Class used to store data and provide information regarding the electrolyte. More...

#include <nafion.h>

Inheritance diagram for FuelCellShop::Material::Nafion:

Collaboration diagram for FuelCellShop::Material::Nafion:

Public Member Functions
Constructors, destructor, and parameter initalization
	Nafion (const bool)
	PROTOTYE Constructor. More...

	Nafion (std::string name="Nafion")
	Constructor The constructor initialize parameters using the default values. More...

	~Nafion ()
	Destructor. More...

virtual void	declare_parameters (ParameterHandler &param) const
	Declare parameters. More...

virtual void	initialize (ParameterHandler &param)
	Member function used to read in data and initialize the necessary data from the parameter file to compute the coefficients. More...

Transport properties and derivatives accessor methods
virtual void	sorption_isotherm (std::vector< double > &) const
	Compute the equilibrium water content, $\lambda_{eq}$ , inside the Nafion for vapor-equilibriated case, at every quadrature point in the cell. More...

virtual void	sorption_isotherm_derivative (std::map< VariableNames, std::vector< double > > &) const
	Compute the derivatives for water sorption source terms, $\frac{\partial \lambda_{eq}}{\partial u}$ , at every quadrature point in the cell. More...

virtual void	proton_conductivity (double &, const double, const double) const
	Compute the proton conductivity, $\sigma_{H^+}$ [`S/cm`], inside the nafion, at every quadrature point in the cell. More...

virtual void	proton_conductivity (double &) const
	Compute the proton conductivity, $\sigma_{H^+}$ [`S/cm`], inside the nafion for a case of constant $\lambda$ and . More...

virtual void	proton_conductivity (std::vector< double > &) const
	Compute the proton conductivity, $\sigma_{H^+}$ [`S/cm`], inside the nafion, at every quadrature point in the cell. More...

virtual void	proton_conductivity_derivative (std::map< VariableNames, std::vector< double > > &) const
	Compute the derivatives of proton conductivity at every quadrature point in the cell. More...

virtual void	water_diffusivity (double &, const double, const double) const
	Compute the water diffusivity, $D_{\lambda}$ [`cm^2/s`], inside the nafion at every quadrature point in the cell. More...

virtual void	water_diffusivity (double &) const
	Compute the water diffusivity, $D_{\lambda}$ [`cm^2/s`], inside the nafion for a case of constant $\lambda$ and . More...

virtual void	water_diffusivity (std::vector< double > &) const
	Compute the water diffusivity, $D_{\lambda}$ [`cm^2/s`], inside the nafion at every quadrature point in the cell. More...

virtual void	water_diffusivity_derivative (std::map< VariableNames, std::vector< double > > &) const
	Compute the derivatives of water diffusivity at every quadrature point in the cell. More...

virtual void	electroosmotic_drag (std::vector< double > &) const
	Compute the electro-osmotic drag coefficient inside the nafion at every quadrature point in the cell. More...

virtual void	electroosmotic_drag_derivative (std::map< VariableNames, std::vector< double > > &) const
	Compute the derivatives of electro-osmotic drag coefficient, at every quadrature point in the cell. More...

virtual void	thermoosmotic_coeff (std::vector< double > &) const
	Compute the thermo-osmotic diffusion coefficient, [`gm/` (cm-s-K )], inside the nafion at every quadrature point in the cell. More...

virtual void	thermoosmotic_coeff_derivative (std::map< VariableNames, std::vector< double > > &) const
	Compute the derivatives of thermo-osmotic diffusion coefficient, at every quadrature point in the cell. More...

virtual void	oxygen_diffusivity (double &, const double) const
	Compute the oxygen diffusivity, [`cm^2/s`], inside the nafion for a given . More...

virtual void	oxygen_diffusivity (double &) const
	Compute the oxygen diffusivity, [`cm^2/s`], inside the nafion for a constant . More...

virtual void	hydrogen_diffusivity (double &) const
	Compute the hydrogen diffusivity, [`cm^2/s`], inside the nafion for a constant . More...

virtual void	oxygen_diffusivity (std::vector< double > &) const
	Compute the oxygen diffusivity, [`cm^2/s`], inside the nafion at every quadrature point in the cell. More...

virtual void	oxygen_diffusivity_derivative (std::map< VariableNames, std::vector< double > > &) const
	Compute the derivatives of oxygen diffusivity, at every quadrature point in the cell. More...

virtual void	proton_diffusivity (double &) const
	Compute the proton diffusivity, [`cm^2/s`], inside the nafion for constant case. More...

virtual void	sorption_enthalpy (std::vector< double > &) const
	Compute the enthalpy of sorption [`J/mol`] of water in Nafion, at all quadrature points in the cell. More...

virtual void	sorption_enthalpy_derivative (std::map< VariableNames, std::vector< double > > &) const
	Compute the derivatives of enthalpy of sorption of water, at every quadrature point in the cell. More...

Accessor methods for molar enthalpy of sorbed water and its derivatives
virtual double	get_Hlambda (const double &) const
	Compute the molar enthalpy, $\bar{H}_{\lambda} ~$ [`J/mol`] of sorbed water in the Nafion as a function of . More...

virtual double	get_dHlambda_dT (const double &) const
	Compute $\frac{\partial \bar{H}_{\lambda}}{\partial T}$ of sorbed water in the Nafion as a function of . More...

virtual double	get_d2Hlambda_dT2 (const double &) const
	Compute $\frac{\partial^2 \bar{H}_{\lambda}}{\partial T^2}$ of sorbed water in the Nafion as a function of . More...

Public Member Functions inherited from FuelCellShop::Material::PolymerElectrolyteBase
double	get_density () const
	Get the density [`gm/cm^3`] of the dry polymer electrolyte material. More...

double	get_H_O2 () const
	Get Henry's constant [`Pa-cm^3/mol`] for oxygen dissolution in the polymer electrolyte. More...

double	get_H_H2 () const
	Get Henry's constant [`Pa-cm^3/mol`] for hydrogen dissolution in the polymer electrolyte. More...

double	get_EW () const
	Get Equivalent Weight (grams of dry polymer electrolyte per moles of ) of the polymer electrolyte material. More...

double	get_permittivity () const
	Get permittivity of the polymer electrolyte material. More...

void	set_p_t (const double &p_t)
	Specify the total pressure in Pascals. More...

void	set_T (const double &Temp)
	Specify the temperature [`Kelvin`] in the polymer electrolyte for isothermal case. More...

void	set_lambda (const double &L)
	Specify the water content in the polymer electrolyte for constant lambda case. More...

void	set_membrane_water_content (const FuelCellShop::SolutionVariable &l_in)
	Set the solution variable, membrane water content $\lambda$ . More...

void	set_temperature (const FuelCellShop::SolutionVariable &T_in)
	Set the solution variable, temperature [`Kelvin`]. More...

void	set_water_molar_fraction (const FuelCellShop::SolutionVariable &x_in)
	Set the solution variable, water vapor molar fraction $x_{H_2O}$ . More...

Public Member Functions inherited from FuelCellShop::Material::BaseMaterial
void	set_derivative_flags (const std::vector< VariableNames > &flags)
	Set the names of FCST solution variables with respect to which you would like to compute the derivatives of material properties. More...

const std::string &	name_material () const
	Return the name of the layer. More...

virtual void	print_material_properties () const
	This function prints out the material properties. More...

Static Public Attributes
static const std::string	concrete_name
	Name of the class. More...

Private Member Functions
void	modify_parameters (const unsigned int &index, const std::string &method)
	Method to modify parameters, without declaring and initializing the parameter file. More...

Private Attributes
std::map< std::string, double >	springer_coeffs
	Map for proton conductivity's coefficients; used with "Springer" method. More...

Friends
Friend class for Unit Testing
class	::NafionTest
	Friend class for testing purposes. More...

Instance Delivery
static Nafion const *	PROTOTYPE
	Create prototype for the layer. More...

virtual boost::shared_ptr < FuelCellShop::Material::PolymerElectrolyteBase >	create_replica ()
	This member function is used to create an object of type Nafion material. More...

Additional Inherited Members
Static Public Member Functions inherited from FuelCellShop::Material::PolymerElectrolyteBase
static void	declare_PolymerElectrolyte_parameters (ParameterHandler &param)
	Function used to declare all the data necessary in the parameter files for all PolymerElectrolyteBase children. More...

static boost::shared_ptr < FuelCellShop::Material::PolymerElectrolyteBase >	create_PolymerElectrolyte (ParameterHandler &param, std::string polymer_electrolyte_name)
	Function called in create_CatalystLayer and used to select the appropriate PolymerElectrolyteBase children that will be used in the layer. More...

Protected Types inherited from FuelCellShop::Material::PolymerElectrolyteBase
typedef std::map< std::string, FuelCellShop::Material::PolymerElectrolyteBase * >	_mapFactory
	This object is used to store all objects of type PolymerElectrolyteBase. More...

Protected Member Functions inherited from FuelCellShop::Material::PolymerElectrolyteBase
	PolymerElectrolyteBase (std::string name)
	Constructor. More...

	PolymerElectrolyteBase ()
	Constructor. More...

virtual	~PolymerElectrolyteBase ()
	Destructor. More...

Protected Member Functions inherited from FuelCellShop::Material::BaseMaterial
	BaseMaterial ()
	Constructor. More...

	BaseMaterial (const std::string &name)
	Constructor. More...

virtual	~BaseMaterial ()
	Destructor. More...

Static Protected Member Functions inherited from FuelCellShop::Material::PolymerElectrolyteBase
static _mapFactory *	get_mapFactory ()

Protected Attributes inherited from FuelCellShop::Material::PolymerElectrolyteBase
FuelCellShop::Material::WaterVapor *	water_mat
	Pointer to FuelCellShop::Material::WaterVapor object, dynamically allocated when the class is constructed. More...

double	EW
	Equivalent weight. More...

double	rho_M
	Dry polymer electrolyte density [`gm/cm^3`]. More...

double	H_O2
	Henry's Constant [`Pa-cm^3/mol`] for dissolution of oxygen. More...

double	H_H2
	Henry's Constant [`Pa-cm^3/mol`] for dissolution of hydroge. More...

double	permittivity
	Permittivity of the material. More...

double	T
	Temperature [`Kelvins`] for isothermal case. More...

double	lambda
	Membrane water content, $\lambda$ for constant lambda case. More...

double	p_total
	Total pressure (in Pascals). More...

double	sigma_p
	Proton conductivity value [`S/cm`], given in the parameter file; used with "Constant" method. More...

double	diffusion_w
	Diffusion of water in polymer electrolyte (if constant option is used), [`cm2/s`]. More...

double	given_n_drag
	Given electroosmotic drag value in the parameter file. More...

double	given_thermoosmotic_coeff
	Given thermo-osmotic diffusion coefficient [`gm/(cm-s-K` )] in the parameter file. More...

double	given_enthalpy_sorption
	Given enthalpy of sorption of water [`J/mol`] in the parameter file. More...

double	D_O2
	Diffusion coefficient of oxygen [`cm^2/s`], given in the parameter file. More...

double	D_H2
	Effective diffusion coefficient of hydrogen [`cm^2/s`], given in the parameter file. More...

double	D_Protons
	Diffusion coefficient of protons [`cm^2/s`], given in the parameter file. More...

std::string	method_conductivity
	Method/Semi-empirical relation to compute protonic conductivity. More...

std::string	method_sorption
	Method to compute equilibrium water content value from sorption isotherm. More...

std::string	method_diffusivity
	Method/semi-empirical relation to compute water diffusivity. More...

std::string	method_electroosmotic_drag
	Method/semi-empirical relation to compute Electro-osmotic drag. More...

std::string	method_thermoosmosis
	Method/semi-empirical relation to compute thermo-osmotic diffusion coefficient. More...

std::string	method_enthalpy_sorption
	Method/semi-empirical relation to compute enthalpy of sorption of water. More...

FuelCellShop::SolutionVariable	lambda_var
	Solution variable, membrane water content $\lambda$ . More...

FuelCellShop::SolutionVariable	T_var
	Solution variable, temperature . More...

FuelCellShop::SolutionVariable	xwater_var
	Solution variable, water vapor molar fraction $x_{H_2O}$ . More...

Protected Attributes inherited from FuelCellShop::Material::BaseMaterial
const std::string	name
	Name of the layer. More...

std::vector< VariableNames >	derivative_flags
	Flags for derivatives: These flags are used to request derivatives of material properties. More...

Detailed Description

Class used to store data and provide information regarding the electrolyte.

In this case the electrolyte that is setup is Nafion. In particular the data coded in this class is obtained from the literature from Nafion 1100, usually from NRE 211 properties.

In the parameter file the following parameters can be specified within the subsections specified below:

* subsection Fuel cell data
*   subsection Materials
*     subsection Nafion
*       set Method for sorption isotherm = Hinatsu        # Options are Hinatsu | Liu09 -- Method to compute equilibrium lambda from sorption isotherm - Depends on Water molar fraction and Temperature
*       set Method to compute proton conductivity = NRE211 # Options are: Constant|Springer|NRE211|Iden11 -- Method used to compute proton conductivity inside the membrane - Depends on lambda and T
*       set Proton conductivity [S/cm] = 0.1                      # Proton conductivity inside the membrane, S/cm
*       set Method to compute water diffusion = Springer   # Options are: "Constant|Springer|Motupally" -- Method used to compute diffusion of water inside the membrane - Depends on lambda and T
*       subsection Springer coefficients --- This section is used to control the coefficients if Springer is used which are of the form: (A \lambda + B) exp [ C (1/303 - 1/T)
*          set Proton conductivity's first coefficient = 0.005139
*          set Proton conductivity's second coefficient = -0.00326
*          set Proton conductivity's third coefficient = 1268.0
*       end
*       set Water diffusion coefficient = 2e-              # Water diffusion coefficient inside the membrane
*       set Electro-osmotic drag method = Springer         # Options are: Constant|Springer -- Method to compute nd. Springer depends on water content
*       set Electro-osmotic drag coefficient = 1.0         # Number of water molecules dragged by one proton
*       set Method to compute thermo-osmotic diffusion coefficient = Kim09 # Options are: Constant | Kim09 -- Method to compute thermo-osmotic diffusion coefficient - Depends on T
*       set Thermo-osmotic diffusion coefficient [gm/(cm-s-K)] = -1.3e-7 # Thermo-osmotic diffusion coefficient inside the membrane [gm/(cm-s-K)].
*       set Method to compute enthalpy of sorption of water = Constant  # Options are: Constant -- Method to compute enthalpy of sorption of water - may depend on lambda and T
*       set Enthalpy of sorption of water [J/mol] = 45000.0     # Heat released when one mole of water is sorbed inside the membrane.
*       set Oxygen diffusion coefficient [cm^2/s] = 9.726e-6    # From J. Peron et al., “Properties of Nafion NR-211 membranes for PEMFCs”
*       set Proton diffusion coefficient [cm^2/s] = 9.2e-5      # Peter Dobsons thesis page 42
*       set Henry's Law Constant for Oxygen [Pa cm^3/mol] = 3.1664e10
*       set Henry's Law Constant for Hydrogen [Pa cm^3/mol] = 6.69e10
*     end
*   end
* end
* 
* 

Usage Details:

As with most routines you need to first declare_parameters, and then initialize. After this the class is ready for use.

See for example FuelCell::OperatingConditions class for more details.

Authors: M. Secanell and M. Bhaiya

Constructor & Destructor Documentation

FuelCellShop::Material::Nafion::Nafion ( const bool )

PROTOTYE Constructor.

Warning: For internal use only.

FuelCellShop::Material::Nafion::Nafion ( std::string name = "Nafion" )

Constructor The constructor initialize parameters using the default values.

This is so that if I do not want to call declare_parameters and initialize, I can still use the routine with the hard coded values.

High Priority Todo:: Make this private and remove name.

FuelCellShop::Material::Nafion::~Nafion ( )

Destructor.

Member Function Documentation

virtual boost::shared_ptr<FuelCellShop::Material::PolymerElectrolyteBase > FuelCellShop::Material::Nafion::create_replica ( )

inlineprivatevirtual

This member function is used to create an object of type Nafion material.

Warning: This class MUST be redeclared in every child.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::declare_parameters ( ParameterHandler & param ) const

virtual

Declare parameters.

High Priority Todo:: Make it protected

In the parameter file the following parameters can be specified within the subsections specified below:

* subsection Fuel cell data
*   subsection Materials
*     subsection Nafion
*       set Method for sorption isotherm = Previous        # Options are Previous | Liu09 -- Method to compute equilibrium lambda from sorption isotherm - Depends on Water molar fraction and Temperature
*       set Method to compute proton conductivity = NRE211 # Options are: Constant|Springer|NRE211|Iden11 -- Method used to compute proton conductivity inside the membrane - Depends on lambda and T
*       set Proton conductivity [S/cm] = 0.1                      # Proton conductivity inside the membrane, S/cm
*       set Method to compute water diffusion = Springer   # Options are: "Constant|Springer|Motupally" -- Method used to compute diffusion of water inside the membrane - Depends on lambda and T
*       set Water diffusion coefficient = 2e-              # Water diffusion coefficient inside the membrane
*       set Electro-osmotic drag method = Springer         # Options are: Constant|Springer -- Method to compute nd. Springer depends on water content
*       set Electro-osmotic drag coefficient = 1.0         # Number of water molecules dragged by one proton
*       set Method to compute thermo-osmotic diffusion coefficient = Kim09 # Options are: Constant | Kim09 -- Method to compute thermo-osmotic diffusion coefficient - Depends on T
*       set Thermo-osmotic diffusion coefficient [gm/(cm-s-K)] = -1.3e-7 # Thermo-osmotic diffusion coefficient inside the membrane [gm/(cm-s-K)].
*       set Method to compute enthalpy of sorption of water = Constant  # Options are: Constant -- Method to compute enthalpy of sorption of water - may depend on lambda and T
*       set Enthalpy of sorption of water [J/mol] = 45000.0     # Heat released when one mole of water is sorbed inside the membrane.
*       set Oxygen diffusion coefficient [cm^2/s] = 9.726e-6    # From J. Peron et al., “Properties of Nafion NR-211 membranes for PEMFCs”
*       set Proton diffusion coefficient [cm^2/s] = 9.2e-5      # Peter Dobsons thesis page 42
*       set Henry's Law Constant for Oxygen [Pa cm^3/mol] = 3.1664e10
*       set Henry's Law Constant for Hydrogen [Pa cm^3/mol] = 6.69e10
*     end
*   end
* end
* 
* 

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::electroosmotic_drag ( std::vector< double > & ) const

virtual

Compute the electro-osmotic drag coefficient inside the nafion at every quadrature point in the cell.

It takes vector as an input argument and values are passed by reference. Note that the double return method is not implemented for electro-osmotic drag coefficients because it is required only when $\lambda$ is one of the solution variables in the application. set_membrane_water_content should be called before using this method.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::electroosmotic_drag_derivative ( std::map< VariableNames, std::vector< double > > & ) const

virtual

Compute the derivatives of electro-osmotic drag coefficient, at every quadrature point in the cell.

The derivatives are computed based on the flags set by the set_derivative_flags method. It takes map as an input argument by reference, in which Key corresponds to the variable about which derivative is being computed, i.e., VariableNames and Value corresponds to the vector storing the derivative values. set_membrane_water_content should be called before using this method. Also, this method should only be called when atleast there is one derivative flag.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual double FuelCellShop::Material::Nafion::get_d2Hlambda_dT2 ( const double & ) const

virtual

Compute $\frac{\partial^2 \bar{H}_{\lambda}}{\partial T^2}$ of sorbed water in the Nafion as a function of $ T $ .

It takes Temperature, $ T ~$ [Kelvin] as input by reference and returns the double value corresponding to the second derivative.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual double FuelCellShop::Material::Nafion::get_dHlambda_dT ( const double & ) const

virtual

Compute $\frac{\partial \bar{H}_{\lambda}}{\partial T}$ of sorbed water in the Nafion as a function of $ T $ .

