Vortex-induced vibration and flow characteristics of a circular cylinder attached with inverted flexible and rigid splitter plates

Vortex-induced vibration and flow characteristics of a circular cylinder attached with inverted flexible and rigid splitter plates | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Vortex-induced vibration and flow characteristics of a circular cylinder attached with inverted flexible and rigid splitter plates Guo-Peng Cui, Li-Hao Feng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7158777/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Nov, 2025 Read the published version in Experiments in Fluids → Version 1 posted 9 You are reading this latest preprint version Abstract In this study, inverted flexible and rigid splitter plates are applied to control the vortex-induced vibration of a circular cylinder. The VIV characteristics and vortex dynamics are experimentally investigated with a Reynold number ranging from 1970 to 10590. To examine the effect of the streamwise length, five different lengths are selected. It is indicated that the VIV of the circular cylinder is suppressed by the inverted rigid splitter plate and the suppression effect is improved with an increase in the streamwise length of the plate, however, the vibration response characteristics remain the same for all streamwise lengths. Compared to the rigid one, the inverted flexible splitter plate causes various vibration responses with the change of its streamwise length. The diverse vibration responses are related to the kinematic characteristics of the inverted flexible splitter plate and the vortex dynamics. Five vortex shedding modes, including “Kármán vortex”, “Bi-LEV + Bi-WV”, “2Bi-LEV + Bi-WV”, “Uni-LEV + Uni-WV”, and “K-H instability”, are found. The correlation between the VIV and the vortex shedding mode is revealed. The “Kármán vortex” and “K-H instability” modes are corresponding to a better effect of suppressing VIV. The control effect of “LEV + WV” modes is affected by the kinematics of the plate, as it is found that the vibration amplitude of the circular cylinder and the inverted flexible splitter plate is positively correlated. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 I. INTRODUCTION The fluid-structure interaction between a flexible body and its surrounding fluid is common in nature. Fish can generate propulsion by using their flexible tail and fins [ 1 ]. When taking off and landing, the flexible bird feathers can rise up to reduce flow separation and enhance flow conditions [ 2 , 3 ]. In order to achieve exceptional maneuverability, bats can alter the shape of their flexible wing [ 4 , 5 ]. These biological behaviors show that flow control using the flexible body is a successful strategy. Wake vortex shedding results in vortex-induced vibration (VIV), which can have an impact on structural reliability and safety. Some investigations have been carried out to provide effective solutions to suppress VIV. Passive control methods such as helical strake [ 6 , 7 ], control rod [ 8 , 9 ], mesh [ 10 , 11 ], and surface roughness [ 12 – 14 ], and active control methods including synthetic jet [ 15 , 16 ], plasma actuator [ 17 ], suction and blowing [ 18 , 19 ], and oscillatory plate [ 20 ] have been developed. In addition, the effect of flexible material on VIV has drawn attention due to its high flow control efficiency in fish swimming and bird flight. The rear flexible splitter plate which is attached to the rear stagnation point of a circular cylinder is a solution to suppress VIV in several investigations. Wu et al . [ 21 ] studied the control effect of the rear flexible splitter plate on the VIV of a circular cylinder at Re = 150. It was found that the flexible splitter plates of different lengths and stiffness could attenuate the VIV of the cylinder, and the suppression effect was better when the plate length was L * ≥ 2 and plate stiffness was 1.7 ≤ ω * ≤ 2.3. The flow field results showed that the flexible splitter plate reduced the pressure difference between the upper and lower surfaces of the cylinder and resulted in a destructive vortex interaction in the cylinder wake, so as to suppress VIV. The numerical results of Sahu et al . [ 22 ] also demonstrated that the rear flexible splitter plate could reduce the cylinder vibration, however, the flexible splitter plate with high stiffness would induce the galloping when the free-stream velocity was large. Xie et al . [ 23 ] also numerically investigated the control effect of the rear flexible splitter plate on VIV, and they mainly considered two key parameters of the bending coefficient and the plate length in their investigation. Liang et al . [ 24 ] experimentally investigated the effect of rear flexible splitter plates of different streamwise lengths (0.5 ≤ L / D ≤ 2.5) on the VIV of a cylinder by wind tunnel experiments with a large mass damping ratio. When the flexible splitter plate's streamwise length was 0.6 ≤ L / D ≤ 1.1, it performed effectively in suppressing VIV; when the plate length was larger than L / D = 1.1, however, the cylinder vibration was even enhanced. Liang et al . [ 24 ] analyzed the streamwise velocity frequency in the cylinder wake and found that high-frequency harmonics appeared in the spectrum when the cylinder vibrated strongly, so they attributed the strong cylinder vibration to the appearance of these high-frequency harmonics in the flow field. Recently, a series of systematic experimental studies conducted by Cui et al [ 25 – 27 ] revealed the better control effect of the rear flexible splitter plate than the rigid one. They studied the effect of the flexible splitter plate including streamwise length, spanwise length, and bending stiffness. Their results showed that a finite-span flexible splitter plate could suppress the cylinder vibration and the effect of the bending stiffness and streamwise length were coupled. Different from the rear flexible splitter plate, an inverted flexible splitter plate which is attached to the front stagnation point of a circular cylinder directly affects the upstream flow field of the circular cylinder. Moreover, compared to the rear flexible splitter plate, the inverted flexible splitter plate can experience large-amplitude vibration at a lower velocity and undergo various vibration modes including straight mode, flapping mode, and deflected mode. Kim et al . [ 28 ] investigated the large-amplitude vibration and vibration modes of the inverted flexible splitter plate and found that the large-amplitude vibration was caused by the formation and development of the leading-edge vortex (LEV). Gurugubelli and Jaiman [ 29 ] further confirmed the occurrence and maintenance mechanism of large-amplitude vibration of inverted flexible splitter plate by numerical simulations. Hu et al . [ 30 – 33 ] systematically studied the flow fields and dynamic behaviors of inverted flexible splitter plates under different arrangements, including single, parallel, tandem, staggered, and triangular ones. In general, the control effect of the rear flexible splitter plate on the VIV of a circular cylinder has been investigated by some researchers. For the inverted flexible splitter plate, researchers mainly studied the kinematic and dynamic characteristics when it was fixed to a stationary blunt body. To the best of our knowledge, its control effect on the VIV of a circular cylinder is still unclear. Thus, in the present work, we apply the inverted flexible splitter plate to control cylinder vibration. The control effect of the inverted flexible splitter plate is discussed and the effect of its streamwise length is also studied. Moreover, the control effect of the inverted rigid splitter plate is also investigated as a comparison. The kinematic characteristics of the plate and vortex dynamics are analyzed and the relationship between the cylinder vibration and the vortex evolution is further revealed. II. EXPERIMENTAL SETUP The experiment was conducted in a high-quality recirculating water tunnel with a length of 3000 mm, a width of 600 mm, and a height of 700 mm at the Beijing University of Aeronautics and Astronautics. The free-stream velocity could be increased up to 600 mm/s. As shown in Fig. 1 , the circular cylinder with a diameter of D = 25 mm was mounted on a vibration platform that could only move in the direction transverse to the free stream. The Reynolds number based on the free-stream velocity and cylinder diameter was in the range 1970 < Re < 10590. The reduced velocity that was normalized by the cylinder diameter and the natural frequency in still water of the vibration system ( f nw ) was over the range 2.56 ≤ U * ≤ 13.74. The damping ratio and mass ratio of the vibration system were ζ = 0.0033 and m * = 7.47, respectively. In the present experiment, the control effect of the flexible and rigid splitter plates on the VIV of the circular cylinder was both investigated. The flexible splitter plate had a thickness of h = 0.24 mm, a Young’s modulus of E = 1173.3 MPa, and a density of ρ s = 1.3 × 10 3 kg/m 3 and was made of polyvinyl chloride. The position of the flexible splitter plate could be extracted by image processing which was introduced in the previous work [ 26 ]. The rigid splitter plate was made of steel and its thickness was the same as that of the flexible splitter plate. The inverted splitter plate was attached to the front stagnation point of the circular cylinder. It covered 30% of the submerged cylinder length, which was 500 mm, and six streamwise lengths in the range of L/D = 0.5 to 3 were selected with an interval of L/D = 0.5. The vibration displacement of the cylinder was measured by a laser displacement sensor installed on one side of the vibration platform. At the measurement range of 0-100 mm, the measurement error of the displacement sensor was less than 0.1% of the full-scale output. The signal of the displacement sensor was recorded by a data acquisition card. When the flow field was measured, the sampling frequency of the vibration displacement was the same as that of the flow field, otherwise, the vibration displacement was captured with a sampling frequency of 400 Hz. The vortex dynamics were studied by the particle image velocimetry (PIV) technique which obtained the flow field information by capturing the motion of tracing particles. In the present experiment, the hollow glass beads with a density of 1.05 g/cm 3 and a diameter of 5–20 µm were selected as tracing particles and were illustrated by a high-speed laser at the measurement region. Two CMOS cameras with a full resolution of 2048 × 2048 pixels were utilized to obtain the upstream and downstream flow field by recording particle images with a sampling frequency between 200 Hz to 300 Hz. The image magnification was 0.1 mm/pix. The velocity field was calculated by the multi-pass iterative Lucas-Kanade (MILK) algorithm which computational efficiency could be increased by graphic processing units (GPU) acceleration [ 34 , 35 ]. The interrogation window was set to 32 pixels × 32 pixels with an overlap of 75%. The vorticity field was calculated from the velocity field by the difference scheme, and the statistical characteristics were further obtained. In the present work, the coherent structure boundary was determined by the ridge in the finite-time Lyapunov exponent (FTLE) field [ 27 ], and then the vortex evolution was investigated. III. EXPERIMENTAL RESULTS A. Vibration response of the circular cylinder The VIV amplitude response of a circular cylinder is a typical three-branch response for the natural case and its comparison with the results in another research confirmed the reliability of the experimental results obtained by the present vibration system [ 26 ]. The control effect of the inverted flexible and rigid plates of different streamwise lengths on VIV is shown in Fig. 2 . The kinematic characteristics of the inverted flexible splitter plate are complicated and are affected by the plate length, so as to result in the change of vibration response with the variation of the plate length. When the streamwise length of the flexible splitter plate is L / D ≤ 1.5, the cylinder vibration is effectively controlled, and the control effect gradually increases with an increase in the plate length. When the plate length is increased to L / D = 2, in addition to the vibration response in the low-speed range that is denoted by region I in Fig. 2 (d), a considerable vibration response occurs in the high-speed range that is denoted by region II in Fig. 2 (d), indicating that the flexible splitter plate begins to exhibit richer kinematic behavior than the shorter one. With a further increase in the plate length ( L / D > 2), the vibration response in the low-speed range disappears, and the amplitude peak of the cylinder vibration in the high-speed range gradually shifts to the lower-speed range. For the inverted rigid splitter plate, the cylinder vibration response is basically the same as that of the inverted flexible splitter plate case when the plate length is L / D ≤ 1.5. Different from the flexible splitter plate, the variation of the vibration amplitude with the reduced velocity does not change with a further increase in plate length, only the maximum vibration amplitude is reduced. The previous study showed that the galloping was excited by the alternate attachment of shear layers on the tip of the rear rigid splitter plate [ 25 ]. However, there is no direct interaction between the shear layers and the rigid splitter plate in the cylinder wake when the plate is attached to the front stagnation point. Thus, Fig. 2 shows that the galloping was not induced by the inverted rigid splitter plate. Figure 3 shows the vibration frequency response of the circular cylinder for several typical cases. The vibration frequency is normalized by the natural frequency of the vibration system of the baseline cylinder in still water. For the natural case, the vibration frequency initially varies along the Strouhal line, then gets close to the natural frequency, and finally is locked into a value slightly greater than the natural frequency. For the flexible splitter plate, the change in the frequency response is minimal compared with the natural case for the L / D = 0.5 case. When its length increases to L / D = 2, the flexible splitter plate vibrates at a greater frequency, causing the vibration frequency of the cylinder to be locked into a larger frequency. As the plate length increases further, the vibration frequency of the circular cylinder starts to decrease due to the decrease in the vibration frequency of the flexible splitter plate. Consistent with the similar amplitude response, the vibration frequency response of the rigid splitter plate case for L / D = 0.5 is similar to that of the flexible case, indicating similar vibration characteristics between them. As the streamwise length of the rigid splitter plate increases, the velocity at which the cylinder vibration is suppressed decreases, causing a dispersed vibration frequency distribution to occur at a smaller velocity. B. Kinematics of the inverted flexible splitter plate and vortex dynamics The inverted flexible splitter plate exhibits a variety of vibration modes such as weak vibration, bilateral vibration, and unilateral vibration with the change of velocity and its streamwise length, which further leads to various vortex evolution modes including “Kármán vortex” mode, “LEV + WV” mode (LEV: leading-edge vortex; WV: wake vortex) and “K-H instability” mode. In this section, the kinematics of the inverted flexible splitter plate and the associated vortex dynamics will be discussed. The flow field around the cylinder for the natural case is presented first (Fig. 4 ). As the cylinder vibrates in the transverse direction, the front stationary point moves up and down in the windward side of the cylinder. The upstream fluid develops from the front stationary point on the cylinder surface to both sides of the cylinder and separates at a certain position to form a free shear layer, and a vortex forms at the end of the shear layer. Along with the cylinder vibration, the shear layer vibrates strongly and the wake vortex develops in a large transverse region. Moreover, the vortex shedding mode is a typical 2P mode for this case, which is in the lower branch, i.e., a pair of wake vortices are generated on each side of the cylinder in a vibration period. When the inverted rigid splitter plate is applied to control the VIV of the cylinder (Fig. 5 ), or when the inverted flexible splitter plate vibrates weakly near the center of the cylinder (Fig. 6 ), the upstream fluids develop along the splitter plate and separates before reaching the cylinder due to the viscosity and the inverse pressure gradient. The separated shear layer is reattached to the cylinder at a certain position, and then continues to develop along the cylinder surface, forming Kármán vortex shedding in the wake, which is referred to as the “Kármán vortex” mode in the present work (Fig. 7 ). It is worth noting that the slight deviation of the splitter plate from the center of the cylinder or the weak vibration of the flexible splitter plate will lead to a small angle of attack between the splitter plate and the incoming flow, further resulting some small vortices upstream of the cylinder. However, the primary vortex evolution process is still the Kármán vortex shedding. Figures 5 and 6 show that the vortex evolution modes for the rigid and flexible splitter plate cases with a small streamwise length ( L / D = 0.5, 1, and 1.5) are similar, which results in a similar vibration response, as has been shown in Fig. 2 . For the “Kármán vortex” mode, the effect of the inverted splitter plate on the upstream flow resembles a conical modification on the windward edge of the cylinder. A conical low-speed area forms upstream of the cylinder, and as the plate length increases, the apex of the cone extends upstream, according to the time-averaged streamwise velocity statistics (Fig. 8 ). In addition, the time-averaged streamwise velocity profiles demonstrate that the inverted splitter plate significantly reduces the streamwise velocity upstream of the cylinder compared to the natural case (Fig. 9 ). The reduced incoming velocity may cause the wake vortex takes longer to reach the strength that can shed from the shear layer, and therefore the shedding position moves downstream, as can be verified by the change of low-speed wake region for the control case in comparison with the natural case (Fig. 8 ). When the streamwise length of the flexible splitter plate is small, it mainly presents a straight mode or a weak vibration mode, and therefore its effect on the flow field is similar to that of the rigid splitter plate. However, as the streamwise length increases, the flexible splitter plate exhibits more complicated vibration state, which makes its control effect different from that of the rigid splitter plate (Fig. 10 ). The vibration process of the flexible splitter plate is caused by the variations in the fluid and elastic forces acting on it. The angle of attack between the flexible splitter plate and the incoming flow increases when the plate deviates from equilibrium due to instability or when the direction of the incoming velocity changes as a result of cylinder vibration. This increases the fluid force acting on the plate and causes it to deflect. Along with the deformation of the flexible splitter plate, a LEV is generated at the tip of the plate. The pressure difference between the two sides of the flexible splitter plate caused by the LEV makes the plate continue to deflect. Once the fluid and elastic forces acting on the flexible splitter plate reach equilibrium, the plate vibrates to the boundary position. The fluid force on the flexible splitter plate then reduces as the LEV continues to develop downstream, and the flexible splitter plate begins to rebound toward the equilibrium position, eventually generating the periodic vibration of the plate. For this typical case of L / D = 2, U * = 4.5, two LEVs form at the tip of the plate in one vibration cycle of the flexible splitter plate. Moreover, the fluid between the LEV and the windward edge of the cylinder bypasses the cylinder while the LEVs develop along the flexible splitter plate, causing the formation of two wake vortices (WVs). The LEV and the wake vortex will merge and gradually dissipate during the downstream convection process. In this paper, the vortex evolution mode in which two LEVs form at the tip of the flexible splitter plate and two wake vortices form on either side of the cylinder in one vibration cycle of the cylinder is referred to as “Bi-LEV + Bi-WV” mode (Bi-LEV: bilateral leading-edge vortex; Bi-WV: bilateral wake vortex). The schematic diagram of this vortex evolution mode is clearly shown in Fig. 11 . When the vibration amplitude of the flexible splitter plate is very large, the vortex evolution becomes different. As shown in Fig. 12 , when the flexible splitter plate is close to the boundary position, a LEV forms at its tip, and the LEV develops downstream along with the rebound of the plate. When the flexible splitter plate rebounds to a certain position, the LEV has developed to a position far from the plate tip. With the further rebound of the flexible splitter plate, a new LEV is rolled up on the shear layer of the leeward side of the plate and convects downstream together with the former LEV. Moreover, a wake vortex is shed from the cylinder together with the shedding process of the two LEVs. Therefore, two pairs of LEVs are shed from the plate tip and two wake vortices are shed from the cylinder in a vibration cycle of the flexible splitter plate, which is referred to as “2Bi-LEV + Bi-WV” mode in this study. The schematic diagram of this vortex evolution mode is shown in Fig. 13 . It is worth noting that the flexible splitter plate switches between bilateral vibration and unilateral vibration rather than always vibrating bilaterally. This suggests that the system may contain two attractors, one of which causes the flexible splitter plate to vibrate unilaterally around a position on one side of the cylinder and the other of which causes the flexible splitter plate to vibrate bilaterally around the cylinder center. Note that Fig. 12 (a) shows there is a variation in the vibration frequency of the flexible splitter plate, which will be discussed in the following section. When the elastic force is unable to cause the rebound of the flexible splitter plate to cross the equilibrium position to the opposite side of the cylinder, the flexible splitter plate vibrates on one side of the cylinder, forming a unilateral vibration mode, as shown in Fig. 14 (a). The vortex evolution brought on by the unilateral vibration of the flexible splitter plate is shown in Figs. 14 (b)-14(e). The incoming flow bypasses the tip of the flexible splitter plate and rolls up into a LEV near the boundary position of the plate vibration. The LEV develops downstream along with the rebound of the flexible plate. It can be found that the lower half of the cylinder is almost always located in the separation region behind the flexible splitter plate due to the unilateral vibration of the plate. The flow velocity in the separation region is extremely low and there also exits backflow, which results in no wake vortex forming in the lower part of the cylinder. However, in the upper half of the cylinder, the fluid flows along the windward side of the flexible splitter plate and the cylinder, and then a vortex forms in the wake of the cylinder. The vortex evolution that a LEV is shed on the vibration side of the flexible splitter plate and a wake vortex is shed from the cylinder on the opposite side is referred to as the “Uni-LEV + Uni-WV” mode (Uni-LEV: unilateral leading-edge vortex; Uni-WV: unilateral wake vortex), which is illustrated in Fig. 15 . The “K-H instability” mode, a new vortex evolution mode, develops when the flexible splitter plate vibrates weakly in a large deformation state. As shown in Fig. 16 , the fluid separates at the tip of the flexible splitter plate and forms a free shear layer behind the plate. Due to the development of the K-H instability in the shear layer, some small-scale vortices form. For the lower half of the cylinder, it is located in the separation region caused by the blocking effect of the flexible splitter plate, so there are no obvious vortex structures forming on this side of the cylinder. However, on the side of the cylinder that is not blocked by the flexible splitter plate, the fluid flows over the surface of the cylinder and, like the shear layer behind the flexible splitter plate, K-H instability also develops in the free shear layer behind the cylinder, which then leads to small-scale vortices. Thus, for the “K-H instability” mode, the primary flow structures are small-scale vortices, and there are no large-scale vortices in the flow field. The schematic diagram of the “K-H instability” mode is shown in Fig. 17 . To further understand the relationship between the vortex evolution and the cylinder vibration, Fig. 18 presents a summary of vortex evolution modes and the associated vibration amplitude of the cylinder for all measured cases in the present work. For the flexible splitter plate with a small streamwise length ( L / D = 0.5 and 1) and the rigid splitter plate, the vortex evolution mode is the “Kármán vortex” mode, which controls the flow field around the cylinder by leading-edge modification and affecting the shedding position of the wake vortex. Figure 18 shows that the vibration amplitude of the cylinder corresponding to the “Kármán vortex” mode is generally smaller, further demonstrating that the “Kármán vortex” mode is efficient in suppressing the cylinder vibration. With an increase in the streamwise length of the flexible splitter plate, its kinematic characteristics become more complicated, thus resulting in more vortex evolution modes. They can be characteristic by the “LEV + WV” modes, including “Bi-LEV + Bi-WV” mode, “2Bi-LEV + Bi-WV” mode, and “Uni-LEV + Uni-WV” mode, where the lift fluctuation of the cylinder is affected by the LEV and the wake vortex. The effect of the LEV on the cylinder vibration is mainly brought about by changes in the force exerted on the flexible splitter plate during its periodic bending and rebounding process. The wake vortex directly affects the vortex force, and further changes the lift fluctuation of the cylinder. The bending and rebound of the flexible plate are the process of energy storage and release. When the vibration amplitude of the flexible plate is not very large (“Bi-LEV + Bi-WV” mode), the energy change during the vibration of the flexible splitter plate is relatively small, and the contribution to the cylinder vibration is small. As the vibration amplitude of the flexible splitter plate increases (“2Bi-LEV + Bi-WV” mode and “Uni-LEV + Uni-WV” mode), the energy changes during the vibration process increases, and thus the contribution to the cylinder vibration increases. Figure 18 shows that the cylinder vibration is relatively stronger for the “LEV + WV” modes where the amplitude of the flexible plate oscillation is larger. Figure 19 further supports the finding that there is a positive correlation between the vibration amplitude of the flexible splitter plate and the cylinder, i.e., that the larger the vibration amplitude of the flexible splitter plate, the larger the vibration amplitude of the cylinder. The dominant flow structures of the “K-H instability” mode are small-scale vortices, which have little impact on cylinder vibration and basically suppress it. Therefore, in general, the cylinder vibration is effectively suppressed, when the “Kármán vortex” mode or “K-H instability” mode is generated, whereas the vibration amplitude of the cylinder for the “LEV + WV” modes is relatively larger because the suppression effect is diminished by the relatively strong vibration of the flexible splitter plate. Figure 20 presents the spectral analysis results for some typical vortex evolution modes. It is clear that there is a strong fluid-structure interaction for all cases since the dominant frequencies of the streamwise velocity and the vibration of the flexible splitter plate and cylinder are locked into each other. In particular, the spectra for both the “Bi-LEV + Bi-WV” mode and “Uni-LEV + Uni-WV” mode have the distinctive feature that, in addition to the fundamental frequency, there are high-order harmonics that correlate to small-amplitude perturbations. The small-amplitude perturbations are related to the sweeping and shear effects of large-scale LEVs and strongly vibrating flow structures on their surrounding fluid. When introducing the “Bi-LEV + Bi-WV” vortex evolution mode, it has been pointed out that the flexible splitter plate of L / D = 2.5 switches between large-amplitude bilateral vibration and unilateral vibration, and the vibration frequency also changes at U * = 10.5, as has been shown in Fig. 12 (a). Moreover, the vibration frequency of the flexible splitter plate with a streamwise length of L / D = 2.5 has the same characteristic at U * = 7.2. To investigate the cause of this frequency variation, the frequency characteristics of these two cases are given in Fig. 21 . It is discovered that the plate vibration presents a low-frequency characteristic when the cylinder is stationary. Moreover, the cylinder tends to vibrate with a frequency close to the natural frequency when its degree of freedom is released. As a result, the plate vibration is affected by both the low-frequency characteristic and the natural frequency of the vibration system, which further leads to the change of vibration frequency of the flexible splitter plate. IV. CONCLUSION The control effect of inverted flexible and rigid splitter plates with different streamwise lengths on the VIV of a circular cylinder is investigated in a water tunnel experiment. The kinematic characteristics of the flexible splitter plate and the resulting various vortex evolution modes are analyzed. The main conclusions are as follows. The control effect of the inverted flexible splitter plate on the cylinder vibration depends on its streamwise length. When the flexible splitter plate is short ( L / D = 0.5–1.5), the plate vibration is weak, thus resulting in the vibration response of the cylinder similar to that of the rigid splitter plate case. With an increase in the streamwise length, the occurrence of various vibration states of the flexible splitter plate leads to different vibration responses of the cylinder. In addition to the vibration response at the low-speed region similar to the short flexible splitter plate cases, obvious cylinder vibration is excited at the high-speed region for long flexible splitter plate cases. Moreover, the cylinder vibration at the low-speed region gradually diminishes, and the vibration response at the high-speed region gradually moves toward the low-speed region with an increase in the plate length. The control effect of the inverted splitter plate in the present work is compared with that of the rear splitter plate in the previous work. It has been discovered that the variation of the vibration characteristics of the cylinder with the plate length is more obvious for the inverted flexible splitter plate, while the suppression effect of the rear flexible splitter plate on VIV is better when the streamwise length is L / D ≥ 1. For the rigid splitter plate, the inverted one has a better control effect than the rear one because the galloping of the cylinder is not excited. The change of kinematic characteristics of the inverted flexible splitter plate leads to different vortex evolution modes in the flow field, including “Kármán vortex” mode, “Bi-LEV + Bi-WV” mode, “2Bi-LEV + Bi-WV” mode, “Uni-LEV + Uni-WV” mode, and “K-H instability” mode. The influence mechanism of the inverted flexible splitter plate on the VIV of the cylinder is revealed based on the investigation of the vortex evolution modes. When the “Kármán vortex” mode is induced, the incoming flow velocity upstream of the cylinder is reduced and the shedding position of the wake vortex is extended downstream, thus reducing the effect of the vortex shedding and suppressing the cylinder vibration. For the “LEV + WV” modes, including the “Bi-LEV + Bi-WV” mode, “2Bi-LEV + Bi-WV” mode, and “Uni-LEV + Uni-WV” mode, the cylinder vibration is affected by both LEV and wake vortex. The effect of LEV is generated by energy change during the bending and rebounding processes of the flexible splitter plate, so the vibration amplitude of the flexible splitter plate is positively correlated with the vibration strength of the cylinder. The control of the wake vortex can reduce the vortex force of the circular cylinder, achieving control of the cylinder vibration. For the “K-H instability” mode, the small-scale flow structure leads to a good suppression of cylinder vibration. Declarations Author contributions Guo-Peng Cui contributes to experimental work, formal analysis, investigation, writing—original draft. Li-Hao Feng contributes to formal analysis, methodology, supervision and writing—review & editing. Data availability The data supporting the findings of this study are available from the corresponding author upon reasonable request. Declarations Conflict of interest The authors declare no conflict of interest. References F. E. Fish and G. V. 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Brankovic, Experimental studies of passive control of vortex-induced vibration, Eur. J. Mech. B-Fluids 23 , 9 (2004). H. Park, R. A. Kumar, and M. M. Bernitsas, Suppression of vortex-induced vibrations of rigid circular cylinder on springs by localized surface roughness at 3×10 4 ≤ Re ≤ 1.2×10 5 , Ocean Eng. 111 , 218 (2016). C. Wang, H. Tang, S. C. Yu, and F. Duan, Control of vortex-induced vibration using a pair of synthetic jets: influence of active lock-on, Phys. Fluids 29 , 083602 (2017). H. Wang, L. Ding, L. Zhang, R. N. Sharma, and L. Yang, Numerical study on two-degree-of-freedom vortex induced vibrations suppression of a circular cylinder via synthetic jets at different excitation frequencies, Int. J. Heat Fluid Flow 84 , 108593 (2020). F. C. Hebrero, J. D'Adamo, R. Sosa, and G. Artana, Vortex induced vibrations suppression for a cylinder with plasma actuators, J. Sound Vibr. 468 , 115121 (2020). W. L. Chen, D. B. Xin, F. Xu, H. Li, J. P. Ou, and H. Hu, Suppression of vortex-induced vibration of a circular cylinder using suction-based flow control, J. Fluids Struct. 42 , 25 (2013). S. Dong, G. S. Triantafyllou, and G. E. Karniadakis, Elimination of vortex streets in bluff-body flows, Phys. Rev. Lett. 100 , 204501 (2008). Y., Ren, Z. Xin, and S. Gu, Active control of vortex-induced vibration of a circular cylinder by using the oscillatory plate immersed in the cylinder wake at low Reynolds number, Acta Mech. Sin. 38 , 321530 (2022). J. Wu, Y. L. Qiu, C. Shu, N. Zhao, Flow control of a circular cylinder by using an attached flexible filament, Phys. Fluids 26 , 103601 (2014). T. R. Sahu, M. Furquan, S. Mittal, Numerical study of flow-induced vibration of a circular cylinder with attached flexible splitter plate at low Re , J. Fluid Mech. 880 , 551 (2019). F. Xie, H. Zheng, J. Deng, and Y. Zheng, Vortex induced vibration of a circular cylinder with a filament by using penalty immersed boundary method, Ocean Eng. 186 , 106078 (2019). S. Liang, J. Wang, B. Xu, W. Wu, and K. Lin, Vortex-induced vibration and structure instability for a circular cylinder with flexible splitter plates, J. Wind Eng. Ind. Aerodyn. 174 , 200 (2018). G. P. Cui, L. H. Feng, and Y. W. Hu, Flow-induced vibration control of a circular cylinder by using flexible and rigid splitter plates, Ocean Eng. 249 , 110939 (2022). G. P. Cui and L. H. Feng, Suppression of vortex-induced vibration of a circular cylinder by a finite-span flexible splitter plate, Phys. Rev. Fluids 7 , 024708 (2022). G. P. Cui and L. H. Feng, Combined effect of bending stiffness and streamwise length of the attached flexible splitter plate on the vortex-induced vibration of a circular cylinder, Exp. Therm. Fluid Sci. 141 , 110787 (2023). D. Kim, J. Cossé, C. H. Cerdeira, and M. Gharib, Flapping dynamics of an inverted flag, J. Fluid Mech. 736 , R1 (2013). P. S. Gurugubelli and R. K. Jaiman, Self-induced flapping dynamics of a flexible inverted foil in a uniform flow, J. Fluid Mech. 781 , 657 (2015). Y. W. Hu, J. S. Wang, J. J. Wang, and C. Breitsamter, Flow-structure interaction of an inverted flag in a water tunnel, Sci. China-Phys. Mech. Astron. 62 , 124711 (2019). Y. W. Hu, L. H. Feng, and J. J. Wang, Passive oscillations of inverted flags in a uniform flow, J. Fluid Mech. 884 , A32 (2020). Y. W. Hu, L. H. Feng, and J. J. Wang, Flow-structure interactions of two tandem inverted flags in a water tunnel, Phys. Fluids 32 , 087114 (2020). Y. W. Hu, L. H. Feng, and J. J. Wang, Flow-structure interactions of two parallel inverted flags with small separation distances in a water tunnel, J. Fluids Struct. 94 , 102960 (2020). F. Champagnat, A. Plyer, G. Le Besnerais, B. Leclaire, S. Davoust, and Y. Le Sant, Fast and accurate PIV computation using highly parallel iterative correlation maximization, Exp. Fluids 50 , 1169 (2011). C. Pan, D. Xue, Y. Xu, J. J. Wang, and R. J. Wei, Evaluating the accuracy performance of Lucas-Kanade algorithm in the circumstance of PIV application, Sci. China-Phys. Mech. Astron. 58 , 1 (2015). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Nov, 2025 Read the published version in Experiments in Fluids → Version 1 posted Editorial decision: Revision requested 14 Aug, 2025 Reviews received at journal 13 Aug, 2025 Reviews received at journal 13 Aug, 2025 Reviewers agreed at journal 25 Jul, 2025 Reviewers agreed at journal 23 Jul, 2025 Reviewers invited by journal 22 Jul, 2025 Editor assigned by journal 21 Jul, 2025 Submission checks completed at journal 18 Jul, 2025 First submitted to journal 18 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7158777","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":489491862,"identity":"b5d6c83c-abf6-41e8-bbf4-4e399d4f197a","order_by":0,"name":"Guo-Peng Cui","email":"","orcid":"","institution":"Beijing University of Aeronautics and Astronautics","correspondingAuthor":false,"prefix":"","firstName":"Guo-Peng","middleName":"","lastName":"Cui","suffix":""},{"id":489491863,"identity":"317c65db-df33-4548-aab9-5c9850611565","order_by":1,"name":"Li-Hao Feng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0ElEQVRIiWNgGAWjYBACPgnGB0DKJgHCZSNCC5sEswGQSiNdy2FStEg3Mz4u+HU+z+D44QcMH8oOM/DPbiCgReYws/HMvtvFBmfSDBhnnDvMIHHnACGH5R+T5u25nbjhQIIBM2/bYQYDiQRCWpLZf/P2nEvccP75B+a/RGphY+b5cSBxw40cA2ZGIrUwS/M2JBdL3nhTcLDnXDqPxA0CWvglkhk/8/yxy+M7n77xwY8yazn+GQS0gAFjG4Q+AMQ8RKgHgT9EqhsFo2AUjIKRCQDK7kJMoRJpzAAAAABJRU5ErkJggg==","orcid":"","institution":"Beijing University of Aeronautics and Astronautics","correspondingAuthor":true,"prefix":"","firstName":"Li-Hao","middleName":"","lastName":"Feng","suffix":""}],"badges":[],"createdAt":"2025-07-18 14:53:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7158777/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7158777/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00348-025-04138-2","type":"published","date":"2025-11-08T15:58:16+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":87567014,"identity":"4eef1ca3-24aa-49bf-9ec9-9d95b4f05e36","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":99918,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the experimental setup. (a) Front view, (b) side view.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/d0fdef204b643c9828f5b242.png"},{"id":87567230,"identity":"855874ba-1621-40c1-b88a-738cc732ce33","added_by":"auto","created_at":"2025-07-25 09:49:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":268230,"visible":true,"origin":"","legend":"\u003cp\u003eVibration amplitude response of the circular cylinder. (a) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 0.5, (b) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e= 1, (c) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1.5, (d) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2, (e) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2.5, (f) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e= 3. FP and RP represent the inverted flexible and rigid splitter plates, respectively.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/7d0ce157ca385dfe385a7c3b.png"},{"id":87567242,"identity":"c5dda6b6-2367-4b98-82ce-7b9e50ee5845","added_by":"auto","created_at":"2025-07-25 09:49:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":182984,"visible":true,"origin":"","legend":"\u003cp\u003eVibration frequency response of the circular cylinder. (a) Natural case, (b)-(d) flexible splitter plate, (e)-(g) rigid splitter plate. (b), (e) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 0.5, (c), (f) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e= 2, (d), (g) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2.5. The black dashed line stands for the Strouhal frequency of a stationary circular cylinder (\u003cem\u003eSt\u003c/em\u003e = 0.2), and the blue dashed line stands for the natural frequency.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/a4c4826a7c02bc39edc0beb0.png"},{"id":87568168,"identity":"bbdc78e1-e28d-44a1-a363-8990b9c246b1","added_by":"auto","created_at":"2025-07-25 09:57:21","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":258968,"visible":true,"origin":"","legend":"\u003cp\u003eVortex evolution in a vibration period for the natural case (\u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 8.5).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/99127cadefc0da9e46ffb047.png"},{"id":87567253,"identity":"baf0f81c-8b3f-4609-87c6-0540bb0a2cdd","added_by":"auto","created_at":"2025-07-25 09:49:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":175269,"visible":true,"origin":"","legend":"\u003cp\u003eVortex evolution of the “Kármán vortex” mode (rigid splitter plate case: \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 8.5). (a) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 0.5, (b) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1, (c) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1.5, (d) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2, (f) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2.5.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/da05419df3fc3319df8791ad.png"},{"id":87567034,"identity":"b62c01a1-cf88-4bf5-af94-c495e87210b8","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":247023,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristics of “Kármán vortex” mode (flexible splitter plate case). (a1)-(d1) Vibration displacement of the tip of the flexible splitter plate, (a2)-(d2) vortex evolution. (a) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 0.5, (b) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1, (c) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1.5, (d) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2. (a)-(c) \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 8.5, (d) \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 5.5.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/9317f2f92dc67997ff9ced0e.png"},{"id":87567055,"identity":"3ef4a76c-6bce-4151-bdc6-ce1ebe7bf788","added_by":"auto","created_at":"2025-07-25 09:41:22","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":30176,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the “Kármán vortex” mode.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/376af04a935533be62cbd9dd.png"},{"id":87567074,"identity":"24968e02-8025-4c4a-bbe9-b740315d5991","added_by":"auto","created_at":"2025-07-25 09:41:23","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":162907,"visible":true,"origin":"","legend":"\u003cp\u003eTime-averaged streamwise velocity (\u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 8.5). (a) Natural case, (b)-(d) flexible splitter plate, (e)-(g) rigid splitter plate. (b), (e) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 0.5, (c), (f) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1, (d), (g) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1.5.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/ad882048ff0a4ae251f96521.png"},{"id":87567040,"identity":"fecab974-d63b-485a-8aef-a7a31507b48b","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":114301,"visible":true,"origin":"","legend":"\u003cp\u003eTime-averaged streamwise velocity profiles at different streamwise positions upstream of the cylinder (\u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 8.5). (a)-(d) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1, (e)-(h) \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 1.5.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/c78b106d62f09b6c890d0342.png"},{"id":87567031,"identity":"fa9c5b0e-ffe8-465a-8ed1-131400da34b3","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":407894,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristics of “Bi-LEV + Bi-WV” mode (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2, \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 4.5). (a) Vibration displacement of the tip of the flexible splitter plate and the vibration sketch of the plate, (b)-(e) vortex evolution in a vibration period of the cylinder.\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/a7e6d130cb8c7f3ed02be18d.png"},{"id":87567068,"identity":"a0205314-243e-4b8a-8a05-43adbc014d54","added_by":"auto","created_at":"2025-07-25 09:41:22","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":57842,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the “Bi-LEV + Bi-WV” mode.\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/17c277791fe13c86c940c2e9.png"},{"id":87568170,"identity":"ff1dd9a7-dd71-4c6f-a174-c13938c8db37","added_by":"auto","created_at":"2025-07-25 09:57:22","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":372663,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristics of “2Bi-LEV + Bi-WV” mode (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2.5, \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 10.5). (a) Vibration displacement of the tip of the flexible splitter plate and the vibration sketch of the plate, (b)-(e) vortex evolution in a vibration period of the cylinder.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/97fce3034b7252fd4a5e7cbf.png"},{"id":87567256,"identity":"e72e5919-2140-4fb0-bcd2-6c72f9134db3","added_by":"auto","created_at":"2025-07-25 09:49:21","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":102656,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the “2Bi-LEV + Bi-WV” mode.\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/04ffd3a7de3013dfc2189831.png"},{"id":87567030,"identity":"d46d6bcc-08d2-42ec-b92f-fd23d90b6f21","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":303067,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristics of “Uni-LEV + Uni-WV” mode (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2.5, \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 8.5). (a) Vibration displacement of the tip of the flexible splitter plate and the vibration sketch of the plate, (b)-(e) vortex evolution in a vibration period of the cylinder.\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/50bd8389fd562c8b316a2f49.png"},{"id":87567045,"identity":"b5fd3b8d-5202-4987-9c6a-cdd5f06c1a01","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":49505,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the “Uni-LEV + Uni-WV” mode.\u003c/p\u003e","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/bc53a939b08dd88d905c8e6f.png"},{"id":87567032,"identity":"300a1677-1a13-45a1-ac03-b14720f8a252","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":259103,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristics of “K-H instability” mode (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2, \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 13.7). (a) Vibration displacement of the tip of the flexible splitter plate and the vibration sketch of the plate, (b)-(e) vortex evolution in a vibration period of the cylinder.\u003c/p\u003e","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/9e757fc76c2388c011d0aba8.png"},{"id":87567036,"identity":"93dd480e-c9c4-477c-a837-dbdab36eeebc","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":44348,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the “K-H instability” mode.\u003c/p\u003e","description":"","filename":"floatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/59858f09b1d8ee769ad92981.png"},{"id":87567265,"identity":"6c780d78-851c-4e9e-a75d-31f2ed14b2ff","added_by":"auto","created_at":"2025-07-25 09:49:22","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":74648,"visible":true,"origin":"","legend":"\u003cp\u003eVortex evolution mode and the corresponding vibration amplitude of cylinder.\u003c/p\u003e","description":"","filename":"floatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/44c7a1b698746689d65496c6.png"},{"id":87567058,"identity":"ffa97f12-515b-48a0-8fe0-54da138b2388","added_by":"auto","created_at":"2025-07-25 09:41:22","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":40291,"visible":true,"origin":"","legend":"\u003cp\u003eRelation between the vibration amplitude of cylinder and flexible splitter plate.\u003c/p\u003e","description":"","filename":"floatimage19.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/62dfd8a6002b0fc3d4909c2c.png"},{"id":87567042,"identity":"1c605479-cc93-465c-8d9b-708c05c6a6f3","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":20,"title":"Figure 20","display":"","copyAsset":false,"role":"figure","size":199876,"visible":true,"origin":"","legend":"\u003cp\u003ePower spectral density of the streamwise velocity, plate vibration, and cylinder vibration (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2). (a) “Bi-LEV + Bi-WV” mode: \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 4.5, (b) “Kármán vortex” mode: \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 5.5, (c) “Uni-LEV + Uni-WV”: \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 10.5, (d) “K-H instability” mode: \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 13.7.\u003c/p\u003e","description":"","filename":"floatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/39867597da3d67f592a1e732.png"},{"id":87567039,"identity":"84a1c2bf-a2fd-447c-84fe-cbfca409fa7d","added_by":"auto","created_at":"2025-07-25 09:41:21","extension":"png","order_by":21,"title":"Figure 21","display":"","copyAsset":false,"role":"figure","size":136492,"visible":true,"origin":"","legend":"\u003cp\u003ePower spectral density of the plate vibration (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 2.5). (a), (b) Vibrating cylinder, (c), (d) stationary cylinder. (a), (c) \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 7.2, (b), (d) \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 10.5.\u003c/p\u003e","description":"","filename":"floatimage21.png","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/02d88160916c02fc4815fad3.png"},{"id":95564107,"identity":"498d854b-9b65-40a7-8766-5302c15a2e9a","added_by":"auto","created_at":"2025-11-10 16:07:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4231871,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7158777/v1/b4f9758c-c96d-4278-a7fc-e7e191078a71.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Vortex-induced vibration and flow characteristics of a circular cylinder attached with inverted flexible and rigid splitter plates","fulltext":[{"header":"I. INTRODUCTION","content":"\u003cp\u003eThe fluid-structure interaction between a flexible body and its surrounding fluid is common in nature. Fish can generate propulsion by using their flexible tail and fins [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. When taking off and landing, the flexible bird feathers can rise up to reduce flow separation and enhance flow conditions [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In order to achieve exceptional maneuverability, bats can alter the shape of their flexible wing [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. These biological behaviors show that flow control using the flexible body is a successful strategy.\u003c/p\u003e\u003cp\u003eWake vortex shedding results in vortex-induced vibration (VIV), which can have an impact on structural reliability and safety. Some investigations have been carried out to provide effective solutions to suppress VIV. Passive control methods such as helical strake [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], control rod [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], mesh [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], and surface roughness [\u003cspan additionalcitationids=\"CR13\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], and active control methods including synthetic jet [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], plasma actuator [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], suction and blowing [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], and oscillatory plate [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] have been developed. In addition, the effect of flexible material on VIV has drawn attention due to its high flow control efficiency in fish swimming and bird flight.\u003c/p\u003e\u003cp\u003eThe rear flexible splitter plate which is attached to the rear stagnation point of a circular cylinder is a solution to suppress VIV in several investigations. Wu \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] studied the control effect of the rear flexible splitter plate on the VIV of a circular cylinder at \u003cem\u003eRe\u003c/em\u003e\u0026thinsp;=\u0026thinsp;150. It was found that the flexible splitter plates of different lengths and stiffness could attenuate the VIV of the cylinder, and the suppression effect was better when the plate length was \u003cem\u003eL\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e \u0026ge; 2 and plate stiffness was 1.7\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003eω\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e\u0026thinsp;\u0026le;\u0026thinsp;2.3. The flow field results showed that the flexible splitter plate reduced the pressure difference between the upper and lower surfaces of the cylinder and resulted in a destructive vortex interaction in the cylinder wake, so as to suppress VIV. The numerical results of Sahu \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] also demonstrated that the rear flexible splitter plate could reduce the cylinder vibration, however, the flexible splitter plate with high stiffness would induce the galloping when the free-stream velocity was large. Xie \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] also numerically investigated the control effect of the rear flexible splitter plate on VIV, and they mainly considered two key parameters of the bending coefficient and the plate length in their investigation.\u003c/p\u003e\u003cp\u003eLiang \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] experimentally investigated the effect of rear flexible splitter plates of different streamwise lengths (0.5\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;2.5) on the VIV of a cylinder by wind tunnel experiments with a large mass damping ratio. When the flexible splitter plate's streamwise length was 0.6\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;1.1, it performed effectively in suppressing VIV; when the plate length was larger than \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.1, however, the cylinder vibration was even enhanced. Liang \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] analyzed the streamwise velocity frequency in the cylinder wake and found that high-frequency harmonics appeared in the spectrum when the cylinder vibrated strongly, so they attributed the strong cylinder vibration to the appearance of these high-frequency harmonics in the flow field.\u003c/p\u003e\u003cp\u003eRecently, a series of systematic experimental studies conducted by Cui \u003cem\u003eet al\u003c/em\u003e [\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] revealed the better control effect of the rear flexible splitter plate than the rigid one. They studied the effect of the flexible splitter plate including streamwise length, spanwise length, and bending stiffness. Their results showed that a finite-span flexible splitter plate could suppress the cylinder vibration and the effect of the bending stiffness and streamwise length were coupled.\u003c/p\u003e\u003cp\u003eDifferent from the rear flexible splitter plate, an inverted flexible splitter plate which is attached to the front stagnation point of a circular cylinder directly affects the upstream flow field of the circular cylinder. Moreover, compared to the rear flexible splitter plate, the inverted flexible splitter plate can experience large-amplitude vibration at a lower velocity and undergo various vibration modes including straight mode, flapping mode, and deflected mode. Kim \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] investigated the large-amplitude vibration and vibration modes of the inverted flexible splitter plate and found that the large-amplitude vibration was caused by the formation and development of the leading-edge vortex (LEV). Gurugubelli and Jaiman [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] further confirmed the occurrence and maintenance mechanism of large-amplitude vibration of inverted flexible splitter plate by numerical simulations. Hu \u003cem\u003eet al\u003c/em\u003e. [\u003cspan additionalcitationids=\"CR31 CR32\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] systematically studied the flow fields and dynamic behaviors of inverted flexible splitter plates under different arrangements, including single, parallel, tandem, staggered, and triangular ones.\u003c/p\u003e\u003cp\u003eIn general, the control effect of the rear flexible splitter plate on the VIV of a circular cylinder has been investigated by some researchers. For the inverted flexible splitter plate, researchers mainly studied the kinematic and dynamic characteristics when it was fixed to a stationary blunt body. To the best of our knowledge, its control effect on the VIV of a circular cylinder is still unclear. Thus, in the present work, we apply the inverted flexible splitter plate to control cylinder vibration. The control effect of the inverted flexible splitter plate is discussed and the effect of its streamwise length is also studied. Moreover, the control effect of the inverted rigid splitter plate is also investigated as a comparison. The kinematic characteristics of the plate and vortex dynamics are analyzed and the relationship between the cylinder vibration and the vortex evolution is further revealed.\u003c/p\u003e"},{"header":"II. EXPERIMENTAL SETUP","content":"\u003cp\u003eThe experiment was conducted in a high-quality recirculating water tunnel with a length of 3000 mm, a width of 600 mm, and a height of 700 mm at the Beijing University of Aeronautics and Astronautics. The free-stream velocity could be increased up to 600 mm/s. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the circular cylinder with a diameter of \u003cem\u003eD\u003c/em\u003e = 25 mm was mounted on a vibration platform that could only move in the direction transverse to the free stream. The Reynolds number based on the free-stream velocity and cylinder diameter was in the range 1970 \u0026lt; \u003cem\u003eRe\u003c/em\u003e \u0026lt; 10590. The reduced velocity that was normalized by the cylinder diameter and the natural frequency in still water of the vibration system (\u003cem\u003ef\u003c/em\u003e\u003csub\u003e\u003cem\u003enw\u003c/em\u003e\u003c/sub\u003e) was over the range 2.56 ≤ \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e ≤ 13.74. The damping ratio and mass ratio of the vibration system were \u003cem\u003eζ\u003c/em\u003e = 0.0033 and \u003cem\u003em\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 7.47, respectively.\u003c/p\u003e\u003cp\u003eIn the present experiment, the control effect of the flexible and rigid splitter plates on the VIV of the circular cylinder was both investigated. The flexible splitter plate had a thickness of \u003cem\u003eh\u003c/em\u003e = 0.24 mm, a Young’s modulus of \u003cem\u003eE\u003c/em\u003e = 1173.3 MPa, and a density of \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e = 1.3 × 10\u003csup\u003e3\u003c/sup\u003e kg/m\u003csup\u003e3\u003c/sup\u003e and was made of polyvinyl chloride. The position of the flexible splitter plate could be extracted by image processing which was introduced in the previous work [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The rigid splitter plate was made of steel and its thickness was the same as that of the flexible splitter plate. The inverted splitter plate was attached to the front stagnation point of the circular cylinder. It covered 30% of the submerged cylinder length, which was 500 mm, and six streamwise lengths in the range of \u003cem\u003eL/D\u003c/em\u003e = 0.5 to 3 were selected with an interval of \u003cem\u003eL/D\u003c/em\u003e = 0.5.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe vibration displacement of the cylinder was measured by a laser displacement sensor installed on one side of the vibration platform. At the measurement range of 0-100 mm, the measurement error of the displacement sensor was less than 0.1% of the full-scale output. The signal of the displacement sensor was recorded by a data acquisition card. When the flow field was measured, the sampling frequency of the vibration displacement was the same as that of the flow field, otherwise, the vibration displacement was captured with a sampling frequency of 400 Hz.\u003c/p\u003e\u003cp\u003eThe vortex dynamics were studied by the particle image velocimetry (PIV) technique which obtained the flow field information by capturing the motion of tracing particles. In the present experiment, the hollow glass beads with a density of 1.05 g/cm\u003csup\u003e3\u003c/sup\u003e and a diameter of 5–20 µm were selected as tracing particles and were illustrated by a high-speed laser at the measurement region. Two CMOS cameras with a full resolution of 2048 × 2048 pixels were utilized to obtain the upstream and downstream flow field by recording particle images with a sampling frequency between 200 Hz to 300 Hz. The image magnification was 0.1 mm/pix. The velocity field was calculated by the multi-pass iterative Lucas-Kanade (MILK) algorithm which computational efficiency could be increased by graphic processing units (GPU) acceleration [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The interrogation window was set to 32 pixels × 32 pixels with an overlap of 75%. The vorticity field was calculated from the velocity field by the difference scheme, and the statistical characteristics were further obtained. In the present work, the coherent structure boundary was determined by the ridge in the finite-time Lyapunov exponent (FTLE) field [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], and then the vortex evolution was investigated.\u003c/p\u003e"},{"header":"III. EXPERIMENTAL RESULTS","content":"\u003cp\u003e\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eA. Vibration response of the circular cylinder\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eThe VIV amplitude response of a circular cylinder is a typical three-branch response for the natural case and its comparison with the results in another research confirmed the reliability of the experimental results obtained by the present vibration system [\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e]. The control effect of the inverted flexible and rigid plates of different streamwise lengths on VIV is shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. The kinematic characteristics of the inverted flexible splitter plate are complicated and are affected by the plate length, so as to result in the change of vibration response with the variation of the plate length. When the streamwise length of the flexible splitter plate is \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;1.5, the cylinder vibration is effectively controlled, and the control effect gradually increases with an increase in the plate length. When the plate length is increased to \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2, in addition to the vibration response in the low-speed range that is denoted by region I in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(d), a considerable vibration response occurs in the high-speed range that is denoted by region II in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(d), indicating that the flexible splitter plate begins to exhibit richer kinematic behavior than the shorter one. With a further increase in the plate length (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;2), the vibration response in the low-speed range disappears, and the amplitude peak of the cylinder vibration in the high-speed range gradually shifts to the lower-speed range.\u003c/p\u003e\n\u003cp\u003eFor the inverted rigid splitter plate, the cylinder vibration response is basically the same as that of the inverted flexible splitter plate case when the plate length is \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;1.5. Different from the flexible splitter plate, the variation of the vibration amplitude with the reduced velocity does not change with a further increase in plate length, only the maximum vibration amplitude is reduced. The previous study showed that the galloping was excited by the alternate attachment of shear layers on the tip of the rear rigid splitter plate [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. However, there is no direct interaction between the shear layers and the rigid splitter plate in the cylinder wake when the plate is attached to the front stagnation point. Thus, Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows that the galloping was not induced by the inverted rigid splitter plate.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows the vibration frequency response of the circular cylinder for several typical cases. The vibration frequency is normalized by the natural frequency of the vibration system of the baseline cylinder in still water. For the natural case, the vibration frequency initially varies along the Strouhal line, then gets close to the natural frequency, and finally is locked into a value slightly greater than the natural frequency. For the flexible splitter plate, the change in the frequency response is minimal compared with the natural case for the \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.5 case. When its length increases to \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2, the flexible splitter plate vibrates at a greater frequency, causing the vibration frequency of the cylinder to be locked into a larger frequency. As the plate length increases further, the vibration frequency of the circular cylinder starts to decrease due to the decrease in the vibration frequency of the flexible splitter plate. Consistent with the similar amplitude response, the vibration frequency response of the rigid splitter plate case for \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.5 is similar to that of the flexible case, indicating similar vibration characteristics between them. As the streamwise length of the rigid splitter plate increases, the velocity at which the cylinder vibration is suppressed decreases, causing a dispersed vibration frequency distribution to occur at a smaller velocity.\u003c/p\u003e\n\u003cp\u003e\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eB. Kinematics of the inverted flexible splitter plate and vortex dynamics\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eThe inverted flexible splitter plate exhibits a variety of vibration modes such as weak vibration, bilateral vibration, and unilateral vibration with the change of velocity and its streamwise length, which further leads to various vortex evolution modes including \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode, \u0026ldquo;LEV\u0026thinsp;+\u0026thinsp;WV\u0026rdquo; mode (LEV: leading-edge vortex; WV: wake vortex) and \u0026ldquo;K-H instability\u0026rdquo; mode. In this section, the kinematics of the inverted flexible splitter plate and the associated vortex dynamics will be discussed.\u003c/p\u003e\n\u003cp\u003eThe flow field around the cylinder for the natural case is presented first (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e). As the cylinder vibrates in the transverse direction, the front stationary point moves up and down in the windward side of the cylinder. The upstream fluid develops from the front stationary point on the cylinder surface to both sides of the cylinder and separates at a certain position to form a free shear layer, and a vortex forms at the end of the shear layer. Along with the cylinder vibration, the shear layer vibrates strongly and the wake vortex develops in a large transverse region. Moreover, the vortex shedding mode is a typical 2P mode for this case, which is in the lower branch, i.e., a pair of wake vortices are generated on each side of the cylinder in a vibration period.\u003c/p\u003e\n\u003cp\u003eWhen the inverted rigid splitter plate is applied to control the VIV of the cylinder (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e), or when the inverted flexible splitter plate vibrates weakly near the center of the cylinder (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e), the upstream fluids develop along the splitter plate and separates before reaching the cylinder due to the viscosity and the inverse pressure gradient. The separated shear layer is reattached to the cylinder at a certain position, and then continues to develop along the cylinder surface, forming K\u0026aacute;rm\u0026aacute;n vortex shedding in the wake, which is referred to as the \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode in the present work (Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e). It is worth noting that the slight deviation of the splitter plate from the center of the cylinder or the weak vibration of the flexible splitter plate will lead to a small angle of attack between the splitter plate and the incoming flow, further resulting some small vortices upstream of the cylinder. However, the primary vortex evolution process is still the K\u0026aacute;rm\u0026aacute;n vortex shedding. Figures \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e show that the vortex evolution modes for the rigid and flexible splitter plate cases with a small streamwise length (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.5, 1, and 1.5) are similar, which results in a similar vibration response, as has been shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eFor the \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode, the effect of the inverted splitter plate on the upstream flow resembles a conical modification on the windward edge of the cylinder. A conical low-speed area forms upstream of the cylinder, and as the plate length increases, the apex of the cone extends upstream, according to the time-averaged streamwise velocity statistics (Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e). In addition, the time-averaged streamwise velocity profiles demonstrate that the inverted splitter plate significantly reduces the streamwise velocity upstream of the cylinder compared to the natural case (Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e). The reduced incoming velocity may cause the wake vortex takes longer to reach the strength that can shed from the shear layer, and therefore the shedding position moves downstream, as can be verified by the change of low-speed wake region for the control case in comparison with the natural case (Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eWhen the streamwise length of the flexible splitter plate is small, it mainly presents a straight mode or a weak vibration mode, and therefore its effect on the flow field is similar to that of the rigid splitter plate. However, as the streamwise length increases, the flexible splitter plate exhibits more complicated vibration state, which makes its control effect different from that of the rigid splitter plate (Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e). The vibration process of the flexible splitter plate is caused by the variations in the fluid and elastic forces acting on it. The angle of attack between the flexible splitter plate and the incoming flow increases when the plate deviates from equilibrium due to instability or when the direction of the incoming velocity changes as a result of cylinder vibration. This increases the fluid force acting on the plate and causes it to deflect. Along with the deformation of the flexible splitter plate, a LEV is generated at the tip of the plate. The pressure difference between the two sides of the flexible splitter plate caused by the LEV makes the plate continue to deflect. Once the fluid and elastic forces acting on the flexible splitter plate reach equilibrium, the plate vibrates to the boundary position. The fluid force on the flexible splitter plate then reduces as the LEV continues to develop downstream, and the flexible splitter plate begins to rebound toward the equilibrium position, eventually generating the periodic vibration of the plate. For this typical case of \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2, \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 4.5, two LEVs form at the tip of the plate in one vibration cycle of the flexible splitter plate. Moreover, the fluid between the LEV and the windward edge of the cylinder bypasses the cylinder while the LEVs develop along the flexible splitter plate, causing the formation of two wake vortices (WVs). The LEV and the wake vortex will merge and gradually dissipate during the downstream convection process. In this paper, the vortex evolution mode in which two LEVs form at the tip of the flexible splitter plate and two wake vortices form on either side of the cylinder in one vibration cycle of the cylinder is referred to as \u0026ldquo;Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; mode (Bi-LEV: bilateral leading-edge vortex; Bi-WV: bilateral wake vortex). The schematic diagram of this vortex evolution mode is clearly shown in Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eWhen the vibration amplitude of the flexible splitter plate is very large, the vortex evolution becomes different. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e, when the flexible splitter plate is close to the boundary position, a LEV forms at its tip, and the LEV develops downstream along with the rebound of the plate. When the flexible splitter plate rebounds to a certain position, the LEV has developed to a position far from the plate tip. With the further rebound of the flexible splitter plate, a new LEV is rolled up on the shear layer of the leeward side of the plate and convects downstream together with the former LEV. Moreover, a wake vortex is shed from the cylinder together with the shedding process of the two LEVs. Therefore, two pairs of LEVs are shed from the plate tip and two wake vortices are shed from the cylinder in a vibration cycle of the flexible splitter plate, which is referred to as \u0026ldquo;2Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; mode in this study. The schematic diagram of this vortex evolution mode is shown in Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e. It is worth noting that the flexible splitter plate switches between bilateral vibration and unilateral vibration rather than always vibrating bilaterally. This suggests that the system may contain two attractors, one of which causes the flexible splitter plate to vibrate unilaterally around a position on one side of the cylinder and the other of which causes the flexible splitter plate to vibrate bilaterally around the cylinder center. Note that Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e(a) shows there is a variation in the vibration frequency of the flexible splitter plate, which will be discussed in the following section.\u003c/p\u003e\n\u003cp\u003eWhen the elastic force is unable to cause the rebound of the flexible splitter plate to cross the equilibrium position to the opposite side of the cylinder, the flexible splitter plate vibrates on one side of the cylinder, forming a unilateral vibration mode, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e(a). The vortex evolution brought on by the unilateral vibration of the flexible splitter plate is shown in Figs. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e(b)-14(e). The incoming flow bypasses the tip of the flexible splitter plate and rolls up into a LEV near the boundary position of the plate vibration. The LEV develops downstream along with the rebound of the flexible plate. It can be found that the lower half of the cylinder is almost always located in the separation region behind the flexible splitter plate due to the unilateral vibration of the plate. The flow velocity in the separation region is extremely low and there also exits backflow, which results in no wake vortex forming in the lower part of the cylinder. However, in the upper half of the cylinder, the fluid flows along the windward side of the flexible splitter plate and the cylinder, and then a vortex forms in the wake of the cylinder. The vortex evolution that a LEV is shed on the vibration side of the flexible splitter plate and a wake vortex is shed from the cylinder on the opposite side is referred to as the \u0026ldquo;Uni-LEV\u0026thinsp;+\u0026thinsp;Uni-WV\u0026rdquo; mode (Uni-LEV: unilateral leading-edge vortex; Uni-WV: unilateral wake vortex), which is illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe \u0026ldquo;K-H instability\u0026rdquo; mode, a new vortex evolution mode, develops when the flexible splitter plate vibrates weakly in a large deformation state. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e16\u003c/span\u003e, the fluid separates at the tip of the flexible splitter plate and forms a free shear layer behind the plate. Due to the development of the K-H instability in the shear layer, some small-scale vortices form. For the lower half of the cylinder, it is located in the separation region caused by the blocking effect of the flexible splitter plate, so there are no obvious vortex structures forming on this side of the cylinder. However, on the side of the cylinder that is not blocked by the flexible splitter plate, the fluid flows over the surface of the cylinder and, like the shear layer behind the flexible splitter plate, K-H instability also develops in the free shear layer behind the cylinder, which then leads to small-scale vortices. Thus, for the \u0026ldquo;K-H instability\u0026rdquo; mode, the primary flow structures are small-scale vortices, and there are no large-scale vortices in the flow field. The schematic diagram of the \u0026ldquo;K-H instability\u0026rdquo; mode is shown in Fig. \u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eTo further understand the relationship between the vortex evolution and the cylinder vibration, Fig. 18 presents a summary of vortex evolution modes and the associated vibration amplitude of the cylinder for all measured cases in the present work. For the flexible splitter plate with a small streamwise length (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e = 0.5 and 1) and the rigid splitter plate, the vortex evolution mode is the \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode, which controls the flow field around the cylinder by leading-edge modification and affecting the shedding position of the wake vortex. Figure 18 shows that the vibration amplitude of the cylinder corresponding to the \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode is generally smaller, further demonstrating that the \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode is efficient in suppressing the cylinder vibration.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWith an increase in the streamwise length of the flexible splitter plate, its kinematic characteristics become more complicated, thus resulting in more vortex evolution modes. They can be characteristic by the \u0026ldquo;LEV + WV\u0026rdquo; modes, including \u0026ldquo;Bi-LEV + Bi-WV\u0026rdquo; mode, \u0026ldquo;2Bi-LEV + Bi-WV\u0026rdquo; mode, and \u0026ldquo;Uni-LEV + Uni-WV\u0026rdquo; mode, where the lift fluctuation of the cylinder is affected by the LEV and the wake vortex. The effect of the LEV on the cylinder vibration is mainly brought about by changes in the force exerted on the flexible splitter plate during its periodic bending and rebounding process. The wake vortex directly affects the vortex force, and further changes the lift fluctuation of the cylinder. The bending and rebound of the flexible plate are the process of energy storage and release. When the vibration amplitude of the flexible plate is not very large (\u0026ldquo;Bi-LEV + Bi-WV\u0026rdquo; mode), the energy change during the vibration of the flexible splitter plate is relatively small, and the contribution to the cylinder vibration is small. As the vibration amplitude of the flexible splitter plate increases (\u0026ldquo;2Bi-LEV + Bi-WV\u0026rdquo; mode and \u0026ldquo;Uni-LEV + Uni-WV\u0026rdquo; mode), the energy changes during the vibration process increases, and thus the contribution to the cylinder vibration increases. Figure 18 shows that the cylinder vibration is relatively stronger for the \u0026ldquo;LEV + WV\u0026rdquo; modes where the amplitude of the flexible plate oscillation is larger.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 19 further supports the finding that there is a positive correlation between the vibration amplitude of the flexible splitter plate and the cylinder, i.e., that the larger the vibration amplitude of the flexible splitter plate, the larger the vibration amplitude of the cylinder. The dominant flow structures of the \u0026ldquo;K-H instability\u0026rdquo; mode are small-scale vortices, which have little impact on cylinder vibration and basically suppress it. Therefore, in general, the cylinder vibration is effectively suppressed, when the \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode or \u0026ldquo;K-H instability\u0026rdquo; mode is generated, whereas the vibration amplitude of the cylinder for the \u0026ldquo;LEV + WV\u0026rdquo; modes is relatively larger because the suppression effect is diminished by the relatively strong vibration of the flexible splitter plate.\u003c/p\u003e\n\u003cp\u003eFigure 20 presents the spectral analysis results for some typical vortex evolution modes. It is clear that there is a strong fluid-structure interaction for all cases since the dominant frequencies of the streamwise velocity and the vibration of the flexible splitter plate and cylinder are locked into each other. In particular, the spectra for both the \u0026ldquo;Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; mode and \u0026ldquo;Uni-LEV\u0026thinsp;+\u0026thinsp;Uni-WV\u0026rdquo; mode have the distinctive feature that, in addition to the fundamental frequency, there are high-order harmonics that correlate to small-amplitude perturbations. The small-amplitude perturbations are related to the sweeping and shear effects of large-scale LEVs and strongly vibrating flow structures on their surrounding fluid.\u003c/p\u003e\n\u003cp\u003eWhen introducing the \u0026ldquo;Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; vortex evolution mode, it has been pointed out that the flexible splitter plate of \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.5 switches between large-amplitude bilateral vibration and unilateral vibration, and the vibration frequency also changes at \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 10.5, as has been shown in Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e(a). Moreover, the vibration frequency of the flexible splitter plate with a streamwise length of \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.5 has the same characteristic at \u003cem\u003eU\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = 7.2. To investigate the cause of this frequency variation, the frequency characteristics of these two cases are given in Fig. \u003cspan class=\"InternalRef\"\u003e21\u003c/span\u003e. It is discovered that the plate vibration presents a low-frequency characteristic when the cylinder is stationary. Moreover, the cylinder tends to vibrate with a frequency close to the natural frequency when its degree of freedom is released. As a result, the plate vibration is affected by both the low-frequency characteristic and the natural frequency of the vibration system, which further leads to the change of vibration frequency of the flexible splitter plate.\u003c/p\u003e"},{"header":"IV. CONCLUSION","content":"\u003cp\u003eThe control effect of inverted flexible and rigid splitter plates with different streamwise lengths on the VIV of a circular cylinder is investigated in a water tunnel experiment. The kinematic characteristics of the flexible splitter plate and the resulting various vortex evolution modes are analyzed. The main conclusions are as follows.\u003c/p\u003e\u003cp\u003eThe control effect of the inverted flexible splitter plate on the cylinder vibration depends on its streamwise length. When the flexible splitter plate is short (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.5\u0026ndash;1.5), the plate vibration is weak, thus resulting in the vibration response of the cylinder similar to that of the rigid splitter plate case. With an increase in the streamwise length, the occurrence of various vibration states of the flexible splitter plate leads to different vibration responses of the cylinder. In addition to the vibration response at the low-speed region similar to the short flexible splitter plate cases, obvious cylinder vibration is excited at the high-speed region for long flexible splitter plate cases. Moreover, the cylinder vibration at the low-speed region gradually diminishes, and the vibration response at the high-speed region gradually moves toward the low-speed region with an increase in the plate length. The control effect of the inverted splitter plate in the present work is compared with that of the rear splitter plate in the previous work. It has been discovered that the variation of the vibration characteristics of the cylinder with the plate length is more obvious for the inverted flexible splitter plate, while the suppression effect of the rear flexible splitter plate on VIV is better when the streamwise length is \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;1. For the rigid splitter plate, the inverted one has a better control effect than the rear one because the galloping of the cylinder is not excited.\u003c/p\u003e\u003cp\u003eThe change of kinematic characteristics of the inverted flexible splitter plate leads to different vortex evolution modes in the flow field, including \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode, \u0026ldquo;Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; mode, \u0026ldquo;2Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; mode, \u0026ldquo;Uni-LEV\u0026thinsp;+\u0026thinsp;Uni-WV\u0026rdquo; mode, and \u0026ldquo;K-H instability\u0026rdquo; mode. The influence mechanism of the inverted flexible splitter plate on the VIV of the cylinder is revealed based on the investigation of the vortex evolution modes. When the \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; mode is induced, the incoming flow velocity upstream of the cylinder is reduced and the shedding position of the wake vortex is extended downstream, thus reducing the effect of the vortex shedding and suppressing the cylinder vibration. For the \u0026ldquo;LEV\u0026thinsp;+\u0026thinsp;WV\u0026rdquo; modes, including the \u0026ldquo;Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; mode, \u0026ldquo;2Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo; mode, and \u0026ldquo;Uni-LEV\u0026thinsp;+\u0026thinsp;Uni-WV\u0026rdquo; mode, the cylinder vibration is affected by both LEV and wake vortex. The effect of LEV is generated by energy change during the bending and rebounding processes of the flexible splitter plate, so the vibration amplitude of the flexible splitter plate is positively correlated with the vibration strength of the cylinder. The control of the wake vortex can reduce the vortex force of the circular cylinder, achieving control of the cylinder vibration. For the \u0026ldquo;K-H instability\u0026rdquo; mode, the small-scale flow structure leads to a good suppression of cylinder vibration.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGuo-Peng Cui contributes to experimental work, formal analysis, investigation, writing\u0026mdash;original draft. Li-Hao Feng\u0026nbsp;contributes to formal analysis, methodology, supervision and writing\u0026mdash;review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data supporting the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclarations Conflict of interest\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eF. E. Fish and G. V. Lauder, Passive and active flow control by swimming fishes and mammals, Annu. Rev. Fluid Mech. \u003cstrong\u003e38\u003c/strong\u003e, 193 (2006).\u003c/li\u003e\n \u003cli\u003eC. Br\u0026uuml;cker and C.Weidner, Influence of self-adaptive hairy flaps on the stall delay of an airfoil in ramp-up motion, J. 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Astron. \u003cstrong\u003e58\u003c/strong\u003e, 1 (2015).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"experiments-in-fluids","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"exif","sideBox":"Learn more about [Experiments in Fluids](http://link.springer.com/journal/348)","snPcode":"348","submissionUrl":"https://submission.nature.com/new-submission/348/3","title":"Experiments in Fluids","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7158777/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7158777/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, inverted flexible and rigid splitter plates are applied to control the vortex-induced vibration of a circular cylinder. The VIV characteristics and vortex dynamics are experimentally investigated with a Reynold number ranging from 1970 to 10590. To examine the effect of the streamwise length, five different lengths are selected. It is indicated that the VIV of the circular cylinder is suppressed by the inverted rigid splitter plate and the suppression effect is improved with an increase in the streamwise length of the plate, however, the vibration response characteristics remain the same for all streamwise lengths. Compared to the rigid one, the inverted flexible splitter plate causes various vibration responses with the change of its streamwise length. The diverse vibration responses are related to the kinematic characteristics of the inverted flexible splitter plate and the vortex dynamics. Five vortex shedding modes, including \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo;, \u0026ldquo;Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo;, \u0026ldquo;2Bi-LEV\u0026thinsp;+\u0026thinsp;Bi-WV\u0026rdquo;, \u0026ldquo;Uni-LEV\u0026thinsp;+\u0026thinsp;Uni-WV\u0026rdquo;, and \u0026ldquo;K-H instability\u0026rdquo;, are found. The correlation between the VIV and the vortex shedding mode is revealed. The \u0026ldquo;K\u0026aacute;rm\u0026aacute;n vortex\u0026rdquo; and \u0026ldquo;K-H instability\u0026rdquo; modes are corresponding to a better effect of suppressing VIV. The control effect of \u0026ldquo;LEV\u0026thinsp;+\u0026thinsp;WV\u0026rdquo; modes is affected by the kinematics of the plate, as it is found that the vibration amplitude of the circular cylinder and the inverted flexible splitter plate is positively correlated.\u003c/p\u003e","manuscriptTitle":"Vortex-induced vibration and flow characteristics of a circular cylinder attached with inverted flexible and rigid splitter plates","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-25 09:41:16","doi":"10.21203/rs.3.rs-7158777/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-14T04:42:36+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-13T09:17:47+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-13T06:57:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"189552037068119079561522906474065226991","date":"2025-07-25T07:17:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"117242139032932674004851396481853547575","date":"2025-07-23T04:30:04+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-23T03:12:50+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-21T14:54:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-19T02:33:47+00:00","index":"","fulltext":""},{"type":"submitted","content":"Experiments in Fluids","date":"2025-07-18T14:38:06+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"experiments-in-fluids","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"exif","sideBox":"Learn more about [Experiments in Fluids](http://link.springer.com/journal/348)","snPcode":"348","submissionUrl":"https://submission.nature.com/new-submission/348/3","title":"Experiments in Fluids","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"9dfe6343-fdc7-421a-a3ed-193b834903bd","owner":[],"postedDate":"July 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-10T16:03:50+00:00","versionOfRecord":{"articleIdentity":"rs-7158777","link":"https://doi.org/10.1007/s00348-025-04138-2","journal":{"identity":"experiments-in-fluids","isVorOnly":false,"title":"Experiments in Fluids"},"publishedOn":"2025-11-08 15:58:16","publishedOnDateReadable":"November 8th, 2025"},"versionCreatedAt":"2025-07-25 09:41:16","video":"","vorDoi":"10.1007/s00348-025-04138-2","vorDoiUrl":"https://doi.org/10.1007/s00348-025-04138-2","workflowStages":[]},"version":"v1","identity":"rs-7158777","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7158777","identity":"rs-7158777","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}