Transport Phenomena in Cathode Catalyst Layer of PEM Fuel Cells

249 Pages·2010·10.36 MB·English

Transport Phenomena in Cathode
Catalyst Layer of PEM Fuel Cells
by
Prodip K. Das
A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Doctor of Philosophy
in
Mechanical Engineering
Waterloo, Ontario, Canada, 2010
© Prodip K. Das 2010
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis,
including any required final revisions, as accepted by my examiners.
I understand that my thesis may be made electronically available to the public.
Prodip K. Das
ii
Abstract
Polymer electrolyte membrane (PEM) fuel cells have increasingly become promising green
energy sources for automobile and stationary cogeneration applications but its success in
commercialization depends on performance optimization and manufacturing cost. The
activation losses, expensive platinum catalyst, and water flooding phenomenon are the
key factors currently hindering commercialization of PEM fuel cells. These factors are
associated with the cathode catalyst layer (CCL), which is about ten micrometers thick.
Given the small scale of this layer, it is extremely difficult to study transport phenomena
inside the catalyst layer experimentally, either intrusively or non-intrusively. Therefore,
mathematical and numerical models become the only means to provide insight on the
physical phenomena occurring inside the CCL and to optimize the CCL designs before
building a prototype for engineering application.
In this thesis research, a comprehensive two-phase mathematical model for the CCL
has been derived from the fundamental conservation equations using a volume-averaging
method. The model also considers several water transport and physical processes that are
involved in the CCL. The processes are: (a) electro-osmotic transport from the membrane
to the CCL, (b) back-diffusion of water from the CCL to the membrane, (c) condensation
and evaporation of water, and (d) removal of liquid water to the gas flow channel through
the gas diffusion layer (GDL). A simple analytical model for the activation overpotential
in the CCL has also been developed and an optimization study has been carried out using
the analytical activation overpotential formulation. Further, the mathematical model has
been simplified for the CCL and an analytical approach has been provided for the liquid
water transport in the catalyst layer.
The volume-averaged mathematical model of the CCL is finally implemented numer-
ically along with an investigation how the physical structure of a catalyst layer affects
fuel cell performance. Since the numerical model requires various effective transport prop-
erties, a set of mathematical expressions has been developed for estimating the effective
transport properties in the CCL and GDL of a PEM fuel cell. The two-dimensional (2D)
numerical model has been compared with the analytical model to validate the numerical
results. Subsequently, using this validated model, 2D numerical studies have been carried
out to investigate the effect of various physical and wetting properties of CCL and GDL
on the performance of a PEM fuel cell. It has been observed that the wetting properties
of a CCL control the flooding behavior, and hydrophilic characteristics of the CCL play a
significant role on the cell performance. To investigate the effect of concentration variation
in the flow channel, a three-dimensional numerical simulation is also presented.
iii
Acknowledgements
This work was supported by the National Research Council (NRC) and Natural Sciences
and Engineering Research Council (NSERC) of Canada. I would also like to thank my
supervisor, Dr. Xianguo Li, and Dr. Zhong-Sheng Liu for their guidance in the production
of this thesis.
I want to extend my thanks to my colleagues at 20/20 Laboratory for Fuel Cells and
Green Energy RD&D and NRC Institute for Fuel Cell Innovation for helping me to un-
derstand many concepts. Thanks to all of my friends from Bangladesh University of
Engineering & Technology, University of Alberta, and Edmonton for their moral support
over the last couple of years. A special thanks to A.K.M. Monjur Morshed (Mridul), Dulal
Laha, Shafique Kamal, and Sukanta Pramanik for inspiring me over the last few years to
finish this Ph.D. degree.
Lastly, but most importantly, I would like to thank my mom and siblings for their
support throughout all my endeavors.
iv
Dedication
This thesis is dedicated to Prof. Subir Bhattacharjee, who encouraged and inspired me to
pursue a PhD and still has a strong influence in my personal life. It is also dedicated to
Dr. Manas Shome and Prof. Abhijit Bhattacharyya, who brought me to the University of
Alberta from a small town in Bangladesh.
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Contents
List of Tables xi
List of Figures xii
List of Symbols xxii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Polymer Electrolyte Membrane Fuel Cells . . . . . . . . . . . . . . . . . . 2
1.2.1 Operation Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 Technical Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Literature Review 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.1 Single-phase Models . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.2 Two-phase Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.3 Cathode Catalyst Layer Models . . . . . . . . . . . . . . . . . . . . 16
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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3 General Formulation 19
3.1 Physical Structure and Nature of Flows . . . . . . . . . . . . . . . . . . . . 19
3.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Multi-phase Volume-averaging Method . . . . . . . . . . . . . . . . . . . . 22
3.4 Conservation of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 Conservation of Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Simplified Formulation for PEM Fuel Cell Cathode 35
4.1 Physical Problem and Assumptions . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Gas Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 Mass Transport in Gas Phase . . . . . . . . . . . . . . . . . . . . . 38
4.2.2 Momentum Transport in Gas Phase . . . . . . . . . . . . . . . . . . 39
4.2.3 Species Transport in Gas Phase . . . . . . . . . . . . . . . . . . . . 41
4.3 Liquid Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.1 Mass Transport in Liquid Phase . . . . . . . . . . . . . . . . . . . . 45
4.3.2 Momentum Transport in Liquid Phase . . . . . . . . . . . . . . . . 46
4.4 Electron and Proton Transports . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 Chemical Reaction in Catalyst Layer . . . . . . . . . . . . . . . . . . . . . 49
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5 Effective Transport Properties 52
5.1 Overview of Empirical Correlations . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Effective Protonic Conductivity . . . . . . . . . . . . . . . . . . . . 57
5.2.2 Effective Electronic Conductivity . . . . . . . . . . . . . . . . . . . 60
5.2.3 Effective Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 Comparisons of Effective Properties . . . . . . . . . . . . . . . . . . . . . . 64
5.3.1 Binary Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
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5.3.2 Effective Protonic Conductivity in Catalyst Layer . . . . . . . . . . 66
5.3.3 Effective Electronic Conductivity . . . . . . . . . . . . . . . . . . . 69
5.3.4 Effective Diffusivity in Catalyst Layer . . . . . . . . . . . . . . . . . 71
5.4 Relative Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.5 Capillary Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6 Analytical Model 80
6.1 Analytical Approach to Performance Optimization . . . . . . . . . . . . . . 80
6.2 Estimation of Activation Overpotential . . . . . . . . . . . . . . . . . . . . 81
6.2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.2.2 One-dimensional Formulation . . . . . . . . . . . . . . . . . . . . . 82
6.2.3 Exact Solution of Activation Overpotential . . . . . . . . . . . . . . 84
6.3 Oxygen Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.3.1 Oxygen Concentration in Flooded GDL . . . . . . . . . . . . . . . . 87
6.3.2 Oxygen Concentration in Dry GDL . . . . . . . . . . . . . . . . . . 90
6.4 Cell Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.4.1 Reversible Cell Potential . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4.2 Ohmic Overpotential . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5 Analytical Approach to Liquid Water Transport . . . . . . . . . . . . . . . 93
6.5.1 One-dimensional Liquid Water Transport . . . . . . . . . . . . . . . 94
6.5.2 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.5.3 Dimensionless Liquid Water Profile . . . . . . . . . . . . . . . . . . 97
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7 Numerical Implementation 100
7.1 Computational Domains and Boundary Conditions . . . . . . . . . . . . . 100
7.2 Numerical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.3 Mesh Generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.4 Convergence Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.5 Grid Independent Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
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8 Results and Discussion 109
8.1 Activation Overpotential Model Comparison . . . . . . . . . . . . . . . . . 110
8.1.1 Comparison with Empirical Correlations . . . . . . . . . . . . . . . 110
8.1.2 Comparison with Experimental Data . . . . . . . . . . . . . . . . . 114
8.1.3 Comparison with Numerical Results . . . . . . . . . . . . . . . . . . 117
8.2 Cell Performance and Optimization . . . . . . . . . . . . . . . . . . . . . . 119
8.2.1 Effect of Operating Conditions . . . . . . . . . . . . . . . . . . . . . 119
8.2.2 Optimization of Platinum Loading . . . . . . . . . . . . . . . . . . 124
8.2.3 Effect of Nafion Fraction . . . . . . . . . . . . . . . . . . . . . . . . 129
8.2.4 Optimization of Catalyst Layer Thickness . . . . . . . . . . . . . . 129
8.3 Analytical Model of Liquid Water Transport . . . . . . . . . . . . . . . . . 134
8.3.1 Liquid Saturation Profile in Cathode Catalyst Layer . . . . . . . . . 134
8.3.2 Effect of Surface Wettability . . . . . . . . . . . . . . . . . . . . . . 135
8.3.3 Effect of Electro-osmotic Drag and Back-diffusion . . . . . . . . . . 139
8.3.4 Effect of Flooding on Performance . . . . . . . . . . . . . . . . . . . 139
8.3.5 Effect of Time Constants . . . . . . . . . . . . . . . . . . . . . . . . 142
8.4 Numerical Model of Agglomerate Catalyst Layer . . . . . . . . . . . . . . . 146
8.4.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.4.2 Model Results: In-line Arrangement . . . . . . . . . . . . . . . . . . 151
8.4.3 Model Results: Uni-directional Staggered Arrangement . . . . . . . 155
8.4.4 Model Results: Bi-directional Staggered Arrangement . . . . . . . . 161
8.5 Two-dimensional Numerical Model . . . . . . . . . . . . . . . . . . . . . . 166
8.5.1 Numerical Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.5.2 Effect of Water Density . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.5.3 Effect of Gas Density . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8.5.4 Effect of CCL Porosity . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.5.5 Effect of CCL Contact Angle . . . . . . . . . . . . . . . . . . . . . 182
8.5.6 Effect of GDL Porosity . . . . . . . . . . . . . . . . . . . . . . . . . 186
8.5.7 Effect of GDL Contact Angle . . . . . . . . . . . . . . . . . . . . . 189
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8.6 Three-dimensional Numerical Model . . . . . . . . . . . . . . . . . . . . . 192
8.6.1 Numerical Accuracy of Three-dimensional Model . . . . . . . . . . 192
8.6.2 Boundary Conditions at GDL/GFC Interface . . . . . . . . . . . . 195
8.6.3 Tetrahedral vs. Hexahedral Mesh . . . . . . . . . . . . . . . . . . . 196
8.6.4 Effect of CCL Contact Angle . . . . . . . . . . . . . . . . . . . . . 198
8.6.5 Condensation/Evaporation of Liquid Water . . . . . . . . . . . . . 199
8.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
9 Summary and Future Work 203
References 210
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