Cantera  2.0
DustyGasTransport Class Reference

Class DustyGasTransport implements the Dusty Gas model for transport in porous media. More...

#include <DustyGasTransport.h>

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## Public Member Functions

DustyGasTransport (thermo_t *thermo=0)
default constructor

DustyGasTransport (const DustyGasTransport &right)
Copy Constructor for the DustyGasTransport object.

DustyGasTransportoperator= (const DustyGasTransport &right)
Assignment operator.

virtual ~DustyGasTransport ()
Destructor.

virtual TransportduplMyselfAsTransport () const
Duplication routine for objects which inherit from Transport.

virtual int model () const
Transport model.

virtual void setParameters (const int type, const int k, const doublereal *const p)
Set the Parameters in the model.

virtual void getMultiDiffCoeffs (const size_t ld, doublereal *const d)
Return the Multicomponent diffusion coefficients. Units: [m^2/s].

virtual void getMolarFluxes (const doublereal *const state1, const doublereal *const state2, const doublereal delta, doublereal *const fluxes)
Get the molar fluxes [kmol/m^2/s], given the thermodynamic state at two nearby points.

void setPorosity (doublereal porosity)
Set the porosity (dimensionless)

void setTortuosity (doublereal tort)
Set the tortuosity (dimensionless)

Set the mean pore radius (m)

void setMeanParticleDiameter (doublereal dbar)
Set the mean particle diameter.

void setPermeability (doublereal B)
Set the permeability of the media.

TransportgasTransport ()
Return a reference to the transport manager used to compute the gas binary diffusion coefficients and the viscosity.

thermo_tthermo ()
Phase object.

Returns true if the transport manager is ready for use.

void setNDim (const int ndim)
Set the number of dimensions to be expected in flux expressions.

size_t nDim () const
Return the number of dimensions in flux expressions.

void checkSpeciesIndex (size_t k) const
Check that the specified species index is in range Throws an exception if k is greater than nSpecies()

void checkSpeciesArraySize (size_t kk) const
Check that an array size is at least nSpecies() Throws an exception if kk is less than nSpecies().

virtual doublereal getElectricConduct ()
Compute the mixture electrical conductivity (S m-1) at the current conditions of the phase (Siemens m-1)

virtual void getElectricCurrent (int ndim, const doublereal *grad_T, int ldx, const doublereal *grad_X, int ldf, const doublereal *grad_V, doublereal *current)
Compute the electric current density in A/m^2.

virtual void getSpeciesFluxes (size_t ndim, const doublereal *const grad_T, size_t ldx, const doublereal *const grad_X, size_t ldf, doublereal *const fluxes)
Get the species diffusive mass fluxes wrt to the specified solution averaged velocity, given the gradients in mole fraction and temperature.

virtual void getSpeciesFluxesES (size_t ndim, const doublereal *grad_T, size_t ldx, const doublereal *grad_X, size_t ldf, const doublereal *grad_Phi, doublereal *fluxes)
Get the species diffusive mass fluxes wrt to the mass averaged velocity, given the gradients in mole fraction, temperature and electrostatic potential.

virtual void getSpeciesVdiff (size_t ndim, const doublereal *grad_T, int ldx, const doublereal *grad_X, int ldf, doublereal *Vdiff)
Get the species diffusive velocities wrt to the mass averaged velocity, given the gradients in mole fraction and temperature.

virtual void getSpeciesVdiffES (size_t ndim, const doublereal *grad_T, int ldx, const doublereal *grad_X, int ldf, const doublereal *grad_Phi, doublereal *Vdiff)
Get the species diffusive velocities wrt to the mass averaged velocity, given the gradients in mole fraction, temperature, and electrostatic potential.

virtual void getMassFluxes (const doublereal *state1, const doublereal *state2, doublereal delta, doublereal *mfluxes)
Get the mass fluxes [kg/m^2/s], given the thermodynamic state at two nearby points.

virtual void getThermalDiffCoeffs (doublereal *const dt)
Return a vector of Thermal diffusion coefficients [kg/m/sec].

virtual void getBinaryDiffCoeffs (const size_t ld, doublereal *const d)
Returns the matrix of binary diffusion coefficients [m^2/s].

virtual void getMixDiffCoeffs (doublereal *const d)
Returns a vector of mixture averaged diffusion coefficients.

virtual void getMixDiffCoeffsMole (doublereal *const d)
Returns a vector of mixture averaged diffusion coefficients.

virtual void getMixDiffCoeffsMass (doublereal *const d)
Returns a vector of mixture averaged diffusion coefficients.

void setVelocityBasis (VelocityBasis ivb)
Sets the velocity basis.

VelocityBasis getVelocityBasis () const
Gets the velocity basis.

Transport Properties
virtual doublereal viscosity ()
The viscosity in Pa-s.

virtual void getSpeciesViscosities (doublereal *const visc)
Returns the pure species viscosities.

virtual doublereal bulkViscosity ()
The bulk viscosity in Pa-s.

virtual doublereal ionConductivity ()
The ionic conductivity in 1/ohm/m.

virtual void getSpeciesIonConductivity (doublereal *const ionCond)
Returns the pure species ionic conductivity.

virtual void mobilityRatio (double *mobRat)
Returns the pointer to the mobility ratios of the species in the phase.

virtual void getSpeciesMobilityRatio (double **mobRat)
Returns the pure species limit of the mobility ratios.

virtual void selfDiffusion (doublereal *const selfDiff)
Returns the self diffusion coefficients of the species in the phase.

virtual void getSpeciesSelfDiffusion (double **selfDiff)
Returns the pure species self diffusion in solution of each species.

virtual doublereal thermalConductivity ()
Returns the mixture thermal conductivity in W/m/K.

virtual doublereal electricalConductivity ()
The electrical conductivity (Siemens/m).

virtual void getMobilities (doublereal *const mobil_e)
Get the Electrical mobilities (m^2/V/s).

virtual void getFluidMobilities (doublereal *const mobil_f)
Get the fluid mobilities (s kmol/kg).

## Protected Member Functions

void initialize (ThermoPhase *phase, Transport *gastr)
Initialization routine called by TransportFactory.

Transport manager construction

These methods are used internally during construction.

virtual bool initGas (GasTransportParams &tr)
Called by TransportFactory to set parameters.

virtual bool initLiquid (LiquidTransportParams &tr)
Called by TransportFactory to set parameters.

void setThermo (thermo_t &thermo)
Specifies the ThermPhase object.

void finalize ()
Enable the transport object for use.

## Protected Attributes

thermo_tm_thermo
pointer to the object representing the phase

true if finalize has been called

size_t m_nsp
Number of species.

size_t m_nDim
Number of dimensions used in flux expressions.

int m_velocityBasis
Velocity basis from which diffusion velocities are computed.

## Private Member Functions

void updateTransport_T ()
Update temperature-dependent quantities within the object.

void updateTransport_C ()
Update concentration-dependent quantities within the object.

void updateBinaryDiffCoeffs ()
Private routine to update the dusty gas binary diffusion coefficients.

void updateMultiDiffCoeffs ()
Private routine to update the Multicomponent diffusion coefficients that are used in the approximation.

void updateKnudsenDiffCoeffs ()
Private routine to update the Knudsen diffusion coefficients.

void eval_H_matrix ()
Private routine to calculate the H matrix.

## Private Attributes

vector_fp m_mw
Local copy of the species molecular weights.

DenseMatrix m_d
binary diffusion coefficients

vector_fp m_x
mole fractions

vector_fp m_dk
Knudsen diffusion coefficients.

doublereal m_temp
temperature

DenseMatrix m_multidiff
Multicomponent diffusion coefficients.

vector_fp m_spwork
work space of size m_nsp;

vector_fp m_spwork2
work space of size m_nsp;

bool m_knudsen_ok
Update-to-date variable for Knudsen diffusion coefficients.

bool m_bulk_ok
Update-to-date variable for Binary diffusion coefficients.

doublereal m_porosity
Porosity.

doublereal m_tortuosity
Tortuosity.

doublereal m_diam
Particle diameter.

doublereal m_perm
Permeability of the media.

Transportm_gastran
Pointer to the transport object for the gas phase.

## Friends

class TransportFactory
Make the TransportFactory object a friend, because this object has restricted its instantiation to classes which are friends.

## Detailed Description

Class DustyGasTransport implements the Dusty Gas model for transport in porous media.

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 $$k$$, $$J_k$$ by the following formula.

$\sum_{j \ne k}{\frac{X_j J_k - X_k J_j}{D^e_{kj}}} + \frac{J_k}{\mathcal{D}^{e}_{k,knud}} = - \nabla C_k - \frac{C_k}{\mathcal{D}^{e}_{k,knud}} \frac{\kappa}{\mu} \nabla p$

$$j$$ is a sum over all species in the gas.

The effective Knudsen diffusion coefficients are given by the following form

$\mathcal{D}^e_{k,knud} = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}$

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).

Definition at line 62 of file DustyGasTransport.h.

## Constructor & Destructor Documentation

 DustyGasTransport ( thermo_t * thermo = 0 )

default constructor

Parameters
 thermo Pointer to the ThermoPhase object for this phase. Defaults to zero.

Definition at line 29 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::duplMyselfAsTransport().

 DustyGasTransport ( const DustyGasTransport & right )

Copy Constructor for the DustyGasTransport object.

Parameters
 right LiquidTransport to be copied

Definition at line 49 of file DustyGasTransport.cpp.

 ~DustyGasTransport ( )
virtual

Destructor.

Definition at line 112 of file DustyGasTransport.cpp.

References DustyGasTransport::m_gastran.

## Member Function Documentation

 DustyGasTransport & operator= ( const DustyGasTransport & right )

Assignment operator.

Warning -> Shallow pointer copies are made of m_thermo and m_gastran.. gastran may not point to the correct object after this copy. The routine initialize() must be called after this routine to complete the copy.

Parameters
 right Reference to DustyGasTransport object to be copied into the current one.

Definition at line 77 of file DustyGasTransport.cpp.

 Transport * duplMyselfAsTransport ( ) const
virtual

Duplication routine for objects which inherit from Transport.

This virtual routine can be used to duplicate Transport objects inherited from Transport even if the application only has a pointer to Transport to work with.

These routines are basically wrappers around the derived copy constructor.

Reimplemented from Transport.

Definition at line 126 of file DustyGasTransport.cpp.

References DustyGasTransport::DustyGasTransport().

Referenced by DustyGasTransport::operator=().

 virtual int model ( ) const
inlinevirtual

Transport model.

The transport model is the set of equations used to compute the transport properties. This virtual method returns an integer flag that identifies the transport model implemented. The base class returns 0.

Reimplemented from Transport.

Definition at line 108 of file DustyGasTransport.h.

 void setParameters ( const int type, const int k, const doublereal *const p )
virtual

Set the Parameters in the model.

Parameters
 type Type of the parameter to set 0 - porosity 1 - tortuosity 2 - mean pore radius 3 - mean particle radius 4 - permeability k Unused int p pointer to double for the input list of parameters

Reimplemented from Transport.

Definition at line 144 of file DustyGasTransport.cpp.

 void getMultiDiffCoeffs ( const size_t ld, doublereal *const d )
virtual

Return the Multicomponent diffusion coefficients. Units: [m^2/s].

Returns the array of multicomponent diffusion coefficients.

Parameters
 ld The dimension of the inner loop of d (usually equal to m_nsp) d flat vector of diffusion coefficients, fortran ordering. d[ld*j+i] is the D_ij diffusion coefficient (the diffusion coefficient for species i due to species j).

Reimplemented from Transport.

Definition at line 394 of file DustyGasTransport.cpp.

 void getMolarFluxes ( const doublereal *const state1, const doublereal *const state2, const doublereal delta, doublereal *const fluxes )
virtual

Get the molar fluxes [kmol/m^2/s], given the thermodynamic state at two nearby points.

$J_k = - \sum_{j = 1, N} \left[D^{multi}_{kj}\right]^{-1} \left( \nabla C_j + \frac{C_j}{\mathcal{D}^{knud}_j} \frac{\kappa}{\mu} \nabla p \right)$

Parameters
 state1 Array of temperature, density, and mass fractions for state 1. state2 Array of temperature, density, and mass fractions for state 2. delta Distance from state 1 to state 2 (m). fluxes Vector of species molar fluxes due to diffusional driving force

Reimplemented from Transport.

Definition at line 299 of file DustyGasTransport.cpp.

 void setPorosity ( doublereal porosity )

Set the porosity (dimensionless)

Parameters
 porosity Set the value of the porosity

Definition at line 436 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::setParameters().

 void setTortuosity ( doublereal tort )

Set the tortuosity (dimensionless)

Tortuosity is considered to be constant within the object

Parameters
 tort Value of the tortuosity

Definition at line 447 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::setParameters().

 void setMeanPoreRadius ( doublereal rbar )

Set the mean pore radius (m)

Parameters
 rbar Value of the pore radius ( m)

Definition at line 458 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::setParameters().

 void setMeanParticleDiameter ( doublereal dbar )

Set the mean particle diameter.

Parameters
 dbar Set the mean particle diameter (m)

Definition at line 468 of file DustyGasTransport.cpp.

References DustyGasTransport::m_diam.

Referenced by DustyGasTransport::setParameters().

 void setPermeability ( doublereal B )

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

$\kappa = \frac{p^3 d^2}{72 t (1 - p)^2}$

Parameters
 B set the permeability of the media (units = m^2)

Definition at line 486 of file DustyGasTransport.cpp.

References DustyGasTransport::m_perm.

Referenced by DustyGasTransport::setParameters().

 Transport & gasTransport ( )

Return a reference to the transport manager used to compute the gas binary diffusion coefficients and the viscosity.

Returns
Returns a reference to the gas transport object

Definition at line 496 of file DustyGasTransport.cpp.

References DustyGasTransport::m_gastran.

 void initialize ( ThermoPhase * phase, Transport * gastr )
protected

Initialization routine called by TransportFactory.

The DustyGas model is a subordinate model to the gas phase transport model. Here we set the gas phase models.

This is a protected routine, so that initialization of the Model must occur within Cantera's setup

Parameters
 phase Pointer to the underlying ThermoPhase model for the gas phase gastr Pointer to the underlying Transport model for transport in the gas phase.

Definition at line 177 of file DustyGasTransport.cpp.

Referenced by TransportFactory::newTransport().

 void updateTransport_T ( )
private

Update temperature-dependent quantities within the object.

The object keeps a value m_temp, which is the temperature at which quantities were last evaluated at. If the temperature is changed, update Booleans are set false, triggering recomputation.

