Class SimpleTransport implements mixture-averaged transport properties for liquid phases. More...

#include <SimpleTransport.h>

Inheritance diagram for SimpleTransport:

Collaboration diagram for SimpleTransport:

Public Member Functions
	SimpleTransport (thermo_t *thermo=0, int ndim=1)
	Default constructor. More...

	SimpleTransport (const SimpleTransport &right)

SimpleTransport &	operator= (const SimpleTransport &right)

virtual Transport *	duplMyselfAsTransport () const
	Duplication routine for objects which inherit from Transport. More...

virtual bool	initLiquid (LiquidTransportParams &tr)
	Initialize the transport object. More...

virtual int	model () const
	Transport model. More...

virtual doublereal	viscosity ()
	Returns the mixture viscosity of the solution. More...

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

virtual void	getBinaryDiffCoeffs (const size_t ld, doublereal *const d)
	Returns the binary diffusion coefficients. More...

virtual void	getMixDiffCoeffs (doublereal *const d)
	Get the Mixture diffusion coefficients. More...

virtual void	getThermalDiffCoeffs (doublereal *const dt)
	Return the thermal diffusion coefficients. More...

virtual doublereal	thermalConductivity ()
	Returns the mixture thermal conductivity of the solution. More...

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

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

virtual void	set_Grad_V (const doublereal *const grad_V)
	Specify the value of the gradient of the voltage. More...

virtual void	set_Grad_T (const doublereal *const grad_T)
	Specify the value of the gradient of the temperature. More...

virtual void	set_Grad_X (const doublereal *const grad_X)
	Specify the value of the gradient of the MoleFractions. More...

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 averaged velocity, given the gradients in mole fraction and temperature. More...

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 averaged velocity, given the gradients in mole fraction, temperature and electrostatic potential. More...

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. More...

virtual void	getSpeciesFluxesExt (size_t ldf, doublereal *fluxes)
	Return the species diffusive mass fluxes wrt to the mass averaged velocity,. More...

Public Member Functions inherited from Transport
	Transport (thermo_t *thermo=0, size_t ndim=1)
	Constructor. More...

	Transport (const Transport &right)

Transport &	operator= (const Transport &right)

thermo_t &	thermo ()

bool	ready ()

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

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

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

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

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

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. More...

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. More...

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

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. More...

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

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

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

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

void	setVelocityBasis (VelocityBasis ivb)
	Sets the velocity basis. More...

VelocityBasis	getVelocityBasis () const
	Gets the velocity basis. More...

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

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

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

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

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

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

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

virtual doublereal	electricalConductivity ()

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

virtual bool	initSolid (SolidTransportData &tr)
	Called by TransportFactory to set parameters. More...

virtual void	setThermo (thermo_t &thermo)
	Specifies the ThermoPhase object. More...

Protected Member Functions
virtual bool	update_T ()
	Handles the effects of changes in the Temperature, internally within the object. More...

virtual bool	update_C ()
	Handles the effects of changes in the mixture concentration. More...

void	updateViscosity_T ()
	Update the temperature-dependent viscosity terms. More...

void	updateCond_T ()
	Update the temperature-dependent parts of the mixture-averaged thermal conductivity. More...

void	updateViscosities_C ()
	Update the concentration parts of the viscosities. More...

void	updateDiff_T ()
	Update the binary diffusion coefficients wrt T. More...

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

Private Attributes
int	tempDepType_
	Temperature dependence type. More...

enum LiquidTranMixingModel	compositionDepType_
	Composition dependence of the transport properties. More...

bool	useHydroRadius_
	Boolean indicating whether to use the hydrodynamic radius formulation. More...

bool	doMigration_
	Boolean indicating whether electro-migration term should be added. More...

vector_fp	m_mw
	Local Copy of the molecular weights of the species. More...

std::vector< LTPspecies * >	m_coeffVisc_Ns
	Pure species viscosities in Arrhenius temperature-dependent form. More...

std::vector< LTPspecies * >	m_coeffLambda_Ns
	Pure species thermal conductivities in Arrhenius temperature-dependent form. More...

std::vector< LTPspecies * >	m_coeffDiff_Ns
	Pure species viscosities in Arrhenius temperature-dependent form. More...

std::vector< LTPspecies * >	m_coeffHydroRadius_Ns
	Hydrodynamic radius in LTPspecies form. More...

vector_fp	m_Grad_X
	Internal value of the gradient of the mole fraction vector. More...

vector_fp	m_Grad_T
	Internal value of the gradient of the Temperature vector. More...

vector_fp	m_Grad_P
	Internal value of the gradient of the Pressure vector. More...

vector_fp	m_Grad_V
	Internal value of the gradient of the Electric Voltage. More...

vector_fp	m_diffSpecies
	Vector of Species Diffusivities. More...

vector_fp	m_viscSpecies
	Species viscosities. More...

vector_fp	m_condSpecies
	Internal value of the species individual thermal conductivities. More...

int	m_iStateMF
	State of the mole fraction vector. More...

vector_fp	m_molefracs
	Local copy of the mole fractions of the species in the phase. More...

vector_fp	m_concentrations
	Local copy of the concentrations of the species in the phase. More...

doublereal	concTot_
	Local copy of the total concentration. More...

doublereal	meanMolecularWeight_
	Mean molecular weight. More...

doublereal	dens_
	Density. More...

vector_fp	m_chargeSpecies
	Local copy of the charge of each species. More...

doublereal	m_temp
	Current Temperature -> locally stored. More...

doublereal	m_press
	Current value of the pressure. More...

doublereal	m_lambda
	Saved value of the mixture thermal conductivity. More...

doublereal	m_viscmix
	Saved value of the mixture viscosity. More...

vector_fp	m_spwork
	work space More...

vector_fp	m_fluxes

bool	m_visc_mix_ok
	Boolean indicating that the top-level mixture viscosity is current. More...

bool	m_visc_temp_ok
	Boolean indicating that weight factors wrt viscosity is current. More...

bool	m_diff_mix_ok
	Boolean indicating that mixture diffusion coeffs are current. More...

bool	m_diff_temp_ok
	Boolean indicating that binary diffusion coeffs are current. More...

bool	m_cond_temp_ok
	Flag to indicate that the pure species conductivities are current wrt the temperature. More...

bool	m_cond_mix_ok
	Boolean indicating that mixture conductivity is current. More...

size_t	m_nDim
	Number of dimensions. More...

double	rhoVc [3]
	Temporary variable that stores the rho Vc value. More...

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

bool	m_ready
	true if finalize has been called More...

size_t	m_nsp
	Number of species. More...

size_t	m_nDim
	Number of dimensions used in flux expressions. More...

int	m_velocityBasis
	Velocity basis from which diffusion velocities are computed. More...

Detailed Description

Class SimpleTransport implements mixture-averaged transport properties for liquid phases.

The model is based on that described by Newman, Electrochemical Systems

The velocity of species i may be described by the following equation p. 297 (12.1)

\[ c_i \nabla \mu_i = R T \sum_j \frac{c_i c_j}{c_T D_{ij}} (\mathbf{v}_j - \mathbf{v}_i) \]

This as written is degenerate by 1 dof.

To fix this we must add in the definition of the mass averaged velocity of the solution. We will call the simple bold-faced \(\mathbf{v} \) symbol the mass-averaged velocity. Then, the relation between \(\mathbf{v}\) and the individual species velocities is \(\mathbf{v}_i\)

\[ \rho_i \mathbf{v}_i = \rho_i \mathbf{v} + \mathbf{j}_i \]

where \(\mathbf{j}_i\) are the diffusional fluxes of species i with respect to the mass averaged velocity and

\[ \sum_i \mathbf{j}_i = 0 \]

and

\[ \sum_i \rho_i \mathbf{v}_i = \rho \mathbf{v} \]

Using these definitions, we can write

\[ \mathbf{v}_i = \mathbf{v} + \frac{\mathbf{j}_i}{\rho_i} \]

\[ c_i \nabla \mu_i = R T \sum_j \frac{c_i c_j}{c_T D_{ij}} (\frac{\mathbf{j}_j}{\rho_j} - \frac{\mathbf{j}_i}{\rho_i}) = R T \sum_j \frac{1}{D_{ij}} (\frac{x_i \mathbf{j}_j}{M_j} - \frac{x_j \mathbf{j}_i}{M_i}) \]

The equations that we actually solve are

\[ c_i \nabla \mu_i = = R T \sum_j \frac{1}{D_{ij}} (\frac{x_i \mathbf{j}_j}{M_j} - \frac{x_j \mathbf{j}_i}{M_i}) \]

and we replace the 0th equation with the following:

\[ \sum_i \mathbf{j}_i = 0 \]

When there are charged species, we replace the RHS with the gradient of the electrochemical potential to obtain the modified equation

\[ c_i \nabla \mu_i + c_i F z_i \nabla \Phi = R T \sum_j \frac{1}{D_{ij}} (\frac{x_i \mathbf{j}_j}{M_j} - \frac{x_j \mathbf{j}_i}{M_i}) \]

With this formulation we may solve for the diffusion velocities, without having to worry about what the mass averaged velocity is.

Viscosity Calculation

The viscosity calculation may be broken down into two parts. In the first part, the viscosity of the pure species are calculated In the second part, a mixing rule is applied. There are two mixing rules. Solvent-only and mixture-averaged.

For the solvent-only mixing rule, we use the pure species viscosity calculated for the solvent as the viscosity of the entire mixture. For the mixture averaged rule we do a mole fraction based average of the pure species viscosities:

Solvent-only:

\[ \mu = \mu_0 \]

Mixture-average:

\[ \mu = \sum_k {\mu_k X_k} \]

Calculate of the Binary Diffusion Coefficients

The binary diffusion coefficients are obtained from the pure species diffusion coefficients using an additive process

\[ D_{i,j} = \frac{1}{2} \left( D^0_i(T) + D^0_j(T) \right) \]

Electrical Mobilities

The mobility \( \mu^e_k \) is calculated from the diffusion coefficient using the Einstein relation.

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

The diffusion coefficients, \( D_k \) , is calculated from a call to the mixture diffusion coefficient routine.

Species Diffusive Fluxes

The diffusive mass flux of species 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.

\[ j_k = - c^T M_k D_k \nabla X_k - \rho Y_k V_c \]

where V_c is the correction velocity

\[ \rho V_c = - \sum_j {c^T M_j D_j \nabla X_j} \]

In the above equation, \( D_k \) is the mixture diffusivity for species k calculated for the current conditions, which may depend on T, P, and X_k. \( C^T \) is the total concentration of the phase.

When this is electrical migration, the formulas above are enhanced to

\[ j_k = - C^T M_k D_k \nabla X_k + F C^T M_k \frac{D_k}{ R T } X_k z_k \nabla V - \rho Y_k V_c \]

where V_c is the correction velocity

\[ \rho V_c = - \sum_j {c^T M_j D_j \nabla X_j} + \sum_j F C^T M_j \frac{D_j}{ R T } X_j z_j \nabla V \]

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, \( V_k^d \)

\[ j_k = \rho Y_k V_k^d \]

   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.

Definition at line 180 of file SimpleTransport.h.

Constructor & Destructor Documentation

SimpleTransport	(	thermo_t *	thermo = `0`,
		int	ndim = `1`
	)

Default constructor.

This requires call to initLiquid(LiquidTransportParams& tr) after filling LiquidTransportParams to complete instantiation. The filling of LiquidTransportParams is currently carried out in the TransportFactory class, but might be moved at some point.

Parameters

thermo	ThermoPhase object holding species information.
ndim	Number of spatial dimensions.

Definition at line 12 of file SimpleTransport.cpp.

Referenced by SimpleTransport::duplMyselfAsTransport().

Member Function Documentation

Transport * duplMyselfAsTransport ( ) const

virtual

Duplication routine for objects which inherit from Transport.

This virtual routine can be used to duplicate objects derived 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 135 of file SimpleTransport.cpp.

References SimpleTransport::SimpleTransport().

bool initLiquid ( LiquidTransportParams & tr )

virtual

Initialize the transport object.

Here we change all of the internal dimensions to be sufficient. We get the object ready to do property evaluations.

Parameters

tr	Transport parameters for all of the species in the phase.

Reimplemented from Transport.

Definition at line 156 of file SimpleTransport.cpp.

virtual int model ( ) const

inlinevirtual

Transport model.

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

Reimplemented from Transport.

Definition at line 209 of file SimpleTransport.h.

doublereal viscosity ( )

virtual

Returns the mixture viscosity of the solution.

The viscosity is computed using the general mixture rules specified in the variable compositionDepType_.

Solvent-only:

\[ \mu = \mu_0 \]

Mixture-average:

\[ \mu = \sum_k {\mu_k X_k} \]

Here \( \mu_k \) is the viscosity of pure species k.

units are Pa s or kg/m/s

See Also: updateViscosity_T();

Reimplemented from Transport.

Definition at line 268 of file SimpleTransport.cpp.

References SimpleTransport::compositionDepType_, SimpleTransport::m_molefracs, Transport::m_nsp, SimpleTransport::m_visc_mix_ok, SimpleTransport::m_visc_temp_ok, SimpleTransport::m_viscmix, SimpleTransport::m_viscSpecies, SimpleTransport::update_C(), SimpleTransport::update_T(), and SimpleTransport::updateViscosity_T().

Referenced by SimpleTransport::updateDiff_T().

void getSpeciesViscosities ( doublereal *const visc )

virtual

Returns the pure species viscosities.

The pure species viscosities are to be given in an Arrhenius form in accordance with activated-jump-process dominated transport.

units are Pa s or kg/m/s

Parameters

visc	Return the species viscosities as a vector of length m_nsp

Reimplemented from Transport.

Definition at line 297 of file SimpleTransport.cpp.

References SimpleTransport::m_visc_temp_ok, SimpleTransport::m_viscSpecies, SimpleTransport::update_T(), and SimpleTransport::updateViscosity_T().

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

virtual

Returns the binary diffusion coefficients.

Parameters

ld
d

Reimplemented from Transport.

Definition at line 306 of file SimpleTransport.cpp.

References SimpleTransport::m_diff_temp_ok, SimpleTransport::m_diffSpecies, Transport::m_nsp, SimpleTransport::update_T(), and SimpleTransport::updateDiff_T().

void getMixDiffCoeffs ( doublereal *const d )

virtual

Get the Mixture diffusion coefficients.

Parameters

d	vector of mixture diffusion coefficients units = m2 s-1. length = number of species

Reimplemented from Transport.

Definition at line 538 of file SimpleTransport.cpp.

References SimpleTransport::m_diff_temp_ok, SimpleTransport::m_diffSpecies, Transport::m_nsp, SimpleTransport::update_C(), SimpleTransport::update_T(), and SimpleTransport::updateDiff_T().

Referenced by SimpleTransport::getFluidMobilities(), SimpleTransport::getMobilities(), and SimpleTransport::getSpeciesFluxesExt().

void getThermalDiffCoeffs ( doublereal *const dt )

virtual

Return the thermal diffusion coefficients.

These are all zero for this simple implementation

Parameters

dt	thermal diffusion coefficients

Reimplemented from Transport.

Definition at line 393 of file SimpleTransport.cpp.

References Transport::m_nsp.

doublereal thermalConductivity ( )

virtual

Returns the mixture thermal conductivity of the solution.

The thermal is computed using the general mixture rules specified in the variable compositionDepType_.

Controlling update boolean = m_condmix_ok

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

Solvent-only:

\[ \lambda = \lambda_0 \]

Mixture-average:

\[ \lambda = \sum_k {\lambda_k X_k} \]

Here \( \lambda_k \) is the thermal conductivity of pure species k.

See Also: updateCond_T();

Reimplemented from Transport.

Definition at line 369 of file SimpleTransport.cpp.

References SimpleTransport::compositionDepType_, SimpleTransport::m_cond_mix_ok, SimpleTransport::m_cond_temp_ok, SimpleTransport::m_condSpecies, SimpleTransport::m_lambda, SimpleTransport::m_molefracs, Transport::m_nsp, SimpleTransport::update_C(), SimpleTransport::update_T(), and SimpleTransport::updateCond_T().

void getMobilities ( doublereal *const mobil_e )

virtual

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 from Transport.

Definition at line 325 of file SimpleTransport.cpp.

References Cantera::Boltzmann, DATA_PTR, SimpleTransport::getMixDiffCoeffs(), Transport::m_nsp, SimpleTransport::m_spwork, and SimpleTransport::m_temp.

void getFluidMobilities ( doublereal *const mobil_f )

virtual

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 from Transport.

Definition at line 334 of file SimpleTransport.cpp.

References DATA_PTR, Cantera::GasConstant, SimpleTransport::getMixDiffCoeffs(), Transport::m_nsp, SimpleTransport::m_spwork, and SimpleTransport::m_temp.

void set_Grad_V ( const doublereal *const grad_V )

virtual

Specify the value of the gradient of the voltage.

Parameters

grad_V Gradient of the voltage (length num dimensions);

Definition at line 343 of file SimpleTransport.cpp.

References SimpleTransport::doMigration_, SimpleTransport::m_Grad_V, and SimpleTransport::m_nDim.

Referenced by SimpleTransport::getSpeciesVdiffES().

void set_Grad_T ( const doublereal *const grad_T )

virtual

Specify the value of the gradient of the temperature.

Parameters

grad_T Gradient of the temperature (length num dimensions);

Definition at line 354 of file SimpleTransport.cpp.

References SimpleTransport::m_Grad_T, and SimpleTransport::m_nDim.

Referenced by SimpleTransport::getSpeciesFluxes(), SimpleTransport::getSpeciesVdiff(), and SimpleTransport::getSpeciesVdiffES().

void set_Grad_X ( const doublereal *const grad_X )

virtual

Specify the value of the gradient of the MoleFractions.

Parameters

grad_X Gradient of the mole fractions(length nsp * num dimensions);

Definition at line 361 of file SimpleTransport.cpp.

References SimpleTransport::m_Grad_X, SimpleTransport::m_nDim, and Transport::m_nsp.

Referenced by SimpleTransport::getSpeciesFluxes(), SimpleTransport::getSpeciesVdiff(), and SimpleTransport::getSpeciesVdiffES().

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

virtual

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.

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. Flat vector with the m_nsp in the inner loop. length = ldx * ndim

Reimplemented from Transport.

Definition at line 400 of file SimpleTransport.cpp.

References DATA_PTR, Phase::density(), SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::m_nDim, Transport::m_nsp, Transport::m_thermo, Phase::massFractions(), SimpleTransport::set_Grad_T(), and SimpleTransport::set_Grad_X().

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

virtual

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.

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 species diffusion velocities Flat vector with the m_nsp in the inner loop. length = ldx * ndim

Reimplemented from Transport.

Definition at line 425 of file SimpleTransport.cpp.

References DATA_PTR, Phase::density(), SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::m_nDim, Transport::m_nsp, Transport::m_thermo, Phase::massFractions(), SimpleTransport::set_Grad_T(), SimpleTransport::set_Grad_V(), and SimpleTransport::set_Grad_X().

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

virtual

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

units = kg/m2/s

The diffusive mass flux of species 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.

\[ j_k = - \rho M_k D_k \nabla X_k - Y_k V_c \]

where V_c is the correction velocity

\[ V_c = - \sum_j {\rho M_j D_j \nabla X_j} \]

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	Gradient of the mole fractions(length nsp * num dimensions);
ldf	Leading dimension of the fluxes array.
fluxes	Output fluxes of species.

Reimplemented from Transport.

Definition at line 449 of file SimpleTransport.cpp.

References SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::set_Grad_T(), and SimpleTransport::set_Grad_X().

void getSpeciesFluxesExt	(	size_t	ldf,
		doublereal *	fluxes
	)

virtual

Return the species diffusive mass fluxes wrt to the mass averaged velocity,.

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 k is computed from the following formula

\[ j_k = - \rho M_k D_k \nabla X_k - Y_k V_c \]

where V_c is the correction velocity

\[ V_c = - \sum_j {\rho M_j D_j \nabla X_j} \]

Parameters

ldf	stride of the fluxes array. Must be equal to or greater than the number of species.
fluxes	Vector of calculated fluxes

Definition at line 458 of file SimpleTransport.cpp.

References AssertThrow, Cantera::Boltzmann, DATA_PTR, SimpleTransport::doMigration_, SimpleTransport::getMixDiffCoeffs(), SimpleTransport::m_chargeSpecies, SimpleTransport::m_Grad_V, SimpleTransport::m_Grad_X, SimpleTransport::m_molefracs, SimpleTransport::m_nDim, Transport::m_nsp, SimpleTransport::m_spwork, SimpleTransport::m_temp, Transport::m_thermo, Transport::m_velocityBasis, Phase::massFractions(), Phase::molarDensity(), Phase::molecularWeights(), SimpleTransport::rhoVc, SimpleTransport::update_C(), SimpleTransport::update_T(), Cantera::VB_MASSAVG, and Cantera::VB_MOLEAVG.

Referenced by SimpleTransport::getSpeciesFluxes(), SimpleTransport::getSpeciesVdiff(), and SimpleTransport::getSpeciesVdiffES().

bool update_T ( void )

protectedvirtual

Handles the effects of changes in the Temperature, internally within the object.

This is called whenever a transport property is requested. The first task is to check whether the temperature has changed since the last call to update_T(). If it hasn't then an immediate return is carried out.

Returns: Returns true if the temperature has changed, and false otherwise

Definition at line 635 of file SimpleTransport.cpp.

References Cantera::fp2str(), SimpleTransport::m_cond_mix_ok, SimpleTransport::m_cond_temp_ok, SimpleTransport::m_diff_mix_ok, SimpleTransport::m_diff_temp_ok, SimpleTransport::m_temp, Transport::m_thermo, SimpleTransport::m_visc_mix_ok, SimpleTransport::m_visc_temp_ok, and Phase::temperature().

Referenced by SimpleTransport::getBinaryDiffCoeffs(), SimpleTransport::getMixDiffCoeffs(), SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::getSpeciesViscosities(), SimpleTransport::thermalConductivity(), and SimpleTransport::viscosity().

bool update_C ( )

protectedvirtual

Handles the effects of changes in the mixture concentration.

This is called for every interface call to check whether the concentrations have changed. Concentrations change whenever the pressure or the mole fraction has changed. If it has changed, the recalculations should be done.

Note this should be a lightweight function since it's part of all of the interfaces.

Definition at line 551 of file SimpleTransport.cpp.

References SimpleTransport::concTot_, DATA_PTR, SimpleTransport::dens_, Phase::density(), Phase::getConcentrations(), Phase::getMoleFractions(), SimpleTransport::m_concentrations, SimpleTransport::m_cond_mix_ok, SimpleTransport::m_diff_mix_ok, SimpleTransport::m_iStateMF, SimpleTransport::m_molefracs, Transport::m_nsp, SimpleTransport::m_press, Transport::m_thermo, SimpleTransport::m_visc_mix_ok, Phase::meanMolecularWeight(), SimpleTransport::meanMolecularWeight_, ThermoPhase::pressure(), and Phase::stateMFNumber().

Referenced by SimpleTransport::getMixDiffCoeffs(), SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::thermalConductivity(), and SimpleTransport::viscosity().

void updateViscosity_T ( )

protected

Update the temperature-dependent viscosity terms.

Updates the array of pure species viscosities, and the weighting functions in the viscosity mixture rule.

The flag m_visc_temp_ok is set to true.

Definition at line 622 of file SimpleTransport.cpp.

References SimpleTransport::compositionDepType_, SimpleTransport::m_coeffVisc_Ns, Transport::m_nsp, SimpleTransport::m_visc_mix_ok, SimpleTransport::m_visc_temp_ok, and SimpleTransport::m_viscSpecies.

Referenced by SimpleTransport::getSpeciesViscosities(), and SimpleTransport::viscosity().

void updateCond_T ( )

protected

Update the temperature-dependent parts of the mixture-averaged thermal conductivity.

Definition at line 587 of file SimpleTransport.cpp.

References SimpleTransport::compositionDepType_, SimpleTransport::m_coeffLambda_Ns, SimpleTransport::m_cond_mix_ok, SimpleTransport::m_cond_temp_ok, SimpleTransport::m_condSpecies, and Transport::m_nsp.

Referenced by SimpleTransport::thermalConductivity().

void updateViscosities_C ( )

protected

Update the concentration parts of the viscosities.

Internal routine is run whenever the update_boolean is false. This routine will calculate internal values for the species viscosities.

Definition at line 618 of file SimpleTransport.cpp.

void updateDiff_T ( )

protected

Update the binary diffusion coefficients wrt T.

These are evaluated from the polynomial fits at unit pressure (1 Pa).

Definition at line 600 of file SimpleTransport.cpp.

References Cantera::GasConstant, SimpleTransport::m_coeffDiff_Ns, SimpleTransport::m_coeffHydroRadius_Ns, SimpleTransport::m_diff_mix_ok, SimpleTransport::m_diff_temp_ok, SimpleTransport::m_diffSpecies, Transport::m_nsp, SimpleTransport::m_temp, Cantera::Pi, SimpleTransport::useHydroRadius_, and SimpleTransport::viscosity().

Referenced by SimpleTransport::getBinaryDiffCoeffs(), and SimpleTransport::getMixDiffCoeffs().

Member Data Documentation

int tempDepType_

private

Temperature dependence type.

The following coefficients are allowed to have simple temperature dependencies: mixture viscosity mixture thermal conductivity diffusitivy

Types of temperature dependencies: 0 - Independent of temperature (only one implemented so far) 1 - extended arrhenius form 2 - polynomial in temperature form

Definition at line 500 of file SimpleTransport.h.

enum LiquidTranMixingModel compositionDepType_

private

Composition dependence of the transport properties.

The following coefficients are allowed to have simple composition dependencies

mixture viscosity
mixture thermal conductivity

Permissible types of composition dependencies 0 - Solvent values (i.e., species 0) contributes only 1 - linear combination of mole fractions;

Definition at line 513 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), SimpleTransport::thermalConductivity(), SimpleTransport::updateCond_T(), SimpleTransport::updateViscosity_T(), and SimpleTransport::viscosity().

bool useHydroRadius_

private

Boolean indicating whether to use the hydrodynamic radius formulation.

If true, then the diffusion coefficient is calculated from the hydrodynamic radius.

Definition at line 520 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), and SimpleTransport::updateDiff_T().

bool doMigration_

private

Boolean indicating whether electro-migration term should be added.

Definition at line 523 of file SimpleTransport.h.

Referenced by SimpleTransport::getSpeciesFluxesExt(), and SimpleTransport::set_Grad_V().

vector_fp m_mw

private

Local Copy of the molecular weights of the species.

Length is Equal to the number of species in the mechanism.

Definition at line 529 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid().

std::vector<LTPspecies*> m_coeffVisc_Ns

private

Pure species viscosities in Arrhenius temperature-dependent form.

Definition at line 532 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), and SimpleTransport::updateViscosity_T().

std::vector<LTPspecies*> m_coeffLambda_Ns

private

Pure species thermal conductivities in Arrhenius temperature-dependent form.

Definition at line 535 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), and SimpleTransport::updateCond_T().

std::vector<LTPspecies*> m_coeffDiff_Ns

private

Pure species viscosities in Arrhenius temperature-dependent form.

Definition at line 538 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), and SimpleTransport::updateDiff_T().

std::vector<LTPspecies*> m_coeffHydroRadius_Ns

private

Hydrodynamic radius in LTPspecies form.

Definition at line 541 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), and SimpleTransport::updateDiff_T().

vector_fp m_Grad_X

private

Internal value of the gradient of the mole fraction vector.

Note, this is the only gradient value that can and perhaps should reflect the true state of the mole fractions in the application solution vector. In other words no cropping or massaging of the values to make sure they are above zero should occur. - developing ....

m_nsp is the number of species in the fluid k is the species index n is the dimensional index (x, y, or z). It has a length equal to m_nDim

m_Grad_X[n*m_nsp + k]

Definition at line 558 of file SimpleTransport.h.

Referenced by SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::initLiquid(), and SimpleTransport::set_Grad_X().

vector_fp m_Grad_T

private

Internal value of the gradient of the Temperature vector.

Generally, if a transport property needs this in its evaluation it will look to this place to get it.

No internal property is precalculated based on gradients. Gradients are assumed to be freshly updated before every property call.

Definition at line 568 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), and SimpleTransport::set_Grad_T().

vector_fp m_Grad_P

private

Internal value of the gradient of the Pressure vector.

Generally, if a transport property needs this in its evaluation it will look to this place to get it.

No internal property is precalculated based on gradients. Gradients are assumed to be freshly updated before every property call.

Definition at line 578 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid().

vector_fp m_Grad_V

private

Internal value of the gradient of the Electric Voltage.

Generally, if a transport property needs this in its evaluation it will look to this place to get it.

No internal property is precalculated based on gradients. Gradients are assumed to be freshly updated before every property call.

Definition at line 588 of file SimpleTransport.h.

Referenced by SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::initLiquid(), and SimpleTransport::set_Grad_V().

vector_fp m_diffSpecies

private

Vector of Species Diffusivities.

Depends on the temperature. We have set the pressure dependence to zero for this liquid phase constituitve model

units m2/s

Definition at line 599 of file SimpleTransport.h.

Referenced by SimpleTransport::getBinaryDiffCoeffs(), SimpleTransport::getMixDiffCoeffs(), SimpleTransport::initLiquid(), and SimpleTransport::updateDiff_T().

vector_fp m_viscSpecies

private

Species viscosities.

Viscosity of the species Length = number of species

Depends on the temperature. We have set the pressure dependence to zero for this model

controlling update boolean -> m_visc_temp_ok

Definition at line 611 of file SimpleTransport.h.

Referenced by SimpleTransport::getSpeciesViscosities(), SimpleTransport::initLiquid(), SimpleTransport::updateViscosity_T(), and SimpleTransport::viscosity().

vector_fp m_condSpecies

private

Internal value of the species individual thermal conductivities.

Then a mixture rule is applied to get the solution conductivities

Depends on the temperature and perhaps pressure, but not the species concentrations

controlling update boolean -> m_cond_temp_ok

Definition at line 622 of file SimpleTransport.h.

Referenced by SimpleTransport::initLiquid(), SimpleTransport::thermalConductivity(), and SimpleTransport::updateCond_T().

int m_iStateMF

private

State of the mole fraction vector.

Definition at line 625 of file SimpleTransport.h.

Referenced by SimpleTransport::update_C().

vector_fp m_molefracs

private

Local copy of the mole fractions of the species in the phase.

The mole fractions here are assumed to be bounded by 0.0 and 1.0 and they are assumed to add up to one exactly. This mole fraction vector comes from the ThermoPhase object. Derivative quantities from this are referred to as bounded.

Update info? length = m_nsp

Definition at line 637 of file SimpleTransport.h.

Referenced by SimpleTransport::getSpeciesFluxesExt(), SimpleTransport::initLiquid(), SimpleTransport::thermalConductivity(), SimpleTransport::update_C(), and SimpleTransport::viscosity().