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Added docs for saturation routines

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Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
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Ian Bell
2014-09-14 22:46:00 +02:00
parent 71556fcffe
commit d47ba92acf
1 changed files with 53 additions and 10 deletions
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63
src/Backends/Helmholtz/VLERoutines.h
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@@ -210,11 +210,35 @@ namespace SaturationSolvers
newton_raphson_twophase_options(){ Nstep_max = 30; Nsteps = 0; beta = -1; omega =1;} // Defaults
};
/** \brief A class to do newton raphson solver for VLE for p,q or T,q
/** \brief 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.
*
* This class only handles bubble and dew lines since the independent variables are N-1 of the mole fractions in the incipient phase along with one of T, p, or rho
* As in Gernert, FPE, 2014, except that only one of T and P are known
*
* The independent variables are \f$N-1\f$ mole fractions in liquid, \f$N-1\f$ mole fractions in vapor, and the non-specified variable in p or T, for a total of \f$2N-1\f$ independent variables
*
* First N residuals are from
*
* \f$F_k = \ln f_i(T,p,\mathbf{x}) - \ln f_i(T,p,\mathbf{y})\f$ for \f$i = 1, ... N\f$ and \f$k=i\f$
*
* Derivatives are the same as for the saturation solver \ref newton_raphson_saturation
*
* Second N-1 residuals are from
*
* \f$F_k = \dfrac{z_i-x_i}{y_i-x_i} - \beta_{spec}\f$ for \f$ i = 1, ... N-2\f$ and \f$k = i+N\f$
*
* Gernert eq. 35
*
* \f$\dfrac{\partial F_k}{\partial x_i} = \dfrac{z_i-y_i}{(y_i-x_i)^2}\f$
*
* Gernert eq. 36
*
* \f$\dfrac{\partial F_k}{\partial y_i} = -\dfrac{z_i-x_i}{(y_i-x_i)^2}\f$
*
* \f$\dfrac{\partial F_k}{\partial T} = 0\f$ Because x, y and T are independent by definition of the formulation
*
* \f$\dfrac{\partial F_k}{\partial p} = 0\f$ Because x, y and p are independent by definition of the formulation
*/
class newton_raphson_twophase
{
@@ -240,7 +264,7 @@ namespace SaturationSolvers
rhomolar_liq = _HUGE; rhomolar_vap = _HUGE; T = _HUGE; p = _HUGE;
};
/** Call the Newton-Raphson VLE Solver
/** \brief 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
@@ -251,11 +275,9 @@ namespace SaturationSolvers
*/
void call(HelmholtzEOSMixtureBackend &HEOS, newton_raphson_twophase_options &IO);
/*! Build the arrays for the Newton-Raphson solve
This method builds the Jacobian matrix, the sensitivity matrix, etc.
/* \brief Build the arrays for the Newton-Raphson solve
*
*/
*/
void build_arrays();
};
@@ -271,11 +293,32 @@ namespace SaturationSolvers
newton_raphson_saturation_options(){ Nstep_max = 30; Nsteps = 0;} // Defaults
};
/** \brief A class to do newton raphson solver for VLE given guess values for vapor-liquid equilibria. This class will then be included in the Mixture class
/** \brief 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.
* 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 \ref PhaseEnvelopeRoutines for the construction of the phase envelope
*
* This class only handles bubble and dew lines since the independent variables are N-1 of the mole fractions in the incipient phase along with one of T, p, or rho
* 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 \f$\rho''\f$.
*
* 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$F_i = \ln f_i(T, p, \mathbf{x}) - \ln f_i(T, p, \mathbf{y})\f$ for \f$i = 1, ... N\f$
*
* if either T or p are imposed. In this case a solver is used to find \f$\rho\f$ given \f$T\f$ and \f$p\f$.
*
* In the case that \f$\rho''\f$ is imposed, the case is much nicer and the first \f$N\f$ residuals are
*
* \f$F_i = \ln f_i(T, \rho', \mathbf{x}) - \ln f_i(T, \rho'', \mathbf{y})\f$ for \f$i = 1, ... N\f$
*
* which requires no iteration. A final residual is set up to ensure the same pressures in the phases:
*
* \f$p(T,\rho',\mathbf{x})-p(T,\rho'',\mathbf{y}) = 0\f$
*
* Documentation of the derivatives needed can be found in the work of Gernert, FPE, 2014
*/
class newton_raphson_saturation
{