The Mu0Poly class implements an interpolation of the Gibbs free energy based on a piecewise constant heat capacity approximation. More...

#include <Mu0Poly.h>

Inheritance diagram for Mu0Poly:

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Detailed Description

The Mu0Poly class implements an interpolation of the Gibbs free energy based on a piecewise constant heat capacity approximation.

The Mu0Poly class implements a piecewise constant heat capacity approximation. of the standard state chemical potential of one species at a single reference pressure. The chemical potential is input as a series of ( \( T \), \( \mu^o(T) \)) values. The first temperature is assumed to be equal to 298.15 K; however, this may be relaxed in the future. This information, and an assumption of a constant heat capacity within each interval is enough to calculate all thermodynamic functions.

The piece-wise constant heat capacity is calculated from the change in the chemical potential over each interval. Once the heat capacity is known, the other thermodynamic functions may be determined. The basic equation for going from temperature point 1 to temperature point 2 are as follows for \( T \), \( T_1 <= T <= T_2 \)

\[ \mu^o(T_1) = h^o(T_1) - T_1 * s^o(T_1) \]

\[ \mu^o(T_2) - \mu^o(T_1) = Cp^o(T_1)(T_2 - T_1) - Cp^o(T_1)(T_2)ln(\frac{T_2}{T_1}) - s^o(T_1)(T_2 - T_1) \]

\[ s^o(T_2) = s^o(T_1) + Cp^o(T_1)ln(\frac{T_2}{T_1}) \]

\[ h^o(T_2) = h^o(T_1) + Cp^o(T_1)(T_2 - T_1) \]

Within each interval the following relations are used. For \( T \), \( T_1 <= T <= T_2 \)

\[ \mu^o(T) = \mu^o(T_1) + Cp^o(T_1)(T - T_1) - Cp^o(T_1)(T_2)ln(\frac{T}{T_1}) - s^o(T_1)(T - T_1) \]

\[ s^o(T) = s^o(T_1) + Cp^o(T_1)ln(\frac{T}{T_1}) \]

\[ h^o(T) = h^o(T_1) + Cp^o(T_1)(T - T_1) \]

Notes about temperature interpolation for \( T < T_1 \) and \( T > T_{npoints} \): These are achieved by assuming a constant heat capacity equal to the value in the closest temperature interval. No error is thrown.

Note: In the future, a better assumption about the heat capacity may be employed, so that it can be continuous.

Definition at line 73 of file Mu0Poly.h.

Public Member Functions
	Mu0Poly (double tlow, double thigh, double pref, const double *coeffs)
	Constructor with all input data.

void	setParameters (double h0, const map< double, double > &T_mu)
	Set parameters for \( \mu^o(T) \).

int	reportType () const override
	Returns an integer representing the type of parameterization.

void	updateProperties (const double tt, double cp_R, double h_RT, double s_R) const override
	Update the properties for this species, given a temperature polynomial.

void	updatePropertiesTemp (const double temp, double cp_R, double h_RT, double *s_R) const override
	Compute the reference-state property of one species.

size_t	nCoeffs () const override
	This utility function returns the number of coefficients for a given type of species parameterization.

void	reportParameters (size_t &n, int &type, double &tlow, double &thigh, double &pref, double *const coeffs) const override
	This utility function returns the type of parameterization and all of the parameters for the species.

void	getParameters (AnyMap &thermo) const override
	Store the parameters of the species thermo object such that an identical species thermo object could be reconstructed using the newSpeciesThermo() function.

Public Member Functions inherited from SpeciesThermoInterpType
	SpeciesThermoInterpType (double tlow, double thigh, double pref)

	SpeciesThermoInterpType (const SpeciesThermoInterpType &b)=delete

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

virtual double	minTemp () const
	Returns the minimum temperature that the thermo parameterization is valid.

virtual void	setMinTemp (double Tmin)
	Set the minimum temperature at which the thermo parameterization is valid.

virtual double	maxTemp () const
	Returns the maximum temperature that the thermo parameterization is valid.

virtual void	setMaxTemp (double Tmax)
	Set the maximum temperature at which the thermo parameterization is valid.

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

virtual void	setRefPressure (double Pref)
	Set the reference pressure [Pa].

virtual void	validate (const string &name)
	Check for problems with the parameterization, and generate warnings or throw and exception if any are found.

virtual int	reportType () const
	Returns an integer representing the type of parameterization.

virtual size_t	temperaturePolySize () const
	Number of terms in the temperature polynomial for this parameterization.

virtual void	updateTemperaturePoly (double T, double *T_poly) const
	Given the temperature T, compute the terms of the temperature polynomial T_poly.

virtual void	updateProperties (const double tt, double cp_R, double h_RT, double s_R) const
	Update the properties for this species, given a temperature polynomial.

virtual void	updatePropertiesTemp (const double temp, double cp_R, double h_RT, double *s_R) const
	Compute the reference-state property of one species.

virtual size_t	nCoeffs () const
	This utility function returns the number of coefficients for a given type of species parameterization.

virtual void	reportParameters (size_t &index, int &type, double &minTemp, double &maxTemp, double &refPressure, double *const coeffs) const
	This utility function returns the type of parameterization and all of the parameters for the species.

AnyMap	parameters (bool withInput=true) const
	Return the parameters of the species thermo object such that an identical species thermo object could be reconstructed using the newSpeciesThermo() function.

virtual double	reportHf298 (double *const h298=0) const
	Report the 298 K Heat of Formation of the standard state of one species (J kmol-1)

virtual void	modifyOneHf298 (const size_t k, const double Hf298New)
	Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1)

virtual void	resetHf298 ()
	Restore the original heat of formation for this species.

const AnyMap &	input () const
	Access input data associated with the species thermo definition.

AnyMap &	input ()

Protected Attributes
size_t	m_numIntervals = 0
	Number of intervals in the interpolating linear approximation.

double	m_H298 = 0.0
	Value of the enthalpy at T = 298.15.

vector< double >	m_t0_int
	Points at which the standard state chemical potential are given.

vector< double >	m_mu0_R_int
	Mu0's are primary input data.

vector< double >	m_h0_R_int
	Dimensionless Enthalpies at the temperature points.

vector< double >	m_s0_R_int
	Entropy at the points.

vector< double >	m_cp0_R_int
	Heat capacity at the points.

Protected Attributes inherited from SpeciesThermoInterpType
double	m_lowT = 0.0
	lowest valid temperature

double	m_highT = 0.0
	Highest valid temperature.

double	m_Pref = 0.0
	Reference state pressure.

AnyMap	m_input

Additional Inherited Members
virtual void	getParameters (AnyMap &thermo) const
	Store the parameters of the species thermo object such that an identical species thermo object could be reconstructed using the newSpeciesThermo() function.

Constructor & Destructor Documentation

◆ Mu0Poly() [1/2]

Mu0Poly ( )

Definition at line 18 of file Mu0Poly.cpp.

◆ Mu0Poly() [2/2]

Mu0Poly	(	double	tlow,
		double	thigh,
		double	pref,
		const double *	coeffs
	)

Constructor with all input data.

Parameters

tlow	Minimum temperature
thigh	Maximum temperature
pref	reference pressure (Pa).
coeffs	Vector of coefficients used to set the parameters for the standard state for species n. There are \( 2+npoints*2 \) coefficients, where \( npoints \) are the number of temperature points. Their identity is further broken down: coeffs[0] = number of points (integer) coeffs[1] = \( h^o(298.15 K) \) (J/kmol) coeffs[2] = \( T_1 \) (Kelvin) coeffs[3] = \( \mu^o(T_1) \) (J/kmol) coeffs[4] = \( T_2 \) (Kelvin) coeffs[5] = \( \mu^o(T_2) \) (J/kmol) coeffs[6] = \( T_3 \) (Kelvin) coeffs[7] = \( \mu^o(T_3) \) (J/kmol) ........

Definition at line 23 of file Mu0Poly.cpp.

Member Function Documentation

◆ setParameters()

void setParameters	(	double	h0,
		const map< double, double > &	T_mu
	)

Set parameters for \( \mu^o(T) \).

Calculates and stores the piecewise linear approximation to the thermodynamic functions.

Parameters

h0	Enthalpy at the reference temperature of 298.15 K [J/kmol]
T_mu	Map with temperature [K] as the keys and the Gibbs free energy [J/kmol] as the values. Must contain one point at 298.15 K.

Definition at line 36 of file Mu0Poly.cpp.

◆ reportType()

int reportType ( ) const

inlineoverridevirtual

Returns an integer representing the type of parameterization.

Reimplemented from SpeciesThermoInterpType.

Definition at line 111 of file Mu0Poly.h.

◆ updateProperties()

void updateProperties	(	const double *	tt,
		double *	cp_R,
		double *	h_RT,
		double *	s_R
	)		const

overridevirtual

Update the properties for this species, given a temperature polynomial.

