Modelling wind turbine acoustics to design quieter wind farms

Where tonal noise from wind turbines comes from

Wind turbines generate several types of sound:

• Aerodynamic noise from the blades moving through turbulent air
• Mechanical noise from the drivetrain and generator
• Structural radiation from large steel components such as the tower

Tonal noise is most often linked to periodic vibration in the drivetrain. A key source is the meshing of gear teeth in multi stage gearboxes. Typical gear mesh frequencies include:

• Low speed stage – around 10 to 30 Hz
• Intermediate stage – around 50 to 150 Hz
• High speed stage – around 300 to 700 Hz

If those excitation frequencies line up with structural resonances in the tower or blades, even relatively modest internal forces can produce clearly audible tones at receptors hundreds of metres away. Tall, lightly damped steel towers are particularly effective radiators because of their large surface area.

When you put that together with sensitive receivers and low background noise in rural locations, you have a strong case for detailed, physics based modelling.

Why modelling acoustics from large turbines is so challenging

From a simulation perspective, wind turbines are an awkward combination:

• Very large, slender structures
• Large regions of air and void space around blades and tower that must be included in the acoustic domain
• Tonal noise at frequencies where wavelengths are no longer large compared with the structure

In a conventional finite element analysis (FEA) approach:

• You create a model of the structure and a surrounding volume of air
• That volume is divided into many small elements
• To represent sound accurately, each wavelength needs several elements across it (a common rule of thumb is around one sixth of a wavelength per element)

The problem is that as frequency increases, wavelength decreases:

• At 100 Hz, sound in air has a wavelength of about 3.4 m, so element sizes of roughly 0.5 to 0.6 m are needed
• At 1000 Hz, the wavelength is around 0.34 m, so element sizes closer to a few centimetres are required

For a turbine with a rotor diameter over 150 m and a tip height exceeding 200 m, that can lead to millions of elements in the acoustic mesh. Memory demand and solve time grow rapidly, to the point where full 3D FEA at higher frequencies becomes impractical.

That is why the choice of modelling approach matters just as much as the model geometry.

Two main approaches: FEA and BEM

Two of the most useful methods for simulating wind turbine acoustics are finite element analysis (FEA) and the boundary element method (BEM). Each has strengths and limitations.

FEA: powerful but mesh hungry

FEA is well suited when you need to model:

• Structural dynamics and acoustics in a coupled way
• Low to mid frequencies where mesh sizes are still manageable
• Near field phenomena close to the turbine

In the Xi study, a 60 m tip height turbine was modelled using FEA at different tonal frequencies. At 50 Hz, the model solved in under half a minute. By 200 Hz, the same model took around half an hour for a single frequency step.

For larger turbines, or for higher frequencies, the number of elements and the time to solution can become prohibitive.

BEM: efficient at higher frequencies

BEM takes a different approach. Instead of meshing the whole volume of air, it:

• Uses the turbine surfaces as the primary mesh
• Represents the acoustic field using Green’s functions to calculate sound at points of interest

The key advantages are:

• No need to mesh the entire surrounding volume of air
• Solve time that is much less sensitive to frequency than FEA

In Xi’s comparison, modelling tonal noise at 100 Hz for a large modern turbine took over 4 hours with FEA and roughly 3 minutes using BEM, for a single frequency.

For this scale of turbine, BEM becomes the practical choice for tonal noise in the 100 Hz and above range.

Keeping models tractable: smart domain design

There are ways to make FEA more efficient, particularly at lower frequencies where it is still attractive.

In the comparison study, Xi reduced computational cost by:

• Surrounding the tower and each blade with local acoustic domains rather than modelling the full volume between blades and tower
• Using a half cylinder around the tower to cut the mesh size
• Applying perfectly matched layers (PMLs) at the outer surfaces so sound could leave the model without artificial reflections
• Using far field analysers on each acoustic domain and summing them to calculate sound pressure levels at distant points

This kind of domain design can make the difference between a model that runs overnight and one that will not run at all on available hardware.

Interpreting and presenting acoustic results

The best simulation is only useful if its results can be understood.

With FEA:

• The volumetric mesh naturally supports cross sections and full field contour plots
• It is straightforward to show sound pressure distribution around the turbine on arbitrary slices

With BEM:

• Results are defined on the boundaries
• To create similar contour plots, you must define grids of receiver points and compute sound level at each, adding post processing time

For many projects, that trade off is worth making because BEM delivers results quickly at the frequencies of interest. The important point is to plan from the start how results will be used in planning submissions, design reviews and communication with non specialist stakeholders.

Beyond FEA and BEM: very high frequencies

At very high frequencies, even BEM starts to struggle. Models become too large and solution times lengthen again.

In those regions, techniques such as:

• Statistical Energy Analysis (SEA)
• Ray tracing and other high frequency asymptotic methods

may be more appropriate. These approaches treat sound more like rays or energy flows than waves, which is a good approximation when wavelengths are very small compared with geometry.

The practical takeaway is that no single method is best everywhere. A robust acoustic strategy often combines multiple techniques across different frequency bands.

How Xi uses measurement and modelling together

For all our wind turbine acoustics work, simulation is only half the story.

Xi’s standard approach includes:

• Field measurements of vibration and far field sound from operating turbines, carried out by engineers trained to work at height on real machines
• Measurements that conform to IEC 61400 11 for both broadband and tonal noise, so that results integrate with established industry practice
• Model calibration and validation against those measurements, rather than relying solely on theoretical inputs

This gives developers, owners and OEMs confidence that the simulated behaviour is anchored in reality, and that predicted changes will translate into real world improvements.