mirror of
https://github.com/CoolProp/CoolProp.git
synced 2026-01-15 00:48:18 -05:00
93f4a986e2
Found via `codespell -i 3 -w -I ../coolprop-word-whitelist.txt` whereby whitelist consists of: ``` cas formate hel nd te tim ue uint ```
1171 lines
51 KiB
C++
1171 lines
51 KiB
C++
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#ifndef HELMHOLTZ_H
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#define HELMHOLTZ_H
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#include <vector>
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#include "rapidjson_include.h"
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//#include "Eigen/Core"
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#include "time.h"
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#include "CachedElement.h"
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#include "Backends/Cubics/GeneralizedCubic.h"
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#include "crossplatform_shared_ptr.h"
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namespace CoolProp{
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// #############################################################################
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// #############################################################################
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// #############################################################################
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// RESIDUAL TERMS
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// #############################################################################
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// #############################################################################
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// #############################################################################
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#define LIST_OF_DERIVATIVE_VARIABLES \
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X(alphar) \
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X(dalphar_ddelta) \
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X(dalphar_dtau) \
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X(d2alphar_ddelta2) \
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X(d2alphar_dtau2) \
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X(d2alphar_ddelta_dtau) \
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X(d3alphar_ddelta3) \
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X(d3alphar_ddelta_dtau2) \
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X(d3alphar_ddelta2_dtau) \
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X(d3alphar_dtau3) \
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X(d4alphar_ddelta4) \
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X(d4alphar_ddelta3_dtau) \
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X(d4alphar_ddelta2_dtau2) \
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X(d4alphar_ddelta_dtau3) \
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X(d4alphar_dtau4) \
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X(delta_x_dalphar_ddelta) \
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X(tau_x_dalphar_dtau) \
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X(delta2_x_d2alphar_ddelta2) \
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X(deltatau_x_d2alphar_ddelta_dtau) \
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X(tau2_x_d2alphar_dtau2) \
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struct HelmholtzDerivatives
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{
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#define X(name) CoolPropDbl name;
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LIST_OF_DERIVATIVE_VARIABLES
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#undef X
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void reset(CoolPropDbl v){
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#define X(name) name = v;
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LIST_OF_DERIVATIVE_VARIABLES
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#undef X
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}
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HelmholtzDerivatives operator+(const HelmholtzDerivatives &other) const
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{
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HelmholtzDerivatives _new;
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#define X(name) _new.name = name + other.name;
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LIST_OF_DERIVATIVE_VARIABLES
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#undef X
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return _new;
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}
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HelmholtzDerivatives operator*(const CoolPropDbl &other) const
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{
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HelmholtzDerivatives _new;
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#define X(name) _new.name = name*other;
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LIST_OF_DERIVATIVE_VARIABLES
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#undef X
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return _new;
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}
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HelmholtzDerivatives(){reset(0.0);};
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/// Retrieve a single value based on the number of derivatives with respect to tau and delta
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double get(std::size_t itau, std::size_t idelta){
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if (itau == 0){
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if (idelta == 0){ return alphar; }
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else if (idelta == 1){ return dalphar_ddelta; }
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else if (idelta == 2){ return d2alphar_ddelta2; }
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else if (idelta == 3){ return d3alphar_ddelta3; }
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else if (idelta == 4){ return d4alphar_ddelta4; }
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else { throw ValueError(); }
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}
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else if (itau == 1){
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if (idelta == 0){ return dalphar_dtau; }
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else if (idelta == 1){ return d2alphar_ddelta_dtau; }
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else if (idelta == 2){ return d3alphar_ddelta2_dtau; }
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else if (idelta == 3){ return d4alphar_ddelta3_dtau; }
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else { throw ValueError(); }
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}
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else if (itau == 2){
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if (idelta == 0){ return d2alphar_dtau2; }
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else if (idelta == 1){ return d3alphar_ddelta_dtau2; }
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else if (idelta == 2){ return d4alphar_ddelta2_dtau2; }
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else { throw ValueError(); }
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}
