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Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers, Incorporated,

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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CFD MODELING AND ANALYSIS OF DIFFERENT NOVEL DESIGNS OF AIR-BREATHING PEM FUEL CELLS

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CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells Maher A.R. Sadiq Al-Baghdadi 2010. ISBN: 978-1-60876-489-1

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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CFD MODELING AND ANALYSIS OF DIFFERENT NOVEL DESIGNS OF AIR-BREATHING PEM FUEL CELLS

MAHER A.R. SADIQ AL-BAGHDADI

Nova Science Publishers, Inc. New York

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Copyright © 2010 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Al-Baghdadi, Maher A. R. Sadiq. CFD modeling and analysis of different novel designs of air-breathing PEM fuel cells / Maher A.R. Sadiq Al-Baghdadi. p. cm. Includes bibliographical references and index.

ISBN:  (eBook)

1. Proton exchange membrane fuel cells--Mathematical models. 2. Proton exchange membrane fuel cells--Computer simulation. 3. Proton exchange membrane fuel cells--Design and construction-Mathematics. 4. Computational fluid dynamics. I. Title. TK2933.P76A53 2009 621.31'2429--dc22 2009041955

Published by Nova Science Publishers, Inc. © New York CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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CONTENTS Preface

ix

Acknowledgments

xi

Nomenclature

xiii

Chapter 1

Introduction

1

Chapter 2

CFD Model

21

Chapter 3

Planar Air-Breathing PEM Fuel Cell

45

Chapter 4

Planar Micro-Structured Air-Breathing PEM Fuel Cell

65

Planar Compacted-Design Micro-Structured Air-Breathing PEM Fuel Cell

85

Chapter 6

Tubular Air-Breathing PEM Fuel Cell

105

Chapter 7

Tubular Micro-Structured Air-Breathing PEM Fuel Cell

127

Tubular Compacted-Design Micro-Structured Air-Breathing PEM Fuel Cell

147

Disk-Shaped Micro-Structured Air-Breathing PEM Fuel Cell

169

Disk-Shaped Compacted-Design Micro-Structured Air-Breathing PEM Fuel Cell

189

Parametric Study

211

Chapter 5

Chapter 8 Chapter 9 Chapter 10 Chapter 11

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

viii

Contents 223

Index

227

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References

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

PREFACE Fuel cell system is an advanced power system for the future that is sustainable, clean and environmental friendly. Fuel cells are electrochemical devices that convert the chemical energy of hydrogen and oxygen directly into electrical energy. Fuel cells are growing in importance as sources of sustainable energy and will doubtless form part of the changing programme of energy resources in the future. Small fuel cells have provided significant advantages in portable electronic applications over conventional battery systems. Competitive costs, instant recharge, and high energy density make fuel cells ideal for supplanting batteries in portable electronic devices. For portable applications like laptops, camcorders, and mobile phones the requirements of the fuel cell systems are even more specific than for stationary and vehicular applications. The requirements for portable applications are mostly focused on size and weight of the system as well as the temperature. Among all kinds of fuel cells, proton exchange membrane (PEM) fuel cells are compact and lightweight, work at low temperatures with a high output power density, and offer superior system start-up and shutdown performance. However, the typical PEM fuel cell system with its heavy reliance on subsystems for cooling, humidification and air supply would not be practical in small applications. The air-breathing PEM fuel cells without moving parts (external humidification instrument, fans or pumps) are one of the most competitive candidates for future portable-power applications. These passive type cells consume ambient air for their operation through natural free convection; as such, they eliminate the need for air-supply subsystems including compressor, humidifier and other components which minimise the Balance-Of-Plant (BOP) cost and complexity. Their hydrogen-supply subsystem can even be miniaturised by combining it with on-demand micro-hydrogen generator/galvanic cell.

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

x

Maher A. R. Sadiq Al-Baghdadi

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Today, the production of the air-breathing fuel cells is linked with high manufacturing costs. Crucial for the successful design of fuel cells is an understanding of how the design influences performance. The small dimensions of the ambient air-breathing PEM fuel cells restrict the use of sensors to monitor the distribution of current density, species, and heat in different parts of the cell. Thus, Computational Fluid Dynamics (CFD) modelling plays a significant and important role in analyzing the performance and transport phenomena in airbreathing PEM fuel cells. The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of the air-breathing PEM fuel cells, the introduction of cheaper materials and fabrication techniques, and the design and development of novel architectures. In the book of CFD MODELLING AND ANALYSIS OF DIFFERENT NOVEL DESIGNS OF AIR-BREATHING PEM FUEL CELLS, different novel designs of the air-breathing PEM fuel cells have been developed in order to achieve an air-breathing PEM fuel cell with much higher power density, long cell life, and lower cost. The CFD models in this book would allow the creation of powerful computational fuel cell engineering tools that lead to dramatic reductions in lead times and development costs, and spur innovative design.

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

ACKNOWLEDGMENTS

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

This work, based on research carried out over several years. My great appreciation is expressed to International Technological University (ITU), London, UK for providing available facilities. My gratitude and appreciation is due to my wife for her patience, care, and support during the period of preparing this Book. Most of all, I want to thank my parents for their unconditional support throughout all the years of my education. This study would not have been possible without them. Many thanks also are due to my brother and sister. Maher A.R. Sadiq AL-Baghdadi

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

NOMENCLATURE Symbol

Description

Units

a

Water activity

-

AMEA

Area of the MEA

m2

Ach

Cross sectional area of flow channel

m2

cW

Water content

-

C

Condensation constant

-

Cf

Fixed charge concentration

mol.m −3

CH2

Local hydrogen concentration

mol.m −3

C Href2

Reference hydrogen concentration

mol.m −3

C O2

Local oxygen concentration

mol.m −3

C Oref2

Reference oxygen concentration

mol.m −3

Cp

Specific heat capacity

J .kg −1 .K −1

D

Diffusion coefficients

m 2 .s −1

DH +

Protonic diffusion coefficient

Ddrop

Diameter of droplet water

m 2 .s −1 m

E

Reversible cell potential

volts

E cell

Cell operating potential

volts

E fc

Thermodynamic efficiency of the cell

-

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Maher A. R. Sadiq Al-Baghdadi

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

xiv Symbol

Description

Units

F

Faraday's constant

G g

Gibb's free energy

96487C.mol −1 J

Specific Gibb’s free energy

J .mol −1

h

Specific enthalpy

J .mol −1

I

Cell operating (nominal) current density

A.m −2

ia

Anode local current density

A.m −3

ic

Cathode local current density

A.m −3

ioref,c

Anode reference exchange current density

A.m −3

ioref,a

Cathode reference exchange current density

A.m −3

i L,a

Anode local limiting current density

A.m −2

i L ,c

Cathode local limiting current density

A.m −2

k

Gases thermal conductivity

W .m −1 .K −1

keff

Effective electrode thermal conductivity

W .m −1 .K −1

k gr

Graphite thermal conductivity

W .m −1 .K −1

kmem

Membrane thermal conductivity

W .m −1 .K −1

k xm

Mass transfer coefficient

mol.m −2 .s −1

Kp

Hydraulic permeability

m2

LHV H 2

Lower heating value of hydrogen

J .kg −1

m& phase

Mass transfer in the form of: evaporation

kg.s −1

m& phase = m& evap

and condensation

m& phase = m& cond M

Molecular weight of mixture gases

kg.mol −1

M H2

Molecular weight of hydrogen

kg.mol −1

M H 2O

Molecular weight of water

kg.mol −1

M O2

Molecular weight of oxygen

kg.mol −1

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Nomenclature

xv

Symbol

Description

Units

NW

Net water flux across the membrane

kg.m −2 .s −1

nd

Electro-osmotic drag coefficient

-

ne

Number of electrons transfer

-

P

Pressure

Pa

Pc

Capillary pressure

Pa

Psat

Water saturation pressure

Pa

q&

Heat generation

W .m −3

rg

Volume fraction of the gas phase

-

rl

Volume fraction of the liquid phase

-

R

Universal gas constant

8.314 J .mol −1 .K −1

s

Specific entropy

J .mol −1 .K −1

sat

Saturation

-

T

Temperature

K

u

Velocity vector

m.s −1

v∞

Free-stream velocity

m.s −1

Wcell

Cell power density

W .m −2

xi

Molar fraction

-

yi

Mass fraction

-

zf

Fixed-site charge

-

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Maher A. R. Sadiq Al-Baghdadi

xvi

Greek Symbols Description Symbol

Description

Units

αa

Charge transfer coefficient, anode side Charge transfer coefficient, cathode side Modified heat transfer coefficient

-

αc

β τ

Chemical potential

τ γH

Electrochemical potential

W .m −3 .K −1 J .mol −1 J .mol −1

Hydrogen concentration parameter

-

Oxygen concentration parameter

-

Enthalpy of evaporation

J .kg −1

Entropy change of cathode side reaction Catalyst layer thickness

Membrane thickness

J mole −1 K −1 m m m

Porosity

-

ξ η

Stoichiometric flow ratio

-

Overpotential

volts

λe λm μ ρ

Electrode electronic conductivity

φGDL

Electric potential inside the gas diffusion layer Electric potential inside the membrane Relative humidity of inlet fuel and air

S .m −1 S .m −1 kg.m −1 .s −1 kg.m −3 volts

γO

2

2

ΔH evap ΔS

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-

δ CL δ GDL δ mem ε

φ mem ℜ

ψ ϕ

ϖ σ

Gas diffusion layer thickness

Membrane ionic conductivity Viscosity Density

Inlet Oxygen/Nitrogen ratio Local relative humidity of the gas phase Scaling parameter for evaporation Surface Tension

volts

% -

N .m −1

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Nomenclature Abbreviations Definition CFD CL GDL MEA MEM PEM sat

Computational Fluid Dynamics Catalyst Layer Gas Diffusion Layer Membrane Electrode Assembly Membrane Proton Exchange Membrane Saturation

Subscript Definition

a c g

Anode

l w

Liquid phase

Cathode Gas phase

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Water

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

xvii

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Chapter 1

1. INTRODUCTION

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1.1. BACKGROUND Fuel cell system is an advanced power system for the future that is sustainable, clean and environmental friendly. Fuel cells are electrochemical devices that convert the chemical energy of hydrogen and oxygen directly into electrical energy. Fuel cells are growing in importance as sources of sustainable energy and will doubtless form part of the changing programme of energy resources in the future. Small fuel cells have provided significant advantages in portable electronic applications over conventional battery systems. Competitive costs, instant recharge, and high energy density make fuel cells ideal for supplanting batteries in portable electronic devices. For portable applications like laptops, camcorders, and mobile phones the requirements of the fuel cell systems are even more specific than for stationary and vehicular applications. The requirements for portable applications are mostly focused on size and weight of the system as well as the temperature. Among all kinds of fuel cells, proton exchange membrane (PEM) fuel cells are compact and lightweight, work at low temperatures with a high output power density, and offer superior system start-up and shutdown performance. However, the typical PEM fuel cell system with its heavy reliance on subsystems for cooling, humidification and air supply would not be practical in small applications. The air-breathing PEM fuel cells without moving parts (external humidification instrument, fans or pumps) are one of the most competitive candidates for future portable-power applications. These passive type cells consume ambient air for their operation through natural free convection; as such, they eliminate the need for air-supply subsystems including compressor,

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

2

Maher A. R. Sadiq Al-Baghdadi

humidifier and other components which minimise the Balance-Of-Plant (BOP) cost and complexity. Their hydrogen-supply subsystem can even be miniaturised by combining it with on-demand micro-hydrogen generator/galvanic cell. In airbreathing PEM fuel cell, the cathode side of the cell is directly open to ambient air. The oxygen needed by the fuel cell electrochemical reaction is taken directly from the surrounding air by natural convection and diffusion through the gas diffusion backing into the cathode electrode. Today, the production of the air-breathing fuel cells is linked with high manufacturing costs. Crucial for the successful design of fuel cells is an understanding of how the design influences performance. In the present book, different novel designs of the air-breathing PEM fuel cells have been developed in order to achieve an air-breathing PEM fuel cell with much higher power density, long cell life, and lower cost.

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

1.2. TYPES OF FUEL CELL According to their electrolytes, fuel cells are classified into four types; PEMFC (Proton Exchange Membrane Fuel Cell), PAFC (Phosphoric Acid Fuel Cell), MCFC (Molten Carbonate Fuel Cell), and SOFC (Solid Oxide Fuel Cell). An exception to this classification is the DMFC (Direct Methanol Fuel Cell) which is a fuel cell in which methanol is directly fed to the anode. The electrolyte of this cell is not determining for the class. A second grouping can be done by looking at the operating temperature for each of the fuel cells. There are, thus, low-temperature and high-temperature fuel cells. Low-temperature fuel cells are the Alkaline Fuel Cell (AFC), the Polymer Electrolyte Fuel Cell (PEMFC), the Direct Methanol Fuel Cell (DMFC) and the Phosphoric Acid Fuel Cell (PAFC). The high-temperature fuel cells operate at temperatures approx. 600±1000 -C and two different types have been developed, the Molten Carbonate Fuel Cell (MCFC) and the Solid Oxide Fuel Cell (SOFC). Table 1.1 compares the different types of fuel cell systems [1-4]. A schematic representation of a fuel cell with reactant and product, and ions flow directions for these types of fuel cells are shown in Figure 1.1. From the Table 1.1 can conclude that the PEMFC is the only fuel cell that excels in all the characteristics essential for private vehicle applications. Additional advantages that the PEMFC offers over some of the other fuel cells are that the PEMFC is a less complicated system to implement and has a longer expected lifetime [5].

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Introduction

3

Table 1.1. The different types of fuel cells AFC Electrolyte

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Electrode Material

NaOH / KOH Metal or carbon

PEMF DMFC C Polymer membrane

PAFC

MCFC

SOFC

H3PO4

LiCO3– K2CO3

ZrO2 with Y2O3 Ni/Y2O3– ZrO2

Pt-on-carbon

Ni +Cr

Operating Temp. (Co)

60-100

50-100

50-200

160-210

650-800

800-1000

Power Density (kW/m2)

0.7 – 8.1

3.8 – 6.5

> 1.5

0.8 – 1.9

0.1 – 1.5

1.5 – 2.6

Practical Efficiency (%)

60

60

60

55

55-65

60-65

Combine heat and power for decentrali zed stationary power systems

Combine heat and power for stationary decentralized systems and for transportation (trains, boats, …)

hrs

hrs

Applications

Transportation, Space, Military, Energy storage systems

Start-Up Time

min

sec

secmin

hrs

Among all kinds of fuel cells, proton exchange membrane (PEM) fuel cells are compact and lightweight, work at low temperatures with a high output power density, and offer superior system start-up and shutdown performance [6]. These advantages have sparked development efforts in various quarters of industry to open up new field of applications for PEM fuel cells, including transportation power supplies, compact cogeneration stationary power supplies, portable power supplies, and emergency and disaster backup power supplies [1-7]. The advantages of fuel cells impact particularly strongly on combined heat and power (CHP) systems (for both large- and small-scale applications), and on mobile power systems, especially for vehicles and electronic equipment such as portable computers, mobile telephones, and military communications equipment. These areas are the major fields in which fuel cells are being used. However, there are varied advantages, which feature more or less strongly for different types and lead to different applications (Figure 1.2)

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Maher A. R. Sadiq Al-Baghdadi

Figure 1.1. Operating principle of various types of fuel cells.

Figure 1.2. Chart to summarize the applications and main advantages of fuel cells of different types, and in different applications.

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Introduction

5

The most important attributes of fuel cells for stationary power generation are the high efficiencies and the possibility for distributed power generation. Both low-temperature and high-temperature fuel cells could, in principle, be utilised for stationary applications. The low-temperature fuel cells have the advantage that usually a faster start-up time can be achieved. The high-temperature systems such as SOFC and MCFC generate high-grade heat which can directly be used in a heat cycle or indirectly used by incorporating the fuel cell system into a combined cycle. SOFCs and MCFCs also have the advantage that they can operate directly on available fuels without the need for external reforming. For a small distributed power system, e.g., single-home or multiple-home power generation, a PEM, SOFC, or PAFC combined with a heat cycle could be used to provide all the needs for a home. The PAFC start-up time is much lower than this for hightemperature systems, which makes it more attractive for small-power generation. The heat generated by the fuel cell system can be employed for heating and providing the home with hot water. The PAFC produces enough steam to operate a steam reforming system whereas the PEM system due to its lower operation temperature is not able to supply the necessary heat. Small power plants in the range above 250 kW can be operated by high-temperature fuel cell systems. The high grade heat obtained from these systems can be exchanged at a broad temperature range leaving the possibility of direct heat use or further electricity generation by steam engines. The start-up time of these systems are longer than for low-temperature systems but the advantages of being able to operate the system without external reforming and the higher efficiencies of SOFCs and MCFCs makes these systems more suitable for large-scale power plants. For vehicular applications fuel cell systems need to be different from stationary power generation. Available space in vehicles is much more critical and fast response times and start-up times are required. The controversial AFC has proven to be a suitable system for hybrid vehicles as long as a circulating electrolyte is used and pure hydrogen is supplied to the fuel cell. Pure hydrogen distribution centres are not widely spread over the world and, thus, it is to be predicted that AFC vehicles will be limited to specified types (e.g., fleet buses and other centralised vehicles). For space vehicles, AFC technology is established and although the tendency to change to PEM fuel cells is also penetrating the space industry it is likely that AFC systems will be employed for many more years in space. PEM systems still need to be tested concerning the stringent requirements (reliability of operation etc.) for space applications. Prototype fuel-cell-powered vehicles have recently been demonstrated by several car manufactures. All of the various demonstration vehicles are based on a basic conceptual design combining the proton exchange membrane (PEM) fuel cell with an electric drive. The

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Maher A. R. Sadiq Al-Baghdadi

PEMFC is regarded as ideally suited for transportation applications due to its high power density, high energy conversion efficiency, compactness, lightweight, and low-operating temperature (below 100 C). The recent PEM driven electric vehicles have demonstrated the technical feasibility of the concept. However, among all applications for fuel cells the transportation application involves the most stringent requirements regarding volumetric and gravimetric power density, reliability, and costs. The higher energy density of a liquid fuel guarantees a driving range similar to that of internal combustion engine vehicles. The fuel favoured by many car manufacturers is methanol from which hydrogen can be produced on-board by steam reforming. The reforming of the fuel, however, leads to slower response times, and extensive gas clean-up procedures need to be carried out to supply the fuel cell with high-grade hydrogen. Because of the difficult thermal integration and the size of the reformer and gas-cleaning unit a direct methanol fuel cell (DMFC), where methanol is oxidized directly at the anode, would be more desirable for mobile systems (higher simplicity of the system). Therefore, in addition to the reformer/ fuel cell combination, DMFCs using methanol/water vapour or liquid methanol/water mixtures as fuel are being investigated and developed. The development of the DMFC for transportation applications, however, is less advanced as compared to the indirect PEMFC and hampered by problems of reduced power density caused by methanol permeation through the membrane and poisoning of the electrocatalysts. Recent progress regarding power density and compactness of DMFC stacks are encouraging and indicate that this concept may be competitive in vehicles. Due to the multitude of realized demonstration vehicles with PEMFC technology it appears a forgone conclusion that only fuel cells based on the PEM technique are suitable for transportation applications. System considerations, however, show beneficial properties of high-temperature fuel cells that could simplify the system considerably. Certainly, proton exchange membrane fuel cells (PEMFCs) have the advantage of the low operating temperature and the high power density. Using alcohols or hydrocarbons as fuel, thermal integration is complicated. The main advantage of SOFCs compared to PEMFCs concerns the unproblematic use of hydrocarbon fuels. SOFCs do not require pure hydrogen as fuel, but can be operated on partially pre-reformed hydrocarbons (e.g., gasoline). They do not exhibit any significant poisoning problem. Several studies have investigated the potential of SOFC for transportation applications and have pointed out this advantage. These beneficial factors have been recognized recently, leading several companies to develop SOFCs as Auxiliary Power Units (APU) for gasoline vehicles. The APU replaces the traditional battery and provides further electrical energy for air conditioning and car electronics. For portable applications like

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Introduction

7

laptops, camcorders, and mobile phones the requirements of the fuel cell systems are even more specific than for vehicle applications. Low temperatures are necessary and therefore PEM fuel cells are chosen. Possibilities for fuel cell systems are the combination of PEM with hydrogen storage by hydrides or gas cartridges. The requirements for portable applications are mostly focused on size and weight of the system (as well as the temperature). Other fuel cells are, therefore, not suitable for this kind of applications. Portable devices need lower power than other fuel cell applications and, thus, PEM fuel cells and DMFC systems may be well suited for this kind of applications. With further technology improvements and better storage systems PEM fuel cells and DMFC systems will continue to compete in this market. The use of portable electronic telecommunication and computing devices has motivated the research of power sources with a long-term operation. The small fuel cell system, especially the small proton exchange membrane fuel cell (PEM), has been developed significantly as a promising electrochemical power source in portable and miniature electronic devices. The small PEM can replace the lithium battery due to its safety, high efficiency, renewable fuel and environmental compatibility.

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1.3. OPERATION PRINCIPLE OF A PEM FUEL CELL The hydrogen diffuses through the anode diffusion layer towards the catalyst layer, where each hydrogen molecule splits up into two hydrogen protons and two electrons on catalyst surface according to: 2 H 2 → 4 H + + 4e −

(1.1)

The protons migrate through the membrane and the electrons travel through the conductive diffusion layer and an external circuit where they produce electric work. On the cathode side the oxygen diffuses through the diffusion layer, splits up at the catalyst layer surface and reacts with the protons and the electrons to form water: O 2 + 4 H + + 4e − → 2 H 2 O

(1.2)

Reaction 1 is slightly endothermic, and reaction 2 is heavily exothermic, so that overall heat is created. From above it can be seen that the overall reaction in a PEM Fuel Cell can be written as:

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Maher A. R. Sadiq Al-Baghdadi

2 H 2 + O2 → 2 H 2 O

(1.3)

Based on its physical dimensions, a single cell produces a total amount of current, which is related to the geometrical cell area by the current density of the cell in [A/cm2]. The cell current density is related to the cell voltage via the polarization curve, and the product of the current density and the cell voltage gives the power density in [W/cm2] of a single cell.

1.4. FUEL CELL COMPONENTS The air-breathing PEM fuel cell consists of a current collector, gas diffusion layer, and catalyst layer on the anode and cathode sides as well as an ion conducting polymer membrane.

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1.4.1. Polymer Electrolyte Membrane An important part of the fuel cell is the electrolyte, which gives every fuel cell its name. At the core of a PEM fuel cell is the polymer electrolyte membrane that separates the anode from the cathode. The desired characteristics of PEMs are high proton conductivity, good electronic insulation, good separation of fuel in the anode side from oxygen in the cathode side, high chemical and thermal stability, and low production cost [8]. One type of PEMs that meets most of these requirements is Nafion. This is why Nafion is the most commonly used and investigated PEM in fuel cells. In the Proton-Exchange Membrane Fuel Cell (or Polymer-Electrolyte Membrane Fuel Cell) the electrolyte consists of an acidic polymeric membrane that conducts protons but repels electrons, which have to travel through the outer circuit providing the electric work. A common electrolyte material is Nafion® (Figure 1.3) from DuPont™, which consists of a fluoro-carbon backbone, similar −

to Teflon, with attached sulfonic acid SO 3 groups (Figure 1.4). The membrane is characterized by the fixed-charge concentration (the acidic groups): the higher the concentration of fixed-charges, the higher is the protonic conductivity of the membrane. Alternatively, the term “equivalent weight” is used to express the mass of electrolyte per unit charge.

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Introduction

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Figure 1.3. The structure of Nafion showing the three different regions the hydrophobic PTFE backbone, the hydrophilic ionic zone, and the intermediate region.

Figure 1.4. Membrane structure.

For optimum fuel cell performance it is crucial to keep the membrane fully humidified at all times, since the conductivity depends directly on water content [9, 10].

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The thickness of the membrane is also important, since a thinner membrane reduces the ohmic losses in a cell. However, if the membrane is too thin, hydrogen, which is much more diffusive than oxygen, will be allowed to crossover to the cathode side and recombine with the oxygen without providing electrons for the external circuit. Typically, the thickness of a membrane is in the range of 5-300 μm [11].

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1.4.2. Catalyst Layer The best catalyst material for both anode and cathode PEM fuel cell is platinum. Since the catalytic activity occurs on the surface of the platinum particles, it is desirable to maximize the surface area of the platinum particles. A common procedure for surface maximization is to deposit the platinum particles on larger carbon black particles [12]. Therefore, the catalyst is characterized by the surface area of platinum by mass of carbon support. The electrochemical half-cell reactions can only occur, where all the necessary reactants have access to the catalyst surface. This means that the carbon particles have to be mixed with some electrolyte material in order to ensure that the hydrogen protons can migrate towards the catalyst surface. This "coating" of electrolyte must be sufficiently thin to allow the reactant gases to dissolve and diffuse towards the catalyst surface (Figure 1.5). Since the electrons travel through the solid matrix of the electrodes, these have to be connected to the catalyst material, i.e. an isolated carbon particle with platinum surrounded by electrolyte material will not contribute to the chemical reaction. Several methods of applying the catalyst layer to the gas diffusion electrode have been reported. These methods are spreading, spraying, and catalyst power deposition. For the spreading method, a mixture of carbon support catalyst and electrolyte is spread on the GDL surface by rolling a metal cylinder on its surface [13]. In the spraying method, the catalyst and electrolyte mixture is repeatedly sprayed onto the GDL surface until a desired thickness is achieved. Although the catalyst layer thickness can be up to 50 μm thick, it has been found that almost all of the electrochemical reaction occurs in a 10

μm thick layer closest to the membrane

[13].

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Introduction

11

Figure 1.5. Catalyst layer structure.

1.4.3. Gas Diffusion Layer The typical materials for gas diffusion layers are carbon paper and carbon cloth. These are porous materials with typical thickness of 100-300 μm [13]. The functions of the gas diffusion layers are to provide structural support for the catalyst layers, passages for reactant gases to reach the catalyst layers and transport of water to or from the catalyst layers, electron transport from the catalyst layer to the bipolar plate in the anode side and from the bipolar plate to the catalyst layer in the cathode side, and heat removal from the catalyst layers.

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12

Gas diffusion layers are usually coated with Teflon to reduce flooding which can significantly reduce fuel cell performance due to poor reactant gas transport.

Figure 1.6. The gas diffusion layer.

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The gas diffusion layers are characterized mainly by their thickness and porosity (Figure 1.6). The hot-pressed assembly of the membrane and the gasdiffusion layer including the catalyst is called the Membrane-Electrode-Assembly (MEA).

1.5. FUEL CELL THERMODYNAMICS 1.5.1. Gibbs Free Energy Change in Fuel Cell Reactions Fuel cell electrochemical reactions convert free energy change associated with the chemical reaction into electrical energy directly. The Gibbs free energy change in a chemical reaction is a measure of the maximum net work obtainable from a chemical reaction [14].

Δg = Δh − TΔs

(1.4)

The basic thermodynamic functions are internal energy U, enthalpy H, entropy S, and Gibbs free energy G. These are extensive properties of a thermodynamic system and they are first order homogenous functions of the components of the system. Pressure and temperature are intensive properties of the system and they are zero-order homogenous functions of the components of

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Introduction

13

the system. Electrochemical potentials are the driving force in an electrochemical system. The electrochemical potential comprises chemical potential and electrostatic potential in the following relation. Chemical potential:

⎛ ∂G ⎞

⎟⎟ τ i = ⎜⎜ ∂ N ⎝ i ⎠T ,P, N

(1.5) j

Electrochemical potential:

τ i = τ i + zFφ where

(1.6)

τ i is the chemical potential, z is the charge number of the ion, φ is the

potential at the location of the particles i.

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1.5.2. Electrode Potential The reversible electrode potential of a chemical reaction can be obtained from the Nernst equation;

⎛ ∑ a vi i ⎜ RT E = Eo − ln⎜ i vj ne F ⎜ ∑ a j ⎜ j ⎝ where E

o

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

(1.7)

is the reversible potential at standard state, ai and a j are activity

coefficients of the products and reactants respectively, v i and v j are the stoichiometric coefficients respectively. The standard state reversible electrode potential can be calculated from the thermodynamic property of standard Gibbs free energy change of the reaction as [14];

Eo = −

ΔG o ne F

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(1.8)

Maher A. R. Sadiq Al-Baghdadi

14

It can be seen from these relations that the reversible potential is dependent on temperature and pressure since the Gibbs free energy is a function of temperature and the activity coefficients are dependent on temperature, pressure for gases and ionic strengths for ionic electrolytes. The Nernst equation (1.7) is used to derive a formula for calculating the reversible cell potential as follows: Anode electrode potential;

Ea =

E ao

2 RT ⎛⎜ a H + + ln 2F ⎜ a H 2 ⎝

⎞ ⎟ ⎟ ⎠

(1.9)

Cathode electrode potential;

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E c = E co +

RT ⎛⎜ a H 2O ( g ) ln 2 F ⎜ a 2 + aO1 2 2 ⎝ H

⎞ ⎟ ⎟ ⎠

(1.10)

The absolute electrode potential of the fuel cell is difficult to measure. However, only the electrode potential difference between the cathode and anode is important in fuel cells. The reversible cell potential can be obtained from the difference between the reversible electrode potentials at the cathode and anode.

E = Eo +

RT ⎛⎜ a H 2O ln 2 F ⎜ a H aO1 2 ⎝ 2 2

⎞ ⎟ ⎟ ⎠

(1.11)

1.5.3. Electrode Kinetics Electrochemical kinetics is a complex process and only a short summary is provided in this section. The first step in understanding the kinetics of the electrode is to determine the governing electrochemical reaction mechanism. The reaction mechanism can be single step or multi-step with electron transfer. The operation of an electrochemical system is a highly non-equilibrium process that involves the transfer of electrons and reactant species at the electrode surface. The reaction rates are directly related to the Faradic current flows through the electrode. This rate depends on three important parameters: exchange current

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Introduction

15

density which is related to catalytic activity of the electrode surface, concentration of oxidizing and reducing species at the electrode surface, and surface activation overpotential. Mathematically, these physical quantities are used to derive the Butler-Volmer equation for calculating the current [14-17].

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1.6. TRANSPORT PHENOMENA IN AIR-BREATHING PEM FUEL CELLS The air-breathing PEM fuel cell, shown schematically in Figure 1.7, provides a good illustration of the complex interplay between various transport phenomena [18]. In air-breathing PEM fuel cell, hydrogen enters the cell through gas channels at the anode and air supply directly from the surrounding air by natural convection at the cathode. The gas diffusion layers (GDL) are used to uniformly distribute the reactants across the surface of the catalyst layers (CL), as well as to provide an electrical connection between the catalyst layers and the current collectors. The electrochemical reactions that drive a fuel cell occur in the catalyst layers which are attached to both sides of the membrane. The catalyst layers must be designed in such a manner as to facilitate the transport of protons, electrons, and gaseous reactants. Protons, produced by the oxidation of hydrogen on the anode, are transported through ion conducting polymer within the catalyst layers and the membrane. Electrons produced at the anode are transported through the electrically conductive portion of the catalyst layers to the gas diffusion layers, then to the collector plates and through the load, and finally to the cathode. Gaseous reactants are transported by both diffusion and advection through pores in the catalyst layers. Protons are conducted across the polymer membrane from the anode, where they are produced, to the cathode where they combine with oxygen and electrons to form water, which may be in vapour or liquid form, depending on the local conditions. Liquid water is transported through the pores in the catalyst and gas diffusion layers through a mechanism that may be similar to capillary flow. Water may also be transported, in dissolved form, through the polymer portion of the catalyst layers and through the membrane. The mechanisms of dissolved water transport are diffusion, due to a concentration gradient between anode and cathode, and electro-osmotic drag. Water management has a significant impact on the overall system performance, and is, therefore, one of the most critical and widely studied issues in PEM fuel cells.

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Maher A. R. Sadiq Al-Baghdadi

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Figure 1.7. Transport of reactants, charged species and products in an air-breathing PEM fuel cell.

Proper water management requires meeting two conflicting needs: adequate membrane hydration and avoidance of water flooding in the catalyst layer and/or gas diffusion layer. To ensure a fully hydrated membrane, fuel and oxidant (air) are preferred to be fully humidified before entering the fuel cell. However, under certain operating conditions, and especially at low temperatures, high humidification levels, and high current densities, the gases inside the fuel cell become oversaturated with water vapour and condensation may occur at the cathode side, resulting in reduced performance. Clearly, adequate understanding of water generation, transport and distribution within the PEM fuel cell is essential. Figure 1.8 schematically depicts water transport in a PEM fuel cell. Water is generated internally at the cathode catalyst–membrane interface as a result of oxygen reduction reaction, and is also supplied to the fuel cell by humidified reactant gases or by direct liquid hydration, represented by anode and cathode inlet relative humidity values. Through the membrane between the anode and the cathode, two modes of water transport occur: electro-osmotic drag transport and back-diffusion transport. The former drives the water migration from the anode to the cathode along with the protons, and the latter, caused by the concentration gradient of water across the membrane, drives the water flux towards the anode.

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Introduction

17

Figure 1.8. Water transport processes in an air-breathing PEM fuel cell.

The water flux due to the electro-osmotic drag effect is proportional to the protonic flux (I/F), and the back-diffusion flux is related to the water diffusion coefficient through the ionomer and the concentration gradient of water. In addition, a sufficient amount of water that is generated at the cathode must be transported away from the catalyst layer by evaporation, water–vapour diffusion and capillary transport of liquid water through the GDL into the outlet. If this does not occur, excess water exists at the cathode side and condenses, thus blocking the

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Maher A. R. Sadiq Al-Baghdadi

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pores of the GDL and reducing the active sites of the cathode catalyst layer. This phenomenon is known as “flooding”, and is an important limiting factor of PEM fuel cell performance (Figure 1.9). The extent of flooding and the effects of flooding depend upon the interaction of the operating conditions and the membrane electrode assembly properties. Generally, flooding of an electrode is linked to high current density operation that results in a water production rate that is higher than the removal rate. However, flooding can also occur even at low current densities under certain operating conditions, such as low temperatures and low gas flow rates, where faster saturation of the gas phase by water–vapour can occur. Therefore, water management is a critical design consideration for PEM fuel cell systems. The amount and disposition of water within the fuel cell strongly affects efficiency and reliability.

Figure 1.9. Schematic of flooding and drying in air-breathing PEM fuel cell.

An increasingly more prevalent driver of fuel cell development for portable devices is the ever-increasing energy density requirements of new consumer electronics, such as mobile phones, laptops, and camcorders. The fact that most

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Introduction

19

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electronic systems are continuously upgrading to more advanced systems of added functionalities, raises more doubts about whether they are capable of fulfilling the energy needs of this broad and important sector. Meanwhile, Air-Breathing Proton Exchange Membrane Fuel Cells are receiving more attention as a potential replacement and, in particular, for systems of high energy storage requirements. These passive type cells consume ambient air for their operation through natural free convection; as such, they eliminate the need for air-supply subsystems including compressor, humidifier and other components which minimise the Balance-Of-Plant (BOP) cost and complexity. Their hydrogen-supply subsystem can even be miniaturised by combining it with on-demand micro-hydrogen generator/galvanic cell. The envisaged implementation of PEM fuel cells for portable devices is in a device integrated form. This entails placing the fuel cell either on, or within portable electronics. For example, fuel cells can be mounted on the exterior surfaces of mobile phones, laptops, or camcorders as illustrated in Figure 1.10.

Figure 1.10. Illustration of an ambient air-breathing PEM fuel cell stack as a power source for a mobile phone, laptop, and camcorder. CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Maher A. R. Sadiq Al-Baghdadi

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The cathode gas diffusion layer is fed ambient air, rather than conditioned air through flow channels, and the fuel (hydrogen) is stored and distributed on the anode side of the fuel cell. One advantage of an air-breathing cathode is that it eliminates the need for manifolding. In addition, the open surface facilitates heat transfer from the fuel cell [19, 20].

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Chapter 2

2. CFD MODEL

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2.1. INTRODUCTION The small dimensions of the ambient air-breathing PEM fuel cells restrict the use of sensors to monitor the distribution of current density, species, and heat in different parts of the cell. Thus, modelling plays a significant and important role in analyzing the performance and transport phenomena in air-breathing PEM fuel cells. The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of fuel cells, the introduction of cheaper materials and fabrication techniques, and the design and development of novel architectures. The difficult experimental environment of fuel cell systems has stimulated efforts to develop models that could simulate and predict multi-dimensional coupled transport of reactants, heat, and charged species using Computational Fluid Dynamics (CFD) methods. The strength of the CFD numerical approach is it provides detailed insight into the various transport mechanisms and their interaction, and the possibility of performing sensitivity analyses of the parameters. Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat transfer, mass transfer, phase change, chemical reaction, mechanical movement, stress or deformation of related solid structures, and related phenomena by solving the mathematical equations that govern these processes using a numerical algorithm on a computer. The results of CFD analyses are relevant in: conceptual studies of new designs, detailed product development, troubleshooting, and redesign. CFD analysis complements testing and

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Maher A. R. Sadiq Al-Baghdadi

experimentation, by reduces the total effort required in the experiment design and data acquisition. CFD complements physical modelling and other experimental techniques by providing a detailed look into our fluid flow problems, including complex physical processes such as turbulence, chemical reactions, heat and mass transfer, and multiphase flows. In many cases, we can build and analyze virtual models at a fraction of the time and cost of physical modelling. This allows us to investigate more design options and "what if" scenarios than ever before. Moreover, flow modelling provides insights into our fluid flow problems that would be too costly or simply prohibitive by experimental techniques alone. The added insight and understanding gained from flow modelling gives us confidence in our design proposals, avoiding the added costs of over-sizing and over-specification, while reducing risk. Prior to setting up and running a CFD simulation there is a stage of identification and formulation of the problem in terms of the physical and chemical phenomena that need to be considered. For a given problem, you will need firstly to define your modelling goal, and create the domain for the problem (model's geometry). Analysis begins with a mathematical model of a physical problem, where the conservation of matter, momentum, and energy must be satisfied throughout the region of interest (specify governing equations). Fluid properties are modelled empirically, and a simplifying assumptions are made in order to make the problem tractable (e.g., steady-state, incompressible, inviscid, two-dimensional, etc.). Provide appropriate initial and boundary conditions for the problem. Domain is discretized into a finite set of control volumes or cells. The discretized domain is called the "grid" or the "mesh". All equations are solved simultaneously to provide solution. The solution is post-processed to extract quantities of interest. Examine the results and consider revisions to the model to ensure property conservation and correct physical behaviour. The flow diagram of the algorithm is shown in Figure 2.1. The CFD models can generally be characterized by the scope of the model. In many cases, modelling efforts focus on a specific part or parts of the fuel cell, such as the cathode catalyst layer, the cathode electrode [gas diffusion layer (GDL) plus catalyst layer], or the membrane electrode assembly (MEA). These models are very useful because they may include a large portion of the relevant fuel cell physics but at the same time having relatively short solution times. In other cases, modelling efforts focus on one important phenomenon in the fuel cell, such as transport mechanisms or heat transfer. However, these narrowly focused models neglect important parts of the fuel cell making it impossible to get a complete picture of the phenomena governing fuel cell behaviour.

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CFD Model

Figure 2.1. Flow diagram of the modelling procedure.

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Maher A. R. Sadiq Al-Baghdadi

Models that include all parts of a fuel cell are typically two- or threedimensional and reflect many of the physical processes occurring within the fuel cell. In a real PEM fuel cell geometry, the gas diffusion layers are used to enhance the reaction area accessible by the reactants. The effect of using these diffusion layers is to allow a spatial distribution in the current density on the membrane in both the direction of bulk flow and the direction orthogonal to the flow but parallel to the membrane. This two-dimensional distribution cannot be modelled with the well-used two-dimensional models where the mass-transport limitation is absent in the third direction. Comprehensive models rely on the determination of a large number of properties and operating parameters and can be much more computationally intensive, leading to longer solution times. However, these disadvantages are typically outweighed by the benefit of being able to assess the influence of a greater number of design parameters and their associated physical processes.

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2.2. MODEL DESCRIPTION The present work presents a comprehensive three–dimensional, multi–phase, non-isothermal CFD model of different novel designs of air-breathing PEM fuel cells that incorporates the significant physical processes and the key parameters affecting fuel cell performance. The following assumptions are made: (1) the fuel cell operates under steady–state conditions; (2) to alleviate the need for air distribution channels, along with the necessary pumps and fans, the cathode gas diffusion layer is in direct contact with the ambient air; (3) the ionic conductivity of the membrane is constant; (4) the membrane is impermeable to gases and cross-over of reactant gases is neglected; (5) the gas diffusion layer is homogeneous and isotropic; (6) the flow in the natural convection region is laminar. (7) the produced water is in the vapour phase; (8) two-phase flow inside the porous media; (9) both phases occupy a certain local volume fraction inside the porous media and their interaction is accounted for through a multi-fluid approach;

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CFD Model

25

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(10) external humidification systems are eliminated and the fuel cell relies on the ambient relative humidity and water production in the cathode for the humidification of the membrane; (11) the circulating ambient air facilitates the cooling of the fuel cell in lieu of a dedicated heat management system. The model accounts for both gas and liquid phase in the same computational domain, and thus allow for the implementation of phase change inside the gas diffusion layers (the porous cathode and anode diffusion layers). The model includes the transport of liquid water within the porous electrodes as well as the transport of gaseous species, protons, and energy. Water is assumed to be exchanged among two phases; liquid and vapour, and equilibrium among these phases is assumed. Water transport inside the porous gas diffusion layer and catalyst layer is described by two physical mechanisms: viscous drag and capillary pressure forces. Liquid water, created by the electrochemical reaction and condensation, is dragged along with the gas phase. At the cathode side, the humidity level of the incoming air determines whether this drag is directed into or out of the gas diffusion layer, whereas at the anode side this drag is always directed into the GDL. The capillary pressure gradient drives the liquid water out of the gas diffusion layers. Water transport across the membrane is also described by two physical mechanisms: electro-osmotic drag and diffusion. The balance between the electroosmotic drag of water from anode to cathode and back diffusion from cathode to anode yields the net water content through the membrane. The model reflects the influence of numerous parameters on fuel cell performance including geometry, materials, operating and others. The present multi-phase model is capable of identifying important parameters for the wetting behaviour of the gas diffusion layers and can be used to identify conditions that might lead to the onset of pore plugging, which has a detrimental effect of the fuel cell performance.

2.3. MODELLING EQUATIONS 2.3.1. Air and Fuel Flow In natural convection region, the transport equations solved in the ambient air include continuity, momentum, energy and mass transport equations. In the fuel channel, the gas-flow field is obtained by solving the steady-state Navier-Stokes

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26

equations, i.e. the continuity equation. The mass conservation equation for each phase yields the volume fraction (r ) and along with the momentum equations the pressure distribution inside the channel. The continuity equation for the gas phase inside the channel is given by [21];

(

)

∇ ⋅ rg ρ g u g = 0

(2.1)

and for the liquid water (liquid phase) inside the channel becomes;

∇ ⋅ (rl ρ l u l ) = 0

(2.2)

Two sets of momentum equations are solved in the channels, and they share the same pressure field;

Pg = Pl = P

(2.3)

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Under these conditions, it can be shown that the momentum equations becomes;

(

[ ( )]

)

2 ⎛ ⎞ ∇ ⋅ ρ g u g ⊗ u g − μ g ∇u g = −∇rg ⎜ P + μ g ∇ ⋅ u g ⎟ + ∇ ⋅ μ g ∇u g 3 ⎝ ⎠

T

(2.4)

and

[

2 ⎛ ⎞ ∇ ⋅ (ρ l u l ⊗ u l − μ l ∇u l ) = −∇rl ⎜ P + μ l ∇ ⋅ u l ⎟ + ∇ ⋅ μ l (∇u l )T 3 ⎝ ⎠

]

(2.5)

The mass balance is described by the divergence of the mass flux through diffusion and convection. Multiple species are considered in the gas phase only, and the species conservation equation in multi-component, multi-phase flow can be written in the following expression for species i; N ⎡ ∇M ⎞ ∇P ⎤ M ⎡⎛ − + ρ r y ⎜ ∇y j + y j ⎟+ xj − yj ⎢ g g i ∑ Dij ⎢ M j ⎣⎝ M ⎠ P ⎥⎦ j =1 ⎢ ∇⋅ ⎢ ∇T rg ρ g y i ⋅ u g + DiT ⎢ T ⎣

(

)

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

⎤ ⎥ ⎥=0 ⎥ ⎥ ⎦

(2.6)

CFD Model

27

where the subscript i denotes oxygen at the cathode side and hydrogen at the anode side, and j is water vapour in both case. Nitrogen is the third species at the cathode side. The Maxwell-Stefan diffusion coefficients of any two species are dependent on temperature and pressure. They can be calculated according to the empirical relation based on kinetic gas theory [22, 23];

Dij = 3.16 × 10

⎡ 1 1 ⎤ + ⎢ ⎥ 1 3 ⎤2 ⎢Mi M j ⎥⎦ ⎣ ⎛ ⎞ + ⎜⎜ ∑ Vkj ⎟⎟ ⎥ ⎝ k ⎠ ⎥⎦

T 1.75

−8

⎡⎛ ⎞ P ⎢⎜⎜ ∑ Vki ⎟⎟ ⎢⎝ k ⎠ ⎣

13

12

(2.7)

In this equation, pressure is in [atm] and the binary diffusion coefficient is in 2

[cm /s]. The values of the molar diffusion volumes,

(∑Vki ), are given by Fuller

et al. [24] as shown in Table 2.1.

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Table 2.1. Molar diffusion volumes of reactants

(∑Vki )

Species

Diffusion Volumes [m3/mole]

O2

16.6 × 10 −6

N2

17.9 × 10 −6

H2

12.7 × 10 −6

H 2O

7.07 × 10 −6

The temperature field is obtained by solving the convective energy equation;

( (

))

∇ ⋅ rg ρ g Cp g u g T − k g ∇T = 0

(2.8)

The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium; hence the temperature of the liquid water is the same as the gas phase temperature. The correlation for the gas viscosity of each species can be expressed as [25];

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(

)

μ i = A + B.T + C.T 2 × 10 −7

(2.9)

where A, B, and C are correlation constants of species i as shown in Table 2.2 [25]. Table 2.2. Constants for gas viscosity equation Species

A

B

C −2

− 187.9 × 10 −6

O2

18.11

66.32 × 10

N2

30.43

49.89 × 10 −2

− 109.3 × 10 −6

H2

21.87

22.20 × 10 −2

− 37.51 × 10 −6

H 2O

− 31.89

41.45 × 10 −2

− 8.272 × 10 −6

The Herning-Zipperer correlation [25] for the calculation of gas mixture viscosity is used in this work;

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n

μ=

∑ μ i .xi .(M i )0.5 i =1 n

(2.10)

∑ xi .(M i )

0.5

i =1

The correlation for the gas thermal conductivity of each species can be expressed as [25];

(

k i = 4.184 × 10 −4 A + B.T + C.T 2 + D.T 3

)

(2.11)

where A, B, C, and D are correlation constants of species i as shown in Table 2.3 [25]. The gas mixture thermal conductivity is calculated as follow; n

k = ∑ k i . yi i =1

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

(2.12)

CFD Model

29

Table 2.3. Constants for gas thermal conductivity equation Species

A

B

C

O2

− 0.7816

23.80 × 10

N2

0.9359

23.44 × 10 −2

− 1.21 × 10 −4

3.591 × 10 −8

H2

19.34

159.74 × 10 −2

− 9.93 × 10 −4

37.29 × 10 −8

H 2O

17.53

− 2.42 × 10 −2

4.3 × 10 −4

− 21.73 × 10 −8

−2

D

− 0.8939 × 10

2.324 × 10 −8

−4

The correlation for the gas specific heat capacity of each species can be expressed as [25];

Cpi =

(

4.1868 × 10 −3 A + B.T + C.T 2 + D.T 3 Mi

)

(2.13)

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where A, B, C, and D are correlation constant of species i as shown in Table 2.4 [25]; The specific heat capacity of the gas mixture is calculated as follow; n

Cp = ∑ Cpi . yi

(2.14)

i =1

Table 2.4. Constants for gas specific heat capacity equation Species

O2 N2 H2 H 2O

A

6.22 7.07 6.88 8.10

B

C −3

2.710 × 10 − 1.320 × 10 −3 − 0.022 × 10 −3 − 0.720 × 10 −3

− 0.37 × 10 3.31 × 10 −6 0.21 × 10 −6 3.63 × 10 −6

D −6

− 0.22 × 10 −9 − 1.26 × 10 −9 0.13 × 10 −9 − 1.16 × 10 −9

2.3.2. Gas Diffusion Layers The physics of multiple phases through a porous medium is further complicated here with phase change and the sources and sinks associated with the

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30

electrochemical reaction. The equations used to describe transport in the gas diffusion layers are given below. & phase > 0 and condensation Mass transfer in the form of evaporation m

(

)

(m& phase < 0) is assumed, so that the mass balance equations for both phases are

[26];

(

)

∇ ⋅ (1 − sat )ρ g εu g = m& phase

(2.15)

∇ ⋅ (sat.ρ l εu l ) = m& phase

(2.16)

and

The momentum equation for the gas phase reduces to Darcy’s law, which is, however, based on the relative permeability for the gas phase (KP ) . The relative

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

permeability accounts for the reduction in pore space available for one phase due to the existence of the second phase. The relative permeability for the gas phase is given by;

KPg = (1 − sat )KP

(2.17)

and for the liquid phase;

KPl = sat.KP

(2.18)

The momentum equation for the gas phase inside the gas diffusion layer becomes;

u g = −(1 − sat )

Kp

μg

∇P

(2.19)

Two liquid water transport mechanisms are considered; shear, which drags the liquid phase along with the gas phase in the direction of the pressure gradient, and capillary forces, which drive liquid water from high to low saturation regions [27, 28]. Starting from Darcy’s law, the following equation can write;

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

CFD Model

ul = −

Kpl

μl

31

∇Pl

(2.20)

where the liquid water pressure stems from the gas-phase pressure and the capillary pressure according to [29, 30];

∇Pl = ∇P − ∇Pc = ∇P −

∂Pc ∇sat ∂sat

(2.21)

Introducing this expression into Equation (2.20) yields a liquid water velocity field equation;

ul = −

KPl

μl

∇P +

KPl ∂Pc ∇sat μ l ∂sat

(2.22)

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The functional variation of capillary pressure with saturation is prescribed following Leverett [31] who has shown that;

⎛ ε ⎞ Pc = σ ⎜ ⎟ ⎝ KP ⎠

12

f (sat )

(2.23)

f (sat ) = 1.417(1 − sat ) − 2.12(1 − sat ) + 1.263(1 − sat ) (2.24) 2

3

The correlation for interfacial liquid/gas tension can be expressed as [25]; Z

(

⎛ T −T ⎞ ⎟⎟ 1 × 10 −3 σ = σ 1 ⎜⎜ c − T T ⎝ c 1⎠ where

σ 1 = 71.97

)

Tc = 647.35

(2.25)

T1 = 298.15

Z = 0.8105 .

The liquid phase consists of pure water, while the gas phase has multi components. The transport of each species in the gas phase is governed by a general convection-diffusion equation in conjunction which the Stefan-Maxwell equations to account for multi species diffusion, with the addition of a source term accounting for phase change [28-32];

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32

N ⎡ M ⎡⎛ ∇M ⎞ ∇P ⎤ ⎤ ⎢− (1 − sat )ρ g εy i ∑ Dij ⎢⎜ ∇y j + y j M ⎟ + x j − y j P ⎥ + ⎥ M ⎝ ⎠ ⎣ ⎦ ⎥ = m& j j = 1 ∇⋅⎢ phase ⎥ ⎢ ∇ (1 − sat )ρ g εyi ⋅ u g + εDiT T ⎥ ⎢ T ⎦ ⎣

(

)

(2.26)

where the subscript i denotes oxygen at the cathode side and hydrogen at the anode side, and j is water vapour in both cases. Nitrogen is the third species at the cathode side. In order to account for geometric constraints of the porous media, the diffusivities are corrected using the Bruggemann correction formula [33, 34].

Dijeff = Dij × ε 1.5

(2.27)

The heat transfer in the gas diffusion layers is governed by the energy equation as follows;

(

(

))

∇ ⋅ (1 − sat ) ρ g εCp g u g T − k eff , g ε∇T = εβ (Tsolid − T ) − εm& phase ΔH evap

(2.28)

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where the term ( εβ (Tsolid − T ) ), on the right hand side, accounts for the heat exchange to and from the solid matrix of the GDL. The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium, i.e., the liquid water and the gas phase are at the same temperature. The enthalpy of evaporation for water is calculated as follow [25]; Z

ΔH evap

⎛ T −T ⎞ ⎟⎟ × 4186.80 = ΔH evap,l ⎜⎜ c ⎝ Tc − T1 ⎠

where ΔH evap ,l = 538.7

Tc = 647.35

(2.29)

T1 = 373.15

Z = 0.38 .

The potential distribution in the gas diffusion layers is governed by;

∇ ⋅ (λe ∇φGDL ) = 0

(2.30)

Implementation of Phase Change In order to account for the magnitude of phase change inside the GDL, expressions are required to relate the level of over- and undersaturation as well as

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

CFD Model

33

the amount of liquid water present to the amount of water undergoing phase change. In the case of evaporation, such relations must be dependent on (i) the level of undersaturation of the gas phase in each control volume and on (ii) the surface area of the liquid water in the control volume. The surface area can be assumed proportional to the volume fraction of the liquid water in each cell. A plausible choice for the shape of the liquid water is droplets, especially since the catalyst area is Teflonated [35]. The evaporation rate of a droplet in a convective stream depends on the rate of undersaturation, the surface area of the liquid droplet, and a (diffusivity dependent) mass-transfer coefficient. The mass flux of water undergoing evaporation in each control volume can be represented by [16, 17];

m& evap = M H 2O ϖ N D k xm π Ddrop

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The bulk concentration

xw∞

x w 0 − x w∞ 1 − x w0

(2.31)

is known by solving the continuity equation of

water vapour. To obtain the concentration at the surface xw0 , it is reasonable to assume thermodynamic equilibrium between the liquid phase and the gas phase at the interface, i.e., the relative humidity of the gas in the immediate vicinity of the liquid is 100%. Under that condition, the surface concentration can be calculated based on the saturation pressure and is only a function of temperature. The heat-transfer coefficient for convection around a sphere is well established, and by invoking the analogy between convective heat and mass transfer, the following mass-transfer coefficient is obtained [16, 17];

k xm

⎛D v ρ cair DH 2O ⎡ ⎢2 + 0.6⎜ drop ∞ g = ⎜ Ddrop ⎢ μg ⎝ ⎣

⎞ ⎟ ⎟ ⎠

12

⎛ μg ⎜ ⎜ ρ g DH O 2 ⎝

⎞ ⎟ ⎟ ⎠

13⎤

⎥ ⎥ ⎦

(2.32)

D It is further assumed that all droplets have a specified diameter drop , and the number of droplets in each control volume is found by dividing the total volume of the liquid phase in each control volume by the volume of one droplet;

ND =

sat.Vcv 1 3 πDdrop 6

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(2.33)

Maher A. R. Sadiq Al-Baghdadi

34

In the case when the calculated relative humidity in a control volume exceeds 100%, condensation occurs and the evaporation term is switched off. The case of condensation is more complex, because it can occur on every solid surface area, but the rate of condensation can be different when it takes place on a wetted surface. In addition, the overall surface area in each control volume available for condensation shrinks with an increasing amount of liquid water present. Berning and Djilali [35] assumed that the rate of condensation depends only on the level of oversaturation of the gas phase multiplied by a condensation constant. Thus, the mass flux of water undergoing condensation in each control volume can be represented by;

m& cond = ϖ C

x w 0 − x w∞ 1 − x w0

(2.34)

The liquid water density is calculated as follow [25];

ρ l = 1 × 10 3. A.B −(1−(T −273.15 ) Tc ) Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

where A = 0.3471

B = 0.274

(2.35)

Tc = 374.2 o C .

The correlation for the liquid water viscosity can be expressed as [25];

−3

μ l = 1 × 10 .10 where A = −10.73

B ⎛ 2⎞ ⎜ A+ + CT + DT ⎟ T ⎝ ⎠

B = 1828

C = 1.966 × 10 −2

(2.36)

D = −14.66 × 10 −6 .

2.3.3. Catalyst Layers The catalyst layer is treated as a thin interface, where sink and source terms for the reactants are implemented. Due to the infinitesimal thickness, the source terms are actually implemented in the last grid cell of the porous medium. At the cathode side, the sink term for oxygen is given by;

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

CFD Model

M O2

S O2 = −

ic

4F

35

(2.37)

Whereas the sink term for hydrogen is specified as;

S H2 = −

M H2 2F

ia

(2.38)

The production of water is modelled as a source terms, and hence can be written as;

S H 2O =

M H 2O

ic

2F

(2.39)

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The generation of heat in the cell is due to entropy changes as well as irreversibilities due to the activation overpotential [36];

⎡ T (− Δs ) ⎤ q& = ⎢ + η act ,c ⎥ ic ⎦ ⎣ ne F

(2.40)

The local current density distribution in the cathode and anode catalyst layers is modelled by the Butler-Volmer equation [30-34];

⎛ CO ic = ioref,c ⎜ ref2 ⎜C ⎝ O2

⎞⎡ ⎛ α F ⎞ ⎛ α F ⎞⎤ ⎟ exp⎜ a η ⎟ + exp⎜ − c η act ,c ⎟⎥ (2.41) act , c ⎢ ⎟ ⎣ ⎝ RT ⎠ ⎝ RT ⎠⎦ ⎠

and

ia =

ioref,a

⎛ CH 2 ⎜ ⎜ C ref ⎝ H2

⎞ ⎟ ⎟ ⎠

12

⎡ ⎛αaF ⎞ ⎛ α F ⎞⎤ η act ,a ⎟ + exp⎜ − c η act ,a ⎟⎥ ⎢exp⎜ ⎠ ⎝ RT ⎠⎦ ⎣ ⎝ RT

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(2.42)

Maher A. R. Sadiq Al-Baghdadi

36

2.3.4. Membrane The balance between the electro-osmotic drag of water from anode to cathode and back diffusion from cathode to anode yields the net water flux through the membrane [30-34];

N W = n d M H 2O

i − ∇ ⋅ (ρDW ∇cW ) F

(2.43)

The water diffusivity in the polymer can be calculated as follow [36];

⎡ 1 ⎞⎤ ⎛ 1 − ⎟⎥ DW = 1.3 × 10 −10 exp ⎢2416⎜ ⎝ 303 T ⎠⎦ ⎣

(2.44)

The variable cW represents the number of water molecules per sulfonic acid −1

group (i.e. mol H 2 O equivalent SO3 ).The water content in the electrolyte

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phase is related to water vapour activity via [16, 17];

cW = 0.043 + 17.81a − 39.85a 2 + 36.0a 3

(0 < a ≤ 1)

cW = 14.0 + 1.4(a − 1)

(1 < a ≤ 3)

cW = 16.8

(a ≥ 3)

(2.45)

The water vapour activity given by;

a=

xW P Psat

(2.46)

Heat transfer in the membrane is governed by;

∇ ⋅ (k mem ⋅ ∇T ) = 0

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

(2.47)

CFD Model

37

The potential loss in the membrane is due to resistance to proton transport across membrane, and is governed by;

∇ ⋅ (λ m ∇φ mem ) = 0

(2.48)

2.3.5. Potential Drop across the Cell 2.3.5.1. Cell Potential Useful work (electrical energy) is obtained from a fuel cell only when a current is drawn, but the actual cell potential, Ecell, is decreased from its equilibrium thermodynamic potential, E, because of irreversible losses. The various irreversible loss mechanisms which are often called overpotentials, η , are defined as the deviation of the cell potential, Ecell, from the equilibrium thermodynamic potential E. The cell potential is obtained by subtracting all overpotentials (losses) from the equilibrium thermodynamic potential as the following expression;

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

E cell = E − η act − η ohm − η mem − η Diff

(2.49)

The equilibrium potential is determined using the Nernst equation [37];

( )

( )

1 ⎤ ⎡ E = 1.229 − 0.83 × 10 −3 (T − 298.15) + 4.308 × 10 −5 T ⎢ln PH 2 + ln PO2 ⎥ 2 ⎦ ⎣

(2.50)

2.3.5.2. Activation Overpotential Activation overpotential arises from the kinetics of charge transfer reaction across the electrode-electrolyte interface. In other words, a portion of the electrode potential is lost in driving the electron transfer reaction. Activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current. The activation overpotential can be divided into the anode and cathode overpotentials. The anode and cathode activation overpotentials are calculated from Butler-Volmer equation (2.41 and 2.42). 2.3.5.3. Ohmic Overpotential in Gas Diffusion Layers The potential loss due to current conduction through the anode and cathode gas diffusion layers can be modelled by equation (2.30).

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2.3.5.4. Membrane Overpotential The membrane overpotential is related to the fact that an electric field is necessary in order to maintain the motion of the hydrogen protons through the membrane. This field is provided by the existence of a potential gradient across the cell, which is directed in the opposite direction from the outer field that gives us the cell potential, and thus has to be subtracted. The overpotential in membrane is calculated from the potential equation (2.48). 2.3.5.5. Diffusion Overpotential Diffusion overpotential is caused by mass transfer limitations on the availability of the reactants near the electrodes. The electrode reactions require a constant supply of reactants in order to sustain the current flow. When the diffusion limitations reduce the availability of a reactant, part of the available reaction energy is used to drive the mass transfer, thus creating a corresponding loss in output voltage. Similar problems can develop if a reaction product accumulates near the electrode surface and obstructs the diffusion paths or dilutes the reactants. Mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes. The mass transport loss at the anode is negligible compared to that at the cathode. At the limiting current density, oxygen at the catalyst layer is depleted and no more current increase can be obtained from the fuel cell. This is responsible for the sharp decline in potential at high current densities. To reduce mass transport loss, the cathode is usually run at high pressure. The anode and cathode diffusion overpotentials are calculated from the following equations [1];

η Diff ,c =

i RT ⎛⎜ ln 1 − c ⎜ 2 F ⎝ i L ,c

⎞ ⎟ ⎟ ⎠

(2.51)

η Diff ,a =

i RT ⎛⎜ ln 1 − a 2 F ⎜⎝ i L,a

⎞ ⎟ ⎟ ⎠

(2.52)

i L ,c =

2 FDO2 CO2

δ GDL

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

(2.53)

CFD Model

i L ,a =

2 FDH 2 C H 2

39

(2.54)

δ GDL

The diffusivity of oxygen and hydrogen are calculated from the following equations [14]; 32

DO2

T ⎞ = 3.2 × 10 ⎜ ⎟ ⎝ 353 ⎠

32

DH 2

T ⎞ = 1.1 × 10 ⎜ ⎟ ⎝ 353 ⎠

−5 ⎛

−4 ⎛

⎛ 101325 ⎞ ⎟ ⎜ ⎝ P ⎠

(2.55)

⎛ 101325 ⎞ ⎟ ⎜ ⎝ P ⎠

(2.56)

2.3.6. Cell Power and Efficiency

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Once the cell potential is determined for a given current density, the output power density is found as [38];

Wcell = I .E cell

(2.57)

The thermodynamic efficiency of the cell can be determined as [39, 40];

E fc =

2 E cell F M H 2 .LHV H 2

(2.58)

2.4. SOLUTION ALGORITHM The solution begins by specifying a desired current density of the cell to be used for calculating the inlet flow rates at the anode and cathode sides. An initial guess of the activation overpotential is obtained from the desired current density using the Butler-Volmer equation. Then follows by computing the flow fields for velocities u,v,w, and pressure P. Once the flow field is obtained, the mass fraction equations are solved for the mass fractions of oxygen, hydrogen, water vapour, and nitrogen. Scalar equations are solved last in the sequence of the transport

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

40

Maher A. R. Sadiq Al-Baghdadi

equations for the temperature field in the cell and potential fields in the gas diffusion layers and the membrane. The local current densities are solved based on the Butler-Volmer equation. After the local current densities are obtained, the local activation overpotentials can be readily calculated from the Butler-Volmer equation. The local activation overpotentials are updated after each global iterative loop. Convergence criteria are then performed on each variable and the procedure is repeated until convergence. The properties and then source terms are updated after each global iterative loop based on the new local gas composition and temperature. Source terms reflect changes in the overall gas phase mass flow due to consumption or production of gas species via reaction and due to mass transfer between water in the vapour phase and water that is in the liquid phase (phase-change). The strength of the current model is clearly to perform parametric studies and explore the impact of various parameters on the transport mechanisms and on fuel cell performance. The new feature of the algorithm developed in this work is its capability for accurate calculation of the local activation overpotentials, which in turn results in improved prediction of the local current density distribution. The flow diagram of the algorithm is shown in Figure 2.2.

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

2.5. MODELLING PARAMETERS Choosing the right modelling parameters is important in establishing the base case validation of the model against experimental results. Since the fuel cell model that is presented in this chapter accounts for all basic transport phenomena simply by virtue of its three-dimensionality, a proper choice of the modelling parameters will make it possible to obtain good agreement with experimental results obtained from a real fuel cell. It is important to note that because this model accounts for all major transport processes and the modelling domain comprises all the elements of a complete cell, no parameters needed to be adjusted in order to obtain physical results. The operational parameters are based on the experimental operating conditions. These values are listed in Table 2.5. Electrode material properties have important impact on fuel cell performance. The base case values are taken from reference [1] and are listed in Table 2.6. The membrane properties are required to model various transport phenomena across the membrane. The values of Table 2.7 are taken from reference [1] and listed the membrane properties taken for the base case. The membrane type is Nafion 117®.

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CFD Model

41

Figure 2.2. Flow diagram of the solution procedure used.

Table 2.5. Operating conditions for base case Parameter

Symbol

Value

Unit

Air pressure (Cathode pressure)

Pc

1

atm

Fuel pressure (Anode pressure)

Pa

1

atm

Fuel stoichiometric flow ratio

ξa

2

-

Fuel cell temperature

Tcell

300.15

K

0.79/0.21

-

Inlet Oxygen/Nitrogen ratio

ψ

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Table 2.6. Electrode properties at base case conditions Parameter Electrode porosity

Symbol

ε

Value 0.4

Unit -

Electrode hydraulic permeability

kp e

1.7 × 10 −11

m2

Electrode thermal conductivity (Ballard AvCarb®-P150)

k eff

17.1223

W / m.K

Electrode electronic conductivity

λe

180

S /m

Transfer coefficient, anode side

αa

0.5

-

Transfer coefficient, cathode side

αc

1

-

Anode ref. exchange current density

ioref,a

1.0 × 10 3

A / m3

Cathode ref. exchange current density

ioref,c

3000

A / m3

Oxygen concentration parameter

γ O2

1

-

Hydrogen concentration parameter

γ H2

.5

-

Entropy change of cathode reaction

ΔS

-326.36

Heat transfer coefficient

β

4 × 10

Electrode density

ρ GDL

400

kg / m 3

Thermal expansion coefficient

℘GDL

− 0.8 × 10 −6

1/ K

Poisson's ratio

ℑGDL

0.25

-

Young's modulus

ΨGDL

1× 1010

Pa

J / mole.K 6

W / m3

2.6. BOUNDARY CONDITIONS Boundary conditions have to be applied for all variables of interest in computational domain. At the inlets of the gas-flow channel, the incoming velocity is calculated as a function of the desired current density and stoichiometric flow ratio. At the outlets, the pressure is prescribed for the momentum equation and a zero-gradient condition is imposed for all scalar equations.

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CFD Model

43

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Table 2.7. Membrane properties at base case conditions Parameter

Symbol

Value

Unit

Protonic diffusion coefficient

DH +

4.5 × 10 −9

m2 / s

Fixed-charge concentration

cf

1200

mole / m 3

Fixed-site charge

zf

-1

-

Electro-osmotic drag coefficient

nd

2.5

-

Membrane thermal conductivity

k mem

0.455

W / m.K

Membrane ionic conductivity (Nafion® 117)

λm

17.1223

S /m

Membrane hydraulic permeability

kp m

7.04 ×10 −11

m2

Membrane density

ρ mem

2000

kg / m 3

Thermal expansion coefficient

℘mem

123 ×10 −6

1/ K

Swelling expansion coefficient

D mem

23 ×10 −4

-

Poisson's ratio

ℑ mem

0.25

-

Young's modulus

Ψmem

249×106

Pa

At the external surfaces of the cell, the convective heat transfer flux is applied. Combinations of Dirichlet and Neumann boundary conditions are used to solve the electronic and protonic potential equations. Dirichlet boundary conditions are applied at the cathode and anode current collectors. Neumann boundary conditions are applied at the interface between the gas inlet surfaces and the gas diffusion layers to give zero potential flux into the gas inlet surfaces. Similarly, the protonic potential field requires a set of potential boundary condition and zero flux boundary condition at the anode catalyst layer interface and cathode catalyst layer interface respectively.

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Chapter 3

3. PLANAR AIR-BREATHING PEM FUEL CELL 3.1. INTRODUCTION

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Planar cell design could be advantageous especially in applications where the area of the power source is not limited, but the thickness is the critical factor. One advantage of the planar air-breathing PEM fuel cell is that it eliminates the need for manifolding. In addition, the open surface facilitates heat transfer from the fuel cell.

3.2. MODELLING DOMAIN AND GEOMETRY The full computational domain for the planar air-breathing PEM fuel cell consists of anode gas flow field and the membrane electrode assembly is shown in Figure 3.1. Table 3.1 shows the dimensions of the computational domain. A schematic description of a planer air-breathing PEM fuel cell stack is shown in Figure 3.2. The cathode side of the cell is directly open to ambient air. The oxygen needed by the fuel cell reaction is transferred by natural convection and diffusion through the gas diffusion backing into the cathode electrode. The perforated current collector plate on the cathode side is used in order to ensure good mechanical, thermal, and electrical contact between the central parts of the gas diffusion backing and MEA.

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Table 3.1. Cell dimensions Parameter

Symbol

Value

Unit

Cell length

L

50 × 10 −3

m

Cell height

H

1.75 × 10 −3

m

Cell width

W

2 × 10 −3

m

Hydrogen channel height

HH2

1 × 10 −3

m

Hydrogen channel width

WH2

1 × 10 −3

m

Land area width

Wland

1 × 10 −3

m

Electrode thickness (GDL)

δ GDL

0.26 × 10 −3

m

Catalyst layer thickness

δ CL

0.0287 × 10 −3

m

Membrane thickness

δ mem

0.23 × 10 −3

m

Figure 3.1. Three-dimensional computational domain of the planar air-breathing PEM fuel cell.

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47

Figure 3.2. Longitudinal cross section of 3-cells fuel cell stack.

3.3. COMPUTATIONAL PROCEDURE The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent numerical tests were performed to ensure that the solutions were independent of the grid size. A computational quadratic finer mesh consisting of a total of 17801 meshes ware found to provide sufficient spatial resolution (Figure 3.3). The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

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Figure 3.3. Computational mesh of the planar air-breathing PEM fuel cell (quadratic).

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3.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

3.4.1. Velocity Profile The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multicomponent, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 3.4 and 3.5 for both gas and

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liquid phase. The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL.

Figure 3.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2.

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While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell. The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the currentcollector/GDL interface.

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3.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 3.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen. The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of oxygen at the ends of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

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Planar Air-Breathing PEM Fuel Cell

Figure 3.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

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Figure 3.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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3.4.3. Hydrogen Distribution

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The hydrogen mass fraction distribution in the anode side is shown in Figure 3.7 for two different nominal current densities. In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. The decrease in mass concentration of the hydrogen across the anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

Figure 3.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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3.4.4. Current Density Distribution

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Figure 3.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities.

Figure 3.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to under-utilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

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3.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment. Figure 3.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities. The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

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Figure 3.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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3.4.6. Activation Overpotential Distribution

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The variation of the cathode activation overpotentials (in V) is shown in Figure 3.10.

Figure 3.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 3.11. It can be seen that the anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials. It can be seen from the Figures 3.10 and 3.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

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3.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 3.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

3.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 3.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller

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gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

Figure 3.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 3.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 3.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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3.4.9. Diffusion Overpotential Distribution

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The variation of the cathode diffusion overpotentials (in V) is shown in Figure 3.14.

Figure 3.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Figure 3.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the diffusion overpotential profile correlates with the local

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current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode diffusion overpotentials (in V) is shown in Figure 3.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials. In addition, it can be seen from Figure 3.14 and Figure 3.15 that the mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

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Chapter 4

4. PLANAR MICRO-STRUCTURED AIRBREATHING PEM FUEL CELL

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4.1. INTRODUCTION The viability of proton exchange membrane (PEM) fuel cells as battery replacements requires that PEM fuel cells undergo significant miniaturization while achieving higher power densities. This presents challenges for small scale and micro-fuel cells in terms of design, materials, effective transport of reactants, and heat management. The planar micro-structured air-breathing PEM fuel cell employs a micro-structured arrangement that enables an active area greater than the planar fuel cell area.

4.2. MODELLING DOMAIN AND GEOMETRY The full computational domain for the planar micro-structured air-breathing PEM fuel cell consists of anode gas flow field and the membrane electrode assembly (MEA) is shown in Figure 4.1. Table 4.1 shows the dimensions of the computational domain. A schematic description of a planar micro-structured airbreathing PEM fuel cell stack is shown in Figure 4.2. The cathode of the cell is directly open to ambient air. The oxygen needed by the fuel cell reaction is transferred by natural convection and diffusion through the gas diffusion backing into the cathode electrode. It breathes the fresh air and routes out the electric current through solid bipolar plate. The hydrogen accesses to the anode are directly through the anode gas diffusion layers.

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Table 4.1. Cell dimensions Parameter

Symbol

Value

Unit

Cell length

L

50 × 10 −3

m

Cell height

H

0.75 × 10 −3

m

Cell width

W

1.5 × 10 −3

m

Electrode thickness (GDL)

δ GDL

0.26 × 10 −3

m

Catalyst layer thickness

δ CL

0.0287 × 10 −3

m

Membrane thickness

δ mem

0.23 × 10 −3

m

Figure 4.1. Three-dimensional computational domain of the planar micro-structured airbreathing PEM fuel cell.

The design can achieve much higher active area to volume ratios, and hence higher volumetric power densities. In this new design, the MEA played an additional function by forming the channels that distribute the fuel and oxidant. Thus, the volume that previously comprised the flow channels could support additional active area and generate increased volumetric power density.

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Figure 4.2. Longitudinal cross section of 3-cells fuel cell stack.

Such fuel cells have the potential to be significantly cheaper, smaller, and lighter than planar plate and frame fuel cells; they could also broaden the range of fuel cell applications.

4.3. COMPUTATIONAL PROCEDURE The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent

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numerical tests were performed to ensure that the solutions were independent of the grid size. A computational quadratic finer mesh consisting of a total of 15814 meshes ware found to provide sufficient spatial resolution (Figure 4.3).

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Figure 4.3. Computational mesh of the planar micro-structured air-breathing PEM fuel cell (quadratic).

The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

4.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

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4.4.1. Velocity Profile

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The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multicomponent, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 4.4 and 4.5 for both gas and liquid phase. The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL. While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell.

Figure 4.4. (Continued).

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Figure 4.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2.

The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the current-collector/GDL interface.

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Figure 4.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

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4.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 4.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen. The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of oxygen at the end of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

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Figure 4.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

4.4.3. Hydrogen Distribution The hydrogen mass fraction distribution in the anode side is shown in Figure 4.7 for two different nominal current densities.

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Figure 4.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. The decrease in mass concentration of the hydrogen across the

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anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

4.4.4. Current Density Distribution

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Figure 4.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities. The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to under-utilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a nonuniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

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Figure 4.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

4.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. Figure 4.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities. The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

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Figure 4.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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4.4.6. Activation Overpotential Distribution

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The variation of the cathode activation overpotentials (in V) is shown in Figure 4.10. For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area.

Figure 4.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 4.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 4.11. It can be seen that the

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anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials. It can be seen from the Figures 4.10 and 4.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

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4.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 4.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

4.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 4.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

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Figure 4.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 4.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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4.4.9. Diffusion Overpotential Distribution

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The variation of the cathode diffusion overpotentials (in V) is shown in Figure 4.14. For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the diffusion overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode diffusion overpotentials (in V) is shown in Figure 4.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials. In addition, it can be seen from Figure 4.14 and Figure 4.15 that the mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

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Figure 4.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

Figure 4.15. (Continued).

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Figure 4.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Chapter 5

5. PLANAR COMPACTED-DESIGN MICROSTRUCTURED AIR-BREATHING PEM FUEL CELL

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5.1. INTRODUCTION In small-scale applications, the fuel cell should be exceptionally small and have highest energy density. One way to achieve these requirements is to reduce the thickness of the cell (compacted-design) for increasing the volumetric power density of a fuel cell power supply. The planar compacted-design microstructured air-breathing PEM fuel cell employs a compacted-design (smallest cell thickness) that enables an active area greatest than the planar fuel cell area.

5.2. MODELLING DOMAIN AND GEOMETRY The full computational domain for the planar compacted-design microstructured air-breathing PEM fuel cell consists of anode gas flow field and the membrane electrode assembly (MEA) is shown in Figure 5.1. Table 5.1 shows the dimensions of the computational domain. A schematic description of a planar compacted-design micro-structured airbreathing PEM fuel cell stack is shown in Figure 5.2. The cathode of the cell is directly open to ambient air. The oxygen needed by the fuel cell reaction is transferred by natural convection and diffusion through the gas diffusion backing into the cathode electrode. It breathes the fresh air and routes out the electric current through solid bipolar plate. The hydrogen accesses to the anode are directly through the anode gas diffusion layers.

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Table 5.1. Cell dimensions Parameter

Symbol

Value

Unit

Cell length

L

50 × 10 −3

m

Cell height

H

0.49 × 10 −3

m

Cell width

W

1.5 × 10 −3

m

Electrode thickness (GDL)

δ GDL

0.26 × 10 −3

m

Catalyst layer thickness

δ CL

0.0287 × 10 −3

m

Membrane thickness

δ mem

0.23 × 10 −3

m

Figure 5.1. Three-dimensional computational domain of the planar compacted-design micro-structured air-breathing PEM fuel cell.

The design can achieve much higher active area to volume ratios, and hence very higher volumetric power densities. In this novel design, the MEA played an additional function by forming the channels that distribute the fuel and oxidant. Thus, the volume that previously comprised the flow channels could support additional active area and generate increased volumetric power density.

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Figure 5.2. Longitudinal cross section of 3-cells fuel cell stack.

The height of the gas diffusion layers (GDLs) decreases along the main flow direction and this leads to improving the gases flow and diffusion through the porous layers, and hence improving the cell performance, furthermore achieve greatly higher active area to volume ratios. Such fuel cells have the potential to be significantly cheaper, very smaller, and lighter than planar micro-structured fuel cells; they could also broaden the range of fuel cell applications.

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5.3. COMPUTATIONAL PROCEDURE

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The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent numerical tests were performed to ensure that the solutions were independent of the grid size. A computational quadratic finer mesh consisting of a total of 12568 meshes ware found to provide sufficient spatial resolution (Figure 5.3). The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

Figure 5.3. Computational mesh of the planar compacted-design micro-structured airbreathing PEM fuel cell (quadratic).

5.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These

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transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

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5.4.1. Velocity Profile The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multicomponent, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 5.4 and 5.5 for both gas and liquid phase. The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL. While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell.

Figure 5.4. (Continued).

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Figure 5.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2.

The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the current-collector/GDL interface.

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Figure 5.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

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5.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 5.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen. The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of oxygen at the end of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities.

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Figure 5.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

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5.4.3. Hydrogen Distribution

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The hydrogen mass fraction distribution in the anode side is shown in Figure 5.7 for two different nominal current densities.

Figure 5.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. The decrease in mass concentration of the hydrogen across the anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

5.4.4. Current Density Distribution

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Figure 5.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities. The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to under-utilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

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Figure 5.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

5.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment. Figure 5.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities. The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is highest.

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Figure 5.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

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5.4.6. Activation Overpotential Distribution

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The variation of the cathode activation overpotentials (in V) is shown in Figure 5.10.

Figure 5.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 5.11.

Figure 5.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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It can be seen that the anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials. It can be seen from the Figures 5.10 and 5.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

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5.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 5.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

Figure 5.12. (Continued).

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Figure 5.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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5.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 5.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

5.4.9. Diffusion Overpotential Distribution The variation of the cathode diffusion overpotentials (in V) is shown in Figure 5.14. For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area.

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Figure 5.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

It can be seen that the diffusion overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations.

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Figure 5.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

The variation of the anode diffusion overpotentials (in V) is shown in Figure 5.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials.

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Figure 5.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

In addition, it can be seen from Figure 5.14 and Figure 5.15 that the mass transport loss becomes significant when the fuel cell is operated at high current

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density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

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5.5. MICRO-SCALE FUEL CELLS The presence of microelectromechanical system (MEMS) technology makes it possible to manufacture the miniaturized fuel cell systems for application in portable electronic devices. The majority of research on micro-scale fuel cells is aimed at micro-power applications. There are many new miniaturized applications which can only be realized if a higher energy density power source is available compared to button cells and other small batteries. Miniaturization down to these dimensions is not possible with conventional design of fuel cell stack technology. Using new technologies and designs it should be possible to significantly improve fuel cell performance when micro-scale phenomena are exploited. However, such benefits can only be realized if the fuel cell devices can be fabricated using available manufacturing techniques. They are in most cases adapted from semiconductor and micro-systems technology. Fuel cells built to exploit micro-scale phenomena would be smaller, make better use of volume and could obtain improved heat and mass transfer.

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Chapter 6

6. TUBULAR AIR-BREATHING PEM FUEL CELL

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6.1. INTRODUCTION The oxygen transport limitation plays a great role in the performance of airbreathing fuel cells. The current production by electrochemical reaction is directly proportional to the local oxygen concentration in the fuel cell. Inadequate airflow in the planar air-breathing PEM fuel cell cannot provide enough oxygen for the electrochemical reaction on the active surfaces under the land areas. It results in heterogeneous current distribution in the electrode that reduces the performance of the fuel cell. Thus, one of the greater challenges in the design of passive fuel cells is how to provide enough oxygen for the electrochemical reaction on the entire active surface. One of the new architectures in PEM fuel cell design is a tubular-shaped fuel cell. There are several reasons that make the tubular design more advantageous than the planar one for medium to high power stacks: (i) elimination of the flow field: lower pressure drop at the anode fields and no time-consuming machinery due to shorter flow fields, (ii) uniform pressure applied to the MEA by the cathode, (iii) quicker response when switching from fuel cell mode to electrolyser mode in a unitized regenerative fuel cell, (iv) greater cathode surface that increases the amount of oxygen reduction, the rate of which is slower than the hydrogen oxidation rate. In addition, (v) tubular designs can achieve much higher active area to volume ratios, and hence higher volumetric power densities.

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6.2. MODELLING DOMAIN AND GEOMETRY The full computational domain for the tubular-shaped air-breathing PEM fuel cell consists of anode gas flow field and the membrane electrode assembly (MEA) is shown in Figure 6.1. Table 6.1 shows the dimensions of the computational domain. Table 6.1. Cell dimensions Parameter Cell length Cell width

Symbol L W

Hydrogen channel diameter

DH2

Electrode thickness (GDL)

δ GDL

Catalyst layer thickness

δ CL δ mem

3 × 10 −3 1× 10 −3 0.26 × 10 −3 0.0287 × 10 −3 0.23 × 10 −3

Unit

m m m m m m

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Membrane thickness

Value 50 ×10 −3

Figure 6.1. Three-dimensional computational domain of the tubular-shaped air-breathing PEM fuel cell.

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Figure 6.2. Longitudinal cross section of 3-cells fuel cell stack.

The porous cathode is attached to a perforated current collector. It breathes the fresh air through the perforations and routes out the electric current through its solid counterpart. Hydrogen access to the anode is through the perforated tubular former anode current collector. The design had to allow for tabs to be used as electrical connectors from the cathode band of one cell to the anode tube of the next cell, in order to build stacks with practical voltages. The nickel foil anode current collector was marginally wider than the MEA which allowed electrical connections to the neighbouring cell to be made, see Figure 6.2.

6.3. COMPUTATIONAL PROCEDURE The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent numerical tests were performed to ensure that the solutions were independent of

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the grid size. A computational quadratic finer mesh consisting of a total of 39658 meshes ware found to provide sufficient spatial resolution (Figure 6.3). The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

Figure 6.3. Computational mesh of the tubular-shaped air-breathing PEM fuel cell (quadratic).

6.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These

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transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

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6.4.1. Velocity Profile The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multicomponent, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 6.4 and 6.5 for both gas and liquid phase. The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL. While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell. The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the current-collector/GDL interface.

6.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 6.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen.

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Figure 6.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2.

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Figure 6.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

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Figure 6.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of oxygen at the end of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

6.4.3. Hydrogen Distribution

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The hydrogen mass fraction distribution in the anode side is shown in Figure 6.7 for two different nominal current densities. In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. The decrease in mass concentration of the hydrogen across the anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

6.4.4. Current Density Distribution Figure 6.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities. The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to under-utilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a nonuniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

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Figure 6.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Figure 6.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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6.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment. Figure 6.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities. The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

6.4.6. Activation Overpotential Distribution The variation of the cathode activation overpotentials (in V) is shown in Figure 6.10. For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 6.11. It can be seen that the anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials. It can be seen from the Figures 6.10 and 6.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

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Figure 6.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Figure 6.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 6.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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6.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 6.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

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6.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 6.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

6.4.9. Diffusion Overpotential Distribution The variation of the cathode diffusion overpotentials (in V) is shown in Figure 6.14. For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the diffusion overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode diffusion overpotentials (in V) is shown in Figure 6.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials.

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Figure 6.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 6.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 6.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Figure 6.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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In addition, it can be seen from Figure 6.14 and Figure 6.15 that the mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

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Chapter 7

7. TUBULAR MICRO-STRUCTURED AIRBREATHING PEM FUEL CELL

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7.1. INTRODUCTION The viability of proton exchange membrane (PEM) fuel cells as battery replacements requires that PEM fuel cells undergo significant miniaturization while achieving higher power densities. This presents challenges for small scale and micro-fuel cells in terms of design, materials, effective transport of reactants, and heat management. The tubular-shaped micro-structured air-breathing PEM fuel cell employs a microstructured arrangement that enables an active area greater than the tubular fuel cell area.

7.2. MODELLING DOMAIN AND GEOMETRY A schematic description of a tubular-shaped micro-structured air-breathing PEM fuel cell is shown in Figure 7.1. The cathode of the cell is directly open to ambient air. The oxygen needed by the fuel cell reaction is transferred by natural convection and diffusion through the gas diffusion backing into the cathode electrode. It breathes the fresh air and routes out the electric current through solid rings. The hydrogen accesses to the anode are through six micro-channels. The tubular-shaped micro-structured air-breathing PEM fuel cell design can achieve much higher active area to volume ratios, and hence higher volumetric power densities. A computational model of an entire cell would require very large computing resources and excessively long simulation times. The computational domain in

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this study is therefore limited to one straight flow channel. The full computational domain consists of anode gas flow field, and the membrane electrode assembly (MEA) is shown in Figure 7.2. Table 7.1 shows the dimensions of the computational domain. Table 7.1. Cell dimensions Parameter Cell length Cell width

Symbol L W

Hydrogen channel diameter

DH2

Electrode thickness (GDL)

δ GDL

Catalyst layer thickness

δ CL δ mem

−3

3 × 10 1× 10 −3 0.26 × 10 −3 0.0287 × 10 −3 0.23 × 10 −3

Unit

m m m m m m

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Membrane thickness

Value 50 ×10 −3

Figure 7.1. Schematic of the tubular-shaped micro-structured air-breathing PEM fuel cell.

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Figure 7.2. Three-dimensional computational domain of the tubular-shaped microstructured air-breathing PEM fuel cell.

7.3. COMPUTATIONAL PROCEDURE The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent numerical tests were performed to ensure that the solutions were independent of the grid size. A computational quadratic finer mesh consisting of a total of 48358 meshes ware found to provide sufficient spatial resolution (Figure 7.3). The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

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Figure 7.3. Computational mesh of the tubular-shaped micro-structured air-breathing PEM fuel cell (quadratic).

7.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

7.4.1. Velocity Profile The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multicomponent, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase

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velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 7.4 and 7.5 for both gas and liquid phase.

Figure 7.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2.

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Figure 7.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

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The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL. While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell. The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the currentcollector/GDL interface.

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7.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 7.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen. The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of oxygen at the end of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

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Figure 7.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

7.4.3. Hydrogen Distribution The hydrogen mass fraction distribution in the anode side is shown in Figure 7.7 for two different nominal current densities.

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Figure 7.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. The decrease in mass concentration of the hydrogen across the anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

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7.4.4. Current Density Distribution

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Figure 7.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities.

Figure 7.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to under-utilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

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7.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment. Figure 7.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities. The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

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Figure 7.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

7.4.6. Activation Overpotential Distribution The variation of the cathode activation overpotentials (in V) is shown in Figure 7.10.

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Figure 7.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area

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and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 7.11. It can be seen that the anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials.

Figure 7.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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It can be seen from the Figures 7.10 and 7.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

7.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 7.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

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7.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 7.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

7.4.9. Diffusion Overpotential Distribution The variation of the cathode diffusion overpotentials (in V) is shown in Figure 7.14. For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the diffusion overpotential profile correlates

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with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations.

Figure 7.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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The variation of the anode diffusion overpotentials (in V) is shown in Figure 7.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials.

Figure 7.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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In addition, it can be seen from Figure 7.14 and Figure 7.15 that the mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

Figure 7.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 7.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

7.5. MICRO-SCALE FUEL CELLS The presence of microelectromechanical system (MEMS) technology makes it possible to manufacture the miniaturized fuel cell systems for application in portable electronic devices.

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The majority of research on micro-scale fuel cells is aimed at micro-power applications. There are many new miniaturized applications which can only be realized if a higher energy density power source is available compared to button cells and other small batteries. Miniaturization down to these dimensions is not possible with conventional design of fuel cell stack technology. Using new technologies and designs it should be possible to significantly improve fuel cell performance when micro-scale phenomena are exploited. However, such benefits can only be realized if the fuel cell devices can be fabricated using available manufacturing techniques. They are in most cases adapted from semiconductor and micro-systems technology. Fuel cells built to exploit micro-scale phenomena would be smaller, make better use of volume and could obtain improved heat and mass transfer.

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Chapter 8

8. TUBULAR COMPACTED-DESIGN MICROSTRUCTURED AIR-BREATHING PEM FUEL CELL

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8.1. INTRODUCTION In small-scale applications, the fuel cell should be small and have high energy density. One way to achieve these requirements in tubular design is to use the compacted-design for increasing the volumetric power density of a fuel cell power supply. The tubular-shaped compacted-design micro-structured air-breathing PEM fuel cell employs a compacted-design that enables an active area greatest than the tubular micro-structured fuel cell area.

8.2. MODELLING DOMAIN AND GEOMETRY A schematic description of a tubular-shaped compacted-design microstructured air-breathing PEM fuel cell is shown in Figure 8.1. It consists from eight sections. Each section represents a unit cell. The cathode of the cell is directly open to ambient air. The oxygen needed by the fuel cell reaction is transferred by natural convection and diffusion through the gas diffusion backing into the cathode electrode. It breathes the fresh air and routes out the electric current through solid bipolar plate. The hydrogen accesses to the anode are directly through the anode gas diffusion layers. A computational model of an entire cell would require very large computing resources and excessively long simulation times. The computational domain in this study is therefore limited to one cell.

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Figure 8.1. Schematic of the tubular-shaped compacted-design micro-structured airbreathing PEM fuel cell.

The full computational domain consists of anode gas flow field, and the MEA is shown in Figure 8.2. Table 8.1 shows the dimensions of the computational domain. The design can achieve much higher active area to volume ratios, and hence very higher volumetric power densities. In this novel design, the MEA played an additional function by forming the channels that distribute the fuel and oxidant. Thus, the volume that previously comprised the flow channels could support additional active area and generate increased volumetric power density. The height of the cathode gas diffusion layer decreases along the main flow direction and this leads to improving the gases flow and diffusion through the porous layers, and hence improving the cell performance, furthermore achieve greatly higher active area to volume ratios. Such fuel cells have the potential to be significantly cheaper, very smaller, and lighter than planar and tubular microstructured fuel cells; they could also broaden the range of fuel cell applications.

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Table 8.1. Cell dimensions Parameter Cell length

Symbol L

Value

Cell width

W

3.4 × 10 −3

Hydrogen channel diameter

DH2

Electrode thickness (GDL)

δ GDL

1× 10 −3 0.26 × 10 −3

m m m m

Catalyst layer thickness

δ CL

0.0287 × 10 −3

m

Membrane thickness

δ mem

0.23 × 10 −3

m

50 ×10

Unit −3

Figure 8.2. Three-dimensional computational domain of the tubular-shaped compacteddesign micro-structured air-breathing PEM fuel cell.

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8.3. COMPUTATIONAL PROCEDURE

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The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent numerical tests were performed to ensure that the solutions were independent of the grid size. A computational quadratic finer mesh consisting of a total of 18112 meshes ware found to provide sufficient spatial resolution (Figure 8.3). The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

Figure 8.3. Computational mesh of the tubular-shaped micro-structured air-breathing PEM fuel cell (quadratic).

8.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These

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transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

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8.4.1. Velocity Profile The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multicomponent, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 8.4 and 8.5 for both gas and liquid phase. The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL. While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell. The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the currentcollector/GDL interface.

8.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 8.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen.

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Figure 8.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2.

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Figure 8.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

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Figure 8.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of

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oxygen at the end of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

8.4.3. Hydrogen Distribution

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The hydrogen mass fraction distribution in the anode side is shown in Figure 8.7 for two different nominal current densities. In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. The decrease in mass concentration of the hydrogen across the anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

8.4.4. Current Density Distribution Figure 8.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities. The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to underutilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

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Figure 8.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 8.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

8.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and

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excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment. Figure 8.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities. The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

8.4.6. Activation Overpotential Distribution The variation of the cathode activation overpotentials (in V) is shown in Figure 8.10. For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 8.11. It can be seen that the anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials. It can be seen from the Figures 8.10 and 8.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

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Figure 8.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 8.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 8.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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8.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 8.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

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8.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 8.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

8.4.9. Diffusion Overpotential Distribution The variation of the cathode diffusion overpotentials (in V) is shown in Figure 8.14. For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the diffusion overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode diffusion overpotentials (in V) is shown in Figure 8.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials.

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Figure 8.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

In addition, it can be seen from Figure 8.14 and Figure 8.15 that the mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

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Figure 8.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 8.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 8.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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8.5. MICRO-SCALE FUEL CELLS

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The presence of microelectromechanical system (MEMS) technology makes it possible to manufacture the miniaturized fuel cell systems for application in portable electronic devices. The majority of research on micro-scale fuel cells is aimed at micro-power applications. There are many new miniaturized applications which can only be realized if a higher energy density power source is available compared to button cells and other small batteries. Miniaturization down to these dimensions is not possible with conventional design of fuel cell stack technology. Using new technologies and designs it should be possible to significantly improve fuel cell performance when micro-scale phenomena are exploited. However, such benefits can only be realized if the fuel cell devices can be fabricated using available manufacturing techniques. They are in most cases adapted from semiconductor and micro-systems technology. Fuel cells built to exploit micro-scale phenomena would be smaller, make better use of volume and could obtain improved heat and mass transfer.

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Chapter 9

9. DISK-SHAPED MICRO-STRUCTURED AIRBREATHING PEM FUEL CELL

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9.1. INTRODUCTION Disk cell design could be advantageous especially in applications where the area of the power source is not limited, but the thickness (cell length) is the critical factor. The advantages of the disk-shaped micro-structured air-breathing PEM fuel cell are that it eliminates the need for manifolding, smallest height, and much higher active area to volume ratios, and hence higher volumetric power densities.

9.2. MODELLING DOMAIN AND GEOMETRY The full computational domain for the disk-shaped micro-structured airbreathing PEM fuel cell consists of anode gas flow field and the membrane electrode assembly (MEA) is shown in Figure 9.1. Table 9.1 shows the dimensions of the computational domain. A schematic description of the diskshaped micro-structured air-breathing PEM fuel cell stack is shown in Figure 9.2. The cathode of the cell is directly open to ambient air. The oxygen needed by the fuel cell reaction is transferred by natural convection and diffusion through the gas diffusion backing into the cathode electrode. It breathes the fresh air and routes out the electric current through solid bipolar plate. The hydrogen accesses to the anode are directly through the anode gas diffusion layers.

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Parameter Cell length

Symbol L

Value

Cell width

W

3 × 10 −3

Hydrogen channel diameter

DH2

Electrode thickness (GDL)

δ GDL

1× 10 −3 0.26 × 10 −3

m m m

Catalyst layer thickness

δ CL

0.0287 × 10 −3

m

Membrane thickness

δ mem

0.23 × 10 −3

m

m

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0.75 × 10 −3

Unit

Figure 9.1. Three-dimensional computational domain of the disk-shaped micro-structured air-breathing PEM fuel cell.

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Figure 9.2. Longitudinal cross section of 3-cells fuel cell stack.

The design can achieve much higher active area to volume ratios, and hence very higher volumetric power densities. In this novel design, the MEA played an additional function by forming the channels that distribute the fuel and oxidant. Thus, the volume that previously comprised the flow channels could support additional active area and generate increased volumetric power density. Such fuel cells have the potential to be significantly cheaper, very smaller, and lighter than planer and tubular micro-structured fuel cells; they could also broaden the range of fuel cell applications.

9.3. COMPUTATIONAL PROCEDURE The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent numerical tests were performed to ensure that the solutions were independent of

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the grid size. A computational quadratic finer mesh consisting of a total of 17298 meshes ware found to provide sufficient spatial resolution (Figure 9.3).

Figure 9.3. Computational mesh of the disk-shaped micro-structured air-breathing PEM fuel cell (quadratic).

The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

9.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

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9.4.1. Velocity Profile

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The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multicomponent, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 9.4 and 9.5 for both gas and liquid phase. The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL. While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell. The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the current-collector/GDL interface.

Figure 9.4. (Continued).

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Figure 9.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2.

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Figure 9.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

9.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 9.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen. The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of oxygen at the end of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities.

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Figure 9.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

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9.4.3. Hydrogen Distribution

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The hydrogen mass fraction distribution in the anode side is shown in Figure 9.7 for two different nominal current densities.

Figure 9.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. The decrease in mass concentration of the hydrogen across the anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

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9.4.4. Current Density Distribution Figure 9.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities. The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to under-utilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

9.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment.

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Figure 9.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

Figure 9.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities. The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is highest.

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Figure 9.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

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9.4.6. Activation Overpotential Distribution

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The variation of the cathode activation overpotentials (in V) is shown in Figure 9.10. For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area.

Figure 9.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 9.11. It can be seen that the anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials. It can be seen from the Figures 9.10 and 9.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

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9.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 9.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

9.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 9.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

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Figure 9.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 9.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 9.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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9.4.9. Diffusion Overpotential Distribution

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The variation of the cathode diffusion overpotentials (in V) is shown in Figure 9.14.

Figure 9.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower). CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Figure 9.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the diffusion overpotential profile correlates with the local

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current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode diffusion overpotentials (in V) is shown in Figure 9.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials. In addition, it can be seen from Figure 9.14 and Figure 9.15 that the mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

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9.5. MICRO-SCALE FUEL CELLS The presence of microelectromechanical system (MEMS) technology makes it possible to manufacture the miniaturized fuel cell systems for application in portable electronic devices. The majority of research on micro-scale fuel cells is aimed at micro-power applications. There are many new miniaturized applications which can only be realized if a higher energy density power source is available compared to button cells and other small batteries. Miniaturization down to these dimensions is not possible with conventional design of fuel cell stack technology. Using new technologies and designs it should be possible to significantly improve fuel cell performance when micro-scale phenomena are exploited. However, such benefits can only be realized if the fuel cell devices can be fabricated using available manufacturing techniques. They are in most cases adapted from semiconductor and micro-systems technology. Fuel cells built to exploit micro-scale phenomena would be smaller, make better use of volume and could obtain improved heat and mass transfer.

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Chapter 10

10. DISK-SHAPED COMPACTED-DESIGN MICRO-STRUCTURED AIR-BREATHING PEM FUEL CELL

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10.1. INTRODUCTION In small-scale applications, the fuel cell should be exceptionally small and have highest energy density. One way to achieve these requirements is to reduce the thickness of the cell (compacted-design) for increasing the volumetric power density of a fuel cell power supply. The disk-shaped compacted-design microstructured air-breathing PEM fuel cell employs a compacted-design (smallest cell thickness) that enables an active area greatest than the disk fuel cell area.

10.2. MODELLING DOMAIN AND GEOMETRY The full computational domain for the disk-shaped micro-structured airbreathing PEM fuel cell consists of anode gas flow field and the membrane electrode assembly (MEA) is shown in Figure 10.1. Table 10.1 shows the dimensions of the computational domain. A schematic description of the diskshaped micro-structured air-breathing PEM fuel cell stack is shown in Figure 10.2. The cathode of the cell is directly open to ambient air. The oxygen needed by the fuel cell reaction is transferred by natural convection and diffusion through the gas diffusion backing into the cathode electrode. It breathes the fresh air and routes out the electric current through solid bipolar plate. The hydrogen accesses to the anode are directly through the anode gas diffusion layers.

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Table 10.1. Cell dimensions Parameter Cell length

Symbol L

Value

Cell width

W

3 × 10 −3

Hydrogen channel diameter

DH2

Electrode thickness (GDL)

δ GDL

1× 10 −3 0.26 × 10 −3

m m m m

Catalyst layer thickness

δ CL

0.0287 × 10 −3

m

Membrane thickness

δ mem

0.23 × 10 −3

m

0.49 × 10

Unit −3

Figure 10.1. Three-dimensional computational domain of the disk-shaped micro-structured air-breathing PEM fuel cell.

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Figure 10.2. Longitudinal cross section of 3-cells fuel cell stack.

The design can achieve much higher active area to volume ratios, and hence very higher volumetric power densities. In this novel design, the MEA played an additional function by forming the channels that distribute the fuel and oxidant. Thus, the volume that previously comprised the flow channels could support additional active area and generate increased volumetric power density. Such fuel cells have the potential to be significantly cheaper, very smaller, and lighter than planer and tubular micro-structured fuel cells; they could also broaden the range of fuel cell applications.

10.3. COMPUTATIONAL PROCEDURE The governing equations in chapter two were discretized using a finite volume method and solved using the multi-physics CFD code. Stringent numerical tests were performed to ensure that the solutions were independent of the grid size. A computational quadratic finer mesh consisting of a total of 14149 meshes ware found to provide sufficient spatial resolution (Figure 10.3).

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Figure 10.3. Computational mesh of the disk-shaped micro-structured air-breathing PEM fuel cell (quadratic).

The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0×10−6. The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2GB RAM) using Windows XP operating system. The number of iterations required to obtain converged solutions dependent on the nominal current density of the cell; the higher the load the slower the convergence.

10.4. RESULTS The three-dimensional model allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These transport phenomena are the velocity flow field, variation of local concentration of gas reactants, local current densities, temperature field, and potential field.

10.4.1. Velocity Profile The operation of a fuel cell and the resulting water and heat distributions depend on numerous transport phenomena including charge-transport and multi-

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component, multiphase flow, and heat transfer in porous media. Multiphase flow is a central issue in PEM fuel cell technology because while water is essential for membrane ionic conductivity, excess liquid water leads to flooding of catalyst layers and gas diffusion layers. Understanding the flow of gas/liquid flows is therefore of major technological as well as scientific interest. The multiphase velocity fields inside the cathodic and anodic gas diffusion layers are shown in Figures 10.4 and 10.5 for both gas and liquid phase.

Figure 10.4. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the cathode GDL at a nominal current density of 0.4 A/cm2. CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

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Figure 10.5. Gas phase velocity vectors (upper) and liquid water velocity vectors (lower) inside the anode GDL at a nominal current density of 0.4 A/cm2.

The pressure gradient induces bulk gas flow from the hydrogen channel and ambient air into the GDL. While the capillary pressure gradient drives the liquid water out of the gas diffusion layers into the hydrogen flow channel and ambient

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air. Therefore, the liquid water flux is directed from the GDL into the hydrogen channel and ambient air, i.e., in the opposite direction of the gas-phase velocity, where it can leave the cell. The velocity of the liquid phase, however, is lower than for the gas phase, which is due to the higher viscosity, and the highest liquid water velocity occurs at the corners of the current-collector/GDL interface. The liquid water oozes out of the GDL, mainly at the corners of the current-collector/GDL interface.

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10.4.2. Oxygen Distribution The detailed distribution of oxygen mass fraction for two different nominal current densities is shown in Figure 10.6. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near the catalyst layer. The non-linear drop in concentration along the cell width of the electrode is the result of oxygen consumption along the diffusion pathway. Although the reduction in oxygen concentration is significant, the fuel cell is still far from being starved of oxygen. The local current density of the cathode side reaction depends directly on the oxygen concentration. At a low current density, the oxygen consumption rate is low enough not to cause diffusive limitations, whereas at a high current density the concentration of oxygen at the end of the cell width of the electrode has already reached low values. It becomes clear that the diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption.

10.4.3. Hydrogen Distribution The hydrogen mass fraction distribution in the anode side is shown in Figure 10.7 for two different nominal current densities. In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed.

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Figure 10.6. Oxygen mass fraction distribution in the cathode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 10.7. Hydrogen mass fraction distribution in the anode side for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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The decrease in mass concentration of the hydrogen across the anode gas diffusion layer is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen.

10.4.4. Current Density Distribution

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Figure 10.8 shows the local current density distribution at the cathode side catalyst layer for two different nominal current densities. The local current densities have been normalized by the nominal current density in each case (i.e. ic/I ). It can be seen that for a low nominal current density, the distribution is quite uniform. This will change for high current density, where a noticeable decrease takes place along the cell width of the electrode. It can be seen that for a high nominal current density, a high fraction of the current is generated at the catalyst layer near the air inlet area, leading to under-utilization of the catalyst at the end of the cell width of the electrode. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers.

10.4.5. Cell Temperature Distribution Thermal management is required to remove the heat produced by the electrochemical reactions in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane or mechanical damage in the cell. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment. Figure 10.9 shows the distribution of the temperature (in K) inside the cell for two different nominal current densities.

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Figure 10.8. Local current density distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 10.9. Temperature distribution inside the cell for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

The result shows that the increase in temperature can exceed several degrees Kelvin near the catalyst layer regions, where the electrochemical activity is

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highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production.

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10.4.6. Activation Overpotential Distribution The variation of the cathode activation overpotentials (in V) is shown in Figure 10.10. For both nominal current densities, the distribution patterns of activation overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the activation overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode activation overpotentials (in V) is shown in Figure 10.11. It can be seen that the anode activation overpotentials is evenly distributed for both nominal current densities and several orders of magnitude smaller than that of cathode activation overpotentials. It can be seen from the Figures 10.10 and 10.11 that the activation overpotential is directly related to the nature of the electrochemical reactions and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by the current.

10.4.7. Ohmic Overpotential Distribution Ohmic overpotential is the loss associated with resistance to electron transport in the gas diffusion layers. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes for two different nominal current densities are shown in Figure 10.12. The potential distributions are normal to the flow inlet of fuel and air where electrons flow into the bipolar plates. The distributions exhibit gradients in both cell width and height directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer near the fuel and air inlet.

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Figure 10.10. Activation overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 10.11. Activation overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 10.12. Ohmic overpotential distribution in the anode and cathode GDLs for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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10.4.8. Membrane Overpotential Distribution The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Figure 10.13 shows the potential loss distribution (in V) in the membrane for two nominal current densities. It can be seen that at a low current density, the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen.

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10.4.9. Diffusion Overpotential Distribution The variation of the cathode diffusion overpotentials (in V) is shown in Figure 10.14. For both nominal current densities, the distribution patterns of diffusion overpotentials are similar, with higher values at the catalyst layer near the air inlet area. It can be seen that the diffusion overpotential profile correlates with the local current density, where the current densities are highest near the air inlet area and coincide with the highest reactant concentrations. The variation of the anode diffusion overpotentials (in V) is shown in Figure 10.15. It can be seen that the anode diffusion overpotentials is evenly distributed for all nominal current densities and several orders of magnitude smaller than that of cathode diffusion overpotentials. In addition, it can be seen from Figure 10.14 and Figure 10.15 that the mass transport loss becomes significant when the fuel cell is operated at high current density. This is created by the concentration gradient due to the consumption of oxygen or fuel at the electrodes.

10.5. MICRO-SCALE FUEL CELLS The presence of microelectromechanical system (MEMS) technology makes it possible to manufacture the miniaturized fuel cell systems for application in portable electronic devices. The majority of research on micro-scale fuel cells is aimed at micro-power applications.

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Figure 10.13. Membrane overpotential distribution across the membrane for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 10.14. Diffusion overpotential distribution at the cathode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

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Figure 10.15. Diffusion overpotential distribution at the anode catalyst layer for two different nominal current densities: 0.2 A/cm2 (upper) and 0.4 A/cm2 (lower).

There are many new miniaturized applications which can only be realized if a higher energy density power source is available compared to button cells and

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other small batteries. Miniaturization down to these dimensions is not possible with conventional design of fuel cell stack technology. Using new technologies and designs it should be possible to significantly improve fuel cell performance when micro-scale phenomena are exploited. However, such benefits can only be realized if the fuel cell devices can be fabricated using available manufacturing techniques. They are in most cases adapted from semiconductor and micro-systems technology. Fuel cells built to exploit micro-scale phenomena would be smaller, make better use of volume and could obtain improved heat and mass transfer.

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Chapter 11

11. PARAMETRIC STUDY

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11.1. INTRODUCTION In addition to revealing the detail of transport phenomena inside the fuel cell, the comprehensive three-dimensional model can also be used to investigate the sensitivity of certain parameters on fuel cell performance. The performance characteristics of the fuel cell based on a certain parameter can be obtained by varying that parameter while keeping all other parameters constant. Results obtained from these parametric studies will allow the identification of the critical parameters for fuel cell performance as well as the sensitivity of the model to these parameters. Results with deferent operating conditions for different cells operate at nominal current density of 0.4 A/cm2 are discussed in the following subsections. In the following subsections only the parameter investigated is changed, all other parameters are at the base case conditions as outlined in Table 2.5, Table 2.6, and Table 2.7.

11.2. EFFECT OF AMBIENT CONDITIONS (AMBIENT TEMPERATURE AND RELATIVE HUMIDITY) Ambient conditions such as temperature and relative humidity of surroundings played an important role on the air-breathing fuel cell performance, because membrane hydration, water removal and oxygen transport at the cathode were influenced by the ambient temperature and humidity. Proper water management requires meeting two conflicting needs: adequate membrane hydration and avoidance of water flooding in the cathode catalyst layer and/or gas diffusion layer. Water management is related with air supply to the cathode and is

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one of the crucial factors in an air-breathing PEM fuel cell system, due the lack of control of ambient air stream conditions (flow stoichiometry, temperature, and humidity). In order to retain the optimum hydration level of the air-breathing PEM fuel cell, water produced at the cathode has to be supplied to the membrane and the anode. However, too much water may lead to cathode flooding, which limits the access of oxygen to the active surface of the catalyst particles. Under certain ambient and operating conditions, such as low humidity, high temperatures, and low current densities, dehumidification of the membrane may occur, resulting in deterioration of protonic conductivity, increasing resistive losses, and increasing membrane electrode assembly (MEA) temperature. In the extreme case of complete drying, local burnout of the membrane may result. Thus, proper hydration of the MEA and removal of water from cathode through water management is critical to maintain membrane conductivity and performance. Thermal management is also required to remove the heat produced by the electrochemical reaction in order to prevent drying out of the membrane, which in turn can result not only in reduced performance but also in eventual rupture of the membrane. Thermal management is also essential for the control of the water evaporation or condensation rates. Diffusion and free convection are the primary transport mechanisms for delivering oxygen to the cathode of air-breathing fuel cells. The oxygen transport limitation plays a great role in the performance of air-breathing fuel cells. The current production by electrochemical reaction is directly proportional to the local oxygen concentration in the fuel cell. Inadequate airflow in the planar airbreathing PEM fuel cell cannot provide enough oxygen for the electrochemical reaction on the active surfaces under the land areas. It results in heterogeneous current distribution in the electrode that reduces the performance of the fuel cell. Thus, one of the greater challenges in the design of passive fuel cells is how to provide enough oxygen for the electrochemical reaction on the entire active surface. The ambient conditions have a strong impact on the fuel cell performance. Ambient temperature and relative humidity impacted all three major electrochemical loss components of the air-breathing fuel cell: activation, resistive, and mass transfer. Activation losses were typically the largest loss component. However, these were affected weakly by varying ambient conditions. A small increase in activation losses was showed at high ambient temperature and low humidity conditions (probably due to catalyst dry-out). Resistive losses were most strongly affected by ambient conditions and dominated fuel cell losses during dry-out. The membrane resistance decreases due to membrane self-

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humidification with product water and self-heating with reaction heat, and membrane resistance increases due to excessive evaporation from the cathode surface. Mass transfer losses typically became important at high current density. Furthermore, low ambient temperatures, and high ambient humidity both tended to increase mass transfer losses due to flooding of the GDL. The temperature distribution in the air-breathing fuel cell is dependent on the membrane electrode assembly water content. The net water balance of the cell is a complex coupling of cell self-heating and water production as well as the convection of heat and water vapour to the environment. The temperature distribution inside the tubular-shaped micro-structured airbreathing PEM fuel cell can be shown in Figures 11.1 and 11.2 for two cases of the ambient relative humidity values. In both cases, the highest temperatures are located at the cathode catalyst layer, implying that major heat generation takes place in this region. The minimum temperature with lower gradient appears in the cell of the higher ambient relative humidity case (Figure 11.1). The temperature difference between the cathode catalyst layer and ambient air temperature is as large as 5 K. Further, the temperature profiles are more uniform compared with the result of the lower ambient relative humidity case (Figure 11.2). This behaviour is consistent with a more hydrated membrane, lower ohmic losses, and reduced joule heating.

Figure 11.1. Temperature distribution inside the cell at ambient temperature of 300.15 K (27 C) and relative humidity of 80%..

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Figure 11.2. Temperature distribution inside the cell at ambient temperature of 300.15 K (27 C) and relative humidity of 20%.

Thermal management is required to remove the heat produced by the electrochemical reaction in order to prevent drying out of the membrane and excessive thermal stresses that result in rupture of the membrane. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM micro fuel cells. As the ambient temperature increases, the air-breathing fuel cell rejects less heat and the GDL temperature increases (Figure 11.3). At high temperature and low relative humidity the membrane dries out due to evaporation of product water from the open cathode surface, and the cell potential drops. At low temperature and high relative humidity the cell floods at high current density. The results showed that the ambient conditions (ambient temperature and relative humidity) have a strong impact on the temperature distribution inside the cell. In conclusion, the self-heating and self-humidifying effects of passive fuel cells are balanced by the transfer of heat and water to the ambient. Optimal performance of air-breathing cells is therefore a complex function of ambient and load conditions as well as the cell design.

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Figure 11.3. Temperature distribution inside the cell at ambient temperature of 320.14 K (47 C) and relative humidity of 80%.

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11.3. EFFECT OF GDL POROSITY The porosity of the gas diffusion layer has two comparing effects on the fuel cell performance; as the porous region provides the space for the reactants to diffuse towards the catalyst region, an increase in the porosity means that the onset of mass transport limitations occurs at higher current densities, i.e. it leads to higher limiting currents. The adverse effect of a high porosity is an expected increase in the contact resistance. Higher gas diffusion layer porosity improves the mass transport within the cell and this leads to reducing the mass transport loss. The molar oxygen fraction at the catalyst layer increases with more even distribution with an increasing in the porosity. This is because of a higher value of the porosity provides less resistance for the oxygen to reach the catalyst layer. A higher porosity evens out the local current density distribution. For a lower value of the porosity a much higher fraction of the total current is generated. This can lead to local hot spots inside the membrane electrode assembly as can be seen in the tubular-shaped airbreathing PEM fuel cell (Figure 11.4).

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Figure 11.4. Temperature distribution inside the cell for two different GDL porosities: 0.3 (upper) and 0.5 (lower).

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These hot spots can lead to a further drying out of the membrane, thus increasing the electric resistance, which in turn leads to more heat generation and can lead to a failure of the membrane. Thus, it is important to keep the current density relatively even throughout the cell. As mentioned above, another loss mechanism that is important when considering different gas diffusion layer porosities is the contact resistance. Contact resistance occurs at all interfaces inside the fuel cell. The magnitude of the contact resistance depends on various parameters such as the surface material and treatment and the applied stack pressure. The electrode porosity has a negative effect on electron conduction, since the solid matrix of the gas diffusion layer provide the pathways for electron transport, the higher volume porosity increases resistance to electron transport in the gas diffusion layers.

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11.4. EFFECT OF GDL THERMAL CONDUCTIVITY Thermal management is required to remove the heat produced by the electrochemical reaction in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane. The small temperature differential between the fuel cell stack and the operating environment make thermal management a challenging problem in PEM fuel cells. The temperature distribution inside the tubular-shaped compacted-design micro-structured air-breathing PEM fuel cell can be shown in Figure 11.5 for two cases of the gas diffusion layer thermal conductivity values. The maximum temperature with higher gradient appears in the cathode side catalyst layer of the lower thermal conductivity. Heat generated in the catalyst layer is primarily removed through the gas diffusion layer to the current collector rib by lateral conduction. This process is controlled by the gas diffusion layer thermal conductivity. Therefore, the membrane temperature is strongly influenced by the gas diffusion layer thermal conductivity, indicating a significant role played by lateral heat conduction through the gas diffusion layer in the removal of waste heat to the ambient. Therefore, a gas diffusion layer material having higher thermal conductivity is strongly recommended for fuel cells designed to operate with high power.

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Figure 11.5. Temperature distribution inside the cell for two different values of the GDL thermal conductivity: 0.5 W/m.K (upper) and 2.9 W/m.K (lower).

11.5. EFFECT OF MEMBRANE THERMAL CONDUCTIVITY The temperature distribution inside the planar micro-structured air-breathing PEM fuel cell can be shown in Figure 11.6 for two cases of the membrane thermal

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conductivity values. The higher membrane conductivity results in more even distribution of the temperature inside the cell.

Figure 11.6. Temperature distribution inside the cell for two different values of the membrane thermal conductivity: 0.3 W/m.K (upper) and 0.6 W/m.K (lower).

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membrane material having higher thermal conductivity is strongly recommended for fuel cells designed to operate with high power density.

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11.6. EFFECT OF GDL THICKNESS The effect of gas diffusion layer thickness on the fuel cell performance is again mostly on the mass transport, as the ohmic losses of the electrons inside the gas diffusion layer are relatively small due to the high conductivity of the carbon fiber paper. A thinner gas diffusion layer increases the mass transport through it, and this leads to reduction the mass transport loss. The molar oxygen fraction at the catalyst layer increases with a decreasing of the gas diffusion layer thickness due to the reduced resistance to the oxygen diffusion by the thinner layer. The distribution of the local current density of the cathode side depends directly on the oxygen concentration. The thicker gas diffusion layer results in more even distribution of the local current density due to the more even distribution of the molar oxygen fraction at the catalyst layer. This leads to the fact that for a thinner gas diffusion layer at a constant current density, there is a much stronger distribution of current inside the cell. Therefore, the maximum temperature gradient appears inside the planar air-breathing PEM fuel cell of the thinner gas diffusion layer case as can be seen in Figure 11.7.

11.7. EFFECT OF MEMBRANE THICKNESS The effect of membrane thickness on the fuel cell performance is mostly on the resistance of the proton transport across the membrane. The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. Therefore, a reduction in the membrane thickness means that the path travelled by the protons will be decreased, thereby reducing the membrane resistance and this leads to reducing the potential loss in the membrane, which in turn leads to less heat generation in the membrane as can be shown in the diskshaped micro-structured air-breathing PEM fuel cell (Figure 11.8). These results suggested that reducing the membrane thickness played a significant role in promoting cell performance.

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Figure 11.7. Temperature distribution inside the cell for two different GDL thicknesses: 0.2 mm (upper) and 0.3 mm (lower).

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Figure 11.8. Temperature distribution inside the cell for two different membrane thicknesses: 0.2 mm (upper) and 0.3 mm (lower).

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[2] [3] [4]

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Maher A.R. Sadiq Al-Baghdadi. CFD Models for Analysis and Design of PEM Fuel Cells. NOVA Sci. Pub. Inc., 400 Oser Avenue, Suite 1600, Hauppauge, NY 11788-3619 USA. 2008. ISBN 9781604569971. Carrette, L.; Friedrich, K.A.; Stimming, U. Fuel Cells J. 2001, 1(1), 5-39. Ernst, W.; Nerschook, J. Fuel Cell Review Magazine. 2004, 1(1), 25-28. Spencer, P.; Barrett, S. Int. Fuel Cell Magazine (fcFOCUS) Fuel Cell Supplement. 2003, 6-9. Okada, O.; Yokoyama, K. Fuel Cells J. 2001, 1(1), 72-77. Bak, P.E. Magazine Hydrogen Cars Business (H2CARSBIZ). 2004, 2(1), pp.12. Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Fuel Cell. 2006, 6(6), 28-31. Eikerling, M.; Kornyshev, A.A. J. Electroanalytical Chemistry. 2001, 502(1-2), 1-14. Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Engineering Applications of Computational Fluid Mechanics Journal. 2007 1(2), 71-87. Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Int. J. of Hydrogen Energy. 2007, 32(17), 4510-4522. Kolde, J.A.; Bahar, B.; Wilson, M.S.; Zawodzinski, T.A.; Gottesfeld. S. Proc. Electrochemical Soc. 1995, 23, 193–201. Eikerling, M.; Kornyshev, A.A.; Kuznetsov, A.M.; Ulstrup, J.; Walbran, S. J. Phys. Chem. B. 2001, 105, 3646-4662. Mehta, M.; Cooper, J.S. J. Power Sources. 2003, 114(1), 32-53. Maher A.R. Sadiq Al-Baghdadi. PEM Fuel Cell Modeling, Chapter 7 in "Fuel Cell Research Trends" (Textbook), NOVA Sci. Pub. Inc, 400 Oser Avenue, Suite 1600, Hauppauge, NY 11788 USA. 2007, pp. 273-379. ISBN 9781600216695.

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[15] Maher A.R. Sadiq Al-Baghdadi. Renewable Energy Journal. 2007, 32(7), 1077-1101. [16] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Journal of Zhejiang University SCIENCE-A. 2007, 8(2), 285-300. [17] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Energy Conversion and Management 2007, 48(12), 3102-3119. [18] Maher A.R. Sadiq Al-Baghdadi. CFD Modelling of Multiphase Flow: Application to Air-Breathing PEM Fuel Cells, Chapter 14 in "Multiphase Flow Research" (Textbook), NOVA Sci. Pub. Inc., 400 Oser Avenue, Suite 1600, Hauppauge, NY 11788-3619 USA. 2009, ISBN 9781606924488. [19] Maher A.R. Sadiq Al-Baghdadi. CFD Models for Analysis and Design of Ambient Air-Breathing PEM Fuel Cells, Chapter 4 in "Polymer Electrolyte Membrane Fuel Cells and Electrocatalysts" (Textbook), NOVA Sci. Pub. Inc, 400 Oser Avenue, Suite 1600, Hauppauge, NY 11788-3619 USA. 2009, ISBN 9781606927731. [20] Maher A.R. Sadiq Al-Baghdadi. Fuel Cell. 2009, Vol.9, Issue 3. [21] Maher A.R. Sadiq Al-Baghdadi. Proceedings of the I MECH ENG. Journal of Power and Energy. 2008, 222 (6), 569-585. [22] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Proceedings of the I MECH ENG. Journal of Power and Energy. 2007, 221 (7), 917-929. [23] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Proceedings of the I MECH ENG. Journal of Power and Energy. 2007, 221 (7) pp. 931-939. [24] Fuller, E.N.; Schettler, P.D.; Giddings, J.C. Ind. Eng. Chem. 1966, 58(5), 18-27. [25] Coker, A.K. FORTRAN programs for chemical process design, analysis, and simulation. Gulf Publishing Company: Houston, Texas, 1995. ISBN 0884152804. [26] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. International Journal of Fluid Mechanics Research. 2008, 35(3), 219-234. [27] Maher A.R. Sadiq Al-Baghdadi. Renewable Energy Journal. 2009, 34(7), 1812-1824. [28] Maher A.R. Sadiq Al-Baghdadi. Journal of Renewable and Sustainable Energy. 2009, Vol.1, Issue 2. [29] Maher A.R. Sadiq Al-Baghdadi. Renewable Energy Journal. 2008, 33(6), 1334-1345. [30] Maher A.R. Sadiq Al-Baghdadi. Fuel Cell. 2008, 8(3), 32-38. [31] Maher A.R. Sadiq Al-Baghdadi. Renewable Energy Journal. 2009, 34(3), 674-682.

