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Zinc Bromine Redox Flow Battery
Introduction
The zinc bromine redox flow battery is an electrochemical energy storage technology suitable for stationary applications.
Compared to other flow battery chemistries, the Zn-Br cell potentially features lower cost, higher energy densities and better energy efficiencies.
In the cell during charge, zinc metal is deposited on the negative electrode, whereas bromine is produced on the positive electrode. The electrolyte in the two porous electrodes compartments is continuously replaced in the cell by the use of external pumps and recirculation tanks as depicted in Figure 1. A separator of low permeability separates the two electrode compartments. During discharge of the cell, the bromine stored in the positive electrolyte tank and the zinc deposited in the negative electrode are consumed.
This tutorial models the cell voltage, as well as the bromine and zinc production-consumption, during a charge-discharge cycle. The model is mainly based on the experimental work and results described in Ref. 1, with some additional model parameters taken from Ref. 2.
Figure 1: Working principle of a zinc bromine redox flow battery.
Model Definition
Figure 2 shows the model geometry. The geometry consists of three rectangular domains, a negative (left-hand side) carbon felt porous electrode, a separator (center), and a positive (right-hand side) carbon felt porous electrode. On the positive side, the electrolyte (posolyte) enters the cell from the bottom and exits the cell at the top.
The bromine-containing posolyte exiting the cell passes an external tank, and is then reinserted at the posolyte cell inlet at a constant volumetric flow rate. Note that in a real cell there is also a recirculation tank for the negative side (see Figure 1). Negative recirculation is however neglected in this model.
Figure 2: Model Geometry.
During charge in the negative porous electrode, zinc metal is deposited according to
(1)
In the positive porous electrode, bromine is produced according to
(2)
Bromine would normally be evolved as a gas, but due to the presence of a complexing agent Q, a complex is formed
(3)
This second complexing reaction step is assumed to be fast and at equilibrium, and the complexing agent Q is assumed to be excess. When referring to Br2 or bromine in the reminder of this document, we hence actually refer to the complexed form of bromine, Br2Q.
The model solves for the electrolyte phase potential and the concentration of the complexed form of bromine in the electrolyte in all three domains using transport equations based on Ohm’s law and the Nernst–Planck equations, respectively. A supporting electrolyte assumption is made, treating all other species concentrations in the electrolyte as constants as well as the electrolyte conductivity. In the two porous electrode domains, also the electrode phase potential is solved for using Ohm’s law.
As mentioned above, convection effects and the corresponding recirculation tank on the negative side are neglected in this tutorial. Convection effects are also neglected in the separator due to a low permeability. In the positive electrode, a uniform velocity in the y direction is assumed.
Due to the lower potential of the negative electrode, bromine is assumed to be instantly oxidized when reaching the negative electrode-separator boundary, setting the Br2 concentration to 0. The corresponding current density, calculated by Faraday’s law of electrolysis, is added as a boundary current density to the charge balance equations.
The left-hand side negative current collector boundary is grounded, whereas at the corresponding positive boundary an average current density boundary condition is applied, featuring a 30 min charge at a constant current density followed by a discharge at an equal current density magnitude.
Tank Model
Assuming a well-mixed system, the recirculation tank is modeled by using an ordinary differential equation, solving for a global dependent variable for the tank concentration of bromine, ctank (mol/m3):
(4)
Here, Vtank is the tank volume (m3), c is the concentration of bromine in the cell (mol/m3), n is the normal vector at the boundary, and u is the convective flow velocity vector (m/s). Furthermore, δΩin and δΩout are the posolyte inlet and outlet boundaries, respectively.
The above expression is valid for the case when the nonconvective parts of the molar flux at the inlet and outlet fluxes are zero. This is accomplished in the electrolyte transport model by the use of a Danckwerts inflow condition at the inlet and an outflow condition at the outlet.
Results and Discussion
Figure 3 shows the cell voltage versus time for various constant current charge/discharge current densities. The cell voltages during the 30 min charging period feature a flat, constant, voltage profile, whereas there is a pronounced decline in voltage towards the end of the discharge period. The voltage curves also feature higher polarization for higher currents, stemming from the ohmic and electrode activation voltage losses in the cell, which increase with a higher current density level.
Figure 3: Cell voltage versus time for various current densities.
Figure 4 depicts the tank concentration levels of bromine versus time for the various current density levels. The levels vary linearly with time. At the end of discharge, the tank concentration levels are not zero, indicating that it is not possible to completely discharge the cell at the chosen current density level.
Figure 4: Tank concentrations versus time for various current densities.
Figure 5 and Figure 6 show the bromine concentration levels in the cell at the end of the charging and the discharging periods, respectively. At the end of charge, the cell concentration is more or less uniform, but at the end of discharge, depletion of bromine becomes more severe for longer distances from the posolyte inlet.
Figure 5: Bromine concentration at the end of the 30 min charge at 40 mA/cm2.
Figure 6: Bromine concentration at the end of the discharge at 40 mA/cm2.
Figure 7: Electrode volume fraction change due to Zn(s) deposition at the end of the 30 min charge period.
Finally, Figure 7 shows the electrode volume fraction change at the end of charge as a result of the deposition of zinc metal. Due to current distribution effects, the highest amount of deposited zinc (2%) is found close to the current collector and separator boundaries. The almost symmetric deposition pattern is a result of the electrolyte and electrode conductivities having similar values in the model parameters.
References
1. S. Suresh, M. Ulaganathan, N. Venkatesan, P. Periasamy, and P. Ragupathy, “High performance zinc-bromine redox flow batteries: Role of various carbon felts and cell configurations,” J. Energy Storage, vol. 20, pp. 134–139, 2018.
2. Z. Xu, J. Wang, S.C. Yan, Q. Fan, and P.D. Lund, “Modeling of Zinc Bromine redox flow battery with application to channel design, J. Power Sources, vol. 450, p. 227436, 2020.
Application Library path: Battery_Design_Module/Flow_Batteries/znbr_flow_battery
Modeling Instructions
This tutorial consists of two parts. In the first part we will set up the electrochemical reactions, the electrolyte transport and the recirculation tank model, and solve for 1 h charge at a constant current. In the second part, we will add the deposition of zinc metal, as well as a charge-discharge current load profile, and solve for a range of different current loads.
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D.
2
In the Select Physics tree, select Electrochemistry>Tertiary Current Distribution, Nernst-Planck>Tertiary, Supporting Electrolyte (tcd).
3
Click Add.
In this tutorial, we will model the transport of one electrolyte species only (Bromine).
4
In the Number of species text field, type 1.
5
In the Concentrations table, enter the following settings:
cBr2
Also add an ODE interface which will be used for setting up the tank model.
6
In the Select Physics tree, select Mathematics>ODE and DAE Interfaces>Global ODEs and DAEs (ge).
7
Click Add.
8
Click  Study.
9
In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Tertiary Current Distribution, Nernst-Planck>Time Dependent with Initialization.
10
Click  Done.
Global Definitions
Parameters 1
Load some parameters from a text file.
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file znbr_flow_battery_parameters.txt.
Geometry 1
The geometry is composed of a single rectangle.
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type W_cell.
4
In the Height text field, type H_cell.
Use Layers to define the internal carbon felt and separator boundaries.
5
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (m)
Layer 1
W_cf
Layer 2
W_sep
6
Select the Layers to the right check box.
7
Clear the Layers on bottom check box.
8
Click  Build All Objects.
The finalized geometry should look as follows:
Definitions
Add some explicitly named selections. These will facilitate setting up the physics later on.
Separator
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Separator in the Label text field.
3
Select Domain 2 only.
Negative Carbon Felt
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Negative Carbon Felt in the Label text field.
3
Select Domain 1 only.
Positive Carbon Felt
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Positive Carbon Felt in the Label text field.
3
Select Domain 3 only.
Posolyte Inlet
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Posolyte Inlet in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 8 only.
Posolyte Outlet
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Posolyte Outlet in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 9 only.
Tertiary Current Distribution, Nernst-Planck (tcd)
Now start defining the current distribution part of the physics, beginning with the separator.
Separator 1
1
In the Model Builder window, under Component 1 (comp1) right-click Tertiary Current Distribution, Nernst-Planck (tcd) and choose Separator.
2
In the Settings window for Separator, locate the Domain Selection section.
3
From the Selection list, choose Separator.
4
Locate the Diffusion section. In the DcBr2 text field, type D_Br2.
5
Locate the Electrolyte Current Conduction section. From the σl list, choose User defined. In the associated text field, type sigmal.
