ENERGY SAVING MECHANISM OF HYDRODYNAMIC COLLECTIVE BEHAVIOR OF MULTIPLE FLEXIBLE BEAMS IN V FORMATION
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摘要: V型排列是自然界中常见的动物(如大雁等迁徙性鸟类)集群模式, 普遍推测该模式可以有效地降低能耗, 然而目前没有研究给出相关的直接数据证据. 开展其节能机理研究有助于提升对集群自然现象的认知水平, 为集群仿生应用打下基础. 本文采用基于Fluent二次开发的数值方法求解多个柔性体−流体介质相互作用的流固耦合问题, 其中流体动力学方程采用有限体积法进行求解, 柔性体动力学控制方程通过用户自定义模块(UDF)嵌入, 并采用模态叠加法和4阶龙格库塔法求解, 流固交界面形变使用动网格技术处理. 实现了多个自推进二维柔性梁自主形成V型集群运动过程的数值模拟, 并将得到的推进性能参数(平均速度, 输入功率和效率)与单独自推进柔性体的数据进行对比. 研究发现: 该V型集群运动中不仅后排柔性梁的速度和推进效率得到提升, 领头柔性梁性能也得到大幅提升, 增幅均超过14%. 此外, 对V型集群运动的流场细节(涡量和压力云图)开展分析, 揭示了多柔性梁V型集群行为产生的原因和节能的内在机理, 特别是对领头柔性梁的节能机理进行了阐述.Abstract: The phenomenon of aggregation of animals in V formation is ubiquitous in our daily life, such as bird flocks in migration. It is commonly recognized that this collective mode helps to save energy of the group. However, little direct evidence is given. Research on the energy saving mechanism of this collective behavior can not only help to improve the understanding of nature secret, but also lay a foundation for its bionic application. In this paper, a simulation method developed based on Fluent is adopted to solve this fluid-structure interaction problem of hydrodynamic collective behavior of multiple flexible beams in V formation. Specifically, finite volume method is used to simulate the flow field, governing equations of Euler-Bernoulli beam are complemented through user-defined function, and then solved by the mode superposition method and fourth-order Runge-Kutta method. Dynamic mesh technique is adopted to trace the coupling interface between flow field and structural field. The hydrodynamic aggregations of multiple (three or five) self-propelled 2D flexible beams in V configuration are simulated. Three propulsive properties (mean velocity, input power and efficiency) of beams in V formation are compared with the corresponding data of single self-propelled beam. It is found that not only the following beams in V formation possess the promotion of mean velocity and propulsive efficiency, the performance of leading beam also increases, and the growing rate surpasses 14%. Those data provide the direct evidence of energy saving in the collective behavior of V formation. In addition, in order to find out the mechanism of the formation of hydrodynamic aggregation behavior and the reason of the energy saving of beams (especially the leading beam) in V formation, the obtained flow details (vortices contour and pressure contour) are analyzed.
