressure, temperature, density, ddensity_dp, ddensity_dT);
111  rho = density;
112  drho_dp = ddensity_dp;
113  drho_dT = ddensity_dT;
114 
115  Real energy, denergy_dp, denergy_dT;
116  e_from_p_T(pressure, temperature, energy, denergy_dp, denergy_dT);
117  e = energy;
118  de_dp = denergy_dp;
119  de_dT = denergy_dT;
120 }
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
const std::string pressure
Definition: NS.h:26
virtual Real e(Real pressure, Real temperature) const
virtual Real e_from_p_T(Real pressure, Real temperature) const override
Internal energy from pressure and temperature.

◆ rho_from_p_s() [1/2]

Real SinglePhaseFluidProperties::rho_from_p_s ( Real  p,
Real  s 
) const
virtualinherited

Density from pressure and specific entropy.

Parameters
[in]ppressure
[in]sspecific entropy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 103 of file SinglePhaseFluidProperties.C.

Referenced by StagnationTemperatureAux::computeValue(), and SinglePhaseFluidProperties::T_from_p_h().

104 {
105  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
106 }
const std::string name
Definition: Setup.h:22

◆ rho_from_p_s() [2/2]

void SinglePhaseFluidProperties::rho_from_p_s ( Real  p,
Real  s,
Real &  rho,
Real &  drho_dp,
Real &  drho_ds 
) const
virtualinherited

Density and its derivatives from pressure and specific entropy.

Parameters
[in]ppressure
[in]sspecific entropy
[out]rhodensity
[out]drho_dpderivative of density w.r.t. pressure
[out]drho_dsderivative of density w.r.t. specific entropy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 109 of file SinglePhaseFluidProperties.C.

110 {
111  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
112 }
const std::string name
Definition: Setup.h:22

◆ rho_from_p_T() [1/2]

Real CO2FluidProperties::rho_from_p_T ( Real  p,
Real  T 
) const
overridevirtual

Density from pressure and temperature.

Parameters
[in]ppressure (Pa)
[in]Ttemperature (K)
Returns
density (kg/m^3)

Reimplemented from HelmholtzFluidProperties.

Definition at line 466 of file CO2FluidProperties.C.

Referenced by k_from_p_T(), and mu_from_p_T().

467 {
468  // Check that the input parameters are within the region of validity
469  if (temperature < 216.0 || temperature > 1100.0 || pressure <= 0.0)
470  throw MooseException("Parameters out of range in " + name() + ": rho_from_p_T()");
471 
472  // Also check that the pressure and temperature are not in the solid phase region
475  throw MooseException("Input pressure and temperature in " + name() +
476  ": rho_from_p_T() correspond to solid CO2 phase");
477 
478  Real density;
479  // Initial estimate of a bracketing interval for the density
480  Real lower_density = 100.0;
481  Real upper_density = 1000.0;
482 
483  // The density is found by finding the zero of the pressure calculated using the
484  // Span and Wagner EOS minus the input pressure
485  auto pressure_diff = [&pressure, &temperature, this](Real x) {
486  return p_from_rho_T(x, temperature) - pressure;
487  };
488 
489  BrentsMethod::bracket(pressure_diff, lower_density, upper_density);
490  density = BrentsMethod::root(pressure_diff, lower_density, upper_density);
491 
492  return density;
493 }
Real sublimationPressure(Real temperature) const
Sublimation pressure.
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
Real root(std::function< Real(Real)> const &f, Real x1, Real x2, Real tol=1.0e-12)
Finds the root of a function using Brent&#39;s method.
Definition: BrentsMethod.C:61
const Real _triple_point_temperature
Triple point temperature (K)
virtual Real p_from_rho_T(Real density, Real temperature) const override
Pressure as a function of density and temperature.
const std::string pressure
Definition: NS.h:26
Real meltingPressure(Real temperature) const
Melting pressure.
void bracket(std::function< Real(Real)> const &f, Real &x1, Real &x2)
Function to bracket a root of a given function.
Definition: BrentsMethod.C:17

◆ rho_from_p_T() [2/2]

void CO2FluidProperties::rho_from_p_T ( Real  p,
Real  T,
Real &  rho,
Real &  drho_dp,
Real &  drho_dT 
) const
overridevirtual

Density and its derivatives from pressure and temperature.

