void GasTransport::getMixDiffCoeffsMass(doublereal* const d)
{
update_T();
update_C();
// update the binary diffusion coefficients if necessary
if (!m_bindiff_ok) {
updateDiff_T();
}
doublereal mmw = m_thermo->meanMolecularWeight();
doublereal p = m_thermo->pressure();
if (m_nsp == 1) {
d[0] = m_bdiff(0,0) / p;
} else {
for (size_t k=0; k<m_nsp; k++) {
double sum1 = 0.0;
double sum2 = 0.0;
for (size_t i=0; i<m_nsp; i++) {
if (i==k) {
continue;
}
sum1 += m_molefracs[i] / m_bdiff(k,i);
sum2 += m_molefracs[i] * m_mw[i] / m_bdiff(k,i);
}
sum1 *= p;
sum2 *= p * m_molefracs[k] / (mmw - m_mw[k]*m_molefracs[k]);
d[k] = 1.0 / (sum1 + sum2);
}
}
}
void AqueousTransport::getMixDiffCoeffs(doublereal* const d)
{
update_T();
update_C();
// update the binary diffusion coefficients if necessary
if (!m_bindiff_ok) {
updateDiff_T();
}
size_t k, j;
doublereal mmw = m_thermo->meanMolecularWeight();
doublereal sumxw = 0.0, sum2;
doublereal p = m_press;
if (m_nsp == 1) {
d[0] = m_bdiff(0,0) / p;
} else {
for (k = 0; k < m_nsp; k++) {
sumxw += m_molefracs[k] * m_mw[k];
}
for (k = 0; k < m_nsp; k++) {
sum2 = 0.0;
for (j = 0; j < m_nsp; j++) {
if (j != k) {
sum2 += m_molefracs[j] / m_bdiff(j,k);
}
}
if (sum2 <= 0.0) {
d[k] = m_bdiff(k,k) / p;
} else {
d[k] = (sumxw - m_molefracs[k] * m_mw[k])/(p * mmw * sum2);
}
}
}
}
void GasTransport::getMixDiffCoeffsMole(doublereal* const d)
{
update_T();
update_C();
// update the binary diffusion coefficients if necessary
if (!m_bindiff_ok) {
updateDiff_T();
}
doublereal p = m_thermo->pressure();
if (m_nsp == 1) {
d[0] = m_bdiff(0,0) / p;
} else {
for (size_t k = 0; k < m_nsp; k++) {
double sum2 = 0.0;
for (size_t j = 0; j < m_nsp; j++) {
if (j != k) {
sum2 += m_molefracs[j] / m_bdiff(j,k);
}
}
if (sum2 <= 0.0) {
d[k] = m_bdiff(k,k) / p;
} else {
d[k] = (1 - m_molefracs[k]) / (p * sum2);
}
}
}
}
void ApproxMixTransport::getMixDiffCoeffs(double* const d)
{
update_T();
update_C();
// update the binary diffusion coefficients if necessary
if (!m_bindiff_ok) {
updateDiff_T();
}
double mmw = m_thermo->meanMolecularWeight();
double sumxw = 0.0, sum2;
double p = m_thermo->pressure();
if (m_nsp == 1) {
d[0] = m_bdiff(0,0) / p;
} else {
for (size_t k = 0; k < m_nsp; k++) {
sumxw += m_molefracs[k] * m_mw[k];
}
for (size_t k = 0; k < m_nsp; k++) {
sum2 = 0.0;
if (m_molefracs[k] >= _threshold) {
for (size_t j = 0; j < m_nsp; j++) {
if (j != k) {
sum2 += m_molefracs[j] / m_bdiff(j,k);
}
}
} else {
for (size_t j : _kMajor) {
if (j != k) {
sum2 += m_molefracs[j] / m_bdiff(j,k);
}
}
}
if (sum2 <= 0.0) {
d[k] = m_bdiff(k,k) / p;
} else {
d[k] = (sumxw - m_molefracs[k] * m_mw[k])/(p * mmw * sum2);
}
}
}
}
void ApproxMixTransport::updateDiff_T()
{
// Evaluate binary diffusion coefficients at unit pressure for
// the species pairs where at least one has a mole fraction above
// the specified threshold.
if (m_mode == Cantera::CK_Mode) {
for (size_t ij=0; ij<_kMajor.size(); ij++) {
size_t j = _kMajor[ij];
for (size_t k=0; k<m_nsp; k++) {
size_t ic = (k > j) ? m_nsp*j - (j-1)*j/2 + k - j
: m_nsp*k - (k-1)*k/2 + j - k;
m_bdiff(j,k) = exp(Cantera::dot4(m_polytempvec, m_diffcoeffs[ic]));
m_bdiff(k,j) = m_bdiff(j,k);
}
}
} else {
for (size_t ij=0; ij<_kMajor.size(); ij++) {
size_t j = _kMajor[ij];
for (size_t k=0; k<m_nsp; k++) {
size_t ic = (k > j) ? m_nsp*j - (j-1)*j/2 + k - j
: m_nsp*k - (k-1)*k/2 + j - k;
m_bdiff(j,k) = m_temp * m_sqrt_t*Cantera::dot5(m_polytempvec, m_diffcoeffs[ic]);
m_bdiff(k,j) = m_bdiff(j,k);
}
}
}
m_bindiff_ok = true;
}
void GasTransport::updateDiff_T()
{
update_T();
// evaluate binary diffusion coefficients at unit pressure
size_t ic = 0;
if (m_mode == CK_Mode) {
for (size_t i = 0; i < m_nsp; i++) {
for (size_t j = i; j < m_nsp; j++) {
m_bdiff(i,j) = exp(dot4(m_polytempvec, m_diffcoeffs[ic]));
m_bdiff(j,i) = m_bdiff(i,j);
ic++;
}
}
} else {
for (size_t i = 0; i < m_nsp; i++) {
for (size_t j = i; j < m_nsp; j++) {
m_bdiff(i,j) = m_temp * m_sqrt_t*dot5(m_polytempvec,
m_diffcoeffs[ic]);
m_bdiff(j,i) = m_bdiff(i,j);
ic++;
}
}
}
m_bindiff_ok = true;
}
/**
* Update the binary diffusion coefficients. These are evaluated
* from the polynomial fits at unit pressure (1 Pa).
*/
void LiquidTransport::updateDiff_temp() {
// evaluate binary diffusion coefficients at unit pressure
int i,j;
int ic = 0;
if (m_mode == CK_Mode) {
for (i = 0; i < m_nsp; i++) {
for (j = i; j < m_nsp; j++) {
m_bdiff(i,j) = exp(dot4(m_polytempvec, m_diffcoeffs[ic]));
m_bdiff(j,i) = m_bdiff(i,j);
ic++;
}
}
}
else {
for (i = 0; i < m_nsp; i++) {
for (j = i; j < m_nsp; j++) {
m_bdiff(i,j) = m_temp * m_sqrt_t*dot5(m_polytempvec,
m_diffcoeffs[ic]);
m_bdiff(j,i) = m_bdiff(i,j);
ic++;
}
}
}
m_diff_temp_ok = true;
m_diff_mix_ok = false;
}
/*
*
* d[ld*j + i] = rp * m_bdiff(i,j);
*
* units of m**2 / s
*
* @param ld offset of rows in the storage
* @param d output vector of diffusion coefficients
*/
void MixTransport::getBinaryDiffCoeffs(const int ld, doublereal* const d) {
update_T();
// if necessary, evaluate the binary diffusion coefficents from the polynomial fits
if (!m_bindiff_ok) updateDiff_T();
if (ld < m_nsp) {
throw CanteraError(" MixTransport::getBinaryDiffCoeffs()", "ld is too small");
}
doublereal rp = 1.0/pressure_ig();
for (int i = 0; i < m_nsp; i++)
for (int j = 0; j < m_nsp; j++) {
d[ld*j + i] = rp * m_bdiff(i,j);
}
}
void LiquidTransport::getBinaryDiffCoeffs(size_t ld, doublereal* d) {
update_temp();
// if necessary, evaluate the binary diffusion coefficents
// from the polynomial fits
if (!m_diff_temp_ok) updateDiff_temp();
doublereal pres = m_thermo->pressure();
doublereal rp = 1.0/pres;
for (size_t i = 0; i < m_nsp; i++)
for (size_t j = 0; j < m_nsp; j++) {
d[ld*j + i] = rp * m_bdiff(i,j);
}
}
/**
* Mixture-averaged diffusion coefficients [m^2/s].
*
* For the single species case or the pure fluid case
* the routine returns the self-diffusion coefficient.
* This is need to avoid a Nan result in the formula
* below.
*/
void LiquidTransport::getMixDiffCoeffs(doublereal* const d) {
update_temp();
update_conc();
// update the binary diffusion coefficients if necessary
if (!m_diff_temp_ok) {
updateDiff_temp();
}
int k, j;
doublereal mmw = m_thermo->meanMolecularWeight();
doublereal sumxw_tran = 0.0;
doublereal sum2;
if (m_nsp == 1) {
d[0] = m_bdiff(0,0);
} else {
for (k = 0; k < m_nsp; k++) {
sumxw_tran += m_molefracs_tran[k] * m_mw[k];
}
for (k = 0; k < m_nsp; k++) {
sum2 = 0.0;
for (j = 0; j < m_nsp; j++) {
if (j != k) {
sum2 += m_molefracs_tran[j] / m_bdiff(j,k);
}
}
// Because we use m_molefracs_tran, sum2 must be positive definate
// if (sum2 <= 0.0) {
// d[k] = m_bdiff(k,k);
// } else {
d[k] = (sumxw_tran - m_molefracs_tran[k] * m_mw[k])/(mmw * sum2);
// }
}
}
}
void AqueousTransport::getBinaryDiffCoeffs(const size_t ld, doublereal* const d)
{
update_T();
// if necessary, evaluate the binary diffusion coefficients
// from the polynomial fits
if (!m_bindiff_ok) {
updateDiff_T();
}
doublereal pres = m_thermo->pressure();
doublereal rp = 1.0/pres;
for (size_t i = 0; i < m_nsp; i++)
for (size_t j = 0; j < m_nsp; j++) {
d[ld*j + i] = rp * m_bdiff(i,j);
}
}
void LiquidTransport::getBinaryDiffCoeffs(size_t ld, doublereal* d)
{
if (ld != m_nsp) {
throw CanteraError("LiquidTransport::getBinaryDiffCoeffs",
"First argument does not correspond to number of species in model.\nDiff Coeff matrix may be misdimensioned");
}
update_T();
// if necessary, evaluate the binary diffusion coefficients
// from the polynomial fits
if (!m_diff_temp_ok) {
updateDiff_T();
}
for (size_t i = 0; i < m_nsp; i++) {
for (size_t j = 0; j < m_nsp; j++) {
d[ld*j + i] = 1.0 / m_bdiff(i,j);
}
}
}
void LiquidTransport::stefan_maxwell_solve()
{
doublereal tmp;
m_B.resize(m_nsp, m_nDim, 0.0);
m_A.resize(m_nsp, m_nsp, 0.0);
//! grab a local copy of the molecular weights
const vector_fp& M = m_thermo->molecularWeights();
//! grad a local copy of the ion molar volume (inverse total ion concentration)
const doublereal vol = m_thermo->molarVolume();
/*
* Update the temperature, concentrations and diffusion coefficients in the mixture.
*/
update_T();
update_C();
if (!m_diff_temp_ok) {
updateDiff_T();
}
double T = m_thermo->temperature();
update_Grad_lnAC();
m_thermo->getActivityCoefficients(DATA_PTR(m_actCoeff));
/*
* Calculate the electrochemical potential gradient. This is the
* driving force for relative diffusional transport.
*
* Here we calculate
*
* X_i * (grad (mu_i) + S_i grad T - M_i / dens * grad P
*
* This is Eqn. 13-1 p. 318 Newman. The original equation is from
* Hershfeld, Curtis, and Bird.
*
* S_i is the partial molar entropy of species i. This term will cancel
* out a lot of the grad T terms in grad (mu_i), therefore simplifying
* the expression.
*
* Ok I think there may be many ways to do this. One way is to do it via basis
* functions, at the nodes, as a function of the variables in the problem.
*
* For calculation of molality based thermo systems, we current get
* the molar based values. This may change.
*
* Note, we have broken the symmetry of the matrix here, due to
* considerations involving species concentrations going to zero.
*/
for (size_t a = 0; a < m_nDim; a++) {
for (size_t i = 0; i < m_nsp; i++) {
m_Grad_mu[a*m_nsp + i] =
m_chargeSpecies[i] * Faraday * m_Grad_V[a]
+ GasConstant * T * m_Grad_lnAC[a*m_nsp+i];
}
}
if (m_thermo->activityConvention() == cAC_CONVENTION_MOLALITY) {
int iSolvent = 0;
double mwSolvent = m_thermo->molecularWeight(iSolvent);
double mnaught = mwSolvent/ 1000.;
double lnmnaught = log(mnaught);
for (size_t a = 0; a < m_nDim; a++) {
for (size_t i = 1; i < m_nsp; i++) {
m_Grad_mu[a*m_nsp + i] -=
m_molefracs[i] * GasConstant * m_Grad_T[a] * lnmnaught;
}
}
}
/*
* Just for Note, m_A(i,j) refers to the ith row and jth column.
* They are still fortran ordered, so that i varies fastest.
*/
double condSum1;
const doublereal invRT = 1.0 / (GasConstant * T);
switch (m_nDim) {
case 1: /* 1-D approximation */
m_B(0,0) = 0.0;
//equation for the reference velocity
for (size_t j = 0; j < m_nsp; j++) {
if (m_velocityBasis == VB_MOLEAVG) {
m_A(0,j) = m_molefracs_tran[j];
} else if (m_velocityBasis == VB_MASSAVG) {
m_A(0,j) = m_massfracs_tran[j];
} else if ((m_velocityBasis >= 0)
&& (m_velocityBasis < static_cast<int>(m_nsp))) {
// use species number m_velocityBasis as reference velocity
if (m_velocityBasis == static_cast<int>(j)) {
m_A(0,j) = 1.0;
} else {
m_A(0,j) = 0.0;
}
} else {
throw CanteraError("LiquidTransport::stefan_maxwell_solve",
"Unknown reference velocity provided.");
}
}
for (size_t i = 1; i < m_nsp; i++) {
m_B(i,0) = m_Grad_mu[i] * invRT;
m_A(i,i) = 0.0;
for (size_t j = 0; j < m_nsp; j++) {
if (j != i) {
tmp = m_molefracs_tran[j] * m_bdiff(i,j);
m_A(i,i) -= tmp;
m_A(i,j) = tmp;
}
}
}
//! invert and solve the system Ax = b. Answer is in m_B
solve(m_A, m_B);
condSum1 = 0;
for (size_t i = 0; i < m_nsp; i++) {
condSum1 -= Faraday*m_chargeSpecies[i]*m_B(i,0)*m_molefracs_tran[i]/vol;
}
break;
case 2: /* 2-D approximation */
m_B(0,0) = 0.0;
m_B(0,1) = 0.0;
//equation for the reference velocity
for (size_t j = 0; j < m_nsp; j++) {
if (m_velocityBasis == VB_MOLEAVG) {
m_A(0,j) = m_molefracs_tran[j];
} else if (m_velocityBasis == VB_MASSAVG) {
m_A(0,j) = m_massfracs_tran[j];
} else if ((m_velocityBasis >= 0)
&& (m_velocityBasis < static_cast<int>(m_nsp))) {
// use species number m_velocityBasis as reference velocity
if (m_velocityBasis == static_cast<int>(j)) {
m_A(0,j) = 1.0;
} else {
m_A(0,j) = 0.0;
}
} else {
throw CanteraError("LiquidTransport::stefan_maxwell_solve",
"Unknown reference velocity provided.");
}
}
for (size_t i = 1; i < m_nsp; i++) {
m_B(i,0) = m_Grad_mu[i] * invRT;
m_B(i,1) = m_Grad_mu[m_nsp + i] * invRT;
m_A(i,i) = 0.0;
for (size_t j = 0; j < m_nsp; j++) {
if (j != i) {
tmp = m_molefracs_tran[j] * m_bdiff(i,j);
m_A(i,i) -= tmp;
m_A(i,j) = tmp;
}
}
}
//! invert and solve the system Ax = b. Answer is in m_B
solve(m_A, m_B);
break;
case 3: /* 3-D approximation */
m_B(0,0) = 0.0;
m_B(0,1) = 0.0;
m_B(0,2) = 0.0;
//equation for the reference velocity
for (size_t j = 0; j < m_nsp; j++) {
if (m_velocityBasis == VB_MOLEAVG) {
m_A(0,j) = m_molefracs_tran[j];
} else if (m_velocityBasis == VB_MASSAVG) {
m_A(0,j) = m_massfracs_tran[j];
} else if ((m_velocityBasis >= 0)
&& (m_velocityBasis < static_cast<int>(m_nsp))) {
// use species number m_velocityBasis as reference velocity
if (m_velocityBasis == static_cast<int>(j)) {
m_A(0,j) = 1.0;
} else {
m_A(0,j) = 0.0;
}
} else {
throw CanteraError("LiquidTransport::stefan_maxwell_solve",
"Unknown reference velocity provided.");
}
}
for (size_t i = 1; i < m_nsp; i++) {
m_B(i,0) = m_Grad_mu[i] * invRT;
m_B(i,1) = m_Grad_mu[m_nsp + i] * invRT;
m_B(i,2) = m_Grad_mu[2*m_nsp + i] * invRT;
m_A(i,i) = 0.0;
for (size_t j = 0; j < m_nsp; j++) {
if (j != i) {
tmp = m_molefracs_tran[j] * m_bdiff(i,j);
m_A(i,i) -= tmp;
m_A(i,j) = tmp;
}
}
}
//! invert and solve the system Ax = b. Answer is in m_B
solve(m_A, m_B);
break;
default:
printf("unimplemented\n");
throw CanteraError("routine", "not done");
break;
}
for (size_t a = 0; a < m_nDim; a++) {
for (size_t j = 0; j < m_nsp; j++) {
m_Vdiff(j,a) = m_B(j,a);
m_flux(j,a) = concTot_ * M[j] * m_molefracs_tran[j] * m_B(j,a);
}
}
}
