We intend to publish a newsletter at irregular intervals, providing some explanation of aeroelasticity on wind turbines and discussing articles or reports that can be of interest to all those designing wind turbines or performing load set calculations, or creating wind turbine controllers. So welcome to our very first newsletter. We hope you will enjoy it.
The Importance of Accurate Structural Damping
First some basics….
In wind turbine aeroelasticity, there are two main problems that one should know about and should avoid in the design: resonance and instability. A resonance occurs when an outside forcing occurs at a frequency that is close to a natural frequency of the system. On wind turbines this will be related to the rotor speed, indicated as 1P and multiples of the rotor speed nP. The forcing comes from e.g. tower shadow, shear flow, misalignment and rotational sampling of turbulence. The other problem, instability, occurs when a natural mode is such that during the vibration in the natural mode, the aerodynamic forces change in such a way, that they are actually adding energy to that motion. So this is not related to the energy that the wind turbine produces, it is purely the change in the velocities of the blade coming from the motion in the natural mode, that change the aerodynamic forces, which can result in an increasing amplitude of the vibration. If you are interested in this subject and want to learn more, why not participate in one of our training courses? Check out our page “training options” at the top of this page.
This flow diagram illustrates when there is a risk of resonance and when it is more likely that an instability is occurring. For resonances, the amount of damping of the mode involved is also very important, if there is little damping, the resonance will result in large vibrations, if there is a lot of damping, the closeness of an excitation frequency to a natural frequency will not cause significant vibrations.
Looking at instabilities, we need all modes to be positively damped. Damping comes mainly from two sources: structural damping and aerodynamic damping. Structural damping will always be positive and is assumed to be higher for higher modes e.g. second edgewise mode is expected to have a higher structural damping than the first edgewise mode, and the third edgewise mode will have higher structural damping than the first and second. Note however that the first torsion mode will have a significantly higher frequency than the second edgewise mode, but will have structural damping that is probably comparable to the first edgewise mode. In some aeroelastic simulation tools, we can set the structural damping for each mode separately, in some tools the damping for the first modes in each direction are provided and for higher modes, the damping is calculated based on a simple damping model.
If we are overestimating the structural damping,
this can significantly impact the calculated loads!
Now, a recent article actually shows that the assumption of higher damping for higher modes may be inaccurate: https://iopscience.iop.org/article/10.1088/1742-6596/2767/2/022069 Edgewise Structural Damping of a 2.8-MW Land-Based Wind Turbine Rotor Blade, from Mayank Chetan and Pietro Bortolotti, J. Phys.: Conf. Ser. 2767 022069. Tests on a full turbine were performed in an attempt to compare the structural damping of the first, second and third edgewise mode. Note that it is stated in the article that the approach used to get the damping, Cov-SSI often results in much lower values than expected, so comparing these new measurements to other results is not valid. The following figure is from that article:
Here we see the results of their experiment on a full wind turbine, but also measured data of blade damping in a laboratory setting. The laboratory settings in blue provide perhaps the easiest comparison. We see that the damping of the first mode is slightly higher than the second mode, not the way we would expected and what is used in some of our aeroelastic codes. The OpenFAST result illustrate the damping we get if we tune the structural damping to either the first or the second mode, clearly, the damping of higher modes is expected to be higher for higher modes in the theory used in OpenFAST.
If we overestimate structural damping, we make mistakes that can result in significant underestimations of fatigue loads and in the case where we actually have situations with instabilities, the resulting vibrations can even become critical. Just think about it, if we have a simulation where the total damping (aerodynamic plus structural damping) of the second edgewise mode is just positive, but in reality we have overestimated the structural damping and the total damping is actually negative, then you will get serious vibrations in the second edgewise mode. This paper illustrates that we need to be careful with the structural damping in the input of aeroelastic simulation tools and that it is vital to further investigate what the structural damping really is.
Example with Reduced Structural Damping
A dramatic example of how much different the loads can be if we reduce structural damping, is shown below:
The simulations for the graphs above were performed using OpenFAST using the Beamdyn model for the blades. As is clearly visible, the reduction in the structural damping has resulted in an instability occurring, resulting in much higher loads, that may increase even further if the simulation would have run longer. This illustrates that the difference in damping cannot be covered by the usual safety factors used in load calculations.
In the case that is shown, the first edgewise mode has become unstable when the structural damping is reduced. Clearly, we need to know the correct values for the structural damping of the relevant modes of the turbine blades, as not to calculate a stable situation and find an unstable situation on the proto type. This is not only true for overspeed simulations, but for all simulations. If in any of the calculated cases, we end up with modes that have low total damping in the simulation, but the structural damping is actually overestimated whereby in reality the total damping of the mode would actually be negative due to negative damping from the aerodynamic forces, the loads on the prototype will be significantly higher than those calculated and it is even possible for the blades to break due to an aeroelastic instability. Therefore we should consider being rather conservative when setting the structural damping values.
If you find this subject interesting, the training we provide on wind turbine aeroelasticity might be a good match for you, please check out our page “training options” at the bottom of this page.