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

#include <MixTransport.h>

Inheritance diagram for MixTransport:

Detailed Description

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

The model is based on that described in Kee, et al. [20].

Specific mixture-averaged formulas are implemented by:

Definition at line 35 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 [kg/m/s].

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

void	getMobilities (double *const mobil) override
	Get the electrical mobilities [m²/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 [kg/m²/s] with respect to the mass averaged velocity, given the gradients in mole fraction and temperature.

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

Public Member Functions inherited from GasTransport
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	electricalConductivity ()
	Get the electrical conductivity [siemens/m].

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

Protected Member Functions inherited from GasTransport
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 [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_cond
	vector of species thermal conductivities [W/m/K]

double	m_lambda = 0.0
	Internal storage for the calculated mixture thermal conductivity [W/m/K].

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 [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

◆ MixTransport()

MixTransport ( )

default

Default constructor.

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.

Reimplemented in UnityLewisTransport.

Definition at line 41 of file MixTransport.h.

◆ getThermalDiffCoeffs()

void getThermalDiffCoeffs ( double *const dt )

overridevirtual

Return the thermal diffusion coefficients [kg/m/s].

Model by S. Chapman and T.G. Cowling [4]. For more information about this implementation and its validation, see T. Zirwes and A. Kronenburg [56].

The thermal diffusion coefficient of species \( k \) is computed from

\[ D_k^{T}= \frac{1}{2}\rho\frac{M_k}{\bar{M}}D_{mk}'\Theta_k \]

with

\[ \Theta_k=\frac{15}{2}\frac{\bar{M}^2}{\rho}\sum_i\left(\frac{1.2C_{ki}^*-1}{D_{ki}}\right)\left(\frac{Y_k\frac{\eta_i}{M_i}a_i-Y_i\frac{\eta_k}{M_k}a_k}{M_k+M_i}\right) \]

where \( C_{k,i}^* \) is a reduced collision integral and

\[ a_k=\left(1+\frac{1.065}{2\sqrt{2}X_k}\sum_{i\ne k}X_i\Phi_{k,i}\right)^{-1}, \]

with \( \Phi_{k,i} \) the Wilke mixing operator. The thermodiffusion coefficients are then normalized with

\[ \hat{D}^T_k=D^T_k-Y_k\sum_i D^T_i. \]

This ensures that the sum of all thermodiffusion coefficients and thus the sum of all thermodiffusion fluxes are zero.

Parameters

[out] dt Vector of thermal diffusion coefficients

Reimplemented from Transport.

Reimplemented in UnityLewisTransport.

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

\[ \mathbf{q} = - \lambda \nabla T \]

Reimplemented from Transport.

Definition at line 32 of file MixTransport.cpp.

◆ getMobilities()

void getMobilities ( double *const mobil )

overridevirtual

Get the electrical mobilities [m²/V/s].

This function returns the mobilities. Here, the mobility is calculated from the diffusion coefficient using the Einstein relation:

\[ \mu^e_k = \frac{F D_{km}'}{R T} \]

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 151 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 164 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 [kg/m²/s] with respect to the mass averaged velocity, given the gradients in mole fraction and temperature.

The diffusive mass flux of species k is computed from

\[ \mathbf{j}_k = -\rho \frac{M_k}{\overline{M}} D_{km}' \nabla X_k. \]

Parameters

	ndim	Number of dimensions in the flux expressions
[in]	grad_T	Gradient of the temperature (length `ndim`)
	ldx	Leading dimension of the `grad_X` array (usually equal to the number of species)
[in]	grad_X	Gradients of the mole fractions; flattened matrix such that \( dX_k/dx_n = \tt{ grad\_X[nldx+k]} \) is the gradient of species k in dimension n. Length is `ldx` `ndim`.
	ldf	Leading dimension of the `fluxes` array (usually equal to the number of species)
[out]	fluxes	The diffusive mass fluxes; flattened matrix such that \( j_{kn} = \tt{ fluxes[nldf+k]} \) is the flux of species k in dimension n. Length is `ldf` `ndim`.

Reimplemented from Transport.

Definition at line 126 of file MixTransport.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 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 178 of file MixTransport.cpp.

Member Data Documentation

◆ m_cond

vector<double> 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. length = m_nsp.

Definition at line 160 of file MixTransport.h.

◆ m_lambda

double m_lambda = 0.0

protected

Internal storage for the calculated mixture thermal conductivity [W/m/K].

Definition at line 163 of file MixTransport.h.

◆ m_spcond_ok

bool m_spcond_ok = false

protected

Update boolean for the species thermal conductivities.

Definition at line 166 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 169 of file MixTransport.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

◆ MixTransport()

Member Function Documentation

◆ transportModel()

◆ getThermalDiffCoeffs()

◆ thermalConductivity()

◆ getMobilities()

◆ update_T()

◆ update_C()

◆ getSpeciesFluxes()

◆ init()

◆ updateCond_T()

Member Data Documentation

◆ m_cond

◆ m_lambda

◆ m_spcond_ok

◆ m_condmix_ok