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, Thesis Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2011
ii
CONTENTS
LIST OF SYMBOLS ........................................................................................................ iv
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
ABSTRACT .................................................................................................................... vii
1. INTRODUCTION/BACKGROUND .................................................................... viii
2. THEORY/METHODOLOGY .................................................................................. x
Stress Theory ............................................................................................................... x
DOE methodology ...................................................................................................... xi
Geometry ................................................................................................................... xii
Materials ................................................................................................................... xiii
4. DISCUSSION .......................................................................................................... xxi
5. CONCLUSIONS .................................................................................................... xxii
1. Bibliography ........................................................................................................... xxiii
APPENDICES ............................................................................................................. xxiv
iii
LIST OF SYMBOLS
E = Modulus of Elasticity (GPa)
ν = Poisson’s Ratio (-)
ε = Strain (-)
ω = Displacement (mm)
σ = Normal Stress (GPa)
τ = Shear Stress (GPa)
G = Shear Modulus (GPa)
p = Applied Load (N)
M = Applied Moment (N*m)
ρ = Density (kg/m^3)
iv
LIST OF TABLES
Table 1: DOE factorial variables for analysis................................................................... xi
Table 2: Material Properties........................................................................................ xiv
v
LIST OF FIGURES
Figure 1 - How a fuel cell works .................................................................................... viii
Figure 2: Geometry of the single cell ............................................................................. xiii
Figure 3: Highlighted surfaces represent symmetry boundary conditions ...................... xv
Figure 4 - Boundary load location on the pressure plate ................................................ xvi
Figure 5: Mesh containing tetrahedrals and triangular prisms. ..................................... xvii
Figure 6 - Side view of cell mesh .................................................................................. xvii
Figure 8 - Stress plot of a cross section of the separator plate. .................................... xviii
Figure 7 – Von Mises stress plot of the pressure plate ................................................... xix
Figure 10: Case 1 ............................................................................................................. xx
vi
ABSTRACT
A PEM fuel cell consists of the electrode assembly, separator 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 crucial for maximum performance and
durability. In general, 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. This study evaluates the factors which affect the pressure on the cell
assembly, within a single cell fuel cell. Using design of experiments 2 factorial methods,
the factors will be optimized for minimum pressure distribution.
vii
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 PEM fuel cells. The fuel
cell type which will be evaluated in this paper is a Proton Exchange Membrane (PEM)
fuel cell. Multiple cells can be 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 fuel cell works
For a PEM fuel cell to function it needs to have an anode plate, a cathode plate, and
an electrolyte. In addition to conducting electricity the anode and cathode plates, also
known as separator plates, all have channels machined into them for the fuel and air to
flow though. These flow channels allow for fuel and air to pass by the electrode
assembly, which contains the electrolyte as well as gas diffusion layers (GDLs) which
are located on either side of the electrode.
viii
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 the hydrogen reacts with a
catalyst in the electrode which causes positive ions to pass through the electrode
membrane, while the negative ions create an electrical current to whatever it is
powering. The positive ions then react with the oxygen in the air on the cathode side of
cell to produce water.
In between them is a membrane which has a GDL on each side. The performance of
the fuel cell is dependent on the load of the GDL (1). Proper load distribution of the fuel
cell is important for performance and durability. Fuel cell stacks with dozens of cells end
up with relatively even distribution due to the ability for the pressures to equilibrate
through the thickness of the cell stack. Single cell assemblies, as well as low power
assemblies which have only a few cells, can have poor load distribution across the cell.
