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

#include <DustyGasTransport.h>

Inheritance diagram for DustyGasTransport:

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.

For references on the Dusty Gas Model, see Zhu and Kee [48]; Zhu, et al. [49]; Mason and Malinauskas [25]; and Veldsink, et al. [45].

Definition at line 52 of file DustyGasTransport.h.

Public Member Functions
	DustyGasTransport (ThermoPhase *thermo=0)
	default constructor

void	setThermo (ThermoPhase &thermo) override
	Specifies the ThermoPhase object.

string	transportModel () const override
	Identifies the model represented by this Transport object.

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

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

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

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

void	setMeanPoreRadius (double rbar)
	Set the mean pore radius (m)

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

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

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

Public Member Functions inherited from Transport
	Transport (ThermoPhase *thermo=0, size_t ndim=npos)
	Constructor.

	Transport (const Transport &)=delete

Transport &	operator= (const Transport &)=delete

virtual string	transportModel () const
	Identifies the model represented by this Transport object.

string	transportType () const
	Identifies the Transport object type.

ThermoPhase &	thermo ()
	Phase object.

bool	ready ()
	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.

void	checkSpeciesArraySize (size_t kk) const
	Check that an array size is at least nSpecies().

virtual double	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 double grad_T, int ldx, const double grad_X, int ldf, const double grad_V, double current)
	Compute the electric current density in A/m^2.

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

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

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

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

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

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

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

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

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

virtual void	getViscosityPolynomial (size_t i, double *coeffs) const
	Return the polynomial fits to the viscosity of species i.

virtual void	getConductivityPolynomial (size_t i, double *coeffs) const
	Return the temperature fits of the heat conductivity of species i.

virtual void	getBinDiffusivityPolynomial (size_t i, size_t j, double *coeffs) const
	Return the polynomial fits to the binary diffusivity of species pair (i, j)

virtual void	getCollisionIntegralPolynomial (size_t i, size_t j, double astar_coeffs, double bstar_coeffs, double *cstar_coeffs) const
	Return the polynomial fits to the collision integral of species pair (i, j)

virtual void	setViscosityPolynomial (size_t i, double *coeffs)
	Modify the polynomial fits to the viscosity of species i.

virtual void	setConductivityPolynomial (size_t i, double *coeffs)
	Modify the temperature fits of the heat conductivity of species i.

virtual void	setBinDiffusivityPolynomial (size_t i, size_t j, double *coeffs)
	Modify the polynomial fits to the binary diffusivity of species pair (i, j)

virtual void	setCollisionIntegralPolynomial (size_t i, size_t j, double astar_coeffs, double bstar_coeffs, double *cstar_coeffs, bool flag)
	Modify the polynomial fits to the collision integral of species pair (i, j)

virtual void	setParameters (const int type, const int k, const double *const p)
	Set model parameters for derived classes.

AnyMap	parameters () const
	Return the parameters for a phase definition which are needed to reconstruct an identical object using the newTransport function.

void	setVelocityBasis (VelocityBasis ivb)
	Sets the velocity basis.

VelocityBasis	getVelocityBasis () const
	Gets the velocity basis.

virtual double	viscosity ()
	The viscosity in Pa-s.

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

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

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

virtual void	getSpeciesIonConductivity (double *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 double	thermalConductivity ()
	Returns the mixture thermal conductivity in W/m/K.

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

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

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

virtual void	init (ThermoPhase *thermo, int mode=0, int log_level=0)
	Initialize a transport manager.

virtual void	setRoot (shared_ptr< Solution > root)
	Set root Solution holding all phase information.

virtual bool	CKMode () const
	Boolean indicating the form of the transport properties polynomial fits.

Protected Member Functions
void	initialize (ThermoPhase phase, Transport gastr)
	Initialization routine called by TransportFactory.

Protected Member Functions inherited from Transport
void	finalize ()
	Enable the transport object for use.

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 ()
	Update the Multicomponent diffusion coefficients that are used in the approximation.

void	updateKnudsenDiffCoeffs ()
	Update the Knudsen diffusion coefficients.

void	eval_H_matrix ()
	Calculate the H matrix.

Private Attributes
vector< double >	m_mw
	Local copy of the species molecular weights.

DenseMatrix	m_d
	binary diffusion coefficients

vector< double >	m_x
	mole fractions

vector< double >	m_dk
	Knudsen diffusion coefficients.

double	m_temp = -1.0
	temperature

DenseMatrix	m_multidiff
	Multicomponent diffusion coefficients.

vector< double >	m_spwork
	work space of size m_nsp;

vector< double >	m_spwork2
	work space of size m_nsp;

double	m_gradP = 0.0
	Pressure Gradient.

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

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

double	m_porosity = 0.0
	Porosity.

double	m_tortuosity = 1.0
	Tortuosity.

double	m_pore_radius = 0.0
	Pore radius (meter)

double	m_diam = 0.0
	Particle diameter.

double	m_perm = -1.0
	Permeability of the media.

unique_ptr< Transport >	m_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.

Additional Inherited Members
Protected Attributes inherited from Transport
ThermoPhase *	m_thermo
	pointer to the object representing the phase

bool	m_ready = false
	true if finalize has been called

size_t	m_nsp = 0
	Number of species.

size_t	m_nDim
	Number of dimensions used in flux expressions.

int	m_velocityBasis = VB_MASSAVG
	Velocity basis from which diffusion velocities are computed.

std::weak_ptr< Solution >	m_root
	reference to Solution

Constructor & Destructor Documentation

◆ DustyGasTransport()

DustyGasTransport ( ThermoPhase * thermo = 0 )

default constructor

Parameters

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

Definition at line 16 of file DustyGasTransport.cpp.

Member Function Documentation

◆ setThermo()

void setThermo ( ThermoPhase & thermo )

overridevirtual

Specifies the ThermoPhase object.

We have relaxed this operation so that it will succeed when the underlying old and new ThermoPhase objects have the same number of species and the same names of the species in the same order. The idea here is to allow copy constructors and duplicators to work. In order for them to work, we need a method to switch the internal pointer within the Transport object after the duplication takes place. Also, different thermodynamic instantiations of the same species should also work.

Parameters

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

Deprecated:: To be removed after Cantera 3.0. The ThermoPhase object should be set as part of the call to init.

Reimplemented from Transport.

Definition at line 21 of file DustyGasTransport.cpp.

◆ transportModel()

string transportModel ( ) const

inlineoverridevirtual

Identifies the model represented by this Transport object.

Each derived class should override this method to return a meaningful identifier.

Since: New in Cantera 3.0. The name returned by this method corresponds to the canonical name used in the YAML input format.

Reimplemented from Transport.

Definition at line 66 of file DustyGasTransport.h.

◆ getMultiDiffCoeffs()

void getMultiDiffCoeffs	(	const size_t	ld,
		double *const	d
	)

overridevirtual

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

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

Parameters

[in]	ld	The dimension of the inner loop of d (usually equal to m_nsp)
[out]	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 concentration gradients in species j). Units: m^2/s

Reimplemented from Transport.

Definition at line 181 of file DustyGasTransport.cpp.

◆ getMolarFluxes()

void getMolarFluxes	(	const double *const	state1,
		const double *const	state2,
		const double	delta,
		double *const	fluxes
	)

overridevirtual

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 105 of file DustyGasTransport.cpp.

◆ setPorosity()

void setPorosity ( double porosity )

Set the porosity (dimensionless)

Parameters

porosity Set the value of the porosity

Definition at line 214 of file DustyGasTransport.cpp.

◆ setTortuosity()

void setTortuosity ( double tort )

Set the tortuosity (dimensionless)

Tortuosity is considered to be constant within the object

Parameters

tort	Value of the tortuosity

Definition at line 221 of file DustyGasTransport.cpp.

◆ setMeanPoreRadius()

void setMeanPoreRadius ( double rbar )

Set the mean pore radius (m)

Parameters

rbar	Value of the pore radius ( m)

Definition at line 228 of file DustyGasTransport.cpp.

◆ setMeanParticleDiameter()

void setMeanParticleDiameter ( double dbar )

Set the mean particle diameter.

Parameters

dbar	Set the mean particle diameter (m)

Definition at line 234 of file DustyGasTransport.cpp.

◆ setPermeability()

void setPermeability ( double 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 239 of file DustyGasTransport.cpp.

◆ gasTransport()

Transport & gasTransport ( )

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

Returns: a reference to the gas transport object

Definition at line 244 of file DustyGasTransport.cpp.

◆ initialize()

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 27 of file DustyGasTransport.cpp.

◆ updateTransport_T()

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 191 of file DustyGasTransport.cpp.

◆ updateTransport_C()

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 201 of file DustyGasTransport.cpp.

◆ updateBinaryDiffCoeffs()

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 54 of file DustyGasTransport.cpp.

◆ updateMultiDiffCoeffs()

void updateMultiDiffCoeffs ( )

private

Update the Multicomponent diffusion coefficients that are used in the approximation.

This routine updates the H matrix and then inverts it.

Definition at line 164 of file DustyGasTransport.cpp.

◆ updateKnudsenDiffCoeffs()

void updateKnudsenDiffCoeffs ( )

private

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 71 of file DustyGasTransport.cpp.

◆ eval_H_matrix()

void eval_H_matrix ( )

private

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 84 of file DustyGasTransport.cpp.

Friends And Related Symbol Documentation

◆ TransportFactory

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 139 of file DustyGasTransport.h.

Member Data Documentation

◆ m_mw

vector<double> m_mw

private

Local copy of the species molecular weights.

units kg /kmol length = m_nsp;

Definition at line 223 of file DustyGasTransport.h.

◆ m_d

DenseMatrix m_d

private

binary diffusion coefficients

Definition at line 226 of file DustyGasTransport.h.

◆ m_x

vector<double> m_x

private

mole fractions

Definition at line 229 of file DustyGasTransport.h.

◆ m_dk

vector<double> m_dk

private

Knudsen diffusion coefficients.

See also: updateKnudsenDiffCoeffs()

Definition at line 232 of file DustyGasTransport.h.

◆ m_temp

double m_temp = -1.0

private

temperature

Definition at line 235 of file DustyGasTransport.h.

◆ m_multidiff

DenseMatrix m_multidiff

private

Multicomponent diffusion coefficients.

See also: eval_H_matrix()

Definition at line 238 of file DustyGasTransport.h.

◆ m_spwork

vector<double> m_spwork

private

work space of size m_nsp;

Definition at line 241 of file DustyGasTransport.h.

◆ m_spwork2

vector<double> m_spwork2

private

work space of size m_nsp;

Definition at line 244 of file DustyGasTransport.h.

◆ m_gradP

double m_gradP = 0.0

private

Pressure Gradient.

Definition at line 247 of file DustyGasTransport.h.

◆ m_knudsen_ok

bool m_knudsen_ok = false

private

Update-to-date variable for Knudsen diffusion coefficients.

Definition at line 250 of file DustyGasTransport.h.

◆ m_bulk_ok

bool m_bulk_ok = false

private

Update-to-date variable for Binary diffusion coefficients.

Definition at line 253 of file DustyGasTransport.h.

◆ m_porosity

double m_porosity = 0.0

private

Porosity.

Definition at line 256 of file DustyGasTransport.h.

◆ m_tortuosity

double m_tortuosity = 1.0

private

Tortuosity.

Definition at line 259 of file DustyGasTransport.h.

◆ m_pore_radius

double m_pore_radius = 0.0

private

Pore radius (meter)

Definition at line 262 of file DustyGasTransport.h.

◆ m_diam

double m_diam = 0.0

private

Particle diameter.

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

Definition at line 268 of file DustyGasTransport.h.

◆ m_perm

double m_perm = -1.0

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 283 of file DustyGasTransport.h.

◆ m_gastran

unique_ptr<Transport> m_gastran

private

Pointer to the transport object for the gas phase.

Definition at line 286 of file DustyGasTransport.h.

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

Detailed Description

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Friends

Additional Inherited Members

Constructor & Destructor Documentation

◆ DustyGasTransport()

Member Function Documentation

◆ setThermo()

◆ transportModel()

◆ getMultiDiffCoeffs()

◆ getMolarFluxes()

◆ setPorosity()

◆ setTortuosity()

◆ setMeanPoreRadius()

◆ setMeanParticleDiameter()

◆ setPermeability()

◆ gasTransport()

◆ initialize()

◆ updateTransport_T()

◆ updateTransport_C()

◆ updateBinaryDiffCoeffs()

◆ updateMultiDiffCoeffs()

◆ updateKnudsenDiffCoeffs()

◆ eval_H_matrix()

Friends And Related Symbol Documentation

◆ TransportFactory

Member Data Documentation

◆ m_mw

◆ m_d

◆ m_x

◆ m_dk

◆ m_temp

◆ m_multidiff

◆ m_spwork

◆ m_spwork2

◆ m_gradP

◆ m_knudsen_ok

◆ m_bulk_ok

◆ m_porosity

◆ m_tortuosity

◆ m_pore_radius

◆ m_diam

◆ m_perm

◆ m_gastran