Designing a 2D Transformer Core: Steady-State Simulation in ElmerFEM (Part 2)

PorThales Maia Geral

In this second part of our series, we transition from geometry preparation in FreeCAD to the simulation environment of ElmerFEM. If you missed Part 1, you can catch up via the link.

ElmerGUI streamlines the workflow by managing the Solver Input File (.sif) directly through its interface. In this stage, we will compute the static magnetic flux generated by the transformer’s primary winding and later apply a load to the secondary winding to validate our Finite Element Method (FEM) results against analytical calculations.

Understanding ElmerGUI

Before we start, it is important to understand that ElmerGUI is a great tool for those starting with Elmer. However, you will soon find that the core configuration eventually leads back to the .sif file, which we will learn to edit in this post.

First Steps: Importing and Scaling

The first task is to import the mesh we generated previously. Go to File >> Open and select your .unv file.

Fig. 1 – The ElmerGUI interface showing the successfully imported transformer mesh, including the core and surrounding air domain.

For the model to work correctly, we need two specific solvers that aren’t active by default in the UI:

  1. Go to File >> Definitions.
  2. Click the Append button.
  3. Navigate to the edf-extra folder and select magnetodynamics2d.xml and magnetodynamics.xml.
Fig. 2 – Appending the Magnetodynamics definitions to enable magnetic field simulation capabilities.

Important Note on Units: If you modeled your geometry in millimeters or inches, you must add a Coordinate Scaling factor. Go to Model >> Setup and set the scale to 0.001 (to convert mm to meters), as Elmer operates in SI units.

Setting Up the Equation

We must inform Elmer what physics it needs to solve.

  1. In the left sidebar, under Model, click Equation >> Add.
  2. In the MgDyn2D tab, activate the solver and apply it to all bodies.
  3. Set the Priority to 2 (higher numbers indicate higher priority).
Fig. 3 – Configuring the 2D Magnetodynamics equation and assigning execution priority 1.
  1. Now look for MgDynPost (used for post-processing results). Activate it and set its Priority to 1.
  2. Name this set “MgDyn” before clicking OK.
Fig. 4 – Configuring the 2D Magnetodynamics equation and assigning execution priority 1.

Materials and Body Identification

Before assigning materials, it is best practice to rename your bodies for better organization. Double-click the numbered bodies in the left menu to rename them (e.g., Core, Coil_A, Air).

Fig. 5 – Renaming the mesh bodies to simplify the assignment of materials and forces.

Now, apply the materials via Model >> Material >> Add:

  • Air and Coils: Choose “Air” from the Material library and apply it to the Air and Coil bodies.
  • Core (Iron): Select “Iron”. In the MgDyn2D tab, set the Relative Permeability to 4000.Now we can go to Material and click in [Add..]. Click in the Material library. Chose Air and Apply to bodies Air and Coils. Follow the same process, but now, select the Iron material.
Fig. 6 – Defining the magnetic properties for the transformer core material.

Body Force: Adding the Current Source

We must add the current source for the primary winding. In ElmerGUI, we enter the total surface current density (J). If we consider a total current of 60\ A.e, the surface current density is calculated as:

J=N.IA=60 A.e70 mm × 17.5 mm=48979.6 A/m2J = \frac{N.I}{A} = \frac{60~A.e}{70~mm~\times~17.5~mm } = 48979.6~A/m^2
  1. Go to Model >> Body Force >> Add.
  2. In the MgDyn2D tab, check Calculate Potential and enter the calculated value above.
  3. Create a second Body Force for the opposite coil using a negative value to represent the return path of the current.
Fig. 7 – Applying the calculated surface current density as a Body Force to the coils. Positive.

Create a new Body force, but now you should choose the opposite coil and put a negative surface current value.

Fig. 8 – Applying the calculated surface current density as a Body Force to the coils. Negative.

Boundary Conditions

Finally, we define the simulation boundary.

  1. Go to Model >> Boundary Condition >> Add.
  2. Select the outer boundary of the air domain.
  3. Set the Dirichlet Potential to 0. This ensures the magnetic flux is contained within our simulation space.
Fig. 9 – Setting the Dirichlet boundary condition to zero at the outer edges of the model.

The Sif File and Running the Simulation

We are now ready for the first simulation run.

  1. Click on Sif in the upper bar menu and select Generate.
  2. Click Sif again and select Edit. You will be able to read every modification we’ve made in text format.
  3. After checking the settings, click the Run icon to start the solver.

Paraview Results

If everything went fine, the solver will finish, and you will be able to view the results in Paraview. We will discuss the visualization of flux lines and density in our next topic!

Fig. 10 – Paraview post-processing.