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

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.

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.

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.

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.

Results presented Isosurfaces of the weight fraction of oxygen at a total

potential drop over the modeled domain of 190 mV.

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.

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.

The local overvoltage is rather even because the porous electrode is a conductor.

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.

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.

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.

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.

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.

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.

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.

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.

Your overpotential plot should now look like this (We have not included the effects of mass transport yet):

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".

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.

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(=)

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!

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.

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.

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).

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.

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.

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.

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).

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 (=).

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.

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.

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.

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.

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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