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Electrical Heating in a Busbar Introduction
The model that you create analyzes a busbar designed to conduct a direct current from
a transformer to an electrical device; see Figure 1. The current conducted in the busbar
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.
Figure 1: Photo of a busbar installation, and the geometry of the busbar used in this model.
The goal of your simulation is to precisely calculate how much the busbar heats up and to study the influence of a design parameter, the width of the device, on the
phenomenon.
Model Definition
The busbar is made of copper while the bolts are made of titanium. This choice of materials is important since titanium has a lower electrical conductivity than copper and is subjected to a higher current density.
All surfaces, except the bolt contact surfaces, are cooled by natural convection in the air surrounding the busbar. You can assume that the bolt cross-section boundaries do not contribute to cooling or heating of the device. The electric potential at the
upper-right vertical bolt surface is 20 mV, and that the potential at the two horizontal surfaces of the lower bolts is 0 V.
Copper Titanium Ground Electric potential: 20mV
All other boundaries: natural convection
Figure 2: Material and boundary settings in the model.
Results and Discussion
The plot shown in Figure 3 displays the temperature in the busbar, which is
substantially higher than the ambient temperature 293 K. The temperature difference in the device is less than 10 K, due to the high thermal conductivity of copper and titanium. The temperature variations are largest on the top bolt, which conducts double the amount of current compared to the two lower ones.
Figure 3: Temperature distribution in the busbar.
The color range of the plot in Figure 4 better illustrates the low temperature variation in the copper part of the device. The temperature distribution is symmetric with a vertical mirror plane running between the two lower titanium bolts and running across the middle of the upper bolt. 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.
Figure 4: Temperature distribution in the copper part of the busbar.
Increasing the width of the busbar while keeping the applied potential constant leads to a lower temperature in the device, as shown in Figure 5. 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.
Figure 5: Average temperature in the busbar plotted against its width.
Notes About the COMSOL Implementation
The busbar geometry you are using in this model comes from a Pro/ENGINEER assembly. The LiveLink interface for Pro/ENGINEER transfers the geometry from Pro/ENGINEER to COMSOL Multiphysics. Using the interface you are also able to update the dimension of the busbar in the Pro/ENGINEER file. In order for this to work you need to have both programs running during modeling, and you need to make sure that the busbar assembly file is the active file in Pro/ENGINEER.
Model Library path: LiveLink_for_ProENGINEER/Tutorial_Models/
busbar_llproe
Modeling Instructions
1In Pro/ENGINEER open the file busbar_assembly.asm, which you find if you browse to the model’s Model Library folder.
2Switch to COMSOL Multiphysics to start setting up the model.
M O D E L W I Z A R D
1Go to the Model Wizard window.
2Click Next.
3In the Add Physics tree, select Heat Transfer>Electromagnetic Heating>Joule Heating (jh).
4Click Next.
5In the Studies tree, select Preset Studies>Stationary.
6Click Finish.
G E O M E T R Y1
In the Model Builder window, expand the Model 1 node.
LiveLink for Pro/ENGINEER 1
1Right-click Model 1>Geometry 1 and choose LiveLink Interfaces>LiveLink for Pro/ ENGINEER.
2Go to the Settings window for LiveLink for Pro/ENGINEER.
3Locate the Synchronize section. Click the Synchronize button.
By this action you transfer the geometry of the busbar from Pro/ENGINEER to COMSOL Multiphysics.
G L O B A L D E F I N I T I O N S
Parameters
1In the Model Builder window, right-click Global Definitions and choose Parameters.
2Go to the Settings window for Parameters.
3Locate the Parameters section. Click Load from File.
4Browse to the model’s Model Library folder and double-click the file busbar_parameters.txt.
You need the width parameter, wbb, to set up the automatic parameter sweep. A parameter sweep can be over multiple parameters, and, although not detailed in this step by step instruction, you may also set up parameter sweeps to study for example the influence of the applied potential, Vtot, or the maximum mesh size parameter, mh.
M A T E R I A L S
1In the Model Builder window, right-click Model 1>Materials and choose Open Material Browser.
2Go to the Material Browser window.
3Locate the Materials section. In the Search edit field, type copper.
4Click the Search button.
5In the Materials tree, select Built-In>Copper.
6Right-click and choose Add Material to Model from the menu.
Copper
1In the Model Builder window, expand the Materials node, then click Copper.
2Select Domain 1, highlighted in the figure below.
3Go to the Material Browser window.
4Locate the Materials section. In the Search edit field, type titanium.
5Click the Search button.
6In the Materials tree, select Built-In>Titanium beta-21S.
7Right-click and choose Add Material to Model from the menu.
Titanium beta-21S
1In the Model Builder window, click Titanium beta-21S.
2Select Domains 2–4, highlighted in the figure below.
J O U L E H E A T I N G(J H)
Heat Flux 1
1In the Model Builder window, right-click Model 1>Joule Heating (jh) and choose the boundary condition Heat Transfer>Heat Flux.
2Go to the Settings window for Heat Flux.
3Locate the Boundaries section. From the Selection list, select All boundaries.
4Remove Boundaries 8,14, and 28, marked in the figure below, from the Selection list.
5Check that the Selection list contains all other boundaries, i.e. Boundaries 1–7, 9–13, and 15–27.
6Go to the Settings window for Heat Flux.
7Locate the Heat Flux section. Click the Inward heat flux button.
8In the h edit field, type htc.
Ground 1
1In the Model Builder window, right-click Joule Heating (jh) and choose the boundary condition Electric Currents>Ground.
2Select Boundaries 8 and 14, highlighted in the figure below.
Electric Potential 1
1In the Model Builder window, right-click Joule Heating (jh) and choose the boundary condition Electric Currents>Electric Potential.
2Select Boundary 28, highlighted in the figure below.
3Go to the Settings window for Electric Potential.
4Locate the Electric Potential section. In the V0 edit field, type Vtot.
M E S H1
In the Model Builder window, right-click Model 1>Mesh 1 and choose Free Tetrahedral.
Size
1In the Model Builder window, expand the Mesh 1 node, then click Size.
2Go to the Settings window for Size.
3Locate the Element Size section. Click the Custom button.
4Locate the Element Size Parameters section. In the Maximum element size edit field, type mh.
5In the Minimum element size edit field, type mh-mh/3.
6In the Resolution of curvature edit field, type 0.2.
7In the Model Builder window, right-click Mesh 1 and choose Build All.
S T U D Y1
In the Model Builder window, right-click Study 1 and choose Compute.
R E S U L T S
Temperature (jh)
1In the Model Builder window, expand the Results node.
2In the Model Builder window, expand the Temperature (jh) node, then click Surface 1. 3Go to the Settings window for Surface.
4Click to expand the Range section.
5Select the Manual color range check box.
6In the Maximum edit field, type 315.8.
G E O M E T R Y1
LiveLink for Pro/ENGINEER 1
1In the Model Builder window, click Model 1>Geometry 1>LiveLink Interfaces>LiveLink for Pro/ENGINEER 1.
2Go to the Settings window for LiveLink for Pro/ENGINEER.
3Click to expand the Parameters in CAD Package section.
4In the table, enter the following settings:
NAME VALUE
d6:0wbb
The entry in the Name column refers to the width dimension of the busbar in the Pro/ENGINEER file. The syntax, which includes the component (session) ID, assures that the correct dimension gets updated, since this is defined in the busbar.prt component (with ID 0) of the assembly you are synchronizing with. By entering the global parameter wbb in the Value column you enable the possibility to automatically trigger an update of the specified dimension as soon as the value of wbb changes during a parameter sweep.
S T U D Y1
Parametric Sweep
1In the Model Builder window, right-click Study 1 and choose Parametric Sweep.
2Go to the Settings window for Parametric Sweep.
3Locate the Study Settings section. Under Parameter names, click Add.
4Go to the Add dialog box.
5In the Parameter names list, select wbb (Width of busbar).
6Click the OK button.
7Go to the Settings window for Parametric Sweep.
8Locate the Study Settings section. Click the Range button.
9Go to the Range dialog box.
10In the Start edit field, type 40.
11In the Stop edit field, type 70.
12In the Step edit field, type 10.
13Click the Replace button.
©2011 C O M S O L 11 | E L E C T R I C A L H E A T I N G I N A B U S B A R
14In the Model Builder window, right-click Study 1 and choose Compute .R E S U L T S
G L O B A L D E F I N I T I O N S
1In the Model Builder window, right-click Model 1>Definitions and choose Probes>Domain Probe .
2In the Settings window, click Update Results .
R E S U L T S
Temperature (jh) 1
1In the Model Builder window, click Results>Temperature (jh) 1.
2Locate the Data section. In the Parameter value (wbb) drop-drown list you can select between the different values of wbb used during the parametric sweep. Select 50.3Click the Plot button.
4Click Temperature (jh) 1>Surface 1.
5Go to the Settings window for Surface.
6Locate the Range section. Adjust the slider for the Minimum value all the way to the left.
7In the Maximum edit field, type 323.5.
8Click the Plot button.
Probe 1D Plot Group 3
1In the Model Builder window, click Results>Probe 1D Plot Group 3.
2Go to the Settings
window for 1D Plot Group.
3Locate the Plot Settings section. In the x-axis label edit field, type busbar width
[mm].
.
4In the y-axis label edit field, type Average temperature [K]
12|E L E C T R I C A L H E A T I N G I N A B U S B A R©2011C O M S O L。