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:

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 by a SpeciesThermoInterpType 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 SpeciesThermoInterpType 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.

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

An example of the specification of a standard state using a temperature dependent standard state volume is given in the YAML API Reference.

Definition at line 111 of file PDSS_SSVol.h.

Public Member Functions
	PDSS_SSVol ()
	Default Constructor.

Molar Thermodynamic Properties of the Species Standard State
double	intEnergy_mole () const override
	Return the molar internal Energy in units of J kmol-1.

double	cv_mole () const override
	Return the molar const volume heat capacity in units of J kmol-1 K-1.

Mechanical Equation of State Properties
void	setPressure (double pres) override
	Sets the pressure in the object.

void	setTemperature (double temp) override
	Set the internal temperature.

void	setState_TP (double temp, double pres) override
	Set the internal temperature and pressure.

Miscellaneous properties of the standard state
double	satPressure (double t) override
	saturation pressure

Initialization of the Object
void	initThermo () override
	Initialization routine.

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

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

void	getParameters (AnyMap &eosNode) const override
	Store the parameters needed to reconstruct a copy of this PDSS object.

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

double	entropy_mole () const override
	Return the molar entropy in units of J kmol-1 K-1.

double	gibbs_mole () const override
	Return the molar Gibbs free energy in units of J kmol-1.

double	cp_mole () const override
	Return the molar const pressure heat capacity in units of J kmol-1 K-1.

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

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

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

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

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

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

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

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

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

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

double	density () const override
	Return the standard state density at standard state.

Public Member Functions inherited from PDSS
virtual void	setTemperature (double temp)
	Set the internal temperature.

virtual double	temperature () const
	Return the current stored temperature.

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

virtual double	critTemperature () const
	critical temperature

virtual double	critPressure () const
	critical pressure

virtual double	critDensity () const
	critical density

virtual double	satPressure (double T)
	saturation pressure

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

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

	PDSS ()=default
	Default Constructor.

	PDSS (const PDSS &b)=delete

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

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

double	minTemp () const
	return the minimum temperature

double	maxTemp () const
	return the minimum temperature

virtual double	pressure () const
	Returns the pressure (Pa)

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

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

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

void	setParameters (const AnyMap &node)
	Set model parameters from an AnyMap phase description, for example from the `equation-of-state` field of a species definition.

Private Types
enum class	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.

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

vector< double >	TCoeff_
	coefficients for the temperature representation

double	dVdT_
	Derivative of the volume wrt temperature.

double	d2VdT2_
	2nd derivative of the volume wrt temperature

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

double	m_cp0_R
	Reference state heat capacity divided by R.

double	m_s0_R
	Reference state entropy divided by R.

double	m_g0_RT
	Reference state Gibbs free energy divided by RT.

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

double	m_hss_RT
	Standard state enthalpy divided by RT.

double	m_cpss_R
	Standard state heat capacity divided by R.

double	m_sss_R
	Standard state entropy divided by R.

double	m_gss_RT
	Standard state Gibbs free energy divided by RT.

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

Protected Attributes inherited from PDSS
double	m_temp = -1.0
	Current temperature used by the PDSS object.

double	m_pres = -1.0
	State of the system - pressure.

double	m_p0 = -1.0
	Reference state pressure of the species.

double	m_minTemp = -1.0
	Minimum temperature.

double	m_maxTemp = 10000.0
	Maximum temperature.

double	m_mw = 0.0
	Molecular Weight of the species.

AnyMap	m_input
	Input data supplied via setParameters.

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

Member Enumeration Documentation

◆ SSVolume_Model

enum class 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 166 of file PDSS_SSVol.h.

Constructor & Destructor Documentation

◆ PDSS_SSVol()

PDSS_SSVol ( )

Default Constructor.

Definition at line 16 of file PDSS_SSVol.cpp.

Member Function Documentation

◆ intEnergy_mole()

double intEnergy_mole ( ) const

overridevirtual

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 84 of file PDSS_SSVol.cpp.

◆ cv_mole()

double cv_mole ( ) const

overridevirtual

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 90 of file PDSS_SSVol.cpp.

◆ setPressure()

void setPressure ( double pres )

overridevirtual

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 116 of file PDSS_SSVol.cpp.

◆ setTemperature()

void setTemperature ( double temp )

overridevirtual

Set the internal temperature.

Parameters

temp	Temperature (Kelvin)

Reimplemented from PDSS.

Definition at line 135 of file PDSS_SSVol.cpp.

◆ setState_TP()

void setState_TP	(	double	temp,
		double	pres
	)

overridevirtual

Set the internal temperature and pressure.

Parameters

temp	Temperature (Kelvin)
pres	pressure (Pascals)

Reimplemented from PDSS.

Definition at line 157 of file PDSS_SSVol.cpp.

◆ satPressure()

double satPressure ( double T )

overridevirtual

saturation pressure

Parameters

T	Temperature (Kelvin)

Reimplemented from PDSS.

Definition at line 163 of file PDSS_SSVol.cpp.

◆ initThermo()

void initThermo ( )

overridevirtual

Initialization routine.

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

Reimplemented from PDSS.

Definition at line 55 of file PDSS_SSVol.cpp.

◆ 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 21 of file PDSS_SSVol.cpp.

◆ 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 28 of file PDSS_SSVol.cpp.

◆ getParameters()

void getParameters ( AnyMap & eosNode ) const

overridevirtual

Store the parameters needed to reconstruct a copy of this PDSS object.

Reimplemented from PDSS.

Definition at line 35 of file PDSS_SSVol.cpp.

◆ calcMolarVolume()

void calcMolarVolume ( )

private

Does the internal calculation of the volume.

Definition at line 95 of file PDSS_SSVol.cpp.

Member Data Documentation

◆ volumeModel_

SSVolume_Model volumeModel_ = SSVolume_Model::tpoly

private

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

Definition at line 183 of file PDSS_SSVol.h.

◆ TCoeff_

vector<double> TCoeff_

private

coefficients for the temperature representation

Definition at line 186 of file PDSS_SSVol.h.

◆ dVdT_

double dVdT_

mutableprivate

Derivative of the volume wrt temperature.

Definition at line 189 of file PDSS_SSVol.h.

◆ d2VdT2_

double d2VdT2_

mutableprivate

2nd derivative of the volume wrt temperature

Definition at line 192 of file PDSS_SSVol.h.

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

Detailed Description

Specification of Species Standard State Properties

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ SSVolume_Model

Constructor & Destructor Documentation

◆ PDSS_SSVol()

Member Function Documentation

◆ intEnergy_mole()

◆ cv_mole()

◆ setPressure()

◆ setTemperature()

◆ setState_TP()

◆ satPressure()

◆ initThermo()

◆ setVolumePolynomial()

◆ setDensityPolynomial()

◆ getParameters()

◆ calcMolarVolume()

Member Data Documentation

◆ volumeModel_

◆ TCoeff_

◆ dVdT_

◆ d2VdT2_