The Effect of Continuous Trapezoidal Straight Spoiler Plates on the Vortex-Induced Vibration of Wind Turbine Towers

Round 1

Reviewer 1 Report

1.- Literature review is not sufficient, there lot of work in the literature on VIV on wind turbine towers and more recent studies should be reviewed and reported.

2.- The units of measures in the figures and tables are confusing. (ie: time/s, W/t).

3.- Perform a dimensional analysis of the experiments to validate the results, such as Geometric Similarity, Kinematic Similarity, and Dynamic Similarity.

4.- According to the FFT spectrum results, the VIV frequencies of the O-tower model (fsw) and the Ts-tower model (fs) are 5.625 Hz and 3.345 Hz, the reduction rate is reached 40.53 %, it is similar to the reduction rate obtained by the simulation analysis (34.3 %). What about the amplitudes?

5.- The results of the paper should be compared with the literature studies in tabulated form. The operating parameters, and outcomes could be considered for this comparison. This will increase the clarity to the reader and highlight the outcome of this article.

6.- The pointwise presentation of conclusions will improve the readability.

Author Response

Response to Reviewer 1 Comments

 

Point 1: Literature review is not sufficient, there lot of work in the literature on VIV on wind turbine towers and more recent studies should be reviewed and reported.

 

Response 1: More literatures have been refered to Introduction section, and the reference list has also been updated. The added literatures are 1、4、11、23-25 and 31.

 

Point 2: The units of measures in the figures and tables are confusing. (ie: time/s, W/t).

 

Response 2: The units of measures in all figures are regulated. (figures 7、8、10、13、19、20)

 

Point 3: Perform a dimensional analysis of the experiments to validate the results, such as Geometric Similarity, Kinematic Similarity, and Dynamic Similarity.

 

Response 3: The geometric similarity and dimensinal analysis of experiments are added in section 4.5 as following:

“For comparison with the actual sizes of the O-tower and TS-tower in Table 4, the di-ameter and height of the test specimens used in the experiment are reduced by 50 times (D = 80 mm and H = 100 mm). On the basis of the model similarity criterion, the TS sizes L2 and L3 are also reduced by 50 times correspondingly. At the same time, the TS numbers and angle remained as 50 pieces and 61 degrees, respectively, because the two parameters are not related to the size difference.”

 

Point 4: According to the FFT spectrum results, the VIV frequencies of the O-tower model (fsw) and the Ts-tower model (fs) are 5.625 Hz and 3.345 Hz, the reduction rate is reached 40.53 %, it is similar to the reduction rate obtained by the simulation analysis (34.3 %). What about the amplitudes?

 

Response 4: The amplitude of FFT spectrum means the power spectral density (PSD) of air pressure signal in unit frequency band, the frequency which is corresponding to maximum PSD is the typical exciting frequency. In this research, it is the VIV frequency, and the explaination has been added to the paragraph.

 

“According to the FFT spectrum results, the VIV frequencies of the O-specimen (fsw) and TS-specimen (fs) are 5.562 Hz and 3.345 Hz (the frequencies that correspond to the maximum power spectral density of air pressure signals), respectively, and a reduction rate of 40.53 % is reached, similar to the reduction rate obtained by the simulation analysis (34.3 %).” (in section 4.5, page 15)

 

Point 5: The results of the paper should be compared with the literature studies in tabulated form. The operating parameters, and outcomes could be considered for this comparison. This will increase the clarity to the reader and highlight the outcome of this article.

 

Response 5: The reduction rates of lift coefficient and drag coefficient after TS addition (see Figure 12, in page 11) are compared with the data derive from literature:

 

 “Figure 12 illustrates the time history curves of the Cl and Cd of the TS-tower. The results indicate that the value of the Cl is within the range of -0.05 to 0.05, the average value of the Cd is 0.25, and that the general trend in the time history is similar to that of the O-tower. The reduction rates of the Cl and Cd after the addition of TS have achieved values of 84.3% and 81.6%, respectively. According to the research conclu-sions of Gustavo R.S. Assi et al. [23], the S45-serrated 45-strake model can supply a 55% lift reduction and 57% drag reduction; comparison of the reduction rates validates and evaluates the effectiveness of reducing VIV due to the addition of TS.”(in section 4.3, page 10-11)

 

Point 6: The pointwise presentation of conclusions will improve the readability.

 

Response 6: The pointwise presentation of concluisions have been revised.

Reviewer 2 Report

The performed study lacks novelty and generality. It looks more like an engineering project than a scientific paper. I do not recommend it for publication in its current form.

Some particular comments are provided below:

• The Abstract is not written clearly and should be rewritten and improved. Overall, the language throughout the paper should be improved.
• Wind turbine towers very much resemble chimneys and industrial stacks. The questions of VIVs are resolved with these structures, and whole chapters of international standards provide guidelines on how to estimate and overcome these issues. This should be clearly mentioned and referenced in the Introduction.
• When mentioning Fig. 1, it should be clearly stated that not all wind speeds induce vortex shedding, and that it happens only at particular regimes (lower speeds).
• U is a very strange notation for kinematic viscosity.
• Provide the actual names of the dimensionless numbers Re and St in the text.
• (7) and (8) are not dimensionless. They are either missing a characteristic length, or forces Fl and Fd are per unit length. This should be corrected or explained better.
• Somewhat arbitrary choice of Re = 100 is not explained well. When would this small Re ever occur with wind turbine tower whose diameter is 4 m? It seems the authors just wanted to simulate a case with vortex shedding, and have not considered the actual structures. This greatly decreases the validity of the performed study.
• It should be clearly stated how big are the generated fluid meshes and if mesh convergence study was performed. It is not sufficient to just say that meshes are “high-quality”. How is this high-quality quantified?
• It should be clearly stated how fluid flow around TS-towers was computed? TS modifications will certainly induce transition to turbulence, so how was turbulence resolved?
• 7 should also contain points clearly showing the angles for which the computations were performed. The same goes for Fig. 9.
• The mentioned effects of TS parameters are highly dependent on the assumed Re. Can the authors provide any recommendations on how these effects would change with Re, since much higher values of Re can be expected at real structures?
• Can a simple point mass adequately represent the nacelle and rotor, particularly if the blades are rotating? Were the two models (this simplified vs. a more realistic one) compared to establish the validity of this assumption? The actual nacelle and rotor quite alter the modal characteristics of the whole structure and should be appropriately modeled. Correct this, or provide an explanation in the text.
• Provide more details on the used numerical set-up of the modal analysis.
• In Table 5, the authors are actually comparing the first three modes, and not the first five as written.
• Can the obtained experimental results even be compared to the numerical ones, when the model is so scaled-down? It is apparent that completely different frequencies of vertex shedding are captured. Therefore, there is no certainty that the obtained conclusions can be simply translated to a bigger structure.

Author Response

Response to Reviewer 2 Comments

 

Point 1: The Abstract is not written clearly and should be rewritten and improved. Overall, the language throughout the paper should be improved.

 

Response 1: The abstract has been rewritten, and the language of the manuscript has been improved carefully:.

 

Abstract: This paper proposes a method of controlling the vortex-induced vibration (VIV) of wind turbine towers by adding continuous trapezoidal straight spoiler plates (TS) onto their outer surface: a fluid–solid coupling model was constructed to simulate the processes of Karman vortex genera-tion and shedding on the different surfaces of an original tower (O-tower) and a tower with TS (TS-tower) with assumed and actual Re, while the VIV frequencies were also calculated and compared; the effects of the TS geometry parameters on the VIV frequency of towers were studied to investigate the recommended size; a modal analysis was carried out to research the effects of TS on the vortex-induced resonance risk of towers; and the simulation results as well as relevant re-search conclusions were validated by an analogical wind tunnel test.

 

Point 2: Wind turbine towers very much resemble chimneys and industrial stacks. The questions of VIVs are resolved with these structures, and whole chapters of international standards provide guidelines on how to estimate and overcome these issues. This should be clearly mentioned and referenced in the Introduction.

 

Response 2: This issues have been mentioned in Introduction section:

 

“……Considering the great influence of VIV on the structural safety of wind turbine towers, it is seriously significant to investigate effective solutions for reducing VIV. In reality, wind turbine towers very much resemble chimneys and industrial stacks, and some of the literature and international standards have provided certain methodologies for resolving VIV issues of similar structures. Generally speaking, there are three common methods to reduce the influence of VIV on large structures:”（the end of first paragraph in page 2, above Figure 1）

 

More relevant literatures have been refered to Introduction section, and the reference list also has been updated. The added literatures are 1、4、11、23-25 and 31.

 

Point 3: When mentioning Fig. 1, it should be clearly stated that not all wind speeds induce vortex shedding, and that it happens only at particular regimes (lower speeds).

 

Response 3: The revision was carried out for the second paragraph of Introduction section in page 1:

 

“Figure 1 indicates the mechanism of VIV generation by towers. If the wind flows through the surface of a tower at particular regimes (i.e., lower speeds, laminar), the airflow will generate periodic vortices on both sides of the tower; consequently, the fluid pressure will be varied when the vortices are shedding from a tower’s surface, and the extra load excitation derived from such differential pressure causes a tower to vibrate periodically.” (the beginning of the second paragraph of section 1: Introduction)

 

Point 4: U is a very strange notation for kinematic viscosity.

 

Response 4: The notation of kinematic viscosity has been changed to v, and U is defined as the notation for flow velosity.

 

Point 5: Provide the actual names of the dimensionless numbers Re and St in the text.

 

Response 5: The actural names of Re and St are provided when they are first mentioned, and are listed in Nomenclature.

 

“The Reynolds number (Re) and the Strouhal number (St) are important dimen-sionless parameters in the flow around circular cylinders.” (in section 2.1, the middle of page 4)

 

Point 6: (7) and (8) are not dimensionless. They are either missing a characteristic length, or forces Fl and Fd are per unit length. This should be corrected or explained better.

 

Response 6: The revision was carried out for the last paragraph of in page 4, it has been corrected:

 

“According to the theory of flow around circular cylinders, the ratios of the lift force and drag force per characteristic length (the diameter of a tower, D) to the dynamic pressure of airflow are defined as the lift coefficient (C_l) and drag coefficient (C_d). These two important coefficients can be obtained as shown in Equations (7) and (8):”

 

Point 7: Somewhat arbitrary choice of Re = 100 is not explained well. When would this small Re ever occur with wind turbine tower whose diameter is 4 m? It seems the authors just wanted to simulate a case with vortex shedding, and have not considered the actual structures. This greatly decreases the validity of the performed study.

 

Response 7: Re is a very important condition which is relative to the accuracy of simulation result definitly, it is really necessary to consider actual Re for the research. At the beginning of the project, the original purpose is to analyze the effects of TS on VIV problem by analyzing the situation of Karman vortex, so the simulation was focus on how to clarify the vortex generation and shedding obviously. Furthermore, the research object derived from a wind turbine which was destroyed by serious VIV resonance, so we tried to carry out the research on the basis of the wind turbine tower.

 

In previous research, we considered the vortex generation should be more clear under laminar flow condition, and the convergence of the solving progress should be better, so we just chose assumed Re = 100 to validate the reasonability of the model and algorithm. Although Re is assumed, the simulation results still could reflect some significant conclusions, so we prepared the manuscript on the basis of the simulation with assumed Re, and we considered that the laminar model and obtained conclusions should be the fundation for further research.

 

Actually, we always keep optimizing the model all the time in order to find resonable method to simulate the vortex under turbulence flow condition with actual Re. During the preparation of the manuscript, we have obtained some expected progress. Our latest model can simulate the vortex generation clearly and calculate VIV frequency with actual Re, the result can also validate the effects of TS on VIV frequency reduction. The updated results and relevant discussions are added to the new section 4.3 in the text (page 11).                 

 

Point 8: It should be clearly stated how big are the generated fluid meshes and if mesh convergence study was performed. It is not sufficient to just say that meshes are “high-quality”. How is this high-quality quantified?

 

Response 8: The specified description of mesh quality and accruacy requirements are added in the text:

 

“The preprocessing is carried out by using Hypermesh software, and the total number of elements totals almost 920000. The fluid elements are meshed under the following quality control parameters:

• All elements are first- order tetrahedral, and the type is Solid185;
• Aspect ratio > 5,
• Tetrahedral collapse ratio < 0.5,
• Equiangle skew ratio > 0.7,
• Volume skew ratio > 0.95;
• Jacobian < 0.7;

After the element quality check process, the unqualified rates of all of the control parameters must be controlled within 1%. In this instance, the simulation results after convergence will not be influenced significantly by variation in element density; con-sequently, the quality of the fluid elements can be considered to satisfy accuracy re-quirements.”(in the first paragrapg of section 3.2, page 7)

 

Point 9: It should be clearly stated how fluid flow around TS-towers was computed? TS modifications will certainly induce transition to turbulence, so how was turbulence resolved?

 

Response 9: The fluid domain around the TS-towers was meshed as boundary layer, and the monitor point should be located in boundary layer to capture the pressure variation. The size of TS is much less than the scale of tower, so we consider that the effectiveness of TS should be mainly performed by varying the roughness of the surface. The velocity streamline results indicates the turbulence around TS-tower is not very obvious under lamina flow condition, so the simulation in this case study does not consider the influence of the turbulence. Actually, the mentioned turbulence in this comment is a very important issue for VIV problem. The research regarding the topic of this paper will be continued to optimized the methodolody to simulate VIV under turbulence flow condition more accurately, and we will consider and disscuss the simulating aglorithm and relevant influence of the mentioned turbulence carefully in our future works.

 

The relevant explainations regarding the specific simulation settings of the CFD model and the velocity streamline result figures are added in the section of 3.1 (in page 6).

 

Point 10: 7 should also contain points clearly showing the angles for which the computations were performed. The same goes for Fig. 9.

 

Response 10: The mentioned figures are replaced by new format which contains computing points.

 

Point 11: The mentioned effects of TS parameters are highly dependent on the assumed Re. Can the authors provide any recommendations on how these effects would change with Re, since much higher values of Re can be expected at real structures?

 

Response 11: The results regarding the effects of TS angle on VIV frequency reduction on the actual Re have been added to a new section 4.3 in page 10-11. The results indicate that to compare with the results on assumed Re, the VIV frequencies of O-tower and TS-tower are overall increased due to the influence of turbulence, and TS is also effective to reduce VIV frequency of tower under real structure and actual fluid state conditions.

 

Point 12: Can a simple point mass adequately represent the nacelle and rotor, particularly if the blades are rotating? Were the two models (this simplified vs. a more realistic one) compared to establish the validity of this assumption? The actual nacelle and rotor quite alter the modal characteristics of the whole structure and should be appropriately modeled. Correct this, or provide an explanation in the text.

 

Response 12: Some particular realistic data regarding the nacelle and blade are difficult to obtain…so we can only consider boundary conditions as many as possible. Furthermore, we considered that the main purpose of modal analysis was to investigate the effects of TS on eigen-frequencies and mode shapes of the tower relatively, and the data of nacelle and blade are common conditions of the two towers, the influences of such conditions on the modes of two towers are identical, the most significant influence should derive from TS. Acturally, the errors of eigen-frequencies and mode shape results may be obvious, but the comparision between the eigen-frequency results of the two towers can also indicate the difference due to TS relatively, and the purpose of modal analysis can be achieved.  

 

The explaination has been added in the text as following (line 4, the first paragraph of section 4.4):

 

“In this paper, the main purpose of the modal analysis was to investigate the effects of the addition of TS on the eigenfrequencies and mode shapes of towers relatively; it is not very essential to consider some common conditions of the two towers specifically, such as the structure of nacelles and blades, some local stiffeners (i.e., inside flanges), the gyroscopic effect of rotating blades, etc., because the influences of such conditions on the modes of the two towers are identical, except for the TS. Consequently, a simpli-fied model of a wind turbine is established for the modal analysis, as displayed in Figure 14.”

 

Point 13: Provide more details on the used numerical set-up of the modal analysis.

 

Response 13: The modal analysis is carried out in Workbench, some specified numerical parameters such as the mass of nacell and rotor system and material data are added in the text:

 

“…the rigid connection element is used to simulate the connection relationship between the nacelle and the tower, and a lumped mass element, Mass21, is used to describe the mass of the nacelle and blades–hub system; the assumed value is defined as 455000 kg according to the common weight data of such a megawatt wind turbine. The tower is the key object of the modal analysis; its mass and flexibility should be determined by the structure and material, so the material parameters, such as the elastic module and Poisson’s ratio, are defined as steel (E = 206 GPa and ε = 0.3).”(in the end of the first paragraph of section 4.4)

 

Point 14: In Table 5, the authors are actually comparing the first three modes, and not the first five as written.

 

Response 14: The eigen-frequencies of first 5 modes in Table 5 have been revised.

 

Point 15: Can the obtained experimental results even be compared to the numerical ones, when the model is so scaled-down? It is apparent that completely different frequencies of vertex shedding are captured. Therefore, there is no certainty that the obtained conclusions can be simply translated to a bigger structure

 

Response 15: The main purpose of the experiment is to validate that to manufacture TS on the outer surface of cylindrical tower can decrease VIV frequency. It is certain that the tunnel test should be carried out by using the specimen with actual dimension, but unfortunately our current experimental conditions are too limited to construct a large enough wind tunnel, so we can only design a small-scale test rig with the consideration of geometric similarity for the experiment. The relevant statement regarding dimensinal analysis has been added in section 4.5:    

 

“For comparison with the actual sizes of the O-tower and TS-tower in Table 4, the di-ameter and height of the test specimens used in the experiment are reduced by 50 times (D = 80 mm and H = 100 mm). On the basis of the model similarity criterion, the TS sizes L2 and L3 are also reduced by 50 times correspondingly. At the same time, the TS numbers and angle remained as 50 pieces and 61 degrees, respectively, because the two parameters are not related to the size difference.” (in the end of the first paragraph of section 4.4)

 

Although the experimental results apparent completely different frequencies from simulation, it also indicates that the VIV frequency of Ts-specimen (3.345 Hz) is much lower than the O-specimen (5.562Hz), and the reduction rate is basically similar to simulation result (40.53%/34.3%). To some extent, the obtained results can validate the expected conclusion, so the small-scale tunnel test should be significant to achieve the main purpose of the experiment.  

Reviewer 3 Report

Accepted as it is

Author Response

Many thanks.

Reviewer 4 Report

The paper investigates a way of vortex-induced vibration control on wind turbine towers where this design approach is usually used on slender structures such as steel industrial chimneys.

The Proposed algorithm of investigation of this phenomenon, shows that by adding trapezoidal shape plates on the outer surface of the wind turbine tower, vortex-induced vibration frequency can be decreased. While maintaining similar values of the eigenfrequency of the original structure, presented results indicate that appropriately applied trapezoidal shape plates can further separate exciting frequency and eigenfrequency values. Numerical analysis is supported by the experimental investigation. Future work is proposed to further investigate this problem approach. 

The potential readers may expect further details of the presented numerical models for both CFD and frequency analysis. 

The few modes of the mode shapes of the wind turbine tower presented in figures 12 and 13 are going to have different features when the numerical model includes local stiffeners existing on the real structure (inside flanges, etc)

Author Response

Response to Reviewer 4 Comments

 

Point 1: The potential readers may expect further details of the presented numerical models for both CFD and frequency analysis.

 

Response 1:

Some further descriptions and soluition settings of CFD model are added to section 3.1 (in page 6).

The detailed descriptions of mesh model and element quality are added to section 3.2 (in page 7).

Some numerical set-up of frequency analysis are added to section 4.4 (in page 12).

 

Point 2: The few modes of the mode shapes of the wind turbine tower presented in figures 12 and 13 are going to have different features when the numerical model includes local stiffeners existing on the real structure (inside flanges, etc)

 

Response 2: Some particular realistic data regarding the components in the real strucure, such as mentioned local stiffeners, nacelle and blade and so on are difficult to obtain…so we can only consider boundary conditions as many as possible. Furthermore, we considered that the main purpose of modal analysis was to investigate the effects of Ts addition on eigen-frequencies and mode shapes of the tower relatively, and the data of such components are common conditions of the two towers, the influences of such conditions on the modes of two towers are identical, the most significant influence should derive from Ts addition. Acturally, the errors of eigen-frequencies and mode shape results may be obvious, but the comparision between the eigen-frequency results of the two towers can also indicate the difference due to Ts addition relatively, and the purpose of modal analysis can be achieved. 

 

The explaination has been added in the text as following (in line 4 of the first paragraph of section 4.4, page 12):

 

“In this paper, the main purpose of the modal analysis was to investigate the effects of the addition of TS on the eigenfrequencies and mode shapes of towers relatively; it is not very essential to consider some common conditions of the two towers specifically, such as the structure of nacelles and blades, some local stiffeners (i.e., inside flanges), the gyroscopic effect of rotating blades, etc., because the influences of such conditions on the modes of the two towers are identical, except for the TS. Consequently, a simpli-fied model of a wind turbine is established for the modal analysis, as displayed in Figure 14.”

Round 2

Reviewer 1 Report

I suggest Improve image quality. ie: Fig. 5, 15 and 16.

The units of measures in the figures and tables are confusing.

ie: Figures 8 y 13.  (degree); table 5.

 

 

Author Response

1. I suggest Improve image quality. ie: Fig. 5, 15 and 16.

Reply: The quality of metioned images has been improved.

2. The units of measures in the figures and tables are confusing. ie: Figures 8 y 13.  (degree); table 5.

Reply: Figures 8, 10 and 13 are revised to clarify the units. The units in Tables 3-6 are also revised.  

 

Reviewer 2 Report

The paper has been improved, all the comments have been adequately answered to and I recommend it for publication.

Author Response

Your significant and valuable suggestions are really important for our future works. Many thanks for your help!