This method is called with a pointer to an array containing the functions of temperature needed by this parameterization, and three pointers to arrays where the computed property values should be written. This method updates only one value in each array.

The form and length of the Temperature Polynomial may vary depending on the parameterization.

Parameters

tt	vector of evaluated temperature functions
cp_R	Vector of Dimensionless heat capacities. (length m_kk).
h_RT	Vector of Dimensionless enthalpies. (length m_kk).
s_R	Vector of Dimensionless entropies. (length m_kk).

Temperature Polynomial: tt[0] = temp (Kelvin)

Reimplemented from SpeciesThermoInterpType.

Definition at line 102 of file Mu0Poly.cpp.

◆ updatePropertiesTemp()

void updatePropertiesTemp	(	const double	temp,
		double *	cp_R,
		double *	h_RT,
		double *	s_R
	)		const

overridevirtual

Compute the reference-state property of one species.

Given temperature T in K, this method updates the values of the non- dimensional heat capacity at constant pressure, enthalpy, and entropy, at the reference pressure, of the species.

Parameters

temp	Temperature (Kelvin)
cp_R	Vector of Dimensionless heat capacities. (length m_kk).
h_RT	Vector of Dimensionless enthalpies. (length m_kk).
s_R	Vector of Dimensionless entropies. (length m_kk).

Reimplemented from SpeciesThermoInterpType.

Definition at line 121 of file Mu0Poly.cpp.

◆ nCoeffs()

size_t nCoeffs ( ) const

overridevirtual

This utility function returns the number of coefficients for a given type of species parameterization.

Reimplemented from SpeciesThermoInterpType.

Definition at line 129 of file Mu0Poly.cpp.

◆ reportParameters()

void reportParameters	(	size_t &	index,
		int &	type,
		double &	minTemp,
		double &	maxTemp,
		double &	refPressure,
		double *const	coeffs
	)		const

overridevirtual

This utility function returns the type of parameterization and all of the parameters for the species.

All parameters are output variables

Parameters

index	Species index
type	Integer type of the standard type
minTemp	output - Minimum temperature
maxTemp	output - Maximum temperature
refPressure	output - reference pressure (Pa).
coeffs	Vector of coefficients used to set the parameters for the standard state.

Reimplemented from SpeciesThermoInterpType.

Definition at line 134 of file Mu0Poly.cpp.

◆ getParameters()

void getParameters ( AnyMap & thermo ) const

overridevirtual

Store the parameters of the species thermo object such that an identical species thermo object could be reconstructed using the newSpeciesThermo() function.

Reimplemented from SpeciesThermoInterpType.

Definition at line 152 of file Mu0Poly.cpp.

Member Data Documentation

◆ m_numIntervals

size_t m_numIntervals = 0

protected

Number of intervals in the interpolating linear approximation.

Number of points is one more than the number of intervals.

Definition at line 137 of file Mu0Poly.h.

◆ m_H298

double m_H298 = 0.0

protected

Value of the enthalpy at T = 298.15.

This value is tied to the Heat of formation of the species at 298.15.

Definition at line 141 of file Mu0Poly.h.

◆ m_t0_int

vector<double> m_t0_int

protected

Points at which the standard state chemical potential are given.

Definition at line 144 of file Mu0Poly.h.

◆ m_mu0_R_int

vector<double> m_mu0_R_int

protected

Mu0's are primary input data.

They aren't strictly needed, but are kept here for convenience.

Definition at line 148 of file Mu0Poly.h.

◆ m_h0_R_int

vector<double> m_h0_R_int

protected

Dimensionless Enthalpies at the temperature points.

Definition at line 151 of file Mu0Poly.h.

◆ m_s0_R_int

vector<double> m_s0_R_int

protected

Entropy at the points.

Definition at line 154 of file Mu0Poly.h.

◆ m_cp0_R_int

vector<double> m_cp0_R_int

protected

Heat capacity at the points.

Definition at line 157 of file Mu0Poly.h.

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

Detailed Description

Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ Mu0Poly() [1/2]

◆ Mu0Poly() [2/2]

Member Function Documentation

◆ setParameters()

◆ reportType()

◆ updateProperties()

◆ updatePropertiesTemp()

◆ nCoeffs()

◆ reportParameters()

◆ getParameters()

Member Data Documentation

◆ m_numIntervals

◆ m_H298

◆ m_t0_int

◆ m_mu0_R_int

◆ m_h0_R_int

◆ m_s0_R_int

◆ m_cp0_R_int