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cantera/src/thermo/RedlichKwongMFTP.cpp
Steven DeCaluwe 14019cfd2e Adding HighPressureGas transport module.
2014-07-28 21:02:18 +00:00

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/**
* @file RedlichKwongMFTP.cpp
* Definition file for a derived class of ThermoPhase that assumes either
* an ideal gas or ideal solution approximation and handles
* variable pressure standard state methods for calculating
* thermodynamic properties (see \ref thermoprops and
* class \link Cantera::RedlichKwongMFTP RedlichKwongMFTP\endlink).
*/
/*
* Copyright (2005) Sandia Corporation. Under the terms of
* Contract DE-AC04-94AL85000 with Sandia Corporation, the
* U.S. Government retains certain rights in this software.
*/
#include "cantera/thermo/RedlichKwongMFTP.h"
#include "cantera/thermo/mix_defs.h"
#include "cantera/thermo/ThermoFactory.h"
#include "cantera/numerics/RootFind.h"
#include "cantera/base/stringUtils.h"
using namespace std;
namespace Cantera
{
const doublereal RedlichKwongMFTP::omega_a = 4.27480233540E-01;
const doublereal RedlichKwongMFTP::omega_b = 8.66403499650E-02;
const doublereal RedlichKwongMFTP::omega_vc = 3.33333333333333E-01;
RedlichKwongMFTP::RedlichKwongMFTP() :
MixtureFugacityTP(),
m_standardMixingRules(0),
m_formTempParam(0),
m_b_current(0.0),
m_a_current(0.0),
a_vec_Curr_(0),
b_vec_Curr_(0),
a_coeff_vec(0,0),
m_pc_Species(0),
m_tc_Species(0),
m_vc_Species(0),
NSolns_(0),
m_pp(0),
m_tmpV(0),
m_partialMolarVolumes(0),
dpdV_(0.0),
dpdT_(0.0),
dpdni_(0)
{
Vroot_[0] = 0.0;
Vroot_[1] = 0.0;
Vroot_[2] = 0.0;
}
RedlichKwongMFTP::RedlichKwongMFTP(const std::string& infile, std::string id_) :
MixtureFugacityTP(),
m_standardMixingRules(0),
m_formTempParam(0),
m_b_current(0.0),
m_a_current(0.0),
a_vec_Curr_(0),
b_vec_Curr_(0),
a_coeff_vec(0,0),
m_pc_Species(0),
m_tc_Species(0),
m_vc_Species(0),
NSolns_(0),
m_pp(0),
m_tmpV(0),
m_partialMolarVolumes(0),
dpdV_(0.0),
dpdT_(0.0),
dpdni_(0)
{
Vroot_[0] = 0.0;
Vroot_[1] = 0.0;
Vroot_[2] = 0.0;
XML_Node* root = get_XML_File(infile);
if (id_ == "-") {
id_ = "";
}
XML_Node* xphase = get_XML_NameID("phase", std::string("#")+id_, root);
if (!xphase) {
throw CanteraError("newPhase",
"Couldn't find phase named \"" + id_ + "\" in file, " + infile);
}
importPhase(*xphase, this);
}
RedlichKwongMFTP::RedlichKwongMFTP(XML_Node& phaseRefRoot, const std::string& id_) :
MixtureFugacityTP(),
m_standardMixingRules(0),
m_formTempParam(0),
m_b_current(0.0),
m_a_current(0.0),
a_vec_Curr_(0),
b_vec_Curr_(0),
a_coeff_vec(0,0),
m_pc_Species(0),
m_tc_Species(0),
m_vc_Species(0),
NSolns_(0),
m_pp(0),
m_tmpV(0),
m_partialMolarVolumes(0),
dpdV_(0.0),
dpdT_(0.0),
dpdni_(0)
{
Vroot_[0] = 0.0;
Vroot_[1] = 0.0;
Vroot_[2] = 0.0;
XML_Node* xphase = get_XML_NameID("phase", std::string("#")+id_, &phaseRefRoot);
if (!xphase) {
throw CanteraError("RedlichKwongMFTP::RedlichKwongMFTP()","Couldn't find phase named \"" + id_ + "\" in XML node");
}
importPhase(*xphase, this);
}
RedlichKwongMFTP::RedlichKwongMFTP(int testProb) :
MixtureFugacityTP(),
m_standardMixingRules(0),
m_formTempParam(0),
m_b_current(0.0),
m_a_current(0.0),
a_vec_Curr_(0),
b_vec_Curr_(0),
a_coeff_vec(0,0),
m_pc_Species(0),
m_tc_Species(0),
m_vc_Species(0),
NSolns_(0),
m_pp(0),
m_tmpV(0),
m_partialMolarVolumes(0),
dpdV_(0.0),
dpdT_(0.0),
dpdni_(0)
{
std::string infile = "co2_redlichkwong.xml";
std::string id_;
if (testProb == 1) {
infile = "co2_redlichkwong.xml";
id_ = "carbondioxide";
} else {
throw CanteraError("", "test prob = 1 only");
}
XML_Node* root = get_XML_File(infile);
if (id_ == "-") {
id_ = "";
}
XML_Node* xphase = get_XML_NameID("phase", std::string("#")+id_, root);
if (!xphase) {
throw CanteraError("newPhase", "Couldn't find phase named \"" + id_ + "\" in file, " + infile);
}
importPhase(*xphase, this);
}
RedlichKwongMFTP::RedlichKwongMFTP(const RedlichKwongMFTP& b) :
MixtureFugacityTP(),
m_standardMixingRules(0),
m_formTempParam(0),
m_b_current(0.0),
m_a_current(0.0),
a_vec_Curr_(0),
b_vec_Curr_(0),
a_coeff_vec(0,0),
m_pc_Species(0),
m_tc_Species(0),
m_vc_Species(0),
NSolns_(0),
m_pp(0),
m_tmpV(0),
m_partialMolarVolumes(0),
dpdV_(0.0),
dpdT_(0.0),
dpdni_(0)
{
*this = b;
}
RedlichKwongMFTP& RedlichKwongMFTP::operator=(const RedlichKwongMFTP& b)
{
if (&b != this) {
/*
* Mostly, this is a passthrough to the underlying
* assignment operator for the ThermoPhae parent object.
*/
MixtureFugacityTP::operator=(b);
/*
* However, we have to handle data that we own.
*/
m_standardMixingRules = b.m_standardMixingRules;
m_formTempParam = b.m_formTempParam;
m_b_current = b.m_b_current;
m_a_current = b.m_a_current;
a_vec_Curr_ = b.a_vec_Curr_;
b_vec_Curr_ = b.b_vec_Curr_;
a_coeff_vec = b.a_coeff_vec;
m_pc_Species = b.m_pc_Species;
m_tc_Species = b.m_tc_Species;
m_vc_Species = b.m_vc_Species;
NSolns_ = b.NSolns_;
Vroot_[0] = b.Vroot_[0];
Vroot_[1] = b.Vroot_[1];
Vroot_[2] = b.Vroot_[2];
m_pp = b.m_pp;
m_tmpV = b.m_tmpV;
m_partialMolarVolumes = b.m_partialMolarVolumes;
dpdV_ = b.dpdV_;
dpdT_ = b.dpdT_;
dpdni_ = b.dpdni_;
}
return *this;
}
ThermoPhase* RedlichKwongMFTP::duplMyselfAsThermoPhase() const
{
return new RedlichKwongMFTP(*this);
}
int RedlichKwongMFTP::eosType() const
{
return cRedlichKwongMFTP;
}
/*
* ------------Molar Thermodynamic Properties -------------------------
*/
doublereal RedlichKwongMFTP::enthalpy_mole() const
{
_updateReferenceStateThermo();
doublereal rt = _RT();
doublereal h_ideal = rt * mean_X(DATA_PTR(m_h0_RT));
doublereal h_nonideal = hresid();
return h_ideal + h_nonideal;
}
doublereal RedlichKwongMFTP::entropy_mole() const
{
_updateReferenceStateThermo();
doublereal sr_ideal = GasConstant * (mean_X(DATA_PTR(m_s0_R))
- sum_xlogx() - std::log(pressure()/m_spthermo->refPressure()));
doublereal sr_nonideal = sresid();
return sr_ideal + sr_nonideal;
}
doublereal RedlichKwongMFTP::cp_mole() const
{
_updateReferenceStateThermo();
doublereal TKelvin = temperature();
doublereal sqt = sqrt(TKelvin);
doublereal mv = molarVolume();
doublereal vpb = mv + m_b_current;
pressureDerivatives();
doublereal cpref = GasConstant * mean_X(DATA_PTR(m_cp0_R));
doublereal dadt = da_dt();
doublereal fac = TKelvin * dadt - 3.0 * m_a_current / 2.0;
doublereal dHdT_V = (cpref + mv * dpdT_ - GasConstant - 1.0 / (2.0 * m_b_current * TKelvin * sqt) * log(vpb/mv) * fac
+1.0/(m_b_current * sqt) * log(vpb/mv) * (-0.5 * dadt));
return dHdT_V - (mv + TKelvin * dpdT_ / dpdV_) * dpdT_;
}
doublereal RedlichKwongMFTP::cv_mole() const
{
throw CanteraError("", "unimplemented");
return cp_mole() - GasConstant;
}
doublereal RedlichKwongMFTP::pressure() const
{
#ifdef DEBUG_MODE
_updateReferenceStateThermo();
// Get a copy of the private variables stored in the State object
double rho = density();
doublereal T = temperature();
doublereal mmw = meanMolecularWeight();
double molarV = mmw / rho;
double pp = GasConstant * T/(molarV - m_b_current) - m_a_current/(sqrt(T) * molarV * (molarV + m_b_current));
if (fabs(pp -m_Pcurrent) > 1.0E-5 * fabs(m_Pcurrent)) {
throw CanteraError(" RedlichKwongMFTP::pressure()", "setState broken down, maybe");
}
#endif
return m_Pcurrent;
}
void RedlichKwongMFTP::calcDensity()
{
/*
* Calculate the molarVolume of the solution (m**3 kmol-1)
*/
const doublereal* const dtmp = moleFractdivMMW();
getPartialMolarVolumes(DATA_PTR(m_tmpV));
double invDens = dot(m_tmpV.begin(), m_tmpV.end(), dtmp);
/*
* Set the density in the parent State object directly,
* by calling the Phase::setDensity() function.
*/
double dens = 1.0/invDens;
Phase::setDensity(dens);
}
void RedlichKwongMFTP::setTemperature(const doublereal temp)
{
Phase::setTemperature(temp);
_updateReferenceStateThermo();
updateAB();
}
void RedlichKwongMFTP::setMassFractions(const doublereal* const x)
{
MixtureFugacityTP::setMassFractions(x);
updateAB();
}
void RedlichKwongMFTP::setMassFractions_NoNorm(const doublereal* const x)
{
MixtureFugacityTP::setMassFractions_NoNorm(x);
updateAB();
}
void RedlichKwongMFTP::setMoleFractions(const doublereal* const x)
{
MixtureFugacityTP::setMoleFractions(x);
updateAB();
}
void RedlichKwongMFTP::setMoleFractions_NoNorm(const doublereal* const x)
{
MixtureFugacityTP::setMoleFractions(x);
updateAB();
}
void RedlichKwongMFTP::setConcentrations(const doublereal* const c)
{
MixtureFugacityTP::setConcentrations(c);
updateAB();
}
void RedlichKwongMFTP::getActivityConcentrations(doublereal* c) const
{
getPartialMolarVolumes(DATA_PTR(m_partialMolarVolumes));
for (size_t k = 0; k < m_kk; k++) {
c[k] = moleFraction(k) / m_partialMolarVolumes[k];
}
}
doublereal RedlichKwongMFTP::standardConcentration(size_t k) const
{
getStandardVolumes(DATA_PTR(m_tmpV));
return 1.0 / m_tmpV[k];
}
void RedlichKwongMFTP::getUnitsStandardConc(double* uA, int, int sizeUA) const
{
//int eos = eosType();
for (int i = 0; i < sizeUA; i++) {
if (i == 0) {
uA[0] = 1.0;
}
if (i == 1) {
uA[1] = -static_cast<int>(nDim());
}
if (i == 2) {
uA[2] = 0.0;
}
if (i == 3) {
uA[3] = 0.0;
}
if (i == 4) {
uA[4] = 0.0;
}
if (i == 5) {
uA[5] = 0.0;
}
}
}
void RedlichKwongMFTP::getActivityCoefficients(doublereal* ac) const
{
doublereal TKelvin = temperature();
doublereal rt = TKelvin * GasConstant;
doublereal mv = molarVolume();
doublereal sqt = sqrt(TKelvin);
doublereal vpb = mv + m_b_current;
doublereal vmb = mv - m_b_current;
for (size_t k = 0; k < m_kk; k++) {
m_pp[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_pp[k] += moleFractions_[i] * a_vec_Curr_[counter];
}
}
doublereal pres = pressure();
for (size_t k = 0; k < m_kk; k++) {
ac[k] = (- rt * log(pres * mv / rt)
+ rt * log(mv / vmb)
+ rt * b_vec_Curr_[k] / vmb
- 2.0 * m_pp[k] / (m_b_current * sqt) * log(vpb/mv)
+ m_a_current * b_vec_Curr_[k] / (m_b_current * m_b_current * sqt) * log(vpb/mv)
- m_a_current / (m_b_current * sqt) * (b_vec_Curr_[k]/vpb)
);
}
for (size_t k = 0; k < m_kk; k++) {
ac[k] = exp(ac[k]/rt);
}
}
/*
* ---- Partial Molar Properties of the Solution -----------------
*/
void RedlichKwongMFTP::getChemPotentials_RT(doublereal* muRT) const
{
getChemPotentials(muRT);
doublereal invRT = 1.0 / _RT();
for (size_t k = 0; k < m_kk; k++) {
muRT[k] *= invRT;
}
}
void RedlichKwongMFTP::getChemPotentials(doublereal* mu) const
{
getGibbs_ref(mu);
doublereal xx;
doublereal rt = temperature() * GasConstant;
for (size_t k = 0; k < m_kk; k++) {
xx = std::max(SmallNumber, moleFraction(k));
mu[k] += rt*(log(xx));
}
doublereal TKelvin = temperature();
doublereal mv = molarVolume();
doublereal sqt = sqrt(TKelvin);
doublereal vpb = mv + m_b_current;
doublereal vmb = mv - m_b_current;
for (size_t k = 0; k < m_kk; k++) {
m_pp[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_pp[k] += moleFractions_[i] * a_vec_Curr_[counter];
}
}
doublereal pres = pressure();
doublereal refP = refPressure();
for (size_t k = 0; k < m_kk; k++) {
mu[k] += (rt * log(pres/refP) - rt * log(pres * mv / rt)
+ rt * log(mv / vmb)
+ rt * b_vec_Curr_[k] / vmb
- 2.0 * m_pp[k] / (m_b_current * sqt) * log(vpb/mv)
+ m_a_current * b_vec_Curr_[k] / (m_b_current * m_b_current * sqt) * log(vpb/mv)
- m_a_current / (m_b_current * sqt) * (b_vec_Curr_[k]/vpb)
);
}
}
void RedlichKwongMFTP::getPartialMolarEnthalpies(doublereal* hbar) const
{
/*
* First we get the reference state contributions
*/
getEnthalpy_RT_ref(hbar);
doublereal rt = GasConstant * temperature();
scale(hbar, hbar+m_kk, hbar, rt);
/*
* We calculate dpdni_
*/
doublereal TKelvin = temperature();
doublereal mv = molarVolume();
doublereal sqt = sqrt(TKelvin);
doublereal vpb = mv + m_b_current;
doublereal vmb = mv - m_b_current;
for (size_t k = 0; k < m_kk; k++) {
m_pp[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_pp[k] += moleFractions_[i] * a_vec_Curr_[counter];
}
}
for (size_t k = 0; k < m_kk; k++) {
dpdni_[k] = rt/vmb + rt * b_vec_Curr_[k] / (vmb * vmb) - 2.0 * m_pp[k] / (sqt * mv * vpb)
+ m_a_current * b_vec_Curr_[k]/(sqt * mv * vpb * vpb);
}
doublereal dadt = da_dt();
doublereal fac = TKelvin * dadt - 3.0 * m_a_current / 2.0;
for (size_t k = 0; k < m_kk; k++) {
m_tmpV[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_tmpV[k] += 2.0 * moleFractions_[i] * TKelvin * a_coeff_vec(1,counter) - 3.0 * moleFractions_[i] * a_vec_Curr_[counter];
}
}
pressureDerivatives();
doublereal fac2 = mv + TKelvin * dpdT_ / dpdV_;
for (size_t k = 0; k < m_kk; k++) {
double hE_v = (mv * dpdni_[k] - rt - b_vec_Curr_[k]/ (m_b_current * m_b_current * sqt) * log(vpb/mv)*fac
+ 1.0 / (m_b_current * sqt) * log(vpb/mv) * m_tmpV[k]
+ b_vec_Curr_[k] / vpb / (m_b_current * sqt) * fac);
hbar[k] = hbar[k] + hE_v;
hbar[k] -= fac2 * dpdni_[k];
}
}
void RedlichKwongMFTP::getPartialMolarEntropies(doublereal* sbar) const
{
getEntropy_R_ref(sbar);
doublereal r = GasConstant;
scale(sbar, sbar+m_kk, sbar, r);
doublereal TKelvin = temperature();
doublereal sqt = sqrt(TKelvin);
doublereal mv = molarVolume();
doublereal refP = refPressure();
for (size_t k = 0; k < m_kk; k++) {
doublereal xx = std::max(SmallNumber, moleFraction(k));
sbar[k] += r * (- log(xx));
}
for (size_t k = 0; k < m_kk; k++) {
m_pp[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_pp[k] += moleFractions_[i] * a_vec_Curr_[counter];
}
}
for (size_t k = 0; k < m_kk; k++) {
m_tmpV[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_tmpV[k] += moleFractions_[i] * a_coeff_vec(1,counter);
}
}
doublereal dadt = da_dt();
doublereal fac = dadt - m_a_current / (2.0 * TKelvin);
doublereal vmb = mv - m_b_current;
doublereal vpb = mv + m_b_current;
for (size_t k = 0; k < m_kk; k++) {
sbar[k] -=(GasConstant * log(GasConstant * TKelvin / (refP * mv))
+ GasConstant
+ GasConstant * log(mv/vmb)
+ GasConstant * b_vec_Curr_[k]/vmb
+ m_pp[k]/(m_b_current * TKelvin * sqt) * log(vpb/mv)
- 2.0 * m_tmpV[k]/(m_b_current * sqt) * log(vpb/mv)
+ b_vec_Curr_[k] / (m_b_current * m_b_current * sqt) * log(vpb/mv) * fac
- 1.0 / (m_b_current * sqt) * b_vec_Curr_[k] / vpb * fac
) ;
}
pressureDerivatives();
getPartialMolarVolumes(DATA_PTR(m_partialMolarVolumes));
for (size_t k = 0; k < m_kk; k++) {
sbar[k] -= -m_partialMolarVolumes[k] * dpdT_;
}
}
void RedlichKwongMFTP::getPartialMolarIntEnergies(doublereal* ubar) const
{
getIntEnergy_RT(ubar);
doublereal rt = GasConstant * temperature();
scale(ubar, ubar+m_kk, ubar, rt);
}
void RedlichKwongMFTP::getPartialMolarCp(doublereal* cpbar) const
{
getCp_R(cpbar);
doublereal r = GasConstant;
scale(cpbar, cpbar+m_kk, cpbar, r);
}
void RedlichKwongMFTP::getPartialMolarVolumes(doublereal* vbar) const
{
for (size_t k = 0; k < m_kk; k++) {
m_pp[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_pp[k] += moleFractions_[i] * a_vec_Curr_[counter];
}
}
for (size_t k = 0; k < m_kk; k++) {
m_tmpV[k] = 0.0;
for (size_t i = 0; i < m_kk; i++) {
size_t counter = k + m_kk*i;
m_tmpV[k] += moleFractions_[i] * a_coeff_vec(1,counter);
}
}
doublereal TKelvin = temperature();
doublereal sqt = sqrt(TKelvin);
doublereal mv = molarVolume();
doublereal rt = GasConstant * TKelvin;
doublereal vmb = mv - m_b_current;
doublereal vpb = mv + m_b_current;
for (size_t k = 0; k < m_kk; k++) {
doublereal num = (rt + rt * m_b_current/ vmb + rt * b_vec_Curr_[k] / vmb
+ rt * m_b_current * b_vec_Curr_[k] /(vmb * vmb)
- 2.0 * m_pp[k] / (sqt * vpb)
+ m_a_current * b_vec_Curr_[k] / (sqt * vpb * vpb)
);
doublereal denom = (m_Pcurrent + rt * m_b_current/(vmb * vmb) - m_a_current / (sqt * vpb * vpb)
);
vbar[k] = num / denom;
}
}
doublereal RedlichKwongMFTP::critTemperature() const
{
double pc, tc, vc;
double a0 = 0.0;
double aT = 0.0;
for (size_t i = 0; i < m_kk; i++) {
for (size_t j = 0; j <m_kk; j++) {
size_t counter = i + m_kk * j;
a0 += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(0, counter);
aT += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(1, counter);
}
}
calcCriticalConditions(m_a_current, m_b_current, a0, aT, pc, tc, vc);
return tc;
}
doublereal RedlichKwongMFTP::critPressure() const
{
double pc, tc, vc;
double a0 = 0.0;
double aT = 0.0;
for (size_t i = 0; i < m_kk; i++) {
for (size_t j = 0; j <m_kk; j++) {
size_t counter = i + m_kk * j;
a0 += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(0, counter);
aT += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(1, counter);
}
}
calcCriticalConditions(m_a_current, m_b_current, a0, aT, pc, tc, vc);
return pc;
}
doublereal RedlichKwongMFTP::critVolume() const
{
double pc, tc, vc;
double a0 = 0.0;
double aT = 0.0;
for (size_t i = 0; i < m_kk; i++) {
for (size_t j = 0; j <m_kk; j++) {
size_t counter = i + m_kk * j;
a0 += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(0, counter);
aT += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(1, counter);
}
}
calcCriticalConditions(m_a_current, m_b_current, a0, aT, pc, tc, vc);
return vc;
}
doublereal RedlichKwongMFTP::critCompressibility() const
{
double pc, tc, vc;
double a0 = 0.0;
double aT = 0.0;
for (size_t i = 0; i < m_kk; i++) {
for (size_t j = 0; j <m_kk; j++) {
size_t counter = i + m_kk * j;
a0 += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(0, counter);
aT += moleFractions_[i] * moleFractions_[j] * a_coeff_vec(1, counter);
}
}
calcCriticalConditions(m_a_current, m_b_current, a0, aT, pc, tc, vc);
return pc*vc/tc/GasConstant;
}
doublereal RedlichKwongMFTP::critDensity() const
{
double pc, tc, vc;
double a0 = 0.0;
double aT = 0.0;
for (size_t i = 0; i < m_kk; i++) {
for (size_t j = 0; j <m_kk; j++) {
size_t counter = i + m_kk * j;
a0 += moleFractions_[i] * moleFractions_[j] *a_coeff_vec(0, counter);
aT += moleFractions_[i] * moleFractions_[j] *a_coeff_vec(1, counter);
}
}
calcCriticalConditions(m_a_current, m_b_current, a0, aT, pc, tc, vc);
double mmw = meanMolecularWeight();
return mmw / vc;
}
void RedlichKwongMFTP::initThermo()
{
initLengths();
MixtureFugacityTP::initThermo();
}
void RedlichKwongMFTP::setToEquilState(const doublereal* mu_RT)
{
double tmp, tmp2;
_updateReferenceStateThermo();
getGibbs_RT_ref(DATA_PTR(m_tmpV));
/*
* Within the method, we protect against inf results if the
* exponent is too high.
*
* If it is too low, we set
* the partial pressure to zero. This capability is needed
* by the elemental potential method.
*/
doublereal pres = 0.0;
double m_p0 = refPressure();
for (size_t k = 0; k < m_kk; k++) {
tmp = -m_tmpV[k] + mu_RT[k];
if (tmp < -600.) {
m_pp[k] = 0.0;
} else if (tmp > 500.0) {
tmp2 = tmp / 500.;
tmp2 *= tmp2;
m_pp[k] = m_p0 * exp(500.) * tmp2;
} else {
m_pp[k] = m_p0 * exp(tmp);
}
pres += m_pp[k];
}
// set state
setState_PX(pres, &m_pp[0]);
}
void RedlichKwongMFTP::initLengths()
{
a_vec_Curr_.resize(m_kk * m_kk, 0.0);
b_vec_Curr_.resize(m_kk, 0.0);
a_coeff_vec.resize(2, m_kk * m_kk, 0.0);
m_pc_Species.resize(m_kk, 0.0);
m_tc_Species.resize(m_kk, 0.0);
m_vc_Species.resize(m_kk, 0.0);
m_pp.resize(m_kk, 0.0);
m_tmpV.resize(m_kk, 0.0);
m_partialMolarVolumes.resize(m_kk, 0.0);
dpdni_.resize(m_kk, 0.0);
}
void RedlichKwongMFTP::initThermoXML(XML_Node& phaseNode, const std::string& id)
{
RedlichKwongMFTP::initLengths();
/*
* Check the model parameter for the Redlich-Kwong equation of state
* two are allowed
* RedlichKwong mixture of species, each of which are RK fluids
* RedlichKwongMFTP mixture of species with cross term coefficients
*/
if (phaseNode.hasChild("thermo")) {
XML_Node& thermoNode = phaseNode.child("thermo");
std::string model = thermoNode["model"];
if (model == "RedlichKwong") {
m_standardMixingRules = 1;
} else if (model == "RedlichKwongMFTP") {
m_standardMixingRules = 0;
} else {
throw CanteraError("RedlichKwongMFTP::initThermoXML",
"Unknown thermo model : " + model);
}
/*
* Go get all of the coefficients and factors in the
* activityCoefficients XML block
*/
XML_Node* acNodePtr = 0;
if (thermoNode.hasChild("activityCoefficients")) {
XML_Node& acNode = thermoNode.child("activityCoefficients");
acNodePtr = &acNode;
size_t nC = acNode.nChildren();
/*
* Loop through the children getting multiple instances of
* parameters
*/
for (size_t i = 0; i < nC; i++) {
XML_Node& xmlACChild = acNodePtr->child(i);
string stemp = xmlACChild.name();
string nodeName = lowercase(stemp);
/*
* Process a binary salt field, or any of the other XML fields
* that make up the Pitzer Database. Entries will be ignored
* if any of the species in the entry isn't in the solution.
*/
if (nodeName == "purefluidparameters") {
readXMLPureFluid(xmlACChild);
}
}
if (m_standardMixingRules == 1) {
applyStandardMixingRules();
}
/*
* Loop through the children getting multiple instances of
* parameters
*/
for (size_t i = 0; i < nC; i++) {
XML_Node& xmlACChild = acNodePtr->child(i);
string stemp = xmlACChild.name();
string nodeName = lowercase(stemp);
/*
* Process a binary salt field, or any of the other XML fields
* that make up the Pitzer Database. Entries will be ignored
* if any of the species in the entry isn't in the solution.
*/
if (nodeName == "crossfluidparameters") {
readXMLCrossFluid(xmlACChild);
}
}
}
}
for (size_t i = 0; i < m_kk; i++) {
double a0coeff = a_coeff_vec(0, i*m_kk + i);
double aTcoeff = a_coeff_vec(1, i*m_kk + i);
double ai = a0coeff + aTcoeff * 500.;
double bi = b_vec_Curr_[i];
calcCriticalConditions(ai, bi, a0coeff, aTcoeff, m_pc_Species[i], m_tc_Species[i], m_vc_Species[i]);
}
MixtureFugacityTP::initThermoXML(phaseNode, id);
}
void RedlichKwongMFTP::readXMLPureFluid(XML_Node& pureFluidParam)
{
vector_fp vParams;
string xname = pureFluidParam.name();
if (xname != "pureFluidParameters") {
throw CanteraError("RedlichKwongMFTP::readXMLPureFluid",
"Incorrect name for processing this routine: " + xname);
}
/*
* Read the species
* Find the index of the species in the current phase. It's not an error to not find the species
*/
string iName = pureFluidParam.attrib("species");
if (iName == "") {
throw CanteraError("RedlichKwongMFTP::readXMLPureFluid", "no species attribute");
}
size_t iSpecies = speciesIndex(iName);
if (iSpecies == npos) {
return;
}
size_t counter = iSpecies + m_kk * iSpecies;
size_t nParamsExpected, nParamsFound;
size_t num = pureFluidParam.nChildren();
for (size_t iChild = 0; iChild < num; iChild++) {
XML_Node& xmlChild = pureFluidParam.child(iChild);
string stemp = xmlChild.name();
string nodeName = lowercase(stemp);
if (nodeName == "a_coeff") {
string iModel = lowercase(xmlChild.attrib("model"));
if (iModel == "constant") {
nParamsExpected = 1;
} else if (iModel == "linear_a") {
nParamsExpected = 2;
if (m_formTempParam == 0) {
m_formTempParam = 1;
}
} else {
throw CanteraError("", "unknown model");
}
ctml::getFloatArray(xmlChild, vParams, true, "Pascal-m6/kmol2", "a_coeff");
nParamsFound = vParams.size();
if (nParamsFound != nParamsExpected) {
throw CanteraError("RedlichKwongMFTP::readXMLPureFluid(for a_coeff" + iName + ")",
"wrong number of params found");
}
for (size_t i = 0; i < nParamsFound; i++) {
a_coeff_vec(i, counter) = vParams[i];
}
} else if (nodeName == "b_coeff") {
ctml::getFloatArray(xmlChild, vParams, true, "m3/kmol", "b_coeff");
nParamsFound = vParams.size();
if (nParamsFound != 1) {
throw CanteraError("RedlichKwongMFTP::readXMLPureFluid(for b_coeff" + iName + ")",
"wrong number of params found");
}
b_vec_Curr_[iSpecies] = vParams[0];
}
}
}
void RedlichKwongMFTP::applyStandardMixingRules()
{
int nParam = 2;
for (size_t i = 0; i < m_kk; i++) {
size_t icounter = i + m_kk * i;
for (size_t j = 0; j < m_kk; j++) {
if (i != j) {
size_t counter = i + m_kk * j;
size_t jcounter = j + m_kk * j;
for (int n = 0; n < nParam; n++) {
a_coeff_vec(n, counter) = sqrt(a_coeff_vec(n, icounter) * a_coeff_vec(n, jcounter));
}
}
}
}
}
void RedlichKwongMFTP::readXMLCrossFluid(XML_Node& CrossFluidParam)
{
vector_fp vParams;
string xname = CrossFluidParam.name();
if (xname != "crossFluidParameters") {
throw CanteraError("RedlichKwongMFTP::readXMLCrossFluid",
"Incorrect name for processing this routine: " + xname);
}
/*
* Read the species
* Find the index of the species in the current phase. It's not an error to not find the species
*/
string iName = CrossFluidParam.attrib("species1");
if (iName == "") {
throw CanteraError("RedlichKwongMFTP::readXMLCrossFluid", "no species1 attribute");
}
size_t iSpecies = speciesIndex(iName);
if (iSpecies == npos) {
return;
}
string jName = CrossFluidParam.attrib("species2");
if (iName == "") {
throw CanteraError("RedlichKwongMFTP::readXMLCrossFluid", "no species2 attribute");
}
size_t jSpecies = speciesIndex(jName);
if (jSpecies == npos) {
return;
}
size_t counter = iSpecies + m_kk * jSpecies;
size_t counter0 = jSpecies + m_kk * iSpecies;
size_t nParamsExpected, nParamsFound;
size_t num = CrossFluidParam.nChildren();
for (size_t iChild = 0; iChild < num; iChild++) {
XML_Node& xmlChild = CrossFluidParam.child(iChild);
string stemp = xmlChild.name();
string nodeName = lowercase(stemp);
if (nodeName == "a_coeff") {
string iModel = lowercase(xmlChild.attrib("model"));
if (iModel == "constant") {
nParamsExpected = 1;
} else if (iModel == "linear_a") {
nParamsExpected = 2;
if (m_formTempParam == 0) {
m_formTempParam = 1;
}
} else {
throw CanteraError("", "unknown model");
}
ctml::getFloatArray(xmlChild, vParams, true, "Pascal-m6/kmol2", "a_coeff");
nParamsFound = vParams.size();
if (nParamsFound != nParamsExpected) {
throw CanteraError("RedlichKwongMFTP::readXMLCrossFluid(for a_coeff" + iName + ")",
"wrong number of params found");
}
for (size_t i = 0; i < nParamsFound; i++) {
a_coeff_vec(i, counter) = vParams[i];
a_coeff_vec(i, counter0) = vParams[i];
}
}
}
}
void RedlichKwongMFTP::setParametersFromXML(const XML_Node& thermoNode)
{
MixtureFugacityTP::setParametersFromXML(thermoNode);
std::string model = thermoNode["model"];
}
doublereal RedlichKwongMFTP::sresid() const
{
// note this agrees with tpx
doublereal rho = density();
doublereal mmw = meanMolecularWeight();
doublereal molarV = mmw / rho;
double hh = m_b_current / molarV;
doublereal zz = z();
doublereal dadt = da_dt();
doublereal T = temperature();
doublereal sqT = sqrt(T);
doublereal fac = dadt - m_a_current / (2.0 * T);
double sresid_mol_R = log(zz*(1.0 - hh)) + log(1.0 + hh) * fac / (sqT * GasConstant * m_b_current);
return GasConstant * sresid_mol_R;
}
doublereal RedlichKwongMFTP::hresid() const
{
// note this agrees with tpx
doublereal rho = density();
doublereal mmw = meanMolecularWeight();
doublereal molarV = mmw / rho;
double hh = m_b_current / molarV;
doublereal zz = z();
doublereal dadt = da_dt();
doublereal T = temperature();
doublereal sqT = sqrt(T);
doublereal fac = T * dadt - 3.0 *m_a_current / (2.0);
return GasConstant * T * (zz - 1.0) + fac * log(1.0 + hh) / (sqT * m_b_current);
}
doublereal RedlichKwongMFTP::liquidVolEst(doublereal TKelvin, doublereal& presGuess) const
{
double v = m_b_current * 1.1;
double atmp;
double btmp;
calculateAB(TKelvin, atmp, btmp);
doublereal pres = std::max(psatEst(TKelvin), presGuess);
double Vroot[3];
bool foundLiq = false;
int m = 0;
do {
int nsol = NicholsSolve(TKelvin, pres, atmp, btmp, Vroot);
if (nsol == 1 || nsol == 2) {
double pc = critPressure();
if (pres > pc) {
foundLiq = true;
}
pres *= 1.04;
} else {
foundLiq = true;
}
} while ((m < 100) && (!foundLiq));
if (foundLiq) {
v = Vroot[0];
presGuess = pres;
} else {
v = -1.0;
}
return v;
}
doublereal RedlichKwongMFTP::densityCalc(doublereal TKelvin, doublereal presPa, int phaseRequested, doublereal rhoguess)
{
/*
* It's necessary to set the temperature so that m_a_current is set correctly.
*/
setTemperature(TKelvin);
double tcrit = critTemperature();
doublereal mmw = meanMolecularWeight();
if (rhoguess == -1.0) {
if (phaseRequested != FLUID_GAS) {
if (TKelvin > tcrit) {
rhoguess = presPa * mmw / (GasConstant * TKelvin);
} else {
if (phaseRequested == FLUID_GAS || phaseRequested == FLUID_SUPERCRIT) {
rhoguess = presPa * mmw / (GasConstant * TKelvin);
} else if (phaseRequested >= FLUID_LIQUID_0) {
double lqvol = liquidVolEst(TKelvin, presPa);
rhoguess = mmw / lqvol;
}
}
} else {
/*
* Assume the Gas phase initial guess, if nothing is
* specified to the routine
*/
rhoguess = presPa * mmw / (GasConstant * TKelvin);
}
}
doublereal volguess = mmw / rhoguess;
NSolns_ = NicholsSolve(TKelvin, presPa, m_a_current, m_b_current, Vroot_);
doublereal molarVolLast = Vroot_[0];
if (NSolns_ >= 2) {
if (phaseRequested >= FLUID_LIQUID_0) {
molarVolLast = Vroot_[0];
} else if (phaseRequested == FLUID_GAS || phaseRequested == FLUID_SUPERCRIT) {
molarVolLast = Vroot_[2];
} else {
if (volguess > Vroot_[1]) {
molarVolLast = Vroot_[2];
} else {
molarVolLast = Vroot_[0];
}
}
} else if (NSolns_ == 1) {
if (phaseRequested == FLUID_GAS || phaseRequested == FLUID_SUPERCRIT || phaseRequested == FLUID_UNDEFINED) {
molarVolLast = Vroot_[0];
} else {
return -2.0;
}
} else if (NSolns_ == -1) {
if (phaseRequested >= FLUID_LIQUID_0 || phaseRequested == FLUID_UNDEFINED || phaseRequested == FLUID_SUPERCRIT) {
molarVolLast = Vroot_[0];
} else if (TKelvin > tcrit) {
molarVolLast = Vroot_[0];
} else {
return -2.0;
}
} else {
molarVolLast = Vroot_[0];
return -1.0;
}
return mmw / molarVolLast;
}
doublereal RedlichKwongMFTP::densSpinodalLiquid() const
{
if (NSolns_ != 3) {
return critDensity();
}
double vmax = Vroot_[1];
double vmin = Vroot_[0];
RootFind rf(fdpdv_);
rf.setPrintLvl(10);
rf.setTol(1.0E-5, 1.0E-10);
rf.setFuncIsGenerallyDecreasing(true);
double vbest = 0.5 * (Vroot_[0]+Vroot_[1]);
double funcNeeded = 0.0;
int status = rf.solve(vmin, vmax, 100, funcNeeded, &vbest);
if (status != ROOTFIND_SUCCESS) {
throw CanteraError(" RedlichKwongMFTP::densSpinodalLiquid() ", "didn't converge");
}
doublereal mmw = meanMolecularWeight();
return mmw / vbest;
}
doublereal RedlichKwongMFTP::densSpinodalGas() const
{
if (NSolns_ != 3) {
return critDensity();
}
double vmax = Vroot_[2];
double vmin = Vroot_[1];
RootFind rf(fdpdv_);
rf.setPrintLvl(10);
rf.setTol(1.0E-5, 1.0E-10);
rf.setFuncIsGenerallyIncreasing(true);
double vbest = 0.5 * (Vroot_[1]+Vroot_[2]);
double funcNeeded = 0.0;
int status = rf.solve(vmin, vmax, 100, funcNeeded, &vbest);
if (status != ROOTFIND_SUCCESS) {
throw CanteraError(" RedlichKwongMFTP::densSpinodalGas() ", "didn't converge");
}
doublereal mmw = meanMolecularWeight();
return mmw / vbest;
}
doublereal RedlichKwongMFTP::pressureCalc(doublereal TKelvin, doublereal molarVol) const
{
doublereal sqt = sqrt(TKelvin);
double pres = GasConstant * TKelvin / (molarVol - m_b_current)
- m_a_current / (sqt * molarVol * (molarVol + m_b_current));
return pres;
}
doublereal RedlichKwongMFTP::dpdVCalc(doublereal TKelvin, doublereal molarVol, doublereal& presCalc) const
{
doublereal sqt = sqrt(TKelvin);
presCalc = GasConstant * TKelvin / (molarVol - m_b_current)
- m_a_current / (sqt * molarVol * (molarVol + m_b_current));
doublereal vpb = molarVol + m_b_current;
doublereal vmb = molarVol - m_b_current;
doublereal dpdv = (- GasConstant * TKelvin / (vmb * vmb)
+ m_a_current * (2 * molarVol + m_b_current) / (sqt * molarVol * molarVol * vpb * vpb));
return dpdv;
}
void RedlichKwongMFTP::pressureDerivatives() const
{
doublereal TKelvin = temperature();
doublereal mv = molarVolume();
doublereal pres;
dpdV_ = dpdVCalc(TKelvin, mv, pres);
doublereal sqt = sqrt(TKelvin);
doublereal vpb = mv + m_b_current;
doublereal vmb = mv - m_b_current;
doublereal dadt = da_dt();
doublereal fac = dadt - m_a_current/(2.0 * TKelvin);
dpdT_ = (GasConstant / (vmb) - fac / (sqt * mv * vpb));
}
void RedlichKwongMFTP::updateMixingExpressions()
{
updateAB();
}
void RedlichKwongMFTP::updateAB()
{
double temp = temperature();
if (m_formTempParam == 1) {
for (size_t i = 0; i < m_kk; i++) {
for (size_t j = 0; j < m_kk; j++) {
size_t counter = i * m_kk + j;
a_vec_Curr_[counter] = a_coeff_vec(0,counter) + a_coeff_vec(1,counter) * temp;
}
}
}
m_b_current = 0.0;
m_a_current = 0.0;
for (size_t i = 0; i < m_kk; i++) {
m_b_current += moleFractions_[i] * b_vec_Curr_[i];
for (size_t j = 0; j < m_kk; j++) {
m_a_current += a_vec_Curr_[i * m_kk + j] * moleFractions_[i] * moleFractions_[j];
}
}
}
void RedlichKwongMFTP::calculateAB(doublereal temp, doublereal& aCalc, doublereal& bCalc) const
{
bCalc = 0.0;
aCalc = 0.0;
if (m_formTempParam == 1) {
for (size_t i = 0; i < m_kk; i++) {
bCalc += moleFractions_[i] * b_vec_Curr_[i];
for (size_t j = 0; j < m_kk; j++) {
size_t counter = i * m_kk + j;
doublereal a_vec_Curr = a_coeff_vec(0,counter) + a_coeff_vec(1,counter) * temp;
aCalc += a_vec_Curr * moleFractions_[i] * moleFractions_[j];
}
}
} else {
for (size_t i = 0; i < m_kk; i++) {
bCalc += moleFractions_[i] * b_vec_Curr_[i];
for (size_t j = 0; j < m_kk; j++) {
size_t counter = i * m_kk + j;
doublereal a_vec_Curr = a_coeff_vec(0,counter);
aCalc += a_vec_Curr * moleFractions_[i] * moleFractions_[j];
}
}
}
}
doublereal RedlichKwongMFTP::da_dt() const
{
doublereal dadT = 0.0;
if (m_formTempParam == 1) {
for (size_t i = 0; i < m_kk; i++) {
for (size_t j = 0; j < m_kk; j++) {
size_t counter = i * m_kk + j;
dadT+= a_coeff_vec(1,counter) * moleFractions_[i] * moleFractions_[j];
}
}
}
return dadT;
}
void RedlichKwongMFTP::calcCriticalConditions(doublereal a, doublereal b, doublereal a0_coeff, doublereal aT_coeff,
doublereal& pc, doublereal& tc, doublereal& vc) const
{
if (m_formTempParam != 0) {
a = a0_coeff;
}
if (b <= 0.0) {
tc = 1000000.;
pc = 1.0E13;
vc = omega_vc * GasConstant * tc / pc;
return;
}
if (a <= 0.0) {
tc = 0.0;
pc = 0.0;
vc = 2.0 * b;
return;
}
double tmp = a * omega_b / (b * omega_a * GasConstant);
double pp = 2./3.;
doublereal sqrttc, f, dfdt, deltatc;
if (m_formTempParam == 0) {
tc = pow(tmp, pp);
} else {
tc = pow(tmp, pp);
for (int j = 0; j < 10; j++) {
sqrttc = sqrt(tc);
f = omega_a * b * GasConstant * tc * sqrttc / omega_b - aT_coeff * tc - a0_coeff;
dfdt = 1.5 * omega_a * b * GasConstant * sqrttc / omega_b - aT_coeff;
deltatc = - f / dfdt;
tc += deltatc;
}
if (deltatc > 0.1) {
throw CanteraError("RedlichKwongMFTP::calcCriticalConditions", "didn't converge");
}
}
pc = omega_b * GasConstant * tc / b;
vc = omega_vc * GasConstant * tc / pc;
}
int RedlichKwongMFTP::NicholsSolve(double TKelvin, double pres, doublereal a, doublereal b,
doublereal Vroot[3]) const
{
Vroot[0] = 0.0;
Vroot[1] = 0.0;
Vroot[2] = 0.0;
if (TKelvin <= 0.0) {
throw CanteraError("RedlichKwongMFTP::NicholsSolve()", "neg temperature");
}
/*
* Derive the coefficients of the cubic polynomial to solve.
*/
doublereal an = 1.0;
doublereal bn = - GasConstant * TKelvin / pres;
doublereal sqt = sqrt(TKelvin);
doublereal cn = - (GasConstant * TKelvin * b / pres - a/(pres * sqt) + b * b);
doublereal dn = - (a * b / (pres * sqt));
double tmp = a * omega_b / (b * omega_a * GasConstant);
double pp = 2./3.;
double tc = pow(tmp, pp);
double pc = omega_b * GasConstant * tc / b;
double vc = omega_vc * GasConstant * tc / pc;
// Derive the center of the cubic, x_N
doublereal xN = - bn /(3 * an);
// Derive the value of delta**2. This is a key quantity that determines the number of turning points
doublereal delta2 = (bn * bn - 3 * an * cn) / (9 * an * an);
doublereal delta = 0.0;
// Calculate a couple of ratios
doublereal ratio1 = 3.0 * an * cn / (bn * bn);
doublereal ratio2 = pres * b / (GasConstant * TKelvin);
if (fabs(ratio1) < 1.0E-7) {
//printf("NicholsSolve(): Alternative solution (p = %g T = %g)\n", pres, TKelvin);
doublereal ratio3 = a / (GasConstant * sqt) * pres / (GasConstant * TKelvin);
if (fabs(ratio2) < 1.0E-5 && fabs(ratio3) < 1.0E-5) {
doublereal zz = 1.0;
for (int i = 0; i < 10; i++) {
doublereal znew = zz / (zz - ratio2) - ratio3 / (zz + ratio1);
doublereal deltaz = znew - zz;
zz = znew;
if (fabs(deltaz) < 1.0E-14) {
break;
}
}
doublereal v = zz * GasConstant * TKelvin / pres;
Vroot[0] = v;
return 1;
}
}
int nSolnValues;
double h2 = 4. * an * an * delta2 * delta2 * delta2;
if (delta2 > 0.0) {
delta = sqrt(delta2);
}
doublereal h = 2.0 * an * delta * delta2;
doublereal yN = 2.0 * bn * bn * bn / (27.0 * an * an) - bn * cn / (3.0 * an) + dn;
doublereal desc = yN * yN - h2;
if (fabs(fabs(h) - fabs(yN)) < 1.0E-10) {
if (desc != 0.0) {
// this is for getting to other cases
printf("NicholsSolve(): numerical issues\n");
throw CanteraError("NicholsSolve()", "numerical issues");
}
desc = 0.0;
}
if (desc < 0.0) {
nSolnValues = 3;
} else if (desc == 0.0) {
nSolnValues = 2;
// We are here as p goes to zero.
} else if (desc > 0.0) {
nSolnValues = 1;
}
/*
* One real root -> have to determine whether gas or liquid is the root
*/
if (desc > 0.0) {
doublereal tmpD = sqrt(desc);
doublereal tmp1 = (- yN + tmpD) / (2.0 * an);
doublereal sgn1 = 1.0;
if (tmp1 < 0.0) {
sgn1 = -1.0;
tmp1 = -tmp1;
}
doublereal tmp2 = (- yN - tmpD) / (2.0 * an);
doublereal sgn2 = 1.0;
if (tmp2 < 0.0) {
sgn2 = -1.0;
tmp2 = -tmp2;
}
doublereal p1 = pow(tmp1, 1./3.);
doublereal p2 = pow(tmp2, 1./3.);
doublereal alpha = xN + sgn1 * p1 + sgn2 * p2;
Vroot[0] = alpha;
Vroot[1] = 0.0;
Vroot[2] = 0.0;
tmp = an * Vroot[0] * Vroot[0] * Vroot[0] + bn * Vroot[0] * Vroot[0] + cn * Vroot[0] + dn;
} else if (desc < 0.0) {
doublereal tmp = - yN/h;
doublereal val = acos(tmp);
doublereal theta = val / 3.0;
doublereal oo = 2. * Cantera::Pi / 3.;
doublereal alpha = xN + 2. * delta * cos(theta);
doublereal beta = xN + 2. * delta * cos(theta + oo);
doublereal gamma = xN + 2. * delta * cos(theta + 2.0 * oo);
Vroot[0] = beta;
Vroot[1] = gamma;
Vroot[2] = alpha;
for (int i = 0; i < 3; i++) {
tmp = an * Vroot[i] * Vroot[i] * Vroot[i] + bn * Vroot[i] * Vroot[i] + cn * Vroot[i] + dn;
if (fabs(tmp) > 1.0E-4) {
for (int j = 0; j < 3; j++) {
if (j != i) {
if (fabs(Vroot[i] - Vroot[j]) < 1.0E-4 * (fabs(Vroot[i]) + fabs(Vroot[j]))) {
writelog("RedlichKwongMFTP::NicholsSolve(T = " + fp2str(TKelvin) + ", p = " +
fp2str(pres) + "): WARNING roots have merged: " +
fp2str(Vroot[i]) + ", " + fp2str(Vroot[j]));
writelogendl();
}
}
}
}
}
} else if (desc == 0.0) {
if (yN == 0.0 && h == 0.0) {
Vroot[0] = xN;
Vroot[1] = xN;
Vroot[2] = xN;
} else {
// need to figure out whether delta is pos or neg
if (yN > 0.0) {
tmp = pow(yN/(2*an), 1./3.);
if (fabs(tmp - delta) > 1.0E-9) {
throw CanteraError("RedlichKwongMFTP::NicholsSolve()", "unexpected");
}
Vroot[1] = xN + delta;
Vroot[0] = xN - 2.0*delta; // liquid phase root
} else {
tmp = pow(yN/(2*an), 1./3.);
if (fabs(tmp - delta) > 1.0E-9) {
throw CanteraError("RedlichKwongMFTP::NicholsSolve()", "unexpected");
}
delta = -delta;
Vroot[0] = xN + delta;
Vroot[1] = xN - 2.0*delta; // gas phase root
}
}
for (int i = 0; i < 2; i++) {
tmp = an * Vroot[i] * Vroot[i] * Vroot[i] + bn * Vroot[i] * Vroot[i] + cn * Vroot[i] + dn;
}
}
/*
* Unfortunately, there is a heavy amount of roundoff error due to bad conditioning in this
*/
double res, dresdV = 0.0;
for (int i = 0; i < nSolnValues; i++) {
for (int n = 0; n < 20; n++) {
res = an * Vroot[i] * Vroot[i] * Vroot[i] + bn * Vroot[i] * Vroot[i] + cn * Vroot[i] + dn;
if (fabs(res) < 1.0E-14) {
break;
}
dresdV = 3.0 * an * Vroot[i] * Vroot[i] + 2.0 * bn * Vroot[i] + cn;
double del = - res / dresdV;
Vroot[i] += del;
if (fabs(del) / (fabs(Vroot[i]) + fabs(del)) < 1.0E-14) {
break;
}
double res2 = an * Vroot[i] * Vroot[i] * Vroot[i] + bn * Vroot[i] * Vroot[i] + cn * Vroot[i] + dn;
if (fabs(res2) < fabs(res)) {
continue;
} else {
Vroot[i] -= del;
Vroot[i] += 0.1 * del;
}
}
if ((fabs(res) > 1.0E-14) && (fabs(res) > 1.0E-14 * fabs(dresdV) * fabs(Vroot[i]))) {
writelog("RedlichKwongMFTP::NicholsSolve(T = " + fp2str(TKelvin) + ", p = " +
fp2str(pres) + "): WARNING root didn't converge V = " + fp2str(Vroot[i]));
writelogendl();
}
}
if (nSolnValues == 1) {
if (TKelvin > tc) {
if (Vroot[0] < vc) {
nSolnValues = -1;
}
} else {
if (Vroot[0] < xN) {
nSolnValues = -1;
}
}
} else {
if (nSolnValues == 2) {
if (delta > 0.0) {
nSolnValues = -2;
}
}
}
return nSolnValues;
}
}
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