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Reporte sobre COMSOL: Simulaciones de Fuel-Cells
Anlisis de los siguientes Model Libraries:
1)Tutorial Models: Fuel Cell cathode.2)PEMFC:pem gdl species
transport 2d.3)PEMFC: passive pem.4)PEMFC: ht pem.
Se da un introduccin a cada modelo y las variantes que se podran
realizar.
Antonio Zegarra Borrero
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1)Tutorial Models: Fuel Cell cathode.One of the most important
and complicated parameters to model in a fuel-cell is the MASS
TRANSPORT through the GDL (Gas Diffusion Layers) and RL (Reactive
Layers). The concentrations of the gases (on the cathode we have
O_{2}, H_{2}O y N_{2} and at the anode H_{2}) are relatively high
and are affected by chemical reactions (Reduction of Oxygen at the
Cathode and Oxidation of Hydrogen at the Anode). These conditions
make Fickian diffusion inappropriate to model mass transport and
one has to rely on the more elaborated Maxwell-Stefan equation.
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In this case the cathode of a fuel-cell with perforated current
collectors is investigated. Due to the perforation layout a 3D
model is needed to study the mass transport, current and reaction
distributions.
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This model investigates such a geometry and the mass transport
that occurs through Maxwell-Stefan diffusion. It couples this mass
transport to a generic, Tafel-like electrochemical kinetics in the
reaction term at a cathode.
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Physical Interfaces used: The electronic and ionic current
balances are
modeled using a Secondary Current Distribution interface.
The species (mass) transport is modeled by the Maxwell-Stefan
equations for oxygen (Species 1) and water (Species 2) in the gas
phase using a Transport of Concentrated Species interface. Mass
transport is solved for in the electrode domain only.
The velocity vector is solved for using a Darcys law
interface.
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Results presented Isosurfaces of the weight fraction of oxygen
at a total
potential drop over the modeled domain of 190 mV.
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Velocity field for the gas phase in the cathodes porous reactive
layer. There is a significant velocity peak at the edge of the
inlet orifice caused by the contributions of the reactive layer
underneath the current collector because in this region the
convective flux dominates the mass transport.
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The electrochemical reaction rate, represented by the local
current density, is related to both the local overvoltage and
oxygen concentration. The next figure depicts the local
overvoltage, which is rather even throughout the cathode. This is
caused by the high electronic conductivity in the porous material.
Another observation is that the maximum overvoltage is -180 mV.
This means that there is a voltage loss of 10 mV in the electrolyte
layer.
Although the local overvoltage distribution is rather even, the
concentration of oxygen is not. This means that the reaction rate
is nonuniform in the reactive layer. One way to study the
distribution of the reaction rate is to plot the ionic current
density at the bottom boundary of the free electrolyte.
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The local overvoltage is rather even because the porous
electrode is a conductor.
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The current-density distribution shows that the variations are
rather large. The reaction rate and the current production are
higher beneath the orifice and decrease as the distance to the gas
inlet increases. This means that the mass transport of reactant
dictates the electrodes efficiency for this design at these
particular conditions.
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Now, an analysis of the ways to introduce modifications to
the
instructions in the manual The simulation starts by adding a
SECONDARY
CURRENT DISTRBUTION Interface and a Stationary Study to set up
and solve for a current distribution model of the cell.
At this stage we don't consider the influence of chemical
species yet because we want to analyze the current distribution
only considering a voltage difference between the electrolyte and
the current collector.
Because of the geometry we need a 3D-model.
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GEOMETRY 1 Use blocks to define the electrolyte and the
porous
electrode domains. Then use a workplane to draw the inlet hole
at the top of the porous electrode. Facilitate geometry selection
later (when setting up the physics) by enabling Create Selections
and renaming the geometry objects.
Block1: Electrolyte, Block 2: Porous Electrode,
Work-Plane-->Circle : Inlet. Then use Form Union.
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GLOBAL DEFINITIONS Load the model parameters and variables from
text
files (We can change these parameters to adapt them to a
particular material/experiment).
Parameters: fuel_cell_cathode_parameters.txt. Variables:
fuel_cell_cathode_variables.txt.
EXPLICIT Manually add selections for the bottom electrolyte
and
top current collector boundaries: Explicit 1---> Boundary
3---> Electrolyte Boundary. Explicit 2---> Boundary 7--->
Current Collector.
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SECONDARY CURRENT DISTRIBUTION Now start defining the physics
for the current distribution
model. Add a porous electrode and specify the electrode reaction
parameters, then add potential boundary nodes for both the
electrolyte and the electrode phase. Note that an Electrolyte node
already has been added automatically by default.
Physics Toolbar-->Porous Electrode 1--> Domain Selection:
Porous Electrode. No correction for the effective
conductivities.
Porous Electrode 1--->Porous Electrode Reaction 1--->
Model Inputs---> T, i0, S (We can change this!)
Potentials at the electrolyte and current collector: 0 at the
electrolyte and E_pol at the current collector. Provide initial
values to reduce computational time.
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MATERIALS The Materials node is marked with a red cross. This
indicates that
there are material parameters missing in the model. Add two
different material nodes for the electrolyte and the porous
electrode, and specify the conductivity values.
Model Builder--->Component 1---->Materials---->New
Material--->Geometric Entity Selection---->
Electrolyte----->Electrolyte Conductivity: sigmal= 5 [S/m].
Model Builder--->Component1---->Materials---->New
Material--->Geometric Entity Selection---->Porous
Electrode----->Electrolyte Conductivity: sigmal= 1 [S/m],
Electrical conductivity sigma=sigma_s.
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MESH 1 Use the default mesh sequence that will be induced by
the physics, but change to a finer size. Model
Builder--->Component 1---->Mesh 1----
>Element Size---->Fine (Here we can increase the accuracy
by choosing Extra Fine)--->Build All.
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STUDY 1: Home Toolbar--->Compute (=).
Add Plot Group----> 3D Plot Group, then Model
Builder---->Results---->3D Plot
Group---->Volume----->Expression----> Replace Expression:
Overpotential (siec.eta_per1)---->Plot----> Rename 3D Plot
Group 3----> New Name: Local Overpotential.
RESULTS: Electrolyte potential plots are created by default. Now
create a plot of the local overpotential by first adding a plot
group, followed by a volume plot.
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Your overpotential plot should now look like this (We have not
included the effects of mass transport yet):
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Data Sets: Create a data set with a selection on the bottom
electrolyte boundary only. Then use this data set to plot a surface
plot of the normal electrolyte current density.
Results Toolbar----->More Data Sets---->Solution.
Model Builder----->Results---->Data Sets: Right click
Solution 2--->Add Selection. Selection settings
window----->Geometric Entity Selection----->Geometric Entity
Level: Boundary------>Selection: Electrolyte
Boundary---->Select "Propagate to lower dimensions".
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3D Plot Group 4
Home toolbar---->Add Plot Group----> 3D Plot Group---->
Data Section---> Data Set: Solution 2. Right Click
Results-----> 3D Plot Group 4--->Surface----->Expression
Section---->Replace Expression: Normal electrolyte current
density (siec.nIl) ----->abs(siec.nIl) (we plot the absolute
value)------>Plot.
Model Builder----> right click 3D Plot Group 4----->
Rename ----> Electrolyte Current Density.
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Now change to second order elements in the finite element
discretization. This will increase the accuracy of the solution and
render a smoother plot. (Alternatively you could increase the
resolution of the mesh). Model Builder----> Show button (the
"eye")----
>Select Discretization. Secondary Current Distribution
settings
window----> Discretization Section ------> Electrolyte
potential: Quadratic, Electric potential: Quadratic.
Study I: Home toolbar---->Compute(=)
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Results: Your current density plot should now look like
this:
We have little current at the inlet because there is like a hole
and the current comes from the electrolyte to the current
collector. We have no added oxygen yet!
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COMPONENT 1 Now, add more physics to the model by adding a
Transport of Concentrated Species interface for gas phase mass
transport and a Darcy's law interface for the convective flow.
Add Physics---->Chemical Species Transport---->Transport
of Concentrated Species (chcs)----->Dependent
Variables------>Number of species=3-----> Add to
Component.
Add Physics---->Fluid Flow---->Porous Media and Subsurface
Flow-----> Darcy's Law (dl)----->Add to Component.
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Transport of Concentrated Species Model Builder---->Component
1---->Transport of
Concentrated Species----->Domain Selection: Porous
Electrode---->Transport Mechanisms----->Diffusion model:
Maxwell-Stefan.
Convection and Diffusion 1 Model Builder----->Transport of
Concentrated
Species----->Convection and Diffusion
1----->Density--->M_n2, M_o2, M_h2o----->Diffusion (Enter
the Data on the Table for D_{i,k})---->Model Inputs---->u
list: Darcy's velocity field (dl/dlm1)---->T--->p: Pressure
(dl/dlm1)----> p_{ref}: p_atm.
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Porous Electrode Coupling 1 Use a porous electrode coupling to
create a mass sink in the
domain corresponding to the oxygen leaving the gas phase due to
the electrochemical reactions.
Physics Toolbar---->Domains---->Porous Electrode
Coupling----->Domain Selection: Porous Electrode.
Reaction Coefficients 1 Model Builder----->Component
1---->Transport of
Concentrated Species---->Porous Electrode Coupling 1----->
Reaction Coefficients----> Model Inputs---->i_{v}: Local
current source (siec/pce1/per1)----> Stoichiometric
Coefficients: n_{m}=4 ------> \nu_{wo2}= -1 (Oxygen is consumed
during the Rxn).
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Model Builder----->Component 1---->Transport of
Concentrated Species ----> Initial Values 1-----> Initial
Values: w_o2_ref, w_h2o_ref.
Initial Values 1
Inflow 1
Physics
Toolbar------>Boundaries----->Inflow----->Bondary
Selection: Inlet----->Inflow: w_o2_ref, w_h2o_ref.
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Model Builder---->Component 1---->Darcy's
Law----->Domain Selection------>Selection list: Porous
Electrode.
Darcy's Law: Now do the settings for Darcy's law. Also here the
electrochemical currents will result in a mass sink due to the
oxygen molecules leaving the domain.
Fluid and Matrix Properties 1 Model Builder----->Darcy's
Law---->Fluid and Matrix
Properties 1---->Fluid Properties----->Density: User
Defined: chcs.rho----> Dynamic viscosity: User Defined: mu
----->Matrix Properties: e_por--->permeability
(\kappa)=perm.
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Physics toolbar----->Domains---->Porous Electrode
Coupling------>Domain Selection----->Selection List: Porous
Electrode------>Species: Add, Add--->Species Table:
Porous Electrode Coupling 1
Reaction Coefficients 1 Model Builder---->Porous Electrode
Coupling 1-----
>Reaction Coefficients 1----->Model
Inputs---->i_{v}:Local current source
(siec/pce1/per1)------>Stoichiometric
Coefficients---->n_{m}=4---->\nu_{2}=-1.
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Physics toolbar---->Boundaries---->Inlet----->Boundary
Selection---->Selection List: Inlet----->U_{0}: v_in.
Inlet 1
SECONDARY CURRENT DISTRIBUTIONPorous Electrode Reaction 1:
Finalize the physics settings by modifying the porous electrode
reaction current density to depend on the oxygen concentration.
Model Builder----->Component 1---->Secondary Current
Distribution---->Porous Electrode 1----->Porous Electrode
Reaction 1-----> Electrode Kinetics----->Kinetics expression
type: Concentration dependent kinetics----->
C_{0}=chcs.c_w_o2/c_o2_ref (chcs.c_w_o2 is the molar concentration
variable defined by the Transport of Concentrated Species
interface).
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Study Toolbar---->Study
Steps---->Stationary---->Physics and Variables
Selection---->Table:
STUDY 1: Add a second study step that solves for all physics.
Modify the first study step so that it only solves for the current
distribution interface.
Step 1: Stationary
Home Toolbar---->Compute (=).
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We notice that there is a higher Overpotential at the inlet, but
the variation is not very large over the porous electrode because
of its conductivity.
RESULTS: Considering now the presence of Oxygen and its
reduction-reaction.
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We notice that the current density (at the electrolyte) is
higher at the inlet and decreases as the distance from the inlet
increases. The reaction rate (proportional to the current density)
is related to both the local overvoltage and the concentration of
oxygen, and since the local overvoltage is rather even, we expect
the concentration of oxygen to show a dependence similar to that
exhibited by the current density.
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Results------>Add Plot Group---->3D Plot
Group---->Results: 3D Plot Group 5----->Isosurface:
Expression----->Replace Expression: Mass fraction
(w_o2)------>Levels: Total Levels =
10------>Plot----->Rename 3D Plot Group: Oxygen Mass
Fraction.
3D Plot Group 5: Create a plot of the mass fraction of oxygen in
the gas phase as follows.
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Results------>Add Plot Group---->3D Plot
Group--->Results---->3D Plot Group 6---->Slice
----->Slice: Expression------>Replace Expression: Darcy's
velocity magnitude (dl.U).
Right click Results----->3D Plot Group 6----->Slice
1----->Duplicate---->Plane
Data----->zx-planes----->Inherit style section------>Plot
List: Slice 1------>Plot----->Rename 3D Plot Group: Oxygen
Mass Fraction.
3D Plot Group 6: Create a slice plot of the gas velocity
magnitude as follows.
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Variantes q se pueden realizar: Change the geometrical
arrangement: the size and shape of
the inlet. Change the Parameters (modify the text-file). The
surface
Specific Area is very important and depend on the
nanomaterial.
Material Properties: change conductivities of the free
electrolyte, porous electrode and pore-electrolyte. We can also
change the porosity and permeability (material-dependent).
Change the Discretization of the Mesh (Both are equivalent) to
improve accuracy.
Change the kinetics....perhaps...but Maxwell-Stefan is the best
suited for this system. However the M-S Diffusivity matrix can be
analyzed in more detail.
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