Thorough Example: The Busbar
Electrical Heating in a Busbar
In order to get acquainted with COMSOL Multiphysics, it is best to work through a basic example step by step. The directions in this section will cover the essential components of the model building procedure, highlighting several features and demonstrating common simulation tasks along the way. At the end, you will have completed building a truly multiphysics model.
The model that you will create analyzes a busbar designed to conduct
a direct current from a transformer to an electric device (see below).
The current conducted in the busbar, from bolt 1 to bolts 2a and 2b,
produces heat due to the resistive losses, a phenomenon referred to as
Joule heating. The busbar is made of copper while the bolts are made of
titanium. This choice of materials is important since titanium has a
lower electric conductivity than copper and will be subjected to a
higher current density.
The goal of your simulation will be to precisely calculate how much the busbar will heat up. Once you have captured the basic multiphysics phenomena, you will also have the chance to investigate thermal expansion yielding structural stresses and strains in the busbar and the effects of cooling by an air stream.
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. 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.
Model Wizard
Start COMSOL by double-clicking its icon on the desktop.
When the Model Wizard
opens, select a space dimension; the default is 3D. Click the Next button 
to continue to the physics page.
In the Add Physics
step, click the Heat Transfer
folder, right-click Joule Heating
and Add Selected.
Click the Next button 
.
The last Model Wizard step is to select the Study Type.
Select the Stationary
study type and click the Finish
button 
. Any selection from the Custom
Studies list needs manual fine-tuning.
Preset Studies contains studies that have solver and equation settings adapted to the Selected physics, in this example, Joule Heating.
Global Definitions
If you are planning to draw the geometry in detail, define the
parameters in this section. If you plan to load the geometry from a
file, you can browse through this section briefly and skip to “Geometry”
on page 11.
The Global Definitions in the Model Builder stores Parameters, Variables, and Functions with a global scope. You can use these operations in several Models. In this case, there is only one Model 1 node where the parameters are used.
Since you will run a geometric parameter study later in the example, define the geometry using parameters from the start. Do this by entering parameters for the length for the lower part of the busbar, L, the radius of the titanium bolts, rad_1, the thickness of the busbar, tbb, and the width of the device, wbb.
Also add the parameters that will control the mesh, mh, a heat transfer coefficient for cooling by natural convection, htc, and a value for the voltage across the busbar, Vtot.
Right-click Global Definitions
and select Parameters to create a
list of parameters In the Parameters
table, click the first row under Name and
enter L.
Click the first row under Expression
and enter the value of L, 9[cm].
Note that you can enter any unit inside the square brackets.
Continue adding the other parameters: L,
rad_1, tbb,
wbb, mh, htc, and Vtot
according to the Parameters
list.
It is a good idea to type in descriptions for variables, in case you forget or share the model with others.
Geometry
Here you can take a shortcut by loading the model geometry from the Model Library.
Open the Model Library
from the File menu.
In the Model Library, select COMSOL Multiphysics>Multiphysics>busbar_geom
and then click Open.
Alternatively, you can construct the busbar geometry using the parameters entered above with the COMSOL geometry tools. If you would like to see this now, have a look at “Geometry Sequences” on page 77.
Once you have created or imported the geometry, experimenting with different dimensions is easy: update the values of L, tbb, or wbb, and rerun the geometry sequence.
Under Global Definitions
click Parameters. In the Settings window, select the wbb parameter’s Expression
column and enter 10[cm] to change the
value of the width wbb.
In the Model Builder,
click the Form Union node 
and then the Build All button 
to
rerun the geometry sequence.
In the Graphics toolbar click the Zoom Extents button 
. You should get a wider busbar.
Left-click and drag in the Graphics window to rotate the
busbar. Right-click and drag to move it. Center-click and drag to zoom
in and out. To get back to the original position, click the Go to Default 3D View button 
on
the Graphics toolbar.
Return to the Parameters
table and change the value of wbb back to
5[cm].
In the Model Builder, click
the Form Union node 
and then the Build All button 
to
rerun the geometry sequence.
On the Graphics toolbar, click the Zoom
Extents button 
.
Now save you work up to this point as busbar.mph.
Experienced users of other CAD programs are already familiar with this approach since all major CAD platforms include parameterized geometries. To support this class of users and to avoid redundancy, COMSOL offers the LiveLink™ family of products. These products connect COMSOL Multiphysics directly with a separate CAD program, so that all parameters specified in CAD can be interactively linked with your simulation geometry. The current product line includes LiveLink™ interfaces for SolidWorks®, Inventor®, and Pro/ENGINEER®.
It is also worth noting that the LiveLink™ interface for Matlab® is available for those who want to incorporate a COMSOL Multiphysics model into an extended programming environment.
Having completed the geometry for your model, it is time to define the materials.
Materials
The Materials node administrates the material properties for all physics and all domains in a Model node. The busbar is made of copper, and the bolts are made of titanium. Both these materials are available from the Built-In material database.
In the Model Builder,
right-click Materials and select
Open Material Browser.
In the Material Browser,
expand the Built-In materials
folder, right-click Copper and
select Add Material to Model.
Click the Material Browser
window tab, and scroll down to Titanium
beta-21S in the Built-In material
folder and add this material to the model.
In the Model Builder,
collapse the Geometry 1 node to
get a better overview of the model.
Under the Materials
node, click Copper.
In the Settings window,
locate the Material Contents
section.
The Material Contents section provides useful feedback on the model’s
material property usage. Properties that are both required by the
physics and available from the material are marked with a green check
mark 
. Properties required by the physics but missing in the
material will result in an error and are therefore marked with a stop
sign 
. A property that is not used in the model is unmarked.
You may note that the Coefficient of thermal expansion at the bottom of the list is not used, but you will need it later for expanding your model with heat induced stresses and strains. Since you added the Copper material first, all parts will by defaults have copper material assigned. In the next step you will assign Titanium properties to the bolts, which will override the Copper material assignment for those parts.
In the Model Builder,
click the Titanium beta-21S node.
Select All Domains in
the Selection list and then click
Domain 1. Click the Remove from Selection button 
.
Cross-check: Domains 2, 3, 4, 5, 6, and 7.
Be sure to investigate the Material
Contents section in the Settings
window. All the properties used by the physics interfaces should have a
green check mark 
.
Close the Material Browser.
Physics
The domain settings for the Joule Heating physics interface are complete now that you have set the material properties for the different domains. Next you will set the proper boundary conditions for the heat transfer problem and the conduction of electric current.
In the Model Builder,
expand the Joule Heating node to
examine the default physics interface nodes.
Joule Heating Model 1 contains the settings for heat conduction and current conduction. The heating effect for Joule heating is set in Electromagnetic Heat Source 1. Thermal Insulation 1 contains the default boundary condition for the heat transfer problem and Electric Insulation 1 corresponds to the conservation of electric current. Initial Values 1 contains initial guesses for the nonlinear solver for stationary problems and initial conditions for time-dependent problems.
Right-click the Joule Heating
node. In the second section of the context menu—the boundary
section—select Heat Transfer >Heat
Flux.
In the Settings window,
select All boundaries in the Selection list.
Assume that the circular bolt boundaries are neither heated nor cooled by the surroundings. Therefore we will in the next step remove them from the heat flux selection list, which leaves them with the default insulating boundary condition for Heat Transfer interfaces.
Rotate the busbar to inspect the back. Click one of the
circular titanium bolt surfaces to highlight it in green. Right-click
anywhere in the Graphics window
to remove this boundary from the Selection
list. Repeat this for the other two bolts.
Cross-check: Boundaries 8, 15, and 43 are removed from the Selection list.
In the Settings window,
click the Inward heat flux radio
button. Enter htc in the Heat transfer coefficient field, h.
Continue by setting the boundary conditions for the electric current.
In the Model Builder,
right-click the Joule Heating
node. In the second section of the context menu—the boundary
section—select Electric
Currents>Electric Potential.
Click the circular face of the upper titanium bolt to
highlight it and right-click anywhere to add it to the Selection list.
Cross-check: Boundary 43.
In the Settings window,
enter Vtot in the Voltage field.
The last step in the physics settings is to set the two remaining bolt surfaces to ground.
In the Model Builder,
right-click the Joule Heating
node. In the boundary section of the context menu, select Electric Currents>Ground.
n the Graphics window,
click one of the remaining bolts to highlight it. Right-click anywhere
to add it to the Selection list.
I
Repeat this procedure for the last bolt.
Cross-check: Boundaries 8 and 15.
Click the Go to Default 3D
View button 
on the Graphics
toolbar.
Mesh
The simplest way to mesh is to create an unstructured tetrahedral mesh. This will do nicely for the busbar. You can also create several mesh sequences, see “Mesh Sequences” on page 44.
In the Model Builder,
right-click the Mesh 1 node and
select Free Tetrahedral. Click
the Size node 
.
In the Settings window,
select the Custom button under Element Size. Enter mh in the Maximum
element size field. Enter mh-mh/3
in the Minimum size edit field,
and enter 0.2 in the Resolution of curvature field.
Note that mh is 6 mm—the value entered earlier as a global parameter.
Click the Build All
button 
to create the mesh.
Study
To run a simulation, in the Model
Builder, right-click Study 1
and select Compute 
.
The Study node automatically defines a solution sequence for the simulation based on the selected physics and the study type.
The simulation only takes a few seconds to solve.
Results
The default plot displays the temperature in the busbar. 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. The temperature is substantially higher
than the ambient temperature 293 K.
Left-click and drag in the Graphics window to rotate the
busbar and visualize the back side.
Click the Go to Default 3D
View button 
on the Graphics
toolbar to go back to the default view.
You can change the Range of the color table to visualize the temperature difference in the copper part.
Click 3D Plot Group
1>Surface 1. In the Settings
window, under Range, select the Manual color range check box. Enter 323 in the Maximum
field.
Click the Plot button 
.
With this solution in hand, you can create an image that will be displayed by COMSOL when browsing for model files.
Go to the File menu and select Save Model Image.
There are two other ways to create images from this plot. One way is
to use the Image Snapshot button 
in the Graphics toolbar for directly creating an image, and
another is to add an Image node 
to the Report by right-clicking the Plot Group of interest.
The second option lets you reuse the Image Settings if you update the
model.
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.
Another plot of interest shows the current density in the device.
In the Model Builder,
right-click Results and select 3D Plot Group.
Right-click 3D Plot Group 3
and select Surface.
In the Settings window,
in the Expression section, click
the Replace Expression button 
.
Select Electric Currents>Current
density norm (jh.normJ). This is the variable for the magnitude,
or absolute value, of the current density vector.
Click the Plot button 
.
The resulting plot is almost uniform due to the high current density
at the contact edges with the bolts. Left-click and drag the busbar in
the Graphics window to view the back side.
Click the Go to Default 3D View
button 
on the Graphics
toolbar. Change the Range of the color table in the Settings window to
visualize the current density distribution.
Under Range, select the
Manual color range check box.
Enter 1e6 in the Maximum field. Click the Plot button 
. Save the model as busbar.mph.
This plot shows how the current takes the shortest path in the
90-degree bend in the busbar. Moreover, the edges of the busbar outside
of the bolts are hardly utilized for current conduction.
Rotate the device to show the back of the busbar where you
will see the high current density around the contact surfaces of the
bolts.
Continue the exercise by adding your own plots and investigating ways of generating cross section plots and cross section line plots.
Now you have completed a basic multiphysics simulation. The following sections are designed to increase your understanding of the steps you implemented up to this point as well as to extend your simulation to include other relevant effects, like thermal expansion and fluid flow.
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