Structural Analysis of Load Distribution within Single Cell Fuel Cell
by
Eric J. O’Brien
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2011
CONTENTS
LIST OF SYMBOLS iv
LIST OF TABLES v
LIST OF FIGURES vi
LIST OF KEY WORDS vii
ABSTRACT viii
1. INTRODUCTION/BACKGROUND 1
2. THEORY/METHODOLOGY 4
2.1. Solid Mechanics of the PEM fuel cell 4
2.2. Design of Experiment Factorial Methodology 5
2.3. Geometry 7
2.4. Materials 9
3. RESULTS 15
3.1. Results Overview 15
3.2. Selecting a Surface for Evaluation 17
3.3. Cell Pressure Results – Z component of Stress 22
3.4. Factorial Analysis Results 28
4. DISCUSSION 32
5. CONCLUSIONS 36
6. BIBLIOGRAPHY 37
7. APPENDICES 39
7.1. Comsol Files: Cases 1-8 39
7.2. Minitab File 39
LIST OF SYMBOLS
σ = Normal Stress (Pa)
τ = Shear Stress (Pa)
λ = Lamé’s Constant (Pa)
ε = True Strain (-)
δ = Elongation (m)
G = Shear Modulus (Pa)
e = Linear Strain
E = Modulus of Elasticity (GPa)
ν = Poisson’s Ratio (-)
ρ = Density (kg/m^3)
F = External Force/Load (N)
A = Area (m2)
p = Pressure (Pa)
L = Length (m)
W = Width (m)
D = Diameter (m)
LIST OF TABLES
Table 1: DOE factorial variables for analysis 7
Table 2: Material Properties 9
Table 3: Compression results by case 22
LIST OF FIGURES
Figure 1 - How a PEM fuel cell works [1] 1
Figure 2: Fuel Cell Stack Diagram 3
Figure 3: Visual representation of a Full Factorial vs. Half Factorial 6
Figure 4: Geometry of the single cell 8
Figure 5: Highlighted surfaces represent symmetry boundary conditions 10
Figure 6 – Applied pressure location on the pressure plate 11
Figure 7 - Side view of cell mesh 13
Figure 8: Mesh containing triangular prisms. 14
Figure 9 – Von Mises stress plot of the pressure plate 16
Figure 10: Cross Section Planes within separator plates. 18
Figure 11 - Plot of Z direction of stress in a cross section of the separator plate. 19
Figure 12: Plots of Z component of stress in different locations within the separator plates (a) 1.5 mm from center anode side (b) 1mm from center anode side (c) 1mm from center cathode side. 20
Figure 13: 3D Plot of Z component stress in baseline separator plate 21
Figure 14 (a,b): Plots of the Z component stress tensor 23
Figure 14 (c,d): Plots of the Z component stress tensor 24
Figure 15 (a,b): Plots of the Z component stress tensor 26
Figure 15 (c,d): Plots of the Z component stress tensor 27
Figure 16: Main Effects plot for Average Values 28
Figure 17: Effects Pareto for Average 29
Figure 18: Effects Pareto for Range 30
Figure 19: Effects Pareto for Max Z Stress 30
Figure 20: Pareto Chart of effects for Min Z stress 31
Figure 21: Optimization of Factorial Analysis 33
Figure 22: Low aspect ratio solution 34
LIST OF KEY WORDS
Fuel Cell
PEM – Polymer Electrolyte Membrane
Pressure Plate
Separator Plate
UEA – Unitized Electrode Assembly
GDL – Gas Diffusion Layer
DOE – Design of Experiments
Factorial Analysis
ABSTRACT
A PEM fuel cell consists of a membrane within an electrode assembly, flow field plates to deliver the reactant gases, and pressure plates to load the system for sealing and conduction. Distribution of pressure on a fuel cell is important for maximum performance and durability of the membrane. This study evaluates the factors which affect the pressure within a single cell fuel cell by performing a structural analysis using a Finite Element model to evaluate eight different cases. The cases were generated using design of experiments factorial methods with four factors and two levels to vary the pressure plate thickness, flow field plate thickness, aspect ratio, and tie rod load in each case. The results show that there are areas of the cell which are not under compressive load. Pressure plate thickness and applied load are the largest factors which affect the load distribution of the cell.
