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Modeling and Simulation of Interacting Wings: Collective Dynamics in Inertial Fluid Flows

相互作用机翼的建模和仿真：惯性流体流动的集体动力学

基本信息

批准号：
2108839
负责人：
Anand Oza
金额：
$ 28万
依托单位：
New Jersey Institute of Technology
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-15 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2108839&HistoricalAwards=false
关键词：
Modeling Simulation Interacting Wings Collective

项目摘要

This project aims to understand how collections of flapping wings propel and interact through a fluid medium, such as water or air. Many living and non-living objects propel themselves by moving a set of propulsors (wings, fins, or a tail) that are attached to a main body. While there has been substantial progress in understanding how microscopic objects (such as bacteria) interact through slow fluid flows, little is known about how macroscopic objects (like fish) are affected by the relatively fast flows they generate. The new mathematical models constructed in this project will be used to assess how fluid flows affect the speed, energy consumption and stability of a collection of flapping wings traveling in different formations. The insights gained from this research have the potential to impact the biology and engineering communities. Specifically, recent experiments have suggested that fish and birds may travel in orderly formations in order to save energy, but the role of fluid flows in mediating schooling and flocking remains poorly understood. On the engineering side, the design of autonomous underwater vehicles is often inspired by the flapping mechanics of fish, and this project could inform new design and control principles. The project will train undergraduate and graduate students in mathematical modeling and physical applied mathematics, giving them tools that can be broadly applied to problems arising in the natural sciences and engineering. Moreover, the beautiful displays exhibited by animal collectives can readily be appreciated by the public, making the project suitable for outreach initiatives conducted by the university.Mathematical models of varying degrees of fidelity and complexity will be constructed and analyzed to probe different aspects of the wings' behavior. A key challenge is that flapping wings generate long-lived fluid flows in the form of complex vortical structures. This leads to temporally nonlocal hydrodynamic interactions between the constituents, wherein the forces between wings at a given time depend on their past positions and velocities. A nonlinear discrete-time delay-difference map, which explicitly models the wings' shed vortices, has been validated against recent experiments and will be used to assess the dependence of a formation’s speed, energy consumption and stability on geometric parameters. Conformal mapping and integral equation techniques will be used to represent two- and three-dimensional flows, respectively, and to assess the influence of wing shape. Furthermore, a continuum PDE theory for a dense collective of wings in a high Reynolds number flow will be systematically derived from the aforementioned models. Traveling wave solutions of the continuum theory will be characterized through numerical simulations, and the emergence of positional and orientational order will be assessed. The goals are to determine the extent to which hydrodynamic interactions alone can account for the spatiotemporally complex formations observed in dense collectives of flapping objects, and to uncover novel emergent phenomena that have been conjectured to arise in systems influenced by inertial fluid flows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目旨在了解扑动翅膀的集合如何通过流体介质（例如水或空气）推动和相互作用。许多生物和非生物物体通过移动附在主体上的一组推进器（机翼、鳍或尾巴）来推动自身。虽然在理解微观物体（如细菌）如何通过缓慢的流体流动相互作用方面取得了实质性进展，但人们对宏观物体（如鱼）如何受到其产生的相对较快的流动的影响知之甚少。该项目构建的新数学模型将用于评估流体流动如何影响以不同编队飞行的一组扑翼的速度、能量消耗和稳定性。从这项研究中获得的见解有可能影响生物学和工程界。具体来说，最近的实验表明，鱼类和鸟类可能会以有序的队形旅行以节省能量，但流体流动在调节鱼群和集群中的作用仍然知之甚少。在工程方面，自主水下航行器的设计通常受到鱼类扑动力学的启发，该项目可以为新的设计和控制原理提供信息。该项目将培训本科生和研究生数学建模和物理应用数学，为他们提供可广泛应用于自然科学和工程中出现的问题的工具。此外，动物集体展示的美丽展示很容易被公众欣赏，使得该项目适合大学开展的推广活动。将构建和分析不同保真度和复杂程度的数学模型，以探讨翅膀行为的不同方面。一个关键的挑战是扑动的翅膀会产生复杂涡流结构形式的长期流体流。这导致了成分之间的暂时非局部流体动力相互作用，其中给定时间机翼之间的力取决于它们过去的位置和速度。非线性离散时间延迟差图明确模拟了机翼脱落的涡流，已根据最近的实验进行了验证，并将用于评估编队速度、能耗和稳定性对几何参数的依赖性。共形映射和积分方程技术将分别用于表示二维和三维流动，并评估机翼形状的影响。此外，高雷诺数流中密集翼群的连续统偏微分方程理论将从上述模型中系统地导出。将通过数值模拟来表征连续介质理论的行波解，并评估位置和方向顺序的出现。其目标是确定仅靠流体动力相互作用在多大程度上可以解释在密集的扑动物体集合中观察到的时空复杂结构，并揭示被推测在受惯性流体流影响的系统中出现的新的涌现现象。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。