Proceedings of the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels
ICNMM2014
August 3-7, 2014, Chicago, Illinois, USA
ICNMM2014-21922
THE EFFECT OF INJECTION AND SUCTION ON THE INTERFACIAL MASS
TRANSPORT RESISTANCE IN A PROTON EXCHANGE MEMBRANE FUEL CELL
AIR CHANNEL
Mustafa Koz
Rochester Institute of Technology, Microsystems
Engineering
Rochester, NY, USA
ABSTRACT
Proton exchange membrane fuel cells are efficient and
environmentally friendly electrochemical engines. The present
work focuses on air channels that bring the oxidant air into the
cell. Characterization of the oxygen concentration drop from
the channel to the gas diffusion layer (GDL)-channel interface
is a need in the modeling community. This concentration drop
is expressed with the non-dimensional Sherwood number (Sh).
At the aforementioned interface, the air can have a non-zero
velocity normal to the interface: injection of air to the channel
and suction of air from the channel. A water droplet in the
channel can constrict the channel cross section and lead to a
flow through the GDL. In this numerical study, a rectangular air
channel, GDL, and a stationary droplet on the GDL-channel
interface are simulated to investigate the Sh under droplet
induced injection/suction conditions. The simulations are
conducted with a commercially available software package,
COMSOL Multiphysics.
NOMENCLATURE
Abbreviations
BPP
bipolar plate
CL
catalyst layer
GDL
gas diffusion layer
PEMFC proton exchange membrane fuel cell
Variables
A
area
C
molar concentration of a gas
DO2-air molar oxygen diffusivity in air
dh
hydraulic diameter
Fc
Faraday’s constant
H
height
hM
mass transport coefficient
Satish G. Kandlikar
Rochester Institute of Technology, Mechanical
Engineering
Rochester, NY, USA
I
i
J
j
L
Nu
p
r
Sh
u
u, v, w
W
x
x, y, z
identity matrix
current density
molar consumption rate of species
molar flux of species
length
Nusselt number
air pressure
droplet radius
Sherwood number
velocity vector
velocity components
width
spatial coordinate vector
spatial coordinate components
Greek
ε
porosity
θ
contact angle on the GDL
λ
stoichiometric ratio
µ
dynamic viscosity of air
ξ
portion of fuel cell generated water in vapor form and
cathode side
ρ
air mass density
τ
exchanged electron per oxidant/reactant
ω
molar fraction
Subscripts
ac
repetitive unit area under a channel and a land
adv
advective
air
air
ch
channel
d
droplet
dif
diffusive
FD
fully developed
GDL
gas diffusion layer
1
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H2O
inj
int
land
O2
suc
0
water
injection
GDL-air channel interface
bipolar plate land width between two channels
oxygen
suction
baseline case: no injection or suction
1. INTRODUCTION
Proton exchange membrane fuel cells (PEMFCs)
efficiently convert the chemical energy in hydrogen and oxygen
into electrical energy. Reactants are supplied into reactant
channels through a pressure difference. Air carries the oxygen
required to the cathode side while hydrogen is supplied to the
anode side. The performance of the cell depends on the oxygen
concentration in the electrochemical reaction sites located
within the cathode catalyst layer (CL). Reactants diffuse from
the respective reactant channel towards the catalyst layer
through a gas diffusion layer (GDL). The interface between the
GDL and air channel has an oxygen transport resistance that
leads to an oxygen concentration drop. In simplified fuel cell
performance models [1], a mass transfer coefficient (hM) has
been used to relate the oxygen consumption of the cell to the
concentration drop at the interface. The mass transfer
coefficient is represented in the non-dimensional form:
Sherwood number (Sh = hmdh/D).
Sherwood number is dependent on the channel cross
section and boundary conditions on the walls. Reactant
channels mostly have a rectangular cross section that consists
of a porous wall (GDL-channel interface) and three non-porous
walls. The porous wall has oxygen transport from the channel
into the GDL while the bulk air can have a non-zero velocity
across this wall (interface). One of the reasons leading to flow
across the interface is the cathode electrochemical reactions
that do not conserve volume of air in the GDL. The consumed
oxygen reduces the volume of air. The produced water vapor
counteracts the effect of oxygen consumption. Additionally,
pressure difference across the membrane can induce cross flow
in between cathode and anode. However, since this cross flow
is strived to be kept at the minimum, its effect on
injection/suction is neglected. Oxygen consumption is constant
with current density. Contrarily, vapor production is a variable
with thermal conditions of the cell even at constant current
density. Air injection into channel from the GDL happens when
the production of vapor is more than the consumption of
oxygen and air pressure at the catalyst side of GDL is higher
than the channel side. When the consumption of oxygen
dominates the vapor production, air suction happens from the
channel to the GDL due to lower pressure at the catalyst layer
than the GDL-channel interface.
Injection and suction can be stronger when the air flow is
directed out of the channel into the GDL due to water features
observed during two phase flow. It has been earlier shown by
Chen et al. [2] that a droplet can constrict a channel and lead to
an air flow bypassing underneath the droplet through the GDL.
As a water feature constricts the channel more, the air flow
through the GDL can be stronger. Air suction and injection are
expected up and down stream of the constrictions, respectively.
The intensity of injection and suction is expected to be the
highest in the immediate vicinity of a constriction and decay to
zero with distance.
The effect of injection and suction on Sherwood number
has been investigated in the literature numerically [3–6]. A
number of these studies utilized parallel plates assumption to
represent reactant channels [3,4]. However, this approach needs
to be refined since reactant channel aspect ratios are close to
unity. Jeng et al. [4] and Hassanzadeh et al. [3] applied injection
and suction, respectively on one channel wall as a boundary
condition and investigated their parametric effect on Sherwood
number. The intensity of injection and suction was calculated
based on the balance between oxygen consumption and vapor
generation. The authors found the effect of injection and
suction on Sherwood number to be negligible. Three
dimensional numerical studies on the effect of stronger
injection and suction are scarcely available in the literature.
Only Beale has published in the aforementioned research area
[5,6]. In these publications, Sherwood number was reported in
the form of mass transfer driving force. Correlations were
established for a wide range of injection/suction intensity and
channel aspect ratio.
The Sherwood number under the effect of spatially varying
injection and suction has not yet been investigated in the
available literature. Spatially varying injection and suction
conditions can happen due to constrictions of water features in
air channels leading into partial air flow through the GDL.
Results for developing Sherwood number can allow researchers
to predict local cell performance in the aforementioned regions.
Droplets emerging from the channel center width can constrict
the channel the most compared to the ones emerging from the
off center width positions.
This numerical study investigates the effect of wall
injection and suction due to a single droplet in the channel on
the local Sherwood number (Sh). Firstly, an isolated channel
was simulated with no droplet while injection and suction were
imposed as a boundary condition. This part establishes an
understanding towards the effect of injection and suction.
Secondly, an isolated channel was simulated with a droplet.
This simulation establishes reference results for a channel with
all impermeable walls. Thirdly and lastly, a droplet was
simulated in a channel that was combined with a GDL. Droplet
radius and superficial air velocity were varied as input
parameters. With one channel wall is permeable, results are
compared against the ones in earlier sections. The effect of
injection and suction induced by the droplet on the Sherwood
number is characterized.
2
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Copyright © 2014 by ASME
it was 3 for 0.1 A cm-2. Oxygen concentration was calculated to
be 3.83 mol m-3 through the ideal gas law and imposed as a
fully developed profile at the inlet. Only convection was
allowed at the outlet.
Superficial velocities of oxygen (uO2,ac) and water vapor
(uH2O,ac) at the active area are required to be expressed to
calculate the net air velocity as a boundary condition at the
GDL-channel interface. They are dependent on their respective
molar fluxes and ultimately, current density. While oxygen is
consumed at the cathode side, water is produced. Hence, these
fluxes have the opposite direction. Molar flux of oxygen (jO2,ac)
and vapor (jH2O,ac) are 𝑗O2,ac = 𝑖 ⁄(𝜏O2 𝐹c ) and 𝑗H2O,ac =
𝑖𝜉 ⁄(𝜏H2O 𝐹c ), respectively. Exchanged number of electrons per
reacting/produced molecule (τ) is 4 and 2, for oxygen and
water, respectively. Depending on the thermal condition of the
cell, a portion of water (ξ) is in the vapor state. For maximum,
injection and suction, ξ corresponds to 1 and 0, respectively.