The pressure within a given single cell has been proven to vary as much as 4x from
the lowest pressure to the highest pressure even with different loads (1). The question ot
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. Threaded tie rods are used to connect the two end plates and apply a
compressive load to the cell stack. The manifolds for the stack design evaluated in this
study are assumed to be external to the cells. Therefore there are no ports on the pressure
plate.
ix
2. THEORY/METHODOLOGY
To ensure proper loading, optimization of the pressure plate and bipolar plate design
is needed. The objective of this task is to evaluate the change in load distribution when
changing the pressure plate structure, including the thickness, tie rod location, and aspect
ratio. Using a constant pressure plate configuration, the pressure on the electrode
assembly will be evaluated. The channel/rib ratio will be varied to analyze the effect on
the electrode assembly. (Karvonen, Hottinen, Ihonen, & Uusalo, 2008)
The model was analyzed in Comsol using the solid mechanics module. 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 will
be made in order to keep the mesh of reasonable size, such as the number of channels in
the bipolar plate. Minitab was used to develop a Design of Experiment series of runs
each with 2 factors each. The results were evaluated for each of the cases required for
the DOE analysis. The thru plane stress will be the main data point compared for each
case. The overall deflection plot as well as other stresses will be examined when
appropriate. The target goal will be to have the smallest range of stresses on the
electrode assembly.
Stress Theory
Since the pressure plate holds most of the structure due to its material properties as well
as its thickness relative to the separator plate. Therefore an estimation of the load within
the cell can be calculated using plate theory with the pressure plate. 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 represented with the following equation:
x
 x  xy  xz
 ij   xy  y  yz
 zx  zy  z
Since the system is in equilibrium the following equation applies:
 *  0
The stress-stain relationship:
 x  E x
Because there are simple and symmetric boundary conditions for this problem in
Cartesian coordinates, the strip theory for plates can be applied to this problem.
DOE methodology
To generate the cases 4 parameters were changed. The Minitab software will be
used to randomly generate a set of tests based on a 2 factorial DOE analysis. These cases
will then be analyzed and the results entered back into Minitab. Minitab can then
generate an optimized solution.
Table 1: DOE factorial variables for analysis
Run #
1
2
3
4
5
6
7
Pressure Plate
Thickness (mm)
10
16
10
16
10
16
10
Load (kPa)
200
200
350
350
200
200
350
xi
Aspect
Ratio
2:1
2:1
2:1
2:1
3:1
3:1
3:1
Tie Rod
Distance
(mm)
0
30
30
0
30
0
0
8
16
350
3:1
30
The table above has the 8 runs which were analyzed. The pressure plate thickness is the
thought thickness of the plate which was varied from 10mm to 16mm. The load is the
pressure on the active area of the cell ranging from 200 kPa to 350 kPa. The aspect ratio
of the cell varied from 2:1 to 3:1. The tie rod distance is the location of the tie rod from
the edge of the active area of the cell.
Geometry
The geometry is a simplified representation of a fuel cell containing pressure plates,
a fuel flow field plate, a fuel flow field plate and an electrode assembly. To reduce the
number of elements needed to run the model was made as ¼ of the actual assembly. This
is possible because the cell is symmetrical in both directions. Symmetry boundary
conditions were used on the symmetrical interfaces. 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 holes for the
tie rods.
xii
Figure 2: Geometry of the single cell
The corner which transitions between the main part of the pressure plate and the
flange had a large radius to account for the high local stresses in the part. Instead of
removing the radius completely it was changed to a small block of material. This way it
was able to be meshed with the rest of the structure.
The hole for the tie rods were removed to create a simpler mesh and not create
unrealistic stresses on the hole due to the coarse mesh in that area. Since that area was
not of concern for this analysis the simplification of it was appropriate.
Materials
xiii
Three different materials are included in the fuel cell. The pressure plate is made of
stainless steel. For the purposes of this analysis the pressure plate is made from Type
316 stainless steel. The flow field plate is made from graphite. The UEA is also made
from a fibrous graphite. The material properties are listed in table X.
Table 2: Material Properties
Material
Density
(g/cc)
Young’s
Modulus
(Gpa)
Poisson's
Ratio
Source
316 SS
7.92
193
.28
Efunda
1.5
10
.27
.9
10
.27
Graftech
Graphite Plate
UEA
Graftech &
NASA
Graftech
Boundary Conditions
In order to simulate the entire cell while still maintaining a manageable model, the
symmetry boundary condition was used on two sides of the cell.
xiv
Figure 3: Highlighted surfaces represent symmetry boundary conditions
The load on the fuel cell is created by 4 tie rods that run between the pressure plates.
The load from the tie rod is distributed onto the pressure plate through a washer. The
load from this washer is added to circular surfaces on the pressure plate flanges. This
load was scaled to a pressure such that the load on the circular area under the washer was
equal to the load on the cell represented in the DOE table.
xv
Figure 4 - Boundary load location on the pressure plate
Mesh
The mesh is made up of triangular prism and quadrilateral elements. In order to
mesh the separator plate with channels, a surface mesh of triangles was first created on
the side of the plate. The triangular prisms were then swept through the plate.
xvi
Figure 5: Mesh containing tetrahedrals and triangular prisms.
The same process of sweeping triangles was used for the all of the pressure plate,
except for the pressure plate flanges. The flanges were made of quadrilateral elements
which meshed properly with the triangular elements at the flanged end of the pressure
plate.
Figure 6 - Side view of cell mesh
xvii
3. RESULTS
The results below show how the pressure within the cell for each case of the DOE
table. The main focus of results is the load distribution across the separator plate. Since
the exact stresses on the UEA show some unrealistically high stresses due to the thinness
of the geometry. Therefore a plane through the center of the separator plate was used to
review the stress distribution across the cell. The place is showed in the plot below. The
remaining plots of this plane will be 2D contour plots of this cross section.
Figure 7 - Stress plot of a cross section of the separator plate.
Since the cell is loaded by the tie rods in the majority of the stress is transferred
through the corners of the pressure plate which is represented by the von mises stress
plot below for case 1. Although only case 1 is shown below, the stress plot looks very
similar for all cases although the values may scale up or down depending on the
variables.
xviii
Figure 8 – Von Mises stress plot of the pressure plate
Below are the cross sections of the separator plate detailed in the beginning of the results
section. These results are of the Z component of stress which is through plane of the
separator plate. Based on the plots below most of the load goes into the top corner of the
cell in all cases, which is to be expected because the load is cantilevered off the end of
the cell.
xix
Figure 9: Case 1
xx
DISCUSSION
xxi
4. CONCLUSIONS
Due to the fact that the load in the middle of the cell is much less than the edge of the
cell, the tie rod load should be moved as close to the active are of the fuel cell as
possible. Also, the thicker the pressure plate is, the less deflection it will have and will
therefore better distribute the load of the fuel cell. A fuel cell which has an aspect ratio
closest to 1:1 will also have the best distribution of load for a given area size because it
will have a maximized area for a given distance from tie rod load to the center of the
cell.
xxii
1. Bibliography
1. The effects of compression and gas diffusion layers on the performance of a PEM fuel
cell. Woo-kum Lee, chien-Hsien Ho, J.W. Van Zee, Mahesh Murthy. 1999, Journal
of Power Sources 84, pp. 45-51.
2. Modeling of Polymer Electrolyte Membrane Fuel Cell Stack End Plates. Karvonen,
Suvi, et al., et al. 2008, Journal of Fuel Cell Science and Technology, pp. 041009-1 to
04009-9.
3. Analyses of the fuel cell stack assembly pressure. Lee, Shuo-Jen, Hsu, Chen-De and
Huang, Ching-Han. 145, TaoYuan : Journal of Power Sources, 2005.
4.
Stainless
Steel
AISI
Type
316.
efunda.com.
[Online]
http://www.efunda.com/Materials/alloys/stainless_steels/show_stainless.cfm?ID=AISI_
Type_316&prop=all&Page_Title=AISI%20Type%20316. (1)
xxiii
APPENDICES
xxiv