vi
1. INTRODUCTION/BACKGROUND
Fuel Cells utilize an electrochemical reaction between a fuel, usually hydrogen, and oxygen, typically from air to generate electricity. There are multiple types of fuel cells which have different benefits for different applications. These include Direct Methanol, Alkaline, Phosphoric Acid, Molten Carbonate, Solid Oxide and Polymer Electrolyte Membrane fuel cells. The fuel cell type which will be evaluated in this paper is a Polymer Electrolyte Membrane (PEM) fuel cell. A single fuel cell does not generate a large amount of electricity; therefore, multiple cells are usually stacked together into a cell stack assembly. The area of each cell and the number of cells in the stack can be varied to meet specific operating conditions.
Figure 1 - How a PEM fuel cell works [1]
As seen in Figure 1, for a PEM fuel cell to function it needs to have a hydrogen flow field plate on the anode side, an oxygen flow field plate on the cathode side, and the polymer electrolyte membrane (PEM) in the center. On either side of the PEM is the anode catalyst and the cathode catalyst as well as backing layers, also known as gas diffusion layers (GDLs). The GDLs help the flow diffuse equally into the membrane, including areas between the actual flow channels. The membrane, catalyst layers, and backing layers are is often bonded into a single assembly [2], or unitized, and referred to as a unitized electrode assembly or UEA. It is referred to as unitized because it is made into a single assembly which is then sandwiched between the flow field plates, also known as separator plates. The flow field plates usually are made from carbon graphite material. This material allows for electrical conductivity through the plates, as well as channels to be machined into them for fuel and air flow. These flow channels allow for fuel and air to pass by the electrode assembly which contains the membrane, catalyst layers as well as gas diffusion layers (GDLs) which are located on either side of the membrane.
Electricity is generated in the fuel cell when a fuel, pure hydrogen in the case of PEM fuel cells, flows over the anode side of the electrode assembly and air flows over the cathode side of the electrode assembly. When this occurs, hydrogen reacts with a catalyst in the electrode which causes positive ions to pass through the membrane, while the negative ions create an electrical current. The positive ions then react with the oxygen in the air on the cathode side of cell to produce water. Below are the following equations for this reaction [3]:
Anode Reaction:
Cathode Reaction:
Overall Cell Reaction:
Although there are many factors which affect the performance of a fuel cell, the load on the UEA and more specifically on the GDL can significantly affect the performance. [4]. Proper load distribution of the fuel cell is important for both performance and durability. Low loads on a cell increases resistance and therefore reduces performance. High loads can create excessive stress on the cell membrane decreasing lifetime of the cell. Fuel cell stacks with dozens of cells end up with relatively even pressure distribution because the ratio of the length of the stack vs. the distance from the tie rod loads to the center of the cell is large. When this number is small the distribution of load at the UEA can be poor, such as in single cell stacks or stacks with only a few cells.
The pressure within a given single cell has been proven to vary as much as 4 times from the lowest pressure to the highest pressure even with different loads [5]. The question to be answered in this study is what variable of the design affect this ratio from the highest load to the lowest load.
To apply load to the stack, there are stainless steel pressure plates on the either end of the assembly with threaded tie rods connecting the two pressure plates as seen in Figure 2 below [6]. The pressure plates are large plates of stainless steel represented by numbers 120 and 140 in the diagram below. The threaded tie rods, represented by number 102 in the figure below, extend through each of the pressure plates and nuts on either side pull the pressure plates together, compressing the cell stack assembly. None of the other features in the diagram represent the fuel cell discussed in this study. For instance, there are coolant ports in the pressure plate below, however the pressure plate used in this study does not have any ports in it.
Figure 2: Fuel Cell Stack Diagram
2. THEORY/METHODOLOGY
To ensure proper loading, optimization of the pressure plate and bipolar plate design is needed. The objective of this paper is to evaluate the change in load distribution when changing the configuration of the cell, including the thickness of the pressure plate, thickness of the separator plate, load on the cell and aspect ratio of the fuel cell. Using a constant pressure plate configuration, the pressure on the electrode assembly (UEA) will be evaluated.
