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Cantera
3.1.0
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The Mu0Poly class implements an interpolation of the Gibbs free energy based on a piecewise constant heat capacity approximation. More...
#include <Mu0Poly.h>
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.
Public Member Functions | |
| Mu0Poly (double tlow, double thigh, double pref, const double *coeffs) | |
| Constructor with all input data. | |
| void | setParameters (double h0, const map< double, double > &T_mu) |
| Set parameters for \( \mu^o(T) \). | |
| int | reportType () const override |
| Returns an integer representing the type of parameterization. | |
| void | updateProperties (const double *tt, double *cp_R, double *h_RT, double *s_R) const override |
| Update the properties for this species, given a temperature polynomial. | |
| void | updatePropertiesTemp (const double temp, double *cp_R, double *h_RT, double *s_R) const override |
| Compute the reference-state property of one species. | |
| size_t | nCoeffs () const override |
| This utility function returns the number of coefficients for a given type of species parameterization. | |
| void | reportParameters (size_t &n, int &type, double &tlow, double &thigh, double &pref, double *const coeffs) const override |
| This utility function returns the type of parameterization and all of the parameters for the species. | |
| void | getParameters (AnyMap &thermo) const override |
| Store the parameters of the species thermo object such that an identical species thermo object could be reconstructed using the newSpeciesThermo() function. | |
 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 double | minTemp () const |
| Returns the minimum temperature that the thermo parameterization is valid. | |
| virtual void | setMinTemp (double Tmin) |
| Set the minimum temperature at which the thermo parameterization is valid. | |
| virtual double | maxTemp () const |
| Returns the maximum temperature that the thermo parameterization is valid. | |
| virtual void | setMaxTemp (double Tmax) |
| Set the maximum temperature at which the thermo parameterization is valid. | |
| virtual double | refPressure () const |
| Returns the reference pressure (Pa) | |
| virtual void | setRefPressure (double Pref) |
| Set the reference pressure [Pa]. | |
| virtual void | validate (const string &name) |
| Check for problems with the parameterization, and generate warnings or throw and exception if any are found. | |
| virtual int | reportType () const |
| Returns an integer representing the type of parameterization. | |
| virtual size_t | temperaturePolySize () const |
| Number of terms in the temperature polynomial for this parameterization. | |
| virtual void | updateTemperaturePoly (double T, double *T_poly) const |
| Given the temperature T, compute the terms of the temperature polynomial T_poly. | |
| virtual void | updateProperties (const double *tt, double *cp_R, double *h_RT, double *s_R) const |
| Update the properties for this species, given a temperature polynomial. | |
| virtual void | updatePropertiesTemp (const double temp, double *cp_R, double *h_RT, double *s_R) const |
| Compute the reference-state property of one species. | |
| virtual size_t | nCoeffs () const |
| This utility function returns the number of coefficients for a given type of species parameterization. | |
| virtual void | reportParameters (size_t &index, int &type, double &minTemp, double &maxTemp, double &refPressure, double *const coeffs) const |
| This utility function returns the type of parameterization and all of the parameters for the species. | |
| 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. | |
| virtual double | reportHf298 (double *const h298=0) const |
| Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) | |
| virtual void | modifyOneHf298 (const size_t k, const double Hf298New) |
| Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1) | |
| virtual void | resetHf298 () |
| Restore the original heat of formation for this species. | |
| const AnyMap & | input () const |
| Access input data associated with the species thermo definition. | |
| AnyMap & | input () |
Protected Attributes | |
| size_t | m_numIntervals = 0 |
| Number of intervals in the interpolating linear approximation. | |
| double | m_H298 = 0.0 |
| Value of the enthalpy at T = 298.15. | |
| vector< double > | m_t0_int |
| Points at which the standard state chemical potential are given. | |
| vector< double > | m_mu0_R_int |
| Mu0's are primary input data. | |
| vector< double > | m_h0_R_int |
| Dimensionless Enthalpies at the temperature points. | |
| vector< double > | m_s0_R_int |
| Entropy at the points. | |
| vector< double > | m_cp0_R_int |
| Heat capacity at the points. | |
| Protected Attributes inherited from SpeciesThermoInterpType | |
| double | m_lowT = 0.0 |
| lowest valid temperature | |
| double | m_highT = 0.0 |
| Highest valid temperature. | |
| double | m_Pref = 0.0 |
| Reference state pressure. | |
| 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. | |
| Mu0Poly | ( | ) |
Definition at line 18 of file Mu0Poly.cpp.
| Mu0Poly | ( | double | tlow, |
| double | thigh, | ||
| double | pref, | ||
| const double * | coeffs | ||
| ) |
Constructor with all input data.
| 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:
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Definition at line 23 of file Mu0Poly.cpp.
| void setParameters | ( | double | h0, |
| const map< double, double > & | T_mu | ||
| ) |
Set parameters for \( \mu^o(T) \).
Calculates and stores the piecewise linear approximation to the thermodynamic functions.
| 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 36 of file Mu0Poly.cpp.
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inlineoverridevirtual |
Returns an integer representing the type of parameterization.
Reimplemented from SpeciesThermoInterpType.
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overridevirtual |
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.
| 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 102 of file Mu0Poly.cpp.
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overridevirtual |
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.
| 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 121 of file Mu0Poly.cpp.
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overridevirtual |
This utility function returns the number of coefficients for a given type of species parameterization.
Reimplemented from SpeciesThermoInterpType.
Definition at line 129 of file Mu0Poly.cpp.
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overridevirtual |
This utility function returns the type of parameterization and all of the parameters for the species.
All parameters are output variables
| 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 134 of file Mu0Poly.cpp.
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overridevirtual |
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 152 of file Mu0Poly.cpp.
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1.9.7