Cantera  2.0
MixTransport Class Reference

Class MixTransport implements mixture-averaged transport properties for ideal gas mixtures. More...

#include <MixTransport.h>

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## Public Member Functions

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

MixTransportoperator= (const MixTransport &right)
Assignment operator.

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

virtual ~MixTransport ()
Destructor.

virtual int model () const
Return the model id for transport.

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

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

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

virtual void update_T ()
Update the internal parameters whenever the temperature has changed.

virtual void update_C ()
Update the internal parameters whenever the concentrations have changed.

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

virtual bool initGas (GasTransportParams &tr)
Initialize the transport object.

struct GasTransportData getGasTransportData (int kspec) const
Return a structure containing all of the pertinent parameters about a species that was used to construct the Transport properties in this object.

virtual doublereal viscosity ()
Viscosity of the mixture (kg /m /s)

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

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

virtual void getMixDiffCoeffs (doublereal *const d)
Returns the Mixture-averaged diffusion coefficients [m^2/s].

virtual void getMixDiffCoeffsMole (doublereal *const d)
Returns the mixture-averaged diffusion coefficients [m^2/s].

virtual void getMixDiffCoeffsMass (doublereal *const d)
Returns the mixture-averaged diffusion coefficients [m^2/s].

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 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 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.

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

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

void setVelocityBasis (VelocityBasis ivb)
Sets the velocity basis.

VelocityBasis getVelocityBasis () const
Gets the velocity basis.

Transport Properties
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 electricalConductivity ()
The electrical conductivity (Siemens/m).

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

## Protected Member Functions

MixTransport ()
Default constructor.

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

Update the pure-species viscosities.

virtual void updateDiff_T ()
Update the binary diffusion coefficients.

Transport manager construction

These methods are used internally during construction.

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

vector_fp m_molefracs
Vector of species mole fractions.

doublereal m_viscmix
Internal storage for the viscosity of the mixture (kg /m /s)

bool m_visc_ok
Update boolean for mixture rule for the mixture viscosity.

bool m_viscwt_ok
Update boolean for the weighting factors for the mixture viscosity.

bool m_spvisc_ok
Update boolean for the species viscosities.

bool m_bindiff_ok
Update boolean for the binary diffusivities at unit pressure.

int m_mode
Type of the polynomial fits to temperature.

DenseMatrix m_phi
m_phi is a Viscosity Weighting Function. size = m_nsp * n_nsp

vector_fp m_spwork
work space length = m_kk

vector_fp m_visc
vector of species viscosities (kg /m /s).

std::vector< vector_fpm_visccoeffs
Polynomial fits to the viscosity of each species.

vector_fp m_mw
Local copy of the species molecular weights.

DenseMatrix m_wratjk
Holds square roots of molecular weight ratios.

DenseMatrix m_wratkj1
Holds square roots of molecular weight ratios.

vector_fp m_sqvisc
vector of square root of species viscosities sqrt(kg /m /s).

vector_fp m_polytempvec
Powers of the ln temperature, up to fourth order.

doublereal m_temp
Current value of the temperature at which the properties in this object are calculated (Kelvin).

doublereal m_kbt
Current value of Boltzman's constant times the temperature (Joules)

doublereal m_sqrt_kbt
current value of Boltzman's constant times the temperature.

doublereal m_sqrt_t
current value of temperature to 1/2 power

doublereal m_logt
Current value of the log of the temperature.

doublereal m_t14
Current value of temperature to 1/4 power.

doublereal m_t32
Current value of temperature to the 3/2 power.

std::vector< vector_fpm_diffcoeffs
Polynomial fits to the binary diffusivity of each species.

DenseMatrix m_bdiff
Matrix of binary diffusion coefficients at the reference pressure and the current temperature Size is nsp x nsp.

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

doublereal pressure_ig () const
Calculate the pressure from the ideal gas law.

void updateCond_T ()
Update the temperature dependent parts of the species thermal conductivities.

## Private Attributes

std::vector< vector_fpm_condcoeffs
Polynomial fits to the thermal conductivity of each species.

vector_fp m_cond
vector of species thermal conductivities (W/m /K)

doublereal m_lambda
Internal storage for the calculated mixture thermal conductivity.

bool m_spcond_ok
Update boolean for the species thermal conductivities.

bool m_condmix_ok
Update boolean for the mixture rule for the mixture thermal conductivity.

vector_fp m_eps
Lennard-Jones well-depth of the species in the current phase.

DenseMatrix m_diam
hard-sphere diameter for (i,j) collision

vector_fp m_dipoleDiag
The effective dipole moment for (i,j) collisions.

vector_fp m_alpha
Polarizability of each species in the phase.

vector_fp m_crot
Dimensionless rotational heat capacity of the species in the current phase.

vector_fp m_zrot
Rotational relaxation number for the species in the current phase.

bool m_debug
Debug flag - turns on more printing.

## Friends

class TransportFactory

## Detailed Description

Class MixTransport implements mixture-averaged transport properties for ideal gas mixtures.

The model is based on that described by Kee, Coltrin, and Glarborg, "Theoretical and Practical Aspects of Chemically Reacting Flow Modeling."

The viscosity is computed using the Wilke mixture rule (kg /m /s)

$\mu = \sum_k \frac{\mu_k X_k}{\sum_j \Phi_{k,j} X_j}.$

Here $$\mu_k$$ is the viscosity of pure species k, and

$\Phi_{k,j} = \frac{\left[1 + \sqrt{\left(\frac{\mu_k}{\mu_j}\sqrt{\frac{M_j}{M_k}}\right)}\right]^2} {\sqrt{8}\sqrt{1 + M_k/M_j}}$

The thermal conductivity is computed from the following mixture rule:

$\lambda = 0.5 \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k/\lambda_k} \right)$

It's used to compute the flux of energy due to a thermal gradient

$j_T = - \lambda \nabla T$

The flux of energy has units of energy (kg m2 /s2) per second per area.

The units of lambda are W / m K which is equivalent to kg m / s^3 K.

Definition at line 67 of file MixTransport.h.

## Constructor & Destructor Documentation

 MixTransport ( )
protected

Default constructor.

Definition at line 30 of file MixTransport.cpp.

Referenced by MixTransport::duplMyselfAsTransport().

 MixTransport ( const MixTransport & right )

Copy Constructor for the MixTransport object.

Parameters
 right LiquidTransport to be copied

Definition at line 46 of file MixTransport.cpp.

 virtual ~MixTransport ( )
inlinevirtual

Destructor.

Definition at line 105 of file MixTransport.h.

## Member Function Documentation

 MixTransport & operator= ( const MixTransport & right )

Assignment operator.

This is NOT a virtual function.

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

Definition at line 71 of file MixTransport.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 103 of file MixTransport.cpp.

References MixTransport::MixTransport().

 virtual int model ( ) const
inlinevirtual

Return the model id for transport.

Returns
cMixtureAverage

Reimplemented from Transport.

Definition at line 111 of file MixTransport.h.

 void getThermalDiffCoeffs ( doublereal *const dt )
virtual

Return the thermal diffusion coefficients.

For this approximation, these are all zero.

Eqns. (12.168) shows how they are used in an expression for the species flux.

Parameters
 dt Vector of thermal diffusion coefficients. Units = kg/m/s

Reimplemented from Transport.

Definition at line 193 of file MixTransport.cpp.

References Transport::m_nsp.

 doublereal thermalConductivity ( )
virtual

Returns the mixture thermal conductivity (W/m /K)

The thermal conductivity is computed from the following mixture rule:

$\lambda = 0.5 \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k/\lambda_k} \right)$

It's used to compute the flux of energy due to a thermal gradient

$j_T = - \lambda \nabla T$

The flux of energy has units of energy (kg m2 /s2) per second per area.

The units of lambda are W / m K which is equivalent to kg m / s^3 K.

Returns
Returns the mixture thermal conductivity, with units of W/m/K

Reimplemented from Transport.

Definition at line 165 of file MixTransport.cpp.

 void getMobilities ( doublereal *const mobil )
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.

Here, the mobility is calculated from the diffusion coefficient using the Einstein relation

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

Parameters
 mobil 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 137 of file MixTransport.cpp.

 void update_T ( void )
virtual

Update the internal parameters whenever the temperature has changed.

This is called whenever a transport property is requested if the temperature has changed since the last call to update_T().

Reimplemented from GasTransport.

Definition at line 259 of file MixTransport.cpp.

Referenced by MixTransport::getSpeciesFluxes(), and MixTransport::thermalConductivity().

 void update_C ( )
virtual

Update the internal parameters whenever the concentrations have changed.

This is called whenever a transport property is requested if the concentrations have changed since the last call to update_C().

Implements GasTransport.

Definition at line 281 of file MixTransport.cpp.

Referenced by MixTransport::getSpeciesFluxes(), and MixTransport::thermalConductivity().

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

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

The diffusive mass flux of species k is computed from

$\vec{j}_k = -n M_k D_k \nabla X_k.$

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 from Transport.

Definition at line 225 of file MixTransport.cpp.

 bool initGas ( GasTransportParams & 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 GasTransport.

Definition at line 110 of file MixTransport.cpp.

 struct GasTransportData getGasTransportData ( int kspec ) const

Return a structure containing all of the pertinent parameters about a species that was used to construct the Transport properties in this object.

Parameters
 kspec Species number to obtain the properties from.
Returns
GasTransportData returned structure.
Deprecated:

Definition at line 322 of file MixTransport.cpp.

 doublereal pressure_ig ( ) const
inlineprivate

Calculate the pressure from the ideal gas law.

Definition at line 232 of file MixTransport.h.

 void updateCond_T ( )
private

Update the temperature dependent parts of the species thermal conductivities.

These are evaluated from the polynomial fits of the temperature and are assumed to be independent of pressure

Definition at line 302 of file MixTransport.cpp.

Referenced by MixTransport::thermalConductivity().

 doublereal viscosity ( )
virtualinherited

Viscosity of the mixture (kg /m /s)

The viscosity is computed using the Wilke mixture rule (kg /m /s)

$\mu = \sum_k \frac{\mu_k X_k}{\sum_j \Phi_{k,j} X_j}.$

Here $$\mu_k$$ is the viscosity of pure species k, and

$\Phi_{k,j} = \frac{\left[1 + \sqrt{\left(\frac{\mu_k}{\mu_j}\sqrt{\frac{M_j}{M_k}}\right)}\right]^2} {\sqrt{8}\sqrt{1 + M_k/M_j}}$

Returns
Returns the viscosity of the mixture ( units = Pa s = kg /m /s)
updateViscosity_T();

Reimplemented from Transport.

Definition at line 166 of file GasTransport.cpp.

 virtual void getSpeciesViscosities ( doublereal *const visc )
inlinevirtualinherited

Get the pure-species viscosities.

Reimplemented from Transport.

Definition at line 44 of file GasTransport.h.

References GasTransport::m_visc, and GasTransport::updateViscosity_T().

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

Returns the matrix of binary diffusion coefficients.

   d[ld*j + i] = rp * m_bdiff(i,j);

Parameters
 ld offset of rows in the storage d output vector of diffusion coefficients. Units of m**2 / s

Reimplemented from Transport.

Definition at line 257 of file GasTransport.cpp.

 void getMixDiffCoeffs ( doublereal *const d )
virtualinherited

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

Returns the mixture averaged diffusion coefficients for a gas, appropriate for calculating the mass averaged diffusive flux with respect to the mass averaged velocity using gradients of the mole fraction. Note, for the single species case or the pure fluid case the routine returns the self-diffusion coefficient. This is needed to avoid a Nan result in the formula below.

This is Eqn. 12.180 from "Chemically Reacting Flow"

$D_{km}' = \frac{\left( \bar{M} - X_k M_k \right)}{ \bar{\qquad M \qquad } } {\left( \sum_{j \ne k} \frac{X_j}{D_{kj}} \right) }^{-1}$

Parameters
 [out] d Vector of mixture diffusion coefficients, $$D_{km}'$$ , for each species (m^2/s). length m_nsp

Reimplemented from Transport.

Definition at line 274 of file GasTransport.cpp.

Referenced by MixTransport::getMobilities(), and MixTransport::getSpeciesFluxes().

 void getMixDiffCoeffsMole ( doublereal *const d )
virtualinherited

Returns the mixture-averaged diffusion coefficients [m^2/s].

These are the coefficients for calculating the molar diffusive fluxes from the species mole fraction gradients, computed according to Eq. 12.176 in "Chemically Reacting Flow":

$D_{km}^* = \frac{1-X_k}{\sum_{j \ne k}^K X_j/\mathcal{D}_{kj}}$

Parameters
 [out] d vector of mixture-averaged diffusion coefficients for each species, length m_nsp.

Reimplemented from Transport.

Definition at line 309 of file GasTransport.cpp.

 void getMixDiffCoeffsMass ( doublereal *const d )
virtualinherited

Returns the mixture-averaged diffusion coefficients [m^2/s].

These are the coefficients for calculating the diffusive mass fluxes from the species mass fraction gradients, computed according to Eq. 12.178 in "Chemically Reacting Flow":

$\frac{1}{D_{km}} = \sum_{j \ne k}^K \frac{X_j}{\mathcal{D}_{kj}} + //! \frac{X_k}{1-Y_k} \sum_{j \ne k}^K \frac{Y_j}{\mathcal{D}_{kj}}$

Parameters
 [out] d vector of mixture-averaged diffusion coefficients for each species, length m_nsp.

Reimplemented from Transport.

Definition at line 339 of file GasTransport.cpp.

 void updateViscosity_T ( )
protectedvirtualinherited

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_ok is set to true.

The formula for the weighting function is from Poling and Prausnitz, Eq. (9-5.14):

$\phi_{ij} = \frac{ \left[ 1 + \left( \mu_i / \mu_j \right)^{1/2} \left( M_j / M_i \right)^{1/4} \right]^2 } {\left[ 8 \left( 1 + M_i / M_j \right) \right]^{1/2}}$

Definition at line 190 of file GasTransport.cpp.

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

protectedvirtualinherited

Update the pure-species viscosities.

These are evaluated from the polynomial fits of the temperature and are assumed to be independent of pressure.

Definition at line 213 of file GasTransport.cpp.

Referenced by MultiTransport::updateThermal_T(), and GasTransport::updateViscosity_T().

 void updateDiff_T ( )
protectedvirtualinherited

Update the binary diffusion coefficients.

These are evaluated from the polynomial fits of the temperature at the unit pressure of 1 Pa.

Definition at line 231 of file GasTransport.cpp.

 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 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 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 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().

 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 getMolarFluxes ( const doublereal *const state1, const doublereal *const state2, const doublereal delta, doublereal *const cfluxes )
inlinevirtualinherited

Get the molar fluxes [kmol/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). cfluxes Output array containing the diffusive molar 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 [kmol/m^2/s].

Reimplemented in MultiTransport, and DustyGasTransport.

Definition at line 650 of file TransportBase.h.

References Transport::err().

 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 getMultiDiffCoeffs ( const size_t ld, doublereal *const d )
inlinevirtualinherited

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
 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 in DustyGasTransport, and MultiTransport.

Definition at line 721 of file TransportBase.h.

References Transport::err().

Referenced by StFlow::updateTransport().

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

Set model parameters for derived classes.

This method may be derived in subclasses to set model-specific parameters. The primary use of this class is to set parameters while in the middle of a calculation without actually having to dynamically cast the base Transport pointer.

Parameters
 type Specifies the type of parameters to set 0 : Diffusion coefficient 1 : Thermal Conductivity The rest are currently unused. k Species index to set the parameters on p Vector of parameters. The length of the vector varies with the parameterization

Reimplemented in DustyGasTransport, and SolidTransport.

Definition at line 105 of file TransportBase.cpp.

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 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.

## Member Data Documentation

 std::vector m_condcoeffs
private

Polynomial fits to the thermal conductivity of each species.

m_condcoeffs[k] is vector of polynomial coefficients for species k that fits the thermal conductivity

Definition at line 252 of file MixTransport.h.

Referenced by MixTransport::initGas(), MixTransport::operator=(), and MixTransport::updateCond_T().

 vector_fp m_cond
private

vector of species thermal conductivities (W/m /K)

These are used in wilke's rule to calculate the viscosity of the solution units = W /m /K = kg m /s^3 /K. length = m_kk

Definition at line 260 of file MixTransport.h.

 doublereal m_lambda
private

Internal storage for the calculated mixture thermal conductivity.

Units = W /m /K

Definition at line 266 of file MixTransport.h.

Referenced by MixTransport::operator=(), and MixTransport::thermalConductivity().

 bool m_spcond_ok
private

Update boolean for the species thermal conductivities.

Definition at line 269 of file MixTransport.h.

 bool m_condmix_ok
private

Update boolean for the mixture rule for the mixture thermal conductivity.

Definition at line 272 of file MixTransport.h.

 vector_fp m_eps
private

Lennard-Jones well-depth of the species in the current phase.

Not used in this routine -> just a passthrough

length is the number of species in the phase Units are Joules (Note this is not Joules/kmol) (note, no kmol -> this is a per molecule amount)

Definition at line 281 of file MixTransport.h.

Referenced by MixTransport::initGas(), and MixTransport::operator=().

 DenseMatrix m_diam
private

hard-sphere diameter for (i,j) collision

Not used in this routine -> just a passthrough

diam(i,j) = 0.5*(tr.sigma[i] + tr.sigma[j]); Units are m (note, no kmol -> this is a per molecule amount)

Length nsp * nsp. This is a symmetric matrix.

Definition at line 292 of file MixTransport.h.

Referenced by MixTransport::initGas(), and MixTransport::operator=().

 vector_fp m_dipoleDiag
private

The effective dipole moment for (i,j) collisions.

tr.dipoleMoment has units of Debye's. A Debye is 10-18 cm3/2 erg1/2

Not used in this routine -> just a passthrough

tr.dipole(i,i) = 1.e-25 * SqrtTen * trdat.dipoleMoment; tr.dipole(i,j) = sqrt(tr.dipole(i,i)*tr.dipole(j,j)); Units are in Debye (note, no kmol -> this is a per molecule amount)

Length nsp. We store only the diagonal component here.

Definition at line 306 of file MixTransport.h.

Referenced by MixTransport::initGas(), and MixTransport::operator=().

 vector_fp m_alpha
private

Polarizability of each species in the phase.

Not used in this routine -> just a passthrough

Length = nsp Units = m^3

Definition at line 315 of file MixTransport.h.

Referenced by MixTransport::initGas(), and MixTransport::operator=().

 vector_fp m_crot
private

Dimensionless rotational heat capacity of the species in the current phase.

Not used in this routine -> just a passthrough

These values are 0, 1 and 1.5 for single-molecule, linear, and nonlinear species respectively length is the number of species in the phase units are dimensionless (Cr / R)

Definition at line 325 of file MixTransport.h.

Referenced by MixTransport::initGas(), and MixTransport::operator=().

 vector_fp m_zrot
private

Rotational relaxation number for the species in the current phase.

Not used in this routine -> just a passthrough

length is the number of species in the phase units are dimensionless

Definition at line 334 of file MixTransport.h.

Referenced by MixTransport::initGas(), and MixTransport::operator=().

 bool m_debug
private

Debug flag - turns on more printing.

Definition at line 337 of file MixTransport.h.

Referenced by MixTransport::operator=().

 vector_fp m_molefracs
protectedinherited

Vector of species mole fractions.

These are processed so that all mole fractions are >= MIN_X. Length = m_kk.

Definition at line 136 of file GasTransport.h.

 doublereal m_viscmix
protectedinherited

Internal storage for the viscosity of the mixture (kg /m /s)

Definition at line 139 of file GasTransport.h.

Referenced by GasTransport::viscosity().

 bool m_visc_ok
protectedinherited

Update boolean for mixture rule for the mixture viscosity.

Definition at line 142 of file GasTransport.h.

Referenced by GasTransport::initGas(), MixTransport::update_C(), and GasTransport::viscosity().

 bool m_viscwt_ok
protectedinherited

Update boolean for the weighting factors for the mixture viscosity.

Definition at line 145 of file GasTransport.h.

 bool m_spvisc_ok
protectedinherited

Update boolean for the species viscosities.

Definition at line 148 of file GasTransport.h.

 bool m_bindiff_ok
protectedinherited

Update boolean for the binary diffusivities at unit pressure.

Definition at line 151 of file GasTransport.h.

 int m_mode
protectedinherited

Type of the polynomial fits to temperature.

CK_Mode means Chemkin mode. Currently CA_Mode is used which are different types of fits to temperature.

Definition at line 155 of file GasTransport.h.

 DenseMatrix m_phi
protectedinherited

m_phi is a Viscosity Weighting Function. size = m_nsp * n_nsp

Definition at line 158 of file GasTransport.h.

 vector_fp m_spwork
protectedinherited

work space length = m_kk

Definition at line 161 of file GasTransport.h.

 vector_fp m_visc
protectedinherited

vector of species viscosities (kg /m /s).

These are used in Wilke's rule to calculate the viscosity of the solution. length = m_kk.

Definition at line 165 of file GasTransport.h.

 std::vector m_visccoeffs
protectedinherited

Polynomial fits to the viscosity of each species.

m_visccoeffs[k] is the vector of polynomial coefficients for species k that fits the viscosity as a function of temperature.

Definition at line 170 of file GasTransport.h.

 vector_fp m_mw
protectedinherited

Local copy of the species molecular weights.

Definition at line 173 of file GasTransport.h.

 DenseMatrix m_wratjk
protectedinherited

Holds square roots of molecular weight ratios.

m_wratjk(j,k) = sqrt(mw[j]/mw[k]) j < k m_wratjk(k,j) = sqrt(sqrt(mw[j]/mw[k])) j < k

Definition at line 180 of file GasTransport.h.

Referenced by GasTransport::initGas(), and GasTransport::updateViscosity_T().

 DenseMatrix m_wratkj1
protectedinherited

Holds square roots of molecular weight ratios.

m_wratjk1(j,k) = sqrt(1.0 + mw[k]/mw[j]) j < k

Definition at line 186 of file GasTransport.h.

Referenced by GasTransport::initGas(), and GasTransport::updateViscosity_T().

 vector_fp m_sqvisc
protectedinherited

vector of square root of species viscosities sqrt(kg /m /s).

These are used in Wilke's rule to calculate the viscosity of the solution. length = m_kk.

Definition at line 191 of file GasTransport.h.

 vector_fp m_polytempvec
protectedinherited

Powers of the ln temperature, up to fourth order.

Definition at line 194 of file GasTransport.h.

 doublereal m_temp
protectedinherited

Current value of the temperature at which the properties in this object are calculated (Kelvin).

Definition at line 198 of file GasTransport.h.

 doublereal m_kbt
protectedinherited

Current value of Boltzman's constant times the temperature (Joules)

Definition at line 201 of file GasTransport.h.

Referenced by MultiTransport::updateThermal_T().

 doublereal m_sqrt_kbt
protectedinherited

current value of Boltzman's constant times the temperature.

(Joules) to 1/2 power

Definition at line 205 of file GasTransport.h.

 doublereal m_sqrt_t
protectedinherited

current value of temperature to 1/2 power

Definition at line 208 of file GasTransport.h.

 doublereal m_logt
protectedinherited

Current value of the log of the temperature.

Definition at line 211 of file GasTransport.h.

Referenced by MultiTransport::updateThermal_T().

 doublereal m_t14
protectedinherited

Current value of temperature to 1/4 power.

Definition at line 214 of file GasTransport.h.

 doublereal m_t32
protectedinherited

Current value of temperature to the 3/2 power.

Definition at line 217 of file GasTransport.h.

 std::vector m_diffcoeffs
protectedinherited

Polynomial fits to the binary diffusivity of each species.

m_diffcoeff[ic] is vector of polynomial coefficients for species i species j that fits the binary diffusion coefficient. The relationship between i j and ic is determined from the following algorithm:

int ic = 0; for (i = 0; i < m_nsp; i++) { for (j = i; j < m_nsp; j++) { ic++; } }

Definition at line 232 of file GasTransport.h.

Referenced by GasTransport::initGas(), and GasTransport::updateDiff_T().

 DenseMatrix m_bdiff
protectedinherited

Matrix of binary diffusion coefficients at the reference pressure and the current temperature Size is nsp x nsp.

Definition at line 236 of file GasTransport.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: