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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Collaboration diagram for RedlichKisterVPSSTP:

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Public Member Functions
	RedlichKisterVPSSTP ()
	Constructor. More...

	RedlichKisterVPSSTP (const std::string &inputFile, const std::string &id="")
	Construct and initialize a RedlichKisterVPSSTP ThermoPhase object directly from an xml input file. More...

	RedlichKisterVPSSTP (XML_Node &phaseRef, const std::string &id="")
	Construct and initialize a RedlichKisterVPSSTP ThermoPhase object directly from an XML database. More...

	RedlichKisterVPSSTP (int testProb)
	Special constructor for a hard-coded problem. More...

	RedlichKisterVPSSTP (const RedlichKisterVPSSTP &b)
	Copy constructor. More...

RedlichKisterVPSSTP &	operator= (const RedlichKisterVPSSTP &b)
	Assignment operator. More...

virtual ThermoPhase *	duplMyselfAsThermoPhase () const
	Duplication routine for objects which inherit from ThermoPhase. More...

void	Vint (double &VintOut, double &voltsOut)
	Utility routine that calculates a literature expression. More...

Utilities
virtual int	eosType () const
	Equation of state type flag. More...

Molar Thermodynamic Properties
virtual doublereal	enthalpy_mole () const
	Molar enthalpy. Units: J/kmol. More...

virtual doublereal	entropy_mole () const
	Molar entropy. Units: J/kmol. More...

virtual doublereal	cp_mole () const
	Molar heat capacity at constant pressure. Units: J/kmol/K. More...

virtual doublereal	cv_mole () const
	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 \[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \] The quantity \(\mu_k^0(T,P)\) is the chemical potential at unit activity, which depends only on temperature and pressure.
virtual void	getLnActivityCoefficients (doublereal *lnac) const
	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
virtual void	getChemPotentials (doublereal *mu) const
	Get the species chemical potentials. Units: J/kmol. More...

virtual void	getPartialMolarEnthalpies (doublereal *hbar) const
	Returns an array of partial molar enthalpies for the species in the mixture. More...

virtual void	getPartialMolarEntropies (doublereal *sbar) const
	Returns an array of partial molar entropies for the species in the mixture. More...

virtual void	getPartialMolarCp (doublereal *cpbar) const
	Returns an array of partial molar entropies for the species in the mixture. More...

virtual void	getPartialMolarVolumes (doublereal *vbar) const
	Return an array of partial molar volumes for the species in the mixture. More...

void	getElectrochemPotentials (doublereal *mu) const
	Get the species electrochemical potentials. More...

virtual void	getd2lnActCoeffdT2 (doublereal *d2lnActCoeffdT2) const
	Get the array of temperature second derivatives of the log activity coefficients. More...

virtual void	getdlnActCoeffdT (doublereal *dlnActCoeffdT) const
	Get the array of temperature derivatives of the log activity coefficients. 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 files importCTML.cpp and ThermoFactory.cpp.
virtual void	initThermo ()

void	initThermoXML (XML_Node &phaseNode, const std::string &id)
	Import and initialize a ThermoPhase object. More...

Derivatives of Thermodynamic Variables needed for Applications
virtual void	getdlnActCoeffds (const doublereal dTds, const doublereal const dXds, doublereal dlnActCoeffds) const
	Get the change in activity coefficients w.r.t. More...

virtual void	getdlnActCoeffdlnX_diag (doublereal *dlnActCoeffdlnX_diag) const
	Get the array of log concentration-like derivatives of the log activity coefficients - diagonal component. More...

virtual void	getdlnActCoeffdlnN_diag (doublereal *dlnActCoeffdlnN_diag) const
	Get the array of derivatives of the log activity coefficients wrt mole numbers - diagonal only. More...

virtual void	getdlnActCoeffdlnN (const size_t ld, doublereal *const dlnActCoeffdlnN)
	Get the array of derivatives of the ln activity coefficients with respect to the ln species mole numbers. More...

Public Member Functions inherited from GibbsExcessVPSSTP
	GibbsExcessVPSSTP ()

	GibbsExcessVPSSTP (const GibbsExcessVPSSTP &b)
	Copy constructor. More...

GibbsExcessVPSSTP &	operator= (const GibbsExcessVPSSTP &b)
	Assignment operator. More...

virtual void	getActivityConcentrations (doublereal *c) const
	This method returns an array of generalized concentrations. More...

virtual doublereal	standardConcentration (size_t k=0) const
	The standard concentration \( C^0_k \) used to normalize the generalized concentration. More...

virtual doublereal	logStandardConc (size_t k=0) const
	Returns the natural logarithm of the standard concentration of the kth species. More...

virtual void	getUnitsStandardConc (double *uA, int k=0, int sizeUA=6) const
	Returns the units of the standard and generalized concentrations Note they have the same units, as their ratio is defined to be equal to the activity of the kth species in the solution, which is unitless. More...

virtual void	getActivities (doublereal *ac) const
	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...

virtual void	getActivityCoefficients (doublereal *ac) const
	Get the array of non-dimensional molar-based activity coefficients at the current solution temperature, pressure, and solution concentration. More...

virtual void	getdlnActCoeffdlnX (doublereal *dlnActCoeffdlnX) const
	Get the array of log concentration-like derivatives of the log activity coefficients. More...

void	getElectrochemPotentials (doublereal *mu) const
	Get the species electrochemical potentials. More...

virtual const vector_fp &	getPartialMolarVolumes () const

virtual void	setState_TP (doublereal t, doublereal p)
	Set the temperature (K) and pressure (Pa) More...

virtual void	setMassFractions (const doublereal *const y)
	Set the mass fractions to the specified values, and then normalize them so that they sum to 1.0. More...

virtual void	setMassFractions_NoNorm (const doublereal *const y)
	Set the mass fractions to the specified values without normalizing. More...

virtual void	setMoleFractions (const doublereal *const x)
	Set the mole fractions to the specified values, and then normalize them so that they sum to 1.0. More...

virtual void	setMoleFractions_NoNorm (const doublereal *const x)
	Set the mole fractions to the specified values without normalizing. More...

virtual void	setConcentrations (const doublereal *const c)
	Set the concentrations to the specified values within the phase. More...

virtual void	setPressure (doublereal p)
	Set the internally stored pressure (Pa) at constant temperature and composition. More...

Public Member Functions inherited from VPStandardStateTP
	VPStandardStateTP ()
	Constructor. More...

	VPStandardStateTP (const VPStandardStateTP &b)
	Copy Constructor. More...

VPStandardStateTP &	operator= (const VPStandardStateTP &b)
	Assignment operator. More...

virtual	~VPStandardStateTP ()
	Destructor. More...

virtual int	standardStateConvention () const
	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	getChemPotentials_RT (doublereal *mu) const
	Get the array of non-dimensional species chemical potentials. More...

virtual void	getStandardChemPotentials (doublereal *mu) const
	Get the array of chemical potentials at unit activity. More...

virtual void	getEnthalpy_RT (doublereal *hrt) const
	Get the nondimensional Enthalpy functions for the species at their standard states at the current T and P of the solution. More...

virtual void	getEntropy_R (doublereal *sr) const
	Get the array of nondimensional Enthalpy functions for the standard state species at the current T and P of the solution. More...

virtual void	getGibbs_RT (doublereal *grt) const
	Get the nondimensional Gibbs functions for the species at their standard states of solution at the current T and P of the solution. More...

void	getPureGibbs (doublereal *gpure) const
	Get the standard state Gibbs functions for each species at the current T and P. More...

virtual void	getIntEnergy_RT (doublereal *urt) const
	Returns the vector of nondimensional internal Energies of the standard state at the current temperature and pressure of the solution for each species. More...

virtual void	getCp_R (doublereal *cpr) const
	Get the nondimensional Heat Capacities at constant pressure for the standard state of the species at the current T and P. More...

virtual void	getStandardVolumes (doublereal *vol) const
	Get the molar volumes of each species in their standard states at the current T and P of the solution. More...

virtual const vector_fp &	getStandardVolumes () const

virtual void	setTemperature (const doublereal temp)
	Set the temperature of the phase. More...

doublereal	pressure () const
	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...

virtual void	getEnthalpy_RT_ref (doublereal *hrt) const
	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...

virtual void	getGibbs_RT_ref (doublereal *grt) const
	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...

virtual void	getGibbs_ref (doublereal *g) const

virtual void	getEntropy_R_ref (doublereal *er) const

virtual void	getCp_R_ref (doublereal *cprt) const

virtual void	getStandardVolumes_ref (doublereal *vol) const
	Get the molar volumes of the species reference states at the current T and P_ref of the solution. More...

virtual void	setParametersFromXML (const XML_Node &eosdata)
	Set equation of state parameter values from XML entries. More...

void	setVPSSMgr (VPSSMgr *vp_ptr)
	set the VPSS Mgr More...

VPSSMgr *	provideVPSSMgr ()
	Return a pointer to the VPSSMgr for this phase. More...

void	createInstallPDSS (size_t k, const XML_Node &s, const XML_Node *phaseNode_ptr)

PDSS *	providePDSS (size_t k)

const PDSS *	providePDSS (size_t k) const

Public Member Functions inherited from ThermoPhase
	ThermoPhase ()
	Constructor. More...

virtual	~ThermoPhase ()
	Destructor. Deletes the species thermo manager. More...

	ThermoPhase (const ThermoPhase &right)
	Copy Constructor for the ThermoPhase object. More...

ThermoPhase &	operator= (const ThermoPhase &right)
	Assignment operator. More...

doublereal	_RT () const
	Return the Gas Constant multiplied by the current temperature. More...

virtual doublereal	refPressure () const
	Returns the reference pressure in Pa. More...

virtual doublereal	minTemp (size_t k=npos) const
	Minimum temperature for which the thermodynamic data for the species or phase are valid. More...

doublereal	Hf298SS (const int k) const
	Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More...

virtual void	modifyOneHf298SS (const int k, const doublereal Hf298New)
	Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1) More...

virtual doublereal	maxTemp (size_t k=npos) const
	Maximum temperature for which the thermodynamic data for the species are valid. More...

bool	chargeNeutralityNecessary () const
	Returns the chargeNeutralityNecessity boolean. More...

virtual doublereal	intEnergy_mole () const
	Molar internal energy. Units: J/kmol. More...

virtual doublereal	gibbs_mole () const
	Molar Gibbs function. Units: J/kmol. More...

virtual doublereal	cv_vib (int, double) const

virtual doublereal	isothermalCompressibility () const
	Returns the isothermal compressibility. Units: 1/Pa. More...

virtual doublereal	thermalExpansionCoeff () const
	Return the volumetric thermal expansion coefficient. Units: 1/K. More...

void	setElectricPotential (doublereal v)
	Set the electric potential of this phase (V). More...

doublereal	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 (doublereal *mu) const
	Get the species electrochemical potentials. More...

virtual void	getPartialMolarIntEnergies (doublereal *ubar) const
	Return an array of partial molar internal energies for the species in the mixture. More...

virtual void	getdPartialMolarVolumes_dT (doublereal *d_vbar_dT) const
	Return an array of derivatives of partial molar volumes wrt temperature for the species in the mixture. More...

virtual void	getdPartialMolarVolumes_dP (doublereal *d_vbar_dP) const
	Return an array of derivatives of partial molar volumes wrt pressure for the species in the mixture. More...

virtual void	getdStandardVolumes_dT (doublereal *d_vol_dT) const
	Get the derivative of the molar volumes of the species standard states wrt temperature at the current T and P of the solution. More...

virtual void	getdStandardVolumes_dP (doublereal *d_vol_dP) const
	Get the derivative molar volumes of the species standard states wrt pressure at the current T and P of the solution. More...

virtual void	getIntEnergy_RT_ref (doublereal *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...

virtual void	setReferenceComposition (const doublereal *const x)
	Sets the reference composition. More...

virtual void	getReferenceComposition (doublereal *const x) const
	Gets the reference composition. More...

doublereal	enthalpy_mass () const
	Specific enthalpy. More...

doublereal	intEnergy_mass () const
	Specific internal energy. More...

doublereal	entropy_mass () const
	Specific entropy. More...

doublereal	gibbs_mass () const
	Specific Gibbs function. More...

doublereal	cp_mass () const
	Specific heat at constant pressure. More...

doublereal	cv_mass () const
	Specific heat at constant volume. More...

virtual void	setToEquilState (const doublereal *lambda_RT)
	This method is used by the ChemEquil equilibrium solver. More...

void	setElementPotentials (const vector_fp &lambda)
	Stores the element potentials in the ThermoPhase object. More...

bool	getElementPotentials (doublereal *lambda) const
	Returns the element potentials stored in the ThermoPhase object. More...

virtual doublereal	critTemperature () const
	Critical temperature (K). More...

virtual doublereal	critPressure () const
	Critical pressure (Pa). More...

virtual doublereal	critDensity () const
	Critical density (kg/m3). More...

virtual doublereal	satTemperature (doublereal p) const
	Return the saturation temperature given the pressure. More...

virtual doublereal	satPressure (doublereal t)
	Return the saturation pressure given the temperature. More...

virtual doublereal	vaporFraction () const
	Return the fraction of vapor at the current conditions. More...

virtual void	setState_Tsat (doublereal t, doublereal x)
	Set the state to a saturated system at a particular temperature. More...

virtual void	setState_Psat (doublereal p, doublereal x)
	Set the state to a saturated system at a particular pressure. More...

void	saveSpeciesData (const size_t k, const XML_Node *const data)
	Store a reference pointer to the XML tree containing the species data for this phase. More...

const std::vector< const XML_Node * > &	speciesData () const
	Return a pointer to the vector of XML nodes containing the species data for this phase. More...

void	setSpeciesThermo (SpeciesThermo *spthermo)
	Install a species thermodynamic property manager. More...

virtual SpeciesThermo &	speciesThermo (int k=-1)
	Return a changeable reference to the calculation manager for species reference-state thermodynamic properties. More...

virtual void	initThermoFile (const std::string &inputFile, const std::string &id)

virtual void	installSlavePhases (Cantera::XML_Node *phaseNode)
	Add in species from Slave phases. More...

virtual void	setParameters (int n, doublereal *const c)
	Set the equation of state parameters. More...

virtual void	getParameters (int &n, doublereal *const c) const
	Get the equation of state parameters in a vector. More...

virtual void	setStateFromXML (const XML_Node &state)
	Set the initial state of the phase to the conditions specified in the state XML element. More...

virtual void	getdlnActCoeffdlnN_numderiv (const size_t ld, doublereal *const dlnActCoeffdlnN)

virtual std::string	report (bool show_thermo=true) const
	returns a summary of the state of the phase as a string More...

virtual void	reportCSV (std::ofstream &csvFile) const
	returns a summary of the state of the phase to a comma separated file. More...

virtual void	setState_TPX (doublereal t, doublereal p, const doublereal *x)
	Set the temperature (K), pressure (Pa), and mole fractions. More...

virtual void	setState_TPX (doublereal t, doublereal p, compositionMap &x)
	Set the temperature (K), pressure (Pa), and mole fractions. More...

virtual void	setState_TPX (doublereal t, doublereal p, const std::string &x)
	Set the temperature (K), pressure (Pa), and mole fractions. More...

virtual void	setState_TPY (doublereal t, doublereal p, const doublereal *y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...

virtual void	setState_TPY (doublereal t, doublereal p, compositionMap &y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...

virtual void	setState_TPY (doublereal t, doublereal p, const std::string &y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...

virtual void	setState_PX (doublereal p, doublereal *x)
	Set the pressure (Pa) and mole fractions. More...

virtual void	setState_PY (doublereal p, doublereal *y)
	Set the internally stored pressure (Pa) and mass fractions. More...

virtual void	setState_HP (doublereal h, doublereal p, doublereal tol=1.e-4)
	Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase. More...

virtual void	setState_UV (doublereal u, doublereal v, doublereal tol=1.e-4)
	Set the specific internal energy (J/kg) and specific volume (m^3/kg). More...

virtual void	setState_SP (doublereal s, doublereal p, doublereal tol=1.e-4)
	Set the specific entropy (J/kg/K) and pressure (Pa). More...

virtual void	setState_SV (doublereal s, doublereal v, doublereal tol=1.e-4)
	Set the specific entropy (J/kg/K) and specific volume (m^3/kg). More...

Public Member Functions inherited from Phase
	Phase ()
	Default constructor. More...

virtual	~Phase ()
	Destructor. More...

	Phase (const Phase &right)
	Copy Constructor. More...

Phase &	operator= (const Phase &right)
	Assignment operator. More...

XML_Node &	xml ()
	Returns a reference to the XML_Node stored for the phase. More...

void	saveState (vector_fp &state) const
	Save the current internal state of the phase Write to vector 'state' the current internal state. More...

void	saveState (size_t lenstate, doublereal *state) const
	Write to array 'state' the current internal state. More...

void	restoreState (const vector_fp &state)
	Restore a state saved on a previous call to saveState. More...

void	restoreState (size_t lenstate, const doublereal *state)
	Restore the state of the phase from a previously saved state vector. More...

doublereal	molecularWeight (size_t k) const
	Molecular weight of species `k`. More...

void	getMolecularWeights (vector_fp &weights) const
	Copy the vector of molecular weights into vector weights. More...

void	getMolecularWeights (doublereal *weights) const
	Copy the vector of molecular weights into array weights. More...

const vector_fp &	molecularWeights () const
	Return a const reference to the internal vector of molecular weights. More...

doublereal	size (size_t k) const
	This routine returns the size of species k. More...

doublereal	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...

doublereal	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 void	freezeSpecies ()
	Call when finished adding species. More...

bool	speciesFrozen ()
	True if freezeSpecies has been called. More...

virtual bool	ready () const

int	stateMFNumber () const
	Return the State Mole Fraction Number. More...

std::string	id () const
	Return the string id for the phase. More...

void	setID (const std::string &id)
	Set the string id for the phase. More...

std::string	name () const
	Return the name of the phase. More...

void	setName (const std::string &nm)
	Sets the string name for the phase. More...

std::string	elementName (size_t m) const
	Name of the element with index m. More...

size_t	elementIndex (const std::string &name) const
	Return the index of element named 'name'. More...

const std::vector< std::string > &	elementNames () const
	Return a read-only reference to the vector of element names. More...

doublereal	atomicWeight (size_t m) const
	Atomic weight of element m. More...

doublereal	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_fp &	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 Throws an exception if m is greater than nElements()-1. More...

void	checkElementArraySize (size_t mm) const
	Check that an array size is at least nElements() Throws an exception if mm is less than nElements(). More...

doublereal	nAtoms (size_t k, size_t m) const
	Number of atoms of element `m` in species `k`. More...

void	getAtoms (size_t k, double *atomArray) const
	Get a vector containing the atomic composition of species k. More...

size_t	speciesIndex (const std::string &name) const
	Returns the index of a species named 'name' within the Phase object. More...

std::string	speciesName (size_t k) const
	Name of the species with index k. More...

std::string	speciesSPName (int k) const
	Returns the expanded species name of a species, including the phase name This is guaranteed to be unique within a Cantera problem. More...

const std::vector< std::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 Throws an exception if k is greater than nSpecies()-1. More...

void	checkSpeciesArraySize (size_t kk) const
	Check that an array size is at least nSpecies() Throws an exception if kk is less than nSpecies(). More...

void	setMoleFractionsByName (compositionMap &xMap)
	Set the species mole fractions by name. More...

void	setMoleFractionsByName (const std::string &x)
	Set the mole fractions of a group of species by name. More...

void	setMassFractionsByName (compositionMap &yMap)
	Set the species mass fractions by name. More...

void	setMassFractionsByName (const std::string &x)
	Set the species mass fractions by name. More...

void	setState_TRX (doublereal t, doublereal dens, const doublereal *x)
	Set the internally stored temperature (K), density, and mole fractions. More...

void	setState_TRX (doublereal t, doublereal dens, compositionMap &x)
	Set the internally stored temperature (K), density, and mole fractions. More...

void	setState_TRY (doublereal t, doublereal dens, const doublereal *y)
	Set the internally stored temperature (K), density, and mass fractions. More...

void	setState_TRY (doublereal t, doublereal dens, compositionMap &y)
	Set the internally stored temperature (K), density, and mass fractions. More...

void	setState_TNX (doublereal t, doublereal n, const doublereal *x)
	Set the internally stored temperature (K), molar density (kmol/m^3), and mole fractions. More...

void	setState_TR (doublereal t, doublereal rho)
	Set the internally stored temperature (K) and density (kg/m^3) More...

void	setState_TX (doublereal t, doublereal *x)
	Set the internally stored temperature (K) and mole fractions. More...

void	setState_TY (doublereal t, doublereal *y)
	Set the internally stored temperature (K) and mass fractions. More...

void	setState_RX (doublereal rho, doublereal *x)
	Set the density (kg/m^3) and mole fractions. More...

void	setState_RY (doublereal rho, doublereal *y)
	Set the density (kg/m^3) and mass fractions. More...

void	getMoleFractionsByName (compositionMap &x) const
	Get the mole fractions by name. More...

doublereal	moleFraction (size_t k) const
	Return the mole fraction of a single species. More...

doublereal	moleFraction (const std::string &name) const
	Return the mole fraction of a single species. More...

doublereal	massFraction (size_t k) const
	Return the mass fraction of a single species. More...

doublereal	massFraction (const std::string &name) const
	Return the mass fraction of a single species. More...

void	getMoleFractions (doublereal *const x) const
	Get the species mole fraction vector. More...

void	getMassFractions (doublereal *const y) const
	Get the species mass fractions. More...

const doublereal *	massFractions () const
	Return a const pointer to the mass fraction array. More...

void	getConcentrations (doublereal *const c) const
	Get the species concentrations (kmol/m^3). More...

doublereal	concentration (const size_t k) const
	Concentration of species k. More...

const doublereal *	moleFractdivMMW () const
	Returns a const pointer to the start of the moleFraction/MW array. More...

doublereal	temperature () const
	Temperature (K). More...

virtual doublereal	density () const
	Density (kg/m^3). More...

doublereal	molarDensity () const
	Molar density (kmol/m^3). More...

doublereal	molarVolume () const
	Molar volume (m^3/kmol). More...

virtual void	setDensity (const doublereal density_)
	Set the internally stored density (kg/m^3) of the phase Note the density of a phase is an independent variable. More...

virtual void	setMolarDensity (const doublereal molarDensity)
	Set the internally stored molar density (kmol/m^3) of the phase. More...

doublereal	mean_X (const doublereal *const Q) const
	Evaluate the mole-fraction-weighted mean of an array Q. More...

doublereal	mean_Y (const doublereal *const Q) const
	Evaluate the mass-fraction-weighted mean of an array Q. More...

doublereal	meanMolecularWeight () const
	The mean molecular weight. Units: (kg/kmol) More...

doublereal	sum_xlogx () const
	Evaluate \( \sum_k X_k \log X_k \). More...

doublereal	sum_xlogQ (doublereal *const Q) const
	Evaluate \( \sum_k X_k \log Q_k \). More...

void	addElement (const std::string &symbol, doublereal weight=-12345.0)
	Add an element. More...

void	addElement (const XML_Node &e)
	Add an element from an XML specification. More...

void	addUniqueElement (const std::string &symbol, doublereal weight=-12345.0, int atomicNumber=0, doublereal entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS)
	Add an element, checking for uniqueness The uniqueness is checked by comparing the string symbol. More...

void	addUniqueElement (const XML_Node &e)
	Add an element, checking for uniqueness The uniqueness is checked by comparing the string symbol. More...

void	addElementsFromXML (const XML_Node &phase)
	Add all elements referenced in an XML_Node tree. More...

void	freezeElements ()
	Prohibit addition of more elements, and prepare to add species. More...

bool	elementsFrozen ()
	True if freezeElements has been called. More...

size_t	addUniqueElementAfterFreeze (const std::string &symbol, doublereal weight, int atomicNumber, doublereal entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS)
	Add an element after elements have been frozen, checking for uniqueness The uniqueness is checked by comparing the string symbol. More...

void	addSpecies (const std::string &name, const doublereal *comp, doublereal charge=0.0, doublereal size=1.0)

void	addUniqueSpecies (const std::string &name, const doublereal *comp, doublereal charge=0.0, doublereal size=1.0)
	Add a species to the phase, checking for uniqueness of the name This routine checks for uniqueness of the string name. More...

