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the Creative Commons Attribution 4.0 License.
| 14 Jan 2025
Investigation into Instantaneous Centre of Rotation for Enhanced Design of Floating Offshore Wind Turbines
Abstract. The dynamic behaviour of Floating Offshore Wind Turbines (FOWT) involves complex interactions of multivariate loads from wind, waves, and currents, which result in complex motion characteristics. Although methods for analysing global motion responses are well-established, the time- and location-dependent kinematics remain underexplored. This paper investigates the Instantaneous Centre of Rotation (ICR), a point of zero velocity at a time instance of general plane motion. Understanding and strategically positioning the ICR can reduce the dynamic motion in critical structural locations, enhancing the performance and structural robustness of FOWTs. The paper presents a method for computing the ICR using time domain simulation results and proposes a statistical analysis approach suitable for design studies. Building on prior research, it examines the sensitivity of the ICR to external loading and design features, providing insights into how these factors influence motion response and how the motion response influences the statistics of the ICR, structural loads, and other performance metrics of interest. The study explores two FOWT configurations, a spar and a semisubmersible, identifying design variables that most effectively control the ICR statistics and identifying the ICR statistics most correlated with the responses of interest. Finally, through two case studies, we demonstrate how to apply these new insights in a practical design scenario. By adjusting the design variables most correlated with the ICR (fairlead vertical position and centre of mass for the spar, and mooring line length and heave plate diameter for the semisubmersible), we successfully modified the designs of the floating support structures to reduce the loads in the mooring lines, tower base, and blade roots, improving the ultimate strength and fatigue characteristics as compared to the original designs.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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CC1: 'Comment on wes-2024-167', Frank Lemmer, 15 Jan 2025
Congratulations to a paper on a very relevant topic!
Please note that the comment about our paper (Lemmer2020) is not correct: We did not use a taut mooring system to achieve the desired center of rotation but a modification of the hull of all semi-submersible geometries.Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2024-167-CC1 -
AC1: 'Reply on CC1', Katarzyna Patryniak, 13 Feb 2025
Thank you very much for your comment and clarification. We have revised the text to accurately reflect the scope of your study:
“The authors modified the semisubmersible floating platform designs to ensure that the system rotates about the hub, thereby achieving preferable dynamic response characteristics, improved power quality, and reduced tower base loads”.
We appreciate your input, and the revised version should now be consistent with your work.
Citation: https://doi.org/10.5194/wes-2024-167-AC1
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AC1: 'Reply on CC1', Katarzyna Patryniak, 13 Feb 2025
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RC1: 'Comment on wes-2024-167', Anonymous Referee #1, 30 Jan 2025
general comments
The centre of rotation is an interesting parameter, it is certainly helpful in interpreting the motion behaviour of the floating wind foundation.
However, it does not seem appropriate to 'optimise' a design using this parameter. It doesn't seem possible to clearly identify the most advantageous (=optimal) ICR position, as it is very dependent on the floater concept and the response parameters you want to optimise.
The correlations between the design parameters, the centre of rotation and the response parameters are not very clear, they seem to depend strongly on the floater concept and configuration. This means that the correlations presented in the paper probably cannot be generalised or applied to another floater design. They would have to be recalculated for each design, which is likely to be a time-consuming task. The practical application of this aspect of the study may therefore be limited.
I suggest to acknowledge this limitations of the study related to practical application explicitly in the Conclusions section of the manuscript. This would help to prevent any “unwise” application by less experienced engineers. See also specific comment below.
However, as mentioned in the first paragraph, the ICR is very interesting when it comes to describing the motion behaviour at a high level. For example, plotting the ICR over different wave periods could be a useful figure, together with the motion RAOs and other hydrodynamic parameters.
specific comments
Line 151-154: Change of underwater geometry is (together with the mooring system design parameters) the main design variable for a FOWT (not considering the WTG design). So, excluding the change of hydrodynamic loading on the structure seems to be a serious limitation.
