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This commit is contained in:
Harry Moffat 2010-08-20 15:40:08 +00:00
parent fc7c88ab91
commit 039b01cbe3
2 changed files with 251 additions and 70 deletions
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151
Cantera/src/transport/DustyGasTransport.cpp
View file

@ -51,8 +51,6 @@ namespace Cantera {
m_gradP(0.0),
m_knudsen_ok(false),
m_bulk_ok(false),
m_gradConc_set(false),
m_gradP_set(false),
m_porosity(0.0),
m_tortuosity(1.0),
m_pore_radius(0.0),
@ -74,8 +72,6 @@ namespace Cantera {
m_gradP(0.0),
m_knudsen_ok(false),
m_bulk_ok(false),
m_gradConc_set(false),
m_gradP_set(false),
m_porosity(0.0),
m_tortuosity(1.0),
m_pore_radius(0.0),
@ -112,8 +108,6 @@ namespace Cantera {
m_gradP = right.m_gradP;
m_knudsen_ok = right.m_knudsen_ok;
m_bulk_ok= right.m_bulk_ok;
m_gradConc_set = right.m_gradConc_set;
m_gradP_set = right.m_gradP_set;
m_porosity = right.m_porosity;
m_tortuosity = right.m_tortuosity;
m_pore_radius = right.m_pore_radius;
@ -193,18 +187,26 @@ namespace Cantera {
// set flags all false
m_knudsen_ok = false;
m_bulk_ok = false;
m_gradConc_set = false;
m_gradP_set = false;
m_spwork.resize(m_nsp);
m_spwork2.resize(m_nsp);
}
//====================================================================================================================
// Private routine to update the dusty gas binary diffusion coefficients
/*
* The dusty gas binary diffusion coefficients \f$ D^{dg}_{i,j} \f$ are evaluated from the binary
* gas-phase diffusion coefficients \f$ D^{bin}_{i,j} \f$ using the following formula
*
* \f[
* D^{dg}_{i,j} = \frac{\phi}{\tau} D^{bin}_{i,j}
* \f]
*
* where \f$ \phi \f$ is the porosity of the media and \f$ \tau \f$ is the tortuosity of the media.
*
*/
void DustyGasTransport::updateBinaryDiffCoeffs() {
if (m_bulk_ok) return;
int n,m;
// get the gaseous binary diffusion coefficients
m_gastran->getBinaryDiffCoeffs(m_nsp, m_d.ptrColumn(0));
doublereal por2tort = m_porosity / m_tortuosity;
@ -216,6 +218,15 @@ namespace Cantera {
m_bulk_ok = true;
}
//====================================================================================================================
// Private routine to update the Knudsen diffusion coefficients
/*
* The Knudsen diffusion coefficients are given by the following form
*
* \f[
* \mathcal{D}^{knud}_k = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}
* \f]
*
*/
void DustyGasTransport::updateKnudsenDiffCoeffs() {
if (m_knudsen_ok) return;
doublereal K_g = m_pore_radius * m_porosity / m_tortuosity;
@ -227,7 +238,21 @@ namespace Cantera {
m_knudsen_ok = true;
}
//====================================================================================================================
//====================================================================================================================
// Private routine to calculate the H matrix
/*
* The H matrix is the term we have given to the matrix of coefficients in the equation for the molar
* fluxes. The matrix must be inverted in order to calculate the molar fluxes.
*
* The multicomponent diffusion H matrix \f$ H_{k,l} \f$ is given by the following formulas
*
* \f[
* H_{k,l} = - \frac{X_k}{D^e_{k,l}}
* \f]
* \f[
* H_{k,k} = \frac{1}{\mathcal(D)^{e}_{k, knud}} + \sum_{j \ne k}^N{ \frac{X_j}{D^e_{k,j}} }
* \f]
*/
void DustyGasTransport::eval_H_matrix() {
updateBinaryDiffCoeffs();
updateKnudsenDiffCoeffs();
@ -258,25 +283,30 @@ namespace Cantera {
int k;
doublereal conc1, conc2;
doublereal* cbar = DATA_PTR(m_spwork);
doublereal* gradc = DATA_PTR(m_spwork2);
doublereal t1 = state1[0];
doublereal t2 = state2[0];
doublereal rho1 = state1[1];
doublereal rho2 = state2[1];
const doublereal* y1 = state1 + 2;
const doublereal* y2 = state2 + 2;
// cbar will be the average concentration between the two points
doublereal * const cbar = DATA_PTR(m_spwork);
doublereal * const gradc = DATA_PTR(m_spwork2);
const doublereal t1 = state1[0];
const doublereal t2 = state2[0];
const doublereal rho1 = state1[1];
const doublereal rho2 = state2[1];
const doublereal* const y1 = state1 + 2;
const doublereal* const y2 = state2 + 2;
doublereal c1sum = 0.0, c2sum = 0.0;
for (k = 0; k < m_nsp; k++) {
conc1 = rho1*y1[k]/m_mw[k];
conc2 = rho2*y2[k]/m_mw[k];
conc1 = rho1 * y1[k] / m_mw[k];
conc2 = rho2 * y2[k] / m_mw[k];
cbar[k] = 0.5*(conc1 + conc2);
gradc[k] = (conc2 - conc1)/delta;
gradc[k] = (conc2 - conc1) / delta;
c1sum += conc1;
c2sum += conc2;
}
doublereal p1 = c1sum * GasConstant * state1[0];
doublereal p2 = c2sum * GasConstant * state2[0];
// Calculate the pressures at p1 p2 and pbar
doublereal p1 = c1sum * GasConstant * t1;
doublereal p2 = c2sum * GasConstant * t2;
doublereal pbar = 0.5*(p1 + p2);
doublereal gradp = (p2 - p1)/delta;
doublereal tbar = 0.5*(t1 + t2);
@ -285,7 +315,9 @@ namespace Cantera {
updateMultiDiffCoeffs();
// Multiply m_multidiff and gradc together and store the result in fluxes[]
multiply(m_multidiff, gradc, fluxes);
divide_each(cbar, cbar + m_nsp, m_dk.begin());
// if no permeability has been specified, use result for
@ -302,11 +334,16 @@ namespace Cantera {
}
b *= gradp / m_gastran->viscosity();
scale(cbar, cbar + m_nsp, cbar, b);
// Multiply m_multidiff with cbar and add it to fluxes
increment(m_multidiff, cbar, fluxes);
scale(fluxes, fluxes + m_nsp, fluxes, -1.0);
}
//====================================================================================================================
// Private routine to update the Multicomponent diffusion coefficients that are used in the approximation
/*
* This routine updates the H matrix and then inverts it.
*/
void DustyGasTransport::updateMultiDiffCoeffs() {
// see if temperature has changed
updateTransport_T();
@ -370,4 +407,68 @@ namespace Cantera {
m_bulk_ok = false;
}
//====================================================================================================================
// Set the porosity (dimensionless)
/*
* @param porosity Set the value of the porosity
*/
void DustyGasTransport::setPorosity(doublereal porosity) {
m_porosity = porosity;
m_knudsen_ok = false;
m_bulk_ok = false;
}
//====================================================================================================================
// Set the tortuosity (dimensionless)
/*
* @param tort Value of the tortuosity
*/
void DustyGasTransport::setTortuosity(doublereal tort) {
m_tortuosity = tort;
m_knudsen_ok = false;
m_bulk_ok = false;
}
//====================================================================================================================
// Set the mean pore radius (m)
/*
* @param rbar Value of the pore radius ( m)
*/
void DustyGasTransport::setMeanPoreRadius(doublereal rbar) {
m_pore_radius = rbar;
m_knudsen_ok = false;
}
//====================================================================================================================
// Set the mean particle diameter
/*
* @param dbar Set the mean particle diameter (m)
*/
void DustyGasTransport::setMeanParticleDiameter(doublereal dbar) {
m_diam = dbar;
}
//====================================================================================================================
// Set the permeability of the media
/*
* If not set, the value for close-packed spheres will be used by default.
*
* The value for close-packed spheres is given below, where p is the porosity,
* t is the tortuosity, and d is the diameter of the sphere
*
* \f[
* \kappa = \frac{p^3 d^2}{72 t (1 - p)^2}
* \f]
*
* @param B set the permeability of the media (units = m^2)
*/
void DustyGasTransport::setPermeability(doublereal B) {
m_perm = B;
}
//====================================================================================================================
// Return a reference to the transport manager used to compute the gas
// binary diffusion coefficients and the visdcosity.
/*
* @return Returns a reference to the gas transport object
*/
Transport& DustyGasTransport::gasTransport() {
return *m_gastran;
}
//====================================================================================================================
}

170
Cantera/src/transport/DustyGasTransport.h
View file

@ -27,6 +27,41 @@ namespace Cantera {
/*!
* As implemented here, only species transport is handled. The viscosity, thermal conductivity, and thermal
* diffusion coefficients are not implemented.
*
* The dusty gas model includes the effects of Darcy's law. There is a net flux of species due to a pressure gradient
* that is part of Darcy's law.
*
* The dusty gas model expresses the value of the molar flux of species \f$ k \f$, \f$ J_k \f$ by the following formula.
*
* \f[
* \sum_{j \ne k}{\frac{X_j J_k - X_k J_j}{D^e_{kj}}} + \frac{J_k}{\mathcal{D}^{e}_{k,knud}} =
* - \nabla C_k - \frac{C_k}{\mathcal{D}^{e}_{k,knud}} \frac{\kappa}{\mu} \nabla p
* \f]
*
* \f$ j \f$ is a sum over all species in the gas.
*
* The effective Knudsen diffusion coefficients are given by the following form
*
* \f[
* \mathcal{D}^e_{k,knud} = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}
* \f]
*
* The effective knudsen diffusion coefficients take into account the effects of collisions of gas-phase
* molecules with the wall.
*
* References for the Dusty Gas Model
*
* (1) H. Zhu, R. J. Kee, "Modeling Electrochemical Impedance Spectra in SOFC Button Cells with
* Internal Methane Reforming," J. Electrochem. Soc., 153(9) A1765-1772 (2006).
*
* (2) H. Zhu, R. J. Kee, V. M. Janardhanan, O. Deutschmann, D. G. Goodwin, J. Electrochem. Soc., 152, A2427 (2005).
*
* (3) E. A. Mason, A. P. Malinauskas," Gas Transport in Porous Media: the Dusty-Gas Model",
* American Elsevier, New York (1983).
*
* (4) J. W. Veldsink, R. M. J. van Damme, G. F. Versteeg, W. P. M. van Swaaij,
* "The use of the dusty gas model for the description of mass transport with chemical reaction in porous media,"
* Chemical Engineering Journal, 57, 115 - 125 (1995).
*/
class DustyGasTransport : public Transport {
@ -89,14 +124,18 @@ namespace Cantera {
*/
virtual void getMultiDiffCoeffs(const int ld, doublereal* const d);
//! Get the molar fluxes [kmol/m^2/s], given the thermodynamic
//! state at two nearby points.
//! Get the molar fluxes [kmol/m^2/s], given the thermodynamic state at two nearby points.
/*!
* @param state1 Array of temperature, density, and mass
* fractions for state 1.
* @param state2 Array of temperature, density, and mass
* fractions for state 2.
* @param delta Distance from state 1 to state 2 (m).
*
* \f[
* J_k = - \sum_{j = 1, N} \left[D^{multi}_{kj}\right]^{-1} \left( \nabla C_j + \frac{C_j}{\mathcal{D}^{knud}_j} \frac{\kappa}{\mu} \nabla p \right)
* \f]
*
* @param state1 Array of temperature, density, and mass fractions for state 1.
* @param state2 Array of temperature, density, and mass fractions for state 2.
* @param delta Distance from state 1 to state 2 (m).
*
* @param fluxes Vector of species molar fluxes due to diffusional driving force
*/
virtual void getMolarFluxes(const doublereal * const state1,
const doublereal* const state2, const doublereal delta,
@ -105,30 +144,31 @@ namespace Cantera {
//-----------------------------------------------------------
// new methods added in this class
/// Set the porosity (dimensionless)
void setPorosity(doublereal porosity) {
m_porosity = porosity;
m_knudsen_ok = false;
m_bulk_ok = false;
}
//! Set the porosity (dimensionless)
/*!
* @param porosity Set the value of the porosity
*/
void setPorosity(doublereal porosity);
/// Set the tortuosity (dimensionless)
void setTortuosity(doublereal tort) {
m_tortuosity = tort;
m_knudsen_ok = false;
m_bulk_ok = false;
}
//! Set the tortuosity (dimensionless)
/*!
* Tortuosity is considered to be constant within the object
*
* @param tort Value of the tortuosity
*/
void setTortuosity(doublereal tort);
/// Set the mean pore radius (m)
void setMeanPoreRadius(doublereal rbar) {
m_pore_radius = rbar;
m_knudsen_ok = false;
}
//! Set the mean pore radius (m)
/*!