Molar fluxes of species at the active area can be
transformed into superficial velocities with the use of
respective molar concentrations (CO2 = 3.83 mol m-3, CH2O =
16.24 mol m-3): uac = jac C-1. The superficial velocities at the
active area can be mapped to the value at the GDL-channel
interface (uint) in isolated channel simulations through a similar
use of Eq. (1).
The molar fraction (ω) averaged velocity of the air is
calculated with superficial oxygen (uO2) and vapor (uH2O)
velocities as expressed in Eq. (2). During this calculation,
superficial nitrogen velocity is zero (uN2= 0) since there is no
transport of nitrogen.
𝑢air = 𝑢O2 × 𝜔O2 + 𝑢H2O × 𝜔H2O + 𝑢N2 × 𝜔N2
constriction of the channel. The average interfacial air velocity
(uair,int) was calculated as a function of streamwise position and
𝑊
−1
along the channel width: 𝑢air,int = 𝑊ch
(∫𝑦=0 𝑤d𝑦). This
resulting velocity is presented as the interfacial Reynolds
number (Reint) as defined in the previous paragraph.
2.3. Expression of Interfacial Mass Transport
Resistance
The molar oxygen flux at the GDL-channel interface
(jO2,int) has advective (jO2,int,adv) and diffusive (jO2,int,dif)
components.
𝑗O2,int = 𝑗O2,int,adv + 𝑗O2,int,dif
This study focuses on the transport resistance against the
diffusive component. The average diffusive transport at the
interface was calculated based on the channel-width-average of
local diffusive flux values.
𝑊
−1
𝑗O2,int,dif = 𝑊ch
∫𝑦=0 (𝐷O2−air
ℎM =
𝐶m =
𝐶int =
Rech
|Reint|×102
0.1
0.4
0.7
1.0
1.34
2.34
3.35
) d𝑦
(4)
𝑗
,
,
(5)
𝐶 −𝐶
𝐶 𝑢 d𝐴
∫
(6)
𝑢 d𝐴
∫
𝐶|
∫
d𝑦
(7)
𝑊
𝜌∇ ⋅ 𝐮 = 0
𝜌(𝐮 ⋅ ∇)𝐮 = ∇ ⋅ [−𝑝𝐈 + 𝜇(∇𝐮 + (∇𝐮)𝑇 )]
(8)
(9)
1.5
41.31 110.16 192.78 275.15 412.85
0.34
|
δ𝑧 𝑧=0
2.4. Numerical Approach
The air flow in the channel is governed by steady state
conservation of mass and momentum (Navier-Stokes) equations
as given in Eq. (8) and (9), respectively.
Table 1: Simulated current densities with the corresponding
channel (Rech) and absolute interfacial (|Reint|) Reynolds
numbers.
i (A cm-2)
δ𝐶
Mass transfer coefficient is the proportionality between the
diffusive flux and concentration drop at the interface. The
concentration drop is specific to streamwise position in the
channel. The concentration drop is expressed as the difference
between the mean concentration in the channel flow (Cm) and
channel-width-average interfacial concentration (Cint).
(2)
Throughout the results, the air velocity at the GDL-channel
interface will be presented with non-dimensional interfacial
Reynolds number (Reint=uair,int×dh×ρ×µ-1). Table 1 shows the
respective channel Reynolds number (Rech=uair,ch×dh×ρ×µ-1),
and the maximum possible absolute interfacial Reynolds
number corresponding to ξ = 0 and 1. Each case of current
density was simulated with the corresponding |Reint| which was
applied as both injection and suction.
(3)
5.01
In the presence of a droplet, injection and suction were not
imposed as a boundary condition at the GDL-channel interface
or at the active area. When the channel was simulated to be
isolated from the GDL, the velocity component across the
interface was imposed to be zero (w=0 at z=0). However, when
the channel was simulated with the GDL, the velocity
component across the interface can be non-zero due to the
The flow in the GDL is governed by steady state Brinkman
equations, a combination of Eqs. (8) and (10). Compared to
Darcy’s flow, Eq. (10) incorporates the shear force, and treats
velocity and pressure as separate variables. This allows
coupling free flow in the channel with the interstitial one in the
GDL.
𝜌
𝜀
(𝐮 ⋅ ∇)
𝐮
𝜀
= −∇𝑝 + ∇ ⋅ [
4
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𝜇
𝜀
𝜇
(∇𝐮 + (∇𝐮)𝑇 )] − 𝐮 (10)
𝐾
Copyright © 2014 by ASME
it was 3 for 0.1 A cm-2. Oxygen concentration was calculated to
be 3.83 mol m-3 through the ideal gas law and imposed as a
fully developed profile at the inlet. Only convection was
allowed at the outlet.
Superficial velocities of oxygen (uO2,ac) and water vapor
(uH2O,ac) at the active area are required to be expressed to
calculate the net air velocity as a boundary condition at the
GDL-channel interface. They are dependent on their respective
molar fluxes and ultimately, current density. While oxygen is
consumed at the cathode side, water is produced. Hence, these
fluxes have the opposite direction. Molar flux of oxygen (jO2,ac)
and vapor (jH2O,ac) are 𝑗O2,ac = 𝑖 ⁄(𝜏O2 𝐹c ) and 𝑗H2O,ac =
𝑖𝜉 ⁄(𝜏H2O 𝐹c ), respectively. Exchanged number of electrons per
reacting/produced molecule (τ) is 4 and 2, for oxygen and
water, respectively. Depending on the thermal condition of the
cell, a portion of water (ξ) is in the vapor state. For maximum,
injection and suction, ξ corresponds to 1 and 0, respectively.
Molar fluxes of species at the active area can be
transformed into superficial velocities with the use of
respective molar concentrations (CO2 = 3.83 mol m-3, CH2O =
16.24 mol m-3): uac = jac C-1. The superficial velocities at the
active area can be mapped to the value at the GDL-channel
interface (uint) in isolated channel simulations through a similar
use of Eq. (1).
The molar fraction (ω) averaged velocity of the air is
calculated with superficial oxygen (uO2) and vapor (uH2O)
velocities as expressed in Eq. (2). During this calculation,
superficial nitrogen velocity is zero (uN2= 0) since there is no
transport of nitrogen.
𝑢air = 𝑢O2 × 𝜔O2 + 𝑢H2O × 𝜔H2O + 𝑢N2 × 𝜔N2
constriction of the channel. The average interfacial air velocity
(uair,int) was calculated as a function of streamwise position and
𝑊
−1
along the channel width: 𝑢air,int = 𝑊ch
(∫𝑦=0 𝑤d𝑦). This
resulting velocity is presented as the interfacial Reynolds
number (Reint) as defined in the previous paragraph.
2.3. Expression of Interfacial Mass Transport
Resistance
The molar oxygen flux at the GDL-channel interface
(jO2,int) has advective (jO2,int,adv) and diffusive (jO2,int,dif)
components.
𝑗O2,int = 𝑗O2,int,adv + 𝑗O2,int,dif
This study focuses on the transport resistance against the
diffusive component. The average diffusive transport at the
interface was calculated based on the channel-width-average of
local diffusive flux values.
𝑊
−1
𝑗O2,int,dif = 𝑊ch
∫𝑦=0 (𝐷O2−air
ℎM =
𝐶m =
𝐶int =
Rech
|Reint|×102
0.1
0.4
0.7
1.0
1.34
2.34
3.35
) d𝑦
(4)
𝑗
,
,
(5)
𝐶 −𝐶
𝐶 𝑢 d𝐴
∫
(6)
𝑢 d𝐴
∫
𝐶|
∫
d𝑦
(7)
𝑊
𝜌∇ ⋅ 𝐮 = 0
𝜌(𝐮 ⋅ ∇)𝐮 = ∇ ⋅ [−𝑝𝐈 + 𝜇(∇𝐮 + (∇𝐮)𝑇 )]
(8)
(9)
1.5
41.31 110.16 192.78 275.15 412.85
0.34
|
δ𝑧 𝑧=0
2.4. Numerical Approach
The air flow in the channel is governed by steady state
conservation of mass and momentum (Navier-Stokes) equations
as given in Eq. (8) and (9), respectively.
Table 1: Simulated current densities with the corresponding
channel (Rech) and absolute interfacial (|Reint|) Reynolds
numbers.
i (A cm-2)
δ𝐶
Mass transfer coefficient is the proportionality between the
diffusive flux and concentration drop at the interface. The
concentration drop is specific to streamwise position in the
channel. The concentration drop is expressed as the difference
between the mean concentration in the channel flow (Cm) and
channel-width-average interfacial concentration (Cint).