Line 166-167: FOWT are designed to a large extend for ultimate limit strength (ULS) and fatigue limit strength (FLS). The proposed averaging process seems to be targeted at "representative" FLS responses. However, ULS responses (maximum responses within all conditions) would be averaged by this process and thus largely underestimated.
Line 167-168: Are the same seeds used for each design variant? If not results between design variants would not be comparable with each other.
Figure 17: Why do the original design values show different ICR values? Shouldn't all original design values share the same ICR value? The original design values should all represent the same original design configuration and thus have same result values.
Table 10. (FAIRTEN2 mean Value 10983.62): This seems to be a very high mean/static tension especially, considering that usually the dynamic tension is the governing mooring line maximum load.
Table 11. (Platform zCM adjusted value -100.00): The vertical CM of a SPAR is usually already as low as technically possible. Thus, reducing the CM without any major changes to geometry seems unlikely. Then, if geometry would change, hydrodynamic loading would change and the correlations might be different.
Table 13. (Offset column d, mean Re-vol. value 8.38): Offset column has a major impact on hydrostatic stiffness and restoring. Reducing the parameter by this extend is would probably result in insufficient floating stability thus large tilt during power production and even risk of capsizing/downflooding.
technical corrections
none
Citation: https://doi.org/10.5194/wes-2024-167-RC1 - AC2: 'Reply on RC1', Katarzyna Patryniak, 02 Apr 2025
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RC2: 'Comment on wes-2024-167', Anonymous Referee #2, 02 Feb 2025
General comments
In this study, time-domain simulations are used for assessing the behaviour of the instantaneous centre of rotation (ICR) of a floating offshore wind turbine (FOWT), under different environmental loading conditions. Then, by considering two different FOWT concepts (a spar and a semi-submersible), the authors evaluate the influence of the ICR on structural responses that are relevant for a FOWT design (e.g. tower base bending moment, blade root bending moment, mooring line tension). A systematic variation of selected design variables is then performed for both floaters, for determining their influence on the ICR variations. Finally, the authors propose a method to design FOWTs using the observed interplaying involving design variables, ICR behaviour, and structural responses.
The procedure introduced in the paper is original, and a convincing strategy is adopted to relate environmental loading, FOWT design variables, the ICR, and structural responses. For this reviewer, the paper fulfils the requirements for scientific significance that is needed for publication in Wind Energy Science (WES). This reviewer deems the paper’s scientific significant as “good”.
However, the paper fails in presenting very important data and equations needed for a proper interpretation of the results and conclusions. In addition, some problematic theoretical assumptions are adopted which, in this reviewer’s opinion, can significantly impair the credibility and reproducibility of the results. In this case, the criteria for scientific quality stated by WES are not met. Please see the discussion below for details on this. This reviewer deems the paper’s scientific quality as “unsatisfactory”.
The paper is well written, and includes clear and informative figures. The placement of the figures through the paper can sometimes be a bit confusing, though. Overall, the ideas are presented in a logic and well-structured sequence. The paper’s presentation quality is deemed as “good”.
Specific comments
Major comments
Section 2 Methodology
Since the analyses and conclusions are highly dependent on the dynamics of both floaters, the authors must introduce a section with detailed data for each of the FOWT models used in the paper. The data has to include at least: mass and moments of inertia (or radii of gyration), centre of gravity, centre of buoyancy, metacentric height, restoring matrix, added mass, Morison model parameters (element length/diameters and drag coefficients), and natural periods for the relevant degrees of freedom. Also, some data about the wind turbine (thrust at rated wind speed, RNA mass), and mooring system (chain properties, pretension, anchor radius), are also necessary. Without this information, it is not possible for the reader to evaluate if the results presented later in the paper are compatible with the conclusions. For example, how can the reader understand the impact of heave plate size in the ICR coordinates response, if there is no explanation about how the heave plates are modelled? In addition, the results are not reproducible.
Please note that it is not enough to just refer to the original publication describing the floater. This information shall be shown in the present article.
In addition, it is necessary to include the equation of motions, indicating how the variation of the design variables affect the dynamics of the floaters. For example, how does the variation in the heave plates affect the floater response? Which forces are affected by variations in the column diameters? It is impossible understand the impact of the design variations in the responses without knowing how the dynamics are modelled.
Section 2.3 Dynamic simulations
The paragraph starting at line 151 says the potential-theory hydrodynamic coefficients are not re-calculated for the design variations. The justification given for this assumption is that the variations of underwater floater dimensions are kept “small”.
This reviewer believes that this is a very problematic assumption. The variations in diameter for both the spar (at the waterline) and semi (columns) will significantly affect both the added mass and the excitation force, which are directly related with the results and conclusions.
Even more serious may be the variation in the heave plates' diameter (from 19.33 m to 27.35 m), which will very significantly affect the heave and pitch added masses, impacting the floater dynamics substantially.
Doing a very simple approximation for the heave added mass of each column + heave plate set, as the mass of a semi-sphere with the heave plate diameter (A33 = pi*rho*D^3/12): we have 1.9e6 kg for D = 19.33 m, and 5.5e6 kg for D = 27.35. Is it reasonable to neglect the added mass variations in this case?
If the authors are not able to run the potential theory analysis for each design variation, an alternative could for example be to use scaling rules for estimating the radiation and diffraction loads of the design variations, and then re-run the analyses with the scaled loads.
If the authors prefer not to re-run analyses, they at the very least must be able to discuss how this assumption (keeping the potential theory loads unchanged for all design variations) will affect the results – and why they think the conclusions are still valid, after adopting the assumption.
Minor comments
Line 71: You say that the method proposed in the paper is “readily applicable” in a practical design. That may be a bit too optimistic, since the analysis may be quite cumbersome. Please re-word.
Line 107: Please explain what is the meaning of "direct proportion".
Lines 117/118: Seems like the references are flipped (regular waves should be Fig 5, irregular waves should be Fig 6).
Line 124: Please add a reference to the Kolmogorov-Smirnov method.
Line 134: The explanation on how to use the Spearman correlation coefficients is a bit confusing. Can you provide an example, showing how you ranked design variables, ICR coordinates, and FOWT responses?
Line 143: The rotor speed actually varies due to the fluctuations on the relative incident wind, caused by a combination of wind speed variations and RNA motions.
Line 161: This is a bit confusing. It is possible to understand that the peak-shape parameter is not "systematically varied" like the other parameters, but the text says it "is not varied" - and right after it says that the parameter is varied together with Hs and Tp. Please, reword.
Line 165: Missing a reference for the metocean data.
Line 171: Is it possible to bring Figure 16 to this section? Then you save the reader from scrolling several pages to see the frames, and at the same time the floaters are shown in the section they are supposed to be described. I also recommend you increase the axes in the figure - they are much smaller than the floaters themselves, which can make it a bit difficult to see them.
Table 2: Can you include the peak-shape factor for groups B and G?
Line 196: Do you assume a constant current profile? Please clarify.
Line 202: It is not very easy to interpret the results, if I am only to look at Fig 2. Are you able to make a plot of the trajectory of the ICR, for one cycle of one of the regular waves, to illustrate a bit better how the ICR moves? You could for example plot also the floater CG trajectory, in the same figure. Very important to show the coordinate-system axes, too.
Line 204: The longest period considered is 17.0 s. It is hard to believe that these waves will excite surge (Tn = 125 s) very significantly. Even the heave natural period (31 s) is a bit far from that. What is the pitch natural period? If it is not much longer than 17 s, could it be that the increased surge motion is actually caused by coupling with pitch?
Line 215: Any possible interpretation for the non-monotonic trend?
Line 224: It seems this change in mooring loads was not mentioned before.
Line 228: You say that the current load on the spar is insignificant, compared with other loads. Still, the variation of z_ICR varies a lot more for the higher current speed. Why?
Figure 17: Apparently there is a typo describing the marker "Waterline R" (should be "Waterline D" instead?)
Line 334: Lower nacelle acceleration may also be associated with lower tower base bending moment (reduced inertial loads, especially at wave frequency).
Figures 25 and 27: If I understood it correctly, the bars in the figure show only the mean and std deviation for the modified design - but normalized with the values of the original design. If that is correct, then the caption of the figure may be a bit misleading, since the reader can expect to see the data for both designs side-by-side. Please consider rewording.
Tables 12 and 13: There is something strange with the two last lines in the table: the design variables (e.g. line length and heave plate) should not have a mean and a std deviation.
Line 429: You say that changing the ICR mean z-coordinate improved the responses, but that is true only when we ignore the non-practical change in draft, right? Please be as precise as possible in your conclusions.
Citation: https://doi.org/10.5194/wes-2024-167-RC2 - AC3: 'Reply on RC2', Katarzyna Patryniak, 02 Apr 2025
Status: closed
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CC1: 'Comment on wes-2024-167', Frank Lemmer, 15 Jan 2025
Congratulations to a paper on a very relevant topic!
Please note that the comment about our paper (Lemmer2020) is not correct: We did not use a taut mooring system to achieve the desired center of rotation but a modification of the hull of all semi-submersible geometries.Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2024-167-CC1 -
AC1: 'Reply on CC1', Katarzyna Patryniak, 13 Feb 2025
Thank you very much for your comment and clarification. We have revised the text to accurately reflect the scope of your study:
“The authors modified the semisubmersible floating platform designs to ensure that the system rotates about the hub, thereby achieving preferable dynamic response characteristics, improved power quality, and reduced tower base loads”.
We appreciate your input, and the revised version should now be consistent with your work.
Citation: https://doi.org/10.5194/wes-2024-167-AC1
-
AC1: 'Reply on CC1', Katarzyna Patryniak, 13 Feb 2025
-
RC1: 'Comment on wes-2024-167', Anonymous Referee #1, 30 Jan 2025
general comments
The centre of rotation is an interesting parameter, it is certainly helpful in interpreting the motion behaviour of the floating wind foundation.
However, it does not seem appropriate to 'optimise' a design using this parameter. It doesn't seem possible to clearly identify the most advantageous (=optimal) ICR position, as it is very dependent on the floater concept and the response parameters you want to optimise.
The correlations between the design parameters, the centre of rotation and the response parameters are not very clear, they seem to depend strongly on the floater concept and configuration. This means that the correlations presented in the paper probably cannot be generalised or applied to another floater design. They would have to be recalculated for each design, which is likely to be a time-consuming task. The practical application of this aspect of the study may therefore be limited.
I suggest to acknowledge this limitations of the study related to practical application explicitly in the Conclusions section of the manuscript. This would help to prevent any “unwise” application by less experienced engineers. See also specific comment below.
However, as mentioned in the first paragraph, the ICR is very interesting when it comes to describing the motion behaviour at a high level. For example, plotting the ICR over different wave periods could be a useful figure, together with the motion RAOs and other hydrodynamic parameters.
specific comments
Line 151-154: Change of underwater geometry is (together with the mooring system design parameters) the main design variable for a FOWT (not considering the WTG design). So, excluding the change of hydrodynamic loading on the structure seems to be a serious limitation.
Line 166-167: FOWT are designed to a large extend for ultimate limit strength (ULS) and fatigue limit strength (FLS). The proposed averaging process seems to be targeted at "representative" FLS responses. However, ULS responses (maximum responses within all conditions) would be averaged by this process and thus largely underestimated.
Line 167-168: Are the same seeds used for each design variant? If not results between design variants would not be comparable with each other.
Figure 17: Why do the original design values show different ICR values? Shouldn't all original design values share the same ICR value? The original design values should all represent the same original design configuration and thus have same result values.
Table 10. (FAIRTEN2 mean Value 10983.62): This seems to be a very high mean/static tension especially, considering that usually the dynamic tension is the governing mooring line maximum load.
Table 11. (Platform zCM adjusted value -100.00): The vertical CM of a SPAR is usually already as low as technically possible. Thus, reducing the CM without any major changes to geometry seems unlikely. Then, if geometry would change, hydrodynamic loading would change and the correlations might be different.
Table 13. (Offset column d, mean Re-vol. value 8.38): Offset column has a major impact on hydrostatic stiffness and restoring. Reducing the parameter by this extend is would probably result in insufficient floating stability thus large tilt during power production and even risk of capsizing/downflooding.
technical corrections
none
Citation: https://doi.org/10.5194/wes-2024-167-RC1 - AC2: 'Reply on RC1', Katarzyna Patryniak, 02 Apr 2025
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RC2: 'Comment on wes-2024-167', Anonymous Referee #2, 02 Feb 2025
General comments
In this study, time-domain simulations are used for assessing the behaviour of the instantaneous centre of rotation (ICR) of a floating offshore wind turbine (FOWT), under different environmental loading conditions. Then, by considering two different FOWT concepts (a spar and a semi-submersible), the authors evaluate the influence of the ICR on structural responses that are relevant for a FOWT design (e.g. tower base bending moment, blade root bending moment, mooring line tension). A systematic variation of selected design variables is then performed for both floaters, for determining their influence on the ICR variations. Finally, the authors propose a method to design FOWTs using the observed interplaying involving design variables, ICR behaviour, and structural responses.
The procedure introduced in the paper is original, and a convincing strategy is adopted to relate environmental loading, FOWT design variables, the ICR, and structural responses. For this reviewer, the paper fulfils the requirements for scientific significance that is needed for publication in Wind Energy Science (WES). This reviewer deems the paper’s scientific significant as “good”.
However, the paper fails in presenting very important data and equations needed for a proper interpretation of the results and conclusions. In addition, some problematic theoretical assumptions are adopted which, in this reviewer’s opinion, can significantly impair the credibility and reproducibility of the results. In this case, the criteria for scientific quality stated by WES are not met. Please see the discussion below for details on this. This reviewer deems the paper’s scientific quality as “unsatisfactory”.
The paper is well written, and includes clear and informative figures. The placement of the figures through the paper can sometimes be a bit confusing, though. Overall, the ideas are presented in a logic and well-structured sequence. The paper’s presentation quality is deemed as “good”.
Specific comments
Major comments
Section 2 Methodology
Since the analyses and conclusions are highly dependent on the dynamics of both floaters, the authors must introduce a section with detailed data for each of the FOWT models used in the paper. The data has to include at least: mass and moments of inertia (or radii of gyration), centre of gravity, centre of buoyancy, metacentric height, restoring matrix, added mass, Morison model parameters (element length/diameters and drag coefficients), and natural periods for the relevant degrees of freedom. Also, some data about the wind turbine (thrust at rated wind speed, RNA mass), and mooring system (chain properties, pretension, anchor radius), are also necessary. Without this information, it is not possible for the reader to evaluate if the results presented later in the paper are compatible with the conclusions. For example, how can the reader understand the impact of heave plate size in the ICR coordinates response, if there is no explanation about how the heave plates are modelled? In addition, the results are not reproducible.
Please note that it is not enough to just refer to the original publication describing the floater. This information shall be shown in the present article.
In addition, it is necessary to include the equation of motions, indicating how the variation of the design variables affect the dynamics of the floaters. For example, how does the variation in the heave plates affect the floater response? Which forces are affected by variations in the column diameters? It is impossible understand the impact of the design variations in the responses without knowing how the dynamics are modelled.
Section 2.3 Dynamic simulations
The paragraph starting at line 151 says the potential-theory hydrodynamic coefficients are not re-calculated for the design variations. The justification given for this assumption is that the variations of underwater floater dimensions are kept “small”.
This reviewer believes that this is a very problematic assumption. The variations in diameter for both the spar (at the waterline) and semi (columns) will significantly affect both the added mass and the excitation force, which are directly related with the results and conclusions.
Even more serious may be the variation in the heave plates' diameter (from 19.33 m to 27.35 m), which will very significantly affect the heave and pitch added masses, impacting the floater dynamics substantially.
Doing a very simple approximation for the heave added mass of each column + heave plate set, as the mass of a semi-sphere with the heave plate diameter (A33 = pi*rho*D^3/12): we have 1.9e6 kg for D = 19.33 m, and 5.5e6 kg for D = 27.35. Is it reasonable to neglect the added mass variations in this case?
If the authors are not able to run the potential theory analysis for each design variation, an alternative could for example be to use scaling rules for estimating the radiation and diffraction loads of the design variations, and then re-run the analyses with the scaled loads.
If the authors prefer not to re-run analyses, they at the very least must be able to discuss how this assumption (keeping the potential theory loads unchanged for all design variations) will affect the results – and why they think the conclusions are still valid, after adopting the assumption.
Minor comments
Line 71: You say that the method proposed in the paper is “readily applicable” in a practical design. That may be a bit too optimistic, since the analysis may be quite cumbersome. Please re-word.
Line 107: Please explain what is the meaning of "direct proportion".
Lines 117/118: Seems like the references are flipped (regular waves should be Fig 5, irregular waves should be Fig 6).
Line 124: Please add a reference to the Kolmogorov-Smirnov method.
Line 134: The explanation on how to use the Spearman correlation coefficients is a bit confusing. Can you provide an example, showing how you ranked design variables, ICR coordinates, and FOWT responses?
Line 143: The rotor speed actually varies due to the fluctuations on the relative incident wind, caused by a combination of wind speed variations and RNA motions.
Line 161: This is a bit confusing. It is possible to understand that the peak-shape parameter is not "systematically varied" like the other parameters, but the text says it "is not varied" - and right after it says that the parameter is varied together with Hs and Tp. Please, reword.
Line 165: Missing a reference for the metocean data.
Line 171: Is it possible to bring Figure 16 to this section? Then you save the reader from scrolling several pages to see the frames, and at the same time the floaters are shown in the section they are supposed to be described. I also recommend you increase the axes in the figure - they are much smaller than the floaters themselves, which can make it a bit difficult to see them.
Table 2: Can you include the peak-shape factor for groups B and G?
Line 196: Do you assume a constant current profile? Please clarify.
Line 202: It is not very easy to interpret the results, if I am only to look at Fig 2. Are you able to make a plot of the trajectory of the ICR, for one cycle of one of the regular waves, to illustrate a bit better how the ICR moves? You could for example plot also the floater CG trajectory, in the same figure. Very important to show the coordinate-system axes, too.
Line 204: The longest period considered is 17.0 s. It is hard to believe that these waves will excite surge (Tn = 125 s) very significantly. Even the heave natural period (31 s) is a bit far from that. What is the pitch natural period? If it is not much longer than 17 s, could it be that the increased surge motion is actually caused by coupling with pitch?
Line 215: Any possible interpretation for the non-monotonic trend?
Line 224: It seems this change in mooring loads was not mentioned before.
Line 228: You say that the current load on the spar is insignificant, compared with other loads. Still, the variation of z_ICR varies a lot more for the higher current speed. Why?
Figure 17: Apparently there is a typo describing the marker "Waterline R" (should be "Waterline D" instead?)
Line 334: Lower nacelle acceleration may also be associated with lower tower base bending moment (reduced inertial loads, especially at wave frequency).
Figures 25 and 27: If I understood it correctly, the bars in the figure show only the mean and std deviation for the modified design - but normalized with the values of the original design. If that is correct, then the caption of the figure may be a bit misleading, since the reader can expect to see the data for both designs side-by-side. Please consider rewording.
Tables 12 and 13: There is something strange with the two last lines in the table: the design variables (e.g. line length and heave plate) should not have a mean and a std deviation.
Line 429: You say that changing the ICR mean z-coordinate improved the responses, but that is true only when we ignore the non-practical change in draft, right? Please be as precise as possible in your conclusions.
Citation: https://doi.org/10.5194/wes-2024-167-RC2 - AC3: 'Reply on RC2', Katarzyna Patryniak, 02 Apr 2025
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