internship report multiphysic simulation in a proton ...€¦ · this internship took place at avl...

BIZOUARD Vincent - - 1 - -

Internship report

Multiphysic simulation in a Proton Exchange Membrane Fuel Cell

Vincent Bizouard (ENSEEIHT)

Supervised by Dr. Alexandre Raulot and Dr. Wolfgang Schwarz (AVL)


Table of contents

1 ABSTRACT ........................................................................................................................................ - 4 -

2 INTRODUCTION ................................................................................................................................ - 5 -

2.1 LIST OF SYMBOLS USED .........................................................................................................................- 5 - 2.2 PRESENTATION OF THE COMPANY AVL.....................................................................................................- 6 - 2.2.1 AVL WORLD .............................................................................................................................................. - 6 - 2.2.2 AVL FRANCE .............................................................................................................................................. - 6 - 2.2.3 AST .......................................................................................................................................................... - 6 - 2.2.4 THE SOFTWARE FIRE ................................................................................................................................... - 6 - 2.3 INDUSTRIAL CONTEXT OF FUEL CELLS [1] ...................................................................................................- 6 - 2.4 DIFFERENT TYPES OF FUEL CELLS .............................................................................................................- 7 - 2.5 MAIN APPLICATIONS [3].......................................................................................................................- 7 -

3 PROTON EXCHANGE MEMBRANE FUEL CELL FUNCTIONING AND MODELIZATION............................... - 8 -

3.1 PEMFC FUNCTIONING OVERVIEW...........................................................................................................- 8 - 3.2 DETAIL OF THE PHYSICAL PHENOMENA OCCURRING IN THE PEMFC AND MODELING ............................................- 9 - 3.2.1 MEA MODEL.............................................................................................................................................. - 9 - 3.2.2 3D CFD MODEL ........................................................................................................................................ - 11 - 3.2.3 CONNECTION IN SERIAL (BIPOLAR PLATE)....................................................................................................... - 13 - 3.3 MESH GENERATION AND INPUT DATA IN FIRE.......................................................................................... - 13 - 3.3.1 GEOMETRIC SETTINGS ................................................................................................................................ - 13 - 3.3.2 DATA SETTINGS......................................................................................................................................... - 13 -

4 VALIDATION OF SUB MODELS ON A SIMPLE CONFIGURATION ..........................................................- 14 -

4.1 MEA MODEL ................................................................................................................................... - 15 - 4.1.1 ELECTROCHEMICAL MODEL (REACTIONS AT THE ELECTRODES) ........................................................................... - 15 - 4.1.2 PROTON EXCHANGE MEMBRANE.................................................................................................................. - 17 - 4.2 GAS DIFFUSION LAYER AND CONDENSATION ............................................................................................ - 20 - 4.3 SIZING THE FUEL CELL ......................................................................................................................... - 23 -

5 EXPERIMENTATION : EFFECT OF TEMPERATURE ...............................................................................- 23 -

5.1 IMPORTANCE OF TEMPERATURE ON FUEL CELL PERFORMANCE ...................................................................... - 23 - 5.1.1 INTRODUCTION: THEORY ............................................................................................................................ - 23 - 5.1.2 EFFECT OF OPERATING TEMPERATURE........................................................................................................... - 24 - 5.1.3 RESULTS .................................................................................................................................................. - 25 - 5.2 IMPACT ON COOLING CHANNELS DESIGN ................................................................................................. - 26 - 5.2.1 SIZING OF HEAT EXCHANGERS ...................................................................................................................... - 26 - 5.2.2 OPTIMIZATION.......................................................................................................................................... - 26 - 5.2.3 TOOLS FOR CALCULATION OF COOLING PROCESS ............................................................................................. - 27 - 5.2.4 FUEL CELLS STACK (SEE PART 3.2.3) ............................................................................................................. - 29 -

6 SOME RESULTS ON A MORE ELABORATED MESH..............................................................................- 30 -


6.1 FUEL CELL GEOMETRY......................................................................................................................... - 30 - 6.2 RESULTS ......................................................................................................................................... - 31 - 6.2.1 SIMILARITY TO SIMPLE FUEL CELL RESULTS...................................................................................................... - 31 - 6.2.2 LOCAL EFFECTS.......................................................................................................................................... - 31 - 6.2.3 GAS VELOCITIES ........................................................................................................................................ - 31 - 6.2.4 TEMPERATURES ........................................................................................................................................ - 31 -

7 PERSONAL IMPROVEMENTS.............................................................................................................- 33 -

7.1 LIQUID COVERAGE ............................................................................................................................. - 33 - 7.2 CATHODE EXCHANGE CURRENT DENSITY.................................................................................................. - 33 -

8 CONCLUSION...................................................................................................................................- 34 -

BIBLIOGRAPHY ......................................................................................................................................- 35 -

TABLE OF ILLUSTRATIONS ......................................................................................................................- 35 -

APPENDIX A : TABLE OF REFERENCE VALUES ..........................................................................................- 36 -

1 Abstract

This internship took place at AVL – France, based in Croissy-sur-Seine, under the direction of Dr. Wolfgang Schwarz

and Dr. Alexandre Raulot. This 5 months placement was focused on multiphysic simulation of a Proton Exchange

Membrane Fuel Cell (PEMFC) with a new module for the CFD software FIRE. The aim of this internship was to validate

physical sub models on simple configuration after having enhanced my knowledge on fuel cells, to investigate on

calculation of cooling process and to evaluate the method reliability for realistic configurations. It also implied

presentations to potential customers and discussions with the project leader in order to improve it.

1 Résumé

Ce stage a eu lieu à AVL – France, basé à Croissy sur Seine, sous la direction des docteurs Wolfgang Schwarz et

Alexandre Raulot. Le sujet de ce stage de fin d’études était la simulation multiphysique d’une pile à combustible de type

membrane échangeuse de proton (PEMFC) avec un nouveau module du logiciel de mécanique des fluides numérique

FIRE. Le but de ce stage était de valider les sous modèles physiques d’une configuration simple après avoir améliorer mes

connaissances sur le sujet, d’enquêter sur le calcul de refroidissement et enfin d’évaluer la fiabilité de la méthode pour

des configurations réalistes. Ce travail a également impliqué des présentations aux clients potentiels ainsi que des

discussions avec le chef du projet, à but d’amélioration du programme.


2 Introduction

2.1 List of symbols used

Symbol Description Unit Subscripts

a sulfonic acid group concentration mol/m^3 ano anode

c concentration mol/m^3 cat cathode

Cb Bulk reactant concentration mol/m^3 cha channel

cp specific heat capacity J/kgK g gas phase index

Cs Reactant concentration at the surface of electrode mol/m^3 j species index

D diffusion coefficient m²/s l

liquid phase

index

F Faraday constant As/mol RL reaction layer

H Henry's constant Pa surf electrode surface

i electric current density A/m² w water

i0 exchange current density A/m^3 + hydronium ion

j diffusive mole flux mol/m²s

jj diffusive mass flux kg/m²s

k electrode transfer coefficient -

K permeability mol/(mPas)

L length m

M molar mass kg/mol

mj,r reactive mass transfer rate kg/m^3s

mlg,j Interfacial mass transfer rate kg/m^3s

n mole flux mol/m²s

nj,e- electrons per react. Molecule -

p pressure Pa

R universal gas constant J/molK

RH Relative humidity -

T temperature K

u velocity m/s

V cell voltage V

x species mole fraction -

y species mass fraction -

z normal direction membrane m

α phase volume fraction -

ε porosity -

τ tortuosity -

η electric potential V

ρ density kg/m^3

Φ electric potential V

Reference values used in simulations are available in appendix A if not specified.


2.2 Presentation of the company AVL

2.2.1 AVL World

Founded in 1948 by Mr. Hans List, AVL is the world's largest privately owned and independent company for the

development of powertrain systems with internal combustion engines as well as instrumentation and test systems. It

develops and improves all kinds of powertrain systems and is a competent partner to the engine and automotive

industry. In addition, AVL develops and markets the simulation methods which are necessary for the development work.

AVL employs today more than 4500 people all over the world and has a turnover of 740 millions of Euros (2008).

2.2.2 AVL France

In September 1990, AVL Graz creates an independent affiliate in France, AVL France SA in order to represent its

research and development activities on instrumentation and test benches. The society is divided in three main divisions:

the Division Instrumentation and Test Systems, the Division Powertrain Engineering and the division Advanced Simulation

Technologies. The AVL France aim is to become the supplier leader of Instrumentation and Test benches for automotive

industry. AVL France employs today around eighty people and has a turnover of 25 millions Euros.

2.2.3 AST

The AST department (Advanced Simulation Technology), to which I belonged, ensures sales, project, support and

training for all numerical simulation software:

• EXCITE : GPM dynamic and acoustic

• EXCITE Piston and Rings : piston and segmentation dynamic

• HYDSIM : injection systems simulation

• BOOST : thermodynamic cycle simulation

• CRUISE : vehicle dynamic simulation

• FIRE : Computational Fluid Dynamic simulation. This is the software that

was used to study fuel cells.

2.2.4 The software FIRE

FIRE is a CFD software developed by AVL. An essentially hexahedral unstructured

automatic mesher is used. It solves multiphase and multi-species tridimensional flows

with an implicit numerical method (finite volume) and a fluid solver with pressure

correction.

AVL FIRE™ is the leading simulation program in the field of combustion engine

analysis and specializes in accurate prediction of engine gas exchange, mixture formation and combustion, as well as

emissions and the exhaust gas after treatment.

Since two years, a module devoted to the simulation of Proton exchange membrane fuel cells is being developed.

2.3 Industrial context of fuel cells [1]

Fuel cells are a way to create electrical energy by conversion from chemical energy. Fuel cells are based on a very

simple chemical transformation:

H2+1/2*O2�H2O+energy They are to offer a clean, high-efficient, silent and renewable source of energy. The emission of pollutants is nearly

zero, considering that water is the only product of the reaction. The fuel is not burnt but oxidized, providing efficiency far

superior to the Carnot limitations imposed to thermal engines. Moreover, the lack of explosions and of mechanical parts

make the power generation silent. In spite of the non-existence of hydrogen in nature because of its volatility, it can be


easily created by electrolyze from every source of energy, or created by reformation of current fuel as methanol or

methane.

Discovered in 1839 by Christian Schoenbein [2] and demonstrated the same year by

William Grove, fuel cells saw their first application in 1954 (Alkaline Fuel Cell) by Francis

Bacon, and then were used in spatial applications in the sixties (Apollo program). With

the first oil price shock in the seventies, the research on fuel cells knew a new lease on

life. Nowadays, the prospect of gas shortage, the growing of environmental concerns

awareness, and the will to be energetically independent from oil-producing countries

encourages the development of fuel cells.

Fuel cells can be used in many ways, from a small power station to a new type of

battery for portable applications (laptop, cell phone,…) : the applications are various.

If the focus is made on transport applications, fuel cells open an interesting

prospect. The objective of reduction by four of greenhouse gases emission in 2050 set

up by France can not be achieved without drastic changes, which have started to occur

with the stress put on biofuels (1,75% of total consumption in France in 2006). However,

due to its dependence to agriculture and arable land, bio-fuels can not answer to this

issue by itself.

Hydrogen cars, although requiring important researches and investments, are a

very interesting prospect. The two reactive are the oxygen, which is taken from the

ambient air, and the hydrogen, which is stored inside the car under its gaseous, liquid or

“solid” form. The estimated efficiency of a fuel cell car (60%) makes that with 1kg of hydrogen, a car equipped with a fuel

cell is able to drive a hundred kilometer.

In its gaseous form, hydrogen is kept under ambient temperature, but has to be stored under very high pressure

(usually 350 bars, up to 700 bars for the last cars). With a compression of 350 bars, 1 kg of hydrogen has a volume of 36L,

against 6 liters of oil for the same distance.

In its liquid form, hydrogen is stored at -253°C in an adiabatic tank. The energy used for the refrigeration is very

important.

In its “solid” form, Hydrogen molecules are trapped into a compact solid. When heated, this solid dilates and releases

the hydrogen. Ideally, the “solid” should be composed of 15% of hydrogen (today: 3%).

The action of reforming transforms a usual gas (methane for instance) into hydrogen, which is then used in the fuel

cell. The efficiency of a fuel cell is twice as much as a combustion engine, so this method is efficient. The particular

interest is that an industrial park of hydrogen cars can be put in place without setting up a hydrogen distribution network

(this can be done in a second step, when enough hydrogen cars are in circulation). However, reforming process for

automotive applications seems to have been abandoned for technical reasons: the hydrogen needed has to be very pure.

2.4 Different types of Fuel cells

There are five main types of fuel cells, which are described in the following table :

• Alkaline fuel cells, with a liquid alkaline electrolyte, had been used by the NASA, operates at 80°C. They are

poisoned by the CO2 and need a very pure supply of H2. Their development has been stopped.

• Phosphoric Acid Fuel Cells, with a liquid acid electrolyte, were thought to be used as small combined heat

and power plants, but do not have a good performance, so they have been abandoned.

• Molten Carbonate Fuel Cells, with a molten sodium-potassium electrolyte, were thought to be used as

megawatt-scale power generation, but its electrode corrosion issue made it abandoned.

• Solid Oxide Fuel Cells, with a solid oxide electrolyte, are developed for a power generation use. Its high

operating temperature makes it possible to power a gas turbine with the exhaust.

• Proton Exchange Membrane Fuel Cells (PEMFC), with an acidic solid polymer membrane, is the candidate to

transport applications. This type and its application are studied thereafter.

2.5 Main applications [3]

PEMFCs (and other fuel cells) can be used for various applications. The most developed of them are those designed

to be backup generators (already serially produced), auxiliary power units (Market and laws encourage their

development), and power generators for electric trolleys (serially produced in 2012).

Figure 1 : Christian

Schoenbein


Combine heat and power domestic units and small and medium power station are going to be serially produced

soon. Use as autonomy extension for electric vehicles and power generator for small electric vehicles will depend on

success of batteries.

Finally, a powerful propulsion application requires long researches. The following study is focused on automotive

application, but it is applicable to every applications described in this paragraph.

3 Proton Exchange Membrane Fuel Cell functioning and modelization

3.1 PEMFC functioning overview

Figure 3: Diagram of a proton exchange membrane fuel cell

Figure 2 : Opel Zafira fuel cell car (2004)


The flow channels transport the fuels (hydrogen and air), and the reaction products (water, fuel exceeding) to or

from the fuel cell. The gases are transported through the gas diffusion layer (GDL) by diffusion to the reaction layer,

where the chemical reactions occur : 2H2�4H++4e

- at the anode side. The protons H

+ created at anode go through the

proton exchange membrane (PEM) due to the concentration gradient between anode and cathode, and react with

oxygen at the cathode reaction layer : 4e-+4H

++O2�2H2O.

The water can cross the membrane by diffusion (concentration gradient), but is retained to do it by the H+ flux

(electronegativity). The gases are not supposed to cross the membrane, but they can do it in a limited manner

(crossover). Liquid water is transported through the GDL to the flow channel by capillarity, and the electrons are

transported through the GDL to the bipolar plate, which plays the role of conveying electricity and heat.

3.2 Detail of the physical phenomena occurring in the PEMFC and modeling

In the software FIRE, the fuel cell is split in two subdivisions:

• The one dimensional Membrane Electrode Assembly model includes the membrane and the electrode. It

rules the electrochemical reactions and species permeation through the proton exchange membrane. This

part is not meshed on Fire, but taken into consideration for computation. The membrane is considered

“multi one-dimensional” (in the through plane direction) while the electrode is “multi 0D”. “multi” means

that each boundary cell on the cathode side is linked to a boundary cell on the anode side by the MEA

model. This constrains the 3D mesh to be symmetric.

• The three dimensional model contains the Gas Diffusion Layer and the flow channels. It is a three phases

model where one can find liquid, solid and gas.

Figure 4 : description of the module functionment

In the different regions of the fuel cell, physics laws described thereafter are applied, as well as equations of

conservation of mass, momentum and energy.

3.2.1 MEA model

3.2.1.1 Electrochemical model (reactions at the electrodes) [4]

The actual potential created at the electrodes is equal to the Nernst potential decreased from activation losses,

ohmic losses and concentration losses:

Actual potential = Nernst – cathode – membrane – anode

• Nernst potential is the ideal open circuit potential, proportional to the number of electrons exchanged during

the reactions


• Membrane losses are ohmic losses due to the resistance to electrons transport in the membrane

• Cathode and anode losses potential are composed of activation and concentration losses.

o Activation losses correspond to the amount of energy used to exceed the activation energy required to

start the reactions at the electrodes. They are high at the cathode.

o Concentration losses are due to the fast consumption of a reactant at the electrode, creating a

concentration gradient. This loss is equal to :

Cb and Cs are respectively the bulk reactant concentration and the reactant concentration at the surface of

electrode. F, the Faraday constant, is the electric charge in one mole of electrons. This loss is especially important for high

current density.

Figure 5: Actual voltage in function of current density

The equations of Butler Volmer connect current density with electrode overpotential. E.g. for cathode :

The exchange current density (i0) represents the readiness of an electrode to proceed with the electrochemical

reaction. The higher it is, the easier it is for a charge to move from electrolyte to the catalyst surface, the more current is

generated and finally lower is the activation overpotential. i0 at anode side is much bigger than i0 at cathode side. This is

why the activation losses on anode side are insignificant.

The mass produced or consumed at the reaction layer is then calculated via the Faraday law:

Where M is the molar mass, i is the averaged current density, and nj,e is the number of electrons in the electro-

chemical reaction per reacting molecule (different for cathode and anode : respectively 4 and 2).

3.2.1.2 Proton exchange membrane

3.2.1.2.1 Water permeation

Two conflicting effects play a role in the transport of water through the membrane:


• Diffusion pushes the water to go from cathode to anode (high concentration to low concentration).

• Osmotic drain (or electro-osmosis) lies on the concept of electronegativity. In the water molecule, the electrons

are lightly more attracted by the Oxygen atom, which is consequently negatively charged. The protons H+

consequently attach to the water molecules, which become H3O+ and go from anode to cathode.

These effects are local: one can prevail in a region of the membrane while the other prevails elsewhere.

3.2.1.2.2 Gas crossover

If oxygen or hydrogen crosses the membrane, the chemical reactions will not take place in the reaction layer,

generating reactant losses. This phenomenon is known as gas crossover and occurs for high pressure of gas.

Knowing the partial pressure, the quantity of dissolved gas in the membrane is calculated by Henry’s law, then

convective and diffusive fluxes are computed, creating parasitic reactions which are taken into account but insignificant

most of the time.

Henry’s law:

3.2.2 3D CFD model

3.2.2.1 Gas diffusion layer

Three phases are defined in the fuel cell : liquid (liquid water), gas (hydrogen, air, gaseous water) and solid (for the

porous medium of the GDL).

The Gas Diffusion Layer is a fibrous, anisotropic structure.

The preferential directions are perpendicular to the flow

direction. This is due to its structure, and the through plane

permeability is lower than the in-plane permeability.

The porosity is about 70-80%, for the gases to have

space to go from the flow channels to the membrane, and for

the liquid water to go from the cathode reaction layer to the

flow channel.

The medium is hydrophobic, limiting the flooding effect

by enhancing the circulation and evacuation of liquid water.

The CFD model considers the GDL as a porous media.

For liquid water and gas, a generalized Darcy-type equation is

used : Forchheimer equation, which links pressure gradient to

velocities, porosity, tortuosity(which corresponds to the

shortest distance made to go through a porous media divided

by the normal distance) and permeability. For gases, a

generalized Fick law is used (links the flow to concentration

gradient).

Figure 6 : Microscopic view of a

GDL


Forchheimer equation :

g,lpuu2

1u

KKM pp

2p

p,rel

p

pp

p,rel

p

p =αηη

ρ−α

µ−= for

rrrr

Generalized Fick’s law

yDj ∇−=⇒

−=∇ ∑

≠=

τ

ερ

M

jx

M

jx

ρ D

M

ε

τx

sn

ij1j i

ij

j

ji

ij

i

rrr

3.2.2.2 Condensation model

The water is allowed to condensate when saturation conditions are fulfilled. The mass transfer between gas and

liquid is equal to : ]xp)(Tp[Cm ilv,im,ilg ⋅−⋅=&

This condensation occurs in the GDL, where it has two effects:

• The presence of liquid water change the permeability of the GDL : if there is too much water, gas is not able to

cross easily, because the liquid water blocks the interstices and decreases the empty pores available for the gas

to reach the reacting sites. Saturation influence is taken into account by the Leverett model (capillary pressure) :

when the water condenses, gas diffusion is reduced.

Figure 7: capillar pressure in the GDL

• Liquid water at the surface of the reaction layer lowers the surface for the reaction to happen.

These two phenomena lead to a decrease of current density.

Thereby, the water has two antagonist effects:

• The membrane has to be humidified for the production of electricity, because protons moves through the

membrane hanged on the water molecules (electro-osmosis, see 3.2.1.2.1).

• Too much water leads to water saturation: liquid water decreases current density.

Finally, there are also heat transfers between the phases:


3.2.3 Connection in serial (bipolar plate)

The terminal voltage of a PEMFC is about 0,7V, which is not enough for transport applications. That is why PEMFCs

are put in serials with bipolar plates to connect them.

Figure 8 : Fuel cells put in serials

Bipolar plates have to have a great electrical and thermal conductivity, not to be corroded by reactants and have a

low permeability to hydrogen. The bipolar plate is cooled down by cooling channels, essential for the fuel cell to stay in its

temperature domain of functioning.

3.3 Mesh generation and input data in FIRE

3.3.1 Geometric settings

In the software FIRE, selections are made in the geometry to define which parts of the model correspond to fuel cells

part : anode and cathode inlet and outlet, GDL, and reaction layer :

Figure 9 : selections in a simple model of PEMFC

Some selections are volume cells (channel, GDL), others are surface cells (RL, boundaries)

3.3.2 Data settings

Many parameters and properties can be set. For boundary conditions, inlet velocities can be determined classically

(velocity inlet), or by Stoechiometric coefficient : ratio of the flow of gas on the flow of gas needed for a stoechiometric

reaction. H2O mass fraction inlet can also be determined classically (mass or molar fraction), or by giving either relative

humidity or dew point temperature.

Every parameter that plays a part in the equations is adjustable by the AVL FIRE workflow manager interface:


Figure 10: Fire data settings interface

4 Validation of sub models on a simple configuration

NB : Every results presented in the following sections are results I have obtained with AVL FIRE, unless otherwise specified.

The configuration studied is very simple (see Figure 11). It is a partial modeling of an actual fuel cell which consists in

13 parallel channels. Only one channel is meshed here in order to save CPU time.

Figure 11 : Real and modelized fuel cell

The goal is to validate the different sub models described in 3.2 by comparing FIRE numerical results to the literature

and/or analyzing them in a physical way. If not specified, the values used in the simulations are given in appendix A.


4.1 MEA model

4.1.1 Electrochemical model (reactions at the electrodes)

In this section the polarization curves of a fuel cell, as well as the influence of various parameters on them, will be

studied.

4.1.1.1 Polarization curve

In order to plot a polarization curve, evolution of potential losses with current density, several simulations are made.

The Nernst potential (open circuit voltage) is set to 1V, while the actual cell voltage is set respectively to 0.9, 0.7, 0.5 and

0.3V, and a steady calculation is run for each of these voltages. The others operating values are indicated in part appendix

A. The average values of cathode activation, cathode concentration, membrane and anode overpotentials, as well as

current density, are noted down. A plot of potentials as function of current densities is shown in Figure 12:

Figure 12 : Polarization curve

The total overpotential loss is the sum of all losses, and is represented by the enveloping curve.

One can notice that at low current densities, the main potential loss is the activation potential of the cathode

reaction : 4e-+4H

++O2�2H2O.

At intermediate current densities, the cell potential variation only depends on membrane overpotential variations,

because activation overpotential is constant while the concentration overpotential is insignificant. Thus, it is a linear

function of the current. This is due to ohmic losses in the membrane (U=RI).

At high current densities, concentration losses become significant, as seen in 3.2.1.1.

The anode overpotential is always very weak. This is due to the easiness of the reaction of transformation of

hydrogen: 2H2�4H++4e

-. In technical terms, the anode exchange current density i0 is much higher than the cathode

exchange current density: therefore the voltage loss is much lower than on cathode side.

4.1.1.2 Effect of porosity

In this part, porosity effect on polarization curve will be studied. Results with a GDL porosity of 0.11 is compared with

a GDL porosity of 0.5, as can be seen in Figure 13:


Figure 13 : Polarization curve with a lower porosity

The best way to see a flooding is by reducing the porosity of the GDL. Then, a high current density induces a high

water production. The water saturates and condensates in the GDL, and so blocks the way to the arrival of fuels

(Hydrogen and oxygen). As the reactants have difficulties to reach the electrodes, they are immediately consumed at high

current densities, creating a high concentration gradient more easily than in the case where reactants have no problems

to progress through the GDL.

When the reactants can not arrive to the reacting layer as fast as required by the consumption, the cell voltage is

almost zero and the current density is at its maximum. The maximum current density is called limiting current.

The voltage drop due to gas transport limitations can not be seen with a porosity of 0.5 (Figure 12), because oxygen

has still enough space to run its way.

The Oxygen molar fraction in the GDL can be visualized on Figure 26.

4.1.1.3 Effect of membrane thickness

In this numerical experience, membrane thickness is alternately set to a very thin value (5E-6m), a standard value

(3.5E-5m) and a thick value (1E-4m).

Polarization curves are plotted on Figure 14.

Figure 14 : Polarization curves and membrane losses for different membrane thicknesses


The thicker the membrane is, the higher the potential losses are for a given current density. This is due to the

membrane potential losses.

These ohmic losses are an increasing function of membrane thickness. As already mentioned, the membrane

potential losses are a linear function of the current density : U=R*i, with R the resistance of the membrane, which grows

with the membrane thickness. The thickness has no major effect on other potential losses, as can be seen on Figure 15.

Activation losses for variouses thicknesses

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0 1 2 3 4 5 6 7 8

I (A/cm²)

Po

ten

tial

loss

thickness=5e-6

thickness=3,5e-5

thickness=1e-4

Concentration losses for variouses thicknesses

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0 1 2 3 4 5 6 7 8

I (A/cm²)

Po

ten

tia

l lo

ss

thickness=5e-6

thickness=3,5e-5

thickness=1e-4

Figure 15 : Activation and concentration losses for various thicknesses

4.1.2 Proton exchange membrane

4.1.2.1 Water permeation

4.1.2.1.1 Introduction

In this section, the description and the physical analysis of water management

within the fuel cell is performed. Results (water fluxes, relative humidity, current

density,…) will be plotted along the cathode and the anode, on the reaction layers

just under the flow channel (Figure 16).

Water content is a measurement of the quantity of water. It represents the

number of water molecules with respect to SO3- molecules in the membrane.

Its value is related to the relative humidity RH : 32

w RH36RH39.85-RH17.810.043c ×+××+=

(fit for Nafion 117 at 30°C). When water condensates (e.g. if volume fraction of liquid becomes non negligible), cw is

forced to cw(RH=1)=14, which is the maximum vapor liquid molecules per SO3- group in the membrane.

The gradient of water content between cathode and anode directly affects the back diffusion water flux (from

cathode to anode) : a big gradient leads to a higher influence of diffusion phenomena. The medium water content is

correlated with the proton conductivity, and so with the osmotic drag. More details are given in part 3.2.1.2.1)

4.1.2.1.2 Results

In this test case, the anode and cathode inlets are moderately humidified: the humidification temperatures are set to

63°C, which corresponds to an inlet relative humidity of 76% for both cathode and anode. Current density, anodic and

cathode water content and membrane water flux are plotted along the membrane:

Figure 16: location of the 2d plotting


Fig

ure

17

: c

urr

en

t d

en

sity

fo

r m

od

era

te c

ase

Fig

ure

21

: W

ate

r co

nte

nt

for

mo

de

rate

ca

se

Fig

ure

19

: M

em

bra

ne

wa

ter

flu

x

Fig

ure

18

: O

xyg

en

mo

le f

ract

ion


For each of these plots, the left side corresponds to the cathode inlet / anode outlet, while the right side

corresponds to the anode inlet / cathode outlet.

The plots can be split into three geometrical parts.

AREA 1 : Close to the cathode inlet the membrane is quite dry (Figure 21), so the current density is not high. Due to

the water production at the cathode, the membrane gets more humid, resulting in higher proton conductivity through

the membrane, involving an increase of current density (Figure 17) and of electro-osmotic drag (Figure 19).

AREA 2 : At the interface between area 1 and 2, there is so much water that the gas becomes over-saturated,

leading to condensation of water and a jump of water content at the cathode side (Figure 21), as seen in introduction.

This jump creates an augmentation of the water content gradient, resulting in a high back diffusion to the anode and

therefore a decrease in the overall membrane water flux, because the electro-osmotic drag is still stronger than

diffusion.

In conjunction, closer to the anode inlet, the water flux remains constant (Figure 19) and so does the diffusive flux

(the cathode and anode water content are constant, Figure 21). Consequently, the osmotic drag and the proton flux are

constant as well, while the oxygen falls due to its consumption (Figure 18), hence the current density falls also (Figure

17).

AREA 3 : The water content at the anode side is set by the boundary conditions. Here the difference of water content

leads to a high diffusion which overcomes the electro-osmosis effect. The diffusion effect becomes weaker with the

humidification of the anode side.

Thereby, operating conditions could be achieved where there would be no need for external water contribution and

where the water produced at the cathode reaction layer would circulate across the membrane in order to humidify its

two sides.

4.1.2.1.3 Comparison to literature

These results shall be compared to the paper of Berg et al. 2004[5], where a similar membrane water flux is found:

Figure 22 : Water crossover along the membrane, Berg model

This model is approximately similar to the one implemented in FIRE, except for the determination of liquid water

existence. FIRE considers there is liquid water and put cathode membrane water content to 14 if the liquid water volume

fraction reaches a certain value, while Berg’s model is a monophasic model: the gas water can saturate but not

condensate. This explains the main difference between the two results, the sharp bend in water flux (area 2).

In reality, the transition liquid/gas is not discontinuous but progressive: the bend is smoother. If there is no

saturation, or if the air introduced on cathode side is already water saturated, there is no bend in the membrane water

flux:


Figure 23 : Water crossover along the membrane, with no saturation

4.1.2.2 Gas crossover

Although the membrane is impermeable to gases, a very small amount of reactant may diffuse to the other side of

fuel cell. This quantity creates a negligible over potential in standard conditions. However, at very low current densities,

this loss may become important, according to the literature. This phenomenon can be visualized with FIRE. In is

represented the percentage of participation of the parasitic overpotential to the total cell losses.

Participation of parasitic overpotential to the total losses

0

0,005

0,01

0,015

0,02

0,025

0,01 0,1 1 10

current density (A/cm²)

Pa

rtic

ipa

tio

n o

f p

ara

sit

ic

ov

erp

ote

nti

al

to t

he

to

tal

los

se

s

(%)

Figure 24 : participation of parasitic overpotential to the total cell losses

Even if the parasic overpotential weight increase for low current densities, it is still very low (0.022%).

4.2 Gas diffusion layer and condensation

In this part, the 3D results are studied within the Gas Diffusion Layer. The effect of porosity on the diffusion of gases

will be studied, in order to validate what was announced in part 3.2.2.1.

The aim is to study the influence of the gas volume fraction (which is equal to the porosity minus the fraction of

space occupied by the liquid) on gases diffusion.

Thereafter is a cut view of the cathode GDL, above the channel.


Figure 25 : Emplacement of visualization cut (GDL)

Below the GDL is the cathode flow channel, and above the GDL is the membrane. O2 mole fraction (Figure 26),

gaseous H2O mole fraction (Figure 27) and gas volume fraction (free pore volume, Figure 28) are represented. Two

porosities (0.11 and 0.50) and two cell voltage (0.3V and 0.7V) are tested.

In paragraph 3.2.2.1, a generalized Fick law was introduced:

One can see in this equation that the gradient of gases molar fraction is inversely proportional to the porosity. This

means that a high porosity will ensure high gas diffusivity, and vice versa.

This effect can be observed on Figure 26 and Figure 27, representing O2 and H2O mole fraction. O2 (or gaseous H2O)

mole fraction is the quantity of O2 (or gaseous H2O) divided by the total quantity of gas. At a voltage of 0.7V, which

means a moderate current density (and so a moderate production of water), a high porosity allows oxygen (or gaseous

water) to cross more easily. This is even more obvious for a high current density (cell voltage of 0.3V), where the oxygen

hardly gets to the reaction layer: the limiting current is reached, as seen on Figure 13. With a low porosity, the oxygen

crossing is locally and globally more difficult not only because the GDL provides less empty space for gas molecules, but

also because the gas diffusivity is reduced.

The real porosity to be taken into account for gases is the gas volume fraction, which represents the space available

for gases. It is equal to the actual porosity minus the space taken by the liquid. One can see that local presence of oxygen

in the GDL is highly correlated to the available space for gases, which depends on water saturation. If there is liquid

water, the gas diffusivity is highly reduced.

yDj ∇−=⇒

−=∇ ∑

≠=

τ

ερ

M

jx

M

jx

ρ D

M

ε

τx

sn

ij1j i

ij

j

ji

ij

i

rrr


Figure 26 : O2 mole fraction in cathode GDL

ε=0.11

V=0.7

ε=0.11

V=0.3

ε=0.5

V=0.7

ε=0.5

V=0.3

Figure 27 : gaseous H2O mole fraction in cathode GDL

ε=0.11

V=0.7

ε=0.11

V=0.3

ε=0.5

V=0.7

ε=0.5

V=0.3

Figure 28 : Gas volume fraction (porosity – liquid volume fraction)

ε=0.11

V=0.7

ε=0.11

V=0.3

ε=0.5

V=0.7

ε=0.5

V=0.3


4.3 Sizing the fuel cell

In order to size the fuel cell (and determine how many stack will have to be put together), power output has to be

determined, as well as the optimal operating conditions.

This power output is the product of the terminal voltage with the current : P=U*I. (see Figure 25)

The energetic efficiency is defined as the ratio between the electricity produced and the hydrogen consumed:

η=P/WH2. WH2 is the energy value of hydrogen consumed in Watts, and is equal to the product of the hydrogen

consumption as defined in 3.2.1.1 (Faraday’s law) and of hydrogen’s higher heating value (286 kJ/mol). A simpler

expression is the relation η= V/1.482 for the H2/O2 couple.

Figure 29 : Output power density

Here, the nominal power density output is obtained for a cell voltage of 0.5V. This means that for a given power, the

cell size is minimal at this cell voltage.

However, this cell voltage implies a low efficiency, which means that the fuel consumption is not optimal. For the

optimization of both power and efficiency, a cell voltage of 0.7V is preferred: the increase of fuel cell size conceded by

the loss of power density is negligible compared to the gain of space obtained by the fuel consumption optimization: as

seen in 2.3, the fuel storage is voluminous, especially in automotive application where the space is limited. Nevertheless,

if a high power is momentarily required, the power can be highly increased by consumption augmentation.

5 Experimentation : Effect of temperature

In this part will be explained the importance of temperature on fuel cell performance and the impact on cooling

channels design. If not specified, the values used in calculations are available in appendix A.

5.1 Importance of temperature on fuel cell performance

5.1.1 Introduction: theory

Due to its effect on water and membrane properties, operating temperature is an interesting field of investigation.

The main effect on water is the modification of the saturation rate, which is inversely proportional to

temperature. For a given mass of water, the relative humidity is higher at low temperatures (see Figure 30).


Furthermore, condensation occurs more easily and liquid water is created, reducing gas permeation in the GDL and the

surface of reacting sites on the electrodes. On the opposite, at high temperatures, the air is not enough saturated in

water, causing membrane dehydration.

Figure 30 : hygrometric chart

In Hu et al. 2003[9], formula (48), relies i0, the cathode exchange current density (3.2.1.1), to the operating

temperature:

This dependency to temperature involves that there are more activation potential losses at low temperatures:

Activation losses

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

315 320 325 330 335 340 345 350 355 360 365

Temperature (K)

Acti

vati

on

lo

sses (

V)

Figure 31 : Evolution of activation losses with temperature

5.1.2 Effect of operating temperature

In order to study the influence of temperature, the fuel cell / bipolar plate interface is set to a wall boundary

condition with a constant temperature. This creates an almost homogeneous temperature in the entire fuel cell. Indeed,

the thermal entry length of a circular tube in laminar case, which is the distance about where the boundary layers merge,

is : [6]

xfd,t/D=0.05*ReD*Pr


Although, the Reynolds number of the flow in the entry channel of the fuel cell is : ReD = U*D/ν (with ν the dynamic

viscosity, D the entry diameter and U the flow velocity) ~ 50 for a typical application (laminar flow), while the Prandtl

number is equal to 0.7. As a result, the thermal entry length is:

xfd,t/D=1.75 So, to set a constant wall boundary temperature sets the temperature in the whole fuel cell, as can be seen

thereafter:

Figure 32 : Temperature imposed by boundary conditions

5.1.3 Results

The variation of temperature in the fuel cell for standard conditions described in appendix A creates a high variation

of current density at constant cell voltage :

Evolution of current density with temperature

0

0,2

0,4

0,6

0,8

1

1,2

1,4

315 320 325 330 335 340 345 350 355 360 365

Temperature (K)

Cu

rren

t d

en

sit

y (

A/c

m²)

Figure 33 : Evolution of current density with temperature

The optimal operating temperature is here around 344 K, with a sharp drop for lower and higher temperatures. This

shows that a fuel cell is very sensitive to temperature: the cooling process is a very important issue.


5.2 Impact on cooling channels design

The results found in 5.1.3 have various impacts on the design of the cooling system. Tools for cooling system

calculation will be presented as well.

5.2.1 Sizing of heat exchangers

Both thermal engines and fuel cell generates a heat equivalent to the effective power (used for the vehicle motion) :

PHEAT=h*A*ΔT with PHEAT the evacuated heat, h the heat transfer coefficient, A the area of the exchanger and ΔT the temperature

gap between the liquid to be cooled down and the environment.

Besides, operating temperature for a thermal engine is around 2000K, while for a standard fuel cell it is about 343 K,

as can be seen on Figure 33. Thus, the temperature gap between the fuel cell and the environment is smaller than in a

thermal engine case.

Consequently, for a same effective power, the surface of a fuel cell heat exchanger has to be bigger than for a

thermal engine. This is why high temperature PEM fuel cells, which will have an operating temperature of about 373-400

K, are currently under development using a totally different membrane, in order to reduce the size of heat exchangers.

5.2.2 Optimization

Optimization is possible by a good design of cooling channels. While the cooling fluid flows through cooling channels,

it compulsory gets warmed by the fuel cell, and so a part of the cooling channels are hotter. This may be utilized to set

hotter cooling point close to regions of the GDL where there is liquid phase, in order to increase the saturation level of

water, and so to make less liquid.

In the following numerical experiment, this concept is illustrated with a simple case: cathode boundary temperature

varies along the channel:

1. Cathode boundary temperature is constant and equal to the optimum temperature as seen in 5.1.3 (343.15K).

2. Cathode boundary temperature is hotter where there is liquid. Average temperature is equal to the temperature

of case 1(343.15K).

3. Cathode boundary temperature is cooler where there is liquid. Average temperature is equal to the temperature

of case 1(343.15K).

The cathode exchange current density is set constant at the reference temperature of 343.15K.

Figure 34 : Efficiency comparison of three temperature distribution


Even though an optimal constant temperature gives better results in term of current density, the most adapted case

between 2 and 3 is the case 2.

This concept may be applied to a more complex case (Figure 35), which requires a more sophisticated simulation

methodology.

Figure 35 : Example of a realistic cooling system

5.2.3 Tools for calculation of cooling process

5.2.3.1 ACCI Calculation

In order to study the influence of cooling process on a fuel cell, a bipolar plate and cooling channels can be added to

the calculation, using ACCI – AVL Code Coupling Interface. ACCI, usually couples FIRE with other softwares. It is here

utilized to link three (or more) FIRE calculation: the fuel cell, the plate and the cooling channels. It is also possible to

extract the volumetric temperature distribution inside the solid, and calculate with structure mechanics software the

thermal stresses. In the plate, only the energy equations are used, while the cooling channel requires both thermal and

flow calculation. Each calculation requires one or more processors. They exchange interfacial data (temperature and heat)

at each iteration.

Figure 36 : parallel calculation using ACCI


Figure 37 : Illustration of ACCI coupling

5.2.3.2 Temperature mapping

If ACCI coupling provides detailed results with various cooling design, it is however a process which consumes CPU

time. Therefore, reducing calculation time may be an issue.

In this case and in order to study small variations of parameters, it is possible to extract a temperature field from an

ACCI cooling calculation on a fuel cell boundary, and use it as a boundary condition in a calculation with a fuel cell only

(no coupling).

After a full calculation of an ACCI calculation, the fuel cell / bipolar plate interface is selected, and the temperature

data field is extracted and stored in an ASCII file. Then, this ASCII file can easily be used to map the boundary temperature

at the wall of the single fuel cell. In the end, the calculation needs less capacity and achieve to the same results as the

ACCI one.

Figure 38 : Temperature mapping

Then, small variations of operating conditions can be made around this case. For instance, in Figure 39 are

represented the polarization curve of an ACCI cooling calculation, and a calculation where boundary temperatures were

mapped from an ACCI calculation at a cell voltage of 0.7V.


Polarisation curves

0,5

0,55

0,6

0,65

0,7

0,75

0,8

0,85

0,9

0,95

1

0 0,5 1 1,5 2 2,5 3

Current density (A/cm²)

Cell

vo

ltag

e

Cooling calculation

Mapping calculation

Figure 39 : Polarisation curves for a full cooling calculation and for a calculation issued from a mapping

This shows that the method is validated for small variations, but bigger variations may ensue wrong results, due to

the retroaction between current density and heat production: the gap of cell voltage between the two calculations

expands with the discrepancy to the reference case.

5.2.4 Fuel cells stack (see part 3.2.3)

Usually, fuel cells are put in stacks (see figure 6) because the power of only one fuel cell is too low. The cooling

process is made on both sides of the stack.

In order to study what influence this stacking has on electricity production, a simulation was led. The following

simulation considers three fuel cells put in serial (see Figure 41 for simulation mesh).

The three fuel cells are linked by a plate. A cooling system refreshes the system.

Figure 40: Example of a four

fuel cells stack Figure 41 : three

fuel cells in serial


As it is impossible with the current version to set constant current densities and that no electronic conduction in

bipolar plates is implemented, power density will be compared. A calculation at Ucell=0.7V gives the following field of

temperature:

Figure 42 : Temperature field of three fuel cells in serial

Due to the heat production, the power density of the central fuel cell is lower than the external fuel cells. Water

condensation creates more heat on the cathode sides of the fuel cells. As the lower fuel cell has its cathode side

refreshed, it has a higher power density than the upper one (anode refreshed). None of these fuel cells matches a single

fuel cell refreshed on both sides, which power density is equal on the same operating conditions to 0.483 W/cm².

6 Some results on a more elaborated mesh

6.1 Fuel cell geometry

For these new calculations, a multichannel serpentine fuel cell is taken.


Figure 43 : Multichannel serpentine fuel cell

This geometry theoretically allows a uniform gas distribution. Other types of flow channels distribution are described

in [4].

Figure 44 : Different types of flow channels distribution

In this part will be studied the influence of this particular geometry on gas distribution, membrane water flux, current

density, condensation and phase temperature.

6.2 Results

The following results refer to Figure 45.

6.2.1 Similarity to simple fuel cell results

Main results already obtained in a simple fuel cell are retrieved: from cathode inlet to cathode outlet, the H2O mole

fraction increases (while O2 mole fraction decreases). Liquid water can be found near cathode outlet. The current density

globally decreases as well, due to O2 depletion and liquid water augmentation. Moreover, the membrane water flux is

also similar to the simple fuel cell case: it is an electro-osmosis driven flux for the vast majority of the fuel cell, while a

significant diffusive flux exists near the cathode outlet.

6.2.2 Local effects

Local effects can be found in the GDL, depending on the position of the channels. Under the channels, there is more

oxygen and hydrogen, and so more current density. Thus, there is more water produced on the cathode reaction layer

under the channel, resulting in a higher importance of diffusion contribution (compared to electro-osmotic drag) in the

membrane water flux. Evaporation process is also located under the channels, because of the heat generated by current

density production. On the contrary local variations of liquid water are less pronounced.

One of the goals of the choice of materials used for the GDL is to enhance gas distribution in order to reduce these

local effects.

6.2.3 Gas velocities

The figures show the projected gas velocities in the GDL and the channels. In the GDL, the in-plane gas flow is much

bigger than the through plane flow. This may be due to the anisotropy of the gas diffusion layer structure, as seen in

3.2.2.1 : the through plane permeability is very small compared to the in-plane permeability. In the plane, the gas flow is

diffusion driven and follows the gas gradient: the serpentine configuration has an extremely large influence on this flow.

6.2.4 Temperatures

Temperature of the different phases can be observed. The solid is mainly heated by the chemical reactions and by

conduction, the gas by interfacial heat transfers and the liquid by condensation. These different heating modes explain

the temperature difference between the phases.


Figure 45 : 3d results for multi channels serpentine fuel cell


7 Personal improvements

My work on fuel cells with the software FIRE implied a certain amount of exchange with the PEMFC module project

leader, Clemens Fink, who has just finished his thesis [8]. By my reports on some divergences with theoretical results

encountered during my tests, he was able to improve his code. The two main enhancements we have made were on

influence of liquid coverage on current density, and on the influence of temperature on cathode exchange current

density.

7.1 Liquid coverage

When I was working on fuel cell flooding, I realized that overpotential losses due to flooding were not enough

important. Actually, only the reduction of gas diffusion by liquid water presence in the GDL was implemented, and the

liquid coverage of the platinum surface was not accounted for. Clemens Fink found that for high amounts of liquid water,

the following formula must be used [7]:

, where Sw is the volume fraction of water divided by the free pore volume (porosity).

Two simulations were run, one with and one without this modification, with a porosity of 0.78 and a cell voltage of

0.7V. The profiles of current density and of 1-Sw are plotted along the membrane.

Figure 46 : current density and 1-Sw profiles plotted along the membrane

The reduction of current density corresponds to 1-Sw. So the lower the porosity, the lower the current density will be

because of liquid coverage.

7.2 Cathode exchange current density

As referred in 5.1.1, the cathode current exchange density largely depends on the operating temperature. This fact

was not known at the beginning, and my results were odd because low temperatures were not creating a loss in current

density. After discussions with Clemens Fink, it was found out that io shall depend on temperature.


8 Conclusion

The software AVL FIRE successfully models a large portion of the fuel cell mechanisms, which I have validated for the

most part, from the MEA to the GDL. It is appropriate to cooling studies thanks to the possibility of coupling different

FIRE cases, and the results obtained with a realistic configuration confirms the method reliability.

The PEMFC module is still under development, and more improvements will be implemented. Among others, the

MEA model will be three dimensional, which will allow visualizing results inside the membrane and the electrode, and

electronic conductivity will be added to the model, which will allow more realism for stack calculation.

During this internship, I have practiced my CFD skills on a very interesting and complex subject. Essentially technical,

the discussions with the project leader and the presentations to potential customers have made the work more varied.

The international dimension of AVL was also interesting, since I had to discuss in English with AVL members from Graz.

I would like to thank the AST team for their warm welcome, their help and advice: Wolfgang Schwarz, Alexandre

Raulot, Steeve del Bellino, Lionel Pyot and Laurent Margerie. I also thank Clemens Fink and Peter Sampl for their patience

and for their answers to my numerous questions.


Bibliography

[1] Beuzit. 2007. Hydrogène, l’avenir de la voiture ? L’Archipel

[2] Young et al., 2007.Thermofluid Modeling of Fuel Cells. Annu. Rev. Fluid Mech.

[3] D’Orsay, 2009, SIA conference on main application of fuel cells.

[4] Barbir, 2005. PEM Fuel cells Theory and practice, Elsevier

[5] Berg & al. 2004. Water Management in PEM Fuel Cells. J. Electrochem.

[6] Incropera & Dewitt., 1996. Fundamentals of heat and mass transfer, fourth edition. John

Wiley&Sons.

[7] Acosta & al., 2005, modeling non-isothermal two-phase multicomponent flow in the cathode of

PEM fuel cells, Journal of power sources.

[8]C. Fink., 2009, Modeling and Simulation of Multiphase Transport Phenomena in Porous Media with

Application to PEM Fuel Cells. PhD thesis, Graz University of Technology.

[9]Hu et al., 2003, Three dimensional, two phase flow mathematical model for PEM fuel cell: Part I.

Model development. Elsevier.

D. Bernardi&al. A mathematical model of the Solid Polymer Electrolyte Fuel Cell

Table of illustrations

Figure 1 : Christian Schoenbein……………………………………………………………………………………………………………………………………….- 4 -

Figure 2 : Opel Zafira fuel cell car (2004)…………………………………………………………………………………………………………………………- 5 -

Figure 3: Diagram of a proton exchange membrane fuel cell ..............................................................................................- 8 -

Figure 4 : description of the module functionment .............................................................................................................- 9 -

Figure 5: Actual voltage in function of current density ......................................................................................................- 10 -

Figure 7: capillar pressure in the GDL.................................................................................................................................- 12 -

Figure 8 : Fuel cells put in serials ........................................................................................................................................- 13 -

Figure 9 : selections in a simple model of PEMFC ..............................................................................................................- 13 -

Figure 10: Fire data settings interface................................................................................................................................- 14 -

Figure 11 : Real and modelized fuel cell .............................................................................................................................- 14 -

Figure 12 : Polarization curve .............................................................................................................................................- 15 -

Figure 13 : Polarization curve with a lower porosity ..........................................................................................................- 16 -

Figure 14 : Polarization curves and membrane losses for different membrane thicknesses.............................................- 16 -

Figure 15 : Activation and concentration losses for various thicknesses ...........................................................................- 17 -

Figure 16: location of the 2d plotting…………………………………………………………………………………………………………………………….- 16 -

Figure 17 : current density for moderate case………………………………………………………………………………………………………………- 17 -

Figure 18 : Oxygen mole fraction…………………………………………………………………………………………………………………………………..- 17 -

Figure 19 : Membrane water flux………………………………………………………………………………………………………………………………….- 17 -

Figure 21 : Water content for moderate case……………………………………………………………………………………………………………….- 17 -

Figure 22 : Water crossover along the membrane, Berg model ........................................................................................- 19 -

Figure 23 : Water crossover along the membrane, with no saturation .............................................................................- 20 -


Figure 24 : Emplacement of visualization cut (GDL)...........................................................................................................- 21 -

Figure 25 : O2 mole fraction in cathode GDL .....................................................................................................................- 22 -

Figure 26 : gaseous H2O mole fraction in cathode GDL .....................................................................................................- 22 -

Figure 27 : Gas volume fraction (porosity – liquid volume fraction) ..................................................................................- 22 -

Figure 28 : Output power density.......................................................................................................................................- 23 -

Figure 29 : hygrometric chart .............................................................................................................................................- 24 -

Figure 30 : Evolution of activation losses with temperature..............................................................................................- 24 -

Figure 31 : Temperature imposed by boundary conditions ...............................................................................................- 25 -

Figure 32 : Evolution of current density with temperature................................................................................................- 25 -

Figure 33 : Efficiency comparison of three temperature distribution................................................................................- 26 -

Figure 34 : Example of a realistic cooling system ...............................................................................................................- 27 -

Figure 35 : parallel calculation using ACCI ..........................................................................................................................- 27 -

Figure 36 : Illustration of ACCI coupling .............................................................................................................................- 28 -

Figure 37 : Temperature mapping......................................................................................................................................- 28 -

Figure 38 : Polarisation curves for a full cooling calculation and for a calculation issued from a mapping .......................- 29 -

Figure 40: Example of a four fuel cells stack………………………………………………………………………………………………………………….- 28 -

Figure 41 : three fuel cells in serial………………………………………………………………………………………………………………………………..- 28 -

Figure 41 : Temperature field of three fuel cells in serial...................................................................................................- 30 -

Figure 42 : Multichannel serpentine fuel cell .....................................................................................................................- 31 -

Figure 43 : Different types of flow channels distribution...................................................................................................- 31 -

Figure 44 : 3d results for multi channels serpentine fuel cell.............................................................................................- 32 -

Figure 45 : current density and 1-Sw profiles plotted along the membrane .....................................................................- 33 -

APPENDIX A : Table of reference values

In simulations, the following values were used, if not specified otherwise:

Reference temperature (boundary temperature conditions, inlets) : 343.15K

Cathode inlet :

O2 molar fraction : 0.21

N2 molar fraction : 0.79

H2O quantity defined by the humidification temperature : 336.15K

Gas velocities defined by the stoichiometry : 2.2

Anode inlet :

H2 molar fraction : 1

H2O quantity defined by the humidification temperature : 336.15K

Gas velocities defined by the stoichiometry : 1.5

GDL :

Porosity : 0.79

Tortuosity : 1

Contact angle : 122°

Surface tension : 0.062N/m

Inverse of in plane permeability : 1.767E11m^(-2)

Inverse of through plane permeability : 5.85E13m^(-2)

MEA :

Open circuit cell voltage : 1V

Cell voltage : 0.7V

Henry constant :

O2 : 4.77E8 Pa

N2 : 8.68E9 Pa

H2 : 1.12E8 Pa

H2O : 0 Pa

Reaction layer thickness : 6.7E-5m

Cathode exchange current density : 650000 A/m^3

Anode exchange current density : 1E11 A/m^3

Sulfonic acid group concentration : 1.762 mol/m^3

internship report multiphysic simulation in a proton ...€¦ · this internship took place at avl...

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