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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
A complete, up-to-date, introductory guide to fuel cell technology and application Fuel Cell Fundamentals provides a thorough introduction to the principles and practicalities behind fuel cell technology. Beginning with the underlying concepts, the discussion explores fuel cell thermodynamics, kinetics, transport, and modeling before moving into the application side with guidance on system types and design, performance, costs, and environmental impact. This new third edition has been updated with the latest technological advances and relevant calculations, and enhanced chapters on advanced fuel cell design and electrochemical and hydrogen energy systems. Worked problems, illustrations, and application examples throughout lend a real-world perspective, and end-of chapter review questions and mathematical problems reinforce the material learned. Fuel cells produce more electricity than batteries or combustion engines, with far fewer emissions. This book is the essential introduction to the technology that makes this possible, and the physical processes behind this cost-saving and environmentally friendly energy source. * Understand the basic principles of fuel cell physics * Compare the applications, performance, and costs of different systems * Master the calculations associated with the latest fuel cell technology * Learn the considerations involved in system selection and design As more and more nations turn to fuel cell commercialization amidst advancing technology and dropping deployment costs, global stationary fuel cell revenue is expected to grow from $1.4 billion to $40.0 billion by 2022. The sector is forecasted to explode, and there will be a tremendous demand for high-level qualified workers with advanced skills and knowledge of fuel cell technology. Fuel Cell Fundamentals is the essential first step toward joining the new energy revolution.
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Table of Contents
Title Page
Copyright
Dedication
Preface
Acknowledgments
Nomenclature
Part I: Fuel Cell Principles
Chapter 1: Introduction
1.1 What Is a Fuel Cell?
1.2 A Simple Fuel Cell
1.3 Fuel Cell Advantages
1.4 Fuel Cell Disadvantages
1.5 Fuel Cell Types
1.6 Basic Fuel Cell Operation
1.7 Fuel Cell Performance
1.8 Characterization and Modeling
1.9 Fuel Cell Technology
1.10 Fuel Cells and the Environment
1.11 Chapter Summary
Chapter Exercises
Chapter 2: Fuel Cell Thermodynamics
2.1 Thermodynamics Review
2.2 Heat Potential of a Fuel: Enthalpy of Reaction
2.3 Work Potential of a Fuel: Gibbs Free Energy
2.4 Predicting Reversible Voltage of a Fuel Cell under Non-Standard-State Conditions
2.5 Fuel Cell Efficiency
2.6 Thermal and Mass Balances in Fuel Cells
2.7 Thermodynamics of Reversible Fuel Cells
2.8 Chapter Summary
Chapter Exercises
Chapter 3: Fuel Cell Reaction Kinetics
3.1 Introduction to Electrode Kinetics
3.2 Why Charge Transfer Reactions Have an Activation Energy
3.3 Activation Energy Determines Reaction Rate
3.4 Calculating Net Rate of a Reaction
3.5 Rate of Reaction at Equilibrium: Exchange Current Density
3.6 Potential of a Reaction at Equilibrium: Galvani Potential
3.7 Potential and Rate: Butler–Volmer Equation
3.8 Exchange Currents and Electrocatalysis: How to Improve Kinetic Performance
3.9 Simplified Activation Kinetics: Tafel Equation
3.10 Different Fuel Cell Reactions Produce Different Kinetics
3.11 Catalyst–Electrode Design
3.12 Quantum Mechanics: Framework for Understanding Catalysis in Fuel Cells
3.13 The Sabatier Principle for Catalyst Selection
3.14 Connecting the Butler–Volmer and Nernst Equations (Optional)
3.15 Chapter Summary
Chapter Exercises
Chapter 4: Fuel Cell Charge Transport
4.1 Charges Move in Response to Forces
4.2 Charge Transport Results in a Voltage Loss
4.3 Characteristics of Fuel Cell Charge Transport Resistance
4.4 Physical Meaning of Conductivity
4.5 Review of Fuel Cell Electrolyte Classes
4.6 More on Diffusivity and Conductivity (Optional)
4.7 Why Electrical Driving Forces Dominate Charge Transport (Optional)
4.8 Quantum Mechanics–Based Simulation of Ion Conduction in Oxide Electrolytes (Optional)
4.9 Chapter Summary
Chapter Exercises
Chapter 5: Fuel Cell Mass Transport
5.1 Transport in Electrode versus Flow Structure
5.2 Transport in Electrode: Diffusive Transport
5.3 Transport in Flow Structures: Convective Transport
5.4 Chapter Summary
Chapter Exercises
Chapter 6: Fuel Cell Modeling
6.1 Putting It All Together: A Basic Fuel Cell Model
6.2 A 1D Fuel Cell Model
6.3 Fuel Cell Models Based on Computational Fluid Dynamics (Optional)
6.4 Chapter Summary
Chapter Exercises
Chapter 7: Fuel Cell Characterization
7.1 What Do We Want to Characterize?
7.2 Overview of Characterization Techniques
7.3 In Situ Electrochemical Characterization Techniques
7.4 Ex Situ Characterization Techniques
7.5 Chapter Summary
Chapter Exercises
Part II: Fuel Cell Technology
Chapter 8: Overview of Fuel Cell Types
8.1 Introduction
8.2 Phosphoric Acid Fuel Cell
8.3 Polymer Electrolyte Membrane Fuel Cell
8.4 Alkaline Fuel Cell
8.5 Molten Carbonate Fuel Cell
8.6 Solid-Oxide Fuel Cell
8.7 Other Fuel Cells
8.8 Summary Comparison
8.9 Chapter Summary
Chapter Exercises
Chapter 9: PEMFC and SOFC Materials
9.1 PEMFC Electrolyte Materials
9.2 PEMFC Electrode/Catalyst Materials
9.3 SOFC Electrolyte Materials
9.4 SOFC Electrode/Catalyst Materials
9.5 Material Stability, Durability, and Lifetime
9.6 Chapter Summary
Chapter Exercises
Chapter 10: Overview of Fuel Cell Systems
10.1 Fuel Cell Subsystem
10.2 Thermal Management Subsystem
10.3 Fuel Delivery/Processing Subsystem
10.4 Power Electronics Subsystem
10.5 Case Study of Fuel Cell System Design: Stationary Combined Heat and Power Systems
10.6 Case Study of Fuel Cell System Design: Sizing a Portable Fuel Cell
10.7 Chapter Summary
Chapter Exercises
Chapter 11: Fuel Processing Subsystem Design
11.1 Fuel Reforming Overview
11.2 Water Gas Shift Reactors
11.3 Carbon Monoxide Clean-Up
11.4 Reformer and Processor Efficiency Losses
11.5 Reactor Design for Fuel Reformers and Processors
11.6 Chapter Summary
Chapter Exercises
Chapter 12: Thermal Management Subsystem Design
12.1 Overview of Pinch Point Analysis Steps
12.2 Chapter Summary
Chapter Exercises
Chapter 13: Fuel Cell System Design
13.1 Fuel Cell Design Via Computational Fluid Dynamics
13.2 Fuel Cell System Design: A Case Study
13.3 Chapter Summary
Chapter Exercises
Chapter 14: Environmental Impact of Fuel Cells
14.1 Life Cycle Assessment
14.2 Important Emissions for LCA
14.3 Emissions Related to Global Warming
14.4 Emissions Related to Air Pollution
14.5 Analyzing Entire Scenarios with LCA
14.6 Chapter Summary
Chapter Exercises
Appendix A: Constants and Conversions
Appendix B: Thermodynamic Data
Appendix C: Standard Electrode Potentials at 25°C
Appendix D: Quantum Mechanics
D.1 Atomic Orbitals
D.2 Postulates of Quantum Mechanics
D.3 One-Dimensional Electron Gas
D.4 Analogy to Column Buckling
D.5 Hydrogen Atom
D.6 Multielectron Systems
D.7 Density Functional Theory
Appendix E: Periodic Table of the Elements
Appendix F: Suggested Further Reading
Appendix G: Important Equations
Appendix H: Answers to Selected Chapter Exercises
Bibliography
Index
End User License Agreement
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Guide
Cover
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 General concept of a (H
2
–O
2
) fuel cell.
Figure 1.2 Schematic of H
2
–O
2
combustion reaction. (Arrows indicate the relative motion of the molecules participating in the reaction.) Starting with the reactant H
2
–O
2
gases (1), hydrogen–hydrogen and oxygen–oxygen bonds must first be broken, requiring energy input (2) before hydrogen–oxygen bonds are formed, leading to energy output (3, 4).
Figure 1.3 Bonding energy versus internuclear separation for hydrogen–hydrogen bond: (1) no bond exists; (2) most stable bonding configuration; (3) further overlap unfavorable due to internuclear repulsion.
Figure 1.4 A simple fuel cell.
Figure 1.5 Schematic comparison of fuel cells, batteries, and combustion engines. (
a
) Fuel cells and batteries produce electricity directly from chemical energy. In contrast, combustion engines first convert chemical energy into heat, then mechanical energy, and finally electricity (alternatively, the mechanical energy can sometimes be used directly). (
b
) In batteries, power and capacity are typically intertwined—the battery is both the energy storage and the energy conversion device. In contrast, fuel cells and combustion engines allow independent scaling between power (determined by the fuel cell or engine size) and capacity (determined by the fuel tank size).
Figure 1.6 Fuel cells versus solar cells versus batteries. This schematic diagram provides another way to look at the similarities and differences between three common energy conversion technologies that provide electricity as an output.
Figure 1.7 Power density comparison of selected technologies (approximate ranges).
Figure 1.8 Energy density comparison of selected fuels (lower heating value).
Figure 1.9 Simplified planar anode–electrolyte–cathode structure of a fuel cell.
Figure 1.10 Cross section of fuel cell illustrating major steps in electrochemical generation of electricity: (1) reactant transport, (2) electrochemical reaction, (3) ionic and electronic conduction, (4) product removal.
Figure 1.11 Schematic of fuel cell
i–V
curve. In contrast to the ideal, thermodynamically predicted voltage of a fuel cell (dashed line), the real voltage of a fuel cell is lower (solid line) due to unavoidable losses. Three major losses influence the shape of this
i–V
curve; they will be described in Chapters 3–5.
Figure 1.12 Combined fuel cell
i–V
and power density curves. The power density curve is constructed from the
i–V
curve by multiplying the voltage at each point on the
i–V
curve by the corresponding current density. Fuel cell power density increases with increasing current density, reaches a maximum, and then falls at still higher current densities. Fuel cells are designed to operate at or below the power density maximum. At current densities below the power density maximum, voltage efficiency improves but power density falls. At current densities above the power density maximum, both voltage efficiency and power density fall.
Figure 1.13 Schematic of hydrogen economy dream.
Chapter 2: Fuel Cell Thermodynamics
Figure 2.1 Although this tank of H
2
gas has no apparent macroscopic energy, it has significant internal energy. Internal energy is associated with microscopic movement (kinetic energy) and interactions between particles (chemical/potential energy) on the atomic scale.
Figure 2.2 (
a
) The entropy of this 100-atom perfect crystal is zero because there is only one possible way to arrange the atoms to produce this configuration. (
b
) When three atoms are removed from the crystal and placed on the surface, the entropy increases. This is because there are many possible ways to conFigure a system of 100 atoms where 3 have been removed.
Figure 2.3 Pictorial summary of the four thermodynamic potentials. They relate to one another by offsets of the “energy from the environment” term
TS
and the “expansion work” term
pV
. Use this diagram to help remember the relationships.
Figure 2.4 Diagram of a reversible thermodynamic engine (or heat engine) operating under constant pressure and temperature. Reactants and products enter and exit from the engine at constant pressure and temperature, respectively. The engine generates external work using the chemical (heat) energy of reactants. Also, the engine releases unused chemical energy to the isothermal and isobaric environment.
Figure 2.5 Reversible voltage versus temperature for electrochemical oxidation of a variety of fuels. (After Broers and Ketelaar [3].)
Figure 2.6 Hydrogen concentration cell. A high-pressure hydrogen compartment and a low-pressure hydrogen compartment are separated by a platinum–electrolyte–platinum membrane structure. This device will develop a voltage due to the difference in the chemical potential of hydrogen between the two compartments.
Figure 2.7 Copper concentration cell.
Figure 2.8 Reversible HHV efficiency of H
2
–O
2
fuel cell compared to reversible efficiency of heat engine (Carnot cycle, rejection temperature 273.15 K). Fuel cells hold a significant thermodynamic efficiency advantage at low temperature but lose this advantage at higher temperatures. The kink in the fuel cell efficiency curve at 100°C arises from the entropy difference between liquid water and water vapor (consider the H
2
O
(l)
vs. H
2
O
(g)
curves from Figure 2.5).
Figure 2.9 Fuel cell efficiency under constant-stoichiometry versus constant-flow-rate conditions. Under a constant-stoichiometry condition , the fuel cell efficiency curve follows the fuel cell
j–V
curve, and efficiency is highest at low current density. Under a constant-flow-rate condition (in this case, 110% of the rate required at maximum current), fuel cell efficiency is poor at low current densities (because most of the fuel is wasted) and reaches a maximum at high current densities when most of the fuel is used.
Figure 2.10 Thermal balance in a fuel cell. The difference between the operation voltage V and an “imaginary” thermoneutral voltage calculated from the enthalpy of reaction represents the total energy loss in a fuel cell. This energy is converted to heat. The input, consumption, and output fluxes of reactants can be converted to equivalent currents to satisfy mass balance.
Figure 2.11 Thermal balance in a reversible fuel cell illustrating both the fuel cell and electrolyzer domains of operation. Under fuel cell operation, the difference between the operation voltage
V
and the thermoneutral voltage
E
H
represents the heat loss in the fuel cell. Under the electrolyzer mode of operation, there is a net
consumption
of heat at low current densities when the operating voltage of the electrolyzer,
V
, is below the thermoneutral voltage,
E
H
. However, above the thermoneutral voltage, net heat is produced in the electrolysis mode because entropic heat consumption is fully offset by irreversible heat production due to activation, ohmic, and mass transport losses in the electrolyzer. Maintaining system temperature during electrolysis under endothermic (net heat consumption) conditions can be difficult. Thus, most electrolyzers are designed to operate at or above the thermoneutral voltage.
Figure 2.12 Reversible HHV efficiency of H
2
O electrolysis compared to an H
2
–O
2
fuel cell. The thermodynamic efficiency of electrolysis increases with increasing temperature, while thermodynamic fuel cell efficiency decreases with increasing temperature.
Chapter 3: Fuel Cell Reaction Kinetics
Figure 3.1 Electrochemical reactions are heterogeneous. As this schematic shows, the HOR is a surface-limited reaction. It can take place only at the interface between an electrode and an electrolyte.
Figure 3.2 Electrode potential can be manipulated to trigger reduction (left) or oxidation (right). The thermodynamic equilibrium electrode potential (middle) corresponds to the situation where the oxidation and reduction processes are balanced.
Figure 3.3 An activation barrier (ΔG
‡
) impedes the conversion of reactants to products. Because of this barrier, the rate at which reactants are converted into products (the reaction rate) is limited.
Figure 3.4 Schematic of chemisorbed hydrogen charge transfer reaction. The reactant state, a chemisorbed hydrogen atom (), is shown at 1. Completion of the charge transfer reaction, as shown at 2, liberates a free electron into the metal and a free proton into the electrolyte .
Figure 3.5 Schematic of energetics of chemisorbed hydrogen charge transfer reaction. Curve 1 shows the free energy of the reactant state ([]) as a function of the distance of separation between the H atom and the metal surface. Curve 2 shows the free energy of the product state as a function of the distance of separation between the ion and the metal surface. The dark line denotes the “easiest” (minimum) energy path for the conversion of [] to []. The activated state is represented by .
Figure 3.6 At equilibrium, the chemical free-energy difference (
a
) across a reaction interface is balanced by an electrical potential difference (
b
), resulting in a zero net reaction rate (
c
).
Figure 3.7 One hypothetical possibility for the shape of the fuel cell voltage profile, since scientists can determine but not or . The Galvani potentials at the anode and cathode of a fuel cell must sum to give the overall thermodynamic cell voltage .
Figure 3.8 If the Galvani potential across a reaction interface is reduced, the free energy of the forward reaction will be favored over the reverse reaction. While the chemical energy (
a
) of the reaction system is the same as before, changing the electrical potential (
b
) upsets the balance between the forward and reverse activation barriers (
c
). In this diagram, reducing the Galvani potential by
η
reduces the forward activation barrier (() and increases the reverse activation barrier ().
Figure 3.9 Extracting a net current from a fuel cell requires sacrificing a portion of both the anode and cathode Galvani potentials. In this figure, the anode Galvani potential is lowered by , while the cathode Galvani potential is lowered by . As the Figure indicates, and are not necessarily equal. For a typical fuel cell, is generally much larger than . Compare the detail view in this Figure with Figure 3.8
b
. You should realize that these Figure are showing the same thing, although Figure 3.8 is plotted with units of energy (), while Figure 3.9 is plotted with units of voltage (V).
Figure 3.10 Relationship between
η
and as given by the Butler–Volmer equation. The fine solid lines show the individual contributions from the forward and reverse current density terms while the dark solid line shows the net current density given by the complete Butler–Volmer equation. Note that the Butler–Volmer curve is distinctly linear at low current density and distinctly exponential at high current density. In these regions, simplifications of the Butler–Volmer equation (as developed in Section 3.9) may be used. Note that the direction (sign) on the
η
axis is switched in this Figure to enable direct comparison with Figure 3.11.
Figure 3.11 Effect of activation overvoltage on fuel cell performance. Reaction kinetics typically inflicts an exponential loss on a fuel cell's
j–V
curve as determined by the Butler–Volmer equation. The magnitude of this loss is influenced by the size of . (Curves calculated for various values with , and .)
Figure 3.12 The
j−η
representation of a hypothetical electrochemical reaction. At high overvoltages, a linear fit of the kinetics to the Tafel approximation allows determination of and
α
. The Tafel approximation deviates from Butler–Volmer kinetics at low overvoltages.
Figure 3.13 Relative contributions to activation loss from H
2
–O
2
fuel cell anode versus cathode. The bulk of the activation overvoltage loss occurs at the cathode due to the sluggishness of the oxygen reduction kinetics.
Figure 3.14 Simplified schematic of electrode–electolyte interface in a fuel cell, illustrating TPB reaction zones where catalytically active electrode particles, electrolyte phase, and gas pores intersect.
Figure 3.15 Evolution of electron orbitals as a hydrogen molecule approaches a cluster of platinum atoms. (
a
) Platinum and hydrogen molecules are not yet interacting. (
b
,
c
) Atomic orbitals begin overlapping and forming bonds. (
d
) Complete separation of hydrogen atoms occurs almost simultaneously with reaching the lowest energy configuration.
Figure 3.16 Formation of hydronium. Water attaches to a positively charged proton on the platinum surface, forming a hydronium ion. The hydronium ion then desorbs from the surface. For simplicity only atomic nuclei (no electron orbitals) are shown.
Figure 3.17 (
a
) Oxygen molecule approaching a platinum catalyst surface. (
b
) Even after having reached lowest energy configuration via hybrid orbital formation, the oxygen molecule is not completely separated into individual oxygen atoms.
Figure 3.18 This “volcano plot” shows that materials with intermediate reaction species absorption strength yield the highest catalytic activity for the oxygen reduction reaction. Platinum and palladium are high on the curve. Adapted from Ref. [6b].
Figure 3.19 The overvoltage at the anode and the cathode modify the activation energy of each electrode according to the current. At steady state, the current at the anode and the cathode should be equal. Overvoltage and species concentrations are determined by satisfying this condition.
Chapter 4: Fuel Cell Charge Transport
Figure 4.1 Schematic of flux. Imagine water flowing down this tube at a volumetric flow rate of 10 L/s. Dividing this flow rate by the cross-sectional area of the tube (
A
) gives the flux
J
A
of water moving down the tube. Generally, flux is measured in molar rather than volumetric quantities, so in this example the liters of water should be converted to moles.
Figure 4.2 In a H
2
–O
2
fuel cell, accumulation of protons/electrons at the anode and depletion of protons/electrons at the cathode lead to voltage gradients which drive charge transport. The electrons move from the negatively charged anode electrode to the positively charged cathode electrode. The protons move from the (relatively) positively charged anode side of the electrolyte to the (relatively) negatively charged cathode side of the electrolyte. The relative charge in the electrolyte at the anode versus the cathode arises due to differences in the concentration of protons. This concentration difference can also contribute to proton transport between the anode and cathode.
Figure 4.3 Illustration of charge transport along a uniform conductor of cross-sectional area
A
, length
L
, and conductivity
σ
. A voltage gradient
dV
/
dx
drives the transport of charge down the conductor. From the charge transport equation and the conductor geometry, we can derive Ohm's law: . The resistance of the conductor is dependent on the conductor's geometry and conductivity: .
Figure 4.4 (
a
) Hypothetical voltage profile of a fuel cell at thermodynamic equilibrium (recall Figure 3.7). The thermodynamic voltage of the fuel cell is given by
E
0
. (
b
) Effect of anode and cathode activation losses on the fuel cell voltage profile (recall Figure 3.9). (
c
) Effect of ohmic losses on fuel cell voltage profile. Although the overall fuel cell voltage increases from the anode to the cathode, the cell voltage must decrease between the anode side of the electrolyte and the cathode side of the electrolyte to provide a driving force for charge transport.
Figure 4.5 Effect of ohmic loss on fuel cell performance. Charge transport resistance contributes a linear decrease in fuel cell operating voltage as determined by Ohm's law (Equation 4.7). The magnitude of this loss is determined by the size of . (Curves calculated for equal , , and , respectively.)
Figure 4.6 The importance of ASR is illustrated by these two fuel cells. Fuel cell 2 has lower total resistance than fuel cell 1 but yields a larger ohmic loss for a given current density. Fuel cell resistance is best compared using ASR rather than
R
.
Figure 4.7 The total ohmic resistance presented by a fuel cell is actually a combination of resistances, each attributed to different components of the fuel cell. In this diagram, fuel cell resistance is divided into interconnect, anode, electrolyte, and cathode components. Since current flows serially through all components, total fuel cell resistance is given by the series sum of the individual resistance components.
Figure 4.8 Illustration of charge transport mechanisms. (
a
) Electron transport in a free-electron metal. Valence electrons detach from immobile metal atom cores and move freely in response to an applied field. Their velocity is limited by scattering from the lattice. (
b
) Charge transport in this crystalline ionic conductor is accomplished by mobile anions, which “hop” from position to position within the lattice. The hopping process only occurs where lattice defects such as vacancies or interstitials are present.
Figure 4.9 Schematic of ion transport between polymer chains. Polymer segments can move or vibrate in the free volume, thus inducing physical transfer of ions from one charged site to another.
Figure 4.10 (
a
) Chemical structure of Nafion. Nafion has a PTFE backbone for mechanical stability with sulfonic groups to promote proton conduction. (
b
) Schematic microscopic view of proton conduction in Nafion. When hydrated, nanometer-sized pores swell and become largely interconnected. Protons bind with water molecules to form hydronium complexes. Sulfonic groups near the pore walls enable hydronium conduction.
Figure 4.11 Water content versus water activity for Nafion 117 at 303 K (30°C) according to Equation (4.34). Water vapor activity is defined as the ratio of the actual water vapor pressure for the system compared to the saturation water vapor pressure for the system at the temperature of interest.
Figure 4.12 Ionic conductivity of Nafion versus water content according to Equations 4.38 and 4.39 at 303 K.
Figure 4.13 Ionic conductivity of Nafion versus temperature according to Equation 4.38 when .
Figure 4.14 Water diffusivity in Nafion versus water content at 303 K.
Figure 4.15 Calculated properties of Nafion membrane for Example 4.4. (
a
) Water content profile across Nafion membrane. (
b
) Local conductivity profile across Nafion membrane.
Figure 4.16 View of the (110) plane in (
a
) pure ZrO
2
and (
b
) YSZ. Charge compensation effects in YSZ lead to creation of oxygen vacancies. One oxygen vacancy is created for every two yttrium atoms doped into the lattice.
Figure 4.17 YSZ conductivity versus %Y
2
O
3
(molar basis) [10]; YSZ conductivity is displayed as . In the next section, Figure 4.18 will clarify why it is convenient to multiply
σ
with
T
.
Figure 4.18 Conductivity of YSZ and GDC electrolytes versus temperature.
Figure 4.19 A standard SOFC cathode electrode (
a
) versus a mixed ionic–electronic conducting (MIEC) SOFC cathode electrode (
b
).
Figure 4.20 (
a
) Macroscopic picture of diffusion. (
b
) Atomistic view of diffusion. The net flux of gray atoms across an imaginary plane
A
in this crystalline lattice is given by the flux of gray atoms hopping from plane 1 to plane 2 minus the flux of gray atoms hopping from plane 2 to plane 1. Since there are more gray atoms on plane 1 than plane 2, there is a net flux of gray atoms from plane 1 to plane 2. This net flux will be proportional to the
concentration difference
of gray atoms between the two planes.
Figure 4.21 Atomistic view of hopping process. (
a
) Physical picture of the hopping process. As the anion (
A
−
) hops from its original lattice site to an adjacent, vacant lattice site, it must squeeze through a tight spot in the crystal lattice. (
b
) Free-energy picture of the hopping process. The tight spot in the crystal lattice represents an energy barrier for the hopping process.
Figure 4.22 Effect of linear voltage gradient on activation barrier for hopping. The linear variation in voltage with distance causes a linear drop in free energy with distance. This reduces the forward activation barrier . Two adjacent lattice sites are separated by ; therefore, the total free-energy drop between them is given by . If the activation barrier occurs halfway between the two lattice sites, will be decreased by . [In other words, .]
Figure 4.23 Illustration of the migration energy barrier. The middle point corresponds to the saddle where the oxygen ion and two cations such as zirconia align in the same plane before the oxide ion continues its path forward creating a vacancy in the location where it started.
Figure 4.24 Logarithmic plot of conductivity times
T
versus mol% Y
2
O
3
in YSZ comparing experiment (open squares) and calculation (closed circles).
Chapter 5: Fuel Cell Mass Transport
Figure 5.1 Convection versus diffusion. (
a
) Convective fluid transport in this system moves material from the upper tank to the lower tank. (
b
) A concentration gradient between white and gray particles results in net diffusive transport of gray particles to the left and white particles to the right.
Figure 5.2 Schematic of diffusion layer that develops at the anode of an operating H
2
–O
2
fuel cell. Consumption of H
2
gas at the anode–electrolyte interface results in a depletion of H
2
within the electrode. The concentration of H
2
gas falls from its bulk value () at the flow channel to a much lower value () at the catalyst layer. The magnitude of the H
2
gas velocity in the flow channel is schematically illustrated by the size of the flow arrows. Near the channel–electrode interface, the H
2
gas velocity drops toward zero, marking the start of the diffusion layer.
Figure 5.3 Schematic of mass transport situation within a typical fuel cell electrode. Convective mixing of reactants and products in the flow channel establishes constant bulk species concentrations outside the diffusion layer ( and ). The consumption/generation of species (at a rate given by
j
rxn
) within the catalyst layer leads to reactant depletion and product accumulation . Across the diffusion layer, a reactant concentration gradient is established between and , while a product concentration gradient is established between and .
Figure 5.4 Time dependence of reactant and product concentration profiles at fuel cell electrode. The fuel cell begins producing current at time . Starting from constant initial values ( and ), the reactant and product concentration profiles evolve with increasing time, as shown for . Eventually the profiles approach a steady-state balance (indicated by the dark solid lines) where concentration varies (approximately) linearly with distance across the diffusion layer. At steady state, the diffusion flux down these linear concentration gradients exactly balances the reaction flux at the catalyst layer.
Figure 5.5 Concentration loss due to Nernstian effects. When the fuel cell operates at a current density
j
, the surface concentration decreases below the bulk value due to reactant consumption. Accordingly, the ideal voltage drops by an amount given by from
E
to
E
′. (For now, we do not consider the additional activation losses due to concentration depletion, and so the activation loss curve () is simply translated from
A
to
A
′).
Figure 5.6 Concentration loss due to Nernstian effects and activation effects. The new activation curve accounts for additional kinetic losses due to the decreasing catalyst surface concentration with increasing current density. The difference between and
A
′ represents this concentration-induced concentration loss ().
Figure 5.7 Effect of concentration loss on fuel cell performance. Concentration effects in the catalyst layer contribute to a characteristic drop in fuel cell operating voltage as determined by Equation 5.25. The shape of this loss is determined by
c
and . (Curves calculated for , respectively, while
c
was held constant;
c
was fixed at 0.0388 V using Equation 5.26 with , , .)
Figure 5.8 Fluid flow between two parallel plates.
Figure 5.9 (
a
) Laminar versus (
b
) turbulent flow.
Figure 5.10 Schematic of 2D mass transport in fuel cell flow channel.
Figure 5.11 Friction factors of circular and rectangular channels.
Figure 5.12 Schematic of a 2D fuel cell transport model including diffusion and convection.
Figure 5.13 Oxygen density profile predicted from Equation 5.65 for the following case: electrode porosity , inlet gas pressure , model temperature , current density , inlet gas velocity cm/s, channel height cm, electrode thickness cm, and the Sherwood number .
Figure 5.14 Major flow channel geometries: (
a
) parallel, (
b
) serpentine, (
c
) parallel–serpentine, (
d
) interdigitated. Flow channel geometries seek to provide homogeneous distribution of reactants across an electrode surface while minimizing pressure drop losses and maximizing water removal capability.
Figure 5.15 Gas transport modes in various flow channel geometries. Each channel type induces a different convective transport scheme in the electrode.
Chapter 6: Fuel Cell Modeling
Figure 6.1 Pictorial summary of major factors that contribute to fuel cell performance. The overall fuel cell
j–V
performance can be determined by starting from the ideal thermodynamic fuel cell voltage and subtracting out the losses from activation, conduction, and concentration.
Figure 6.2 Pictorial illustration of the effect of a leakage current loss on overall fuel cell performance. A leakage current effectively “offsets” a fuel cell's
j–V
curve, as shown by the dotted curve in the Figure This has a significant effect on the open-circuit voltage of the fuel cell (
y
-axis intercept), which is reduced below its thermodynamically predicted value.
Figure 6.3 Comparison of our simple model results for a typical PEMFC versus a typical SOFC. As shown by the shape of the curves, the PEMFC benefits from a higher thermodynamic voltage but suffers from larger kinetic losses. SOFC performance is dominated by ohmic and concentration losses. The input parameters used to generate these model results are summarized in Table 6.1.
Figure 6.4 Flux details for (
a
) 1D PEMFC model and (
b
) 1D SOFC model. (
a
) In a PEMFC, water (H
2
O) and protons (H
+
) transport through the electrolyte. (
b
) In a SOFC, oxygen ions (O
2–
) transport through the electrolyte.
Figure 6.5 The
j–V
curve of 1D SOFC model from simplified governing equations. The activation overvoltage is prominent at low current density while the ohmic overvoltage is dominant throughout the entire range of current density. The concentration overvoltage increases sharply at high current density.
Figure 6.6 The
j–V
curve of 1D PEMFC model from simplified governing equations. Please notice the sharp drop of the voltage near zero current density due to large activation overvoltage (typical behavior for PEMFC). The gradual change of slope of the
j–V
curve after 1 A/cm
2
represents the increase of the ohmic resistance in the proton exchange membrane due to the water depletion. Remember (from Chapter 4) that the electro-osmotic drag of water increases with current density, which reduces the water content in the membrane. In the previous 1D SOFC example, the concentration overvoltage was clearly observed at high current density due to the thick cathode (800 µm in Table 6.4). In this example, the concentration overvoltage is not observable since the thickness of the cathode is small (350 µm in Table 6.5).
Figure 6.7 The
j–V
curve of 1D SOFC model considering stoichiometry number. Two curves represent cases where the oxygen stoichiometries are 1.5 (example case in the text) and 5, respectively. The behavior of the concentration overvoltage is quite different from Figure 6.5 where no stoichiometry effect was considered. The example in Figure 6.5 considered only the diffusion limit at the cathode. In other words, the oxygen stoichiometry number was assumed to be infinitely large. In this example, the concentration overvoltage is much larger and limiting current density is greatly reduced.
Figure 6.8 Isometric view of serpentine flow channel fuel cell model (500 µm channel feature size). Since no repetitive unit exists, the entire physical domain is modeled.
Figure 6.9 Cell
j–V
curves for serpentine flow channel model. Activation, ohmic, and concentration losses are clearly observed.
Figure 6.10 Oxygen concentration in cathode at 0.8 V overvoltage. This cross-sectional cut across the center of the serpentine pattern illustrates how the oxygen concentration in the flow channel slowly decreases from inlet to outlet.
Figure 6.11 Oxygen concentration in cathode at 0.8 V overvoltage. The plan view shows the oxygen concentration profile across the cathode surface. Low oxygen concentration is observed under the channel ribs due to the blockage of oxygen flux.
Figure 6.12 Curves for problem 6.1.
Chapter 7: Fuel Cell Characterization
Figure 7.1 (
a
) Typical PEMFC test station. Pressures, temperatures, humidity levels, and flow rates of gases are controlled. (
b
) Typical SOFC test station. Compared to the PEMFC test station, the SOFC test station is more elaborate due to the challenges associated with working at high temperatures.
Figure 7.2 (
a
) Typical log-scaled curve. The activation loss contribution is plotted by the dashed line. (
b
) The low-current-density regimen of the curve shows linear behavior on a log scale. Fitting this line to the Tafel equation gives the transfer coefficient and the exchange current density. (
c
) Activation loss is plotted throughout the curve. The difference between the activation loss and the curve represents the sum of ohmic and concentration losses.
Figure 7.3 A sinusoidal voltage perturbation and resulting sinusoidal current response. The current response will possess the same period (frequency) as the voltage perturbation but will generally be phase shifted by an amount .
Figure 7.4 Application of a small-signal voltage perturbation confines the impedance measurement to a pseudolinear portion of a fuel cell's curve.
Figure 7.5 Example Nyquist plot from a hypothetical fuel cell. The three regions marked on the impedance plot are attributed to the ohmic, anode activation, and cathode activation losses. The relative size of the three regions provides information about the relative magnitude of the three losses in this fuel cell.
Figure 7.6 Circuit diagram and Nyquist plot for a simple resistor. The impedance of a resistor is a single point of value
R
on the real impedance axis (
x
-axis). The impedance of a resistor is independent of frequency.
Figure 7.7 Physical representation and proposed equivalent circuit model of an electrochemical reaction interface. The impedance behavior of an electrochemical reaction interface can be modeled as a parallel combination of a capacitor and a resistor. The capacitor () describes the charge separation between ions and electrons across the interface. The resistor () describes the kinetic resistance of the electrochemical reaction process.
Figure 7.8 Circuit diagram and Nyquist plot for a series
RC
. The impedance is a vertical line that increases with decreasing
w
. The real component of the impedance is given by the value of the resistor. As frequency decreases, the imaginary component of the impedance (as given by the capacitor) dominates the response of the circuit.
Figure 7.9 Circuit diagram and Nyquist plot for a parallel
RC
. This semicircular impedance response is typical of an electrochemical reaction interface. The high-frequency intercept of the semicircle is zero, while the low-frequency intercept of the impedance semicircle is . The diameter of the semicircle () gives information about the reaction kinetics of the electrochemical interface. A small loop indicates facile reaction kinetics while a large loop indicates sluggish reaction kinetics.
Figure 7.10 Circuit diagram and Nyquist plot for a Warburg element used to model diffusion processes. The impedance response is a diagonal line with a slope of 1. Impedance increases from left to right with decreasing frequency.
Figure 7.11 Circuit diagram and Nyquist plot for a porous bounded Warburg element, which is used to model finite diffusion processes (with diffusion occurring through a fixed diffusion layer thickness from an inexhaustible bulk supply of reactants). This situation is typical in fuel cell systems. At high frequency, the porous bounded Warburg impedance response mirrors the behavior of an infinite Warburg; at low frequency, it returns toward the real impedance axis. (This makes intuitive sense: A finite diffusion layer thickness should yield finite real impedance.) The low-frequency real axis impedance intercept yields information about the diffusion layer thickness.
Figure 7.12 Physical picture, circuit diagram, and Nyquist plot for a simple fuel cell impedance model. The equivalent circuit for this fuel cell consists of two parallel
RC
elements to model the anode and cathode activation kinetics, an infinite Warburg element to simulate cathode mass transfer effects, and an ohmic resistor to simulate the ohmic losses. While schematically shown in the electrolyte region, the ohmic resistor models the ohmic losses arising from all parts of the fuel cell (electrolyte, electrodes, etc.). The impedance response shown in the Nyquist plot is based on the circuit element values given in Table 7.2. Each circuit element contributes to the shape of the Nyquist plot, as indicated in the diagram. The ohmic resistor determines the high-frequency impedance intercept. The small semicircle is due to the anode
RC
element, while the large semicircle is due to the cathode
RC
element. The low-frequency diagonal line comes from the infinite Warburg element.
Figure 7.13 In fuel cells the cathode impedance is often significantly larger than the anode impedance. In these cases, the cathode impedance can mask the impedance of the anode, as shown to varying degrees in (
a
) and (
b
). This masking (or “merging”) also occurs if the
RC
time constants for the anode and cathode reactions overlap. If for the anode is extremely small, the
RC
time constant for the anode may correspond to frequencies that are beyond the limits of most impedance hardware. (EIS is usually limited to .) In these cases, the anode impedance may be unmeasurable.
Figure 7.14 EIS characterization of a fuel cell requires impedance measurements at several different points along an curve. The impedance response will change depending on the operating voltage. (
a
) At low current, the activation kinetics dominate and is large, while the mass transport effects can be neglected. (
b
) At intermediate current (higher activation overvoltages), the activation loops decrease since decreases with increasing . (Refer to Equation 7.15.) (
c
) At high current, the activation loops may continue to decrease, but the mass transport effects begin to intercede, resulting in the diagonal Warburg response at low frequency.
Figure 7.15 (
a
) Simplified equivalent circuit of a fuel cell system. The
RC
components from the anode and cathode have been consolidated into a single branch. (
b
) Hypothetical current interrupt profile applied to the circuit in (
a
). In this example, an original steady-state current load of 500 mA is abruptly zeroed. (
c
) Hypothetical time response of fuel cell voltage when the current interrupt in (
b
) is applied to the system. The instantaneous rebound in the voltage is associated with the pure ohmic losses in the system. The time-dependent voltage rebound is associated with the activation and mass transport losses in the system.
Figure 7.16 Schematic of a (CV) waveform and typical resulting current response. (
a
) In a CV experiment, the voltage is swept linearly back and forth between two voltage limits (denoted
V
1
and
V
2
on the diagram). (
b
) The resulting current is plotted
as a function of voltage
. When the voltage sweeps past a potential corresponding to an active electrochemical reaction, the current response will spike. After this initial spike, the current will drop off as most of the readily available reactants are consumed. On the reverse voltage scan, the reverse electrochemical reaction (with a corresponding reverse current direction) may be observed. The shape and size of the peaks give information about the relative rates of reaction and diffusion in the system.
Figure 7.17 Fuel cell CV curve. The peaks marked and represent the hydrogen adsorption and desorption peaks on the platinum fuel cell catalyst surface, respectively. The gray rectangular area between the two peaks denotes the approximate contribution from the capacitive charging current. The active catalyst surface area can be calculated from the area under the or peak (recognizing that the voltage axis can be converted to a time axis if the scan rate of the experiment is known).
Chapter 8: Overview of Fuel Cell Types
Figure 8.1 Schematic of H
2
–O
2
PAFC. The phosphoric acid electrolyte is immobilized within a porous SiC matrix. Porous graphitic electrodes coated with a Pt catalyst mixture are used for both the anode and the cathode. Water is produced at the cathode.
Figure 8.2 Photograph of PureCell™ 200 power system, a commercial 200-kW PAFC. The unit includes a reformer, which processes natural gas into H
2
for fuel. This system provides clean, reliable power at a range of locations from a New York City police station to a major postal facility in Alaska to a credit-card processing system facility in Nebraska to a science center in Japan. It also can provide heat for the building.
Figure 8.3 Schematic of H
2
–O
2
PEMFC. Porous carbon electrodes (often made from carbon paper or carbon cloth) are used for both the anode and the cathode. The electrodes are coated with a Pt catalyst mixture. Water is produced at the cathode.
Figure 8.4 (
a
) Rendering of the 2015 Hyundai ix35 fuel cell car power train. The PEMFC stack generates 100 kW of electricity. The 24–kW Li-ion battery delivers a high rate of electrical energy to the motor during startup and acceleration and stores electricity recovered during braking. The drive train consists of a motor, transmission, and drive shaft, with the AC induction motor producing 100 kW maximum power and 302.8 N · m maximum torque. The inverter converts DC electric power from the fuel cell stack to AC electrical power for motive force. The high-pressure hydrogen tank can store 5.64 kg of hydrogen at 700 atm. The fuel economy of the vehicle is 0.95 kg H
2
/ 100 km, which means the car can travel 594 km with a full tank of hydrogen. Maximum speed of the car is 160 km/h and 0–100 km acceleration takes 12.5 s. (
b
) The Hyundai ix35 fuel cell car undergoing cold- and hot-weather testing. Beside the durability issue during the lifetime of the vehicle operation, PEMFCs face several other big challenges for automotive application. These include cold-start operation and cooling of the fuel cell stack. The water in the fuel cell stack and system will freeze under cold weather after the vehicle turns off. When turned on, a “frozen” fuel cell will not operate normally until the ice in the fuel cell melts. Through clever design and control of fuel cell systems, a state-of-the-art fuel cell engine can start even at –25°C. Cooling of the fuel cell stack is also a big challenge. Since the ideal operating temperature of the PEMFC is around 80°C, hot weather (∼45°C) easily overloads the fuel cell cooling system because all the heat generated by the 100-kW fuel cell must be rejected by the cooling system even if the temperature difference is only 35°C! Thus, as automotive manufacturers continue to test out their fuel cell cars in exotic mountain or desert locations, they aren't just having fun, they're performing serious research! (Images courtesy of Hyundai Motor Company).
Figure 8.5 Schematic of an H
2
–O
2
AFC. Porous carbon or nickel electrodes are used for both the anode and the cathode. Either Pt or nonprecious metal catalyst alternatives can be used. Water is produced at the anode and consumed at the cathode; therefore, the water must be extracted from the anode waste stream or recycled through the electrolyte, using electrolyte recirculation.
Figure 8.6 Photograph of United Technologies Corporation(UTC) AFC. These fuel cell units supplied the primary electric power for the Apollo space missions. The units were rated to 1.5 kW with a peak power capability of 2.2 kW, weighed 250 lb, and were fueled with cryogenic H
2
and O
2
. Fuel cell performance during the
Apollo
missions was exemplary. Over 10,000 h of operation were accumulated in 18 missions without an in-flight incident.
Figure 8.7 Schematic of H
2
–O
2
MCFC. The molten carbonate electrolyte is immobilized in a ceramic matrix. Nickel-based electrodes provide corrosion resistance, electrical conductivity, and catalytic activity. The CO
2
must be recycled from the anode to the cathode to sustain MCFC operation since CO
3
2–
ions are otherwise depleted. Water is produced at the anode.
Figure 8.8 Photograph of a 2.5-MW MCFC system. (
a
) The system can power roughly 3500 individual homes using liquefied natural gas, biogas, or synthesized natural gas as fuel. The footprint of the system is 500 m
2
. (
b
) The system is composed of a fuel cell stack, an MBOP (Mechanical Balance of Plant), and an EBOP (Electrical Balance of Plant). The functions of the MBOP include treatment, preheating, and humidification of the fuel, air, and process water. The system supplies heated water for neighborhood or industrial use via the waste heat from the fuel cell. Through the EBOP, the fuel cell is connected to the electric grid, thereby providing electricity to the end user. The EBOP includes a DC/AC converter, power metering, switching equipment, and a voltage transformer. (Images courtesy of POSCO Energy.)
Figure 8.9 Schematic of H
2
–O
2
SOFC. The ceramic electrolyte is solid state. A nickel–YSZ cermet anode and a mixed conducting ceramic cathode provide the required thermal, mechanical, and catalytic properties at high SOFC operating temperatures. Water is produced at the anode.
Figure 8.10 Photograph of Siemens-Westinghouse 220-kW hybrid SOFC/micro gas-turbine system. This system was delivered to Southern California Edison in May 2000.
Figure 8.11 Recent example prototype portable DMFC systems. (
a
) A 20-W DMFC notebook computer charger can directly power a notebook or recharge the battery in the computer to extend the operating time. The methanol cartridge (the small box detached from the 540-cm
3
main unit at the back of the computer) stores 130cm
3
of pure methanol fuel. The system provides up to 160 Wh with an overall energy density of 230 Wh/L. (
b
) A 2-W prototype DMFC system can charge a cell phone in 2 h using a 10-cm
3
methanol fuel cartridge. The system occupies roughly 150 cm
3
.
Figure 8.12 A membraneless fuel cell design based on a Y-shaped microfluidic channel configuration that places fuel and oxidant streams into diffusional contact without mixing. The left-hand oxygenated electrolyte stream passes over a cathode electrode, while the right-hand fuel-saturated electrolyte stream passes over the anode. Protons can transport across the stream, but fuel and oxygen do not mix because of the laminar flow. However, fuel and oxidant will be depleted near the electrodes and will begin to mix in the center region by diffusion; these two processes set a maximum effective length for the fuel cell (typically micrometers to millimeters).
Figure 8.13 Schematic diagram of a zinc–air cell. A zinc metal anode and a porous air-breathing cathode are separated by a porous, KOH electrolyte saturated membrane. Oxygen from the air reacts with the zinc metal anode to create ZnO, producing electricity in the process. The anode and cathode electrodes are typically housed inside a two-piece coin-cell arrangement, with electrical isolation and sealing provided by an insulating ring gasket.
Figure 8.14 Operating principle of the single-chamber SOFC. The single-chamber SOFC employs a selective anode that only reacts with fuel species and a selective cathode that only reacts with oxygen. Because of this selectivity, both fuel and air can be simultaneously introduced into a single chamber, greatly simplifying fuel cell design and sealing.
Figure 8.15 Schematic illustration of the direct flame fuel cell. A direct flame fuel cell is designed to operate in a “zero-chamber” mode, where the anode side is exposed to a flame combustion source, which provides both heat and partially combusted fuel species, while the cathode faces the ambient air.
Figure 8.16 Operating principle of the liquid-tin anode SOFC (LTA-SOFC). Based on a conventional SOFC electrolyte and cathode, the LTA-SOFC employs liquid tin for the anode, enabling direct utilization of virtually any hydrocarbon species. The liquid tin functions as a reaction “intermediate” by undergoing a redox cycle, converting to SnO
2
at the liquid tin–YSZ interface, then reducing back to Sn at the liquid tin–fuel interface.
Figure 8.17 Schematic diagram of a single cell of a PEM water electrolyzer that electrochemically converts water to hydrogen and oxygen.
Figure 8.18 Graphical comparison of the main fuel cell classes.
Chapter 9: PEMFC and SOFC Materials
Figure 9.1 General chemical structure of sulfonated PEEK.
Figure 9.2 Chemical structure of poly-2,2′-
m
-(phenylene)-5,5′-bibenzimidazole, commonly called polybenzimidazole, or PBI.
Figure 9.3 Typical PEMFC MEA fabrication process. (1) Pt/C catalysts are mixed with water, 5% Nafion solution, and ethylene glycol to form a catalyst ink. (2) The catalyst ink is applied to the electrolyte membrane using one of several techniques. (3) Carbon cloth or carbon paper electrodes are hot-press bonded onto either side of the catalyst-coated membrane. Detail drawing shows the desired final MEA microstructure.
Figure 9.4 Gas and electron transport within the fuel cell GDL. In the GDL, lateral (in-plane) transport is more important than vertical (out-of-plane) transport. For example, electrons generated under the middle of a fuel cell flow channel must be transported laterally 1–2 mm, but must only transport vertically to reach the current collecting rib structures. Similarly, gas from the flow channel must transport nm laterally, but only vertically to reach reaction zones under the channel ribs.
Figure 9.5 Conductivity of a proton-conducting polymer (Nafion), a solid acid (CsH
2
O
4
), an oxide ion conductor (YSZ), and a proton-conducting oxide (BZY) as a function of 1/
T
.
Figure 9.6 The fluorite crystal structure exhibited by stabilized zirconia and by doped ceria.
Figure 9.7 Ionic conductivity of representative examples from the various electrolyte materials groups discussed in this chapter. Conductivity is oxygen ionic, with the exception of BZY, where it is protonic [103–105].
Figure 9.8 Ionic and electronic conductivities of CGO10 (GDC10) in reducing atmosphere (10% H
2
, 2.3% H
2
O) [103].
Figure 9.9 Perovskite structure, exhibited by oxygen-ion-conducting LaGaO
3
and by proton-conducting BaZrO
3
.
Figure 9.10 SOFC MEA fabrication approaches: (
a
) electrolyte supported (the electrolyte forms the primary structural support for the cell), (
b
) cathode supported (the cathode forms the primary structural support for the cell), and (c) anode supported (the anode forms the primary structural support for the cell).
Figure 9.11 Electrical conductivity of Ni–YSZ cermet as a function of nickel concentration (conductivity
measured
at 1000°C in all cases but shown for cermet samples
fired
at various temperatures) [109].
Figure 9.12 Mixed conductive cathode, oxide ions flow perpendicular to cathode, electrons flow parallel to the plane.
Figure 9.13 Composite electrolyte consisting of a layer of GDC and one layer of YSZ with catalyst particles decorating the electrolyte surface.
Chapter 10: Overview of Fuel Cell Systems
Figure 10.1 Schematic of two fuel cell systems: (
a
) stationary residential-scale fuel cell system, (
b
) portable fuel cell system.
Figure 10.2 Vertical stack interconnection. Fuel cells are serially interconnected via bipolar plates. A bipolar plate simultaneously acts as the anode of one cell and cathode of the neighboring cell. In this diagram, the flow structures, which must be conductive, act as bipolar plates.
Figure 10.3 A 3D view of a fuel cell bipolar stack. Unless edge seals are provided around each cell, it is clear that this stack will leak.
Figure 10.4 An example of a sealing method that incorporates gaskets around the edges of each cell.
Figure 10.5 Planar series interconnection. Two planar interconnection schemes are shown, the banded and flip-flop designs. In contrast to the banded configuration, the flip-flop scheme has single-level interconnects that never cross the electrolyte plane.
Figure 10.6 End and side views of tubular SOFC design employed by Siemens-Westinghouse. Air is fed through the inside of the tubes, while the fuel stream is fed along the outside of the tubes. Series stacking is accomplished by the continuation of more cells in the same plane as the electrode and electrolyte, while parallel stacking can be accomplished by the addition of cells in the plane perpendicular to the electrode and electrolyte.
Figure 10.7 Photograph and end-on detail of a small (24-cell) stack of Siemens-Westinghouse tubular SOFCs. Each tube is 150 cm long with a diameter of 2.2 cm.
Figure 10.8 Examples of fuel cell bipolar plates with additional internal channels provided for integrated cooling of fuel cell stack.
Figure 10.9 Two examples of external reformers. (
a
) A Honda Home Energy Station that generates hydrogen from natural gas for use in fuel cell vehicles, while supplying electricity and hot water to the home through fuel cell cogeneration functions. This unit, located in New York, is a second-generation model (developed in collaboration with Plug Power Inc.), which unifies a natural gas reformer and pressurizing units into one compact component to reduce the volume. The unit can produce up to 2 standard cubic meters of hydrogen per hour. (
b
) A Pacific Northwest National Laboratory microfuel processor that converts methanol into hydrogen and carbon dioxide. The system includes a catalytic combustor, a steam reformer, two vaporizers, and a recuperative heat exchanger embedded in a device no larger than a dime! When first built, it was the smallest integrated catalytic fuel processor in the world.
Figure 10.10 Example current–voltage–power relationships for (
a
) a step-up converter and (
b
) a step-down converter.
Figure 10.11 A DC–DC converter may be used to transform a fuel cell's variable curve behavior into a constant-voltage output. Up conversion to the higher fixed-voltage output of the converter is accompanied by a commensurate reduction in current, as shown by points vs. and vs. .
Figure 10.12 Pulse-width voltage modulation allows DC to be transformed into an approximately sinusoidal current waveform.
Figure 10.13 Schematic diagram of a simple fuel cell system with a control system.
Figure 10.14 Process diagram of CHP fuel cell system.
Figure 10.15 Fuel processing subsystem.
Figure 10.16 Fuel cell subsystem.
Figure 10.17 Gross and net efficiency of a fuel cell subsystem.
Figure 10.18 Power electronics subsystem.
Figure 10.19 Thermal management subsystem.
Figure 10.20 Optimizing a portable fuel cell system's design involves finding the best ratio between fuel cell stack size and fuel reservoir size so that the system provides the required electric power for the longest possible time.
Figure 10.21 Gravimetric Ragone plots for a variety of portable power solutions showing trade-offs between system power density and system energy density. The dashed diagonal lines indicate contours of constant lifetime for various power density/energy density ratios.
Figure 10.22 System size versus operating lifetime comparison of a liquid-fueled portable power fuel cell system versus a battery system. The large upfront size cost of the portable fuel cell system is recouped for long operating missions by the higher energy density of the fuel cell's liquid fuel.
Chapter 11: Fuel Processing Subsystem Design
Figure 11.1 Fuel processing subsystem. Repeated from Chapter 10 for clarity.
Chapter 12: Thermal Management Subsystem Design
Figure 12.1 Process diagram of CHP fuel cell system. Repeated from Chapter 10 for reference.
Figure 12.2 Temperature profiles of hot and cold streams in counter-flow heat exchanger.
Figure 12.3 Temperature–enthalpy diagram for a hot stream and a cold stream not connected by a heat exchanger. External heat transfer is maximal. The hot stream rejects 3370 W to the environment. The cold stream absorbs 3370 W from an external heat source. Arrow heads on the plots indicate the direction of stream flow. The schematic at the bottom illustrates the processes occurring by showing pipes carrying fluid and the heat transfer through these pipes. The change in enthalpy is roughly commensurate with the change in the length along a pipe.
Figure 12.4 Temperature–enthalpy diagram for hot and cold streams in Figure 12.3 but connected by a heat exchanger (shown at bottom). External heat transfer is zero. The hot stream rejects 3370 W to the cold stream. The pinch point, the minimum temperature difference between hot and cold streams, appears to be at the entrance to the cold stream and has a value of 40°C, based on our available data. The Figure at the bottom depicts the combined streams in a counter-flow double-pipe heat exchanger.
Figure 12.5 Temperature–enthalpy diagram for a hot and a cold stream connected by a heat exchanger, with the hot stream changing phase from gas to liquid in the middle. The change in phase is marked by the hot stream's abrupt change in slope, where slope is the inverse of the heat flow capacity . The change in phase causes a pinch point. Aggregate conservation-of-energy calculations would not have detected the pinch.
Figure 12.6 Temperature–enthalpy diagram for hot and cold streams from fuel cell system of Figure 12.1. The two separate hot streams are from two different parts of the system. They heat the cold stream in series. First, the cold stream absorbs heat from (1) the fuel cell stack, (2) the aftercooler, (3) a selective oxidation reactor, and (4) the reformate leaving the water gas shift reactor. Second, the cold stream absorbs heat from a condenser. The curves were plotted using the data from Table 12.1.
Chapter 13: Fuel Cell System Design
Figure 13.1 A single-channel fuel cell geometry, including computational grid and boundary conditions. A fine grid structure is deployed in the thin electrode layer to monitor the steep changes in gas concentration, temperature, and voltage that are expected in this domain. In the flow plates, a coarse grid is deployed, since steep changes in the physical variables are not expected here. The grid associated with the flow channels has been removed to distinguish the fluid domain from the solid domain. This model is used to investigate a “counterflow” arrangement, where the flow of fuel and air are in opposite directions.
Figure 13.2 Solutions obtained from a solid-oxide fuel cell model: (
a
) hydrogen concentration profile; (
b
) oxygen concentration profile; (
c
) temperature profile; (
d
) current density profile. The total overpotential is 0.3 V and the inlet gas temperatures are 900°C.
Figure 13.3 Schematic of a simple portable SOFC system.
Figure 13.4 Polarization curve of SOFC obtained from a CFD solid-oxide fuel cell model. The model calculation is based on a stoichiometry of 1.2 for hydrogen and 8.0 for air at 1 atm.
Chapter 14: Environmental Impact of Fuel Cells
Figure 14.1 Supply chain for today's conventional gasoline internal combustion engine vehicles. Energy is consumed (bottom arrows) and emissions are produced (top arrows) during the primary processes (represented as boxes) from petroleum fuel extraction to its use on a vehicle.
Figure 14.2 Supply chain for hydrogen fuel cell vehicle fleet that obtains its hydrogen fuel from steam reforming of natural gas. Approximately 30% of the HHV of natural gas is needed for the operation of the steam reformer (box 6). Approximately 10% of the HHV of is required for compression (box 7). These are the most energy-intensive links in the supply chain.
Figure 14.3 Most U.S. electric power derives from conventional coal-fired power plants, which burn coal in a boiler to generate steam that runs through a steam turbine. The second largest portion of electric power comes from nuclear power plants, which extract heat from nuclear fission reactions to generate steam in a boiler that is then run through a steam turbine. The third most prevalent form of electric power production is from natural gas plants, which burn gas in a turbine.
Figure 14.4 Annual hydrogen consumption by fuel cell vehicles by county, plotted at the center of each U.S. county, assuming a complete switch of fleet from conventional vehicles to fuel cell vehicles.
Figure 14.5 Left: Sunlight hits Earth's surface and is partly absorbed. Earth reemits some of this energy as IR radiation (thermal energy). Greenhouse gases, including , , , and , selectively absorb this IR radiation and reemit it out to space and back toward Earth's surface and thereby warm Earth's surface. Center: Sunlight hits dark-colored particles, such as black carbon, suspended in Earth's atmosphere. These dark particles absorb the light and reemit this energy as IR radiation, some of which may reach Earth's surface and may warm it. Organic matter focuses light onto black carbon, thereby enhancing black carbon's warming effect. Right: Light-colored particles, including sulfates and nitrates, reflect sunlight and have a cooling effect.
Figure 14.6 Between the ∼1860s and recent times, concentrations of the primary greenhouse gases and in the lower atmosphere have increased by about ∼30% and ∼140%, respectively.
Figure 14.7 Since the 1860s, Earth's average, near-surface temperature has increased by over ∼0.6°C.
Figure 14.8 Supply chain for conventional electricity generation from coal. The most energy and emission intensive process in the chain is electricity generation (box 4).
Figure 14.9 Supply chain for coal gasification plant. The most energy-intensive processes in the chain are coal gasification (box 4) and electricity generation at the stationary fuel cell system (box 8).
List of Tables
Chapter 1: Introduction
Table 1.1 Description of Major Fuel Cell Types
Chapter 2: Fuel Cell Thermodynamics
Table 2.1 Selected List of Standard Electrode Potentials
Chapter 3: Fuel Cell Reaction Kinetics