Parameters
[in]ppressure (Pa)
[in]Ttemperature (K)
[out]rhodensity (kg/m^3)
[out]drho_dpderivative of density w.r.t. pressure
[out]drho_dTderivative of density w.r.t. temperature

Reimplemented from HelmholtzFluidProperties.

Definition at line 496 of file CO2FluidProperties.C.

498 {
500 }
const std::string temperature
Definition: NS.h:27
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
const std::string pressure
Definition: NS.h:26

◆ rho_mu()

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

Density and viscosity.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
[out]rhodensity (kg/m^3)
[out]muviscosity (Pa.s)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 173 of file HelmholtzFluidProperties.C.

174 {
177 }
virtual Real mu_from_p_T(Real pressure, Real temperature) const
virtual Real mu(Real pressure, Real temperature) const
Dynamic viscosity.
const std::string temperature
Definition: NS.h:27
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
const std::string pressure
Definition: NS.h:26

◆ rho_mu_dpT()

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

Density and viscosity and their derivatives wrt pressure and temperature.

Parameters
pressurefluid pressure (Pa)
temperaturefluid temperature (K)
[out]rhodensity (kg/m^3)
[out]drho_dpderivative of density wrt pressure
[out]drho_dTderivative of density wrt temperature
[out]muviscosity (Pa.s)
[out]dmu_dpderivative of viscosity wrt pressure
[out]dmu_dTderivative of viscosity wrt temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 180 of file HelmholtzFluidProperties.C.

188 {
189  rho_from_p_T(pressure, temperature, rho, drho_dp, drho_dT);
190  mu_from_p_T(pressure, temperature, mu, dmu_dp, dmu_dT);
191 }
virtual Real mu_from_p_T(Real pressure, Real temperature) const
virtual Real mu(Real pressure, Real temperature) const
Dynamic viscosity.
const std::string temperature
Definition: NS.h:27
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
const std::string pressure
Definition: NS.h:26

◆ s()

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

◆ s_from_h_p() [1/2]

Real SinglePhaseFluidProperties::s_from_h_p ( Real  h,
Real  p 
) const
virtualinherited

Specific entropy from specific enthalpy and pressure.

Parameters
[in]hspecific enthalpy
[in]ppressure

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 92 of file SinglePhaseFluidProperties.C.

Referenced by SinglePhaseFluidProperties::T_from_p_h().

93 {
94  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
95 }
const std::string name
Definition: Setup.h:22

◆ s_from_h_p() [2/2]

void SinglePhaseFluidProperties::s_from_h_p ( Real  h,
Real  p,
Real &  s,
Real &  ds_dh,
Real &  ds_dp 
) const
virtualinherited

Specific entropy and its derivatives from specific enthalpy and pressure.

Parameters
[in]hspecific enthalpy
[in]ppressure
[out]sspecific entropy
[out]ds_dhderivative of specific entropy w.r.t. specific enthalpy
[out]ds_dpderivative of specific entropy w.r.t. pressure

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 98 of file SinglePhaseFluidProperties.C.

99 {
100  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
101 }
const std::string name
Definition: Setup.h:22

◆ s_from_p_T() [1/2]

Real HelmholtzFluidProperties::s_from_p_T ( Real  p,
Real  T 
) const
overridevirtualinherited

Specific entropy from pressure and temperature.

Parameters
[in]ppressure
[in]Ttemperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 194 of file HelmholtzFluidProperties.C.

Referenced by HelmholtzFluidProperties::s_from_p_T().

195 {
196  // Require density first
197  const Real density = rho_from_p_T(pressure, temperature);
198  // Scale the input density and temperature
199  const Real delta = density / criticalDensity();
200  const Real tau = criticalTemperature() / temperature;
201 
202  return _R * (tau * dalpha_dtau(delta, tau) - alpha(delta, tau)) / molarMass();
203 }
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real dalpha_dtau(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt tau.
virtual Real alpha(Real delta, Real tau) const =0
Helmholtz free energy.
virtual Real criticalDensity() const
Critical density.
const std::string pressure
Definition: NS.h:26

◆ 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

Specific entropy and its derivatives from pressure and temperature.

Parameters
[in]ppressure
[in]Ttemperature
[out]sspecific entropy
[out]ds_dpderivative of specific entropy w.r.t. pressure
[out]ds_dTderivative of specific entropy w.r.t. temperature

Reimplemented from SinglePhaseFluidProperties.

Definition at line 206 of file HelmholtzFluidProperties.C.

208 {
209  s = this->s_from_p_T(pressure, temperature);
210 
211  // Require density first
212  const Real density = rho_from_p_T(pressure, temperature);
213  // Scale the input density and temperature
214  const Real delta = density / criticalDensity();
215  const Real tau = criticalTemperature() / temperature;
216 
217  const Real da_dd = dalpha_ddelta(delta, tau);
218  const Real da_dt = dalpha_dtau(delta, tau);
219  const Real d2a_dd2 = d2alpha_ddelta2(delta, tau);
220  const Real d2a_dt2 = d2alpha_dtau2(delta, tau);
221  const Real d2a_ddt = d2alpha_ddeltatau(delta, tau);
222 
223  ds_dp = tau * (d2a_ddt - da_dd) / (density * temperature * (2.0 * da_dd + delta * d2a_dd2));
224  ds_dT = -_R * tau * (da_dt - alpha(delta, tau) + tau * (d2a_dt2 - da_dt)) /
225  (molarMass() * temperature);
226 }
virtual Real d2alpha_ddeltatau(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta and tau.
virtual Real d2alpha_dtau2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt tau.
virtual Real s(Real pressure, Real temperature) const
virtual Real molarMass() const
Molar mass [kg/mol].
const std::string density
Definition: NS.h:17
const std::string temperature
Definition: NS.h:27
virtual Real d2alpha_ddelta2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta.
const Real _R
Universal gas constant (J/mol/K)
virtual Real criticalTemperature() const
Critical temperature.
virtual Real dalpha_ddelta(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt delta.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Density from pressure and temperature.
virtual Real dalpha_dtau(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt tau.
virtual Real alpha(Real delta, Real tau) const =0
Helmholtz free energy.
virtual Real criticalDensity() const
Critical density.
virtual Real s_from_p_T(Real pressure, Real temperature) const override
Specific entropy from pressure and temperature.
const std::string pressure
Definition: NS.h:26

◆ s_from_T_v() [1/2]

Real SinglePhaseFluidProperties::s_from_T_v ( Real  T,
Real  v 
) const
virtualinherited

Specific entropy from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 557 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::s_from_T_v().

558 {
559  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
560 }
const std::string name
Definition: Setup.h:22

◆ s_from_T_v() [2/2]

void SinglePhaseFluidProperties::s_from_T_v ( Real  T,
Real  v,
Real &  s,
Real &  ds_dT,
Real &  ds_dv 
) const
virtualinherited

Specific entropy and its derivatives from temperature and specific volume.

Parameters
[in]Ttemperature
[in]vspecific volume
[out]sspecific entropy (J/kg)
[out]ds_dTderivative of specific entropy w.r.t. temperature
[out]ds_dvderivative of specific entropy w.r.t. specific volume

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 563 of file SinglePhaseFluidProperties.C.

564 {
565  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
566 }
const std::string name
Definition: Setup.h:22

◆ s_from_v_e() [1/2]

Real SinglePhaseFluidProperties::s_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Specific entropy from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 81 of file SinglePhaseFluidProperties.C.

Referenced by StagnationPressureAux::computeValue(), and StagnationTemperatureAux::computeValue().

82 {
83  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
84 }
const std::string name
Definition: Setup.h:22

◆ s_from_v_e() [2/2]

void SinglePhaseFluidProperties::s_from_v_e ( Real  v,
Real  e,
Real &  s,
Real &  ds_dv,
Real &  ds_de 
) const
virtualinherited

Specific entropy and its derivatives from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy
[out]sspecific entropy
[out]ds_dvderivative of specific entropy w.r.t. specific volume
[out]ds_dederivative of specific entropy w.r.t. specific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 87 of file SinglePhaseFluidProperties.C.

88 {
89  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
90 }
const std::string name
Definition: Setup.h:22

◆ 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
temperatureCO2 temperature (K)
Returns
saturated liquid density (kg/m^3)

Definition at line 124 of file CO2FluidProperties.C.

Referenced by p_from_rho_T().

125 {
126  if (temperature < _triple_point_temperature || temperature > _critical_temperature)
127  throw MooseException("Temperature is out of range in " + name() + ": saturatedLiquiDensity()");
128 
129  Real Tstar = temperature / _critical_temperature;
130 
131  Real logdensity = 1.9245108 * std::pow(1.0 - Tstar, 0.34) -
132  0.62385555 * std::pow(1.0 - Tstar, 0.5) -
133  0.32731127 * std::pow(1.0 - Tstar, 10.0 / 6.0) +
134  0.39245142 * std::pow(1.0 - Tstar, 11.0 / 6.0);
135 
136  return _critical_density * std::exp(logdensity);
137 }
const Real _critical_density
Critical density (kg/m^3)
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const Real _critical_temperature
Critical temperature (K)

◆ 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
temperatureCO2 temperature (K)
Returns
saturated vapor density (kg/m^3)

Definition at line 140 of file CO2FluidProperties.C.

Referenced by p_from_rho_T().

141 {
142  if (temperature < _triple_point_temperature || temperature > _critical_temperature)
143  throw MooseException("Temperature is out of range in " + name() + ": saturatedVaporDensity()");
144 
145  Real Tstar = temperature / _critical_temperature;
146 
147  Real logdensity =
148  (-1.7074879 * std::pow(1.0 - Tstar, 0.34) - 0.82274670 * std::pow(1.0 - Tstar, 0.5) -
149  4.6008549 * (1.0 - Tstar) - 10.111178 * std::pow(1.0 - Tstar, 7.0 / 3.0) -
150  29.742252 * std::pow(1.0 - Tstar, 14.0 / 3.0));
151 
152  return _critical_density * std::exp(logdensity);
153 }
const Real _critical_density
Critical density (kg/m^3)
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const Real _critical_temperature
Critical temperature (K)

◆ subdomainSetup()

virtual void FluidProperties::subdomainSetup ( )
inlinefinalvirtualinherited

Definition at line 32 of file FluidProperties.h.

32 {}

◆ 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
temperatureCO2 temperature (K)
Returns
sublimation pressure (Pa)

Definition at line 91 of file CO2FluidProperties.C.

Referenced by rho_from_p_T().

92 {
94  throw MooseException("Temperature is above the triple point temperature in " + name() +
95  ": sublimationPressure()");
96 
98 
100  std::exp((-14.740846 * (1.0 - Tstar) + 2.4327015 * std::pow(1.0 - Tstar, 1.9) -
101  5.3061778 * std::pow(1.0 - Tstar, 2.9)) /
102  Tstar);
103 
104  return pressure;
105 }
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
const Real _triple_point_temperature
Triple point temperature (K)
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const std::string pressure
Definition: NS.h:26
const Real _triple_point_pressure
Triple point pressure (Pa)

◆ T_from_p_h()

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

Temperature from pressure and specific enthalpy.

Parameters
[in]pressurepressure (Pa)
[in]enthalpyenthalpy (J/kg)
Returns
Temperature (K)

Reimplemented in IdealGasFluidProperties.

Definition at line 601 of file SinglePhaseFluidProperties.C.

602 {
603  const Real s = s_from_h_p(h, p);
604  const Real rho = rho_from_p_s(p, s);
605  const Real v = 1. / rho;
606  const Real e = e_from_v_h(v, h);
607  return T_from_v_e(v, e);
608 }
virtual Real T_from_v_e(Real v, Real e) const
Temperature from specific volume and specific internal energy.
virtual Real s(Real pressure, Real temperature) const
virtual Real h(Real p, Real T) const
virtual Real s_from_h_p(Real h, Real p) const
Specific entropy from specific enthalpy and pressure.
virtual Real rho(Real p, Real T) const
virtual Real e_from_v_h(Real v, Real h) const
Specific internal energy as a function of specific volume and specific enthalpy.
virtual Real rho_from_p_s(Real p, Real s) const
Density from pressure and specific entropy.
virtual Real e(Real pressure, Real temperature) const

◆ T_from_v_e() [1/2]

Real SinglePhaseFluidProperties::T_from_v_e ( Real  v,
Real  e 
) const
virtualinherited

Temperature from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy
Returns
sound speed

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 39 of file SinglePhaseFluidProperties.C.

Referenced by FluidPropertiesMaterial::computeQpProperties(), StagnationTemperatureAux::computeValue(), TemperatureAux::computeValue(), IdealRealGasMixtureFluidProperties::p_T_from_v_e(), and SinglePhaseFluidProperties::T_from_p_h().

40 {
41  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
42 }
const std::string name
Definition: Setup.h:22

◆ T_from_v_e() [2/2]

void SinglePhaseFluidProperties::T_from_v_e ( Real  v,
Real  e,
Real &  T,
Real &  dT_dv,
Real &  dT_de 
) const
virtualinherited

Temperature and its derivatives from specific volume and specific internal energy.

Parameters
[in]vspecific volume
[in]especific internal energy
[out]Ttemperature
[out]dT_dvderivative of temperature w.r.t. specific volume
[out]dT_dederivative of temperature w.r.t. specific internal energy

Reimplemented in IdealGasFluidProperties, and StiffenedGasFluidProperties.

Definition at line 45 of file SinglePhaseFluidProperties.C.

46 {
47  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
48 }
const std::string name
Definition: Setup.h:22

◆ threadJoin()

virtual void FluidProperties::threadJoin ( const UserObject &  )
inlinefinalvirtualinherited

Definition at line 31 of file FluidProperties.h.

31 {}

◆ 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.

67 {
69 }
const Real _triple_point_pressure
Triple point pressure (Pa)

◆ 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.

73 {
75 }
const Real _triple_point_temperature
Triple point temperature (K)

◆ 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]Ttemperature
[in]vspecific volume

Reimplemented in StiffenedGasFluidProperties.

Definition at line 524 of file SinglePhaseFluidProperties.C.

Referenced by IdealRealGasMixtureFluidProperties::v_from_p_T().

525 {
526  mooseError(name(), ": ", __PRETTY_FUNCTION__, " not implemented.");
527 }
const std::string name
Definition: Setup.h:22

◆ 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]ppressure
[in]Ttemperature

Definition at line 151 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().

152 {
153  Real rho = rho_from_p_T(p, T);
154  return 1.0 / rho;
155 }
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real p, Real T) const
Density from pressure and temperature.

