Class for pressure dependent standard states that uses a standard state volume model of some sort. More...

#include <PDSS_SSVol.h>

Inheritance diagram for PDSS_SSVol:

Collaboration diagram for PDSS_SSVol:

Public Member Functions
	PDSS_SSVol ()
	Default Constructor. More...

Molar Thermodynamic Properties of the Species Standard State in the Solution
virtual doublereal	intEnergy_mole () const
	Return the molar internal Energy in units of J kmol-1. More...

virtual doublereal	cv_mole () const
	Return the molar const volume heat capacity in units of J kmol-1 K-1. More...

Mechanical Equation of State Properties
virtual void	setPressure (doublereal pres)
	Sets the pressure in the object. More...

virtual void	setTemperature (doublereal temp)
	Set the internal temperature. More...

virtual void	setState_TP (doublereal temp, doublereal pres)
	Set the internal temperature and pressure. More...

virtual void	setState_TR (doublereal temp, doublereal rho)
	Set the internal temperature and density. More...

Miscellaneous properties of the standard state
virtual doublereal	satPressure (doublereal t)
	saturation pressure More...

Initialization of the Object
virtual void	initThermo ()
	Initialization routine. More...

void	setVolumePolynomial (double *coeffs)
	Set polynomial coefficients for the standard state molar volume as a function of temperature. More...

void	setDensityPolynomial (double *coeffs)
	Set polynomial coefficients for the standard state density as a function of temperature. More...

virtual void	setParametersFromXML (const XML_Node &speciesNode)
	Initialization routine for the PDSS object based on the speciesNode. More...

Public Member Functions inherited from PDSS_Nondimensional
virtual doublereal	enthalpy_mole () const
	Return the molar enthalpy in units of J kmol-1. More...

virtual doublereal	entropy_mole () const
	Return the molar entropy in units of J kmol-1 K-1. More...

virtual doublereal	gibbs_mole () const
	Return the molar Gibbs free energy in units of J kmol-1. More...

virtual doublereal	cp_mole () const
	Return the molar const pressure heat capacity in units of J kmol-1 K-1. More...

virtual double	enthalpy_RT_ref () const
	Return the molar enthalpy divided by RT at reference pressure. More...

virtual double	entropy_R_ref () const
	Return the molar entropy divided by R at reference pressure. More...

virtual double	gibbs_RT_ref () const
	Return the molar Gibbs free energy divided by RT at reference pressure. More...

virtual double	cp_R_ref () const
	Return the molar heat capacity divided by R at reference pressure. More...

virtual double	molarVolume_ref () const
	Return the molar volume at reference pressure. More...

virtual double	enthalpy_RT () const
	Return the standard state molar enthalpy divided by RT. More...

virtual double	entropy_R () const
	Return the standard state entropy divided by RT. More...

virtual double	gibbs_RT () const
	Return the molar Gibbs free energy divided by RT. More...

virtual double	cp_R () const
	Return the molar const pressure heat capacity divided by RT. More...

virtual double	molarVolume () const
	Return the molar volume at standard state. More...

virtual double	density () const
	Return the standard state density at standard state. More...

Public Member Functions inherited from PDSS
	PDSS ()
	Default Constructor. More...

	PDSS (const PDSS &b)=delete

PDSS &	operator= (const PDSS &b)=delete

virtual	~PDSS ()

virtual doublereal	enthalpyDelp_mole () const
	Get the difference in the standard state enthalpy between the current pressure and the reference pressure, p0. More...

virtual doublereal	entropyDelp_mole () const
	Get the difference in the standard state entropy between the current pressure and the reference pressure, p0. More...

virtual doublereal	gibbsDelp_mole () const
	Get the difference in the standard state Gibbs free energy between the current pressure and the reference pressure, p0. More...

virtual doublereal	cpDelp_mole () const
	Get the difference in standard state heat capacity between the current pressure and the reference pressure, p0. More...

doublereal	refPressure () const
	Return the reference pressure for this phase. More...

doublereal	minTemp () const
	return the minimum temperature More...

doublereal	maxTemp () const
	return the minimum temperature More...

virtual doublereal	pressure () const
	Returns the pressure (Pa) More...

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

virtual doublereal	temperature () const
	Return the current stored temperature. More...

virtual doublereal	critTemperature () const
	critical temperature More...

virtual doublereal	critPressure () const
	critical pressure More...

virtual doublereal	critDensity () const
	critical density More...

doublereal	molecularWeight () const
	Return the molecular weight of the species in units of kg kmol-1. More...

void	setMolecularWeight (doublereal mw)
	Set the molecular weight of the species. More...

void	setReferenceThermo (shared_ptr< SpeciesThermoInterpType > stit)
	Set the SpeciesThermoInterpType object used to calculate reference state properties. More...

virtual bool	useSTITbyPDSS () const
	Returns 'true' if this object should be used in an STITbyPDSS object in the phase's reference thermo manager, or 'false' if a separate SpeciesThermoInterpType should be constructed. More...

virtual void	setParent (VPStandardStateTP *phase, size_t k)
	Set the parent VPStandardStateTP object of this PDSS object. More...

virtual void	reportParams (size_t &kindex, int &type, doublereal *const c, doublereal &minTemp, doublereal &maxTemp, doublereal &refPressure) const
	This utility function reports back the type of parameterization and all of the parameters for the species, index. More...

Private Types
enum	SSVolume_Model { tpoly, density_tpoly }
	Types of general formulations for the specification of the standard state volume. More...

Private Member Functions
void	calcMolarVolume ()
	Does the internal calculation of the volume. More...

Private Attributes
SSVolume_Model	volumeModel_
	Enumerated data type describing the type of volume model used to calculate the standard state volume of the species. More...

vector_fp	TCoeff_
	coefficients for the temperature representation More...

doublereal	dVdT_
	Derivative of the volume wrt temperature. More...

doublereal	d2VdT2_
	2nd derivative of the volume wrt temperature More...

Additional Inherited Members
Protected Attributes inherited from PDSS_Nondimensional
double	m_h0_RT
	Reference state enthalpy divided by RT. More...

double	m_cp0_R
	Reference state heat capacity divided by R. More...

double	m_s0_R
	Reference state entropy divided by R. More...

double	m_g0_RT
	Reference state Gibbs free energy divided by RT. More...

double	m_V0
	Reference state molar volume (m^3/kmol) More...

double	m_hss_RT
	Standard state enthalpy divided by RT. More...

double	m_cpss_R
	Standard state heat capacity divided by R. More...

double	m_sss_R
	Standard state entropy divided by R. More...

double	m_gss_RT
	Standard state Gibbs free energy divided by RT. More...

double	m_Vss
	Standard State molar volume (m^3/kmol) More...

Protected Attributes inherited from PDSS
doublereal	m_temp
	Current temperature used by the PDSS object. More...

doublereal	m_pres
	State of the system - pressure. More...

doublereal	m_p0
	Reference state pressure of the species. More...

doublereal	m_minTemp
	Minimum temperature. More...

doublereal	m_maxTemp
	Maximum temperature. More...

doublereal	m_mw
	Molecular Weight of the species. More...

shared_ptr< SpeciesThermoInterpType >	m_spthermo
	Pointer to the species thermodynamic property manager. More...

Detailed Description

Class for pressure dependent standard states that uses a standard state volume model of some sort.

Attention: This class currently does not have any test cases or examples. Its implementation may be incomplete, and future changes to Cantera may unexpectedly cause this class to stop working. If you use this class, please consider contributing examples or test cases. In the absence of new tests or examples, this class may be deprecated and removed in a future version of Cantera. See https://github.com/Cantera/cantera/issues/267 for additional information.

Class PDSS_SSVol is an implementation class that compute the properties of a single species in a phase at its standard states, for a range of temperatures and pressures. This particular class assumes that the calculation of the thermodynamics functions can be separated into a temperature polynomial representation for thermo functions that can be handled bey a SimpleThermo object and a separate calculation for the standard state volume. The Models include a cubic polynomial in temperature for either the standard state volume or the standard state density. The manager uses a SimpleThermo object to handle the calculation of the reference state. This object then adds the pressure dependencies and the volume terms to these thermo functions to complete the representation.

The class includes the following models for the representation of the standard state volume:

Temperature polynomial for the standard state volume
- This standard state model is invoked with the keyword "temperature_polynomial". The standard state volume is considered a function of temperature only.
  \[ V^o_k(T,P) = a_0 + a_1 T + a_2 T^2 + a_3 T^3 \]
Temperature polynomial for the standard state density
- This standard state model is invoked with the keyword "density_temperature_polynomial". The standard state density, which is the inverse of the volume, is considered a function of temperature only.
  \[ {\rho}^o_k(T,P) = \frac{M_k}{V^o_k(T,P)} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 \]

Specification of Species Standard State Properties

The standard molar Gibbs free energy for species k is determined from the enthalpy and entropy expressions

\[ G^o_k(T,P) = H^o_k(T,P) - S^o_k(T,P) \]

The enthalpy is calculated mostly from the MultiSpeciesThermo object's enthalpy evaluator. The dependence on pressure originates from the Maxwell relation

\[ {\left(\frac{dH^o_k}{dP}\right)}_T = T {\left(\frac{dS^o_k}{dP}\right)}_T + V^o_k \]

which is equal to

\[ {\left(\frac{dH^o_k}{dP}\right)}_T = V^o_k - T {\left(\frac{dV^o_k}{dT}\right)}_P \]

The entropy is calculated mostly from the MultiSpeciesThermo objects entropy evaluator. The dependence on pressure originates from the Maxwell relation:

\[ {\left(\frac{dS^o_k}{dP}\right)}_T = - {\left(\frac{dV^o_k}{dT}\right)}_P \]

The standard state constant-pressure heat capacity expression is obtained from taking the temperature derivative of the Maxwell relation involving the enthalpy given above to yield an expression for the pressure dependence of the heat capacity.

\[ {\left(\frac{d{C}^o_{p,k}}{dP}\right)}_T = - T {\left(\frac{{d}^2{V}^o_k}{{dT}^2}\right)}_T \]

The standard molar Internal Energy for species k is determined from the following relation.

\[ U^o_k(T,P) = H^o_k(T,P) - p V^o_k \]

XML Example

An example of the specification of a standard state for the LiCl molten salt which has a temperature dependent standard state volume.

<speciesData id="species_MoltenSalt">
<species name="LiCl(L)">
   <atomArray> Li:1 Cl:1 </atomArray>
   <standardState  model="density_temperature_polynomial">
      <densityTemperaturePolynomial units="gm/cm3" >
         1.98715, -5.890906E-4, 0.0, 0.0
      </densityTemperaturePolynomial>
   </standardState>
   <thermo>
     <Shomate Pref="1 bar" Tmax="2000.0" Tmin="700.0">
       <floatArray size="7">
         73.18025, -9.047232, -0.316390,
         0.079587, 0.013594, -417.1314,
         157.6711
       </floatArray>
     </Shomate>
   </thermo>
 </species>
 </speciesData>

Definition at line 133 of file PDSS_SSVol.h.

Member Enumeration Documentation

◆ SSVolume_Model

enum SSVolume_Model

strongprivate

Types of general formulations for the specification of the standard state volume.

Enumerator

tpoly

This approximation is for a species with a cubic polynomial in temperature.

V^ss = a_0 + a_1 T + a_2 T^2 + a_3 T^3

density_tpoly

This approximation is for a species where the density is expressed as a cubic polynomial in temperature.

V^ss = M / (a_0 + a_1 T + a_2 T^2 + a_3 T^3)

Definition at line 188 of file PDSS_SSVol.h.

Constructor & Destructor Documentation

◆ PDSS_SSVol()

PDSS_SSVol ( )

Default Constructor.

Definition at line 19 of file PDSS_SSVol.cpp.

Member Function Documentation

◆ intEnergy_mole()

doublereal intEnergy_mole ( ) const

virtual

Return the molar internal Energy in units of J kmol-1.

Returns: The species standard state internal Energy in J kmol-1 at the current temperature and pressure.

Reimplemented from PDSS.

Definition at line 74 of file PDSS_SSVol.cpp.

References Cantera::GasConstant, PDSS_Nondimensional::m_h0_RT, PDSS::m_pres, PDSS::m_temp, and PDSS_Nondimensional::m_Vss.

◆ cv_mole()

doublereal cv_mole ( ) const

virtual

Return the molar const volume heat capacity in units of J kmol-1 K-1.

Returns: The species standard state Cv in J kmol-1 K-1 at the current temperature and pressure.

Reimplemented from PDSS.

Definition at line 80 of file PDSS_SSVol.cpp.

References PDSS_Nondimensional::cp_mole(), and PDSS_Nondimensional::m_V0.

◆ setPressure()

void setPressure ( doublereal pres )

virtual

Sets the pressure in the object.

Currently, this sets the pressure in the PDSS object. It is indeterminant what happens to the owning VPStandardStateTP object.

Parameters

pres	Pressure to be set (Pascal)

Reimplemented from PDSS.

Definition at line 106 of file PDSS_SSVol.cpp.

References PDSS::m_p0, and PDSS::m_pres.

◆ setTemperature()

void setTemperature ( doublereal temp )

virtual

Set the internal temperature.

Parameters

temp	Temperature (Kelvin)

Reimplemented from PDSS.

Definition at line 125 of file PDSS_SSVol.cpp.

References PDSS_SSVol::calcMolarVolume(), PDSS_Nondimensional::m_cp0_R, PDSS_Nondimensional::m_g0_RT, PDSS_Nondimensional::m_h0_RT, PDSS::m_p0, PDSS::m_pres, PDSS_Nondimensional::m_s0_R, PDSS::m_spthermo, and PDSS::m_temp.

Referenced by PDSS_SSVol::setState_TP(), and PDSS_SSVol::setState_TR().

◆ setState_TP()

void setState_TP	(	doublereal	temp,
		doublereal	pres
	)

virtual

Set the internal temperature and pressure.

Parameters

temp	Temperature (Kelvin)
pres	pressure (Pascals)

Reimplemented from PDSS.

Definition at line 147 of file PDSS_SSVol.cpp.

References PDSS::m_pres, and PDSS_SSVol::setTemperature().

◆ setState_TR()

void setState_TR	(	doublereal	temp,
		doublereal	rho
	)

virtual

Set the internal temperature and density.

Parameters

temp	Temperature (Kelvin)
rho	Density (kg m-3)

Reimplemented from PDSS.

Definition at line 153 of file PDSS_SSVol.cpp.

References PDSS::m_mw, PDSS_Nondimensional::m_Vss, and PDSS_SSVol::setTemperature().

◆ satPressure()

doublereal satPressure ( doublereal T )

virtual

saturation pressure

Parameters

T	Temperature (Kelvin)

Reimplemented from PDSS.

Definition at line 163 of file PDSS_SSVol.cpp.

◆ initThermo()

void initThermo ( )

virtual

Initialization routine.

This is a cascading call, where each level should call the the parent level.

Reimplemented from PDSS.

Definition at line 66 of file PDSS_SSVol.cpp.

References PDSS::initThermo(), PDSS::m_maxTemp, PDSS::m_minTemp, PDSS::m_p0, and PDSS::m_spthermo.

◆ setVolumePolynomial()

void setVolumePolynomial ( double * coeffs )

Set polynomial coefficients for the standard state molar volume as a function of temperature.

Cubic polynomial (4 coefficients). Leading coefficient is the constant (temperature-independent) term [m^3/kmol].

Definition at line 52 of file PDSS_SSVol.cpp.

References PDSS_SSVol::TCoeff_, PDSS_SSVol::tpoly, and PDSS_SSVol::volumeModel_.

Referenced by PDSS_SSVol::setParametersFromXML().

◆ setDensityPolynomial()

void setDensityPolynomial ( double * coeffs )

Set polynomial coefficients for the standard state density as a function of temperature.

Cubic polynomial (4 coefficients). Leading coefficient is the constant (temperature-independent) term [kg/m^3].

Definition at line 59 of file PDSS_SSVol.cpp.

References PDSS_SSVol::density_tpoly, PDSS_SSVol::TCoeff_, and PDSS_SSVol::volumeModel_.

Referenced by PDSS_SSVol::setParametersFromXML().

◆ setParametersFromXML()

void setParametersFromXML ( const XML_Node & speciesNode )

virtual

Initialization routine for the PDSS object based on the speciesNode.

This is a cascading call, where each level should call the the parent level. This function is called before initThermo()

Reimplemented from PDSS.

Definition at line 25 of file PDSS_SSVol.cpp.

References XML_Node::attrib(), XML_Node::findByName(), Cantera::getFloatArray(), XML_Node::name(), PDSS_SSVol::setDensityPolynomial(), PDSS::setParametersFromXML(), and PDSS_SSVol::setVolumePolynomial().

◆ calcMolarVolume()

void calcMolarVolume ( )

private

Does the internal calculation of the volume.

Definition at line 85 of file PDSS_SSVol.cpp.

References PDSS_SSVol::d2VdT2_, PDSS_SSVol::density_tpoly, PDSS_SSVol::dVdT_, PDSS::m_mw, PDSS::m_temp, PDSS_Nondimensional::m_V0, PDSS_Nondimensional::m_Vss, PDSS_SSVol::TCoeff_, PDSS_SSVol::tpoly, and PDSS_SSVol::volumeModel_.

Referenced by PDSS_SSVol::setTemperature().

Member Data Documentation

◆ volumeModel_

SSVolume_Model volumeModel_

private

Enumerated data type describing the type of volume model used to calculate the standard state volume of the species.

Definition at line 205 of file PDSS_SSVol.h.

Referenced by PDSS_SSVol::calcMolarVolume(), PDSS_SSVol::setDensityPolynomial(), and PDSS_SSVol::setVolumePolynomial().

◆ TCoeff_

vector_fp TCoeff_

private

coefficients for the temperature representation

Definition at line 208 of file PDSS_SSVol.h.

Referenced by PDSS_SSVol::calcMolarVolume(), PDSS_SSVol::setDensityPolynomial(), and PDSS_SSVol::setVolumePolynomial().

◆ dVdT_

doublereal dVdT_

mutableprivate

Derivative of the volume wrt temperature.

Definition at line 211 of file PDSS_SSVol.h.

Referenced by PDSS_SSVol::calcMolarVolume().

◆ d2VdT2_

doublereal d2VdT2_

mutableprivate

2nd derivative of the volume wrt temperature

Definition at line 214 of file PDSS_SSVol.h.

Referenced by PDSS_SSVol::calcMolarVolume().

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

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Specification of Species Standard State Properties

XML Example

Member Enumeration Documentation

◆ SSVolume_Model

Constructor & Destructor Documentation

◆ PDSS_SSVol()

Member Function Documentation

◆ intEnergy_mole()

◆ cv_mole()

◆ setPressure()

◆ setTemperature()

◆ setState_TP()

◆ setState_TR()

◆ satPressure()

◆ initThermo()

◆ setVolumePolynomial()

◆ setDensityPolynomial()

◆ setParametersFromXML()

◆ calcMolarVolume()

Member Data Documentation

◆ volumeModel_

◆ TCoeff_

◆ dVdT_

◆ d2VdT2_