diff --git a/Cantera/src/transport/LiquidTransport.h b/Cantera/src/transport/LiquidTransport.h
index 352687c47..080790f5f 100644
--- a/Cantera/src/transport/LiquidTransport.h
+++ b/Cantera/src/transport/LiquidTransport.h
@@ -482,8 +482,7 @@ namespace Cantera {
doublereal* current);
- //! Get the species diffusive velocities wrt to
- //! the averaged velocity,
+ //! Get the species diffusive velocities wrt to the averaged velocity,
//! given the gradients in mole fraction and temperature
/*!
* The average velocity can be computed on a mole-weighted
diff --git a/Cantera/src/transport/SimpleTransport.cpp b/Cantera/src/transport/SimpleTransport.cpp
index 6c9b62c64..cfd84f401 100644
--- a/Cantera/src/transport/SimpleTransport.cpp
+++ b/Cantera/src/transport/SimpleTransport.cpp
@@ -598,6 +598,104 @@ namespace Cantera {
dt[k] = 0.0;
}
}
+
+ //====================================================================================================================
+ //! Get the species diffusive velocities wrt to the averaged velocity,
+ //! given the gradients in mole fraction and temperature
+ /*!
+ * The average velocity can be computed on a mole-weighted
+ * or mass-weighted basis, or the diffusion velocities may
+ * be specified as relative to a specific species (i.e. a
+ * solvent) all according to the velocityBasis input parameter.
+ *
+ * Units for the returned velocities are m s-1.
+ *
+ * @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 Vdiff Output of the diffusive velocities.
+ * Flat vector with the m_nsp in the inner loop.
+ * length = ldx * ndim
+ */
+ void SimpleTransport::getSpeciesVdiff(int ndim,
+ const doublereal* grad_T,
+ int ldx,
+ const doublereal* grad_X,
+ int ldf,
+ doublereal* Vdiff) {
+ set_Grad_T(grad_T);
+ set_Grad_X(grad_X);
+ const doublereal* y = m_thermo->massFractions();
+ const doublereal rho = m_thermo->density();
+
+ getSpeciesFluxesExt(m_nsp, DATA_PTR(Vdiff));
+
+ for (int n = 0; n < m_nDim; n++) {
+ for (int k = 0; k < m_nsp; k++) {
+ if (y[k] > 1.0E-200) {
+ Vdiff[n * m_nsp + k] *= 1.0 / (rho * y[k]);
+ } else {
+ Vdiff[n * m_nsp + k] = 0.0;
+ }
+ }
+ }
+ }
+ //================================================================================================
+ // Get the species diffusive velocities wrt to the averaged velocity,
+ // given the gradients in mole fraction, temperature and electrostatic potential.
+ /*
+ * The average velocity can be computed on a mole-weighted
+ * or mass-weighted basis, or the diffusion velocities may
+ * be specified as relative to a specific species (i.e. a
+ * solvent) all according to the velocityBasis input parameter.
+ *
+ * Units for the returned velocities are m s-1.
+ *
+ * @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 grad_Phi Gradients of the electrostatic potential
+ * (length = ndim)
+ * @param Vdiff Output of the species diffusion velocities
+ * Flat vector with the m_nsp in the inner loop.
+ * length = ldx * ndim
+ */
+ void SimpleTransport::getSpeciesVdiffES(int ndim, const doublereal* grad_T,
+ int ldx, const doublereal* grad_X,
+ int ldf, const doublereal* grad_Phi,
+ doublereal* Vdiff) {
+ set_Grad_T(grad_T);
+ set_Grad_X(grad_X);
+ set_Grad_V(grad_Phi);
+ const doublereal* y = m_thermo->massFractions();
+ const doublereal rho = m_thermo->density();
+
+ getSpeciesFluxesExt(m_nsp, DATA_PTR(Vdiff));
+
+ for (int n = 0; n < m_nDim; n++) {
+ for (int k = 0; k < m_nsp; k++) {
+ if (y[k] > 1.0E-200) {
+ Vdiff[n * m_nsp + k] *= 1.0 / (rho * y[k]);
+ } else {
+ Vdiff[n * m_nsp + k] = 0.0;
+ }
+ }
+ }
+ }
//================================================================================================
// Get the species diffusive mass fluxes wrt to the specified solution averaged velocity,
// given the gradients in mole fraction and temperature
@@ -673,33 +771,34 @@ namespace Cantera {
const array_fp& mw = m_thermo->molecularWeights();
const doublereal* y = m_thermo->massFractions();
- doublereal conc = m_thermo->molarDensity();
+ doublereal concTotal = m_thermo->molarDensity();
// Unroll wrt ndim
- vector_fp sum(m_nDim, 0.0);
-
+
if (doMigration_) {
double FRT = ElectronCharge / (Boltzmann * m_temp);
for (n = 0; n < m_nDim; n++) {
+ rhoVc[n] = 0.0;
for (k = 0; k < m_nsp; k++) {
- fluxes[n*ldf + k] = -conc * mw[k] * m_spwork[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]);
- sum[n] += fluxes[n*ldf + k];
+ rhoVc[n] += fluxes[n*ldf + k];
}
}
} else {
for (n = 0; n < m_nDim; n++) {
+ rhoVc[n] = 0.0;
for (k = 0; k < m_nsp; k++) {
- fluxes[n*ldf + k] = -conc * mw[k] * m_spwork[k] * m_Grad_X[n*m_nsp + k];
- sum[n] += fluxes[n*ldf + k];
+ fluxes[n*ldf + k] = - concTotal * mw[k] * m_spwork[k] * m_Grad_X[n*m_nsp + k];
+ rhoVc[n] += fluxes[n*ldf + k];
}
}
}
- // add correction flux to enforce sum to zero
+ // Add correction flux to enforce sum to zero
for (n = 0; n < m_nDim; n++) {
for (k = 0; k < m_nsp; k++) {
- fluxes[n*ldf + k] -= y[k]*sum[n];
+ fluxes[n*ldf + k] -= y[k] * rhoVc[n];
}
}
}
diff --git a/Cantera/src/transport/SimpleTransport.h b/Cantera/src/transport/SimpleTransport.h
index 2d7c2734d..3c60f1b90 100644
--- a/Cantera/src/transport/SimpleTransport.h
+++ b/Cantera/src/transport/SimpleTransport.h
@@ -156,6 +156,53 @@ namespace Cantera {
* The diffusion coefficients, \f$ D_k \f$ , is calculated from a call to the mixture diffusion
* coefficient routine.
*
+ * Species Diffusive Fluxes
+ *
+ * The diffusive mass flux of species \e k is computed from the following
+ * formula
+ *
+ * Usually the specified solution average velocity is the mass averaged velocity.
+ * This is changed in some subclasses, however.
+ *
+ * \f[
+ * j_k = - c^T M_k D_k \nabla X_k - \rho Y_k V_c
+ * \f]
+ *
+ * where V_c is the correction velocity
+ *
+ * \f[
+ * \rho V_c = - \sum_j {c^T M_j D_j \nabla X_j}
+ * \f]
+ *
+ * In the above equation, \f$ D_k \f$ is the mixture diffusivity for species k calculated for the current
+ * conditions, which may depend on T, P, and X_k. \f$ C^T \f$ is the total concentration of the phase.
+ *
+ * When this is electrical migration, the formulas above are enhanced to
+ *
+ * \f[
+ * j_k = - C^T M_k D_k \nabla X_k + F C^T M_k \frac{D_k}{ R T } X_k z_k \nabla V - \rho Y_k V_c
+ * \f]
+ *
+ * where V_c is the correction velocity
+ *
+ * \f[
+ * \rho V_c = - \sum_j {c^T M_j D_j \nabla X_j} + \sum_j F C^T M_j \frac{D_j}{ R T } X_j z_j \nabla V
+ * \f]
+ *
+ *
+ * Species Diffusional Velocities
+ *
+ * Species diffusional velocities are calculated from the species diffusional fluxes, within this object,
+ * using the following formula for the diffusional velocity of the kth species, \f$ V_k^d \f$
+ *
+ * \f[
+ * j_k = \rho Y_k V_k^d
+ * \f]
+ *
+ *
+ * TODO
+ * This object has to be made compatible with different types of reference velocities. Right now, elements
+ * of the formulas are only compatible with the mass-averaged velocity.
*
* @ingroup tranprops
*
@@ -364,6 +411,69 @@ namespace Cantera {
*/
virtual void set_Grad_X(const doublereal * const grad_X);
+ //! Get the species diffusive velocities wrt to the averaged velocity,
+ //! given the gradients in mole fraction and temperature
+ /*!
+ * The average velocity can be computed on a mole-weighted
+ * or mass-weighted basis, or the diffusion velocities may
+ * be specified as relative to a specific species (i.e. a
+ * solvent) all according to the velocityBasis input parameter.
+ *
+ * Units for the returned velocities are m s-1.
+ *
+ * @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 Vdiff Output of the diffusive velocities.
+ * Flat vector with the m_nsp in the inner loop.
+ * length = ldx * ndim
+ */
+ virtual void getSpeciesVdiff(int ndim,
+ const doublereal* grad_T,
+ int ldx,
+ const doublereal* grad_X,
+ int ldf,
+ doublereal* Vdiff);
+
+ //! Get the species diffusive velocities wrt to the averaged velocity,
+ //! given the gradients in mole fraction, temperature and electrostatic potential.
+ /*!
+ * The average velocity can be computed on a mole-weighted
+ * or mass-weighted basis, or the diffusion velocities may
+ * be specified as relative to a specific species (i.e. a
+ * solvent) all according to the velocityBasis input parameter.
+ *
+ * Units for the returned velocities are m s-1.
+ *
+ * @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 grad_Phi Gradients of the electrostatic potential
+ * (length = ndim)
+ * @param Vdiff Output of the species diffusion velocities
+ * Flat vector with the m_nsp in the inner loop.
+ * length = ldx * ndim
+ */
+ virtual void getSpeciesVdiffES(int ndim, const doublereal* grad_T,
+ int ldx, const doublereal* grad_X,
+ int ldf, const doublereal* grad_Phi,
+ doublereal* Vdiff);
+
+
//! Get the species diffusive mass fluxes wrt to the specified solution averaged velocity,
//! given the gradients in mole fraction and temperature
/*!
@@ -723,6 +833,8 @@ namespace Cantera {
*/
vector_fp m_spwork;
+ vector_fp m_fluxes;
+
private:
@@ -755,6 +867,9 @@ namespace Cantera {
*/
int m_nDim;
+ //! Temporary variable that stores the rho Vc value
+ double rhoVc[3];
+
private:
//! Throw an exception if this method is invoked.