This class implements methods for calculating geometric parameters of a spherical agglomerate surrounded by a thin ionomer film. More...

#include <agglomerate_base.h>

Inheritance diagram for FuelCellShop::MicroScale::SphericalAgglomerateGeometry:

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Protected Types
typedef FuelCellShop::Layer::MultiScaleCL < deal_II_dimension > ::Properties	CLPropNames

typedef std::map< CLPropNames, double >	CL_Properties

Protected Member Functions
	SphericalAgglomerateGeometry ()

virtual double	compute_thickness_agg (FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > *layer)
	Member function to compute the thickness of the agglomerate thin film based on the radius and structure. More...

virtual double	compute_epsilon_agg (FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > *layer)
	Compute the volume fraction of nafion inside the agglomerate given the catalyst layer ionomer volume fraction , $\epsilon_N$ ; size of the agglomerate, $r_{agg}$ ; and, porosity inside the agglomerate, $\epsilon_{agg}$ , the necessary ionomer thin film thickness is computed such that the correct volume fractions are obtained. More...

virtual double	compute_epsilon_N (const double delta_agg, const double thickness_agg) const
	Function used to compute the amount of electrolyte in the catalyst layer. More...

virtual double	compute_depsilonN_dthickness (const double thickness_agg) const
	Function to compute $\frac{\partial \epsilon_N^{cat}}{\partial thickness_{agg}}$ This function should only be used to calculate the thin film thickness using Newton's method. More...

virtual double	compute_depsilonN_depsilon_agg (FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > *layer) const
	Function to compute $\frac{\partial \epsilon_N^{cat}}{\partial \epsilon_{agg}}$ This function should only be used to calculate the thin film thickness using Newton's method. More...

virtual double	compute_n (FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > *layer) const
	Member function to compute the number of agglomerates. More...

virtual double	compute_dn_depsilon_agg (FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > *layer) const
	Compute the derivative of n with respect to the porosity of the agglomerate. More...

Protected Attributes
double	pi

double	r_agg

double	delta_agg

double	epsilon_agg

double	n_agg

Detailed Description

This class implements methods for calculating geometric parameters of a spherical agglomerate surrounded by a thin ionomer film.

Note: This class is used by Agglomerate base (which is used by most agglomerates) and ICCP. Some virtual methods are reimplemented in hybrid agglomerate.

Usage details

Child class should set inherited members r_agg, delta_agg and epsilon_agg. Then base class can use member functions to calculate agglomerate geometry.

Author: Philip Wardlaw, Peter Dobson, Marc Secanell

Date: 2015

Member Typedef Documentation

typedef std::map<CLPropNames, double> FuelCellShop::MicroScale::SphericalAgglomerateGeometry::CL_Properties

protected

typedef FuelCellShop::Layer::MultiScaleCL<deal_II_dimension>::Properties FuelCellShop::MicroScale::SphericalAgglomerateGeometry::CLPropNames

protected

Constructor & Destructor Documentation

FuelCellShop::MicroScale::SphericalAgglomerateGeometry::SphericalAgglomerateGeometry ( )

inlineprotected

References Constants::Pi(), and pi.

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Member Function Documentation

virtual double FuelCellShop::MicroScale::SphericalAgglomerateGeometry::compute_depsilonN_depsilon_agg ( FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > * layer ) const

protectedvirtual

Function to compute

$\frac{\partial \epsilon_N^{cat}}{\partial \epsilon_{agg}}$

This function should only be used to calculate the thin film thickness using Newton's method.

Physically, the thickness of the thin film should not have an effect on the volume fractions defined in ConventionalCL

virtual double FuelCellShop::MicroScale::SphericalAgglomerateGeometry::compute_depsilonN_dthickness ( const double thickness_agg ) const

protectedvirtual

Function to compute

$\frac{\partial \epsilon_N^{cat}}{\partial thickness_{agg}}$

This function should only be used to calculate the thin film thickness using Newton's method.

Physically, the thickness of the thin film should not have an effect on the volume fractions defined in ConventionalCL

virtual double FuelCellShop::MicroScale::SphericalAgglomerateGeometry::compute_dn_depsilon_agg ( FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > * layer ) const

protectedvirtual

Compute the derivative of n with respect to the porosity of the agglomerate.

For a spherical agglomerate:

$\frac{\partial n_{agg}}{\partial \epsilon_agg} = \frac{\epsilon_S}{\frac{4}{3} \pi r_{agg}^3 (1 - \epsilon_{agg})^2}$

virtual double FuelCellShop::MicroScale::SphericalAgglomerateGeometry::compute_epsilon_agg ( FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > * layer )

protectedvirtual

Compute the volume fraction of nafion inside the agglomerate given the catalyst layer ionomer volume fraction , $\epsilon_N$ ; size of the agglomerate, $r_{agg}$ ; and, porosity inside the agglomerate, $\epsilon_{agg}$ , the necessary ionomer thin film thickness is computed such that the correct volume fractions are obtained.

A Newton loop is used in order to obtain the correct value for the agglomerate porosity, $\epsilon_{agg}$ .

Note: compute_thickness_agg and compute_epsilon_agg are mutually exclusive and the selection between using one method or the other depends on the inpu parameter:
* set Constant agglomerate parameter [Thickness | Porosity] = Thickness

* set Agglomerate porosity = 0.25 #specify if Porosity is selected in variable above

* set Thickness of the agglomerate film [nm] = 80 #specify if Thickness is selected in property above

*

virtual double FuelCellShop::MicroScale::SphericalAgglomerateGeometry::compute_epsilon_N	(	const double	delta_agg,
		const double	thickness_agg
	)		const

protectedvirtual

Function used to compute the amount of electrolyte in the catalyst layer.

This is given by the agglomerate sturcture and the amount of solid phase. In particular,

$\epsilon_N^{cat} = n \frac{4.0}{3.0}3.1416({r_agg*1e-7})^{3.0}*(\epsilon_agg-1) + (r_{agg}1e-4 + \delta_{agg}1e-4)^{3.0};$

where n is computed by another function. For details on this equation and other see, M.Secanell et al., "",...

virtual double FuelCellShop::MicroScale::SphericalAgglomerateGeometry::compute_n ( FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > * layer ) const

protectedvirtual

Member function to compute the number of agglomerates.

The number of agglomerates is computed differently depending on the type of agglomerate and depends on the agglomerate radius, amount of ionomer per agglomerate and the solid phase volume fraction in the CL.

For a spherical agglomerate

$n_{agg} = \frac{\epsilon_S}{\frac{4}{3} \pi r_{agg}^3 (1 - \epsilon_{agg})}$

virtual double FuelCellShop::MicroScale::SphericalAgglomerateGeometry::compute_thickness_agg ( FuelCellShop::Layer::MultiScaleCL< deal_II_dimension > * layer )

protectedvirtual

Member function to compute the thickness of the agglomerate thin film based on the radius and structure.

For a given ionomer volume fraction, $\epsilon_N$ ; size of the agglomerate, $r_{agg}$ ; and, porosity inside the agglomerate, $\epsilon_{agg}$ , the necessary ionomer thin film thickness is computed such that the correct volume fractions are obtained.

A Newton loop is used in order to obtain the correct value for the thickness of the agglomerate film, $\delta_{agg}$

Note: compute_thickness_agg and compute_epsilon_agg are mutually exclusive and the selection between using one method or the other depends on the inpu parameter:
* set Constant agglomerate parameter [Thickness | Porosity] = Thickness

* set Agglomerate porosity = 0.25 #specify if Porosity is selected in variable above

* set Thickness of the agglomerate film [nm] = 80 #specify if Thickness is selected in property above

*