Cantera  3.1.0a1
RedlichKisterVPSSTP Class Reference

RedlichKisterVPSSTP is a derived class of GibbsExcessVPSSTP that employs the Redlich-Kister approximation for the excess Gibbs free energy. More...

#include <RedlichKisterVPSSTP.h>

Inheritance diagram for RedlichKisterVPSSTP:
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Detailed Description

RedlichKisterVPSSTP is a derived class of GibbsExcessVPSSTP that employs the Redlich-Kister approximation for the excess Gibbs free energy.

RedlichKisterVPSSTP derives from class GibbsExcessVPSSTP which is derived from VPStandardStateTP, and overloads the virtual methods defined there with ones that use expressions appropriate for the Redlich Kister Excess Gibbs free energy approximation.

The independent unknowns are pressure, temperature, and mass fraction.

Specification of Species Standard State Properties

All species are defined to have standard states that depend upon both the temperature and the pressure. The Redlich-Kister approximation assumes symmetric standard states, where all of the standard state assume that the species are in pure component states at the temperature and pressure of the solution. I don't think it prevents, however, some species from being dilute in the solution.

Specification of Solution Thermodynamic Properties

The molar excess Gibbs free energy is given by the following formula which is a sum over interactions i. Each of the interactions are binary interactions involving two of the species in the phase, denoted, Ai and Bi. This is the generalization of the Redlich-Kister formulation for a phase that has more than 2 species.

\[ G^E = \sum_{i} G^E_{i} \]

where

\[ G^E_{i} = n X_{Ai} X_{Bi} \sum_m \left( A^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right) \]

where n is the total moles in the solution and where we can break down the Gibbs free energy contributions into enthalpy and entropy contributions by defining \( A^i_m = H^i_m - T S^i_m \) :

\[ H^E_i = n X_{Ai} X_{Bi} \sum_m \left( H^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right) \]

\[ S^E_i = n X_{Ai} X_{Bi} \sum_m \left( S^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right) \]

The activity of a species defined in the phase is given by an excess Gibbs free energy formulation:

\[ a_k = \gamma_k X_k \]

where

\[ R T \ln( \gamma_k )= \frac{d(n G^E)}{d(n_k)}\Bigg|_{n_i} \]

Taking the derivatives results in the following expression

\[ R T \ln( \gamma_k )= \sum_i \delta_{Ai,k} (1 - X_{Ai}) X_{Bi} \sum_m \left( A^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right) + \sum_i \delta_{Ai,k} X_{Ai} X_{Bi} \sum_m \left( A^{i}_0 + A^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^{m-1} (1 - X_{Ai} + X_{Bi}) \right) \]

Evaluating thermodynamic properties requires the following derivatives of \( \ln(\gamma_k) \):

\[ \frac{d \ln( \gamma_k )}{dT} = - \frac{1}{RT^2} \left( \sum_i \delta_{Ai,k} (1 - X_{Ai}) X_{Bi} \sum_m \left( H^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right) + \sum_i \delta_{Ai,k} X_{Ai} X_{Bi} \sum_m \left( H^{i}_0 + H^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^{m-1} (1 - X_{Ai} + X_{Bi}) \right) \right) \]

and

\[ \frac{d^2 \ln( \gamma_k )}{dT^2} = -\frac{2}{T} \frac{d \ln( \gamma_k )}{dT} \]

This object inherits from the class VPStandardStateTP. Therefore, the specification and calculation of all standard state and reference state values are handled at that level. Various functional forms for the standard state are permissible. The chemical potential for species k is equal to

\[ \mu_k(T,P) = \mu^o_k(T, P) + R T \ln(\gamma_k X_k) \]

The partial molar entropy for species k is given by the following relation,

\[ \tilde{s}_k(T,P) = s^o_k(T,P) - R \ln( \gamma_k X_k ) - R T \frac{d \ln(\gamma_k) }{dT} \]

The partial molar enthalpy for species k is given by

\[ \tilde{h}_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT} \]

The partial molar volume for species k is

\[ \tilde V_k(T,P) = V^o_k(T,P) + R T \frac{d \ln(\gamma_k) }{dP} \]

The partial molar Heat Capacity for species k is

\[ \tilde{C}_{p,k}(T,P) = C^o_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma_k )}{dT} - R T^2 \frac{d^2 \ln(\gamma_k) }{{dT}^2} = C^o_{p,k}(T,P) \]

Application within Kinetics Managers

\( C^a_k \) are defined such that \( a_k = C^a_k / C^s_k, \) where \( C^s_k \) is a standard concentration defined below and \( a_k \) are activities used in the thermodynamic functions. These activity (or generalized) concentrations are used by kinetics manager classes to compute the forward and reverse rates of elementary reactions. The activity concentration, \( C^a_k \),is given by the following expression.

\[ C^a_k = C^s_k X_k = \frac{P}{R T} X_k \]

The standard concentration for species k is independent of k and equal to

\[ C^s_k = C^s = \frac{P}{R T} \]

For example, a bulk-phase binary gas reaction between species j and k, producing a new gas species l would have the following equation for its rate of progress variable, \( R^1 \), which has units of kmol m-3 s-1.

\[ R^1 = k^1 C_j^a C_k^a = k^1 (C^s a_j) (C^s a_k) \]

where

\[ C_j^a = C^s a_j \mbox{\quad and \quad} C_k^a = C^s a_k \]

\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C^s \) is the standard concentration. \( a_j \) is the activity of species j which is equal to the mole fraction of j.

The reverse rate constant can then be obtained from the law of microscopic reversibility and the equilibrium expression for the system.

\[ \frac{a_j a_k}{ a_l} = K_a^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} ) \]

\( K_a^{o,1} \) is the dimensionless form of the equilibrium constant, associated with the pressure dependent standard states \( \mu^o_l(T,P) \) and their associated activities, \( a_l \), repeated here:

\[ \mu_l(T,P) = \mu^o_l(T, P) + R T \ln a_l \]

We can switch over to expressing the equilibrium constant in terms of the reference state chemical potentials

\[ K_a^{o,1} = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{P} \]

The concentration equilibrium constant, \( K_c \), may be obtained by changing over to activity concentrations. When this is done:

\[ \frac{C^a_j C^a_k}{ C^a_l} = C^o K_a^{o,1} = K_c^1 = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{RT} \]

Kinetics managers will calculate the concentration equilibrium constant, \( K_c \), using the second and third part of the above expression as a definition for the concentration equilibrium constant.

For completeness, the pressure equilibrium constant may be obtained as well

\[ \frac{P_j P_k}{ P_l P_{ref}} = K_p^1 = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) \]

\( K_p \) is the simplest form of the equilibrium constant for ideal gases. However, it isn't necessarily the simplest form of the equilibrium constant for other types of phases; \( K_c \) is used instead because it is completely general.

The reverse rate of progress may be written down as

\[ R^{-1} = k^{-1} C_l^a = k^{-1} (C^o a_l) \]

where we can use the concept of microscopic reversibility to write the reverse rate constant in terms of the forward rate constant and the concentration equilibrium constant, \( K_c \).

\[ k^{-1} = k^1 K^1_c \]

\( k^{-1} \) has units of s-1.

Definition at line 232 of file RedlichKisterVPSSTP.h.

Public Member Functions

 RedlichKisterVPSSTP (const string &inputFile="", const string &id="")
 Construct a RedlichKisterVPSSTP object from an input file. More...
 
string type () const override
 String indicating the thermodynamic model implemented. More...
 
void getd2lnActCoeffdT2 (double *d2lnActCoeffdT2) const
 Get the array of temperature second derivatives of the log activity coefficients. More...
 
void getdlnActCoeffdT (double *dlnActCoeffdT) const override
 Get the array of temperature derivatives of the log activity coefficients. More...
 
Molar Thermodynamic Properties
double enthalpy_mole () const override
 Molar enthalpy. Units: J/kmol. More...
 
double entropy_mole () const override
 Molar entropy. Units: J/kmol/K. More...
 
double cp_mole () const override
 Molar heat capacity at constant pressure. Units: J/kmol/K. More...
 
double cv_mole () const override
 Molar heat capacity at constant volume. Units: J/kmol/K. More...
 
Activities, Standard States, and Activity Concentrations

The activity \( a_k \) of a species in solution is related to the chemical potential by

\[ \mu_k = \mu_k^0(T) + \hat R T \ln a_k. \]

The quantity \( \mu_k^0(T,P) \) is the chemical potential at unit activity, which depends only on temperature and pressure.

void getLnActivityCoefficients (double *lnac) const override
 Get the array of non-dimensional molar-based ln activity coefficients at the current solution temperature, pressure, and solution concentration. More...
 
Partial Molar Properties of the Solution
void getChemPotentials (double *mu) const override
 Get the species chemical potentials. Units: J/kmol. More...
 
void getPartialMolarEnthalpies (double *hbar) const override
 Returns an array of partial molar enthalpies for the species in the mixture. More...
 
void getPartialMolarEntropies (double *sbar) const override
 Returns an array of partial molar entropies for the species in the mixture. More...
 
void getPartialMolarCp (double *cpbar) const override
 Returns an array of partial molar heat capacities for the species in the mixture. More...
 
void getPartialMolarVolumes (double *vbar) const override
 Return an array of partial molar volumes for the species in the mixture. More...
 
Initialization

The following methods are used in the process of constructing the phase and setting its parameters from a specification in an input file.

They are not normally used in application programs. To see how they are used, see importPhase().

void initThermo () override
 Initialize the ThermoPhase object after all species have been set up. More...
 
void getParameters (AnyMap &phaseNode) const override
 Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function. More...
 
void addBinaryInteraction (const string &speciesA, const string &speciesB, const double *excess_enthalpy, size_t n_enthalpy, const double *excess_entropy, size_t n_entropy)
 Add a binary species interaction with the specified parameters. More...
 
Derivatives of Thermodynamic Variables needed for Applications
void getdlnActCoeffds (const double dTds, const double *const dXds, double *dlnActCoeffds) const override
 Get the change in activity coefficients wrt changes in state (temp, mole fraction, etc) along a line in parameter space or along a line in physical space. More...
 
void getdlnActCoeffdlnX_diag (double *dlnActCoeffdlnX_diag) const override
 Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only. More...
 
void getdlnActCoeffdlnN_diag (double *dlnActCoeffdlnN_diag) const override
 Get the array of log species mole number derivatives of the log activity coefficients. More...
 
void getdlnActCoeffdlnN (const size_t ld, double *const dlnActCoeffdlnN) override
 Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers. More...
 
- Public Member Functions inherited from GibbsExcessVPSSTP
bool addSpecies (shared_ptr< Species > spec) override
 Add a Species to this Phase. More...
 
 GibbsExcessVPSSTP ()
 
Units standardConcentrationUnits () const override
 Returns the units of the "standard concentration" for this phase. More...
 
void getActivityConcentrations (double *c) const override
 This method returns an array of generalized concentrations. More...
 
double standardConcentration (size_t k=0) const override
 The standard concentration \( C^0_k \) used to normalize the generalized concentration. More...
 
double logStandardConc (size_t k=0) const override
 Natural logarithm of the standard concentration of the kth species. More...
 
void getActivities (double *ac) const override
 Get the array of non-dimensional activities (molality based for this class and classes that derive from it) at the current solution temperature, pressure, and solution concentration. More...
 
void getActivityCoefficients (double *ac) const override
 Get the array of non-dimensional molar-based activity coefficients at the current solution temperature, pressure, and solution concentration. More...
 
virtual void getdlnActCoeffdlnX (double *dlnActCoeffdlnX) const
 Get the array of log concentration-like derivatives of the log activity coefficients. More...
 
- Public Member Functions inherited from VPStandardStateTP
void setTemperature (const double temp) override
 Set the temperature of the phase. More...
 
void setPressure (double p) override
 Set the internally stored pressure (Pa) at constant temperature and composition. More...
 
void setState_TP (double T, double pres) override
 Set the temperature and pressure at the same time. More...
 
double pressure () const override
 Returns the current pressure of the phase. More...
 
virtual void updateStandardStateThermo () const
 Updates the standard state thermodynamic functions at the current T and P of the solution. More...
 
double minTemp (size_t k=npos) const override
 Minimum temperature for which the thermodynamic data for the species or phase are valid. More...
 
double maxTemp (size_t k=npos) const override
 Maximum temperature for which the thermodynamic data for the species are valid. More...
 
PDSSprovidePDSS (size_t k)
 
const PDSSprovidePDSS (size_t k) const
 
 VPStandardStateTP ()
 Constructor. More...
 
 ~VPStandardStateTP () override
 
bool isCompressible () const override
 Return whether phase represents a compressible substance. More...
 
int standardStateConvention () const override
 This method returns the convention used in specification of the standard state, of which there are currently two, temperature based, and variable pressure based. More...
 
void getStandardChemPotentials (double *mu) const override
 Get the array of chemical potentials at unit activity for the species at their standard states at the current T and P of the solution. More...
 
void getEnthalpy_RT (double *hrt) const override
 Get the nondimensional Enthalpy functions for the species at their standard states at the current T and P of the solution. More...
 
void getEntropy_R (double *sr) const override
 Get the array of nondimensional Entropy functions for the standard state species at the current T and P of the solution. More...
 
void getGibbs_RT (double *grt) const override
 Get the nondimensional Gibbs functions for the species in their standard states at the current T and P of the solution. More...
 
void getPureGibbs (double *gpure) const override
 Get the Gibbs functions for the standard state of the species at the current T and P of the solution. More...
 
void getIntEnergy_RT (double *urt) const override
 Returns the vector of nondimensional Internal Energies of the standard state species at the current T and P of the solution. More...
 
void getCp_R (double *cpr) const override
 Get the nondimensional Heat Capacities at constant pressure for the species standard states at the current T and P of the solution. More...
 
void getStandardVolumes (double *vol) const override
 Get the molar volumes of the species standard states at the current T and P of the solution. More...
 
virtual const vector< double > & getStandardVolumes () const
 
void initThermo () override
 Initialize the ThermoPhase object after all species have been set up. More...
 
void getSpeciesParameters (const string &name, AnyMap &speciesNode) const override
 Get phase-specific parameters of a Species object such that an identical one could be reconstructed and added to this phase. More...
 
bool addSpecies (shared_ptr< Species > spec) override
 Add a Species to this Phase. More...
 
void installPDSS (size_t k, unique_ptr< PDSS > &&pdss)
 Install a PDSS object for species k More...
 
virtual bool addSpecies (shared_ptr< Species > spec)
 Add a Species to this Phase. More...
 
void getEnthalpy_RT_ref (double *hrt) const override
 Returns the vector of nondimensional enthalpies of the reference state at the current temperature of the solution and the reference pressure for the species. More...
 
void getGibbs_RT_ref (double *grt) const override
 Returns the vector of nondimensional Gibbs Free Energies of the reference state at the current temperature of the solution and the reference pressure for the species. More...
 
void getGibbs_ref (double *g) const override
 Returns the vector of the Gibbs function of the reference state at the current temperature of the solution and the reference pressure for the species. More...
 
void getEntropy_R_ref (double *er) const override
 Returns the vector of nondimensional entropies of the reference state at the current temperature of the solution and the reference pressure for each species. More...
 
void getCp_R_ref (double *cprt) const override
 Returns the vector of nondimensional constant pressure heat capacities of the reference state at the current temperature of the solution and reference pressure for each species. More...
 
void getStandardVolumes_ref (double *vol) const override
 Get the molar volumes of the species reference states at the current T and P_ref of the solution. More...
 
- Public Member Functions inherited from ThermoPhase
 ThermoPhase ()=default
 Constructor. More...
 
double RT () const
 Return the Gas Constant multiplied by the current temperature. More...
 
double equivalenceRatio () const
 Compute the equivalence ratio for the current mixture from available oxygen and required oxygen. More...
 
string type () const override
 String indicating the thermodynamic model implemented. More...
 
virtual bool isIdeal () const
 Boolean indicating whether phase is ideal. More...
 
virtual string phaseOfMatter () const
 String indicating the mechanical phase of the matter in this Phase. More...
 
virtual double refPressure () const
 Returns the reference pressure in Pa. More...
 
double Hf298SS (const size_t k) const
 Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More...
 
virtual void modifyOneHf298SS (const size_t k, const double Hf298New)
 Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1) More...
 
virtual void resetHf298 (const size_t k=npos)
 Restore the original heat of formation of one or more species. More...
 
bool chargeNeutralityNecessary () const
 Returns the chargeNeutralityNecessity boolean. More...
 
virtual double intEnergy_mole () const
 Molar internal energy. Units: J/kmol. More...
 
virtual double gibbs_mole () const
 Molar Gibbs function. Units: J/kmol. More...
 
virtual double isothermalCompressibility () const
 Returns the isothermal compressibility. Units: 1/Pa. More...
 
virtual double thermalExpansionCoeff () const
 Return the volumetric thermal expansion coefficient. Units: 1/K. More...
 
virtual double soundSpeed () const
 Return the speed of sound. Units: m/s. More...
 
void setElectricPotential (double v)
 Set the electric potential of this phase (V). More...
 
double electricPotential () const
 Returns the electric potential of this phase (V). More...
 
virtual int activityConvention () const
 This method returns the convention used in specification of the activities, of which there are currently two, molar- and molality-based conventions. More...
 
void getElectrochemPotentials (double *mu) const
 Get the species electrochemical potentials. More...
 
virtual void getPartialMolarIntEnergies (double *ubar) const
 Return an array of partial molar internal energies for the species in the mixture. More...
 
virtual void getIntEnergy_RT_ref (double *urt) const
 Returns the vector of nondimensional internal Energies of the reference state at the current temperature of the solution and the reference pressure for each species. More...
 
double enthalpy_mass () const
 Specific enthalpy. Units: J/kg. More...
 
double intEnergy_mass () const
 Specific internal energy. Units: J/kg. More...
 
double entropy_mass () const
 Specific entropy. Units: J/kg/K. More...
 
double gibbs_mass () const
 Specific Gibbs function. Units: J/kg. More...
 
double cp_mass () const
 Specific heat at constant pressure. Units: J/kg/K. More...
 
double cv_mass () const
 Specific heat at constant volume. Units: J/kg/K. More...
 
virtual void setState_TPX (double t, double p, const double *x)
 Set the temperature (K), pressure (Pa), and mole fractions. More...
 
virtual void setState_TPX (double t, double p, const Composition &x)
 Set the temperature (K), pressure (Pa), and mole fractions. More...
 
virtual void setState_TPX (double t, double p, const string &x)
 Set the temperature (K), pressure (Pa), and mole fractions. More...
 
virtual void setState_TPY (double t, double p, const double *y)
 Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...
 
virtual void setState_TPY (double t, double p, const Composition &y)
 Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...
 
virtual void setState_TPY (double t, double p, const string &y)
 Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...
 
virtual void setState_HP (double h, double p, double tol=1e-9)
 Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase. More...
 
virtual void setState_UV (double u, double v, double tol=1e-9)
 Set the specific internal energy (J/kg) and specific volume (m^3/kg). More...
 
virtual void setState_SP (double s, double p, double tol=1e-9)
 Set the specific entropy (J/kg/K) and pressure (Pa). More...
 
virtual void setState_SV (double s, double v, double tol=1e-9)
 Set the specific entropy (J/kg/K) and specific volume (m^3/kg). More...
 
virtual void setState_ST (double s, double t, double tol=1e-9)
 Set the specific entropy (J/kg/K) and temperature (K). More...
 
virtual void setState_TV (double t, double v, double tol=1e-9)
 Set the temperature (K) and specific volume (m^3/kg). More...
 
virtual void setState_PV (double p, double v, double tol=1e-9)
 Set the pressure (Pa) and specific volume (m^3/kg). More...
 
virtual void setState_UP (double u, double p, double tol=1e-9)
 Set the specific internal energy (J/kg) and pressure (Pa). More...
 
virtual void setState_VH (double v, double h, double tol=1e-9)
 Set the specific volume (m^3/kg) and the specific enthalpy (J/kg) More...
 
