Force Element Analysis in Vortex-Induced Vibrations of Side-by-Side Dual Cylinders: A Numerical Study

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have investigated the vortex-induced vibration (VIV) mechanism of side-by-side dual cylinders with spacing ratios L/D ranging from 3 to 6 utilizing numerical approach for mass ratio and Reynolds number of 100 and 10, respectively. A user-defined function and fourth order Runge-Kutta method is utilized to investigate the mutual interaction during VIV for side-by-side dual cylinders. It has been shown that for side-by-side positioned dual cylinders outside the "lock-in region", the lift and drag forces are predominantly effected by the volume vorticity forces in conjunction with surface vortices (including frictional) forces. However, within the "lock-in region", the surface acceleration lift forces provide greater force contributions, and the volume vorticity lift force contributes significantly with negative values. Moreover, the "slapping" phenomenon near the "lock-in region" leads to "bounded" trajectories of cylinders.

In general, results are well-presented and discussed. However, some minor revisions and further explanations are essential as summarized below:

1-     Please consider giving the relation between the definition of “reduced velocity” and Strouhal number in the initial parts of the manuscript.

2-     It would be beneficial to represent the near-wall first grid height information in terms of y⁺ values while discussing the grid dependency.

3-     It is crucial to provide some introductory level information about the “Pressure Method” mentioned in Line 245.

4-     Figure 7 needs more clarification in the caption as well as within the text. Specially a legend table describing the variables is essential. Please also include the variables in the nomenclature list. It seems vital to briefly describe all variables before starting to discuss their behavior individually.

5-     Starting from Figure 7, it is not clear how the authors have decomposed the lift and drag forces to the variables presented in Figure 7 to 10. Please include appropriate descriptive text.

6-     It would be beneficial to have the same axis ranges for all subfigures in Figures 11 to 14 in order to have a healthy comparison.

7-     The information in Figures 11 to 14 could be summarized and depicted in one Table in terms of maximum/minimum and standard deviation for X and Y components. It will result in a full picture useful for a healthier comparison.

8-     Please include the definition of f* (Frequency ratio) and consider revising the caption of Figure 18(a).

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Review of:

Force Element Analysis in Vortex-Induced Vibrations of Side-2 by-Side Dual Cylinders: A Numerical Study

by

Mengtian Song, Suxiang Guo, Hailong Xu, Weijian Tao, Jiechao Lei and Chien-Cheng Chang

This manuscript presents a 2D numerical study on vortex induced vibrations of two side-by-side cylinders under varying distance ratios and reduced freestream velocities. The main focus of the study is to analyze this problem using a force decomposition method introduced by one of the co-authors in previous articles. Since an incompressible potential flow does not exert any force on a body, any fluid element or flow structure with non-zero vorticity can by interpreted as a source for the force acting on a body. This analysis allows for a decomposition of the force components in each direction into five parts, and the present study applies this decomposition on the mentioned VIV-case.

This analysis is certainly valuable and can help to better understand the sources of vortex induced vibrations. The presented methodology is sound and the results are certainly plausible.

The quality of the manuscript suffers from being relatively repetitive in certain sections, e.g. when describing the results at high L/D-ratios. It would be beneficial if the authors would not only describe what the different figures show. It would be good if, for some selected cases, the authors would perform a more in-depth combined analysis by discussing the results for the different force components together with the vorticity contours and pressure contours at different times and the different frequencies of the vibrational response. The manuscript does not really demonstrate what the additional insights are, which can be gained from the force decomposition applied.  Therefore, even though the study design and the results are valuable, I am not enthusiastic about this manuscript.

Besides the prior general comments, the following remarks should be addressed to improve the manuscript:

1.       Since equation (3) is pivotal for the subsequent analysis, the authors might want to expand their explanations regarding its interpretation and be more careful regarding the introduced quantities. First of all, the potential phi is not introduced. Second, the equation is in nondimensional form, hence F_total is a dimensionless force – here the manuscript is inconsistent, since the dimensionless force coefficients are introduced later. In addition, it might help with the interpretation to point out that the formulation of this equation is not general, but has already been adapted to the case under consideration. That is why, e.g. the acceleration term is not integrated over S_R,  but only over S_1 (the body experiences acceleration, the incoming flow has constant velocity).
This part must be improved.

2.       It might be good to include the formula for the natural frequency f_n.

3.       Figure 6: Were the results for the single cylinder case taken from a reference?

4.       The figures 7 to 10, which can be considered the most interesting and novel part of this manuscript, should be improved in order to facilitate the analysis of the results for the reader. Particularly the plots in the lock-in regime require some effort to identify, which curves contribute to lift and drag. In the IB and DB results the drag variations are much smaller than the lift variations. It might be helpful to use different scales for C_L and C_D on the left and right side of the graphs, respectively. It is understandable that the authors want to present the results in a compact form, but some considerations regarding the different colors used or the usage of solid and dashed line might help to make these plots easier to read.

5.       In lines 334 and 422 the authors use the term “inter-cylinder interaction forces”. This term can easily be confused with the interaction forces (acceleration and surface vorticity) which one cylinder exerts on the other. A better clarification of the terms used would facilitate the interpretation.

6.       Line 341f: “the surface vorticity lift components C_lv12 and C_lv21 of the two cylinders have equal amplitudes but opposite phases, being numerical negations of each other” … this is confusing … the curves have different signs?

7.       Line 346: Is this really a ‘beating’ phenomenon? Which relevant force components show slightly different frequencies=

8.       Line 458: “This trajectory is characterized by being narrow at the top 458 and wider at the bottom.” … this only refers to U_r=2, not to U_r=3.

9.       Line 479: “he trajectory becomes an irregular yet somewhat regular motion curve” … this is confusing and should be reworded.

10.   Line 517: This should read ‘Modal analyses’, however, what follows is not really a modal analysis. This would require a more in-depth analysis of the different frequencies and modes of vibration and their superposition. What is presented is a rather half-hearted intent to better understand the trajectory patterns observed for three different cases, but the analysis does not provide too many additional insights. The link between the different force components and the observed trajectory patterns is not really demonstrated.

11. Line 520: The term "aspect ratio" is not correct.      

Comments on the Quality of English Language

The manuscript is reasonably well written. It still contains several minor grammatical and wording errors; however, those do not impede readability too much. A careful read-through would still be beneficial.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf