Thank you for your reply. I am trying to find damping of the system to find aerodynamic damping. I read that one way is to analyse decay of free vibration of the tower top after a pulse loading.
Based on my understanding, I need to apply loading till a given time (Lets say it Tfree) and then let it vibrate and find the damping based on free decay vibration. So, I need to have wind (steady) blowing till Tfree and also apply wave till Tfree (WaveTMax=Tfree).
What else should I do for this time (Tfree)? Do I need to change some settings in servodyn (for example turn off generator by TimGenOf=Tfree)?
And also, I reckon I cant do this for stochastic wind? I tried to apply stochastic wind with duration of less than simulation time, but FAST gave me error.
You must specify wind and wave data for the entire simulation time.
Instead of applying loading till some given time (Tfree), in FAST you can set nonzero initial platform displacements and look at the free-decay starting from model initialization (t=0). What you want enabled (control, etc.) when calculating damping from free-decay likely depends on what type of aerodynamic damping you want to calculate (e.g. based on closed-loop control or open-loop behavior). You may also want to disable the wave excitation (using WaveMod = 0 in HydroDyn). Regardless, when analyzing the free-decay behavior to assess damping, you’ll still need to isolate the aerodynamic damping from other potential sources of damping e.g. hydrodynamic or mooring damping.
Thank you for your reply. I would like to identify total damping. So,if I define initial displacement and also wind (probably steady or stochastic) and wave ( probably regular), then I can calculate total damping from free decay. What can I do with transient period?
I calculated damping with and without initial displacement for three situations (1- just steady wind 2- steady wind + regular wave 3-stochastic wind + regular wave). As you can see in the figure, left figures are time history of top tower displacement without initial displacement. And in the right figure, I applied 1 m F-A displacement at top of tower.
First, the damping I get depends on the length of time history ( the higher, the less damping) and also depends on the initial displacements (the higher, the higher damping). How should I determine which length and initial displacement is fine for calculating damping?
Second, in the case of initial displacement, the transient period is bolder and fluctuating. Should I remove it? If yes what is the point in having initial displacement?
I don’t see a figure attached to your post. Perhaps this is explained in the absent figure, but you also haven’t explained how you are deriving damping from the time history. So, I can’t really answer your questions.
Regardless, damping is often derived from a free-decay simulation, but such a simulation should be performed in still water (WaveMod=0 in HydroDyn) and with steady wind or without wind.
Thank you for your reply. I was trying to upload the figure but it constantly gave error. Regarding the way I am trying to find damping, I am using free decay simulation.
But I am not sure about:
I need to apply initial displacement (how much? ).
in the formula of free decay it is quite important how many cycles after t=0 I should consider. For example, if I calculate damping after about 8 cycles (tn=30 sec), I get damping ( about 6%). However, if I consider more cycles (tn=60), I get much less damping (2%)
The reason I ran simulation with waves as well was that I wanted to include damping of hydrodynamic as well. I reckon the damping I get comprises of three sources (structural, aerodynamic, and hydrodynamic).
Thank you for your support. I am looking forward to hearing back from you.
Are you trying to estimate linear damping or linear + quadratic damping (p+q)? If the damping is changing depending on how many cycles you are taking, my guess is you are trying to extract a linear damping value from a model that is dominated by quadratic damping. Viscous effects e.g. from aerodynamics and hydrodynamics are quadratic in nature, so, a deriving only a linear damping coefficient from the free-decay response will yield different values depending on the amplitude of the oscillation.
Depending on what features you’ve enabled in your HydroDyn model, hydrodynamic damping can come e.g. from the strip-theory solution (quadratic, via the relative form of Morison’s equation) or the potential-flow solution (linear, via the radiation term). These terms also provide damping in still water.
Thank you very much for your reply. So you mean that aerodynamic damping is quadratic and it is not correct to use free decay formula for that?
I am trying to extract damping of system to incorporate in my structural model (I guess damping I get comes from aerodynamic+hydrodynamic+structural).
Lets assume I just wish to find damping for the condition without waves. Should I impose initial displacement in steady wind? Or should I impose a pulse wind (for example having a steady wind with 8 m/s till T=50 sec (dying out transient period), then at this time a wind pulse of 14 m/s for 10 sec. Does this give a more realistic aeroelastic damping rather than imposing an initial displacement at the beginning of simulation?
You can use a free-decay simulation to quantify linear and/or quadratic damping. I was simply saying that you can’t expect to calculate constant linear damping for different cycles of the free-decay response if the damping is dominated by quadratic effects.
It shouldn’t matter how you initialize your free-decay simulation (whether by initial conditions or forced motion), as long as you neglect the first couple cycles of the free-decay response before calculating the damping.
I calculated the aerodynamic damping based on free decay simulation for different wind speeds and I came up with this graph (app.box.com/s/4kq7or4ubbt8ot2y4jg8p1fzfh97m7r8). As you can see in low wind speeds aerodynamic is low (around 1%) and it reaches to the maximum in the rated wind speed and again it falls as wind speed increases. Do you think the trend and values are correct?
I am trying to find aerodynamic damping ratio from free decay simulation. I used to calculate aerodynamic damping from the initial period ( Usually after removing two first cycles ).
Now I tried to do another approach. What I am doing now is to apply uniform wind till time=40s and then for 4 sec I increase wind speed by 50%, then after time =44 sec again wind speed comes back to its constant value and then I calculate damping ratio because of this pulse wind speed.
The thing that is interesting is that for wind speed less than 12m/s, the results are similar to the ones I get from initial period (after removing first two cycles), but for wind speeds more than 12 m/s, in some wind speed, literally there is negligible damping and for some wind speed there is high damping.
To illustrate, I uploaded the time history plot for 16m/s, 18m/s and 20 m/s. You can see for 18 m/s, vibration dies out quickly, but for 20m/s and 16m/s, it almost does not dampen at all. Also, I uploaded the aerodynamic damping obtained from two approaches (Figure A).
Please find the figures here (app.box.com/s/rjdn2r9jc24damv2yr3wuqq2e6317zgh)
What do you think is the reason that the results differ this much? Please note that all situations are the same, I just changed wind speed (uniform wind speed).
I agree that the results look odd, but I’m not sure what the problem might be. One guess is that the controller is not behaving as you’d expect–have you looked at the rotor speed, pitch angle, and generator torque to see if the responses are reasonable during the transient? It is hard for me to identify the problem without knowing anything about your model. Perhaps you should run the same study with the rotor speed spinning at a fixed rate to see if the results are as you expect.
By the aerodynamic damping, are you referring to the effects because of “structural velocity of blade” and “structural velocity of tower” which are considered in the calculation of “resultant velocity” seen by blade which in turn is used for aerodynamic force calculations? This may have influence on blade oscillations but not so much on tower oscillations. Right?
or , the tower aerodynamic loads (i.e since tower is oscillating in wind, it experiences drag force as a distributed load) ? Also, when we specify damping ratios (zeta) for fore-aft or side-side modes in FAST, how are the damping Coefficients (c) calculated inside FAST? using the formula c= 2zetamass*omega_n?
In my response to Arash, I was referring to the aerodynamic damping of the rotor, which results from a combination of blade, tower, and wind velocities. For most wind turbines operating normally, the aerodynamic damping from the rotor dominates over the aerodynamic damping from the tower, at least in the fore-aft direction (along the wind direction). But the aerodynamic damping of the rotor has a strong impact on the tower response.
Yes, your equation for the tower structural damping (c) is correct, except that FAST uses the equivalent expression in terms of stiffness, rather than mass: