Detailed Description

A class to do newton raphson solver mixture bubble point and dew point calculations.

A class is used rather than a function so that it is easier to store iteration histories, additional output values, etc. This class is used in PhaseEnvelopeRoutines for the construction of the phase envelope

This class only handles bubble and dew lines. The independent variables are the first N-1 mole fractions in the incipient phase along with one of T, p, or \(\rho''\).

These methods are based on the work of Gernert, FPE, 2014, the thesis of Gernert, as well as much help from Andreas Jaeger of Uni. Bochum.

There are N residuals from

\(F_i = \ln f_i(T, p, \mathbf{x}) - \ln f_i(T, p, \mathbf{y})\) for \(i = 1, ... N\)

if either T or p are imposed. In this case a solver is used to find \(\rho\) given \(T\) and \(p\).

In the case that \(\rho''\) is imposed, the case is much nicer and the first \(N\) residuals are

\(F_i = \ln f_i(T, \rho', \mathbf{x}) - \ln f_i(T, \rho'', \mathbf{y})\) for \(i = 1, ... N\)

which requires no iteration. A final residual is set up to ensure the same pressures in the phases:

\(p(T,\rho',\mathbf{x})-p(T,\rho'',\mathbf{y}) = 0\)

Documentation of the derivatives needed can be found in the work of Gernert, FPE, 2014

Definition at line 476 of file VLERoutines.h.

#include <VLERoutines.h>

Public Member Functions
	newton_raphson_saturation ()

void	resize (std::size_t N)

void	pre_call ()

void	call (HelmholtzEOSMixtureBackend &HEOS, const std::vector< CoolPropDbl > &z, std::vector< CoolPropDbl > &z_incipient, newton_raphson_saturation_options &IO)
	Call the Newton-Raphson VLE Solver. More...

void	build_arrays ()
	Build the arrays for the Newton-Raphson solve. More...

void	check_Jacobian ()
	Check the derivatives in the Jacobian using numerical derivatives. More...

Public Attributes
newton_raphson_saturation_options::imposed_variable_options	imposed_variable

CoolPropDbl	error_rms

CoolPropDbl	rhomolar_liq

CoolPropDbl	rhomolar_vap

CoolPropDbl	T

CoolPropDbl	p

CoolPropDbl	min_rel_change

std::size_t	N

bool	logging

bool	bubble_point

int	Nsteps

Eigen::MatrixXd	J

HelmholtzEOSMixtureBackend *	HEOS

CoolPropDbl	dTsat_dPsat

CoolPropDbl	dPsat_dTsat

std::vector< CoolPropDbl >	K

std::vector< CoolPropDbl >	x

std::vector< CoolPropDbl >	y

Eigen::VectorXd	r

Eigen::VectorXd	err_rel

std::vector< SuccessiveSubstitutionStep >	step_logger

Constructor & Destructor Documentation

◆ newton_raphson_saturation()

CoolProp::SaturationSolvers::newton_raphson_saturation::newton_raphson_saturation ( )

inline

Definition at line 492 of file VLERoutines.h.

Member Function Documentation

◆ build_arrays()

void CoolProp::SaturationSolvers::newton_raphson_saturation::build_arrays ( )

Build the arrays for the Newton-Raphson solve.

This method builds the Jacobian matrix, the sensitivity matrix, etc.

Definition at line 1384 of file VLERoutines.cpp.

◆ call()

void CoolProp::SaturationSolvers::newton_raphson_saturation::call	(	HelmholtzEOSMixtureBackend &	HEOS,
		const std::vector< CoolPropDbl > &	z,
		std::vector< CoolPropDbl > &	z_incipient,
		newton_raphson_saturation_options &	IO
	)

Call the Newton-Raphson VLE Solver.

This solver must be passed reasonable guess values for the mole fractions, densities, etc. You may want to take a few steps of successive substitution before you start with Newton Raphson.

Parameters

HEOS	HelmholtzEOSMixtureBackend instance
z	Bulk mole fractions [-]
z_incipient	Initial guesses for the mole fractions of the incipient phase [-]
IO	The input/output data structure

Definition at line 1284 of file VLERoutines.cpp.

◆ check_Jacobian()

void CoolProp::SaturationSolvers::newton_raphson_saturation::check_Jacobian ( )

Check the derivatives in the Jacobian using numerical derivatives.

Definition at line 1204 of file VLERoutines.cpp.

◆ pre_call()

void CoolProp::SaturationSolvers::newton_raphson_saturation::pre_call ( )

inline

Definition at line 497 of file VLERoutines.h.

◆ resize()

void CoolProp::SaturationSolvers::newton_raphson_saturation::resize ( std::size_t N )

Definition at line 1187 of file VLERoutines.cpp.

Member Data Documentation

◆ bubble_point

bool CoolProp::SaturationSolvers::newton_raphson_saturation::bubble_point

Definition at line 483 of file VLERoutines.h.

◆ dPsat_dTsat

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::dPsat_dTsat

Definition at line 487 of file VLERoutines.h.

◆ dTsat_dPsat

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::dTsat_dPsat

Definition at line 487 of file VLERoutines.h.

◆ err_rel

Eigen::VectorXd CoolProp::SaturationSolvers::newton_raphson_saturation::err_rel

Definition at line 489 of file VLERoutines.h.

◆ error_rms

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::error_rms

Definition at line 480 of file VLERoutines.h.

◆ HEOS

HelmholtzEOSMixtureBackend* CoolProp::SaturationSolvers::newton_raphson_saturation::HEOS

Definition at line 486 of file VLERoutines.h.

◆ imposed_variable

newton_raphson_saturation_options::imposed_variable_options CoolProp::SaturationSolvers::newton_raphson_saturation::imposed_variable

Definition at line 479 of file VLERoutines.h.

◆ J

Eigen::MatrixXd CoolProp::SaturationSolvers::newton_raphson_saturation::J

Definition at line 485 of file VLERoutines.h.

◆ K

std::vector<CoolPropDbl> CoolProp::SaturationSolvers::newton_raphson_saturation::K

Definition at line 488 of file VLERoutines.h.

◆ logging

bool CoolProp::SaturationSolvers::newton_raphson_saturation::logging

Definition at line 482 of file VLERoutines.h.

◆ min_rel_change

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::min_rel_change

Definition at line 480 of file VLERoutines.h.

◆ N

std::size_t CoolProp::SaturationSolvers::newton_raphson_saturation::N

Definition at line 481 of file VLERoutines.h.

◆ Nsteps

int CoolProp::SaturationSolvers::newton_raphson_saturation::Nsteps

Definition at line 484 of file VLERoutines.h.

◆ p

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::p

Definition at line 480 of file VLERoutines.h.

◆ r

Eigen::VectorXd CoolProp::SaturationSolvers::newton_raphson_saturation::r

Definition at line 489 of file VLERoutines.h.

◆ rhomolar_liq

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::rhomolar_liq

Definition at line 480 of file VLERoutines.h.

◆ rhomolar_vap

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::rhomolar_vap

Definition at line 480 of file VLERoutines.h.

◆ step_logger

std::vector<SuccessiveSubstitutionStep> CoolProp::SaturationSolvers::newton_raphson_saturation::step_logger

Definition at line 490 of file VLERoutines.h.

◆ T

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_saturation::T

Definition at line 480 of file VLERoutines.h.

◆ x

std::vector<CoolPropDbl> CoolProp::SaturationSolvers::newton_raphson_saturation::x

Definition at line 488 of file VLERoutines.h.

◆ y

std::vector<CoolPropDbl> CoolProp::SaturationSolvers::newton_raphson_saturation::y

Definition at line 488 of file VLERoutines.h.

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

src/Backends/Helmholtz/VLERoutines.h
src/Backends/Helmholtz/VLERoutines.cpp

Detailed Description

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

◆ newton_raphson_saturation()

Member Function Documentation

◆ build_arrays()

◆ call()

◆ check_Jacobian()

◆ pre_call()

◆ resize()

Member Data Documentation

◆ bubble_point

◆ dPsat_dTsat

◆ dTsat_dPsat

◆ err_rel

◆ error_rms

◆ HEOS

◆ imposed_variable

◆ J

◆ K

◆ logging

◆ min_rel_change

◆ N

◆ Nsteps

◆ p

◆ r

◆ rhomolar_liq

◆ rhomolar_vap

◆ step_logger

◆ T

◆ x

◆ y