Definition at line 409 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::updateMultiDiffCoeffs().

 void updateTransport_C ( )
private

Update concentration-dependent quantities within the object.

The object keeps a value m_temp, which is the temperature at which quantities were last evaluated at. If the temperature is changed, update Booleans are set false, triggering recomputation.

Definition at line 419 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::updateMultiDiffCoeffs().

 void updateBinaryDiffCoeffs ( )
private

Private routine to update the dusty gas binary diffusion coefficients.

The dusty gas binary diffusion coefficients $$D^{dg}_{i,j}$$ are evaluated from the binary gas-phase diffusion coefficients $$D^{bin}_{i,j}$$ using the following formula

$D^{dg}_{i,j} = \frac{\phi}{\tau} D^{bin}_{i,j}$

where $$\phi$$ is the porosity of the media and $$\tau$$ is the tortuosity of the media.

Definition at line 221 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::eval_H_matrix().

 void updateMultiDiffCoeffs ( )
private

Private routine to update the Multicomponent diffusion coefficients that are used in the approximation.

This routine updates the H matrix and then inverts it.

Definition at line 366 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::getMolarFluxes(), and DustyGasTransport::getMultiDiffCoeffs().

 void updateKnudsenDiffCoeffs ( )
private

Private routine to update the Knudsen diffusion coefficients.

The Knudsen diffusion coefficients are given by the following form

$\mathcal{D}^{knud}_k = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}$

Definition at line 247 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::eval_H_matrix().

 void eval_H_matrix ( )
private

Private routine to calculate the H matrix.

The multicomponent diffusion H matrix $$H_{k,l}$$ is given by the following form

$H_{k,l} = - \frac{X_k}{D_{k,l}}$

$H_{k,k} = \frac{1}{\mathcal(D)^{knud}_{k}} + \sum_{j \ne k}^N{ \frac{X_j}{D_{k,j}} }$

Definition at line 276 of file DustyGasTransport.cpp.

Referenced by DustyGasTransport::updateMultiDiffCoeffs().

 thermo_t& thermo ( )
inlineinherited

Phase object.

Every transport manager is designed to compute properties for a specific phase of a mixture, which might be a liquid solution, a gas mixture, a surface, etc. This method returns a reference to the object representing the phase itself.

Definition at line 239 of file TransportBase.h.

References Transport::m_thermo.

Referenced by Transport::setThermo().

inherited

Returns true if the transport manager is ready for use.

Definition at line 75 of file TransportBase.cpp.

Referenced by Transport::finalize(), and Transport::setThermo().

 void setNDim ( const int ndim )
inherited

Set the number of dimensions to be expected in flux expressions.

Internal memory will be set with this value.

Parameters
 ndim Number of dimensions in flux expressions

Definition at line 83 of file TransportBase.cpp.

References Transport::m_nDim.

 size_t nDim ( ) const
inlineinherited

Return the number of dimensions in flux expressions.

Returns
Returns the number of dimensions

Definition at line 261 of file TransportBase.h.

References Transport::m_nDim.

 void checkSpeciesIndex ( size_t k ) const
inherited

Check that the specified species index is in range Throws an exception if k is greater than nSpecies()

Definition at line 88 of file TransportBase.cpp.

References Transport::m_nsp.

 void checkSpeciesArraySize ( size_t kk ) const
inherited

Check that an array size is at least nSpecies() Throws an exception if kk is less than nSpecies().

Used before calls which take an array pointer.

Definition at line 95 of file TransportBase.cpp.

References Transport::m_nsp.

 virtual doublereal viscosity ( )
inlinevirtualinherited

The viscosity in Pa-s.

Reimplemented in SimpleTransport, LiquidTransport, AqueousTransport, WaterTransport, FtnTransport, and GasTransport.

Definition at line 283 of file TransportBase.h.

References Transport::err().

Referenced by DustyGasTransport::getMolarFluxes(), and StFlow::updateTransport().

 virtual void getSpeciesViscosities ( doublereal *const visc )
inlinevirtualinherited

Returns the pure species viscosities.

The units are Pa-s and the length is the number of species

Parameters
 visc Vector of viscosities

Reimplemented in SimpleTransport, LiquidTransport, AqueousTransport, and GasTransport.

Definition at line 293 of file TransportBase.h.

References Transport::err().

 virtual doublereal bulkViscosity ( )
inlinevirtualinherited

The bulk viscosity in Pa-s.

The bulk viscosity is only non-zero in rare cases. Most transport managers either overload this method to return zero, or do not implement it, in which case an exception is thrown if called.

Reimplemented in WaterTransport, and FtnTransport.

Definition at line 303 of file TransportBase.h.

References Transport::err().

 virtual doublereal ionConductivity ( )
inlinevirtualinherited

The ionic conductivity in 1/ohm/m.

Reimplemented in LiquidTransport.

Definition at line 310 of file TransportBase.h.

References Transport::err().

 virtual void getSpeciesIonConductivity ( doublereal *const ionCond )
inlinevirtualinherited

Returns the pure species ionic conductivity.

The units are 1/ohm/m and the length is the number of species

Parameters
 ionCond Vector of ionic conductivities

Reimplemented in LiquidTransport.

Definition at line 320 of file TransportBase.h.

References Transport::err().

 virtual void mobilityRatio ( double * mobRat )
inlinevirtualinherited

Returns the pointer to the mobility ratios of the species in the phase.

Parameters
 mobRat Returns a matrix of mobility ratios for the current problem. The mobility ratio mobRat(i,j) is defined as the ratio of the mobility of species i to species j.

mobRat(i,j) = mu_i / mu_j

It is returned in fortran-ordering format. ie. it is returned as mobRat[k], where

k = j * nsp + i


The size of mobRat must be at least equal to nsp*nsp

Deprecated:
This doesn't seem to be the essential input; it should just be the mobility.

Reimplemented in LiquidTransport.

Definition at line 342 of file TransportBase.h.

References Transport::err().

 virtual void getSpeciesMobilityRatio ( double ** mobRat )
inlinevirtualinherited

Returns the pure species limit of the mobility ratios.

The value is dimensionless and the length is the number of species

Parameters
 mobRat Vector of mobility ratios

Reimplemented in LiquidTransport.

Definition at line 352 of file TransportBase.h.

References Transport::err().

 virtual void selfDiffusion ( doublereal *const selfDiff )
inlinevirtualinherited

Returns the self diffusion coefficients of the species in the phase.

The self diffusion coefficient is the diffusion coefficient of a tracer species at the current temperature and composition of the species. Therefore, the dilute limit of transport is assumed for the tracer species. The effective formula may be calculated from the stefan-maxwell formulation by adding another row for the tracer species, assigning all D's to be equal to the respective species D's, and then taking the limit as the tracer species mole fraction goes to zero. The corresponding flux equation for the tracer species k in units of kmol m-2 s-1 is.

$J_k = - D^{sd}_k \frac{C_k}{R T} \nabla \mu_k$

The derivative is taken at constant T and P.

The self diffusion calculation is handled by subclasses of LiquidTranInteraction as specified in the input file. These in turn employ subclasses of LTPspecies to determine the individual species self diffusion coeffs.

Parameters
 selfDiff Vector of self-diffusion coefficients Length = number of species in phase units = m**2 s-1

Reimplemented in LiquidTransport.

Definition at line 382 of file TransportBase.h.

References Transport::err().

 virtual void getSpeciesSelfDiffusion ( double ** selfDiff )
inlinevirtualinherited

Returns the pure species self diffusion in solution of each species.

The pure species molar volumes are evaluated using the appropriate subclasses of LTPspecies as specified in the input file.

Parameters
 selfDiff array of length "number of species" to hold returned self diffusion coeffs.

Reimplemented in LiquidTransport.

Definition at line 396 of file TransportBase.h.

References Transport::err().

 virtual doublereal thermalConductivity ( )
inlinevirtualinherited

Returns the mixture thermal conductivity in W/m/K.

Units are in W / m K or equivalently kg m / s3 K

Returns
returns thermal conductivity in W/m/K.

Reimplemented in SimpleTransport, LiquidTransport, AqueousTransport, MixTransport, WaterTransport, MultiTransport, FtnTransport, and SolidTransport.

Definition at line 406 of file TransportBase.h.

References Transport::err().

Referenced by StFlow::updateTransport().

 virtual doublereal electricalConductivity ( )
inlinevirtualinherited

The electrical conductivity (Siemens/m).

Reimplemented in SolidTransport, and FtnTransport.

Definition at line 413 of file TransportBase.h.

References Transport::err().

 virtual void getMobilities ( doublereal *const mobil_e )
inlinevirtualinherited

Get the Electrical mobilities (m^2/V/s).

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

$\mu^e_k = \frac{F D_k}{R T}$

Parameters
 mobil_e Returns the mobilities of the species in array mobil_e. The array must be dimensioned at least as large as the number of species.

Reimplemented in LiquidTransport, SimpleTransport, AqueousTransport, MixTransport, FtnTransport, and SolidTransport.

Definition at line 435 of file TransportBase.h.

References Transport::err().

 virtual void getFluidMobilities ( doublereal *const mobil_f )
inlinevirtualinherited

Get the fluid mobilities (s kmol/kg).

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

$\mu^f_k = \frac{D_k}{R T}$

Parameters
 mobil_f Returns the mobilities of the species in array mobil. The array must be dimensioned at least as large as the number of species.

Reimplemented in LiquidTransport, SimpleTransport, and AqueousTransport.

Definition at line 457 of file TransportBase.h.

References Transport::err().

 virtual doublereal getElectricConduct ( )
inlinevirtualinherited

Compute the mixture electrical conductivity (S m-1) at the current conditions of the phase (Siemens m-1)

The electrical conductivity, $$\sigma$$, relates the electric current density, J, to the electric field, E.

