CoolProp
6.6.1dev
An open-source fluid property and humid air property database
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The base class class for the Helmholtz energy terms.
Residual Helmholtz Energy Terms:
Term | Helmholtz Energy Contribution |
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ResidualHelmholtzPower | \( \alpha^r=\left\lbrace\begin{array}{cc}\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} & l_i=0\\ \displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) & l_i\neq 0\end{array}\right.\) |
ResidualHelmholtzExponential | \( \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\gamma_i\delta^{l_i}) \) |
ResidualHelmholtzLemmon2005 | \( \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}-\tau^{m_i})\) |
ResidualHelmholtzGaussian | \( \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\tau-\gamma_i)^2)\) |
ResidualHelmholtzGERG2008Gaussian | \( \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\delta-\gamma_i))\) |
ResidualHelmholtzNonAnalytic | \( \begin{array}{c}\alpha^r&=&\displaystyle\sum_i n_i \Delta^{b_i}\delta\psi \\ \Delta & = & \theta^2+B_i[(\delta-1)^2]^{a_i}\\ \theta & = & (1-\tau)+A_i[(\delta-1)^2]^{1/(2\beta_i)}\\ \psi & = & \exp(-C_i(\delta-1)^2-D_i(\tau-1)^2) \end{array}\) |
ResidualHelmholtzSAFTAssociating | \( \alpha^r = am\left(\ln X-\frac{X}{2}+\frac{1}{2}\right); \) |
Ideal-Gas Helmholtz Energy Terms:
Term | Helmholtz Energy Contribution |
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IdealHelmholtzLead | \( \alpha^0 = n_1 + n_2\tau + \ln\delta \) |
IdealHelmholtzEnthalpyEntropyOffset | \( \alpha^0 = \displaystyle\frac{\Delta s}{R_u/M}+\frac{\Delta h}{(R_u/M)T}\tau \) |
IdealHelmholtzLogTau | \( \alpha^0 = n_1\log\tau \) |
IdealHelmholtzPower | \( \alpha^0 = \displaystyle\sum_i n_i\tau^{t_i} \) |
IdealHelmholtzPlanckEinsteinGeneralized | \( \alpha^0 = \displaystyle\sum_i n_i\log[c_i+d_i\exp(\theta_i\tau)] \) |
Definition at line 161 of file Helmholtz.h.
#include <Helmholtz.h>
Public Member Functions | |
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 () |
virtual void | all (const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs)=0 throw () |
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inline |
Definition at line 164 of file Helmholtz.h.
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inlinevirtual |
Definition at line 165 of file Helmholtz.h.
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pure virtual |
Implemented in CoolProp::IdealHelmholtzGERG2004Cosh, CoolProp::IdealHelmholtzGERG2004Sinh, CoolProp::IdealHelmholtzCP0PolyT, CoolProp::IdealHelmholtzCP0Constant, CoolProp::IdealHelmholtzPlanckEinsteinGeneralized, CoolProp::IdealHelmholtzPower, CoolProp::IdealHelmholtzLogTau, CoolProp::IdealHelmholtzEnthalpyEntropyOffset, CoolProp::IdealHelmholtzLead, CoolProp::ResidualHelmholtzXiangDeiters, CoolProp::ResidualHelmholtzGaoB, CoolProp::ResidualHelmholtzGeneralizedCubic, CoolProp::ResidualHelmholtzNonAnalytic, CoolProp::ResidualHelmholtzGeneralizedExponential, and CoolProp::ResidualHelmholtzSAFTAssociating.
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inlinevirtual |
Returns the base, non-dimensional, Helmholtz energy term (no derivatives) [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 171 of file Helmholtz.h.
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inlinevirtual |
Returns the first partial derivative of Helmholtz energy term with respect to delta [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 207 of file Helmholtz.h.
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inlinevirtual |
Returns the second partial derivative of Helmholtz energy term with respect to delta [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 216 of file Helmholtz.h.
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inlinevirtual |
Returns the third mixed partial derivative (delta2,dtau1) of Helmholtz energy term with respect to delta and tau [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 225 of file Helmholtz.h.
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inlinevirtual |
Reimplemented in CoolProp::ResidualHelmholtzSAFTAssociating.
Definition at line 271 of file Helmholtz.h.
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inlinevirtual |
Returns the third partial derivative of Helmholtz energy term with respect to delta [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 252 of file Helmholtz.h.
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inlinevirtual |
Reimplemented in CoolProp::ResidualHelmholtzSAFTAssociating.
Definition at line 276 of file Helmholtz.h.
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inlinevirtual |
Reimplemented in CoolProp::ResidualHelmholtzSAFTAssociating.
Definition at line 281 of file Helmholtz.h.
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inlinevirtual |
Returns the second mixed partial derivative (delta1,dtau1) of Helmholtz energy term with respect to delta and tau [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 198 of file Helmholtz.h.
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inlinevirtual |
Returns the third mixed partial derivative (delta1,dtau2) of Helmholtz energy term with respect to delta and tau [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 234 of file Helmholtz.h.
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inlinevirtual |
Reimplemented in CoolProp::ResidualHelmholtzSAFTAssociating.
Definition at line 266 of file Helmholtz.h.
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inlinevirtual |
Returns the first partial derivative of Helmholtz energy term with respect to tau [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 180 of file Helmholtz.h.
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inlinevirtual |
Returns the second partial derivative of Helmholtz energy term with respect to tau [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 189 of file Helmholtz.h.
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inlinevirtual |
Returns the third partial derivative of Helmholtz energy term with respect to tau [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Definition at line 243 of file Helmholtz.h.
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inlinevirtual |
Returns the fourth partial derivative of Helmholtz energy term with respect to tau [-].
tau | Reciprocal reduced temperature where \(\tau=T_c / T\) |
delta | Reduced density where \(\delta = \rho / \rho_c \) |
Reimplemented in CoolProp::ResidualHelmholtzSAFTAssociating.
Definition at line 261 of file Helmholtz.h.