Pore Scale Modelling of Porous Layers Used in Fuel Cells · Pore Scale Modelling of Porous Layers...

© Fraunhofer ITWM1

Special Semester RICAM Linz 05.10.2011

Pore Scale Modelling of Porous Layers Used in Fuel Cells

Jürgen Becker

Fraunhofer Institute for Industrial Mathematics ITWM

Kaiserslautern, Germany

© Fraunhofer ITWM2

Pore Scale Modelling of Porous Layers Used in Fuel Cells

Department 'Flow and Material Simulation'

Groups:

Hydrodynamics and CFD

Complex Fluids

Micro-structure simulation and virtual material design

A. Wiegmann, S.Rief, L. Cheng, E. Glatt, N. Zamel. S. Linden

Mechanics of Materials

© Fraunhofer ITWM3

Outline

1. Introduction to PEM fuel cells

2. Pore scale modelling of porous layers used in fuel cells

a) Creation of virtual 3D structure models

b) Determination of effective properties

c) Validation

d) Some results

3. The general idea

4. Other fields of applications

© Fraunhofer ITWM4

Proton Exchange Membrane (PEM) Fuel Cell

© Fraunhofer ITWM5

Porous Layers in a PEM Fuel Cell

Gas Diffusion Layer

Micro-porous Layer

Catalyst Layer

Membrane

Find layers with optimal properties!

Properties of a porous medium are influenced by:

Material

Pore structure

© Fraunhofer ITWM6

Gas Diffusion Layer (GDL)

Carbon Fibers ( 7 µm diam.)

Teflon Coating

Pore Sizes ~ 30 µm

Thickness 200-400 µm

Optional:

Binder

Entangled Fibers

Filling

Alternative:

Woven Carbon Paper

© Fraunhofer ITWM7

Microporous Layer (MPL)

Carbon Agglomerates

Pore Sizes ~ 100 nm

Chun et al, Int. J. Hydrogen Energy 35, 2010

© Fraunhofer ITWM8

GDL and MPL

© Fraunhofer ITWM9

Catalyst Layer

Carbon Agglomerates

Ionomer

Platinum Particles

Pore Sizes ~ 100 nm

FIB-SEM image by S. Thiele, IMTEK Freiburg

© Fraunhofer ITWM10

Outline





c) Validation

d) Some results

3. The general idea



3D Structure Model

Two sources:1) Tomography image (segmentation)

(needed for validation)

2) Virtually generated (stochastic geometry)

(needed for virtual material design)


3D Models: Gas Diffusion Layer (GDL)

Nonwoven fibres

Input: Porosity Fibre diameter and type Anisotropy

Agorithm: Poisson line process

Production process not modeled



Nonwoven fibres plus binder


Weight% binder



Nonwoven fibres (entangled)


Fibre crimp


Curved Fibers

Idea: create curved fibres out of straight segments

Algorithm: 1. start with one segment2. add segments until desired fibre length is reached

How to determine the direction of the next segment? Many possibilities: keep previous direction + random deviation or: keep previous curvature + random deviation anisotropy of main fibre direction anisotropy of deviations


Curved Fibers

Determine fiber direction dn+1 :

α = 0 : maintain curvatureα = 1 : maintain direction

α=1, β=1:

Anisotropy:

α: "straightness"β: "force"σ: randomness


3D Models: Microporous Layer (MPL)

Typically: carbon agglomerates

Input: Particle size Particles per Agglomerate Porosity

Becker, Wieser, Fell, Steiner, Int J. Heat Mass Transfer2010


3D Models: Catalyst Layer (CL)

Carbon agglomerates plus electrolyte/ionomer

Elect. surrounds

C. particles

Elect. between

C. particles

Elect. surrounds

C. particles but

not in between


Model example:

Porosity 33.3 %Carbon/Pt 50.1 vol%Electrolyte 16.6 vol%

Size: (800 nm)³, voxel length 1 nm

3D Models: Catalyst Layer (CL)


Outline





c) Validation

d) Some results

3. The general idea



Determination of Effective Properties

Common approach:

1. Start with a given 3D voxel mesh

2. Find effective properties

a) Geometrical properties: • pore size distribution, pore morphology, surface area

b) Transport properties:i. Solve PDE on the voxel gridii. Find effective property by upscaling / averaging


Diffusivity

Macroscopic description (homogenized porous media model)Fick's first law:

D* : effective diffusivity [m²/s] unknownj : diffusion flux [mol/m²/s]c : concentration [mol/m³]

Microscopic description (pore structure model)Laplace equation:

Boundary conditions: no-flux on fibre surface, concentration drop

D* can be determined from the solution!

c=1

c=0


Knudsen Diffusivity

Macroscopic description (homogenized porous media model)Fick's first law:

D* : effective diffusivity [m²/s] unknownj : diffusion flux [mol/m²/s]c : concentration [mol/m³]

Diffusion mechanisms1. Kn << 1 (bulk diffusion) Diffusion by particle-particle collisions Mathematical model: Laplace equation

2. Kn >> 1 (Knudsen diffusion) Diffusion by particle-wall collisions Mathematical model: random walk methods

3. Kn ~ 1 (transition regime diffusion) Both mechanisms are present, Bosanquet:

[( )( ) ]2

TKn t o t oD E x x x x

t

ε= − −


Electric Conductivity

Macroscopic description (homogenized porous media model)Macroscopic description (homogenized porous media model)Macroscopic description (homogenized porous media model)Macroscopic description (homogenized porous media model)

Ohm’s law :

j : current density [A/m2]σ¤: effective conductivity [1/Ω/m]φ : potential [V]

Microscopic description (pore structure model)Microscopic description (pore structure model)Microscopic description (pore structure model)Microscopic description (pore structure model)

Conduction equation:

Boundary conditions: potential drop

σ* can be determined from the solution!


Permeability

Macroscopic description (homogenized porous media model)

Darcy’s law :

u : average flow velocityκ : permeability tensor unknownµ : viscosityp : pressure

Microscopic description (pore structure model)

Stokes equation:

Boundary conditions: no-slip on fibre surface, pressure dropκ can be determined from the solution!


Two-step approach:

1. Use pore morphology method (Hilpert, 2001) to determine distribution of air and water phase.

Idea: a pore is filled with the non-wetting fluid (=water), if

2. Solve Stokes equation on the remaining pore space to determine wetting phase (=air) permebility

Relative Permeability

non-wetting fluid

wetting fluid

r

β


Properties Overview

GDL: (saturation dependent) diffusivity, (saturation dependent) permeability, electric conductivity, heat conductivity pore size distribution

MPL (Knudsen) diffusivity, electric conductivity, heat conductivity pore size distribution

CL pore size distribution, surface or contact areas, contact lines protonic conductivity, electronic conductivity, (Knudsen) diffusivity

Caveat: Results cannot be better than the 3D structure model permits.


Outline





c) Validation

d) Some results

3. The general idea



Validation: Toray TGP H 060 Gas Diffusion Layer

Data from PSI: Tomography images of Toray TGP H 060 at different compression levels Diffusivity, permeability and conductivity were measured at different compression levels experimentally

Now: compute diffusivity, permeability and conductivity numerically and compare results

Becker, Flückiger, Reum, Büchi, Marone, Stampanoni, 2009, J. Electrochem. Soc. 156


Diffusivity

Perfect in tp-direction

Small differences in ip-direction

• ip-measurememts performed

on a stack of GDLs

• tomography image shows

single layer between sample

holder


Permeability

Perfect in tp-direction

Small differences in ip-direction

• ip-measurememts performed

on a stack of GDLs

• tomography image shows

single layer between sample

holder


Electric Conductivity

Tp-conductivity too high!

Reason: model assumes a

perfect contact between the

fibres (and the binder)


Outline





c) Validation

d) Some results

3. The general idea



Comparison of GDL Designs

same fibre diameters

different orientations

all fibres in-plane

isotropic

in-plane + through-plane

Zamel, Li, Shen, Becker, Wiegmann, Chem. Engineering Sci. 65, pp 3994-4006, 2010.


Comparison of Different MPL

Create MPLs with

same porosity & particle sizes

different pore size distributions


Comparison of Different MPL

Case Conductivity Diffusivity

I 0.094 1.92

II 0.120 1.78

III 0.104 1.65

IV 0.092 1.59

V 0.095 1.67


Outline





c) Validation

d) Some results

3. The general idea



The General Approach: Computer Aided Material Engineering

Properties

Model

Properties

Voxel Mesh

generate

compute

measure

Properties are:• pore size distribution• permeability• diffusivity• capillary pressure curve• ...

Lab Computer

?

PorousMaterial

manufacturenext material

try nextset of

parameters


Validation - Step 1: Property Computations

Porous Material

Properties

CT Image

Voxel Mesh

Properties

compute

filter &segment

image

measure

compare

... and image acquisition

... and image processing

... and measurements


Validation - Step 2: Material Models

CT Image

Voxel Mesh

Model

Properties Properties

VoxelMesh

generate

computecompute

filter &segment

compare


filter &segment

Computer Aided Material Engineering

Porous Material CT Image

Voxel Mesh

Model

Properties

generate

compute

Properties

image

measure

Lab Tomograph


The GeoDict Software

3d Image

Voxel Mesh

NonwovenModel

Permea-bility

Sintered Structures

Model

Woven Model

DiffusivityCapillary Pressure

Pore Size Distribution

metry

pre ions

...

...


Modules of the GeoDict Software

Generators:Generators:Generators:Generators:

- FiberFiberFiberFiberGeo Geo Geo Geo

- SinterSinterSinterSinterGeoGeoGeoGeo

- WeaveWeaveWeaveWeaveGeoGeoGeoGeo

- GridGridGridGridGeoGeoGeoGeo

- PackPackPackPackGeo Geo Geo Geo

- PleatPleatPleatPleatGeo Geo Geo Geo

- PaperPaperPaperPaperGeo Geo Geo Geo

Modifiers:Modifiers:Modifiers:Modifiers:

- ProcessProcessProcessProcessGeoGeoGeoGeo (3d image processing)

- LayerLayerLayerLayerGeoGeoGeoGeo (layered media)

- ImportImportImportImportGeoGeoGeoGeo (e.g. tomographie, .stl)

- ExportExportExportExportGeoGeoGeoGeo (e.g. Fluent, Abaqus)

Simple Properties Predictors:Simple Properties Predictors:Simple Properties Predictors:Simple Properties Predictors:

- FlowFlowFlowFlowDictDictDictDict (single phase flow properties)

- ElastoElastoElastoElastoDictDictDictDict (effective elastic properties)

- ConductoConductoConductoConductoDictDictDictDict (effective conductivity)

- DiffuDiffuDiffuDiffuDictDictDictDict (effective diffusivity)

Complex Properties Predictors:Complex Properties Predictors:Complex Properties Predictors:Complex Properties Predictors:

- FilterFilterFilterFilterDictDictDictDict (pressure drop, efficiency, life time)

- SatuSatuSatuSatuDictDictDictDict (two phase flow properties)

- PoroPoroPoroPoroDictDictDictDict (pore size measures)

- AcoustoAcoustoAcoustoAcoustoDictDictDictDict (acoustic absorption)

- PleatPleatPleatPleatDictDictDictDict (porous media flow)


Outline





c) Validation

d) Some results

3. The general idea



Other Industrial Applications

Filtration

Paper dewatering felts

Sintered ceramics

Woven metal wire meshes

Diapers and hygiene products


Filtration


Tomography and Models of Felts

Tomography

Paper machine

1mm

10m

Forming fabric and dewatering felt


Sintered Ceramics

• top: binarized SEM image• bottom: cross section through virtually created medium


Computed vs measured porosities and permeabilities

simulation

measurement


Woven Metal Wire Meshes: Complex weave models

Left: Model of a two-layer weave based on a CT-scan.Right: Model of a complex one-layer twill Dutch-weave.


Woven Metal Wire Meshes: Geometric Validation

(a): CT of a twill Dutch-weave. (b): Geometry model. (c)-(d): Geometric validation.


Woven Metal Wire Meshes: Measurement and Simulation

Velocity dependent pressure drop: Comparison between measurements and simulationson corresponding geometry models.


Thank You !Geometry generator, property

predictor and virtual material

designer

www.geodict.com

BMBF project PemCaD

Pore Scale Modelling of Porous Layers Used in Fuel Cells · Pore Scale Modelling of Porous Layers...

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