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

#include <MixTransport.h>

Inheritance diagram for MixTransport:

Collaboration diagram for MixTransport:

Public Member Functions
	MixTransport (const MixTransport &right)

MixTransport &	operator= (const MixTransport &right)

virtual Transport *	duplMyselfAsTransport () const
	Duplication routine for objects which inherit from Transport. More...

virtual int	model () const
	Return the model id for transport. More...

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

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

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

virtual bool	initGas (GasTransportParams &tr)
	Initialize the transport object. More...

Public Member Functions inherited from GasTransport
	GasTransport (const GasTransport &right)

GasTransport &	operator= (const GasTransport &right)

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

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	getMixDiffCoeffs (doublereal *const d)
	Returns the Mixture-averaged diffusion coefficients [m^2/s]. 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 &right)

Transport &	operator= (const Transport &right)

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 Throws an exception if k is greater than nSpecies() More...

void	checkSpeciesArraySize (size_t kk) const
	Check that an array size is at least nSpecies() Throws an exception if kk is less than nSpecies(). 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 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	selfDiffusion (doublereal *const selfDiff)
	Returns the self diffusion coefficients of the species in the phase. More...

virtual void	getSpeciesSelfDiffusion (double **selfDiff)
	Returns the pure species self diffusion in solution of each species. More...

virtual doublereal	electricalConductivity ()

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

virtual bool	initSolid (SolidTransportData &tr)
	Called by TransportFactory to set parameters. More...

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

Public Attributes
vector_fp	m_eps

vector_fp	m_sigma

vector_fp	m_alpha

DenseMatrix	m_dipole

vector_fp	m_zrot

vector_fp	m_crot

Protected Member Functions
	MixTransport ()
	Default constructor. 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...

Protected Member Functions inherited from Transport
virtual bool	initLiquid (LiquidTransportParams &tr)
	Called by TransportFactory to set parameters. More...

void	finalize ()
	Enable the transport object for use. More...

Private Member Functions
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...

Private Attributes
std::vector< vector_fp >	m_condcoeffs
	Polynomial fits to the thermal conductivity of each species. More...

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...

bool	m_debug
	Debug flag - turns on more printing. More...

Friends
class	TransportFactory

Additional Inherited Members
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 Boltzman's constant times the temperature (Joules) More...

doublereal	m_sqrt_kbt
	current value of Boltzman's 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...

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...

Detailed Description

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

The model is based on that described by Kee, Coltrin, and Glarborg, "Theoretical and Practical Aspects of Chemically Reacting Flow Modeling."

The viscosity is computed using the Wilke mixture rule (kg /m /s)

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

Here \( \mu_k \) is the viscosity of pure species k, and

\[ \Phi_{k,j} = \frac{\left[1 + \sqrt{\left(\frac{\mu_k}{\mu_j}\sqrt{\frac{M_j}{M_k}}\right)}\right]^2} {\sqrt{8}\sqrt{1 + M_k/M_j}} \]

The thermal conductivity is computed from the following mixture rule:

\[ \lambda = 0.5 \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k/\lambda_k} \right) \]

It's used to compute the flux of energy due to a thermal gradient

\[ j_T = - \lambda \nabla T \]

The flux of energy has units of energy (kg m2 /s2) per second per area.

The units of lambda are W / m K which is equivalent to kg m / s^3 K.

Definition at line 56 of file MixTransport.h.

Constructor & Destructor Documentation

MixTransport ( )

protected

Default constructor.

Definition at line 19 of file MixTransport.cpp.

Referenced by MixTransport::duplMyselfAsTransport().

Member Function Documentation

Transport * duplMyselfAsTransport ( ) const

virtual

Duplication routine for objects which inherit from Transport.

This virtual routine can be used to duplicate objects derived from Transport even if the application only has a pointer to Transport to work with.

These routines are basically wrappers around the derived copy constructor.

Reimplemented from Transport.

Definition at line 58 of file MixTransport.cpp.

References MixTransport::MixTransport().

virtual int model ( ) const

inlinevirtual

Return the model id for transport.

Returns: cMixtureAverage

Reimplemented from Transport.

Definition at line 73 of file MixTransport.h.

void getThermalDiffCoeffs ( doublereal *const dt )

virtual

Return the thermal diffusion coefficients.

For this approximation, these are all zero.

Eqns. (12.168) shows how they are used in an expression for the species flux.

Parameters

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

Reimplemented from Transport.

Definition at line 115 of file MixTransport.cpp.

References Transport::m_nsp.

doublereal thermalConductivity ( )

virtual

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

The thermal conductivity is computed from the following mixture rule:

\[ \lambda = 0.5 \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k/\lambda_k} \right) \]

It's used to compute the flux of energy due to a thermal gradient

\[ j_T = - \lambda \nabla T \]

The flux of energy has units of energy (kg m2 /s2) per second per area.

The units of lambda are W / m K which is equivalent to kg m / s^3 K.

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

Reimplemented from Transport.

Definition at line 95 of file MixTransport.cpp.

References MixTransport::m_cond, MixTransport::m_condmix_ok, MixTransport::m_lambda, GasTransport::m_molefracs, Transport::m_nsp, MixTransport::m_spcond_ok, MixTransport::update_C(), MixTransport::update_T(), and MixTransport::updateCond_T().

void getMobilities ( doublereal *const mobil )

virtual

Get the Electrical mobilities (m^2/V/s).

This function returns the mobilities. In some formulations this is equal to the normal mobility multiplied by Faraday's constant.

Here, the mobility is calculated from the diffusion coefficient using the Einstein relation

\[ \mu^e_k = \frac{F D_k}{R T} \]

Parameters

mobil Returns the mobilities of the species in array mobil. The array must be dimensioned at least as large as the number of species.

Reimplemented from Transport.

Definition at line 86 of file MixTransport.cpp.

References Cantera::Boltzmann, DATA_PTR, GasTransport::getMixDiffCoeffs(), Transport::m_nsp, GasTransport::m_spwork, and GasTransport::m_temp.

void update_T ( void )

virtual

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 150 of file MixTransport.cpp.

References Cantera::fp2str(), GasTransport::m_bindiff_ok, MixTransport::m_condmix_ok, MixTransport::m_spcond_ok, GasTransport::m_temp, Transport::m_thermo, and Phase::temperature().

Referenced by MixTransport::getSpeciesFluxes(), and MixTransport::thermalConductivity().

void update_C ( )

virtual

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 167 of file MixTransport.cpp.

References DATA_PTR, Phase::getMoleFractions(), MixTransport::m_condmix_ok, GasTransport::m_molefracs, Transport::m_nsp, Transport::m_thermo, GasTransport::m_visc_ok, and Cantera::Tiny.

Referenced by MixTransport::getSpeciesFluxes(), and MixTransport::thermalConductivity().

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

virtual

Get the species diffusive mass fluxes wrt to the mass averaged velocity, given the gradients in mole fraction and temperature.

Units for the returned fluxes are kg m-2 s-1.

The diffusive mass flux of species k is computed from

\[ \vec{j}_k = -n M_k D_k \nabla X_k. \]

Parameters

ndim	Number of dimensions in the flux expressions
grad_T	Gradient of the temperature (length = ndim)
ldx	Leading dimension of the grad_X array (usually equal to m_nsp but not always)
grad_X	Gradients of the mole fraction Flat vector with the m_nsp in the inner loop. length = ldx * ndim
ldf	Leading dimension of the fluxes array (usually equal to m_nsp but not always)
fluxes	Output of the diffusive mass fluxes Flat vector with the m_nsp in the inner loop. length = ldx * ndim