It takes Temperature, $ T ~$ [Kelvin] as input by reference and returns the double value corresponding to the derivative.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual double FuelCellShop::Material::Nafion::get_Hlambda ( const double & ) const

virtual

Compute the molar enthalpy, $\bar{H}_{\lambda} ~$ [J/mol] of sorbed water in the Nafion as a function of $ T $ .

It takes Temperature, $ T ~$ [Kelvin] as input by reference and returns the double value corresponding to molar enthalpy.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::hydrogen_diffusivity ( double & ) const

virtual

Compute the hydrogen diffusivity, [cm^2/s], inside the nafion for a constant $ T $ .

Before calling this method, set_T method should be used for setting the constant temperature value. It takes a double as an input argument and value is passed by reference.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::initialize ( ParameterHandler & param )

virtual

Member function used to read in data and initialize the necessary data from the parameter file to compute the coefficients.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

void FuelCellShop::Material::Nafion::modify_parameters	(	const unsigned int &	index,
		const std::string &	method
	)

inlineprivate

Method to modify parameters, without declaring and initializing the parameter file.

It takes two arguments, first one (unsigned int) corresponds to a particular type of method and second one (std::string) corresponds to various implementations for that method type. index corresponds to following methods:

1: protonic conductivity methods
2: water diffusivity methods
3: electro-osmotic drag methods
4: thermo-osmotic coefficient methods
5: sorption isotherm methods
6: sorption enthalpy methods
Note
This function is used by the unit testing for this class. For method strings, look at declare_parameters() method.

References FuelCellShop::Material::PolymerElectrolyteBase::method_conductivity, FuelCellShop::Material::PolymerElectrolyteBase::method_diffusivity, FuelCellShop::Material::PolymerElectrolyteBase::method_electroosmotic_drag, FuelCellShop::Material::PolymerElectrolyteBase::method_enthalpy_sorption, FuelCellShop::Material::PolymerElectrolyteBase::method_sorption, and FuelCellShop::Material::PolymerElectrolyteBase::method_thermoosmosis.

virtual void FuelCellShop::Material::Nafion::oxygen_diffusivity	(	double &	,
		const double
	)		const

virtual

Compute the oxygen diffusivity, [cm^2/s], inside the nafion for a given $ T $ .

It can be called by either constant or variable solution setting methods to avoid duplicate equations. The first parameter is the output oxygen diffusivity and the second one is temperature, $ T $ [K], used as input parameter.

virtual void FuelCellShop::Material::Nafion::oxygen_diffusivity ( double & ) const

virtual

Compute the oxygen diffusivity, [cm^2/s], inside the nafion for a constant $ T $ .

Before calling this method, set_T method should be used for setting the constant temperature value. It takes a double as an input argument and value is passed by reference.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::oxygen_diffusivity ( std::vector< double > & ) const

virtual

Compute the oxygen diffusivity, [cm^2/s], inside the nafion at every quadrature point in the cell.

It takes vector as an input argument and values are passed by reference. set_temperature should be called before using this method.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::oxygen_diffusivity_derivative ( std::map< VariableNames, std::vector< double > > & ) const

virtual

Compute the derivatives of oxygen diffusivity, at every quadrature point in the cell.

The derivatives are computed based on the flags set by the set_derivative_flags method. It takes map as an input argument by reference, in which Key corresponds to the variable about which derivative is being computed, i.e., VariableNames and Value corresponds to the vector storing the derivative values. set_temperature should be called before using this method. Also, this method should only be called when atleast there is one derivative flag.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::proton_conductivity	(	double &	,
		const double	,
		const double
	)		const

virtual

Compute the proton conductivity, $\sigma_{H^+}$ [S/cm], inside the nafion, at every quadrature point in the cell.

It is computed \ as a function of $\lambda$ and $ T $ . It can be called by either constant or variable solution setting methods to avoid duplicate equations. The first parameter is the output bulk proton conductivity and the two following are input parameters such as temperature, $ T $ [K], and water content, $\lambda$ [-].

virtual void FuelCellShop::Material::Nafion::proton_conductivity ( double & ) const

virtual

Compute the proton conductivity, $\sigma_{H^+}$ [S/cm], inside the nafion for a case of constant $\lambda$ and $ T $ .

Before calling this method, set_T method should be used for setting the constant temperature value. If the constant $\lambda$ value is required to be different from the default value 12.0, then set_lambda method should be used. It takes a double as an input argument and value is passed by reference.

Remarks: This method is recommended only for multi-scale models. In case of macrohomogeneous models, constant values should always be set before the variable ones, otherwise it may give erroneous results.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::proton_conductivity ( std::vector< double > & ) const

virtual

Compute the proton conductivity, $\sigma_{H^+}$ [S/cm], inside the nafion, at every quadrature point in the cell.

It is computed as a function of $\lambda$ and $ T $ , hence solution setting methods should be called accordingly for them, whether constant or variable. It is recommended to set the constant ones in the initialization of the application, unless you are solving for multi-scale model. It takes vector as an input argument and values are passed by reference.

Warning: Precaution must be used while using two different solution setting methods, i.e., either constant or variable for a single solution variable on the same electrolyte object. You cannot use constant solution setting methods for this object, if variable solution setting methods are already used for a single solution variable. In case of constant $\lambda$ and , vector size should be set equal to the number of quadrature points, before passing to this function.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::proton_conductivity_derivative ( std::map< VariableNames, std::vector< double > > & ) const

virtual

Compute the derivatives of proton conductivity at every quadrature point in the cell.

The derivatives are computed based on the flags set by the set_derivative_flags method. It takes map as an input argument by reference, in which Key corresponds to the variable about which derivative is being computed, i.e., VariableNames and Value corresponds to the vector storing the derivative values. Note that this method should not be used when both $\lambda$ and $ T $ are constant. Hence, atleast set_membrane_water_content or set_temperature should be called before using this method. Also, this method should only be called when atleast there is one derivative flag.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::proton_diffusivity ( double & ) const

virtual

Compute the proton diffusivity, [cm^2/s], inside the nafion for constant case.

It takes a double as an input argument and value is passed by reference. It basically returns a constant value specified using the parameter file.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::sorption_enthalpy ( std::vector< double > & ) const

virtual

Compute the enthalpy of sorption [J/mol] of water in Nafion, at all quadrature points in the cell.

It takes vector as an input argument and values are passed by reference. Note that the double return method is not implemented for thermo-osmotic diffusion coefficients because it is required only when $ T$ is one of the solution variables in the application. set_temperature should be called before using this method.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::sorption_enthalpy_derivative ( std::map< VariableNames, std::vector< double > > & ) const

virtual

Compute the derivatives of enthalpy of sorption of water, at every quadrature point in the cell.

The derivatives are computed based on the flags set by the set_derivative_flags method. It takes map as an input argument by reference, in which Key corresponds to the variable about which derivative is being computed, i.e., VariableNames and Value corresponds to the vector storing the derivative values. set_temperature should be called before using this method. Also, this method should only be called when atleast there is one derivative flag.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::sorption_isotherm ( std::vector< double > & ) const

virtual

Compute the equilibrium water content, $\lambda_{eq}$ , inside the Nafion for vapor-equilibriated case, at every quadrature point in the cell.

It takes a vector as an input argument and values are passed by reference. It is required to call set_water_molar_fraction method atleast before computing sorption isotherm values.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::sorption_isotherm_derivative ( std::map< VariableNames, std::vector< double > > & ) const

virtual

Compute the derivatives for water sorption source terms, $\frac{\partial \lambda_{eq}}{\partial u}$ , at every quadrature point in the cell.

The derivatives are computed based on the flags set by the set_derivative_flags method. It takes map as an input argument by reference, in which Key corresponds to the variable about which derivative is being computed, i.e., VariableNames and Value corresponds to the vector storing the derivative values. It is required to call set_water_molar_fraction method atleast before computing sorption isotherm values. Also, this method should only be called when atleast there is one derivative flag.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::thermoosmotic_coeff ( std::vector< double > & ) const

virtual

Compute the thermo-osmotic diffusion coefficient, [gm/ (cm-s-K )], inside the nafion at every quadrature point in the cell.

It takes vector as an input argument and values are passed by reference. Note that the double return method is not implemented for thermo-osmotic diffusion coefficients because it is required only when $ T$ is one of the solution variables in the application. set_temperature should be called before using this method.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::thermoosmotic_coeff_derivative ( std::map< VariableNames, std::vector< double > > & ) const

virtual

Compute the derivatives of thermo-osmotic diffusion coefficient, at every quadrature point in the cell.

The derivatives are computed based on the flags set by the set_derivative_flags method. It takes map as an input argument by reference, in which Key corresponds to the variable about which derivative is being computed, i.e., VariableNames and Value corresponds to the vector storing the derivative values. set_temperature should be called before using this method. Also, this method should only be called when atleast there is one derivative flag.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::water_diffusivity	(	double &	,
		const double	,
		const double
	)		const

virtual

Compute the water diffusivity, $D_{\lambda}$ [cm^2/s], inside the nafion at every quadrature point in the cell.

It is computed as a function of $\lambda$ and $ T $ . It can be called by either constant or variable solution setting methods to avoid duplicate equations. The first parameter is the output water diffusivity and the two following are input parameters such as temperature, $ T $ [K], and water content, $\lambda$ [-].

virtual void FuelCellShop::Material::Nafion::water_diffusivity ( double & ) const

virtual

Compute the water diffusivity, $D_{\lambda}$ [cm^2/s], inside the nafion for a case of constant $\lambda$ and $ T $ .

Before calling this method, set_T method should be used for setting the constant temperature value. If the constant $\lambda$ value is required to be different from the default value 12.0, then set_lambda method should be used. It takes a double as an input argument and value is passed by reference.

Remarks: This method is recommended only for multi-scale models. In case of macrohomogeneous models, it's not required in particular because $D_{\lambda}$ is required only when $\lambda$ is one of the solution variables in the application.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::water_diffusivity ( std::vector< double > & ) const

virtual

Compute the water diffusivity, $D_{\lambda}$ [cm^2/s], inside the nafion at every quadrature point in the cell.

It is computed as a function of $\lambda$ and $ T $ , hence solution setting methods should be called accordingly for them, whether constant or variable. It is recommended to set the constant ones in the initialization of the application. Note that this method should not be used when both $\lambda$ and $ T $ are constant. Hence, atleast set_membrane_water_content or set_temperature should be called before using this method. It takes vector as an input argument and values are passed by reference.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

virtual void FuelCellShop::Material::Nafion::water_diffusivity_derivative ( std::map< VariableNames, std::vector< double > > & ) const

virtual

Compute the derivatives of water diffusivity at every quadrature point in the cell.

The derivatives are computed based on the flags set by the set_derivative_flags method. It takes map as an input argument by reference, in which Key corresponds to the variable about which derivative is being computed, i.e., VariableNames and Value corresponds to the vector storing the derivative values. Note that this method should not be used when both $\lambda$ and $ T $ are constant. Hence, atleast set_membrane_water_content or set_temperature should be called before using this method. Also, this method should only be called when atleast there is one derivative flag.

Reimplemented from FuelCellShop::Material::PolymerElectrolyteBase.

Friends And Related Function Documentation

friend class ::NafionTest

friend

Friend class for testing purposes.

Member Data Documentation

const std::string FuelCellShop::Material::Nafion::concrete_name

static

Name of the class.

This name is used to select the layer.

Nafion const* FuelCellShop::Material::Nafion::PROTOTYPE

staticprivate

Create prototype for the layer.

std::map<std::string, double> FuelCellShop::Material::Nafion::springer_coeffs

private

Map for proton conductivity's coefficients; used with "Springer" method.

Conductivity is given by

$\quad \sigma = \left( A \lambda + B \right) exp \left[ C \left( \frac{1}{303} - \frac{1}{T} \right) \right] \quad$ [S/cm]

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

nafion.h

Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Friends

Instance Delivery

Additional Inherited Members

Detailed Description

Usage Details:

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation