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Finished documenting reducing functions

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Closes https://github.com/CoolProp/CoolProp/issues/112

Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-10-03 13:15:55 +02:00
parent 379be8831d
commit 16b15a395e
2 changed files with 83 additions and 19 deletions
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6
src/Backends/Helmholtz/ReducingFunctions.cpp
View File

@@ -96,7 +96,7 @@ long double GERG2008ReducingFunction::d2Trdxi2__constxj(const std::vector<long d
}
long double GERG2008ReducingFunction::d2Trdxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return d2Yrdxidxj__constxj(x, i, j, beta_T, gamma_T, T_c, Yc_T, xN_flag);
return d2Yrdxidxj(x, i, j, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
long double GERG2008ReducingFunction::rhormolar(const std::vector<long double> &x)
{
@@ -116,7 +116,7 @@ long double GERG2008ReducingFunction::d2vrmolardxi2__constxj(const std::vector<l
}
long double GERG2008ReducingFunction::d2vrmolardxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return d2Yrdxidxj__constxj(x, i, j, beta_v, gamma_v, v_c, Yc_v, xN_flag);
return d2Yrdxidxj(x, i, j, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
long double GERG2008ReducingFunction::d2rhormolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
@@ -232,7 +232,7 @@ long double GERG2008ReducingFunction::d2Yrdxi2__constxj(const std::vector<long d
}
}
long double GERG2008ReducingFunction::d2Yrdxidxj__constxj(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag)
long double GERG2008ReducingFunction::d2Yrdxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag)
{
if (xN_flag == XN_INDEPENDENT){
if (i == j)

96
src/Backends/Helmholtz/ReducingFunctions.h
View File

@@ -129,23 +129,77 @@ public:
/// Default destructor
~GERG2008ReducingFunction(){};
/// The reduced temperature
/** \brief The reducing temperature
* Calculated from \ref Yr with \f$T = Y\f$
*/
long double Tr(const std::vector<long double> &x);
/// The derivative of reduced temperature with respect to component i mole fraction
/** \brief The derivative of reducing temperature with respect to component i mole fraction
*
* Calculated from \ref dYrdxi__constxj with \f$T = Y\f$
*/
long double dTrdxi__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
/// The molar reducing density
long double rhormolar(const std::vector<long double> &x);
///Derivative of the molar reducing density with respect to component i mole fraction
long double drhormolardxi__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
long double dvrmolardxi__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_fla);
long double d2vrmolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
long double d2rhormolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
long double d2vrmolardxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
long double d2rhormolardxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
long double d2Trdxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
/** \brief The second derivative of reducing temperature with respect to component i mole fraction
*
* Calculated from \ref d2Yrdxi2__constxj with \f$T = Y\f$
*/
long double d2Trdxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
/** \brief The second derivative of reducing temperature with respect to component i and j mole fractions
*
* Calculated from \ref d2Yrdxidxj with \f$T = Y\f$
*/
long double d2Trdxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
/** \brief The derivative of reducing molar volume with respect to component i mole fraction
*
* Calculated from \ref dYrdxi__constxj with \f$v = Y\f$
*/
long double dvrmolardxi__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_fla);
/** \brief The second derivative of reducing molar volume with respect to component i mole fraction
*
* Calculated from \ref d2Yrdxi2__constxj with \f$v = Y\f$
*/
long double d2vrmolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
/** \brief The second derivative of reducing molar volume with respect to component i and j mole fractions
*
* Calculated from \ref d2Yrdxidxj with \f$v = Y\f$
*/
long double d2vrmolardxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
/** \brief The molar reducing density
*
* Given by \f$ \rho_r = 1/v_r \f$
*/
long double rhormolar(const std::vector<long double> &x);
/** \brief Derivative of the molar reducing density with respect to component i mole fraction
*
* See also GERG 2004, Eqn. 7.57
* \f[
* \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}}
* \f]
*/
long double drhormolardxi__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
/** \brief Derivative of the molar reducing density with respect to component i mole fraction
*
* See also GERG 2004, Eqn. 7.58
* \f[
* \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)
* \f]
*/
long double d2rhormolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag);
/** \brief Derivative of the molar reducing density with respect to component i and j mole fractions
*
* See also GERG 2004, Eqn. 7.59
* \f[
* \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)
* \f]
*/
long double d2rhormolardxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
/** \brief Generalized reducing term \f$Y_r\f$
*
* \f[
* 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)
* \f]
*/
long double Yr(const std::vector<long double> &x, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc);
/** \brief First composition derivative of \f$Y_r\f$ with \f$x_i\f$
*
@@ -192,10 +246,20 @@ public:
* \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}
* \f]
*/
long double d2Yrdxidxj__constxj(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag);
long double d2Yrdxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag);
/** \brief The coefficient \f$ c_{Y,ij} \f$
*
* \f[
* c_{Y,ij} = 2\beta_{Y,ij}\gamma_{Y,ij}Y_{c,ij}
* \f]
*/
long double c_Y_ij(std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c);
/** \brief The function \f$ f_{Y,ij}(x_i,x_j) \f$
*
* \f[ f_{Y,ij}(x_i,x_j) = x_ix_j\frac{x_i+x_j}{\beta_{Y,ij}^2x_i+x_j} \f]
*/
long double f_Y_ij(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta);
/**
*
* \f[