◆ 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]ppressure
[in]Ttemperature
[out]vspecific volume
[out]dv_dpderivative of specific volume w.r.t. pressure
[out]dv_dTderivative of specific volume w.r.t. temperature

Definition at line 158 of file SinglePhaseFluidProperties.C.

159 {
160  Real rho, drho_dp, drho_dT;
161  rho_from_p_T(p, T, rho, drho_dp, drho_dT);
162 
163  v = 1.0 / rho;
164  const Real dv_drho = -1.0 / (rho * rho);
165 
166  dv_dp = dv_drho * drho_dp;
167  dv_dT = dv_drho * drho_dT;
168 }
virtual Real rho(Real p, Real T) const
virtual Real rho_from_p_T(Real p, Real T) const
Density from pressure and temperature.

◆ vaporPressure()

Real CO2FluidProperties::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
temperaturewater temperature (K)
Returns
saturation pressure (Pa)

Reimplemented from SinglePhaseFluidProperties.

Definition at line 108 of file CO2FluidProperties.C.

Referenced by p_from_rho_T().

109 {
110  if (temperature < _triple_point_temperature || temperature > _critical_temperature)
111  throw MooseException("Temperature is out of range in " + name() + ": vaporPressure()");
112 
113  Real Tstar = temperature / _critical_temperature;
114 
115  Real logpressure =
116  (-7.0602087 * (1.0 - Tstar) + 1.9391218 * std::pow(1.0 - Tstar, 1.5) -
117  1.6463597 * Utility::pow<2>(1.0 - Tstar) - 3.2995634 * Utility::pow<4>(1.0 - Tstar)) /
118  Tstar;
119 
120  return _critical_pressure * std::exp(logpressure);
121 }
const Real _critical_pressure
Critical pressure (Pa)
const std::string temperature
Definition: NS.h:27
const std::string name
Definition: Setup.h:22
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
const Real _critical_temperature
Critical temperature (K)

◆ vaporPressure_dT()

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

Vapor pressure.

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

Parameters
temperaturewater temperature (K)
[out]saturationpressure (Pa)
[out]derivativeof saturation pressure wrt temperature (Pa/K)

Reimplemented in Water97FluidProperties.

Definition at line 351 of file SinglePhaseFluidProperties.C.

Referenced by PorousFlowWaterNCG::equilibriumMassFractions(), and PorousFlowWaterNCG::gasProperties().

354 {
355  mooseError(name(), ": vaporPressure_dT() is not implemented");
356 }
const std::string name
Definition: Setup.h:22

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 181 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

◆ _A4

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

◆ _alpha3

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

◆ _b4

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

◆ _B4

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

◆ _beta3

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

◆ _beta4

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

◆ _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 207 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

◆ _critical_density

const Real CO2FluidProperties::_critical_density = 467.6
protected

Critical density (kg/m^3)

Definition at line 172 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 168 of file CO2FluidProperties.h.

Referenced by criticalPressure(), and vaporPressure().

◆ _critical_temperature

const Real CO2FluidProperties::_critical_temperature = 304.1282
protected

◆ _d1

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

◆ _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 202 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

◆ _D4

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

◆ _eps3

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

◆ _gamma3

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

◆ _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 239 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 232 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 233 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 234 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 235 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 236 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 237 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 166 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 227 of file CO2FluidProperties.h.

Referenced by mu_drhoT_from_rho_T(), and 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 228 of file CO2FluidProperties.h.

Referenced by mu_drhoT_from_rho_T(), and 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 185 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 194 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 209 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

◆ _R

const Real SinglePhaseFluidProperties::_R
protectedinherited

◆ _Rco2

const Real CO2FluidProperties::_Rco2 = 188.9241
protected

Specific gas constant (J/mol/K)

Definition at line 178 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

◆ _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 204 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

◆ _T_c2k

const Real SinglePhaseFluidProperties::_T_c2k
protectedinherited

◆ _theta0

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

Definition at line 182 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 174 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 176 of file CO2FluidProperties.h.

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


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