/*!
* This function returns the fluid mobilities. Usually, you have
* to multiply Faraday's constant into the resulting expression
* to general a species flux expression.
*
* Frequently, but not always, the mobility is calculated from the
* diffusion coefficient using the Einstein relation
*
* \f[
* \mu^f_k = \frac{D_k}{R T}
* \f]
*
*
* @param mobil_f Returns the mobilities of
* the species in array \c mobil. The array must be
* dimensioned at least as large as the number of species.
*/
void LiquidTransport::getFluidMobilities(doublereal* const mobil_f) {
getMixDiffCoeffs(DATA_PTR(m_spwork));
doublereal c1 = 1.0 / (GasConstant * m_temp);
for (size_t k = 0; k < m_nsp; k++) {
mobil_f[k] = c1 * m_spwork[k];
}
}
void AqueousTransport::getSpeciesFluxesExt(size_t ldf, doublereal* const fluxes)
{
update_T();
update_C();
getMixDiffCoeffs(DATA_PTR(m_spwork));
const vector_fp& mw = m_thermo->molecularWeights();
const doublereal* y = m_thermo->massFractions();
doublereal rhon = m_thermo->molarDensity();
// Unroll wrt ndim
vector_fp sum(m_nDim,0.0);
for (size_t n = 0; n < m_nDim; n++) {
for (size_t k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] = -rhon * mw[k] * m_spwork[k] * m_Grad_X[n*m_nsp + k];
sum[n] += fluxes[n*ldf + k];
}
}
// add correction flux to enforce sum to zero
for (size_t n = 0; n < m_nDim; n++) {
for (size_t k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] -= y[k]*sum[n];
}
}
}
/*
* This function returns the mobilities. In some formulations
* this is equal to the normal mobility multiplied by faraday's constant.
*
* Frequently, but not always, the mobility is calculated from the
* diffusion coefficient using the Einstein relation
*
* \f[
* \mu^e_k = \frac{F D_k}{R T}
* \f]
*
* @param mobil_e Returns the mobilities of
* the species in array \c mobil_e. The array must be
* dimensioned at least as large as the number of species.
*/
void LiquidTransport::getMobilities(doublereal* const mobil) {
getMixDiffCoeffs(DATA_PTR(m_spwork));
doublereal c1 = ElectronCharge / (Boltzmann * m_temp);
for (size_t k = 0; k < m_nsp; k++) {
mobil[k] = c1 * m_spwork[k];
}
}
void LiquidTransport::getSpeciesDiffusiveMassFluxes(doublereal* const fluxes) {
int n, k;
update_temp();
update_conc();
getMixDiffCoeffs(DATA_PTR(m_spwork));
const array_fp& mw = m_thermo->molecularWeights();
const doublereal* const y = m_thermo->massFractions();
const doublereal rhon = m_thermo->molarDensity();
// Unroll wrt ndim
vector_fp sum(m_nDim,0.0);
for (n = 0; n < m_nDim; n++) {
for (k = 0; k < m_nsp; k++) {
fluxes[n*m_nsp + k] = -rhon * mw[k] * m_spwork[k] * m_Grad_X[n*m_nsp + k];
sum[n] += fluxes[n*m_nsp + k];
}
}
// add correction flux to enforce sum to zero
for (n = 0; n < m_nDim; n++) {
for (k = 0; k < m_nsp; k++) {
fluxes[n*m_nsp + k] -= y[k]*sum[n];
}
}
}
/*
* Units for the returned fluxes are kg m-2 s-1.
*
*
* The diffusive mass flux of species \e k is computed from
* \f[
* \vec{j}_k = -n M_k D_k \nabla X_k.
* \f]
*
* @param ndim Number of dimensions in the flux expressions
* @param grad_T Gradient of the temperature
* (length = ndim)
* @param ldx Leading dimension of the grad_X array
* (usually equal to m_nsp but not always)
* @param grad_X Gradients of the mole fraction
* Flat vector with the m_nsp in the inner loop.
* length = ldx * ndim
* @param ldf Leading dimension of the fluxes array
* (usually equal to m_nsp but not always)
* @param fluxes Output of the diffusive mass fluxes
* Flat vector with the m_nsp in the inner loop.
* length = ldx * ndim
*/
void MixTransport::getSpeciesFluxes(int ndim,
const doublereal* grad_T, int ldx, const doublereal* grad_X,
int ldf, doublereal* fluxes) {
int n, k;
update_T();
update_C();
getMixDiffCoeffs(DATA_PTR(m_spwork));
const array_fp& mw = m_thermo->molecularWeights();
const doublereal* y = m_thermo->massFractions();
doublereal rhon = m_thermo->molarDensity();
vector_fp sum(ndim,0.0);
for (n = 0; n < ndim; n++) {
for (k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] = -rhon * mw[k] * m_spwork[k] * grad_X[n*ldx + k];
sum[n] += fluxes[n*ldf + k];
}
}
// add correction flux to enforce sum to zero
for (n = 0; n < ndim; n++) {
for (k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] -= y[k]*sum[n];
}
}
}
void LiquidTransport::getMobilities(doublereal* const mobil) {
// this needs to be checked out.
int k;
getMixDiffCoeffs(DATA_PTR(m_spwork));
doublereal c1 = ElectronCharge / (Boltzmann * m_temp);
for (k = 0; k < m_nsp; k++) {
mobil[k] = c1 * m_spwork[k] * m_thermo->charge(k);
}
}
/**
* Compute the mobilities of the species from the diffusion coefficients,
* using the Einstein relation.
*/
void SolidTransport::getMobilities(doublereal* const mobil) {
int k;
getMixDiffCoeffs(mobil);
doublereal t = m_thermo->temperature();
int nsp = m_thermo->nSpecies();
doublereal c1 = ElectronCharge / (Boltzmann * t);
for (k = 0; k < nsp; k++) {
mobil[k] *= c1 * fabs(m_thermo->charge(k));
}
}
/*
*
* units = kg/m2/s
*
* Internally, gradients in the in mole fraction, temperature
* and electrostatic potential contribute to the diffusive flux
*
*
* The diffusive mass flux of species \e k is computed from the following
* formula
*
* \f[
* j_k = - M_k z_k u^f_k F c_k \nabla \Psi - c M_k D_k \nabla X_k - Y_k V_c
* \f]
*
* where V_c is the correction velocity
*
* \f[
* V_c = - \sum_j {M_k z_k u^f_k F c_k \nabla \Psi + c M_j D_j \nabla X_j}
* \f]
*
* @param ldf stride of the fluxes array. Must be equal to
* or greater than the number of species.
* @param fluxes Vector of calculated fluxes
*/
void SimpleTransport::getSpeciesFluxesExt(size_t ldf, doublereal* fluxes)
{
AssertThrow(ldf >= m_nsp ,"SimpleTransport::getSpeciesFluxesExt: Stride must be greater than m_nsp");
update_T();
update_C();
getMixDiffCoeffs(DATA_PTR(m_spwork));
const vector_fp& mw = m_thermo->molecularWeights();
const doublereal* y = m_thermo->massFractions();
doublereal concTotal = m_thermo->molarDensity();
// Unroll wrt ndim
if (doMigration_) {
double FRT = ElectronCharge / (Boltzmann * m_temp);
for (size_t n = 0; n < m_nDim; n++) {
rhoVc[n] = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] = - concTotal * mw[k] * m_spwork[k] *
(m_Grad_X[n*m_nsp + k] + FRT * m_molefracs[k] * m_chargeSpecies[k] * m_Grad_V[n]);
rhoVc[n] += fluxes[n*ldf + k];
}
}
} else {
for (size_t n = 0; n < m_nDim; n++) {
rhoVc[n] = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] = - concTotal * mw[k] * m_spwork[k] * m_Grad_X[n*m_nsp + k];
rhoVc[n] += fluxes[n*ldf + k];
}
}
}
if (m_velocityBasis == VB_MASSAVG) {
for (size_t n = 0; n < m_nDim; n++) {
rhoVc[n] = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
rhoVc[n] += fluxes[n*ldf + k];
}
}
for (size_t n = 0; n < m_nDim; n++) {
for (size_t k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] -= y[k] * rhoVc[n];
}
}
} else if (m_velocityBasis == VB_MOLEAVG) {
for (size_t n = 0; n < m_nDim; n++) {
rhoVc[n] = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
rhoVc[n] += fluxes[n*ldf + k] / mw[k];
}
}
for (size_t n = 0; n < m_nDim; n++) {
for (size_t k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] -= m_molefracs[k] * rhoVc[n] * mw[k];
}
}
} else if (m_velocityBasis >= 0) {
for (size_t n = 0; n < m_nDim; n++) {
rhoVc[n] = - fluxes[n*ldf + m_velocityBasis] / mw[m_velocityBasis];
for (size_t k = 0; k < m_nsp; k++) {
rhoVc[n] += fluxes[n*ldf + k] / mw[k];
}
}
for (size_t n = 0; n < m_nDim; n++) {
for (size_t k = 0; k < m_nsp; k++) {
fluxes[n*ldf + k] -= m_molefracs[k] * rhoVc[n] * mw[k];
}
fluxes[n*ldf + m_velocityBasis] = 0.0;
}
} else {
throw CanteraError("SimpleTransport::getSpeciesFluxesExt()",
"unknown velocity basis");
}
}