The Shomate polynomial parameterization for two temperature ranges for one species. More...

#include <ShomatePoly.h>

Inheritance diagram for ShomatePoly2:

Detailed Description

The Shomate polynomial parameterization for two temperature ranges for one species.

Seven coefficients \( (A,\dots,G) \) are used to represent \( c_p^0(T) \), \( h^0(T) \), and \( s^0(T) \) as polynomials in the temperature, \( T \), in one temperature region:

\[ \tilde{c}_p^0(T) = A + B t + C t^2 + D t^3 + \frac{E}{t^2} \]

\[ \tilde{h}^0(T) = A t + \frac{B t^2}{2} + \frac{C t^3}{3} + \frac{D t^4}{4} - \frac{E}{t} + F. \]

\[ \tilde{s}^0(T) = A\ln t + B t + \frac{C t^2}{2} + \frac{D t^3}{3} - \frac{E}{2t^2} + G. \]

In the above expressions, the thermodynamic polynomials are expressed in dimensional units, but the temperature, \( t \), is divided by 1000. The following dimensions are assumed in the above expressions:

\( \tilde{c}_p^0(T) \) = Heat Capacity (J/gmol*K)
\( \tilde{h}^0(T) \) = standard Enthalpy (kJ/gmol)
\( \tilde{s}^0(T) \)= standard Entropy (J/gmol*K)
\( t \)= temperature (K) / 1000.

For more information about Shomate polynomials, see the NIST website, http://webbook.nist.gov/

Before being used within Cantera, the dimensions must be adjusted to those used by Cantera (for example, Joules and kmol).

This function uses two temperature regions, each with a Shomate polynomial representation to represent the thermo functions. There are 15 coefficients, therefore, in this representation. The first coefficient is the midrange temperature.

Definition at line 232 of file ShomatePoly.h.

Public Member Functions
	ShomatePoly2 (double tlow, double thigh, double pref, const double *coeffs)
	Constructor with all input data.

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

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

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

void	setParameters (double Tmid, const vector< double > &low, const vector< double > &high)

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

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

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

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.

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

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

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

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
double	m_midT
	Midrange temperature (kelvin)

ShomatePoly	msp_low
	Shomate polynomial for the low temperature region.

ShomatePoly	msp_high
	Shomate polynomial for the high temperature region.

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

◆ ShomatePoly2() [1/2]

ShomatePoly2 ( )

inline

Definition at line 235 of file ShomatePoly.h.

◆ ShomatePoly2() [2/2]

ShomatePoly2	(	double	tlow,
		double	thigh,
		double	pref,
		const double *	coeffs
	)

inline

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. [Tmid, 7 low-T coeffs, 7 high-T coeffs]

Definition at line 245 of file ShomatePoly.h.

Member Function Documentation

◆ setMinTemp()

void setMinTemp ( double Tmin )

inlineoverridevirtual

Set the minimum temperature at which the thermo parameterization is valid.

Reimplemented from SpeciesThermoInterpType.

Definition at line 253 of file ShomatePoly.h.

◆ setMaxTemp()

void setMaxTemp ( double Tmax )

inlineoverridevirtual

Set the maximum temperature at which the thermo parameterization is valid.

Reimplemented from SpeciesThermoInterpType.

Definition at line 258 of file ShomatePoly.h.

◆ setRefPressure()

void setRefPressure ( double Pref )

inlineoverridevirtual

Set the reference pressure [Pa].

Reimplemented from SpeciesThermoInterpType.

Definition at line 263 of file ShomatePoly.h.

◆ setParameters()

void setParameters	(	double	Tmid,
		const vector< double > &	low,
		const vector< double > &	high
	)

inline

Parameters

Tmid	Temperature [K] at the boundary between the low and high temperature polynomials
low	Vector of 7 coefficients for the low temperature polynomial
high	Vector of 7 coefficients for the high temperature polynomial

Definition at line 275 of file ShomatePoly.h.

◆ reportType()

int reportType ( ) const

inlineoverridevirtual

Returns an integer representing the type of parameterization.

Reimplemented from SpeciesThermoInterpType.

Definition at line 283 of file ShomatePoly.h.

◆ temperaturePolySize()

size_t temperaturePolySize ( ) const

inlineoverridevirtual

Number of terms in the temperature polynomial for this parameterization.

Reimplemented from SpeciesThermoInterpType.

Definition at line 287 of file ShomatePoly.h.

◆ updateTemperaturePoly()

void updateTemperaturePoly	(	double	T,
		double *	T_poly
	)		const

inlineoverridevirtual

Given the temperature T, compute the terms of the temperature polynomial T_poly.

Reimplemented from SpeciesThermoInterpType.

Definition at line 289 of file ShomatePoly.h.

◆ updateProperties()

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

inlineoverridevirtual

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).

Form of the temperature polynomial:

t is T/1000.
t[0] = t
t[1] = t*t
t[2] = t[1]*t
t[3] = 1.0/t[1]
t[4] = log(t)
`t[5] = 1.0/t;

Reimplemented from SpeciesThermoInterpType.

Definition at line 294 of file ShomatePoly.h.

◆ updatePropertiesTemp()

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

inlineoverridevirtual

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 304 of file ShomatePoly.h.

◆ nCoeffs()

size_t nCoeffs ( ) const

inlineoverridevirtual

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

Reimplemented from SpeciesThermoInterpType.

Definition at line 313 of file ShomatePoly.h.

◆ reportParameters()

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

inlineoverridevirtual

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 315 of file ShomatePoly.h.

◆ getParameters()

void getParameters ( AnyMap & thermo ) const

inlineoverridevirtual

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 322 of file ShomatePoly.h.

◆ reportHf298()

double reportHf298 ( double *const h298 = nullptr ) const

inlineoverridevirtual

Report the 298 K Heat of Formation of the standard state of one species (J kmol-1)

The 298K Heat of Formation is defined as the enthalpy change to create the standard state of the species from its constituent elements in their standard states at 298 K and 1 bar.

Parameters

h298	If this is nonnull, the current value of the Heat of Formation at 298K and 1 bar for species m_speciesIndex is returned in h298[m_speciesIndex].

Returns: the current value of the Heat of Formation at 298K and 1 bar for species m_speciesIndex.

Reimplemented from SpeciesThermoInterpType.

Definition at line 332 of file ShomatePoly.h.

◆ modifyOneHf298()

void modifyOneHf298	(	const size_t	k,
		const double	Hf298New
	)

inlineoverridevirtual

Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1)

The 298K heat of formation is defined as the enthalpy change to create the standard state of the species from its constituent elements in their standard states at 298 K and 1 bar.

Parameters

k	Species k
Hf298New	Specify the new value of the Heat of Formation at 298K and 1 bar

Reimplemented from SpeciesThermoInterpType.

Definition at line 345 of file ShomatePoly.h.

◆ resetHf298()

void resetHf298 ( )

inlineoverridevirtual

Restore the original heat of formation for this species.

Resets changes made by modifyOneHf298().

Reimplemented from SpeciesThermoInterpType.

Definition at line 356 of file ShomatePoly.h.

Member Data Documentation

◆ m_midT

double m_midT

protected

Midrange temperature (kelvin)

Definition at line 363 of file ShomatePoly.h.

◆ msp_low

ShomatePoly msp_low

protected

Shomate polynomial for the low temperature region.

Definition at line 365 of file ShomatePoly.h.

◆ msp_high

ShomatePoly msp_high

protected

Shomate polynomial for the high temperature region.

Definition at line 367 of file ShomatePoly.h.

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

ShomatePoly.h

Detailed Description

Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ ShomatePoly2() [1/2]

◆ ShomatePoly2() [2/2]

Member Function Documentation

◆ setMinTemp()

◆ setMaxTemp()

◆ setRefPressure()

◆ setParameters()

◆ reportType()

◆ temperaturePolySize()

◆ updateTemperaturePoly()

◆ updateProperties()

◆ updatePropertiesTemp()

◆ nCoeffs()

◆ reportParameters()

◆ getParameters()

◆ reportHf298()

◆ modifyOneHf298()

◆ resetHf298()

Member Data Documentation

◆ m_midT

◆ msp_low

◆ msp_high