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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Collaboration diagram for Mu0Poly:

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Public Member Functions
	Mu0Poly ()
	Constructor.

	Mu0Poly (size_t n, doublereal tlow, doublereal thigh, doublereal pref, const doublereal *coeffs)
	Constructor used in templated instantiations.

	Mu0Poly (const Mu0Poly &)
	Copy constructor.

Mu0Poly &	operator= (const Mu0Poly &)
	Assignment operator.

virtual	~Mu0Poly ()
	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 tPoly, 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
size_t	m_numIntervals
	Number of intervals in the interpolating linear approximation.

doublereal	m_H298
	Value of the enthalpy at T = 298.15.

vector_fp	m_t0_int
	Points at which the standard state chemical potential are given.

vector_fp	m_mu0_R_int
	Mu0's are primary input data.

vector_fp	m_h0_R_int
	Dimensionless Enthalpies at the temperature points.

vector_fp	m_s0_R_int
	Entropy at the points.

vector_fp	m_cp0_R_int
	Heat capacity at the points.

doublereal	m_lowT
	Limiting low temperature.

doublereal	m_highT
	Limiting high temperature.

doublereal	m_Pref
	Reference pressure.

size_t	m_index
	Species index.

Private Member Functions
void	processCoeffs (const doublereal *coeffs)
	process the coefficients

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 71 of file Mu0Poly.h.

Constructor & Destructor Documentation

Mu0Poly ( )

Constructor.

Definition at line 22 of file Mu0Poly.cpp.

Referenced by Mu0Poly::duplMyselfAsSpeciesThermoInterpType().

Mu0Poly	(	size_t	n,
		doublereal	tlow,
		doublereal	thigh,
		doublereal	pref,
		const doublereal *	coeffs
	)

Constructor used in templated instantiations.

In the constructor, we calculate and store the piecewise linear approximation to the thermodynamic functions.

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 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 48 of file Mu0Poly.cpp.

References Mu0Poly::processCoeffs().

Mu0Poly ( const Mu0Poly & b )

Copy constructor.

Definition at line 63 of file Mu0Poly.cpp.

~Mu0Poly ( )

virtual

Destructor.

Definition at line 99 of file Mu0Poly.cpp.

Member Function Documentation

Mu0Poly & operator= ( const Mu0Poly & b )

Assignment operator.

Definition at line 78 of file Mu0Poly.cpp.

References Mu0Poly::m_cp0_R_int, Mu0Poly::m_h0_R_int, Mu0Poly::m_H298, Mu0Poly::m_highT, Mu0Poly::m_index, Mu0Poly::m_lowT, Mu0Poly::m_mu0_R_int, Mu0Poly::m_numIntervals, Mu0Poly::m_Pref, Mu0Poly::m_s0_R_int, and Mu0Poly::m_t0_int.

SpeciesThermoInterpType * duplMyselfAsSpeciesThermoInterpType ( ) const

virtual

Duplicator.

Implements SpeciesThermoInterpType.

Definition at line 104 of file Mu0Poly.cpp.

References Mu0Poly::Mu0Poly().

doublereal minTemp ( ) const

virtual

Returns the minimum temperature that the thermo parameterization is valid.

Implements SpeciesThermoInterpType.

Definition at line 110 of file Mu0Poly.cpp.

References Mu0Poly::m_lowT.

doublereal maxTemp ( ) const

virtual

Returns the maximum temperature that the thermo parameterization is valid.

Implements SpeciesThermoInterpType.

Definition at line 114 of file Mu0Poly.cpp.

References Mu0Poly::m_highT.

doublereal refPressure ( ) const

virtual

Returns the reference pressure (Pa)

Implements SpeciesThermoInterpType.

Definition at line 118 of file Mu0Poly.cpp.

References Mu0Poly::m_Pref.

virtual int reportType ( ) const

inlinevirtual

Returns an integer representing the type of parameterization.

Implements SpeciesThermoInterpType.

Definition at line 134 of file Mu0Poly.h.

References MU0_INTERP.

virtual size_t speciesIndex ( ) const

inlinevirtual

Returns an integer representing the species index.

Implements SpeciesThermoInterpType.

Definition at line 139 of file Mu0Poly.h.

References Mu0Poly::m_index.

void updateProperties	(	const doublereal *	tPoly,
		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:

tPoly[0] = temp (Kelvin)

Parameters

tPoly	vector of temperature polynomials. Length = 1
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 138 of file Mu0Poly.cpp.

References Mu0Poly::m_cp0_R_int, Mu0Poly::m_h0_R_int, Mu0Poly::m_index, Mu0Poly::m_numIntervals, Mu0Poly::m_s0_R_int, and Mu0Poly::m_t0_int.

Referenced by Mu0Poly::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.

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 160 of file Mu0Poly.cpp.

References Mu0Poly::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.

Implements SpeciesThermoInterpType.

Definition at line 174 of file Mu0Poly.cpp.

References Cantera::GasConstant, Mu0Poly::m_H298, Mu0Poly::m_highT, Mu0Poly::m_index, Mu0Poly::m_lowT, Mu0Poly::m_mu0_R_int, Mu0Poly::m_numIntervals, Mu0Poly::m_Pref, Mu0Poly::m_t0_int, and MU0_INTERP.

void modifyParameters ( doublereal * coeffs )

virtual

Modify parameters for the standard state.

Parameters

coeffs Vector of coefficients used to set the parameters for the standard state.

Reimplemented from SpeciesThermoInterpType.

Definition at line 194 of file Mu0Poly.cpp.

References Mu0Poly::processCoeffs().

void processCoeffs ( const doublereal * coeffs )

private

process the coefficients

Mu0Poly():

In the constructor, we calculate and store the piecewise linear approximation to the thermodynamic functions.

Parameters

coeffs coefficients. These are defined as follows:

coeffs[0] = number of points (integer) 1 = H298(J/kmol) 2 = T1 (Kelvin) 3 = mu1 (J/kmol) 4 = T2 (Kelvin) 5 = mu2 (J/kmol) 6 = T3 (Kelvin) 7 = mu3 (J/kmol) ........

Definition at line 307 of file Mu0Poly.cpp.

References Cantera::GasConstant, Mu0Poly::m_cp0_R_int, Mu0Poly::m_h0_R_int, Mu0Poly::m_H298, Mu0Poly::m_mu0_R_int, Mu0Poly::m_numIntervals, Mu0Poly::m_s0_R_int, Mu0Poly::m_t0_int, and Cantera::npos.

Referenced by Mu0Poly::modifyParameters(), and Mu0Poly::Mu0Poly().