$\vec{J} = \sigma \vec{E}$

We assume here that the mixture electrical conductivity is an isotropic quantity, at this stage. Tensors may be included at a later time.

The conductivity is the reciprocal of the resistivity.

The units are Siemens m-1, where 1 S = 1 A / volt = 1 s^3 A^2 /kg /m^2

Reimplemented in LiquidTransport.

Definition at line 482 of file TransportBase.h.

References Transport::err().

 virtual void getElectricCurrent ( int ndim, const doublereal * grad_T, int ldx, const doublereal * grad_X, int ldf, const doublereal * grad_V, doublereal * current )
inlinevirtualinherited

Compute the electric current density in A/m^2.

Calculates the electric current density as a vector, given the gradients of the field variables.

Parameters
 ndim The number of spatial dimensions (1, 2, or 3). grad_T The temperature gradient (ignored in this model). ldx Leading dimension of the grad_X array. grad_X The gradient of the mole fraction ldf Leading dimension of the grad_V and current vectors. grad_V The electrostatic potential gradient. current The electric current in A/m^2. This is a vector of length ndim

Reimplemented in LiquidTransport.

Definition at line 500 of file TransportBase.h.

References Transport::err().

 void getSpeciesFluxes ( size_t ndim, const doublereal *const grad_T, size_t ldx, const doublereal *const grad_X, size_t ldf, doublereal *const fluxes )
virtualinherited

Get the species diffusive mass fluxes wrt to the specified solution averaged velocity, given the gradients in mole fraction and temperature.

Units for the returned fluxes are kg m-2 s-1.

Usually the specified solution average velocity is the mass averaged velocity. This is changed in some subclasses, however.

Parameters
 ndim Number of dimensions in the flux expressions grad_T Gradient of the temperature (length = ndim) ldx Leading dimension of the grad_X array (usually equal to m_nsp but not always) grad_X Gradients of the mole fraction Flat vector with the m_nsp in the inner loop. length = ldx * ndim ldf Leading dimension of the fluxes array (usually equal to m_nsp but not always) fluxes Output of the diffusive mass fluxes Flat vector with the m_nsp in the inner loop. length = ldx * ndim

Reimplemented in LiquidTransport, SimpleTransport, AqueousTransport, MixTransport, and MultiTransport.

Definition at line 146 of file TransportBase.cpp.

References Transport::err().

Referenced by Transport::getSpeciesFluxesES().

 virtual void getSpeciesFluxesES ( size_t ndim, const doublereal * grad_T, size_t ldx, const doublereal * grad_X, size_t ldf, const doublereal * grad_Phi, doublereal * fluxes )
inlinevirtualinherited

Get the species diffusive mass fluxes wrt to the mass averaged velocity, given the gradients in mole fraction, temperature and electrostatic potential.

Units for the returned fluxes are kg m-2 s-1.

Parameters
 ndim Number of dimensions in the flux expressions grad_T Gradient of the temperature (length = ndim) ldx Leading dimension of the grad_X array (usually equal to m_nsp but not always) grad_X Gradients of the mole fraction Flat vector with the m_nsp in the inner loop. length = ldx * ndim ldf Leading dimension of the fluxes array (usually equal to m_nsp but not always) grad_Phi Gradients of the electrostatic potential (length = ndim) fluxes Output of the diffusive mass fluxes Flat vector with the m_nsp in the inner loop. length = ldx * ndim

Definition at line 560 of file TransportBase.h.

References Transport::getSpeciesFluxes().

 virtual void getSpeciesVdiff ( size_t ndim, const doublereal * grad_T, int ldx, const doublereal * grad_X, int ldf, doublereal * Vdiff )
inlinevirtualinherited

Get the species diffusive velocities wrt to the mass averaged velocity, given the gradients in mole fraction and temperature.

Units for the returned velocities are m s-1

Parameters
 ndim Number of dimensions in the flux expressions grad_T Gradient of the temperature (length = ndim) ldx Leading dimension of the grad_X array (usually equal to m_nsp but not always) grad_X Gradients of the mole fraction Flat vector with the m_nsp in the inner loop. length = ldx * ndim ldf Leading dimension of the fluxes array (usually equal to m_nsp but not always) Vdiff Output of the diffusive velocities wrt the mass-averaged velocity Flat vector with the m_nsp in the inner loop. length = ldx * ndim units are m / s.

Reimplemented in LiquidTransport, and SimpleTransport.

Definition at line 593 of file TransportBase.h.

References Transport::err().

Referenced by Transport::getSpeciesVdiffES().

 virtual void getSpeciesVdiffES ( size_t ndim, const doublereal * grad_T, int ldx, const doublereal * grad_X, int ldf, const doublereal * grad_Phi, doublereal * Vdiff )
inlinevirtualinherited

Get the species diffusive velocities wrt to the mass averaged velocity, given the gradients in mole fraction, temperature, and electrostatic potential.

Units for the returned velocities are m s-1.

Parameters
 ndim Number of dimensions in the flux expressions grad_T Gradient of the temperature (length = ndim) ldx Leading dimension of the grad_X array (usually equal to m_nsp but not always) grad_X Gradients of the mole fraction Flat vector with the m_nsp in the inner loop. length = ldx * ndim ldf Leading dimension of the fluxes array (usually equal to m_nsp but not always) grad_Phi Gradients of the electrostatic potential (length = ndim) Vdiff Output of the diffusive velocities wrt the mass-averaged velocity Flat vector with the m_nsp in the inner loop. length = ldx * ndim units are m / s.

Reimplemented in LiquidTransport, and SimpleTransport.

Definition at line 625 of file TransportBase.h.

References Transport::getSpeciesVdiff().

 virtual void getMassFluxes ( const doublereal * state1, const doublereal * state2, doublereal delta, doublereal * mfluxes )
inlinevirtualinherited

Get the mass fluxes [kg/m^2/s], given the thermodynamic state at two nearby points.

Parameters
 state1 Array of temperature, density, and mass fractions for state 1. state2 Array of temperature, density, and mass fractions for state 2. delta Distance from state 1 to state 2 (m). mfluxes Output array containing the diffusive mass fluxes of species from state1 to state2. This is a flat vector with the m_nsp in the inner loop. length = ldx * ndim. Units are [kg/m^2/s].

Reimplemented in MultiTransport.

Definition at line 671 of file TransportBase.h.

References Transport::err().

 virtual void getThermalDiffCoeffs ( doublereal *const dt )
inlinevirtualinherited

Return a vector of Thermal diffusion coefficients [kg/m/sec].

The thermal diffusion coefficient $$D^T_k$$ is defined so that the diffusive mass flux of species k induced by the local temperature gradient is given by the following formula

$M_k J_k = -D^T_k \nabla \ln T.$

The thermal diffusion coefficient can be either positive or negative.

Parameters
 dt On return, dt will contain the species thermal diffusion coefficients. Dimension dt at least as large as the number of species. Units are kg/m/s.

Reimplemented in LiquidTransport, SimpleTransport, AqueousTransport, MixTransport, MultiTransport, and FtnTransport.

Definition at line 693 of file TransportBase.h.

References Transport::err().

Referenced by StFlow::updateTransport().

 virtual void getBinaryDiffCoeffs ( const size_t ld, doublereal *const d )
inlinevirtualinherited

Returns the matrix of binary diffusion coefficients [m^2/s].

Parameters
 ld Inner stride for writing the two dimension diffusion coefficients into a one dimensional vector d Diffusion coefficient matrix (must be at least m_k * m_k in length.

Reimplemented in SimpleTransport, LiquidTransport, AqueousTransport, and GasTransport.

Definition at line 705 of file TransportBase.h.

References Transport::err().

Referenced by DustyGasTransport::updateBinaryDiffCoeffs().

 virtual void getMixDiffCoeffs ( doublereal *const d )
inlinevirtualinherited

Returns a vector of mixture averaged diffusion coefficients.

Mixture-averaged diffusion coefficients [m^2/s]. If the

transport manager implements a mixture-averaged diffusion model, then this method returns the array of mixture-averaged diffusion coefficients. Otherwise it throws an exception.

Parameters
 d Return vector of mixture averaged diffusion coefficients Units = m2/s. Length = n_sp

Reimplemented in LiquidTransport, SimpleTransport, AqueousTransport, FtnTransport, GasTransport, and SolidTransport.

Definition at line 738 of file TransportBase.h.

References Transport::err().

Referenced by StFlow::updateTransport().

 virtual void getMixDiffCoeffsMole ( doublereal *const d )
inlinevirtualinherited

Returns a vector of mixture averaged diffusion coefficients.

Reimplemented in GasTransport.

Definition at line 744 of file TransportBase.h.

References Transport::err().

 virtual void getMixDiffCoeffsMass ( doublereal *const d )
inlinevirtualinherited

Returns a vector of mixture averaged diffusion coefficients.

Reimplemented in GasTransport.

Definition at line 749 of file TransportBase.h.

References Transport::err().

 void setVelocityBasis ( VelocityBasis ivb )
inlineinherited

Sets the velocity basis.

What the transport object does with this parameter is up to the individual operator. Currently, this is not functional for most transport operators including all of the gas-phase operators.

Parameters
 ivb Species the velocity basis

Definition at line 777 of file TransportBase.h.

References Transport::m_velocityBasis.

 VelocityBasis getVelocityBasis ( ) const
inlineinherited

Gets the velocity basis.

What the transport object does with this parameter is up to the individual operator. Currently, this is not functional for most transport operators including all of the gas-phase operators.

Returns
Returns the velocity basis

Definition at line 789 of file TransportBase.h.

References Transport::m_velocityBasis.

 virtual bool initGas ( GasTransportParams & tr )
inlineprotectedvirtualinherited

Called by TransportFactory to set parameters.

Called by TransportFactory to set parameters.

This is called by classes that use the gas phase parameter list to initialize themselves.

Parameters
 tr Reference to the parameter list that will be used to initialize the class

Reimplemented in MixTransport, MultiTransport, and GasTransport.

Definition at line 819 of file TransportBase.h.

References Transport::err().

Referenced by TransportFactory::initTransport().

 virtual bool initLiquid ( LiquidTransportParams & tr )
inlineprotectedvirtualinherited

Called by TransportFactory to set parameters.

This is called by classes that use the liquid phase parameter list to initialize themselves.

Parameters
 tr Reference to the parameter list that will be used to initialize the class

Reimplemented in AqueousTransport, SimpleTransport, and LiquidTransport.

Definition at line 832 of file TransportBase.h.

References Transport::err().

Referenced by TransportFactory::initLiquidTransport().

 void setThermo ( thermo_t & thermo )
protectedinherited

Specifies the ThermPhase object.

Parameters
 thermo Reference to the ThermoPhase object that the transport object will use

Definition at line 112 of file TransportBase.cpp.

Referenced by TransportFactory::newTransport().

 void finalize ( )
protectedinherited

Enable the transport object for use.

Once finalize() has been called, the transport manager should be ready to compute any supported transport property, and no further modifications to the model parameters should be made.

Definition at line 136 of file TransportBase.cpp.

## Friends And Related Function Documentation

 friend class TransportFactory
friend

Make the TransportFactory object a friend, because this object has restricted its instantiation to classes which are friends.

Definition at line 210 of file DustyGasTransport.h.

## Member Data Documentation

 vector_fp m_mw
private

Local copy of the species molecular weights.

units kg /kmol length = m_nsp;

Definition at line 293 of file DustyGasTransport.h.

 DenseMatrix m_d
private

binary diffusion coefficients

Definition at line 296 of file DustyGasTransport.h.

 vector_fp m_x
private

mole fractions

Definition at line 299 of file DustyGasTransport.h.

 vector_fp m_dk
private

Knudsen diffusion coefficients.

The Knudsen diffusion coefficients are given by the following form

$\mathcal{D}^{knud}_k = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}$

Definition at line 310 of file DustyGasTransport.h.

 doublereal m_temp
private

temperature

Definition at line 313 of file DustyGasTransport.h.

 DenseMatrix m_multidiff
private

Multicomponent diffusion coefficients.

The multicomponent diffusion matrix $$H_{k,l}$$ is given by the following form

$H_{k,l} = - \frac{X_k}{D_{k,l}}$

$H_{k,k} = \frac{1}{\mathcal(D)^{knud}_{k}} + \sum_{j \ne k}^N{ \frac{X_j}{D_{k,j}} }$

Definition at line 326 of file DustyGasTransport.h.

 vector_fp m_spwork
private

work space of size m_nsp;

Definition at line 329 of file DustyGasTransport.h.

 vector_fp m_spwork2
private

work space of size m_nsp;

Definition at line 332 of file DustyGasTransport.h.

private

Definition at line 335 of file DustyGasTransport.h.

Referenced by DustyGasTransport::operator=().

 bool m_knudsen_ok
private

Update-to-date variable for Knudsen diffusion coefficients.

Definition at line 338 of file DustyGasTransport.h.

 bool m_bulk_ok
private

Update-to-date variable for Binary diffusion coefficients.

Definition at line 341 of file DustyGasTransport.h.

 doublereal m_porosity
private

Porosity.

Definition at line 344 of file DustyGasTransport.h.

 doublereal m_tortuosity
private

Tortuosity.

Definition at line 347 of file DustyGasTransport.h.

private

Definition at line 350 of file DustyGasTransport.h.

 doublereal m_diam
private

Particle diameter.

The medium is assumed to consist of particles of size m_diam units = m

Definition at line 357 of file DustyGasTransport.h.

 doublereal m_perm
private

Permeability of the media.

The permeability is the proportionality constant for Darcy's law which relates discharge rate and viscosity to the applied pressure gradient.

Below is Darcy's law, where $$\kappa$$ is the permeability

$v = \frac{\kappa}{\mu} \frac{\delta P}{\delta x}$

units are m2

Definition at line 373 of file DustyGasTransport.h.

 Transport* m_gastran
private

Pointer to the transport object for the gas phase.

Note, this object owns the gastran object

Definition at line 379 of file DustyGasTransport.h.

protectedinherited

true if finalize has been called

Definition at line 860 of file TransportBase.h.

Referenced by Transport::finalize(), Transport::operator=(), Transport::ready(), and Transport::Transport().

 size_t m_nDim
protectedinherited

Number of dimensions used in flux expressions.

Definition at line 866 of file TransportBase.h.

Referenced by Transport::nDim(), Transport::operator=(), Transport::setNDim(), and Transport::Transport().

 int m_velocityBasis
protectedinherited

Velocity basis from which diffusion velocities are computed.

Defaults to the mass averaged basis = -2

Definition at line 870 of file TransportBase.h.

The documentation for this class was generated from the following files: