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Wang C, Tang H, Zhang X. Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics. BIOINSPIRATION & BIOMIMETICS 2022; 17:041002. [PMID: 35443232 DOI: 10.1088/1748-3190/ac68ba] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Accepted: 04/20/2022] [Indexed: 06/14/2023]
Abstract
Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.
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Affiliation(s)
- Chenglei Wang
- Research Center for Fluid Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, People's Republic of China
- The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, Guangdong 518057, People's Republic of China
| | - Hui Tang
- Research Center for Fluid Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, People's Republic of China
- The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, Guangdong 518057, People's Republic of China
| | - Xing Zhang
- The State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
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Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle. J Math Biol 2021; 83:56. [PMID: 34731319 DOI: 10.1007/s00285-021-01678-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Revised: 08/04/2021] [Accepted: 10/13/2021] [Indexed: 10/19/2022]
Abstract
Jellyfish have been called one of the most energy-efficient animals in the world due to the ease in which they move through their fluid environment, by product of their bell kinematics coupled with their morphological, muscular, material properties. We investigated jellyfish locomotion by conducting in silico comparative studies and explored swimming performance across different fluid scales (i.e., Reynolds Number), bell contraction frequencies, and contraction phase kinematics (duty cycle) for a jellyfish with a fineness ratio of 1 (ratio of bell height to bell diameter). To study these relationships, an open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid-structure interaction problem of a flexible jellyfish bell in a viscous fluid. Thorough 2D parameter subspace explorations illustrated optimal parameter combinations in which give rise to enhanced swimming performance. All performance metrics indicated a higher sensitivity to bell actuation frequency than fluid scale or duty cycle, via Sobol sensitivity analysis, on a higher performance parameter subspace. Moreover, Pareto-like fronts were identified in the overall performance space involving the cost of transport and forward swimming speed. Patterns emerged within these performance spaces when highlighting different parameter regions, which complemented the global sensitivity results. Lastly, an open source computational model for jellyfish locomotion is offered to the science community that can be used as a starting place for future numerical experimentation.
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Baldwin T, Battista NA. Hopscotching jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance. BIOINSPIRATION & BIOMIMETICS 2021; 16:066021. [PMID: 34584025 DOI: 10.1088/1748-3190/ac2afe] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 09/28/2021] [Indexed: 06/13/2023]
Abstract
Jellyfish (Medusozoa) have been deemed the most energy-efficient animals in the world. Their bell morphology and relatively simple nervous systems make them attractive to robotocists. Although, the science community has devoted much attention to understanding their swimming performance, there is still much to be learned about the jet propulsive locomotive gait displayed by prolate jellyfish. Traditionally, computational scientists have assumed uniform duty cycle kinematics when computationally modeling jellyfish locomotion. In this study we used fluid-structure interaction modeling to determine possible enhancements in performance from shuffling different duty cycles together across multiple Reynolds numbers and contraction frequencies. Increases in speed and reductions in cost of transport were observed as high as 80% and 50%, respectively. Generally, the net effects were greater for cases involving lower contraction frequencies. Overall, robust duty cycle combinations were determined that led to enhanced or impeded performance.
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Affiliation(s)
- Tierney Baldwin
- Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, Ewing Township, NJ 08628, United States of America
| | - Nicholas A Battista
- Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, Ewing Township, NJ 08628, United States of America
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Alben S, Puritz C. Intermittent sliding locomotion of a two-link body. Phys Rev E 2020; 101:052613. [PMID: 32575270 DOI: 10.1103/physreve.101.052613] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 05/07/2020] [Indexed: 11/07/2022]
Abstract
We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes improves the efficiency further only when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction.
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Affiliation(s)
- Silas Alben
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Connor Puritz
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA
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Abstract
Snakes' bodies are covered in scales that make it easier to slide in some directions than in others. This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots, for example) but is less understood. In this work we regularize a model for sliding locomotion to allow for static friction. We then propose a robust iterative numerical method to study the efficiency of a wide range of motions under isotropic Coulomb friction. We find that simple undulatory motions give little net locomotion in the isotropic regime. We compute general time-harmonic motions of three-link bodies and find three local optima for efficiency. The top two involve static friction to some extent. We then propose a class of smooth body motions that have similarities to concertina locomotion (including the involvement of static friction) and can achieve optimal efficiency for both isotropic and anisotropic friction.
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Affiliation(s)
- Silas Alben
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA
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Gemmell BJ, Troolin DR, Costello JH, Colin SP, Satterlie RA. Control of vortex rings for manoeuvrability. J R Soc Interface 2016; 12:20150389. [PMID: 26136226 DOI: 10.1098/rsif.2015.0389] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Manoeuvrability is critical to the success of many species. Selective forces acting over millions of years have resulted in a range of capabilities currently unmatched by machines. Thus, understanding animal control of fluids for manoeuvring has both biological and engineering applications. Within inertial fluid regimes, propulsion involves the formation and interaction of vortices to generate thrust. We use both volumetric and planar imaging techniques to quantify how jellyfish (Aurelia aurita) modulate vortex rings during turning behaviour. Our results show that these animals distort individual vortex rings during turns to alter the force balance across the animal, primarily through kinematic modulation of the bell margin. We find that only a portion of the vortex ring separates from the body during turns, which may increase torque. Using a fluorescent actin staining method, we demonstrate the presence of radial muscle fibres lining the bell along the margin. The presence of radial muscles provides a mechanistic explanation for the ability of scyphomedusae to alter their bell kinematics to generate non-symmetric thrust for manoeuvring. These results illustrate the advantage of combining imaging methods and provide new insights into the modulation and control of vorticity for low-speed animal manoeuvring.
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Affiliation(s)
- Brad J Gemmell
- Eugene Bell Center, Marine Biological Laboratory, Woods Hole, MA 02543, USA Biology Department, Providence College, Providence, RI 02908, USA
| | | | - John H Costello
- Eugene Bell Center, Marine Biological Laboratory, Woods Hole, MA 02543, USA Biology Department, Providence College, Providence, RI 02908, USA
| | - Sean P Colin
- Eugene Bell Center, Marine Biological Laboratory, Woods Hole, MA 02543, USA Marine Biology and Environmental Science, Roger Williams University, Bristol, RI 02809, USA
| | - Richard A Satterlie
- Biology and Marine Biology, University of North Carolina Wilmington, Wilmington, NC 28403, USA
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Sledge I, Krieg M, Lipinski D, Mohseni K. Identifying and modeling motion primitives for the hydromedusae Sarsia tubulosa and Aequorea victoria. BIOINSPIRATION & BIOMIMETICS 2015; 10:066001. [PMID: 26495992 DOI: 10.1088/1748-3190/10/6/066001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The movements of organisms can be thought of as aggregations of motion primitives: motion segments containing one or more significant actions. Here, we present a means to identify and characterize motion primitives from recorded movement data. We address these problems by assuming that the motion sequences can be characterized as a series of dynamical-system-based pattern generators. By adopting a nonparametric, Bayesian formalism for learning and simplifying these pattern generators, we arrive at a purely data-driven model to automatically identify breakpoints in the movement sequences. We apply this model to swimming sequences from two hydromedusa. The first hydromedusa is the prolate Sarsia tubulosa, for which we obtain five motion primitives that correspond to bell cavity pressurization, jet formation, jetting, cavity fluid refill, and coasting. The second hydromedusa is the oblate Aequorea victoria, for which we obtain five motion primitives that correspond to bell compression, vortex separation, cavity fluid refill, vortex formation, and coasting. Our experimental results indicate that the breakpoints between primitives are correlated with transitions in the bell geometry, vortex formation and shedding, and changes in derived dynamical quantities. These dynamics quantities include terms like pressure, power, drag, and thrust. Such findings suggest that dynamics information is inherently present in the observed motions.
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Affiliation(s)
- Isaac Sledge
- Department of Electrical and Computer Engineering, University of Florida, USA. Institute for Networked Autonomous Systems, University of Florida, USA
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Ristroph L, Childress S. Stable hovering of a jellyfish-like flying machine. J R Soc Interface 2014; 11:20130992. [PMID: 24430122 PMCID: PMC3899867 DOI: 10.1098/rsif.2013.0992] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2013] [Accepted: 12/18/2013] [Indexed: 11/12/2022] Open
Abstract
Ornithopters, or flapping-wing aircraft, offer an alternative to helicopters in achieving manoeuvrability at small scales, although stabilizing such aerial vehicles remains a key challenge. Here, we present a hovering machine that achieves self-righting flight using flapping wings alone, without relying on additional aerodynamic surfaces and without feedback control. We design, construct and test-fly a prototype that opens and closes four wings, resembling the motions of swimming jellyfish more so than any insect or bird. Measurements of lift show the benefits of wing flexing and the importance of selecting a wing size appropriate to the motor. Furthermore, we use high-speed video and motion tracking to show that the body orientation is stable during ascending, forward and hovering flight modes. Our experimental measurements are used to inform an aerodynamic model of stability that reveals the importance of centre-of-mass location and the coupling of body translation and rotation. These results show the promise of flapping-flight strategies beyond those that directly mimic the wing motions of flying animals.
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Affiliation(s)
- Leif Ristroph
- Applied Math Lab, Courant Institute, New York University, 251 Mercer St., New York, NY 10012, USA
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Abstract
We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we show that retrograde travelling waves are optimal. We give an asymptotic analysis showing that the optimal wave amplitude decays as the
power of the coefficient of transverse friction. This result agrees well with the numerical optima. At the other extreme, zero coefficient of transverse friction, we propose a triangular direct wave that is optimal. Between these two extremes, a variety of complex, locally optimal motions are found. Some of these can be classified as standing waves (or ratcheting motions).
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Affiliation(s)
- Silas Alben
- Department of Mathematics, University of Michigan, Ann Arbor, MI, USA
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