Cantera  2.4.0
Public Member Functions | Protected Attributes | Private Member Functions | List of all members

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)
 Normal constructor. 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 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. More...
 
- Public Member Functions inherited from SpeciesThermoInterpType
 SpeciesThermoInterpType (double tlow, double thigh, double pref)
 
 SpeciesThermoInterpType (const SpeciesThermoInterpType &b)=delete
 
SpeciesThermoInterpTypeoperator= (const SpeciesThermoInterpType &b)=delete
 
virtual doublereal minTemp () const
 Returns the minimum temperature that the thermo parameterization is valid. More...
 
virtual doublereal maxTemp () const
 Returns the maximum temperature that the thermo parameterization is valid. More...
 
virtual doublereal refPressure () const
 Returns 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 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 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...
 

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...
 

Private Member Functions

void processCoeffs (const doublereal *coeffs)
 process the coefficients 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 73 of file Mu0Poly.h.

Constructor & Destructor Documentation

◆ Mu0Poly()

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

Normal constructor.

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

Parameters
tlowMinimum temperature
thighMaximum temperature
prefreference pressure (Pa).
coeffsVector 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 21 of file Mu0Poly.cpp.

References Mu0Poly::processCoeffs().

Member Function Documentation

◆ reportType()

virtual int reportType ( ) const
inlinevirtual

Returns an integer representing the type of parameterization.

Implements SpeciesThermoInterpType.

Definition at line 101 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
ttvector of evaluated temperature functions
cp_RVector of Dimensionless heat capacities. (length m_kk).
h_RTVector of Dimensionless enthalpies. (length m_kk).
s_RVector of Dimensionless entropies. (length m_kk).

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

Reimplemented from SpeciesThermoInterpType.

Definition at line 29 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
tempTemperature (Kelvin)
cp_RVector of Dimensionless heat capacities. (length m_kk).
h_RTVector of Dimensionless enthalpies. (length m_kk).
s_RVector of Dimensionless entropies. (length m_kk).

Implements SpeciesThermoInterpType.

Definition at line 48 of file Mu0Poly.cpp.

◆ reportParameters()

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

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

All parameters are output variables

Parameters
indexSpecies index
typeInteger type of the standard type
minTempoutput - Minimum temperature
maxTempoutput - Maximum temperature
refPressureoutput - reference pressure (Pa).
coeffsVector of coefficients used to set the parameters for the standard state.

Implements SpeciesThermoInterpType.

Definition at line 56 of file Mu0Poly.cpp.

◆ 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
coeffscoefficients. These are defined as follows:
  • 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 137 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, and Mu0Poly::m_t0_int.

Referenced by Mu0Poly::Mu0Poly().

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 127 of file Mu0Poly.h.

Referenced by Mu0Poly::processCoeffs(), 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 131 of file Mu0Poly.h.

Referenced by Mu0Poly::processCoeffs().

◆ m_t0_int

vector_fp m_t0_int
protected

Points at which the standard state chemical potential are given.

Definition at line 134 of file Mu0Poly.h.

Referenced by Mu0Poly::processCoeffs().

◆ 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 138 of file Mu0Poly.h.

Referenced by Mu0Poly::processCoeffs().

◆ m_h0_R_int

vector_fp m_h0_R_int
protected

Dimensionless Enthalpies at the temperature points.

Definition at line 141 of file Mu0Poly.h.

Referenced by Mu0Poly::processCoeffs().

◆ m_s0_R_int

vector_fp m_s0_R_int
protected

Entropy at the points.

Definition at line 144 of file Mu0Poly.h.

Referenced by Mu0Poly::processCoeffs().

◆ m_cp0_R_int

vector_fp m_cp0_R_int
protected

Heat capacity at the points.

Definition at line 147 of file Mu0Poly.h.

Referenced by Mu0Poly::processCoeffs().


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