* @param rbar Value of the pore radius ( m)
*/
void setMeanPoreRadius(doublereal rbar);
/// Set the mean particle diameter
void setMeanParticleDiameter(doublereal dbar) {
m_diam = dbar;
}
//! Set the mean particle diameter
/*!
* @param dbar Set the mean particle diameter (m)
*/
void setMeanParticleDiameter(doublereal dbar);
//! Set the permeability of the media
/*!
@ -143,15 +183,18 @@ namespace Cantera {
*
* @param B set the permeability of the media (units = m^2)
*/
void setPermeability(doublereal B) {
m_perm = B;
}
void setPermeability(doublereal B);
//! Return a reference to the transport manager used to compute the gas
//! binary diffusion coefficients and the visdcosity.
Transport& gasTransport() { return *m_gastran; }
/*!
* @return Returns a reference to the gas transport object
*/
Transport& gasTransport();
//! Make the TransportFactory object a friend, because this object has restricted its
//! instantiation to classes which are friends.
friend class TransportFactory;
@ -186,9 +229,48 @@ namespace Cantera {
*/
void updateTransport_C();
//! Private routine to update the dusty gas binary diffusion coefficients
/*!
* The dusty gas binary diffusion coefficients \f$ D^{dg}_{i,j} \f$ are evaluated from the binary
* gas-phase diffusion coefficients \f$ D^{bin}_{i,j} \f$ using the following formula
*
* \f[
* D^{dg}_{i,j} = \frac{\phi}{\tau} D^{bin}_{i,j}
* \f]
*
* where \f$ \phi \f$ is the porosity of the media and \f$ \tau \f$ is the tortuosity of the media.
*
*/
void updateBinaryDiffCoeffs();
//! Private routine to update the Multicomponent diffusion coefficients that are used in the approximation
/*!
* This routine updates the H matrix and then inverts it.
*/
void updateMultiDiffCoeffs();
//! Private routine to update the Knudsen diffusion coefficients
/*!
* The Knudsen diffusion coefficients are given by the following form
*
* \f[
* \mathcal{D}^{knud}_k = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}
* \f]
*
*/
void updateKnudsenDiffCoeffs();
//! Private routine to calculate the H matrix
/*!
* The multicomponent diffusion H matrix \f$ H_{k,l} \f$ is given by the following form
*
* \f[
* H_{k,l} = - \frac{X_k}{D_{k,l}}
* \f]
* \f[
* H_{k,k} = \frac{1}{\mathcal(D)^{knud}_{k}} + \sum_{j \ne k}^N{ \frac{X_j}{D_{k,j}} }
* \f]
*/
void eval_H_matrix();
@ -203,10 +285,10 @@ namespace Cantera {
vector_fp m_mw;
//! binary diffusion coefficients
DenseMatrix m_d;
DenseMatrix m_d;
//! mole fractions
vector_fp m_x;
vector_fp m_x;
//! Knudsen diffusion coefficients
/*!
@ -217,10 +299,10 @@ namespace Cantera {
* \f]
*
*/
vector_fp m_dk;
vector_fp m_dk;
//! temperature
doublereal m_temp;
doublereal m_temp;
//! Multicomponent diffusion coefficients
/*!
@ -233,14 +315,13 @@ namespace Cantera {
* H_{k,k} = \frac{1}{\mathcal(D)^{knud}_{k}} + \sum_{j \ne k}^N{ \frac{X_j}{D_{k,j}} }
* \f]
*/
DenseMatrix m_multidiff;
DenseMatrix m_multidiff;
//! work space of size m_nsp;
vector_fp m_spwork;
//! work space of size m_nsp;
vector_fp m_spwork2;
//! Pressure Gradient
doublereal m_gradP;
@ -248,19 +329,17 @@ namespace Cantera {
//! Update-to-date variable for Knudsen diffusion coefficients
bool m_knudsen_ok;
//! Update-to-date variable for Binary diffusion coefficients
//! Update-to-date variable for Binary diffusion coefficients
bool m_bulk_ok;
bool m_gradConc_set;
bool m_gradP_set;
//! Porosity
doublereal m_porosity;
//! Tortuosity
doublereal m_tortuosity;
doublereal m_pore_radius; /// pore radius (m)
//! Pore radius (meter)
doublereal m_pore_radius;
//! Particle diameter
/*!
@ -285,7 +364,8 @@ namespace Cantera {
*/
doublereal m_perm;
Transport* m_gastran; /// pointer to gas transport manager
//! Pointer to the transport object for the gas phase
Transport* m_gastran;
};
}