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CoolProp/src/Backends/Helmholtz/ReducingFunctions.cpp

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#include "ReducingFunctions.h"
namespace CoolProp{
CoolPropDbl ReducingFunction::d_ndTrdni_dxj__constxi(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
if (xN_flag == XN_INDEPENDENT){
CoolPropDbl s = 0;
for (std::size_t k = 0; k < N; k++)
{
s += x[k]*d2Trdxidxj(x,j,k, xN_flag);
}
return d2Trdxidxj(x,i,j, xN_flag)-dTrdxi__constxj(x,j, xN_flag)-s;
}
else if (xN_flag == XN_DEPENDENT){
if (j == N-1){ return 0;}
CoolPropDbl s = 0;
for (std::size_t k = 0; k < N-1; k++)
{
s += x[k]*d2Trdxidxj(x,k,j, xN_flag);
}
CoolPropDbl val = d2Trdxidxj(x,j,i,xN_flag)-dTrdxi__constxj(x,j, xN_flag)-s;
return val;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl ReducingFunction::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)
{
if (xN_flag == XN_INDEPENDENT){
CoolPropDbl s = 0;
for (std::size_t m = 0; m < N; m++)
{
s += x[m]*d3Trdxidxjdxk(x, j, k, m, xN_flag);
}
return d3Trdxidxjdxk(x, i, j, k, xN_flag) - 2*d2Trdxidxj(x, j, k, xN_flag)-s;
}
else if (xN_flag == XN_DEPENDENT){
if (j == N-1){ return 0; }
CoolPropDbl s = 0;
for (std::size_t m = 0; m < N-1; m++)
{
s += x[m]*d3Trdxidxjdxk(x, k, j, m, xN_flag);
}
CoolPropDbl val = d3Trdxidxjdxk(x, i, j, k,xN_flag)-d2Trdxidxj(x, j, k, xN_flag)-s;
return val;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl ReducingFunction::d_ndrhorbardni_dxj__constxi(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
CoolPropDbl s = 0;
for (std::size_t k = 0; k < N; k++)
{
s += x[k]*d2rhormolardxidxj(x,j,k, xN_flag);
}
return d2rhormolardxidxj(x,j,i, xN_flag)-drhormolardxi__constxj(x,j, xN_flag)-s;
}
CoolPropDbl ReducingFunction::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)
{
CoolPropDbl s = 0;
for (std::size_t m = 0; m < N; m++)
{
s += x[m]*d3rhormolardxidxjdxk(x, j, k, m, xN_flag);
}
return d3rhormolardxidxjdxk(x, i, j, k, xN_flag)-2*d2rhormolardxidxj(x, j, k, xN_flag)-s;
}
CoolPropDbl ReducingFunction::ndrhorbardni__constnj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
if (xN_flag == XN_INDEPENDENT){
CoolPropDbl summer_term1 = 0;
for (std::size_t j = 0; j < N; j++)
{
summer_term1 += x[j]*drhormolardxi__constxj(x,j, xN_flag);
}
return drhormolardxi__constxj(x,i, xN_flag)-summer_term1;
}
else if (xN_flag == XN_DEPENDENT){
CoolPropDbl summer_term1 = 0;
for (std::size_t k = 0; k < N-1; ++k)
{
summer_term1 += x[k]*drhormolardxi__constxj(x, k, xN_flag);
}
return drhormolardxi__constxj(x, i, xN_flag)-summer_term1;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl ReducingFunction::ndTrdni__constnj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
if (xN_flag == XN_INDEPENDENT){
// GERG Equation 7.54
CoolPropDbl summer_term1 = 0;
for (std::size_t j = 0; j < N; j++)
{
summer_term1 += x[j]*dTrdxi__constxj(x,j, xN_flag);
}
return dTrdxi__constxj(x,i, xN_flag)-summer_term1;
}
else if (xN_flag == XN_DEPENDENT){
CoolPropDbl summer_term1 = 0;
for (std::size_t k = 0; k < N-1; ++k)
{
summer_term1 += x[k]*dTrdxi__constxj(x, k, xN_flag);
}
return dTrdxi__constxj(x, i, xN_flag)-summer_term1;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl ReducingFunction::PSI_rho(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return 1-1/rhormolar(x)*ndrhorbardni__constnj(x, i, xN_flag);
}
CoolPropDbl ReducingFunction::d_PSI_rho_dxj(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return -1/rhormolar(x)*(d_ndrhorbardni_dxj__constxi(x, i, j, xN_flag) - drhormolardxi__constxj(x, j, xN_flag)*(1 - PSI_rho(x, i, xN_flag))) ;
}
CoolPropDbl ReducingFunction::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)
{
double line1 = d2_ndrhorbardni_dxj_dxk__constxi(x, i, j, k, xN_flag);
double line2 = -1/rhormolar(x)*drhormolardxi__constxj(x, k, xN_flag)*d_ndrhorbardni_dxj__constxi(x, i, j, xN_flag);
double line3 = drhormolardxi__constxj(x, j, xN_flag)*d_PSI_rho_dxj(x, i, k, xN_flag);
double line4 = -(d2rhormolardxidxj(x, j, k, xN_flag)-1/rhormolar(x)*drhormolardxi__constxj(x, k, xN_flag)*drhormolardxi__constxj(x, j, xN_flag))*(1-PSI_rho(x, i, xN_flag));
return -1/rhormolar(x)*(line1 + line2 + line3 + line4);
}
CoolPropDbl ReducingFunction::PSI_T(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return 1/Tr(x)*ndTrdni__constnj(x, i, xN_flag);
}
CoolPropDbl ReducingFunction::d_PSI_T_dxj(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return 1/Tr(x)*(d_ndTrdni_dxj__constxi(x, i, j, xN_flag) - dTrdxi__constxj(x, j, xN_flag)*PSI_T(x, i, xN_flag));
}
CoolPropDbl ReducingFunction::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)
{
double line1 = d2_ndTrdni_dxj_dxk__constxi(x, i, j, k, xN_flag);
double line2 = -1/Tr(x)*dTrdxi__constxj(x, k, xN_flag)*d_ndTrdni_dxj__constxi(x, i, j, xN_flag);
double line3 = -dTrdxi__constxj(x, j, xN_flag)*d_PSI_T_dxj(x, i, k, xN_flag);
double line4 = -(d2Trdxidxj(x, j, k, xN_flag)-1/Tr(x)*dTrdxi__constxj(x, k, xN_flag)*dTrdxi__constxj(x, j, xN_flag))*PSI_T(x, i, xN_flag);
return 1/Tr(x)*(line1 + line2 + line3 + line4);
}
CoolPropDbl GERG2008ReducingFunction::Tr(const std::vector<CoolPropDbl> &x)
{
return Yr(x, beta_T, gamma_T, T_c, Yc_T);
}
CoolPropDbl GERG2008ReducingFunction::dTrdxi__constxj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return dYrdxi__constxj(x, i, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::d2Trdxi2__constxj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return d2Yrdxi2__constxj(x, i, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::d2Trdxidxj(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return d2Yrdxidxj(x, i, j, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
CoolPropDbl 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)
{
return d3Yrdxidxjdxk(x, i, j, k, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::rhormolar(const std::vector<CoolPropDbl> &x)
{
return 1/Yr(x, beta_v, gamma_v, v_c, Yc_v);
}
CoolPropDbl GERG2008ReducingFunction::drhormolardxi__constxj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return -pow(rhormolar(x),2)*dvrmolardxi__constxj(x, i, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::dvrmolardxi__constxj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return dYrdxi__constxj(x, i, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::d2vrmolardxi2__constxj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return d2Yrdxi2__constxj(x, i, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::d2vrmolardxidxj(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return d2Yrdxidxj(x, i, j, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
CoolPropDbl 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)
{
return d3Yrdxidxjdxk(x, i, j, k, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::d2rhormolardxi2__constxj(const std::vector<CoolPropDbl> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
CoolPropDbl rhor = this->rhormolar(x);
CoolPropDbl dvrbardxi = this->dvrmolardxi__constxj(x,i, xN_flag);
return 2*pow(rhor,3)*pow(dvrbardxi,2)-pow(rhor,2)*this->d2vrmolardxi2__constxj(x,i, xN_flag);
}
CoolPropDbl GERG2008ReducingFunction::d2rhormolardxidxj(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
double rhor = this->rhormolar(x);
double dvrbardxi = this->dvrmolardxi__constxj(x,i, xN_flag);
double dvrbardxj = this->dvrmolardxi__constxj(x,j, xN_flag);
return 2*pow(rhor,3)*dvrbardxi*dvrbardxj-pow(rhor,2)*this->d2vrmolardxidxj(x,i,j, xN_flag);
}
CoolPropDbl 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)
{
double rhor = this->rhormolar(x);
double line1 = -pow(rhor, 2)*d3vrmolardxidxjdxk(x, i, j, k, xN_flag);
double line2 = 2*pow(rhor, 3)*(dvrmolardxi__constxj(x, k, xN_flag)*d2vrmolardxidxj(x, i, j, xN_flag)
+ dvrmolardxi__constxj(x, j, xN_flag)*d2vrmolardxidxj(x, i, k, xN_flag)
+ dvrmolardxi__constxj(x, i, xN_flag)*d2vrmolardxidxj(x, j, k, xN_flag));
double line3 = -6*pow(rhor, 4)*dvrmolardxi__constxj(x, i, xN_flag)*dvrmolardxi__constxj(x, j, xN_flag)*dvrmolardxi__constxj(x, k, xN_flag);
return line1 + line2 + line3;
}
CoolPropDbl GERG2008ReducingFunction::Yr(const std::vector<CoolPropDbl> &x, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<CoolPropDbl> &Yc)
{
CoolPropDbl Yr = 0;
for (std::size_t i = 0; i < N; i++)
{
double xi = x[i];
Yr += xi*xi*Yc[i];
// The last term is only used for the pure component, as it is sum_{i=1}^{N-1}sum_{j=1}^{N}
if (i==N-1){ break; }
for (std::size_t j = i+1; j < N; j++)
{
Yr += c_Y_ij(i, j, beta, gamma, Y_c_ij)*f_Y_ij(x, i, j, beta);
}
}
return Yr;
}
CoolPropDbl 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)
{
if (xN_flag == XN_INDEPENDENT){
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
CoolPropDbl xi = x[i];
CoolPropDbl dYr_dxi = 2*xi*Yc[i];
for (std::size_t k = 0; k < i; k++)
{
dYr_dxi += c_Y_ij(k,i,beta,gamma,Y_c_ij)*dfYkidxi__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N; k++)
{
dYr_dxi += c_Y_ij(i,k,beta,gamma,Y_c_ij)*dfYikdxi__constxk(x,i,k,beta);
}
return dYr_dxi;
}
else if (xN_flag == XN_DEPENDENT){
// Table S1 from Gernert, 2014, supplemental information
if (i == N-1){return 0.0;}
CoolPropDbl dYr_dxi = 2*x[i]*Yc[i] - 2*x[N-1]*Yc[N-1];
for (std::size_t k = 0; k < i; k++)
{
dYr_dxi += c_Y_ij(k, i, beta, gamma, Y_c_ij)*dfYkidxi__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N-1; k++)
{
dYr_dxi += c_Y_ij(i, k, beta, gamma, Y_c_ij)*dfYikdxi__constxk(x,i,k,beta);
}
double beta_Y_iN = beta[i][N-1], xN = x[N-1];
dYr_dxi += c_Y_ij(i, N-1, beta, gamma, Y_c_ij)*(xN*(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2));
for (std::size_t k = 0; k < N-1; ++k)
{
double beta_Y_kN = beta[k][N-1];
dYr_dxi += c_Y_ij(k, N-1, beta, gamma, Y_c_ij)*(-x[k]*(x[k]+xN)/(pow(beta_Y_kN,2)*x[k]+xN)+(1-beta_Y_kN*beta_Y_kN)*xN*x[k]*x[k]/pow(beta_Y_kN*beta_Y_kN*x[k]+xN, 2));
}
return dYr_dxi;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl 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)
{
if (xN_flag == XN_INDEPENDENT){
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
CoolPropDbl d2Yr_dxi2 = 2*Yc[i];
for (std::size_t k = 0; k < i; k++)
{
d2Yr_dxi2 += c_Y_ij(k,i,beta,gamma,Y_c_ij)*d2fYkidxi2__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N; k++)
{
d2Yr_dxi2 += c_Y_ij(i,k,beta,gamma,Y_c_ij)*d2fYikdxi2__constxk(x,i,k,beta);
}
return d2Yr_dxi2;
}
else if (xN_flag == XN_DEPENDENT){
// Table S1 from Gernert, 2014, supplemental information
if (i == N-1){return 0.0;}
CoolPropDbl d2Yr_dxi2 = 2*Yc[i] + 2*Yc[N-1];
for (std::size_t k = 0; k < i; k++)
{
d2Yr_dxi2 += c_Y_ij(k, i, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N-1; k++)
{
d2Yr_dxi2 += c_Y_ij(i, k, beta, gamma, Y_c_ij)*d2fYikdxi2__constxk(x,i,k,beta);
}
double beta_Y_iN = beta[i][N-1], xN = x[N-1];
d2Yr_dxi2 += 2*c_Y_ij(i, N-1, beta, gamma, Y_c_ij)*(-(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*(xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)+((1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN-beta_Y_iN*beta_Y_iN*x[i]*x[i]*xN)/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)));
for (std::size_t k = 0; k < N-1; ++k)
{
double beta_Y_kN = beta[k][N-1];
d2Yr_dxi2 += 2*c_Y_ij(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(pow(beta_Y_kN,2)*x[k]+xN, 2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
}
return d2Yr_dxi2;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl 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)
{
if (std::abs(x[i]) < 10*DBL_EPSILON && std::abs(x[j]) < 10*DBL_EPSILON){return 0;}
if (xN_flag == XN_INDEPENDENT){
if (i == j)
{
return d2Yrdxi2__constxj(x, i, beta, gamma, Y_c_ij, Yc, xN_flag);
}
else
{
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
return c_Y_ij(i, j, beta, gamma, Y_c_ij)*d2fYijdxidxj(x, i, j, beta);
}
}
else if (xN_flag == XN_DEPENDENT){
// Table S1 from Gernert, 2014, supplemental information
if (j == N-1 || i == N-1){ return 0.0; }
if (i == j){ return d2Yrdxi2__constxj(x, i, beta, gamma, Y_c_ij, Yc, xN_flag); }
CoolPropDbl xN = x[N-1];
CoolPropDbl d2Yr_dxidxj = 2*Yc[N-1];
d2Yr_dxidxj += c_Y_ij(i, j, beta, gamma, Y_c_ij)*d2fYijdxidxj(x,i,j,beta);
for (std::size_t k = 0; k < N-1; k++)
{
CoolPropDbl beta_Y_kN = beta[k][N-1];
d2Yr_dxidxj += 2*c_Y_ij(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(beta_Y_kN*beta_Y_kN*x[k]+xN,2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
}
{
CoolPropDbl beta_Y_iN = beta[i][N-1];
d2Yr_dxidxj += c_Y_ij(i, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_iN*beta_Y_iN)*(2*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)-x[i]*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)) - (x[i]+xN)/(beta_Y_iN*beta_Y_iN*x[i]+xN));
}
{
CoolPropDbl beta_Y_jN = beta[j][N-1];
d2Yr_dxidxj += -c_Y_ij(j, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_jN*beta_Y_jN)*(2*x[j]*x[j]*xN*beta_Y_jN*beta_Y_jN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 3)-x[j]*xN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 2)) + (x[j]+xN)/(beta_Y_jN*beta_Y_jN*x[j]+xN));
}
return d2Yr_dxidxj;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl 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)
{
if (std::abs(x[i]) < 10 * DBL_EPSILON && std::abs(x[j]) < 10 * DBL_EPSILON){ return 0; }
if (xN_flag == XN_INDEPENDENT){
if (i != j && j != k && k != i){
return 0;
}
else if (k == i && i != j){
return c_Y_ij(i, j, beta, gamma, Y_c_ij)*d3fYijdxi2dxj(x, i, j, beta);
}
else if (k == j && i != j){
return c_Y_ij(i, j, beta, gamma, Y_c_ij)*d3fYijdxidxj2(x, i, j, beta);
}
else if (i == j && i != k){
return c_Y_ij(i, k, beta, gamma, Y_c_ij)*d3fYijdxi2dxj(x, i, k, beta);
}
else{
CoolPropDbl d3Yr_dxi3 = 0;
for (std::size_t m = 0; m < i; m++)
{
d3Yr_dxi3 += c_Y_ij(m, i, beta, gamma, Y_c_ij)*d3fYkidxi3__constxk(x, m, i, beta);
}
for (std::size_t m = i + 1; m < N; m++)
{
d3Yr_dxi3 += c_Y_ij(i, m, beta, gamma, Y_c_ij)*d3fYikdxi3__constxk(x, i, m, beta);
}
return d3Yr_dxi3;
}
}
else if (xN_flag == XN_DEPENDENT){
throw ValueError("d3Yrdxidxjdxk not implemented yet");
// Table S1 from Gernert, 2014, supplemental information
if (j == N - 1 || i == N - 1){ return 0.0; }
if (i == j){ return d2Yrdxi2__constxj(x, i, beta, gamma, Y_c_ij, Yc, xN_flag); }
CoolPropDbl xN = x[N - 1];
CoolPropDbl d2Yr_dxidxj = 2 * Yc[N - 1];
d2Yr_dxidxj += c_Y_ij(i, j, beta, gamma, Y_c_ij)*d2fYijdxidxj(x, i, j, beta);
for (std::size_t k = 0; k < N - 1; k++)
{
CoolPropDbl beta_Y_kN = beta[k][N - 1];
d2Yr_dxidxj += 2 * c_Y_ij(k, N - 1, beta, gamma, Y_c_ij)*x[k] * x[k] * (1 - beta_Y_kN*beta_Y_kN) / pow(beta_Y_kN*beta_Y_kN*x[k] + xN, 2)*(xN / (beta_Y_kN*beta_Y_kN*x[k] + xN) - 1);
}
{
CoolPropDbl beta_Y_iN = beta[i][N - 1];
d2Yr_dxidxj += c_Y_ij(i, N - 1, beta, gamma, Y_c_ij)*((1 - beta_Y_iN*beta_Y_iN)*(2 * x[i] * xN*xN / pow(beta_Y_iN*beta_Y_iN*x[i] + xN, 3) - x[i] * xN / pow(beta_Y_iN*beta_Y_iN*x[i] + xN, 2)) - (x[i] + xN) / (beta_Y_iN*beta_Y_iN*x[i] + xN));
}
{
CoolPropDbl beta_Y_jN = beta[j][N - 1];
d2Yr_dxidxj += -c_Y_ij(j, N - 1, beta, gamma, Y_c_ij)*((1 - beta_Y_jN*beta_Y_jN)*(2 * x[j] * x[j] * xN*beta_Y_jN*beta_Y_jN / pow(beta_Y_jN*beta_Y_jN*x[j] + xN, 3) - x[j] * xN / pow(beta_Y_jN*beta_Y_jN*x[j] + xN, 2)) + (x[j] + xN) / (beta_Y_jN*beta_Y_jN*x[j] + xN));
}
return d2Yr_dxidxj;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
CoolPropDbl GERG2008ReducingFunction::dfYkidxi__constxk(const std::vector<CoolPropDbl> &x, std::size_t k, std::size_t i, const STLMatrix &beta)
{
double xk = x[k], xi = x[i], beta_Y = beta[k][i];
if (std::abs(xi) < 10*DBL_EPSILON && std::abs(xk) < 10*DBL_EPSILON){return 0;}
return xk*(xk+xi)/(beta_Y*beta_Y*xk+xi)+xk*xi/(beta_Y*beta_Y*xk+xi)*(1-(xk+xi)/(beta_Y*beta_Y*xk+xi));
}
CoolPropDbl GERG2008ReducingFunction::dfYikdxi__constxk(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t k, const STLMatrix &beta)
{
double xk = x[k], xi = x[i], beta_Y = beta[i][k];
if (std::abs(xi) < 10*DBL_EPSILON && std::abs(xk) < 10*DBL_EPSILON){return 0;}
return xk*(xi+xk)/(beta_Y*beta_Y*xi+xk)+xi*xk/(beta_Y*beta_Y*xi+xk)*(1-beta_Y*beta_Y*(xi+xk)/(beta_Y*beta_Y*xi+xk));
}
CoolPropDbl GERG2008ReducingFunction::c_Y_ij(std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c)
{
return 2*beta[i][j]*gamma[i][j]*Y_c[i][j];
}
CoolPropDbl GERG2008ReducingFunction::f_Y_ij(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, const STLMatrix &beta)
{
double xi = x[i], xj = x[j], beta_Y = beta[i][j];
if (std::abs(xi) < 10*DBL_EPSILON && std::abs(xj) < 10*DBL_EPSILON){return 0;}
return xi*xj*(xi+xj)/(beta_Y*beta_Y*xi+xj);
}
CoolPropDbl GERG2008ReducingFunction::d2fYikdxi2__constxk(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t k, const STLMatrix &beta)
{
double xi = x[i], xk = x[k], beta_Y = beta[i][k];
if (std::abs(xi) < 10*DBL_EPSILON && std::abs(xk) < 10*DBL_EPSILON){return 0;}
return 1/(beta_Y*beta_Y*xi+xk)*(1-beta_Y*beta_Y*(xi+xk)/(beta_Y*beta_Y*xi+xk))*(2*xk-xi*xk*2*beta_Y*beta_Y/(beta_Y*beta_Y*xi+xk));
}
CoolPropDbl GERG2008ReducingFunction::d2fYkidxi2__constxk(const std::vector<CoolPropDbl> &x, std::size_t k, std::size_t i, const STLMatrix &beta)
{
double xi = x[i], xk = x[k], beta_Y = beta[k][i];
if (std::abs(xi) < 10*DBL_EPSILON && std::abs(xk) < 10*DBL_EPSILON){return 0;}
return 1/(beta_Y*beta_Y*xk+xi)*(1-(xk+xi)/(beta_Y*beta_Y*xk+xi))*(2*xk-xk*xi*2/(beta_Y*beta_Y*xk+xi));
}
CoolPropDbl GERG2008ReducingFunction::d2fYijdxidxj(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, const STLMatrix &beta)
{
double xi = x[i], xj = x[j], beta_Y = beta[i][j], beta_Y2 = beta_Y*beta_Y;
if (std::abs(xi) < 10*DBL_EPSILON && std::abs(xj) < 10*DBL_EPSILON){return 0;}
return (xi+xj)/(beta_Y2*xi+xj) + xj/(beta_Y2*xi+xj)*(1-(xi+xj)/(beta_Y2*xi+xj))
+xi/(beta_Y2*xi+xj)*(1-beta_Y2*(xi+xj)/(beta_Y2*xi+xj))
-xi*xj/pow(beta_Y2*xi+xj,2)*(1+beta_Y2-2*beta_Y2*(xi+xj)/(beta_Y2*xi+xj));
}
CoolPropDbl GERG2008ReducingFunction::d3fYijdxi2dxj(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, const STLMatrix &beta)
{
double x_i = x[i], x_j = x[j], beta_Y = beta[i][j], beta_Y2 = beta_Y*beta_Y;
double den = pow(beta_Y, 8)*pow(x_i, 4) + 4*pow(beta_Y, 6)*pow(x_i, 3)*x_j + 6*pow(beta_Y, 4)*pow(x_i*x_j, 2) + 4*beta_Y2*x_i*pow(x_j, 3) + pow(x_j, 4);
return -6*beta_Y2*x_i*x_j*x_j*(beta_Y2-1)/den;
}
CoolPropDbl GERG2008ReducingFunction::d3fYijdxidxj2(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t j, const STLMatrix &beta)
{
double x_i = x[i], x_j = x[j], beta_Y = beta[i][j], beta_Y2 = beta_Y*beta_Y;
double den = pow(beta_Y, 8)*pow(x_i, 4) + 4*pow(beta_Y, 6)*pow(x_i, 3)*x_j + 6*pow(beta_Y, 4)*pow(x_i*x_j, 2) + 4*beta_Y2*x_i*pow(x_j, 3) + pow(x_j, 4);
return 6*beta_Y2*x_i*x_i*x_j*(beta_Y2-1)/den;
}
CoolPropDbl GERG2008ReducingFunction::d3fYikdxi3__constxk(const std::vector<CoolPropDbl> &x, std::size_t i, std::size_t k, const STLMatrix &beta)
{
double x_i = x[i], x_k = x[k], beta_Y = beta[i][k], beta_Y2 = beta_Y*beta_Y;
double den = pow(beta_Y, 8)*pow(x_i, 4) + 4*pow(beta_Y, 6)*pow(x_i, 3)*x_k + 6*pow(beta_Y, 4)*pow(x_i*x_k, 2) + 4*beta_Y2*x_i*pow(x_k, 3) + pow(x_k, 4);
return 6*beta_Y2*x_k*x_k*x_k*(beta_Y2-1)/den;
}
CoolPropDbl GERG2008ReducingFunction::d3fYkidxi3__constxk(const std::vector<CoolPropDbl> &x, std::size_t k, std::size_t i, const STLMatrix &beta)
{
double x_i = x[i], x_k = x[k], beta_Y = beta[k][i], beta_Y2 = beta_Y*beta_Y;
double den = pow(beta_Y, 8)*pow(x_i, 4) + 4*pow(beta_Y, 6)*pow(x_i, 3)*x_k + 6*pow(beta_Y, 4)*pow(x_i*x_k, 2) + 4*beta_Y2*x_i*pow(x_k, 3) + pow(x_k, 4);
return 6*beta_Y2*x_k*x_k*x_k*(1-beta_Y2)/pow(beta_Y2*x_k+x_i, 4);
}
} /* namespace CoolProp */
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