Optimizing fuel cell design with Optimizing fuel cell design with COMSOLCOMSOL M l i h iM l i h iCOMSOL COMSOL MultiphysicsMultiphysics

Presenter: Dr. Kai Fei (費凱)Dr Chin-Hsien Cheng(鄭欽獻)Dr. Chin-Hsien Cheng(鄭欽獻)

COMSOL User Conference 2012 Nov. 9 2012 Taipei Taiwan

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OutlineOutline

• Fuel cell introduction

• Simulation detail

• FC applicationsFC applications– 2D MEA model (HT-PBI)– Multi-scale simulations (conceptual)

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How fuel cell worksHow fuel cell worksBipolar plate

•Bipolar plate (graphite): ~10000 μmC h dBipolar plate

electron conduction

•Gas channel : ~1000 μm

Cathode

O2 O2 μ

gas transport

•GDL (Carbon cloth/paper): ~250 μmGDL

Catalyst layerH+

e-

GDL

MembraneCatalyst layer

GDL (Carbon cloth/paper): 250 μm

electron conduction and gas/water transport

•CL (Pt Carbon Nafion): ~10 μm

y y

GDL •CL (Pt, Carbon, Nafion): ~10 μmelectron conduction, gas/water transport

d i d h i l iMEAH2 H2

Bipolar plateproton conduction and chemical reaction

•Membrane (Nafion): ~100 μmAnode

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proton conduction and water transportOver all: H2+O2→H2O

Components single cell and stackComponents, single cell and stack

Polymer electrolytePolymer electrolyte

Carbon paper

Single cell

FC stackFC stack

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Bipolar plate Catalyst layer

Complex species transportComplex species transport

Liquid waterMulti-componentMulti-phase

ChannelPorous media

Gas(H O )

proton

water vapor Temperature(H2, O2 etc)

electron

p p

Dissolve water

Couple/dependentCouple/dependentMesh problem User input equations

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Couple/dependentCouple/dependentMesh problem User input equations

Governing equationsGoverning equations• Conservation of species: • Bulter Volmer equation

O2O2O2eff, SCD- Conservation of species:

RT

Fexp

RTF

exp)(jj ,,0jcja

ref

i

CC

• Bulter-Volmer equation

H2H2H2 eff, SCD- SCD

f

• Agglomerate model is used wvwvwveff, SCD-

eff• Conservation of charge: PBI O2Pt/C

eSolideffe S- peelectrolyteffP S-

Pt/C

Pt/C

Pt/CPt/C

peelectrolytP

Tff STk- • Conservation of energy: Pt/C Pt/C

Pt/C

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Teff STk

Source termsSource termsS AGDL ACL PEM CCL CGDLSourceTerms

AGDL ACL PEM CCL CGDL

SO2 mol/(m3 s) 0Fjc 4/O2 ( )

SH2 mol/(m3 s) 0

S mol/(m3 s) MS /

Fja 2/

SMS /

jc

MS / MS /Swv mol/(m s)

Sλ mol/(m3 s) 0OHl MS 2/ SMS OHl 2/

)( eqMa EW

OHl MS 2/

)( eqM

a EW

OHl MS 2/

Sl (kg/m3s)

Se (A /m3) 0 0lS lS

j

OHc

OHl

MFj

MSS

2

2

4

cjlS

e ( / )

Sp (A/m3) 0

S (W/m3) 2I

aj

aj2I I 2

cj

cj)( STj 2I

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ST (W/m ) lghSI

leffe

lg

hSIj leff

effp lg

2

)(

hSInF

j

leff

lghSI

leffe

Transport parametersTransport parameters751400 )/101325()333/(10055.1 75.140 2

02 PTDD OHH

)/101325()333/(102982.0 75.140 2 PTD OH

)/101325()333/(102652.0 75.140 2 PTDO

))/2768exp(1013 70 2 TD fO ))/2768exp(101.3,2 TD nafionO

30 )1(101.3 )/2436(28.070 ,2 TnafionOH eeD

173)1161(10174 )/2436(80 TeeD 173 )1161(1017.4 )(,2 nafionOH eeD

)/666exp(1033.1 52 THNafionO

11 1 ))13031(1268exp()326.0514.0(0

Tp

1))11(1268exp(187900

8

1 ))303

(1268exp(1879.0 Tp

Kinetic parametersKinetic parameters 0 eelectroltysolid

)1

3431(exp)/( 0343,0,0 TR

EVSij

acta

Kref

aref

a

RTF

jFC

k crefcrefO

exp4

1,0

2 343 TR

)1

3431(exp)/( 0343,0,0 TR

EVSij

actc

Kref

cref

c

O2

FFP )1( MXs

0P : lcondl sPKS

)exp()exp()(

2

2,0 RT

FRT

FPPjj ref

H

Hrefaa

kP

Fj O24

0P : )1( 2

RTMXs

PKS OHwvcondl

)1(/3 ,2 CL

effeffO

agg Dkr

kHFj Naf

Oc

2

4

3 ff

)3/(1)3coth(3 2

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Simulation flow chartSimulation flow chartCOMSOL geometry toolsModel geometry COMSOL geometry toolsImport from CAD files

Parameters input ConstantSubdomain expresses

•ConvergenceM hp

Direct (UMFPACK)

•Mesh

Solve equations( )

Stationary/parametricsAdaptive mesh refinement

Post processing COMSOL postprocessing toolsExport according to your own need

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Export according to your own need

Challenges & solutionsChallenges & solutions

•• ConvergenceConvergence– Mainly due to coupled equations (8) and lots of y p q ( )

variable dependent parameters.Appropriate value of initial valuepp op ate va e o t a va eUsing RESTART to solve equations step by step

•• MeshMesh•• MeshMesh– Finer or coarser mesh are both possible to solve the

bl d h d b dproblem (adaptive method can be used)

G i f 2 3 4 2 !!!11

Great improvement form ver.2.3 ver.4.2 !!!

Models used in COMSOLModels used in COMSOL

• Chemical Engineering Module– Mass Transport Convection and Diffusion (4)p ( )– Energy Transport Convection and Conduction(1)

AC/DC M d l• AC/DC Module– Conductive Media DC (2)

• COMSOL Multiphysics ModulePDE Coefficient Form(1)– PDE, Coefficient Form(1)

All solved variables are dependent

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p

What we need isWhat we need is…

User friendly interfaceFlexible mesh generation

Couple different User friendly interface

variables at willUser friendly interface

COMSOL Multiphysics

Easy user define functioninputPowerful post-processing

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Examples solved by COMSOLProton exchange membrane fuel cell- Proton exchange membrane fuel cell

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2D simulations2D simulationsRibGas• Simulation domain Rib

Gas channel

RibGas channelchannel

Cathode GDLC h d GDL 200Cathode CL

Anode CL

Cathode GDL: 200μmCathode CL: 20μmElectrolyte: 50μmAnode CL 10μm

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Anode GDLAnode CL: 10μmAnode GDL 200μm

INCREASE REDUCEINCREASECL performance

REDUCECL cost

Pt loadingPBI contentP /C %Pt/C wt%Support materialCL thicknessAlternative catalyst material

CL ith diff r nt PBI t% mp iti nCL with different PBI wt% compositionsPerformance can be increased!

Cost can be reduced!

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Multi layer CL designMulti-layer CL designN if iti f PBI t tNon-uniform composition of PBI content

CGDLCGDL

CCL (multi-layer)

MEM

ACL ( i l l )ACL (single layer)

AGDL

MEA structure

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Case studied(1/2) single layerCase studied(1/2) – single layerPBI 含量 5 t% 10 t% 20 t% 30 t%PBI 含量 5wt% 10wt% 20wt% 30wt%

觸媒層厚度 2e-5m 2.05e-5m 2.3e-5m 2.35e-5m

PBI薄膜厚度 1e-8m 2.4e-8m 5.5e-8m 6e-8m

孔隙率 0.439 0.436 0.404 0.382

Pt/C體積分率 0.510 0.459 0.386 0.267

PBI體積分率 0.0506 0.104 0.209 0.3507

彎曲率 1.3 1.6 2.8 4.5

Pt loading 0.5mg/cm2 0.5mg/cm2 0.5mg/cm2 0.5mg/cm2g g g g g

Optimizing PBI content in single CL design

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p g g g

Case studied(2/2) multi layerCase studied(2/2) – multi-layer

觸媒層結構 %PBI Pt loading 觸媒層厚度 PBI薄膜厚度

(a) cathode 5wt% 0.333mg/cm2 2e-5/2 m 1e-8m

30wt% 0.167mg/cm2 2.35e-5/2m 3e-8m

(b) cathode 10wt% 0.333mg/cm2 2.05e-5/2m 2e-8m

30wt% 0.167mg/cm2 2.35e-5/2m 3e-8m

(c) cathode 5wt% 0.167mg/cm2 2e-5/3m 1e-8m

10wt% 0 167mg/cm2 2 05e 5/3m 2e-8m10wt% 0.167mg/cm2 2.05e-5/3m 2e 8m

20wt% 0.166mg/cm2 2.3e-5/3m 2.2e-8m

Optimizing PBI content distribution in multi-CL design

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Experimental validation- single layer

5 wt% of PBI5 wt% of PBI

is the best

G d m t h ith p rim nt l d t

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Good match with experimental data

Detail analysis (single layer)Detail analysis (single layer)

DaR PBIratiodiff OPBI

2

16Ld

ma Ptratio

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Resistivity of gas diffusion

Lda catPtPtratio

Effective Pt reaction area

Parametric study (1/2)Parametric study (1/2)

Temperature effect Porosity effect

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p

Parametric study (2/2)Parametric study (2/2)

Totuorsity effect Thickness effect

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Cathode O distributionCathode O2 distribution

channel rib U=0.2V

5wt% 20wt%

10wt% 30wt%

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Temperature distributionTemperature distributionU=0.2Vchannel rib

5wt% 20wt%

2510wt% 30wt%

Experimental validation- multi-layer

Good match with experimental data

Higher PBI content is required g qfor sub-layer close to membrane- For increasing proton conductivity

Lower PBI content is required for sub-layer close to GDL- For increasing gas diffusivity

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Detail analysis (multi layer)Detail analysis (multi-layer)

Resistivity of diff i n

Effective Pt r ti n r

Proton conductivitygas diffusion Pt reaction area

Different effect for different physical properties

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for different regions is observed

Internal distributionsInternal distributions

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Oxygen distribution Temperature distribution

New multi layer CL designNew multi-layer CL design

A new triple-layer CL designis proposed (3-5-7wt%) and is p p ( )shown to have better performancethan single layer design

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Examples solved by COMSOLConceptual multi scale simulation- Conceptual multi-scale simulation

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Why multi scale simulation?Why multi-scale simulation?

• From fundamental point of view…– All macroscopic transport properties (eg. diffusivity) p p p p ( g y)

are ensemble average of microscopic transport phenomenap

– Traditional correlations is inadequate to describe what really happenwhat really happen

• Challenges…– No real couple multi-scale simulation package can be

found– Alternative way to do this is necessary

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Concept of multi scaleConcept of multi-scale

Macro nanoField distribution Transport properties

Done by

Semi-empirical relation derived base on atomistic scale simulation

yCOMSOL

base on atomistic scale simulation

Take advantage of COMSOL’s very flexible and user friendly /

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interface/functions!

Simulation proceduresSimulation procedures1299 )(104589.210438.5 1299,2 smD NafionO

)(104678.3108814.2 12109,2 smD NafionOH

Estimated by molecular dynamics simulations

COMSOLInput into COMSOL

simulation

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Diffusivity distributionDiffusivity distributionCMD Conventional

O2 diffusivity inside Nafion

CMD Conventional

H2O diffusivity inside Nafion

Similar performance but different internal distribution

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p Different optimization design will be proposed !!!

Thanks for your attention!Thanks for your attention!

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