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

#include <IonGasTransport.h>

Inheritance diagram for IonGasTransport:

Collaboration diagram for IonGasTransport:

Public Member Functions
virtual std::string	transportType () const
	Identifies the Transport object type. More...

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

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

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

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

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

virtual double	electricalConductivity ()

Public Member Functions inherited from MixTransport
	MixTransport ()
	Default constructor. More...

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

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

virtual void	update_C ()
	Update the internal parameters whenever the concentrations have changed. 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 mass averaged velocity, given the gradients in mole fraction and temperature. More...

Public Member Functions inherited from GasTransport
virtual void	getSpeciesViscosities (doublereal *const visc)
	Get the pure-species viscosities. More...

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

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

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

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

	Transport (const Transport &)=delete

Transport &	operator= (const Transport &)=delete

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. More...

void	checkSpeciesArraySize (size_t kk) const
	Check that an array size is at least nSpecies(). 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	getFluidMobilities (doublereal *const mobil_f)
	Get the fluid mobilities (s kmol/kg). 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	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. 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 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	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 void	setThermo (thermo_t &thermo)
	Specifies the ThermoPhase object. More...

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

Protected Member Functions
void	setupN64 ()
	setup parameters for n64 model More...

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

double	omega11_n64 (const double tstar, const double gamma)

Protected Member Functions inherited from MixTransport
doublereal	pressure_ig () const
	Calculate the pressure from the ideal gas law. More...

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

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

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

virtual void	updateSpeciesViscosities ()
	Update the pure-species viscosities. More...

virtual void	updateDiff_T ()
	Update the binary diffusion coefficients. More...

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

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

void	getTransportData ()
	Read the transport database. More...

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

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

virtual void	fitProperties (MMCollisionInt &integrals)
	Generate polynomial fits to the viscosity and conductivity. More...

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

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

Protected Attributes
vector_fp	m_speciesCharge
	electrical properties More...

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

std::vector< size_t >	m_kNeutral
	index of neutral species More...

size_t	m_kElectron
	index of electron More...

DenseMatrix	m_gamma
	parameter of omega11 of n64 More...

vector_fp	m_om11_O2
	polynomial of the collision integral for O2/O2- More...

Protected Attributes inherited from MixTransport
vector_fp	m_cond
	vector of species thermal conductivities (W/m /K) More...

doublereal	m_lambda
	Internal storage for the calculated mixture thermal conductivity. More...

bool	m_spcond_ok
	Update boolean for the species thermal conductivities. More...

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

Protected Attributes inherited from GasTransport
vector_fp	m_molefracs
	Vector of species mole fractions. More...

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

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

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

bool	m_spvisc_ok
	Update boolean for the species viscosities. More...

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

int	m_mode
	Type of the polynomial fits to temperature. More...

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

vector_fp	m_spwork
	work space length = m_kk More...

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

std::vector< vector_fp >	m_visccoeffs
	Polynomial fits to the viscosity of each species. More...

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

DenseMatrix	m_wratjk
	Holds square roots of molecular weight ratios. More...

DenseMatrix	m_wratkj1
	Holds square roots of molecular weight ratios. More...

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

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

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

doublereal	m_kbt
	Current value of Boltzmann constant times the temperature (Joules) More...

doublereal	m_sqrt_kbt
	current value of Boltzmann constant times the temperature. More...

doublereal	m_sqrt_t
	current value of temperature to 1/2 power More...

doublereal	m_logt
	Current value of the log of the temperature. More...

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

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

std::vector< vector_fp >	m_diffcoeffs
	Polynomial fits to the binary diffusivity of each species. More...

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

std::vector< vector_fp >	m_condcoeffs
	temperature fits of the heat conduction More...

std::vector< vector_int >	m_poly
	Indices for the (i,j) interaction in collision integral fits. More...

std::vector< vector_fp >	m_omega22_poly
	Fit for omega22 collision integral. More...

std::vector< vector_fp >	m_astar_poly
	Fit for astar collision integral. More...

std::vector< vector_fp >	m_bstar_poly
	Fit for bstar collision integral. More...

std::vector< vector_fp >	m_cstar_poly
	Fit for cstar collision integral. More...

vector_fp	m_zrot
	Rotational relaxation number for each species. More...

vector_fp	m_crot
	Dimensionless rotational heat capacity of each species. More...

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

vector_fp	m_alpha
	Polarizability of each species in the phase. More...

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

vector_fp	m_sigma
	Lennard-Jones diameter of the species in the current phase. More...

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

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

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

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

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

vector_fp	m_w_ac
	Pitzer acentric factor. More...

vector_fp	m_disp
	Dispersion coefficient. More...

vector_fp	m_quad_polar
	Quadrupole polarizability. More...

int	m_log_level
	Level of verbose printing during initialization. More...

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...

std::weak_ptr< Solution >	m_root
	reference to Solution More...

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, Stefan, and Uwe Riedel. "Transport properties of ionized species." Annals of the New York Academy of Sciences 891.1 (1999): 72-80.
Selle, Stefan, and Uwe Riedel. "Transport coefficients of reacting air at high temperatures." 38th Aerospace Sciences Meeting and Exhibit. 1999.
Han, Jie, et al. "Numerical modelling of ion transport in flames." Combustion Theory and Modelling 19.6 (2015): 744-772. DOI: 10.1080/13647830.2015.1090018
Chiflikian, R. V. "The analog of Blanc’s law for drift velocities of electrons in gas mixtures in weakly ionized plasma." Physics of Plasmas 2.10 (1995): 3902-3909.
Viehland, L. A., et al. "Tables of transport collision integrals for (n, 6, 4) ion-neutral potentials." Atomic Data and Nuclear Data Tables 16.6 (1975): 495-514.

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:

Prager, Jens. Modeling and simulation of charged species in lean methane-oxygen flames. Diss. 2005. Page 104.

Definition at line 49 of file IonGasTransport.h.

Member Function Documentation

◆ transportType()

virtual std::string transportType ( ) const

inlinevirtual

Identifies the Transport object type.

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

Reimplemented from MixTransport.

Definition at line 54 of file IonGasTransport.h.

◆ init()

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

virtual

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 MixTransport.

Definition at line 18 of file IonGasTransport.cpp.

References Cantera::npos, Phase::nSpecies(), and Cantera::polyfit().

◆ viscosity()

double viscosity ( )

virtual

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

Only Neutral species contribute to Viscosity.

Reimplemented from GasTransport.

Definition at line 87 of file IonGasTransport.cpp.

References Cantera::multiply().

◆ thermalConductivity()

double thermalConductivity ( )

virtual

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

Only Neutral species contribute to thermal conductivity.

Reimplemented from MixTransport.

Definition at line 111 of file IonGasTransport.cpp.

◆ getMobilities()

void getMobilities ( double *const mobi )

virtual

The mobilities for ions in gas.

The ion mobilities are calculated by Blanc's law.

Reimplemented from MixTransport.

Definition at line 373 of file IonGasTransport.cpp.

References Cantera::ElectronCharge.

◆ getMixDiffCoeffs()

void getMixDiffCoeffs ( double *const d )

virtual

The mixture transport for ionized gas.

The binary transport between two charged species is neglected.

Reimplemented from GasTransport.

Definition at line 338 of file IonGasTransport.cpp.

References Cantera::ElectronCharge.

◆ electricalConductivity()

double electricalConductivity ( )

virtual

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 130 of file IonGasTransport.cpp.

References Cantera::ElectronCharge, and Cantera::npos.

◆ setupN64()

void setupN64 ( )

protected

setup parameters for n64 model

Definition at line 238 of file IonGasTransport.cpp.

References Cantera::ElectronCharge, Cantera::epsilon_0, and Cantera::Pi.

◆ fitDiffCoeffs()

void fitDiffCoeffs ( MMCollisionInt & integrals )

protectedvirtual

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 147 of file IonGasTransport.cpp.

References Cantera::Boltzmann, Cantera::Pi, Cantera::poly4(), Cantera::poly5(), Cantera::polyfit(), Cantera::vec2str(), Cantera::writelog(), and Cantera::writelogf().

◆ 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 306 of file IonGasTransport.cpp.

Member Data Documentation

◆ m_speciesCharge

vector_fp m_speciesCharge

protected

electrical properties

Definition at line 101 of file IonGasTransport.h.

◆ m_kIon

std::vector<size_t> m_kIon

protected

index of ions (exclude electron.)

Definition at line 104 of file IonGasTransport.h.

◆ m_kNeutral

std::vector<size_t> m_kNeutral

protected

index of neutral species

Definition at line 107 of file IonGasTransport.h.

◆ m_kElectron

size_t m_kElectron

protected

index of electron

Definition at line 110 of file IonGasTransport.h.

◆ m_gamma

DenseMatrix m_gamma

protected

parameter of omega11 of n64

Definition at line 113 of file IonGasTransport.h.

◆ m_om11_O2

vector_fp m_om11_O2

protected

polynomial of the collision integral for O2/O2-

Definition at line 116 of file IonGasTransport.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

◆ transportType()

◆ 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