Introduction to COMSOL Multiphysics 4: Building a model

Adding Physics to a Model

COMSOL's distinguishing characteristics of adaptability and compatibility are prominently displayed when you add physics to an existing model. In this section, you will realize the ease with which this seemingly difficult task is performed. By following these directions, you can add structural mechanics and fluid flow to the busbar model.

Structural Mechanics

After completing the Joule heating simulation, you now know that there is temperature rise in the busbar. So it is logical to ask: What kind of mechanical stress is induced by thermal expansion? To answer this question, COMSOL Multiphysics makes it easy for you to expand your model to include the physics associated with structural mechanics. The following set of instructions, which requires the Structural Mechanics Module, shows you how to do this. If you are more interested in adding cooling by fluid flow, you can skip to the next section, “Fluid Flow” .

Open the model busbar.mph that you created earlier.

Adding Solid Mechanics

In the Model Builder, right-click the Busbar node and select Add Physics .

In the Model Wizard, select Structural Mechanics>Solid Mechanics. There are three ways to add this node: double-click, right-click and Add Selected, or click the Add Selected button .

Click the Finish button .

Save the model with a new name, busbar_II.mph. You will use it shortly.

When adding more physics interfaces, you need to make sure that any materials included in Materials have all the required properties for the selected physics interfaces. In this example, you know that all properties are available for copper and titanium.

You can start by adding the effect of thermal expansion to the structural analysis. Note that there is also a predefined multiphysics interface for thermal stresses and strains in the Structural Mechanics Module.

In the Model Builder, under Solid Mechanics, right-click the Linear Elastic Material Model 1 node and select Thermal Expansion.

On the Thermal Expansion page, under Thermal Expansion, select Temperature (jh/jh1) from the Temperature list.

This is the temperature field from the Joule Heating physics interface (jh/jhm1) and couples the Joule heating effect to the thermal expansion of the busbar.

Next, fix the busbar at the position of the titanium bolts.

In the Model Builder, right-click Solid Mechanics and select Fixed Constraint.

In the Graphics window, rotate the busbar to access the back. Click one of the bolts to highlight it and right-click to add the bolt to the Selection list. Repeat this procedure for the remaining bolts.

Cross-check: Boundaries 8, 15, and 43.

You can now update the Study to take the added effects into account.

Running a Study Sequence—Joule Heating and Thermal Expansion

The Joule heating effect is independent of the stresses and strains in the busbar, assuming small deformations and ignoring the effects of electric contact pressure. This means that you can run the simulation using the temperature as input to the structural analysis. In other words, the extended multiphysics problem is weakly coupled. As such, you can solve it in two separate study steps—one for the strongly coupled Joule heating problem and a second one for the structural analysis.

In the Model Builder, right-click the Study 1 node and select Stationary to add a second stationary study step.

When adding study steps you need to manually connect the correct physics with the correct study step.

Start by removing the structural analysis from the first step.

Under Study 1, click the Stationary 1 node.

In the Settings window, under Physics Selection, select the Solid mechanics (solid) interface in the Physics interfaces list.

Clear the Use in this study check box.

Then remove Joule heating from the second step.

Under Study 1, click the Stationary 2 node.

In the Settings window, under Physics Selection, select Joule heating (jh) from the Physics interfaces list.

Clear the Use in this study check box. Save the model.

Right-click Solver Configurations and select Delete Solvers.

Right-click the Study 1 node and select Compute to automatically create a solver sequence that solves the problems in sequence.

Resulting Deformation

Click Results>Plot Group 3>Surface 1. In the Settings window, click the Replace Expression button and select Solid Mechanics>Total Displacements from the context menu. You can also type solid.disp in the Expression field.

The local displacement, due to thermal expansion, is displayed by COMSOL as a surface plot. Next add exaggerated deformation information.

In the Model Builder, Results>Plot Group 3, right-click the Surface 1 node and select Deformation. Save the model.

You can also plot the von Mises and principal stresses to assess the structural integrity of the busbar and the bolts and to check for the susceptibility to fatigue.

Fluid Flow

After analyzing the heat generated in the busbar and possibly the induced thermal stresses, you might want to investigate ways of cooling it by letting air flow over its surfaces.

Adding the fluid flow to the Joule heating model forms a new multiphysics coupling. To simulate the flow domain, you need to create an air box around the busbar. You can do this manually by altering the geometry from your first model. Alternatively, you can load a file including the geometry and the solution to the Joule heating problem. In the Model Library, select COMSOL Multiphysics>Multiphysics>busbar_box and then click Open.

Having loaded or created the geometry, now simulate the air flow according to the figure below.

Start by adding a new parameter for the inlet flow velocity.

Defining Inlet Velocity

In the Model Builder, click Parameters in Global Definitions.

In the Settings window, click the last row in the Parameters table. Type Vin in the Name column and 1e-1[m/s] in the Expression column. Enter a description of your choice.

The next step is to add the material properties of air in Materials.

Adding Air

In the Model Builder, right-click Materials and select Open Material Browser.

In the Material Browser, expand the Built-In tree. Right-click Air and select Add Material to Model.

Close the Material Browser.

In the Model Builder, click Air in the Materials node.

In the Graphics window, click the air box to highlight it and right-click to add it to the selection list.

Cross-check: Domain 1.

Now you can add the physics of fluid flow.

Adding Fluid Flow

In the Model Builder, right-click the Model 1 node and select Add Physics .

In the Model Wizard, select Fluid Flow>Single-Phase Flow>Laminar Flow.

Click the Add Selected button and click the Finish button .

Save the model with a new name, busbar_box_I.mph.

Click the Wireframe rendering button in the Graphics window toolbar to look inside of the box.

Now that you have added fluid flow to the model, you need to couple the heat transfer part of the Joule Heating Physics Interface to the fluid flow.

In the Model Builder, right-click Joule Heating. In the first section of the context menu, select Heat Transfer>Heat Transfer in Fluids.

The Settings window for Heat Transfer in Fluids should now be active. Make sure this is the case.

In the Graphics window select the air domain to highlight it (in red) and right-click to add it to the Selection list (which changes the color to blue).

Cross-check: Domain 1.

Now couple fluid flow with heat transfer.

In the Settings window, locate the Velocity field list. In the list, select Velocity field (spf/fp1).

This identifies the flow field from the Laminar Flow Physics Interface and couples it to heat transfer.

Moving on to the boundary conditions, specify the inlet and outlet for the heat transfer in the fluid domain.

In the Model Builder, right-click Joule Heating. In the second section of the context menu, the boundary section, select Heat Transfer>Temperature.

In the Graphics window, click the inlet boundary, boundary number 2, and right-click to add it to the Selection list in the Settings window.

This sets the inlet temperature to 293 K, the default setting.

Continue with the outlet.

In the Model Builder, right-click Joule Heating. In the second section of the context menu, select Heat Transfer>Outflow.

In the Graphics window, click the outlet boundary, boundary number 5, and right-click to add it to the Selection list in the Settings window.

The settings for the busbar, bolts, and for the Electric Potential 1 and Ground 1 boundaries have retained the correct selection, even though you added the box geometry for the air domain. To see this, click Electric Potential 1 and then Ground 1 in the Model Builder to verify that they have the correct boundary selection.

Continuing with the settings for the flow, you need to indicate that fluid flow only takes place in the fluid domain. Then you need to set the inlet, outlet, and symmetry conditions.

In the Model Builder, click Laminar Flow. In the Settings window, locate the Selection list and click the Clear Selection button .

In the Graphics window, click the air box (domain number 1) and right-click to add it to the Selection list.

You can also verify that Air in Materials has all the properties that this multiphysics combination requires. In the Model Builder, in Materials, click Air. In the Settings window’s Material Contents list, verify that there are no missing properties, which would be marked by a stop sign .

Continue with the boundaries.

In the Model Builder, right-click Laminar Flow. From the context menu’s second section, select Inlet. This opens the Settings window.

In the Graphics window, select the inlet boundary and right-click to add it to the Selection list.

Cross-check: Boundary 2.

Go back to the Settings window. In the U0 field, type Vin to set the Normal inflow velocity.

Right-click Laminar Flow and select Outlet.

In the Graphics window, select the outlet boundary and right-click.

Cross-check: Boundary 5.

The last step is to add symmetry boundaries. You can assume that the flow just outside of the faces of the channel is similar to the flow just inside these faces. This is correctly expressed by the symmetry condition.

Right-click Laminar Flow and select Symmetry.

In the Graphics window, click one of the blue faces in the figure and right-click to add it to the Selection list. Continue with the three other faces.

Cross-check: Boundaries 1, 3, 4 and 48.

The next step is to change the mesh slightly in order to get a quick solution. The current mesh settings would take a relatively long time to solve, and you can always refine it later. So for now, make the mesh coarser.

Coarsening the Mesh

Go to the Model Builder, in Mesh 1, and click Size.

In the Settings window, click the Predefined button to use the Normal element size.

Click the Build All button .

You can assume that the flow velocity is large enough to neglect the influence of the temperature increase in the flow field. It follows that you can solve for the flow field first and subsequently solve for the temperature using the results from the flow field as input. You can implement this by running a Study Sequence.

Running a Study Sequence—Fluid Flow and Joule Heating

Solving the flow field first and then the temperature field yields a weakly coupled multiphysics problem. The Study sequence below solves such a weak coupling automatically.

In the Model Builder, right-click the Study 1 node and select Stationary to add a second stationary study step.

Next you need to connect the correct physics with the correct study step. Start by removing Joule heating from the first step.

Under Study 1, click the Stationary 1 node.

In the Settings window, under Physics Selection, select the Joule heating (jh) interface in the Physics interfaces list. Clear the Use in this study check box.

Remove the fluid flow from the second step.

Under Study 1, click the Stationary 2 node. In the Settings window, under Physics Selection, select Laminar flow (spf) from the Physics interface list and clear the Use in this study check box.

Save the model with Ctrl-s.

Right-click Solver Configurations and select Delete Solvers.

This clears any solver settings that may be kept from last solution.

Right-click the Study 1 node and select Compute to automatically create a new solver sequence that solves the two problems in sequence. The simulation takes a few minutes to run.

After the solution is complete, click the Transparency button on the Graphics toolbar to visualize the temperature field inside the box.

The plot shows that the temperature in the busbar has decreased slightly compared to the model without fluid flow. Even for this moderate flow field, the effective heat transfer coefficient seems to be larger than the value of htc used in the previous model.

You can also see that the temperature field is not smooth due to the relatively coarse mesh. A good strategy to get a smoother solution would be to refine the mesh to estimate the accuracy.

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