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Tutorial: Harmonic Analysis of an Airfoil (2/2)

This article provides a step-by-step tutorial for a harmonic analysis simulation of an airfoil, including post-processing. It is a continuation of the Frequency Analysis of an Airfoil (1/2) tutorial.

harmonic analysis shape animation airfoil at 25 Hz
Animation 1: Displacement of the airfoil due to harmonic excitation at 25 Hz. Displacements are magnified by a factor of 10.

This tutorial teaches how to:

  • Set up and run a harmonic simulation;
  • Assign boundary conditions, material and other properties to the simulation;
  • Mesh with the SimScale standard meshing algorithm.

We are following the typical SimScale workflow:

  1. Prepare the CAD model for the simulation;
  2. Set up the simulation;
  3. Create the mesh;
  4. Run the simulation and analyze the results.

1. Prepare the CAD Model and Select the Analysis Type

In case you already have a project from the Frequency Analysis of an Airfoil Tutorial, feel free to continue using that workbench. The geometry and mesh are the same as the frequency analysis tutorial.

Otherwise, you can click the button below. It will copy the tutorial project containing the geometry into your workbench.

The following picture demonstrates what should be visible after importing the tutorial project.

harmonics analysis using an airfoil
Figure 1: Airfoil geometry loaded in the workbench

1.1 Create the Simulation

As a first step, click on the geometry name.

creating a new simulation for a project
Figure 2: Creating a new simulation in the SimScale workbench

Hitting the ‘Create simulation’ button leads to the following options:

analysis types available in simscale
Figure 3: List of analysis types available.

Choose ‘Harmonic‘ as the analysis type and ‘Create the simulation‘.

2. Assigning the Material and Boundary Conditions

To have an overview, the following picture shows the boundary conditions applied for this simulation:

harmonics analysis boundary conditions
Figure 4: Overview of the boundary conditions for the harmonics analysis.

We will assign a pressure load at different eigenfrequencies based on the results of the frequency analysis tutorial as well as fixed support. Furthermore, we are going to use aluminum as a material for the wing.

2.1 Define a Material

In the left-hand side panel, click on the ‘+ button‘ next to the Materials. In doing so, a list of pre-defined material appears.

materials list simscale
Figure 5: List of materials pre-defined in the library.

Choose ‘Aluminium‘ from the library and hit ‘Apply‘.

Now you successfully created the material. The blade is assigned to it automatically. All you need to do is confirm it by hitting the checkbox next to Aluminium.

2.2 Assign the Boundary Conditions

In the next step, boundary conditions need to be assigned, using Figure 4 as a reference. For an overview of the boundary conditions available, please have a look at this documentation page.

a. Fixed Support

The first boundary condition is a fixed support. It represents zero displacement in all directions. Proceed as below:

fixed support boundary condition fea
Figure 6: Steps to create a fixed support boundary condition.

After hitting the ‘+ button’ next to boundary conditions, a drop-down menu opens. From it, one can choose between different boundary conditions. After choosing ‘Fixed support‘, assign it to one of the airfoil’s tips:

assigning boundary condition to an entity
Figure 7: Assigning the fixed support boundary condition to a face.

b. Pressure

Still based on figure 4, create a second boundary condition and choose ‘Pressure‘. This will be used for the harmonic excitation. Let’s apply a pressure of ‘500‘ \(Pa\) on the bottom face of the airfoil. Phase angle should be kept at 0 degrees in case of a single force.

harmonic excitation force
Figure 8: Setting up the pressure boundary condition. It is applied to the bottom face of the airfoil.

For applications where more than one force is applied, oftentimes a non-zero phase angle will be specified. For example, in a car engine analysis, we have several pistons with unsynchronized forces. In this case, you can set one of the forces with a phase angle of 0 and define the phase of the other forces accordingly.


For harmonic analysis, at least one load-related boundary condition needs to be defined. Otherwise, there is no prescribed load for the harmonic excitation and the simulation will fail.

Valid load boundary conditions are: centrifugal force, force, nodal load, pressure, remote force, surface load and volume load.

2.3 Numerics and Simulation Control

Under Numerics, change the Linear system relative residual to ‘1e-4‘. This value is the maximum relative residual tolerated by the solver.

numerics settings for a harmonic analysis type
Figure 9: Numerics settings for the harmonic analysis.

Under Simulation control, you can specify a list of Excitation frequencies, at which the loads will be excited. To specify meaningful excitations for the harmonic analysis, it is important to perform a frequency analysis on the geometry, to gain more insight about the natural frequencies.

Therefore, the results from the frequency analysis tutorial are important in this step. These are the first 10 modes for the airfoil geometry, and their respective natural frequencies. You can find the following figure in the results of the frequency analysis tutorial here:

airfoil eigenmodes and eigenfrequencies
Figure 10: Results from the frequency analysis tutorial, showing eigenfrequencies for the airfoil geometry.

These 10 frequencies span from 4 to 255 \(Hz\). Let’s focus on the first 3 modes for the harmonic analysis.

