The Mu0Poly class implements an interpolation of the Gibbs free energy based on a piecewise constant heat capacity approximation. More...
#include <Mu0Poly.h>
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 | |
| SpeciesThermoInterpType & | operator= (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.
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
-
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 21 of file Mu0Poly.cpp.
References Mu0Poly::processCoeffs().
Member Function Documentation
◆ reportType()
|
inlinevirtual |
Returns an integer representing the type of parameterization.
Implements SpeciesThermoInterpType.
Definition at line 101 of file Mu0Poly.h.
References MU0_INTERP.
◆ updateProperties()
|
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 29 of file Mu0Poly.cpp.
References Mu0Poly::m_numIntervals.
◆ updatePropertiesTemp()
|
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).
Implements SpeciesThermoInterpType.
Definition at line 48 of file Mu0Poly.cpp.
◆ reportParameters()
|
virtual |
This utility function reports back 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.
Implements SpeciesThermoInterpType.
Definition at line 56 of file Mu0Poly.cpp.
◆ processCoeffs()
|
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)
- 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
|
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
|
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
|
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
|
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
|
protected |
Dimensionless Enthalpies at the temperature points.
Definition at line 141 of file Mu0Poly.h.
Referenced by Mu0Poly::processCoeffs().
◆ 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
|
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:
