Introduction to Batteries and Fuelcells Module

VERSION 4.3

Introduction toBatteries & Fuel Cells Module

C o n t a c t I n f o r m a t i o n

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Part No. CM021502

I n t r o d u c t i o n t o t h e B a t t e r i e s & F u e l C e l l s M o d u l e 19982012 COMSOLProtected by U.S. Patents 7,519,518; 7,596,474; and 7,623,991. Patents pending.

This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/sla) and may be used or copied only under the terms of the license agree-ment.

COMSOL, COMSOL Desktop, COMSOL Multiphysics, and LiveLink are registered trademarks or trade-marks of COMSOL AB. Other product or brand names are trademarks or registered trademarks of their respective holders.

Version: May 2012 COMSOL 4.3

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Battery Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

The Battery Modeling Interfaces . . . . . . . . . . . . . . . . . . 11

Fuel Cell Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

The

Physics

The Mo

Tutoria

Tutoria

Mod

Resu | 3

Fuel Cell Modeling Interfaces . . . . . . . . . . . . . . . . 14

List by Space Dimension and Study Type. . . . . . 16

del Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

l Model of a Lithium-Ion Battery. . . . . . . . . . . . . . 19

l Model: Fuel Cell Cathode . . . . . . . . . . . . . . . . . . 31

el Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

lts and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 33

IntroductionThe Batteries & Fuel Cells Module models and simulates the fundamental processes in the electrodes and electrolytes of batteries and fuel cells. These simulations may involve the transport of charged and neutral species, current conduction, fluid flow, heat transfer, and electrochemical reactions in porous electrodes.

You can use this module to investigate the performance of batteries and fuel cells at different operating conditions for different electrode configurations, separators, current collectoinvolved procedifferent hypotstudy the influecomposition, a

The figure belointerfaces in COthe Heat Trans

Figure 1: The 3D mIntroduction | 5

rs and feeders, materials, and chemistry. The description of the sses and phenomena is rather detailed and you can therefore apply heses to gain an understanding of the investigated systems. You can nce of different electrocatalysts, pore distribution, electrolyte

nd other fundamental parameters directly in the user interface.

w shows the Batteries & Fuel Cells interfaces and other physics MSOL Multiphysics that are modified by the module, for example

fer interfaces.

odel physics list for the Batteries & Fuel Cells Module as shown in the Model Wizard.

6 | Introduction

The modules interfaces describe different phenomena in batteries and fuel cells and are based on the conservation of current, charge, chemical species, and energy.

The Battery with Binary Electrolyte ( ), the Lead-Acid Battery ( ), and the Lithium-Ion Battery ( ) interfaces form the basis for battery modeling. In addition, the Primary Current Distribution ( ), Secondary Current Distribution ( ), and Tertiary Current Distribution, Nernst-Planck ( ) interfaces are general physics interfaces to model any electrochemical cell. The Chemical Species Transport ( ), the Fluid Flow ( ) and the Heat Transfer ( ) interfaces are also extended with functionality fo

The Primary, Sewith the interfaform the basis fr battery modeling, as discussed in Battery Modeling on page 7.

condary, and Tertiary Current Distribution interfaces, in combination ces for Chemical Species Transport, Fluid Flow, and Heat Transfer, or fuel cell modeling, as discussed in Fuel Cell Modeling on page 12.

Battery ModelingThe Batteries & Fuel Cells Module has a number of physics interfaces to model battery unit cells that consist of:

Current collectors and current feeders

Porous electrodes

The electrolyte that separates the anode and cathode

The module treats both rechargeable batteries (secondary cells) and non-rechargeab

This module carechargeable b

Figure 2: Directionelectrodes.

During dischartransfer reactioenergy during dcurrent, transpflow, and the redue to activatio

anode

negativeiloc

iloc, a

iloc, cBattery Modeling | 7

le batteries (primary cells).

n be used to study the charge and discharge processes in a attery as described below.

of the current and charge transfer current during discharge in a battery with porous

ge, chemical energy is transferred to electrical energy in the charge ns at the anode and cathode. The conversion of chemical to electrical ischarge may involve electrochemical reactions, transport of electric

ort of ions in the electrolyte, neutral chemical species transport, fluid lease of heat in irreversible losses, such as ohmic losses and losses n energies.

Cathodic charge transfer reaction

Anodic charge transfer reactionCurrent in positive electrodeCurrent in the electrolyteCurrent in negative electrode

negative electrode positive electrode

cathode

electrode positive electrode

EcellE

8 | Battery Mode

Figure 2 shows a schematic picture of the discharge process. The current enters the cell from the current feeder at the negative electrode. The charge transfer reaction occurs at the interface between the electrode material and electrolyte contained in the porous electrode, also called the pore electrolyte. Here, an oxidation of the electrode material may take place through an anodic charge transfer reaction, denoted iloc, a in Figure 2. The shapes of the two curves in the graph are described by the electrode kinetics for the specific materials. The reaction may also involve the transport of chemical species from the pore electrolyte and also from the electrode particles.

From the pore the electrolyte electrolyte in th

At the interfaceporous electrocurrent conducreduction of threaction, denotinvolve the tranparticles.

Figure 3: Electrode

The current leaand the electrolosses, activatio

iloc

iloc, a

iloc, c

anodeling

electrolyte, the current is conducted by the transport of ions through that separates the positive and negative electrode to the pore e positive electrode.

between the pore electrolyte and the surface of the particles in the de, the charge transfer reaction transfers the electrolyte current to ted by electrons in the positive electrode. At this interface, a e electrode material takes place through a cathodic charge transfer ed iloc, c in Figure 3. Also here, the charge transfer reaction may sport of chemical species in the electrolyte and in the electrode

polarization during discharge.

ves the cell through the current collector. The conduction of current chemical charge transfer reactions also releases heat due to ohmic n losses, and other irreversible processes.

positive electrodenegative electrode

cathode

Ecell

Eocv

E

The graph in Figure 3 plots the charge transfer current density, iloc, as a function of the electrode potential, E. These curves describe the polarization of the electrodes during discharge.

The negative electrode is polarized anodically during discharge, positive current as indicated by the arrow in Figure 3. The potential of the negative electrode increases. The positive electrode is polarized cathodically, a negative current as indicated by the arrow. The potential of the positive electrode decreases.

Consequently, Figure 3 also shows that the potential difference between the electrodes, hervoltage, here dif the ohmic losbatteries. This shown in Figure

During rechargtransformed to

Figure 4: During recathode. The cell v

The current enoxidation of th

negative e

cathode

iloc

iloc, a

iloc, cBattery Modeling | 9

e denoted Ecell, decreases during discharge compared to the open cell enoted Eocv. The value of Ecell is the cell voltage at a given current iloc, ses in the cell are negligible. This is usually not the case in most

implies that the cell voltage in most cases is slightly smaller than that 3.

e, the processes are reversed; see Figure 4. Electrical energy is chemical energy that is stored in the battery.

charge, the positive electrode acts as the anode while the negative one acts as the oltage increases, at a give current, compared to the open cell voltage.

ters the cell at the positive electrode. Here, during recharge, an e products from the discharge takes place through an anodic charge

Anodic charge transfer reaction

Cathodic charge transfer reactionCurrent in positive electrodeCurrent in the electrolyteCurrent in negative electrode

lectrode positive electrode

anode

EcellE

negative electrode positive electrode

10 | Battery Mo

transfer reaction. The positive electrode is polarized anodically, with a positive current, and the electrode potential increases.

The current is then conducted from the pore electrolyte, through the electrolyte that separates the electrodes, to the negative electrode.

In the negative electrode, a reduction of the reduced products from the previous discharge reaction takes place through a cathodic charge transfer reaction. The negative electrode is polarized cathodically and the electrode potential decreases.

Figure 5: Electrode

The difference increases durinThe value of Eccells, these loss

The battery prinvestigated usimodule allow ymanagement o

Choice of m

Dimensions

Dimension a

Size of the p

Porosity and

Configuratio

iloc

iloc, a

iloc, c

cathodedeling

polarization during recharge.

in potential between the electrodes, here denoted Ecell, at a given iloc, g recharge, compared to the open cell voltage, here denoted Eocv.

ell is equal to the cell voltage when ohmic losses are neglected. In most es are not negligible and they would add to the cell voltage.

ocesses and phenomena described in the figures above can all be ng the Batteries & Fuel Cells Module. The physics included in the ou to investigate the influence on battery performance and thermal f parameters such as the:

aterials and chemistry

and geometry of the current collectors and feeders

nd geometry of the electrodes

ar ticles that the porous electrodes are made of

specific surface area of the porous electrode

n of the battery components

positive electrodenegative electrode

anodeEocv

Ecell

E

The Battery Modeling InterfacesThe Battery with Binary Electrolyte interface ( ) describes the conduction of electric current in the electrodes, the charge transfer reactions in the porous electrodes, the mass transport of ions in the pore electrolyte and in the electrolyte that separates the electrodes, and the intercalation of species in the particles that form the porous electrodes. The descriptions are available for cells with basic binary electrolyte, which covers the nickel-metal hydride and the nickel-cadmium batteries.

The Lead-Acid Battery interface ( ) is tailored for this type of battery and includes functionality threactions, the vsuperficial velo

The Lithium-Ionfunctionality threactions, inter

The Tertiary Ctransport of chconvection. In non-porous elethe electronic c

The Chemical the pore electrOther reactionexample to deSecondary CurSpecies interfacbe used to modin most battery

The Fluid Flowin free media if of lead-acid ba

The Heat TransThis includes thelectrolyte, heathe net changeelectrochemicaBattery Modeling | 11

at describes the transport of charged species, charge transfer ariation of porosity due to charge and discharge, and the average city of the electrolyte caused by the change in porosity.

Battery interface ( ) is tailored for this type of battery and includes at describes the transport of charged species, charge transfer nal par ticle diffusion, and the solid electrolyte interface (SEI).

urrent Distribution, Nernst-Planck, interface ( ) describes the arged species in electrolytes through diffusion, migration, and addition, it also includes ready-made formulations for porous and ctrodes, including charge transfer reactions and current conduction in onductors.

Species Transport interfaces ( ) describe the transport of ions in olyte and in the electrolyte that separates the anode and cathode. s can be added other than pure electrochemical reactions, for scribe the degradation of materials. In combination with the rent Distribution interface ( ), the Transport of Concentrated e ( ) and the Species Transport in Porous Media interface ( ) can el the transport of charged species and the electrochemical reactions systems.

interfaces ( ) describe the fluid flow in the porous electrodes and this is relevant for a specific type of battery, for example certain types tteries.

fer in Porous Media interface ( ) describes heat transfer in the cells. e effects of Joule heating in the electrode material and in the ting due to activation losses in the electrochemical reactions, and of of entropy. The heat of reactions from other reactions than the l reactions can also be described by these interfaces.

12 | Fuel Cell M

Fuel Cell ModelingThis module includes functionality to model fuel cell unit cells that consist of:

Current collectors and current feeders

Gas channels usually formed by grooves in the current collectors and feeders

Porous gas diffusion electrodes (GDEs)

An electrolyte that separates the anode and cathode

Figure 6 shows a schematic drawing of a fuel cell unit cell and the structure of one of the GDEs. ItGDE and its co

Figure 6: Fuel cell uelectrolyte.

Oxygen and hycollector and cfeeder are usuagrooves that foside facing the

The current coto the load. Threquired during

load

cu

cuodeling

represents a fuel cell unit cell and a magnified section of the cathode ntact with the electrolyte.

nit cell and a magnified section of the cathode GDE and its contact with the

drogen are supplied to the cell through the gas channels in the current urrent feeder, respectively. The current collector and the current lly made of electronic conducting materials and are equipped with rm the gas channels. These grooves are open channels with the open surface of the GDEs.

llectors and feeders also conduct the current to the wires connected ey can also supply cooling required during operation and heating star t-up of the cell.

Cathode

AnodeElectrolyte

electrolyte

pore electrolyte GDE

gas

rrent collector

rrent feeder

Direction of the current

Gas channels in current collectors and current feeders

The GDE magnified in Figure 6 is an oxygen-reducing cathode in a fuel cell with acidic electrolyte, for example the PEMFC. In the PEMFC, the active GDE is confined to a thin active layer supported by a pure gas diffusion layer (GDE).

Figure 7 shows the principle of the oxygen reduction process in the electrode.

Figure 7: Transportreducing GDE.

From the free ecalled pore elecharge transferinterface betweelectrolyte.

Figure 7 also dcurrent in the pelectrolyte as itthe current in t

H+

e-

Current by ion transport

Current by electron transport

electro

electrodeFuel Cell Modeling | 13

of oxygen, water, protons, and electrons to and from the reaction site in an oxygen

lectrolyte, current enters the electrolyte contained in the GDE (also ctrolyte) as protons, and is transferred to electron current in the reaction at the reaction sites. These reaction sites are situated at the en the electrocatalyst in the electrode material and the pore

escribes the schematic path of the current in the electrode. The ore electrolyte decreases as a function of the distance from the free is transferred to electron current in the electrode. The direction of he electrode is opposite to that of the electrons, by definition.

2H++1/2O2+2e- = H2OO2

H2O

Charge transfer reaction

Oxygen transport

Water transport

Charge transfer reaction:

lyte

gas

14 | Fuel Cell M

The supply of oxygen takes place in conjunction with the charge transfer reaction and can be subject to mass transport resistance both in the gas phase and in the thin layer of pore electrolyte that covers the reaction site.