Protected Attributes
size_t	numBinaryInteractions_
	number of binary interaction expressions More...

std::vector< size_t >	m_pSpecies_A_ij
	vector of species indices representing species A in the interaction More...

std::vector< size_t >	m_pSpecies_B_ij
	vector of species indices representing species B in the interaction More...

std::vector< size_t >	m_N_ij
	Vector of the length of the polynomial for the interaction. More...

std::vector< vector_fp >	m_HE_m_ij
	Enthalpy term for the binary mole fraction interaction of the excess gibbs free energy expression. More...

std::vector< vector_fp >	m_SE_m_ij
	Entropy term for the binary mole fraction interaction of the excess gibbs free energy expression. More...

int	formRedlichKister_
	form of the RedlichKister interaction expression More...

int	formTempModel_
	form of the temperature dependence of the Redlich-Kister interaction expression More...

Array2D	dlnActCoeff_dX_
	Two dimensional array of derivatives of activity coefficients wrt mole fractions. More...

Protected Attributes inherited from GibbsExcessVPSSTP
std::vector< doublereal >	moleFractions_
	Storage for the current values of the mole fractions of the species. More...

std::vector< doublereal >	lnActCoeff_Scaled_
	Storage for the current values of the activity coefficients of the species. More...

std::vector< doublereal >	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...

std::vector< doublereal >	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...

std::vector< doublereal >	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...

std::vector< doublereal >	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...

std::vector< doublereal >	m_pp
	Temporary storage space that is fair game. More...

Protected Attributes inherited from VPStandardStateTP
doublereal	m_Pcurrent
	Current value of the pressure - state variable. More...

doublereal	m_Tlast_ss
	The last temperature at which the standard statethermodynamic properties were calculated at. More...

doublereal	m_Plast_ss
	The last pressure at which the Standard State thermodynamic properties were calculated at. More...

doublereal	m_P0

VPSSMgr *	m_VPSS_ptr
	Pointer to the VPSS manager that calculates all of the standard state info efficiently. More...

std::vector< PDSS * >	m_PDSS_storage
	Storage for the PDSS objects for the species. More...

Protected Attributes inherited from ThermoPhase
SpeciesThermo *	m_spthermo
	Pointer to the calculation manager for species reference-state thermodynamic properties. More...

std::vector< const XML_Node * >	m_speciesData
	Vector of pointers to the species databases. More...

doublereal	m_phi
	Stored value of the electric potential for this phase. More...

vector_fp	m_lambdaRRT
	Vector of element potentials. More...

bool	m_hasElementPotentials
	Boolean indicating whether there is a valid set of saved element potentials for this phase. More...

bool	m_chargeNeutralityNecessary
	Boolean indicating whether a charge neutrality condition is a necessity. More...

int	m_ssConvention
	Contains the standard state convention. More...

std::vector< doublereal >	xMol_Ref
	Reference Mole Fraction Composition. More...

Protected Attributes inherited from Phase
size_t	m_kk
	Number of species in the phase. More...

size_t	m_ndim
	Dimensionality of the phase. More...

vector_fp	m_speciesComp
	Atomic composition of the species. More...

vector_fp	m_speciesSize
	Vector of species sizes. More...

vector_fp	m_speciesCharge
	Vector of species charges. length m_kk. More...

Private Member Functions
void	readXMLBinarySpecies (XML_Node &xmlBinarySpecies)
	Process an XML node called "binaryNeutralSpeciesParameters". More...

void	resizeNumInteractions (const size_t num)
	Resize internal arrays within the object that depend upon the number of binary Redlich-Kister interaction terms. More...

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...

doublereal	err (const std::string &msg) const
	Error function. More...

Additional Inherited Members
Protected Member Functions inherited from GibbsExcessVPSSTP
double	checkMFSum (const doublereal *const x) const
	utility routine to check mole fraction sum More...

void	calcDensity ()
	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...

const vector_fp &	Gibbs_RT_ref () const

Protected Member Functions inherited from ThermoPhase
virtual void	getCsvReportData (std::vector< std::string > &names, std::vector< vector_fp > &data) const
	Fills `names` and `data` with the column names and species thermo properties to be included in the output of the reportCSV method. More...

Protected Member Functions inherited from Phase
void	init (const vector_fp &mw)

void	setMolecularWeight (const int k, const double mw)
	Set the molecular weight of a single species to a given value. More...

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.

Several concepts are introduced. The first concept is there are temporary variables for holding the species standard state values of Cp, H, S, G, and V at the last temperature and pressure called. These functions are not recalculated if a new call is made using the previous temperature and pressure. Currently, these variables and the calculation method are handled by the VPSSMgr class, for which VPStandardStateTP owns a pointer to.

To support the above functionality, pressure and temperature variables, m_plast_ss and m_tlast_ss, are kept which store the last pressure and temperature used in the evaluation of standard state properties.

This class is usually used for nearly incompressible phases. For those phases, it makes sense to change the equation of state independent variable from density to pressure. The variable m_Pcurrent contains the current value of the pressure within the phase.

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

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

and where we can break down the gibbs free energy contributions into enthalpy and entropy contributions

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

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

where n is the total moles in the solution.

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

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

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

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

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:

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

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 reate 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 260 of file RedlichKisterVPSSTP.h.

Constructor & Destructor Documentation

RedlichKisterVPSSTP ( )

Constructor.

This doesn't do much more than initialize constants with default values.

Definition at line 26 of file RedlichKisterVPSSTP.cpp.

Referenced by RedlichKisterVPSSTP::duplMyselfAsThermoPhase().

RedlichKisterVPSSTP	(	const std::string &	inputFile,
		const std::string &	id = `""`
	)

Construct and initialize a RedlichKisterVPSSTP ThermoPhase object directly from an xml input file.

Parameters

inputFile	Name of the input file containing the phase XML data to set up the object
id	ID of the phase in the input file. Defaults to the empty string.

Definition at line 40 of file RedlichKisterVPSSTP.cpp.

References ThermoPhase::initThermoFile().

RedlichKisterVPSSTP	(	XML_Node &	phaseRef,
		const std::string &	id = `""`
	)

Construct and initialize a RedlichKisterVPSSTP ThermoPhase object directly from an XML database.

Parameters

phaseRef	XML phase node containing the description of the phase
id	id attribute containing the name of the phase. (default is the empty string)

Definition at line 56 of file RedlichKisterVPSSTP.cpp.

References Cantera::findXMLPhase(), and Cantera::importPhase().

RedlichKisterVPSSTP ( int testProb )

Special constructor for a hard-coded problem.

Parameters

testProb Hard-coded value. Only the value of 1 is used. It's for a LiKCl system -> test to predict the eutectic and liquidus correctly.

Deprecated:: To be refactored into a standalone test

Definition at line 72 of file RedlichKisterVPSSTP.cpp.

References ThermoPhase::initThermoFile(), RedlichKisterVPSSTP::m_HE_m_ij, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, Cantera::npos, RedlichKisterVPSSTP::numBinaryInteractions_, and Phase::speciesIndex().

RedlichKisterVPSSTP ( const RedlichKisterVPSSTP & b )

Copy constructor.

Parameters

b	class to be copied

Definition at line 119 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::operator=().

Member Function Documentation

RedlichKisterVPSSTP & operator= ( const RedlichKisterVPSSTP & b )

Assignment operator.

Parameters

b	class to be copied.

Definition at line 135 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::dlnActCoeff_dX_, RedlichKisterVPSSTP::formRedlichKister_, RedlichKisterVPSSTP::formTempModel_, RedlichKisterVPSSTP::m_HE_m_ij, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, RedlichKisterVPSSTP::numBinaryInteractions_, and GibbsExcessVPSSTP::operator=().

Referenced by RedlichKisterVPSSTP::RedlichKisterVPSSTP().

ThermoPhase * duplMyselfAsThermoPhase ( ) const

virtual

Duplication routine for objects which inherit from ThermoPhase.

This virtual routine can be used to duplicate thermophase objects inherited from ThermoPhase even if the application only has a pointer to ThermoPhase to work with.

Reimplemented from GibbsExcessVPSSTP.

Definition at line 157 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::RedlichKisterVPSSTP().

int eosType ( ) const

virtual

Equation of state type flag.

The ThermoPhase base class returns zero. Subclasses should define this to return a unique non-zero value. Known constants defined for this purpose are listed in mix_defs.h.

Reimplemented from GibbsExcessVPSSTP.

Definition at line 162 of file RedlichKisterVPSSTP.cpp.

Referenced by RedlichKisterVPSSTP::err().

doublereal enthalpy_mole ( ) const

virtual

Molar enthalpy. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 223 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::getPartialMolarEnthalpies(), GibbsExcessVPSSTP::moleFractions_, and Phase::nSpecies().

doublereal entropy_mole ( ) const

virtual

Molar entropy. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 235 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::getPartialMolarEntropies(), GibbsExcessVPSSTP::moleFractions_, and Phase::nSpecies().

doublereal cp_mole ( ) const

virtual

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

Reimplemented from ThermoPhase.

Definition at line 247 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::getPartialMolarCp(), GibbsExcessVPSSTP::moleFractions_, and Phase::nSpecies().

Referenced by RedlichKisterVPSSTP::cv_mole().

doublereal cv_mole ( ) const

virtual

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

Reimplemented from ThermoPhase.

Definition at line 259 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::cp_mole(), and Cantera::GasConstant.

void getLnActivityCoefficients ( doublereal * lnac ) const

virtual

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

Parameters

lnac	Output vector of ln activity coefficients. Length: m_kk.

Reimplemented from ThermoPhase.

Definition at line 171 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::lnActCoeff_Scaled_, Phase::m_kk, and RedlichKisterVPSSTP::s_update_lnActCoeff().

void getChemPotentials ( doublereal * mu ) const

virtual

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

mu	Output vector of species chemical potentials. Length: m_kk. Units: J/kmol

Reimplemented from ThermoPhase.

Definition at line 199 of file RedlichKisterVPSSTP.cpp.

References Cantera::GasConstant, VPStandardStateTP::getStandardChemPotentials(), GibbsExcessVPSSTP::lnActCoeff_Scaled_, Phase::m_kk, GibbsExcessVPSSTP::moleFractions_, RedlichKisterVPSSTP::s_update_lnActCoeff(), Cantera::SmallNumber, and Phase::temperature().

Referenced by RedlichKisterVPSSTP::getElectrochemPotentials().

void getPartialMolarEnthalpies ( doublereal * hbar ) const

virtual

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

hbar	Vector of returned partial molar enthalpies (length m_kk, units = J/kmol)

Reimplemented from ThermoPhase.

Definition at line 264 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::dlnActCoeffdT_Scaled_, Cantera::GasConstant, VPStandardStateTP::getEnthalpy_RT(), Phase::m_kk, RedlichKisterVPSSTP::s_update_dlnActCoeff_dT(), RedlichKisterVPSSTP::s_update_lnActCoeff(), and Phase::temperature().

Referenced by RedlichKisterVPSSTP::enthalpy_mole().

void getPartialMolarEntropies ( doublereal * sbar ) const

virtual

Returns an array of partial molar entropies 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 activity coefficient wrt temperature

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

Parameters

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

Reimplemented from ThermoPhase.

Definition at line 315 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::dlnActCoeffdT_Scaled_, Cantera::GasConstant, VPStandardStateTP::getEntropy_R(), GibbsExcessVPSSTP::lnActCoeff_Scaled_, Phase::m_kk, GibbsExcessVPSSTP::moleFractions_, RedlichKisterVPSSTP::s_update_dlnActCoeff_dT(), RedlichKisterVPSSTP::s_update_lnActCoeff(), Cantera::SmallNumber, and Phase::temperature().

Referenced by RedlichKisterVPSSTP::entropy_mole().

void getPartialMolarCp ( doublereal * cpbar ) const

virtual

Returns an array of partial molar entropies 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 activity coefficient wrt temperature

\[ ??????????????? \bar s_k(T,P) = s^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT} - R \ln( \gamma_k X_k) - R T \frac{d \ln(\gamma_k) }{dT} ??????????????? \]

Parameters

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

Reimplemented from ThermoPhase.

Definition at line 290 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::d2lnActCoeffdT2_Scaled_, GibbsExcessVPSSTP::dlnActCoeffdT_Scaled_, Cantera::GasConstant, VPStandardStateTP::getCp_R(), Phase::m_kk, RedlichKisterVPSSTP::s_update_dlnActCoeff_dT(), RedlichKisterVPSSTP::s_update_lnActCoeff(), and Phase::temperature().

Referenced by RedlichKisterVPSSTP::cp_mole().

void getPartialMolarVolumes ( doublereal * vbar ) const

virtual

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

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

Reimplemented from GibbsExcessVPSSTP.

Definition at line 342 of file RedlichKisterVPSSTP.cpp.

References VPStandardStateTP::getStandardVolumes(), and Phase::m_kk.

void getElectrochemPotentials ( doublereal * mu ) const

Get the species electrochemical potentials.

These are partial molar quantities. This method adds a term \( Fz_k \phi_k \) to the to each chemical potential.

Units: J/kmol

Parameters

mu	output vector containing the species electrochemical potentials. Length: m_kk., units = J/kmol

Definition at line 190 of file RedlichKisterVPSSTP.cpp.

References Phase::charge(), ThermoPhase::electricPotential(), RedlichKisterVPSSTP::getChemPotentials(), and Phase::m_kk.

void getd2lnActCoeffdT2 ( doublereal * d2lnActCoeffdT2 ) const

virtual

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

This function is a virtual class, but it first appears in GibbsExcessVPSSTP class and derived classes from GibbsExcessVPSSTP.

units = 1/Kelvin

Parameters

d2lnActCoeffdT2 Output vector of temperature 2nd derivatives of the log Activity Coefficients. length = m_kk

Definition at line 560 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::d2lnActCoeffdT2_Scaled_, Phase::m_kk, and RedlichKisterVPSSTP::s_update_dlnActCoeff_dT().

void getdlnActCoeffdT ( doublereal * dlnActCoeffdT ) const

virtual

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

This function is a virtual class, but it first appears in GibbsExcessVPSSTP class and derived classes from GibbsExcessVPSSTP.

units = 1/Kelvin

Parameters

dlnActCoeffdT Output vector of temperature derivatives of the log Activity Coefficients. length = m_kk

Reimplemented from GibbsExcessVPSSTP.

Definition at line 552 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::dlnActCoeffdT_Scaled_, Phase::m_kk, and RedlichKisterVPSSTP::s_update_dlnActCoeff_dT().

void initThermo ( )

virtual

Initialize. 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. When importing a CTML phase description, this method is called just prior to returning from function importPhase.

See Also: importCTML.cpp

Reimplemented from GibbsExcessVPSSTP.

Definition at line 361 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::initLengths(), and GibbsExcessVPSSTP::initThermo().

void initThermoXML	(	XML_Node &	phaseNode,
		const std::string &	id
	)

virtual

Import and initialize a ThermoPhase object.

Parameters

phaseNode	This object must be the phase node of a complete XML tree description of the phase, including all of the species data. In other words while "phase" must point to an XML phase object, it must have sibling nodes "speciesData" that describe the species in the phase.
id	ID of the phase. If nonnull, a check is done to see if phaseNode is pointing to the phase with the correct id.

Reimplemented from VPStandardStateTP.

Definition at line 373 of file RedlichKisterVPSSTP.cpp.

References XML_Node::attrib(), XML_Node::child(), XML_Node::hasChild(), XML_Node::id(), VPStandardStateTP::initThermoXML(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), and RedlichKisterVPSSTP::readXMLBinarySpecies().

void getdlnActCoeffds	(	const doublereal	dTds,
		const doublereal *const	dXds,
		doublereal *	dlnActCoeffds
	)		const

virtual

Get the change in activity coefficients w.r.t.

change in state (temp, mole fraction, etc.) along a line in parameter space or along a line in physical space

Parameters

dTds	Input of temperature change along the path
dXds	Input 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.
dlnActCoeffds	Output 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 639 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::dlnActCoeff_dX_, GibbsExcessVPSSTP::dlnActCoeffdT_Scaled_, Phase::m_kk, RedlichKisterVPSSTP::s_update_dlnActCoeff_dT(), and RedlichKisterVPSSTP::s_update_dlnActCoeff_dX_().

void getdlnActCoeffdlnX_diag ( doublereal * dlnActCoeffdlnX_diag ) const

virtual

Get the array of log concentration-like derivatives of the log activity coefficients - diagonal component.

This function is a virtual method. 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.

units = dimensionless

Parameters

dlnActCoeffdlnX_diag Output vector of the diagonal component of the log(mole fraction) derivatives of the log Activity Coefficients. length = m_kk

Reimplemented from ThermoPhase.

Definition at line 663 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::dlnActCoeffdlnX_diag_, Phase::m_kk, and RedlichKisterVPSSTP::s_update_dlnActCoeff_dX_().

void getdlnActCoeffdlnN_diag ( doublereal * dlnActCoeffdlnN_diag ) const

virtual

Get the array of derivatives of the log activity coefficients wrt mole numbers - diagonal only.

This function is a virtual method. 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 (i.e. mole fraction, molality, etc.) that represents the standard state.

units = dimensionless

Parameters

dlnActCoeffdlnN_diag Output vector of the diagonal entries for the log(mole fraction) derivatives of the log Activity Coefficients. length = m_kk

Reimplemented from VPStandardStateTP.

Definition at line 652 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::dlnActCoeff_dX_, Phase::m_kk, GibbsExcessVPSSTP::moleFractions_, and RedlichKisterVPSSTP::s_update_dlnActCoeff_dX_().

void getdlnActCoeffdlnN	(	const size_t	ld,
		doublereal *const	dlnActCoeffdlnN
	)

virtual

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

Implementations should take the derivative of the logarithm of the activity coefficient with respect to a log of a species mole number (with all other species mole numbers held constant)

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.

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

Parameters

ld	Number of rows in the matrix
dlnActCoeffdlnN	Output vector of derivatives of the log Activity Coefficients. length = m_kk * m_kk

Reimplemented from GibbsExcessVPSSTP.

Definition at line 671 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::dlnActCoeffdlnN_, Phase::m_kk, and RedlichKisterVPSSTP::s_update_dlnActCoeff_dX_().

void readXMLBinarySpecies ( XML_Node & xmlBinarySpecies )

private

Process an XML node called "binaryNeutralSpeciesParameters".

This node contains all of the parameters necessary to describe the Redlich-Kister model for a particular binary interaction. This function reads the XML file and writes the coefficients it finds to an internal data structures.

Parameters

xmlBinarySpecies Reference to the XML_Node named "binaryNeutralSpeciesParameters" containing the binary interaction

Definition at line 693 of file RedlichKisterVPSSTP.cpp.

References XML_Node::attrib(), Phase::charge(), XML_Node::child(), ctml::getFloatArray(), Cantera::lowercase(), RedlichKisterVPSSTP::m_HE_m_ij, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, XML_Node::name(), XML_Node::nChildren(), Cantera::npos, RedlichKisterVPSSTP::numBinaryInteractions_, RedlichKisterVPSSTP::resizeNumInteractions(), Phase::speciesIndex(), and Phase::speciesName().

Referenced by RedlichKisterVPSSTP::initThermoXML().

void resizeNumInteractions ( const size_t num )

private

Resize internal arrays within the object that depend upon the number of binary Redlich-Kister interaction terms.

Parameters

num	Number of binary Redlich-Kister interaction terms

Definition at line 682 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::dlnActCoeff_dX_, RedlichKisterVPSSTP::m_HE_m_ij, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, Cantera::npos, RedlichKisterVPSSTP::numBinaryInteractions_, and Array2D::resize().

Referenced by RedlichKisterVPSSTP::readXMLBinarySpecies().

void initLengths ( )

private

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

Definition at line 367 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::dlnActCoeffdlnN_, Phase::m_kk, Phase::nSpecies(), and Array2D::resize().

Referenced by RedlichKisterVPSSTP::initThermo().

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 435 of file RedlichKisterVPSSTP.cpp.

References Cantera::GasConstant, GibbsExcessVPSSTP::lnActCoeff_Scaled_, RedlichKisterVPSSTP::m_HE_m_ij, Phase::m_kk, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, GibbsExcessVPSSTP::moleFractions_, RedlichKisterVPSSTP::numBinaryInteractions_, and Phase::temperature().

Referenced by RedlichKisterVPSSTP::getChemPotentials(), RedlichKisterVPSSTP::getLnActivityCoefficients(), RedlichKisterVPSSTP::getPartialMolarCp(), RedlichKisterVPSSTP::getPartialMolarEnthalpies(), and RedlichKisterVPSSTP::getPartialMolarEntropies().

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 506 of file RedlichKisterVPSSTP.cpp.

References GibbsExcessVPSSTP::d2lnActCoeffdT2_Scaled_, GibbsExcessVPSSTP::dlnActCoeffdT_Scaled_, Phase::m_kk, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, GibbsExcessVPSSTP::moleFractions_, and RedlichKisterVPSSTP::numBinaryInteractions_.

Referenced by RedlichKisterVPSSTP::getd2lnActCoeffdT2(), RedlichKisterVPSSTP::getdlnActCoeffds(), RedlichKisterVPSSTP::getdlnActCoeffdT(), RedlichKisterVPSSTP::getPartialMolarCp(), RedlichKisterVPSSTP::getPartialMolarEnthalpies(), and RedlichKisterVPSSTP::getPartialMolarEntropies().

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 568 of file RedlichKisterVPSSTP.cpp.

References RedlichKisterVPSSTP::dlnActCoeff_dX_, RedlichKisterVPSSTP::m_HE_m_ij, Phase::m_kk, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, GibbsExcessVPSSTP::moleFractions_, RedlichKisterVPSSTP::numBinaryInteractions_, Phase::temperature(), and Array2D::zero().

Referenced by RedlichKisterVPSSTP::getdlnActCoeffdlnN(), RedlichKisterVPSSTP::getdlnActCoeffdlnN_diag(), RedlichKisterVPSSTP::getdlnActCoeffdlnX_diag(), and RedlichKisterVPSSTP::getdlnActCoeffds().

void Vint	(	double &	VintOut,
		double &	voltsOut
	)

Utility routine that calculates a literature expression.

Parameters

VintOut	Output contribution to the voltage corresponding to nonideal term
voltsOut	Output contribution to the voltage corresponding to nonideal term and mf term

Definition at line 782 of file RedlichKisterVPSSTP.cpp.

References Cantera::GasConstant, GibbsExcessVPSSTP::lnActCoeff_Scaled_, RedlichKisterVPSSTP::m_HE_m_ij, Phase::m_kk, RedlichKisterVPSSTP::m_N_ij, RedlichKisterVPSSTP::m_pSpecies_A_ij, RedlichKisterVPSSTP::m_pSpecies_B_ij, RedlichKisterVPSSTP::m_SE_m_ij, GibbsExcessVPSSTP::moleFractions_, RedlichKisterVPSSTP::numBinaryInteractions_, and Phase::temperature().