A critical part of wind turbine design is making them as quiet as possible, as noise can affect people living close to wind farms. Modelling the acoustic design of wind turbines is extremely challenging due to the very large physical sizes of the turbines compared to the wavelengths of the sound they produce. To select the correct modelling technique for successfully simulating wind turbine acoustics, we need to understand first, where and how the noise is generated and secondly, it’s frequency. Two typical modelling approaches are finite element analysis (FEA) and boundary element method (BEM). Here, we explore some of the advantages and disadvantages of each approach and examine how computation times compare.
When does noise from wind turbines becomes a problem?
Broadband and tonal noise produced by wind turbines can have detrimental effects on neighbouring residential communities. Tones are very easily perceived by human hearing. As a result, the tonal noise from wind turbines often increases the annoyance of receiver to such an extent that has been identified as the primary cause for complaint. Consequently, legislation has been put into place to regulate tonal noise emitted from wind turbines which can lead to financial penalties, curtailment, or even closure of a turbine site. The risk of such economic losses has influenced the wind turbine industry to develop solutions to address the issue.
What causes wind turbine tonal noise?
Tonal noise on wind turbines is commonly caused by the vibrations produced by the rotating components of the drivetrain. For example, vibration can be caused by the interlocking of gear teeth in the gearbox. This is commonly referred to as gear meshing. Normally, gearboxes have three step-up stages:
- low-speed stage with meshing in the 10 to 30 Hz range
- intermediate stage with 50 to 150 Hz meshing
- high-speed stage with 300 to 700 Hz meshing
These vibrations, while causing tonal noise, may not necessarily be problematic as the drivetrain is often a considerable distance away from the nearest receiver. However, if the frequency of vibration is closely aligned with structural resonant frequencies of the tower and/or blades, then the modal response can be excited. Therefore, amplifying and radiating tonal noise. Wind turbine towers are commonly lightly damped steel structures with very large surface areas, making them extremely efficient radiation surfaces for tonal noise.
Challenge of modelling large objects at high frequency
Modelling the acoustic output of an object using conventional finite element analysis typically involves creating the geometry of the object and the surrounding fluid through which the sound waves pass. This surrounding fluid is the acoustic domain of the model and it is normally divided up into a numeric mesh. To correctly model sound, the size of the elements that make up the mesh should be around one-sixth of the wavelength of the sound being modelled.
As the frequency of sound increases the wavelength decreases along with the mesh size required. For example, the wavelength of 100 Hz in air is 3.4 m requiring a mesh size of 57 cm. At 1000 Hz the mesh size required is 5.7 cm. When the geometric size becomes very large compared to the wavelength (i.e. at a higher frequency) the number of mesh elements required by the simulation becomes so high that it is no longer feasible to compute the simulation.
Why is modelling acoustics from wind turbines so challenging?
Wind turbines by nature are formed by large, almost linear objects with large regions of void space between the blades and tower. These void spaces must also be modelled accentuating problems involved in the size of the numeric mesh. Furthermore, wind turbines can also be very large, with rotor diameters exceeding 150 m and the length from the ground to tip exceeding 200 m. As we shall see below, a common complaint is the emission of tonal noise between 100 and 700 Hz, requiring mesh size in the order of 8 cm. This very fine mesh size, compared to the scale of the wind turbine, makes computing simulations close to impossible.
An alternative approach is to use BEM, which does not require a numeric mesh. BEM solves a series of Green’s functions to calculate the noise at any given point in space. The lack of mesh makes BEM very attractive for wind turbine problems, however, it is a computationally expensive method. So, when should we use FEA or BEM?
Comparing the performance of FEA and BEM
To examine how FEA and BEM methods compare, we’ll look at three different sizes of wind turbines that produce tonal noise at 100 Hz.
- 60 m tip height
- 120 m tip height
- 200 m tip height
The models are produced with COMSOL Multiphysics and run on a computer with 16 cores, 128 GB of RAM using an AMD 1st Generation Threadripper processor. In our example, the wind turbines were modelled using a combination of shell and solid elements in the structural module. The structural model was coupled to acoustic domains and solved in the frequency domain with either an FEA or BEM approach.
A trick to reduce the mesh size of the FEA
To reduce the size of the mesh in the FEA models, both the tower and each blade were surrounded by a cylinder of air modelled as an acoustic domain, thereby avoiding having to model void space. To reduce the mesh size the tower was modelled with a half-cylinder. The external layers of these acoustic domains were modelled with perfectly matched layers to allow the acoustic waves to propagate out of the model space. Each of the acoustic domains had an individual far-field analyser and the sound pressure level at any point in space calculated by summing the four far-field analysers.
Results: FEA at low frequency, BEM above 100 Hz.
The time it takes to solve the FEA models are strongly dependent on the frequency being modelled.
This is because as the frequency increases the mesh element size decreases and the number of mesh elements increases exponentially. Conversely, the time it takes to solve the BEM is hardly affected by the frequency.
For the wind turbine with a tip height of 60 m, the FEA solved the 50 Hz tone in 24 seconds compared to the BEM 76 seconds. At 90 Hz both took 79 seconds, while at 200 Hz the FEA took 30 minutes compared to the BEM which only took 93 seconds.
For this relatively small scale of with turbine, we would use FEA below 90 Hz and BEM above 100 Hz.
Results: BEM for large scale turbine
The table below shows the run times for the two modelling approaches when modelling different scale wind turbines at 100 Hz. For the largest turbine over 4 hours of computation time is required to solve a single frequency using FEA. Typically, dozens of frequencies are required to model the acoustic output of a turbine making FEA to computationally expense to solve these large wind turbines. The rapid solve time of ~ 3 minutes using BEM makes it a viable approach to modelling large modern wind turbines. The table below also includes the degrees of freedom that each simulation uses; this number directly relates to the model’s mesh size and can be considered a gauge of the model’s complexity and difficulty to solve.
One draw-back with BEM
One thing that should be remembered when considering which approach to model wind turbines, or any acoustic applications, is how to present results. The best simulation is useless if you can’t convey the results effectively. A common way to show results from an acoustic simulation is to slice through the three-dimensional acoustic field. This is easy to generate with an FEA simulation as the mesh contains all the information required for the false-colour plot. However, to plot a similar diagram with a BEM requires time-consuming post-post-processing set where an array of grid points is defined, and the Green’s functions are used to calculate acoustic pressure at every point. In a BEM the time is taken to post-process the results may out weight the advantages in computation times used to solve to the model.
Other advanced modelling techniques to consider
At very high frequencies solving BEM models also become nonviable. At very high frequencies you may need to consider other simulation techniques such as statistical energy analysis or ray tracing.
What we used to make these models
The models presented here used COMSOL Multiphysics. The module used were:
- Structural Dynamics
- Acoustics
Since adopting COMSOL, Xi has continued to push the boundaries of what is possible through simulation. Xi works closely with COMSOL and is one of only five certified COMSOL consultants in the UK and one of less than 60 worldwide.
Why choose Xi for your next project
Xi’s approach to all modelling problems is that the validation of the simulation is vital. The approach with wind turbine simulations is no different. Typically, Xi would accompany wind turbine simulations with field measurements of vibration and far-field sound. Our engineers are accredited for working at heights in wind turbines, so our modellers have real-life experience working on these machines. Our acoustic measurements of wind turbines conform to the international standard IEC 61400-11 for both broadband and tonal noise.
The simulation approach discussed above is also applicable to other objects where the physical size is large compared to the wavelength of noise. Examples include medium to high-frequency noise in auto interiors and how Hi-Fi speakers interact with room acoustics.
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Xi Engineering – A comparison of modelling wind turbine noise using FEA and BEM approaches
