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

#include <ShomatePoly.h>

Inheritance diagram for ShomatePoly2:

Collaboration diagram for ShomatePoly2:

Public Member Functions
	ShomatePoly2 ()
	Empty constructor.

	ShomatePoly2 (size_t n, doublereal tlow, doublereal thigh, doublereal pref, const doublereal *coeffs)
	Constructor used in templated instantiations.

	ShomatePoly2 (const ShomatePoly2 &b)
	Copy constructor.

ShomatePoly2 &	operator= (const ShomatePoly2 &b)
	Assignment operator.

virtual	~ShomatePoly2 ()
	Destructor.

virtual SpeciesThermoInterpType *	duplMyselfAsSpeciesThermoInterpType () const
	duplicator

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

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

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

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

virtual size_t	speciesIndex () const
	Returns an integer representing the species index.

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

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

virtual void	reportParameters (size_t &n, int &type, doublereal &tlow, doublereal &thigh, doublereal &pref, doublereal *const coeffs) const
	This utility function reports back the type of parameterization and all of the parameters for the species, index.

virtual void	modifyParameters (doublereal *coeffs)
	Modify parameters for the standard state.

Protected Attributes
doublereal	m_lowT
	Minimum temperature the representation is valid(kelvin)

doublereal	m_midT
	Midrange temperature (kelvin)

doublereal	m_highT
	Maximum temperature the representation is valid (kelvin)

doublereal	m_Pref
	Reference pressure (Pascal)

ShomatePoly *	msp_low
	Pointer to the Shomate polynomial for the low temperature region.

ShomatePoly *	msp_high
	Pointer to the Shomate polynomial for the high temperature region.

vector_fp	m_coeff
	Array of the original coefficients.

size_t	m_index
	Species index.

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 (i.e., 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 410 of file ShomatePoly.h.

Constructor & Destructor Documentation

ShomatePoly2 ( )

inline

Empty constructor.

Definition at line 415 of file ShomatePoly.h.

References ShomatePoly2::m_coeff.

Referenced by ShomatePoly2::duplMyselfAsSpeciesThermoInterpType().

ShomatePoly2	(	size_t	n,
		doublereal	tlow,
		doublereal	thigh,
		doublereal	pref,
		const doublereal *	coeffs
	)

inline

Constructor used in templated instantiations.

Parameters

n	Species index
tlow	Minimum temperature
thigh	Maximum temperature
pref	reference pressure (Pa).
coeffs	Vector of coefficients used to set the parameters for the standard state. There are 15 coefficients for the 2-zone Shomate polynomial. The first coefficient is the value of Tmid. The next 7 coefficients are the low temperature range Shomate coefficients. The last 7 are the high temperature range Shomate coefficients.

Definition at line 439 of file ShomatePoly.h.

References ShomatePoly2::m_coeff, ShomatePoly2::m_midT, ShomatePoly2::msp_high, and ShomatePoly2::msp_low.

ShomatePoly2 ( const ShomatePoly2 & b )

inline

Copy constructor.

Parameters

b	object to be copied.

Definition at line 459 of file ShomatePoly.h.

References ShomatePoly2::m_coeff, ShomatePoly2::m_highT, ShomatePoly2::m_index, ShomatePoly2::m_lowT, ShomatePoly2::m_midT, ShomatePoly2::m_Pref, ShomatePoly2::msp_high, and ShomatePoly2::msp_low.

virtual ~ShomatePoly2 ( )

inlinevirtual

Destructor.

Definition at line 506 of file ShomatePoly.h.

References ShomatePoly2::msp_high, and ShomatePoly2::msp_low.

Member Function Documentation

ShomatePoly2& operator= ( const ShomatePoly2 & b )

inline

Assignment operator.

Parameters

b	object to be copied.

Definition at line 481 of file ShomatePoly.h.

References ShomatePoly2::m_coeff, ShomatePoly2::m_highT, ShomatePoly2::m_index, ShomatePoly2::m_lowT, ShomatePoly2::m_midT, ShomatePoly2::m_Pref, ShomatePoly2::msp_high, and ShomatePoly2::msp_low.

virtual SpeciesThermoInterpType* duplMyselfAsSpeciesThermoInterpType ( ) const

inlinevirtual

duplicator

Implements SpeciesThermoInterpType.

Definition at line 514 of file ShomatePoly.h.

References ShomatePoly2::ShomatePoly2().

virtual doublereal minTemp ( ) const

inlinevirtual

Returns the minimum temperature that the thermo parameterization is valid.

Implements SpeciesThermoInterpType.

Definition at line 521 of file ShomatePoly.h.

References ShomatePoly2::m_lowT.

virtual doublereal maxTemp ( ) const

inlinevirtual

Returns the maximum temperature that the thermo parameterization is valid.

Implements SpeciesThermoInterpType.

Definition at line 527 of file ShomatePoly.h.

References ShomatePoly2::m_highT.

virtual doublereal refPressure ( ) const

inlinevirtual

Returns the reference pressure (Pa)

Implements SpeciesThermoInterpType.

Definition at line 532 of file ShomatePoly.h.

References ShomatePoly2::m_Pref.

virtual int reportType ( ) const

inlinevirtual

Returns an integer representing the type of parameterization.

Implements SpeciesThermoInterpType.

Definition at line 537 of file ShomatePoly.h.

References SHOMATE2.

virtual size_t speciesIndex ( ) const

inlinevirtual

Returns an integer representing the species index.

Implements SpeciesThermoInterpType.

Definition at line 542 of file ShomatePoly.h.

References ShomatePoly2::m_index.

virtual void updateProperties	(	const doublereal *	tt,
		doublereal *	cp_R,
		doublereal *	h_RT,
		doublereal *	s_R
	)		const

inlinevirtual

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.

Temperature Polynomial: tt[0] = t; tt[1] = t*t; tt[2] = m_t[1]*t; tt[3] = m_t[2]*t; tt[4] = 1.0/t; tt[5] = std::log(t);

Parameters

tt	vector of temperature polynomials
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 569 of file ShomatePoly.h.

References ShomatePoly2::m_midT, ShomatePoly2::msp_high, ShomatePoly2::msp_low, and ShomatePoly::updateProperties().

virtual void updatePropertiesTemp	(	const doublereal	temp,
		doublereal *	cp_R,
		doublereal *	h_RT,
		doublereal *	s_R
	)		const

inlinevirtual

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, Pref of one of the species. The species index is used to reference into the cp_R, h_RT, and s_R arrays.

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).

Implements SpeciesThermoInterpType.

Definition at line 597 of file ShomatePoly.h.

References ShomatePoly2::m_midT, ShomatePoly2::msp_high, ShomatePoly2::msp_low, and ShomatePoly::updatePropertiesTemp().

virtual void reportParameters	(	size_t &	n,
		int &	type,
		doublereal &	tlow,
		doublereal &	thigh,
		doublereal &	pref,
		doublereal *const	coeffs
	)		const

inlinevirtual

This utility function reports back the type of parameterization and all of the parameters for the species, index.

All parameters are output variables

Parameters

n	Species index
type	Integer type of the standard type
tlow	output - Minimum temperature
thigh	output - Maximum temperature
pref	output - reference pressure (Pa).
coeffs	Vector of coefficients used to set the parameters for the standard state.