The water balance in the electrode is maintained through evaporation and transport through the gas pores.

The pore electrolyte has to form an unbroken path from the free electrolyte, between the anode and the cathode, to the reaction site. Also, the electrode material and the gas pores must each form an unbroken path to the reaction site or to the pore ele

The processes transfer, currenand the electrocharacteristics

Several importprocesses. Amo

Porosity, acti

Geometry orelation to th

Geometry ocurrent colle

The Fuel CellThe fluid flow iinterfacestheLaw ( ) inter

The transport electrolyte is hhave nodes thareactions. The Flow interfacescomposition.

The Heat Tranelectrolyte, in tcontribution toactivation overodeling

ctrolyte covering the reaction site.

described above including fluid flow, chemical species transport, heat t conduction in the collectors, feeders, electrodes and electrolytes, chemical reactions are all coupled together, and determine the of a unit cell.

ant design parameters can be investigated by modeling these ng these parameters are:

ve surface area, and pore electrolyte content of the GDEs

f the GDEs (active layer and GDL for the PEMFC) and electrolyte in e gas channels, the current collectors, and feeders

f the grooves that form the gas channels and dimensions of the ctors and feeders

Modeling Interfacesn the gas channels and in the GDEs are addressed by the Fluid Flow Laminar Flow ( ), Free and Porous Media Flow ( ), and Darcys faces.

of gaseous species and the mass transport resistance in the pore andled by the Chemical Species Transport interfaces ( ), which all t couple the transport in the gas phase to the electrochemical Chemical Species Transport interfaces are also coupled to the Fluid ( ) through the gas density, which is influenced by the gas

sfer interfaces ( ) handle the effects of Joule heating in the he pore electrolyte, and in the electrodes. They include the the thermal balance from the electrochemical reactions due to the potential and the net change of entropy.

The current transport by ions in the free electrolyte and in the pore electrolyte, the current transport by electrons, and the charge transfer reactions are all treated in the Secondary Current Distribution ( ) and the Tertiary Current Distribution, Nernst-Planck ( ) interfaces. In the Secondary Current Distribution interface, the variations in composition in the electrolyte are neglected. In the Tertiary Current Distribution, Nernst-Planck interface, also the contribution of diffusion to the transport of ions, and thus the contribution to the current in the electrolyte, is taken into account.

The Electrode,tangential direcwhere the poteThis assumptiodifferential eqube reduced, anavoided.Fuel Cell Modeling | 15

Shell interface ( ) models electric current conduction in the tion on a boundary. The interface is suitable to use for thin electrodes ntial variation in the normal direction to the electrode is negligible.

n allows for the thin electrode domain to be replaced by a partial ation formulation on the boundary. In this way the problem size can d potential problems with mesh anisotropy in the thin layer can be

16 | Physics List

Physics List by Space Dimension and Study TypeThe table lists the physics interfaces available with this module in addition to those included with the COMSOL basic license.

PHYSICS ICON TAG SPACE DIMENSION PRESET STUDIES

Chemical Species Transport

Surface Reactions chsr all dimensions stationary; time dependent

Transport of ConceSpecies

Species Transport in

Reacting Flow, ConcSpecies

Reacting Flow, Dilut

Electroche

Primary Current Di

Secondary Current

Tertiary Current DiNernst-Planck

Electrode. Shell

Battery Inter

Lithium-Ion Battery

Battery with Binary

Lead Acid Battery by Space Dimension and Study Type

ntrated chcs all dimensions stationary; time dependent

Porous Media chpm all dimensions stationary; time dependent

entrated rfcs 3D, 2D, 2D axisymmetric

stationary; time dependent

ed Species rfds 3D, 2D, 2D axisymmetric


mistry

stribution piec all dimensions stationary

Distribution siec all dimensions stationary; time dependent; AC impedance stationary; AC impedance time dependent

stribution, tcdee all dimensions stationary; time dependent; AC impedance stationary; AC impedance time dependent

els 3D, 2D, 2D axisymmetric


faces

liion all dimensions stationary; time dependent; AC impedance stationary; AC impedance time dependent

Electrolyte batbe all dimensions stationary; time dependent; AC impedance stationary; AC impedance time dependent

leadbat all dimensions stationary; time dependent; AC impedance stationary; AC impedance time dependent

Fluid Flow

Porous Media and Subsurface Flow

Brinkman Equations br 3D, 2D, 2D axisymmetric


Darcys Law dl all dimensions stationary; time dependent

Free and Porous Me

Heat Trans

Heat Transfer in Po

PHYSICS ICON TAG SPACE DIMENSION PRESET STUDIESPhysics List by Space Dimension and Study Type | 17

dia Flow fp 3D, 2D, 2D axisymmetric


fer

rous Media ht all dimensions stationary; time dependent

18 | The Model

The Model LibraryTo open a Batteries & Fuel Cells Module Model Library model, select View > Model Library from the main menu in COMSOL Multiphysics. In the Model Library window that opens, expand the Batteries & Fuel Cells Module folder and browse or search the contents. Click Open Model and PDF to open the model in COMSOL Multiphysics and a PDF to read background theory about the model including the step-by-step instructions to build it.

The MPH-files ior Compact M

Full MPH-filemodels appethe text Larmodels node

Compact MPsolution dataother reasonre-solve the and solutionModel Librarat a compactappears. If a context men

Two models froModel of a LithCell Cathode

The next two s Library

n the COMSOL model libraries can have two formatsFull MPH-files PH-files.

s, including all meshes and solutions. In the Model Library these ar with the icon. If the MPH-files size exceeds 25MB, a tip with ge file and the file size appears when you position the cursor at the in the Model Library tree.

H-files with all settings for the model but without built meshes and to save space on the DVD (a few MPH-files have no solutions for s). You can open these models to study the settings and to mesh and models. It is also possible to download the full versionswith meshes sof most of these models through Model Library Update. In the y these models appear with the icon. If you position the cursor model in the Model Library window, a No solutions stored message full MPH-file is available for download, the corresponding nodes u includes a Model Library Update item.

m the Model Library are used as tutorials in this guide. See Tutorial ium-Ion Battery star ting on page 19 and the Tutorial Model: Fuel star ting on page 31.

ections introduce you to the battery and fuel cell modeling basics.

Tutorial Model of a Lithium-Ion BatteryThe following is a two-dimensional model of a lithium-ion battery. The cell geometry could be a small part of an experimental cell but here it is only meant to demonstrate a 2D model setup. A realistic 2D geometry is shown in the model Edge Effects in a Spirally Wound Li-Ion Battery available in the Batteries & Fuel Cells Module Model Library (see The Model Library on page 18 to access this model).

The cell geometry is shown in the figure below. Due to symmetry along the height of the battery, tshows the posicollector and fe

During discharg(red face, middfaces, middle).

The resulting 2positive electro

positive electrode

electrTutorial Model of a Lithium-Ion Battery | 19

he 3D geometry can be modeled using a 2D cross section. The figure tion of the positive and negative electrode, and the position of the eder contacts during discharge.

e, the current collector is in contact with the outer face of the battery le) while the current feeder runs inside of the folded structure (blue The modeled 2D cross section is shown in light blue (right).

D cell geometry is shown in the next figure. During discharge, the de acts as the cathode and the contact of the metallic tab acts as a

olyte negative electrode

cross-sectioncurrent collector (discharge)

current feeder (discharge)

20 | Tutorial Mo

current collector. The negative electrode then acts as the anode and the contact of the metallic tab acts as the current feeder.

The model defbattery. The intelectrode is soland t are the otthe material anequations are fooriginally formuUniversity of C

The purpose odischarge, as a This distributiothickness of theand transport p

The following i

current collector

current feeder

positive electrode

negative electrodedel of a Lithium-Ion Battery

ines and solves the current and material balances in the lithium-ion ercalation of lithium inside the par ticles in the positive and negative ved using a fourth independent variable for the particle radius (x, y, her three). The reaction kinetics and the intercalation are coupled to d current balances at the surface of the particles. The model und in the Batteries & Fuel Cells Module Users Guide. The model was lated for 1D simulations by John Newman and his co-workers at the alifornia at Berkeley.

f the 2D simulation is to reveal the distribution of the depth of function of discharge time, in the different parts of the electrodes. n is caused by the position of the current collector and feeder and the electrodes and electrolyte in combination with the electrode kinetics roperties.

nstructions show how to formulate, solve, and reproduce this model.

1.3 mm

MODEL WIZARD

1 Open COMSOL Multiphysics.

2 In the Model Wizard, click the 2D button. Click Next .

3 On the Add Physics window, under Electrochemistry>Battery Interfaces , double-click Lithium-Ion Battery (liion) to add it to the Selected physics list. Click Next .

4 On the Studies window under Preset Studies, click Time Dependent .

5 Click Finish .

GLOBAL D

Load the param

Parameters1 In the Model B

2 In the setting

3 Browse to thfolder on youDouble-click

Note: The locaCOMSOL Multmight be similar

The parameterTutorial Model of a Lithium-Ion Battery | 21

EFINITIONS

eter values to be used in the model from a parameter file.

uilder, right-click Global Definitions and choose Parameters .

s window under Parameters, click Load from File .

e file li_battery_tutorial_2d_parameters.txt in the Model Library r computer, models\Batteries_and_Fuel_Cells_Module\Tutorial Models. to add or click Open.

tion of the file used in this exercise varies based on the installation of iphysics. For example, if the installation is on your hard drive, the file path to C:\Program Files\COMSOL43\models\.

s are added to the table as in this figure.

22 | Tutorial Mo

GEOMETRY 1

Also import the geometry from a file.

1 In the Model Builder under Model 1, right-click Geometry 1 and choose Import .

2 In the settings window under Import, click the Browse button.

3 Browse to the file li_battery_tutorial_2d.mphbin in the Model Library folder on your computer, Batteries_and_Fuel_Cells_Module\Tutorial Models. Double-click to add or click Open.

Note: The locatCOMSOL Multmight be similar

4 Click Import a

MATERIAL

Use the Batterfor the electrolmodel first, thisdel of a Lithium-Ion Battery

ion of the file used in this exercise varies based on the installation of iphysics. For example, if the installation is on your hard drive, the file path to C:\Program Files\COMSOL43\models\.

nd then the Build All button .

S

ies and Fuel Cells Material Library to set up the material properties yte and electrode materials. By adding the electrolyte material to the material becomes the default material for all domains.

1:2 EC:DMC / LiPF6 (Li-ion Battery)1 Select View>Material Browser from the main menu.

2 In the Material Browser window in the tree under Batteries and Fuel Cells, right-click 1:2 EC:DMC / LiPF6 (Li-ion Battery) and choose Add Material to Model from the menu.

LixC6 Electrode1 Go to the Ma

2 In the tree unBattery) and

LixMn2O4 Elec1 Go to the Ma

2 In the Materia(Positive, Li-ioTutorial Model of a Lithium-Ion Battery | 23

(Negative, Li-ion Battery)terial Browser window.

der Batteries and Fuel Cells, right-click LixC6 Electrode (Negative, Li-ion choose Add Material to Model from the menu.

trode (Positive, Li-ion Battery)terial Browser window.

ls tree under Batteries and Fuel Cells, right-click LixMn2O4 Electrode n Battery) and choose Add Material to Model from the menu.

The node sequence in the Model Builder under the Materials node should match this figure.

24 | Tutorial Mo

LITHIUM-ION BATTERY INTERFACE

Now set up the physics in the domains. Star t with the negative porous electrode.

Porous Electrode 11 Right-click Lithium-Ion Battery and choose Porous Electrode .

2 Select Domain 3 only.

Note: There are many ways to select geometric entities. When you know the geometric entitybutton and eselecting geomeUsers Guide.

3 Go to the PoElectrolyte sal

4 Under ElectroElectrode mat

5 Under ParticlParticle materElectrode (Neg

6 Enter cs0_neconcentration the Particle mdistance (rp) fdel of a Lithium-Ion Battery

to add, such as in these exercises, you can click the Paste Selection nter the information in the Selection field. For more information about tric entities in the Graphics window, see the COMSOL Multiphysics

rous Electrode settings window. Under Model Inputs, from the c list, select t concentration (liion/liion).

de Properties, select LixC6 Electrode (Negative, Li-ion Battery) from the erial list.

e Intercalation from the ial list, select LixC6 ative, Li-ion Battery).

g as the Initial species (cs,init) and rp_neg in ean center-surface ield.

7 Under Volume Fractions, in the Electrode volume fraction (s) field, enter epss_neg. In the Electrolyte volume fraction (l) field enter epsl_neg.

8 Under Effective Transport Parameter Correction, choose Bruggeman from all the listsElectrolyte conductivity, Electrical conductivity and Diffusion.

Porous Electrod1 In the Model B

node and clicnode.The Dmeans it is a

2 Under Model select Insertiosurface (liion/p

3 Under EquilibFrom material

4 Under Materi(Negative, Li-i

Now set up thelectrode in a s

Porous Electrod1 Right-click Lit

2 Select DomaTutorial Model of a Lithium-Ion Battery | 25

e Reaction 1uilder, expand the Porous Electrode 1 k the Porous Electrode Reaction 1 in the upper left corner of a node default node.

Inputs from the c list, n particle concentration, ce1).

rium Potential, select .

als select LixC6 Electrode on Battery) from the list.

e positive porous imilar way.

e 2hium-Ion Battery and add another Porous Electrode node.

in 1 only.

26 | Tutorial Mo

3 In the Porous Electrode settings window, under Model Inputs, select Electrolyte salt concentration (liion/liion) from the c list.

4 Under Electrode Properties, select LixMn2O4 Electrode (Positive, Li-ion Battery) from the Electrode material list.

5 Under Particle Intercalation, select LixMn2O4 Electrode (Positive, Li-ion Battery) from the Particle material list. Enter cs0_pos in the Initial species concentration (cs,init) field, and enter rp_pos in the Particle mean center-surface distance (rp) field.

6 Under Volume Fractions, enter epss_pos in the Electrode volume fraction (s) field. In the Electrolyte vo

7 Under EffectiElectrolyte con

Porous Electrode1 In the Model B

node and clic

2 Under Model particle conce

3 Under Equilib

4 Under MateriLi-ion Battery)

Electrolyte is theDomain 2 only.

Initial Values 2Initial values are

1 Right-click Lit

2 Select Doma

3 In the Initial VValues, enter (phil) field anfield.del of a Lithium-Ion Battery

lume fraction (l) field, enter epsl_pos.ve Transport Parameter Correction, choose Bruggeman from all the listsductivity, Electrical conductivity, and Diffusion.

Reaction 1uilder, expand the Porous Electrode 2 k Porous Electrode Reaction 1 .

Inputs from the c list, select Insertion ntration, surface (liion/liion).

rium Potential, select From material.

als select LixMn2O4 Electrode (Positive, from the list.

default domain node . This default node is now applied to No additional settings are needed for this node.

needed for the solver to converge. Star t with the positive electrode.

hium-Ion Battery and choose Initial Values .

in 1 only.

alues settings window under Initial -0.2 in the Electrolyte potential d 4.1 the Electric potential (phis)

Initial Values 1 (the Default Node)The default Initial Values node is now applied to the negative electrode and the electrolyte domains only.

1 In the Model Builder, click Initial Values 1 .

2 Go to the Initial Values settings window. Under Initial Values enter -0.2 in the Electrolyte potential (phil) field.

Finish the model by setting up the boundary conditions. Grofeeder, and apppositive curren

Electric Ground1 Right-click Lit

2 Select bound9, 15 in the P

Electrode Curre1 Right-click Lit

Electrode>Ele

2 Select Bound

3 In the settingDensity, entercurrent densit

MESH 1

Modify the def

1 In the Model B

2 In the Mesh seExtra fine.Tutorial Model of a Lithium-Ion Battery | 27

und the negative electrode current ly a current density condition at the t collector.

1hium-Ion Battery and choose Electrode>Electric Ground .

aries 7, 9, and 15 only (or click the Paste Selection button and enter 7, aste Selection window).

nt Density 1hium-Ion Battery and choose ctrode Current Density .

ary 14 only.

s window under Electrode Current -200[A/m^2] in the Inward electrode y (in,s) field.

ault mesh by choosing a finer size.

uilder under Model 1, click Mesh 1 .

ttings window under Mesh Settings, from the Element size list choose

28 | Tutorial Mo

3 Click the Build All button .

STUDY 1

Set up a 100 s tfirst 10 s, and 1

Step 1: Time De1 In the Model B

2 In the settingSettings, in thcopy and pasrange(20,10

3 Choose the Rbox and ente

4 In the Model Bdel of a Lithium-Ion Battery

ime-dependent solver to store the solution at 1 s intervals during the 0 s intervals during the last 90 s. Then solve the problem.

pendentuilder expand the Study 1 node and click Step 1: Time Dependent .

s window under Study e Times field enter (or te) range(0,1,10), ,100).

elative tolerance check r 0.001.

uilder, right-click Study 1 and choose Compute .

RESULTS

2D Plot Group 3The following steps create a plot of the solid lithium concentration at the surface of the electrode particles at 100 s.

1 In the Model Builder, right-click Results and choose 2D Plot Group .

2 In the 2D Plot Group settings window under Data, choose 100 from the Time list.

3 Right-click 2D

4 In the Surfacechoose Lithiu

5 Click the Plot

6 On the Graph

1D Plot Group 4The following s

1 In the Model B

2 Right-click 1D

3 Select Point 1

4 In the Point GTutorial Model of a Lithium-Ion Battery | 29

Plot Group 3 and choose Surface .

settings window under Expression, click Replace Expression and m-Ion Battery>Insertion particle concentration, surface (liion.cs_surface).

button .

ics toolbar click the Zoom Extents button .

teps create a plot of the cell potential during the simulation.

uilder, right-click Results and choose 1D Plot Group .

Plot Group 4 and choose Point Graph .

1 only.

raph settings window under Expression, enter phis in the Expression field.

30 | Tutorial Mo

5 Click the Plot button .del of a Lithium-Ion Battery

Tutorial Model: Fuel Cell CathodeOne of the most importantand most difficultparameters to model in a fuel cell is the mass transport through gas diffusion and reactive layers. Gas concentrations are often quite large and are significantly affected by the reactions that take place. This makes Fickian diffusion an inappropriate assumption to model the mass transport.

Figure 8 shows an example 3D geometry of a cathode from a fuel cell with perforated curexperimental cof the mass tra

Figure 8: A fuel ce

This model inveMaxwell-StefanelectrochemicaTutorial Model: Fuel Cell Cathode | 31

rent collectors. It is often seen in self-breathing cathodes or in small ells. Due to the perforation layout, a 3D model is needed in the study nsport, current, and reaction distributions.

ll cathode with a perforated current collector.

stigates such a geometry and the mass transport that occurs through diffusion. It couples this mass transport to a generic, Tafel-like l kinetics in the reaction term at a cathode.

gas inlet hole

unit cell

reactive

layer

electrolyt

e layer

32 | Tutorial Mo

Model DefinitionFigure 9 shows details for a unit cell from Figure 8. The circular hole in the collector is where the gas enters the modeling domain, where the composition is known. The upper rectangular domain is the reaction-zone electrode. It is a porous structure that contains the feed-gas mixture, an electronically conducting material covered with an electrocatalyst, and an electrolyte. The lower domain corresponds to a free electrolyte ionically interconnecting the two electrodes of the fuel cell. No reaction takes place in this domain. Neither are there pores to allow gas to flow or material for electronic c

The reaction zomm in surface,

Figure 9: The modopen to the feed gunit cell the top do

The electronic Distribution int

The species (m(Species 1) andSpecies interfac

The velocity vedel: Fuel Cell Cathode

urrentcurrent is conducted ionically.

ne is 75 mm thick, as is the electrolyte layer. The unit cell is 1.5-by-1.5 and the gas inlet hole has a radius of 1.0 mm.

eled fuel cell cathode unit cell. The marked zone is the surface of the cathode that is as inlet, while the rest of the top surface sits flush against the current collector. In the main is the porous cathode, while the bottom domain is the free electrolyte.

and ionic current balances are modeled using a Secondary Current erface.

ass) transport is modeled by the Maxwell-Stefan equations for oxygen water (Species 2) in the gas phase using a Transport of Concentrated e. Mass transport is solved for in the electrode domain only.

ctor is solved for using a Darcys law interface.

