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Electrical Heating in a Busbar Assembly
Introduction
This tutorial analyzes the anode to busbar coupling designed to conduct a direct current from a current source to the anode in an electrolysis process, such as the chlor alkali process for the production of chlorine and sodium. The current that passes from the intercell busbar to the anode produces heat due to the resistive losses, a phenomenon referred to as Joule heating. The Joule heating effect is described by conservation laws for electric current and energy. Once solved for, the two conservation laws give the temperature and electric field, respectively.
The geometry for the simulation, displayed in Figure 1, includes the coupling components for one cell, and a section of the intercell busbar that is connected to the power source. It consists of the top of the anode with four central columns holding copper rods attached to copper bars.
Figure 1: The geometry of the anode to busbar coupling used in this example.
When designing the coupling to the busbar it is important to aim for a low operational temperature for the copper components to avoid excessive oxidation and to maintain a high electrical conductivity. The goal of your simulation is to precisely calculate how much the busbar heats up, and to study the influence of two design parameters, the diameter of the rods rising from the top of the anode and the width of the copper connectors that link to the intercell busbar, on the phenomenon. By conducting a parametric sweep you can determine which combinations of these parameters result in a maximum temperature in the copper components should preferably be less than 90°C. Above this temperature the oxidation rate of copper starts to increase.
Model Definition
The intercell busbar, the various connector bars, and the rods rising from the anode are made of copper. For the components of the anode and the bolts that hold the copper busbars together, choose titanium assuming a highly corrosive environment.
All surfaces, except the anode bottom surface in contact with the electrolyte and the grounded surfaces of the intercell busbar, are cooled by natural convection in the air surrounding the busbar. Use the convective heat flux boundary condition for the purpose, assuming a cell room temperature of to 35°C. The same boundary condition is applied at the bottom surface of the anode, where the temperature of the surrounding electrolyte is set to 100°C. The intercell busbar cross section boundaries do not contribute to cooling or heating of the device. The electric potential at these boundaries is 0 V. At the bottom surface of the anode the normal current density is set to 8000 A/m2.
Figure 2: Boundary settings in the model.
Results and Discussion
The plot shown in Figure 3 displays the temperature in the device, which is substantially higher than the ambient temperature of 35°C. The highest temperature is experienced by the titanium parts in contact with the hot electrolyte. For the copper components, the temperature variation is largest in the copper rods.
Figure 3: Temperature distribution in the busbar.
The temperature distribution is symmetric with a vertical mirror plane running through the anode at a right angle to the intercell busbar. In this case, the model does not require much computing power and you can model the whole geometry. For more complex models, you should consider using symmetries in order to reduce the size of the model.
Increasing the diameter of the copper rod and the width of the connector rods, while keeping the applied current density constant, leads to a lower temperature in the device. While the increased cross-sectional area leads to more heat produced by resistive losses, there is an even larger increase in the cooling effect as the total surface area increases, resulting in the lowering of the temperature.
By plotting the maximum temperature in the copper components against the diameter and width parameters, and formatting the plot according to Figure 4, you can easily determine the combinations of the diameter and width parameters that lead to an acceptable value of the maximum temperature.
Figure 4: Maximum temperature in the busbar assembly plotted against the rod diameter and the connector width parameters, and formatted to show the parameter combinations that lead to a maximum temperature of less than 90°C.
Application Library path: COMSOL_Multiphysics/Multiphysics/busbar_assembly
Modeling Instructions
COMSOL Desktop
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Heat Transfer>Electromagnetic Heating>Joule Heating.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Geometry 1
The geometry sequence for this model is inserted to focus on the physics setup and the parametric sweep. This also inserts the parameters required for creating the geometry.
1
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
2
Browse to the model’s Application Libraries folder and double-click the file busbar_assembly_geom_sequence.mph.
3
In the Insert Sequence dialog box, select Geometry 1 in the Select geometry sequence to insert list.
4
Click OK to insert the finalized geometry.
5
In the Geometry toolbar, click  Build All.
The inserted geometry sequence is created using geometry parts. In another version of the busbar the geometry sequence is instead structured by group nodes. Both busbar versions contain the same selections and parameters, but illustrate different ways of creating the geometry. To insert the alternative geometry sequence, browse to COMSOL Multiphysics/Multiphysics/busbar_assembly_groups_geom_sequence.mph.
Global Definitions
Parameters 1
Global parameters in a model allow you to parameterize settings and can be controlled by the parametric solver to perform parametric sweeps.
Continue with loading additional parameters for setting up the physics.
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 busbar_assembly_parameters.txt.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Copper.
4
Click Add to Component in the window toolbar.
Materials
Copper (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Copper.
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in>Titanium beta-21S.
3
Click Add to Component in the window toolbar.
4
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Titanium beta-21S (mat2)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Titanium.
Electric Currents (ec)
Ground 1
1
In the Model Builder window, under Component 1 (comp1) right-click Electric Currents (ec) and choose Ground.
2
In the Settings window for Ground, locate the Boundary Selection section.
3
From the Selection list, choose Grounded boundary (Intercell busbar 1).
Normal Current Density 1
1
In the Physics toolbar, click  Boundaries and choose Normal Current Density.
2
In the Settings window for Normal Current Density, locate the Boundary Selection section.
3
From the Selection list, choose Electrolyte boundary (Cell grid top 1).
4
Locate the Normal Current Density section. In the Jn text field, type Jan.
Heat Transfer in Solids (ht)
In the Model Builder window, under Component 1 (comp1) click Heat Transfer in Solids (ht).
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Heat flux boundaries.
4
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
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In the h text field, type htca.
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In the Text text field, type Ta.
Heat Flux 2
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Electrolyte boundary (Cell grid top 1).
4
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
5
In the h text field, type htce.
6
In the Text text field, type Te.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Sequence Type section.
3
From the list, choose User-controlled mesh.
Size
1
In the Model Builder window, under Component 1 (comp1)>Mesh 1 click Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Element Size Parameters section. In the Minimum element size text field, type mh.
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Click  Build All.
Study 1
Parametric Sweep
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
From the list in the Parameter name column, choose the rod diameter r_d.
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Click  Range.
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In the Range dialog box, type 16[mm] in the Start text field.
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In the Step text field, type 2[mm].
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In the Stop text field, type 20[mm].
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Click Replace.
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In the Parameter unit column, enter mm.
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In the Settings window for Parametric Sweep, locate the Study Settings section.
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Click  Add.
13
From the list in the Parameter name column, choose the width of the angle connector a_c_w.
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Click  Range.
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In the Range dialog box, type 60[mm] in the Start text field.
16
In the Step text field, type 10[mm].
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In the Stop text field, type 90[mm].
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Click Replace.
19
In the Parameter unit column, enter mm.
As the last step before computing the solution, configure the sweep to include all combinations of the two parameters.
20
In the Settings window for Parametric Sweep, locate the Study Settings section.
21
From the Sweep type list, choose All combinations.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1 node, then click Segregated 1.
4
In the Settings window for Segregated, locate the General section.
5
From the Stabilization and acceleration list, choose Anderson acceleration.
6
In the Study toolbar, click  Compute.
Results
Temperature (ht)
1
In the Model Builder window, under Results click Temperature (ht).
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
From the Color list, choose Gray.
Surface
1
In the Model Builder window, expand the Temperature (ht) node, then click Surface.
2
In the Settings window for Surface, locate the Expression section.
3
From the Unit list, choose degC.
4
Locate the Coloring and Style section. Click  Change Color Table.
5
In the Color Table dialog box, select Thermal>HeatCameraLight in the tree.
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Click OK.
7
In the Temperature (ht) toolbar, click  Plot.
8
You should now see a plot similar to the one in Figure 3.
Definitions
Add a domain probe to calculate the average temperature increase from ambient temperature in the device.
Domain Probe 1 (dom1)
1
In the Definitions toolbar, click  Probes and choose Domain Probe.
2
In the Settings window for Domain Probe, locate the Probe Type section.
3
From the Type list, choose Maximum.
4
Locate the Source Selection section. From the Selection list, choose Copper.
5
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Heat Transfer in Solids>Temperature>T - Temperature - K.
6
Locate the Expression section. From the Table and plot unit list, choose degC.
7
Click  Update Results.
Table
1
Go to the Table window.
2
Click Table Surface in the window toolbar.
A plot similar to the one displayed below appears.
Results
In the last few steps you can add annotations and format the plot to make it easier to read which parameter combinations result in an accepted temperature increase.
Table Surface 2
1
In the Model Builder window, under Results>2D Plot Group 6 right-click Table Surface 1 and choose Duplicate.
2
In the Settings window for Table Surface, click to expand the Title section.
3
From the Title type list, choose None.
4
Click to expand the Range section. Select the Manual data range check box.
5
In the Maximum text field, type 90.
6
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
7
From the Color list, choose Green.
Table Surface 1
1
In the Model Builder window, click Table Surface 1.
2
In the Settings window for Table Surface, locate the Range section.
3
Select the Manual data range check box.
4
In the Minimum text field, type 90.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
2D Plot Group 6
1
In the Model Builder window, click 2D Plot Group 6.
2
In the Settings window for 2D Plot Group, locate the Plot Settings section.
3
Select the x-axis label check box. In the associated text field, type Rod diameter (r_d) (mm).
4
Select the y-axis label check box. In the associated text field, type Angle connector width (a_c_w) (mm).
Annotation 1
1
Right-click 2D Plot Group 6 and choose Annotation.
2
In the Settings window for Annotation, locate the Data section.
3
From the Dataset list, choose Domain Probe 1.
4
Locate the Annotation section. In the Text text field, type $T_\max\ >\ 90 \degree \mathrm{C}$.
5
Locate the Position section. In the x text field, type 16.8[mm].
6
In the y text field, type 69[mm].
7
Locate the Annotation section. Select the LaTeX markup check box.
8
Locate the Coloring and Style section. Clear the Show point check box.
Annotation 2
1
Right-click 2D Plot Group 6 and choose Annotation.
2
In the Settings window for Annotation, locate the Data section.
3
From the Dataset list, choose Domain Probe 1.
4
Locate the Annotation section. In the Text text field, type $T_\max\ <\ 90 \degree \mathrm{C}$.
5
Locate the Position section. In the x text field, type 18.2[mm].
6
In the y text field, type 79[mm].
7
Locate the Annotation section. Select the LaTeX markup check box.
8
Locate the Coloring and Style section. Clear the Show point check box.
9
In the 2D Plot Group 6 toolbar, click  Plot.
The plot in the Graphics window should now look similar to the one in Figure 4.