Detailed Description
\[ \alpha^0 = \displaystyle\sum_i n_i\log[c_i+d_i\exp(\theta_i\tau)] \]
To convert conventional Plank-Einstein forms, given by \( \frac{c_p^0}{R} = a_k\displaystyle\frac{\left( b_k/T \right)^2\exp \left( b_k/T \right)}{\left(\exp \left(b_k/T\right) - 1 \right)^2} \) and \( \alpha^0 = a_k\ln \left[1 - \exp \left( \frac{-b_k\tau}{T_c} \right) \right] \) use \(c = 1\), \(d = -1\), \(n = a\), \(\theta = -\displaystyle\frac{b_k}{T_c}\)
To convert the second form of Plank-Einstein terms, given by \( \frac{c_p^0}{R} = a_k\displaystyle\frac{\left( -b_k/T \right)^2\exp \left( b_k/T \right)}{c\left(\exp \left(-b_k/T\right) + 1 \right)^2} \) and \( \alpha^0 = a_k\ln \left[c + \exp \left( \frac{b_k\tau}{T_c} \right) \right] \) use \(c = 1\), \(d = 1\), \(n = -a\), \(\theta = \displaystyle\frac{b_k}{T_c}\)
Converting Aly-Lee tems is a bit more complex
Aly-Lee starts as
\[\frac{c_p^0}{R_u} = A + B\left(\frac{C/T}{\sinh(C/T)}\right)^2 + D\left(\frac{E/T}{\cosh(E/T)}\right)^2\]
Constant is separated out, and handled separately. sinh part can be expanded as
\[B\left(\frac{C/T}{\sinh(C/T)}\right)^2 = \frac{B(-2C/T)^2\exp(-2C/T)}{(1-\exp(-2C/T))^2}\]
where
\[n_k = B\]
\[\theta_k = -\frac{2C}{T_c}\]
\[c_k = 1\]
\[d_k = -1\]
cosh part can be expanded as
\[D\left(\frac{E/T}{\cosh(E/T)}\right)^2 = \frac{D(-2E/T)^2\exp(-2E/T)}{(1+\exp(-2E/T))^2}\]
where
\[n_k = -D\]
\[\theta_k = -\frac{2E}{T_c}\]
\[c_k = 1\]
\[d_k = 1\]
Definition at line 1036 of file Helmholtz.h.
#include <Helmholtz.h>
Public Member Functions | |
| IdealHelmholtzPlanckEinsteinGeneralized () | |
| IdealHelmholtzPlanckEinsteinGeneralized (const std::vector< CoolPropDbl > &n, const std::vector< CoolPropDbl > &theta, const std::vector< CoolPropDbl > &c, const std::vector< CoolPropDbl > &d) | |
| void | extend (const std::vector< CoolPropDbl > &n, const std::vector< CoolPropDbl > &theta, const std::vector< CoolPropDbl > &c, const std::vector< CoolPropDbl > &d) |
| bool | is_enabled () const |
| void | to_json (rapidjson::Value &el, rapidjson::Document &doc) |
| void | all (const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw () |
 Public Member Functions inherited from CoolProp::BaseHelmholtzTerm | |
| BaseHelmholtzTerm () | |
| virtual | ~BaseHelmholtzTerm () |
| virtual CoolPropDbl | base (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the base, non-dimensional, Helmholtz energy term (no derivatives) [-]. More... | |
| virtual CoolPropDbl | dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the first partial derivative of Helmholtz energy term with respect to tau [-]. More... | |
| virtual CoolPropDbl | dTau2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the second partial derivative of Helmholtz energy term with respect to tau [-]. More... | |
| virtual CoolPropDbl | dDelta_dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the second mixed partial derivative (delta1,dtau1) of Helmholtz energy term with respect to delta and tau [-]. More... | |
| virtual CoolPropDbl | dDelta (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the first partial derivative of Helmholtz energy term with respect to delta [-]. More... | |
| virtual CoolPropDbl | dDelta2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the second partial derivative of Helmholtz energy term with respect to delta [-]. More... | |
| virtual CoolPropDbl | dDelta2_dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the third mixed partial derivative (delta2,dtau1) of Helmholtz energy term with respect to delta and tau [-]. More... | |
| virtual CoolPropDbl | dDelta_dTau2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the third mixed partial derivative (delta1,dtau2) of Helmholtz energy term with respect to delta and tau [-]. More... | |
| virtual CoolPropDbl | dTau3 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the third partial derivative of Helmholtz energy term with respect to tau [-]. More... | |
| virtual CoolPropDbl | dDelta3 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the third partial derivative of Helmholtz energy term with respect to delta [-]. More... | |
| virtual CoolPropDbl | dTau4 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| Returns the fourth partial derivative of Helmholtz energy term with respect to tau [-]. More... | |
| virtual CoolPropDbl | dDelta_dTau3 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| virtual CoolPropDbl | dDelta2_dTau2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| virtual CoolPropDbl | dDelta3_dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
| virtual CoolPropDbl | dDelta4 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw () |
Constructor & Destructor Documentation
◆ IdealHelmholtzPlanckEinsteinGeneralized() [1/2]
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inline |
Definition at line 1045 of file Helmholtz.h.
◆ IdealHelmholtzPlanckEinsteinGeneralized() [2/2]
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inline |
Definition at line 1047 of file Helmholtz.h.
Member Function Documentation
◆ all()
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virtual | ||||||||||||||||||||||||
Implements CoolProp::BaseHelmholtzTerm.
Definition at line 1099 of file Helmholtz.cpp.
◆ extend()
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inline |
Definition at line 1052 of file Helmholtz.h.
◆ is_enabled()
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inline |
Definition at line 1061 of file Helmholtz.h.
◆ to_json()
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inline |
Definition at line 1065 of file Helmholtz.h.
The documentation for this class was generated from the following files:
- include/Helmholtz.h
- src/Helmholtz.cpp
