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- Worked on the equation section.
This commit is contained in:
Harry Moffat 2007-03-06 17:14:41 +00:00
parent 924afeceb4
commit aa7e70a2ad
2 changed files with 120 additions and 36 deletions
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12
Cantera/src/thermo/DebyeHuckel.cpp
View file

@ -1015,7 +1015,7 @@ namespace Cantera {
* -------------- Utilities -------------------------------
*/
/**
/*
* Initialization routine for a DebyeHuckel phase.
*
* This is a virtual routine. This routine will call initThermo()
@ -1026,7 +1026,7 @@ namespace Cantera {
initLengths();
}
/**
/*
* constructPhaseFile
*
* Initialization of a Debye-Huckel phase using an
@ -1100,7 +1100,7 @@ namespace Cantera {
return rval;
}
/**
/*
* Import and initialize a DebyeHuckel phase
* specification in an XML tree into the current object.
* Here we read an XML description of the phase.
@ -1229,7 +1229,7 @@ namespace Cantera {
}
/**
/*
* Process the XML file after species are set up.
*
* This gets called from importPhase(). It processes the XML file
@ -2013,7 +2013,7 @@ namespace Cantera {
return lac;
}
/**
/*
* s_update_lnMolalityActCoeff():
*
* Using internally stored values, this function calculates
@ -2071,7 +2071,7 @@ namespace Cantera {
m_IionicMolalityStoich = m_maxIionicStrength;
}
/**
/*
* Possibly update the storred value of the
* Debye-Huckel parameter A_Debye
* This parameter appears on the top of the activity

144
Cantera/src/thermo/DebyeHuckel.h
View file

@ -34,7 +34,7 @@ namespace Cantera {
* This form assumes a dilute limit to DH, and is mainly
* for informational purposes:
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I)
* ln(gamma_k) = -z_k**2 * alpha * sqrt(I)
*
* where I = 1/2 sum_k( molality_k * z_k**2)
*
@ -42,7 +42,7 @@ namespace Cantera {
*
* This form assumes Bethke's format for the DH coefficient
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a_k * sqrt(I))
* ln(gamma_k) = -z_k**2 * alpha * sqrt(I) / (1 + B * a_k * sqrt(I))
* + bdot_k * I
*
* (note, this particular form where a_k can differ in
@ -54,7 +54,7 @@ namespace Cantera {
*
* This form assumes Bethke's format for the DH coefficient
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* ln(gamma_k) = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* + bdot_k * I
*
* The value of a is determined at the beginning of the
@ -67,7 +67,7 @@ namespace Cantera {
* more complex treatments for stronger electrolytes, like Pitzer
* and HMW treatments.
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* ln(gamma_k) = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* + 2* sum_j (beta_jk m_j)
*
* DHFORM_PITZER_BETAIJ = 4
@ -75,7 +75,7 @@ namespace Cantera {
* This form assumes an activity coefficient formulation consistent
* with a truncated form of Pitzer's formulation.
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* ln(gamma_k) = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* -2 * z_k**2 * alpha * ln(1 + B * a * sqrt(I)) / (B * a)
* + 2 * sum_j (beta_jk m_j)
*
@ -199,53 +199,122 @@ namespace Cantera {
* This form assumes a dilute limit to DH, and is mainly
* for informational purposes:
* \f[
* \frac{\ln(\gamma_k^\triangle)}{ R T} = - z_k^2 A_{Debye} \sqrt{I}
* \ln(\gamma_k^\triangle) = - z_k^2 A_{Debye} \sqrt{I}
* \f]
* where I is the ionic strength
* \f[
* I = \frac{1}{2} \sum_k{m_k z_k^2}
* \f]
*
* DHFORM_BDOT_AK = 1
* The activity for the solvent water,\f$ a_o \f$, is not independent and must be
* determined from the Gibbs-Duhem relation.
*
* This form assumes Bethke's format for the DH coefficient
* \f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2}
* \f]
*
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a_k * sqrt(I))
* + bdot_k * I
*
* (note, this particular form where a_k can differ in
* <H3> Bdot Formulation </H3>
*
* DHFORM_BDOT_AK = 1
*
* This form assumes Bethke's format for the Debye Huckel activity coefficient:
*
* \f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a_k \sqrt{I}}
* + \log(10) B^{dot}_k I
* \f]
*
* Note, this particular form where \f$ a_k \f$ can differ in
* multielectrolyte
* solutions has problems wrt a gibbs-duhem analysis. However
* we include it here because there is a lot of data fit to it)
* 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 DH coefficient
* This form assumes Bethke's format for the Debye-Huckel activity coefficient
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* + bdot_k * I
* \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 Newmann's book, and is the beginning of
* more complex treatments for stronger electrolytes, like Pitzer
* and HMW treatments.
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* + 2* sum_j (beta_jk m_j)
* It is used extensively in the book by Newmann, Electrochemistry, 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]
*
*
* <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.
* 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]
*
*
* ln(gamma_k)/RT = -z_k**2 * alpha * sqrt(I) / (1 + B * a * sqrt(I))
* -2 * z_k**2 * alpha * ln(1 + B * a * sqrt(I)) / (B * a)
* + 2 * sum_j (beta_jk m_j)
* <HR>
* <b> %Application within %Kinetics Managers </b>
* <HR>
@ -1130,10 +1199,25 @@ namespace Cantera {
* with the correct id.
*/
virtual void constructPhaseXML(XML_Node& phaseNode, std::string id="");
//! Process the XML file after species are set up.
/*!
* This gets called from importPhase(). It processes the XML file
* after the species are set up. This is the main routine for
* reading in activity coefficient parameters.
*
* @param phaseNode This object must be the phase node of a
* complete XML tree
* description of the phase, including all of the
* species data. In other words while "phase" must
* point to an XML phase object, it must have
* sibling nodes "speciesData" that describe
* the species in the phase.
* @param id ID of the phase. If nonnull, a check is done
* to see if phaseNode is pointing to the phase
* with the correct id.
*/
virtual void initThermoXML(XML_Node& phaseNode, std::string id);
//! Return the Debye Huckel constant as a function of temperature
//! and pressure (Units = sqrt(kg/gmol))