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图 1 多个柔性体自推进V型排列计算模型示意图
Figure 1. Schematic of multiple self-propelled flexible beams in V configuration
图 4 纵向排列柔性梁导边运动参数时历曲线对比: (a) 水平运动速度; (b) 纵向间距
Figure 4. Comparison of time history of (a) streamwise velocity and (b) longitudinal separation distance of two tandem beams between the present solutions and Ref. [23]
5 柔性梁导边水平运动速度时历曲线对比: (a) 网格无关性分析; (b) 时间步长无关性分析; (c) 模态截断分析
5. Comparison of streamwise velocity curves of the leading edge in (a) grid independence study, (b) time-step independence study, and (c) mode truncation study
5 柔性梁导边水平运动速度时历曲线对比: (a) 网格无关性分析; (b) 时间步长无关性分析; (c) 模态截断分析(续)
5. Comparison of streamwise velocity curves of the leading edge in (a) grid independence study, (b) time-step independence study, and (c) mode truncation study (continued)
图 6 3个柔性梁V型排列运动参数时历曲线: (a) 速度差值Uij(t) = ui(t)−uj(t); (b) 纵向间距Hij(t) = Xi(s = 0, t)−Xj(s = 0, t) (i, j = 1, 2, 3)
Figure 6. Time history of (a) velocity difference Uij(t) = ui(t)−uj(t), and (b) longitudinal separation distance Hij(t) = Xi(s = 0, t)−Xj(s = 0, t) (i, j = 1, 2, 3) of three beams in V configuration
7 3个柔性梁V型排列流场细节图: (a~d) 涡量云图; (e~h) 压力云图. 特征值ωref=Uref /L和pref=ρf
$U_{ref}^2 $ 分别被用来无因次化计算得到的涡量和压力7. Fluid details: (a~d) vortices contour and (e~h) pressure contour of three beams in V configuration. The vortices and pressures are normalized by ωref=Uref /L, pref=ρf
$U_{ref}^2 $ , respectively
图 8 3个柔性梁水平受力时历曲线, 特征值Fref=(1/2)ρf
$U_{ref}^2{L}$ 被用来无因次化计算得到的合力Figure 8. Hydrodynamic force experienced by three flexible beams in the horizontal direction during one heaving motion period. The forces are normalized by Fref=(1/2)ρf
$U_{ref}^2{L}$ 
图 9 5个柔性梁V型排列运动参数时历曲线: (a, b) 速度差值Uij(t) = ui(t)−uj(t); (c, d) 纵向间距Hij(t) = Xi(s = 0, t)−Xj(s = 0, t) (i, j = 1, 2, 3, 4, 5)
Figure 9. Time history of (a, b) velocity difference Uij(t) = ui(t)−uj(t), and (c, d) longitudinal separation distance Hij(t) = Xi(s = 0, t)−Xj(s = 0, t) (i, j = 1, 2, 3, 4, 5) of five beams in V configuration
图 10 5个柔性梁V型排列流场涡量云图. 特征值ωref = Uref /L被用来无因次化计算得到的涡量
Figure 10. Vortices contour of five beams in V configuration. The vortices are normalized by ωref = Uref /L
图 11 5个柔性梁V型排列流场压力云图. 特征值pref = ρf
$U_{ref}^2 $ 被用来无因次化计算得到的压力Figure 11. Pressure contour of five beams in V configuration. The pressures are normalized by pref = ρf
$U_{ref}^2 $ 
图 12 5个柔性梁水平受力时历曲线, 特征值Fref = (1/2)ρf
$U_{ref}^2{L}$ 被用来无因次化计算得到的合力Figure 12. Hydrodynamic force experienced by five flexible beams in the horizontal direction during three heaving motion periods. The forces are normalized by Fref = (1/2)ρf
$U_{ref}^2{L}$ 
图 13 领头柔性梁对比: (a) 水平受力时历曲线; (b) 横向形变时历曲线. 特征值Fref = (1/2)ρf
$U_{ref}^2{L} $ 被用来无因次化计算得到的合力Figure 13. The comparison of the leading beams: (a) hydrodynamic force in the horizontal direction and (b) lateral deformation during one heaving motion period. The forces are normalized by Fref = (1/2)ρf
$U_{ref}^2{L}$ 
14 单柔性体和3个柔性梁流场细节图: (a~c) 涡量云图; (d~f) 压力云图. 特征值ωref = Uref /L和pref = ρf
$U_{ref}^2$ 分别被用来无因次化计算得到的涡量和压力14. Fluid details of single beam and 3 beams: (a-c) vortices contour and (d-f) pressure contour. The vortices and pressures are normalized by ωref = Uref /L, pref = ρf
$U_{ref}^2$ , respectively表 1 多个自推进柔性体性能参数比较
Table 1. Propulsive performance of multiple self-propelled flexible beams
Collective behavior Velocity Input power Efficiency/% U P1 P2 P3 P4 P5 η1 η2 η3 η4 η5 single beam 1.74 1.22 7.90 3 beams 2.01 1.26 1.29 1.28 10.2 10.0 10.1 5 beams 2.02 1.24 1.44 1.44 1 27 1.28 10.5 9.05 9.05 10.3 10.2 
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