Cantera  2.5.1
Public Member Functions | Protected Member Functions | Protected Attributes | List of all members

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

#include <IonGasTransport.h>

Inheritance diagram for IonGasTransport:
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Collaboration diagram for IonGasTransport:
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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
 
Transportoperator= (const Transport &)=delete
 
thermo_tthermo ()
 
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_fpm_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_fpm_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_fpm_condcoeffs
 temperature fits of the heat conduction More...
 
std::vector< vector_intm_poly
 Indices for the (i,j) interaction in collision integral fits. More...
 
std::vector< vector_fpm_omega22_poly
 Fit for omega22 collision integral. More...
 
std::vector< vector_fpm_astar_poly
 Fit for astar collision integral. More...
 
std::vector< vector_fpm_bstar_poly
 Fit for bstar collision integral. More...
 
std::vector< vector_fpm_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_tm_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< Solutionm_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:

  1. Selle, Stefan, and Uwe Riedel. "Transport properties of ionized species." Annals of the New York Academy of Sciences 891.1 (1999): 72-80.
  2. Selle, Stefan, and Uwe Riedel. "Transport coefficients of reacting air at high temperatures." 38th Aerospace Sciences Meeting and Exhibit. 1999.
  3. 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
  4. 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.
  5. 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
thermoPointer to the ThermoPhase object
modeChemkin compatible mode or not. This alters the specification of the collision integrals. defaults to no.
log_levelDefaults 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: