# Experimental Investigation on Flow-Induced Rotation of Two Mechanically Tandem-Coupled Cylinders
## 5 Conclusions  
In this paper, an experimental investigation on the flow-induced rotation (FIR) of two mechanically tandem-coupled cylinders at different spacing ratios (\(L/D\)) was carried out with the help of a self-circulating water tank. The Reynolds number ranged from 20,105 to 96,575. The complete rotation responses of the FIR system with \(L/D=4.0\)-9.0 were analyzed emphatically. The major conclusions are as follows:  
(1) For \(L/D=4.0\) and 4.5: The rotation response of the FIR system is similar to the VIV response, on the whole. The rotational oscillation is at a low level and the maximum arc length ratio (\(A^{\star}\)) is less than 0.56. Compared with the typical VIV response, the difference is that the arc length response appears as a re-growth region with the increase of velocity after entering the lower branch of VIV, but the oscillation is still suppressed in this region. As \(L/D\) increases, the re-growth region is no longer significant.  
(2) For \(L/D=5.0\), 5.5 and 6.0: The rotation responses of the FIR system present the typical VIV response, and the oscillation reaches a high level with the maximum \(A^{\star}\) exceeding 0.85. Additionally, the vibration structure with \(L/D=6.0\) is more suitable for flow-induced motion power generation because of the longer arc length and the wider range of synchronization interval.  
(3) For \(L/D=7.0\), 8.0 and 9.0: The rotation responses still show the VIV law. The oscillation is at the medium level, and the maximum \(A^{\star}\) is between 0.53 and 0.72. Compared with the other cases, the oscillation response of these three cases have a wider range of synchronization interval, and the range shows an increasing trend with the growth of the spacing ratio.  
In this paper, the flow-induced rotation characteristics of two tandem-coupled cylinders at different spacing ratios were investigated. Nevertheless, the two key parameter \(c_{\text{tangent},up}\) and \(c_{\text{tangent},down}\) in Equation (22) were not actually measured in the existing experiments. A torque sensor will be introduced to measure these two parameters in future research. Additionally, the more definite influence of the term containing \(\left(\dot{\theta}\right)^{2}\) in Equation (18) on the FIR system will also be a focus of subsequent research. Finally, a generator will be installed, on the basis of the present experimental device, to evaluate the power generation level of the FIR system. Meanwhile, the new system's dynamic equation can be further analyzed and solved after considering the generator damping.  
Conceptualization, F.L. and X.Y.; methodology, F.L., W.F., X.Y., D.R. and N.S.; software, W.F., X.Y., X.W. and D.Y.; validation, W.F., X.Y. and D.R.; formal analysis, F.L., W.F. and W.F.; investigation, W.F. and X.Y.; resources, F.L. and X.Y.; data curation, F.L., W.F. and X.Y.; writing--original draft preparation, W.F.; writing--review and editing, F.L., X.Y., D.R., N.S., X.W. and D.Y.; visualization, W.F. and X.Y.; supervision, F.L. and X.Y.; project administration, F.L. and X.Y.; funding acquisition, F.L. and X.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51909190.  
Not applicable.  
Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available, due to privacy.  
The authors would like to thank the peer reviewers and editors for their hard work and constructive feedback, which made a significant contribution to improving the paper.  
The authors declare no conflict of interest.