I approximate the NREL 5-MW monopile wind turbine model by the mathematical model given in the first attachment, where the subscripts t and x denote derivatives with respect to the time t and the position x, respectively. w stands for the transverse displacement of the tower, l is the height of the tower and E I and rho are the flexural rigidity function and mass density function. m > 0 and J > 0 are the mass and the moment of inertia of the RNA (assumed to be rigid). -(E I (x)wxx (x, t))xx dx is the total lateral force acting on a slice of the tower of height dx, located at the position x and the time t. (E Iwxx )x (l, t) and -E I (l)wxx (l, t) are the force and the torque acting on the RNA from the tower at the time t. f(t) and v(t) are the applied force and torque acting on the RNA.

I use FEM and FDM to discretize the mathematical model in tower span and time respectively. To validate that the mathematical model can simulate movements of the tower, I compare the results from my model with those from FAST coupled with the NREL 5-MW monopile wind turbine model.

Before conducting the comparison, I set all the tower mode structural damping ratio to 0. There is no aerodynamic load on the tower and no hydrodynamic load. The wind profile is a constant 8 m/s wind. f(t) is obtained by summing all the FSTipDrag(K,:), FSAero(K,J,:)*DRNodes(J) and FKAero terms in the FAST code, and is computed as the dot product of the vector sum and the inertia frame vector (z1/-z3) since the mathematical model is in the inertia frame.

I never think the results obtained from my code will be much consistent with those from FAST but I expected at least the variation trend would be similar. Yes the trend is similar for the side-side direction. But for the fore-aft direction, the tower-top fore-aft displacement (YawBrTDxt) from FAST tends to decay quickly while it is oscillating for my model, as shown in the second attachment, where the blue line is from my code while the red one is from FAST. I wonder I neglect a ‘damping effect’ in the fore-aft direction, but I don’t know where this damping comes from as there is no tower mode structural damping and I think the aerodynamic damping force is included in f(t).

Unless the applied force is properly in phase with the velocity, the resulting damping may be very different. Your results clearly show phase differences in the displacement, so, my guess is this is the reason your model has a different level of damping. My guess is that you’ll have to introduce an aerodynamic damping term to your model if you wish to capture that effect.

You mentioned that it is needed to introduce aerodynamic damping to model. I have seen structural damping parameters in elastodyn and subdyn modules. But I could not find the way to define aerodynamic damping term. Could you please tell how to change aerodynamic damping as it is important for idling analysis.

I was suggesting that you would have to add an aerodynamic damping term to your mathematical model, not to your FAST model.

Aerodynamic damping is not directly specified in the FAST input files, but is included intrinsically as part of the aero-elastic solution. That is, the aerodynamic force calculated within FAST is dependent on the structural velocity. In your mathematical model, the aerodynamic force is taken from FAST and is not directly dependent on the structural velocity of your mathematical model. Thus, a difference in phasing of the structural velocity between the models will lead to a different level of aerodynamic damping between them.

Thank you for reply. I don’t have mathematical model( I am not Xin Tong ).

I am just using FAST and for my design. I was faced with this graph that says for different loadcases I need to alter aerodynamic damping. I was wondering how to change these aerodynamic damping in FAST?

For structural damping, I altered it in Elastodyn and subdyn input file. But for aerodynamic damping, I have no clue what to do.

I would appreciate if you could tell how to change these parameters?

Regardless, as I said, aerodynamic damping is not directly specified in the FAST input files, but is included intrinsically as part of the aero-elastic solution. In general, the damping will depend on the control region (torque or pitch control region), the slope of the lift coefficient versus angle of attack curve, the rotor speed, the tower natural frequency, etc. I’ve seen papers where explicit approximations of the aerodynamic damping are given; I suggest you review these to gage the effect.

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?

Thank you for your reply. I did not change the settings of Pitch control and Generator control. Both of them are user-defined from Bladed-style DLL as below.

PCMode=5
VSContrl=5

And about active pitch control, I defined start time of override pitch maneuver as longer than time simulation

0 TPCOn - Time to enable active pitch control (s) [unused when PCMode=0]
9999.9 TPitManS(1) - Time to start override pitch maneuver for blade 1 and end standard pitch control (s)

It would appreciate if you could tell me I need to change it?