A finite element model was developed using the program Comsol. The geometry was originally modeled in Pro/Engineer and was then refined within Comsol such that the parametric features could be used within Comsol. Some simplifications were made in order to keep the mesh of reasonable size, such as the number of channels in the separator plates as well as having the channels run parallel instead of perpendicular. Meshing the perpendicular flow field would have exponentially increased the amount of elements needed. Minitab was used to develop a set of analyses with two levels for each variable using Design of Experiment (DOE) factorial methods. The results were evaluated for each of the cases required for the DOE analysis. The thru plane stress was the main output compared for each case. Because good load distribution on the cell is important for its performance, as stated above in the introduction, reducing the pressure distribution at the surface of the UEA was the goal of the analysis.
2.1. Solid Mechanics of the PEM fuel cell
It is assumed that there are no initial stresses on the materials from machining or material processing and all materials are assumed to be isotropic. Due to the relatively low temperature of a PEM fuel cell, which is usually less than 100C, the material properties are assumed to be the same as room temperature. There is also assumed to be no thermal stress in the system.
The stress within the material is therefore represented with the following equations [7]:
[1]
Since the system is in equilibrium the following equation applies:
[2]
The stress-stain relationship is Hooke’s Law:
[3]
Where:
[4a]
[4b]
2.2. Design of Experiment Factorial Methodology
Design of Experiments is a method of experimentation to test or establish a hypothesis to see which inputs have the greatest effect on the output. Generally used for physical experiments to ensure variation is of the experiment does not affect the outcome, it can also be used for a set of analyses used to determine which parameters in the analysis have the greatest effect on the output. One type of analysis method is factorial analysis. The factorial analysis is a statistical method to describe the effect of variables on a system with a reduced number of factors. In this case there are four factors being analyzed with two levels for each factor. To produce a full factorial of tests, 16 analyses would have to be run because the factorial equation is the number of levels raised to the power of the number of factors as represented in equation. However, a full factorial compares all interactions between all of the factors. For this case the assumption is that the higher level interactions are not large factors and a half factorial can be used. This allows for the most significant data to be collected with half of the cases, which would now be 8.
The half factorial set selects 8 of the cases in a logical manner which allows for the least error. A graphical representation of full factorial vs. ½ factorial can be seen in Figure 3. This figure represents a three factor experiment where the number of cases reduces from 8 to 4; however the same logic applies to four factors.
Figure 3: Visual representation of a Full Factorial vs. Half Factorial
The experiment variables were selected to be the pressure plate thickness, tie rod load, aspect ratio of the cell, and the separator thickness. Minitab’ half factorial logic was used to calculate the set of cases and these are shown below in Table 1. In general the table is just a set of zeros or ones representing the two levels of each factor. To generate the cases specific to this analysis, the following four parameters were entered into Minitab: pressure plate thickness, load, aspect ratio, tie rod location. These cases were entered as variables within a finite analysis model as parameter such that the model could be run with any set of variables. The outputs from the analysis were then entered back into Minitab for post processing. The details of the post processing are within the Results and Discussion sections below.
Table 1: DOE factorial variables for analysis
The table above contains the 8 cases which were analyzed. The factors were selected as bounds of the design space for each of the variables. The pressure plate thickness is the through thickness of the plate which was varied from 16mm to 20mm which is scaled for size from similar documented analyses [5]. The load is the pressure on the active area of the cell ranging from 200 kPa to 350 kPa which are standard loads on a fuel cell. The aspect ratio of the cell varied from 1.5:1 to 2:1 which is within a standard range of aspect ratios where fuel cells are not perfectly square as found in various studies [8]. The separator thickness was set to 2mm because standard fuel cell channels are around 1mm deep or less [9] . To add significant thickness the high level of the factor was set to 4mm.
2.3. Geometry
The geometry is a simplified representation of a single cell fuel cell containing pressure plates, a fuel flow field plate, an air flow field plate and an electrode assembly (UEA). To reduce the number of elements needed, the model was made as ¼ of the actual assembly by taking advantage of symmetry. This is possible because the cell is symmetrical in both directions. This means instead of four tie rod loading points in the model, there is only one corner which is loaded. The gaskets within the flow field plates were ignored as they are only on the very edge of the plate and this study is focused on the lack of pressure within the center of the assembly. The cell stack is assumed to have external manifolds for the reactants and coolant flows. Therefore, there are no features on the pressure plates other than the flanges for the tie rods.