In Simulation control, change the settings to the following:

harmonic analysis frequency list
Figure 11: Simulation control set up for the harmonic analysis.
  • Set Excitation frequencies to ‘Frequency list‘;
  • Change Start frequency to ‘2.5‘ \(1/s\);
  • End frequency is ‘30‘ \(1/s\);
  • Frequency stepping will be ‘2.5‘ \(1/s\). With these settings, a total of 12 frequencies will be analyzed.

2.4 Result Control

With result controls, users can monitor parameters in points of interest within the geometry.

To set up a point control, proceed as below:

data point result control harmonic analysis
Figure 12: Creating a data point result control.
  1. Click on the ‘+ button‘ next to Point data;
  2. Make sure Field selection is set to ‘Displacement‘. Component selection is ‘All‘ and Complex number is ‘Magnitude and phase‘;
  3. Lastly, click on the ‘+ button‘ next to Geometry primitives to specify a point.

For the coordinates, specify ‘0.1‘ in the x-direction, ‘0‘ in the y-direction and ‘-0.8‘ in the z-direction:

probe point creation harmonics
Figure 13: Coordinates for the data point. More points can be created, to monitor areas of interest.

Note that, after creating the probe point, it’s necessary to assign it to the result control.

assigning a probe point to a result control
Figure 14: Assigning the newly created point to the result control

3. Mesh

To get the mesh, we recommend using the Standard algorithm, which is a good choice in general as it is quite automated and delivers good results for the most geometries.

The mesh is the same used for the frequency analysis test. Therefore, change the global Fineness to ‘2‘. 2nd order elements will also be used here, to provide more accurate results. Lastly, the Gap refinement factor should be set to ‘0.5‘. Finally, ‘Generate‘ the mesh.

mesh harmonic analysis set up
Figure 15: Standard mesh settings for the harmonic analysis.

After a few minutes, the mesh is ready and looks like this:

airfoil fea mesh
Figure 16: Mesh of the airfoil. This is the same mesh used for the frequency analysis tutorial.

4. Start the Simulation

starting a simulation run
Figure 17: Simulation tree ready to start a simulation run.

Now you can start the simulation. While the results are being calculated you can already have a look at the intermediate results in the post-processor. They are being updated in real-time!

possibilities of accessing the post processor
Figure 18: Accessing the post-processing environment.

5. Post-Processing

After about 35 minutes, the results should be available.

5.1 Displacement Plots

First, let’s have a look at the result controls that we specified. Recalling the natural frequencies, we can see that peaks in displacement occur around those frequencies:

displacement harmonic analysis results
Figure 19: Displacement on the result control point. For 25 Hertz, the displacement was the biggest.

The phase angles observed for this simulation are either 0 or 180 degrees. This indicates that the peaks in both displacement and forces occur at the same time.


If we were modeling damping, a phase shift would occur, and phase angles between 0 and 180 would also be observed. This is caused by the energy being dissipated out of the system. In SimScale, damping is modeled under the Materials node.

Phase angles between 0 and 180 are also observed when two or more forces are present, with a phase angle between them.

5.2 Surface Visualization

In order to view the results of your harmonic analysis, click on the ‘Post-process results‘ tab under your finished run.

post-processing the results after the  run is finished
Figure 20: After the simulation is finished, you can check the results in the post-processor.

Select the ‘Von Mises Stress’ to display on the part, under the Coloring section. In order to improve the quality of your visualization, and make the color transition between blocks smoother, right-click on the legend bar at the bottom of the page, and select the ‘Use continuous scale’ option:

continuous scale for smoother visualization of stress distribution on surface
Figure 21: Choose the ‘Use continuous scale‘ option, for smoother transition between different levels of stress.

You can visualize more parameters by changing the Coloring input:

surface visualization available parameters for distribution inspection on airfoil after harmonic analysis
Figure 22: All the available parameters to use for your surface visualization

For example, this is what the surface visualization with the real displacement values looks like when the continuous scale feature is also added:

changing the coloring of the surface visualization top real displacement
Figure 23: Real displacement distribution on the surface of the airfoil, with the highest values, colored in warm tones, placed at the center of the airfoil.

5.3 Displacement

There are more features to use in order to post-process the results of the run, and you can access them by clicking on the ‘Add filter’ option. Then the menu with all the available options appears:

post processing filters for results visualization
Figure 24: All the available filters are listed on this menu

Plotting displacement contours can also provide valuable insight into the behavior of the parts. Below, we have activated the visualization of displacements. For 25 \(Hz\), a bending effect occurs and the displacement is the biggest, as seen in Figure 19. You can check this by implementing the following:

  • Change the Fields to ‘Displacement(real)‘;
  • Set the Scaling factor to 10, making the displacement easier to identify;
  • Rollback to the timestep that corresponds to 25 \(Hz\), using the slider at the top. You can check other frequencies as well by changing this input.
visual representation of displacements harmonic analysis
Figure 25: Visually inspecting displacement of the airfoil, magnified by a factor of 10, so the results are enhanced.

Analyze your results with the SimScale post-processor. Have a look at our post-processing guide to learn how to use the post-processor.

Congratulations! You finished the tutorial!


If you have questions or suggestions, please reach out either via the forum or contact us directly.

Last updated: May 20th, 2021

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