phir_Lemmon2005 Class Reference

#include <Helmholtz.h>

Inheritance diagram for phir_Lemmon2005:

Public Member Functions
	phir_Lemmon2005 (std::vector< double >, std::vector< double >, std::vector< double >, std::vector< double >, std::vector< double >, int, int)
	phir_Lemmon2005 (const double[], const double[], const double[], const double[], const double[], int, int, int)
	phir_Lemmon2005 (double[], double[], double[], double[], double[], int, int, int)
	Destructor for the phir_Lemmon2005 class. No implementation. More...
	~phir_Lemmon2005 ()
void	to_json (rapidjson::Value &el, rapidjson::Document &doc)
double	base (double tau, double delta) throw ()
double	dDelta (double tau, double delta) throw ()
double	dTau (double tau, double delta) throw ()
double	dDelta2 (double tau, double delta) throw ()
double	dDelta_dTau (double tau, double delta) throw ()
double	dTau2 (double tau, double delta) throw ()
double	dDelta3 (double tau, double delta) throw ()
double	dDelta2_dTau (double tau, double delta) throw ()
double	dDelta_dTau2 (double tau, double delta) throw ()
double	dTau3 (double tau, double delta) throw ()
Public Member Functions inherited from phi_BC
	phi_BC ()
virtual	~phi_BC ()

Detailed Description

This class implements residual Helmholtz Energy terms of the form

\[ \phi_r = n \delta^d \tau^t \exp(-\delta^l) \exp(-\tau^m) \]

Definition at line 361 of file Helmholtz.h.

Constructor & Destructor Documentation

phir_Lemmon2005::phir_Lemmon2005	(	std::vector< double >	n,
		std::vector< double >	d,
		std::vector< double >	t,
		std::vector< double >	l,
		std::vector< double >	m,
		int	iStart_in,
		int	iEnd_in
	)

Definition at line 573 of file Helmholtz.cpp.

phir_Lemmon2005::phir_Lemmon2005	(	const double	n[],
		const double	d[],
		const double	t[],
		const double	l[],
		const double	m[],
		int	iStart_in,
		int	iEnd_in,
		int	N
	)

Definition at line 583 of file Helmholtz.cpp.

phir_Lemmon2005::phir_Lemmon2005	(	double	[],
		double	[],
		double	[],
		double	[],
		double	[],
		int	,
		int	,
		int
	)

Destructor for the phir_Lemmon2005 class. No implementation.

phir_Lemmon2005::~phir_Lemmon2005 ( )

inline

Definition at line 384 of file Helmholtz.h.

Member Function Documentation

double phir_Lemmon2005::base ( double  tau, double  delta  ) throw ( )

virtual

Returns the base, non-dimensional, Helmholtz energy term (no derivatives) [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc/T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 605 of file Helmholtz.cpp.

double phir_Lemmon2005::dDelta ( double  tau, double  delta  ) throw ( )

virtual

Returns the first partial derivative of Helmholtz energy term with respect to delta [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 721 of file Helmholtz.cpp.

double phir_Lemmon2005::dDelta2 ( double  tau, double  delta  ) throw ( )

virtual

Returns the second partial derivative of Helmholtz energy term with respect to delta [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 740 of file Helmholtz.cpp.

double phir_Lemmon2005::dDelta2_dTau ( double  tau, double  delta  ) throw ( )

virtual

Returns the third mixed partial derivative (delta2,dtau1) of Helmholtz energy term with respect to delta and tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 783 of file Helmholtz.cpp.

double phir_Lemmon2005::dDelta3 ( double  tau, double  delta  ) throw ( )

virtual

Returns the third partial derivative of Helmholtz energy term with respect to delta [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 760 of file Helmholtz.cpp.

double phir_Lemmon2005::dDelta_dTau ( double  tau, double  delta  ) throw ( )

virtual

Returns the second mixed partial derivative (delta1,dtau1) of Helmholtz energy term with respect to delta and tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 804 of file Helmholtz.cpp.

double phir_Lemmon2005::dDelta_dTau2 ( double  tau, double  delta  ) throw ( )

virtual

Returns the third mixed partial derivative (delta1,dtau2) of Helmholtz energy term with respect to delta and tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 700 of file Helmholtz.cpp.

double phir_Lemmon2005::dTau ( double  tau, double  delta  ) throw ( )

virtual

Returns the first partial derivative of Helmholtz energy term with respect to tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc/T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 619 of file Helmholtz.cpp.

double phir_Lemmon2005::dTau2 ( double  tau, double  delta  ) throw ( )

virtual

Returns the second partial derivative of Helmholtz energy term with respect to tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc/T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 635 of file Helmholtz.cpp.

