The Pennsylvania State University. The Graduate School. College of Engineering COMPUTATIONAL EXPLORATION OF HIGH POWER OPERATION IN POROUS FLOW

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1 The Pennsylvania State University The Graduate School College of Engineering COMPUTATIONAL EXPLORATION OF HIGH POWER OPERATION IN POROUS FLOW FIELD POLYMER ELECTROLYTE FUEL CELLS WITH A VALIDATED MODEL A Dissertation in Mechanical Engineering by Lijuan Zheng 013 Lijuan Zheng Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 013

2 The dissertation of Lijuan Zheng was reviewed and approved* by the following: Matthew M. Mench Adjunct Professor of Mechanical Engineering Dissertation Advisor Co-Chair of Committee Adri C. T. van Duin Associate Professor of Mechanical Engineering Co-Chair of Committee Jack S. Brenizer J. Lee Everett Professor of Mechanical and Nuclear Engineering John M. Regan Associate Professor of Environmental Engineering Karen Thole Professor of Mechanical Engineering Department Head of Mechanical and Nuclear Engineering *Signatures are on file in the Graduate School. ii

3 ABSTRACT As one of the most promising hydrogen-based energy conversion devices, the polymer electrolyte fuel cell (PEFC) has been through intense development in the last two decades. Ultra-high current operation, which cannot be normally achieved at a reasonable voltage by the commonly used cell architecture, has been enabled by material advancement and cell design lately. However, a robust model is needed to rise to the unprecedented challenges in heat and water management. A comprehensive D + 1 computational model has been developed in this work to explore the operation of a PEFC with open metallic element (OME) porous flow field in the ultra-high current regime. In most of previous modeling works, the model validation has been generally limited to polarization curve comparison under single selected condition. This model distinguishes itself from the others in that it has been validated to a greater extent, including in-situ experimental measurement of performance, area specific resistance (ASR), and net water drag (NWD) coefficient. Data furnished by experimental diagnostics under a wide range of operating parameters serve as benchmark for model validation. Results also highlight the utility of experimentally-determined anode dry-out limits for validating multi-phase models. The collaborative experimental and modeling investigation shows that gas phase oxygen transport, which is responsible for limiting current density observed with conventional parallel flow field, is not the limiting factor in OME porous flow field, even in the ultra-high current regime. Notwithstanding the significant performance improvement of OME porous flow field at high current, anode dry-out limits the performance, as confirmed by NWD data from both experiment and model. Moreover, diffusive transport has been determined to be the dominant mode of water removal from the catalyst layer in an OME porous flow field, compared to capillary action and convective flux. Thermo-osmosis, which is a regularly-observed mode of water transport across membrane in experiments but relatively minor due to low performance and low temperature gradient achieved in conventional iii

4 parallel flow field, demonstrates its non-negligible effect in comparison to electro-osmosis, especially under hot and dry high power density conditions, even with thin polymer electrolyte membranes. The extensively-validated model is then applied to engineer cell operation so that anode dry-out can be mitigated in high temperature high power density operating regime, desired for automotive application. Predictions of internal water distribution demonstrate that moderate changes in operating parameters, such as pressure, stoichiometry and humidity, help maintain a hydrated anode stream and therefore enable a 0 ⁰ C increase in stable operating temperature than the baseline case, making heat dissipation to the cooling system more efficient. iv

5 Table of Contents List of Symbols... vii List of Tables... xiii List of Figures... xiv 1. Introduction Electrochemical Reaction Classification of Fuel Cells Working Principle of PEFC Literature Survey Model Dimensionality Model Treatment of Multi-Phase Flow Model Treatment of Catalyst Layer Flow Field Study Experimental Diagnostics Motivation Model Development Model Assumption Governing Equations and Boundary Conditions of -D Sub-Model Transport in Membrane Transport in Diffusion Media Transport in Catalyst Layer Boundary Conditions of -D Sub-Model Parameters and Correlations for -D Simulation Determination of Water Content Ionic Conductivity in MEA Dissolved Water Diffusion Coefficient in MEA Other Parameters and Correlations Agglomerate Model in Cathode Catalyst Layer Simplified +1 Formulation Along Flow Exploration of Ultra-High Current PEFC Operation with Porous Flow Field v

6 3.1. Experimental Details Model Validation Transport Study in Porous Flow Field Conclusions Operation Engineering to Enable High Temperature High Power Density Operation Literature Review Experimental Details Significance of Thermo-osmotic Flux Anode Dehydration Induced at High Temperature Operation Engineering to Mitigate Anode Dehydration Impact of Pressure Differential on Limiting Temperature Impact of Cathode Stoichiometry on Limiting Temperature Impact of Cathode Humidification on Limiting Temperature Combined Impact on Limiting Temperature Conclusion Conclusions and Future Work Conclusions Recommendations for Future Work Reference vi

7 List of Symbols a activity of water vapor, unitless roughness factor, cm Pt/cm 3 A effective surface area to dissolve oxygen into agglomerate per catalyst layer agg volume, m /m 3 A geometric active area, m Apt accessible specific Pt surface area, m Pt/g Pt C concentration of species i, mol/m 3 i C total concentration of gas phase, mol/m 3 T c p specific heat capacity, J/kg K D int diffusion coefficient of water transport in membrane with respect to gradient in ra chemical potential, m /s Dd diffusion coefficient of water transport in membrane with respect to gradient in concentration, m /s D, binary diffusion coefficient between species i and j, m /s i j Eth Erev Ecell Er EW F H H vl thermal voltage, V reversible voltage, V cell voltage, V effectiveness factor, unitless equivalent weight of ionomer, kg/equiv Faraday s constant, C/equiv Henry s constant, unitless latent heat of vaporization, J/mol i current density, A/m vii

8 i exchange current density, A/m 0 J transfer current density, A/m 3 gen K effective permeability, m K r kth relative permeability, unitless thermal conductivity, W/m K k reaction rate constant, s -1 c kvl mass transfer coefficient between gas and liquid phase, mol/m 3 s Pa L catalyst loading, mg Pt /cm M m N i n nd ni P Pe Ru ragg S Svl s T molecular weight, kg/mol coolant flow rate, kg/s molar flux of species i, mol/m s number of electrons transferred in electrode reaction, unitless electro-osmotic drag coefficient, unitless molar flow rate of species i, mol/s pressure, Pa Peclet number, unitless universal gas constant, J/mol K radius of agglomerate, m entropy change of reaction, J/mol K phase change between vapor and liquid water, mol/m 3 s saturation, unitless temperature, K viii

9 t u V0 Vm w wt xi thickness, m velocity, m/s molar volume of dissolved water, m 3 /mol molar volume of dry membrane, m 3 /mol velocity in through-plane direction, m/s weight percentage of PTFE, unitless mole fraction of species i x y z in-plane direction along-channel direction through-plane direction Greek Letters d charge transfer coefficient, unitless net water drag coefficient, unitless reaction order, unitless surface tension, N/m 0 i L thickness of thin film surrounding the agglomerate, m porosity, unitless volume fraction, unitless stoichiometry of species i, unitless overpotential, V Thiele modulus, unitless ionic conductivity, S/m water content, unitless ix

10 viscosity, Pa s density of dry membrane, kg/m 3 dry electronic conductivity, S/m potential, V Subscripts / Superscripts 0 intrinsic value a agg c cond conv cap d diff e eff G Kn L N ref s sat W anode agglomerate cathode conduction convection capillary flow dissolved phase of water diffusion ionically conducting phase effective value gas phase Knudsen liquid phase ionomer parameter evaluated at reference conditions electronically conducting phase at saturated state liquid water Abbreviation x

11 ASR AFC CL DM DMFC EOD EIS FF GDL HFR HOR MCFC MEA MPL NWD ODE OME ORR PAFC PCI PEFC PEM PEMFC area specific resistance alkaline fuel cell catalyst layer diffusion media direct methanol fuel cell electro-osmotic drag electrochemical impedance spectroscopy flow field gas diffusion layer high frequency resistance hydrogen oxidation reaction molten carbonate fuel cell membrane electrode assembly micro-porous layer net water drag ordinary differential equation open metallic element oxygen reduction reaction phosphoric acid fuel cell phase change induced polymer electrolyte fuel cell polymer electrolyte fuel cell proton exchange membrane fuel cell polymer electrolyte membrane fuel cell SEM SOFC scanning electron microscopy solid oxide fuel cell xi

12 SPEFC TOD solid polymer electrolyte fuel cell thermo-osmotic drag xii

13 List of Tables Table 1-I Classification and Description of Fuel Cells. From [6] Table 1-II Contributions to Non-Membrane ASR Table 1-III Summary of visualization techniques applied to PEFC. From [6] Table -I Boundary Conditions of -D Sub-Model Table -II Prevalent Water Uptake Isotherm Table -III Prevalent Correlations of Membrane Ionic Conductivity Table -IV Prevalent Correlations of Water Diffusion Coefficient in Membrane Table -V Parameters Used in -D Simulation Table -VI Correlations used in -D Simulation... 8 Table -VII Values and Constitutive Relations in Agglomerate Catalyst Model Table 3-I Operating conditions with varying inlet RH Table 3-II Changes in transport parameters to fit measured NWD coefficient Table 3-III Binary diffusion coefficient between N, He and H O, O Table 4-I Test Conditions to Engineer Operation (Difference from Condition 0 is highlighted) Table 4-II Major parameters of temperature dependence in the model xiii

14 List of Figures Figure 1.1 Basic Electrochemical Reactions. From [6] Figure 1. Schematic of a generic fuel cell. From [6] Figure 1.3 Scanning Electron Microscope (SEM) Image of (a) Woven Carbon Cloth (b) Non-woven Carbon Paper. From [6] Figure 1.4 Typical Polarization Curve of Fuel Cell. From [6] Figure 1.5 Tafel plot of oxygen reduction reaction as current-overpotential curve. Different cathode catalyst loadings are tested in H -O PEFC at 80 C. Tafel slope for all conditions is approximately 65mV/decade. From [3] Figure 1.6 Computational domain of 1D model. From [16] Figure 1.7 Sample results of 1D model: (a) Computed water profiles in Nafion 117 for four current densities under base-case conditions at constant gas flow rate equivalent to unity stoichiometry at 1A/cm. From [15] (b) Model calculation of concentrations of dissolved gas in the membrane phase throughout the fuel cell (base case operating conditions). From [16]... 4 Figure 1.8 Computational domain of D model incorporating through-plane and (a) in-plane From [70] (b) along-channel direction From [97] Figure 1.9 Sample results of D model incorporating through-plane and in-plane direction: (a) Effect of differential pressure on the local current density profiles along the electrode width From [55] (b) Lateral current variation inside the membrane at three different cathode gas humidity conditions From [73] Figure 1.10 Sample result of D model incorporating through-plane and along-channel direction: mole fraction of hydrogen, oxygen and water in the gas channel. Local current density is shown by the solid line. From [93] Figure 1.11 Computational Domain of 3D model. From [14] Figure 1.1 Structural picture of cathode catalyst layer depicting (a) various components and porous structure at macro-homogeneous scale (b) composition and reaction spots inside single agglomerate. From [8] Figure 1.13 Schematic of parallel flow field. From [175] Figure 1.14 Schematic of serpentine flow field (a) single serpentine (b) double serpentine (c) triple serpentine. From [136] Figure 1.15 Schematic of interdigitated flow field. From [185] Figure 1.16 Schematic of porous flow field. From [188] Figure 1.17 Schematic of water transport plate as bipolar plate (a) cross-section view From [189] (b) close-up of porous backing plate From [174]... 5 Figure 1.18 (a) Schematic picture of catalyst layer structure (b) one-dimensional transmission line equivalent circuit with proton resistance R p, charge transfer resistance R ct, electronic resistance R el and double layer capacitance C dl. From [196] Figure 1.19 Ideal Nyquist plot showing general regions of polarization losses. From [6] Figure 1.0 Schematic of test cell and imaging area. From [3] Figure 1.1 Evolution of water build-up inside the test cell (a) Neutron image (b) liquid water content reduced from neutron image. From [3] xiv

15 Figure.1 Schematics of computational domain: three-dimensional structure of single fuel cell; close-up of catalyst layer; idealized spherical agglomerate particle (not to scale) Figure. Time series of fuel cell voltage at consecutive current densities at 0.1, 0. and 0.3A/cm for the non-porous graphite plate and the porous carbon wick plate. From [174] Figure.3 Flow in a very small channel. The molecular interactions with the channel wall are no longer negligible compared to the collisions with other molecules. From [6] Figure.4 High-resolution neutron image of through-plane liquid water profile for cell at 60 C and 0.5A/cm. ( ) two stoichiometry anode flow ( ) high anode flow, 480 std cm 3 min -1 constant. Solid line demarks the center of the membrane; dashed line demarks the micro-porous layer / macro-porous layer boundary from the image dat. From [19] Figure.5 Evolution of membrane structure as a function of water content. the gray area is the fluorocarbon matrix, the black is the polymer side-chain, the light gray is the liquid water, and the dotted line is a collapsed channel. From [34] Figure 3.1 Comparison between conventional land / channel flow field (on the left) with Nuvera OME flow field (on the right) Figure 3. Experimental comparison between Parallel flow field and OME flow field on voltage and power density Figure 3.3 Comparison between experiment and model using air on OME flow field under baseline condition (a) polarization curve and ASR (symbol represents experiment and line represents model) (b) net water drag coefficient with conventional transport parameters. Error bars represents the range of water measurement from multiple test runs Figure 3.4 Pore size distribution curves for GDL as a function of carbon loading in MPL. From [01]. 107 Figure 3.5 Comparison of net water drag coefficient between experiment and model with conventional and adjusted transport parameters using air on OME flow field under baseline condition. Error bars represents the range of water measurement from multiple test runs Figure 3.6 Comparison between experiment and model using air on OME flow field under Condition 1 (a) polarization curve and ASR (symbol represents experiment and line represents model) (b) net water drag coefficient with adjusted transport parameters. Error bars represents the range of water measurement from multiple test runs Figure 3.7 Comparison between experiment and model using air on OME flow field under Condition (a) polarization curve and ASR (symbol represents experiment and line represents model) (b) net water drag coefficient with adjusted transport parameters. Error bars represents the range of water measurement from multiple test runs Figure 3.8 Experimental effect of inert gas on cell performance and ASR (a) parallel flow field (b) OME flow field Figure 3.9 Comparison of polarization curve and ASR between experiment and model using heliox on OME flow field under baseline conditions Figure 3.10 Comparison of predicted net water drag coefficient between air and heliox under baseline condition Figure 3.11 Comparison of predicted average water content in anode catalyst layer between heliox and air under baseline condition Figure 3.1 Effect of MPL permeability on net water drag coefficient under baseline condition xv

16 Figure 3.13 Predicted relative influence of convection measured by Peclet number under baseline condition Figure 3.14 Predicted effect of water vapor diffusivity on (a) voltage (b) net water drag coefficient under baseline condition Figure 4.1 Schematic of the single cell fixture (Courtesy of Nuvera Fuel Cells Inc.) Figure 4. Experimental polarization curve, heat dissipation and electrical power density under specified operating conditions Figure 4.3 Experimental comparison of (a) polarization curve (b) net water drag coefficient (c) gas stream humidity at exit over the range of operating current density between three gas feed RH conditions. Error bars represent the range of water measurement from multiple test runs Figure 4.4 (a) Predicted NWD with and without thermo-osmotic drag contribution under Condition 0 (b) Impact of cell operating temperature on thermo-osmotic drag coefficient and temperature gradient across membrane under Condition 0. Error bars represent the range of water measurement from multiple test runs Figure 4.5 Comparison of voltage, ASR and NWD between experiment (EXP) and model (MOD) under Condition 0. Error bars represent the range of water measurement from multiple test runs Figure 4.6 Comparison of local distribution of (a) water molar flow rate (b) NWD (c) gas stream RH between 60 and 70 C under Condition 0. Arrow indicates flow direction Figure 4.7 Comparison of voltage, ASR and NWD between experiment (EXP) and model (MOD) under Condition 1 and their comparison with Condition 0. Error bars represent the range of water measurement from multiple test runs Figure 4.8 Comparison of local distribution of (a) water molar flow rate (b) gas stream RH between Condition 0 and 1 under 60 C. Arrow indicates flow direction Figure 4.9 Comparison of local distribution of (a) water molar flow rate (b) gas stream RH between Condition 0 and 1 under 70 C. Arrow indicates flow direction Figure 4.10 Comparison of voltage, ASR and NWD between experiment (EXP) and model (MOD) under Condition and their comparison with Condition 0. Error bars represent the range of water measurement from multiple test runs Figure 4.11 Comparison of local distribution of (a) water molar flow rate (b) gas stream RH between Condition 0 and under 70 C. Arrow indicates flow direction Figure 4.1 Comparison of voltage, ASR and NWD between experiment (EXP) and model (MOD) under Condition 3 and their comparison with Condition 0. Error bars represent the range of water measurement from multiple test runs Figure 4.13 Comparison of local distribution of gas stream RH between Condition 0 and 3 under (a) 60 C (b)70 C. Arrow indicates flow direction Figure 4.14 Comparison of voltage, ASR and NWD between experiment (EXP) and model (MOD) under Condition 4. Error bars represent the range of water measurement from multiple test runs xvi

17 1. Introduction 1.1. Electrochemical Reaction For a basic electrochemical reaction to occur, there are several necessary components, as shown in Figure 1.1. The electrode is where the electrochemical reactions occur. Electrochemical oxidation reactions occur at the anode surface, resulting in the transport of electrons and increase in the valence state of reactant. Electrochemical reduction reactions occur at the cathode, resulting in consumption of electrons and decrease in the valence state. Reduction and oxidation accompany each other and are referred to as a redox reaction. The electrolyte, which can be liquid or solid, serves the purpose of conducting ions from one electrode to another, separating fuel and oxidizer, and preventing an electronic short-circuit between the electrodes. An external connection between electrodes is necessary to ensure continuous current flow in the circuit. Electrochemical reaction is similar to a purely chemical reaction in some aspects. Both utilize fuel and oxidizer as reactants. Both derive the desired output of useful work from chemical bond energy released via fuel oxidation. For the same fuel and oxidizer, the overall chemical reaction and the potential energy release by the reaction are identical. However, a clear distinction can be made between electrochemical reaction and purely chemical reaction. Usually in chemical reactions, heat is first generated by fuel and oxidizer reaction and then converted to useful work via mechanical process. In contrast, in electrochemical reactions the same enthalpy of reaction is directly converted into electrical current via electrochemical process. The process of conversion of the enthalpy of reaction to useful work is the fundamental difference between electrochemical reaction system and chemical reaction system. Another difference between two systems is fuel and oxidizer must be separated by electrolyte in electrochemical system, while they are generally preferred to be well mixed in chemical system. Fuel cells and batteries are the two most common electrochemical energy conversion devices. They differ from each other in that in the battery, fuel and oxidizer are continuously depleted and performance can 1

18 only be recovered by recharging; in the fuel cell, performance will not degrade as long as fuel and oxidizer are continuously fed into the system. 1.. Classification of Fuel Cells Fuel cells can be classified based on the electrolyte material, fuel utilized or operating temperature. As fuel cell classification by temperature has become relatively blurred, it is more common to categorize fuel cells by electrolyte material first and use fuel for sub-classification. Table 1-I lists the electrolyte material, operating temperature, major poison, advantage, disadvantage and application of major types of fuel cell. Polymer Electrolyte Fuel Cell (PEFC) PEFC, also referred to as solid polymer electrolyte fuel cell (SPEFC), proton exchange membrane fuel cell (PEMFC), or polymer electrolyte membrane fuel cell (PEMFC), uses flexible perfluorosulfonic acid polymer as electrolyte. Hydrogen PEFC and direct methanol PEFC are the two types of most-seen fuel cells. Hydrogen PEFCs are fueled by either pure hydrogen or hydrogen mixture generated from a reformate. Hydrogen PEFCs are considered as the most viable alternative to heat engines in automotive, stationary and portable power application. Main technical challenges on research and development include cost reduction due to noble metal catalyst and other components, heat and water management due to relatively low operating temperature, and durability. Hydrogen PEFC will be discussed in much greater detail in the following chapters. Direct methanol fuel cell (DMFC) is the most developed direct alcohol fuel cell. The electrochemical reactions involved are: oxidation reaction on anode: CH3OH HO 6e 6H CO reduction reaction on cathode: 3 6H O 6e 3HO

19 Compared with hydrogen PEFC, DMFC overcomes the problems of fuel storage and transportation, hydrogen availability and ancillary components in that it is directly fed by liquid methanol and requires less ancillary equipment. Although its efficiency, performance and cost is inferior to hydrogen PEFC, this does not preclude its attractiveness as the most viable alternative to lithium ion batteries in portable applications and in stationary and distributed power area as well. The major limiting factors to DMFC development include: water management issues as seen in other low-temperature fuel cells; methanol crossover that causes significant reduction in open-circuit voltage; poor anode kinetics; two-phase flow regime on both anode and cathode, especially the counter-flow and removal of carbon dioxide. Alkaline Fuel Cell (AFC) Similar to PEFC, AFC is operating under relatively low temperature range. It utilizes a solution of potassium hydroxide (KOH) in water as alkaline liquid electrolyte. Its global anode and cathode reactions are oxidation reaction on anode: H OH HO e reduction reaction on cathode: 1 O H O e OH Its advantages in low cost of raw materials, high demonstrated efficiency, and robust operation under a wide range of operating conditions make it suitable for its original space application. However, the intolerance to even a small fraction of carbon dioxide and complicated system design resulting from water and electrolyte management hinders its commercial development and application. Phosphoric Acid Fuel Cell (PAFC) PAFC is named by its acidic liquid electrolyte of high concentration phosphoric acid contained by a porous silicon carbide ceramic matrix. PAFC is similar to PEFC in many ways, except the acid-based electrolyte is in liquid form and the operating temperature is slightly higher. Its global anode and cathode reactions are the same as hydrogen PEFC: 3

20 oxidation reaction on anode: H H e reduction reaction on cathode: 1 O H e HO The advantages of PAFC have been shown in the following aspects: ease of water management because flooding is not an issue at operating temperature and highly concentrated acid electrolyte does not require water for conductivity; higher tolerance to CO than PEFC due to higher operating temperature; demonstrated long-life reliability. However the following issues need to be addressed for its commercial application at a large scale: bulky system and resulting low system power density makes it not competitive for automotive application; relatively long warm-up time due to its operating temperature; loss of electrolyte in vapor phase over time is substantial; high costs make it not commercially competitive with other types of fuel cells. Solid Oxide Fuel Cell (SOFC) SOFC is one of the representatives of higher temperature fuel cell, where solid ceramic is used as electrolyte. Its global anode and cathode reactions are: oxidation reaction on anode: H O HO e reduction reaction on cathode: 1 O e O This means in the solid state electrolyte, O - ions are passed from the cathode to the anode via oxygen vacancies in the electrolyte and water is produced at the anode, which is different from other fuel cells. The high temperature operation of SOFC eliminates some technical barriers common to low and medium temperature fuel cells: noble catalyst utilization is not necessary at high temperature; ionic loss is negligible if the temperature is sufficiently high; water management is not a headache at all because of the physical state; waste heat is of good quality and can be used in cogeneration system; CO can act as a fuel 4

21 instead of poison and therefore increase fuel flexibility. However, it suffers its own limitations: high temperature operation requires long start-up time; ionic conductivity is adversely impacted if operating temperature is reduced; durability of components is reduced under high temperature; proper cell sealing is not easy to achieve due to non-uniform thermal stress. Molten Carbonate Fuel Cell (MCFC) MCFC is another example of high temperature fuel cell. It utilizes molten mixture of alkali metal carbonates retained in a solid ceramic porous matrix. The global anode and cathode reactions involved are: oxidation reaction on anode: 3 H CO H O CO e reduction reaction on cathode: 1 O CO e CO 3 Unique to such fuel cell systems is CO is consumed in electrochemical reaction at the cathode, converted into carbonate anion, carrying the current through electrolyte, and converted back into CO at the anode. While it eliminates technical barriers in low and medium temperature fuel cell by operating at higher temperature, such as fuel flexibility since CO can act as fuel instead of poison, inexpensive catalyst because of high temperature operation, and quality waste heat, it suffers similar problems to SOFC, such as long start-up time and durability. Different from SOFC, MCFC has its unique drawbacks: carbon dioxide needs to be injected into the cathode stream to maintain electrolyte stability; and the liquid electrolyte needs to be well maintained or it will be lost in vapor form. In summary, different types of fuel cells have their own advantages and disadvantages and accordingly their application realm. In the following text, focus will be exclusively on PEFCs, and hydrogen PEFCs in particular, since they are believed to be the most logical choice for future power. 5

22 1.3. Working Principle of PEFC Figure 1. is a schematic of generic fuel cell with components common to most types of fuel cells. Fuel and oxidizer stream, in either liquid- or gas-phase, enter the flow channels separately. Reactant flow channels can collect current as well. Some fuel cells have a porous layer between electrode and reactant flow channel to transport electrons and species to and from the electrode surface. Reactants are transported by diffusion and / or convection to the electrode (catalyst layer). At the anode electrode, the electrochemical oxidation of the fuel produces electrons that flow through the bipolar plate (also called cell interconnect) to the external circuit. The ions generated migrate through the electrolyte to complete the circuit. The electrons in the external circuit drive the load and return to the cathode electrode, where they recombine with the oxidizer through electrochemical reduction reaction. The products of the fuel cells are chemical products, waste heat and electrical power. Specific to PEFC, each basic component has its unique materials, structure and design features. Component A and H in Figure 1. are called anodic and cathodic current collectors since the flow is fuel and oxidizer, respectively. They are also called bipolar plates or cell interconnect in a stack arrangement, where the anodic current collector is also the cathodic current collector on the opposing side. They collect current in a single cell and connect the anode or cathode of adjacent cells in series in a stack. The main functions of current collectors include: conduct electrons to / from external circuit in a single cell or adjacent cell in a stack; deliver reactant flow through the flow channels, labeled B and G, by diffusion and / or convection to electrode, where fuel oxidation or oxidizer reduction occurs; provide structural integrity of stack; and dissipate waste heat generated by reaction with coolant flow through current collector. Component B and G in Figure 1. are the flow field. They can be machined directly in the current collector plate, as in most cases, or be a discrete part. The main functions of flow field include: facilitate fuel and oxidizer transport to respective electrode; and facilitate product removal from catalyst layer. Because of the highly-coupled heat transfer, mass transfer and electrochemical phenomena, significance of flow field design should not be under-estimated. A variety of flow field designs have been proposed to 6

23 optimize reactant delivery, product removal, heat transport, parasitic loss and machinability, although each design has particular advantages and disadvantages. Most mainstream flow fields will be examined in detail in next chapter. Component C and F in Figure 1. are anode and cathode electrode, respectively. This thin layer is the location of the complicated electrochemical reaction. The main functions of the catalyst layers include: facilitate reactant transport to the reaction sites; facilitate product removal from the reaction sites; enable fuel oxidation and oxidizer reduction reaction via catalyst; conduct ions from the reaction site to the electrolyte labeled as E; and conduct electrons from the reaction site to the current collector labeled as A and H. Since the electrochemical oxidation and reduction reaction occur only at the simultaneous presence of reactant, catalyst, ion conductor with continuous path to the main electrolyte, and electron conductor with continuous path to the current collector, the electrode must have a high degree of mixed ionic and electronic conductivity and porosity. To achieve this, catalyst layer is made a porous, highly three-dimensional structure consisting of catalyst, electrolyte, electron conductor and voids for reactant transport. Therefore, the true active area of the porous electrode available for reaction is orders of magnitude higher than the geometric area of the electrode which is typically used for current density calculation. Although not shown in Figure 1., there is usually an electron-conducting porous layer, called diffusion media (DM) or gas diffusion layer (GDL), between the catalyst layer and the current collector. Its primary functions include: transport electrons to and from the electrode surface; and transport species to and from the electrode. Usually a woven carbon cloth or non-woven carbon paper is used in PEFC, the scanning electron microscopy (SEM) image of which are shown in Figure 1.3 (a) and (b) respectively. Component E in Figure 1. is the electrolyte. Its main functions include: physically separate the reactants; conduct the charge-carrying ions from one electrode to the other; and prevent electronic conduction between anode and cathode. 7

24 1.4. Literature Survey Model Dimensionality As depicted in Figure 1., the fuel cell is a three-dimensional structure in nature. The through-plane direction (indicated as z ) accounts for transport phenomenon across different layers. The in-plane direction (indicated as x ) takes into consideration the transport inhibited by flow field architecture in parallel with layer surface plane. The transport in the same direction as the gas feed is solved by the along-flow direction (indicated as y ). The progress made in dimensionality is one of the most important indicators of ever-improving fuel cell computational models in the past several decades. Zero-Dimensional Models Zero-dimensional models are the simplest description of the polarization behavior. They do not have any resolution inside the fuel cell and therefore are classified as zero-dimensional. They are in the form of a single equation, usually filled with empirical values or expressions. Despite their simplicity, they are a very useful experimental tool to decompose the overall over-potential into various losses and determine kinetics parameters [1]. A typical expression to describe the departure of the operating cell voltage from an ideal one is E cell E, T Pkinetics ohmic concentrat ion [1-1] As illustrated by Figure 1.4, the y axis of E cell is the cell voltage measured. E is the theoretical opencircuit voltage calculated by Nernst Equation, depending on hydrogen and oxygen partial pressure as well as temperature: E 3 T, P T 98 R ut P.303 log 4F P H H PO PO [1-] where kinetics, ohmic and concentrat ion represent the kinetics, ohmic and concentration over-potential, respectively. Although all types of losses contribute throughout the entire operating current range, one 8

25 type of loss dominates in a specific region. For example, Regions I, II and III in Figure 1.4 are dominated by kinetics, ohmic and concentration over-potential, respectively. Moreover, each loss term in Equation [1-1] can be expanded on as needed. Ohmic over-potential ohmic is usually expressed as: where ohmic ir [1-3] R refers to the sum of ohmic area specific resistance (ASR) contributions from flow field / DM contact resistance, DM / CL contact resistance, CL / membrane contact resistance, bulk resistance in DM, bulk resistance in catalyst layer as well as protonic resistance in the membrane. Table 1-II lists the typical value of non-membrane ohmic ASR from these contributions, which is the total ohmic ASR excluding protonic resistance in the membrane and highly dependent on compression and surface morphology. Zero-dimensional models are widely used in kinetics parameter determination [-8]. Kinetics overpotential kinetics is the kinetics loss from hydrogen oxidation resistance (HOR) and oxygen reduction resistance (ORR), i.e. kinetics [1-4] HOR Owning to the fast HOR kinetics on Pt, hydrogen oxidation loss HOR can be negligible [7]. Oxygen ORR reduction loss ORR, however, is much more significant because of sluggish ORR and is usually expressed as: where i x is the crossover current, i i x ORR blog [1-5] L ca APt, eli0 T, P O L ca is the Pt loading on the cathode. A, is the electrochemically available Pt surface area in the membrane electrode assembly (MEA). i 0 is the exchange current density Pt el 9

26 for ORR, which depends on temperature and oxygen partial pressure. b in Equation [1-5] is the Tafel slope, resulting from Tafel approximation of the Butler-Volmer Equation: where j is the charge transfer coefficient. RuT b.303 [1-6] F j Equation [1-1], [1-5] and [1-6] can be combined for a cell without mass transport loss to be: E cell E R ut T, P.303 log jf L ca i ix APt, eli0 T, P O ir [1-7] Experimentally, the exchange current density i 0 and charge transfer coefficient j can be found with a Tafel plot, as demonstrated by Figure 1.5. In this figure, i eff in x axis represents the measured current density corrected for crossover current as i. EiR free is the voltage corrected with experimentally ix determined ASR R as E cell ir. Therefore, charge transfer coefficient j can be determined from the slope of a semilog plot of corrected voltage versus corrected current and the exchange current density i 0 can be found with the intercept. The concentration over-potential way is [9-11] concentrat ion is primarily formulated in two empirical ways. One empirical mexp n i [1-8] concentrat ion where m and n are fitted by polarization curve data. Another way, which makes more physical sense, is [1] 10

27 i mlog 1 [1-9] concentrat ion ilim where i lim is the limiting current density, which occurs at the extreme of mass transport. Theoretically, at the mass transport limiting current density, the rate of mass transport to the catalyst surface is insufficient to keep up with the consumption rate required for reaction and thus local reactant concentration will be reduced to zero. Again, m is a fitting parameter to the polarization curve. In summary, the zero-dimensional models show the advantage of their simplicity especially in the experimental work. However, since there is no built-in resolution in any dimension, their robustness is limited to cases where some composition of over-potential can be neglected or clearly quantified. One-Dimensional Models The essence of the sandwich-like structure of fuel cell is its layer-by-layer design. The pioneering modeling work focused exclusively on the transport normal to various layers, shown as z in Figure 1., since it is the primary pathway of reactant transport for reaction [13-17]. The computational domain, as depicted in Figure 1.6, is generally comprised of flow fields, diffusion media, catalyst layers and a membrane. Governing ordinary differential equations (ODEs) which describe the transport and reaction process inside layers are solved computationally. In addition to the general polarization behavior, the model is capable of predicting the profile of a specific quantity of interest, the sample of which is presented in Figure 1.7. Those seminal one-dimensional models have their derivatives [18-3]. Major improvements include the capability to handle two-phase flow or flooding issues in porous layer [4-41], resolve catalyst layer [4, 7, 40, 4-48] or simulate dynamic response [45, 49, 50]. Pasaogullari et al. [8] examined specifically the diffusion media flooding with the one-dimensional twophase model. Analytical solution of the governing equations showed that diminished oxygen delivery to 11

28 the active site and surface coverage of active catalyst by liquid water are the limiting factor at higher current density. Weber et al. [34] simulated the intricate interplay between thermal and water management. The impact of the heat pipe effect and the corresponding phase-change-induced flow was examined. The necessity of a non-isothermal two-phase model was highlighted to better handle the highly coupled heat and water management. Yoon et al. [40] put their agglomerate particle in catalyst layer into the context of porous electrode of the 1D model. The mass transport limitations observed in experiment with low platinum loading was found to result from increased oxygen flux and diffusion pathway through the film. Two-Dimensional Models In terms of the additional dimension on top of the through-plane one, there are two choices available: one is in-plane and the other is along-channel, the schematic of which is shown in Figure 1.8 (a) and (b), respectively. The need for additional in-plane resolution results from the conventional channel / land flow field design [51-75]. The two-dimensional multi-component transport model by Yi et al. [54] was used to study the interdigitated gas distributor. It was demonstrated that the forced flow-through condition created by interdigitation could result from narrower shoulder widths between inlet and outlet channel. It was also pointed out that diffusion still played important role in oxygen transport to reaction site although convection was greatly promoted by interdigitated flow distributor. He et al. [55] developed a model to examined the -D rib effect in their interdigitated flow field. The existence of the rib turned out to affect the overall performance to a significant extent in that gas is forced by both convection and diffusion through diffusion media to reach the next channel. As shown in Figure 1

29 1.9 (a), the effect of differential pressure across the inlet and outlet channels on local current density profile along the electrode width was examined. Natarajan et al. [56] applied their two phase model to the land / channel structure and clearly demonstrated the entrainment of liquid water in the gas diffusion layer under the rib. Their transient results also supported the conclusion that liquid water transport is the slowest mass transport phenomenon in the cathode and therefore is primarily responsible for the mass transfer restriction, especially over the shoulder. The importance of in-plane charged species transport was highlighted by Sun et al. [60]. They found it as important as oxygen diffusion in determining the overall electrode reaction rate. Unlike the majority of multi-dimensional models that predicted higher current density either under the land or under the channel, they believed it was non-uniform due to land / channel geometry and was a combined effect of electron, proton and oxygen species. Lin et al. [6] conducted a parametric study on relative dimension of land / channel as well as anisotropic properties in diffusion media. It was concluded that more channels, smaller shoulder width and higher inplane permeability of diffusion media would enhance liquid water transport, and thus better performance could be achieved. Meng et al. [65] developed a non-isothermal two-phase model to investigate the land / channel structure. The existence of the evaporation / condensation interface was highlighted and its location changed with humidification. The non-isothermal behavior confirmed the experimental observation that porous media directly under the channel was relatively dry. Water management coupled with thermal management was explored by Meng et al. [73] in their twophase model. Land / channel effects on liquid water formation, transport and distribution were revealed. The move of lateral current density peak from under-the-channel to under-the-land indicated dictating mechanism from oxygen supply to membrane hydration, as highlighted in Figure 1.9 (b). 13

30 The effects of spatially-varying GDL properties and non-uniform land compression were considered by Wang et al. [75]. It was shown that in-plane GDL property variation caused by land compression could impact local water distribution inside the diffusion media. The varying gas composition and resulting non-uniform distribution of reactant, water and current are typical along-the-channel effects and lead to the necessity to account for transport in the along-channel direction. Although transport in the along-channel direction is solved to full extent in some work [76-9], there were numerous work that treated it in a simplified fashion [93-104]. Singh et al. [77] solved transport in the through-plane and along-channel directions completely to study the -D nature of fuel cell. It was found that the counter-current flow configuration yields worse performance than co-current one because of severe polarization. The net water transport across the membrane along the channel led to the significance of two-dimensionality on water management. Fuller et al. [93] established a psudo-d model to capture the along-channel effects in a simplified fashion. The varying gas composition and non-uniform current were shown in Figure 1.10 along with non-uniform temperature and net water transport along the channel, which elucidated the necessity to account for the along-channel effects. The D model developed by Nguyen et al. [94] was slightly different than others in that through-plane direction is simplified while attention was paid to flow along the channel. In addition to the along-channel effects, such as local gas composition, temperature, performance and water transport, they emphasized the importance of humidifying anode stream due to insufficient back diffusion to keep up with electroosmotic drag at high current density. The issue associated with dry gas feed at low pressure was addressed by the pseudo D model developed by van Bussel et al. [95]. The advantage of counter-flow arrangement as a result of anode recirculation was confirmed by their modeling results under dry feeding gas. Additionally, the severe non-uniformity of local performance along the channel was revealed under such conditions. 14

31 Water transport was fully explored by the phenomenological model of Janssen et al. [99]. The more accurate prediction of local effective drag coefficient along the channel was enabled by treating water transport through membrane as under chemical potential gradient. The model was validated through direct comparison with experimental measurement and demonstrated the capability to predict local flooding and dry-out, both of which are detrimental to cell operation. Attention was paid to the impact of flow arrangement and pressure differential on overall performance in the pseudo D model established by Ge et al. [100]. A detailed comparison between co-flow and counterflow arrangement showed the internal humidification in counter-flow configuration and thus its advantage in dry or low humidity environment, but no significant improvement otherwise. It was also revealed that pressure differential could better hydrate the membrane along the channel and improve the overall performance. Sensitivity of along-channel current density distribution was evaluated by Berg et al. [101] in their 1D + 1 model under different flow arrangement, inlet humidity, gas stream composition and stoichiometry. Weber et al. [10] cast their previously-developed 1-D comprehensive sandwich model into the alongthe-channel context. The gas channel was divided into several elements, which were linked together by mass balance. Temperature effect on net water transport across membrane was examined specifically, and the through-plane resolution was also used to further explain observed modeling results. Three-Dimensional Model Figure 1.11 shows the computational domain of fully three-dimensional models, which combines the additional in-plane and along-channel resolution with the principal through-plane one and realistically reflects the fuel cell operation [ ]. One of the bonuses of having all three dimensions in the model is the capability to study non-conventional flow fields [13, 136, 14, 153]. However, the substantial increase in computational costs from fully solving mass, momentum, heat and charge conservation equations in three dimensions might outweigh those benefits. The computational issues which might arise 15

32 in this situation are convergence difficulties. On one hand, it has been well-recognized that transport in the in-plane direction has to be solved completely since no simplification can be made without neglecting the land / channel existence. On the other hand, pseudo two-dimensional models seem to work as well as full two-dimensional ones since they also capture all the same along-channel effects. Because of this, the full three-dimensional models were reduced by some researchers to the combination of pseudo 1D down the channel plus full resolution in the other two dimensions [156, 157]. In summary, although all dimensions need to be resolved to the full extent in the ideal situation, the associated computational cost is expensive and would not be a practical solution considering the computational resources available in most cases. For a conventional flow field, a pseudo threedimensional model, which can capture all the features in through-plane and in-plane transport while not missing along-channel effects, is a practical solution at much lower computational cost and is believed to be the best compromise between dimensional resolution and computational costs Model Treatment of Multi-Phase Flow Performance improvement has made fuel cell operation more and more plagued by water management issues, especially the delicate balance between dry-out and flooding. On one hand, efforts have been made on reducing the hydration-dependent resistance, such as making the membrane thinner and thinner, developing more conductive membrane material under relatively dry environment. On the other hand, a modeling tool that can help better understand flooding phenomenon becomes necessary. The following discussion only applies to models that have resolution in at least one dimension to solve multi-phase transport. Single-Phase Model During the initial period of fuel cell research and development, a single-phase model, which accounts for no more than gas phase transport, seems satisfactory [13, 19-1, 31, 4, 44, 47, 51, 53, 54, 57, 60, 69, 70, 78-80, 83, 84, 87, 91, 93, 95, 97, 98, 10, 107, 110, 111, , 119, 13-15, 130, 14, ]. 16

33 Simplified Two-Phase Model As the fuel cell performance progressed, water as a result of electrochemical reaction leads to local water vapor activity higher than unity. As the importance of two-phase flow in porous media became more and more recognized, the liquid water existence in the porous media could not be neglected anymore. In some early work where liquid water was accounted for explicitly in the model, its treatment was considerably simplified. It was considered to be a stationary phase only occupying the voids in porous media, or its transport was solved but phase transfer was not, or both transport and phase change were solved but the capability to predict local saturation was lost since it was assumed constant [1, 14-18, 3-5, 43, 45, 46, 55, 76, 77, 94, 96, 100, 101, 109, 135, 136, 138, 15, 154, 159]. The flooding phenomenon observed in experiment cannot be elucidated in a meaningful sense in these cases. Rigorous Two-Phase Model The most rigorous treatment of two-phase behavior should incorporate transport, phase interaction and local liquid phase volume fraction prediction [6-30, 3, 34-36, 38, 39, 41, 49, 50, 56, 58, 59, 61-66, 7-75, 8, 85, 86, 88-90, 104, 108, 114, 16, 18, 19, , 137, , 143, , 150, 151, 160]. Although multiphase mixture model is formulated differently, similar description of liquid water effects can be achieved [81, 105, 11, 113, 155, 161, 16]. In summary, two-phase flow in porous media is of great interest for water management because of its existence under most operating conditions especially under higher current density, its close relation to water removal mechanism in porous media, and its significant impact on performance from experimental observation. The presence of liquid water in diffusion media has been more and more recognized as one of the major limiting factors to higher current operation in fuel cell. The resulting blockage of diffusion pathways inside porous media is more severe under the rib in the conventional land / channel architecture. One thing that needs to be clarified is that some seemingly rigorous two-phase models[7, 3, 6, 89] made assumptions about isothermal conditions, therefore they were not able to capture the phase-changeinduced (PCI) flow, which has been proved to be another primary way of removing water out of cathode 17

34 besides capillary flow [163]. Instead, a truly rigorous two-phase model to account for liquid effects should take into account the temperature effects as well as capillary action, vapor-liquid interaction and local saturation Model Treatment of Catalyst Layer Although it is normally the thinnest layer in the fuel cell assembly, catalyst layer is undoubtedly the most complicated one. Transport of ions, electrons, mass and heat occurs here and electro-chemical reaction takes place at the phase boundary. In terms of the catalyst layer modeling, the complexity lies in the combination of membrane and diffusion media treatment while agglomerate particles need more specific description. Upon the review of catalyst layer modeling work, it is obvious that much more focus has been on cathode catalyst layer than the anode one. The underlying reason is the water production and removal and the sluggish oxygen reduction reaction kinetics. Interface Model In the early work of fuel cell modeling, the catalyst layer was not the focus and therefore was simplified to a considerable extent. The easiest level of catalyst layer treatment is to consider it as an interface between the membrane and diffusion media while neglecting its detailed structure. These models might differ from each other in that potential might not be predicted, or potential could be predicted from an overall polarization equation as the zero-dimensional model, or non-uniform current distribution could be yielded from kinetics inclusion. But one thing in common among all these interface models is the assumption of an infinitely thin catalyst layer [15, 6, 30, 51, 5, 54-56, 77-79, 81, 94, 98-10, 108, 109, 11, 114, 155, 157]. Weber et al. [10] put their detailed membrane model in the full cell context. To focus on their membrane model validation, catalyst layer kinetics was not considered explicitly while Faraday s Law was applied to account for reactant consumption and water production at the interface between membrane and catalyst layer. 18

35 In order to better examine the two-phase behavior in diffusion media, Weber et al. [30] ignored the water transport effects in the catalyst layer while keeping the polarization and ohmic effects. By assuming water transport in this thin layer would not significantly alter the overall water transport, the catalyst layer was reduced to an interface situated between diffusion media and membrane and a polarization equation was used instead of kinetics. The superiority of interdigitated flow field over conventional land / channel flow field was investigated by Kazim et al. with a mathematical model[5]. In order to elucidate the performance enhancement due to improved mass transfer under the rib, Butler-Volmer kinetics were used at the catalyst layer interface. Payoff from under-the-rib convection in interdigitated flow field can be discerned from direct comparison of local oxygen concentration and resultant current density distribution. Although the rationale behind interface model is the thickness of the catalyst layer itself, such resolution is far from adequate to account for relevant interactions in this layer. More details are required to ensure the proper evaluation of impact of either structure or operating parameters. Porous Electrode Model or Agglomerate Model The physical picture of the catalyst layer, as illustrated by Figure 1.1, reveals that it is in reality a structure of two length scales: through the porous layer and over the agglomerate particle. Therefore the level higher than ignoring catalyst layer structure is to model one of these two length scales, called porous electrode model and agglomerate model, respectively. With catalyst layer thickness as the characteristic length scale, porous electrode model cares about the reaction distribution across the catalyst layer [1, 14, 16, 18, 3, 43, 45, 76, 115, ]. The underlying assumption of porous electrode model is that there is no transport or reaction resistance inside the agglomerate. They differ from the interface catalyst layer model in that catalyst layer has a finite thickness and allows for diffusion in it. 19

36 Eikerling et al. [164] developed a macro-homogeneous model to find the distinguishing limiting factor in different regions of the polarization curve. Oxygen diffusion, proton migration and reaction kinetics were coupled to find the optimal catalyst layer thickness. In contrast to the porous electrode model, the agglomerate model uses agglomerate radius as the characteristic length scale [13, 46, 83, ]. Uniform gas concentration and surface over-potential are implied to neglect the non-uniform reaction rate distribution across the catalyst layer thickness. The actual reaction rate is solved by the information of effectiveness factor. Different analytical expressions are the results of different proposed geometrical descriptions of the agglomerate. Siegel et al. [83] modeled the catalyst layer based on an agglomerate geometry and investigated the impact of agglomerate size on performance. It was found that the reactant diffusion distance to reach reaction site and agglomerate radius were correlated and optimal agglomerate size did exist in the case of reaction rate dominating mass transfer rate. Gloaguen et al. [166] compared the macro-homogeneous model with the agglomerate model and concluded that macro-homogeneous model overestimated the oxygen transport limitation. In contrast, agglomerate model was a better representation of cathode catalyst layer in predicting mass transport resistance. Although there is no conclusive answer to whether porous electrode model is superior to agglomerate model or the opposite, the pros and cons of each one can be appreciated. Compared with using porous electrode model, the incentive of using agglomerate model is to enable the parameter optimization, such as agglomerate radius, catalyst loading and ionomer / carbon ratio. The drawback of the agglomerate model is its inability to account for distribution across the layer, such as reaction rate and proton migration. 0

37 Combined Porous Electrode and Agglomerate Model The catalyst layer model which combines the length scale of catalyst layer thickness with agglomerate radius is the state-of-the-art macroscopic treatment of the complex catalyst layer. Typically the agglomerate model is embedded in the porous electrode to account for both length scales [7, 40, 44, 47, 48, 60, 6, 67, 97]. Numerical optimization algorithm was applied by Secanell et al. [67] to find the optimal catalyst layer parameter to maximize the electrode performance under specific operating conditions. The specific catalyst-layer-related parameters under inspection were platinum loading, platinum to carbon ratio and ionomer volume fraction in the agglomerate. Different limiting factors, whether proton transport or mass transfer in high and low current density regimes, result in different schemes to improve performance effectively. The variations in optimal value with different agglomerate sizes and ionomer film thicknesses were also discussed. Yoon et al. [40] used the modeling tool to test the widely-used assumption in agglomerate model that the agglomerate is an equi-potential and isothermal particle and oxygen reduction is first-order reaction. Evaluating the effects of platinum oxide, ionomer film and non-unity reaction order was enabled by casting their rigorous agglomerate model in the porous electrode. It was concluded that the ionomer film and longer diffusion path can cause additional mass transfer resistance under lower platinum loading. Properties of the catalyst layer are closely related to water management and the interplay between dry-out and flooding. Limiting factors associated with the catalyst layer include: dry-out, which can be represented by proton resistance in the ionomer phase of catalyst layer; and flooding, which can be represented by oxygen transport resistance through gas voids of the catalyst layer; flooding, which can be represented by oxygen transport resistance through ionomer and / or water film. In particular, flooding in the catalyst layer, either described as water film on top of ionomer film or as covering the interfacial area of reaction site, is a major limiting factor to higher performance. 1

38 In summary, more and more insight into cathode catalyst layer has been provided through experimental observation and test. In the meantime, the findings using rigorous catalyst layer models have improved significantly the understanding of this complex layer and beyond. Design of cathode catalyst layer has been guided with the help of modeling work under specific operating conditions. Therefore, it is well expected that implementing a rigorous catalyst layer model can, to a great extent, determine the robustness of the full cell model and enable better understanding of the associated limiting factors Flow Field Study Flow field design is believed to be both the cause and solution to problems seen in fuel cell operation. In this respect, a valid model can be of great help in better understanding the pros and cons of each flow field. Proper water management is top concern of flow field design along with volume, cost and ease of manufacture. Some mainstream flow field prototypes are discussed in the following sections along with the corresponding modeling work. Parallel Flow Field Parallel flow field, as shown in Figure 1.13, is the earliest flow field structure proposed and is still widely-used in the fuel cell community due to its simplicity. Parallel flow field used to be the primary flow field design in numerous modeling work. With the recognition of its drawbacks and rapid development of improved design, such as serpentine, interdigitated, porous flow field and water transport plate, now the parallel flow field appears more often in flow field comparison study [116, 153, ]. Serpentine Flow Field and its Derivatives Serpentine flow field and some of its derivatives are shown in Figure There are flow field studies which focused on serpentine flow field[111, 11, 136, ], while it is often one of the subjects in flow field comparison study [116, 153, 175]. Compared with parallel flow field, the serpentine flow field has been found to have better water removal mechanisms at the price of a more significant pressure drop from gas inlet to outlet.

39 Interdigitated Flow Field Having recognized the limited in-plane diffusion in conventional land / channel architecture, researchers started to work on its improvement, such as an interdigitated flow field. Interdigitated flow fields were initially proposed by Nguyen et al. [185], the architecture of which is shown in Figure The rationale behind this design is by making the inlet and outlet channels deadended the reactant gas is forced to flow into the porous electrode and exit the cell. The significant performance improvement has been observed with such designs and the flow mechanism has been disclosed by both experiment and model [5, 54, 55, 117, 118, 13, 144, 151, 158, 175, 177, 18, 185, 186]. As the advocates of the interdigitated flow field, Nguyen et al. [185] used the extended mass-transferlimited region in their test results to support the idea that this flow field design converted gas transport from diffusion to convection mechanism, gas diffusion layer could be greatly reduced and the shear force of the flow could help remove entrapped water. Wood et al. [158] used direct liquid water injection as the gas humidification scheme on interdigitated flow field. In addition to the extended mass-transfer-limited region, interdigitated flow fields turned out to be capable of handling higher water flow rate and achieve effective water management with direct liquid injection. Yi et al. [54] found out the diffusion layer thickness could be greatly reduced thanks to the forced flowthrough condition created by interdigitated gas distributor design while diffusion still played significant role in oxygen transport to reaction site. A narrower shoulder between inlet and outlet channels was found to further increase the average current density. The two-phase flow solved by He et al. [55] in an interdigitated flow distributor revealed the two primary mechanisms to remove water entrapped in porous electrode: shear force and capillary force. Higher 3

40 differential pressure between inlet and outlet channels could lead to higher oxygen transport rate and more effective liquid water removal and therefore enhanced performance. Darling et al. [177] used porous bipolar plates (called water transport plate) together with an interdigitated air distributor. Due to the facile water evaporation from the water transport plate and well-controlled saturation in channel and GDL, oxygen delivery inside the cell can be approximated as occurring under fully humidified conditions everywhere. Interdigitation was found to transport more oxygen by convection and diffusion to the cathode catalyst layer occluded by the ribs. In summary, since the interdigitated flow distributor kept the traditional land / channel structure, reactant delivery to and product removal from under-the-rib region was the top concern. The capability of interdigitated flow field in promoting forced convection under the rib was identified as the fundamental reason for mass transfer enhancement. Porous Flow Field and its Derivatives Porous flow field simply eliminates rib from the flow distributor and is another way to circumvent the drawbacks associated with rib existence. It is technically an open area for flow distribution, as shown in Figure Substantial performance improvement has been observed as well[106, 110, 116, 13, 187, 188]. Kumar et al. [110] compared the metal foam flow field with the conventional multi-parallel flow field design. The superiority of metal foam flow field can be attributed to the more uniform distribution of current density. The performance was found to increase with metal foam permeability decrease in the range of 10-6 to 10-1 m but slower increase rate below the order of electrode permeability (10-1 m ). Senn et al. [116] showed the advantage of porous flow distributor over ribbed flow field in terms of enhanced mass transfer and substantially higher cell performance accordingly. Moreover, reduction in stack weight and manufacturing costs were also suggested. 4

41 Bigersson et al. [13] compared the parallel, interdigitated and porous flow distributor in terms of cell performance and current distribution over the catalyst layer. The interdigitated distributor was found to yield the highest performance followed by foam, counter-flow parallel and co-flow parallel. Foam was found to yield the most uniform local current distribution. However, care was suggested on permeability of the foam flow field to avoid unreasonably high pressure drop. The feasibility of using metal foam as flow distributor was explored by Arisetty et al. [187] in direct methanol fuel cell. A parametric study on pore size distribution demonstrated the competing effects on current collection capability and gas transport characteristics with varying pore size. The feasibility of using metal foam as gas diffusion layer was discussed as well. Performance gain and susceptibility to corrosion were found to be the pro and con, respectively. The feasibility of using porous carbon foam in polymer electrolyte fuel cell was investigated by Kim et al. [188]. The impact of material properties, such as PPI and thickness, on performance was studied and competing effects between effective electronic conductivity and effective area for reactant gas distribution were evaluated. It was confirmed that porous carbon foam possessed acceptable stability and showed its advantage under well-humidified conditions. Water Transport Plate and its Derivatives Porous bipolar plates, or called water transport plate, were another good example of solving water management issue with flow field design [104, 174, 176, 177, 189]. This flow field design was mostly practiced by UTC and limited information has been disclosed to open literature probably due to proprietary issues. According to the description, the schematic of such flow field is similar to Figure It differs from the porous flow field introduced above in that the rib structure was kept along with the flow channel but was made porous and permeable (only to liquid) instead of solid. Yi et al. [189] identified the liquid water in the gas channel as an unavoidable issue for fuel cells of any practical size. The contradicting needs between higher pressure drop for better performance and lower 5

42 pressure drop for less parasitic loss made overall system design tricky. As it was suggested, the intra-cell water exchange scheme, which replaced the solid rib with a porous water transport plate, could remove or supply water within the cell depending on local demand. Such design could therefore minimize issues associated with liquid water existence and MEA dry out. Another feature pointed out was the feasibility of operation under ambient pressure since high pressure drop was not required in the flow channel. Numerical simulation was conducted by Weber et al. [104] on water transport plate in comparison to conventional solid plates. Performance was observed to be substantially improved on water transport plate, which could be attributed to the effective liquid water removal into the water plate under wet conditions and spontaneous reactant stream humidification under dry conditions from water in the plate. Properties of the water transport plate, such as pressure differential between the reactant and coolant stream, was investigated as well. Darling et al. [177] tried to combine the benefits of interdigitated flow field with water transport plate. It was reasoned that the coupling between liquid water and gas transport in interdigitated flow field with solid rib could be eliminated by the replacement with a water transport plate. Since the water transport plate played the role of removing excess liquid water and compensating for insufficient water, the gas feed was saturated and the liquid and gas transport in the gas diffusion layer could be decoupled. Litster et al. [174] compared the performance of a standard, non-porous graphite plate with a porous, hydrophilic carbon plate. The concerns with non-porous plates, including electrolyte dry-out, severe flooding and power density transient were mitigated in porous plates. Better water management was hypothesized to result from capillary action in the porous plate, removing the excess water downstream from the channel, pumping water upstream to the dry inlet and redistributing water throughout the cell. With the help of the porous plate, flooding can be avoided even with low stoichiometry and membrane can be ensured to be fully humidified. 6

43 Similarly, Strickland et al. [176] coated the channel flow field with a polymer wick to achieve passive water management. It was demonstrated that the flood-free operating with wick channel can reduce required air stoichiometry and minimize parasitic loss while ensuring oxygen delivery. In summary, the ultimate goal of a good flow field design is the proper water management scheme, including excess liquid water removal, reactant delivery, water replenishment in dry region and parasitic loss reduction. Spontaneous internal water circulation would be preferred so that humidification load can be greatly reduced Experimental Diagnostics Although current work is model-based, the importance of experiments in model development, validation and application is never under-estimated. The accuracy of the model is, to a large extent, relying on the accuracy of the experimental characterization. The significance of experimental efforts in current modelbased work is even more than that: the experimental diagnostics will provide benchmark data for model validation and thus have profound impact on model parameter tuning. DC Polarization The capability to predict polarization behavior is one of the basic functions of model. Therefore, the polarization curve becomes a natural choice to test the model validity. Validation of the developed model in terms of polarization behavior was seen in almost every modeling work, if the model was validated at all. Usually if the polarization curves from experiment and model under the same specific operating conditions compared favorably with each other, the model was considered to be accurate and the modeling results followed were considered to be convincing [14, 16, 55, 76, 77, 80, 95, 165]. This tool seemed very useful at a time when experimental diagnostics were relatively undeveloped. As explained in Chapter 1.4.1, polarization behavior is a lumped result, including kinetics, ohmic, concentration and other losses. Although information can be gleaned by different polarization curves corresponding to varying operating conditions, it is not straightforward to distinguish each contributing 7

44 loss in the polarization behavior. Therefore, it is somewhat dubious to draw conclusions on the model s accuracy based on the polarization curve agreement alone. Area Specific Resistance (ASR) The ohmic parameters and polarization need to be quantified. At very high frequencies the alternating current will render the various electrochemical double-layer capacitances to zero so that only purely ohmic resistance will be left and captured. This in-situ diagnostic tool is called ASR to eliminate the difference in cell geometric area or more often high frequency resistance (HFR) due to its working principle. ASR measurement is interpreted as purely ohmic resistance, i.e. the sum of contact resistance between components, ionic resistance in membrane and electronic resistance in all components. It has been believed to be the most reliable experimental method found so far to quantify ohmic losses. While the contribution of contact resistance is a strong function of compression and surface morphology, the contribution of ionic resistance is deemed as an indicator of membrane hydration. However, caution should be taken in ASR data analysis in that this approach only measures the path of least resistance. The problem with separating ionic loss from other losses in the electrode cannot be solved by ASR. The underlying reason is the electrical resistance is generally much less than the ionic resistance in the mixed conductivity structure, therefore ASR normally measures the electrical resistance only. Water Measurement As another in-situ experimental diagnostic tool, water measurement and the calculation of net water drag (NWD) coefficient inside the cell is supposed to be straightforward. However, it is somehow rarely seen in either experimental or modeling work [15, 3, 94, 99, ]. One common way to measure the water balance in an operating fuel cell is through effluent collection. In this approach, the humidified effluent gas from the fuel cell is chilled through a condensing bath or desiccant and the total water content removed over time can be determined. Although this approach cannot provide distributed information on 8

45 local water transport across the membrane, NWD coefficient can be calculated, which gives some idea about overall water balance. Electrochemical Impedance Spectroscopy (EIS) EIS has become more and more popular these years in study of complex electrochemical problems, such as fuel cells [196-07]. Its working principle is: the total voltage loss in a fuel cell at a given current density is a result of combinations of ohmic and non-ohmic contributions; The ohmic contributions can be studied using direct current (DC) techniques while non-ohmic contributions normally have frequencydependent response times, which makes them suitable for alternating current (AC) techniques. The characteristic response of the electrochemical system to the applied AC signal of varying frequency can be used to discern qualitative details of the kinetics and concentration polarization behavior at the electrode. The real difficulty of experimental diagnostics lies in cathode catalyst layer, the schematic picture and one-dimensional transmission line equivalent circuit are shown in Figure The result of EIS is usually demonstrated by the Nyquist plot of imaginary versus real impedance. Figure 1.19 shows a generalized Nyquist plot. As can be observed, at high frequencies the intercept with real impedance represents the ohmic resistance, as mentioned above about ASR; at medium frequencies the semicircle response is a result of charge transfer resistance across double layer; at very low frequencies the mass transport resistance dominates the response. Despite the limitation of EIS on quantitative description of individual loss and heavy reliance on equivalent circuit selection, a wealth of qualitative information can still be gained for better understanding of the polarization behavior. Distributed Measurement It was realized early that the fuel cell performance varied with location in a single cell, such as the coexistence of local flooding and dry-out inside the cell. The bulk voltage, current and ASR data is far from sufficient to explore the cell limitations in this respect. Spatial variations in terms of current, 9

46 temperature, reactant concentration, and ASR can be easily calculated from the model that is twodimensional and up. The experimental diagnostic tools, however, were developed much later to improve fundamental understanding of local competing physiochemical phenomenon[08-15]. The local variation in current distribution is obvious among fuel cells, especially for those with large geometric area. A cell with small active area may have a nearly uniform current distribution, while larger area cells may have steep gradients resulting from local humidity, flooding, species concentration and temperature. The gradient in local species concentration is well-expected, especially when the stoichiometry is not high. Under low stoichiometry operation, the depleting reactants towards the flow field exit may result in considerable concentration limitation. The variation in local temperature inside the single cell can be significant if the cooling scheme is not effective or if the cell is operated under high current density. The local hot and cold is a contributing factor to local flooding or dry-out observed. The net water transport across the membrane along the channel and the corresponding impact on local amount of water is the ultimate reason for local flooding and dry-out. Distributed EIS measurement can give qualitative idea about local ohmic, charge transfer and mass transfer loss and can verify model prediction to a certain extent. Direct Visualization Technique Several major direct visualization techniques which have been applied to PEFC study are summarized in Table 1-III. Among the techniques listed in the table, neutron radiography is most widely-applied [41, 16-5], the working principle of which can be illustrated by Figure 1.0. The sample results of neutron image and reduced liquid water amount are shown in Figure 1.1 (a) and (b) respectively. Neutron radiography is good at distinguishing liquid water from gas phase species and can therefore provide good information about amount of liquid water and its spatial distribution inside the cell. However there is still room for improvement with regard to the spatial and temporal resolution. In the meanwhile advanced data analysis technique needs to be developed to quantify liquid water amount with less error. 30

47 1.6. Motivation A porous flow field has demonstrated its capability to enable ultra-high current operation. However, the details in performance improvement have not been given in past literature. The underlying reasons for the significant performance improvement associated with such design have not been explored in depth. The ultimate performance limitation in such design has not been fully understood yet. Therefore, this flow field was examined in detail in this work. The ultra-high current operation of PEFCs has been hampered by water management issues for long time. The most recent advances in the materials and designs have demonstrated stable operation at a current density greater than A/cm. The achievement of such high current density, however, is expected to be accompanied by unprecedented challenges in heat and water management. Because it is normally unable to reach this level of high current at a reasonable voltage, this operating regime has been largely unexplored in the scientific literature from either experimental or modeling perspective. Ultra-high current operation and the possible related new operating features were the subject of this work. A comprehensive model is needed to rise to the challenges in ultra-high current operation. Rigorous treatment of multi-phase water transport is a must. The length scales of porous electrode and agglomerate particle need to be both covered in the catalyst layer. Unlike most half-cell agglomerate models published so far, water balance between electrodes need to be simulated. Two-dimensional models, which accounted for either in-plane or along-flow direction in addition to through-plane transport, may not be sufficient to resolve all the transport issues in high current regime. Considering the computational resources and efficiencies, a compromise between the computational cost and dimensional resolution needs to be reached. Such a model was developed in this work to better handle all these complexities in the operating regime at a reasonable cost. The close collaboration between experiment and model is demonstrated throughout this work. Structural and transport parameters and correlations implemented into the model rely heavily on experimental 31

48 measurement and characterization, which is ubiquitous in our model development. Moreover, experimental diagnostics can produce benchmark data for model validation. However, model validation has been difficult and generally limited to polarization curve comparison under few, if more than one, selected test conditions. The robustness of the model is going to be tested more extensively in this work. In turn, predictions from a validated model can improve the understanding of what is observed in experiments. Typically the model can give much more details than what experiments can offer due to limitations in experimental techniques. In this work, the information contained in the wealth of model prediction is going to shed light on some experimental observations which cannot be sufficiently resolved by diagnostic tools. Moreover, the validated model can be utilized to engineer cell operation in this work to overcome potential limiting factors and enable stable and high performance under desired conditions. 3

49 Table 1-I Classification and Description of Fuel Cells. From [6] 33

50 Table 1-II Contributions to Non-Membrane ASR Contributions ASR ( m cm ) Reference Two FF / DM contact resistance 13 ~ 16 [00], [7] Two DM / CL contact resistance 3.4 [00] Two CL / membrane contact resistance 3.5 ~ 5.5 [7] Two bulk DM electronic resistance.8 [00] Two bulk CL electronic resistance 1. [00] Total 6 34

51 Table 1-III Summary of visualization techniques applied to PEFC. From [6] 35

52 Figure 1.1 Basic Electrochemical Reactions. From [6] 36

53 Figure 1. Schematic of a generic fuel cell. From [6] 37

54 (a) (b) Figure 1.3 Scanning Electron Microscope (SEM) Image of (a) Woven Carbon Cloth (b) Non-woven Carbon Paper. From [6] 38

55 Figure 1.4 Typical Polarization Curve of Fuel Cell. From [6] 39

56 Figure 1.5 Tafel plot of oxygen reduction reaction as current-overpotential curve. Different cathode catalyst loadings are tested in H -O PEFC at 80 C. Tafel slope for all conditions is approximately 65mV/decade. From [3] 40

57 Figure 1.6 Computational domain of 1D model. From [16] 41

58 (a) (b) Figure 1.7 Sample results of 1D model: (a) Computed water profiles in Nafion 117 for four current densities under base-case conditions at constant gas flow rate equivalent to unity stoichiometry at 1A/cm. From [15] (b) Model calculation of concentrations of dissolved gas in the membrane phase throughout the fuel cell (base case operating conditions). From [16] 4

59 (a) (b) Figure 1.8 Computational domain of D model incorporating through-plane and (a) in-plane From [70] (b) along-channel direction From [97] 43

60 (a) (b) Figure 1.9 Sample results of D model incorporating through-plane and in-plane direction: (a) Effect of differential pressure on the local current density profiles along the electrode width From [55] (b) Lateral current variation inside the membrane at three different cathode gas humidity conditions From [73] 44

61 Figure 1.10 Sample result of D model incorporating through-plane and along-channel direction: mole fraction of hydrogen, oxygen and water in the gas channel. Local current density is shown by the solid line. From [93] 45

62 Figure 1.11 Computational Domain of 3D model. From [14] 46

63 Figure 1.1 Structural picture of cathode catalyst layer depicting (a) various components and porous structure at macro-homogeneous scale (b) composition and reaction spots inside single agglomerate. From [8] 47

64 Figure 1.13 Schematic of parallel flow field. From [175] 48

65 Figure 1.14 Schematic of serpentine flow field (a) single serpentine (b) double serpentine (c) triple serpentine. From [136] 49

66 Figure 1.15 Schematic of interdigitated flow field. From [185] 50

67 Figure 1.16 Schematic of porous flow field. From [188] 51

68 (a) (b) Figure 1.17 Schematic of water transport plate as bipolar plate (a) cross-section view From [189] (b) close-up of porous backing plate From [174] 5

69 Figure 1.18 (a) Schematic picture of catalyst layer structure (b) one-dimensional transmission line equivalent circuit with proton resistance R p, charge transfer resistance R ct, electronic resistance R el and double layer capacitance C dl. From [196] 53

70 Figure 1.19 Ideal Nyquist plot showing general regions of polarization losses. From [6] 54

71 Figure 1.0 Schematic of test cell and imaging area. From [3] 55

72 (a) (b) Figure 1.1 Evolution of water build-up inside the test cell (a) Neutron image (b) liquid water content reduced from neutron image. From [3] 56

73 . Model Development The computational domain of the D + 1 model is shown in Figure.1. The computational domain of the -D sub-model is comprised of the polymer electrolyte membrane (PEM), sandwiched by catalyst layer (CL), micro-porous layer (MPL), macro-porous diffusion medium (DM) and flow field (FF) on anode and cathode side, respectively. This model formulation is applicable to both parallel land / channel flow field and porous flow field by simply replacing the corresponding layer in the computational domain..1. Model Assumption Strictly speaking, the fuel cell operation is a dynamic process, as can be confirmed by dynamic water transport in Figure.. The transient phenomena inside the fuel cell, especially the non-equilibrium phase transfer between liquid water and water vapor and non-equilibrium membrane sorption / desorption process, will exert influence on the dynamic response of the cell to load change or step change in operating conditions [49, 56, 64, 69, 70, 80, 89, 103, 1, 17, 146, 148, 180, 181, 9]. However, since steady-state operation is of more interest in current work, the transient nature exhibited during start-up, shut-down and operating condition change will not be addressed and the phase change phenomena such as evaporation / condensation and membrane water sorption / desorption will be approximated as occurring at an infinite rate. As found by Ge et al. [103], absorption / desorption of water in membrane occurs at different rates. In a steady-state model, however, water vapor in MEA is assumed to dissolve into the ionomer phase instantly based on equilibrium water sorption. Namely, the membrane sorption / desorption process occurs at an infinite rate and thus the transient nature of membrane water sorption / desorption is neglected. As another major dynamic process, phase transfer between liquid water and water vapor, is assumed to occur until phase equilibrium is achieved. Namely, the evaporation / condensation process occurs at an infinite rate and thus the its transient nature is overlooked. 57

74 There is wide controversy in multi-phase models regarding whether the product water is in vapor, liquid or dissolved form [147]. It makes physical sense that in the electrochemical reaction water is produced in dissolved form and transfer between vapor, liquid and dissolved phase occurs simultaneously but at different rates. However, since phase equilibrium is assumed between all three phases in this work, the form of product water in electrochemical reaction will not make difference in numerical solution. In the case of flow in very small pores or channels, as illustrated by Figure.3, molecular collision with solid walls or channels might be as significant as collision with another molecule to make the overall diffusion behavior deviate from Fickian diffusion theory. The dominance of Knudsen diffusion increases as pore size decreases and molecular interaction with wall becomes more and more significant. Considering the relative pore size of the individual layer, Knudsen diffusion is taken into consideration only in the catalyst layer and micro-porous layer [30]. The effective diffusion coefficient is calculated as Knudsen diffusion in series with molecular diffusion in terms of gas phase transport. Local maximum and minimum are typically observed in through-plane water profile from high-resolution neutron imaging or X-ray, as shown in Figure.4. However, monotonic change in liquid profile across GDL is usually seen in model prediction. Wang et al. [75] attributed this discrepancy in water content across GDL to the assumption that GDL is a uniform media with constant property throughout GDL thickness. They calculated spatially varying GDL properties resulting from uneven compression and predicted the local peaks in liquid water profile across GDL. However, since the local peaks and water traps in GDL is not of interest in current work, material properties in each layer are assumed to be homogeneous, but can be anisotropic in through-plane and in-plane direction. The diffusion media and micro-porous layer are assumed to be hydrophobic for better water removal. Therefore liquid is the non-wetting phase and gas is the wetting phase. In the agglomerate catalyst layer model on the cathode side, the agglomerate particle is assumed to be a sphere. The assumption of isothermal and equi-potential particle widely used in agglomerate models has 58

75 been confirmed by Yoon et. al [40] to be valid. ORR is widely assumed to be first order reaction although it was found by some work to deviate from unity [5, 40, 31]. Reactant crossover is not considered in current model. Mathematical simulations conducted by Weber [3] shows that the crossover current resulting from oxygen / hydrogen reaching the other electrode through membrane is low if permeation coefficient is below the threshold value under normal fuel cell operating conditions. Two-phase flow in the channel is not explicitly accounted for. It is assumed that if there is liquid water in the flow field, it exists in the form of water droplet suspended in the gas flow or water film attached to the channel wall. Thus gas transport is not affected by liquid existence. The pressure drop in the flow field is neglected. Mass balance of each species is applied down the channel (i.e. in the same direction as reactant stream)... Governing Equations and Boundary Conditions of -D Sub-Model..1. Transport in Membrane There are three species in the membrane: protons, water and membrane. The most rigorous account of all relevant interactions between species is the concentrated solution theory, which couples transport phenomenon in the following way [33] N L C L C C [-1a] N [-1b] 0 L0 CC0 L00C0 0 where N i is the molar flux of species i, L ij can be related to experimentally measured transport parameters, C i is the concentration of species i, and i is the electrochemical potential of species i. Here three measurable transport properties are defined to further simplify Equation [-1a] and [-1b]. Firstly, Ohm s Law is applied to define the ionic conductivity : 59

76 i e [-] where i is the current density and e is the potential in the electrolyte phase. Secondly, electro-osmotic drag coefficient,, is defined as the number of water molecules carried EOD across the membrane with each hydrogen ion in the absence of chemical potential gradient: The last is the transport coefficient, the absence of current: N0 [-3] N EOD D 0, to relate the flux of water to its chemical potential gradient in N [-4] 0 D 0 0 Equation [-1a] and [-1b] can be rewritten in terms of above three transport properties as i e F i N EOD D F EOD [-5a] [-5b] In contrast, the dilute solution theory considers only the interaction between each dissolved species and the solvent. The resulting Nernst-Plank Equation can be applied to the membrane system as N i z u FC DC C v [-6] i i i e i i i where the first term on the right represents the migration flux, which is related to the potential gradient by charge number z i, mobility u i and concentration C i. The second term on the right is the diffusive flux related to concentration gradient. The last term is the convective flux related to the bulk motion of solvent carrying the species. Considering that the solvent is stationary membrane ( v 0 ) and water has zero valence, the above Nernst-Plank Equation can be reduced in the membrane system to 60

77 N i e 0 D 0 0 [-7a] [-7b] Such water and proton treatment are too trivial and miss an important phenomenon that as the protons move across the membrane they include flux of water in the same direction. Since this electro-osmotic flow is the result of proton-water interaction, it is not considered in dilute solution theory. It can be easily deduced by comparing Equation [-5a] and [-5b] with Equation [-7a] and [-7b] that the better compromise between concentrated and dilute solution theory is N i e i F 0 EOD D 0 0 [-8a] [-8b] Because of electroneutrality and no charge accumulation in the membrane, i 0 [-9] Because of no water accumulation or reaction in the membrane, N 0 0 [-10] In contrast to the diffusive model of membrane described above, which corresponds to vapor-equilibrated membrane, the hydraulic model corresponds to liquid-equilibrated membrane. The hydraulic model treats the membrane as having pores filled with liquid water and therefore can sustain pressure gradient across the membrane. As found by Yi et al. [96], a pressure differential is going to help the membrane retain more water and be better hydrated and more conductive. The proton transport is treated in the same way as in diffusive model while the driving force for water transport is replaced by hydraulic pressure gradient and transport coefficient is permeability as in Darcy s Law: 61

78 i W K N0 EOD P [-11] F M In order to account for the water movement driving force of both concentration and pressure gradient, diffusive and hydraulic model has to be combined somehow. The way to incorporate both types of transport in current work is where W i W K N0 EOD DdCd P [-1] F M C d is the concentration of dissolved water in the membrane and dissolved water in the membrane. W D d is the diffusion coefficient of In addition to the transport of dissolved species of proton and water, heat transport is solved in membrane as well. The general heat transport equation can be expanded by considering heat conduction based on Fourier s Law q th S T [-13] q cond th k T th [-14] and Joule heating as the heat source term i S T [-15] Equations [-8a], [-9], [-10], [-1] and [-13] constitute a closed set of equations that completely describe the transport of water, proton, and heat in membrane.... Transport in Diffusion Media The diffusion media, either with or without MPL, is a multi-functional porous backing layer between catalyst layer and flow field. It also provides the pathway for gas, liquid water and electron movement to and from the catalyst layer as well as structural support. 6

79 The transport of gas phase species is composed of diffusive and convective flux. For the ternary system on the cathode side, Stefan-Maxwell multi-species diffusion theory is applied as x i i j x N i diff j C x N T D j eff i, j diff i [-16] For the binary system on the anode side, Stefan-Maxwell multi-species diffusion theory can be reduced to Fick s diffusion law as N diff i eff CT Di, j x i [-17] where x i is the mole fraction of species i, which can be oxygen/helium or water vapor on the cathode side and hydrogen or water vapor on the anode side. C T is the total concentration of all species. D, is the effective binary diffusion coefficient between species i and j, which has been corrected by Bruggeman relation for porous media, partial saturation and Knudsen effects. The convective flux for the gas phase, conv N, as formulated below i eff i j can be added to the diffusive flux diff N i N conv i u C [-18] G i, where u G is the gas phase velocity and C i is the concentration of species i. The source / sink term in gas phase is the phase transfer between water vapor and liquid, S vl S vl vl v sat P P [-19] where vl is the transfer coefficient between water vapor and liquid, P v is the vapor pressure, and P sat is the saturation pressure. Therefore the transport of gas phase species can be summarized as 63

80 conv N i N diff i 0 if i = O, H [-0] Here the velocity field of the total gas phase u G S vl if i = H O is calculated by Darcy s Law as u G KG G P G [-1] where K is the gas permeability, G is the gas viscosity, and G P is the gas phase pressure. G The equation governing total gas phase is therefore C T K G PG S G vl [-] Similarly, the equation governing total liquid phase can be written as where 0 is the porosity, s is the saturation, molecular weight, pressure. 0 sw KL PL Svl M [-3] W L W is the density of liquid water, M W is the water K L is the liquid permeability, L is the liquid viscosity, and P L is the liquid phase In addition to mass transport, heat transport in the form of conduction and convection is also solved in diffusion media. In addition to heat conduction as formulated in Equation [-14] for membrane, convective heat flux, conv q th, is also included in terms of gas and liquid phase transport q conv th where is the density and c p is the specific heat. [-4] C u T C u T P G 64 P L

81 As for the heat transport, the only heat source / sink term in the diffusion media is the latent heat as a result of evaporation / condensation, where H is the latent heat of vaporization. vl S H S [-5] T vl vl Final heat transport equation can be arrived at by casting Equation [-14], [-4] and [-5] into the general form of heat equation as q conv th q cond th S T [-6] The electron transport in diffusion media can be derived from Ohm s law as i s [-7] where is the electronic conductivity and s is the potential in electron-conducting phase. because of no reaction in the diffusion media i 0 [-8]..3. Transport in Catalyst Layer The complexity of catalyst layer lies in the fact that this thin layer is where all species coexist and electrochemical reaction takes place. Therefore, additional terms for electrochemical kinetics need to be solved in the porous electrode on top of the proton, water and heat transport in membrane and electron, electron and heat transport in diffusion medium as formulated above. Cathode catalyst layer is modeled in a rigorous manner in this work so that both through-the-porouselectrode and over-the-agglomerate length scales can be accounted for, as shown in the upper right corner of Figure.1 As the electrochemical reaction occurs in the catalyst layer, the source / sink term for proton / electron transport is not zero as in membrane and diffusion media. 65

82 Similarly, the source / sink term for species transport and corresponding total gas phase transport is the reactant consumption and water production, where S S S J gen [-9a] 4F O J gen [-9b] F H H J gen O [-9c] F J gen is the transfer current density, which will be further explained in the context of agglomerate catalyst model in the following section. In addition to the Joule heating and latent heat release from vapor-liquid phase change, reversible and irreversible heat is added to the heat source term S T i H vl S vl J gen TS nf [-30] where S is the entropy change of reaction and is the overpotential, defined as where E rev is the maximum reversible voltage, labeled as..4. Boundary Conditions of -D Sub-Model s e at anode [-31a] E at cathode [-31b] s e rev E in Figure 1.4. The boundary conditions for the to-be-solved variables in the -D sub-model are listed in Table -I..3. Parameters and Correlations for -D Simulation.3.1. Determination of Water Content Water content,, defined as moles of water per mole of sulfonic acid sites, is a critical parameter of the membrane. As a representation of membrane hydration, it is closely related to transport parameters, such 66

83 as electro-osmotic drag coefficient n d, ionic conductivity, and dissolved water diffusion coefficient D d. Weber et al. [34] summarized the wealth of information contained in the literature, developed a semi-phenomenological membrane model and gave a physical picture of the membrane structure evolution with water content, as illustrated by Figure.5. Transport in the membrane is dependent on whether the membrane is in vapor-equilibrated or liquidequilibrated mode. For the membrane in equilibrium with water vapor, an uptake isotherm, which relates water content,, with water vapor activity, a, is needed. There are a variety of experimental ~a correlations in the literature, as summarized in Table -II. In common, these water uptake isotherms exhibit similar shape over the whole range of water vapor activity and decrease with temperature. As observed by Hinatsu et al. [35], the water uptake is influenced by ion exchange capacity as well. Weber et al. [33] made minor changes on the isotherm calculated by the chemical model of Meyers et al. [36] and is the only correlation that takes into account the effect of both temperature and membrane equivalent weight. Therefore, it was implemented in current model to account for membrane equivalent weight other than 1100 and temperature other than 30⁰C..3.. Ionic Conductivity in MEA As an indicator of membrane hydration, membrane resistance accounts for a significant portion of ASR. A good water management strategy can ensure a highly conductive membrane and thus minimal ASR while a bad one will result in local dry-out and appreciable voltage loss accordingly. Ionic conductivity of the membrane is measured as function of membrane hydration, usually water content,. Although there is discrepancy in experimental measurement about the activation energy, it is agreed that an Arrhenius type of relation is sufficient to account for the strong temperature effect on membrane conductivity. As listed in Table -III, the membrane development has witnessed a more conductive membrane and therefore lower membrane resistance in the cell. 67

84 While ionic resistance in the membrane can be measured by ASR, ionic resistance in the catalyst layer is not captured by ASR due to much higher local electronic conductivity. The major reason which makes ionic resistance in the anode catalyst layer negligible is the facile HOR kinetics. The reaction rate of ORR, however, is several orders of magnitude lower than that of HOR and therefore the pathway for the proton to be released from the reaction site to the membrane needs to be taken into consideration. The simple calculation done by Makharia et al. [00] used the transmission line model to fit the EIS data so that catalyst layer electrolyte resistance can be separated from cell ohmic resistance. Their study showed substantial voltage loss from catalyst layer proton resistance, especially under low RH conditions. Neyerlin et al. [6] further studied the voltage loss within the cathode catalyst layer according to the ratio of ohmic to charge transfer resistance. They figured out from the cathode catalyst utilization perspective the conditions under which the approximation of sheet resistance to cathode proton resistance is valid. Liu et al. [8] further clarified the effect of ionomer/carbon ratio on effective proton resistance through corresponding ionomer volume fraction and tortuosity value. Their following work [37] investigated the effect of electrode thickness, Pt loading, ionomer loading and ionomer EW on electrode proton resistivity. In summary, the proton resistance in the cathode catalyst layer, R H, ccl, is accounted for in the following way: where R R 1 t 1 t 1 t sheet ccl ccl ccl [-3] H, ccl 3 3 eff 3 i 3 i R sheet is the sheet proton resistance of the cathode catalyst layer, t ccl is the cathode catalyst layer thickness, eff is the effective ionic conductivity in the cathode catalyst layer, is the ionic conductivity in the bulk membrane, i is the ionomer volume fraction, and is the tortuosity in the cathode catalyst layer. 68

85 .3.3. Dissolved Water Diffusion Coefficient in MEA Diffusion is one of the major forms of water transport across MEA. As transport theory is applied to water diffusion in the MEA, the diffusive flux can be related to gradient and corresponding diffusion coefficient. There are several ways in the literature to describe the driving force for water diffusion in the MEA, i.e. gradient in terms of water content,, gradient in terms of dissolved water concentration, and gradient in terms of chemical potential,. Regardless of the driving force for water diffusion in the membrane, diffusion coefficient is a parameter highly dependent on membrane hydration. Zawodzinski et al. [38] measured the intra-diffusion coefficient for Nafion 117 at 30⁰C in terms of chemical potential and explained how to convert it to chemical diffusion coefficient in terms of membrane water concentration. This work was followed by Springer et al. [15], who took into account membrane swelling and used a polynomial to represent the water diffusion coefficient with respect to water content gradient. Motupally et al. [39] called the conversion between intra-diffusion and Fickian diffusion Darken factor and compared some previous work on Fickian diffusion coefficient. Weber et al. [33] fitted the experimental data of the intra-diffusion coefficient by a nearly linear function of water content and Arrhenius dependence on temperature. Ye et al. [40] measured the water diffusion coefficient for Gore- Select membrane and used a scaling factor to account for the difference between Gore-Select and Nafion membrane. The diffusion coefficient correlations widely used in the literature are briefly summarized in Table -IV. C d,.3.4. Other Parameters and Correlations The material properties of individual layers, including thickness t, porosity 0, permeability K 0, thermal conductivity k th, electronic conductivity and hydrophobicity (e.g. contact angle or PTFE content wt ) are either provided by manufacture or measured in-house. In addition, the parameters and correlations implemented in the model and used in the simulation are listed in Table -V and Table -VI, respectively. 69

86 .4. Agglomerate Model in Cathode Catalyst Layer Besides porous electrode thickness, the other characteristic length in the robust cathode catalyst layer model is agglomerate particle radius, as shown in the bottom right corner of Figure.1. The volumetric transfer current density, J gen, resulting from the agglomerate catalyst layer model can be derived as J gen c W C O H O ragg i ragg i F 1 W i 4 i CL i H O 1 0 E rkc H O AaggDO, W ragg i W AaggDO, i r agg 1 1 s [-33] where i HO and W HO are the dimensionless Henry s constant values of oxygen dissolved into ionomer and water thin film respectively, i and W are the thickness of ionomer and water thin film respectively and D O, i D, and O W are diffusion coefficient of oxygen in ionomer and liquid water respectively. The radius of the idealized spherical agglomerate is r agg and the effective surface area to dissolve oxygen into agglomerate is A agg. In Equation [-33], the effectiveness factor, E r, describes the simultaneous reaction and diffusion in agglomerate. For a first-order reaction with no other transport limitation, an analytical expression for effectiveness factor is [41] E r L tanh 3 3 L L [-34] Here L is the Thiele modulus for the ORR and can be written as [41] 70

87 r k agg c L eff [-35] 3 DO, agg Here agg r D eff O, agg represents the mass transfer portion of Thiele modulus, where eff D O, agg is the effective diffusion coefficient of oxygen inside the agglomerate written as D eff O agg O, i, agg1.5 i D [-36] agg where i is the volume fraction of ionomer inside the agglomerate. The kinetics portion of Thiele modulus can be represented by the reaction rate constant k c [41] k c ai ref 0, c c, cf exp ref c C RuT 4F O [-37] where a is the roughness factor per unit volume, is the reference oxygen concentration. ref i 0,c is the reference exchange current density and Compared to the sluggish ORR in the cathode catalyst layer, HOR in the anode catalyst layer is facile and can be formulated by Butler-Volmer kinetics without agglomerate effects as ref CO J gen a C ref H F F a, a c, a ai 0, a 1 s exp exp [-38] ref CH RuT RuT The details of values and relations applied in the agglomerate model are presented in Table -VII. It is worth mentioning the uncertainties associated with these parameters, especially exchange current density 0, Henry s constant H O, i / W, radius of agglomerate particle r agg, and film thickness i / W ref i, a / c. As briefly summarized by Dobson et al. [4], there is order of magnitude difference in the structural and kinetics parameters between different works, even from experimental observation. Such discrepancy is 71

88 expected to impose significant impact on modeling the kinetics and mass transport in cathode catalyst layer. Therefore it is critical to make sure the set of parameters fall under the range of experimental data and make physical sense..5. Simplified +1 Formulation Along Flow As briefly reviewed above, in addition to the through-plane and in-plane transport, a higher-dimension model is needed to account for the varying gas composition along the channel, especially in the case of low to medium stoichiometry, so that local reactant starvation or flooding will not be missed. The internal humidification effects resulting from counter-current configuration will not be captured either if alongflow direction is not solved. A fully three-dimensional model, however, requires much greater computing resources. In comparison, a pseudo 3-D, or D + 1 model, is based on the -D model introduced above and discretizes the along-flow direction into a limited number of segments. As pointed out in the model assumptions, this D + 1 model is differentiated from a fully 3-D model by not solving the along-flow direction to the full extent. The simplified solution in the along-flow direction is a compromise between computational cost and dimensional resolution. Information is passed in the along-flow direction by satisfying mass and heat balance of each species in the +1 direction. The resulting species concentration changes correspond to changes in boundary conditions of the adjacent -D control volumes. At respective inlet, the molar flow rate of each species can be specified as: a, in ia n H H [-39a] F T RH T RH a, in a, in Psat n H O n H [-39b] P P a sat c, in ia n O O [-39c] 4F 7

89 , in c, in 79% ia 79% n c n N O O [-39d] 1% 4F 1% c, in c, in Psat T n n c, in RH n H O O N [-39e] P P c sat T RH Here j is the stoichiometry of species j, i is the average current density, A is the total active area, P a / c is the total pressure in the flow field, sat P is the saturation pressure, and RH is the relative humidity of gas feed. The mass balance of each species and heat balance with coolant are formulated in the following way: a, k1 a, k n H n H a, k1 a, k n H O n H O k i A F k net k k i A F k [-40a] [-40b] c, k 1 c, k n O n O k i A 4F k [-40c] c, k 1 c, k n N n N [-40d] k k c, k1 c, k k i A n n 0. [-40e] F H O H O net 5 T k1 T k k i A mc k p E th E cell [-40f] where k 1 N 73

90 Here k represents the discretized segment along the flow, N is the total number of segments in the along-flow direction, k n j is the local molar flow rate of species j in the flow field, i k is the local current density, k A is the local active area, k is the local NWD coefficient, net k T is the local coolant temperature, m is the mass flow rate of coolant, c p is the specific heat of coolant, voltage, and E th is the thermal E cell is the cell voltage. The plus or minus sign in Equation [-40] depends on whether the sweeping direction is with or against the flow direction. It is plus sign if the sweeping direction is same as the flow and it is minus sign otherwise. In this way, the D + 1 model can be applicable to both co-flow and counter-flow configuration. As formulated by Berg et al. [101], the molar flow rate of H, O, N and H O are then converted to concentration profile in the following manner: for the under-saturated gas flow in the flow field, n where j represents H or H O [-41a] a, k a, k Pa j C j k a, k a, k RuT n H n H O c, k c, k Pc j C j k c, k c, k c, k RuT n O n N n H O n where j represents O, N or H O [-41b] for the saturated gas flow in the flow field, C a / c, k j P ( T ) k sat k RuT where j represents H O [-4a] C a, k j Pa P R T sat k u T k where j represents H [-4b] k c, k c, k Pc Psat T j C j k c, k c, k RuT n O n N n where j represents O or N [-4c] 74

91 75 The molar concentration of H, O, N and H O are then specified as boundary conditions of -D submodel as in Table -I. Whether the gas flow in the flow field is under-saturated or saturated is determined in the following way: anode: 0,,, T P n n n P sat k a O H k a H k a O H a saturated 0,,, T P n n n P sat k a O H k a H k a O H a under-saturated cathode: 0,,,, T P n n n n P sat k c O H k c N k c O k c O H c saturated 0,,,, T P n n n n P sat k c O H k c N k c O k c O H c under-saturated

92 Table -I Boundary Conditions of -D Sub-Model z=0 ampl acl acl PEM PEM ccl ccl cmpl z=l x=0 & x=w C / / / O 0 O C / specified C O C O C O 0 C H specified CH C H / H 0 C / / / C H 0 C H O specified CH O CH O / / / / C H C specified O C 0 H O H O T specified T T / / / / specified T T T 0 P G specified PG P G / / / / P P 0 specified G P G G P L specified PL P L / / / / P P 0 specified L P L L / 0 / / 0 e e e / 0 e s specified s / / / / s 0 0 s 76

93 Table -II Prevalent Water Uptake Isotherm Mathematical Description Reference Comments a 39.85a 36.0a [38] Nafion 117 membrane, 30⁰C; a 16.0a 14.1a [35] Nafion 117 membrane, 80⁰C; solve ~ a from the following two equations H3O exp 1 exp K H 1 3O 1 H O 3 H O 3 exp 3 a K exp H O 3 H O 3 [33] associated values are fitted to 1100EW and 30⁰C; EW and temperature dependent; 77

94 Table -III Prevalent Correlations of Membrane Ionic Conductivity Mathematical Description Reference Comments exp [15] R 303 T Nafion 117, measured in the range of 30 ~ 80⁰C f 0.06 exp V0 where f V V m 0 R 303 T [33] data fit in the range of 5 ~ 85⁰C RH exp R 353 T [7] 1050EW, measured at 80⁰C Nafion 117, RH [43] data fit of measurement at 80⁰C RH range 34% ~ 100% RH [40] Gore-Select, data fit of measurement at 80⁰C 78

95 Table -IV Prevalent Correlations of Water Diffusion Coefficient in Membrane Mathematical Description Reference Comments Nafion 117; D 4 D F exp T e exp W, for 0 3 T D F D D f 1 161e exp W, for 3 17 T 4 V exp T V0 V V m 9 0 f V 0000 exp R T [15] [39] [40] [33] converted from measurement at 30⁰C; relative to water content gradient; Nafion 117; converted from measurement at 30⁰C; relative to water content gradient; Gore-Select membrane; measured at 80⁰C; relative to water content gradient; empirical scaling factor of 0.5; fit a wide range of data; relative to chemical potential gradient; 79

96 Table -V Parameters Used in -D Simulation Symbol Unit Value Reference S J/mol K for HOR for ORR [44] D O, H O, H O,O D m /s [45] D N, H O, H O,N D m /s [45] D O,N, N,O D m /s [45] D He, H O, D H O, He m /s [45] D O, He D m /s [45] He,O, D H, H O, H O,H D m /s [45] dry kg/m [46] EW kg/equiv 1.1 manufacturer CL i 0. [8] W kg/m M w kg/mol

97 Pa s for liquid for gas H gl J/mol N/m Uth V 1.3 [6] 81

98 Table -VI Correlations used in -D Simulation Symbol Unit Expression Reference 3 P Pa T C T C T C sat 846 [6] a CH ORuT defined P sat P cap Pa 0 K 0 g 1/ gs, where s wt wt% 3 % s 0.143s [47] lns K m K 0 Kr defined K r Dd m /s s for non-wetting phase, s nw 1 nw for wetting phase [48] d ln a D intra [38] d ln Cd mol/m 3 dry EW [115] D Kn m /s 4r 3 p RuT M [49] D, m /s eff i j s Di, jdkn s Di, j DKn empirical D T mol/m s K exp exp 98 T 36 T for Gore-Select membrane for Nafion membrane [50] 8

99 S m 3 /s k C RT P vl vl H O sat defined 83

100 Table -VII Values and Constitutive Relations in Agglomerate Catalyst Model Symbol Units Value / Expression Reference L a, L c mg Pt /cm 0.15, 0.4 manufacturer A Pt m Pt/g Pt 5.4 [3] a,a, c, a 1, 1 [115] c,c 1 [115] a, c 0.5, 1 [115] C, C mol/m 3 40, 40 [115] ref H ref O ref i 0,a A/cm Pt [7] ref i 0,c A/cm Pt fitted H O, i H O, W exp RT exp RT 666 /T 498/T [16] [51] H H, i RT 3 [16] r agg m based on [60] agg i 0.5 based on [60] i m based on [60] W m CL 0 a s agg [7] V s e at anode defined 84

101 E s e rev at cathode D O, i m /s exp T [5] D O, W m 9 /s [7] CL 31 A agg m /m 3 0 r agg N [7] LA a m Pt/m 3 tcl Pt [40] 85

102 Figure.1 Schematics of computational domain: three-dimensional structure of single fuel cell; close-up of catalyst layer; idealized spherical agglomerate particle (not to scale) 86

103 Figure. Time series of fuel cell voltage at consecutive current densities at 0.1, 0. and 0.3A/cm for the non-porous graphite plate and the porous carbon wick plate. From [174] 87

104 Figure.3 Flow in a very small channel. The molecular interactions with the channel wall are no longer negligible compared to the collisions with other molecules. From [6] 88

105 Figure.4 High-resolution neutron image of through-plane liquid water profile for cell at 60 C and 0.5A/cm. ( ) two stoichiometry anode flow ( ) high anode flow, 480 std cm 3 min -1 constant. Solid line demarks the center of the membrane; dashed line demarks the micro-porous layer / macroporous layer boundary from the image dat. From [19] 89

106 Figure.5 Evolution of membrane structure as a function of water content. the gray area is the fluorocarbon matrix, the black is the polymer side-chain, the light gray is the liquid water, and the dotted line is a collapsed channel. From [34] 90

107 3. Exploration of Ultra-High Current PEFC Operation with Porous Flow Field The comprehensive D + 1 model developed in previous chapter was applied to a PEFC with porous flow field, called open metallic element (OME), to explore its operation in the ultra-high current density regime (>A/cm ). This model was validated by in-situ experimental measurement to a greater extent than previously published models. Polarization curve, ASR and water measurement were taken to test the model validity under a wide range of input RH conditions. The major reason for significant performance improvement was identified. The merit and potential limitation of such flow field were revealed by model as well Experimental Details Fuel Cell Components The single cell with OME flow field (basically a porous medium) used in this study was designed by Nuvera Fuel Cells Inc. As compared in Figure 3.1, the use of Nuvera OME flow field instead of conventional land / channel flow field eliminated the need for in-plane diffusion. The reactant delivery to and product removal from the active sites were expected to be considerably facilitated and therefore the mass transport limitation usually resulting from the mask of catalytic active area under the land was expected to be greatly removed. The GDL used at both electrodes was Sigracet GDL 5BC from SGL Group, which included a 5% PTFE-treated, hydrophobized substrate and a 3% PTFE treated MPL on one side. The nominal thickness was 35 μm and porosity was 80%. The MEA used in the testing was Gore Primea series 57 from W. L. Gore and Associates Inc. The loadings were 0.15 and 0.4 mg/cm Pt on the anode and cathode, respectively. The single cell had an active area of 50cm. The thickness of dry membrane, anode and cathode catalyst layers were 18, 4 and 13 μm, respectively. 91

108 Fuel Cell Test Conditions The cell operated at a nominal temperature of 60 C since coolant water was recirculated in the compression plate on the outer boundary of the flow field plates to keep the outer boundaries of the cell fixed at this desired temperature. The back pressure of the flow exit was throttled to 1.8 bar on both anode and cathode sides and maintained at all current densities. Pure hydrogen, humidified or not, was supplied to the anode. In the air tests, breathing grade air, either humidified or dry, was supplied to the cathode. In the comparative study, heliox, humidified or not, was supplied to the cathode. Heliox used was a mixture of helium and oxygen (1% oxygen, bal. helium in dry state). Stoichiometry of hydrogen and oxygen was kept a constant of.0 at all current densities. The RH of reactants at their respective inlets was varied in three conditions: partially humidified anode dry cathode, fully humidified anode dry cathode, and dry anode fully humidified cathode. The RH of a stream was defined as the ratio of saturation pressure at the dew point temperature T dew and saturation pressure at nominal cell temperature T cell. P P sat T T cell sat dew RH [3-1] The operating conditions were summarized in Table 3-I and labeled as Condition 0, Condition 1 and Condition, respectively. Fuel Cell Test System A fuel cell test station designed by Arbin Instruments was used to control the gas flow rates and the electronic load. A Nafion type membrane humidifier system from Fuel Cell Technologies Inc. controlled reactants dew point. Lines between humidifiers and the fuel cell were heated to avoid condensation. Back pressure was controlled with a back pressure module by Scribner Associates Inc. Performance curves were recorded by taking the 45 minute average potential response of each operating point in galvanostatic mode. The ASR was monitored with a miliohmmeter from Agilent Technologies Inc. 9

109 Water Balance Measurement and Calculation To calculate the NWD coefficient, water measurement needed to be taken at the anode and cathode outlet. The water flow rate was measured by two humidity sensors by Vaisala, one at the anode outlet and the other at the cathode outlet. Outlet lines and sensors were heated to avoid water condensation and moist flow before reaching the humidity sensor. The dew point temperature, T dew, read from the humidity sensor along with the back pressure information was used to calculate water molar flow rate at the anode outlet and cathode outlet a out n, HO : c out n, HO ia Psat T dew 1 a, out n H O H [3-a] F P P T a sat dew n c, out O H O xo ia 1 4F c Psat Tdew P P T sat dew [3-b] Although the water flow rate at cathode exit was not required for computing NWD coefficient, it was used to check the overall water balance. Other information necessary for overall water balance was the water molar flow rate at the anode inlet a in n, HO, cathode inlet and water generation rate c in n, HO : gen nh O n n a, in H O H c, in O H O xo ia F ia 4F a Psat Tdew P P T c sat sat Psat Tdew P P T dew dew [3-3a] [3-3b] ia n gen H O [3-3c] F In the ideal case of steady-state operation, the sum of incoming water and generated water should be equal to the sum of outgoing water: 93

110 n a, in HO n n n n [3-4] c, in HO gen HO The water measurement was considered valid if the amount of outgoing water was within 90% ~ 110% that of the incoming plus generated water. Fluctuation in dew-point temperature was believed to be the major contributor to the experiment uncertainties. Multiple runs were performed on the same build in order to quantify such uncertainties. a, out HO c, out HO For a legitimate water measurement, the NWD coefficient, net, defined as the net number of water molecules dragged by each proton from anode to cathode, was calculated in the following way: a, in a, out n H O n HO net [3-5] ia / F 3.. Model Validation As compared in Figure 3., in the performance curve of a conventional land / channel parallel flow field, mass transport limitation is consistently observed at high current density, which is usually attributed to the flooding in the CL that blocks the catalytic active sites and / or flooding in the DM that blocks the path of reactant delivery to active sites. In contrast, the concentration polarization region is barely noticeable throughout the performance curve with OME, resulting in a substantially improved limiting current density, as high as 3.0A/cm. The model is first validated under baseline conditions, medium-rh anode and dry cathode. As shown in Figure 3.3 (a), the model prediction of performance agrees well with experimental measurement. The reasonably close agreement is also observed with regard to ASR, indicating that the model is capable of capturing the membrane internal humidification. In addition to performance and ASR validation, as done by other modeling work, this model is further validated by NWD coefficient, net, calculated from water measurement. The definition in Equation [3-5] implies that the positive NWD coefficient corresponds to net water transport across the membrane from anode to cathode. The more positive the NWD coefficient, the more the electro-osmotic drag 94

111 dominates the back transport and vice versa. The physical limits of the NWD coefficient are defined by two extreme cases: one is there is no water coming out of anode exit and thus NWD coefficient reaches its upper limit; the other is all the incoming and produced water come out of anode exit and thus NWD coefficient reaches its lower limit. Under the baseline operating conditions, the upper physical limit is a constant of 0.06 and the lower limit is a constant of -0.5 throughout the current density range. To the author s best knowledge, no other published models to date have been validated with the NWD coefficient over such a wide range of operating current density and RH conditions. As revealed by Figure 3.3 (b), by using the correlations available in the literature and widely-used in the modeling work, the model prediction of NWD coefficient is close in absolute value but different in qualitative trend from repeated experimental measurement. The fact that NWD is not quantitatively matched indicates that despite the performance and ASR agreement additional modification of the transport relationships is necessary to match the repeated experimental results. It has been well acknowledged that electro-osmotic drag and back transport are the primary mechanism of water transport across the membrane under normal circumstances with nearly zero temperature gradient across the membrane. Therefore, the parameters of electro-osmotic drag coefficient and dissolved water diffusion coefficient are expected to have the most significant impact on the resulting through-plane net water transport. Firstly, considering the wide discrepancy in the literature on dissolved water diffusion coefficient, it is appropriate to adjust this parameter within a reasonable range represented by the scatter in measured experimental data in the literature. Due to the similarity in functional groups and difference in microscopic structures between different membranes, the water diffusion coefficient was assumed to exhibit similar functional forms but differ by a scaling factor. The scaling factor of 1.5 is determined empirically to match the measured NWD coefficient. 95

112 The second parameter adjusted is the electro-osmotic drag. Instead of being discontinuous between vaporand liquid-equilibrated mode, it was made continuous in between and more sensitive to hydration and temperature. The physical idea behind this is similar to the reasoning proposed by Weber et al. [34]: a continuous transition is assumed between vapor-equilibrate and liquid-equilibrated mode; when the membrane is neither fully vapor-equilibrated nor fully liquid-equilibrated, the transport mode is assumed to be a superposition between the two. Such treatment technically bridges the gap between vapor- and liquid-equilibrated transport mode. The third adjustment is made on the correlation between relative permeability and liquid saturation in MPL. Most of the work so far on correlating relative permeability with liquid saturation was about macroporous GDL substrate while the work on MPL was rarely seen. Considering the distinct difference in pore size distribution, as illustrated by Figure 3.4, it might not be appropriate to apply the widely-used correlation measured specifically for macro-porous GDL substrate directly to MPL. The same functional form is assumed between macro-porous GDL and MPL for lack of experimental evidence. Considering the combined effect of much lower intrinsic permeability and liquid saturation in MPL than that in macroporous GDL, the exponent in the functional form is empirically reduced from 3 to 1 to make MPL less restrictive to liquid flow. Note such adjustment will not change the fact that MPL is much more restrictive to liquid flow than macro-porous GDL substrate. This power reduction could physically represent a reduction in flow resistance resulting from cracks observed on MPL surface, as done by Hizir et al. [53]. The details of all three adjustment are listed in Table 3-II. As shown in Figure 3.5, all three attempts to fit the experimental data bring the predicted NWD closer to the measured one in the whole operating regime. Now the model and experiment share the same qualitative trend in NWD coefficient over the range of operating current density: the dominance of electro-osmotic drag increases with current density. Under this trend, the cell dies out from anode dry-out beyond 3.0A/cm, since the NWD is approaching the upper limit. It should be pointed out that in contrast to the considerable impact on NWD coefficient, performance measured by i-v polarization behavior is hardly influenced by this fitting procedure. It 96

113 implies that caution should be taken to validate the model with only performance curve because it can be misleading. In addition to ASR, which is a good indicator of membrane hydration, NWD coefficient can be a useful and necessary parameter to test the validity of the multi-phase model. Figure 3.6 shows the comparison between experiment and model under fully-humidified anode and dry cathode conditions, labeled as Condition 1 in Table 3-I. The model prediction coincides with the experimental data in terms of performance, ASR and NWD coefficient. However, the dominance of electro-osmotic drag is still slightly under-estimated in the ultra-high current regime, which might be attributed to some physics that come into strong effect at high current density. The thermo-osmosis observed experimentally might be it [50], and its impact is going to be evaluated in next chapter. A third case in the series of model validation is Condition : dry anode and fully humidified cathode. In Figure 3.7 model predictions of performance and NWD coefficient compare favorably with experiment, indicating the validity of the model in capturing correct water balance. To the author s best knowledge, this is the first published model that is validated by accompanying experimental work under drastically different RH conditions Transport Study in Porous Flow Field Helium has a much smaller molecular weight than nitrogen, therefore water vapor diffusion and oxygen diffusion in helium is about twice higher than that in nitrogen, as compared in Table 3-III. This explains why mass transport limitations can be improved by replacing the constituent of nitrogen in the air with helium. In a parallel flow field the limiting current density typically results from the difficulty of water vapor in moving out of the cell and oxygen in reaching reaction sites. This replacement typically improves oxygen transport to a significant extent in the high current regime, as depicted by Figure 3.8 (a). The physical mechanism for such improvement is two-fold: diffusion process in the multi-component cathode system is promoted, especially under restrictive land locations; and facilitated diffusion process 97