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else if (itau == 3){
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if (idelta == 0){ return d3alphar_dtau3; }
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else if (idelta == 1){ return d4alphar_ddelta_dtau3; }
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else { throw ValueError(); }
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}
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else if (itau == 4){
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if (idelta == 0){ return d4alphar_dtau4; }
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else { throw ValueError(); }
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}
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else { throw ValueError(); }
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}
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};
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#undef LIST_OF_DERIVATIVE_VARIABLES
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/// The base class class for the Helmholtz energy terms
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/**
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Residual Helmholtz Energy Terms:
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Term | Helmholtz Energy Contribution
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---------- | ------------------------------
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ResidualHelmholtzPower | \f$ \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.\f$
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ResidualHelmholtzExponential | \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\gamma_i\delta^{l_i}) \f$
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ResidualHelmholtzLemmon2005 | \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}-\tau^{m_i})\f$
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ResidualHelmholtzGaussian | \f$ \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)\f$
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ResidualHelmholtzGERG2008Gaussian | \f$ \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))\f$
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ResidualHelmholtzNonAnalytic | \f$ \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}\f$
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ResidualHelmholtzSAFTAssociating | \f$ \alpha^r = am\left(\ln X-\frac{X}{2}+\frac{1}{2}\right); \f$
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Ideal-Gas Helmholtz Energy Terms:
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Term | Helmholtz Energy Contribution
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---------- | ------------------------------
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IdealHelmholtzLead | \f$ \alpha^0 = n_1 + n_2\tau + \ln\delta \f$
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IdealHelmholtzEnthalpyEntropyOffset | \f$ \alpha^0 = \displaystyle\frac{\Delta s}{R_u/M}+\frac{\Delta h}{(R_u/M)T}\tau \f$
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IdealHelmholtzLogTau | \f$ \alpha^0 = n_1\log\tau \f$
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IdealHelmholtzPower | \f$ \alpha^0 = \displaystyle\sum_i n_i\tau^{t_i} \f$
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IdealHelmholtzPlanckEinsteinGeneralized | \f$ \alpha^0 = \displaystyle\sum_i n_i\log[c_i+d_i\exp(\theta_i\tau)] \f$
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*/
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class BaseHelmholtzTerm{
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public:
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BaseHelmholtzTerm(){};
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virtual ~BaseHelmholtzTerm(){};
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/// Returns the base, non-dimensional, Helmholtz energy term (no derivatives) [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl base(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.alphar;};
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/// Returns the first partial derivative of Helmholtz energy term with respect to tau [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.dalphar_dtau;};
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/// Returns the second partial derivative of Helmholtz energy term with respect to tau [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dTau2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d2alphar_dtau2;};
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/// Returns the second mixed partial derivative (delta1,dtau1) of Helmholtz energy term with respect to delta and tau [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dDelta_dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d2alphar_ddelta_dtau;};
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/// Returns the first partial derivative of Helmholtz energy term with respect to delta [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dDelta(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.dalphar_ddelta;};
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/// Returns the second partial derivative of Helmholtz energy term with respect to delta [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dDelta2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d2alphar_ddelta2;};
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/// Returns the third mixed partial derivative (delta2,dtau1) of Helmholtz energy term with respect to delta and tau [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dDelta2_dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d3alphar_ddelta2_dtau;};
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/// Returns the third mixed partial derivative (delta1,dtau2) of Helmholtz energy term with respect to delta and tau [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dDelta_dTau2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d3alphar_ddelta_dtau2;};
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/// Returns the third partial derivative of Helmholtz energy term with respect to tau [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dTau3(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d3alphar_dtau3;};
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/// Returns the third partial derivative of Helmholtz energy term with respect to delta [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dDelta3(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d3alphar_ddelta3;};
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/// Returns the fourth partial derivative of Helmholtz energy term with respect to tau [-]
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/** @param tau Reciprocal reduced temperature where \f$\tau=T_c / T\f$
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* @param delta Reduced density where \f$\delta = \rho / \rho_c \f$
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*/
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virtual CoolPropDbl dTau4(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d4alphar_dtau4;};
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virtual CoolPropDbl dDelta_dTau3(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d4alphar_ddelta_dtau3;};
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virtual CoolPropDbl dDelta2_dTau2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d4alphar_ddelta2_dtau2;};
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virtual CoolPropDbl dDelta3_dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d4alphar_ddelta3_dtau;};