double phir_Lemmon2005::dTau3 ( double  tau, double  delta  ) throw ( )

virtual

\[ \frac{{{\partial ^2}{\alpha ^r}}}{{\partial {\tau ^2}}} = {N_k}{\delta ^{{d_k}}}{\tau ^{{t_k} - 2}}\exp \left( { - {\delta ^{{l_k}}}} \right)\exp \left( { - {\tau ^{{m_k}}}} \right)\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right]\\ \]

\[ \frac{{{\partial ^2}{\alpha ^r}}}{{\partial {\tau ^2}}} = {N_k}{\delta ^{{d_k}}}\exp \left( { - {\delta ^{{l_k}}}} \right){\tau ^{{t_k} - 2}}\exp \left( { - {\tau ^{{m_k}}}} \right)\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right]\\ \]

Group all the terms that don't depend on $ $

\[ \frac{{{\partial ^2}{\alpha ^r}}}{{\partial {\tau ^2}}} = A{\tau ^{{t_k} - 2}}\exp \left( { - {\tau ^{{m_k}}}} \right)\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right]\\ \]

\[ \frac{1}{A}\frac{{{\partial ^3}{\alpha ^r}}}{{\partial {\tau ^3}}} = {\tau ^{{t_k} - 2}}\exp \left( { - {\tau ^{{m_k}}}} \right)\frac{\partial }{{\partial \tau }}\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right] + \frac{\partial }{{\partial \tau }}\left[ {{\tau ^{{t_k} - 2}}\exp \left( { - {\tau ^{{m_k}}}} \right)} \right]\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right]\\ \]

\[ \frac{\partial }{{\partial \tau }}\left[ {{\tau ^{{t_k} - 2}}\exp \left( { - {\tau ^{{m_k}}}} \right)} \right] = ({t_k} - 2){\tau ^{{t_k} - 3}}\exp \left( { - {\tau ^{{m_k}}}} \right) + {\tau ^{{t_k} - 2}}\exp \left( { - {\tau ^{{m_k}}}} \right)( - {m_k}{\tau ^{{m_k} - 1}}) = \exp \left( { - {\tau ^{{m_k}}}} \right)\left( {({t_k} - 2){\tau ^{{t_k} - 3}} - {\tau ^{{t_k} - 2}}{m_k}{\tau ^{{m_k} - 1}}} \right)\\ \]

\[ \frac{\partial }{{\partial \tau }}\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right] = \left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( { - m_k^2{\tau ^{{m_k} - 1}}} \right) + \left( { - m_k^2{\tau ^{{m_k} - 1}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^3{\tau ^{{m_k} - 1}} = - m_k^2{\tau ^{{m_k} - 1}}\left[ {{t_k} - {m_k}{\tau ^{{m_k}}} + {t_k} - 1 - {m_k}{\tau ^{{m_k}}} + {m_k}} \right] = - m_k^2{\tau ^{{m_k} - 1}}\left[ {2{t_k} - 2{m_k}{\tau ^{{m_k}}} - 1 + {m_k}} \right]\\ \]

\[ \frac{1}{A}\frac{{{\partial ^3}{\alpha ^r}}}{{\partial {\tau ^3}}} = {\tau ^{{t_k} - 2}}\exp \left( { - {\tau ^{{m_k}}}} \right)\left( { - m_k^2{\tau ^{{m_k} - 1}}\left[ {2{t_k} - 2{m_k}{\tau ^{{m_k}}} - 1 + {m_k}} \right]} \right) + \exp \left( { - {\tau ^{{m_k}}}} \right)\left( {({t_k} - 2){\tau ^{{t_k} - 3}} - {\tau ^{{t_k} - 2}}{m_k}{\tau ^{{m_k} - 1}}} \right)\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right]\\ \]

\[ \frac{1}{A}\frac{{{\partial ^3}{\alpha ^r}}}{{\partial {\tau ^3}}} = \exp \left( { - {\tau ^{{m_k}}}} \right)\left[ { - {\tau ^{{t_k} - 2}}m_k^2{\tau ^{{m_k} - 1}}\left[ {2{t_k} - 2{m_k}{\tau ^{{m_k}}} - 1 + {m_k}} \right] + \left( {({t_k} - 2){\tau ^{{t_k} - 3}} - {\tau ^{{t_k} - 2}}{m_k}{\tau ^{{m_k} - 1}}} \right)\left[ {\left( {{t_k} - {m_k}{\tau ^{{m_k}}}} \right)\left( {{t_k} - 1 - {m_k}{\tau ^{{m_k}}}} \right) - m_k^2{\tau ^{{m_k}}}} \right]} \right] \]

Implements phi_BC.

Definition at line 681 of file Helmholtz.cpp.

void phir_Lemmon2005::to_json ( rapidjson::Value &  el, rapidjson::Document &  doc  )

virtual

Implements phi_BC.

Definition at line 553 of file Helmholtz.cpp.

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The documentation for this class was generated from the following files:

• CoolProp/Helmholtz.h
• CoolProp/Helmholtz.cpp