Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition
Proceedings of the ASME 2009 International Mechanical Engineering Congress &IMECE2009
Exposition
November 13-19, Lake Buena Vista, Florida,
USA
IMECE2009
November 13-19, Lake Buena Vista, Florida, USA
IMECE2009-11425
IMECE2009-11425
INVESTIGATION OF WATER VAPOR DIFFUSIVITY THROUGH GDL OF A PEMFC
Jacob LaManna*, Satish G. Kandlikar
Mechanical Engineering Department
Kate Gleason College of Engineering
Rochester Institute of Technology, Rochester, NY USA
*[email protected]
ABSTRACT
Water transport through the gas diffusion layer (GDL) of a
proton exchange membrane (PEM) fuel cell is of critical
importance in the operation of the fuel cell. In this study, the
transport of water vapor through the GDL is investigated. A
one-dimensional, single-phase heat and mass transfer model is
developed to investigate the diffusivity of water vapor through
the GDL of a PEMFC. An experimental apparatus is developed
to induce water vapor gradients across the GDL while varying
humidity levels and flow rates comparable to actual fuel cell
operational conditions. Experimental data is then used to
extract an effective water vapor diffusivity from the numerical
model. Effective diffusivity was found to be 0.104x10-4 m2/s
and the overall mass transfer coefficient was found to be 0.019
m/s at a temperature of 40°C.
1 INTRODUCTION
Proton exchange membrane (PEM) fuel cells have
come to the foreground as one of the potential choices for
replacement of petroleum fueled internal combustion engines.
In this role as primary power for transportation, high
performance and long life will be demanded from the fuel cell.
One of the factors that cause degradation in performance and
cell life is water content in the fuel cell; too much water lowers
performance while too little water will result in membrane
dehydration which causes lower performance and shortens the
life of the cell. Due to this limited range of acceptable water
levels, proper water management in the fuel cell is critical to
operation. The gas diffusion layer (GDL) plays an important
role in water management as it provides water removal,
reactant gas diffusion, and thermal management.
The GDL is typically constructed of carbon fibers either in
a woven cloth or a non-woven paper. There are five primary
tasks a GDL must perform for optimal fuel cell performance:
mechanical backing of catalyst layers and proton exchange
membrane, low resistance electron conductivity, thermal
management of the catalyst layer and membrane, water removal
from the catalyst layer to the flow fields, and reactant gas
distribution. To improve its water removal abilities, the GDL is
often treated with polytetrafluoroethylene (PTFE) to increase
its hydrophobicity.
Even though PTFE is used to improve water transport
through the GDL it often reduces the average pore sizes
available to the transport of both water and oxygen. Because of
the effect of wet-proofing on the inherent structure of the GDL,
it is important to understand the transport coefficients for the
GDL. There have been several experimental efforts to measure
the permeability of a GDL. This permeability is based on bulk
flow through the GDL and is calculated using Darcy’s law.
Ihonen et al. [1] and Feser et al. [2] both investigated the
effects of compression on through-plane permeability and
found that compression restricts the available pores thus
lowering the permeability of the GDL. Gostick et al. [3]
experimentally determined both the through-plane and in-plane
permeability for GDL and found that the in-plane permeability
is greater than the through-plane permeability. Gas phase
permeability was studied by Gurau et al. [4] and Williams et al.
[5] with the use of dry nitrogen gas. This dry nitrogen analysis
neglects the potential effects of oxygen and water vapor
concentrations to the overall flow properties.
Efforts have been made to understand the optimal
permeability of a GDL numerically. Pharoah [6] and Pharoah
et al. [7] investigated the differences between isotropic and
anisotropic permeability properties, it was found that
significant differences can exist between the through-plane and
in-plane permeability. Inoue et al. [8] developed a threedimensional reconstruction of carbon paper to analyze gas
permeability with the lattice Boltzmann method.
Experimental efforts to determine water vapor permeability
through the GDL is lacking in the literature. As stated by
Mathias et al. [9], the typical transport mode is diffusion in the
through-plane direction. It is necessary to analyze water vapor
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Copyright © 2009 by ASME
diffusion as water vapor can be present in the cell along with
liquid water. This investigation will develop a predictive
model that will reduce experimental data to determine a water
vapor diffusivity specific to a GDL and an overall mass transfer
coefficient. Permeability is not calculated in this investigation
as it is not valid for diffusion based transport. Viscosity is not a
governing property for diffusion; therefore the Darcy equation
is not applicable as it requires viscosity to calculate
permeability.
The model developed in this paper considers onedimensional coupled heat and mass transfer. It considers
convective heat and mass transfer on the channel GDL interface
on either side of the GDL and heat conduction and mass
diffusion through the GDL. The mass flux is then used to back
out an overall mass transfer coefficient similar to an overall
heat transfer coefficient. To adjust this overall mass transfer
coefficient and obtain an adjusted water vapor diffusivity,
experimental data will be used as inputs to the model. This
experimental data will allow the diffusivity to be adjusted until
the mass fluxes predicted by the model match the
experimentally obtained values.
The experimental setup mimics the same conditions that
are modeled. The test setup consists of 1 mm square channels
machined in polycarbonate that sandwich a sample of GDL.
Grafil U-105 GDL with General Motors sourced microporous
layer (MPL) is used for this study. Humidity is measured at the
inlets and outlets of the test section to determine the amount of
water vapor transferred through the GDL. Inlet gases are
passed through the channels to place varying water vapor
concentration gradients across the GDL. This design is similar
to test sections used in polymer membrane diffusion research
[10, 11].
The overall mass transfer coefficient developed in this
paper will be useful for future modeling efforts. It is critical to
understand the transport parameters of all the phases and gas
constituents flowing through the GDL when modeling twophase flow. When the GDL is saturated with higher levels of
liquid water, convective flow may be extremely limited and
therefore diffusive properties are needed.
h
k
km
Κ
Le
m&
N
Nu
P
Pr
Q
R
Ru
t
Binary diffusion coefficient for water in air
Convective coefficient
Thermal conductivity
Permeance
Overall mass transfer coefficient
Lewis number
Mass flow rate
Mass transfer rate
Nusselt number
Pressure
Prandtl number
Heat transfer rate
Resistance
Universal gas constant
GDL thickness
Temperature
Humidity ratio
Subscripts
1
2
a
h
i
j
m
tot
w
Channel 1
Channel 2
Air
Heat transfer terms
ith element
jth channel
Mass transfer terms
Total
Water
2 MODEL DEVELOPMENT
2.1 COMPUTATIONAL DOMAIN
The computational domain represents the same
configuration used in the experimental test section which is
described in Section 3.1. This configuration compresses a GDL
sample between two 1 mm square flow channels. Onedimensional elements are sliced through the length of the
channels as seen below in Figure 1.
Gas Channel #1
GDL
Gas Channel #2
Element i
T1,i +1
T1,i
m& 1,i
Q
W1,i
NOMENCLATURE
A
Area
C
Concentration
Cp
Specific heat
Dh
Hydraulic diameter
D H 2O
T
W
m& w
m& 1,i +1
W1,i +1
T2,i
T2,i +1
m& 2,i
m& 2,i +1
W2,i
W2,i +1
Figure 1: Computational Domain
2.2 ASSUMPTIONS
The assumptions for the model are as follows:
1. Steady state assumed for heat and mass transfer.
2. No pressure drop along the length of the channel
3. The Bulk pressure difference between the two
channels is zero. This assumption ensures that the
only driving force for water vapor from one channel to
the other is vapor partial pressure.
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Copyright © 2009 by ASME
T2,i +1 =
Fluid Properties:
Overall Pressure, Patm
101.3 kPa
Thermal conductivity of air, ka
0.0299 W/m-K
H O
-4
2
Binary diffusivity of H2O in air, D 2 0.26*10 m /s
Channel Properties:
Channel width
Channel height
Channel length
1 mm
1 mm
25 cm
GDL Properties:
Thickness, t
Thermal conductivity, kGDL
230 µm
1.7 W/m-K
5.
Adiabatic channel walls. The thermal conductivity of
polycarbonate is low enough to assume heat transfer
primarily occurs through the GDL and negligible heat
is lost through the polycarbonate.
Heat transfer only occurs in the through-plane
direction of the GDL due to the thickness being much
smaller than the length of the GDL.
2.3 HEAT TRANSFER
To accurately predict the mass transfer through the GDL,
heat transfer and temperature effects must be accounted for.
Heat transfer is modeled as the convection on one wall of an
internal flow.
A series resistance model was used to determine the heat
transfer from one channel to the other. The resistances in the
model were composed of a convection resistance from the first
channel, heat conduction through the GDL, and a convection
resistance to the second channel. Once these resistances were
determined it was possible to find the total resistance to heat
transfer as seen in Eq. 1.
Rh,tot =
1
h1,h A
+
t
K GDL A
+
1
h2 , h A
Qi =
Qi
m& C p1,i
(3)
C p1, i = C p , a1, i + W1,iC p , w1, i
(5)
C p 2,i = C p , a 2,i + W2, iC p , w 2,i
(6)
Mass transfer was calculated using the heat transfer
analogy. A mass transfer resistance network was developed to
model the water vapor transport from one channel to the other.
This resistance network includes mass convective resistances
for each channel and a diffusion resistance for the GDL. The
total mass transfer resistance is shown in Eq. 7.
Rm ,tot =
1
hm,1 A
+
t
D
H 2O
A
+
1
hm, 2 A
(7)
The mass convective coefficients were found utilizing the
Lewis relation [12] which relates the thermal and mass
convective coefficients, Eq. 8.
2
h
= ρC p Le 3
hm
(8)
The mass convective coefficient is obtained after
rearranging Eq. 8 to get Eq. 9.
hm =
(2)
Rh,tot
T1,i +1 = T1,i −
(4)
2.4 MASS TRANSFER
(1)
To find the temperature changes along the length of each
channel, the heat transfer rate was calculated using Eq. 2. This
rate was then used to calculate the change in temperature
through one element in each channel, Eq. 3 and Eq. 4.
T1,i − T2,i
+ T2,i
m& C p2 ,i
To account for the effects on heat transfer of water vapor
in the air streams, moist air properties are considered. Specific
heat is affected by the quantity of water vapor present in the air.
At each element along the length of the channel specific heat
was calculated by combining the specific heats of air and water
for the given temperature as shown in Eq. 5 for channel 1 and
Eq. 6 for channel 2. In both equations W represents the
humidity ratio for that element and Cpa and Cpw represent the
specific heats of air and water respectively.
Table 1: Model properties
4.
Qi
h
ρC p Le
2
(9)
3
The value for the Lewis number was obtained from
Kusuda [13]. Lewis number was set to 0.851 for zero
saturation and 0.841 for full saturation. With the mass
convection coefficient tied to the thermal convective
coefficient, it is even more critical to obtain an appropriate
Nusselt number for the system. The Nusselt number used for
this analysis is 2.76 from Shah and London [14]. This Nusselt
number is specific to square channel geometries and includes
entrance region effects.
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Copyright © 2009 by ASME
Before calculating the mass transfer in each element it is
necessary to calculate the local concentration of water vapor in
each channel. The concentration was calculated from the
partial pressure of water vapor using Eq. 10 where Ru is the
universal gas constant.
Pw, ji
Ci =
j
(10)
Ru T j ,i
C1,i − C2, i
Rm ,tot
(11)
The mass transfer for each element is then used to find the
change in water vapor concentration across the element for
each channel using Eq. 12 for channel 1 and Eq. 13 for channel
2.
C1, i +1 = C1,i −
C 2 , i +1 =
N i ρ1, i
m&
N i ρ 2, i
+ C2 , i
m&
(12)
(13)
Moist air density, ρ, is considered for each of the channels
in Eq. 12 and Eq. 13. This density is calculated at each element
using Eq. 14 [15].
 Pbulk
R T
 a j ,i
ρ j ,i = 

(1 + W j ,i )


 1 + W j ,i Rw 
Ra 

Κ
A( Pw,1 − Pw, 2 )
RuT
NRuT
A( Pw,1 − Pw, 2 )
Where,
In Eq. 17 Κ is the overall mass transfer coefficient and km
is the permeance for the GDL.
The computational domain was discretized into onedimensional elements along the length of the channels. Each
element includes both channels and the GDL as shown in
Figure 1. The 25 cm channel was divided into 10,000
elements, which was necessary to provide stability in the
solution. Governing equations were solved in a marching
scheme starting from the first element. Each element was
solved to provide the input to the next element. The model is
capable of producing plots for the partial pressure and
concentration of water vapor, humidity ratio, relative humidity,
and temperature profiles for the entire channel length.
To determine the resistance due to the structure of the
GDL, experimental data is collected and used as inputs for the
model. Initial conditions for the model are pulled from the
experimental channel temperatures and relative humidities.
Starting with the standard binary diffusivity of water vapor in
air, the effective diffusivity is found by adjusting the original
diffusivity to compensate for the resistance of the GDL. The
diffusivity of water vapor in GDL is adjusted until the predicted
results for exit relative humidity match the data obtained from
the experimentation. The overall mass transfer coefficient was
determined from the model using Eq. 16. The convective
coefficients used to determine the resistances are found
theoretically.
3 EXPERIMENTAL SETUP
3.1 HARDWARE
(15)
Reorganizing Eq. 15 yields Eq. 16.
Κ=
(17)
(14)
Where Pbulk is the overall pressure in element i, and Ra and Rw
are the specific gas constants for air and water, respectively.
To find the overall mass transfer coefficient for the GDL,
the permeance of the system was considered. Equation 15
represents another form for finding mass transfer with partial
pressure differences.
N=
1
1
1
1
+
+
hm ,1 km hm , 2
2.5 SOLUTION METHODOLOGY
Using the concentrations of each channel and the total
mass transfer resistance it is possible to calculate the total mass
transfer from one channel to the other for each element.
Ni =
Κ=
(16)
The experimental setup consists of the test fixture and
supporting equipment. Two polycarbonate channels sandwich
the GDL sample in the test fixture as seen below in Fig 2. The
test fixture allows for a 1400 kPa compressive force to be
applied to the GDL sample. Cutouts in the stainless steel side
plates provide visual access of the gas channels for verification
that excessive condensation is not occurring within the
channels.
Air is supplied to the test section through two separate
supply lines. Ultra zero grade air is supplied by two air bottles
which then flows into an Arbin DPHS-50 dew point humidifier.
The humidifier is capable of fully humidifying two streams up
to flow rates of 50 slpm. Humidity in the air is controlled by
setting the dew point temperature on the temperature
controllers for the system. Supply line gas temperatures can
also be controlled by the humidifier.
After humidification, the moist air passes through humidity
sensor chambers before entering the test section. The humidity
chambers provide a means of mounting the humidity sensors
and help to protect the sensors from any condensed water that
may be present. Once the air has passed through the test
section, the air passes through another humidity sensor chamber
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Copyright © 2009 by ASME
before being exhausted to atmosphere.
Temperature
measurements are taken at the inlet and outlet headers of the
channels. Thermocouple probes are inserted directly into the
flows and are placed as closely to the channel transitions as
possible. Figure 3 shows the location of the humidity chambers
and thermocouple wells with respect to the test section.
thermocouples that are integrated with the humidifier at the
inlet to the test section and E-type thermocouples on the test
section exhaust. Dry air flow rates are measured using a pair of
Omega FMA1816 electronic flow meters. To ensure that no
differential pressure exists between the channels, an Omega
PX143-2.5BD5V differential pressure transducer was placed at
the inlets of the channels. Flow rates were adjusted to achieve
zero differential pressure. Figure 4 displays the locations for
data measurements.
T
T
H
H
DP
H
H
T
T
Figure 3: Location of sensors with respect to test section where
H represents humidity sensors, T represents thermocouples, and
DP represents the differential pressure transducer. Inlet on left
side, outlet on right side.
Figure 2: Exploded view of test section. 1: Stainless steel side
plates; 2: Stainless Steel end plate; 3: Posts to fit inner diameter
of the springs; 4: Aluminum lower plate; 5: Springs; 6:
polycarbonate channel plates; 7: GDL; 8: Stainless steel top
plate.
3.2 DATA ACQUISITION
Parameters collected from the experimental setup consist
of the inlet and outlet channel humidity, inlet and outlet channel
temperature, humidifier dew point temperature, and dry air
mass flow rate.