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virtual CoolPropDbl dDelta4(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){HelmholtzDerivatives deriv; all(tau,delta,deriv); return deriv.d4alphar_ddelta4;};
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virtual void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw() = 0;
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};
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struct ResidualHelmholtzGeneralizedExponentialElement
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{
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/// These variables are for the n*delta^d_i*tau^t_i part
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CoolPropDbl n,d,t;
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/// These variables are for the exp(u) part
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/// u is given by -c*delta^l_i-omega*tau^m_i-eta1*(delta-epsilon1)-eta2*(delta-epsilon2)^2-beta1*(tau-gamma1)-beta2*(tau-gamma2)^2
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CoolPropDbl c, l_double, omega, m_double, eta1, epsilon1, eta2, epsilon2, beta1, gamma1, beta2, gamma2;
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/// If l_i or m_i are integers, we will store them as integers in order to call pow(double, int) rather than pow(double, double)
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int l_int, m_int;
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/// If l is an integer, store a boolean flag so we can evaluate the correct pow() function
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bool l_is_int, m_is_int;
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ResidualHelmholtzGeneralizedExponentialElement()
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{
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n = 0; d = 0; t = 0; c = 0;
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l_double = 0; omega = 0; m_double = 0;
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eta1 = 0; epsilon1 = 0; eta2 = 0; epsilon2 = 0;
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beta1 = 0; gamma1 = 0; beta2 = 0; gamma2 = 0;
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l_int = 0; m_int = 0; l_is_int = false; m_is_int = true;
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};
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};
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/** \brief A generalized residual helmholtz energy container that can deal with a wide range of terms which can be converted to this general form
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*
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* \f$ \alpha^r=\sum_i n_i \delta^{d_i} \tau^{t_i}\exp(u_i) \f$
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*
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* where \f$ u_i \f$ is given by
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*
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* \f$ u_i = -c_i\delta^{l_i}-\omega_i\tau^{m_i}-\eta_{1,i}(\delta-\epsilon_{1,i})-\eta_{2,i}(\delta-\epsilon_{2,i})^2-\beta_{1,i}(\tau-\gamma_{1,i})-\beta_{2,i}(\tau-\gamma_{2,i})^2 \f$
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*/
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class ResidualHelmholtzGeneralizedExponential : public BaseHelmholtzTerm{
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public:
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bool delta_li_in_u, tau_mi_in_u, eta1_in_u, eta2_in_u, beta1_in_u, beta2_in_u, finished;
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std::vector<CoolPropDbl> s;
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std::size_t N;
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// These variables are for the exp(u) part
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// u is given by -c*delta^l_i-omega*tau^m_i-eta1*(delta-epsilon1)-eta2*(delta-epsilon2)^2-beta1*(tau-gamma1)-beta2*(tau-gamma2)^2
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std::vector<double> n,d,t,c, l_double, omega, m_double, eta1, epsilon1, eta2, epsilon2, beta1, gamma1, beta2, gamma2;
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// If l_i or m_i are integers, we will store them as integers in order to call pow(double, int) rather than pow(double, double)
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std::vector<int> l_int, m_int;
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//Eigen::ArrayXd uE, du_ddeltaE, du_dtauE, d2u_ddelta2E, d2u_dtau2E, d3u_ddelta3E, d3u_dtau3E;
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std::vector<ResidualHelmholtzGeneralizedExponentialElement> elements;
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// Default Constructor
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ResidualHelmholtzGeneralizedExponential()
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: delta_li_in_u(false),tau_mi_in_u(false),eta1_in_u(false),
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eta2_in_u(false),beta1_in_u(false),beta2_in_u(false),finished(false), N(0) {};
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/** \brief Add and convert an old-style power (polynomial) term to generalized form
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*
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* Term of the format
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* \f$ \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.\f$
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*/
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void add_Power(const std::vector<CoolPropDbl> &n, const std::vector<CoolPropDbl> &d,
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const std::vector<CoolPropDbl> &t, const std::vector<CoolPropDbl> &l)
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{
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for (std::size_t i = 0; i < n.size(); ++i)
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{
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ResidualHelmholtzGeneralizedExponentialElement el;
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el.n = n[i];
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el.d = d[i];
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el.t = t[i];
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el.l_double = l[i];
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el.l_int = (int)el.l_double;
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if (el.l_double > 0)
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el.c = 1.0;
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else
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el.c = 0.0;
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elements.push_back(el);
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}
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delta_li_in_u = true;
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};
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/** \brief Add and convert an old-style exponential term to generalized form
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*
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* Term of the format
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* \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-g_i\delta^{l_i}) \f$
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*/
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void add_Exponential(const std::vector<CoolPropDbl> &n, const std::vector<CoolPropDbl> &d,
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const std::vector<CoolPropDbl> &t, const std::vector<CoolPropDbl> &g,
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const std::vector<CoolPropDbl> &l)