Results and DiscussionFigure 10 shows the oxygen concentration at a total potential drop over the modeled domain of 190 mV. The figure shows that concentration variations are small along the thickness of the cathode for this relatively small current density, while they are substantially larger along the electrodes width.

Figure 10: Isosurfacof 190 mV.

Figure 11 showpeak at the edglayer underneadominates the properly. In thiseliminates the pmodel.

The electrocheto both the locovervoltage, welectronic condmaximum overin the electrolyTutorial Model: Fuel Cell Cathode | 33

es of the weight fraction of oxygen at a total potential drop over the modeled domain

s the gas velocity in the porous cathode. There is a significant velocity e of the inlet orifice. This is caused by the contributions of the reactive th the current collector because in this region the convective flux mass transport. Thus it is important to model the velocity field case, the combination of a circular orifice and square unit cell ossibility to approximate the geometry with a rotationally symmetric

mical reaction rate, represented by the local current density, is related al overvoltage and oxygen concentration. Figure 12 depicts the local hich is rather even throughout the cathode. This is caused by the high uctivity in the porous material. Another observation is that the voltage is -180 mV. This means that there is a voltage loss of 10 mV te layer.

34 | Tutorial Mo

Figure 11: Velocity

Figure 12: Local ovdel: Fuel Cell Cathode

field for the gas phase in the cathodes porous reactive layer.

ervoltage in the cathode reactive layer.

Although the local overvoltage distribution is rather even, the concentration of oxygen is not. This means that the reaction rate is nonuniform in the reactive layer. One way to study the distribution of the reaction rate is to plot the ionic current density at the bottom boundary of the free electrolyte. Figure 13 shows such a plot.

Figure 13: Current

The current-dereaction rate anas the distancereactant dictateconditions.

The following i

MODEL WI

1 Open the MoTutorial Model: Fuel Cell Cathode | 35

density perpendicular to the lower, free electrolyte boundary.

nsity distribution shows that the variations are rather large. The d the current production are higher beneath the orifice and decrease

to the gas inlet increases. This means that the mass transport of s the electrodes efficiency for this design at these particular

nstructions show how to formulate, solve, and reproduce this model.

ZARD

del Wizard. The Space Dimension defaults to 3D. Click Next .

36 | Tutorial Mo

2 Under Electrochemistry double-click Secondary Current Distribution (siec) to add it to the Selected physics list.

3 Under Chemical Species Transport, double-click to add a Transport of Concentrated Species (chcs) interface .

4 For this interface:

- Under Dependent variables, in the Number of species field, enter 3.

- Enter w_n2, w_o2, and w_h2o in the Mass fractions ta

5 Under Fluid FFlow, double-interface .

6 Click Next

7 On the Studie

8 Click Finish

GEOMETRY

Create Work Pla1 In the Model B

2 Under Work P

3 In the Square

4 Right-click Ge

5 In the DistancDistances (m)

6 Click the BuilGraphics toolb

Add Work Plane1 Right-click Ge

2 In the settingdel: Fuel Cell Cathode

ble, one name per row.

low>Porous Media and Subsurface click to add a Darcy's Law (dl)

.

s window under Preset Studies for Selected Physics, click Stationary .

.

1

ne1, Add a Square and Extrude It uilder under Model 1, right-click Geometry 1 and choose Work Plane .

lane 1 right-click Plane Geometry and choose Square .

settings window under Size, enter 1.5e-3 in the Side length field.

ometry 1 and choose Extrude .

es from Plane table, enter these 0.75e-4 and 1.5e-4

d Selected button and on the ar the Zoom Extents button .

2, Add a Square and Circle, and Intersectometry 1 and add another Work Plane node.

s window under Work Plane, enter 1.5e-4 in the z-coordinate field.

3 Under Work Plane 2 right-click Plane Geometry and add a Square .

4 Under Size, in the Side length field, enter 1.5e-3.

5 Under Work Plane 2, right-click Plane Geometry and add a Circle .

6 Under Size and Shape, enter 1e-3 in the Radius field.

7 Under Position, enter 1.5e-3 in both the xw and the yw fields.

8 Click the Builbutton .

9 Under Work Operations>InTutorial Model: Fuel Cell Cathode | 37

d Selected button and on the Graphics toolbar the Zoom Extents

Plane 2, right-click Plane Geometry and choose Boolean tersection .

38 | Tutorial Mo

10Add the objects sq1 and c1 to the Input objects section. Click the Build Selected button .

11Right-click ForSelected . Con the Graphidel: Fuel Cell Cathode

m Union and choose Build lick the Zoom Extents button cs toolbar.

The sequence of Geometry nodes in the Model Builder should match this figure.

GLOBAL DEFINITIONS AND DEFINITIONS

Load the model parameters and variables from text files.

Import Parameters 1 In the Model Builder, right-click Global Definitions and choose Parameters .

2 In the settings window, under Parameters, click the Load from File button.

3 In the Model Library folder on your computer, models\Batterfuel_cell_c

Note: The locatFor example, if C:\Program Fi

The parameter

Import Variable1 Under Model

2 In the settingTutorial Model: Fuel Cell Cathode | 39

ies_and_Fuel_Cells_Module\Tutorial Models, double-click the file athode_parameters.txt to import it to the Parameters table.

ion of the files used in this exercise may varies based on the installation. the installation is on your hard drive, the file path might be similar to les\COMSOL43\models\.

s are added to the table as in this figure.

s1, right-click Definitions and choose Variables .

s window, under Variables, click the Load from File button.

40 | Tutorial Mo

3 In the Model Library folder on your computer, models\Batteries_and_Fuel_Cells_Module\Tutorial Models double-click the file fuel_cell_cathode_variables.txt to import it to the Variables table.

Create Two Exp1 In the Model B

2 Select Domain

3 Right-click Exelectrolyte

4 Repeat theseDomain 2 onlyClick OK.

Define Two SetsThe electrolytedomain specific

1 Add a second

2 In the Variabl

3 From the Seledel: Fuel Cell Cathode

licit Selection Nodes and Renameuilder, right-click Definitions and choose Selections>Explicit .

