Dancing in the wind

I have discussed in other post the phenomenal growth of the dimensions of wind turbines in the last 2 decades. Bigger rotors, taller towers and more MW has been the industry trend year after year.

There is some evidence that we are reaching the limit – blades of more than 50m length pose significant logistic challenges, while steel tower more than 100 meters tall can be subject to strong vibrations and dangerous oscillations under certain circumstances.

Such vibrations can be induced by several external sources such as an unbalanced rotor, an earthquake or the wind itself.

They are dangerous because they can damage the turbine due to fatigue loading (the weakening of materials due to cyclical loads). Some type of foundation can also partially lose stiffness – for instance monopile foundations.

Additionally, these vibrations can also trigger resonance phenomenons in the tower – you can follow this link to see of how “soft soft” and “stiff” tower are designed based on the blade passing frequency.

You can see a good full scale example of this problem in the video above and read here more about wind turbine vibrations.

There are several technical solutions currently being studied to dampen the tower reducing the vibrations.

Among the most interesting concept that I have seen I would mention tuned mass dampers – basically an auxiliary mass connected to the structure with spring and dashpots (viscous friction dampers), friction plates or similar energy dissipating elements.

These dumpers are called “tuned” because they have been designed keeping in mind the natural oscillation frequencies of the structure they have to protect. The two main parameters are the spring constant and the damping ratio: by varying them it is possible to damp harmonic vibrations.

I do not know if tuned mass dampers that can work with the first fundamental frequency of  industrial size wind turbines (below 1 Hz) are currently available – however I have found quite a lot of  studies on the topic.

A similar technological solution is the tuned liquid column damper. In this case a liquid inside an U shaped tank. By varying the geometry of the tank and the depth of the liquid different damping frequencies can be achieved.

The main benefits of this solution are the geometrical flexibility (you have to put the dumper somewhere inside the tower or the nacelle – I can assure you that the space there is very reduces) and low cost.

Another variant is the pendulum damper. In this solution, the length of the pendulum is calculated to match the fundamental frequency of the WTG.

Mass Damper (a) and Pendulum Damper (b)
Copyright O. Altay, C. Butenweg, S. Klinkel, F. Taddei
Vibration Mitigation of Wind Turbine Towers by Tuned Liquid Column Dampers
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

Good vibrations: wind induced resonance and turbines oscillations

Have you ever wondered why sometimes the wind turbines (and other similar tall structure) sometime vibrate?

Under some conditions the wind blowing on the tower create vortices.

These vortices appears regularly on both sides of the tower, creating low pressure zones first on one side and then in the other.

This beautiful sequence of vortices is called von Karman vortex street. von Karman has been a pioneer of aeronautics

For these reason the tower will start moving perpendicularly to the wind, first toward one side and after toward the opposite.

The tower has a very low structural damping – when the oscillation start its reduction is very slow because the steel tower has a limited capacity to absorb the kinetic energy.

It also has a very low natural frequency (the frequency at which the tower will tend to vibrate when subjected to external forces).

The vortices created by the wind will appear at a frequency that depends on the speed of the wind and the diameter of the tower.

The formula to calculate this frequency is very simple:

f = St · U / D

where

f is the vortex shedding frequency

St is a value called Strouhal number (in our case it is around 0,2)

U is the wind speed

D is the diameter of the tower

At a certain wind speed the vortices will appear and shed at a frequency equal to the natural frequency and the tower will resonate. The wind speed that start the resonance is called the critical speed.

If the wind blow at the critical speed for enough time the amplitude of the vibration will increase and you will see the tower oscillating.

This is a simplistic summary of a very complex phenomenon. It is however a limiting factor for the use of higher steel tower. In additional to the risk of catastrophic failure the wind induce vibrations will also generate additional fatigue loads, shortening the life of the tower.

It is also interesting to observe that a structure has more than a natural frequency.

Vibrations in the lowest natural frequency (first mode) will have this shape:

First wind turbine tower vibration mode

However, sometime a turbine can vibrate in what is called “the second mode” the second lowest natural frequency):

Second wind turbine tower vibration mode

Following this link you can see a real world example of how is a tower vibrating in the second mode.

What can we do to avoid these dangerous vibrations?

Some solutions are structural - basically aimed at increasing the damping of the tower or changing the way the mass is distributed.

It is not easy to change the mass distribution in a wind turbine tower (basically its an inverted pendulum).

Nevertheless it is possible (and it is becoming increasingly common) to install dampers in the wind turbines, either only temporarily during the installation or as a permanent feature.

Other solutions are aerodynamic - the idea is to change the shape of the tower adding elements that disrupt (or "spoil") the vortices. Conceptually they are similar to the spoilers used in cars or planes, in the sense that they are intended to mitigate an unwanted aerodynamic effect.

An example are helical strakes, sometimes called "coils" "ropes". This is a concept developed by Christopher Scruton and other scientist such as William Weaver in the fifties and sixities and used often in chimney and similar structures.

However sometimes they do not work as you can see in the video below.

In general, the effectiveness of this solution is driven by two parameters:

  1. Diameter of the strake (usually defined as a ratio of the diameter of the tower)
  2. Pitch (the distance along the cylinder axis that is needed to complete one full turn of the strake)

Definition of pitch and height

From experimental tests in wind tunnels it has been found that the optimum height of the strake is approximately 10% of the diameter of the tower (that is, around 40 cm for a standard steel tower with a diameter of around 4 meters).

For the pitch the results of the test shown an optimum value in the region between 5 and 15 diameters (that is, one full turn of the rope should be done between 20 and 60 meters).

Obviously the smaller the pitch, the more the strake is parallel to the tower.

There are however other secondary factors that influence the efficiency of this solution, such as the area of the cylinder covered by protrusions (usually called “strake coverage”) and the pattern of the ropes (usually three or four independent ropes are used to create the helix).

One of the biggest problems of the strakes is that they greatly increase the drag coefficient (the resistance opposed by the wind turbine tower to the flow of the wind).

The implication is that the loads at the bottom of the tower will increase as well, so that a bigger foundation could be needed.

For this reason strakes are normally used as a temporary solution only during the installation – above all in the most critical part of the procedure, when the tower is installed but there is still no nacelle on top.

Removable strakes are wrapped around the tower, either before the lift while the tower segment is on the ground or after installation.