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  1. Abstract

    This study investigates the interaction of a two-manta-ray school using computational fluid dynamics simulations. The baseline case consists of two in-phase undulating three-dimensional manta models arranged in a stacked configuration. Various vertical stacked and streamwise staggered configurations are studied by altering the locations of the top manta in the upstream and downstream directions. Additionally, phase differences between the two mantas are considered. Simulations are conducted using an in-house developed incompressible flow solver with an immersed boundary method. The results reveal that the follower will significantly benefit from the upstroke vortices (UVs) and downstroke vortices depending on its streamwise separation. We find that placing the top manta 0.5 body length (BL) downstream of the bottom manta optimizes its utilization of UVs from the bottom manta, facilitating the formation of leading-edge vortices (LEVs) on the top manta’s pectoral fins during the downstroke. This LEV strengthening mechanism, in turn, generates a forward suction force on the follower that results in a 72% higher cycle-averaged thrust than a solitary swimmer. This benefit harvested from UVs can be further improved by adjusting the phase of the top follower. By applying a phase difference ofπ/3to the top manta, the follower not only benefits from the UVs of the bottom manta but also leverages the auxiliary vortices during the upstroke, leading to stronger tip vortices and a more pronounced forward suction force. The newfound interaction observed in schooling studies offers significant insights that can aid in the development of robot formations inspired by manta rays.

     
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  2. Abstract

    To understand the governing mechanisms of bio-inspired swimming has always been challenging due to intense interactions between flexible bodies of natural aquatic species and water around them. Advanced modal decomposition techniques provide us with tools to develop more in-depth understating about these complex dynamical systems. In this paper, we employ proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques to extract energetically strongest spatio-temporal orthonormal components of complex kinematics of a Crevalle jack (Caranx hippos) fish. Then, we present a computational framework for handling fluid–structure interaction related problems in order to investigate their contributions towards the overall dynamics of highly nonlinear systems. We find that the undulating motion of this fish can be described by only two standing-wave like spatially orthonormal modes. Constructing the data set from our numerical simulations for flows over the membranous caudal fin of the jack fish, our modal analyses reveal that only the first few modes receive energy from both the fluid and structure, but the contribution of the structure in the remaining modes is minimal. For the viscous and transitional flow conditions considered here, both spatially and temporally orthonormal modes show strikingly similar coherent flow structures. Our investigations are expected to assist in developing data-driven reduced-order mathematical models to examine the dynamics of bio-inspired swimming robots and develop new and effective control strategies to bring their performance closer to real fish species.

     
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  3. The shape of a foil undergoing a combined pitching heaving motion is critical to its design in applications that demand high efficiency and thrust. This study focuses on understanding of how the shape of a foil affects its propulsive performance. We perform two-dimensional numerical simulations of fluid flows around a flapping foil for different governing parameters in the range of biological swimmers and bio-inspired underwater vehicles. By varying the foil shape using a class-shape transformation method, we investigate a broad range of foil-like shapes. In the study, we also show consistent results with previous studies that a thicker leading-edge and sharper trailing-edge makes for a more efficient foil shape undergoing a flapping motion. In addition, we explain that the performance of the foil is highly sensitive to its shape, specifically the thickness of the foil between the 18th and 50th percent along the chord of the foil. Moreover, we elucidate the flow mechanisms behind variations in performance metrics, particularly focused on constructive interference between the vortices generated at the leading-edge with the trailing-edge vortex, as well as the pressure field differences that lead to higher power consumption in less efficient foil shapes. 
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  4. Mechanisms for hydrodynamic benefit via fluid interactions in large planar fish schools ( n ≥ 10) are investigated by two-dimensional numerical simulations of carangiform fish swimming. It is observed that the average swimming efficiency of the 10-fish school is increased by 30% over a single swimmer, along with a thrust production improvement of 114%. The performance and flow analyses characterize the associated hydrodynamic interaction mechanisms in large dense schools leading to enhanced performance. First, anterior body suction arises from the proximity of the suction side of the flapping tail to the head of the following fish. Next, the block effect is observed as another fish body blocks the flow behind a fish. Finally, the wall effect enhances the flow of momentum downstream where the body of a neighboring fish acts as a wall for the flapping of a fish tail moving toward it. Because these primary body–body interactions are based on the arrangement of surrounding fish, a classification of the individual fish within the school is presented based on the intra-fish interactions and is reflected in the performance of the individuals. It is shown that the school can be separated as front fish, middle fish, edge fish, and back fish based on the geometric position, performance, and wake characteristics. Finally, groupings and mechanisms observed are proven to be consistent over a range of Reynolds numbers and school arrangements. 
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  5. This paper develops a tree-topological local mesh refinement (TLMR) method on Cartesian grids for the simulation of bio-inspired flow with multiple moving objects. The TLMR nests refinement mesh blocks of structured grids to the target regions and arrange the blocks in a tree topology. The method solves the time-dependent incompressible flow using a fractional-step method and discretizes the Navier-Stokes equation using a finite-difference formulation with an immersed boundary method to resolve the complex boundaries. When iteratively solving the discretized equations across the coarse and fine TLMR blocks, for better accuracy and faster convergence, the momentum equation is solved on all blocks simultaneously, while the Poisson equation is solved recursively from the coarsest block to the finest ones. When the refined blocks of the same block are connected, the parallel Schwarz method is used to iteratively solve both the momentum and Poisson equations. Convergence studies show that the algorithm is second-order accurate in space for both velocity and pressure, and the developed mesh refinement technique is benchmarked and demonstrated by several canonical flow problems. The TLMR enables a fast solution to an incompressible flow problem with complex boundaries or multiple moving objects. Various bio-inspired flows of multiple moving objects show that the solver can save over 80% computational time, proportional to the grid reduction when refinement is applied. 
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  6. In recent years, there has been a growing interest in using tandem foils to mimic and study fish swimming, and to inform underwater vehicle design. Though much effort has been put to understanding the propulsion mechanisms of a tandem-foil system, the stability of such a system and the mechanisms for maintaining it remain an open question. In this study, a 3-foil system in an in-line configuration is used towards understanding the hydrodynamics of lateral stability. The foils actively pitch with varying phase. To quantify lateral force oscillation, the standard deviation of the lateral force, 𝝈𝝈𝒀𝒀, calculated over one typical flapping cycle is used, to account for the amount of variation in the lateral force experienced by the system of 3 foils. The higher the standard deviation, the more the spread in the lateral force cycle data, the more lateral momentum exchanged between the flow and the foils, and the less stable the system is. Through phase variations, it is found that the lateral force is minimized when the phases of the three foils are approximately, though not exactly, evenly distributed. The least stable system is found to be the one with the foils all in phase. Systems that are more laterally stable are found to tend to have narrower envelopes of regions around the foils with high momentum. Near-wake of the foils, the envelopes of stable systems are also found to have pronounced convergent sections, whereas the envelope of the less stable systems are found to diverge without much interruption. In the far wake, coherent, singular thrust jets, along with orderly 2-S vortices are found to form in the two best performing cases. In less stable cases, the thrust jets are found to be branched. Corresponding to the width of the high-momentum envelopes, lateral jets are found to exist in the gaps between neighboring foils, the strengths of which vary based on stability, with the lateral jets being more pronounced in the less stable cases (cases with high amount of lateral force oscillation). Peak lateral forces are found to coincide with moments of pressure gradient build-up across the foils. The pressure-driven flow near the trailing edge of the foils then creates trailing-edge vortices, and correspondingly, lateral gap flows. Moments of peak and plateau lateral force on an individual foil in the system are found to coincide with the initiation and shedding of trailing-edge vortices, respectively. The formation of trailing-edge vortices, lateral jets and cross-stream flows in gaps are closely intertwined, and all are 1. Indicative of large lateral momentum oscillation, and 2. The results of pressure gradient build-up across foils. 
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  7. Flapping flight is a commonly used mechanism of micro aerial vehicles and insects alike. Dragonflies use their four-winged anatomy to navigate the environment, maneuver around obstacles, and perform other essential flight patterns. The flight performance and aerodynamics of intact flapping wings is well known; however, this study aims to clarify how wing damage affects the flight performance. First, high speed videos of the damaged wing flight, a takeoff performed by a dragonfly, is captured, and subsequently digitally reconstructed to create a three-dimensional model. Second, using an immersed-boundary method (IBM) based incompressible Navier-Stokes direct numerical simulation (DNS) solver, we resolve the aerodynamic forces and wake topology of the dragonfly’s damaged wing flapping flight in high detail. We found that spanwise damage doesn’t cause any detriment to the force capabilities of the damaged wing which is due to increased pitch angles of the damaged wing. As a consequence, fliers with spanwise damaged and intact wings may be able to utilize similar strategies to achieve takeoffs. The wake topology of the wing damaged flight is also examined. This work serves as a baseline for studying the effect of wing damage for flapping flight and could provide useful insights to micro-aerial vehicle (MAV) designers as some degree of wing damage may be an inevitable occurrence for winged fliers. 
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  8. The canonical motion of foils has been studied extensively in many applications, including energy harvesting. The advantage of undulating foils is often realized in their ability to positively interfere with neighboring foils. However, more research is needed in understanding different arrangements of undulating foils, along with the fluid dynamics interactions involved in enhancing the performance of the foils for this advantage to properly scale to a large number of foils. This work utilizes the concept of subgroups within a school, borrowed from biological studies of fish schools, along with an immersed boundary methodbased computational fluids solver to investigate how these larger groups of undulating foils interact. A parametric study is completed around the spacing of the back subgroup, and the vortex formation and wake structures are analyzed, revealing that the back subgroup gains efficiency via interactions with the wake of the front subgroup. The present study gives insight into how groups of undulating foils interact and uncovers mechanisms that enhance performance through their interaction. 
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  9. In this study, we numerically investigate the effects of the tail-beat phase differences between the trailing fish and its neighboring fish on the hydrodynamic performance and wake dynamics in a two-dimensional high-density school. Foils undulating with a wavy-like motion are employed to mimic swimming fish. The phase difference varies from 0° to 360°. A sharp-interface immersed boundary method is used to simulate flows over the fish-like bodies and provide quantitative analysis of the hydrodynamic performance and wakes of the school. It is found that the highest net thrust and swimming efficiency can be reached at the same time in the fish school with a phase difference of 180°. In particular, when the phase difference is 90°, the trailing fish achieves the highest efficiency, 58% enhancement compared with a single fish, while it has the highest thrust production, increased by 108% over a single fish, at a phase difference of 0°. The performance and flow visualization results suggest that the phase of the trailing fish in the dense school can be controlled to improve thrust and propulsive efficiency, and these improvements occur through the hydrodynamic interactions with the vortices shed by the neighboring fish and the channel formed by the side fish. In addition, the investigation of the phase difference effects on the wake dynamics of schools performed in this work represents the first study in which the wake patterns for systems consisting of multiple undulating bodies are categorized. In particular, a reversed Bénard–von Kármán vortex wake is generated by the trailing fish in the school with a phase difference of 90°, while a Bénard–von Kármán vortex wake is produced when the phase difference is 0°. Results have revealed that the wake patterns are critical to predicting the hydrodynamic performance of a fish school and are highly dependent on the phase difference.

     
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  10. Through direction numerical simulation (DNS) of a model manta ray body, pectoral fin scaled pitching effect on hydrodynamic performance and wake is investigated. The manta ray model is derived from high-speed video of manta ray swimming with motion of the model prescribed to match the actual manta ray. Rotation angles of the model skeletal joints is altered to scale the pitching. This results in four manta ray models with different pectoral fin pitching ratios. The models are simulated using an in-house developed immersed boundary method-based numerical solver. Notable discrepancies in thrust production during the downstroke are observed, with the θ =1.0 case producing instantaneous thrust peak that is 19% higher than the θ =0.72 model. Cycle averaged thrust is highest for the θ =0.72 model case, however, which can be attributed to extended reverse thrust for the θ =1.0 model. Through analysis of the near-body wake structures produced during the downstroke, late leading-edge vortex (LEV) formation is discovered to be primarily responsible for the detrimental reverse thrust seen for the θR =1.0 model. Surface pressure contours confirm this finding. Meanwhile the upstroke possesses less pronounced force production. 
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