1 only.

plicit 1 and Rename the node as Free . Click OK.

steps. Add a second Explicit node, select and Rename the node Porous cathode.

of Variables conductivity will be different in the two different domains. Create variables for this parameter.

Variables node. Right-click Definitions and choose Variables .

es settings window, select Domain from the Geometric entity level list.

ction list, choose Free electrolyte (the explicit selection just defined).

4 In the Variables table, enter the following settings:

5 Repeat these steps. Add a second Variables node, select Domain from the Geometric entity level list, and Porous solid from the Selection list.

6 In the Variables table, enter the following settings:

SECONDA

Now apply the

1 Click the Sho

2 Under Model

3 In the settingDiscretization potential list,

Define the Poro1 Expand the Se

then right-clicnode .

2 In the settingchoose Poroulist.

NAME EXPRESSION DESCRIPTION

k_l 5[S/m] Conductivity, free electrolyte

NAME EXPRESSION DESCRIPTION

k_lTutorial Model: Fuel Cell Cathode | 41

The node sequence under Definitions should match the figure.

RY CURRENT DISTRIBUTION

settings for the current distribution model.

w button and choose Discretization.

1 in the Model Builder click the Secondary Current Distribution node.

s window, click to expand the section. From the Electrolyte choose Quadratic.

us Electrode and Electrolyte Nodescondary Current Distribution node, k and add a Porous Electrode

s window, under Domain Selection, s solid (Domain 2) from the Selection

1[S/m] Effective conductivity, electrolyte

42 | Tutorial Mo

3 Under Electrolyte Current Conduction, from the Electrolyte conductivity list (l), choose User defined. In the field, enter k_l.

4 From the Effective conductivity correction list, choose No correction.

5 Under Electrode Current Conduction, the Electrical conductivity (s) list, choose User defined. In the field, enter k_s.

6 From the Effective conductivity correction list, choose No correction.

7 In the Model Builder, click the Electrolyte 1 node, which is added by default to the interface.

8 In the settingthe Electrolytedefined. Enter

Define the Elect1 Right-click Sec

menu, add an

2 In the Electricthe Selection

3 Under Electridel: Fuel Cell Cathode

s window under Electrolyte, from conductivity list (l), choose User k_l in the field.

ric Potential and Electrolyte Potential Nodesondary Current Distribution and from the boundary level Electrode Electric Potential node.

Potential settings window, click the Paste Selection button . Enter 7 in field. Click OK.

c Potential, in the Boundary electric potential (s,bnd) field, enter V_cell.

4 Right-click Secondary Current Distribution and from the boundary level Electrolyte menu, add an Electrolyte Potential node.

5 In the Electroin the Selectio

6 Under Electroelectrolyte poTutorial Model: Fuel Cell Cathode | 43

lyte Potential settings window, click the Paste Selection button . Enter 3 n field and click OK.

lyte Potential, in the Boundary tential (l,bnd) field, enter phi0.

44 | Tutorial Mo

Define the Porous Electrode Reaction NodeNow set up the porous electrode reaction current density. The current density depends on the oxygen concentration.

1 In the Model Builder, click to expand the Porous Electrode 1 node. Click the Porous Electrode Reaction 1 node.

2 Under Model

3 Under Equilib

4 Under Electroexpression typdependent kin

5 Replace the dcurrent densit

6 Replace the dspecies expreschcs.c_w_o2

7 Under Active Active specific (replace the ddel: Fuel Cell Cathode

Inputs section, replace the default Temperature value with T.

rium Potential, in the E0,ref field, enter dphi_eq.

de Kinetics, from the Kinetics e list, select Concentration etics.

efault value in the Exchange y i0 field with i0.

efault value in the Oxidized sion C0 field with /c_o2_ref.

Specific Surface Area, in the surface area (av) field, enter S efault value).

Define the Initial Values Node1 In the Model Builder, click the Initial

Values 1 node.

2 Under Initial Values, enter phi0 in the Electrolyte potential (phil) field and V_cell in the Electric potential (phis) field.

TRANSPOR

1 Click the Tran

2 In the settingSelection, choSelection list.

3 Under TranspMaxwell-Stefan

Define the Conv1 In the Model B

the ConvectioTutorial Model: Fuel Cell Cathode | 45

T OF CONCENTRATED SPECIES

sport of Concentrated Species node.

s window, under Domain ose Porous cathode from the

ort Mechanisms, choose from the Diffusion model list.

ection and Diffusion Nodeuilder, expand the Transport of Concentrated Species node, then click

n and Diffusion 1 node.

46 | Tutorial Mo

2 In the Convection and Diffusion settings window under Density, replace all the defaults with the following:

- in the Mwn2 field enter M_n2.

- In the Mwo2 field, enter M_o2.

- In the Mwh2o field, enter M_h2o.

3 Under Diffusion, in the Maxwell-Stefan diffusivity matrix Dik table, enter the following

- in the first D_o2n2_ef

- in the first

- in the seco

The table sho

4 Both the veloto Darcy's lawthe Velocity fivelocity field (

5 In the Temperdefault value

Define the PoroCouple the rea

1 Right-click Tranode.

2 In the Porous solid from thedel: Fuel Cell Cathode

row, second column, enter f

row, third column, enter D_n2h2o_eff

nd row, third column, enter D_o2h2o_eff

uld match this figure:

city and pressure are coupled . Under Model Inputs, from

eld u list, choose Darcys dl/dlm1).

ature T field, replace the with T.

us Electrode Coupling and Reaction Coefficients Nodesction rate of oxygen to the electrochemical currents.

nsport of Concentrated Species and add a Porous Electrode Coupling

Electrode Coupling settings window, under Domain Selection, choose Porous Selection list.

3 Expand the Porous Electrode Coupling node and click Reaction Coefficients 1 .

4 Under Model Inputs, from the Coupled reaction iv list, choose Local current source (siec/per1).

5 Under Stoichiof participatinthe Stoichiom

Define the Initia1 Click the Initi

2 In the settingsMass fraction and w_h2o_r

Define the Inflo1 Right-click th

Species noadd an Inflow

2 In the Inflow Selection buttand click OK.

3 Under Inflow,w_o2_ref anw_h2o_ref.Tutorial Model: Fuel Cell Cathode | 47

ometric Coefficients, in the Number g electrons nm field, enter 4 and in etric Coefficient w_o2 field, enter -1.

l Values Nodeal Values 1 node.

window, under Initial Values, enter values: w_o2_ref in the w_o2 field ef in the w_h2o field.

w Nodee Transport of Concentrated de and from the boundary level node.

settings window, click the Paste on . Enter 10 in the Selection field

in the w0,wo2 field, enter d in the w0,wh2o field, enter

48 | Tutorial Mo

DARCY'S LAW

Now do the settings for Darcy's law. The electrochemical currents will result in a mass sink due to the oxygen molecules leaving the domain.

