research/cantera
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Doxygen Update

Browse source 
Worked on the class header information.
This commit is contained in:
Harry Moffat 2007-06-14 23:40:49 +00:00
parent 56155a1d27
commit fa0cc67986
2 changed files with 57 additions and 132 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

1
Cantera/src/thermo/HMWSoln.cpp
View file

@ -1,6 +1,5 @@
/**
* @file HMWSoln.cpp
*
* Member functions of Pitzer activity coefficient implementation.
*/
/*

188
Cantera/src/thermo/HMWSoln.h
View file

@ -83,18 +83,26 @@ namespace Cantera {
class WaterPDSS;
/**
* Class %HMWSoln represents a dilute or conetrated liquid electrolyte phase which
* obeys the Pitzer formulation for nonideality.
* Class %HMWSoln represents a dilute or concentrated liquid electrolyte
* phase which obeys the Pitzer formulation for nonideality.
*
* The concentrations of the ionic species are assumed to obey the electroneutrality
* condition.
* As a prerequisite to the specification of thermodynamic quantities,
* The concentrations of the ionic species are assumed to obey the
* electroneutrality condition.
*
* <HR>
* <H2> Specification of Species Standard %State Properties </H2>
* <HR>
*
* The standard states are on the unit molality basis. Therefore, in the
* documentation below, the normal \f$ o \f$ superscript is replaced with
* The solvent is assumed to be liquid water. A real model for liquid
* water (IAPWS 1995 formulation) is used as its standard state.
* All standard state properties for the solvent are based on
* this real model for water, and involve function calls
* to the object that handles the real water model, #WaterPropsIAPWS.
*
* The standard states for solutes are on the unit molality basis.
* Therefore, in the documentation below, the normal \f$ o \f$
* superscript is replaced with
* the \f$ \triangle \f$ symbol. The reference state symbol is now
* \f$ \triangle, ref \f$.
*
@ -104,19 +112,24 @@ namespace Cantera {
* manager class (see ThermoPhase::m_spthermo). How to relate pressure
* changes to the reference state thermodynamics is resolved at this level.
*
* For an incompressible,
* stoichiometric substance, the molar internal energy is
* independent of pressure. Since the thermodynamic properties
* are specified by giving the standard-state enthalpy, the
* term \f$ P_0 \hat v\f$ is subtracted from the specified molar
* enthalpy to compute the molar internal energy. The entropy is
* assumed to be independent of the pressure.
* For solutes that rely on ThermoPhase::m_spthermo, are assumed to
* have an incompressible standard state mechanical property.
* In other words, the molar volumes are independent of temperature
* and pressure.
*
* For these incompressible,
* standard states, the molar internal energy is
* independent of pressure. Since the thermodynamic properties
* are specified by giving the standard-state enthalpy, the
* term \f$ P_0 \hat v\f$ is subtracted from the specified molar
* enthalpy to compute the molar internal energy. The entropy is
* assumed to be independent of the pressure.
*
* The enthalpy function is given by the following relation.
*
* \f[
* \raggedright h^\triangle_k(T,P) = h^{\triangle,ref}_k(T)
* + \tilde v \left( P - P_{ref} \right)
* + \tilde{v}_k \left( P - P_{ref} \right)
* \f]
*
* For an incompressible,
@ -127,19 +140,19 @@ namespace Cantera {
* enthalpy to compute the molar internal energy.
*
* \f[
* u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde v
* u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde{v}_k
* \f]
*
*
* The standard state heat capacity and entropy are independent
* of pressure. The standard state gibbs free energy is obtained
* The solute standard state heat capacity and entropy are independent
* of pressure. The solute standard state gibbs free energy is obtained
* from the enthalpy and entropy functions.
*
* The vector Constituents::m_speciesSize[] is used to hold the
* base values of species sizes. These are defined as the
* molar volumes of species at infinite dilution at 300 K and 1 atm
* of water. m_speciesSize are calculated during the initialization of the
* %DebyeHuckel object and are then not touched.
* %HMWSoln object and are then not touched.
*
* The current model assumes that an incompressible molar volume for
* all solutes. The molar volume for the water solvent, however,
@ -168,7 +181,12 @@ namespace Cantera {
* \f$k\f$.
*
* Individual activity coefficients of ions can not be independently measured. Instead,
* only binary pairs forming electroneutral solutions can be measured.
* only binary pairs forming electroneutral solutions can be measured. This problem
* leads to a redundancy in the evaluation of species standard state properties.
* The redundancy issue is resolved by setting the standard state chemical potential
* enthalpy, entropy, and volume for the hydrogen ion, H+, to zero, for every temperature
* and pressure. After this convention is applied, all other standard state
* properties of ionic species contain meaningfull information.
*
*
* <H3> Ionic Strength </H3>
@ -279,20 +297,32 @@ namespace Cantera {
