The NASA 9 polynomial parameterization for one temperature range. More...

#include <Nasa9Poly1.h>

Inheritance diagram for Nasa9Poly1:

Collaboration diagram for Nasa9Poly1:

Public Member Functions
	Nasa9Poly1 ()
	Empty constructor.

	Nasa9Poly1 (size_t n, doublereal tlow, doublereal thigh, doublereal pref, const doublereal *coeffs)
	constructor used in templated instantiations

	Nasa9Poly1 (const Nasa9Poly1 &b)
	copy constructor

Nasa9Poly1 &	operator= (const Nasa9Poly1 &b)
	assignment operator

virtual	~Nasa9Poly1 ()
	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
	lowest valid temperature

doublereal	m_highT
	highest valid temperature

doublereal	m_Pref
	standard-state pressure

size_t	m_index
	species index

vector_fp	m_coeff
	array of polynomial coefficients

Detailed Description

The NASA 9 polynomial parameterization for one temperature range.

This parameterization expresses the heat capacity via a 7 coefficient polynomial. Note that this is the form used in the 2002 NASA equilibrium program. A reference to the form is provided below:

"NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species," B. J. McBride, M. J. Zehe, S. Gordon NASA/TP-2002-211556, Sept. 2002

Nine coefficients \((a_0,\dots,a_6)\) are used to represent \( C_p^0(T)\), \( H^0(T)\), and \( S^0(T) \) as polynomials in \( T \) :

\[ \frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T + a_4 T^2 + a_5 T^3 + a_6 T^4 \]

\[ \frac{H^0(T)}{RT} = - a_0 T^{-2} + a_1 \frac{\ln(T)}{T} + a_2 + a_3 T + a_4 T^2 + a_5 T^3 + a_6 T^4 + \frac{a_7}{T} \]

\[ \frac{s^0(T)}{R} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln(T) + + a_3 T \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8 \]

The standard state is assumed to be an ideal gas at the standard pressure of 1 bar, for gases. For condensed species, the standard state is the pure crystalline or liquid substance at the standard pressure of 1 atm.

These NASA representations may have multiple temperature regions through the use of the Nasa9PolyMultiTempRegion object, which uses multiple copies of this Nasa9Poly1 object to handle multiple temperature regions.

Definition at line 71 of file Nasa9Poly1.h.

Constructor & Destructor Documentation

Nasa9Poly1 ( )

Empty constructor.

Definition at line 65 of file Nasa9Poly1.cpp.

Referenced by Nasa9Poly1::duplMyselfAsSpeciesThermoInterpType().

Nasa9Poly1	(	size_t	n,
		doublereal	tlow,
		doublereal	thigh,
		doublereal	pref,
		const doublereal *	coeffs
	)

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.

Definition at line 79 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_coeff.

Nasa9Poly1 ( const Nasa9Poly1 & b )

copy constructor

Parameters

b	object to be copied

Definition at line 95 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_coeff.

~Nasa9Poly1 ( )

virtual

Destructor.

Definition at line 126 of file Nasa9Poly1.cpp.

Member Function Documentation

Nasa9Poly1 & operator= ( const Nasa9Poly1 & b )

assignment operator

Parameters

b	object to be copied

Definition at line 111 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_coeff, Nasa9Poly1::m_highT, Nasa9Poly1::m_index, Nasa9Poly1::m_lowT, and Nasa9Poly1::m_Pref.

SpeciesThermoInterpType * duplMyselfAsSpeciesThermoInterpType ( ) const

virtual

duplicator

Implements SpeciesThermoInterpType.

Definition at line 132 of file Nasa9Poly1.cpp.

References Nasa9Poly1::Nasa9Poly1().

doublereal minTemp ( ) const

virtual

Returns the minimum temperature that the thermo parameterization is valid.

Implements SpeciesThermoInterpType.

Definition at line 140 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_lowT.

doublereal maxTemp ( ) const

virtual

Returns the maximum temperature that the thermo parameterization is valid.

Implements SpeciesThermoInterpType.

Definition at line 147 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_highT.

doublereal refPressure ( ) const

virtual

Returns the reference pressure (Pa)

Implements SpeciesThermoInterpType.

Definition at line 153 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_Pref.

int reportType ( ) const

virtual

Returns an integer representing the type of parameterization.

Implements SpeciesThermoInterpType.

Definition at line 159 of file Nasa9Poly1.cpp.

References NASA9.

size_t speciesIndex ( ) const

virtual

Returns an integer representing the species index.

Implements SpeciesThermoInterpType.

Definition at line 165 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_index.

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

virtual

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] = t*t*t; tt[3] = t*t*t*t; tt[4] = 1.0/t; tt[5] = 1.0/(t*t); tt[6] = 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 194 of file Nasa9Poly1.cpp.

References Nasa9Poly1::m_coeff, Nasa9Poly1::m_index, and Cantera::OneThird.

Referenced by Nasa9Poly1::updatePropertiesTemp().

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

virtual

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.

Temperature Polynomial: tt[0] = t; tt[1] = t*t; tt[2] = t*t*t; tt[3] = t*t*t*t; tt[4] = 1.0/t; tt[5] = 1.0/(t*t); tt[6] = std::log(t);

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 249 of file Nasa9Poly1.cpp.

References Nasa9Poly1::updateProperties().

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

virtual

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. There are 12 of them, designed to be compatible with the multiple temperature formulation. coeffs[0] is equal to one. coeffs[1] is min temperature coeffs[2] is max temperature coeffs[3+i] from i =0,9 are the coefficients themselves