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

Doxygen update.

Browse source 
completed HMWSoln header information.
This commit is contained in:
Harry Moffat 2007-06-26 22:28:53 +00:00
parent edd8584dda
commit d7fb2d6ffa
3 changed files with 139 additions and 31 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

34
Cantera/src/thermo/HMWSoln.cpp
View file

@ -940,7 +940,6 @@ namespace Cantera {
}
/*
*
* getPartialMolarEntropies() (virtual, const)
*
* Returns an array of partial molar entropies of the species in the
@ -954,10 +953,14 @@ namespace Cantera {
* Combining this with the expression H = G + TS yields:
*
* \f[
* \bar s_k(T,P) = \hat s^0_k(T) - R log(M0 * molality[k] ac[k])
* - R T^2 d log(ac[k]) / dT
* \bar s_k(T,P) = s^{\triangle}_k(T,P)
* - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}}))
* - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT}
* \f]
*
* \f[
* \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o)
* - R T \frac{d \ln(a_o)}{dT}
* \f]
*
* The reference-state pure-species entropies,\f$ \hat s^0_k(T) \f$,
* at the reference pressure, \f$ P_{ref} \f$, are computed by the
@ -1011,7 +1014,7 @@ namespace Cantera {
}
}
/**
/*
* getPartialMolarVolumes() (virtual, const)
*
* Returns an array of partial molar volumes of the species
@ -1053,7 +1056,16 @@ namespace Cantera {
* enthalpy of the kth species in the solution at constant
* P and composition (p. 220 Smith and Van Ness).
*
* Cp = -T d2(chemPot_i)/dT2
* \f[
* \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P)
* - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT}
* - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2}
* \f]
* \f[
* \bar C_{p,o}(T,P) = C^o_{p,o}(T,P)
* - 2 R T \frac{d \ln(a_o)}{dT}
* - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2}
* \f]
*/
void HMWSoln::getPartialMolarCp(doublereal* cpbar) const {
/*
@ -1086,7 +1098,7 @@ namespace Cantera {
* in the Solution ------------------
*/
/**
/*
* getStandardChemPotentials() (virtual, const)
*
*
@ -1115,7 +1127,7 @@ namespace Cantera {
mu[0] = m_waterSS->gibbs_mole();
}
/**
/*
* Get the nondimensional gibbs function for the species
* standard states at the current T and P of the solution.
*
@ -1138,7 +1150,7 @@ namespace Cantera {
}
}
/**
/*
*
* getPureGibbs()
*
@ -1227,7 +1239,7 @@ namespace Cantera {
sr[0] /= GasConstant;
}
/**
/*
* Get the nondimensional heat capacity at constant pressure
* function for the species
* standard states at the current T and P of the solution.
@ -1250,7 +1262,7 @@ namespace Cantera {
cpr[0] /= GasConstant;
}
/**
/*
* Get the molar volumes of each species in their standard
* states at the current
* <I>T</I> and <I>P</I> of the solution.

132
Cantera/src/thermo/HMWSoln.h
View file

@ -276,8 +276,8 @@ namespace Cantera {
*
* Polar and non-polar neutral species are differentiated, because some additions
* to the activity
* coefficient expressions distinguish between these two types of solutes. This is the so-called
* salt-out effect.
* coefficient expressions distinguish between these two types of solutes.
* This is the so-called salt-out effect.
*
* The type of species is specified in the <TT>electrolyteSpeciesType</TT> XML block.
* Note, this is not
@ -346,13 +346,15 @@ namespace Cantera {
* <I>a</I> is a subscribt over all anions, <I>c</I> is a subscript extending over all
* cations, and <I>i</I> is a subscrit that extends over all anions and cations.
* <I>n</I> is a subscript that extends only over neutral solute molecules.
* The second line contains cross terms where cations affect cations and/or cation/anion pairs,
* The second line contains cross terms where cations affect
* cations and/or cation/anion pairs,
* and anions affect anions or cation/anion pairs. Note part of the coefficients,
* \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$ stem from the theory
* of unsymmetrical mixing of electrolytes with different charges. This
* theory depends on the total ionic stregnth of the solution, and therefore,
* \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$ will depend on <I>I</I>, the
* ionic strength. \f$ B_{ca}\f$ is a strong function of the total ionic strength, <I>I</I>,
* ionic strength. \f$ B_{ca}\f$ is a strong function of the
* total ionic strength, <I>I</I>,
* of the electrolyte. The rest of the coefficients are assumed to be independent of the
* molalities or ionic strengths. However, all coefficients are potentially functions
* of the temperature and pressure of the solution.
@ -519,6 +521,14 @@ namespace Cantera {
* \frac{1}{\sum_{i \ne 0} m_i}
* \f]
*
* The osmotic coefficient may be related to the water activity by the following relation:
*
* \f[
* \phi = - \frac{1}{\tilde{M}_o \sum_{i \neq o} m_i} \ln(a_o)
* = - \frac{n_o}{\sum_{i \neq o}n_i} \ln(a_o)
* \f]
*
*
* The result is the following
*
* \f[
@ -688,7 +698,7 @@ namespace Cantera {
* Dependent in general on temperature and pressure, it's ionic
* strength dependence is ignored in Pitzer's approach.
* \f$ \,^E\Theta_{ij}(I) \f$ accounts for the electrostatic
* unsymmetrical mixing effects and is depeendnet only on the
* unsymmetrical mixing effects and is dependent only on the
* charges of the ions i, j, the total ionic strength and on
* the dielectric constant and density of the solvent.
* This seems to be a relatively well-documented part of the theory.
@ -925,10 +935,68 @@ namespace Cantera {
* <H3> Temperature and Pressure Dependence of the Activity Coefficients </H3>
*
* Temperature dependence of the activity coefficients leads to nonzero terms
* for the excess enthalpy of solution.
* for the excess enthalpy and entropy of solution. This means that the
* partial molar enthalpies, entropies, and heat capacities are all
* non-trivial to compute. The following formulas are used.
*
* The partial molar enthalpy, \f$ \bar s_k(T,P) \f$:
*
* \f[
* \bar h_k(T,P) = h^{\triangle}_k(T,P)
* - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT}
* \f]
* The solvent partial molar enthalpy is equal to
* \f[
* \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT}
* = h^{o}_o(T,P)
* + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT})
* \f]
*
* The partial molar entropy, \f$ \bar s_k(T,P) \f$:
*
* \f[
* \bar s_k(T,P) = s^{\triangle}_k(T,P)
* - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}}))
* - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT}
* \f]
* \f[
* \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o)
* - R T \frac{d \ln(a_o)}{dT}
* \f]
*
* The partial molar heat capacity, \f$ C_{p,k}(T,P)\f$:
*
* \f[
* \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P)
* - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT}
* - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2}
* \f]
* \f[
* \bar C_{p,o}(T,P) = C^o_{p,o}(T,P)
* - 2 R T \frac{d \ln(a_o)}{dT}
* - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2}
* \f]
*
* The pressure dependence of the activity coefficients leads to non-zero terms
* for the excess Volume of the solution.
* Therefore, the partial molar volumes are functions
* of the pressure derivatives of the activity coefficients.
* \f[
* \bar V_k(T,P) = V^{\triangle}_k(T,P)
* + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP}
* \f]
* \f[
* \bar V_o(T,P) = V^o_o(T,P)
* + R T \frac{d \ln(a_o)}{dP}
* \f]
*
* The majority of work for these functions take place in the internal
* routines that calculate the first and second derivatives of the log
* of the activity coefficients wrt temperature,
* s_update_dlnMolalityActCoeff_dT(), s_update_d2lnMolalityActCoeff_dT2(),
* and the first
* derivative of the log activity coefficients wrt pressure,
* s_update_dlnMolalityActCoeff_dP().
*
* <HR>
* <H2> %Application within %Kinetics Managers </H2>
@ -941,7 +1009,8 @@ namespace Cantera {
* kinetic rate constant specified
* as if all reactants were on a concentration basis.
*
* For example, a bulk-phase binary reaction between liquid species <I>j</I> and <I>k</I>, producing
* For example, a bulk-phase binary reaction between liquid species
* <I>j</I> and <I>k</I>, producing
* a new liquid species <I>l</I> would have the
* following equation for its rate of progress variable, \f$ R^1 \f$, which has
* units of kmol m-3 s-1.
@ -966,7 +1035,7 @@ namespace Cantera {
* and the equilibrium expression for the system.
*
* \f[
* \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
* \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
* \f]
*
* \f$ K^{o,1} \f$ is the dimensionless form of the equilibrium constant.
@ -1591,12 +1660,14 @@ namespace Cantera {
* molality-based activity coefficent wrt temperature
*
* \f[
* \bar h_k(T,P) = h^{\triangle}_k(T,P) - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT}
* \bar h_k(T,P) = h^{\triangle}_k(T,P)
* - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT}
* \f]
* The solvent partial molar enthalpy is equal to
* \f[
* \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT}
* = h^{o}_o(T,P) + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT})
* = h^{o}_o(T,P)
* + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT})
* \f]
*
*
@ -1609,7 +1680,7 @@ namespace Cantera {
//! Returns an array of partial molar entropies of the species in the
//! solution. Units: J/kmol/K.
/*!
* Maxwell's equations provide an insight in how to calculate this
* Maxwell's equations provide an answer for how calculate this
* (p.215 Smith and Van Ness)
*
* d(chemPot_i)/dT = -sbar_i
@ -1620,11 +1691,13 @@ namespace Cantera {
* temperature derivative of the activity coefficents.
*
* \f[
* \bar s_k(T,P) = \hat s^0_k(T) - R log(M0 * molality[k])
* \bar s_k(T,P) = s^{\triangle}_k(T,P)
* - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}}))
* - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT}
* \f]
* \f[
* \bar s_solvent(T,P) = \hat s^0_solvent(T)
* - R ((xmolSolvent - 1.0) / xmolSolvent)
* \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o)
* - R T \frac{d \ln(a_o)}{dT}
* \f]
*
* @param sbar Output vector of species partial molar entropies.
@ -1638,6 +1711,15 @@ namespace Cantera {
* For this solution, the partial molar volumes are functions
* of the pressure derivatives of the activity coefficients.
*
* \f[
* \bar V_k(T,P) = V^{\triangle}_k(T,P)
* + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP}
* \f]
* \f[
* \bar V_o(T,P) = V^o_o(T,P)
* + R T \frac{d \ln(a_o)}{dP}
* \f]
*
* @param vbar Output vector of speciar partial molar volumes.
* Length = m_kk. units are m^3/kmol.
*/
@ -1646,13 +1728,26 @@ namespace Cantera {
//! Return an array of partial molar heat capacities for the
//! species in the mixture. Units: J/kmol/K
/*!
* The following formulas are implemented within the code.
*
* \f[
* \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P)
* - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT}
* - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2}
* \f]
* \f[
* \bar C_{p,o}(T,P) = C^o_{p,o}(T,P)
* - 2 R T \frac{d \ln(a_o)}{dT}
* - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2}
* \f]
*
*
* @param cpbar Output vector of species partial molar heat
* capacities at constant pressure.
* Length = m_kk. units are J/kmol/K.
*/
virtual void getPartialMolarCp(doublereal* cpbar) const;
//@}
/// @name Properties of the Standard State of the Species
@ -1661,7 +1756,8 @@ namespace Cantera {
//! Get the array of chemical potentials at unit activity for the species
//! at their standard states at the current <I>T</I> and <I>P</I> of the solution.
//! at their standard states at the current <I>T</I> and <I>P</I>
//! of the solution.
/*!
* These are the standard state chemical potentials \f$ \mu^0_k(T,P)
* \f$. The values are evaluated at the current
@ -2992,12 +3088,12 @@ namespace Cantera {
//! This function calculates the temperature derivative of the
//! natural logarithm of the molality activity coefficients.
/*!
* Private function does the work
* This is the private function. It does all of the direct work.
*/
void s_update_dlnMolalityActCoeff_dT() const;
/**
* This function calcultes the temperature second derivative
* This function calculates the temperature second derivative
* of the natural logarithm of the molality activity
* coefficients.
*/

4
Cantera/src/thermo/IdealMolalSoln.h
View file

@ -560,7 +560,7 @@ namespace Cantera {
* standard state species entropies plus the ideal molal solution contribution.
*
* \f[
* \bar{s}_k(T,P) = s^0_k(T) - R log( m_k )
* \bar{s}_k(T,P) = s^0_k(T) - R \ln( \frac{m_k}{m^{\triangle}} )
* \f]
* \f[
* \bar{s}_w(T,P) = s^0_w(T) - R ((X_w - 1.0) / X_w)
@ -615,8 +615,8 @@ namespace Cantera {
// in the Solution --
//@{
//! Get the standard state chemical potentials of the species.
/*!
* Get the standard state chemical potentials of the species.
* This is the array of chemical potentials at unit activity
* \f$ \mu^0_k(T,P) \f$.
* We define these here as the chemical potentials of the pure