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Some formatting changes, also added a reference for the acentric factor
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value for CO2 in 'critProperties.xml' file.
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@gkogekar @bryanwweber
gkogekar authored and bryanwweber committed Jul 21, 2021
1 parent ab42372 commit cff20f3
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Showing 3 changed files with 46 additions and 28 deletions.
4 changes: 4 additions & 0 deletions data/inputs/critProperties.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -77,6 +77,10 @@
<Vc value="0.0948"/>
<Zc value="0.275"/>
<omega value="0.228"/>
<source>
The acentric factor is taken from Yaws, Carl L. (2001).
Matheson Gas Data Book. McGraw-Hill.
</source>
</species>
<species name="COS">
<ChemName name="carbonyl-sulfide"/>
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66 changes: 40 additions & 26 deletions include/cantera/thermo/PengRobinson.h
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Original file line number Diff line number Diff line change
Expand Up @@ -68,7 +68,7 @@ class PengRobinson : public MixtureFugacityTP
* \kappa = \left(0.379642 + 1.487503\omega - 0.164423\omega^2 + 0.016667\omega^3 \right), \qquad \text{For } \omega > 0.491
* \f]
*
* Coefficients \f$ a_mix, b_mix \f$ and \f$(a \alpha)_{mix}\f$ are calculated as
* Coefficients \f$ a_{mix}, b_{mix} \f$ and \f$(a \alpha)_{mix}\f$ are calculated as
*
* \f[
* a_{mix} = \sum_i \sum_j X_i X_j a_{i, j} = \sum_i \sum_j X_i X_j \sqrt{a_i a_j}
Expand Down Expand Up @@ -120,13 +120,17 @@ class PengRobinson : public MixtureFugacityTP
virtual void getPartialMolarEnthalpies(double* hbar) const;
virtual void getPartialMolarEntropies(double* sbar) const;
virtual void getPartialMolarIntEnergies(double* ubar) const;
//! Calculate species-specific molar specific heats
/*!
* This function is currently not implemented for Peng-Robinson phase.
*/
virtual void getPartialMolarCp(double* cpbar) const;
virtual void getPartialMolarVolumes(double* vbar) const;

//! Calculate species-specific critical temperature
/*!
* The temperature dependent parameter in P-R EoS is calculated as
* \f$ T_{crit} = (0.0778 a)/(0.4572 b R) \f$
* \f[ T_{crit} = (0.0778 a)/(0.4572 b R) \f]
* Units: Kelvin
*
* @param a species-specific coefficients used in P-R EoS
Expand All @@ -147,11 +151,11 @@ class PengRobinson : public MixtureFugacityTP
virtual bool addSpecies(shared_ptr<Species> spec);
virtual void initThermo();

//! Retrieve a and b coefficients by looking up tabulated critical parameters
//! Retrieve \f$a\f$ and \f$b\f$ coefficients by looking up tabulated critical parameters
/*!
* If pureFluidParameters are not provided for any species in the phase,
* consult the critical properties tabulated in data/inputs/critProperties.xml.
* If the species is found there, calculate pure fluid parameters a_k and b_k as:
* If `pureFluidParameters` are not provided for any species in the phase,
* consult the critical properties tabulated in `data/inputs/critProperties.xml`.
* If the species is found there, calculate pure fluid parameters \f$a_k\f$ and \f$b_k\f$ as:
* \f[ a_k = 0.4278 R^2 T_c^2 / P_c \f]
*
* and:
Expand All @@ -164,8 +168,8 @@ class PengRobinson : public MixtureFugacityTP
//! Set the pure fluid interaction parameters for a species
/*!
* @param species Name of the species
* @param a "a" parameter in the Peng-Robinson model [Pa-m^6/kmol^2]
* @param b "b" parameter in the Peng-Robinson model [m^3/kmol]
* @param a \f$a\f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2]
* @param b \f$a\f$ parameter in the Peng-Robinson model [m^3/kmol]
* @param w acentric factor
*/
void setSpeciesCoeffs(const std::string& species, double a, double b,
Expand All @@ -175,8 +179,8 @@ class PengRobinson : public MixtureFugacityTP
/*!
* @param species_i Name of one species
* @param species_j Name of the other species
* @param a constant term in the "a" expression [Pa-m^6/kmol^2]
* @param alpha dimensionless function of T_r and \omega
* @param a constant term in the \f$a\f$ expression [Pa-m^6/kmol^2]
* @param alpha dimensionless function of \f$T_r\f$ and \f$\omega\f$
*/
void setBinaryCoeffs(const std::string& species_i,
const std::string& species_j, double a);
Expand All @@ -195,35 +199,35 @@ class PengRobinson : public MixtureFugacityTP

// Special functions not inherited from MixtureFugacityTP

//! Calculate temperature derivative d(a*alpha)/dT
//! Calculate temperature derivative \f$d(a \alpha)/dT\f$
/*!
* These are stored internally.
*/
double daAlpha_dT() const;

//! Calculate second derivative d2(a*alpha)/dT2
//! Calculate second derivative \f$d^2(a \alpha)/dT^2\f$
/*!
* These are stored internally.
*/
double d2aAlpha_dT2() const;

public:

//! Calculate dpdV and dpdT at the current conditions
//! Calculate \f$dp/dV\f$ and \f$dp/dT\f$ at the current conditions
/*!
* These are stored internally.
*/
void calculatePressureDerivatives() const;

//! Update the a, b and alpha parameters
//! Update the \f$a\f$, \f$b\f$, and \f$\alpha\f$ parameters
/*!
* The a and the b parameters depend on the mole fraction and the
* parameter alpha depends on the temperature. This function updates
* The \f$a\f$ and the \f$b\f$ parameters depend on the mole fraction and the
* parameter $\f\alpha\f$ depends on the temperature. This function updates
* the internal numbers based on the state of the object.
*/
virtual void updateMixingExpressions();

//! Calculate the a, b and the alpha parameters given the temperature
//! Calculate the \f$a\f$, \f$b\f$, and \f$\alpha\f$ parameters given the temperature
/*!
* This function doesn't change the internal state of the object, so it is a
* const function. It does use the stored mole fractions in the object.
Expand All @@ -240,27 +244,34 @@ class PengRobinson : public MixtureFugacityTP
int solveCubic(double T, double pres, double a, double b, double aAlpha,
double Vroot[3]) const;
protected:
//! Value of b in the equation of state
//! Value of \f$b\f$ in the equation of state
/*!
* m_b is a function of the mole fractions and species-specific b values.
* `m_b` is a function of the mole fractions and species-specific b values.
*/
double m_b;

//! Value of a and alpha in the equation of state
//! Value of \f$a\f$ in the equation of state
/*!
* m_aAlpha_mix is a function of the temperature and the mole fractions. m_a depends only on the mole fractions.
* `m_a` depends only on the mole fractions.
*/
double m_a;

//! Value of \f$\alpha\f$ in the equation of state
/*!
* `m_aAlpha_mix` is a function of the temperature and the mole fractions.
*/
double m_aAlpha_mix;

// Vectors required to store a_coeff, b_coeff, alpha, kappa and other values for every species. Length = m_kk
// Vectors required to store species-specific a_coeff, b_coeff, alpha, kappa and other derivatives.
// Length = m_kk
vector_fp m_b_coeffs;
vector_fp m_kappa;
mutable vector_fp m_dalphadT;
mutable vector_fp m_d2alphadT2;
vector_fp m_alpha;

//Matrices for Binary coefficients a_{i,j} and {a*alpha}_{i.j} are saved in an Array form. Length = (m_kk, m_kk)
// Matrices for Binary coefficients a_{i,j} and {a*alpha}_{i.j} are saved in an Array form.
// Length = (m_kk, m_kk)
Array2D m_a_coeffs;
Array2D m_aAlpha_binary;

Expand Down Expand Up @@ -296,13 +307,16 @@ class PengRobinson : public MixtureFugacityTP
mutable vector_fp m_dpdni;

private:
//! Omega constants: a0 (= omega_a) and b0 (= omega_b) values used in Peng-Robinson equation of state
//! Omega constant: a0 (= omega_a) used in Peng-Robinson equation of state
/*!
* These values are calculated by solving P-R cubic equation at the critical point.
* This value is calculated by solving P-R cubic equation at the critical point.
*/
static const double omega_a;

//! Omega constant for b
//! Omega constant: b0 (= omega_b) used in Peng-Robinson equation of state
/*!
* This value is calculated by solving P-R cubic equation at the critical point.
*/
static const double omega_b;

//! Omega constant for the critical molar volume
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4 changes: 2 additions & 2 deletions src/thermo/PengRobinson.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -426,8 +426,8 @@ vector<double> PengRobinson::getCoeff(const std::string& iName)
void PengRobinson::initThermo()
{
for (auto& item : m_species) {
// Read a and b coefficients and acentric factor w_ac from species 'input'
// information (i.e. as specified in a YAML input file)
// Read a and b coefficients and acentric factor w_ac from species input
// information, specified in a YAML input file.
if (item.second->input.hasKey("equation-of-state")) {
auto eos = item.second->input["equation-of-state"].getMapWhere(
"model", "Peng-Robinson");
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