CoolProp::SaturationSolvers::newton_raphson_twophase Class Reference

Detailed Description

A class to do newton raphson solver for mixture VLE for p,Q or T,Q.

A class is used rather than a function so that it is easier to store iteration histories, additional output values, etc.

As in Gernert, FPE, 2014, except that only one of T and P are known

The independent variables are \(N-1\) mole fractions in liquid, \(N-1\) mole fractions in vapor, and the non-specified variable in p or T, for a total of \(2N-1\) independent variables

First N residuals are from

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

Derivatives are the same as for the saturation solver newton_raphson_saturation

Second N-1 residuals are from

\(F_k = \dfrac{z_i-x_i}{y_i-x_i} - \beta_{spec}\) for \( i = 1, ... N-2\) and \(k = i+N\)

Gernert eq. 35

\(\dfrac{\partial F_k}{\partial x_i} = \dfrac{z_i-y_i}{(y_i-x_i)^2}\)

Gernert eq. 36

\(\dfrac{\partial F_k}{\partial y_i} = -\dfrac{z_i-x_i}{(y_i-x_i)^2}\)

\(\dfrac{\partial F_k}{\partial T} = 0\) Because x, y and T are independent by definition of the formulation

\(\dfrac{\partial F_k}{\partial p} = 0\) Because x, y and p are independent by definition of the formulation

Definition at line 354 of file VLERoutines.h.

#include <VLERoutines.h>

Public Member Functions
	newton_raphson_twophase ()
void	resize (unsigned int N)
void	pre_call ()
void	call (HelmholtzEOSMixtureBackend &HEOS, newton_raphson_twophase_options &IO)
	Call the Newton-Raphson VLE Solver. More...
void	build_arrays ()

Public Attributes
HelmholtzEOSMixtureBackend *	HEOS
newton_raphson_twophase_options::imposed_variable_options	imposed_variable
CoolPropDbl	error_rms
CoolPropDbl	rhomolar_liq
CoolPropDbl	rhomolar_vap
CoolPropDbl	T
CoolPropDbl	p
CoolPropDbl	min_rel_change
CoolPropDbl	beta
std::size_t	N
bool	logging
int	Nsteps
Eigen::MatrixXd	J
Eigen::Vector2d	r
Eigen::Vector2d	err_rel
std::vector< CoolPropDbl >	K
std::vector< CoolPropDbl >	x
std::vector< CoolPropDbl >	y
std::vector< CoolPropDbl >	z
std::vector< SuccessiveSubstitutionStep >	step_logger

Constructor & Destructor Documentation

newton_raphson_twophase()

CoolProp::SaturationSolvers::newton_raphson_twophase::newton_raphson_twophase ( )

inline

Definition at line 368 of file VLERoutines.h.

Member Function Documentation

build_arrays()

void CoolProp::SaturationSolvers::newton_raphson_twophase::build_arrays

(

)

Definition at line 1598 of file VLERoutines.cpp.

call()

void CoolProp::SaturationSolvers::newton_raphson_twophase::call	(	HelmholtzEOSMixtureBackend &	HEOS,
		newton_raphson_twophase_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
IO	The input/output data structure

Definition at line 1514 of file VLERoutines.cpp.

pre_call()

void CoolProp::SaturationSolvers::newton_raphson_twophase::pre_call ( )

inline

Definition at line 385 of file VLERoutines.h.

resize()

void CoolProp::SaturationSolvers::newton_raphson_twophase::resize

(

unsigned int

N

)

Member Data Documentation

beta

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_twophase::beta

Definition at line 359 of file VLERoutines.h.

err_rel

Eigen::Vector2d CoolProp::SaturationSolvers::newton_raphson_twophase::err_rel

Definition at line 364 of file VLERoutines.h.

error_rms

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_twophase::error_rms

Definition at line 359 of file VLERoutines.h.

HEOS

HelmholtzEOSMixtureBackend* CoolProp::SaturationSolvers::newton_raphson_twophase::HEOS

Definition at line 357 of file VLERoutines.h.

imposed_variable

newton_raphson_twophase_options::imposed_variable_options CoolProp::SaturationSolvers::newton_raphson_twophase::imposed_variable

Definition at line 358 of file VLERoutines.h.

J

Eigen::MatrixXd CoolProp::SaturationSolvers::newton_raphson_twophase::J

Definition at line 363 of file VLERoutines.h.

K

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

Definition at line 365 of file VLERoutines.h.

logging

bool CoolProp::SaturationSolvers::newton_raphson_twophase::logging

Definition at line 361 of file VLERoutines.h.

min_rel_change

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_twophase::min_rel_change

Definition at line 359 of file VLERoutines.h.

N

std::size_t CoolProp::SaturationSolvers::newton_raphson_twophase::N

Definition at line 360 of file VLERoutines.h.

Nsteps

int CoolProp::SaturationSolvers::newton_raphson_twophase::Nsteps

Definition at line 362 of file VLERoutines.h.

p

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_twophase::p

Definition at line 359 of file VLERoutines.h.

r

Eigen::Vector2d CoolProp::SaturationSolvers::newton_raphson_twophase::r

Definition at line 364 of file VLERoutines.h.

rhomolar_liq

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_twophase::rhomolar_liq

Definition at line 359 of file VLERoutines.h.

rhomolar_vap

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_twophase::rhomolar_vap

Definition at line 359 of file VLERoutines.h.

step_logger

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

Definition at line 366 of file VLERoutines.h.

T

CoolPropDbl CoolProp::SaturationSolvers::newton_raphson_twophase::T

Definition at line 359 of file VLERoutines.h.

x

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

Definition at line 365 of file VLERoutines.h.

y

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

Definition at line 365 of file VLERoutines.h.

z

std::vector<CoolPropDbl> CoolProp::SaturationSolvers::newton_raphson_twophase::z

Definition at line 365 of file VLERoutines.h.

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

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