[论文解读] Two-dimensionally stable self-organization arises in simple schooling swimmers through hydrodynamic interactions

Pedro C. Ormonde, Melike Kurt+2 more|arXiv (Cornell University)|Feb 6, 2021

Micro and Nano Robotics被引用 6

一句话总结

本研究表明，通过单纯的流体动力相互作用，简单水翼对可在二维空间中被动形成稳定的群体游动构型；其中并列排列的构型由于尾缘涡机制而表现出超稳定平衡状态。该构型在受到扰动时仍保持稳定，集体效率最高可提升84%，在轻微错列构型下推力可提升87%，表明流体动力学力可能比以往认为的在鱼类群体结构形成中起着更为关键的作用。

ABSTRACT

We present new constrained and free-swimming experiments and simulations of a pair of pitching hydrofoils interacting in a minimal school. The hydrofoils have an out-of-phase synchronization and they are varied through in-line, staggered, and side-by-side formations within the two-dimensional interaction plane. It is discovered that there is a extit{two-dimensionally} stable equilibrium point for a side-by-side formation. In fact, this formation is super-stable, meaning that hydrodynamic forces will passively maintain this formation even under external perturbations and the school as a whole has no net forces acting on it that cause it to drift to one side or the other. Moreover, previously discovered extit{one-dimensionally} stable equilibria driven by wake vortex interactions are shown to be, in fact, two-dimensionally extit{unstable}, at least for an out-of-phase synchronization. Additionally, it is discovered that a trailing-edge vortex mechanism provides the restorative force to stabilize a side-by-side formation. The stable equilibrium is further verified by experiments and simulations for freely-swimming foils where dynamic recoil motions are present. When constrained, swimmers in compact side-by-side formations experience collective efficiency and thrust increases up to 40\% and 100\%, respectively, whereas slightly staggered formations output an even higher efficiency improvement of 84\% with a 87\% increase in thrust. Freely-swimming foils in a stable side-by-side formation show an efficiency and speed enhancement of up to 9\% and 15\%, respectively. These newfound schooling performance and stability characteristics suggest that fluid-mediated equilibria may play a role in the control strategies of schooling fish and fish-inspired robots.

研究动机与目标

• 研究仅靠流体动力相互作用是否能在简单游泳者中产生二维稳定的群体游动构型。
• 确定在考虑横向扰动时，已知的一维平衡状态是否仍保持稳定。
• 识别稳定并列构型中恢复力的物理机制。
• 量化在不同流体动力构型下集体效率和推力的性能提升。
• 在受约束和自由游动的实验与模拟条件下，验证并列构型的稳定性和性能。

提出的方法

• 在二维流场平面内，对以反相位同步（φ = π）正弦俯仰运动的NACA 0012水翼进行受约束的水翼实验。
• 通过流场可视化和力测量分析顺排、错列和并列构型下的尾迹涡动力学与流体动力相互作用。
• 数值模拟采用基于势流理论的二维边界元法（BEM），模拟具有规定俯仰运动的非定常自推进水翼。
• 使用Lighthill数（Li = C_D * S_wp）平衡推力与阻力，自由游动模拟中选择Li = 0.3以保证数值稳定性。
• 采用无量纲参数如雷诺数（Re）、斯特劳哈尔数（St）和折合频率（k）来表征流动状态和性能。
• 通过赋予真实附加质量（顺流方向m* = 2.76，横向方向m* = 1.74），在模拟中引入动态回弹运动，实现真实的自由游动行为。

实验结果

研究问题

• RQ1 仅靠流体动力相互作用是否能产生无主动控制的二维稳定群体游动构型？
• RQ2 此前报道的一维稳定顺排构型在横向方向上是否实际上稳定？
• RQ3 何种流体动力机制提供了维持稳定并列构型的恢复力？
• RQ4 不同水翼构型（顺排、错列、并列）下的性能指标（如效率和推力）如何变化？
• RQ5 自由游动水翼中的动态回弹运动在多大程度上影响群体的稳定性和性能？

主要发现

• 两个水翼的并列构型表现出二维超稳定平衡状态，流体动力力能被动维持构型，即使在外部扰动下也保持稳定。
• 此前报道的一维稳定顺排构型在反相位同步下被发现具有二维不稳定性，挑战了其鲁棒性的既有假设。
• 尾缘涡机制产生恢复力，通过抵消横向位移来稳定并列构型。
• 在受约束条件下，轻微错列构型的效率最高可比孤立游泳者提高84%，推力提高87%。
• 自由游动的并列水翼构型效率最高可提升9%，速度提高15%，得益于集体流体动力优势。
• 本研究证实，通过涡旋动力学实现的流体介导平衡态——尤其是其在自组织与性能增强中的核心作用——在群体游泳者中具有关键意义。