Humidity measurements are obtained using Honeywell
HIH-4602-L-CP capacitive humidity sensors. These sensors
can measure relative humidity to ±2% RH with factory
calibration.
Temperature is measured using T-type
Figure 4: Piping and instrumentation diagram for experimental
setup
Data collection for the humidity sensors and the E-type
thermocouples, humidity sensors, and pressure transducer is
performed using a National Instruments cDAQ-9172 compact
USB data acquisition device. The flow meters and the
humidifier data are collected through direct serial interfacing
with the computer. A LabVIEW interface is used to collect the
data from the DAQ and the serial interface devices.
3.3 TEST CASES
Test cases selected for this work include both strictly heat
transfer and strictly mass transfer tests. Heat transfer tests were
performed using an aluminum foil sheet in place of a GDL
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Copyright © 2009 by ASME
sample. Each channel was operated independently and together
to gain insight into the heat transfer characteristics of the entire
test section. Flow rates for heat transfer testing were varied
from 0.25 slpm to 1.75 slpm.
Mass transfer cases were selected at 40°C as this represents
a typical operating temperature for fuel cells during short
driving distances. The test section was wrapped in several
layers of insulation and allowed to operate at an isothermal
condition at this temperature. Isothermal operation was
selected as losses were found to be too great during the heat
transfer testing stated in the previous paragraph. Flow rates of
0.5, 1.0, and 1.5 slpm were utilized. Relative humidity was set
at approximately 95% and 0% for the two channel inlets. Flow
rates, temperatures, and relative humidity were selected to
remain below the maximum operational conditions of the flow
and humidity sensors.
4 RESULTS
4.1 EXPERIMENTAL RESULTS
The mass transfer testing was performed using Grafil U105 GDL manufactured by Mitsubishi Rayon Corporation with
7% by mass PTFE and a MPL as provided by General Motors.
This GDL is a non-woven carbon fiber substrate with carbon
black MPL. The GDL was oriented so that the MPL was
interfaced with the humidified channel. This was done to
simulate actual fuel cell conditions where the MPL is typically
mated to the cathode catalyst layer where the water is produced.
Data was collected continuously in LabVIEW at a rate of
300Hz. Data collection for the output files lasted over 10
seconds to allow for data averaging once steady state was
achieved. Steady state was determined by the relative humidity
change between channel inlets and outlets. Relative humidity
was plotted in LabVIEW to determine the change over time.
Once the plot became level, steady state was reached. Output
files were then averaged to reduce noise in output data.
Experimental results for the mass transfer test cases can be
seen in Table 2. As expected from heat transfer analysis, the
relative humidity change from the inlet to the outlet decreases
with increased flow rate.
The temperatures were stable to within 1°C from inlet to
outlet of the channels. The variability in change in relative
humidity can be attributed to changes in the operational
temperatures, dew point temperatures, and the error in the
humidity sensors themselves.
4.2 NUMERICAL RESULTS
To obtain the effective diffusivity of water vapor in the
GDL, the experimental results from Table 2 were used as inputs
to the numerical model. Inputs consisted of the dry bulb
temperatures and dew point temperatures, which are obtained
from the relative humidities. This allowed for calibration of the
model and allowed the model to simulate each of the
experimental test cases. The model was initially run for each
test case using the water vapor-air binary diffusivity at
atmospheric pressure and temperature of 0.26x10-4 m2/s. Initial
conditions for each case were inspected to ensure that the
model was calculating properties correctly. The conditions
inspected included the initial relative humidity and partial
pressures of water vapor in each channel.
Graphical outputs from the model were used in this
verification. Examples of graphical outputs can be seen in
Figures 5 and 6. Relative humidity was verified to not exceed
100% at the entrance and to closely match the averaged
measured experimental data. Partial pressure was verified to
not exceed the saturation pressure at the given temperature.
These checks were used to ensure that the model was
calculating physically possible values. Mass was verified
through density to be conserved from inlet to outlet.
Channel Channel
∆Relative
Average Dew Point
Humidity
Temp [°C]
[°C]
43.0
42.1
30.5
43.7
42.7
31.2
43.7
42.8
28.6
43.6
42.6
20.0
1.0
43.5
42.5
20.8
43.3
42.3
20.5
41.3
40.5
14.8
1.5
43.5
42.6
14.4
43.7
42.7
15.7
Table 2: Experimental results showing average channel
temperature, channel dew point, and the change in relative
humidity across the channel.
0.5
Figure 5: Relative humidity model output for 40°C, 0.5 slpm
test case.
Once the model was verified for initial conditions on each
test case, adjustment of the water vapor diffusivity took place.
For all cases, the diffusivity had to be lowered to account for
lower experimental mass transfer than originally numerically
predicted with the standard value of diffusivity. A lower
diffusivity is expected from this work as the GDL itself will
provide higher resistance to mass transfer while the MPL will
provide significant additional resistance due to its small pore
size distribution. The effective diffusivity determined by the
model can be seen in Table 3. The table gives the calculated
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Copyright © 2009 by ASME
Overall Mass Transfer Coefficient [m/s]
Flow Rate
Calculated
Average
0.020
0.5
0.019
0.019
0.016
0.019
1
0.020
0.020
0.020
0.019
1.5
0.020
0.018
0.021
Figure 6: Water partial pressure model output for 40°C, 0.5
slpm test case.
diffusivity x104 [m2/s]
Flow Rate
Calculated
Average
0.119
0.5
0.098
0.100
0.074
0.100
1.0
0.108
0.114
0.109
0.103
1.5
0.107
0.095
0.124
Overall Temp average
0.104
Table 3: Effective diffusivity results from numerical model.
Shows effective diffusivity for each experimental test case,
flow rate average, and the averaged diffusivity for the test
temperature.
Overall Temp average
0.019
Table 4: Fully developed overall mass transfer coefficient for
water vapor through the GDL for each test case and an overall
averaged property.
shown in this paper, the actual diffusivity in a GDL can be as
little as half the value of water vapor and air. This discrepancy
could result in models that over-approximate the amount of
diffusion occurring within the cell. With higher diffusion rates,
models should over predict the limiting current and power
output of the cell.
It is important to ensure accurate properties when modeling
fuel cells as the scale makes it susceptible to large variations
from small changes in property values. The new effective
diffusivity found in this work should help to make more
accurate models and increase fundamental understanding of
PEM fuel cell operation.
5 CONCLUSIONS
effective diffusivity for each flow rate and the averaged
effective diffusivity for each temperature case.
An overall mass transfer coefficient for fully developed
flow was also determined for a GDL using the model. The
individual test case and total averaged value of the transfer
coefficient is shown in Table 4. The fully developed flow
value for Κ was determined with a ratio of the fully developed
convective coefficient to the mean convective coefficient. This
ratio allowed the effects of the entrance region to be neglected
from the data. Future work will include testing the same GDL
without the MPL to determine the individual resistances to
water vapor transport. This future work should show higher
individual resistances for the MPL due to its inherent smaller
pore structures.
In this study the effective diffusivity and overall mass
transfer coefficient for water vapor is calculated for a GDL
with MPL. A numerical model is used to determine the
effective diffusivity and mass transfer coefficient from inputs
derived from experimental data. The effective diffusivity gives
a more accurate value for modeling diffusion through the GDL
of a PEM fuel cell. It was found to be 0.104x10-4 m2/s, which
is significantly less than the standard value of 0.26x10-4 m2/s.
Models that use the latter value would over predict the
diffusion in the cell which would lead to over prediction of the
limiting current density and maximum power of the cell. This
improved value is critical as most water vapor and gas property
experiments rely on bulk flow based calculations. Bulk flow
may not occur within portions of the cell during operation and
therefore render those properties unusable. Higher accuracy
models can shed light on the inner dynamics of a fuel cell that
are hard to determine with experiments. It will be critical to
ensure the properties used are as accurate as possible as shown
with this work.
4.2 DISCUSSION
ACKNOWLEDGMENTS
The effective diffusivity of water vapor developed in this
paper will give an important parameter to fuel cell modeling
efforts. Currently, the standard binary diffusivity of water
vapor and air is used in most models that look at diffusion. As
This work was supported by the Department of Energy
under Award Number DE-FG36-07GO17018.
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Copyright © 2009 by ASME
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