Class GasTransport implements some functions and properties that are shared by the MixTransport and MultiTransport classes. More...

#include <GasTransport.h>

Inheritance diagram for GasTransport:

[legend]

Detailed Description

Class GasTransport implements some functions and properties that are shared by the MixTransport and MultiTransport classes.

For details, see Kee, et al. [20] and [21].

Definition at line 25 of file GasTransport.h.

Public Member Functions
double	viscosity () override
	Get the viscosity [Pa·s] of the mixture.

void	getSpeciesViscosities (double *const visc) override
	Get the pure-species viscosities [Pa·s].

void	getBinaryDiffCoeffs (const size_t ld, double *const d) override
	Returns the matrix of binary diffusion coefficients [m²/s].

void	getMixDiffCoeffs (double *const d) override
	Returns the Mixture-averaged diffusion coefficients [m²/s].

void	getMixDiffCoeffsMole (double *const d) override
	Returns the mixture-averaged diffusion coefficients [m²/s].

void	getMixDiffCoeffsMass (double *const d) override
	Returns the mixture-averaged diffusion coefficients [m²/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) override
	Initialize a transport manager.

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

void	invalidateCache () override
	Invalidate any cached values which are normally updated only when a change in state is detected.

Public Member Functions inherited from Transport
	Transport ()=default
	Constructor.

	Transport (const Transport &)=delete

Transport &	operator= (const Transport &)=delete

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

ThermoPhase &	thermo ()
	Phase object.

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 m_nsp.

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 [kg/m²/s] with respect to the specified solution averaged velocity, given the mole fraction and temperature gradients.

virtual void	getMolarFluxes (const double const state1, const double const state2, const double delta, double *const cfluxes)
	Get the molar fluxes [kmol/m²/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/m²/s], given the thermodynamic state at two nearby points.

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

virtual void	getBinaryDiffCoeffs (const size_t ld, double *const d)
	Returns the matrix of binary diffusion coefficients [m²/s].

virtual void	getMultiDiffCoeffs (const size_t ld, double *const d)
	Return the multicomponent diffusion coefficients [m²/s].

virtual void	getMixDiffCoeffs (double *const d)
	Return a vector of mixture averaged diffusion coefficients [m²/s].

virtual void	getMixDiffCoeffsMole (double *const d)
	Returns a vector of mixture averaged diffusion coefficients [m²/s].

virtual void	getMixDiffCoeffsMass (double *const d)
	Returns a vector of mixture averaged diffusion coefficients [m²/s].

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)

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

AnyMap	fittingErrors () const
	Get error metrics about any functional fits calculated for pure species transport properties.

virtual void	invalidateCache ()
	Invalidate any cached values which are normally updated only when a change in state is detected.

virtual double	bulkViscosity ()
	The bulk viscosity [Pa·s].

virtual double	thermalConductivity ()
	Get the mixture thermal conductivity [W/m/K].

virtual double	electricalConductivity ()
	Get the electrical conductivity [siemens/m].

virtual void	getMobilities (double *const mobil_e)
	Get the electrical mobilities [m²/V/s].

Protected Member Functions
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.

Initialization
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 [31].

virtual 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 \( \lambda \).

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 Attributes
vector< double >	m_molefracs
	Vector of species mole fractions.

double	m_viscmix = 0.0
	Internal storage for the viscosity of the mixture [Pa·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
	Viscosity weighting function. size = m_nsp * m_nsp.

vector< double >	m_spwork
	work space length = m_nsp

vector< double >	m_visc
	vector of species viscosities [Pa·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.

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

double	m_temp = -1.0
	Current value of the temperature [K] at which the properties in this object are calculated.

double	m_kbt = 0.0
	Current value of Boltzmann constant times the temperature [J].

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 m_nsp x m_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 [m³] of each species in the phase.

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

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

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

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

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

DenseMatrix	m_dipole
	The effective dipole moment [Coulomb·m] for (i,j) collisions.

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

vector< double >	m_w_ac
	Pitzer acentric factor [dimensionless].

vector< double >	m_disp
	Dispersion coefficient normalized by the square of the elementary charge [m⁵].

vector< double >	m_quad_polar
	Quadrupole polarizability.

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

size_t	m_nsp = 0
	Number of species in the phase.

AnyMap	m_fittingErrors
	Maximum errors associated with fitting pure species transport properties.

Constructor & Destructor Documentation

◆ GasTransport()

GasTransport ( )

protected

Definition at line 23 of file GasTransport.cpp.

Member Function Documentation

◆ viscosity()

double viscosity ( )

overridevirtual

Get the viscosity [Pa·s] of the mixture.

The viscosity is computed using the Wilke mixture rule, as given in Poling et al. [38], Eqs. (9-5.13 and 9-5.14):

\[ \eta = \sum_k \frac{\eta_k X_k}{\sum_j \Phi_{k,j} X_j}. \]

Here, \( \eta_k \) is the viscosity of pure species k and the weighting function \( \Phi_{k,j} \) is:

\[ \Phi_{k,j} = \frac{ \left[ 1 + \left( \eta_k / \eta_j \right)^{1/2} \left( M_j / M_k \right)^{1/4} \right]^2 } {\left[ 8 \left( 1 + M_k / M_j \right) \right]^{1/2}} \]

See also: updateViscosity_T()

Reimplemented from Transport.

Reimplemented in HighPressureGasTransport, and IonGasTransport.

Definition at line 60 of file GasTransport.cpp.

◆ getSpeciesViscosities()

void getSpeciesViscosities ( double *const visc )

inlineoverridevirtual

Get the pure-species viscosities [Pa·s].

Reimplemented from Transport.

Definition at line 48 of file GasTransport.h.

◆ getBinaryDiffCoeffs()

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

overridevirtual

Returns the matrix of binary diffusion coefficients [m²/s].

Parameters

[in]	ld	Leading dimension of the flattened array `d` used to store the diffusion coefficient matrix; usually equal to the number of species.
[out]	d	Diffusion coefficient matrix stored in column-major (Fortran) order, such that \( \mathcal{D}_{ij} = \tt{d[ld*j + i]} \); must be at least `ld` times the number of species in length.

See also: GasTransport::fitDiffCoeffs()

Reimplemented from Transport.

Reimplemented in HighPressureGasTransportBase.

Definition at line 149 of file GasTransport.cpp.

◆ getMixDiffCoeffs()

void getMixDiffCoeffs ( double *const d )

overridevirtual

Returns the Mixture-averaged diffusion coefficients [m²/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"

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

Parameters

[out] d Vector of mixture diffusion coefficients, \( D_{km}' \) , for each species; length is the number of species.

Reimplemented from Transport.

Reimplemented in HighPressureGasTransportBase, IonGasTransport, and UnityLewisTransport.

Definition at line 167 of file GasTransport.cpp.

◆ getMixDiffCoeffsMole()

void getMixDiffCoeffsMole ( double *const d )

overridevirtual

Returns the mixture-averaged diffusion coefficients [m²/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.

Reimplemented in HighPressureGasTransportBase, and UnityLewisTransport.

Definition at line 198 of file GasTransport.cpp.

◆ getMixDiffCoeffsMass()

void getMixDiffCoeffsMass ( double *const d )

overridevirtual

Returns the mixture-averaged diffusion coefficients [m²/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.

Reimplemented in HighPressureGasTransportBase, and UnityLewisTransport.

Definition at line 228 of file GasTransport.cpp.

◆ getViscosityPolynomial()

void getViscosityPolynomial	(	size_t	i,
		double *	coeffs
	)		const

overridevirtual

Return the polynomial fits to the viscosity of species i.

See also: fitProperties()

Reimplemented from Transport.

Definition at line 753 of file GasTransport.cpp.

◆ getConductivityPolynomial()

void getConductivityPolynomial	(	size_t	i,
		double *	coeffs
	)		const

overridevirtual

Return the temperature fits of the heat conductivity of species i.