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{
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for (std::size_t i = 0; i < n.size(); ++i)
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{
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ResidualHelmholtzGeneralizedExponentialElement el;
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el.n = n[i];
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el.d = d[i];
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el.t = t[i];
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el.c = g[i];
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el.l_double = l[i];
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el.l_int = (int)el.l_double;
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elements.push_back(el);
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}
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delta_li_in_u = true;
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}
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/** \brief Add and convert an old-style Gaussian term to generalized form
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*
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* Term of the format
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* \f$ \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)\f$
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*/
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void add_Gaussian(const std::vector<CoolPropDbl> &n,
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const std::vector<CoolPropDbl> &d,
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const std::vector<CoolPropDbl> &t,
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const std::vector<CoolPropDbl> &eta,
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const std::vector<CoolPropDbl> &epsilon,
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const std::vector<CoolPropDbl> &beta,
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const std::vector<CoolPropDbl> &gamma
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)
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{
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for (std::size_t i = 0; i < n.size(); ++i)
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{
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ResidualHelmholtzGeneralizedExponentialElement el;
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el.n = n[i];
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el.d = d[i];
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el.t = t[i];
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el.eta2 = eta[i];
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el.epsilon2 = epsilon[i];
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el.beta2 = beta[i];
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el.gamma2 = gamma[i];
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elements.push_back(el);
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}
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eta2_in_u = true;
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beta2_in_u = true;
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};
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/** \brief Add and convert an old-style Gaussian term from GERG 2008 natural gas model to generalized form
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*
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* Term of the format
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* \f$ \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))\f$
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*/
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|
void add_GERG2008Gaussian(const std::vector<CoolPropDbl> &n,
|
|
const std::vector<CoolPropDbl> &d,
|
|
const std::vector<CoolPropDbl> &t,
|
|
const std::vector<CoolPropDbl> &eta,
|
|
const std::vector<CoolPropDbl> &epsilon,
|
|
const std::vector<CoolPropDbl> &beta,
|
|
const std::vector<CoolPropDbl> &gamma)
|
|
{
|
|
for (std::size_t i = 0; i < n.size(); ++i)
|
|
{
|
|
ResidualHelmholtzGeneralizedExponentialElement el;
|
|
el.n = n[i];
|
|
el.d = d[i];
|
|
el.t = t[i];
|
|
el.eta2 = eta[i];
|
|
el.epsilon2 = epsilon[i];
|
|
el.eta1 = beta[i];
|
|
el.epsilon1 = gamma[i];
|
|
elements.push_back(el);
|
|
}
|
|
eta2_in_u = true;
|
|
eta1_in_u = true;
|
|
};
|
|
/** \brief Add and convert a term from Lemmon and Jacobsen (2005) used for R125
|
|
*
|
|
* Term of the format
|
|
* \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}-\tau^{m_i})\f$
|
|
*/
|
|
void add_Lemmon2005(const std::vector<CoolPropDbl> &n,
|
|
const std::vector<CoolPropDbl> &d,
|
|
const std::vector<CoolPropDbl> &t,
|
|
const std::vector<CoolPropDbl> &l,
|
|
const std::vector<CoolPropDbl> &m)
|
|
{
|
|
for (std::size_t i = 0; i < n.size(); ++i)
|
|
{
|
|
ResidualHelmholtzGeneralizedExponentialElement el;
|
|
el.n = n[i];
|
|
el.d = d[i];
|
|
el.t = t[i];
|
|
el.c = 1.0;
|
|
el.omega = 1.0;
|
|
el.l_double = l[i];
|
|
el.m_double = m[i];
|
|
el.l_int = (int)el.l_double;
|
|
el.m_int = (int)el.m_double;
|
|
elements.push_back(el);
|
|
}
|
|
delta_li_in_u = true;
|
|
tau_mi_in_u = true;
|
|
};
|
|
|
|
void finish(){
|
|
n.resize(elements.size()); d.resize(elements.size());
|
|
t.resize(elements.size()); c.resize(elements.size());
|
|
omega.resize(elements.size());
|
|
l_double.resize(elements.size()); l_int.resize(elements.size());
|
|
m_double.resize(elements.size()); m_int.resize(elements.size());
|
|
epsilon2.resize(elements.size()); eta2.resize(elements.size());
|
|
gamma2.resize(elements.size()); beta2.resize(elements.size());
|
|
|
|
for (std::size_t i = 0; i < elements.size(); ++i){
|
|
n[i] = elements[i].n;
|
|
d[i] = elements[i].d;
|
|
t[i] = elements[i].t;
|
|
c[i] = elements[i].c;
|
|
omega[i] = elements[i].omega;
|
|
l_double[i] = elements[i].l_double;
|
|
l_int[i] = elements[i].l_int;
|
|
m_double[i] = elements[i].m_double;
|
|
m_int[i] = elements[i].m_int;
|
|
epsilon2[i] = elements[i].epsilon2;
|
|
eta2[i] = elements[i].eta2;
|
|
gamma2[i] = elements[i].gamma2;
|
|
beta2[i] = elements[i].beta2;
|
|
|
|
// See if l is an integer, and store a flag if it is
|
|
elements[i].l_is_int = ( std::abs(static_cast<long>(elements[i].l_double) - elements[i].l_double) < 1e-14 );
|
|
}
|
|
// uE.resize(elements.size());
|
|
// du_ddeltaE.resize(elements.size());
|
|
// du_dtauE.resize(elements.size());
|
|
// d2u_ddelta2E.resize(elements.size());
|
|
// d2u_dtau2E.resize(elements.size());
|
|
// d3u_ddelta3E.resize(elements.size());
|
|
// d3u_dtau3E.resize(elements.size());
|
|
|
|
finished = true;
|
|
};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc);
|
|
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
//void allEigen(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
struct ResidualHelmholtzNonAnalyticElement
|
|
{
|
|
CoolPropDbl n, a, b, beta, A, B, C, D;
|
|
};
|
|
class ResidualHelmholtzNonAnalytic : public BaseHelmholtzTerm{
|
|
|
|
public:
|
|
std::size_t N;
|
|
std::vector<CoolPropDbl> s;
|
|
std::vector<ResidualHelmholtzNonAnalyticElement> elements;
|
|
/// Default Constructor
|
|
ResidualHelmholtzNonAnalytic(){N = 0;};
|
|
/// Destructor. No implementation
|
|
~ResidualHelmholtzNonAnalytic(){};
|
|
/// Constructor
|
|
ResidualHelmholtzNonAnalytic(const std::vector<CoolPropDbl> &n,
|
|
const std::vector<CoolPropDbl> &a,
|
|
const std::vector<CoolPropDbl> &b,
|
|
const std::vector<CoolPropDbl> &beta,
|
|
const std::vector<CoolPropDbl> &A,
|
|
const std::vector<CoolPropDbl> &B,
|
|
const std::vector<CoolPropDbl> &C,
|
|
const std::vector<CoolPropDbl> &D
|
|
)
|
|
{
|
|
N = n.size();
|
|
s.resize(N);
|
|
for (std::size_t i = 0; i < n.size(); ++i)
|
|
{
|
|
ResidualHelmholtzNonAnalyticElement el;
|
|
el.n = n[i];
|
|
el.a = a[i];
|
|
el.b = b[i];
|
|
el.beta = beta[i];
|
|
el.A = A[i];
|
|
el.B = B[i];
|
|
el.C = C[i];
|
|
el.D = D[i];
|
|
elements.push_back(el);
|
|
}
|
|
};
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc);
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
class ResidualHelmholtzGeneralizedCubic : public BaseHelmholtzTerm{
|
|
protected:
|
|
shared_ptr<AbstractCubic> m_abstractcubic;
|
|
std::vector<double> z; /// Vector of mole fractions, will be initialized to [1.0] since this is a pure fluid
|
|
public:
|
|
bool enabled;
|
|
|
|
/// Default Constructor
|
|
ResidualHelmholtzGeneralizedCubic() { enabled = false; };
|
|
/// Constructor given an abstract cubic instance
|
|
ResidualHelmholtzGeneralizedCubic(shared_ptr<AbstractCubic> & ac) : m_abstractcubic(ac){
|
|
enabled = true;
|
|
z = std::vector<double>(1,1); // Init the vector to [1.0]
|
|
};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc);
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
/// The generalized Lee-Kesler formulation of Xiang & Deiters: doi:10.1016/j.ces.2007.11.029
|
|
class ResidualHelmholtzXiangDeiters : public BaseHelmholtzTerm{
|
|
|
|
public:
|
|
bool enabled;
|
|
ResidualHelmholtzGeneralizedExponential phi0, phi1, phi2;
|
|
CoolPropDbl Tc, pc, rhomolarc, acentric, R, theta;
|
|
/// Default Constructor
|
|
ResidualHelmholtzXiangDeiters() : Tc(_HUGE), pc(_HUGE), rhomolarc(_HUGE), acentric(_HUGE), R(_HUGE), theta(_HUGE)
|
|
{
|
|
enabled = false;
|
|
};
|
|
/// Constructor
|
|
ResidualHelmholtzXiangDeiters(
|
|
const CoolPropDbl Tc,
|
|
const CoolPropDbl pc,
|
|
const CoolPropDbl rhomolarc,
|
|
const CoolPropDbl acentric,
|
|
const CoolPropDbl R
|
|
);
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
class ResidualHelmholtzSAFTAssociating : public BaseHelmholtzTerm{
|
|
|
|
protected:
|
|
double a, m,epsilonbar, vbarn, kappabar;
|
|
|
|
CoolPropDbl Deltabar(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl dDeltabar_ddelta__consttau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d2Deltabar_ddelta2__consttau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl dDeltabar_dtau__constdelta(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d2Deltabar_dtau2__constdelta(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d2Deltabar_ddelta_dtau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d3Deltabar_dtau3__constdelta(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d3Deltabar_ddelta_dtau2(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d3Deltabar_ddelta3__consttau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d3Deltabar_ddelta2_dtau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
|
|
CoolPropDbl X(const CoolPropDbl &delta, const CoolPropDbl &Deltabar) const;
|
|
CoolPropDbl dX_dDeltabar__constdelta(const CoolPropDbl &delta, const CoolPropDbl &Deltabar) const;
|
|
CoolPropDbl dX_ddelta__constDeltabar(const CoolPropDbl &delta, const CoolPropDbl &Deltabar) const;
|
|
CoolPropDbl dX_dtau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl dX_ddelta(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d2X_dtau2(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d2X_ddeltadtau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d2X_ddelta2(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
|
|
CoolPropDbl d3X_dtau3(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d3X_ddelta3(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d3X_ddeltadtau2(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
CoolPropDbl d3X_ddelta2dtau(const CoolPropDbl &tau, const CoolPropDbl &delta) const;
|
|
|
|
CoolPropDbl g(const CoolPropDbl &eta) const;
|
|
CoolPropDbl dg_deta(const CoolPropDbl &eta) const;
|
|
CoolPropDbl d2g_deta2(const CoolPropDbl &eta) const;
|
|
CoolPropDbl d3g_deta3(const CoolPropDbl &eta) const;
|
|
CoolPropDbl eta(const CoolPropDbl &delta) const;
|
|
|
|
public:
|
|
/// Default constructor
|
|
ResidualHelmholtzSAFTAssociating() : a(_HUGE), m(_HUGE), epsilonbar(_HUGE), vbarn(_HUGE), kappabar(_HUGE)
|
|
{ disabled = true; };
|
|
|
|
// Constructor
|
|
ResidualHelmholtzSAFTAssociating(double a, double m, double epsilonbar, double vbarn, double kappabar)
|
|
: a(a), m(m), epsilonbar(epsilonbar), vbarn(vbarn), kappabar(kappabar)
|
|
{
|
|
disabled = false;
|
|
};
|
|
|
|
bool disabled;
|
|
|
|
//Destructor. No Implementation
|
|
~ResidualHelmholtzSAFTAssociating(){};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc);
|
|
|
|
CoolPropDbl dTau4(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 1e99;};
|
|
CoolPropDbl dDelta_dTau3(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 1e99;};
|
|
CoolPropDbl dDelta2_dTau2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 1e99;};
|
|
CoolPropDbl dDelta3_dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 1e99;};
|
|
CoolPropDbl dDelta4(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 1e99;};
|
|
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &deriv) throw();
|
|
};
|
|
|
|
class BaseHelmholtzContainer{
|
|
protected:
|
|
CachedElement _base, _dDelta, _dTau, _dDelta2, _dTau2, _dDelta_dTau, _dDelta3, _dDelta2_dTau, _dDelta_dTau2, _dTau3;
|
|
CachedElement _dDelta4, _dDelta3_dTau, _dDelta2_dTau2, _dDelta_dTau3, _dTau4;
|
|
public:
|
|
void clear(){
|
|
_base.clear();
|
|
_dDelta.clear(); _dTau.clear();
|
|
_dDelta2.clear(); _dTau2.clear(); _dDelta_dTau.clear();
|
|
_dDelta3.clear(); _dTau3.clear(); _dDelta2_dTau.clear(); _dDelta_dTau2.clear();
|
|
_dDelta4.clear(); _dDelta3_dTau.clear(); _dDelta2_dTau2.clear(); _dDelta_dTau3.clear(); _dTau4.clear();
|
|
};
|
|
|
|
virtual void empty_the_EOS() = 0;
|
|
virtual HelmholtzDerivatives all(const CoolPropDbl tau, const CoolPropDbl delta, bool cache_values) = 0;
|
|
|
|
CoolPropDbl base(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_base || dont_use_cache)
|
|
return all(tau, delta, false).alphar;
|
|
else
|
|
return _base;
|
|
};
|
|
CoolPropDbl dDelta(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dDelta || dont_use_cache)
|
|
return all(tau, delta, false).dalphar_ddelta;
|
|
else
|
|
return _dDelta;
|
|
};
|
|
CoolPropDbl dTau(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dTau || dont_use_cache)
|
|
return all(tau, delta, false).dalphar_dtau;
|
|
else
|
|
return _dTau;
|
|
};
|
|
CoolPropDbl dDelta2(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dDelta2 || dont_use_cache)
|
|
return all(tau, delta, false).d2alphar_ddelta2;
|
|
else
|
|
return _dDelta2;
|
|
};
|
|
CoolPropDbl dDelta_dTau(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dDelta_dTau || dont_use_cache)
|
|
return all(tau, delta, false).d2alphar_ddelta_dtau;
|
|
else
|
|
return _dDelta_dTau;
|
|
};
|
|
CoolPropDbl dTau2(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dTau2 || dont_use_cache)
|
|
return all(tau, delta, false).d2alphar_dtau2;
|
|
else
|
|
return _dTau2;
|
|
};
|
|
CoolPropDbl dDelta3(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dDelta3 || dont_use_cache)
|
|
return all(tau, delta, false).d3alphar_ddelta3;
|
|
else
|
|
return _dDelta3;
|
|
};
|
|
CoolPropDbl dDelta2_dTau(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dDelta2_dTau || dont_use_cache)
|
|
return all(tau, delta, false).d3alphar_ddelta2_dtau;
|
|
else
|
|
return _dDelta2_dTau;
|
|
};
|
|
CoolPropDbl dDelta_dTau2(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dDelta_dTau2 || dont_use_cache)
|
|
return all(tau, delta, false).d3alphar_ddelta_dtau2;
|
|
else
|
|
return _dDelta_dTau2;
|
|
};
|
|
CoolPropDbl dTau3(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) {
|
|
if (!_dTau3 || dont_use_cache)
|
|
return all(tau, delta, false).d3alphar_dtau3;
|
|
else
|
|
return _dTau3;
|
|
};
|
|
CoolPropDbl dDelta4(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) { return all(tau, delta, false).d4alphar_ddelta4; };
|
|
CoolPropDbl dDelta3_dTau(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) { return all(tau, delta, false).d4alphar_ddelta3_dtau; };
|
|
CoolPropDbl dDelta2_dTau2(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) { return all(tau, delta, false).d4alphar_ddelta2_dtau2; };
|
|
CoolPropDbl dDelta_dTau3(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) { return all(tau, delta, false).d4alphar_ddelta_dtau3; };
|
|
CoolPropDbl dTau4(CoolPropDbl tau, CoolPropDbl delta, const bool dont_use_cache = false) { return all(tau, delta, false).d4alphar_dtau4; };
|
|
};
|
|
|
|
class ResidualHelmholtzContainer : public BaseHelmholtzContainer
|
|
{
|
|
public:
|
|
ResidualHelmholtzNonAnalytic NonAnalytic;
|
|
ResidualHelmholtzSAFTAssociating SAFT;
|
|
ResidualHelmholtzGeneralizedExponential GenExp;
|
|
ResidualHelmholtzGeneralizedCubic cubic;
|
|
ResidualHelmholtzXiangDeiters XiangDeiters;
|
|
|
|
void empty_the_EOS(){
|
|
NonAnalytic = ResidualHelmholtzNonAnalytic();
|
|
SAFT = ResidualHelmholtzSAFTAssociating();
|
|
GenExp = ResidualHelmholtzGeneralizedExponential();
|
|
cubic = ResidualHelmholtzGeneralizedCubic();
|
|
XiangDeiters = ResidualHelmholtzXiangDeiters();
|
|
};
|
|
|
|
HelmholtzDerivatives all(const CoolPropDbl tau, const CoolPropDbl delta, bool cache_values = false)
|
|
{
|
|
HelmholtzDerivatives derivs; // zeros out the elements
|
|
GenExp.all(tau, delta, derivs);
|
|
NonAnalytic.all(tau, delta, derivs);
|
|
SAFT.all(tau, delta, derivs);
|
|
cubic.all(tau, delta, derivs);
|
|
XiangDeiters.all(tau, delta, derivs);
|
|
if (cache_values){
|
|
_base = derivs.alphar;
|
|
_dDelta = derivs.dalphar_ddelta;
|
|
_dTau = derivs.dalphar_dtau;
|
|
_dDelta2 = derivs.d2alphar_ddelta2;
|
|
_dTau2 = derivs.d2alphar_dtau2;
|
|
_dDelta_dTau = derivs.d2alphar_ddelta_dtau;
|
|
_dDelta3 = derivs.d3alphar_ddelta3;
|
|
_dTau3 = derivs.d3alphar_dtau3;
|
|
_dDelta2_dTau = derivs.d3alphar_ddelta2_dtau;
|
|
_dDelta_dTau2 = derivs.d3alphar_ddelta_dtau2;
|
|
}
|
|
return derivs;
|
|
};
|
|
};
|
|
|
|
// #############################################################################
|
|
// #############################################################################
|
|
// #############################################################################
|
|
// IDEAL GAS TERMS
|
|
// #############################################################################
|
|
// #############################################################################
|
|
// #############################################################################
|
|
|
|
/// The leading term in the EOS used to set the desired reference state
|
|
/**
|
|
\f[
|
|
\alpha^0 = \log(\delta)+a_1+a_2\tau
|
|
\f]
|
|
*/
|
|
class IdealHelmholtzLead : public BaseHelmholtzTerm{
|
|
|
|
private:
|
|
CoolPropDbl a1, a2;
|
|
bool enabled;
|
|
public:
|
|
// Default constructor
|
|
IdealHelmholtzLead() :a1(_HUGE), a2(_HUGE), enabled(false) {}
|
|
|
|
// Constructor
|
|
IdealHelmholtzLead(CoolPropDbl a1, CoolPropDbl a2)
|
|
:a1(a1), a2(a2), enabled(true) {}
|
|
|
|
bool is_enabled() const {return enabled;}
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc){
|
|
el.AddMember("type","IdealHelmholtzLead",doc.GetAllocator());
|
|
el.AddMember("a1", static_cast<double>(a1), doc.GetAllocator());
|
|
el.AddMember("a2", static_cast<double>(a2), doc.GetAllocator());
|
|
};
|
|
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
|
|
};
|
|
|
|
/// The term in the EOS used to shift the reference state of the fluid
|
|
/**
|
|
\f[
|
|
\alpha^0 = a_1+a_2\tau
|
|
\f]
|
|
*/
|
|
class IdealHelmholtzEnthalpyEntropyOffset : public BaseHelmholtzTerm{
|
|
private:
|
|
CoolPropDbl a1,a2; // Use these variables internally
|
|
std::string reference;
|
|
bool enabled;
|
|
public:
|
|
IdealHelmholtzEnthalpyEntropyOffset():a1(_HUGE),a2(_HUGE),enabled(false){}
|
|
|
|
// Constructor
|
|
IdealHelmholtzEnthalpyEntropyOffset(CoolPropDbl a1, CoolPropDbl a2, const std::string &ref):a1(a1),a2(a2),reference(ref),enabled(true) {}
|
|
|
|
// Set the values in the class
|
|
void set(CoolPropDbl a1, CoolPropDbl a2, const std::string &ref){
|
|
// If it doesn't already exist, just set the values
|
|
if (enabled == false){
|
|
this->a1 = a1; this->a2 = a2;
|
|
enabled = true;
|
|
}
|
|
else if(ref == "DEF"){
|
|
this->a1 = 0.0; this->a2 = 0.0; enabled = false;
|
|
}
|
|
else{
|
|
// Otherwise, increment the values
|
|
this->a1 += a1; this->a2 += a2;
|
|
enabled = true;
|
|
}
|
|
this->reference = ref;
|
|
}
|
|
|
|
bool is_enabled() const {return enabled;};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc){
|
|
el.AddMember("type","IdealHelmholtzEnthalpyEntropyOffset",doc.GetAllocator());
|
|
el.AddMember("a1", static_cast<double>(a1), doc.GetAllocator());
|
|
el.AddMember("a2", static_cast<double>(a2), doc.GetAllocator());
|
|
};
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
|
|
/**
|
|
\f[
|
|
\alpha^0 = a_1\ln\tau
|
|
\f]
|
|
*/
|
|
class IdealHelmholtzLogTau : public BaseHelmholtzTerm
|
|
{
|
|
private:
|
|
CoolPropDbl a1;
|
|
bool enabled;
|
|
public:
|
|
|
|
/// Default constructor
|
|
IdealHelmholtzLogTau():a1(_HUGE),enabled(false){}
|
|
|
|
// Constructor
|
|
IdealHelmholtzLogTau(CoolPropDbl a1):a1(a1),enabled(true){}
|
|
|
|
bool is_enabled() const {return enabled;};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc){
|
|
el.AddMember("type", "IdealHelmholtzLogTau", doc.GetAllocator());
|
|
el.AddMember("a1", static_cast<double>(a1), doc.GetAllocator());
|
|
};
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
/**
|
|
\f[
|
|
\alpha^0 = \displaystyle\sum_i n_i\tau^{t_i}
|
|
\f]
|
|
*/
|
|
class IdealHelmholtzPower : public BaseHelmholtzTerm{
|
|
|
|
private:
|
|
std::vector<CoolPropDbl> n, t; // Use these variables internally
|
|
std::size_t N;
|
|
bool enabled;
|
|
public:
|
|
IdealHelmholtzPower():N(0),enabled(false){};
|
|
// Constructor
|
|
IdealHelmholtzPower(const std::vector<CoolPropDbl> &n, const std::vector<CoolPropDbl> &t)
|
|
:n(n), t(t), N(n.size()), enabled(true) {};
|
|
|
|
bool is_enabled() const {return enabled;};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc)
|
|
{
|
|
el.AddMember("type","IdealHelmholtzPower",doc.GetAllocator());
|
|
cpjson::set_long_double_array("n",n,el,doc);
|
|
cpjson::set_long_double_array("t",t,el,doc);
|
|
};
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
/**
|
|
\f[
|
|
\alpha^0 = \displaystyle\sum_i n_i\log[c_i+d_i\exp(\theta_i\tau)]
|
|
\f]
|
|
|
|
To convert conventional Plank-Einstein forms, given by
|
|
\f$
|
|
\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}
|
|
\f$
|
|
and
|
|
\f$
|
|
\alpha^0 = a_k\ln \left[1 - \exp \left( \frac{-b_k\tau}{T_c} \right) \right]
|
|
\f$
|
|
use \f$c = 1\f$, \f$d = -1\f$, \f$n = a\f$, \f$\theta = -\displaystyle\frac{b_k}{T_c}\f$
|
|
|
|
To convert the second form of Plank-Einstein terms, given by
|
|
\f$
|
|
\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}
|
|
\f$
|
|
and
|
|
\f$
|
|
\alpha^0 = a_k\ln \left[c + \exp \left( \frac{b_k\tau}{T_c} \right) \right]
|
|
\f$
|
|
use \f$c = 1\f$, \f$d = 1\f$, \f$n = -a\f$, \f$\theta = \displaystyle\frac{b_k}{T_c}\f$
|
|
|
|
Converting Aly-Lee tems is a bit more complex
|
|
|
|
Aly-Lee starts as
|
|
\f[\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\f]
|
|
|
|
Constant is separated out, and handled separately. sinh part can be expanded as
|
|
\f[B\left(\frac{C/T}{\sinh(C/T)}\right)^2 = \frac{B(-2C/T)^2\exp(-2C/T)}{(1-\exp(-2C/T))^2}\f]
|
|
where
|
|
\f[n_k = B\f]
|
|
\f[\theta_k = -\frac{2C}{T_c}\f]
|
|
\f[c_k = 1\f]
|
|
\f[d_k = -1\f]
|
|
|
|
cosh part can be expanded as
|
|
\f[D\left(\frac{E/T}{\cosh(E/T)}\right)^2 = \frac{D(-2E/T)^2\exp(-2E/T)}{(1+\exp(-2E/T))^2}\f]
|
|
where
|
|
\f[n_k = -D\f]
|
|
\f[\theta_k = -\frac{2E}{T_c}\f]
|
|
\f[c_k = 1\f]
|
|
\f[d_k = 1\f]
|
|
*/
|
|
class IdealHelmholtzPlanckEinsteinGeneralized : public BaseHelmholtzTerm{
|
|
|
|
private:
|
|
std::vector<CoolPropDbl> n,theta,c,d; // Use these variables internally
|
|
std::size_t N;
|
|
bool enabled;
|
|
public:
|
|
IdealHelmholtzPlanckEinsteinGeneralized():N(0),enabled(false){}
|
|
// Constructor with std::vector instances
|
|
IdealHelmholtzPlanckEinsteinGeneralized(const std::vector<CoolPropDbl> &n, const std::vector<CoolPropDbl> &theta, const std::vector<CoolPropDbl> &c, const std::vector<CoolPropDbl> &d)
|
|
:n(n), theta(theta), c(c), d(d), N(n.size()), enabled(true) {}
|
|
|
|
// Extend the vectors to allow for multiple instances feeding values to this function
|
|
void extend(const std::vector<CoolPropDbl> &n, const std::vector<CoolPropDbl> &theta, const std::vector<CoolPropDbl> &c, const std::vector<CoolPropDbl> &d)
|
|
{
|
|
this->n.insert(this->n.end(), n.begin(), n.end());
|
|
this->theta.insert(this->theta.end(), theta.begin(), theta.end());
|
|
this->c.insert(this->c.end(), c.begin(), c.end());
|
|
this->d.insert(this->d.end(), d.begin(), d.end());
|
|
N += n.size();
|
|
}
|
|
|
|
bool is_enabled() const {return enabled;};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc)
|
|
{
|
|
el.AddMember("type","IdealHelmholtzPlanckEinsteinGeneralized",doc.GetAllocator());
|
|
cpjson::set_long_double_array("n",n,el,doc);
|
|
cpjson::set_long_double_array("theta",theta,el,doc);
|
|
};
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
class IdealHelmholtzCP0Constant : public BaseHelmholtzTerm{
|
|
|
|
private:
|
|
double cp_over_R,Tc,T0,tau0; // Use these variables internally
|
|
bool enabled;
|
|
public:
|
|
/// Default constructor
|
|
IdealHelmholtzCP0Constant() : cp_over_R(_HUGE), Tc(_HUGE), T0(_HUGE), tau0(_HUGE)
|
|
{enabled = false;};
|
|
|
|
/// Constructor with just a single double value
|
|
IdealHelmholtzCP0Constant(CoolPropDbl cp_over_R, CoolPropDbl Tc, CoolPropDbl T0)
|
|
: cp_over_R(cp_over_R), Tc(Tc), T0(T0)
|
|
{
|
|
enabled = true; tau0 = Tc/T0;
|
|
};
|
|
|
|
/// Destructor
|
|
~IdealHelmholtzCP0Constant(){};
|
|
|
|
bool is_enabled() const {return enabled;};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc)
|
|
{
|
|
el.AddMember("type","IdealGasHelmholtzCP0Constant", doc.GetAllocator());
|
|
el.AddMember("cp_over_R", cp_over_R, doc.GetAllocator());
|
|
el.AddMember("Tc", Tc, doc.GetAllocator());
|
|
el.AddMember("T0", T0, doc.GetAllocator());
|
|
};
|
|
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
class IdealHelmholtzCP0PolyT : public BaseHelmholtzTerm{
|
|
private:
|
|
std::vector<CoolPropDbl> c, t;
|
|
CoolPropDbl Tc, T0, tau0; // Use these variables internally
|
|
std::size_t N;
|
|
bool enabled;
|
|
public:
|
|
IdealHelmholtzCP0PolyT()
|
|
: Tc(_HUGE), T0(_HUGE), tau0(_HUGE), N(0), enabled(false) {}
|
|
|
|
/// Constructor with std::vectors
|
|
IdealHelmholtzCP0PolyT(const std::vector<CoolPropDbl> &c, const std::vector<CoolPropDbl> &t, double Tc, double T0)
|
|
: c(c), t(t), Tc(Tc), T0(T0), tau0(Tc/T0), N(c.size()), enabled(true)
|
|
{ assert(c.size() == t.size()); }
|
|
|
|
void extend(const std::vector<CoolPropDbl> &c, const std::vector<CoolPropDbl> &t)
|
|
{
|
|
this->c.insert(this->c.end(), c.begin(), c.end());
|
|
this->t.insert(this->t.end(), t.begin(), t.end());
|
|
N += c.size();
|
|
}
|
|
|
|
bool is_enabled() const {return enabled;};
|
|
|
|
void to_json(rapidjson::Value &el, rapidjson::Document &doc);
|
|
void all(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw();
|
|
};
|
|
|
|
///// Term in the ideal-gas specific heat equation that is based on Aly-Lee formulation
|
|
///** Specific heat is of the form:
|
|
//\f[
|
|
//\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
|
|
//\f]
|
|
//Second partial of ideal-gas Helmholtz energy given directly by specific heat (\f$\displaystyle\alpha_{\tau\tau}^0=-\frac{1}{\tau^2}\frac{c_p^0}{R_u} \f$) - this is obtained by real gas \f$c_p\f$ relationship, and killing off residual Helmholtz terms
|
|
//\f[
|
|
//\alpha^0_{\tau\tau} = -\frac{A}{\tau^2} - \frac{B}{\tau^2}\left(\frac{C/T}{\sinh(C/T)}\right)^2 - \frac{D}{\tau^2}\left(\frac{E/T}{\cosh(E/T)}\right)^2
|
|
//\f]
|
|
//or in terms of \f$ \tau \f$:
|
|
//\f[
|
|
//\alpha^0_{\tau\tau} = -\frac{A}{\tau^2} - \frac{BC^2}{T_c^2}\left(\frac{1}{\sinh(C\tau/T_c)}\right)^2 - \frac{DE^2}{T_c^2}\left(\frac{1}{\cosh(E\tau/T_c)}\right)^2
|
|
//\f]
|
|
//Third partial:
|
|
//\f[
|
|
//\alpha^0_{\tau\tau\tau} = 2\frac{A}{\tau^3} + 2\frac{BC^3}{T_c^3}\frac{\cosh(C\tau/T_c)}{\sinh^3(C\tau/T_c)} +2 \frac{DE^3}{T_c^3}\frac{\sinh(E\tau/T_c)}{\cosh^3(E\tau/T_c)}
|
|
//\f]
|
|
//Now coming back to the ideal gas Helmholtz energy definition:
|
|
//\f[
|
|
//\alpha^0 = -\tau\displaystyle\int_{\tau_0}^{\tau} \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau+\displaystyle\int_{\tau_0}^{\tau} \frac{1}{\tau}\frac{c_p^0}{R_u}d\tau
|
|
//\f]
|
|
//Applying derivative
|
|
//\f[
|
|
//\alpha^0_{\tau} = -\displaystyle\int_{\tau_0}^{\tau} \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau-\tau\frac{\partial}{\partial \tau}\left[\displaystyle\int_{\tau_0}^{\tau} \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau \right]+\frac{\partial}{\partial \tau}\left[\displaystyle\int_{\tau_0}^{\tau} \frac{1}{\tau}\frac{c_p^0}{R_u}d\tau \right]
|
|
//\f]
|
|
//Fundamental theorem of calculus
|
|
//\f[
|
|
//\alpha^0_{\tau} = -\int_{\tau_0}^{\tau} \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau-\tau \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau+\frac{1}{\tau}\frac{c_p^0}{R_u}
|
|
//\f]
|
|
//Last two terms cancel, leaving
|
|
//\f[
|
|
//\alpha^0_{\tau} = -\int_{\tau_0}^{\tau} \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau
|
|
//\f]
|
|
//Another derivative yields (from fundamental theorem of calculus)
|
|
//\f[
|
|
//\alpha^0_{\tau\tau} = - \frac{1}{\tau^2}\frac{c_p^0}{R_u}
|
|
//\f]
|
|
//
|
|
//see also Jaeschke and Schley, 1995, (http://link.springer.com/article/10.1007%2FBF02083547#page-1)
|
|
//*/
|
|
///*
|
|
//class IdealHelmholtzCP0AlyLee : public BaseHelmholtzTerm{
|
|
//private:
|
|
// std::vector<CoolPropDbl> c;
|
|
// CoolPropDbl Tc, tau0, T0; // Use these variables internally
|
|
// bool enabled;
|
|
//public:
|
|
// IdealHelmholtzCP0AlyLee(){enabled = false;};
|
|
//
|
|
// /// Constructor with std::vectors
|
|
// IdealHelmholtzCP0AlyLee(const std::vector<CoolPropDbl> &c, double Tc, double T0)
|
|
// :c(c), Tc(Tc), T0(T0)
|
|
// {
|
|
// tau0=Tc/T0;
|
|
// enabled = true;
|
|
// };
|
|
//
|
|
// /// Destructor
|
|
// ~IdealHelmholtzCP0AlyLee(){};
|
|
//
|
|
// bool is_enabled() const {return enabled;};
|
|
//
|
|
// void to_json(rapidjson::Value &el, rapidjson::Document &doc);
|
|
//
|
|
//
|
|
// /// The antiderivative given by \f$ \displaystyle\int \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau \f$
|
|
// /**
|
|
// sympy code for this derivative:
|
|
//
|
|
// from sympy import *
|
|
// a1,a2,a3,a4,a5,Tc,tau = symbols('a1,a2,a3,a4,a5,Tc,tau', real = True)
|
|
// integrand = a1 + a2*(a3/Tc/sinh(a3*tau/Tc))**2 + a4*(a5/Tc/cosh(a5*tau/Tc))**2
|
|
// integrand = integrand.rewrite(exp)
|
|
// antideriv = trigsimp(integrate(integrand,tau))
|
|
// display(antideriv)
|
|
// print latex(antideriv)
|
|
// print ccode(antideriv)
|
|
//
|
|
// \f[
|
|
// \displaystyle\int \frac{1}{\tau^2}\frac{c_p^0}{R_u}d\tau = -\frac{a_0}{\tau}+\frac{2a_1a_2}{T_c\left[\exp\left(-\frac{2a_2\tau}{T_c}\right)-1\right]}+\frac{2a_3a_4}{T_c\left[\exp\left(-\frac{2a_4\tau}{T_c}\right)+1\right]}
|
|
// \f]
|
|
// */
|
|
// CoolPropDbl anti_deriv_cp0_tau2(const CoolPropDbl &tau);
|
|
//
|
|
// /// The antiderivative given by \f$ \displaystyle\int \frac{1}{\tau}\frac{c_p^0}{R_u}d\tau \f$
|
|
// /**
|
|
// sympy code for this derivative:
|
|
//
|
|
// a_0,a_1,a_2,a_3,a_4,Tc,tau = symbols('a_0,a_1,a_2,a_3,a_4,Tc,tau', real = True)
|
|
// integrand = a_0/tau + a_1/tau*(a_2*tau/Tc/sinh(a_2*tau/Tc))**2 + a_3/tau*(a_4*tau/Tc/cosh(a_4*tau/Tc))**2
|
|
//
|
|
// term2 = a_1/tau*(a_2*tau/Tc/sinh(a_2*tau/Tc))**2
|
|
// term2 = term2.rewrite(exp) # Unpack the sinh to exp functions
|
|
// antideriv2 = trigsimp(integrate(term2,tau))
|
|
// display(antideriv2)
|
|
// print latex(antideriv2)
|
|
// print ccode(antideriv2)
|
|
//
|
|
// term3 = a_3/tau*(a_4*tau/Tc/cosh(a_4*tau/Tc))**2
|
|
// term3 = term3.rewrite(exp) # Unpack the cosh to exp functions
|
|
// antideriv3 = factor(trigsimp(integrate(term3,tau).rewrite(exp)))
|
|
// display(antideriv3)
|
|
// print latex(antideriv3)
|
|
// print ccode(antideriv3)
|
|
//
|
|
// Can be broken into three parts (trick is to express \f$sinh\f$ and \f$cosh\f$ in terms of \f$exp\f$ function)
|
|
//
|
|
// Term 2:
|
|
// \f[
|
|
// \displaystyle\int \frac{a_1a_2^2}{T_c^2}\frac{\tau}{\sinh\left(\displaystyle\frac{a_2\tau}{T_c}\right)^2} d\tau = \frac{2 a_{1} a_{2} \tau}{- Tc + Tc e^{- \frac{2 a_{2}}{Tc} \tau}} + a_{1} \log{\left (-1 + e^{- \frac{2 a_{2}}{Tc} \tau} \right )} + \frac{2 a_{1}}{Tc} a_{2} \tau
|
|
// \f]
|
|
//
|
|
// Term 3:
|
|
// \f[
|
|
// \displaystyle\int \frac{a_1a_2^2}{T_c^2}\frac{\tau}{\cosh\left(\displaystyle\frac{a_2\tau}{T_c}\right)^2} d\tau = - \frac{a_{3}}{Tc \left(e^{\frac{2 a_{4}}{Tc} \tau} + 1\right)} \left(Tc e^{\frac{2 a_{4}}{Tc} \tau} \log{\left (e^{\frac{2 a_{4}}{Tc} \tau} + 1 \right )} + Tc \log{\left (e^{\frac{2 a_{4}}{Tc} \tau} + 1 \right )} - 2 a_{4} \tau e^{\frac{2 a_{4}}{Tc} \tau}\right)
|
|
// \f]
|
|
// */
|
|
// CoolPropDbl anti_deriv_cp0_tau(const CoolPropDbl &tau);
|
|
//
|
|
// CoolPropDbl base(const CoolPropDbl &tau, const CoolPropDbl &delta) throw();
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// CoolPropDbl dDelta(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 0.0;};
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// CoolPropDbl dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw();
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// CoolPropDbl dDelta2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 0.0;};
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// CoolPropDbl dDelta_dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 0.0;};
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// CoolPropDbl dTau2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw();
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// CoolPropDbl dDelta3(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 0.0;};
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// CoolPropDbl dDelta2_dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 0.0;};
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// CoolPropDbl dDelta_dTau2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw(){return 0.0;};
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// CoolPropDbl dTau3(const CoolPropDbl &tau, const CoolPropDbl &delta) throw();
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// CoolPropDbl dTau4(const CoolPropDbl &tau, const CoolPropDbl &delta) throw();
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//
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//};
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class IdealHelmholtzContainer : public BaseHelmholtzContainer
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{
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public:
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IdealHelmholtzLead Lead;
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IdealHelmholtzEnthalpyEntropyOffset EnthalpyEntropyOffsetCore, EnthalpyEntropyOffset;
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IdealHelmholtzLogTau LogTau;
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IdealHelmholtzPower Power;
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IdealHelmholtzPlanckEinsteinGeneralized PlanckEinstein;
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IdealHelmholtzCP0Constant CP0Constant;
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IdealHelmholtzCP0PolyT CP0PolyT;
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void empty_the_EOS(){
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Lead = IdealHelmholtzLead();
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EnthalpyEntropyOffsetCore = IdealHelmholtzEnthalpyEntropyOffset();
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EnthalpyEntropyOffset = IdealHelmholtzEnthalpyEntropyOffset();
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LogTau = IdealHelmholtzLogTau();
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Power = IdealHelmholtzPower();
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PlanckEinstein = IdealHelmholtzPlanckEinsteinGeneralized();
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CP0Constant = IdealHelmholtzCP0Constant();
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CP0PolyT = IdealHelmholtzCP0PolyT();
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};
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HelmholtzDerivatives all(const CoolPropDbl tau, const CoolPropDbl delta, bool cache_values = false)
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{
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HelmholtzDerivatives derivs; // zeros out the elements
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Lead.all(tau, delta, derivs);
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EnthalpyEntropyOffsetCore.all(tau, delta, derivs);
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EnthalpyEntropyOffset.all(tau, delta, derivs);
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LogTau.all(tau, delta, derivs);
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Power.all(tau, delta, derivs);
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PlanckEinstein.all(tau, delta, derivs);
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CP0Constant.all(tau, delta, derivs);
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CP0PolyT.all(tau, delta, derivs);
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if (cache_values){
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_base = derivs.alphar;
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_dDelta = derivs.dalphar_ddelta;
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_dTau = derivs.dalphar_dtau;
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_dDelta2 = derivs.d2alphar_ddelta2;
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_dTau2 = derivs.d2alphar_dtau2;
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_dDelta_dTau = derivs.d2alphar_ddelta_dtau;
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_dDelta3 = derivs.d3alphar_ddelta3;
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_dTau3 = derivs.d3alphar_dtau3;
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_dDelta2_dTau = derivs.d3alphar_ddelta2_dtau;
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_dDelta_dTau2 = derivs.d3alphar_ddelta_dtau2;
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}
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return derivs;
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};
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};
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}; /* namespace CoolProp */
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#endif
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