* category. A neutral solute species is put into the "nonpolarNeutral" category by default.
*
*
* <H3> Debye-Huckel Dilute Limit </H3>
* <H3> Multicomponent Activity Coefficients for Solutes </H3>
*
* In the formulas below the following conventions are used. The subscript <I>M</I> refers
* to a particular cation. The subscript X refers to a particular anion, whose
* activity is being currently evaluated. the subscript <I>a</I> refers to a summation
* over all anions in the solution, while the subscript <I>c</I> refers to a summation
* over all cations in the solutions.
*
* The activity coefficient for a particular cation <I>M</I> is given by
*
* \f[
* \ln(\gamma_M^\triangle) = -z_M^2(F) + \sum_a m_a \left( 2 B_{Ma} + Z C_{Ma} \right)
* + z_M \left( \sum_a \sum_c m_a m_c C_{Ma} \right)
* + \sum_c m_c \left[ 2 \Phi_{Mc} + \sum_a m_a \psi_{Mca} \right]
* + \sum_{a < a'} \sum m_a m_{a'} \psi_{Ma{a'}}
* + 2 \sum_n m_n \lambda_{nM}
* \f]
*
* DHFORM_DILUTE_LIMIT = 0
*
* This form assumes a dilute limit to DH, and is mainly
* for informational purposes:
* \f[
* \ln(\gamma_k^\triangle) = - z_k^2 A_{Debye} \sqrt{I}
* \f]
* where \f$ I\f$ is the ionic strength
* \f[
* I = \frac{1}{2} \sum_k{m_k z_k^2}
* \f]
*
* <H3> Activity of the Water Solvent </H3>
*
* The activity for the solvent water,\f$ a_o \f$, is not independent and must be
* determined from the Gibbs-Duhem relation.
*
@ -301,91 +331,7 @@ namespace Cantera {
* \f]
*
*
* <H3> Bdot Formulation </H3>
*
* DHFORM_BDOT_AK = 1
*
* This form assumes Bethke's format for the Debye Huckel activity coefficient:
*
* \f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a_k \sqrt{I}}
* + \log(10) B^{dot}_k I
* \f]
*
* Note, this particular form where \f$ a_k \f$ can differ in
* multielectrolyte
* solutions has problems with respect to a Gibbs-Duhem analysis. However,
* we include it here because there is a lot of data fit to it.
*
* The activity for the solvent water,\f$ a_o \f$, is not independent and must be
* determined from the Gibbs-Duhem relation. Here, we use:
*
* \f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{1/2}
* \left[ \sum_k{\frac{1}{2} m_k z_k^2 \sigma( B_{Debye} a_k \sqrt{I} ) } \right]
* - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k}
* \f]
* where
* \f[
* \sigma (y) = \frac{3}{y^3} \left[ (1+y) - 2 \ln(1 + y) - \frac{1}{1+y} \right]
* \f]
*
* Additionally, Helgeson's formulation for the water activity is offered as an
* alternative.
*
* <H3> Bdot Formulation with Uniform Size Parameter in the Denominator </H3>
*
* DHFORM_BDOT_AUNIFORM = 2
*
* This form assumes Bethke's format for the Debye-Huckel activity coefficient
*
* \f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}}
* + \log(10) B^{dot}_k I
* \f]
*
* The value of a is determined at the beginning of the
* calculation, and not changed.
*
* \f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} )
* - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k}
* \f]
*
*
* <H3> Beta_IJ formulation </H3>
*
* DHFORM_BETAIJ = 3
*
* This form assumes a linear expansion in a virial coefficient form
* It is used extensively in the book by Newmann, "Electrochemistry Systems",
* and is the beginning of
* more complex treatments for stronger electrolytes, fom Pitzer
* and from Harvey, Moller, and Weire.
*
* \f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}}
* + 2 \sum_j \beta_{j,k} m_j
* \f]
*
* In the current treatment the binary interaction coefficients, \f$ \beta_{j,k}\f$, are
* independent of temperature and pressure.
*
* \f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} )
* - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k
* \f]
*
* In this formulation the ionic radius, \f$ a \f$, is a constant. This must be supplied to the
* model, in an <DFN> ionicRadius </DFN> XML block.
*
* The \f$ \beta_{j,k} \f$ parameters are binary interaction parameters. They are supplied to
* the object in an <TT> DHBetaMatrix </TT> XML block. There are in principle \f$ N (N-1) /2 \f$
* different, symmetric interaction parameters, where \f$ N \f$ are the number of solute species in the
* mechanism.
* An example is given below.
*
* An example <TT> activityCoefficients </TT> XML block for this formulation is supplied below
@ -413,26 +359,6 @@ namespace Cantera {
* </activityCoefficients>
* @endcode
*
* <H3> Pitzer Beta_IJ formulation </H3>
*
* DHFORM_PITZER_BETAIJ = 4
*
* * This form assumes an activity coefficient formulation consistent
* with a truncated form of Pitzer's formulation. Pitzer's formulation is equivalent
* to the formulations above in the dilute limit, where rigorous theory may be applied.
*
* \f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye}}{3} \frac{\sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}}
* -2 z_k^2 \frac{A_{Debye}}{3} \frac{\ln(1 + B_{Debye} a \sqrt{I})}{ B_{Debye} a}
* + 2 \sum_j \beta_{j,k} m_j
* \f]
*
*
* \f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} \frac{(I)^{3/2} }{1 + B_{Debye} a \sqrt{I} }
* - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k
* \f]
*
* <H3> Specification of the Debye Huckel Constants </H3>
*