Cantera 2.6.0

Public Member Functions | Protected Attributes | List of all members
Mu0Poly Class Reference
Models of Phases of Matter » Thermodynamic Properties » Species Reference-State Thermodynamic Properties

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 (double tlow, double thigh, double pref, const double *coeffs)
| Constructor with all input data. More...
void | setParameters (double h0, const std::map< double, double > &T_mu)
| Set parameters for \( \mu^o(T) \). More...
virtual int | reportType () const
| Returns an integer representing the type of parameterization. More...
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. More...
virtual void | updatePropertiesTemp (const doublereal temp, doublereal *cp_R, doublereal *h_RT, doublereal *s_R) const
| Compute the reference-state property of one species. More...
virtual size_t | nCoeffs () const
| This utility function returns the number of coefficients for a given type of species parameterization. More...
virtual void | reportParameters (size_t &n, int &type, doublereal &tlow, doublereal &thigh, doublereal &pref, doublereal *const coeffs) const
| This utility function returns the type of parameterization and all of the parameters for the species. More...
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. More...
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 doublereal | minTemp () const
| Returns the minimum temperature that the thermo parameterization is valid. More...
virtual void | setMinTemp (double Tmin)
| Set the minimum temperature at which the thermo parameterization is valid. More...
virtual doublereal | maxTemp () const
| Returns the maximum temperature that the thermo parameterization is valid. More...
virtual void | setMaxTemp (double Tmax)
| Set the maximum temperature at which the thermo parameterization is valid. More...
virtual doublereal | refPressure () const
| Returns the reference pressure (Pa) More...
virtual void | setRefPressure (double Pref)
| Set the reference pressure [Pa]. More...
virtual void | validate (const std::string &name)
| Check for problems with the parameterization, and generate warnings or throw and exception if any are found. More...
virtual int | reportType () const
| Returns an integer representing the type of parameterization. More...
virtual size_t | temperaturePolySize () const
| Number of terms in the temperature polynomial for this parameterization. More...
virtual void | updateTemperaturePoly (double T, double *T_poly) const
| Given the temperature T, compute the terms of the temperature polynomial T_poly. More...
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. More...
virtual void | updatePropertiesTemp (const doublereal temp, doublereal *cp_R, doublereal *h_RT, doublereal *s_R) const
| Compute the reference-state property of one species. More...
virtual size_t | nCoeffs () const
| This utility function returns the number of coefficients for a given type of species parameterization. More...
virtual void | reportParameters (size_t &index, int &type, doublereal &minTemp, doublereal &maxTemp, doublereal &refPressure, doublereal *const coeffs) const
| This utility function returns the type of parameterization and all of the parameters for the species. More...
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. More...
virtual doublereal | reportHf298 (doublereal *const h298=0) const
| Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More...
virtual void | modifyOneHf298 (const size_t k, const doublereal Hf298New)
| Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1) More...
virtual void | resetHf298 ()
| Restore the original heat of formation for this species. More...
const AnyMap & | input () const
| Access input data associated with the species thermo definition. More...
AnyMap & | input ()

## Protected Attributes
size_t | m_numIntervals
| Number of intervals in the interpolating linear approximation. More...
doublereal | m_H298
| Value of the enthalpy at T = 298.15. More...
vector_fp | m_t0_int
| Points at which the standard state chemical potential are given. More...
vector_fp | m_mu0_R_int
| Mu0's are primary input data. More...
vector_fp | m_h0_R_int
| Dimensionless Enthalpies at the temperature points. More...
vector_fp | m_s0_R_int
| Entropy at the points. More...
vector_fp | m_cp0_R_int
| Heat capacity at the points. More...
Protected Attributes inherited from SpeciesThermoInterpType
doublereal | m_lowT
| lowest valid temperature More...
doublereal | m_highT
| Highest valid temperature. More...
doublereal | m_Pref
| Reference state pressure. More...
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. More...

## 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 74 of file Mu0Poly.h.

## Constructor & Destructor Documentation

## ◆ Mu0Poly() [1/2]

Mu0Poly | ( |  | ) |

Definition at line 21 of file Mu0Poly.cpp.

## ◆ Mu0Poly() [2/2]

Mu0Poly | ( | double | tlow,
|  | double | thigh,
|  | double | pref,
|  | const double * | coeffs
| ) |  |

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 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 28 of file Mu0Poly.cpp.

References Mu0Poly::setParameters().

## Member Function Documentation

## ◆ setParameters()

void setParameters | ( | double | h0,
|  | const std::map< double, double > & | T_mu
| ) |  |

Set parameters for \( \mu^o(T) \).

Calculates and stores the piecewise linear approximation to the thermodynamic functions.

Parameters

  h0 | Enthalpy at the reference temperature of 298.15 K [J/kmol]
  T_mu | Map with temperature [K] as the keys and the Gibbs free energy [J/kmol] as the values. Must contain one point at 298.15 K.

Definition at line 41 of file Mu0Poly.cpp.

References Cantera::GasConstant, Mu0Poly::m_H298, Mu0Poly::m_numIntervals, and Cantera::npos.

Referenced by Mu0Poly::Mu0Poly().

## ◆ reportType()

virtual int reportType | ( |  | ) | const
| inline virtual

Returns an integer representing the type of parameterization.

Reimplemented from SpeciesThermoInterpType.

Definition at line 113 of file Mu0Poly.h.

References MU0_INTERP.

## ◆ updateProperties()

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.

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).

Temperature Polynomial: tt[0] = temp (Kelvin)

Reimplemented from SpeciesThermoInterpType.

Definition at line 108 of file Mu0Poly.cpp.

References Mu0Poly::m_numIntervals.

## ◆ 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, 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 127 of file Mu0Poly.cpp.

## ◆ nCoeffs()

size_t nCoeffs | ( |  | ) | const
| virtual

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

Reimplemented from SpeciesThermoInterpType.

Definition at line 135 of file Mu0Poly.cpp.

References Mu0Poly::m_numIntervals.

## ◆ reportParameters()

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

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 140 of file Mu0Poly.cpp.

## ◆ getParameters()

void getParameters | ( | AnyMap & | thermo | ) | const
| virtual

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 160 of file Mu0Poly.cpp.

References Cantera::GasConstant, AnyMap::getBool(), SpeciesThermoInterpType::getParameters(), Mu0Poly::m_H298, Mu0Poly::m_mu0_R_int, Mu0Poly::m_numIntervals, and Mu0Poly::m_t0_int.

## Member Data Documentation

## ◆ m_numIntervals

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 144 of file Mu0Poly.h.

Referenced by Mu0Poly::getParameters(), Mu0Poly::nCoeffs(), Mu0Poly::setParameters(), and Mu0Poly::updateProperties().

## ◆ m_H298

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 148 of file Mu0Poly.h.

Referenced by Mu0Poly::getParameters(), and Mu0Poly::setParameters().

## ◆ m_t0_int

vector_fp m_t0_int
| protected

Points at which the standard state chemical potential are given.

Definition at line 151 of file Mu0Poly.h.

Referenced by Mu0Poly::getParameters().

## ◆ m_mu0_R_int

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 155 of file Mu0Poly.h.

Referenced by Mu0Poly::getParameters().

## ◆ m_h0_R_int

vector_fp m_h0_R_int
| protected

Dimensionless Enthalpies at the temperature points.

Definition at line 158 of file Mu0Poly.h.

## ◆ m_s0_R_int

vector_fp m_s0_R_int
| protected

Entropy at the points.

Definition at line 161 of file Mu0Poly.h.

## ◆ m_cp0_R_int

vector_fp m_cp0_R_int
| protected

Heat capacity at the points.

Definition at line 164 of file Mu0Poly.h.

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

- Mu0Poly.h
- Mu0Poly.cpp