CoolProp::GERG2008ReducingFunction Class Reference

Detailed Description

The reducing function model of GERG-2008.

Used by the GERG-2008 formulation to yield the reducing parameters \( \rho_r \) and \( T_r \) and derivatives thereof

Definition at line 143 of file ReducingFunctions.h.

#include <ReducingFunctions.h>

Inheritance diagram for CoolProp::GERG2008ReducingFunction:

Public Member Functions
	GERG2008ReducingFunction (const std::vector< CoolPropFluid > &pFluids, const STLMatrix &beta_v, const STLMatrix &gamma_v, STLMatrix beta_T, const STLMatrix &gamma_T)
ReducingFunction *	copy ()
	~GERG2008ReducingFunction ()
	Default destructor. More...
void	set_binary_interaction_double (const std::size_t i, const std::size_t j, double betaT, double gammaT, double betaV, double gammaV)
	Set all beta and gamma values in one shot. More...
virtual void	set_binary_interaction_double (const std::size_t i, const std::size_t j, const std::string &parameter, double value)
	Set a parameter. More...
virtual double	get_binary_interaction_double (const std::size_t i, const std::size_t j, const std::string &parameter) const
	Get a parameter. More...
CoolPropDbl	Tr (const std::vector< CoolPropDbl > &x) const
	The reducing temperature Calculated from Yr with \(T = Y\). More...
CoolPropDbl	dTr_dgammaT (const std::vector< CoolPropDbl > &x) const
	The derivative of reducing temperature with respect to gammaT Calculated from dYr_gamma with \(T = Y\). More...
CoolPropDbl	dTr_dbetaT (const std::vector< CoolPropDbl > &x) const
	The derivative of reducing temperature with respect to betaT Calculated from dYr_beta with \(T = Y\). More...
CoolPropDbl	d2Tr_dxidgammaT (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing temperature with respect to gammaT and composition. More...
CoolPropDbl	d2Tr_dxidbetaT (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing temperature with respect to betaT and composition. More...
CoolPropDbl	dTrdxi__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing temperature with respect to component i mole fraction. More...
CoolPropDbl	d2Trdxi2__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The second derivative of reducing temperature with respect to component i mole fraction. More...
CoolPropDbl	d2Trdxidxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag) const
	The second derivative of reducing temperature with respect to component i and j mole fractions. More...
CoolPropDbl	d3Trdxidxjdxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag) const
	The third derivative of reducing temperature with respect to component i, j and k mole fractions. More...
CoolPropDbl	dvrmolardxi__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing molar volume with respect to component i mole fraction. More...
CoolPropDbl	d2vrmolardxi2__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The second derivative of reducing molar volume with respect to component i mole fraction. More...
CoolPropDbl	d2vrmolardxidxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag) const
	The second derivative of reducing molar volume with respect to component i and j mole fractions. More...
CoolPropDbl	d3vrmolardxidxjdxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag) const
	The third derivative of reducing molar volume with respect to component i, j and k mole fractions. More...
CoolPropDbl	rhormolar (const std::vector< CoolPropDbl > &x) const
	The molar reducing density. More...
CoolPropDbl	drhormolar_dgammaV (const std::vector< CoolPropDbl > &x) const
	The derivative of reducing density with respect to gammaV Calculated from dYr_gamma with \(v = Y\). More...
CoolPropDbl	drhormolar_dbetaV (const std::vector< CoolPropDbl > &x) const
	The derivative of reducing density with respect to betaV Calculated from dYr_beta with \(v = Y\). More...
CoolPropDbl	d2vrmolar_dxidgammaV (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing volume with respect to gammaV and composition. More...
CoolPropDbl	d2vrmolar_dxidbetaV (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing volume with respect to betaV and composition. More...
CoolPropDbl	d2rhormolar_dxidbetaV (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing density with respect to betaV and composition. More...
CoolPropDbl	d2rhormolar_dxidgammaV (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	The derivative of reducing density with respect to gammaV and composition. More...
CoolPropDbl	drhormolardxi__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	Derivative of the molar reducing density with respect to component i mole fraction. More...
CoolPropDbl	d2rhormolardxi2__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
	Derivative of the molar reducing density with respect to component i mole fraction. More...
CoolPropDbl	d2rhormolardxidxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag) const
	Derivative of the molar reducing density with respect to component i and j mole fractions. More...
CoolPropDbl	d3rhormolardxidxjdxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag) const
	Derivative of the molar reducing density with respect to component i, j, and k mole fractions. More...
CoolPropDbl	Yr (const std::vector< CoolPropDbl > &x, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc) const
	Generalized reducing term \(Y_r\). More...
CoolPropDbl	dYr_dgamma (const std::vector< CoolPropDbl > &x, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc) const
	Derivative of reducing term \(Y_r\) with respect to \(\gamma\). More...
CoolPropDbl	dYr_dbeta (const std::vector< CoolPropDbl > &x, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc) const
	Derivative of reducing term \(Y_r\) with respect to \(\beta\). More...
CoolPropDbl	dYrdxi__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc, x_N_dependency_flag xN_flag) const
	First composition derivative of \(Y_r\) with \(x_i\). More...
CoolPropDbl	d2Yrdxidgamma (const std::vector< CoolPropDbl > &x, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc, x_N_dependency_flag xN_flag) const
	Derivative of derivative of reducing term \(\frac{\partial Y_r}{\partial x_i}\) with respect to \(\beta\). More...
CoolPropDbl	d2Yrdxidbeta (const std::vector< CoolPropDbl > &x, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc, x_N_dependency_flag xN_flag) const
	Derivative of derivative of reducing term \(\frac{\partial Y_r}{\partial x_i}\) with respect to \(\gamma\). More...
CoolPropDbl	d2Yrdxi2__constxj (const std::vector< CoolPropDbl > &x, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc, x_N_dependency_flag xN_flag) const
	Second composition derivative of \(Y_r\) with \(x_i\). More...
CoolPropDbl	d2Yrdxidxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc, x_N_dependency_flag xN_flag) const
	Second mixed composition derivative of \(Y_r\) with \(x_i\) and \(x_j\). More...
CoolPropDbl	d3Yrdxidxjdxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector< CoolPropDbl > &Yc, x_N_dependency_flag xN_flag) const
	Third mixed composition derivative of \(Y_r\) with \(x_i\) and \(x_j\) and \(x_k\). More...
const CoolPropDbl	c_Y_ij (const std::size_t i, const std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c) const
	The coefficient \( c_{Y,ij} \). More...
CoolPropDbl	f_Y_ij (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, const STLMatrix &beta) const
	The function \( f_{Y,ij}(x_i,x_j) \). More...
CoolPropDbl	dfYkidxi__constxk (const std::vector< CoolPropDbl > &x, std::size_t k, std::size_t i, const STLMatrix &beta) const
CoolPropDbl	dfYikdxi__constxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t k, const STLMatrix &beta) const
CoolPropDbl	d2fYkidxi2__constxk (const std::vector< CoolPropDbl > &x, std::size_t k, std::size_t i, const STLMatrix &beta) const
CoolPropDbl	d2fYikdxi2__constxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t k, const STLMatrix &beta) const
CoolPropDbl	d2fYijdxidxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t k, const STLMatrix &beta) const
CoolPropDbl	d3fYijdxi2dxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, const STLMatrix &beta) const
CoolPropDbl	d3fYijdxidxj2 (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, const STLMatrix &beta) const
CoolPropDbl	d3fYkidxi3__constxk (const std::vector< CoolPropDbl > &x, std::size_t k, std::size_t i, const STLMatrix &beta) const
CoolPropDbl	d3fYikdxi3__constxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t k, const STLMatrix &beta) const
Public Member Functions inherited from CoolProp::ReducingFunction
	ReducingFunction ()
virtual	~ReducingFunction ()
virtual CoolPropDbl	d_ndTrdni_dxj__constxi (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag) const
	GERG 2004 Monograph equation 7.56: More...
virtual CoolPropDbl	d2_ndTrdni_dxj_dxk__constxi (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	d_ndrhorbardni_dxj__constxi (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag) const
	GERG 2004 Monograph equation 7.55: If the \(x_i\) are all independent. More...
virtual CoolPropDbl	d2_ndrhorbardni_dxj_dxk__constxi (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	ndrhorbardni__constnj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	ndTrdni__constnj (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	PSI_rho (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	d_PSI_rho_dxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	d2_PSI_rho_dxj_dxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	PSI_T (const std::vector< CoolPropDbl > &x, std::size_t i, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	d_PSI_T_dxj (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag) const
virtual CoolPropDbl	d2_PSI_T_dxj_dxk (const std::vector< CoolPropDbl > &x, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag) const

Protected Attributes
STLMatrix	v_c
	\( v_{c,ij} = \frac{1}{8}\left(v_{c,i}^{1/3}+v_{c,j}^{1/3}\right)^{3}\) from GERG-2008 More...
STLMatrix	T_c
	\( T_{c,ij} = \sqrt{T_{c,i}T_{c,j}} \) from GERG=2008 More...
STLMatrix	beta_v
	\( \beta_{v,ij} \) from GERG-2008 More...
STLMatrix	gamma_v
	\( \gamma_{v,ij} \) from GERG-2008 More...
STLMatrix	beta_T
	\( \beta_{T,ij} \) from GERG-2008 More...
STLMatrix	gamma_T
	\( \gamma_{T,ij} \) from GERG-2008 More...
std::vector< CoolPropDbl >	Yc_T
	Vector of critical temperatures for all components. More...
std::vector< CoolPropDbl >	Yc_v
	Vector of critical molar volumes for all components. More...
std::vector< CoolPropFluid >	pFluids
	List of fluids. More...
Protected Attributes inherited from CoolProp::ReducingFunction
std::size_t	N

Additional Inherited Members
Static Public Member Functions inherited from CoolProp::ReducingFunction
static shared_ptr< ReducingFunction >	factory (const std::vector< CoolPropFluid * > &components, STLMatrix &F)
	A factory function to generate the required reducing function. More...

Constructor & Destructor Documentation

GERG2008ReducingFunction()

CoolProp::GERG2008ReducingFunction::GERG2008ReducingFunction ( const std::vector< CoolPropFluid > &  pFluids, const STLMatrix &  beta_v, const STLMatrix &  gamma_v, STLMatrix  beta_T, const STLMatrix &  gamma_T  )

inline

Definition at line 159 of file ReducingFunctions.h.

~GERG2008ReducingFunction()

CoolProp::GERG2008ReducingFunction::~GERG2008ReducingFunction ( )

inline

Default destructor.

Definition at line 186 of file ReducingFunctions.h.

Member Function Documentation

c_Y_ij()

const CoolPropDbl CoolProp::GERG2008ReducingFunction::c_Y_ij	(	const std::size_t	i,
		const std::size_t	j,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c
	)		const

The coefficient \( c_{Y,ij} \).

\[ c_{Y,ij} = 2\beta_{Y,ij}\gamma_{Y,ij}Y_{c,ij} \]

Definition at line 561 of file ReducingFunctions.cpp.

copy()

ReducingFunction* CoolProp::GERG2008ReducingFunction::copy ( )

inlinevirtual

Implements CoolProp::ReducingFunction.

Definition at line 181 of file ReducingFunctions.h.

d2fYijdxidxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2fYijdxidxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	k,
		const STLMatrix &	beta
	)		const

\begin{eqnarray*} \left(\frac{\partial^2 f_{Y,ki}(x_k, x_i)}{\partial x_i\partial x_j}\right)_{x_{k\neq j\neq i}} &=& \frac{x_i+x_j}{\beta_{Y,ij}^2x_i+x_j} + \frac{x_j}{\beta_{Y,ij}^2x_i+x_j}\left(1-\frac{x_i+x_j}{\beta_{Y,ij}^2x_i+x_j}\right) \\ &+& \frac{x_i}{\beta_{Y,ij}^2x_i+x_j}\left(1-\beta_{Y,ij}^2\frac{x_i+x_j}{\beta_{Y,ij}^2x_i+x_j}\right) - \frac{x_ix_j}{(\beta_{Y,ij}^2x_i+x_j)^2}\left(1+\beta_{Y,ij}^2-2\beta_{Y,ij}^2\frac{x_i+x_j}{\beta_{Y,ij}^2x_i+x_j}\right) \end{eqnarray*}

Definition at line 580 of file ReducingFunctions.cpp.

d2fYikdxi2__constxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2fYikdxi2__constxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	k,
		const STLMatrix &	beta
	)		const

\[ \left(\frac{\partial^2 f_{Y,ik}(x_i, x_k)}{\partial x_i^2}\right)_{x_{k}} = \frac{1}{\beta_{Y,ik}^2x_i+x_k}\left(1-\beta_{Y,ik}^2\frac{x_i+x_k}{\beta_{Y,ik}^2x_i+x_k}\right)\left(2x_k-\frac{2x_ix_k\beta_{Y,ik}^2}{\beta_{Y,ik}^2x_i+x_k}\right) \]

Definition at line 569 of file ReducingFunctions.cpp.

d2fYkidxi2__constxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2fYkidxi2__constxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	k,
		std::size_t	i,
		const STLMatrix &	beta
	)		const

\[ \left(\frac{\partial^2 f_{Y,ki}(x_k, x_i)}{\partial x_i^2}\right)_{x_{k\neq i}} = \frac{1}{\beta_{Y,ki}^2x_k+x_i}\left(1-\frac{x_k+x_i}{\beta_{Y,ki}^2x_k+x_i}\right)\left(2x_k-\frac{2x_kx_i}{\beta_{Y,ki}^2x_k+x_i}\right) \]

Definition at line 575 of file ReducingFunctions.cpp.

d2rhormolar_dxidbetaV()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2rhormolar_dxidbetaV ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

The derivative of reducing density with respect to betaV and composition.

Reimplemented from CoolProp::ReducingFunction.

Definition at line 182 of file ReducingFunctions.cpp.

d2rhormolar_dxidgammaV()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2rhormolar_dxidgammaV ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

The derivative of reducing density with respect to gammaV and composition.

Reimplemented from CoolProp::ReducingFunction.

Definition at line 177 of file ReducingFunctions.cpp.

d2rhormolardxi2__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2rhormolardxi2__constxj ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

Derivative of the molar reducing density with respect to component i mole fraction.

See also GERG 2004, Eqn. 7.58

\[ \left(\frac{\partial^2 \rho_r}{\partial x_i^2}\right)_{x_{i\neq j}} = 2\rho_r^3\left(\left(\frac{\partial v_r}{\partial x_i}\right)_{x_{i\neq j}}\right)^2-\rho_r\left(\left(\frac{\partial^2 v_r}{\partial x_i^2}\right)_{x_{i\neq j}}\right) \]

Implements CoolProp::ReducingFunction.

Definition at line 219 of file ReducingFunctions.cpp.

d2rhormolardxidxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2rhormolardxidxj ( const std::vector< CoolPropDbl > &  x, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  ) const

virtual

Derivative of the molar reducing density with respect to component i and j mole fractions.

See also GERG 2004, Eqn. 7.59

\[ \left(\frac{\partial^2 \rho_r}{\partial x_i\partial x_j}\right) = 2\rho_r^3\left(\left(\frac{\partial v_r}{\partial x_i}\right)_{x_{i\neq j}}\right)\left(\left(\frac{\partial v_r}{\partial x_j}\right)_{x_{i\neq j}}\right)-\rho_r^2\left(\left(\frac{\partial v_r}{\partial x_i\partial x_j}\right)\right) \]

Implements CoolProp::ReducingFunction.

Definition at line 224 of file ReducingFunctions.cpp.

d2Tr_dxidbetaT()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Tr_dxidbetaT ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

The derivative of reducing temperature with respect to betaT and composition.

Reimplemented from CoolProp::ReducingFunction.

Definition at line 156 of file ReducingFunctions.cpp.

d2Tr_dxidgammaT()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Tr_dxidgammaT ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

The derivative of reducing temperature with respect to gammaT and composition.

Reimplemented from CoolProp::ReducingFunction.

Definition at line 153 of file ReducingFunctions.cpp.

d2Trdxi2__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Trdxi2__constxj ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

The second derivative of reducing temperature with respect to component i mole fraction.

Calculated from d2Yrdxi2__constxj with \(T = Y\)

Implements CoolProp::ReducingFunction.

Definition at line 163 of file ReducingFunctions.cpp.

d2Trdxidxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Trdxidxj ( const std::vector< CoolPropDbl > &  x, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  ) const

virtual

The second derivative of reducing temperature with respect to component i and j mole fractions.

Calculated from d2Yrdxidxj with \(T = Y\)

Implements CoolProp::ReducingFunction.

Definition at line 166 of file ReducingFunctions.cpp.

d2vrmolar_dxidbetaV()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2vrmolar_dxidbetaV	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		x_N_dependency_flag	xN_flag
	)		const

The derivative of reducing volume with respect to betaV and composition.

Definition at line 190 of file ReducingFunctions.cpp.

d2vrmolar_dxidgammaV()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2vrmolar_dxidgammaV	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		x_N_dependency_flag	xN_flag
	)		const

The derivative of reducing volume with respect to gammaV and composition.

Definition at line 187 of file ReducingFunctions.cpp.

d2vrmolardxi2__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2vrmolardxi2__constxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		x_N_dependency_flag	xN_flag
	)		const

The second derivative of reducing molar volume with respect to component i mole fraction.

Calculated from d2Yrdxi2__constxj with \(v = Y\)

Definition at line 208 of file ReducingFunctions.cpp.

d2vrmolardxidxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2vrmolardxidxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	j,
		x_N_dependency_flag	xN_flag
	)		const

The second derivative of reducing molar volume with respect to component i and j mole fractions.

Calculated from d2Yrdxidxj with \(v = Y\)

Definition at line 211 of file ReducingFunctions.cpp.

d2Yrdxi2__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Yrdxi2__constxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc,
		x_N_dependency_flag	xN_flag
	)		const

Second composition derivative of \(Y_r\) with \(x_i\).

If \(x_N\) is given by \( x_N = 1-\sum_{i=1}^{N-1}x_i\) (Gernert, FPE, 2014, Table S1):

\begin{eqnarray*} \left(\frac{\partial^2 Y_r}{\partial x_i^2}\right)_{\substack{x_{j\neq i} \\ i<N}} &=& 2(Y_{c,i}+Y_{c,N}) + \sum_{k=1}^{i-1}c_{Y,ki}\frac{\partial^2 f_{Y,ki}(x_k, x_i)}{\partial x_i^2}+\sum_{k=i+1}^{N-1}c_{Y,ik}\frac{\partial^2 f_{Y,ik}(x_i, x_k)}{\partial x_i^2} \\ &&+2c_{Y,iN}\left(-\frac{x_i+x_N}{\beta_{Y,iN}^2x_i+x_N}+(1-\beta_{Y,iN}^2)\left( \frac{x_N^2}{(\beta_{Y,iN}^2x_i+x_N)^2} + \frac{(1-\beta_{Y,iN}^2)x_ix_{N}^2-\beta_{Y,iN}^2x_i^2x_N}{(\beta_{Y,iN}^2x_i+x_N)^3}\right)\right) \\ &&+\sum_{k=1}^{N-1}2c_{Y,kN}x_k^2\frac{1-\beta_{Y,kN}^2}{(\beta_{Y,kN}^2x_k+x_N)^2} \left(\frac{x_N}{\beta_{Y,kN}^2 x_k+x_N}-1\right) \end{eqnarray*}

Otherwise, if \(x_i\) are all independent:

\[ \left(\frac{\partial^2 Y_r}{\partial x_i^2}\right)_{x_{j\neq i}} = 2Y_{c,i} + \sum_{k=1}^{i-1}c_{Y,ki}\frac{\partial^2 f_{Y,ki}(x_k,x_i)}{\partial x_i^2} + \sum_{k=i+1}^{N}c_{Y,ik}\frac{\partial^2 f_{Y,ik}(x_i,x_k)}{\partial x_i^2} \]

Definition at line 415 of file ReducingFunctions.cpp.

d2Yrdxidbeta()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Yrdxidbeta	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc,
		x_N_dependency_flag	xN_flag
	)		const

Derivative of derivative of reducing term \(\frac{\partial Y_r}{\partial x_i}\) with respect to \(\gamma\).

Definition at line 339 of file ReducingFunctions.cpp.

d2Yrdxidgamma()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Yrdxidgamma	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc,
		x_N_dependency_flag	xN_flag
	)		const

Derivative of derivative of reducing term \(\frac{\partial Y_r}{\partial x_i}\) with respect to \(\beta\).

Definition at line 377 of file ReducingFunctions.cpp.

d2Yrdxidxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d2Yrdxidxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	j,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc,
		x_N_dependency_flag	xN_flag
	)		const

Second mixed composition derivative of \(Y_r\) with \(x_i\) and \(x_j\).

If \(x_N\) is given by \( x_N = 1-\sum_{i=1}^{N-1}x_i\) (Gernert, FPE, 2014, Table S1):

\begin{eqnarray*} \left(\frac{\partial^2 Y_r}{\partial x_i\partial x_j}\right)_{\substack{x_{k\neq j\neq i} \\ i<N \\ j < N}} &=& 2Y_{c,N} + c_{Y,ij}\frac{\partial^2 f_{Y,ij}(x_i, x_j)}{\partial x_i\partial x_j}+\sum_{k=1}^{N-1}2c_{Y,kN}x_k^2 \frac{1-\beta_{Y,kN}^2}{(\beta_{Y,kN}^2x_k+x_N)^2} \left(\frac{x_N}{\beta_{Y,kN}^2 x_k+x_N}-1\right) \\ &&+c_{Y,iN}\left((1-\beta_{Y,iN}^2)\left(\frac{2x_ix_N^2}{(\beta_{Y,iN}^2x_i+x_N)^3}-\frac{x_ix_N}{(\beta_{Y,iN}^2x_i+x_N)^2}\right) - \frac{x_i+x_N}{\beta_{Y,iN}^2x_i+x_N} \right) \\ &&-c_{Y,jN}\left((1-\beta_{Y,jN}^2)\left(\frac{2x_j^2x_N\beta_{Y,jN}^2}{(\beta_{Y,jN}^2x_j+x_N)^3}-\frac{x_jx_N}{(\beta_{Y,jN}^2x_j+x_N)^2}\right) + \frac{x_j+x_N}{\beta_{Y,jN}^2x_j+x_N} \right) \end{eqnarray*}

Otherwise, if \(x_i\) are all independent:

\[ \left(\frac{\partial^2 Y_r}{\partial x_i\partial x_j}\right)_{\substack{x_{k\neq j\neq i}}} = c_{Y,ij}\frac{\partial^2f_{Y,ij}(x_i,x_j)}{\partial x_i\partial x_j} \]

Definition at line 458 of file ReducingFunctions.cpp.

d3fYijdxi2dxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3fYijdxi2dxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	j,
		const STLMatrix &	beta
	)		const

Definition at line 586 of file ReducingFunctions.cpp.

d3fYijdxidxj2()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3fYijdxidxj2	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	j,
		const STLMatrix &	beta
	)		const

Definition at line 592 of file ReducingFunctions.cpp.

d3fYikdxi3__constxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3fYikdxi3__constxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	k,
		const STLMatrix &	beta
	)		const

Definition at line 598 of file ReducingFunctions.cpp.

d3fYkidxi3__constxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3fYkidxi3__constxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	k,
		std::size_t	i,
		const STLMatrix &	beta
	)		const

Definition at line 605 of file ReducingFunctions.cpp.

d3rhormolardxidxjdxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3rhormolardxidxjdxk ( const std::vector< CoolPropDbl > &  x, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  ) const

virtual

Derivative of the molar reducing density with respect to component i, j, and k mole fractions.

Implements CoolProp::ReducingFunction.

Definition at line 231 of file ReducingFunctions.cpp.

d3Trdxidxjdxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3Trdxidxjdxk ( const std::vector< CoolPropDbl > &  x, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  ) const

virtual

The third derivative of reducing temperature with respect to component i, j and k mole fractions.

Calculated from d3Yrdxidxjdxk with \(T = Y\)

Implements CoolProp::ReducingFunction.

Definition at line 169 of file ReducingFunctions.cpp.

d3vrmolardxidxjdxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3vrmolardxidxjdxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		x_N_dependency_flag	xN_flag
	)		const

The third derivative of reducing molar volume with respect to component i, j and k mole fractions.

Calculated from d3Yrdxidxjdxk with \(v = Y\)

Definition at line 215 of file ReducingFunctions.cpp.

d3Yrdxidxjdxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::d3Yrdxidxjdxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc,
		x_N_dependency_flag	xN_flag
	)		const

Third mixed composition derivative of \(Y_r\) with \(x_i\) and \(x_j\) and \(x_k\).

Definition at line 490 of file ReducingFunctions.cpp.

dfYikdxi__constxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dfYikdxi__constxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	k,
		const STLMatrix &	beta
	)		const

\[ \left(\frac{\partial f_{Y,ik}(x_i, x_k)}{\partial x_i}\right)_{x_k} = x_k\frac{x_i+x_k}{\beta_{Y,ik}^2x_i+x_k} + \frac{x_ix_k}{\beta_{Y,ik}^2x_i+x_k}\left(1-\beta_{Y,ik}^2\frac{x_i+x_k}{\beta_{Y,ik}^2x_i+x_k}\right) \]

Definition at line 555 of file ReducingFunctions.cpp.

dfYkidxi__constxk()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dfYkidxi__constxk	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	k,
		std::size_t	i,
		const STLMatrix &	beta
	)		const

\[ \left(\frac{\partial f_{Y,ki}(x_k, x_i)}{\partial x_i}\right)_{x_{k\neq i}} = x_k\frac{x_k+x_i}{\beta_{Y,ki}^2x_k+x_i} + \frac{x_kx_i}{\beta_{Y,ki}^2x_k+x_i}\left(1-\frac{x_k+x_i}{\beta_{Y,ki}^2x_k+x_i}\right) \]

Definition at line 550 of file ReducingFunctions.cpp.

drhormolar_dbetaV()

CoolPropDbl CoolProp::GERG2008ReducingFunction::drhormolar_dbetaV ( const std::vector< CoolPropDbl > &  x ) const

virtual

The derivative of reducing density with respect to betaV Calculated from dYr_beta with \(v = Y\).

Reimplemented from CoolProp::ReducingFunction.

Definition at line 197 of file ReducingFunctions.cpp.

drhormolar_dgammaV()

CoolPropDbl CoolProp::GERG2008ReducingFunction::drhormolar_dgammaV ( const std::vector< CoolPropDbl > &  x ) const

virtual

The derivative of reducing density with respect to gammaV Calculated from dYr_gamma with \(v = Y\).

Reimplemented from CoolProp::ReducingFunction.

Definition at line 193 of file ReducingFunctions.cpp.

drhormolardxi__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::drhormolardxi__constxj ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

Derivative of the molar reducing density with respect to component i mole fraction.

See also GERG 2004, Eqn. 7.57

\[ \left(\frac{\partial \rho_r}{\partial x_i}\right)_{x_{i\neq j}} = -\rho_r^2\left(\frac{\partial v_r}{\partial x_i}\right)_{x_{i\neq j}} \]

Implements CoolProp::ReducingFunction.

Definition at line 201 of file ReducingFunctions.cpp.

dTr_dbetaT()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dTr_dbetaT ( const std::vector< CoolPropDbl > &  x ) const

virtual

The derivative of reducing temperature with respect to betaT Calculated from dYr_beta with \(T = Y\).

Reimplemented from CoolProp::ReducingFunction.

Definition at line 147 of file ReducingFunctions.cpp.

dTr_dgammaT()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dTr_dgammaT ( const std::vector< CoolPropDbl > &  x ) const

virtual

The derivative of reducing temperature with respect to gammaT Calculated from dYr_gamma with \(T = Y\).

Reimplemented from CoolProp::ReducingFunction.

Definition at line 150 of file ReducingFunctions.cpp.

dTrdxi__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dTrdxi__constxj ( const std::vector< CoolPropDbl > &  x, std::size_t  i, x_N_dependency_flag  xN_flag  ) const

virtual

The derivative of reducing temperature with respect to component i mole fraction.

Calculated from dYrdxi__constxj with \(T = Y\)

Implements CoolProp::ReducingFunction.

Definition at line 160 of file ReducingFunctions.cpp.

dvrmolardxi__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dvrmolardxi__constxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		x_N_dependency_flag	xN_flag
	)		const

The derivative of reducing molar volume with respect to component i mole fraction.

Calculated from dYrdxi__constxj with \(v = Y\)

Definition at line 205 of file ReducingFunctions.cpp.

dYr_dbeta()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dYr_dbeta	(	const std::vector< CoolPropDbl > &	x,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc
	)		const

Derivative of reducing term \(Y_r\) with respect to \(\beta\).

Definition at line 277 of file ReducingFunctions.cpp.

dYr_dgamma()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dYr_dgamma	(	const std::vector< CoolPropDbl > &	x,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc
	)		const

Derivative of reducing term \(Y_r\) with respect to \(\gamma\).

\[ \frac{\partial Y_r}{\partial \gamma} = \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} 2\beta_{ij}Y_{c,ij}f_{Y,ij}(x_i,x_j) \]

Definition at line 263 of file ReducingFunctions.cpp.

dYrdxi__constxj()

CoolPropDbl CoolProp::GERG2008ReducingFunction::dYrdxi__constxj	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc,
		x_N_dependency_flag	xN_flag
	)		const

First composition derivative of \(Y_r\) with \(x_i\).

If \(x_N\) is given by \( x_N = 1-\sum_{i=1}^{N-1}x_i\) (Gernert, FPE, 2014, Table S1):

\begin{eqnarray*} \left(\frac{\partial Y_r}{\partial x_i}\right)_{\substack{x_{j\neq i} \\ i<N}} &=& 2x_iY_{c,j}-2x_NY_{c,N} + \sum_{k=1}^{i-1}c_{Y,ki}\frac{\partial f_{Y,ki}(x_k, x_i)}{\partial x_i}+\sum_{k=i+1}^{N-1}c_{Y,ik}\frac{\partial f_{Y,ik}(x_i, x_k)}{\partial x_i} \\ &&+c_{Y,iN}\left(\frac{x_{N}(x_i+x_{N})}{\beta_{Y,iN}^2x_i+x_{N}}+(1-\beta_{Y,iN}^2)\frac{x_ix_{N}^2}{(\beta_{Y,i(N)}^2x_i+x_{N})^2}\right) \\ &&+\sum_{k=0}^{N-2}c_{Y,kN}\left(-\frac{x_k(x_k+x_N)}{\beta_{Y,kN}^2 x_k+x_N}+(1-\beta_{Y,kN}^2)\frac{x_Nx_k^2}{(\beta_{Y,kN}^2x_k+x_N)^2}\right) \end{eqnarray*}

Otherwise, if \(x_i\) are all independent:

\[ \left(\frac{\partial Y_r}{\partial x_i}\right)_{\substack{x_{j\neq i}}} = 2x_iY_{c,i} + \sum_{k=1}^{i-1}c_{Y,ki}\frac{\partial f_{Y,ki}(x_k,x_i)}{\partial x_i} + \sum_{k=i+1}^{N}c_{Y,ik}\frac{\partial f_{Y,ik}(x_i,x_k)}{\partial x_i} \]

Definition at line 298 of file ReducingFunctions.cpp.

f_Y_ij()

CoolPropDbl CoolProp::GERG2008ReducingFunction::f_Y_ij	(	const std::vector< CoolPropDbl > &	x,
		std::size_t	i,
		std::size_t	j,
		const STLMatrix &	beta
	)		const

The function \( f_{Y,ij}(x_i,x_j) \).

\[ f_{Y,ij}(x_i,x_j) = x_ix_j\frac{x_i+x_j}{\beta_{Y,ij}^2x_i+x_j} \]

Definition at line 565 of file ReducingFunctions.cpp.

get_binary_interaction_double()

virtual double CoolProp::GERG2008ReducingFunction::get_binary_interaction_double ( const std::size_t  i, const std::size_t  j, const std::string &  parameter  ) const

inlinevirtual

Get a parameter.

Implements CoolProp::ReducingFunction.

Definition at line 239 of file ReducingFunctions.h.

rhormolar()

CoolPropDbl CoolProp::GERG2008ReducingFunction::rhormolar ( const std::vector< CoolPropDbl > &  x ) const

virtual

The molar reducing density.

Given by \( \rho_r = 1/v_r \)

Implements CoolProp::ReducingFunction.

Definition at line 173 of file ReducingFunctions.cpp.

set_binary_interaction_double() [1/2]

virtual void CoolProp::GERG2008ReducingFunction::set_binary_interaction_double ( const std::size_t  i, const std::size_t  j, const std::string &  parameter, double  value  )

inlinevirtual

Set a parameter.

Implements CoolProp::ReducingFunction.

Definition at line 211 of file ReducingFunctions.h.

set_binary_interaction_double() [2/2]

void CoolProp::GERG2008ReducingFunction::set_binary_interaction_double ( const std::size_t  i, const std::size_t  j, double  betaT, double  gammaT, double  betaV, double  gammaV  )

inline

Set all beta and gamma values in one shot.

Definition at line 189 of file ReducingFunctions.h.

Tr()

CoolPropDbl CoolProp::GERG2008ReducingFunction::Tr ( const std::vector< CoolPropDbl > &  x ) const

virtual

The reducing temperature Calculated from Yr with \(T = Y\).

Implements CoolProp::ReducingFunction.

Definition at line 144 of file ReducingFunctions.cpp.

Yr()

CoolPropDbl CoolProp::GERG2008ReducingFunction::Yr	(	const std::vector< CoolPropDbl > &	x,
		const STLMatrix &	beta,
		const STLMatrix &	gamma,
		const STLMatrix &	Y_c_ij,
		const std::vector< CoolPropDbl > &	Yc
	)		const

Generalized reducing term \(Y_r\).

\[ Y_r = \sum_{i=1}^{N}x_iY_{c,i}^2+\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} c_{Y,ij}f_{Y,ij}(x_i,x_j) \]

Definition at line 244 of file ReducingFunctions.cpp.

Member Data Documentation

beta_T

STLMatrix CoolProp::GERG2008ReducingFunction::beta_T

protected

\( \beta_{T,ij} \) from GERG-2008

Definition at line 152 of file ReducingFunctions.h.

beta_v

STLMatrix CoolProp::GERG2008ReducingFunction::beta_v

protected

\( \beta_{v,ij} \) from GERG-2008

Definition at line 150 of file ReducingFunctions.h.

gamma_T

STLMatrix CoolProp::GERG2008ReducingFunction::gamma_T

protected

\( \gamma_{T,ij} \) from GERG-2008

Definition at line 153 of file ReducingFunctions.h.

gamma_v

STLMatrix CoolProp::GERG2008ReducingFunction::gamma_v

protected

\( \gamma_{v,ij} \) from GERG-2008

Definition at line 151 of file ReducingFunctions.h.

pFluids

std::vector<CoolPropFluid> CoolProp::GERG2008ReducingFunction::pFluids

protected

List of fluids.

Definition at line 156 of file ReducingFunctions.h.

T_c

STLMatrix CoolProp::GERG2008ReducingFunction::T_c

protected

\( T_{c,ij} = \sqrt{T_{c,i}T_{c,j}} \) from GERG=2008

Definition at line 149 of file ReducingFunctions.h.

v_c

STLMatrix CoolProp::GERG2008ReducingFunction::v_c

protected

\( v_{c,ij} = \frac{1}{8}\left(v_{c,i}^{1/3}+v_{c,j}^{1/3}\right)^{3}\) from GERG-2008

Definition at line 148 of file ReducingFunctions.h.

Yc_T

std::vector<CoolPropDbl> CoolProp::GERG2008ReducingFunction::Yc_T

protected

Vector of critical temperatures for all components.

Definition at line 154 of file ReducingFunctions.h.

Yc_v

std::vector<CoolPropDbl> CoolProp::GERG2008ReducingFunction::Yc_v

protected

Vector of critical molar volumes for all components.

Definition at line 155 of file ReducingFunctions.h.

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

• src/Backends/Helmholtz/ReducingFunctions.h
• src/Backends/Helmholtz/ReducingFunctions.cpp