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MixTransport Class Reference

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

#include <MixTransport.h>

Inheritance diagram for MixTransport:
[legend]

## Detailed Description

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

The model is based on that described in Kee, et al. [15].

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 54 of file MixTransport.h.

## Public Member Functions

MixTransport ()=default
Default constructor.

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

void getThermalDiffCoeffs (double *const dt) override
Return the thermal diffusion coefficients.

double thermalConductivity () override
Returns the mixture thermal conductivity (W/m /K)

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

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

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

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

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

Public Member Functions inherited from GasTransport
double viscosity () override
Viscosity of the mixture (kg /m /s)

void getSpeciesViscosities (double *const visc) override
Get the pure-species viscosities.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Transport (const Transport &)=delete

Transportoperator= (const Transport &)=delete

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

string transportType () const
Identifies the Transport object type.

ThermoPhasethermo ()
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.

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

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

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

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

## Protected Member Functions

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

Protected Member Functions inherited from GasTransport
GasTransport (ThermoPhase *thermo=0)

virtual void update_T ()

virtual void update_C ()=0

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

Update the pure-species viscosities.

virtual void updateDiff_T ()
Update the binary diffusion coefficients.

virtual void setupCollisionParameters ()
Setup parameters for a new kinetic-theory-based transport manager for low-density gases.

void setupCollisionIntegral ()
Setup range for polynomial fits to collision integrals of Monchick & Mason [27].

void getTransportData ()

void makePolarCorrections (size_t i, size_t j, double &f_eps, double &f_sigma)
Corrections for polar-nonpolar binary diffusion coefficients.

void fitCollisionIntegrals (MMCollisionInt &integrals)
Generate polynomial fits to collision integrals.

virtual void fitProperties (MMCollisionInt &integrals)
Generate polynomial fits to the viscosity $$\eta$$ and conductivity $$\lambda$$.

virtual void fitDiffCoeffs (MMCollisionInt &integrals)
Generate polynomial fits to the binary diffusion coefficients.

void getBinDiffCorrection (double t, MMCollisionInt &integrals, size_t k, size_t j, double xk, double xj, double &fkj, double &fjk)
Second-order correction to the binary diffusion coefficients.

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

## Protected Attributes

vector< double > m_cond
vector of species thermal conductivities (W/m /K)

double m_lambda = 0.0
Internal storage for the calculated mixture thermal conductivity.

bool m_spcond_ok = false
Update boolean for the species thermal conductivities.

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

Protected Attributes inherited from GasTransport
vector< double > m_molefracs
Vector of species mole fractions.

double m_viscmix = 0.0
Internal storage for the viscosity of the mixture (kg /m /s)

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

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

bool m_spvisc_ok = false
Update boolean for the species viscosities.

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

int m_mode = 0
Type of the polynomial fits to temperature.

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

vector< double > m_spwork
work space length = m_kk

vector< double > m_visc
vector of species viscosities (kg /m /s).

vector< vector< double > > m_visccoeffs
Polynomial fits to the viscosity of each species.

vector< double > 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< double > m_sqvisc
vector of square root of species viscosities sqrt(kg /m /s).

vector< double > m_polytempvec
Powers of the ln temperature, up to fourth order.

double m_temp = -1.0
Current value of the temperature at which the properties in this object are calculated (Kelvin).

double m_kbt = 0.0
Current value of Boltzmann constant times the temperature (Joules)

double m_sqrt_t = 0.0
current value of temperature to 1/2 power

double m_logt = 0.0
Current value of the log of the temperature.

double m_t14 = 0.0
Current value of temperature to 1/4 power.

vector< vector< double > > m_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.

vector< vector< double > > m_condcoeffs
temperature fits of the heat conduction

vector< vector< int > > m_poly
Indices for the (i,j) interaction in collision integral fits.

vector< vector< double > > m_omega22_poly
Fit for omega22 collision integral.

vector< vector< int > > m_star_poly_uses_actualT
Flag to indicate for which (i,j) interaction pairs the actual temperature is used instead of the reduced temperature.

vector< vector< double > > m_astar_poly
Fit for astar collision integral.

vector< vector< double > > m_bstar_poly
Fit for bstar collision integral.

vector< vector< double > > m_cstar_poly
Fit for cstar collision integral.

vector< double > m_zrot
Rotational relaxation number for each species.

vector< double > m_crot
Dimensionless rotational heat capacity of each species.

vector< bool > m_polar
Vector of booleans indicating whether a species is a polar molecule.

vector< double > m_alpha
Polarizability of each species in the phase.

vector< double > m_eps
Lennard-Jones well-depth of the species in the current phase.

vector< double > m_sigma
Lennard-Jones diameter of the species in the current phase.

DenseMatrix m_reducedMass
This is the reduced mass of the interaction between species i and j.

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

DenseMatrix m_epsilon
The effective well depth for (i,j) collisions.

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

DenseMatrix m_delta
Reduced dipole moment of the interaction between two species.

vector< double > m_w_ac
Pitzer acentric factor.

vector< double > m_disp
Dispersion coefficient.

int m_log_level = 0
Level of verbose printing during initialization.

Protected Attributes inherited from Transport
ThermoPhasem_thermo
pointer to the object representing the phase

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< Solutionm_root
reference to Solution

## ◆ MixTransport()

 MixTransport ( )
default

Default constructor.

## ◆ 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.

Reimplemented in UnityLewisTransport.

Definition at line 60 of file MixTransport.h.

## ◆ getThermalDiffCoeffs()

 void getThermalDiffCoeffs ( double *const dt )
overridevirtual

Return the thermal diffusion coefficients.

For this approximation, these are all zero.

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

Reimplemented from Transport.

Definition at line 51 of file MixTransport.cpp.

## ◆ thermalConductivity()

 double thermalConductivity ( )
overridevirtual

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

Reimplemented from Transport.

Definition at line 32 of file MixTransport.cpp.

## ◆ getMobilities()

 void getMobilities ( double *const mobil )
overridevirtual

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 23 of file MixTransport.cpp.

## ◆ update_T()

 void update_T ( )
overridevirtual

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 83 of file MixTransport.cpp.

## ◆ update_C()

 void update_C ( )
overridevirtual

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 100 of file MixTransport.cpp.

## ◆ getSpeciesFluxes()

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

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 58 of file MixTransport.cpp.

## ◆ init()

 void init ( ThermoPhase * thermo, int mode = 0, int log_level = 0 )
overridevirtual

Initialize a transport manager.

This routine sets up a transport manager. It calculates the collision integrals and populates species-dependent data structures.

Parameters
 thermo Pointer to the ThermoPhase object mode Chemkin compatible mode or not. This alters the specification of the collision integrals. defaults to no. log_level Defaults to zero, no logging

Reimplemented from GasTransport.

Definition at line 17 of file MixTransport.cpp.

## ◆ updateCond_T()

 void updateCond_T ( )
protected

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 114 of file MixTransport.cpp.

## ◆ m_cond

 vector m_cond
protected

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 166 of file MixTransport.h.

## ◆ m_lambda

 double m_lambda = 0.0
protected

Internal storage for the calculated mixture thermal conductivity.

Units = W /m /K

Definition at line 172 of file MixTransport.h.

## ◆ m_spcond_ok

 bool m_spcond_ok = false
protected

Update boolean for the species thermal conductivities.

Definition at line 175 of file MixTransport.h.

## ◆ m_condmix_ok

 bool m_condmix_ok = false
protected

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

Definition at line 178 of file MixTransport.h.

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