Seakeeping Tests of a FOWT in Wind and Waves: An Analysis of Dynamic Coupling Effects and Their Impact on the Predictions of Pitch Motion Response

Round 1

Reviewer 1 Report

Review of:

Article title: Seakeeping tests of a FOWT in wind and waves: an analysis of dynamic coupling effects and their impact on the predictions of pitch motion response

Authors: Giovanni A. Amaral , Pedro C. Mello, Lucas H. S. do Carmo , Izabela F. Alberto, Edgard B.

Malta, Alexandre N. Simos, Guilherme R. Franzini, Hideyuki Suzuki and Rodolfo T. Gonçalves3

The present article is focused on the numerical and experimental investigation of dynamic coupling effects on FOWT motions in wind and waves. The FOWT has a semi-submersible substructure and it is moored by means of three catenary lines.  Experimental tests were done for the FOWT model on regular and irregular waves for different wave angles and wind velocities. An active fan was used to emulate the rotor thrust during the tests, according to the loads predicted by a code integrated to the experimental tests in a SIL scheme. The calibration of wind thrust actuator as well as the experimental tests were properly described. The experimental results were compared with numerical ones in order to investigate a parametric optimization of the floater and mooring system geometries.

Comments:

I enjoyed reading the present article that provides consistent information about the studies made on FOWT in wind and waves. Here are my observations:

1) Please provide more information about the waves characteristics, especially for transient waves, for a better understanding of the hydrodynamic response of the FOWT model.

2) At Paragraph 2.6. Numerical model, please provide more information about grid features.

3) Line 7  “a non-negligible tilt angle..” – there is an extra dot?

4) Line13  “the simulation of FOWTs in waves and in in” – in appears for two times.

5) In the title there is written “Seakeeping”  and, for example,  at Line 25 “sea – keeping”.

6)) Line 59 “second approach, no compensation was made, allowing situations with somewhat çarge tilt angles” – the word/sentence should be revised.

7) Line 80 “hydrodynamic model will be evaluated by confronting the predictions with the to experimental results”   - maybe the phrase should be revised.

8) Please consider to describe the numerical and experimental results representation before Figure 16 and 17. The description appear at Line 292, after Figure 18:

“ 291 Finally, Fig. 18 presents the numerical model calibration versus the experimental data. The red

292 cross marks are the experimental curve for the model with the turbine on at the 11.6 m/s wind speed.

293 The black curve is the numerical model with the even keel configuration. The red line is the model

 294 heeled at the angle of 4 degrees due to the turbine moments.”

9) Please consider to add a Nomenclature section to the article, since there are parameters with no descriptions (for example PSD -Line 123).

Comments for author File: Comments.pdf

Author Response

First of all, we thank the reviewers for their constructive criticism, comments and suggestions. We also acknowledge that they helped us improve the paper quality. The modifications in the new version are highlighted in blue. Here, we address the points raised.

Q1) Please provide more information about the waves characteristics, especially for transient waves, for a better understanding of the hydrodynamic response of the FOWT model.

A1) We would like to thank you for this comment. For the present paper, just white-noise type waves were analyzed. This information was not clear in the text, as we tried to inform that as part of the whole project work test with other types of waves were carried out. Thus, we removed this misinformation and focused on the white-noise type wave only. The characteristics of this wave are still in the text can be found in lines 120-124, and the wave measurements and PSD derived from it can be found in Figure 4.

Q2) At Paragraph 2.6. Numerical model, please provide more information about grid features.

A2) Once more, we thank you for your comment. We added in the text the grid information (Line 181). Indeed, the numerical mesh was represented in high-order surfaces with panel size 5.

Q3-Q6) Typographical errors.

A3-A6) These errors were corrected in the text. Thank you for pointing them out.

Q7) Line 80 “hydrodynamic model will be evaluated by confronting the predictions with the to experimental results”   - maybe the phrase should be revised.

A7) We agree with your comment. In fact, we reorganized the introduction as a whole, in order to be more precise in informing the developments and contributions of the present work. This phrase in specific was removed, the last paragraph from the introduction section was rewritten and can be found in lines 80-88.

Q8) Please consider to describe the numerical and experimental results representation before Figure 16 and 17. The description appear at Line 292, after Figure 18:

“ 291 Finally, Fig. 18 presents the numerical model calibration versus the experimental data. The red

292 cross marks are the experimental curve for the model with the turbine on at the 11.6 m/s wind speed.

293 The black curve is the numerical model with the even keel configuration. The red line is the model

 294 heeled at the angle of 4 degrees due to the turbine moments.”

A8) We kindly accepted your advice and reorganized the Results section. Now, the description of the numerical and experimental results is placed before the first Figure (Fig. 16). It can be found in lines 281 - 283.

Q9) Please consider to add a Nomenclature section to the article, since there are parameters with no descriptions (for example PSD -Line 123).

A9) We thoughtfully considered your comment, and decided to include the description to all acronyms used in the text at their first appearance. For instance, PSD (power spectrum density) can be found in line 123.

Reviewer 2 Report

The topic of investigation is interesting. In particular the results of model tests are valuable and may be of interest for the researchers and designers of FOWTs. In order to make the results feasible for the others, the authors should give all the relevant data of the investigated structure. In particular, I miss the information of mass moments of inertia. The Authors used both regular (monochromatic), and what they call white-noise, waves. I would suggest that they use the term white-noise type waves. The reason for this is the fact that the PSD of thus generated waves is restricted to a certain bandwidth and not even.

While the experimental part is pretty well documented, the same can’t be said about the numerical model. The description is very sketchy and full of errors. You do not present mathematical model, transfer function nor Response Amplitude Operator function (modulus of the latter), although in line 192 you refer to Eq. 4 as RAO. There are some formulas given without a proper definition of the variables used in them. Actually, some of them are mis-used or at least mis-printed; for instance Act of Eq. 1. It seems for me that turbine area is A and Ct some coefficient. How do you define turbine area? Is it disk area of rotor or for instance projected blade area? What is FWind? Is it the same as thrust T? You should list your assumptions, like for instance quasi-steadiness assumption behind the formula 3, which does not take into account rotor pitch setting and inertia.

You tend to form very long and complex sentences which make difficult your arguments. In particular lines 272- 283 are difficult to follow.

What do you mean by calibration of the numerical model? I guess you make some kind of adjustment of it, based on the test data.

Section 4 that is Conclusions should be shortened. In particular you should not repeat yourself and describe what you have done once again. Present the conclusions of your research, only.  In lines 321-322 you claim you used transient waves. As I understood from your earlier description you used regular and irregular (white-noise type) waves only. Transient waves are completely another story.

I suggest that you correct carefully the numerical model description or leave it away completely. In the present form it does not qualify for publication. Other correction as suggested by me, are easy to implement.

Author Response

First of all, we thank the reviewers for their constructive criticism, comments and suggestions. We also acknowledge that they helped us improve the paper quality. The modifications in the new version are highlighted in blue. Here, we address the points raised.

Q1) The topic of investigation is interesting. In particular the results of model tests are valuable and may be of interest for the researchers and designers of FOWTs. In order to make the results feasible for the others, the authors should give all the relevant data of the investigated structure. In particular, I miss the information of mass moments of inertia.

A1) We thank you and agree with your comments. Indeed, some important information was missing in the first version of the paper. Thus, we included the mass/inertia matrix, which can be found in Eq. 1 with comments in lines 182-186. We also included more information, in special the hull mass, in the model characterization Section in Table 1.

Q2) The Authors used both regular (monochromatic), and what they call white-noise, waves. I would suggest that they use the term white-noise type waves. The reason for this is the fact that the PSD of thus generated waves is restricted to a certain bandwidth and not even.

A2) We agree with your pertinent comment and implemented it in the text. The corrected terms can be found in different parts of the text, in special in the wave characterization in line 118. Additionally, we would like to clarify that for the present just white-noise type waves were analyzed. This information was not clear in the text, as we tried to inform that as part of the whole project work, tests with other types of waves were carried out. Thus, we removed this misinformation and focused on the white-noise type wave only.