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[32] Maher A.R. Sadiq Al-Baghdadi. Recent Patents on Mechanical Engineering. 2009, 2(1), 26-39. [33] Maher A.R. Sadiq Al-Baghdadi. Energy Conversion and Management. 2008, 49(11), 2986-2996. [34] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Proceedings of the I MECH ENG. Journal of Power and Energy. 2007, 221 (7), 941-953. [35] Berning, T.; Djilali, N. J. Electrochem. Soc. 2003, 150(12), A1589-A1598. [36] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Energy and Fuels Journal. 2007, 21(4), 2258-2267. [37] Maher A.R. Sadiq Al-Baghdadi. Renewable Energy Journal. 2005, 30(10), 1587-1599. [38] Maher A.R. Sadiq Al-Baghdadi; Shahad HAK. Turkish Journal of Engineering and Environmental Sciences. 2005, 29(4), 235-240. [39] Maher A.R. Sadiq Al-Baghdadi. International Journal of Sustainable Energy. 2007, 26(2), 79-90. [40] Maher A.R. Sadiq Al-Baghdadi. Fuel Cell, 2007, 7(3), 36-38.

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INDEX A 



accounting, 31  acid, 8, 36  acidic, 8  activation, 15, 35, 37, 39, 57, 58, 77, 78, 79,  97, 98, 99, 116, 138, 139, 141, 158, 181,  182, 201, 212  activation energy, 37, 58, 79, 99, 116, 141,  158, 182, 201  active site, 18  AFC, 2, 3, 5  alcohols, 6  algorithm, 21, 22, 40  ambient air, ix, x, 1, 19, 20, 21, 24, 25, 45, 49,  50, 65, 69, 71, 85, 89, 91, 109, 127, 133,  147, 151, 169, 173, 175, 189, 194, 195,  212, 213  ambient air temperature, 213  application, 6, 104, 145, 167, 188, 205  assessment, 48, 68, 88, 108, 130, 150, 172,  192  assumptions, 22, 24  availability, 38  avoidance, 16, 211 

base case, 40, 41, 42, 43, 211  batteries, ix, 1, 6, 65, 104, 127, 146, 167, 188,  209  benefits, 104, 146, 167, 188, 209  bipolar, 11, 58, 65, 79, 85, 99, 120, 141, 147,  162, 169, 182, 189, 201  boats, 3  BOP, ix, 2, 19  boundary conditions, 22, 43  burnout, 212  buses, 5 

C  camcorders, ix, 1, 7, 18  candidates, ix, 1  capillary, 15, 17, 25, 30, 31, 50, 69, 89, 109,  133, 151, 173, 194  carbon, 3, 8, 10, 11, 220  carbon cloth, 11  carbon paper, 11  catalytic activity, 10, 15  channels, 15, 20, 24, 26, 66, 86, 127, 148,  171, 191  chemical energy, ix, 1 

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228

Index

chemical reactions, 22  CHP, 3  classification, 2  cleaning, 6  combustion, 6  compatibility, 7  complexity, ix, 2, 19  components, ix, 2, 12, 19, 31, 212  composition, 40  Computational Fluid Dynamics (CFD) i, iii, iv,  v, vi, vii, x, xvii, 21, 22, 24, 47, 67, 88, 107,  129, 150, 171, 191, 223, 224  computer simulation, vi  computing, 7, 39, 127, 147  condensation, xiv, 16, 25, 30, 34, 212  conditioning, 6  conduction, 37, 217  conductive, 7, 15  conductivity, xiv, xvi, 8, 9, 24, 28, 29, 42, 43,  48, 69, 89, 109, 130, 151, 173, 193, 212,  217, 218, 219, 220  confidence, 22  congress, vi  conservation, 22, 26  constraints, 32  construction, vi  consumer electronics, 18  consumption, 38, 40, 50, 64, 71, 82, 91, 92,  104, 109, 113, 125, 133, 144, 151, 154,  155, 163, 175, 176, 188, 195, 205  continuity, 25, 33  control, 22, 33, 34, 212  convection, ix, 1, 15, 19, 24, 25, 26, 31, 33,  45, 55, 65, 85, 95, 116, 127, 137, 147, 158,  169, 178, 189, 198, 212, 213  convective, 27, 33, 43  convergence, 40, 47, 68, 88, 108, 129, 150,  172, 192  conversion, 6  cooling, ix, 1, 25  correlation, 27, 28, 29, 31, 34  costs, ix, x, 1, 2, 6, 22  coupling, 55, 95, 116, 137, 158, 178, 198, 213 

D  deformation, 21  deposition, 10  deviation, 37  diffusivity, 32, 33, 36, 39, 50, 53, 59, 71, 74,  79, 91, 92, 94, 100, 109, 113, 120, 133,  135, 141, 151, 155, 162, 175, 176, 178,  182, 195, 198, 205  dimensionality, 40  Dirichlet boundary conditions, 43  disaster, 3  disposition, 18  divergence, 26  drying, 18, 55, 75, 95, 116, 137, 157, 178,  198, 212, 214, 217 

E  electric current, 65, 85, 107, 127, 147, 169,  189  electric field, 38  electricity, 5  electrochemical reaction, 2, 10, 12, 14, 15,  25, 30, 37, 55, 58, 75, 79, 95, 99, 105, 116,  137, 141, 157, 158, 178, 182, 198, 201,  212, 214, 217  electrodes, 10, 25, 38, 58, 64, 79, 82, 99, 104,  120, 125, 141, 144, 162, 163, 182, 188,  201, 205  electrolyte, 2, 5, 8, 10, 14, 36, 37  electronic systems, 19  electrons, xv, 7, 8, 10, 11, 14, 15, 37, 58, 79,  99, 120, 141, 162, 182, 201, 217, 220  endothermic, 7  energy, ix, 1, 6, 12, 18, 22, 25, 27, 32, 37, 38,  85, 104, 146, 147, 167, 188, 189, 208  energy density, ix, 1, 6, 18, 85, 104, 146, 147,  167, 188, 189, 208  engines, 5  enthalpy, xvi 

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Index entropy, xv, 12, 35, 55, 75, 96, 116, 137, 158,  180, 201  environment, 21, 55, 75, 95, 116, 137, 158,  178, 198, 213, 214, 217  equilibrium, 14, 25, 37  ethanol, iii  evaporation, xiv, xvi, 17, 30, 32, 33, 34, 213,  214 

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F  fabrication, x, 21  failure, 55, 75, 95, 116, 137, 158, 178, 198,  217  fiber, 220  finite volume, 47, 67, 88, 107, 129, 150, 171,  191  finite volume method, 47, 67, 88, 107, 129,  150, 171, 191  flooding, 12, 16, 18, 48, 69, 89, 109, 130, 151,  173, 193, 211, 212, 213  flow field, 25, 39, 45, 48, 65, 68, 85, 89, 105,  106, 109, 128, 130, 148, 151, 169, 172,  189, 192  flow rate, 18, 39  fluid, vi, 21, 22, 24  free energy, xiv, 12, 13, 14 

G  gas phase, xv, xvi, 18, 25, 26, 27, 30, 31, 32,  33, 34, 40, 50, 70, 90, 109, 133, 151, 173,  195  gasoline, 6  generation, xv, 5, 16, 35, 55, 74, 75, 94, 96,  113, 116, 137, 155, 158, 178, 180, 198,  201, 213, 217, 220  Gibbs free energy, 12, 13, 14  grouping, 2  groups, 8 

229

H  heat capacity, xiii  heat removal, 11  heat transfer, xvi, 20, 21, 22, 32, 43, 45, 48,  69, 89, 109, 130, 151, 173, 193  heating, xiv, 5, 55, 95, 116, 137, 158, 178,  198, 213, 214  height, 46, 58, 66, 79, 86, 87, 99, 120, 141,  148, 162, 169, 182, 201  heterogeneous, 105, 212  high power density, 6, 220  high pressure, 38  high temperature, 212, 214  homogenous, 12  hot spots, 215, 217  hot water, 5  humidity, xvi, 16, 25, 33, 34, 211, 212, 213,  214, 215  hybrid, 5  hydration, 16, 211, 212  hydrides, 7  hydro, 6, 9  hydrocarbon fuels, 6  hydrophilic, 9  hydrophobic, 9 

I  identification, 22, 211  implementation, 19, 25  incompressible, 22  industry, 3, 5  injury, vi  insight, 21, 22  insulation, 8  integration, 6  interaction, 18, 21, 24  interface, 16, 33, 34, 37, 43, 50, 70, 90, 109,  133, 151, 173, 195  internal combustion, 6 

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Index

230 ionic, xvi, 9, 14, 24, 43, 48, 69, 89, 109, 130,  151, 173, 193  ions, 2  isothermal, 24  isotropic, 24 

K  kinetics, 14, 37  KOH, 3 

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L  lack of control, 212  laminar, 24  land, 105, 212  laptop, 19  large‐scale, 5  law, 30  lifetime, 2  limitations, 24, 38, 50, 71, 91, 105, 113, 133,  154, 175, 195, 212, 215  linear, 50, 71, 91, 109, 133, 151, 175, 195  liquid phase, xv, 25, 26, 27, 30, 31, 32, 33, 40,  49, 50, 69, 70, 89, 90, 109, 131, 133, 151,  173, 193, 195  liquid water, 17, 25, 26, 27, 30, 31, 32, 33, 34,  48, 49, 50, 51, 69, 70, 71, 89, 90, 91, 109,  110, 111, 130, 131, 132, 133, 151, 152,  153, 173, 174, 175, 193, 194, 195  lithium, 7  location, 13  losses, 10, 37, 58, 79, 99, 120, 141, 162, 182,  201, 212, 213, 220  low temperatures, ix, 1, 2, 3, 5, 16, 18 

M  machinery, 105  magnetic, vi 

management, 15, 16, 18, 25, 55, 65, 75, 95,  116, 127, 137, 157, 178, 198, 211, 212,  214, 217  manufacturing, x, 2, 104, 146, 167, 188, 209  market, 7  mass transfer, 21, 22, 33, 38, 40, 104, 146,  167, 188, 209, 212  mass‐transport, 24  matrix, 10, 32, 217  Maxwell equations, 31  media, 24, 32, 48, 69, 89, 109, 130, 151, 173,  193  MEMS, 104, 145, 167, 188, 205  methanol, 2, 6  migration, 16  military, 3  miniaturization, 65, 127  mobile phone, ix, 1, 7, 18, 19  modeling, vi  models, vi, x, 21, 22, 24  modulus, 42, 43  mole, 27  molecules, 36  momentum, 22, 25, 26, 30, 42  motion, 38  movement, 21  multiphase flow, 22, 48, 69, 89, 109, 130,  151, 173, 193 

N  Nafion, 8, 9, 40, 43  natural, ix, 1, 15, 19, 24, 25, 45, 65, 85, 127,  147, 169, 189  Navier‐Stokes, 25  Navier‐Stokes equation, 26  neglect, 22  nickel, 107  nitrogen, 39  non‐uniform, 55, 58, 74, 79, 94, 99, 113, 120,  137, 141, 155, 162, 178, 182, 198, 201  normal, 58, 79, 99, 120, 141, 162, 182, 201 

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Index

porous materials, 11  porous media, 24, 32, 48, 69, 89, 109, 130,  151, 173, 193  oil, 107  power, ix, x, xv, 1, 2, 3, 5, 8, 10, 19, 39, 45, 65,  operating system, 47, 68, 88, 108, 129, 150,  66, 85, 86, 104, 105, 127, 146, 147, 148,  172, 192  167, 169, 171, 188, 189, 191, 205, 208,  optimization, x, 21  217, 220  osmotic, xv, 15, 16, 17, 25, 36, 43  power plant, 5  oxidation, 15, 105  prediction, 40  oxidation rate, 105  pressure, xv, 14, 25, 26, 27, 30, 31, 33, 38, 39,  oxygen consumption, 50, 71, 91, 92, 109, 113,  41, 42, 49, 50, 69, 89, 105, 109, 133, 151,  133, 151, 154, 155, 175, 176, 195  173, 194, 217  oxygen consumption rate, 50, 71, 91, 113,  private, 2  133, 154, 175, 195  production, x, 2, 8, 18, 25, 35, 40, 55, 58, 75,  79, 95, 96, 99, 105, 116, 120, 137, 141,  P  158, 162, 178, 180, 182, 198, 201, 212, 213  property, vi, 13, 22  PAFC, 2, 3, 5  proton exchange membrane, ix, 1, 3, 5, 65,  parameter, xvi, 42, 211  127  parents, xi  protons, 7, 8, 10, 15, 16, 25, 38, 58, 79, 100,  particles, 10, 13, 212  120, 141, 162, 182, 205, 220  passive, ix, 1, 19, 105, 212, 214  PTFE, 9  passive type, ix, 1, 19  pumps, ix, 1, 24  pathways, 217  pure water, 31  PEMFC, 2, 3, 6  permeability, xiv, 30, 42, 43  R  permeation, 6  phone, 19  range, 5, 6, 10, 67, 87, 148, 171, 191  physical mechanisms, 25  reaction mechanism, 14  physics, 22, 29, 47, 67, 88, 107, 129, 150, 171,  reaction rate, 14  191  reliability, 5, 18  planar, 45, 46, 48, 65, 66, 67, 68, 85, 86, 87,  resistance, 37, 58, 79, 99, 100, 120, 141, 162,  88, 105, 148, 212, 218, 220  182, 201, 205, 212, 215, 217, 220  plants, 5  resolution, 47, 68, 88, 108, 129, 150, 172, 191  platinum, 10  resources, ix, 1, 127, 147  poisoning, 6  response time, 5  polarization, 8  rings, 127  polymer, 8, 15, 36  risk, 22  poor, 12  rolling, 10  pores, 15, 18, 25, 30  porosity, 12, 42, 215, 217  porous, 11, 24, 25, 29, 32, 34, 48, 69, 87, 89,  107, 109, 130, 148, 151, 173, 193, 215 



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231

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Index

232

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S  safety, 7  saturation, xv, 18, 30, 31, 33  scalar, 39, 42  semiconductor, 104, 146, 167, 188, 209  sensitivity, 21, 211  sensors, x, 21  separation, 8  services, vi  shape, 33  shear, 30  simulation, vi, x, 21, 22, 127, 147, 224  sites, 18  SOFC, 2, 3, 5, 6  solid matrix, 10, 32, 217  spatial, 24, 47, 68, 88, 108, 129, 150, 172, 191  species, x, 14, 16, 21, 25, 26, 27, 28, 29, 31,  32, 40  specific heat, 29  stability, 8  stoichiometry, 212  storage, 3, 7, 19  strength, 21, 40  stress, 21  supply, ix, 1, 5, 6, 15, 19, 38, 85, 147, 189,  211  surface area, 10, 33, 34  switching, 105  systems, ix, 1, 2, 3, 5, 18, 19, 21, 25, 104, 145,  146, 167, 188, 205, 209 

T  technology, 5, 48, 69, 89, 104, 109, 130, 145,  146, 151, 167, 173, 188, 193, 205, 209  Teflon, 8, 12  telecommunication, 7  temperature gradient, 220  tension, 31  Thermal Conductivity, 217, 218  thermal stability, 8 

thermodynamic, 12, 13, 27, 32, 33, 37, 39  thermodynamic equilibrium, 27, 32, 33  thermodynamic function, 12  three‐dimensional, 24, 40, 48, 68, 88, 108,  130, 150, 172, 192, 211  three‐dimensional model, 48, 68, 88, 108,  130, 150, 172, 192, 211  time, 5, 22, 105  transfer, xiv, xv, xvi, 14, 20, 21, 22, 30, 32, 33,  36, 37, 38, 42, 43, 45, 48, 69, 89, 109, 130,  151, 173, 193, 213, 214  transport phenomena, x, 15, 21, 40, 48, 55,  68, 69, 75, 88, 89, 95, 108, 109, 116, 130,  137, 150, 151, 158, 172, 173, 178, 192,  198, 211  transport processes, 17, 40  transportation, 3, 6  travel, 7, 8, 10  troubleshooting, 21  tubular, 105, 106, 107, 108, 127, 128, 129,  130, 147, 148, 149, 150, 171, 191, 213,  215, 217  turbulence, 22  two‐dimensional, 22, 24 

U  uniform, 55, 58, 74, 79, 94, 99, 105, 113, 120,  137, 141, 155, 162, 178, 182, 198, 201, 213 

V  validation, 40  values, 16, 27, 40, 50, 58, 63, 71, 77, 82, 91,  98, 100, 113, 116, 120, 133, 139, 141, 155,  158, 162, 175, 181, 187, 195, 201, 205,  213, 217, 218, 219  variables, 42  variation, 31, 48, 57, 58, 62, 64, 68, 77, 78,  82, 89, 97, 98, 100, 102, 109, 116, 120,  130, 138, 140, 141, 143, 151, 158, 162,  172, 181, 182, 186, 188, 192, 201, 205 

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,

Index

W  water, xiii, xiv, xv, 6, 7, 9, 11, 15, 16, 17, 24,  25, 27, 30, 31, 32, 33, 34, 35, 36, 39, 48,  50, 55, 69, 70, 89, 90, 95, 109, 116, 130,  133, 137, 151, 158, 173, 178, 192, 195,  198, 211, 212, 213, 214  water diffusion, 17  water evaporation, 212  water vapour, 6, 16, 27, 32, 33, 36, 39, 55, 95,  116, 137, 158, 178, 198, 213  wetting, 25 

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vector, xv  vehicles, 3, 5  velocity, xv, 31, 42, 48, 49, 50, 51, 68, 69, 70,  71, 89, 90, 91, 109, 110, 111, 130, 131,  132, 133, 151, 152, 153, 172, 173, 174,  175, 192, 193, 194, 195  viscosity, 27, 28, 34, 50, 70, 90, 109, 133, 151,  173, 195 

233

CFD Modeling and Analysis of Different Novel Designs of Air-Breathing Pem Fuel Cells, Nova Science Publishers,