Class IonGasTransport implements Stockmayer-(n,6,4) model for transport of ions. More...

#include <IonGasTransport.h>

Inheritance diagram for IonGasTransport:

Detailed Description

Class IonGasTransport implements Stockmayer-(n,6,4) model for transport of ions.

As implemented here, only binary transport between neutrals and ions is considered for calculating mixture-average diffusion coefficients and mobilities. When polarizability is not provide for an ion, LJ model is used instead of n64 model. Only neutral species are considered for thermal conductivity and viscosity.

References for Stockmayer-(n,6,4) model: Selle and Riedel [36], [37]; Han et al. [11]; Chiflikian [4]; and Viehland et al. [46].

Stockmayer-(n,6,4) model is not suitable for collision between O2/O2- due to resonant charge transfer. Therefore, an experimental collision data is used instead.

Data taken from [34].

Definition at line 34 of file IonGasTransport.h.

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

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

double	viscosity () override
	Viscosity of the mixture (kg/m/s).

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

void	getMobilities (double *const mobi) override
	The mobilities for ions in gas.

void	getMixDiffCoeffs (double *const d) override
	The mixture transport for ionized gas.

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

Public Member Functions inherited from MixTransport
	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

Transport &	operator= (const Transport &)=delete

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

string	transportType () const
	Identifies the Transport object type.

ThermoPhase &	thermo ()
	Phase object.

bool	ready ()
	Returns true if the transport manager is ready for use.

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

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

void	checkSpeciesIndex (size_t k) const
	Check that the specified species index is in range.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	setVelocityBasis (VelocityBasis ivb)
	Sets the velocity basis.

VelocityBasis	getVelocityBasis () const
	Gets the velocity basis.

virtual double	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 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	setupN64 ()
	setup parameters for n64 model

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

double	omega11_n64 (const double tstar, const double gamma)
	Collision integral of omega11 of n64 collision model.

Protected Member Functions inherited from MixTransport
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.

virtual void	updateSpeciesViscosities ()
	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 ()
	Read the transport database.

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 \( \lambda \).

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_speciesCharge
	electrical properties

vector< size_t >	m_kIon
	index of ions (exclude electron.)

vector< size_t >	m_kNeutral
	index of neutral species

size_t	m_kElectron = npos
	index of electron

DenseMatrix	m_gamma
	parameter of omega11 of n64

vector< double >	m_om11_O2
	polynomial of the collision integral for O2/O2-

Protected Attributes inherited from MixTransport
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.

vector< double >	m_quad_polar
	Quadrupole polarizability.

int	m_log_level = 0
	Level of verbose printing during initialization.

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

bool	m_ready = false
	true if finalize has been called

size_t	m_nsp = 0
	Number of species.

size_t	m_nDim
	Number of dimensions used in flux expressions.

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

std::weak_ptr< Solution >	m_root
	reference to Solution

Member Function Documentation

◆ transportModel()

string transportModel ( ) const

inlineoverridevirtual

Identifies the model represented by this Transport object.

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

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

Reimplemented from Transport.

Definition at line 39 of file IonGasTransport.h.

◆ init()

void init	(	ThermoPhase *	thermo,
		int	mode,
		int	log_level
	)

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 IonGasTransport.cpp.

◆ viscosity()

double viscosity ( )

overridevirtual

Viscosity of the mixture (kg/m/s).

Only Neutral species contribute to Viscosity.

Reimplemented from GasTransport.

Definition at line 96 of file IonGasTransport.cpp.

◆ thermalConductivity()

double thermalConductivity ( )

overridevirtual

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

Only Neutral species contribute to thermal conductivity.

Reimplemented from Transport.

Definition at line 120 of file IonGasTransport.cpp.

◆ getMobilities()

void getMobilities ( double *const mobi )

overridevirtual

The mobilities for ions in gas.

The ion mobilities are calculated by Blanc's law.

Reimplemented from Transport.

Definition at line 382 of file IonGasTransport.cpp.

◆ getMixDiffCoeffs()

void getMixDiffCoeffs ( double *const d )

overridevirtual

The mixture transport for ionized gas.

The binary transport between two charged species is neglected.

Reimplemented from GasTransport.

Definition at line 347 of file IonGasTransport.cpp.

◆ electricalConductivity()

double electricalConductivity ( )

overridevirtual

The electrical conductivity (Siemens/m).

\[ \sigma = \sum_k{\left|C_k\right| \mu_k \frac{X_k P}{k_b T}} \]

Reimplemented from Transport.

Definition at line 139 of file IonGasTransport.cpp.

◆ setupN64()

void setupN64 ( )

protected

setup parameters for n64 model

Definition at line 247 of file IonGasTransport.cpp.

◆ fitDiffCoeffs()

void fitDiffCoeffs ( MMCollisionInt & integrals )

overrideprotectedvirtual

Generate polynomial fits to the binary diffusion coefficients.

Use Stockmayer-(n,6,4) model for collision between charged and neutral species.

Reimplemented from GasTransport.

Definition at line 156 of file IonGasTransport.cpp.

◆ omega11_n64()

double omega11_n64	(	const double	tstar,
		const double	gamma
	)

protected

Collision integral of omega11 of n64 collision model.

The collision integral was fitted by Han et al. using the table by Viehlan et al. Note: Han release the range to 1000, but Selle suggested that a high temperature model is needed for T* > 10.

Definition at line 315 of file IonGasTransport.cpp.

Member Data Documentation

◆ m_speciesCharge

vector<double> m_speciesCharge

protected

electrical properties

Definition at line 87 of file IonGasTransport.h.

◆ m_kIon

vector<size_t> m_kIon

protected

index of ions (exclude electron.)

Definition at line 90 of file IonGasTransport.h.

◆ m_kNeutral

vector<size_t> m_kNeutral

protected

index of neutral species

Definition at line 93 of file IonGasTransport.h.

◆ m_kElectron

size_t m_kElectron = npos

protected

index of electron

Definition at line 96 of file IonGasTransport.h.

◆ m_gamma

DenseMatrix m_gamma

protected

parameter of omega11 of n64

Definition at line 99 of file IonGasTransport.h.

◆ m_om11_O2

vector<double> m_om11_O2

protected

polynomial of the collision integral for O2/O2-

Definition at line 102 of file IonGasTransport.h.

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

Detailed Description

Public Member Functions

Protected Member Functions

Protected Attributes

Member Function Documentation

◆ transportModel()

◆ init()

◆ viscosity()

◆ thermalConductivity()

◆ getMobilities()

◆ getMixDiffCoeffs()

◆ electricalConductivity()

◆ setupN64()

◆ fitDiffCoeffs()

◆ omega11_n64()

Member Data Documentation

◆ m_speciesCharge

◆ m_kIon

◆ m_kNeutral

◆ m_kElectron

◆ m_gamma

◆ m_om11_O2