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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. 

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. 

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. 

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. 

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. 

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. 

In this study, numerical simulations are performed to study the effects of body shape on propulsive performance in a carangiform-like swimming motion. A focus is given to the variation in performance due to changes in the maximum thickness, maximum thickness location, leading-edge radius, and boattail angle of an undulating foil. An immersed boundary method-based incompressible flow solver is implemented to solve for the propulsive performance of two-dimensional undulating foils. The resulting flow simulations yield the thrust, drag, efficiency, and flow for each body shape. From this study, we have found that better propulsive performance comes from a thinner maximum thickness, a maximum thickness location closer to the head of the fish, a narrower boattail angle, and a larger leading-edge radius. Particular care is given to the analysis of the boattail angle, because of the surprising and significant results. In changing only the boattail angle the efficiency is shown to vary by 10.3%. Changes in the leading-edge radius varies the efficiency by 4.4%, the maximum thickness by 4.0%, and the maximum thickness location along the body by 5.0%. The large improvement observed in the thinner boattail angle cases are caused by the increased curvature around the middle of the fish body leading to a high-pressure region at the tail that improves the thrust performance. The results can be used to improve understanding of fish body shapes observed in nature as well as better informing the design of bioinspired underwater robots. 

In this work, numerical simulations are employed to study hydrodynamic interactions in trout-like three-dimensional(3D) fish bodies arranged in vertical and horizontal planes. The fish body is modeled on a juvenile rainbow trout (Oncorhynchus mykiss) and is imposed on a traveling wave to mimic trout swimming. Three typical minimal schools are studied, including the in-line, the side-by-side, and the vertical school. A sharp interface immersed-boundary-based incompressible Navier-Strokes flow solver is then used to quantitively simulate the resulting flow and hydrodynamic performance of the schools. The results show that the hydrodynamic efficiency of the leading fish in the in-line school increases by 5.28%, and the thrust production and efficiency of the side-by-side school are enhanced by 2.28% and 3.86%, respectively. Besides, the thrust production of the vertical school increases by 21.6%. The results suggest great potential in exploiting the hydrodynamic benefits in fish schools arranged in three-dimensional space.