6
Locate the Porous Matrix Properties section. In the εl text field, type epsl_sep.
Porous Electrode - Negative
Continue with the negative carbon felt electrode as follows:
1
In the Physics toolbar, click  Domains and choose Porous Electrode.
2
In the Settings window for Porous Electrode, type Porous Electrode - Negative in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Negative Carbon Felt.
4
Locate the Diffusion section. In the DcBr2 text field, type D_Br2.
5
Locate the Electrolyte Current Conduction section. From the σl list, choose User defined. In the associated text field, type sigmal.
6
Locate the Electrode Current Conduction section. From the σs list, choose User defined. In the associated text field, type sigmas_cf.
7
Locate the Porous Matrix Properties section. In the εs text field, type 1-epsl_cf.
8
In the εl text field, type epsl_cf.
Porous Electrode Reaction 1
Set up the zinc deposition reaction as follows:
1
In the Model Builder window, click Porous Electrode Reaction 1.
2
In the Settings window for Porous Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the n text field, type 2.
4
Locate the Equilibrium Potential section. In the Eeq,ref(T) text field, type Eeq_ref_Zn.
5
Locate the Electrode Kinetics section. In the i0,ref(T) text field, type i0_ref_Zn.
6
In the αa text field, type alpha_a_Zn.
7
Locate the Active Specific Surface Area section. In the av text field, type Av_cf.
Porous Electrode - Positive
1
In the Physics toolbar, click  Domains and choose Porous Electrode.
2
In the Settings window for Porous Electrode, type Porous Electrode - Positive in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Positive Carbon Felt.
In the separator and the negative electrode, the velocity is assumed to be 0. Set the electrolyte to flow at a constant rate in the y-direction in the positive carbon felt electrode as follows:
4
Locate the Convection section. Specify the u vector as
0
x
U
y
5
Locate the Diffusion section. In the DcBr2 text field, type D_Br2.
6
Locate the Electrolyte Current Conduction section. From the σl list, choose User defined. In the associated text field, type sigmal.
7
Locate the Electrode Current Conduction section. From the σs list, choose User defined. In the associated text field, type sigmas_cf.
8
Locate the Porous Matrix Properties section. In the εs text field, type 1-epsl_cf.
9
In the εl text field, type epsl_cf.
Porous Electrode Reaction 1
Set up the bromine redox reaction as follows:
1
In the Model Builder window, click Porous Electrode Reaction 1.
2
In the Settings window for Porous Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the n text field, type 2.
4
In the νcBr2 text field, type -1.
5
Locate the Equilibrium Potential section. In the Eeq,ref(T) text field, type Eeq_ref_Br.
6
Locate the Electrode Kinetics section. In the i0,ref(T) text field, type i0_ref_Br.
7
In the αa text field, type alpha_a_Br.
8
Locate the Active Specific Surface Area section. In the av text field, type Av_cf.
The domain physics settings for the current distribution model are now complete. Continue to define the boundary conditions.
The cell will be set to run galvanostatically, using the negative electrode as ground.
Electric Ground 1
1
In the Physics toolbar, click  Boundaries and choose Electric Ground.
2
Select Boundary 1 only.
Electrode Current 1
1
In the Physics toolbar, click  Boundaries and choose Electrode Current.
2
Select Boundary 10 only.
3
In the Settings window for Electrode Current, locate the Electrode Current section.
4
From the list, choose Average current density.
5
In the is,average text field, type i_app.
6
In the φs,bnd,init text field, type E_cell_init.
Internal Electrode Surface 1
Add the parasitic oxidation reaction of bromine at the negative electrode-separator boundary.
1
In the Physics toolbar, click  Boundaries and choose Internal Electrode Surface.
2
Select Boundary 4 only.
Electrode Reaction 1
1
In the Model Builder window, click Electrode Reaction 1.
2
In the Settings window for Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the n text field, type 2.
4
In the νcBr2 text field, type -1.
5
Locate the Equilibrium Potential section. In the Eeq,ref(T) text field, type Eeq_ref_Br.
6
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Fast irreversible electrode reaction.
Global ODEs and DAEs - Tank Model
Now define the tank model. The tank model will provide the inflow concentration to the posolyte inlet boundary.
1
In the Model Builder window, under Component 1 (comp1) click Global ODEs and DAEs (ge).
2
In the Settings window for Global ODEs and DAEs, type Global ODEs and DAEs - Tank Model in the Label text field.
Global Equations 1
Load the needed equation definitions from a text file.
1
In the Model Builder window, under Component 1 (comp1)>Global ODEs and DAEs - Tank Model (ge) click Global Equations 1.
2
In the Settings window for Global Equations, locate the Global Equations section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file znbr_flow_battery_global_equation.txt.
The imported expression is marked in orange, indicating a missing operator. Add the operator as follows:
Definitions
Integration - Posolyte Outlet
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type Integration - Posolyte Outlet in the Label text field.
3
In the Operator name text field, type intop_pos_out.
4
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
5
From the Selection list, choose Posolyte Outlet.
The intop_pos_out operator can now be used to integrate any variable along the posolyte outlet boundary.
Global ODEs and DAEs - Tank Model (ge)
Global Equations 1
The global equation expression is still marked in orange, indicating a unit error. Set the correct units as follows:
1
In the Model Builder window, under Component 1 (comp1)>Global ODEs and DAEs - Tank Model (ge) click Global Equations 1.
2
In the Settings window for Global Equations, locate the Units section.
3
Click  Select Dependent Variable Quantity.
4
In the Physical Quantity dialog box, type concentration in the text field.
5
Click  Filter.
6
In the tree, select General>Concentration (mol/m^3).
7
Click OK.
8
In the Settings window for Global Equations, locate the Units section.
9
Click  Define Source Term Unit.
10
In the Source term quantity table, enter the following settings:
Source term quantity
Unit
Custom unit
mol/s
Tertiary Current Distribution, Nernst-Planck (tcd)
Now go back to the current distribution model and set the inflow and outflow conditions.
1
In the Model Builder window, under Component 1 (comp1) click Tertiary Current Distribution, Nernst-Planck (tcd).
Inflow 1
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
In the Settings window for Inflow, locate the Boundary Selection section.
3
From the Selection list, choose Posolyte Inlet.
4
Locate the Concentration section. In the c0,cBr2 text field, type cBr2_tank.
5
Locate the Boundary Condition Type section. From the list, choose Flux (Danckwerts).
The Danckwerts condition will set an inflow molar flux based on the tank concentration and the electrolyte convective velocity. This will ensure that the amount of Bromine that enters domain equals that of what exits the tank.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
In the Settings window for Outflow, locate the Boundary Selection section.
3
From the Selection list, choose Posolyte Outlet.
To finalize the setup of the model, provide also initial values for potentials in the different domains. This will improve convergence of the Current Distribution Initialization study step.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the phil text field, type -Eeq_ref_Zn.
Initial Values 2
1
In the Physics toolbar, click  Domains and choose Initial Values.
2
In the Settings window for Initial Values, locate the Domain Selection section.
3
From the Selection list, choose Positive Carbon Felt.
4
Locate the Initial Values section. In the phil text field, type -Eeq_ref_Zn.
5
In the phis text field, type E_cell_init.
Mesh 1
A mapped mesh is suitable for this rectangular geometry.
Mapped 1
In the Mesh toolbar, click  Mapped.
Distribution 1
Use Distribution nodes to improve the mesh resolution in different parts of the geometry.
1
Right-click Mapped 1 and choose Distribution.
2
Select Boundaries 2 and 3 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 10.
6
In the Element ratio text field, type 4.
As you will see when inspecting the deposited zinc distribution (once the second part of the tutorial has been solved), a symmetric distribution in the x direction is suitable in the negative electrode.
7
Select the Symmetric distribution check box.
8
Click  Build Selected.
Distribution 2
1
In the Model Builder window, right-click Mapped 1 and choose Distribution.
2
Select Boundaries 5, 6, 8, and 9 only.
3
In the Settings window for Distribution, click  Build Selected.
Distribution 3
1
Right-click Mapped 1 and choose Distribution.
2
Select Boundaries 1 and 10 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
In the Number of elements text field, type 10.
5
Click  Build All.
Definitions
Before setting up the solver, add a probe to monitor the cell voltage while solving.
Global Variable Probe 1 (var1)
1
In the Definitions toolbar, click  Probes and choose Global Variable Probe.
2
In the Settings window for Global Variable Probe, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Tertiary Current Distribution, Nernst-Planck>tcd.phis0_ec1 - Electric potential on boundary - V.
The variable represents the electrode phase potential of the positive electrode current boundary. The variable is defined by the Electrode Current node. (The same variable will also be used in the second part of this tutorial for defining a stop expression for the solver.)
Study 1
The study you added at the beginning of the tutorial contains two study steps. The first step is only used to compute suitable potential initial values for the second time-dependent step.
Step 1: Current Distribution Initialization
Since we are using 0 as initial values for the bromine concentration in the cell, the equilibrium potential is not well-defined. Hence a primary current distribution cannot be calculated for the initial values.
1
In the Model Builder window, under Study 1 click Step 1: Current Distribution Initialization.
2
In the Settings window for Current Distribution Initialization, locate the Study Settings section.
3
From the Current distribution type list, choose Secondary.
The tank model should not be solved for in the first study step.
4
Locate the Physics and Variables Selection section. In the table, enter the following settings:
Physics interface
Solve for
Equation form
Tertiary Current Distribution, Nernst-Planck (tcd)
√
Automatic (Current distribution initialization)
Global ODEs and DAEs - Tank Model (ge)
 
Not applicable
Step 2: Time Dependent
Simulate the cell during a 1 h charge.
1
In the Model Builder window, click Step 2: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
From the Time unit list, choose h.
4
In the Home toolbar, click  Compute.
The model should take a few seconds to solve.
Results
Boundary Electrode Potential with Respect to Ground (tcd)
A number of default plots where created. Inspect the plots for the cell voltage, the bromine concentration and the tank concentration.
1
In the Boundary Electrode Potential with Respect to Ground (tcd) toolbar, click  Plot.
Concentration (tcd)
1
In the Model Builder window, click Concentration (tcd).
2
In the Concentration (tcd) toolbar, click  Plot.
1D Plot Group 8
1
In the Model Builder window, click 1D Plot Group 8.
2
In the 1D Plot Group 8 toolbar, click  Plot.
Tertiary Current Distribution, Nernst-Planck (tcd)
Now we start with the second part of the tutorial. First add the deposition of zinc metal as follows:
Porous Electrode - Negative
1
In the Model Builder window, under Component 1 (comp1)>Tertiary Current Distribution, Nernst-Planck (tcd) click Porous Electrode - Negative.
2
In the Settings window for Porous Electrode, click to expand the Dissolving-Depositing Species section.
3
Click  Add.
4
In the table, enter the following settings:
Species
Density (kg/m^3)
Molar mass (kg/mol)
Zn
rho_Zn
M_Zn
Note that the added the electrolyte volume fraction of deposited zinc is set to be subtracted from the electrolyte volume fraction by default.
Porous Electrode Reaction 1
Set up the stoichiometry for zinc deposition as follows:
1
In the Model Builder window, click Porous Electrode Reaction 1.
2
In the Settings window for Porous Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the Stoichiometric coefficients for dissolving-depositing species: table, enter the following settings:
Species
Stoichiometric coefficient (1)
Zn
1
Definitions
Next change the cell current profile to also include discharge. Use a step function for this.
Step 1 (step1)
1
In the Home toolbar, click  Functions and choose Local>Step.
2
In the Settings window for Step, locate the Parameters section.
3
In the From text field, type 1.
4
In the To text field, type -1.
5
Click to expand the Smoothing section. In the Size of transition zone text field, type 1.
6
Click  Plot.
Tertiary Current Distribution, Nernst-Planck (tcd)
This step function will now be used to reverse the current after completion of the charge period (30 min).
Electrode Current 1
1
In the Model Builder window, under Component 1 (comp1)>Tertiary Current Distribution, Nernst-Planck (tcd) click Electrode Current 1.
2
In the Settings window for Electrode Current, locate the Electrode Current section.
3
In the is,average text field, type i_app*step1((t-t_charge)/1[s]).
Study 1
Solver Configurations
Remove the old solver sequence. This will remove the old default plots, solvers and data sets pertaining to the old study. Also remove the old probe plot.
1
In the Model Builder window, under Study 1 right-click Solver Configurations and choose Delete Configurations.
Results
Probe Plot Group 9
In the Model Builder window, under Results right-click Probe Plot Group 9 and choose Delete.
Study 1
Parametric Sweep
Add a Parametric Sweep to perform the simulation for three different applied current density levels.
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
i_app (Applied current density)
10 20 40
mA/cm^2
Step 2: Time Dependent
Use a smaller step size to store the solution more often during the charge-discharge cycle. This will render smoother voltage vs time plots later on when post processing the solution.
1
In the Model Builder window, click Step 2: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
Click  Range.
4
In the Range dialog box, type 0.025 in the Step text field.
5
Click Replace.
Solution 1 (sol1)
Generate the solver sequence and modify it by adding a stop condition.
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
Right-click Study 1>Solver Configurations>Solution 1 (sol1)>Time-Dependent Solver 1 and choose Stop Condition.
4
In the Settings window for Stop Condition, locate the Stop Expressions section.
5
Click  Add.
Define the stop condition to terminate the simulation when the electrode phase potential of the positive electrode drops below 1.45 V.
6
In the table, enter the following settings:
Stop expression
Stop if
Active
Description
comp1.tcd.phis0_ec1<1.45[V]
True (>=1)
√
Stop expression 1
7
Locate the Output at Stop section. Clear the Add warning check box.
8
In the Study toolbar, click  Compute.
The model should take about a minute to solve, depending on computer.
Results
Cell Voltage vs Time
A number new default plots where created. Modify them as follows:
1
In the Settings window for 1D Plot Group, type Cell Voltage vs Time in the Label text field.
2
Click to expand the Title section. From the Title type list, choose None.
3
Locate the Plot Settings section. Select the y-axis label check box.
4
In the associated text field, type Cell voltage (V).
Global 1
1
In the Model Builder window, expand the Cell Voltage vs Time node, then click Global 1.
2
In the Settings window for Global, click to expand the Legends section.
3
From the Legends list, choose Evaluated.
4
In the Legend text field, type i<sub>app</sub>=eval(i_app/10) mA/cm<sup>2</sup>.
5
In the Cell Voltage vs Time toolbar, click  Plot.
Bromine Concentration
1
In the Model Builder window, under Results click Concentration (tcd).
2
In the Settings window for 2D Plot Group, type Bromine Concentration in the Label text field.
3
Click to expand the Title section. Find the Type and data subsection. Clear the Type check box.
Streamline 1
1
In the Model Builder window, expand the Results>Bromine Concentration node, then click Streamline 1.
2
In the Settings window for Streamline, click to expand the Title section.
3
From the Title type list, choose None.
4
Locate the Streamline Positioning section. From the Positioning list, choose On selected boundaries.
5
Locate the Selection section. From the Selection list, choose Posolyte Inlet.
6
Locate the Streamline Positioning section. In the Number text field, type 5.
Bromine Concentration
1
In the Model Builder window, click Bromine Concentration.
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Time (h) list, choose 0.5.
4
In the Bromine Concentration toolbar, click  Plot.
From the Time (h) list, choose the last stored time.
5
Click  Plot.
Tank concentration
1
In the Model Builder window, under Results click 1D Plot Group 8.
2
In the Settings window for 1D Plot Group, type Tank concentration in the Label text field.
Global 1
1
In the Model Builder window, expand the Tank concentration node, then click Global 1.
2
In the Settings window for Global, locate the Legends section.
3
From the Legends list, choose Evaluated.
4
In the Legend text field, type i<sub>app</sub>=eval(i_app/10) mA/cm<sup>2</sup>.
5
In the Tank concentration toolbar, click  Plot.
Tank concentration
1
In the Model Builder window, click Tank concentration.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
Deposited Zinc Volume Fraction
You may also add you own plots. Proceed as follows to plot the volume fraction of the deposited zinc layer.
1
In the Home toolbar, click  Add Plot Group and choose 2D Plot Group.
2
In the Settings window for 2D Plot Group, type Deposited Zinc Volume Fraction in the Label text field.
Surface 1
1
Right-click Deposited Zinc Volume Fraction and choose Surface.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Tertiary Current Distribution, Nernst-Planck>Dissolving-depositing species>tcd.deltaeps_pce1_Zn - Volume fraction change.
Deposited Zinc Volume Fraction
1
In the Model Builder window, click Deposited Zinc Volume Fraction.
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Time (h) list, choose 0.5.
4
Click to expand the Number Format section. Select the Manual color legend settings check box.
5
From the Notation list, choose Engineering.
6
In the Deposited Zinc Volume Fraction toolbar, click  Plot.