Fluid–structure interaction modes under complex unsteady vortices: a review
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摘要: 在复杂非定常涡流环境中, 结构所激发的流固耦合模态可能与均匀来流下的模式显著不同, 并伴随丰富的力学机制. 本文结合作者团队多年在该领域的研究与实践经验, 围绕三类流固耦合现象——即圆柱流致振动、柔性薄板拍动以及生物游动/飞行——系统介绍了当前研究进展. 所述三类现象广泛存在于自然界及工程应用, 并涵盖了自激型和自驱型流固耦合作用. 首先, 本文梳理了结构在均匀流与复杂非定常涡流作用下的流固耦合响应模态. 研究表明, 来流涡结构可显著增强圆柱与柔性薄板的振动幅值, 诱发新的失稳模式; 而生物体则可能通过调整运动模式, 主动利用来流漩涡以实现更高效的推进性能. 进一步地, 本文分析了复杂涡环境下的流固耦合模态的可能应用方向, 包括提高流致振动能量俘获效率以及发展具备更强感知与决策能力的仿生机器人. 最后, 本文对当前研究的挑战与未来的发展方向进行了总结与展望, 以期为相关研究提供参考.Abstract: In complex unsteady wakes, the fluid–structure interaction (FSI) modes can differ significantly from those under uniform flows, often involving rich physical mechanisms. This paper reviews recent advances in three representative FSI phenomena: vortex-induced vibration (VIV) of cylinders, flapping of flexible plates, and locomotion of swimming/flying organisms. These phenomena are widely observed in both nature and engineering applications and span self-excited, active, and hybrid FSI modes. First, we compare the response modes under uniform and unsteady wake inflows. Results show that incoming vortices can substantially amplify vibration amplitudes of cylinders and plates, potentially triggering new instabilities. In contrast, biological swimmers may actively exploit incoming vortices by modulating their motions to enhance propulsion efficiency. Furthermore, this paper discusses potential applications of such FSI modes in complex wake flows, including enhanced energy harvesting from flow-induced vibrations and the development of bioinspired robots with improved sensing and decision-making capabilities. Finally, the challenges and future research directions in this area are outlined to guide further exploration.
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图 1 自然界和工程中发生的自激与自驱型流固耦合现象(图片来源于网络, 由作者整理)
Figure 1. Self-excited and active fluid–structure interaction (FSI) phenomena occurring in nature and engineering (schematic illustration compiled by the authors). (Figures from the internet).
图 2 本文研究对象示意图. 复杂涡环境中的自激型流固耦合: (a)圆柱流致振动(Flow-induced vibration, FIV), (b)柔性薄板拍动; 以及自驱型流固耦合: (c)生物游动/飞行
Figure 2. Schematic of the research subjects considered in this study. Self-excited fluid–structure interaction in complex vortex environments: (a) flow-induced vibration (FIV) of circular cylinders; (b) flapping of flexible plates; and active fluid–structure interaction: (c) biological swimming/flying.
图 4 不同质量−阻尼参数下单圆柱涡激振动的流固耦合响应模态示意图: ($ a $)质量比$ \sim \mathcal{O}(10^{2}) $, 主要包含初始与下分支; ($ b $)质量比$ \sim \mathcal{O}(10^{1}) $, 主要包含初始、上和下分支; ($ c $)质量比$ \sim \mathcal{O}(10^{0}) $, 表现出永久涡激振动分支. 数据来源于Han et al. (2023b); Williamson & Govardhan (2004, 2008)
Figure 4. Schematic of FSI modes of vortex-induced vibration of a single cylinder under different mass–damping parameters: (a) mass ratio $ \sim \mathcal{O}(10^{2}) $, mainly exhibiting the initial and lower branches; (b) mass ratio $ \sim \mathcal{O}(10^{1}) $, mainly exhibiting the initial, upper, and lower branches; (c) mass ratio $ \sim \mathcal{O}(10^{0}) $, exhibiting the branch of infinite VIV. Data from Han et al. (2023b); Williamson & Govardhan(2004, 2008).
图 5 固定双圆柱绕流在不同间距比与交错角下的流动模态图(Alam & Meyer, 2013)
Figure 5. Flow modes around two fixed cylinders as functions of spacing ratio and stagger angle (Alam & Meyer, 2013).
图 6 不同间距比下串列双圆柱绕流的脱涡模拟结果(Zeng et al., 2024)
Figure 6. Vortex shedding simulation results of tandem cylinders at different spacing ratios (Zeng et al., 2024).
图 7 非定常涡流中下游弹性支撑圆柱的流致振动模态: (a)纯涡流共振(Pure VR); (b)涡流共振与尾流驰振耦合(Combined VR and WIG); (c)涡流共振与尾流驰振分离(Separated VR and WIG). 其中, VR表示vortex resonance, WIG表示wake-induced galloping (Hu et al., 2020c)
Figure 7. Flow-induced vibration modes of a downstream elastically mounted cylinder under unsteady wakes: (a) pure vortex resonance (Pure VR); (b) combined vortex resonance and wake-induced galloping (Combined VR and WIG); (c) separated vortex resonance and wake-induced galloping (Separated VR and WIG) (Hu et al., 2020c).
图 8 (a)串列圆柱系统中上游圆柱流固耦合振动模态响应随间距比—来流折合速度相图; (b)谐波锁定模态下的脱涡云图. 其中, ID表示初始非同步(Initial desynchronization), IB表示初支(Initial branch), LN表示锁定(Lock-in), HLN表示谐波锁定(Harmonic lock-in), UB表示上支锁定(Upper branch lock-in), LB表示下支锁定(Lower branch lock-in), FD表示最终非同步(Final desynchronization). (Li et al., 2024)
Figure 8. (a) Phase diagram of FSI modes of the upstream cylinder in a tandem cylinder system with respect to spacing ratio and reduced velocity, including the initial desynchronization (ID), initial branch (IB), lock-in (LN), harmonic lock-in (HLN), upper branch lock-in (UB), lower branch lock-in (LB), and final desynchronization (FD); (b) Vortex shedding patterns under harmonic lock-in mode (Li et al., 2024).
图 9 不同工况分支下的锁定(Lock-in)机制示意图: (a)UB(Upper-branch lock-in, 上分支锁定); (b)LB(Lower-branch lock-in, 下分支锁定); (c)与(d)为LN(Lock-in, 锁定分支)(Sharma & Bhardwaj, 2023). 其中, 在图(a)与(b)中, UB工况主要表现为上游圆柱主导的涡结构对下游圆柱的诱导激励; 而LB工况则由间隙射流驱动剪切层发展并促成下游强涡形成, 从而维持系统的锁定响应. 在图(c)与(d)中, LN工况体现为通过弹性耦合实现流能在上下游圆柱之间的传递, 从而支撑锁定或反相锁定振动
Figure 9. Schematic illustration of the lock-in mechanisms under different response branches: (a) UB (Upper-branch lock-in); (b) LB (Lower-branch lock-in); and (c, d) LN (Lock-in branch) (Sharma & Bhardwaj, 2023). In panels (a) and (b), the UB regime is primarily characterized by vortex structures dominated by the upstream cylinder, which induce excitation on the downstream cylinder, whereas in the LB regime, the lock-in response is sustained by the gap flow that drives shear-layer development and promotes the formation of strong downstream vortices. In panels (c) and (d), the LN regime reflects the transfer of flow energy between the upstream and downstream cylinders through elastic coupling, thereby supporting vibrations.
图 10 串列薄板的拍动模态: (a)同相模态(Ristroph & Zhang, 2008); (b)反相模态(Ristroph & Zhang, 2008); (c)增强模式(Kim et al., 2010); (d)削弱模式(Kim et al., 2010)
Figure 10. Flapping modes of tandem filaments: (a) in-phase mode (Ristroph & Zhang, 2008); (b) out-of-phase mode (Ristroph & Zhang, 2008); (c) constructive mode (Kim et al., 2010); (d) destructive mode (Kim et al., 2010).
图 11 串列双薄板的拍动模态: (a)直模态; (b)拍动模态(下游薄板拍动幅度较大); (c)拍动模态(上游薄板拍动幅度较大); (d)偏转模态(上游薄板偏转, 下游薄板几乎保持直模态); (e)偏转模态(上下游薄板均偏转向一侧)(Hu et al., 2020a)
Figure 11. The motion modes of tandem inverted filaments: (a) straight mode, (b) flapping mode with with a larger amplitude in the downstream filament, (c) flapping mode with with a larger amplitude in the upstream filament, (d) deflected mode with the upstream filament deflected and the downstream one almost straight and (e) deflected mode with both the upstream and downstream filaments deflected to one side (Hu et al., 2020a).
图 12 串列双薄板的拍动模态. 等长双薄板: (a)伏贴模态、(b)规则涡激振动模态、(c)静重构模态、(d)空腔振动模态(Zhang et al., 2020c); 非等长双薄板: (e)双伏贴模态、(f)拍动−伏贴模态、(g)双拍动模态、(h)静重构−拍动模态以及(i)双静重构模态(Xiong et al., 2025)
Figure 12. The motion modes of the tandem flexible filaments. For equal-length filaments: (a) lodging mode, (b) regular VIV mode, (c) static reconfiguration mode and (d) cavity oscillation mode (Zhang et al., 2020c). For unequal-length filaments: (e) dual collapse mode, (f) flapping collapse mode, (g) dual flapping mode, (h) static flapping mode and (i) dual static mode (Xiong et al., 2025).
图 13 800根固壁细丝湍流的瞬时相干结构: (a)开尔文−赫姆霍兹涡(KH vortex); (b)高速条带(High-speed streaks, HS-streaks)、低速条带(Low-speed streaks, LS-streaks)与发卡涡(Hairpin vortex, HP-vortex)(Tschisgale et al., 2021)
Figure 13. Instantaneous coherent vortex structures induced by 800 wall-mounted filaments. (a) KH-vortex; (b) HS-streaks, LS-streaks and HP-vortex (Tschisgale et al., 2021).
图 14 生物游动与飞行中涡结构相互作用示意图: (a)蜂与湍流环境相互作用; (b)鱼在卡门涡街中游动; (c)大雁“人”字形排列中个体间相互作用; (d)鱼群中个体间相互作用; (e)蜻蜓前后翅相互作用; (f)鱼背鳍尾鳍相互作用
Figure 14. Schematics of vortex interactions in biological swimming and flying: (a) honeybee interacting with a turbulent flow environment; (b) fish swimming in a Kármán vortex street; (c) mutual interactions among individuals in a V-formation of geese; (d) interactions between individuals in fish schooling; (e) aerodynamic interplay between the forewings and hindwings of a dragonfly; (f) hydrodynamic coupling between the dorsal fin and caudal fin of a fish.
图 15 仿生运动模型示意图: (a)拍动翼模型; (b)波动模型
Figure 15. Schematic of (a) flapping-foil model and (b) undulatory propulsion model.
图 16 卡门涡街中的两种相互作用模态: (a)回转模态(Slalom mode, S模式); (b)拦截模态(Interception mode, I模式)
Figure 16. Schematics of two modes in Kármán vortex street: (a) slalom mode; (b) interception mode.
图 17 金枪鱼(a)与太阳鱼(b)背鳍−尾鳍间三维相互作用(Zhang et al., 2022b)
Figure 17. Three-dimensional interaction between dorsal fin and caudal fin in (a) tuna and (b) sunfish (Zhang et al., 2022b).
图 18 多体相互作用模态: (a)快速模式与慢速模式(Peng et al., 2018a); (b)紧密串联模式(Lin et al., 2020b); (c)主动控制与被动控制(Zhang & Huang, 2022)
Figure 18. Modes of interactions between multiple bodies: (a) fast mode and slow mode (Peng et al., 2018a); (b) compact mode (Lin et al., 2020b); (c) active and passive control (Zhang & Huang, 2022).
图 19 真实生物实验观测: (a)蜻蜓前后翅相互作用流动显示(Thomas et al., 2004); (b)鱼类背鳍尾鳍PIV测量结果(Drucker & Lauder, 2001); (c)鹮集群飞行实验观测数据(Portugal et al., 2014)
Figure 19. Experimental observations of biological systems: (a) flow visualization of dorsal fin-caudal fin interaction in dragonflies (Thomas et al., 2004); (b) PIV measurements of dorsal fin-caudal fin kinematics in fish (Drucker & Lauder, 2001); (c) experimental flying data of ibis flocking dynamics (Portugal et al., 2014).
图 20 真实模型相互作用: (a)鱼背鳍尾鳍相互作用(Liu et al., 2017a); (b)蜻蜓前后翅相互作用(Li & Dong, 2017)
Figure 20. Interactions in realistic numerical models: (a) interaction between dorsal fin and caudal fin in sunfish (Liu et al., 2017a); (b) ineraction between forewing and hindwing in dragonfly (Li & Dong, 2017).
图 21 (a)复杂涡环境中的流致振动俘能设定示意图; (b)不同风速、间距比下的最大俘能性能(Usman et al., 2018)
Figure 21. (a) Schematic diagram of a FIV energy harvesting setup in unsteady vortex flows; (b) maximum energy harvesting performance under different wind speeds and spacing ratios (Usman et al., 2018).
图 22 结合涡流发生器的轻质圆柱流致旋转能量采集系统设计与应用实现示意图(Li et al., 2025a)
Figure 22. Schematic of the design and application implementation of a lightweight cylinder flow-induced rotation energy harvesting system behind a vortex generator (Li et al., 2025a).
图 23 (a)流动下的反置柔性薄板系统示意图; (b)基于柔性薄板的俘能装置(Mazharmanesh et al., 2020)
Figure 23. (a) Schematic of an inverted flexible flag system under flows; (b) energy harvesting device based on flexible flags (Mazharmanesh et al., 2020).
图 24 基于非定常流场中的生物飞行(Lisca, 1957)与游动(Liao et al., 2003)原理设计的仿生机器复杂环境中稳定运动的策略(Ajanic et al., 2020; Feng et al., 2024)
Figure 24. Strategies for stable locomotion of biomimetic robots (Ajanic et al., 2020; Feng et al., 2024) in complex environments, inspired by principles of biological flying (Lisca, 1957) and swimming (Liao et al., 2003) in unsteady flow fields.
图 25 对于生物集群运动中流动控制的研究正帮助海空机器人复杂集群作业成为现实(Berlinger et al., 2021; Soria et al., 2021)
Figure 25. Research on flow control in biological collective motion is facilitating the realization of complex swarm operations for marine and aerial robots(Berlinger et al., 2021; Soria et al., 2021).
表 1 相关综述文献分类汇总
Table 1. Summary and classification of relevant review literature
综述文献 研究类别 具体设定 Williamson & Govardhan(2004, 2008) 流致振动 单个圆柱 Gabbai & Benaroya (2005) 流致振动 单个圆柱 Païdoussis et al. (2010) 流致振动 柱群 Zhou & Alam (2016) 流致振动 柱群 Liu et al. (2020) 流致振动 柱群 Ali et al. (2021) 流致振动 柱群 Shelley & Zhang (2011) 柔性薄板拍动 单个薄板 Yu et al. (2019) 柔性薄板拍动 单个薄板 Gallegos & Sharma (2017) 柔性薄板拍动 单个薄板 Choi et al. (2012) 生物游动飞行 单个生物 Liu et al. (2017b) 生物游动飞行 单个生物 Zhang et al. (2022a) 生物游动飞行 单个/多个生物 Zhang & Lauder (2025) 生物游动 多个生物 
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