See also: fitProperties()

Reimplemented from Transport.

Definition at line 761 of file GasTransport.cpp.

◆ getBinDiffusivityPolynomial()

void getBinDiffusivityPolynomial	(	size_t	i,
		size_t	j,
		double *	coeffs
	)		const

overridevirtual

Return the polynomial fits to the binary diffusivity of species pair (i, j)

See also: fitDiffCoeffs()

Reimplemented from Transport.

Definition at line 769 of file GasTransport.cpp.

◆ getCollisionIntegralPolynomial()

void getCollisionIntegralPolynomial	(	size_t	i,
		size_t	j,
		double *	astar_coeffs,
		double *	bstar_coeffs,
		double *	cstar_coeffs
	)		const

overridevirtual

Return the polynomial fits to the collision integral of species pair (i, j)

See also: fitCollisionIntegrals()

Reimplemented from Transport.

Definition at line 786 of file GasTransport.cpp.

◆ setViscosityPolynomial()

void setViscosityPolynomial	(	size_t	i,
		double *	coeffs
	)

overridevirtual

Modify the polynomial fits to the viscosity of species i

See also: fitProperties()

Reimplemented from Transport.

Definition at line 800 of file GasTransport.cpp.

◆ setConductivityPolynomial()

void setConductivityPolynomial	(	size_t	i,
		double *	coeffs
	)

overridevirtual

Modify the temperature fits of the heat conductivity of species i

See also: fitProperties()

Reimplemented from Transport.

Definition at line 809 of file GasTransport.cpp.

◆ setBinDiffusivityPolynomial()

void setBinDiffusivityPolynomial	(	size_t	i,
		size_t	j,
		double *	coeffs
	)

overridevirtual

Modify the polynomial fits to the binary diffusivity of species pair (i, j)

See also: fitDiffCoeffs()

Reimplemented from Transport.

Definition at line 818 of file GasTransport.cpp.

◆ setCollisionIntegralPolynomial()

void setCollisionIntegralPolynomial	(	size_t	i,
		size_t	j,
		double *	astar_coeffs,
		double *	bstar_coeffs,
		double *	cstar_coeffs,
		bool	actualT
	)

overridevirtual

Modify the polynomial fits to the collision integral of species pair (i, j)

See also: fitCollisionIntegrals()

Reimplemented from Transport.

Definition at line 836 of file GasTransport.cpp.

◆ init()

void init	(	ThermoPhase *	thermo,
		int	mode = `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.

Reimplemented from Transport.

Reimplemented in IonGasTransport, HighPressureGasTransport, MixTransport, and MultiTransport.

Definition at line 261 of file GasTransport.cpp.

◆ CKMode()

bool CKMode ( ) const

inlineoverridevirtual

Boolean indicating the form of the transport properties polynomial fits.

Returns true if the Chemkin form is used.

Reimplemented from Transport.

Definition at line 144 of file GasTransport.h.

◆ invalidateCache()

void invalidateCache ( )

overridevirtual

Invalidate any cached values which are normally updated only when a change in state is detected.

Since: New in Cantera 3.1.

Reimplemented from Transport.

Reimplemented in MultiTransport.

Definition at line 353 of file GasTransport.cpp.

◆ update_T()

void update_T ( )

protectedvirtual

Reimplemented in MixTransport, and MultiTransport.

Definition at line 28 of file GasTransport.cpp.

◆ update_C()

virtual void update_C ( )

protectedpure virtual

Implemented in MixTransport, and MultiTransport.

◆ updateViscosity_T()

void updateViscosity_T ( )

protectedvirtual

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.

See also: viscosity()

Definition at line 84 of file GasTransport.cpp.

◆ updateSpeciesViscosities()

void updateSpeciesViscosities ( )

protectedvirtual

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 105 of file GasTransport.cpp.

◆ updateDiff_T()

void updateDiff_T ( )

protectedvirtual

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 123 of file GasTransport.cpp.

