Dear authors,

thank you very much for the very well elaborated work. It is rare to have a submitted paper to be so well prepared on first submission. Thus, I only have a few very minor aspects to improve:

1. Please make sure, that all variables in the equations are explained at least once. Even if they seem very clear, in other papers, someone might use the exact same variable for something different, which also seems clear. To avoid this confusion, please define once. In most cases this is done, but not in all. So check.

2. On line 303 there seems to be a typo before “LC 2.12”

3. In the paragraph from line 317 on, please use one or two sentences to explain first what step tests are and what they are used for before you go into the discussion.

4. The sentence starting in line 320 is not really good and hard to read. Please check it.

5. On line 331 “and on the operating point in exam.” What is exam?

6. In line 340 the sentence “While not to the same extend, this consideration holds true for most of the blade.” is not very specific and clear. Either leave it away or get or precise, I would say.

7. In line 352 “This is indeed very different form a step test”, most likely it is “from a step test”, isn’t it?

8. On line 416: “BEM-based models are called to perform reliably in …”, I would always say: “BEM-based models are said to perform reliably in …”. What do you think?

9. On line 539 you write about windmill wakes – do you really mean windmills?

Otherwise, the paper opens a lot of room for specific aerodynamic discussion, which most likely cannot be finalized in one single paper. Thus, I find it good this way. But there are still open questions also coming from this paper, which will most likely need to be answered in the further discussions. I’m looking forward to it.

The topic of investigating the performance of BEM codes for FOWT is very interesting and of big practical importance, but not very new. A very similar study was made 10 years ago by

J.B. de Vaal et al., Effect of wind turbine surge motion on rotor thrust and induced velocity, Wind Energy (2012)

The conclusion in the submitted paper is reconfirmed, that a BEM code with a proper dynamic inflow model and an empirical Glauert model for high thrust coefficients used on FOWTs performs quite well for the exposed structural oscillations (amplitudes and frequencies). It would be really nice, if the expected range of frequencies and amplitudes for the DTU 10MW rotor (pitch and surge) was included in the paper for different foundation types. This will also show if going above possible frequencies in the PoliMi tunnel is of practical importance for a real FOWT.

The paper discusses different ways reported in the literature of how to treat the momentum equation in case of a dynamically oscillating wind turbine rotor. In basic fluid mechanics the conservation of momentum is used to determine an unknown force by keeping track of the total momentum deficit out of a control volume and including an inertia term in case of unsteadiness. The mean position of the turbine is not moving, so the control volume and velocities at the boundaries should be in a fixed frame of reference and not include the velocities of the rotor. These should in my opinion only be used when evaluating the angles of attack for the blade elements.

On page 5 and 6 the LLFVW is described as a dynamic vortex model where the vorticity is shed as vortex rings. Note that the coefficients in the Øye Dynamic Inflow model are actually calibrated from a similar dynamic ring vortex approach and the results using an unsteady BEM are therefore expected to be similar to the LLFVW output.

The axial induction velocities from the LLFVW shown in Figure 7 are very small and in the order of 0.03 m/s and compared to the inflow velocity of 4 m/s correspond to an axial induction factor of around a=0.03/4=0.008. If this is true then there is practically no induction for this case and what is the corresponding C_T ?

On page 14 is reported a time constant for the dynamic wake LLFVW computations of around 3-4 seconds. In the Øye Dynamic Wake model the time constant is approximately the rotor diameter divided by the free wind speed and in the case of the UNAFLOW wind turbine should be around tau=2.4/4=0.6 seconds. That is the LLFVW model responds quite much slower to a dynamically changed force than will the Øye model. Since both the Øye dynamic wake model and LLFVW are based on a similar vortex ring model for the shed vorticity what is then the reason for this difference in time constant ? An Actuator Line simulation that through the N-S equations resolves the real physics and inertia of the wake response could be used to check these LLFVW results.  

The result shown in figure 12 is interesting. Here the simulations show that the axial induction factor for a pitching motion of amplitude between 1 and 2 degrees at a frequency of 0.1Hz and at a wind speed of 5 m/s can be as high as a=4 near the blade tip, meaning that the blade will experience a velocity from behind of about 3 times the wind speed. This is estimated to occur at wave heights of 10-13 meters. Is it a realistic scenario to have a wind speed of only 5 m/s at wave heights of more than 10 meters ? And how should a Glauert correction be when the axial induction becomes so large corresponding to a thrust coefficient way above 2 ? And is it the free wind speed or the apparent wind speed taking the structural velocity into account one should use when computing the thrust coefficient CT in a BEM based model ?

It is well known that BEM becomes inaccurate for large blade deflections for a bottom fixed wind turbine. This is because the blade elements are moved away from the rotor plane where the induction is computed combined with a strong streamwise gradient of the induced velocity near the rotor. This effect can become very severe in the case of a floating wind turbine where the position of the rotor plane is continuously moving along the wind direction and how to possibly treat this in a dynamic BEM code should also be discussed in a paper like this. The question is whether the induced velocity field follows the oscillating FOWT or the rotor moves in a velocity gradient fixed in space. This effect is very important and depends on the time constants of the rotor oscillation compared to the inertia (time constants) of the flow as also discussed in the paper by   J.B. de Vaal et al.