Q3) While the experimental part is pretty well documented, the same can’t be said about the numerical model. The description is very sketchy and full of errors. You do not present mathematical model, transfer function nor Response Amplitude Operator function (modulus of the latter), although in line 192 you refer to Eq. 4 as RAO. There are some formulas given without a proper definition of the variables used in them. Actually, some of them are mis-used or at least mis-printed; for instance Act of Eq. 1. It seems for me that turbine area is A and Ct some coefficient. How do you define turbine area? Is it disk area of rotor or for instance projected blade area? What is FWind? Is it the same as thrust T? You should list your assumptions, like for instance quasi-steadiness assumption behind the formula 3, which does not take into account rotor pitch setting and inertia. (...) I suggest that you correct carefully the numerical model description or leave it away completely. In the present form it does not qualify for publication. Other correction as suggested by me, are easy to implement.

A3) Thank you again for your great comment. We agree that the numerical model characterization was not in a proper form. Thus, we decided to rewrite it with all the needed corrections. All variables are now well defined and the assumptions are presented. All corrections can be found in lines 193-209.

Q4) You tend to form very long and complex sentences which make difficult your arguments. In particular lines 272- 283 are difficult to follow.

A4) We agree with your comment. The results description and discussion was not written in a good way. We tried to be more precise and clear, rewriting the numerical-experimental correlation part of the text. In this sense, we accepted your advice and tried to reduce our sentences. The corrections can be found in lines 278-295. 

Q5) What do you mean by calibration of the numerical model? I guess you make some kind of adjustment of it, based on the test data.

A5) Yes, we have made an empirical adjustment based on the test data and the wind turbine response curve. We included this information in the text in order to clarify this point in lines 295-297.

Q6) Section 4 that is Conclusions should be shortened. In particular you should not repeat yourself and describe what you have done once again. Present the conclusions of your research, only.  In lines 321-322 you claim you used transient waves. As I understood from your earlier description you used regular and irregular (white-noise type) waves only. Transient waves are completely another story.

A6) We agree with this very pertinent comment. Indeed, the Conclusion section was too long and repetitive.  In this sense, we rewrote and shortened it, focusing only on the most relevant conclusions. Once more, all the misinformation related to the type of wave used for the tests were verified.

Reviewer 3 Report

Fine Journal with some good experiments. 

Though, some general comments which should be corrected before publications:

1. All units should be written according to the MDPI layout guide. With space and non-italic font.  
2. Be more consistent in your terminology of things, like e.g.
   1. wave basin, basin, tank, ocean basin
3. Do a final spell check on the paper, I have highlighted some in the attached pdf.
4. A replacement of the figures in the journal would benefit the readability of the journal. The latter figures are often placed 2-3 pages after their first citation.  
5. The conclusion is a bit too long in my opinion. Reduce it and make in more precise.
6. The State of Art chapter is limited, a more thorough analysis must be conducted. Thereby, also a more detailed and concrete explanation of the novelty of the work can be made. 

Questions: 

1. What type of scaling law have you used? I know that e.g. Froude scaling is preferred by many for FOWT, but I could not find what law you have used.
2. Have you tested for more trim adjustments then +5 deg, which shows the same results of reduced motion in pitch ? Otherwise, two scenarios are maybe a bit risky to draw a general conclusion on. 

Additional Questions in the attached PDF.

Best regards. 

Comments for author File: Comments.pdf

Author Response

First of all, we thank the reviewers for their constructive criticism, comments and suggestions. We also acknowledge that they helped us improve the paper quality. The modifications in the new version are highlighted in blue. Here, we address the points raised.

Some general comments which should be corrected before publications:

Q1) All units should be written according to the MDPI layout guide. With space and non-italic font.  

A1) All units and algorisms were verified. In particular, the damping coefficients can be found in lines 312-313.

Q2) Be more consistent in your terminology of things, like e.g. wave basin, basin, tank, ocean basin.

A2) We agree with this pertinent comment. We decided to use the term "wave basin" whole text. Corrections can be found all over the text, highlighted in blue.

Q3) Do a final spell check on the paper, I have highlighted some in the attached pdf.

A3) We thank you for your advice and for having pointed out some typographical mistakes. We have corrected them all and the corrections are highlighted in the text.

Q4) A replacement of the figures in the journal would benefit the readability of the journal. The latter figures are often placed 2-3 pages after their first citation.  

A4) We kindly agree with your pertinent comment. We tried to reorganize the positions of the figures in the text. In particular, the figures in the Results and Discussion section are now placed closer to their first citation. We hope this improves the readability of the article. Thank you for this advice.

Q5) The conclusion is a bit too long in my opinion. Reduce it and make in more precise.

A5) We agree with this very pertinent comment. Indeed, the Conclusion section was too long and repetitive. In this sense, we rewrote and shortened it, focusing only on the most relevant conclusions of the work.

Q6) The State of Art chapter is limited, a more thorough analysis must be conducted. Thereby, also a more detailed and concrete explanation of the novelty of the work can be made. 

A6) Firstly, we would like to thank you for this comment. We included a literature review on experimental methodologies for FOWT. In special, details on different approaches for the wind force emulations are now presented. In particular, we included a recent work from the OC6 research project that also discusses heave-pitch couplings noticed in an experimental campaign with a semisubmersible FOWT under waves and constant wind thrust. This result has just been presented to the public at the 2021 DeepWind Conference. At least for the authors' knowledge, there are no other articles reporting these effects of the platform tilt.

Questions: 

Q1) What type of scaling law have you used? I know that e.g. Froude scaling is preferred by many for FOWT, but I could not find what law you have used.

A1) We have used Froude scaling law for both hydro and aerodynamic loads. This was possible due to the SIL approach implemented for the model tests. We added this information in the text in line 136, to clarify this doubt.

Q2) Have you tested for more trim adjustments then +5 deg, which shows the same results of reduced motion in pitch ? Otherwise, two scenarios are maybe a bit risky to draw a general conclusion on.

A2) We thank you for this great question. We would like to test other trim adjustments other than +5 deg. However, we believe that 10 deg higher than mort of the FOWT projects have been considering recently. We agree that two scenarios could be not sufficient for strong conclusions, but the tilt range seems to be representative enough. In any case, we decided to soften the conclusion and point out that higher tilt angles should at least be the subject of a more cautious analysis. This discussion can be found in lines 288-291. 

Additional Questions in the pdf:

Q1) Concerning typographical errors and minor text corrections.

A1) We thank you for having pointed out some typographical errors and minor text corrections. We corrected them all, and the corrections can be found in blue all over the text.

Q2) Do you not have a better picture of the FOWT model other then figure 3. It is very hard to see. 

A2) We decided to include a picture of the model hull in Fig. 1.

Q3) Lines 121-122: "The white-noise wave had a duration of 1315 s with energy
ranging from 6.4 s to 27 s." Do not understand, please reformulate. 

A3) We corrected the phrase to be more precise. "The significant wave height was equivalent to 1.9 m with constant energy distribution over a range of period from 6.4 s to 27 s", in lines 121-122.

Q4) Confusing to talk about full scale range, when talking about measurements from the load cell. maybe shift around. the scaled model peaks seems higer on figure 6 (approx 0.15N) ?

A4) We thank you for your comment. We have chosen to present this physical quantity in fullscale to make them compatible with all information exposed in the paper, even though it is a load cell reading. Fig. 6 is a step response typical of the actuator in the model scale of 4 N of constant thrust. It is not the same test from Fig. 7 that shows a thrust input from BEMT.

Q5) How to you make sure to only measure the thrust force, when you have a length between the load cell and the actuator ?
Hard to see the full setup on picture. 

A5) We agree it is not visible the pivot point of the bench in the original Figure. We decided to change it for a new better picture of the bench. The new one shows the pivot point, composed of a bearing. The pivot point length between load cells and propeller are different, and we took the load cells readings and adjusted the force scaled by the summing of the moment in the pivot point. Then, we have obtained the exact thrust on the propeller height. At the resting condition, we have made a zeroing on load cell readings at the amplifier to null the weight of the bench. The propeller thrust was then read without any other force influences over the bench.

Q6) Please state in caption if the values are found experimentally or obtained numerically.

A6) We agreed on adding in the caption this additional information.

Q7) Line 250 "Only the cases without trim adjustment (TA) are shown.". Why are they now shown?

A7) We decided to present the results in a way that could contribute to the understanding of the effects that were under investigation. In this sense, first, only results without TA were presented, in order to show de worst tilt scenario and its impact on the RAOs. Then, the TA was investigated experimentally, followed for the progressive numerical approach was presented.

Q8) what is the "proper" mooring system stiffness?

A8) We have modeled the mooring system taking into account the correct offset and attitude of the case under investigation. For instance, for the 11.6 m/s wind case without TA, the offset and tilt were 10.3 m and -9.2°, respectively. The stiffness coefficients were then calculated around this mean (static) position. 

Q9) Figure 13. Make the Figure a 2x3 plot, and move the legend into one of the figures.

A9) We thank you for your comment and understand your request. However, the plots in Fig. 13 represent the coefficients of the 3x3 mooring system stiffness matrix, and they are presented in a matrix form (considering the symmetry). We decided to keep the plot, clarifying this important doubt in the text in lines 230-232.

Round 2

Reviewer 2 Report

I am satisfied with most of the corrections&revisions of the paper. Unfortunately, I find that the Authors have problems with the presentation of the numerical model. Variable omega, used in Eq. 3, is not defined. The reader has to guess that the Authors mean by it angular frequency of the motion. If this is the case, Equation 3 applies for monochromatic motion with surge and pitch being in-phase, ie no phase difference of these two motion components. Moreover, if X5 stands for pitch RAO with the units [deg/m], as defined for instance in Fig. 14, there is a confict of units. Same applies to Eq. 4. There must be something wrong with Eq. 5 when used in Eq. 4 as such. Checking the units of it:

[kg/m3][m2][s/m][m2|s2]=[kg/s]

gives the units for force Fwind due to surge motion [kg/s2], which is obviously wrong.

The formulas would be correct if instead of the so-called RAOs X1 and X5 multiplied by angular frequency omega surge and pitch velociteies were used.

Author Response

Once more, we thank the reviewer for your comments and suggestions, that will help us improve the paper quality. Again, the modifications in the new version are highlighted in blue (keeping the old corrections also in blue). Here, we address the point raised.

Q1) I am satisfied with most of the corrections&revisions of the paper. Unfortunately, I find that the Authors have problems with the presentation of the numerical model. Variable omega, used in Eq. 3, is not defined. The reader has to guess that the Authors mean by it angular frequency of the motion. If this is the case, Equation 3 applies for monochromatic motion with surge and pitch being in-phase, ie no phase difference of these two motion components.

A1) We thank you for this really pertinent comment. We reformulated the text about the numerical model in order to make it clearer. As suggested, the definition of the surge and pitch motions as used in Eqs 3 to 5 were made clearer. We also tried to emphasize that the model is linear, hence the different wave components of a real sea are indeed treated as if they were independent monochromatic waves inducing monochromatic motions at their corresponding frequencies. This can be found in lines 196-199.

Q2) Moreover, if X5 stands for pitch RAO with the units [deg/m], as defined for instance in Fig. 14, there is a confict of units. Same applies to Eq. 4.

We agree with this comment. If numerical values were to be substitute into the equations, they should be in radians. However, we decided to plot in the figures the pitch motion degrees, to simply make it easier for the reader to have a physical grasp of the results. 

Q3) There must be something wrong with Eq. 5 when used in Eq. 4 as such. Checking the units of it:

[kg/m3][m2][s/m][m2|s2]=[kg/s]

gives the units for force Fwind due to surge motion [kg/s2], which is obviously wrong.

The formulas would be correct if instead of the so-called RAOs X1 and X5 multiplied by angular frequency omega surge and pitch velociteies were used.

We thank you again for this comment. Following the definition of the aerodynamic force, as given by Eq. 4, the units of coefficient B given in Eq 5 are [N.s/m], or [kg/s], i.e. a force divided by a velocity (a consequence of the derivative with respect to V). Hence, when this relation is used in Eq. 4, the resulting units are newtons, as they should be. We rewrite the text in order to make it clearer, in lines 200-204.