◆ setupCollisionParameters()

void setupCollisionParameters ( )

protectedvirtual

Setup parameters for a new kinetic-theory-based transport manager for low-density gases.

Definition at line 292 of file GasTransport.cpp.

◆ setupCollisionIntegral()

void setupCollisionIntegral ( )

protected

Setup range for polynomial fits to collision integrals of Monchick & Mason [31].

Definition at line 363 of file GasTransport.cpp.

◆ getTransportData()

void getTransportData ( )

protectedvirtual

Read the transport database.

Read transport property data from a file for a list of species. Given the name of a file containing transport property parameters and a list of species names.

Reimplemented in HighPressureGasTransportBase.

Definition at line 389 of file GasTransport.cpp.

◆ makePolarCorrections()

void makePolarCorrections	(	size_t	i,
		size_t	j,
		double &	f_eps,
		double &	f_sigma
	)

protected

Corrections for polar-nonpolar binary diffusion coefficients.

Calculate corrections to the well depth parameter and the diameter for use in computing the binary diffusion coefficient of polar-nonpolar pairs. For more information about this correction, see Dixon-Lewis [7].

Parameters

i	Species one - this is a bimolecular correction routine
j	species two - this is a bimolecular correction routine
f_eps	Multiplicative correction factor to be applied to epsilon(i,j)
f_sigma	Multiplicative correction factor to be applied to diam(i,j)

Definition at line 426 of file GasTransport.cpp.

◆ fitCollisionIntegrals()

void fitCollisionIntegrals ( MMCollisionInt & integrals )

protected

Generate polynomial fits to collision integrals.

Parameters

integrals interpolator for the collision integrals

Definition at line 451 of file GasTransport.cpp.

◆ fitProperties()

void fitProperties ( MMCollisionInt & integrals )

protectedvirtual

Generate polynomial fits to the viscosity \( \eta \) and conductivity \( \lambda \).

If CKMode(), then the fits are of the form

\[ \ln \eta(i) = \sum_{n=0}^3 a_n(i) \, (\ln T)^n \]

and

\[ \ln \lambda(i) = \sum_{n=0}^3 b_n(i) \, (\ln T)^n \]

Otherwise the fits are of the form

\[ \left(\eta(i)\right)^{1/2} = T^{1/4} \sum_{n=0}^4 a_n(i) \, (\ln T)^n \]

and

\[ \lambda(i) = T^{1/2} \sum_{n=0}^4 b_n(i) \, (\ln T)^n \]

Parameters

integrals interpolator for the collision integrals

Definition at line 494 of file GasTransport.cpp.

◆ fitDiffCoeffs()

void fitDiffCoeffs ( MMCollisionInt & integrals )

protectedvirtual

Generate polynomial fits to the binary diffusion coefficients.

If CKMode(), then the fits are of the form

\[ \ln \mathcal{D}(i,j) = \frac{1}{p} \sum_{n=0}^3 c_n(i,j) \, (\ln T)^n \]

Otherwise the fits are of the form

\[ \mathcal{D}(i,j) = \frac{T^{3/2}}{p} \sum_{n=0}^4 c_n(i,j) \, (\ln T)^n \]

Parameters

integrals interpolator for the collision integrals

Reimplemented in IonGasTransport.

Definition at line 630 of file GasTransport.cpp.

◆ getBinDiffCorrection()

void getBinDiffCorrection	(	double	t,
		MMCollisionInt &	integrals,
		size_t	k,
		size_t	j,
		double	xk,
		double	xj,
		double &	fkj,
		double &	fjk
	)

protected

Second-order correction to the binary diffusion coefficients.

Calculate second-order corrections to binary diffusion coefficient pair (dkj, djk). At first order, the binary diffusion coefficients are independent of composition, and d(k,j) = d(j,k). But at second order, there is a weak dependence on composition, with the result that d(k,j) != d(j,k). This method computes the multiplier by which the first-order binary diffusion coefficient should be multiplied to produce the value correct to second order. The expressions here are taken from Marerro and Mason [28].

Parameters

t	Temperature (K)
integrals	interpolator for the collision integrals
k	index of first species
j	index of second species
xk	Mole fraction of species k
xj	Mole fraction of species j
fkj	multiplier for d(k,j)
fjk	multiplier for d(j,k)

Note: This method is not used currently.

Definition at line 701 of file GasTransport.cpp.

Member Data Documentation

◆ m_molefracs

vector<double> m_molefracs

protected

Vector of species mole fractions.

These are processed so that all mole fractions are >= Tiny. Length = m_nsp.

Definition at line 284 of file GasTransport.h.

◆ m_viscmix

double m_viscmix = 0.0

protected

Internal storage for the viscosity of the mixture [Pa·s].

Definition at line 287 of file GasTransport.h.

◆ m_visc_ok

bool m_visc_ok = false

protected

Update boolean for mixture rule for the mixture viscosity.

Definition at line 290 of file GasTransport.h.

◆ m_viscwt_ok

bool m_viscwt_ok = false

protected

Update boolean for the weighting factors for the mixture viscosity.

Definition at line 293 of file GasTransport.h.

◆ m_spvisc_ok

bool m_spvisc_ok = false

protected

Update boolean for the species viscosities.

Definition at line 296 of file GasTransport.h.

◆ m_bindiff_ok

bool m_bindiff_ok = false

protected

Update boolean for the binary diffusivities at unit pressure.

Definition at line 299 of file GasTransport.h.

◆ m_mode

int m_mode = 0

protected

Type of the polynomial fits to temperature.

CK_Mode means Chemkin mode. Any other value means to use Cantera's preferred fitting functions.

Definition at line 303 of file GasTransport.h.

◆ m_phi

DenseMatrix m_phi

protected

Viscosity weighting function. size = m_nsp * m_nsp.

Definition at line 306 of file GasTransport.h.

◆ m_spwork

vector<double> m_spwork

protected

work space length = m_nsp

Definition at line 309 of file GasTransport.h.

◆ m_visc

vector<double> m_visc

protected

vector of species viscosities [Pa·s].

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

Definition at line 313 of file GasTransport.h.

◆ m_visccoeffs

vector<vector<double> > m_visccoeffs

protected

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 318 of file GasTransport.h.

◆ m_mw

vector<double> m_mw

protected

Local copy of the species molecular weights.

Definition at line 321 of file GasTransport.h.

◆ m_wratjk

DenseMatrix m_wratjk

protected

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

Cantera::GasTransport::m_wratjk

DenseMatrix m_wratjk

Holds square roots of molecular weight ratios.

Definition GasTransport.h:330

Definition at line 330 of file GasTransport.h.

◆ m_wratkj1

DenseMatrix m_wratkj1

protected

Holds square roots of molecular weight ratios.

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

Definition at line 336 of file GasTransport.h.

◆ m_sqvisc

vector<double> m_sqvisc

protected

vector of square root of species viscosities.

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

Definition at line 340 of file GasTransport.h.

◆ m_polytempvec

vector<double> m_polytempvec

protected

Powers of the ln temperature, up to fourth order.

Definition at line 343 of file GasTransport.h.

◆ m_temp

double m_temp = -1.0

protected

Current value of the temperature [K] at which the properties in this object are calculated.

Definition at line 347 of file GasTransport.h.

◆ m_kbt

double m_kbt = 0.0

protected

Current value of Boltzmann constant times the temperature [J].

Definition at line 350 of file GasTransport.h.

◆ m_sqrt_t

double m_sqrt_t = 0.0

protected

current value of temperature to 1/2 power

Definition at line 353 of file GasTransport.h.

◆ m_logt

double m_logt = 0.0

protected

Current value of the log of the temperature.

Definition at line 356 of file GasTransport.h.

◆ m_t14

double m_t14 = 0.0

protected

Current value of temperature to 1/4 power.

Definition at line 359 of file GasTransport.h.

◆ m_diffcoeffs

vector<vector<double> > m_diffcoeffs

protected

Polynomial fits to the binary diffusivity of each species.

m_diffcoeff[ic] is the vector of polynomial coefficients that fits the binary diffusion coefficient for species i and j. 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 375 of file GasTransport.h.

◆ m_bdiff

DenseMatrix m_bdiff

protected

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

Definition at line 379 of file GasTransport.h.

◆ m_condcoeffs

vector<vector<double> > m_condcoeffs

protected

temperature fits of the heat conduction

Dimensions are number of species (m_nsp) and polynomial order of the collision integral fit (degree+1).

Definition at line 386 of file GasTransport.h.

◆ m_poly

vector<vector<int> > m_poly

protected

Indices for the (i,j) interaction in collision integral fits.

m_poly[i][j] contains the index for (i,j) interactions in m_omega22_poly, m_astar_poly, m_bstar_poly, and m_cstar_poly.

Definition at line 393 of file GasTransport.h.

◆ m_omega22_poly

vector<vector<double> > m_omega22_poly

protected

Fit for omega22 collision integral.

m_omega22_poly[m_poly[i][j]] is the vector of polynomial coefficients (length degree+1) for the collision integral fit for the species pair (i,j).

Definition at line 400 of file GasTransport.h.

◆ m_star_poly_uses_actualT

vector<vector<int> > m_star_poly_uses_actualT

protected

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

Definition at line 404 of file GasTransport.h.

◆ m_astar_poly

vector<vector<double> > m_astar_poly

protected

Fit for astar collision integral.

m_astar_poly[m_poly[i][j]] is the vector of polynomial coefficients (length degree+1) for the collision integral fit for the species pair (i,j).

Definition at line 411 of file GasTransport.h.

◆ m_bstar_poly

vector<vector<double> > m_bstar_poly

protected

Fit for bstar collision integral.

m_bstar_poly[m_poly[i][j]] is the vector of polynomial coefficients (length degree+1) for the collision integral fit for the species pair (i,j).

Definition at line 418 of file GasTransport.h.

◆ m_cstar_poly

vector<vector<double> > m_cstar_poly

protected

Fit for cstar collision integral.

m_bstar_poly[m_poly[i][j]] is the vector of polynomial coefficients (length degree+1) for the collision integral fit for the species pair (i,j).

Definition at line 425 of file GasTransport.h.

◆ m_zrot

vector<double> m_zrot

protected

Rotational relaxation number for each species.

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

Definition at line 431 of file GasTransport.h.

◆ m_crot

vector<double> m_crot

protected

Dimensionless rotational heat capacity of each species.

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. Dimensionless (Cr / R)

Definition at line 439 of file GasTransport.h.

◆ m_polar

vector<bool> m_polar

protected

Vector of booleans indicating whether a species is a polar molecule.

Length is m_nsp.

Definition at line 445 of file GasTransport.h.

◆ m_alpha

vector<double> m_alpha

protected

Polarizability [m³] of each species in the phase.

Definition at line 448 of file GasTransport.h.

◆ m_eps

vector<double> m_eps

protected

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

length is the number of species in the phase. Note this is not J/kmol; this is a per molecule amount.

Definition at line 455 of file GasTransport.h.

◆ m_sigma

vector<double> m_sigma

protected

Lennard-Jones diameter [m] of the species in the current phase.

Definition at line 458 of file GasTransport.h.

◆ m_reducedMass

DenseMatrix m_reducedMass

protected

This is the reduced mass [kg] of the interaction between species i and j.

\[ m_{ij} = \frac{M_i M_j}{N_A (M_i + M_j)} \]

Length m_nsp * m_nsp. This is a symmetric matrix

Definition at line 467 of file GasTransport.h.

◆ m_diam

DenseMatrix m_diam

protected

hard-sphere diameter [m] for (i,j) collision

\[ \sigma_{ij} = \frac{\sigma_i + \sigma_j}{2} \]

Length m_nsp * m_nsp. This is a symmetric matrix.

Definition at line 476 of file GasTransport.h.

◆ m_epsilon

DenseMatrix m_epsilon

protected

The effective well depth [J] for (i,j) collisions.

\[ \epsilon_{ij} = \sqrt{\epsilon_i \epsilon_j} \]

Length m_nsp * m_nsp. This is a symmetric matrix.

Definition at line 485 of file GasTransport.h.

◆ m_dipole

DenseMatrix m_dipole

protected

The effective dipole moment [Coulomb·m] for (i,j) collisions.

\[ \mu_{ij} = \sqrt{\mu_i \mu_j} \]

Dipole moments are conventionally given in Debye. The conversion factor to Coulomb·m is \( 10^{-21} / c \approx 3.335 \times 10^{-30} \).

Length m_nsp * m_nsp. This is a symmetric matrix.

Definition at line 498 of file GasTransport.h.

◆ m_delta

DenseMatrix m_delta

protected

Reduced dipole moment of the interaction between two species.

\[ \tilde{\delta}^*_{ij} = \frac{ \mu_{ij}^2 }{ 8 \pi \varepsilon_0 \epsilon_{ij} \sigma_{ij}^3 } \]

Length m_nsp * m_nsp. This is a symmetric matrix

Definition at line 508 of file GasTransport.h.

◆ m_w_ac

vector<double> m_w_ac

protected

Pitzer acentric factor [dimensionless].

Length is the number of species in the phase.

Definition at line 514 of file GasTransport.h.

◆ m_disp

vector<double> m_disp

protected

Dispersion coefficient normalized by the square of the elementary charge [m⁵].

Definition at line 517 of file GasTransport.h.

◆ m_quad_polar

vector<double> m_quad_polar

protected

Quadrupole polarizability.

Definition at line 520 of file GasTransport.h.

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

Detailed Description

Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ GasTransport()

Member Function Documentation

◆ viscosity()

◆ getSpeciesViscosities()

◆ getBinaryDiffCoeffs()

◆ getMixDiffCoeffs()

◆ getMixDiffCoeffsMole()

◆ getMixDiffCoeffsMass()

◆ getViscosityPolynomial()

◆ getConductivityPolynomial()

◆ getBinDiffusivityPolynomial()

◆ getCollisionIntegralPolynomial()

◆ setViscosityPolynomial()

◆ setConductivityPolynomial()

◆ setBinDiffusivityPolynomial()

◆ setCollisionIntegralPolynomial()

◆ init()

◆ CKMode()

◆ invalidateCache()

◆ update_T()

◆ update_C()

◆ updateViscosity_T()

◆ updateSpeciesViscosities()

◆ updateDiff_T()

◆ setupCollisionParameters()

◆ setupCollisionIntegral()

◆ getTransportData()

◆ makePolarCorrections()

◆ fitCollisionIntegrals()

◆ fitProperties()

◆ fitDiffCoeffs()

◆ getBinDiffCorrection()

Member Data Documentation

◆ m_molefracs

◆ m_viscmix

◆ m_visc_ok

◆ m_viscwt_ok

◆ m_spvisc_ok

◆ m_bindiff_ok

◆ m_mode

◆ m_phi

◆ m_spwork

◆ m_visc

◆ m_visccoeffs

◆ m_mw

◆ m_wratjk

◆ m_wratkj1

◆ m_sqvisc

◆ m_polytempvec

◆ m_temp

◆ m_kbt

◆ m_sqrt_t

◆ m_logt

◆ m_t14

◆ m_diffcoeffs

◆ m_bdiff

◆ m_condcoeffs

◆ m_poly

◆ m_omega22_poly

◆ m_star_poly_uses_actualT

◆ m_astar_poly

◆ m_bstar_poly

◆ m_cstar_poly

◆ m_zrot

◆ m_crot

◆ m_polar

◆ m_alpha

◆ m_eps

◆ m_sigma

◆ m_reducedMass

◆ m_diam

◆ m_epsilon

◆ m_dipole

◆ m_delta

◆ m_w_ac