Cantera  2.0

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

#include <Mu0Poly.h>

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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.

Mu0Polyoperator= (const Mu0Poly &)
Assignment operator.

virtual ~Mu0Poly ()
Destructor.

virtual SpeciesThermoInterpTypeduplMyselfAsSpeciesThermoInterpType () 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.

 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.

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.

 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

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.

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

## Member Data Documentation

 size_t m_numIntervals
protected

Number of intervals in the interpolating linear approximation.

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

Definition at line 220 of file Mu0Poly.h.

 doublereal m_H298
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 227 of file Mu0Poly.h.

Referenced by Mu0Poly::operator=(), Mu0Poly::processCoeffs(), and Mu0Poly::reportParameters().

 vector_fp m_t0_int
protected

Points at which the standard state chemical potential are given.

Definition at line 233 of file Mu0Poly.h.

 vector_fp 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 239 of file Mu0Poly.h.

Referenced by Mu0Poly::operator=(), Mu0Poly::processCoeffs(), and Mu0Poly::reportParameters().

 vector_fp m_h0_R_int
protected

Dimensionless Enthalpies at the temperature points.

Definition at line 242 of file Mu0Poly.h.

Referenced by Mu0Poly::operator=(), Mu0Poly::processCoeffs(), and Mu0Poly::updateProperties().

 vector_fp m_s0_R_int
protected

Entropy at the points.

Definition at line 245 of file Mu0Poly.h.

Referenced by Mu0Poly::operator=(), Mu0Poly::processCoeffs(), and Mu0Poly::updateProperties().

 vector_fp m_cp0_R_int
protected

Heat capacity at the points.

Definition at line 248 of file Mu0Poly.h.

Referenced by Mu0Poly::operator=(), Mu0Poly::processCoeffs(), and Mu0Poly::updateProperties().

 doublereal m_lowT
protected

Limiting low temperature.

Definition at line 250 of file Mu0Poly.h.

Referenced by Mu0Poly::minTemp(), Mu0Poly::operator=(), and Mu0Poly::reportParameters().

 doublereal m_highT
protected

Limiting high temperature.

Definition at line 252 of file Mu0Poly.h.

Referenced by Mu0Poly::maxTemp(), Mu0Poly::operator=(), and Mu0Poly::reportParameters().

 doublereal m_Pref
protected

Reference pressure.

Definition at line 255 of file Mu0Poly.h.

Referenced by Mu0Poly::operator=(), Mu0Poly::refPressure(), and Mu0Poly::reportParameters().

 size_t m_index
protected

Species index.

Definition at line 258 of file Mu0Poly.h.

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