(2)
Throughout the results, the air velocity at the GDL-channel
interface will be presented with non-dimensional interfacial
Reynolds number (Reint=uair,int×dh×ρ×µ-1). Table 1 shows the
respective channel Reynolds number (Rech=uair,ch×dh×ρ×µ-1),
and the maximum possible absolute interfacial Reynolds
number corresponding to ξ = 0 and 1. Each case of current
density was simulated with the corresponding |Reint| which was
applied as both injection and suction.
(3)
5.01
In the presence of a droplet, injection and suction were not
imposed as a boundary condition at the GDL-channel interface
or at the active area. When the channel was simulated to be
isolated from the GDL, the velocity component across the
interface was imposed to be zero (w=0 at z=0). However, when
the channel was simulated with the GDL, the velocity
component across the interface can be non-zero due to the
The flow in the GDL is governed by steady state Brinkman
equations, a combination of Eqs. (8) and (10). Compared to
Darcy’s flow, Eq. (10) incorporates the shear force, and treats
velocity and pressure as separate variables. This allows
coupling free flow in the channel with the interstitial one in the
GDL.
𝜌
𝜀
(𝐮 ⋅ ∇)
𝐮
𝜀
= −∇𝑝 + ∇ ⋅ [
4
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𝜇
𝜀
𝜇
(∇𝐮 + (∇𝐮)𝑇 )] − 𝐮 (10)
𝐾
Copyright © 2014 by ASME
Conservation of species equation, as given in Eq. (11), was
solved in the channel and GDL. Oxygen diffusivity (D) took
domain specific values within the channel (DO2-air) and GDL
(DO2-GDL).
∇ ⋅ (−𝐷∇𝐶 + 𝐮𝐶) = 0
(11)
Equations (8-10) were first solved coupled, and then Eq.
(11) was solved based on the formerly obtained results (u and
p). As a result of governing equations the unknowns of velocity
(u), pressure (p) and oxygen concentration (C) were obtained.
The numerical domain meshed with 723,030 tetrahedral
elements. Velocity and oxygen concentration were represented
with second order shape functions while pressure was
represented with linear shape functions. As a result, the
resulting degrees of freedom were 3,292,745. Generalized
Minimum Residual Method (GMRES) was used to iteratively
solve the numerical problem along with geometric multigrid
scheme. Automatically scaled residuals of unknowns were
required to converge to 10-3.
3. RESULTS
3.1. Validation of the Numerical Model
The numerical model was validated against experimental
injection and suction studies. Since there was no experimental
study available on the exact problem that is studied here, the
heat transfer analogue of the problem was used for validation.
Experiments by Cheng and Hwang [14] and Hwang et al. [15]
provided heat transfer data under injection and suction
conditions, respectively. The heat transfer at the porous surface
was characterized with Nusselt number (Nu) which is the heat
transfer analogue of Sherwood number. The aforementioned
studies reported mean Nusselt number (Num) in the streamwise
direction, in the developing entrance region of the flow. The
mathematical definition of Num at a given streamwise position,
𝑥
x1 is Num |𝑥 = (∫𝑥=0 Nu d𝑥 )𝑥1−1 .
The entrance region Num profiles are shown in Fig. 2 and 3
for conditions of injection and suction, respectively. The
streamwise distance in the channel is presented in a normalized
way with hydraulic diameter (dh), channel-based Reynolds
number (Rech), and Prandtl number (Pr). These two cases are
challenging enough as validation cases since their Rech values
was almost identical (Rech=400.00) or higher (Rech=500.00)
than the maximum Rech=412.85 used in the present study (as
shown in Table 1).
Figure 2 shows the streamwise Num variation for the case
with injection, Reint = 20.00. The values at each point are lower
compared to the case with no injection. The reason behind this
trend can be explained by the temperature difference between
the mean fluid temperature and interfacial temperature. The
fluid injected to the channel is at the same temperature with the
interface. In the vicinity of the interface, temperature values
start resembling the interface more closely due to injection.
Consequently, the temperature drop needs to become larger.
The largest error in the simulation results is 17% while all other
points have an error equal or below 10%.
Figure 2. Comparison of experimental [14] and numerical
mean Nusselt number (Num) at channel Reynolds number of
Rech = 400.00 and the interfacial Reynolds number of Reint =
20.00 (corresponding to injection).
Figure 3 presents the comparison of experimental and
numerical data for suction conditions, Reint = -5. The values of
Num were obtained to be higher than the case with no suction.
The reasoning behind this observation can be borrowed from
the paragraph above and be applied to suction conditions. The
maximum numerical error is 7%. Both simulations suggest that
the numerical technique is accurate.
Figure 3. Comparison of experimental [15] and numerical
mean Nusselt number (Num) at channel Reynolds number of
Rech = 500.00 and the interfacial Reynolds number of Reint =
-5.00 (corresponding to suction).
3.2. Effect of Injection and Suction on Sherwood
number in an Isolated Channel
In the baseline condition, in which there is no injection or
suction at the GDL-air channel interface, fully developed
Sherwood number was obtained to be ShFD,0 = 3.35. This value
was also obtained for all injection/suction cases shown in Table
1. Therefore, it can be claimed that injection and suction due to
oxygen consumption or vapor generation are not strong enough
to alter baseline fully developed Sherwood number.
Table 2 presents fully developed Sherwood numbers
calculated at injection (ShFD,inj) and suction (ShFD,suc) conditions
and normalized with the baseline value, ShFD,0. The results are
presented as a function of absolute interfacial Reynolds number
(|Reint|). Since Reint changes its sign at injection and suction
conditions, the absolute value of Reint is utilized. When suction
has an intensity larger than 0.4 (Reint < -0.4), advection
overtakes diffusion. Hence, Table 2 compares Sh up to |Reint| =
0.4. The lowest |Reint| was selected as the highest |Reint| from
5
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Copyright © 2014 by ASME
Table 1. Since all |Reint| values in Table 1 led to the same result,
the highest value is representative of other |Reint| values.
Table 2. Values of fully developed Sherwood number in
injection (ShFD,inj) and suction (ShFD,suc) conditions (|Reint| ≤
0.4) normalized with baseline fully developed value (ShFD,0).
|Reint|
5.01×10-2
10-1
2×10-1
4×10-1
ShFD,inj/ShFD,0
ShFD,suc/ShFD,0
1.00
1.00
0.99
1.01
0.98
1.02
0.96
1.03
Table 2 leads to the conclusion that suction cannot lead to a
significant change in Sherwood number under conditions that
diffusion is not completely replaced by advection due to strong
suction.
Table 3 extends the intensity of injection to a Reint value of
5 and shows Sherwood number as a function of Reint. By
analyzing the data in Tables 2 and 3 together, it can be seen that
Sherwood number deviates from the fully developed value at
least 11% when injection Reint exceeds 1. For the entire range
of injection shown in Tables 2 and 3, a linear variation of
Sherwood number is seen. The same trend is valid for the
suction cases in Table 2. Moreover, all values in Tables 2 and 3
match with the correlation provided by Beale [5].
Table 3. Values of fully developed Sherwood number in
injection (ShFD,inj) conditions (6×10-1 ≤ |Reint| ≤ 5) normalized
with baseline fully developed value (ShFD,0).
|Reint|
6×10-1
8×10-1
1
2.5
5
ShFD,inj/ShFD,0
0.93
0.91
0.89
0.73
0.52
3.3. Effect of a Droplet on Sherwood number in an
Isolated Channel
A droplet was simulated in an isolated channel to have a
reference case to be compared against simulations of a droplet
in the combined domain of channel and GDL. The problem
presented in this section has been studied extensively by Koz
and Kandlikar earlier [11]. Three configurations of Rech and r
were selected to provide the highest possible Rech for the
droplet sizes of r=0.10, 0.15, and 0.20 mm. This selection was
based on the droplet detachment criterion as presented earlier
[11]. Figure 4 shows the resulting Sh profiles for the selected
configurations of Rech and r.
Figure 4. Results of local Sherwood number in an isolated
channel with varying channel based Reynolds number
(Rech) and droplet radius (r).
Figure 4 shows that the major effect of a droplet on local
Sherwood number can be seen in the wake region. The largest
Sherwood number leading configuration (Rech=275.15, r=0.15
mm) will be used in the following section to demonstrate the
effect of GDL addition to the existing isolated channel.
3.4. Effect of a Droplet on Sherwood number in a
Channel Coupled with a GDL
A single droplet was placed in a channel with a GDL
adjacent to it. Flow could go through the GDL as the channel
was constricted by the droplet. The average interfacial velocity
induced by the droplet is expressed by interfacial Reynolds
number (Reint). Figure 5 shows a typical interfacial velocity
profile from the case Rech=275.15 and r=0.15 mm. Upstream of
the droplet (x<3.00 mm), suction can be seen with the
maximum intensity nearly Reint=-10. Downstream of the
droplet (x>3.00 mm), injection is present with a maximum
intensity almost half of the suction. Injection downstream of the
droplet is more evenly distributed along the length of the
channel compared to suction upstream.
Figure 5. Induced injection and suction by the droplet with a
radius of r=0.15 mm at a channel based Reynolds number of
Rech=275.15. Droplet induced injection/suction is expressed by
interfacial Reynolds number (Reint).
The highest intensity of suction and injection was obtained
in the case Rech=412.85 and r=0.10 mm with the corresponding
values of Reint=-9.6 and 5.6, respectively. The lowest intensities
were obtained in Rech=110.16 and r=0.20 mm with the
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intensities Reint=-3.0 and 2.9, respectively. All the
aforementioned intensities of injection and suction led to
significant changes in ShFD as presented in Table 3. The Sh
variation in the vicinity of the droplet was analyzed with
expectations parallel to results in Table 3.
Figure 6 compares local Sherwood number variations
under conditions of Rech=275.15 and r=0.15 mm for channelonly and channel-GDL simulations. The fully developed
Sherwood number under zero injection/suction (ShFD,0) differed
slightly. Channel-only and channel-GDL cases led to ShFD,0 of
3.35 and 3.20, respectively. Local Sh values are normalized
with the respective ShFD,0 to provide a better comparison
ground.
Results in Figure 6 show that injection and suction caused
led to increase and decrease, respectively in the immediate
vicinity of the droplet. This trend was seen in all three
configurations of Rech and r. Contrarily, an opposite trend was
obtained in Section 3.2 when injection/suction was enforced as
a boundary condition. Therefore, velocity profile caused by the
droplet is a stronger effect than the local injection and suction.
This trend is consistent in the remaining two cases.
The first scenario of injection/suction was studied to
investigate the effect of oxygen consumption and water vapor
production, and applied as a boundary condition at the GDLchannel interface of an isolated air channel. Fully developed
Sherwood number (ShFD) was investigated as a function of
Reynolds number defined at the GDL-channel interface.
Injection and suction led to linear decrease and increase of
ShFD, respectively. It was shown that ShFD cannot differ under
fuel cell operating conditions due to oxygen consumption and
vapor production.
By incorporating a GDL adjacent to the channel, ShFD was
compared (3.20) to the isolated channel case (3.35). No
significant difference was found between them. This slight
difference between the two values provides a reason why
numerical investigation of interfacial oxygen transport
resistance can be conducted in an isolated air channel.
The second scenario of injection and suction was studied to
investigate the effect of a water droplet that constricts the
channel and leads to air flow through the GDL. It was shown
that up and downstream of the droplet is subjected to suction
and injection, respectively. However, their effects are shown to
be very limited to the immediate vicinity of the droplet. Along
with the conclusion about ShFD in the paragraph above, it can
be concluded that two-phase flow features can be simulated in
an isolated air channel without incorporating the GDL.
ACKNOWLEDGMENTS
This work was conducted in the Thermal Analysis,
Microfluidics, and Fuel Cell Laboratory in the Mechanical
Engineering Department at Rochester Institute of Technology.
Support for this project was provided by the U.S. department of
energy under award number: DE-EE0000470.
Figure 6. Normalized local Sherwood numbers (Sh) with the
respective zero injection/suction fully developed values
(ShFD,0). Changes induced by a droplet with a radius of 0.15
mm at channel based Reynolds number of 275.15.
Comparison made between channel-only and channel-GDL
simulations.
With the addition of the GDL into the simulation, the local
maximum of Sherwood number that is seen in the wake of the
droplet is increased negligibly in all simulated configurations of
Rech and r. This maximum Sherwood number affects a
significant channel length downstream. The negligible change
in this parameter allows the investigation of two-phase flow
Sherwood number in isolated air channels by neglecting the
GDL effect.
CONCLUSIONS
Interfacial oxygen transport resistance in proton exchange
membrane fuel cell air channels was investigated under
injection and suction conditions at the gas diffusion layer –
channel interface. The injection and suction conditions were
studied under two conditions.
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