114 can ensure better oxygen delivery to the active layer as well as enhanced evaporative water removal and thereby less water coverage in the catalyst layer. However, Figure 3.8 (b) shows this substitution of heliox in the OME flow field under baseline conditions does not improve the performance, implying that the cell performance is not limited by gas phase oxygen transport in OME flow field, even in the high current regime. In Figure 3.9, modeling and experimental results consistently show that the cell is unable to reach stable performance beyond.0a/cm with heliox due to anode dry-out, which cannot be elucidated by slight increase in ASR. As mentioned briefly in previous chapter, because electronic resistance in the catalyst layer can be orders of magnitude lower than ionic resistance, ASR is mostly a measurement of membrane hydration and cell contact. The cause of anode dehydration can be found in the apparent difference in predicted NWD coefficient, shown in Figure The more positive NWD coefficient with heliox than that with air results from the further enhanced water vapor transport, greater loss of water to the cathode gas flow and relatively reduced back diffusion in the heliox environment. As NWD coefficient approaches its upper limit, the back diffusion is insufficient to make up for the water dragged by electro-osmosis and thus local dry-out occurs. As illustrated by Figure 3.11, the prediction of average water content in the anode catalyst layer as a function of current is an evidence that anode dry-out is responsible for the reduced ion transport in electrolyte and unstable operation in the high current regime for the OME cell architecture. It is important to realize that multi-phase model validation at anode dry-out conditions can be used to verify internal water balance and represents a key operating point in the overall model validation process. Since the merit of OME flow field has been determined to be facilitated mass transport, it is of interest to identify the primary mode of water transport from catalyst layer to flow field so that material properties and / or operating conditions can be engineered to mitigate the limitations in high current regime. It was found that one of the functions of MPL is to restrict liquid water passage and push it back to anode side [33]. The significance of capillary flow in comparison to gas phase transport can be revealed by a 98

115 parametric study on the intrinsic permeability of MPL with relative permeability adjusted as above. As depicted in Figure 3.1, the order of magnitude change in MPL permeability has little impact on the water management, as well as performance. This implies that capillary action is not a significant mode of water transport through porous layers under these conditions. In terms of gas phase transport, both convective and diffusive flux are accounted for in the model. The non-dimensional Peclet number is calculated as below to measure the relative importance of convection to diffusion. wt Pe [3-6] D where w is the average velocity in the through-plane direction, t is the characteristic length, thickness in this case, and D is the diffusion coefficient. As illustrated by Figure 3.13, although Peclet number increases with current density, it is still orders of magnitude lower than unity, indicating insignificant convective compared to diffusive transport rate, even at high current density. To confirm the dominating role of diffusion in water transport inside porous media, a parametric study has been done on diffusion coefficient between water vapor and inert gas. Although the performance is similar between three cases, the water balance is sensitive to varying diffusion coefficient, as presented in Figure Another implication from the result is that cell performance alone is a lumped metric and seemingly identical performance might result from a totally different internal water balance. The necessity of further validating multi-phase model beyond polarization data alone can be demonstrated by comparison of the internal water balance with similar voltage at dry-out, normal and flooded status Conclusions The comprehensive D + 1 mathematical model developed in Chapter and applied to the OME porous flow field has demonstrated its capability to simulate water balance across the membrane, resolve porous 99

116 electrode and agglomerate particle length scales, and account for non-isothermal multi-phase effects at ultra-high current density. The model has been validated with polarization curve, area-specific resistance and net water drag coefficient under drastically different humidity conditions. The necessity of further validating multi-phase models beyond polarization curve alone has been emphasized by comparing the internal water balance with similar voltage. In particular, validation at anode dry-out limiting conditions is useful to ensure internal water transport is accounted for properly. The validated model is then used to elucidate features of OME cell architecture which enables ultra-high current operation. The study with heliox captures the unstable performance and shows the merit of OME flow field in facilitating mass transport and its potential limiting factor of anode dry-out, especially in the high current regime. With OME flow field, the diffusive flux has been determined to be the primary mode of water transport from catalyst layer to flow field in comparison to convective transport and capillary action. 100

117 Table 3-I Operating conditions with varying inlet RH Operating Condition # T cell ( C) Stoich A C RH A C Condition 0 (baseline condition) Back Pressure A C (bar) % 0% Condition % 0% Condition % 100%

118 Table 3-II Changes in transport parameters to fit measured NWD coefficient Parameter Conventional Value Reference Adjusted Value D intra 9 V exp V V R T [33] m 9 V exp 0 u ref V V R T T m 0 u ref n d 1.0 for vapor-equilibrated [54] 1 1 max 1, exp.5 for liquid-equilibrated R u T ref T K r in MPL 3 s Wyllie Model s 10

119 Table 3-III Binary diffusion coefficient between N, He and H O, O Symbol Unit Value Reference D D m -5 /s [45] N, H O, H O,N D O,N, D D N,O m /s [45] He, H O, D H O, He D O, He He,O, m -5 /s [45] D m -5 /s [45] 103

120 Figure 3.1 Comparison between conventional land / channel flow field (on the left) with Nuvera OME flow field (on the right) 104

121 Figure 3. Experimental comparison between Parallel flow field and OME flow field on voltage and power density 105

122 (a) (b) Figure 3.3 Comparison between experiment and model using air on OME flow field under baseline condition (a) polarization curve and ASR (symbol represents experiment and line represents model) (b) net water drag coefficient with conventional transport parameters. Error bars represents the range of water measurement from multiple test runs. 106

123 Figure 3.4 Pore size distribution curves for GDL as a function of carbon loading in MPL. From [01] 107

124 Figure 3.5 Comparison of net water drag coefficient between experiment and model with conventional and adjusted transport parameters using air on OME flow field under baseline condition. Error bars represents the range of water measurement from multiple test runs. 108

125 (a) (b) Figure 3.6 Comparison between experiment and model using air on OME flow field under Condition 1 (a) polarization curve and ASR (symbol represents experiment and line represents model) (b) net water drag coefficient with adjusted transport parameters. Error bars represents the range of water measurement from multiple test runs. 109

126 (a) (b) Figure 3.7 Comparison between experiment and model using air on OME flow field under Condition (a) polarization curve and ASR (symbol represents experiment and line represents model) (b) net water drag coefficient with adjusted transport parameters. Error bars represents the range of water measurement from multiple test runs. 110

127 (a) (b) Figure 3.8 Experimental effect of inert gas on cell performance and ASR (a) parallel flow field (b) OME flow field 111

128 Figure 3.9 Comparison of polarization curve and ASR between experiment and model using heliox on OME flow field under baseline conditions 11

129 Figure 3.10 Comparison of predicted net water drag coefficient between air and heliox under baseline condition 113

130 Figure 3.11 Comparison of predicted average water content in anode catalyst layer between heliox and air under baseline condition 114

131 Figure 3.1 Effect of MPL permeability on net water drag coefficient under baseline condition 115

132 Figure 3.13 Predicted relative influence of convection measured by Peclet number under baseline condition 116

133 (a) (b) Figure 3.14 Predicted effect of water vapor diffusivity on (a) voltage (b) net water drag coefficient under baseline condition 117

134 4. Operation Engineering to Enable High Temperature High Power Density Operation In previous chapter, it was reported that a total noble metal power density of 7.3 W/mg Pt has been achieved on Nuvera single cell with OME porous flow field architecture. Significant performance improvement has been demonstrated by direct comparison with land / channel structure, especially in high current density regime. Rather than flooding or oxygen mass transport limitations as in conventional flow field, anode dehydration has been identified as the potential limiting factor preventing higher current density operation in the OME porous flow field. In this chapter, efforts are focused on elucidating the operating strategies which enable stable operation at elevated temperature in dry environments, suitable for automotive application. The significance of experimentally-observed thermo-osmosis phenomenon is evaluated quantitatively to compare with electro-osmosis. Operating conditions are designed to study the impact of temperature, pressure, stoichiometry and gas feed RH separately and collectively. The model, validated under a wide range of operating conditions, is used to provide insight about the impact on internal water distribution and the underlying mechanisms how the anode dry-out can be further reduced at high power density Literature Review The delicate interplay between dehydration and flooding is the core of water management issue and critical not only in porous flow field. Actually it has been widely studied in conventional land / channel architecture because flooding in the catalyst layer, diffusion media, and / or flow channel is a major concern. As reviewed by Li et al. [55], both experimental and modeling efforts on flooding reduction included adjusting operation to achieve better water management. Water management can be investigated in-situ by water balance measurement. The impact of operating condition on NWD coefficient has been addressed in several experimental works, e.g. [191, 194, 56-58]. Janssen et al. [191] investigated the impact of varied operating conditions (gas humidification, temperature, pressure, current density and stoichiometry) and material configurations on the measured effective drag coefficient and performance, 118

135 providing ample benchmark data for model validation. Colinart et al. [194] did a systematic investigation on water transport coefficient under a wide range of operating conditions (current density, gas stoichiometry, gas inlet RH, temperature, pressure) and identified parameters of the most significant impact on water transport. As summarized in the review paper by Dai et al. [195], NWD coefficient could be used to analyze the effect of component design, material properties and operating conditions on water balance. As proposed in previous chapter, NWD coefficient can be a necessary and complementary tool for multiphase model validation along with voltage and ASR comparison. Besides the overall water balance measurement, more information on internal water transport can be gleaned from distributed measurement. Dong et al. [08] measured the performance, HFR and species distributions simultaneously at different RH levels under co-flow arrangement. The diffusion reversal process was identified to explain the generalized local current distribution proposed for co-current configuration. Using a similar technique, Yang et al. [09] found the presence of strong back-diffusion of water toward the anode, even with a dry cathode stream. In contrast to the abundance of literature on mitigating flooding in a conventional flow field, the effectiveness of adjusting operating parameters to alleviate anode dehydration in open porous flow field has never been investigated. The impact of specific modes of transport on internal water distribution in PEFCs with porous flow field is systematically addressed in this chapter for the first time with a highly validated computational model. 4.. Experimental Details The counter-current anode / cathode configuration and the coolant flow were illustrated in Figure 4.1. The fuel cell components and test systems were mostly the same as described in previous chapter except ASR and water balance measurement. EIS was collected using a Zahner IM6ex potentiostat by Zahner Elektrik (Kronach, Germany). The frequency was swept from 5 khz to 100 mhz using alternating current 119

136 perturbation with a 50 mv amplitude. ASR corresponded to the real part of the impedance at the frequency of about 3 khz. Condenser and desiccant were used instead of RH sensors to collect water from the effluent gas at the anode and cathode exit, respectively, after stable operation was achieved. The water measurement was considered to be valid if the overall mass balance of water under steady operation was reasonably precise, i.e. the difference between the outgoing water and the incoming plus generated water was within 5% of the amount required for mass conservation at steady state, unless otherwise specified. The selection of operating current density was based on the compromise between electrical power density and efficiency during operation. As shown in Figure 4., electrical power density increases steadily with current density in the range from 0 to.0 A/cm, and plateaus at about 1. W/cm. Heat dissipation, however, increases strongly non-linearly with current density in the whole range from 0 to 3.0 A/cm. Since efficiency has to be addressed to achieve parity with combustion-based propulsion systems,.0 A/cm is believed to be a reasonable operating point considering the high power density achieved with reasonable efficiency in OME design. The selection of gas feed RH was based on the parametric study completed in previous chapter and summarized in Figure 4.3. Three humidification schemes, i.e. sub-saturated anode and dry cathode stream, fully-saturated anode and dry cathode stream, and dry anode and fully-saturated cathode stream, are compared in terms of cell performance, NWD coefficient, and humidity level of effluent gas. The humidity level of outgoing gas is calculated as: At anode exit, RH out a n a, out HO out n H sat Pa Psat T P T cell cell [4-1] At cathode exit, 10

137 where out RH and a RH out c n n c, out HO out out O n N sat Pc Psat T P T out RH are the relative humidity at anode and cathode exit, respectively; c cell cell, n out H O [4-], n out H n out O and are the molar flow rate of water, hydrogen, oxygen and nitrogen at the outlet, respectively; n out N and P is the saturation pressure at cell operating temperature sat T ; cell P and a P is the total back pressure c applied to anode and cathode side, respectively. As shown in Figure 4.3 (a), operation with fully-saturated anode stream produces no better performance than that with sub-saturated one, indicating no incentive to humidify the anode stream more than 50% RH at given operating conditions. Similar qualitative trend can be discerned in Figure 4.3 (b) with regard to NWD coefficient between three humidification scenarios. As presented by Figure 4.3 (c), under all three scenarios, both anode and cathode stream at respective exits are over-saturated at the current density of.5a/cm, especially in the case of fully-saturated cathode. Due to dilution and stoichiometric ratios the amount of water contained in fully-saturated cathode incoming gas is.38 times that contained in fullysaturated anode income gas. However, it still does not lead to increased performance or stability. As can be discerned in Figure 4.3 (a), the cell operating with dry anode and fully-saturated cathode stream is the worst performer out of the three with regard to not only performance but also operation since no stability can be achieved beyond.5a/cm. The lower performance might be explained by local flooding considering the resistance to water removal from cathode side under high humidity level of the cathode stream. The instability might be attributed to dry anode gas feed and insufficient internal humidification in anode inlet region even in counter-flow configuration. The maldistribution of water in the case of dry anode and fully-saturated cathode gas feed is believed to result in co-existence of local flooding and dehydration responsible for the lower performance and instability. Therefore, for the operating conditions design, anode stream is hydrated to achieve better performance and stability with minimum humidification. The cathode humidification is applied only if necessary. 11

138 Operating parameters that can be adjusted include temperature, back pressure, stoichiometry and gas feed RH. The operating conditions chosen for testing (listed in Table 4-I) represent a wide range of inlet humidity, flow rate, and back pressure conditions relevant to automotive applications and provide ample validation space for the model. The fuel cell is starting from 60 C, with temperature increasing until operation becomes unstable. High operating temperature capability is sought in automotive applications to facilitate heat dissipation. A constant dew point temperature, T dew, is set at different operating temperatures to achieve exactly the same flow rate of water into to the fuel cell, as implied by Equation [3-3], for better comparison between different test cases. In the base case, i.e. Condition 0, equal back pressure of 1.8 bar and equal stoichiometry of.0 are applied to both anode and cathode, and T is set dew at a constant of 60 C. Condition 1 differs from Condition 0 in that higher back pressure of.4 bar is applied to cathode side to create a pressure differential across the cell. The difference between Condition and Condition 0 lies in the lower stoichiometry of 1.5 on cathode side. Under Condition 3, cathode humidification is added to Condition 0 with the cathode gas feed at a constant T of 60 C. After dew investigating the impact of pressure, stoichiometry and cathode humidification separately, Condition 4 was designed to evaluate the combined effect of the varied operating parameters. The gas stream humidification in this case is slightly different in that constant RH is applied to Condition 4 instead of constant dew point temperature, as in Condition Significance of Thermo-osmotic Flux Thermo-osmosis is a temperature-driven water transport mode across membrane, in addition to the conventional electro-osmotic flux, diffusive flux and / or hydraulic flux in the membrane. It is a phenomenon regularly observed in similar ion exchange membranes in experiments outside the fuel cell field [50, 59-6]. As directly measured by Kim et al. [50], thermo-osmotic flow was observed in membranes subject to even a small temperature gradient. The direction of water flux in perfluorinated sulfonic acid (PFSA) membrane such as Nafion was determined to be from the cold to hot side. In a 1

139 similar way to mass diffusive flux in a single-component system, thermo-osmotic water flux can be expressed as: N TOD D TOD T [4-3] where N TOD is the thermo-osmotic water molar flux in the unit of molm - s -1, D can be considered as TOD thermo-osmotic diffusivity with units of molm -1 s -1 K -1, T indicates that thermo-osmotic water flux is driven by temperature gradient. The temperature dependence of thermo-osmotic diffusivity, Gore-Select membrane was correlated by Kim et al. [50] as: D TOD, for 4 D TOD 9.10 exp 97/T [4-4] and is applied here. The relative impact of thermo-osmosis is highly dependent on operating conditions and material properties. In conventional land / channel systems, the temperature gradient across the membrane is expected not to be significant due to the relatively low performance achieved, therefore its effect is relatively minor (and arguably within the margin of experimental uncertainty). For a high power density system, however, this effect can become significant, even for thin membranes. This thermo-osmotic flow under temperature gradient can be incorporated into all other modes of water transport as i w K N0 EOD DdCd P DT T [4-5] F M In order to compare the relative magnitude of thermo-osmotic flux, a parameter called thermo-osmotic drag coefficient is defined as the equivalent to electro-osmotic drag coefficient EOD in thermo-osmosis: w 13

140 N TOD i TOD [4-6] F Considering Equation [4-3] and Equation[4-6], the thermo-osmotic drag coefficient estimated as TOD can be where DTODTMEM / tmem TOD [4-7] i / F TMEM is the temperature gradient across the membrane, and t MEM is the membrane thickness. The contribution from thermo-osmosis to predicted NWD under Condition 0 is demonstrated by Figure 4.4 (a). Figure 4.4 (b) shows that under such condition the temperature gradient across the membrane varies from 0.65 to 0.75 ⁰ C and the normalized thermo-osmotic drag coefficient varies from 0.18 to 0.1 in the operating temperature range and is a function of temperature. Compared to electro-osmotic drag coefficient, which is in the range between 1.0 and.55, depending on whether the membrane is in vapor-, transitional or liquid-equilibrated mode, the significance of thermo-osmosis cannot be neglected even for membranes as thin as 18 μm, especially under hot and dry operating conditions. Therefore thermo-osmosis is implemented into the model and included in all the results shown below Anode Dehydration Induced at High Temperature The cell operating temperature where anode dry-out becomes limiting was explored under the baseline Condition 0. Figure 4.5 shows the model prediction compared to the experimental measurement of voltage, ASR and NWD coefficient. In the temperature range from 60 to 70 ⁰ C, the model predicts both the qualitative shape and quantitative values of the voltage, ASR, and NWD coefficient. At 70 ⁰ C, the model under-predicts the performance drop by about 10 mv, which can be mainly attributed to the underprediction of the ASR spike by about 3 mωcm (5.7%). In regard to the limiting temperature where anode dry-out begins, the model prediction is.5 ⁰ C higher than experimental measurement. It is important to 14

141 note that Condition 0 has a fixed amount of water in the cell at all temperatures since inlet dew point temperature, T, is kept constant with only the cell temperature increased. dew The temperature effect can be seen primarily through the physical properties and parameters included in the model. Generally, the deviation of the temperature-dependent transport and reaction parameters from their reference values can be mathematically described by the Arrhenius type of equation: Q T Q Tref E a 1 1 exp [4-8] Ru Tref T where Q T is the value at temperature T, activation energy, and Q T ref is the value at reference temperature T ref, E is the a R is the universal gas constant. In the case of positive u result of increasing T, while in the case of negative E, a Q T increases as a E, a Q T decreases as a result of increasing T. The major parameters implemented in the model with temperature dependence are listed in Table 4-II along with their activation energy E a. Among these parameters, exchange current density, ref i 0,c, ionic conductivity,, and water content : water activity a correlation have direct relevance to performance and ASR. On one hand, as the cell temperature increases, the lower hydration state results in greater resistivity in the electrolyte phase, as implied by the progressive ASR increase. It should be noted however that experimental measurement of the ASR generally does not include ionic losses in the catalyst layers, thus only represents average membrane hydration and does not precisely reflect anode dry-out limitations. On the other hand, at higher temperature, better kinetics can lead to reduced activation polarization, vapor phase mass transport can be further enhanced, and water coverage in the catalyst layer is reduced. Therefore the performance variation with temperature can be interpreted as a competition between these highly non-linear effects. The gradual performance increase from 60 ⁰ C to 67.5 ⁰ C is because of enhanced reaction kinetics and facilitated mass transport at little cost of membrane water content. Beyond 67.5 ⁰ C 15

142 the membrane dehydration is triggered and loss in ionic conductivity dominates the voltage response over activation and transport incentives. As defined in Equation [3-5], global NWD coefficient is positive if net water transport is from anode to cathode. It is a representation of competition between electro-osmosis (always toward the cathode), thermo-osmosis (toward the hotter side), and transport under chemical potential gradient (toward either anode or cathode side). In most cases, thermo-osmotic drag is towards the cathode due to the higher heat generation in the ORR compared to that in the HOR. Increasing dominance of positive water flux toward the cathode with increasing temperature is shown in the inset of Figure 4.5, indicating that the cell is prone to anode dehydration at elevated temperature. The maximum stable cell operation temperature is limited to 70 ⁰ C at this baseline condition as a consequence of severe membrane dehydration, as inferred by the overall trend of NWD coefficient. It is important to note that although the net cell NWD may be positive, given the counter-flow configuration, the local NWD may change from negative to positive along the flow direction and is certainly not constant. Figure 4.6 (a) shows the predicted internal water distribution in terms of molar flow rate along the flow field at two different temperatures, 60 and 70 ⁰ C. The flow direction in the distributor is indicated by the arrow. The salient feature of internal humidification in counter-current configuration can be further elucidated by Figure 4.6 (b). As illustrated by Figure 4.1, at the cathode inlet / anode outlet, the cathode stream is dry, while the anode stream is not. Water transport under chemical potential gradient is positive (from anode to cathode) or slightly negative (from cathode to anode) but insufficient to counteract the combination of electro-osmosis and thermo-osmosis. Therefore, the local net water transport across the membrane is positive, i.e. towards cathode, as supported by Figure 4.6 (b). As the cathode reactant flows downstream, water is accumulated and cathode stream becomes more saturated. The stronger back diffusion makes the positive local NWD coefficient decrease and eventually approach zero. At some point in the along-the-flow direction, the back transport of water becomes significant enough to counteract the positive water flux so that water lost from the anode side through the membrane can be fully replenished, 16

143 which corresponds to the turning point in net water transport from positive to negative. It is noted that the turning point in NWD coefficient corresponds to where anode water flux switches the trend. The direct comparison between 60 and 70 C shows that at higher temperature it is more difficult to saturate the cathode stream, the transition occurs further downstream on the cathode side, i.e. upper-stream on the anode side, water loss from the anode stream is more severe, promoting more severe anode dehydration. Figure 4.6 (c) shows appreciable difference between two temperatures in the overall and local hydration level, especially in the anode outlet / cathode inlet region Operation Engineering to Mitigate Anode Dehydration Impact of Pressure Differential on Limiting Temperature Compared with Condition 0, Condition 1 includes a pressure differential. The cathode back pressure is increased to.4 bar while keeping all other operating parameters the same. As shown in Figure 4.7, the model again quantitatively and qualitatively show close agreement. Although both experiment and model show there is no as obvious ASR spike under Condition 1 as in Condition 0, the model over-predicts ASR by up to 4 mωcm (8.4%), which, along with the ionic loss contribution in cathode catalyst layer, can account for the maximum performance deviation of 15 mv at 75 C. The anode dry-out limiting temperature is over-predicted by.5 C as well. Higher oxygen partial pressure can account for the performance improvement throughout the operating temperature, as observed in Figure 4.7. In the lowertemperature regime, where the membrane is well-hydrated and no noticeable difference is detected in ASR, enhanced oxygen partial pressure is responsible for the performance difference. In the highertemperature regime, where the cell performance is more limited by membrane hydration, the pressure differential between the cathode and anode induces convective flux of water toward the anode, resulting in the significant ASR drop under Condition 1. Although Condition 0 and 1 share the same overall trend in NWD as temperature increases, and the cell dies out eventually from anode dehydration in both cases, considerable difference between two conditions can still be discerned in the inset of Figure 4.7. The underlying mechanism, however, is different with 17

144 temperature. At lower operating temperature, the cell is well-hydrated and the membrane is mostly liquidequilibrated, as shown in Figure 4.8 under both conditions. (In theory Condition 0 and 1 should have the same stream RH at anode inlet. The slight discrepancy observed in Figure 4.8 (b) results from the iterative nature of the solver. The computational model does not necessarily give exact amount of water molar flux at anode inlet as specified by operating conditions. The deviation from theoretical calculation is within %.) Although there is some controversy between use of a diffusive or hydraulic model to represent water transport mode across the membrane [15, 16], these two types of physical behavior can be described in a consistent manner by the driving force of chemical potential, as suggested by Weber et al. [63] in the following formula: 0 0 RTln a0 V P [4-9] where is the chemical potential of water, 0 a is the water activity, 0 V 0 is the molar volume of water, and P is the pressure. In this theory, the water transport in saturated membrane is under the gradient of hydraulic pressure, which can be written as 0 0 V P L [4-10] Therefore at lower temperature (saturated conditions) another major impact of higher cathode pressure is the significant hydraulic permeation through the membrane from cathode to anode side. Based on the pressure differential applied and the NWD difference between two conditions, the effective hydraulic permeability of the membrane can be calculated from experimental measurement to be around m, which is towards the lower end of values presented in literature (between 10-0 and m [16, 64]) The value of m taken from experimental values here is implemented in the model. At higher operating temperature (unsaturated conditions), hydraulic permeation is not the primary mode of water transport in the ionomer phase since the membrane is not hydrated enough to be in liquid- 18

145 equilibrium. Higher cathode back pressure, however, affects the amount of water needed to saturate the cathode gas stream, as implied by the following equation: Psat T cell n n sat n H O O N [4-11] P P T c sat cell where is the local minimum molar flow rate of water required to saturate the gas stream, sat nh O n O and n N are the local molar flow rate of O and N, respectively. This can explain the observation in Figure 4.9 that under Condition 1 there is less water in the cathode stream but the local relative humidity is higher than that under Condition 0. On the anode side, the turning point where the net water transport across the membrane switches direction is closely related to the internal water movement, and the anode stream humidification is affected by the saturation level in cathode stream. Under Condition 1, the cathode stream reaches full saturation more rapidly, lower gradient is created for water to be removed from the cathode side, and therefore more cathode water is pushed back toward the anode. It is evident from Figure 4.9 (a) that under Condition 1 the turning point occurs much further down the anode flow direction, closer to anode exit, compared to at the middle of the flow path under Condition 0. As a result, anode stream starts to lose water to the cathode side at a much later phase and therefore stays better hydrated throughout the flow direction, as shown in Figure 4.9 (b). With exactly the same amount of water inside the cell, the consequence of increasing cathode back pressure by 0.6 bar from Condition 0 to Condition 1 is much stronger back transport, considerably lower global NWD, a better-humidified anode stream and a resultant 5 C increase in the limiting operating temperature, as highlighted in Figure Impact of Cathode Stoichiometry on Limiting Temperature Compared to the baseline Condition 0, Condition reduces the cathode stoichiometry from.0 to 1.5 while keeping all other operating conditions the same. As shown in Figure 4.10, the difference between model prediction and experimental measurement is also satisfactory. The maximum deviations are 11 mv in performance at 60 C due to overestimated flooding severity, 4 mωcm (8.89%) in ASR towards higher temperature, and.5 C in limiting temperature. On one hand, it can be deduced from Equation [4-11] 19

146 that lower cathode stoichiometry can improve the hydration state of the cathode stream, similar to the case of imposing higher cathode pressure. Lower ASR (shown in Figure 4.10) throughout the operating temperature is a result of a better-hydrated membrane, especially in the higher temperature regime. On the other hand, lower cathode stoichiometry can be directly translated to lower average oxygen concentration in the fuel cell. The dramatic performance drop from Condition 0 to Condition, as observed in Figure 4.10, can be interpreted as follows: at lower temperature the cell is well-humidified and more limited by mass transport, so the performance loss by oxidizer availability outweighs the performance gain by better hydration. As the temperature increases, the performance difference between the two conditions decreases and Condition extends the limiting operating temperature by.5 C to 7.5 C with same amount of internal water. More insight of cathode stoichiometry impact on internal water distribution at higher temperature (70 C) is provided by Figure 4.11 (a). On the cathode side, while the water flow rate in the stream is similar between two conditions, the humidity level is much higher under Condition, the underlying reason can be traced to Equation [4-11]. On the anode side, since the cathode stream can absorb moisture in a more efficient way under Condition, the load for anode to internally humidify the cathode stream is reduced, and the turning point occurs closer to cathode inlet / anode outlet, and therefore anode dehydration is greatly mitigated, as shown in Figure 4.11 (b). As a good indicator of internal water transport, NWD coefficient is compared in the inset of Figure Although the overall trend in NWD as a function of temperature and the cell limiting factor are similar to those in other conditions, both experiment and model show a lower NWD throughout the operating temperature, inferring stronger back diffusion and thus better membrane hydration, especially at higher temperature. At lower temperature (saturated conditions), however, the model gives a higher global NWD value than the measurement. As the cathode stoichiometry is reduced, the capability of the cathode stream to carry the water droplets away from the diffusion media diminishes, and water accumulated on the cathode side is more likely to move back to the anode side, making back-transport more dominant in 130

147 lower temperature regime. This impact of cathode flow stoichiometry on water management, however, is not fully addressed by pseudo-three-dimensional model since transport in the along-the-flow direction is simplified to conservation of mass. This may therefore explain the discrepancy between experiment and model in NWD at lower operating temperature Impact of Cathode Humidification on Limiting Temperature Compared to the baseline Condition 0, Condition 3 is tested to understand the impact of humidification of the cathode stream on prevention of anode dry-out. The dew point temperature, T, is kept at a constant dew of 60 C to ensure same amount of water inside the cell at all temperatures. As shown in Figure 4.1, the model is in qualitative agreement with experiment. The maximum quantitative discrepancy is 11 mv in performance, which occurs at 60 ⁰ C due to over-prediction of performance loss from flooding for fullysaturated gas stream. Other discrepancies are only mωcm, 0.03 and.5 C with respect to ASR, NWD and limiting temperature, respectively. The inset of Figure 4.1 shows that by humidifying the cathode stream, much lower NWD coefficient results. Humidified cathode stream and thus stronger back diffusion naturally lead to better-hydrated membrane, as indicated by ASR drop of approximately 4 mωcm at lower temperature and as much as 10 mωcm at higher temperature from Condition 0 to Condition 3, effectively extending the maximum stable cell operation at these conditions by 5 C. However, both experiment and model show reduced performance in Condition 3 at 60 C. As the temperature goes up, the performance under Condition 3 gets closer to that under Condition 0. In the higher temperature regime, Condition 3 shows its superiority to Condition 0 not only in stable operation but also in performance. Figure 4.13 depicts RH of both anode and cathode stream to make direct comparison between Condition 0 and Condition 3. Dramatic distinction can be observed in the saturation level of cathode stream as well as anode stream towards its outlet. In lower temperature mass transport dominated regime, as shown in Figure 4.13 (a), the added humidity to the cathode stream in Condition 3 does not give advantage over Condition 0. Conversely, the over-saturation of both streams is believed to be responsible for the difficulty of water removal from either side, cathode components flooding and thus performance drop. In 131

148 higher temperature regime shown in Figure 4.13 (b), where water loss from the anode to the cathode stream towards anode outlet becomes limiting factor, Condition 3 is observed to result in better-saturated anode stream along with the gradual relief of cathode flooding, which is the key to stable operation towards higher operating temperature Combined Impact on Limiting Temperature Condition 4 combines the pressure differential as in Condition 1, lower cathode stoichiometry as in Condition, and cathode humidification as in Condition 3. This conditions is tested to evaluate the combined impact of tested parameters in extending the maximum operational temperature. Again, dew point temperature is maintained constant in Condition 3 to ensure same amount of internal water at all temperatures, while constant RH is more realistic for fuel cell operation. As demonstrated by Figure 4.14, the model prediction agrees reasonably with the experimental value, especially with respect to NWD coefficient. Note here the water measurement is considered to be valid if the difference in overall mass balance under steady operation is within 10%, considering the significant amount of water involved. The performance, ASR, and maximum temperature predictions are also in reasonable agreement with measured values. The slight deviation in ASR (5 mωcm ) and anode dry-out limiting temperature (.5 ⁰ C) is similar to other cases. The underlying reason for such numerical deviation in ASR towards higher temperature and in anode dry-out limiting temperature may be model assumption of phase equilibrium of water in MEA. The non-equilibrium water uptake in membrane has been studied by several models [103, 148]. In our work, however, the finite rate of water adsorption / desorption process is neglected, which can explain the inaccuracy in predicted ionic loss of not only membrane but also cathode catalyst layer, especially in the dry environment at elevated temperature. The experimental observation of anode dry-out without dramatic ASR spike towards higher operating temperature is an evidence of its transient nature. Moreover, considering such small deviation and relatively large experimental and published transport value uncertainty, a specific reason is hard to pinpoint, as it is more likely the combined effects or varying compression. 13

149 As shown in Figure 4.14, under conditions of uniform 1.8 bar back pressure, uniform stoichiometry of.0 and 50% anode RH, the maximum stable cell operation is limited to 67.5 C. By increasing cathode back pressure to.4 bar, reducing cathode stoichiometry to 1.5 and humidifying the cathode gas stream to 50% RH, cell can reach 87.5 C in stable operation, which can be attributed to better water management as a result of optimizing operating parameters. This 0 C increase in maximum stable cell limiting temperature is achieved with no change in materials or cell architecture Conclusion Anode dry-out has been shown in Chapter 3 to limit cell performance for these porous flow fields as opposed to flooding or oxygen transport. In this chapter, the comprehensive D+1 multi-phase computational model developed in Chapter has been utilized to investigate operating strategies which enable high power density operation in dry, elevated temperature environment. Extensive experimental model validation has been completed under a wide range of temperature, pressure, reactant stoichiometry and humidity conditions. Both qualitative and quantitative agreement has been achieved in regard to voltage, area-specific resistance, and net water drag coefficient. Under saturated conditions, higher cathode pressure can enhance water transport through the membrane in the form of hydraulic permeation; under unsaturated conditions, higher cathode pressure can facilitate cathode stream saturation. In either case the anode stream can be better saturated for higher temperature operation. Lower cathode stoichiometry is demonstrated to have diminishing capability to remove water droplet from cathode side under saturated conditions and facilitate cathode stream saturation under unsaturated conditions, which leads to better-hydrated anode stream in both cases. Internal water distribution predictions show that moderate operating parameter adjustments can maximize water transport to the anode in a counter-current configuration and thus effectively push the envelope of stable operating temperature 0 C higher than the baseline case, enabling more efficient heat dissipation in coolant system. 133

150 Additionally, the significance of thermo-osmotic relative to electro-osmotic flux has been evaluated and is non-negligible for membranes as thin as 18 μm for high current density operation achievable with porous flow fields (> A/cm ). 134

151 Table 4-I Test Conditions to Engineer Operation (Difference from Condition 0 is highlighted) # Current Density Back Pressure A C λ H λ O Relative Humidity A C 0 A/cm 1.8 bar 1.8 bar.0.0 T dew =60 C dry 1 A/cm 1.8 bar.4 bar.0.0 T dew =60 C dry A/cm 1.8 bar 1.8 bar T dew =60 C dry 3 A/cm 1.8 bar 1.8 bar.0.0 T dew =60 C T dew =60 C 4 A/cm 1.8 bar.4 bar % 50% 135

152 Table 4-II Major parameters of temperature dependence in the model Activation Parameters Energy, E a Reference [kj mol -1 ] Correlation between water content, and water activity, a negative, no direct [33] correlation Ionic conductivity, 15 [33] Dissolved water diffusion coefficient, D 0 [33] d Electro-osmotic drag coefficient, 4 [33] Exchange current density, EOD ref i 0,c 67 [5] Diffusion coefficient of oxygen in electrolyte, D O, N 4 [5] Henry s constant for oxygen dissolved into electrolyte, H O, N 6 [14] 136

153 Figure 4.1 Schematic of the single cell fixture (Courtesy of Nuvera Fuel Cells Inc.) 137