1 Click the Darcy's Law node.

2 In the Darcy's Law settings window, under Domain Selection, choose Porous solid from the Selection list.

3 In the Model Builder, expand the Darcy's Law node, then the click

4 In the Fluid anwindow unde

- From the Dand enter

- From the Ddefined and

5 Under Matrix

- From the Pdefined and

- From the Pand enter

Define the Poro1 Right-click Da

2 Under Domaidel: Fuel Cell Cathode

Fluid and Matrix Properties 1 node.

d Matrix Properties settings r Fluid Properties:

ensity list choose User defined chcs.rho in the field.

ynamic viscosity list, choose User enter mu in the field.

Properties:

ermeability list, choose User enter perm in the field.

orosity p list, choose User defined e_por in the field.

us Electrode Coupling and Reaction Coefficients Nodesrcy's Law and add a Porous Electrode Coupling node.

n Selection, choose Porous solid from the Selection list.

3 Under Species, click the Add button twice and in the table, for each species, enter M_n2, M_o2, and M_h2o in the Molar mass column.

4 In the Model BCoupling 1 no

5 Under Model choose Local

6 Under Stoichinm field and

Define the Initia1 Click the Initi

p_atm in the

Define the InfloSet an inflow coIn this way ver

1 Right-click Da

2 Select Boundthe Paste SeleSelection field

3 Under Inlet, e1[mm] in theTutorial Model: Fuel Cell Cathode | 49

uilder, expand the Porous Electrode de and click Reaction Coefficients 1 .

Inputs, from the Coupled reaction iv list, current source (siec/per1).

ometric Coefficients, enter 4 in the -1 in the 2 field.

l Values Nodeal Values 1 node. In the settings window under Initial Values, enter p field.

w Boundary Nodendition assuming an atmospheric pressure 1 mm above the inlet hole.

y steep pressure gradients at the hole edge are avoided.

rcy's Law and add an Inlet node.

ary 10 only. In the settings window, click ction button . Enter 10 in the and click OK.

nter (perm/mu)*(p_atm-p)/ Normal inflow velocity U0 field.

50 | Tutorial Mo

MESH 1

You can use a fairly coarse mesh for this problem. The solution accuracy is increased by using quadratic elements for the ionic potential.

1 In the Model Builder, right-click Mesh 1 and choose Free Tetrahedral .

2 Click the Sizewindow undefrom the Pred

3 Click the Buildel: Fuel Cell Cathode

node , and in the settings r Element Size, choose Extra fine efined list.

d All button .

STUDY

1 In the Model Builder, right-click Study 1 and choose Compute .

RESULTS

Several default Results and Dmore plots to

Plot the Velocity1 In the Model B

node is adde

2 Right-click th

3 In the upper-section, click

4 From the mevelocity magnExpression fie

5 Right-click Sli

6 In the settingColoring and Sbox.

7 Under Plane

8 Click the Plot

The plot in FTutorial Model: Fuel Cell Cathode | 51

plots are generated under the Results node as discussed in the section iscussion on page 33. The following set of instructions involve adding analyze the data even more.

Magnitudeuilder, right-click Results and choose 3D Plot Group . A 3D Plot Group 7 d to the Model Builder.

e 3D Plot Group 7 node and choose Slice .

right corner of the Expression Replace Expression .

nu, choose Darcy's Law>Darcys itude (dl.U) (or enter dl.U in the ld).

ce 1 and choose Duplicate .

s window for Slice 2, under tyle, clear the Color legend check

Data from the Plane list, choose zx-planes.

button .

igure 11 on page 34 displays in the Graphics window.

52 | Tutorial Mo

9 Right-click 3D Plot Group 7 and Rename the node to Velocity Magnitude.

10Click the Velocity Magnitude node and in the settings window, click to expand the Title section. Select Manual and edit the plot name.

Plot the Local Overvoltage 1 Add another 3D Plot Group to the Model Builder and right-click to add a Slice plot.

2 Under Expression in the Expression field, enter siec.eta_per1 (replace any default).

3 Click the Plot button .

4 Right-click Sli

5 Under Plane Dzx-planes. UndColor legend c

6 Click the Plot

The plot in F

7 Right-click an

8 Click the Locasection. Selec

Plot the Oxygen1 Add another

2 Click Replace Species>SpecieExpression fiel

3 Under Levels

The plot in F

4 Right-click an

Add a Data Set1 In the Model Bdel: Fuel Cell Cathode

ce 1 and choose Duplicate .

ata from the Plane list, choose er Coloring and Style clear the

heck box.

button .


d rename 3D Plot Group 8 to Local Overvoltage.

l Overvoltage node and in the settings window, click to expand the Title t Manual and edit the plot name.

Mass Fraction 3D Plot Group with an Isosurface plot.

Expression and from the menu Transport of Concentrated s w_o2> menu, choose Mass fraction (w_o2) (or enter w_o2 in the d).

in the Total levels field, enter 10. Click the Plot button .


d rename 3D Plot Group 9 to Oxygen Mass Fraction.

and a Surface Plotuilder under Results, right-click Data Sets and choose Cut Plane .

2 Under Plane Data from the Plane list, choose xy-planes.

3 Add another 3D Plot Group .

4 Under Data fr

5 Add a Surface

6 Click Replace Distribution>Ez component

7 Click the Plot

The plot in F

8 Right-click an

As a final step,

1 In the Model B

2 From the File

To view the thusection. Make abuttons until thTutorial Model: Fuel Cell Cathode | 53

om the Data set list, choose Cut Plane 1.

plot to 3D Plot Group 10 .

Expression and from the menu, choose Secondary Current lectrolyte current density vector>Electrolyte current density vector,

(siec.Ilz). Or enter siec.Ilz in the Expression field.

button .


d rename 3D Plot Group 10 to Electrolyte Current Density.

pick one of the plots to use as a model thumbnail.

uilder under Results click Local Overvoltage .

menu, choose Save Model Thumbnail.

mbnail image, click the Root node and look under the Model Thumbnail djustments to the image in the Graphics window using the toolbar e image is one that is suitable to your purposes.

54 | Tutorial Model: Fuel Cell Cathode

IntroductionBattery ModelingFuel Cell ModelingPhysics List by Space Dimension and Study TypeThe Model LibraryTutorial Model of a Lithium-Ion BatteryModel WizardGlobal DefinitionsGeometry 1MaterialsLithium-Ion Battery InterfaceMesh 1Study 1Results

Tutorial Model: Fuel Cell CathodeModel WizardGeometry 1Global Definitions and DefinitionsSecondary Current DistributionTransport of Concentrated SpeciesDarcy's LawMesh 1StudyResults

Documents

Introduction to Batteries and Fuelcells Module