virtual void setState_TH (double t, double h, double tol=1e-9)
 Set the temperature (K) and the specific enthalpy (J/kg) More...
 
virtual void setState_SH (double s, double h, double tol=1e-9)
 Set the specific entropy (J/kg/K) and the specific enthalpy (J/kg) More...
 
virtual void setState_DP (double rho, double p)
 Set the density (kg/m**3) and pressure (Pa) at constant composition. More...
 
virtual void setState (const AnyMap &state)
 Set the state using an AnyMap containing any combination of properties supported by the thermodynamic model. More...
 
void setMixtureFraction (double mixFrac, const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar)
 Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More...
 
void setMixtureFraction (double mixFrac, const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar)
 Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More...
 
void setMixtureFraction (double mixFrac, const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar)
 Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More...
 
double mixtureFraction (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const
 Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More...
 
double mixtureFraction (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const
 Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More...
 
double mixtureFraction (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const
 Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More...
 
void setEquivalenceRatio (double phi, const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar)
 Set the mixture composition according to the equivalence ratio. More...
 
void setEquivalenceRatio (double phi, const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar)
 Set the mixture composition according to the equivalence ratio. More...
 
void setEquivalenceRatio (double phi, const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar)
 Set the mixture composition according to the equivalence ratio. More...
 
double equivalenceRatio (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) const
 Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More...
 
double equivalenceRatio (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) const
 Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More...
 
double equivalenceRatio (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) const
 Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More...
 
double stoichAirFuelRatio (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) const
 Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More...
 
double stoichAirFuelRatio (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) const
 Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More...
 
double stoichAirFuelRatio (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) const
 Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More...
 
void equilibrate (const string &XY, const string &solver="auto", double rtol=1e-9, int max_steps=50000, int max_iter=100, int estimate_equil=0, int log_level=0)
 Equilibrate a ThermoPhase object. More...
 
virtual void setToEquilState (const double *mu_RT)
 This method is used by the ChemEquil equilibrium solver. More...
 
virtual bool compatibleWithMultiPhase () const
 Indicates whether this phase type can be used with class MultiPhase for equilibrium calculations. More...
 
virtual double critTemperature () const
 Critical temperature (K). More...
 
virtual double critPressure () const
 Critical pressure (Pa). More...
 
virtual double critVolume () const
 Critical volume (m3/kmol). More...
 
virtual double critCompressibility () const
 Critical compressibility (unitless). More...
 
virtual double critDensity () const
 Critical density (kg/m3). More...
 
virtual double satTemperature (double p) const
 Return the saturation temperature given the pressure. More...
 
virtual double satPressure (double t)
 Return the saturation pressure given the temperature. More...
 
virtual double vaporFraction () const
 Return the fraction of vapor at the current conditions. More...
 
virtual void setState_Tsat (double t, double x)
 Set the state to a saturated system at a particular temperature. More...
 
virtual void setState_Psat (double p, double x)
 Set the state to a saturated system at a particular pressure. More...
 
void setState_TPQ (double T, double P, double Q)
 Set the temperature, pressure, and vapor fraction (quality). More...
 
void modifySpecies (size_t k, shared_ptr< Species > spec) override
 Modify the thermodynamic data associated with a species. More...
 
virtual MultiSpeciesThermospeciesThermo (int k=-1)
 Return a changeable reference to the calculation manager for species reference-state thermodynamic properties. More...
 
virtual const MultiSpeciesThermospeciesThermo (int k=-1) const
 
void initThermoFile (const string &inputFile, const string &id)
 Initialize a ThermoPhase object using an input file. More...
 
virtual void setParameters (const AnyMap &phaseNode, const AnyMap &rootNode=AnyMap())
 Set equation of state parameters from an AnyMap phase description. More...
 
AnyMap parameters (bool withInput=true) const
 Returns the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function. More...
 
const AnyMapinput () const
 Access input data associated with the phase description. More...
 
AnyMapinput ()
 
virtual void getdlnActCoeffdlnN_numderiv (const size_t ld, double *const dlnActCoeffdlnN)
 
virtual string report (bool show_thermo=true, double threshold=-1e-14) const
 returns a summary of the state of the phase as a string More...
 
- Public Member Functions inherited from Phase
 Phase ()=default
 Default constructor. More...
 
 Phase (const Phase &)=delete
 
Phaseoperator= (const Phase &)=delete
 
virtual bool isPure () const
 Return whether phase represents a pure (single species) substance. More...
 
virtual bool hasPhaseTransition () const
 Return whether phase represents a substance with phase transitions. More...
 
virtual map< string, size_t > nativeState () const
 Return a map of properties defining the native state of a substance. More...
 
string nativeMode () const
 Return string acronym representing the native state of a Phase. More...
 
virtual vector< string > fullStates () const
 Return a vector containing full states defining a phase. More...
 
virtual vector< string > partialStates () const
 Return a vector of settable partial property sets within a phase. More...
 
virtual size_t stateSize () const
 Return size of vector defining internal state of the phase. More...
 
void saveState (vector< double > &state) const
 Save the current internal state of the phase. More...
 
virtual void saveState (size_t lenstate, double *state) const
 Write to array 'state' the current internal state. More...
 
void restoreState (const vector< double > &state)
 Restore a state saved on a previous call to saveState. More...
 
virtual void restoreState (size_t lenstate, const double *state)
 Restore the state of the phase from a previously saved state vector. More...
 
double molecularWeight (size_t k) const
 Molecular weight of species k. More...
 
void getMolecularWeights (double *weights) const
 Copy the vector of molecular weights into array weights. More...
 
const vector< double > & molecularWeights () const
 Return a const reference to the internal vector of molecular weights. More...
 
const vector< double > & inverseMolecularWeights () const
 Return a const reference to the internal vector of molecular weights. More...
 
void getCharges (double *charges) const
 Copy the vector of species charges into array charges. More...
 
virtual void setMolesNoTruncate (const double *const N)
 Set the state of the object with moles in [kmol]. More...
 
double elementalMassFraction (const size_t m) const
 Elemental mass fraction of element m. More...
 
double elementalMoleFraction (const size_t m) const
 Elemental mole fraction of element m. More...
 
double charge (size_t k) const
 Dimensionless electrical charge of a single molecule of species k The charge is normalized by the the magnitude of the electron charge. More...
 
double chargeDensity () const
 Charge density [C/m^3]. More...
 
size_t nDim () const
 Returns the number of spatial dimensions (1, 2, or 3) More...
 
void setNDim (size_t ndim)
 Set the number of spatial dimensions (1, 2, or 3). More...
 
virtual bool ready () const
 Returns a bool indicating whether the object is ready for use. More...
 
int stateMFNumber () const
 Return the State Mole Fraction Number. More...
 
bool caseSensitiveSpecies () const
 Returns true if case sensitive species names are enforced. More...
 
void setCaseSensitiveSpecies (bool cflag=true)
 Set flag that determines whether case sensitive species are enforced in look-up operations, for example speciesIndex. More...
 
vector< double > getCompositionFromMap (const Composition &comp) const
 Converts a Composition to a vector with entries for each species Species that are not specified are set to zero in the vector. More...
 
void massFractionsToMoleFractions (const double *Y, double *X) const
 Converts a mixture composition from mole fractions to mass fractions. More...
 
void moleFractionsToMassFractions (const double *X, double *Y) const
 Converts a mixture composition from mass fractions to mole fractions. More...
 
string name () const
 Return the name of the phase. More...
 
void setName (const string &nm)
 Sets the string name for the phase. More...
 
string elementName (size_t m) const
 Name of the element with index m. More...
 
size_t elementIndex (const string &name) const
 Return the index of element named 'name'. More...
 
const vector< string > & elementNames () const
 Return a read-only reference to the vector of element names. More...
 
double atomicWeight (size_t m) const
 Atomic weight of element m. More...
 
double entropyElement298 (size_t m) const
 Entropy of the element in its standard state at 298 K and 1 bar. More...
 
int atomicNumber (size_t m) const
 Atomic number of element m. More...
 
int elementType (size_t m) const
 Return the element constraint type Possible types include: More...
 
int changeElementType (int m, int elem_type)
 Change the element type of the mth constraint Reassigns an element type. More...
 
const vector< double > & atomicWeights () const
 Return a read-only reference to the vector of atomic weights. More...
 
size_t nElements () const
 Number of elements. More...
 
void checkElementIndex (size_t m) const
 Check that the specified element index is in range. More...
 
void checkElementArraySize (size_t mm) const
 Check that an array size is at least nElements(). More...
 
double nAtoms (size_t k, size_t m) const
 Number of atoms of element m in species k. More...
 
size_t speciesIndex (const string &name) const
 Returns the index of a species named 'name' within the Phase object. More...
 
string speciesName (size_t k) const
 Name of the species with index k. More...
 
const vector< string > & speciesNames () const
 Return a const reference to the vector of species names. More...
 
size_t nSpecies () const
 Returns the number of species in the phase. More...
 
void checkSpeciesIndex (size_t k) const
 Check that the specified species index is in range. More...
 
void checkSpeciesArraySize (size_t kk) const
 Check that an array size is at least nSpecies(). More...
 
void setMoleFractionsByName (const Composition &xMap)
 Set the species mole fractions by name. More...
 
void setMoleFractionsByName (const string &x)
 Set the mole fractions of a group of species by name. More...
 
void setMassFractionsByName (const Composition &yMap)
 Set the species mass fractions by name. More...
 
void setMassFractionsByName (const string &x)
 Set the species mass fractions by name. More...
 
void setState_TD (double t, double rho)
 Set the internally stored temperature (K) and density (kg/m^3) More...
 
Composition getMoleFractionsByName (double threshold=0.0) const
 Get the mole fractions by name. More...
 
double moleFraction (size_t k) const
 Return the mole fraction of a single species. More...
 
double moleFraction (const string &name) const
 Return the mole fraction of a single species. More...
 
Composition getMassFractionsByName (double threshold=0.0) const
 Get the mass fractions by name. More...
 
double massFraction (size_t k) const
 Return the mass fraction of a single species. More...
 
double massFraction (const string &name) const
 Return the mass fraction of a single species. More...
 
void getMoleFractions (double *const x) const
 Get the species mole fraction vector. More...
 
virtual void setMoleFractions (const double *const x)
 Set the mole fractions to the specified values. More...
 
virtual void setMoleFractions_NoNorm (const double *const x)
 Set the mole fractions to the specified values without normalizing. More...
 
void getMassFractions (double *const y) const
 Get the species mass fractions. More...
 
const double * massFractions () const
 Return a const pointer to the mass fraction array. More...
 
virtual void setMassFractions (const double *const y)
 Set the mass fractions to the specified values and normalize them. More...
 
virtual void setMassFractions_NoNorm (const double *const y)
 Set the mass fractions to the specified values without normalizing. More...
 
virtual void getConcentrations (double *const c) const
 Get the species concentrations (kmol/m^3). More...
 
virtual double concentration (const size_t k) const
 Concentration of species k. More...
 
virtual void setConcentrations (const double *const conc)
 Set the concentrations to the specified values within the phase. More...
 
virtual void setConcentrationsNoNorm (const double *const conc)
 Set the concentrations without ignoring negative concentrations. More...
 
double temperature () const
 Temperature (K). More...
 
virtual double electronTemperature () const
 Electron Temperature (K) More...
 
virtual double density () const
 Density (kg/m^3). More...
 
virtual double molarDensity () const
 Molar density (kmol/m^3). More...
 
virtual double molarVolume () const
 Molar volume (m^3/kmol). More...
 
virtual void setDensity (const double density_)
 Set the internally stored density (kg/m^3) of the phase. More...
 
virtual void setElectronTemperature (double etemp)
 Set the internally stored electron temperature of the phase (K). More...
 
double mean_X (const double *const Q) const
 Evaluate the mole-fraction-weighted mean of an array Q. More...
 
double mean_X (const vector< double > &Q) const
 Evaluate the mole-fraction-weighted mean of an array Q. More...
 
double meanMolecularWeight () const
 The mean molecular weight. Units: (kg/kmol) More...
 
double sum_xlogx () const
 Evaluate \( \sum_k X_k \ln X_k \). More...
 
size_t addElement (const string &symbol, double weight=-12345.0, int atomicNumber=0, double entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS)
 Add an element. More...
 
void addSpeciesAlias (const string &name, const string &alias)
 Add a species alias (that is, a user-defined alternative species name). More...
 
virtual vector< string > findIsomers (const Composition &compMap) const
 Return a vector with isomers names matching a given composition map. More...
 
virtual vector< string > findIsomers (const string &comp) const
 Return a vector with isomers names matching a given composition string. More...
 
shared_ptr< Speciesspecies (const string &name) const
 Return the Species object for the named species. More...
 
shared_ptr< Speciesspecies (size_t k) const
 Return the Species object for species whose index is k. More...
 
void ignoreUndefinedElements ()
 Set behavior when adding a species containing undefined elements to just skip the species. More...
 
void addUndefinedElements ()
 Set behavior when adding a species containing undefined elements to add those elements to the phase. More...
 
void throwUndefinedElements ()
 Set the behavior when adding a species containing undefined elements to throw an exception. More...
 

Protected Attributes

vector< size_t > m_pSpecies_A_ij
 vector of species indices representing species A in the interaction More...
 
vector< size_t > m_pSpecies_B_ij
 vector of species indices representing species B in the interaction More...
 
vector< vector< double > > m_HE_m_ij
 Enthalpy term for the binary mole fraction interaction of the excess Gibbs free energy expression. More...
 
vector< vector< double > > m_SE_m_ij
 Entropy term for the binary mole fraction interaction of the excess Gibbs free energy expression. More...
 
Array2D dlnActCoeff_dX_
 Two dimensional array of derivatives of activity coefficients wrt mole fractions. More...
 
- Protected Attributes inherited from GibbsExcessVPSSTP
vector< double > moleFractions_
 Storage for the current values of the mole fractions of the species. More...
 
vector< double > lnActCoeff_Scaled_
 Storage for the current values of the activity coefficients of the species. More...
 
vector< double > dlnActCoeffdT_Scaled_
 Storage for the current derivative values of the gradients with respect to temperature of the log of the activity coefficients of the species. More...
 
vector< double > d2lnActCoeffdT2_Scaled_
 Storage for the current derivative values of the gradients with respect to temperature of the log of the activity coefficients of the species. More...
 
vector< double > dlnActCoeffdlnN_diag_
 Storage for the current derivative values of the gradients with respect to logarithm of the mole fraction of the log of the activity coefficients of the species. More...
 
vector< double > dlnActCoeffdlnX_diag_
 Storage for the current derivative values of the gradients with respect to logarithm of the mole fraction of the log of the activity coefficients of the species. More...
 
Array2D dlnActCoeffdlnN_
 Storage for the current derivative values of the gradients with respect to logarithm of the species mole number of the log of the activity coefficients of the species. More...
 
- Protected Attributes inherited from VPStandardStateTP
double m_Pcurrent = OneAtm
 Current value of the pressure - state variable. More...
 
double m_minTemp = 0.0
 The minimum temperature at which data for all species is valid. More...
 
double m_maxTemp = BigNumber
 The maximum temperature at which data for all species is valid. More...
 
double m_Tlast_ss = -1.0
 The last temperature at which the standard state thermodynamic properties were calculated at. More...
 
double m_Plast_ss = -1.0
 The last pressure at which the Standard State thermodynamic properties were calculated at. More...
 
vector< unique_ptr< PDSS > > m_PDSS_storage
 Storage for the PDSS objects for the species. More...
 
vector< double > m_h0_RT
 Vector containing the species reference enthalpies at T = m_tlast and P = p_ref. More...
 
vector< double > m_cp0_R
 Vector containing the species reference constant pressure heat capacities at T = m_tlast and P = p_ref. More...
 
vector< double > m_g0_RT
 Vector containing the species reference Gibbs functions at T = m_tlast and P = p_ref. More...
 
vector< double > m_s0_R
 Vector containing the species reference entropies at T = m_tlast and P = p_ref. More...
 
vector< double > m_V0
 Vector containing the species reference molar volumes. More...
 
vector< double > m_hss_RT
 Vector containing the species Standard State enthalpies at T = m_tlast and P = m_plast. More...
 
vector< double > m_cpss_R
 Vector containing the species Standard State constant pressure heat capacities at T = m_tlast and P = m_plast. More...
 
vector< double > m_gss_RT
 Vector containing the species Standard State Gibbs functions at T = m_tlast and P = m_plast. More...
 
vector< double > m_sss_R
 Vector containing the species Standard State entropies at T = m_tlast and P = m_plast. More...
 
vector< double > m_Vss
 Vector containing the species standard state volumes at T = m_tlast and P = m_plast. More...
 
- Protected Attributes inherited from ThermoPhase
MultiSpeciesThermo m_spthermo
 Pointer to the calculation manager for species reference-state thermodynamic properties. More...
 
AnyMap m_input
 Data supplied via setParameters. More...
 
double m_phi = 0.0
 Stored value of the electric potential for this phase. Units are Volts. More...
 
bool m_chargeNeutralityNecessary = false
 Boolean indicating whether a charge neutrality condition is a necessity. More...
 
int m_ssConvention = cSS_CONVENTION_TEMPERATURE
 Contains the standard state convention. More...
 
double m_tlast = 0.0
 last value of the temperature processed by reference state More...
 
- Protected Attributes inherited from Phase
ValueCache m_cache
 Cached for saved calculations within each ThermoPhase. More...
 
size_t m_kk = 0
 Number of species in the phase. More...
 
size_t m_ndim = 3
 Dimensionality of the phase. More...
 
vector< double > m_speciesComp
 Atomic composition of the species. More...
 
vector< double > m_speciesCharge
 Vector of species charges. length m_kk. More...
 
map< string, shared_ptr< Species > > m_species
 
UndefElement::behavior m_undefinedElementBehavior = UndefElement::add
 Flag determining behavior when adding species with an undefined element. More...
 
bool m_caseSensitiveSpecies = false
 Flag determining whether case sensitive species names are enforced. More...
 

Private Member Functions

void initLengths ()
 Initialize lengths of local variables after all species have been identified. More...
 
void s_update_lnActCoeff () const
 Update the activity coefficients. More...
 
void s_update_dlnActCoeff_dT () const
 Update the derivative of the log of the activity coefficients wrt T. More...
 
void s_update_dlnActCoeff_dX_ () const
 Internal routine that calculates the derivative of the activity coefficients wrt the mole fractions. More...
 
void s_update_dlnActCoeff_dlnX_diag () const
 Internal routine that calculates the total derivative of the activity coefficients with respect to the log of the mole fractions. More...
 

Additional Inherited Members

- Protected Member Functions inherited from GibbsExcessVPSSTP
void compositionChanged () override
 Apply changes to the state which are needed after the composition changes. More...
 
void calcDensity () override
 Calculate the density of the mixture using the partial molar volumes and mole fractions as input. More...
 
- Protected Member Functions inherited from VPStandardStateTP
virtual void _updateStandardStateThermo () const
 Updates the standard state thermodynamic functions at the current T and P of the solution. More...
 
void invalidateCache () override
 Invalidate any cached values which are normally updated only when a change in state is detected. More...
 
const vector< double > & Gibbs_RT_ref () const
 
- Protected Member Functions inherited from Phase
void assertCompressible (const string &setter) const
 Ensure that phase is compressible. More...
 
void assignDensity (const double density_)
 Set the internally stored constant density (kg/m^3) of the phase. More...
 
void setMolecularWeight (const int k, const double mw)
 Set the molecular weight of a single species to a given value. More...
 

Constructor & Destructor Documentation

◆ RedlichKisterVPSSTP()

RedlichKisterVPSSTP ( const string &  inputFile = "",
const string &  id = "" 
)
explicit

Construct a RedlichKisterVPSSTP object from an input file.

Parameters
inputFileName of the input file containing the phase definition. If blank, an empty phase will be created.
idname (ID) of the phase in the input file. If empty, the first phase definition in the input file will be used.

Definition at line 20 of file RedlichKisterVPSSTP.cpp.

Member Function Documentation

◆ type()

string type ( ) const
inlineoverridevirtual

String indicating the thermodynamic model implemented.

Usually corresponds to the name of the derived class, less any suffixes such as "Phase", TP", "VPSS", etc.

Since
Starting in Cantera 3.0, the name returned by this method corresponds to the canonical name used in the YAML input format.

Reimplemented from Phase.

Definition at line 244 of file RedlichKisterVPSSTP.h.

◆ enthalpy_mole()

double enthalpy_mole ( ) const
overridevirtual

Molar enthalpy. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 53 of file RedlichKisterVPSSTP.cpp.

◆ entropy_mole()

double entropy_mole ( ) const
overridevirtual

Molar entropy. Units: J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 64 of file RedlichKisterVPSSTP.cpp.

◆ cp_mole()

double cp_mole ( ) const
overridevirtual

Molar heat capacity at constant pressure. Units: J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 75 of file RedlichKisterVPSSTP.cpp.

◆ cv_mole()

double cv_mole ( ) const
overridevirtual

Molar heat capacity at constant volume. Units: J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 86 of file RedlichKisterVPSSTP.cpp.

◆ getLnActivityCoefficients()

void getLnActivityCoefficients ( double *  lnac) const
overridevirtual

Get the array of non-dimensional molar-based ln activity coefficients at the current solution temperature, pressure, and solution concentration.

Parameters
lnacOutput vector of ln activity coefficients. Length: m_kk.

Reimplemented from ThermoPhase.

Definition at line 27 of file RedlichKisterVPSSTP.cpp.

◆ getChemPotentials()

void getChemPotentials ( double *  mu) const
overridevirtual

Get the species chemical potentials. Units: J/kmol.

This function returns a vector of chemical potentials of the species in solution at the current temperature, pressure and mole fraction of the solution.

Parameters
muOutput vector of species chemical potentials. Length: m_kk. Units: J/kmol

Reimplemented from ThermoPhase.

Definition at line 39 of file RedlichKisterVPSSTP.cpp.

◆ getPartialMolarEnthalpies()

void getPartialMolarEnthalpies ( double *  hbar) const
overridevirtual

Returns an array of partial molar enthalpies for the species in the mixture.

Units (J/kmol)

For this phase, the partial molar enthalpies are equal to the standard state enthalpies modified by the derivative of the molality-based activity coefficient wrt temperature

\[ \bar h_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT} \]

Parameters
hbarVector of returned partial molar enthalpies (length m_kk, units = J/kmol)

Reimplemented from ThermoPhase.

Definition at line 91 of file RedlichKisterVPSSTP.cpp.

◆ getPartialMolarEntropies()

void getPartialMolarEntropies ( double *  sbar) const
overridevirtual

Returns an array of partial molar entropies for the species in the mixture.

For this phase, the partial molar entropies are equal to the standard state entropies modified by the derivative of the activity coefficient with respect to temperature:

\[ \bar s_k(T,P) = s^o_k(T,P) - R \ln( \gamma_k X_k) - R T \frac{d \ln(\gamma_k) }{dT} \]

Parameters
sbarVector of returned partial molar entropies (length m_kk, units = J/kmol/K)

Reimplemented from ThermoPhase.

Definition at line 119 of file RedlichKisterVPSSTP.cpp.

◆ getPartialMolarCp()

void getPartialMolarCp ( double *  cpbar) const
overridevirtual

Returns an array of partial molar heat capacities for the species in the mixture.

Units (J/kmol/K)

For this phase, the partial molar heat capacities are equal to the standard state heat capacities:

\[ \tilde{C}_{p,k}(T,P) = C^o_{p,k}(T,P) \]

Parameters
cpbarVector of returned partial molar heat capacities (length m_kk, units = J/kmol/K)

Reimplemented from ThermoPhase.

Definition at line 110 of file RedlichKisterVPSSTP.cpp.

◆ getPartialMolarVolumes()

void getPartialMolarVolumes ( double *  vbar) const
overridevirtual

Return an array of partial molar volumes for the species in the mixture.

Units: m^3/kmol.

Frequently, for this class of thermodynamics representations, the excess Volume due to mixing is zero. Here, we set it as a default. It may be overridden in derived classes.

Parameters
vbarOutput vector of species partial molar volumes. Length = m_kk. units are m^3/kmol.

Reimplemented from GibbsExcessVPSSTP.

Definition at line 140 of file RedlichKisterVPSSTP.cpp.

◆ getd2lnActCoeffdT2()

void getd2lnActCoeffdT2 ( double *  d2lnActCoeffdT2) const

Get the array of temperature second derivatives of the log activity coefficients.

units = 1/Kelvin

Parameters
d2lnActCoeffdT2Output vector of temperature 2nd derivatives of the log Activity Coefficients. length = m_kk

Definition at line 293 of file RedlichKisterVPSSTP.cpp.

◆ getdlnActCoeffdT()

void getdlnActCoeffdT ( double *  dlnActCoeffdT) const
overridevirtual

Get the array of temperature derivatives of the log activity coefficients.

units = 1/Kelvin

Parameters
dlnActCoeffdTOutput vector of temperature derivatives of the log Activity Coefficients. length = m_kk

Reimplemented from GibbsExcessVPSSTP.

Definition at line 285 of file RedlichKisterVPSSTP.cpp.

◆ initThermo()

void initThermo ( )
overridevirtual

Initialize the ThermoPhase object after all species have been set up.

This method is provided to allow subclasses to perform any initialization required after all species have been added. For example, it might be used to resize internal work arrays that must have an entry for each species. The base class implementation does nothing, and subclasses that do not require initialization do not need to overload this method. Derived classes which do override this function should call their parent class's implementation of this function as their last action.

When importing from an AnyMap phase description (or from a YAML file), setupPhase() adds all the species, stores the input data in m_input, and then calls this method to set model parameters from the data stored in m_input.

Reimplemented from ThermoPhase.

Definition at line 149 of file RedlichKisterVPSSTP.cpp.

◆ getParameters()

void getParameters ( AnyMap phaseNode) const
overridevirtual

Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function.

This does not include user-defined fields available in input().

Reimplemented from ThermoPhase.

Definition at line 165 of file RedlichKisterVPSSTP.cpp.

◆ addBinaryInteraction()

void addBinaryInteraction ( const string &  speciesA,
const string &  speciesB,
const double *  excess_enthalpy,
size_t  n_enthalpy,
const double *  excess_entropy,
size_t  n_entropy 
)

Add a binary species interaction with the specified parameters.

Parameters
speciesAname of the first species
speciesBname of the second species
excess_enthalpycoefficients of the excess enthalpy polynomial
n_enthalpynumber of excess enthalpy polynomial coefficients
excess_entropycoefficients of the excess entropy polynomial
n_entropynumber of excess entropy polynomial coefficients

Definition at line 455 of file RedlichKisterVPSSTP.cpp.

◆ getdlnActCoeffds()

void getdlnActCoeffds ( const double  dTds,
const double *const  dXds,
double *  dlnActCoeffds 
) const
overridevirtual

Get the change in activity coefficients wrt changes in state (temp, mole fraction, etc) along a line in parameter space or along a line in physical space.

Parameters
dTdsInput of temperature change along the path
dXdsInput vector of changes in mole fraction along the path. length = m_kk Along the path length it must be the case that the mole fractions sum to one.
dlnActCoeffdsOutput vector of the directional derivatives of the log Activity Coefficients along the path. length = m_kk units are 1/units(s). if s is a physical coordinate then the units are 1/m.

Reimplemented from ThermoPhase.

Definition at line 412 of file RedlichKisterVPSSTP.cpp.

◆ getdlnActCoeffdlnX_diag()

void getdlnActCoeffdlnX_diag ( double *  dlnActCoeffdlnX_diag) const
overridevirtual

Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only.

For ideal mixtures (unity activity coefficients), this can return zero. Implementations should take the derivative of the logarithm of the activity coefficient with respect to the logarithm of the mole fraction variable that represents the standard state. This quantity is to be used in conjunction with derivatives of that mole fraction variable when the derivative of the chemical potential is taken.

units = dimensionless

Parameters
dlnActCoeffdlnX_diagOutput vector of derivatives of the log Activity Coefficients wrt the mole fractions. length = m_kk

Reimplemented from ThermoPhase.

Definition at line 436 of file RedlichKisterVPSSTP.cpp.

◆ getdlnActCoeffdlnN_diag()

void getdlnActCoeffdlnN_diag ( double *  dlnActCoeffdlnN_diag) const
overridevirtual

Get the array of log species mole number derivatives of the log activity coefficients.

For ideal mixtures (unity activity coefficients), this can return zero. Implementations should take the derivative of the logarithm of the activity coefficient with respect to the logarithm of the concentration- like variable (for example, moles) that represents the standard state. This quantity is to be used in conjunction with derivatives of that species mole number variable when the derivative of the chemical potential is taken.

units = dimensionless

Parameters
dlnActCoeffdlnN_diagOutput vector of derivatives of the log Activity Coefficients. length = m_kk

Reimplemented from ThermoPhase.

Definition at line 425 of file RedlichKisterVPSSTP.cpp.

◆ getdlnActCoeffdlnN()

void getdlnActCoeffdlnN ( const size_t  ld,
double *const  dlnActCoeffdlnN 
)
overridevirtual

Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers.

Implementations should take the derivative of the logarithm of the activity coefficient with respect to a species log mole number (with all other species mole numbers held constant). The default treatment in the ThermoPhase object is to set this vector to zero.

units = 1 / kmol

dlnActCoeffdlnN[ ld * k + m] will contain the derivative of log act_coeff for the m-th species with respect to the number of moles of the k-th species.

\[ \frac{d \ln(\gamma_m) }{d \ln( n_k ) }\Bigg|_{n_i} \]

When implemented, this method is used within the VCS equilibrium solver to calculate the Jacobian elements, which accelerates convergence of the algorithm.

Parameters
ldNumber of rows in the matrix
dlnActCoeffdlnNOutput vector of derivatives of the log Activity Coefficients. length = m_kk * m_kk

Reimplemented from GibbsExcessVPSSTP.

Definition at line 444 of file RedlichKisterVPSSTP.cpp.

◆ initLengths()

void initLengths ( )
private

Initialize lengths of local variables after all species have been identified.

Definition at line 188 of file RedlichKisterVPSSTP.cpp.

◆ s_update_lnActCoeff()

void s_update_lnActCoeff ( ) const
private

Update the activity coefficients.

This function will be called to update the internally stored natural logarithm of the activity coefficients

Definition at line 193 of file RedlichKisterVPSSTP.cpp.

◆ s_update_dlnActCoeff_dT()

void s_update_dlnActCoeff_dT ( ) const
private

Update the derivative of the log of the activity coefficients wrt T.

This function will be called to update the internally stored derivative of the natural logarithm of the activity coefficients wrt temperature.

Definition at line 240 of file RedlichKisterVPSSTP.cpp.

◆ s_update_dlnActCoeff_dX_()

void s_update_dlnActCoeff_dX_ ( ) const
private

Internal routine that calculates the derivative of the activity coefficients wrt the mole fractions.

This routine calculates the the derivative of the activity coefficients wrt to mole fraction with all other mole fractions held constant. This is strictly not permitted. However, if the resulting matrix is multiplied by a permissible deltaX vector then everything is ok.

This is the natural way to handle concentration derivatives in this routine.

Definition at line 350 of file RedlichKisterVPSSTP.cpp.

◆ s_update_dlnActCoeff_dlnX_diag()

void s_update_dlnActCoeff_dlnX_diag ( ) const
private

Internal routine that calculates the total derivative of the activity coefficients with respect to the log of the mole fractions.

This function will be called to update the internally stored vector of the total derivatives (that is, not assuming other mole fractions are constant) of the natural logarithm of the activity coefficients with respect to the log of the mole fraction.

Definition at line 301 of file RedlichKisterVPSSTP.cpp.

Member Data Documentation

◆ m_pSpecies_A_ij

vector<size_t> m_pSpecies_A_ij
protected

vector of species indices representing species A in the interaction

Each Redlich-Kister excess Gibbs free energy term involves two species, A and B. This vector identifies species A.

Definition at line 422 of file RedlichKisterVPSSTP.h.

◆ m_pSpecies_B_ij

vector<size_t> m_pSpecies_B_ij
protected

vector of species indices representing species B in the interaction

Each Redlich-Kister excess Gibbs free energy term involves two species, A and B. This vector identifies species B.

Definition at line 429 of file RedlichKisterVPSSTP.h.

◆ m_HE_m_ij

vector<vector<double> > m_HE_m_ij
protected

Enthalpy term for the binary mole fraction interaction of the excess Gibbs free energy expression.

Definition at line 433 of file RedlichKisterVPSSTP.h.

◆ m_SE_m_ij

vector<vector<double> > m_SE_m_ij
protected

Entropy term for the binary mole fraction interaction of the excess Gibbs free energy expression.

Definition at line 437 of file RedlichKisterVPSSTP.h.

◆ dlnActCoeff_dX_

Array2D dlnActCoeff_dX_
mutableprotected

Two dimensional array of derivatives of activity coefficients wrt mole fractions.

Definition at line 441 of file RedlichKisterVPSSTP.h.


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